Expand model tag support: add GLM-5.1, simplify Anthropic IDs, scan tags anywhere in message
- Flink update_bars debouncing - update_bars subscription idempotency bugfix - Price decimal correction bugfix of previous commit - Add GLM-5.1 model tag alongside renamed GLM-5 - Use short Anthropic model IDs (sonnet/haiku/opus) instead of full version strings - Allow @tags anywhere in message content, not just at start - Return hasOtherContent flag instead of trimmed rest string - Only trigger greeting stream when tag has no other content - Update workspace knowledge base references to platform/workspace and platform/shapes - Hierarchical knowledge base catalog - 151 Trading Strategies knowledge base articles - Shapes knowledge base article - MutateShapes tool instead of workspace patch
This commit is contained in:
@@ -6,7 +6,7 @@ description: "API and patterns for writing custom Python indicator scripts that
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Custom indicators are Python scripts saved in the `indicator` category. They compute values from OHLCV data and are plotted live on the TradingView chart alongside built-in indicators.
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See [`../pandas-ta-reference.md`](../pandas-ta-reference.md) for the full catalog of built-in indicators available via `pandas_ta`.
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See [`pandas-ta-reference`](pandas-ta-reference.md) for the full catalog of built-in indicators available via `pandas_ta`.
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---
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@@ -109,7 +109,7 @@ To shade between two output series (e.g. upper/lower bands), add a `filled_areas
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3. **Add to workspace** with `WorkspacePatch("indicators", ...)` using `pandas_ta_name: "custom_<sanitized_name>"`. Include `custom_metadata` in the patch value so the web client can render it.
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4. **Use in strategies** via `ta.custom_<sanitized_name>(...)`. See [`../strategies/strategy-development.md`](strategy-development.md) for details.
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4. **Use in strategies** via `ta.custom_<sanitized_name>(...)`. See [`strategy-development`](strategy-development.md) for details.
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---
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@@ -163,6 +163,6 @@ if vw_rsi.isna().all() or len(df) < min_required:
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## See Also
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- [`../pandas-ta-reference.md`](../pandas-ta-reference.md) — Full catalog of built-in indicators and calling conventions
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- [`../api-reference.md`](../api-reference.md) — DataAPI and ChartingAPI for research scripts
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- [`../strategies/strategy-development.md`](strategy-development.md) — Using custom indicators in strategies via `ta.custom_*`
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- [`pandas-ta-reference`](pandas-ta-reference.md) — Full catalog of built-in indicators and calling conventions
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- [`api-reference`](api-reference.md) — DataAPI and ChartingAPI for research scripts
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- [`strategy-development`](strategy-development.md) — Using custom indicators in strategies via `ta.custom_*`
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4
gateway/knowledge/platform/index.md
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4
gateway/knowledge/platform/index.md
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@@ -0,0 +1,4 @@
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---
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description: "Platform documentation index: workspace API reference, chart shape types, and MCP sandbox lifecycle."
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tags: [platform, index]
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---
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131
gateway/knowledge/platform/shapes.md
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131
gateway/knowledge/platform/shapes.md
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@@ -0,0 +1,131 @@
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---
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description: "Chart shape types (trend lines, Fibonacci, rectangles, channels, etc.), point requirements, override properties, and WorkspacePatch patterns for adding/modifying/deleting shapes on the TradingView chart."
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---
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# Chart Shapes
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Shapes are persistent TradingView chart drawings stored in the `shapes` workspace store. Read them with `WorkspaceRead("shapes")` and create/modify/delete them with `ShapesMutate`. Do **not** use `WorkspacePatch` for shapes — it requires knowledge of the internal path structure and is error-prone.
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Always read `chartState` first to get the current `symbol` and visible `start_time`/`end_time` for placing points correctly.
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---
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## Shape Object
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```json
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{
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"id": "string — unique ID you assign (e.g. 'trendline-btc-1')",
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"type": "string — see type table below",
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"points": [{ "time": 1700000000, "price": 45000.0, "channel": "optional" }],
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"color": "#2962FF",
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"line_width": 2,
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"line_style": "solid",
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"properties": {},
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"symbol": "BTC/USDT.BINANCE",
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"created_at": 1700000000,
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"modified_at": 1700000000
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}
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```
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- `line_style`: `"solid"` | `"dashed"` | `"dotted"`
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- `properties`: passed directly as TradingView overrides (see [Drawings Overrides](https://www.tradingview.com/charting-library-docs/latest/customization/overrides/Drawings-Overrides))
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- `time` values must be Unix timestamps in **seconds**; they are snapped to the nearest candle boundary automatically
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---
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## Supported Shape Types
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| `type` | Description | Points |
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|---|---|---|
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| `trend_line` | Trend line between two price/time points | 2 |
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| `horizontal_line` | Horizontal price level across the chart | 1 |
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| `vertical_line` | Vertical time marker | 1 |
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| `rectangle` | Price/time rectangle (two corners) | 2 |
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| `circle` | Circle centered at first point, edge at second | 2 |
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| `arrow` | Arrow from point 1 to point 2 | 2 |
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| `fib_retracement` | Fibonacci retracement levels between two points | 2 |
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| `fib_trend_ext` | Trend-based Fibonacci extension (A→B→C) | 3 |
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| `parallel_channel` | Parallel channel (two-line + channel width) | 3 |
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| `pitchfork` | Andrews pitchfork (handle + two tines) | 3 |
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| `gannbox_fan` | Gann fan from a pivot point | 2 |
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| `path` | Free-form polyline through 2+ points | 2+ |
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| `text` | Text label anchored at a price/time location | 1 |
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| `head_and_shoulders` | Head and shoulders pattern overlay | 7 |
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> For the full TradingView drawing catalog (including Elliott waves, patterns, annotations, etc.) see [Drawings List](https://www.tradingview.com/charting-library-docs/latest/ui_elements/drawings/Drawings-List/) and [CreateShapeOptions](https://www.tradingview.com/charting-library-docs/latest/api/interfaces/Charting_Library.CreateShapeOptions/#shape).
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---
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## ShapesMutate Patterns
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Use `ShapesMutate` — not `WorkspacePatch` — to add, update, or remove shapes. Any combination of operations can be sent in a single call.
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### Add a shape
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```
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ShapesMutate({
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add: [{
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id: "trendline-1",
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type: "trend_line",
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points: [
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{ time: 1700000000, price: 42000 },
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{ time: 1700172800, price: 45000 }
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],
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color: "#2962FF",
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line_width: 2,
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line_style: "solid",
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symbol: "BTC/USDT.BINANCE"
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}]
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})
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```
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### Update a property
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```
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ShapesMutate({ update: [{ id: "trendline-1", color: "#FF5722" }] })
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```
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### Delete a shape
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```
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ShapesMutate({ remove: ["trendline-1"] })
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```
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### Combined (add + remove in one call)
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```
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ShapesMutate({
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add: [{ id: "hline-support", type: "horizontal_line", points: [{ time: 0, price: 42000 }], symbol: "BTC/USDT.BINANCE" }],
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remove: ["trendline-1"]
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})
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```
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---
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## Override Properties
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These map to TradingView drawing override keys passed in the `properties` field:
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| Property key | Type | Notes |
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|---|---|---|
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| `linecolor` | string (hex) | Same as top-level `color` — prefer `color` |
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| `linewidth` | number | Same as top-level `line_width` — prefer `line_width` |
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| `linestyle` | number | 0 = solid, 1 = dashed, 2 = dotted — prefer `line_style` |
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| `fillBackground` | boolean | Fill enclosed areas (rectangles, circles, etc.) |
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| `backgroundColor` | string (hex) | Fill color when `fillBackground` is true |
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| `transparency` | number | Fill transparency 0–100 |
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| `extendLeft` | boolean | Extend line left (rays, horizontal lines) |
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| `extendRight` | boolean | Extend line right |
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| `showLabel` | boolean | Show price/time label on the shape |
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For the complete per-type override reference, consult [Drawings Overrides](https://www.tradingview.com/charting-library-docs/latest/customization/overrides/Drawings-Overrides).
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---
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## Notes
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- **ID collisions**: read the `shapes` store first to check existing IDs before adding
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- **Symbol filter**: the web client only renders shapes where `shape.symbol` matches the current chart symbol — always set it
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- **Horizontal lines** only need a `price` in their single point; `time` is ignored
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- **Vertical lines** only need a `time` in their single point; `price` is ignored
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- **Text shapes**: set `properties.text` to the label string
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@@ -1,5 +1,5 @@
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---
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description: "Workspace store schema, available stores, and WorkspaceRead/WorkspacePatch usage for reading and updating the user's UI state."
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description: "Workspace store schema: chartState (symbol/period/time range), indicators, shapes (chart drawings/annotations — see platform/shapes), and WorkspaceRead/WorkspacePatch usage."
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---
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# Workspace
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@@ -70,20 +70,7 @@ A flat map of `indicator_id → IndicatorInstance`. Each entry represents one st
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{ "shapes": { "<shape_id>": Shape } }
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```
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Each `Shape` has:
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| Field | Type | Description |
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|---|---|---|
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| `id` | string | Unique shape ID |
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| `type` | string | Drawing type (e.g. `"trend_line"`, `"horizontal_line"`, `"rectangle"`) |
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| `points` | array | Control points: `{ time: unix_ts, price: number, channel?: string }` |
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| `color` | string? | Hex color |
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| `line_width` | number? | Line thickness |
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| `line_style` | string? | `"solid"`, `"dotted"`, `"dashed"` |
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| `properties` | object? | Additional type-specific properties |
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| `symbol` | string? | Symbol the shape belongs to |
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| `created_at` | number? | Unix timestamp |
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| `modified_at` | number? | Unix timestamp |
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For the complete shapes reference — all supported types, point counts, override properties, and WorkspacePatch examples — see **`platform/shapes`** (`MemoryLookup({page: "platform/shapes"})`).
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---
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@@ -6,7 +6,7 @@ description: "PandasStrategy class API, order placement, backtesting, and paper
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Strategies on Dexorder are `PandasStrategy` subclasses that receive a live stream of OHLCV bars and call `self.buy()` / `self.sell()` / `self.flatten()` to place orders.
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See [`../api-reference.md`](../api-reference.md) for the DataAPI and ChartingAPI used in research scripts. For indicator calculations, see [`../pandas-ta-reference.md`](../pandas-ta-reference.md).
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See [`api-reference`](api-reference.md) for the DataAPI and ChartingAPI used in research scripts. For indicator calculations, see [`pandas-ta-reference`](pandas-ta-reference.md).
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---
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@@ -78,7 +78,7 @@ ema = ta.ema(df["close"], length=20)
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atr = ta.atr(df["high"], df["low"], df["close"], length=14)
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```
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See [`../pandas-ta-reference.md`](../pandas-ta-reference.md) for the full indicator catalog and multi-output column extraction patterns.
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See [`pandas-ta-reference`](pandas-ta-reference.md) for the full indicator catalog and multi-output column extraction patterns.
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---
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@@ -104,7 +104,7 @@ def evaluate(self, dfs):
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self.sell(0.01)
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```
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Custom indicator names follow the pattern `ta.custom_{sanitized_name}`. See [`../indicators/indicator-development.md`](../indicators/indicator-development.md) for naming rules and how to create custom indicators.
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Custom indicator names follow the pattern `ta.custom_{sanitized_name}`. See [`indicator-development`](indicator-development.md) for naming rules and how to create custom indicators.
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---
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@@ -260,7 +260,7 @@ A strategy with a lower win rate can still be profitable if winners are larger t
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## See Also
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- [`../pandas-ta-reference.md`](../pandas-ta-reference.md) — Indicator catalog and usage examples
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- [`../indicators/indicator-development.md`](../indicators/indicator-development.md) — Creating custom indicators
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- [`../api-reference.md`](../api-reference.md) — DataAPI reference (for research scripts)
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- [`../usage-examples.md`](../usage-examples.md) — Research script patterns
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- [`pandas-ta-reference`](pandas-ta-reference.md) — Indicator catalog and usage examples
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- [`indicator-development`](indicator-development.md) — Creating custom indicators
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- [`api-reference`](api-reference.md) — DataAPI reference (for research scripts)
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- [`usage-examples`](usage-examples.md) — Research script patterns
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4
gateway/knowledge/trading/index.md
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---
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description: "Trading knowledge index: signal combination theory, technical analysis, and a master catalog of 150+ strategies by asset class."
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tags: [trading, index]
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---
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121
gateway/knowledge/trading/signal-combination.md
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121
gateway/knowledge/trading/signal-combination.md
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---
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description: "Institutional alpha combination: how to merge multiple weak signals into a single high-conviction output using the 11-step procedure and the Fundamental Law of Active Management."
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tags: [signals, alpha, portfolio, kelly, statistics]
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---
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# Signal Combination — Alpha Stacking
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## Core Law
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Do not search for one perfect signal. Combine many weak, independent signals.
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**Fundamental Law of Active Management:**
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```
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IR = IC × √N
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```
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- `IR` = Information Ratio of the combined system (risk-adjusted edge)
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- `IC` = average Information Coefficient per signal (correlation of prediction to outcome)
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- `N` = number of *genuinely independent* signals
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Real institutional signals have IC = 0.05–0.15. A single signal at IC=0.10 is outperformed by 50 signals at IC=0.05 (IR = 0.05 × √50 = 0.354, over 3× better).
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**Critical:** N counts *effective independent signals*, not raw signal count. Fifty correlated signals may yield only 10–15 effective ones. The 11-step procedure below forces honest accounting.
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---
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## Five Signal Categories
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| Category | What it measures | Why it persists |
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|---|---|---|
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| **Momentum / Price** | Direction/rate of price movement over lookback `d` | Underreaction causes short-term trend persistence |
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| **Mean Reversion** | Deviation from cross-sectional fair value | Related instruments maintain consistent relative pricing |
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| **Volatility** | Implied vs. realized volatility gap | Vol risk premium: sellers demand compensation |
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| **Factor** | Value, momentum, carry, quality, low-vol premiums | Persistent behavioral/structural inefficiencies |
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| **Microstructure** | Order book imbalance, bid-ask spread, VPIN | Informed order flow leads price movement |
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> **Dexorder scope**: Only crypto OHLCV data is available. Factor signals (value, carry, quality) require TradFi data not available here. Momentum, mean reversion, volatility, and microstructure signals are all applicable.
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---
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## 11-Step Combination Engine
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Given N signals with historical returns R(i,s) over M periods:
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**Step 1.** Collect realized return series R(i,s) for each signal i, each period s.
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**Step 2.** Remove drift — serially demean:
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```
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X(i,s) = R(i,s) − mean(R(i,·))
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```
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**Step 3.** Compute variance per signal:
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```
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σ(i)² = (1/M) × Σ X(i,s)²
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```
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**Step 4.** Normalize to common scale:
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```
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Y(i,s) = X(i,s) / σ(i)
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```
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Makes signals with different magnitudes directly comparable.
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**Step 5.** Drop the most recent observation from Y — use only out-of-sample history.
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**Step 6.** Cross-sectionally demean at each time period:
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```
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Λ(i,s) = Y(i,s) − avg_j(Y(j,s))
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```
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Removes any market-wide effect driving all signals simultaneously at that moment.
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**Step 7.** Drop the final period from Λ to eliminate residual look-ahead.
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**Step 8.** Estimate expected forward return per signal using d-day moving average, normalize:
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```
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E(i) = (1/d) × Σ R(i,s) over recent d periods
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E_normalized(i) = E(i) / σ(i)
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```
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**Step 9. (Critical)** Regress E_normalized over Λ(i,s) without intercept, unit weights. Residuals `ε(i)` are each signal's *independent* forward-looking contribution — the component not explained by any other signal in the stack.
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**Step 10.** Set weights:
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```
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w(i) = η × ε(i) / σ(i)
|
||||
```
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High independent edge + low noise → high weight. No subjective judgment.
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**Step 11.** Normalize: scale η so `Σ|w(i)| = 1`. No unintended leverage.
|
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|
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**Combined output = Σ w(i) × signal_i_current_value**
|
||||
|
||||
---
|
||||
|
||||
## Empirical Kelly Sizing
|
||||
|
||||
```
|
||||
f_empirical = f_kelly × (1 − CV_edge)
|
||||
|
||||
f_kelly = (p × b − q) / b
|
||||
```
|
||||
- `CV_edge` = coefficient of variation of edge estimates across 10,000 Monte Carlo path simulations of historical returns
|
||||
- Higher uncertainty → smaller fraction. The formula automatically scales confidence to what is warranted.
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||||
|
||||
---
|
||||
|
||||
## Key Failure Mode: Correlation Blindness
|
||||
|
||||
Believing you have 3 independent reasons for a trade when you have 1 reason expressed 3 times, sized as if for 3. This is the mechanism behind most systematic blowups where the trader was directionally correct but over-sized.
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||||
|
||||
The cross-sectional demeaning (Step 6) and regression residualization (Step 9) structurally prevent this by exposing shared variance before weights are assigned.
|
||||
|
||||
---
|
||||
|
||||
## Dexorder Application Note
|
||||
|
||||
When combining multiple indicators into a single entry/exit signal:
|
||||
|
||||
1. Each indicator (momentum, RSI divergence, volume profile, spread, etc.) is a signal producing a score or directional estimate.
|
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2. Run the 11-step engine over backtested signal histories to derive weights.
|
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3. Combined score = weighted sum of current signal outputs.
|
||||
4. Size the resulting position using empirical Kelly with CV_edge from simulation.
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|
||||
If computing probability estimates (e.g. probability of upward breakout), substitute probability estimates for return estimates at each step — the math is identical.
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||||
---
|
||||
description: "A portfolio strategy that optimally determines how much cash to hold to meet unforeseen liquidity demands while minimizing the drag from uninvested capital."
|
||||
tags: [cash, liquidity, risk-management]
|
||||
---
|
||||
|
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# Liquidity Management
|
||||
|
||||
**Section**: 17.3 | **Asset Class**: Cash | **Type**: Risk management / Portfolio construction
|
||||
|
||||
## Overview
|
||||
|
||||
From a portfolio management perspective, this strategy amounts to optimally defining the amount of cash to be held in the portfolio to meet liquidity demands generated by unforeseen events. Cash provides immediate liquidity, whereas other assets would have to be liquidated first, which can be associated with substantial transaction costs — especially if liquidation is abrupt. From a corporate perspective, holding cash can be a precautionary measure aimed at avoiding cash flow shortfalls that can yield, inter alia, loss of investment opportunities, financial distress, etc.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
The strategy involves three distinct roles for cash as an asset:
|
||||
|
||||
1. **Risk management tool** — Cash held as a buffer mitigates drawdowns and volatility by providing a shock absorber when other assets decline or become illiquid.
|
||||
|
||||
2. **Opportunity management tool** — A cash reserve allows the investor to take advantage of specific or unusual situations (e.g., distressed asset purchases, sudden dislocations) without needing to liquidate existing positions.
|
||||
|
||||
3. **Liquidity management tool** — In unexpected situations requiring liquid funds, cash is the only immediately available resource without liquidation costs.
|
||||
|
||||
Liquid cash equivalents that can be held in a portfolio include:
|
||||
- U.S. Treasury bills
|
||||
- Bank deposit certificates (CDs)
|
||||
- Commercial paper
|
||||
- Banker's acceptances
|
||||
- Eurodollars
|
||||
- Repurchase agreements (repos)
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The direct return on cash is low (near the risk-free rate). The strategy's value lies in its option-like properties: the ability to act quickly when opportunities arise and to avoid forced liquidation at disadvantageous prices. The optimal cash level trades off the opportunity cost of holding cash against the cost of unexpected forced liquidation.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Liquidity buffer target**: sized to expected maximum drawdown of cash needs over some horizon
|
||||
- **Opportunity reserve**: discretionary allocation kept available for tactical deployment
|
||||
- **Kelly-based sizing**: related to Kelly criterion strategies; the cash fraction can be derived from portfolio growth optimization
|
||||
- **Liquidation cost model**: transaction costs and market impact of rapidly liquidating other assets inform the minimum required cash buffer
|
||||
|
||||
## Variations
|
||||
|
||||
- **Corporate treasury liquidity management**: focused on operating cash flow needs, payroll, and debt service
|
||||
- **Hedge fund liquidity management**: sized to potential investor redemptions and margin call scenarios
|
||||
- **Tactical cash allocation**: dynamically increasing cash weight as a defensive signal during high-volatility regimes
|
||||
|
||||
## Notes
|
||||
|
||||
The optimal cash holding is not the same as the rationale behind Kelly strategies. The appropriate cash level depends on the investor's specific liability structure, redemption profile, and the liquidity of the remaining portfolio. Holding too little cash forces costly liquidation; holding too much creates unacceptable opportunity cost drag. The strategy is foundational to virtually all portfolio management frameworks.
|
||||
49
gateway/knowledge/trading/strategies/cash/loan-sharking.md
Normal file
49
gateway/knowledge/trading/strategies/cash/loan-sharking.md
Normal file
@@ -0,0 +1,49 @@
|
||||
---
|
||||
description: "An illegal lending practice involving loans at excessively high interest rates without collateral, enforced through coercion; documented here for educational and awareness purposes only."
|
||||
tags: [cash, illegal, lending, awareness]
|
||||
---
|
||||
|
||||
# Loan Sharking
|
||||
|
||||
**Section**: 17.6 | **Asset Class**: Cash | **Type**: Illegal activity (documented for educational/awareness purposes only)
|
||||
|
||||
## Overview
|
||||
|
||||
Loan sharking consists of offering loans at excessively high — often usurious — interest rates. Unlike pawnbroking, loan sharking in many jurisdictions is illegal, and the loan is not necessarily secured by collateral. This activity is documented here solely for educational and awareness purposes. It is not a legitimate trading strategy and constitutes criminal conduct in most jurisdictions.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Loan structure:**
|
||||
- Cash is lent to a borrower at interest rates far above legal usury limits — rates can be expressed in weekly or daily terms (e.g., "2 for 1" means repay double within a fixed period)
|
||||
- No formal legal documentation is typically used; the arrangement is informal and unenforceable through normal legal channels
|
||||
- The loan is typically unsecured — there is no collateral pledge
|
||||
|
||||
**Enforcement:**
|
||||
- Because the loan cannot be enforced through the legal system, the lender (loan shark) may resort to extralegal means of enforcement
|
||||
- This can include blackmail, threats, and physical violence to compel repayment
|
||||
- The borrower has no legal recourse against abusive enforcement methods
|
||||
|
||||
**Relationship to legitimate lending:**
|
||||
- Loan sharks operate in the same economic niche as payday lenders and pawnbrokers but without legal constraints on rates or enforcement methods
|
||||
- They typically serve borrowers with no access to formal credit (e.g., due to criminal records, immigration status, or existing debt)
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The stated "return" is the extremely high interest charged. In practice, the loan shark often profits more from the coercive control over the borrower than from pure interest income — borrowers may be exploited for labor or other services. The high nominal returns are offset by significant legal, personal safety, and operational risks.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Interest rate**: typically far above legal usury limits; often quoted in short-period terms to obscure the true APR
|
||||
- **Enforcement mechanism**: the primary differentiator from legal lending; ranges from social pressure to physical violence
|
||||
- **Borrower desperation**: loan sharks target individuals with no alternative credit access
|
||||
- **Rollover/compound traps**: unpaid interest may compound rapidly, trapping borrowers in escalating debt
|
||||
|
||||
## Variations
|
||||
|
||||
- **Organized crime lending**: loan sharking as a service offered by criminal organizations, often linked to other illegal activities
|
||||
- **Predatory lending (grey area)**: legal but extremely high-rate lenders (payday loans, rent-to-own) operating at the edge of legality
|
||||
- **Salary lending / advance-fee lending**: informal arrangements common in some developing markets
|
||||
|
||||
## Notes
|
||||
|
||||
Loan sharking is **illegal** in most jurisdictions. It is documented here exclusively for educational purposes — to illustrate the spectrum of cash-based financial activities, support awareness of predatory lending, and assist in compliance or regulatory analysis. Any actual participation in loan sharking carries severe criminal penalties including imprisonment. The key distinction from legal high-rate lending (e.g., payday loans) is the use of illegal coercion and the absence of legal licensing and rate-cap compliance.
|
||||
@@ -0,0 +1,42 @@
|
||||
---
|
||||
description: "A three-stage process (placement, layering, integration) by which illegal cash is transformed into legitimate-appearing assets; documented here for educational and awareness purposes only."
|
||||
tags: [cash, illegal, awareness]
|
||||
---
|
||||
|
||||
# Money Laundering — The Dark Side of Cash
|
||||
|
||||
**Section**: 17.2 | **Asset Class**: Cash | **Type**: Illegal activity (documented for educational/awareness purposes only)
|
||||
|
||||
## Overview
|
||||
|
||||
Money laundering is an activity wherein cash is used as a vehicle to transform illegal profits into legitimate-appearing assets. It is documented here solely for educational and awareness purposes — this is an illegal activity in virtually all jurisdictions and is not a legitimate trading strategy. Understanding its mechanics is relevant for compliance, AML (anti-money-laundering) system design, and regulatory awareness.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
There are three main steps in a money laundering process:
|
||||
|
||||
1. **Placement** — The first and riskiest step. Illegal funds are introduced into the legal economy via fraudulent means, e.g., by dividing funds into small amounts and depositing them into multiple bank accounts (structuring/smurfing) to avoid detection thresholds.
|
||||
|
||||
2. **Layering** — Moving the money around between different accounts and even countries, thereby creating complexity and separating the money from its source by several degrees. The goal is to obscure the audit trail.
|
||||
|
||||
3. **Integration** — Money launderers recover the funds via legitimate-looking sources, e.g., cash-intensive businesses such as bars, restaurants, car washes, hotels (in some countries), gambling establishments, and parking garages.
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The "return" is the successful conversion of illicit proceeds into spendable, untraceable wealth. The primary risk is detection and prosecution at the placement stage, which is why smurfing and structuring techniques are employed to stay below reporting thresholds.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Placement risk**: highest at initial deposit stage; mitigated by structuring below reporting thresholds
|
||||
- **Layering complexity**: number of intermediary accounts, jurisdictions, and transactions used to obscure origin
|
||||
- **Integration vehicles**: choice of business type affects detectability (high-cash-volume businesses preferred)
|
||||
|
||||
## Variations
|
||||
|
||||
- **Trade-based laundering**: over- or under-invoicing international trade transactions
|
||||
- **Real estate laundering**: purchasing and reselling property through shell companies
|
||||
- **Cryptocurrency layering**: use of mixers, privacy coins, and cross-chain swaps to layer funds
|
||||
|
||||
## Notes
|
||||
|
||||
This strategy is **illegal** in all major jurisdictions. It is documented here exclusively for educational purposes, AML awareness, and to support the design of detection and compliance systems. Financial institutions are required by law (e.g., BSA/AML regulations, FATF guidelines) to implement controls to detect and report suspicious activity consistent with these patterns.
|
||||
51
gateway/knowledge/trading/strategies/cash/pawnbroking.md
Normal file
51
gateway/knowledge/trading/strategies/cash/pawnbroking.md
Normal file
@@ -0,0 +1,51 @@
|
||||
---
|
||||
description: "A secured short-term lending strategy where a pawnbroker extends a cash loan against physical collateral, retaining the right to sell the collateral if the loan is not repaid."
|
||||
tags: [cash, lending, collateral, alternative]
|
||||
---
|
||||
|
||||
# Pawnbroking
|
||||
|
||||
**Section**: 17.5 | **Asset Class**: Cash | **Type**: Collateralized lending
|
||||
|
||||
## Overview
|
||||
|
||||
Pawnbroking is conceptually similar to repurchase agreements (REPOs) but operates in retail/consumer markets and has ancient historical roots. A pawnbroker extends a secured cash loan with a pre-agreed interest rate and period (which can sometimes be extended). The loan is secured with a collateral item of value; if the loan is not repaid with interest as agreed, the collateral is forfeited by the borrower and the pawnbroker can keep it or sell it.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Loan origination:**
|
||||
- Borrower presents a physical item of value as collateral (jewelry, electronics, vehicles, rare books, musical instruments, etc.)
|
||||
- Pawnbroker appraises the item and offers a loan amount at a significant discount to appraised value (e.g., 25–60% of estimated resale value)
|
||||
- Borrower receives cash; pawnbroker retains physical possession of the item
|
||||
- A loan ticket is issued specifying the principal, interest rate, fees, and redemption deadline
|
||||
|
||||
**Redemption or forfeiture:**
|
||||
- If borrower repays principal plus interest within the agreed period, the item is returned
|
||||
- If borrower fails to repay, the pawnbroker takes full ownership of the collateral and may sell it to recover the loan amount plus a profit margin
|
||||
|
||||
**From an investment perspective:**
|
||||
- The pawnbroker's strategy profits from: (a) interest income on repaid loans, and (b) resale margin on forfeited collateral
|
||||
- The deep discount on collateral valuation provides a cushion against mispriced or illiquid items
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
Returns come from two sources: interest income on performing loans (typically high, reflecting the high-risk, unbanked borrower profile) and trading profit on forfeited collateral items sold at or above the appraised value. The high interest rates compensate for the non-recourse nature of many pawn loans (the lender's only recourse is the collateral, not the borrower personally).
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Loan-to-value (LTV) ratio**: loan amount as a fraction of collateral's estimated resale value; typically 25–60%
|
||||
- **Interest rate / fees**: high relative to bank rates; regulated in many jurisdictions with rate caps
|
||||
- **Loan term**: typically 1–4 months; extensions often available
|
||||
- **Collateral liquidity**: items with active resale markets (gold jewelry, electronics) command better LTV ratios
|
||||
- **Forfeiture rate**: the fraction of loans that are not redeemed; drives the resale revenue component
|
||||
|
||||
## Variations
|
||||
|
||||
- **Online pawnbroking**: digital platforms for luxury goods, collectibles, and watches
|
||||
- **Commodity pawnbroking**: pawnbrokers dealing specifically in precious metals and gems (overlap with commodity trading)
|
||||
- **Title lending / auto pawn**: loans secured against vehicle titles; borrower retains use of the vehicle while the title is held
|
||||
- **Jewelry/gold dealers**: effectively pawnbrokers who specialize in precious metals with spot-price-linked valuations
|
||||
|
||||
## Notes
|
||||
|
||||
Pawnbroking is legal and regulated in most jurisdictions, with interest rates and practices governed by consumer lending laws. The pawnbroker trades physical commodities such as silver and gold as a byproduct of forfeited collateral. The strategy is highly local and operationally intensive. It is conceptually the retail analogue of institutional repo markets — both involve a cash loan secured by an asset with a right to liquidate the asset upon default.
|
||||
53
gateway/knowledge/trading/strategies/cash/repo.md
Normal file
53
gateway/knowledge/trading/strategies/cash/repo.md
Normal file
@@ -0,0 +1,53 @@
|
||||
---
|
||||
description: "A repurchase agreement strategy that borrows or lends cash at a preset interest rate for 1 day to 6 months using securities as collateral, providing immediate liquidity."
|
||||
tags: [cash, fixed-income, collateral, short-term]
|
||||
---
|
||||
|
||||
# Repurchase Agreement (REPO)
|
||||
|
||||
**Section**: 17.4 | **Asset Class**: Cash | **Type**: Collateralized lending / Cash equivalent
|
||||
|
||||
## Overview
|
||||
|
||||
A repurchase agreement (REPO) is a cash-equivalent asset that provides immediate liquidity at a preset interest rate for a specific period of time in exchange for another asset used as collateral. A REPO strategy amounts to borrowing (or lending) cash with interest in exchange for securities, with the commitment of repurchasing them from (or reselling them to) the counterparty at the end of the term. This type of transaction typically spans from 1 day to 6 months.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**From the borrower's perspective (classic repo):**
|
||||
- The borrower sells securities to the lender at a spot price
|
||||
- Simultaneously agrees to repurchase those securities at a future date at a higher price
|
||||
- The difference in prices represents the repo interest (the "repo rate")
|
||||
- The securities serve as collateral; the lender has recourse to them if the borrower defaults
|
||||
|
||||
**From the lender's perspective (reverse repo):**
|
||||
- The lender buys securities and simultaneously agrees to resell them at a later date
|
||||
- Effectively a collateralized cash loan earning the repo rate
|
||||
- Counterparty credit risk is mitigated by holding the collateral
|
||||
|
||||
**Mechanics summary:**
|
||||
- Term: overnight (O/N) to 6 months; "open" repos have no fixed term
|
||||
- Collateral: typically government securities, though agency bonds and other high-grade paper are used
|
||||
- Haircut: the collateral is valued at a discount to market price to provide a buffer against collateral price declines
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The strategy earns (or pays) the repo rate, which is typically close to but slightly below the risk-free rate (for general collateral) or can be significantly below (even negative) for "special" securities in high demand. The primary objective is efficient short-term cash management — deploying idle cash at near-risk-free rates while maintaining near-immediate liquidity.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Repo rate**: the annualized interest rate on the transaction; general collateral (GC) rate vs. specific/special rates
|
||||
- **Haircut**: discount applied to collateral value (e.g., 2% for Treasuries, higher for lower-grade collateral)
|
||||
- **Term**: overnight, term (fixed date), or open
|
||||
- **Collateral type**: determines applicable haircut and rate; GC repos use any acceptable security vs. specific repos tied to a named security
|
||||
- **Margin calls**: triggered if collateral value falls below the required threshold during the term
|
||||
|
||||
## Variations
|
||||
|
||||
- **Reverse repo**: the lender's side; used by central banks as a monetary policy tool and by money market funds as an investment
|
||||
- **Tri-party repo**: a clearing bank acts as intermediary, handling collateral management for both parties
|
||||
- **Securities lending**: conceptually similar; the security owner lends it out for a fee, receiving cash or other securities as collateral
|
||||
- **GC pooling**: centralized clearing of general collateral repos to improve netting and efficiency
|
||||
|
||||
## Notes
|
||||
|
||||
REPOs are a foundational instrument in money markets and are used by banks, broker-dealers, money market funds, and central banks. The 2008 financial crisis revealed the fragility of repo markets when collateral quality deteriorated rapidly (the "run on repo"). Counterparty credit risk, collateral quality, and the potential for "fire-sale" dynamics during stress are the primary risk considerations. REPOs are conceptually similar to pawnbroking but operate in institutional markets at vastly larger scale.
|
||||
@@ -0,0 +1,56 @@
|
||||
---
|
||||
description: "Commodity futures strategy that uses CFTC Commitments of Traders (COT) hedging pressure data to identify long/short opportunities based on hedger and speculator positioning."
|
||||
tags: [commodities, futures, cot, hedging-pressure, positioning]
|
||||
---
|
||||
|
||||
# Trading Based on Hedging Pressure
|
||||
|
||||
**Section**: 9.2 | **Asset Class**: Commodities | **Type**: Positioning / Sentiment
|
||||
|
||||
## Overview
|
||||
Hedgers and speculators have systematically different objectives in commodity futures markets. High hedger long positioning signals contango (excess hedging demand pushes futures prices up); high speculator long positioning signals backwardation. By reading the CFTC Commitments of Traders (COT) report, a trader can construct a zero-cost portfolio that exploits these positioning signals with a 6-month typical holding period.
|
||||
|
||||
## Construction / Mechanics
|
||||
The "hedging pressure" (HP) for each group is defined as:
|
||||
|
||||
```
|
||||
HP = (number of long contracts) / (total contracts: long + short)
|
||||
```
|
||||
|
||||
HP lies between 0 and 1.
|
||||
|
||||
**Interpretation:**
|
||||
- High hedgers' HP → indicative of contango
|
||||
- Low hedgers' HP → indicative of backwardation
|
||||
- High speculators' HP → indicative of backwardation
|
||||
- Low speculators' HP → indicative of contango
|
||||
|
||||
**Portfolio construction:**
|
||||
1. Rank all commodity futures by speculators' HP; divide the cross-section into upper and lower halves.
|
||||
2. Within the upper half (higher speculator HP, i.e., backwardation signal):
|
||||
- **Buy** futures that are in the **bottom quintile** by hedgers' HP (confirming low hedger demand, strong backwardation signal)
|
||||
3. Within the lower half (lower speculator HP, i.e., contango signal):
|
||||
- **Sell** futures that are in the **top quintile** by hedgers' HP (confirming high hedger demand, strong contango signal)
|
||||
|
||||
The portfolio is zero-cost and rebalanced with typical formation and holding periods of 6 months.
|
||||
|
||||
## Return Profile
|
||||
Profits when commodity futures that show strong backwardation signals (low hedger HP, high speculator HP) outperform those with strong contango signals. The strategy earns a risk premium for providing liquidity to hedgers who are willing to pay above-fair-value forward prices.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| HP (hedgers) | Long / (long + short) for commercial hedgers from COT report |
|
||||
| HP (speculators) | Long / (long + short) for non-commercial speculators from COT |
|
||||
| Holding period | Typically 6 months |
|
||||
| Data source | CFTC Commitments of Traders (weekly) |
|
||||
|
||||
## Variations
|
||||
- Use the net position (long minus short) as the signal rather than the ratio HP.
|
||||
- Combine COT positioning with the roll-yield signal (Section 9.1) for a multi-factor commodity model.
|
||||
|
||||
## Notes
|
||||
- COT data is published weekly with a 3-day lag, so the signal has limited use for high-frequency trading.
|
||||
- The classification of "hedger" vs. "speculator" in COT data is self-reported and can be noisy; large commodity index funds are classified differently across report types (legacy vs. disaggregated COT).
|
||||
- The 6-month holding period smooths over reporting noise but requires patience through short-term adverse moves.
|
||||
- Strategy performance can degrade when large commodity index investors distort the COT positioning signals.
|
||||
@@ -0,0 +1,46 @@
|
||||
---
|
||||
description: "Portfolio diversification strategy that adds commodity exposure to equity portfolios to exploit their historically low cross-asset correlation and improve risk-adjusted returns."
|
||||
tags: [commodities, diversification, portfolio-construction, asset-allocation]
|
||||
---
|
||||
|
||||
# Portfolio Diversification with Commodities
|
||||
|
||||
**Section**: 9.3 | **Asset Class**: Commodities | **Type**: Portfolio Construction / Asset Allocation
|
||||
|
||||
## Overview
|
||||
Commodity markets typically exhibit low correlation with equity markets. Adding commodity exposure can improve the return-to-risk characteristics of equity-dominant portfolios. Two broad approaches exist: a passive buy-and-hold allocation, and an active tactical allocation that adjusts commodity exposure based on macroeconomic signals such as the Federal Reserve discount rate.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Passive Approach
|
||||
1. Allocate a preset fraction of available capital to commodity futures (or commodity indices).
|
||||
2. Hold the commodity position and rebalance periodically (e.g., monthly or annually) back to the target weight.
|
||||
3. No active signal required; the diversification benefit arises purely from low cross-asset correlation.
|
||||
|
||||
### Active (Tactical) Approach
|
||||
1. Monitor the Federal Reserve discount rate (or a proxy monetary policy indicator).
|
||||
2. **Increase** commodity exposure when the discount rate decreases (accommodative policy), since commodity returns are empirically positively correlated with monetary easing.
|
||||
3. **Decrease** commodity exposure when the discount rate increases (tightening policy).
|
||||
4. The tactical adjustment exploits the empirical link between commodity returns and Fed monetary policy.
|
||||
|
||||
## Return Profile
|
||||
The passive approach targets improved risk-adjusted returns through diversification without requiring any predictive signal. The active approach additionally aims to capture the positive correlation between commodity returns and accommodative monetary conditions, increasing commodity weights when they are most likely to outperform.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| Commodity allocation (passive) | Fixed % of portfolio (e.g., 5–20%) |
|
||||
| Rebalancing frequency | Monthly or annual for passive; signal-triggered for active |
|
||||
| Fed discount rate | Primary macro signal for active tactical allocation |
|
||||
| Cross-asset correlation | Empirically low between commodities and equities; drives diversification benefit |
|
||||
|
||||
## Variations
|
||||
- Use commodity indices (e.g., GSCI, BCOM) for passive exposure rather than individual futures contracts.
|
||||
- Active allocation can use other macro signals: inflation expectations, industrial production growth, credit spreads.
|
||||
- Risk-parity weighting (equalising volatility contribution of commodities and equities) rather than fixed notional allocation.
|
||||
|
||||
## Notes
|
||||
- The low equity-commodity correlation is not constant; during crisis periods (e.g., 2008), correlations can spike, reducing diversification benefit at exactly the wrong time.
|
||||
- The empirical link to Fed policy is regime-dependent; the relationship may be weaker during prolonged zero-rate environments.
|
||||
- Commodity exposure via futures introduces roll costs (see Section 9.1); the net diversification benefit must be assessed after roll costs.
|
||||
- Inflation-sensitive commodities (energy, metals) may provide additional value as inflation hedges alongside diversification benefits.
|
||||
@@ -0,0 +1,69 @@
|
||||
---
|
||||
description: "Commodity futures pricing strategy that fits a mean-reverting stochastic model to the term structure and trades futures identified as rich or cheap relative to model-implied fair value."
|
||||
tags: [commodities, futures, stochastic-model, ornstein-uhlenbeck, pricing, term-structure]
|
||||
---
|
||||
|
||||
# Trading with Pricing Models
|
||||
|
||||
**Section**: 9.6 | **Asset Class**: Commodities | **Type**: Relative Value / Model-Based
|
||||
|
||||
## Overview
|
||||
Commodity futures term structures are non-trivial and can be modelled via stochastic processes. Fitting a parametric model (e.g., the Ornstein-Uhlenbeck mean-reverting process) to historical data allows the identification of futures that are rich (sell signal) or cheap (buy signal) relative to the model's predicted fair value. The approach acknowledges that structural mean reversion is a reasonable property for commodity prices.
|
||||
|
||||
## Construction / Mechanics
|
||||
Let S(t) be the spot price and X(t) = ln(S(t)). Model X(t) as a mean-reverting Brownian motion (Ornstein-Uhlenbeck):
|
||||
|
||||
```
|
||||
dX(t) = κ[a - X(t)] dt + σ dW(t) (459)
|
||||
```
|
||||
|
||||
Parameters:
|
||||
- κ: mean-reversion speed
|
||||
- a: long-run mean of ln(S)
|
||||
- σ: log-volatility
|
||||
- W(t): Q-Brownian motion under risk-free measure Q
|
||||
|
||||
Under the standard pricing argument, the futures price F(t,T) is:
|
||||
|
||||
```
|
||||
F(t,T) = E_t(S(T)) (460)
|
||||
ln(F(t,T)) = E_t(X(T)) + (1/2) V_t(X(T)) (461)
|
||||
```
|
||||
|
||||
This gives the closed-form futures price:
|
||||
|
||||
```
|
||||
ln(F(t,T)) = exp(-κ(T-t)) X(t) + a[1 - exp(-κ(T-t))]
|
||||
+ (σ²/4κ)[1 - exp(-2κ(T-t))] (462)
|
||||
```
|
||||
|
||||
**Calibration and trading:**
|
||||
1. Fit κ, a, σ to historical data (e.g., nonlinear least squares on observed futures prices).
|
||||
2. Compute the model-implied futures price for each contract.
|
||||
3. Compare market price to model price:
|
||||
- Market price > model price: **sell signal** (futures is rich)
|
||||
- Market price < model price: **buy signal** (futures is cheap)
|
||||
|
||||
Note: as κ → 0, a → ∞ with κa fixed, this model reduces to the Black-Scholes model.
|
||||
|
||||
## Return Profile
|
||||
Profits when market prices revert toward the model-implied fair values. Returns are driven by mean-reversion in the spread between market and model prices. In-sample fit may be strong but out-of-sample predictive power is model-dependent.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| κ | Mean-reversion speed; higher κ → faster reversion |
|
||||
| a | Long-run mean of log-spot price |
|
||||
| σ | Log-volatility of the spot price |
|
||||
| F(t,T) model vs. market | Rich/cheap signal: sell if market > model, buy if market < model |
|
||||
|
||||
## Variations
|
||||
- **Multifactor models**: add stochastic convenience yield or stochastic volatility for richer term structure fitting.
|
||||
- **Black-box / ML models**: fit any model with desirable qualitative properties (e.g., mean reversion) using machine learning, without explicit stochastic dynamics; valid as long as out-of-sample predictive power is demonstrated.
|
||||
- Combine with roll-yield (Section 9.1) as a complementary signal.
|
||||
|
||||
## Notes
|
||||
- In-sample fit can be excellent even for models with poor predictive power; out-of-sample backtesting is essential (see Paschke and Prokopczuk, 2012).
|
||||
- Model mis-specification risk: the true dynamics may not be OU; using a flexible model without theoretical grounding is equally valid if it works out-of-sample.
|
||||
- Parameter instability: κ, a, σ estimated on historical data may shift during structural changes (supply shocks, geopolitical events).
|
||||
- "Fancy does not equal better" — complex models do not necessarily outperform simple ones out-of-sample.
|
||||
@@ -0,0 +1,51 @@
|
||||
---
|
||||
description: "Commodity futures roll-yield strategy that goes long backwardated and short contangoed futures based on the ratio of front-month to second-month prices."
|
||||
tags: [commodities, futures, roll-yield, term-structure, carry]
|
||||
---
|
||||
|
||||
# Roll Yields
|
||||
|
||||
**Section**: 9.1 | **Asset Class**: Commodities | **Type**: Carry / Term Structure
|
||||
|
||||
## Overview
|
||||
When commodity futures are in backwardation (downward-sloping term structure), long futures positions generate positive roll yield because as contracts approach expiry they roll up toward the higher spot price. In contango (upward-sloping term structure), the roll yield is negative. A zero-cost long-short portfolio can be constructed by going long commodities in backwardation and short those in contango.
|
||||
|
||||
## Construction / Mechanics
|
||||
Define the backwardation/contango ratio for each commodity:
|
||||
|
||||
```
|
||||
φ = P₁ / P₂ (454)
|
||||
```
|
||||
|
||||
where P₁ is the front-month futures price and P₂ is the second-month futures price.
|
||||
|
||||
- φ > 1: backwardation (front-month > second-month); long futures position earns positive roll yield
|
||||
- φ < 1: contango (front-month < second-month); short futures position earns positive roll yield
|
||||
|
||||
**Portfolio construction:**
|
||||
- Rank all N commodity futures by φ
|
||||
- Buy futures with higher values of φ (stronger backwardation)
|
||||
- Sell futures with lower values of φ (deeper contango)
|
||||
- Dollar-neutral (zero-cost) implementation
|
||||
|
||||
Roll yield is realised when the near-expiry contract is sold (covered) and a longer-dated contract is purchased, or vice versa for short positions.
|
||||
|
||||
## Return Profile
|
||||
Profits from the periodic rolling of positions: as a backwardated contract approaches expiry, its price converges upward to the spot, generating a positive roll return. In contango the opposite holds and short positions benefit. Roll yield is distinct from spot price returns.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| φ = P₁/P₂ | Backwardation ratio; φ > 1 → backwardation, φ < 1 → contango |
|
||||
| Ranking quantile | Top/bottom quantile cut-off for long/short selection |
|
||||
| Roll frequency | Determined by contract expiry calendar |
|
||||
|
||||
## Variations
|
||||
- Extend the ratio beyond the first two contracts to capture the broader term structure slope.
|
||||
- Combine with hedging pressure (Section 9.2) or momentum signals for a multi-factor commodity strategy.
|
||||
|
||||
## Notes
|
||||
- Roll yields can be substantial in commodities with high storage costs (energy) or seasonal supply/demand patterns (agricultural).
|
||||
- The ratio φ is a snapshot measure; persistent backwardation or contango is more reliable than transient conditions.
|
||||
- Transaction costs from rolling (bid-ask spreads on each roll) must be weighed against the expected roll yield.
|
||||
- Convenience yield (the benefit of holding physical inventory) is the economic driver of backwardation in many commodity markets.
|
||||
@@ -0,0 +1,55 @@
|
||||
---
|
||||
description: "Commodity futures strategy that captures the negative skewness premium by buying low-skewness and selling high-skewness commodity futures, exploiting the empirical negative relationship between return skewness and expected returns."
|
||||
tags: [commodities, futures, skewness, premium, cross-sectional]
|
||||
---
|
||||
|
||||
# Skewness Premium
|
||||
|
||||
**Section**: 9.5 | **Asset Class**: Commodities | **Type**: Skewness / Risk Premium
|
||||
|
||||
## Overview
|
||||
There is an empirically observed negative correlation between the skewness of historical returns and future expected returns across commodity futures. Commodities with highly negatively skewed returns have, on average, higher future expected returns, while those with positively skewed returns have lower expected returns. This mirrors the skewness premium observed in equity options markets and reflects investor preference for positive skewness ("lottery" demand).
|
||||
|
||||
## Construction / Mechanics
|
||||
The skewness of returns for commodity i (i = 1,...,N) over T observations is:
|
||||
|
||||
```
|
||||
S_i = (1 / (σ_i³ T)) Σ [R_is - R̄_i]³ (456)
|
||||
```
|
||||
|
||||
where:
|
||||
|
||||
```
|
||||
R̄_i = (1/T) Σ R_is (457)
|
||||
|
||||
σ_i² = (1/(T-1)) Σ [R_is - R̄_i]² (458)
|
||||
```
|
||||
|
||||
and R_is are the historical return observations.
|
||||
|
||||
**Portfolio construction:**
|
||||
- Rank all N commodity futures by S_i
|
||||
- **Buy** futures in the **bottom quintile** by skewness (most negatively skewed, highest expected return)
|
||||
- **Sell** futures in the **top quintile** by skewness (most positively skewed, lowest expected return)
|
||||
- Zero-cost portfolio; rebalanced periodically
|
||||
|
||||
## Return Profile
|
||||
Profits when the negative skewness-expected return relationship holds out-of-sample: low-skewness (left-tail-heavy) commodities outperform high-skewness (right-tail-heavy) ones. The premium compensates investors for bearing left-tail (crash) risk.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| S_i | Third standardised moment of historical returns |
|
||||
| T | Estimation window length (number of return observations) |
|
||||
| Quintile cut-offs | Bottom quintile (buy) vs. top quintile (sell) |
|
||||
| Rebalancing | Periodic (monthly or quarterly) |
|
||||
|
||||
## Variations
|
||||
- Use option-implied skewness (from commodity options) instead of realised skewness for a forward-looking signal.
|
||||
- Combine with value (Section 9.4) or roll yield (Section 9.1) in a multi-factor commodity model.
|
||||
|
||||
## Notes
|
||||
- Realised skewness is estimated with substantial noise, particularly for commodities with short or infrequently traded histories.
|
||||
- The skewness premium can be concentrated in a small number of time periods; the strategy may have poor risk-adjusted returns in normal markets and large gains during commodity stress events.
|
||||
- Tail risk is inherent in this strategy: buying low-skewness commodities means accepting left-tail exposure.
|
||||
- Sufficient sample size T is needed for reliable skewness estimates; skewness estimation requires more data than mean or variance estimation.
|
||||
52
gateway/knowledge/trading/strategies/commodities/value.md
Normal file
52
gateway/knowledge/trading/strategies/commodities/value.md
Normal file
@@ -0,0 +1,52 @@
|
||||
---
|
||||
description: "Commodity value strategy that buys commodities whose current spot price is low relative to their spot price five years ago, and sells those with relatively high current prices."
|
||||
tags: [commodities, value, mean-reversion, cross-sectional]
|
||||
---
|
||||
|
||||
# Value
|
||||
|
||||
**Section**: 9.4 | **Asset Class**: Commodities | **Type**: Value / Mean-Reversion
|
||||
|
||||
## Overview
|
||||
Analogous to the value strategy in equities (Section 3.3), the commodity value strategy is based on the premise that commodities with currently depressed prices relative to their historical levels are cheap and likely to revert upward, while those at elevated prices are expensive and likely to revert downward. The value ratio uses the 5-year-ago spot price as the benchmark for fair value.
|
||||
|
||||
## Construction / Mechanics
|
||||
The value signal for each commodity is defined as:
|
||||
|
||||
```
|
||||
v = P₅ / P₀ (455)
|
||||
```
|
||||
|
||||
where:
|
||||
- P₅ is the spot price 5 years ago (alternatively, the average spot price between 4.5 and 5.5 years ago)
|
||||
- P₀ is the current spot price
|
||||
|
||||
A high v means the commodity is currently cheap relative to its 5-year-ago price (good value); a low v means the commodity is currently expensive.
|
||||
|
||||
**Portfolio construction:**
|
||||
- Rank all N commodity futures by v
|
||||
- **Buy** futures in the top tercile by v (cheapest relative to 5-year history)
|
||||
- **Sell** futures in the bottom tercile by v (most expensive relative to 5-year history)
|
||||
- Rebalance monthly
|
||||
|
||||
## Return Profile
|
||||
Profits when commodity prices exhibit long-term mean reversion to their historical levels. The strategy is contrarian over a 5-year horizon, expecting that extreme deviations from historical prices will eventually correct.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| v = P₅/P₀ | Value ratio; high v → cheap (buy), low v → expensive (sell) |
|
||||
| Look-back period | 5 years (or average between 4.5 and 5.5 years ago) |
|
||||
| Portfolio terciles | Top tercile long, bottom tercile short |
|
||||
| Rebalancing | Monthly |
|
||||
|
||||
## Variations
|
||||
- Use different look-back horizons (e.g., 3 years or 7 years) to capture different mean-reversion cycles.
|
||||
- Combine value with momentum (e.g., buy commodities with high v AND positive recent momentum) to avoid "value traps".
|
||||
- Apply to commodity sub-sectors (energy, metals, agriculture) separately to account for different structural price cycles.
|
||||
|
||||
## Notes
|
||||
- Commodity prices are subject to structural breaks (technological change, supply shocks) that can make historical prices poor benchmarks for fair value.
|
||||
- The 5-year look-back is long enough to smooth business cycle effects but may include obsolete price regimes.
|
||||
- Unlike equities, commodities have no earnings or book value; the purely price-based value measure has higher model risk.
|
||||
- Roll costs from maintaining long futures positions in contangoed commodities can erode value-strategy returns.
|
||||
@@ -0,0 +1,44 @@
|
||||
---
|
||||
description: "Buy an undervalued convertible bond and short the underlying stock using a delta-based hedge ratio to capture the mispricing between the convertible's market price and its fair value."
|
||||
tags: [convertibles, arbitrage]
|
||||
---
|
||||
|
||||
# Convertible Arbitrage
|
||||
|
||||
**Section**: 12.1 | **Asset Class**: Convertibles (Hybrid: Fixed Income + Equity) | **Type**: Arbitrage
|
||||
|
||||
## Overview
|
||||
A convertible bond is a hybrid security with an embedded option to convert the bond to a preset number of the issuer's shares (the conversion ratio) when the stock price reaches the conversion price. Empirically, convertibles at issuance tend to be undervalued relative to their fair value, creating arbitrage opportunities. The strategy buys the convertible bond and simultaneously shorts the underlying stock to hedge the equity exposure.
|
||||
|
||||
## Construction / Mechanics
|
||||
The hedge ratio (number of shares to short) is:
|
||||
|
||||
```
|
||||
h = Δ × C (492)
|
||||
Δ = ∂V/∂S (493)
|
||||
```
|
||||
|
||||
- `C` = conversion ratio (number of shares per bond)
|
||||
- `V` = value of the conversion option (model-dependent)
|
||||
- `S` = underlying stock price
|
||||
- `Δ` = option delta (model-dependent)
|
||||
|
||||
The position is typically held for 6–12 months starting at the convertible's issuance date. The hedge ratio is updated daily as delta changes with the stock price.
|
||||
|
||||
## Return Profile
|
||||
Profits when the market price of the convertible converges toward its theoretical fair value. The long convertible position captures the undervaluation premium. The short stock position hedges directional equity risk, leaving exposure primarily to the convergence of the mispricing.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Conversion ratio** `C`: fixed at issuance
|
||||
- **Delta** `Δ = ∂V/∂S`: requires a model for the conversion option value `V`; changes daily with stock price `S`
|
||||
- **Gamma hedging**: since delta itself changes with `S`, the option gamma can be used to refine dynamic hedging (see Section 7.4.1)
|
||||
- **Entry timing**: position typically initiated at issuance when undervaluation is most pronounced
|
||||
|
||||
## Variations
|
||||
- **Gamma hedging overlay**: use gamma to dynamically adjust the hedge ratio as the stock moves, capturing additional convexity profits
|
||||
|
||||
## Notes
|
||||
- Hedge ratios are model-dependent; model risk is a key concern
|
||||
- Nonparametric hedge estimation using historical data (constrained regression of MBS price P w.r.t. swap rate R) is an alternative to model-based delta
|
||||
- Liquidity risk: convertible bonds are less liquid than the underlying stock
|
||||
- Crowding risk: convertible arbitrage is a well-known strategy; forced unwinds by other funds can cause losses
|
||||
@@ -0,0 +1,46 @@
|
||||
---
|
||||
description: "Simultaneously buy and sell two convertible bonds from the same issuer, long the higher option-adjusted spread and short the lower, profiting when the spreads converge."
|
||||
tags: [convertibles, arbitrage, fixed-income]
|
||||
---
|
||||
|
||||
# Convertible Option-Adjusted Spread (OAS) Arbitrage
|
||||
|
||||
**Section**: 12.2 | **Asset Class**: Convertibles (Hybrid: Fixed Income + Equity) | **Type**: Relative Value / Arbitrage
|
||||
|
||||
## Overview
|
||||
This strategy simultaneously buys and sells two different convertible bonds issued by the same company. The long position is in the bond with the higher option-adjusted spread (OAS) and the short position is in the bond with the lower OAS. The trade is profitable when the two spreads converge toward each other.
|
||||
|
||||
## Construction / Mechanics
|
||||
The price of a convertible bond is decomposed as:
|
||||
|
||||
```
|
||||
P_C = P_B + V (494)
|
||||
```
|
||||
|
||||
- `P_C` = convertible bond price
|
||||
- `P_B` = straight bond price (the bond without the embedded option), computed via standard discounting of future cash flows
|
||||
- `V` = value of the conversion option (a call option on the issuer's stock)
|
||||
|
||||
**OAS Calculation Procedure:**
|
||||
1. At the initial iteration, compute `V^(0)` using a call option pricing model with the zero-coupon government Treasury curve as the risk-free rate
|
||||
2. Check if `V^(0)` matches the market-implied option value `P_C^mkt - P_B`
|
||||
3. If not, iteratively parallel-shift the Treasury curve (e.g., using bisection) until the computed `V` equals `P_C^mkt - P_B`
|
||||
4. The parallel shift obtained is the OAS
|
||||
|
||||
## Return Profile
|
||||
Profits when the OAS of the long bond decreases (price rises) and/or the OAS of the short bond increases (price falls), i.e., when the two spreads converge. Returns are driven by relative mispricing between the two convertibles of the same issuer, not by the absolute level of spreads or interest rates.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **OAS differential**: the spread between the two bonds' OAS values; wider differential implies larger potential profit but also higher risk if divergence continues
|
||||
- **Same-issuer requirement**: both bonds must be from the same issuer to neutralize credit risk
|
||||
- **Convergence horizon**: the expected time for OAS convergence to occur
|
||||
|
||||
## Variations
|
||||
- **Multi-bond basket**: extend to a basket of convertibles from the same issuer, weighting by OAS rank
|
||||
- **Cross-issuer OAS**: relax the same-issuer constraint and use credit hedges to neutralize issuer-level credit risk
|
||||
|
||||
## Notes
|
||||
- The OAS computation requires an option pricing model for `V`; model risk affects both legs
|
||||
- The iterative parallel-shift procedure assumes the Treasury curve shape is fixed; actual curve shape changes can affect the OAS estimate
|
||||
- Liquidity mismatch between the two convertible bonds can create mark-to-market losses even when the fundamental trade thesis is correct
|
||||
- This strategy is distinct from straight convertible arbitrage (12.1): there is no stock short; both legs are bonds from the same issuer
|
||||
175
gateway/knowledge/trading/strategies/crypto/ann-strategy.md
Normal file
175
gateway/knowledge/trading/strategies/crypto/ann-strategy.md
Normal file
@@ -0,0 +1,175 @@
|
||||
---
|
||||
description: "An artificial neural network (ANN) strategy that forecasts short-term BTC price movements using technical indicators (EMA, EMSD, RSI) as inputs and quantile-based classification as output."
|
||||
tags: [crypto, machine-learning, ann, bitcoin, technical-analysis]
|
||||
---
|
||||
|
||||
# Artificial Neural Network (ANN) Strategy
|
||||
|
||||
**Section**: 18.2 | **Asset Class**: Cryptocurrencies | **Type**: Machine learning / Price prediction
|
||||
|
||||
## Overview
|
||||
|
||||
This strategy uses an ANN to forecast short-term movements of BTC price based on input technical indicators. Unlike equities, cryptocurrencies have no evident "fundamentals" on which to build value-based strategies, so cryptocurrency trading strategies tend to rely on trend data mining via machine learning techniques. The ANN classifies the future normalized return into quantile buckets and generates buy/sell signals accordingly.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Price and Return Normalization
|
||||
|
||||
Let `P(t)` be the BTC price at time `t`, where `t = 1, 2, ...` is measured in some units (e.g., 15-minute intervals; `t = 1` is the most recent time).
|
||||
|
||||
**Return:**
|
||||
```
|
||||
R(t) = P(t)/P(t+1) - 1 (521)
|
||||
```
|
||||
|
||||
**Serial mean return** over T₁ periods:
|
||||
```
|
||||
R_bar(t, T₁) = (1/T₁) * sum_{t'=t+1}^{t+T₁} R(t') (523)
|
||||
```
|
||||
|
||||
**Serially demeaned return:**
|
||||
```
|
||||
R_tilde(t, T₁) = R(t) - R_bar(t, T₁) (522)
|
||||
```
|
||||
|
||||
**Variance:**
|
||||
```
|
||||
[sigma(t, T₁)]² = (1/(T₁-1)) * sum_{t'=t+1}^{t+T₁} [R_tilde(t', T₁)]² (525)
|
||||
```
|
||||
|
||||
**Normalized (serially demeaned) return:**
|
||||
```
|
||||
R_hat(t, T₁) = R_tilde(t, T₁) / sigma(t, T₁) (524)
|
||||
```
|
||||
|
||||
For notational simplicity the T₁ parameter is omitted below and `R_hat(t)` denotes the normalized return. T₁ should be chosen long enough to provide a reasonable volatility estimate.
|
||||
|
||||
### Input Layer: Technical Indicators
|
||||
|
||||
**Exponential Moving Average (EMA):**
|
||||
```
|
||||
EMA(t, lambda, tau) = ((1-lambda)/(1-lambda^tau)) * sum_{t'=t+1}^{t+tau} lambda^{t'-t-1} * R_hat(t') (526)
|
||||
```
|
||||
|
||||
**Exponential Moving Standard Deviation (EMSD):**
|
||||
```
|
||||
[EMSD(t, lambda, tau)]² = ((1-lambda)/(lambda - lambda^tau)) * sum_{t'=t+1}^{t+tau} lambda^{t'-t-1} * [R_hat(t') - EMA(t, lambda, tau)]² (527)
|
||||
```
|
||||
|
||||
**Relative Strength Index (RSI):**
|
||||
```
|
||||
RSI(t, tau) = nu_+(t, tau) / [nu_+(t, tau) + nu_-(t, tau)] (528)
|
||||
|
||||
nu_±(t, tau) = sum_{t'=t+1}^{t+tau} max(±R_hat(t'), 0) (529)
|
||||
```
|
||||
|
||||
Where: `tau` is the moving average length; `lambda` is the exponential smoothing parameter (to reduce parameters, one can set `lambda = (tau-1)/(tau+1)`).
|
||||
|
||||
Typically RSI > 0.7 is interpreted as overbought; RSI < 0.3 as oversold.
|
||||
|
||||
### Input Layer Construction
|
||||
|
||||
The input layer consists of:
|
||||
- `R_hat(t)` — the current normalized return
|
||||
- `EMA(t, lambda_a, tau_a)` for `a = 1, ..., m`
|
||||
- `EMSD(t, lambda_a, tau_a)` for `a = 1, ..., m`
|
||||
- `RSI(t, tau_{a'})` for `a' = 1, ..., m'`
|
||||
|
||||
Example parameter choices (from the literature):
|
||||
- `tau_a` corresponding to 30 min, 1 hr, 3 hrs, 6 hrs (so `m = 4`)
|
||||
- `tau_{a'}` corresponding to 3 hrs, 6 hrs, 12 hrs (so `m' = 3`)
|
||||
|
||||
### Output Layer: Quantile Classification
|
||||
|
||||
The objective is to forecast which quantile the future normalized return `R_hat(t)` will belong to.
|
||||
|
||||
Let `K` be the number of quantiles. For training dataset `D_train`, compute the `(K-1)` quantile values `q_alpha`, `alpha = 1, ..., K-1`, of `R_hat(t)`, `t in D_train`.
|
||||
|
||||
Define supervisory K-vectors `S_alpha(t)`, `alpha = 1, ..., K`:
|
||||
```
|
||||
S_1(t) = 1, if R_hat(t) <= q_1
|
||||
S_alpha(t) = 1, if q_{alpha-1} <= R_hat(t) < q_alpha, for 1 < alpha < K (530)
|
||||
S_K(t) = 1, if q_{K-1} <= R_hat(t)
|
||||
S_alpha(t) = 0, otherwise
|
||||
```
|
||||
|
||||
The output layer produces a nonnegative K-vector `p_alpha(t)` of class probabilities:
|
||||
```
|
||||
sum_{alpha=1}^{K} p_alpha(t) = 1 (531)
|
||||
```
|
||||
|
||||
### Network Architecture
|
||||
|
||||
The ANN has `L` layers labeled `l = 1, ..., L`:
|
||||
- `l = 1`: input layer
|
||||
- `l = L`: output layer
|
||||
- Intermediate layers: hidden layers
|
||||
|
||||
At each layer `l`, there are `N^(l)` nodes with vectors `X_vec^(l)` having components `X_{i(l)}^(l)`:
|
||||
|
||||
**Forward propagation:**
|
||||
```
|
||||
X_{i(l)}^(l) = h_{i(l)}^(l)(Y_vec^(l)), l = 2, ..., L (532)
|
||||
|
||||
Y_{i(l)}^(l) = sum_{j(l-1)=1}^{N^(l-1)} A_{i(l)j(l-1)}^(l) * X_{j(l-1)}^(l-1) + B_{i(l)}^(l) (533)
|
||||
```
|
||||
|
||||
Where: `A_{i(l)j(l-1)}^(l)` are the weights; `B_{i(l)}^(l)` are the biases (both determined via training).
|
||||
|
||||
**Activation functions:**
|
||||
|
||||
Hidden layers use ReLU:
|
||||
```
|
||||
h_{i(l)}^(l)(Y_vec^(l)) = max(Y_{i(l)}^(l), 0), l = 2, ..., L-1 (534)
|
||||
```
|
||||
|
||||
Output layer uses softmax (ensuring probabilities sum to 1):
|
||||
```
|
||||
h_{i(L)}^(L)(Y_vec^(L)) = Y_{i(L)}^(L) * [sum_{j(L)=1}^{N(L)} Y_{j(L)}^(L)]^{-1} (535)
|
||||
```
|
||||
|
||||
ReLU fires a neuron only if `Y_{i(l)}^(l) > 0`; softmax enforces condition (531).
|
||||
|
||||
### Training: Cross-Entropy Loss
|
||||
|
||||
The error function to minimize is the cross-entropy:
|
||||
```
|
||||
E = - sum_{t in D_train} sum_{alpha=1}^{K} S_alpha(t) * ln(p_alpha(t)) (536)
|
||||
```
|
||||
|
||||
Minimized via stochastic gradient descent (SGD), which iterates until convergence.
|
||||
|
||||
### Trading Signal
|
||||
|
||||
```
|
||||
Signal = Buy, iff max(p_alpha(t)) = p_K(t) (537)
|
||||
Sell, iff max(p_alpha(t)) = p_1(t)
|
||||
```
|
||||
|
||||
The trader buys BTC if the predicted class is `p_K(t)` (the top quantile) and sells if it is `p_1(t)` (the bottom quantile). This rule can be modified — e.g., buy on top 2 quantiles and sell on bottom 2 quantiles.
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The strategy profits when the ANN correctly classifies the direction and magnitude of short-term BTC price movements. Returns are driven by the quality of the technical indicator signals and the ability of the trained network to generalize out-of-sample. Given BTC's high volatility, even modest directional accuracy can produce significant returns.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- `T₁`: lookback for return normalization (volatility estimation window)
|
||||
- `tau_a`: EMA/EMSD lookback periods (e.g., 30 min, 1 hr, 3 hrs, 6 hrs)
|
||||
- `tau_{a'}`: RSI lookback periods (e.g., 3 hrs, 6 hrs, 12 hrs)
|
||||
- `lambda`: exponential smoothing factor; can be set to `(tau-1)/(tau+1)`
|
||||
- `K`: number of quantile classes (e.g., K=2 for simple up/down)
|
||||
- `N^(l)`: number of nodes at each hidden layer
|
||||
- `L`: total number of layers
|
||||
- `d_1`: number of most-recent time points excluded from training data to ensure all indicators are computed on sufficient data
|
||||
|
||||
## Variations
|
||||
|
||||
- **K=2 binary classification**: simple up/down forecast; buy/sell signal directly
|
||||
- **K>2 multi-quantile**: more granular signal strength; trade only on extreme quantiles
|
||||
- **Extended indicator set**: add MACD, Bollinger Bands, volume indicators to the input layer
|
||||
- **LSTM/RNN variant**: replace feedforward ANN with recurrent architecture to better capture time-series dependencies
|
||||
|
||||
## Notes
|
||||
|
||||
The primary risk is overfitting: many free parameters (`tau_a`, `lambda_a`, `tau_{a'}`, `N^(l)`, `K`) must be chosen and the ever-present danger of overfitting various free parameters necessitates careful out-of-sample backtesting. The training dataset must exclude the most recent `d_1` time points to ensure all EMA, EMSD, and RSI values are computed using the required number of data points. This strategy is conceptually similar to the single-stock KNN trading strategy (Section 3.17) but uses ANN instead of k-nearest neighbors. No fundamental valuation of BTC is implied.
|
||||
@@ -0,0 +1,128 @@
|
||||
---
|
||||
description: "A naïve Bayes Bernoulli classifier applied to Twitter sentiment data to forecast BTC price direction, generating buy/sell signals from keyword-frequency feature vectors."
|
||||
tags: [crypto, machine-learning, nlp, sentiment, bitcoin, naive-bayes]
|
||||
---
|
||||
|
||||
# Sentiment Analysis — Naïve Bayes Bernoulli
|
||||
|
||||
**Section**: 18.3 | **Asset Class**: Cryptocurrencies | **Type**: Machine learning / NLP sentiment
|
||||
|
||||
## Overview
|
||||
|
||||
This strategy applies a social media sentiment analysis classification scheme to forecast the direction (or quantile) of BTC price movements based on Twitter data. It uses the naïve Bayes Bernoulli model to classify tweets into outcome classes and generate trading signals. The premise is that aggregate social media sentiment contains predictive information about short-term crypto price movements.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Data Collection and Preprocessing
|
||||
|
||||
1. Collect all tweets containing at least one keyword from a pertinent learning vocabulary `V` over some timeframe
|
||||
2. Clean data: remove duplicate tweets from bots, remove stop-words (e.g., "the", "is", "in", "which"), perform stemming (reduce words to base forms, e.g., "investing" and "invested" → "invest")
|
||||
3. Stemming can be performed using the Porter stemming algorithm
|
||||
|
||||
Let:
|
||||
- `M = |V|` = number of keywords in the learning vocabulary
|
||||
- `N` = number of tweets in the dataset
|
||||
- `i = 1, ..., N` labels tweets
|
||||
- `a = 1, ..., M` labels words `w_a` in `V`
|
||||
|
||||
### Feature Vector Construction (Bernoulli Model)
|
||||
|
||||
Assign a feature M-vector `X_i` to each tweet `i`:
|
||||
|
||||
**Bernoulli (binary presence/absence):**
|
||||
```
|
||||
X_{ia} = 0 if word w_a not present in tweet T_i
|
||||
X_{ia} = 1 if word w_a is present in tweet T_i (Bernoulli)
|
||||
```
|
||||
|
||||
Alternative (multinomial): `X_{ia} = n_{ia}`, the number of times `w_a` appears in `T_i`.
|
||||
|
||||
The Bernoulli case is the focus of this strategy.
|
||||
|
||||
### Classification Framework
|
||||
|
||||
Define `K` outcome classes `C_alpha`, `alpha = 1, ..., K`:
|
||||
- Simplest case: `K = 2` (BTC goes up or down) — provides buy/sell signal
|
||||
- Alternative: `K` quantiles of the normalized return `R_hat(t)` (as in the ANN strategy, Section 18.2)
|
||||
|
||||
**Goal:** given the `N` feature vectors `X_1, ..., X_N`, predict class `C_alpha`.
|
||||
|
||||
### Bayesian Foundation
|
||||
|
||||
By Bayes' theorem:
|
||||
```
|
||||
P(A|B) = P(B|A) * P(A) / P(B) (538)
|
||||
```
|
||||
|
||||
The posterior probability of class `C_alpha` given features `X_1, ..., X_N`:
|
||||
```
|
||||
P(C_alpha | X_1, ..., X_N) = P(X_1, ..., X_N | C_alpha) * P(C_alpha) / P(X_1, ..., X_N) (539)
|
||||
```
|
||||
|
||||
Note `P(X_1, ..., X_N)` is independent of `C_alpha` and acts only as a normalization constant.
|
||||
|
||||
### Naïve (Conditional Independence) Assumption
|
||||
|
||||
The naïve Bayes simplification assumes that for a given class `C_alpha`, all features `X_i` are conditionally independent:
|
||||
```
|
||||
P(X_i | C_alpha, X_1, ..., X_{i-1}, X_{i+1}, ..., X_N) = P(X_i | C_alpha) (540)
|
||||
```
|
||||
|
||||
This gives:
|
||||
```
|
||||
P(C_alpha | X_1, ..., X_N) = gamma * P(C_alpha) * prod_{i=1}^{N} P(X_i | C_alpha) (541)
|
||||
|
||||
gamma = 1 / P(X_1, ..., X_N) (542)
|
||||
```
|
||||
|
||||
### Bernoulli Likelihood
|
||||
|
||||
For the Bernoulli model, the conditional probability of feature vector `X_i` given class `C_alpha`:
|
||||
```
|
||||
P(X_i | C_alpha) = prod_{a=1}^{M} Q_{ia alpha} (543)
|
||||
```
|
||||
|
||||
Where:
|
||||
```
|
||||
Q_{ia alpha} = P(w_a | C_alpha), if X_{ia} = 1 (544)
|
||||
Q_{ia alpha} = 1 - P(w_a | C_alpha), if X_{ia} = 0 (545)
|
||||
```
|
||||
|
||||
The conditional probabilities `P(w_a | C_alpha)` are estimated from word occurrence frequencies in the training data. Similarly, `P(C_alpha)` is estimated from the training data class frequencies.
|
||||
|
||||
### Prediction Rule
|
||||
|
||||
Set the forecasted class `C_pred` to the one with maximum posterior probability:
|
||||
```
|
||||
C_pred = argmax_{C_alpha in {1,...,K}} P(C_alpha) * prod_{i=1}^{N} prod_{a=1}^{M} [P(w_a | C_alpha)]^{X_{ia}} * [1 - P(w_a | C_alpha)]^{1 - X_{ia}} (546)
|
||||
```
|
||||
|
||||
### Trading Signal
|
||||
|
||||
- For `K = 2`: `C_pred = 1` → Sell; `C_pred = 2` → Buy (consistent with ANN signal convention)
|
||||
- For `K` quantiles: trade on extreme quantile predictions analogously to the ANN strategy
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
Returns are driven by the predictive content of Twitter sentiment about short-term BTC price direction. The strategy profits when aggregate social media tone (bullish vs. bearish language in the vocabulary) correlates with subsequent price movements. High crypto volatility means that even modest accuracy gains over random can generate meaningful returns.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Vocabulary `V`**: the set of keywords relevant to BTC price forecasting; quality of `V` critically affects performance
|
||||
- **`K`**: number of outcome classes (2 for binary up/down, or quantile-based)
|
||||
- **`M = |V|`**: vocabulary size; larger vocabulary increases model complexity and overfitting risk
|
||||
- **Training window**: timeframe for estimating `P(C_alpha)` and `P(w_a | C_alpha)`
|
||||
- **Stemming algorithm**: Porter or similar; affects effective vocabulary size
|
||||
- **Stop-word list**: removal of common non-informative words reduces noise
|
||||
|
||||
## Variations
|
||||
|
||||
- **Multinomial naïve Bayes**: uses word count `n_{ia}` instead of binary presence; can better capture emphasis
|
||||
- **Support vector machine (SVM)**: alternative classifier on the same feature vectors
|
||||
- **Logistic regression**: another popular alternative to naïve Bayes for text classification
|
||||
- **Tree boosting**: gradient boosting applied to tweet feature vectors for BTC direction prediction
|
||||
- **Multi-source sentiment**: extend beyond Twitter to Reddit (r/bitcoin), news feeds, Telegram channels
|
||||
|
||||
## Notes
|
||||
|
||||
The naïve (conditional independence) assumption is rarely exactly true but often works well in practice for text classification. The key challenge is vocabulary construction — the learning vocabulary `V` must be chosen to be informative about BTC price movements specifically, not just generally related to Bitcoin. Laplace smoothing (adding a pseudo-count) is typically applied to avoid zero probabilities for words not observed in a given class. Compared to the ANN strategy, naïve Bayes is more interpretable and computationally cheaper to train. Social media strategies are vulnerable to coordinated manipulation (pumping sentiment with bots) and regime changes in platform usage patterns.
|
||||
@@ -0,0 +1,50 @@
|
||||
---
|
||||
description: "Actively acquire distressed assets with the goal of obtaining management control, then drive reorganization through planning a restructuring, buying outstanding debt for equity conversion, or providing secured loans that convert to equity upon reorganization."
|
||||
tags: [distressed-assets, credit, active-investing, private-equity]
|
||||
---
|
||||
|
||||
# Active Distressed Investing
|
||||
|
||||
**Section**: 15.2 | **Asset Class**: Distressed Assets | **Type**: Active / Control-Oriented
|
||||
|
||||
## Overview
|
||||
Unlike passive distressed debt buying (Section 15.1), active distressed investing aims to acquire sufficient ownership or control to influence the management and direction of the distressed company. When a company faces financial distress, it can file for Chapter 11 bankruptcy protection to reorganize under U.S. court supervision, or it can work directly with creditors outside of court. Active investors participate in or drive this reorganization process to generate returns.
|
||||
|
||||
## Construction / Mechanics
|
||||
The active investor accumulates a significant position in the distressed company's debt or equity to obtain standing and leverage in the reorganization process. Larger debt holders tend to submit more competitive reorganization plans. Three primary sub-strategies are described below (as Variations).
|
||||
|
||||
## Return Profile
|
||||
Returns are driven by the successful increase in the company's enterprise value through the reorganization process. Active investors can extract value through:
|
||||
- Control of the reorganized entity
|
||||
- Conversion of debt to equity at favorable terms
|
||||
- Secured loan conversion to equity with control rights
|
||||
|
||||
Returns can be very large but require significant legal, operational, and financial expertise. The investment horizon is typically multi-year.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Debt claim size**: larger positions give more influence in Court and in out-of-court negotiations
|
||||
- **Debt seniority**: senior secured creditors have more leverage; subordinated debt holders have less but more upside on equity conversion
|
||||
- **Chapter 11 vs. out-of-court**: Chapter 11 provides a formal legal framework; out-of-court is faster but requires creditor consensus
|
||||
- **Enterprise valuation**: ability to assess the reorganized company's value is critical to determine fair exchange ratios
|
||||
|
||||
## Variations
|
||||
|
||||
### 15.2.1 Planning a Reorganization
|
||||
An investor submits a reorganization plan to Court with the objective of obtaining participation in the management of the company, increasing its value, and generating profits. Plans submitted by significant debt holders tend to be more competitive and are more likely to be approved by the Court and creditors.
|
||||
|
||||
### 15.2.2 Buying Outstanding Debt
|
||||
The investor buys outstanding debt of the distressed firm at a discount with the view that, after reorganization, part of this debt will be converted into the firm's equity, thereby giving the investor a certain level of control of the reorganized company. The discount at which debt is purchased represents the potential upside if the company's equity value post-reorganization exceeds the implied value in the purchase price.
|
||||
|
||||
### 15.2.3 Loan-to-Own
|
||||
The investor finances (via secured loans) a distressed firm that is not yet bankrupt, with the view that the firm either:
|
||||
- (i) overcomes its distress, avoids bankruptcy, and increases its equity value (the secured loan is repaid at a premium), or
|
||||
- (ii) files for Chapter 11 protection, upon reorganization the secured loan is converted into the firm's equity with control rights
|
||||
|
||||
This strategy is particularly attractive when the investor believes the firm's assets are worth more under new management.
|
||||
|
||||
## Notes
|
||||
- Requires deep operational, legal, and financial restructuring expertise; typically executed by specialist hedge funds and private equity firms
|
||||
- Intercreditor conflicts: multiple classes of creditors with competing interests can delay or complicate the reorganization
|
||||
- Regulatory considerations: acquiring control of a company through debt conversion may trigger regulatory approvals (antitrust, industry-specific)
|
||||
- Time horizon uncertainty: Chapter 11 cases can last from months to several years; secured loans may be tied up indefinitely if bankruptcy is protracted
|
||||
- The "loan-to-own" strategy (15.2.3) has attracted regulatory scrutiny in some jurisdictions as potentially predatory toward the distressed borrower
|
||||
@@ -0,0 +1,44 @@
|
||||
---
|
||||
description: "Passively buy a diversified portfolio of deeply discounted distressed debt (yield spread >1,000 bps over Treasuries) and hold through reorganization, expecting high returns on the subset of positions that recover."
|
||||
tags: [distressed-assets, credit, fixed-income, value]
|
||||
---
|
||||
|
||||
# Buying and Holding Distressed Debt (Passive)
|
||||
|
||||
**Section**: 15.1 | **Asset Class**: Distressed Assets (Fixed Income / Credit) | **Type**: Value / Passive
|
||||
|
||||
## Overview
|
||||
Distressed securities are those whose issuers are undergoing financial or operational distress, default, or bankruptcy. A common definition of distressed debt is when the yield spread between the issuer's bonds and Treasury bonds exceeds a preset threshold (e.g., 1,000 basis points). This passive strategy buys distressed debt at a steep discount and holds it, expecting (hoping) the company will repay its debt. The portfolio is diversified across industries, entities, and debt seniority levels.
|
||||
|
||||
## Construction / Mechanics
|
||||
- **Definition**: distressed debt = yield spread over Treasuries > ~1,000 basis points
|
||||
- **Diversification**: spread across industries, issuers, and debt seniority levels (senior secured, senior unsecured, subordinated)
|
||||
- **Entry timing**: two common approaches:
|
||||
1. At the end of the default month
|
||||
2. At the end of the bankruptcy-filing month
|
||||
— both aim to exploit overreaction in the distressed debt market at these key dates
|
||||
- **Hold**: position is held passively through the reorganization/recovery process
|
||||
|
||||
Passive strategies may also use models (see Section 15.3) to pre-screen assets and predict which companies are likely to declare bankruptcy, selecting only those positioned for successful reorganization.
|
||||
|
||||
## Return Profile
|
||||
Only a small fraction of held assets are expected to have positive returns, but those that do provide high rates of return (e.g., full par recovery from a deeply discounted purchase). Returns are highly skewed and non-normal. The driver of returns is successful company reorganization — either an out-of-court debt restructuring or a Chapter 11 bankruptcy reorganization.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Yield spread threshold**: typically >1,000 bps over comparable-maturity Treasuries as a distress indicator
|
||||
- **Entry timing**: end of default month or end of bankruptcy-filing month captures the overreaction premium
|
||||
- **Debt seniority**: senior secured debt has higher recovery rates; subordinated debt offers higher upside if the company fully recovers
|
||||
- **Industry and issuer diversification**: essential due to high idiosyncratic default risk; a single large default can dominate portfolio returns
|
||||
- **Bankruptcy prediction models**: logistic regression or similar models on financial ratios to pre-screen for likely successful reorganizations (see Section 15.3)
|
||||
|
||||
## Variations
|
||||
- **Focus on defaults**: buy at the end of the default month, targeting market overreaction to default events
|
||||
- **Focus on bankruptcy filings**: buy at the end of the bankruptcy-filing month, targeting overreaction to Chapter 11 filings
|
||||
- **Seniority-focused**: concentrate in senior secured debt for higher recovery certainty (lower return, lower variance)
|
||||
|
||||
## Notes
|
||||
- Illiquidity: distressed debt is highly illiquid; exit before resolution may require large price concessions
|
||||
- Workout timeline: bankruptcy proceedings can take years; capital is tied up for an uncertain duration
|
||||
- Legal complexity: debt holders in bankruptcy proceedings face complex intercreditor disputes, cram-down risks, and professional fees
|
||||
- Expected value of total portfolio is positive but heavily dependent on the few positions that recover fully
|
||||
- This is a passive strategy — the investor does not seek to influence the reorganization process (contrast with Section 15.2)
|
||||
@@ -0,0 +1,58 @@
|
||||
---
|
||||
description: "Exploit the distress risk puzzle by going long the safest (lowest bankruptcy probability) stocks and short the riskiest, constructing a zero-cost HMD (healthy-minus-distressed) portfolio rebalanced monthly."
|
||||
tags: [distressed-assets, equities, factor-investing, long-short]
|
||||
---
|
||||
|
||||
# Distress Risk Puzzle
|
||||
|
||||
**Section**: 15.3 | **Asset Class**: Distressed Assets (Equities) | **Type**: Factor / Long-Short
|
||||
|
||||
## Overview
|
||||
Early studies suggested that companies more prone to bankruptcy offer higher returns as a risk premium. However, more recent and robust studies find the opposite: distressed (high bankruptcy probability) companies do not outperform healthier ones, and healthier companies actually offer higher returns. This is the "distress risk puzzle." The strategy exploits it by buying the safest companies and selling the riskiest (a healthy-minus-distressed, or HMD, zero-cost long-short portfolio).
|
||||
|
||||
## Construction / Mechanics
|
||||
1. **Estimate bankruptcy probability** `P_i` for each stock `i = 1, ..., N` using, e.g., logistic regression on financial variables:
|
||||
```
|
||||
logit(P_i) = β_0 + β_1 × (leverage) + β_2 × (profitability) + ...
|
||||
```
|
||||
2. **Sort stocks** into deciles by `P_i`
|
||||
3. **Construct zero-cost portfolio**:
|
||||
- **Short** the top decile (highest `P_i` — most distressed)
|
||||
- **Long** the bottom decile (lowest `P_i` — healthiest)
|
||||
4. **Rebalance** monthly (annual rebalancing produces similar returns)
|
||||
|
||||
## Return Profile
|
||||
The HMD portfolio profits when healthy stocks outperform distressed stocks, which empirical evidence suggests happens persistently. Returns are driven by the cross-sectional spread in returns between the safest and riskiest firms. The strategy has equity-like volatility and is exposed to periods of market stress.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Bankruptcy probability `P_i`**: core signal; modeled via logistic regression or other classification methods on financial variables (leverage, profitability, coverage ratios, market-to-book, etc.)
|
||||
- **Decile cutoffs**: top and bottom decile are standard; tighter cutoffs increase signal strength but reduce breadth
|
||||
- **Rebalancing frequency**: monthly is standard; annual rebalancing yields similar returns with lower turnover
|
||||
|
||||
## Variations
|
||||
|
||||
### 15.3.1 Distress Risk Puzzle — Risk Management
|
||||
The standard HMD strategy has a high time-varying market beta that turns significantly negative following market downturns (associated with increased volatility). This can cause large losses when the market rebounds abruptly. To mitigate this, a volatility-scaled version is used:
|
||||
|
||||
```
|
||||
HMD* = (σ_target / σ_hat) × HMD (519)
|
||||
```
|
||||
|
||||
- `HMD` = standard HMD portfolio return (from Section 15.3)
|
||||
- `σ_target` = target volatility level, typically 10%–15% (set per trader preferences)
|
||||
- `σ_hat` = estimated realized volatility over the prior year using daily data
|
||||
|
||||
**Interpretation**:
|
||||
- If `σ_hat = σ_target`: 100% of the investment is allocated
|
||||
- If `σ_hat > σ_target`: allocation is reduced below 100% (de-leverage in high-vol regimes)
|
||||
- If `σ_hat < σ_target`: allocation exceeds 100% (leverage in low-vol regimes)
|
||||
|
||||
Alternatively, the allocation can be capped at 100% (`min(σ_target / σ_hat, 1)`) to avoid leverage entirely.
|
||||
|
||||
## Notes
|
||||
- The distress risk puzzle is a well-documented anomaly but its persistence is debated; it may partly reflect data-mining or survivorship bias
|
||||
- The HMD strategy has high time-varying beta to the equity market; risk management via volatility scaling (15.3.1) is essential for production use
|
||||
- Bankruptcy probability models require regular recalibration; financial ratios used as inputs are sensitive to accounting changes
|
||||
- Short-selling the most distressed stocks can be expensive (high borrow costs) and difficult (low float, high short interest)
|
||||
- Regulatory restrictions on short selling may limit implementation in certain markets or during market stress periods
|
||||
- Similar time-varying beta behavior is observed in other factor-based strategies (momentum, value, etc.), suggesting a common structural risk
|
||||
46
gateway/knowledge/trading/strategies/etfs/alpha-rotation.md
Normal file
46
gateway/knowledge/trading/strategies/etfs/alpha-rotation.md
Normal file
@@ -0,0 +1,46 @@
|
||||
---
|
||||
description: "Rotates into sector ETFs with the highest Jensen's alpha estimated from a Fama-French factor regression, replacing raw cumulative return momentum with factor-adjusted alpha as the ranking signal."
|
||||
tags: [etfs, alpha, momentum, fama-french, rotation]
|
||||
---
|
||||
|
||||
# Alpha Rotation
|
||||
|
||||
**Section**: 4.2 | **Asset Class**: ETFs | **Type**: Momentum / Factor-Adjusted Rotation
|
||||
|
||||
## Overview
|
||||
Alpha rotation is structurally the same as the sector momentum rotation strategy (Section 4.1), but replaces cumulative ETF returns `R_i^cum` with ETF alphas `alpha_i`. These alphas are the Jensen's alpha regression coefficients from a serial regression of each ETF's returns on the Fama-French factors, representing the ETF's return unexplained by common risk factors.
|
||||
|
||||
## Construction / Signal
|
||||
Run a serial regression of ETF returns `R_i(t)` on the 3 Fama-French factors (MKT, SMB, HML):
|
||||
|
||||
```
|
||||
R_i(t) = alpha_i + beta_{1,i} MKT(t) + beta_{2,i} SMB(t) + beta_{3,i} HML(t) + epsilon_i(t) (364)
|
||||
```
|
||||
|
||||
The regression coefficient `alpha_i` (Jensen's alpha) corresponds to the intercept and measures the ETF's risk-adjusted excess return relative to the Fama-French model. This alpha replaces `R_i^cum` as the ranking criterion.
|
||||
|
||||
ETFs are ranked by `alpha_i` (descending). Buy top-decile ETFs (highest alpha) and optionally short bottom-decile ETFs (lowest/most-negative alpha).
|
||||
|
||||
## Entry / Exit Rules
|
||||
- **Entry**: At rebalance, estimate alpha for each ETF over the estimation period; rank and enter positions in top-decile (long) and optionally bottom-decile (short).
|
||||
- **Exit**: Hold for the standard holding period; rebalance at next scheduled interval.
|
||||
- **Estimation period**: Typically 1 year; returns `R_i(t)` are daily or weekly.
|
||||
|
||||
## Key Parameters
|
||||
- **Factor model**: 3 Fama-French factors (MKT, SMB, HML); note alpha here is Jensen's alpha for ETF returns, not mutual fund alpha
|
||||
- **Estimation period**: Typically 1 year
|
||||
- **Return frequency for regression**: Daily or weekly `R_i(t)`
|
||||
- **Holding period**: Same as sector momentum rotation (1–3 months)
|
||||
- **Ranking criterion**: `alpha_i` (intercept of Fama-French regression)
|
||||
|
||||
## Variations
|
||||
- **4-factor model**: Add Carhart momentum factor MOM(t) to regression for a 4-factor alpha
|
||||
- **R-squared augmentation**: Combine alpha ranking with R-squared selectivity measure (see Section 4.3)
|
||||
- **Long-only**: Buy only top-decile ETFs by alpha
|
||||
|
||||
## Notes
|
||||
- Estimation period is typically 1 year with daily or weekly return data.
|
||||
- Jensen's alpha here is defined for ETF returns (not mutual fund returns as in Jensen, 1968).
|
||||
- Alpha rotation is analytically cleaner than raw momentum rotation as it removes systematic factor exposures from the ranking signal.
|
||||
- The MA filter and dual-momentum variations from Section 4.1.1 and 4.1.2 can also be applied here.
|
||||
- Can be combined with R-squared (Section 4.3) to further refine ETF selection.
|
||||
49
gateway/knowledge/trading/strategies/etfs/leveraged-etfs.md
Normal file
49
gateway/knowledge/trading/strategies/etfs/leveraged-etfs.md
Normal file
@@ -0,0 +1,49 @@
|
||||
---
|
||||
description: "Exploits the negative drift of leveraged ETF pairs by simultaneously shorting both a leveraged ETF and its inverse counterpart tracking the same index, capturing decay from daily rebalancing compounding."
|
||||
tags: [etfs, leveraged-etf, letf, short-volatility, decay]
|
||||
---
|
||||
|
||||
# Leveraged ETFs (LETFs)
|
||||
|
||||
**Section**: 4.5 | **Asset Class**: ETFs | **Type**: Short-Volatility / Structural Decay
|
||||
|
||||
## Overview
|
||||
A leveraged (or inverse) ETF seeks to deliver a fixed multiple (2x, 3x) or the inverse (-1x, -2x, -3x) of the daily return of its underlying index. To maintain the target daily leverage, LETFs must rebalance every day — buying when the market is up and selling when it is down. This daily rebalancing creates a negative drift (volatility decay) in the long run, which can be exploited by shorting both a leveraged ETF and its corresponding leveraged inverse ETF on the same underlying index.
|
||||
|
||||
## Construction / Signal
|
||||
A leveraged ETF with leverage factor L rebalances daily to maintain L × (daily index return). This requires:
|
||||
- **On up days**: Buy more of the underlying index
|
||||
- **On down days**: Sell the underlying index
|
||||
|
||||
The compounding of daily returns with daily rebalancing creates a path-dependent negative drift over time:
|
||||
|
||||
```
|
||||
LETF cumulative return < L × (index cumulative return) [for L > 1 or L < -1]
|
||||
```
|
||||
|
||||
**Strategy**: Short both a leveraged ETF (e.g., 2x) and its leveraged inverse ETF (-2x) on the same underlying index. Both positions decay in value over time due to daily rebalancing, generating profit from the combined negative drift.
|
||||
|
||||
Proceeds from both short positions can be invested in an uncorrelated asset (e.g., a Treasury ETF).
|
||||
|
||||
## Entry / Exit Rules
|
||||
- **Entry**: Simultaneously short a leveraged ETF (e.g., 2x long) and its corresponding inverse leveraged ETF (e.g., 2x inverse) on the same underlying index.
|
||||
- **Exit**: Positions are held as long as both ETFs continue to decay; may require periodic rebalancing of the short pair as relative prices change.
|
||||
- **Capital deployment**: Invest the short proceeds into a Treasury ETF or other low-risk asset.
|
||||
|
||||
## Key Parameters
|
||||
- **Leverage factor**: 2x or 3x (and their -2x or -3x inverses)
|
||||
- **Underlying index**: Same index for both the leveraged and inverse leveraged ETF
|
||||
- **Rebalancing of short pair**: Periodically rebalance the short positions to maintain equal dollar exposure
|
||||
- **Volatility regime**: Decay is larger in high-volatility regimes
|
||||
|
||||
## Variations
|
||||
- **3x pair**: Short a 3x leveraged ETF and its -3x inverse (higher decay, higher risk)
|
||||
- **Single-leg short**: Short only the leveraged (not inverse) ETF when directional bias exists
|
||||
- **Volatility regime filter**: Enter positions only in high-volatility environments where decay is expected to be larger
|
||||
|
||||
## Notes
|
||||
- The negative drift from daily rebalancing is mathematically guaranteed over time for both the leveraged and inverse ETF, making this a structural (not purely alpha-dependent) source of return.
|
||||
- **Key risk**: In the short term, if one leg of the short pair (e.g., the inverse ETF) has a large positive return (the market rallies strongly), the short position in the inverse ETF suffers a sizable loss. This short-term risk can be significant even though the long-term drift is negative.
|
||||
- The strategy can have a significant downside in the short term if one short leg moves sharply against the position.
|
||||
- Transaction costs (borrow costs for short selling LETFs, bid-ask spreads) must be carefully considered; LETF borrow rates can be elevated.
|
||||
- Volatility decay is proportional to variance: approximately `L(L-1)/2 × sigma^2` per period for a leverage factor L.
|
||||
57
gateway/knowledge/trading/strategies/etfs/mean-reversion.md
Normal file
57
gateway/knowledge/trading/strategies/etfs/mean-reversion.md
Normal file
@@ -0,0 +1,57 @@
|
||||
---
|
||||
description: "Constructs a dollar-neutral ETF portfolio by selling ETFs with high Internal Bar Strength (IBS, close near daily high) and buying ETFs with low IBS (close near daily low), exploiting short-term mean-reversion."
|
||||
tags: [etfs, mean-reversion, ibs, internal-bar-strength]
|
||||
---
|
||||
|
||||
# Mean-Reversion (ETFs)
|
||||
|
||||
**Section**: 4.4 | **Asset Class**: ETFs | **Type**: Mean-Reversion
|
||||
|
||||
## Overview
|
||||
This strategy applies mean-reversion to ETFs using the Internal Bar Strength (IBS) indicator, derived from the previous day's close, high, and low prices. ETFs with a close near their daily high (high IBS) are considered "rich" and likely to revert downward; ETFs with a close near their daily low (low IBS) are "cheap" and likely to revert upward. A dollar-neutral portfolio sells high-IBS ETFs and buys low-IBS ETFs.
|
||||
|
||||
## Construction / Signal
|
||||
**Internal Bar Strength (IBS)**:
|
||||
```
|
||||
IBS = (P_C - P_L) / (P_H - P_L) (370)
|
||||
```
|
||||
|
||||
Where:
|
||||
- `P_C` = previous day's closing price
|
||||
- `P_H` = previous day's high price
|
||||
- `P_L` = previous day's low price
|
||||
|
||||
IBS ranges from 0 to 1:
|
||||
- IBS close to 1: price closed near the daily high → ETF is "rich"
|
||||
- IBS close to 0: price closed near the daily low → ETF is "cheap"
|
||||
|
||||
An equivalent symmetric measure: `Y = IBS - 1/2 = (P_C - P_*) / (P_H - P_L)` where `P_* = (P_H + P_L) / 2`; Y ranges from -1/2 to +1/2.
|
||||
|
||||
**Portfolio construction**:
|
||||
- Sort ETFs cross-sectionally by IBS.
|
||||
- Sell ETFs in the top decile (high IBS, "rich").
|
||||
- Buy ETFs in the bottom decile (low IBS, "cheap").
|
||||
- Dollar-neutral construction.
|
||||
|
||||
## Entry / Exit Rules
|
||||
- **Entry**: Each day after the close, compute IBS for all ETFs, rank, and enter positions for the next day's open or close.
|
||||
- **Exit**: Typically hold for 1 day (short-term mean-reversion); close at next day's close.
|
||||
- **Rebalance**: Daily.
|
||||
|
||||
## Key Parameters
|
||||
- **IBS computation**: Daily, using previous day's high, low, and close
|
||||
- **Holding period**: Short-term (typically 1 day)
|
||||
- **Portfolio construction**: Dollar-neutral long/short decile
|
||||
- **Weights**: Uniform for all long and all short ETFs, or volatility-weighted
|
||||
|
||||
## Variations
|
||||
- **Volatility-weighted positions**: Weight positions by historical ETF volatility rather than equal-weighting
|
||||
- **Stock mean-reversion methods**: Mean-reversion strategies from Section 3 (cluster, weighted regression) can also be adapted to ETFs
|
||||
- **IBS threshold**: Instead of top/bottom decile, use a fixed IBS threshold (e.g., IBS > 0.8 = short, IBS < 0.2 = long)
|
||||
|
||||
## Notes
|
||||
- IBS is a simple, daily-bar indicator requiring only OHLC (open-high-low-close) data.
|
||||
- Mean-reversion in ETFs can be stronger than in individual stocks because ETFs represent diversified baskets where idiosyncratic volatility is reduced, and market-maker arbitrage constrains large deviations from NAV.
|
||||
- Holding period is very short (1 day); transaction costs can be significant for daily rebalancing.
|
||||
- The strategy can be combined with other signals (e.g., sector momentum) for confirmation.
|
||||
- All stock-based mean-reversion strategies (clusters, weighted regression) can be adapted for ETF universes.
|
||||
@@ -0,0 +1,70 @@
|
||||
---
|
||||
description: "Builds a long-only trend-following portfolio across multiple asset classes using ETFs, allocating weights proportional to cumulative momentum and optionally risk-adjusted by historical volatility, with an optional MA filter."
|
||||
tags: [etfs, trend-following, multi-asset, momentum, long-only]
|
||||
---
|
||||
|
||||
# Multi-Asset Trend Following
|
||||
|
||||
**Section**: 4.6 | **Asset Class**: ETFs | **Type**: Trend-Following / Multi-Asset
|
||||
|
||||
## Overview
|
||||
ETFs allow efficient diversification across sectors, countries, asset classes, and factors in a relatively small number of instruments. This strategy constructs a long-only trend-following portfolio across multiple ETFs (and thus multiple asset classes) by allocating weights based on cumulative momentum, optionally filtered by a moving average, and weighted by historical volatility to manage risk.
|
||||
|
||||
## Construction / Signal
|
||||
**Step 1 — Compute cumulative returns** over a T-month formation period (T = 6–12 months):
|
||||
```
|
||||
R_i^cum = P_i(t) / P_i(t+T) - 1
|
||||
```
|
||||
|
||||
**Step 2 — Filter**: Keep only ETFs with positive `R_i^cum` (positive momentum required for long-only).
|
||||
|
||||
**Step 3 — Optional MA filter**: Additionally keep only ETFs whose last closing price P_i exceeds their moving average MA_i(T') (typically T' = 100–200 days):
|
||||
```
|
||||
P_i > MA_i(T')
|
||||
```
|
||||
|
||||
**Step 4 — Assign weights** to all surviving ETFs (not just top decile, since the universe is small):
|
||||
|
||||
Option A — proportional to cumulative return:
|
||||
```
|
||||
w_i = gamma_1 * R_i^cum (371)
|
||||
```
|
||||
|
||||
Option B — momentum divided by volatility (Sharpe-like weighting):
|
||||
```
|
||||
w_i = gamma_2 * R_i^cum / sigma_i (372)
|
||||
```
|
||||
|
||||
Option C — momentum divided by variance (Sharpe ratio optimization for diagonal covariance):
|
||||
```
|
||||
w_i = gamma_3 * R_i^cum / sigma_i^2 (373)
|
||||
```
|
||||
|
||||
where `sigma_i` is historical ETF volatility and normalization coefficients `gamma_1`, `gamma_2`, `gamma_3` are computed to satisfy `sum_{i=1}^{N} w_i = 1` (N = number of ETFs with nonzero weights after filtering).
|
||||
|
||||
Option C (Eq. 373) optimizes the Sharpe ratio of the ETF portfolio assuming a diagonal covariance matrix `C_ij = diag(sigma_i^2)` (ignoring cross-ETF correlations).
|
||||
|
||||
## Entry / Exit Rules
|
||||
- **Entry**: At each rebalance, apply momentum and MA filters, compute weights, and enter long positions in all surviving ETFs.
|
||||
- **Exit**: Rebalance monthly (or per the formation period schedule); ETFs with negative cumulative momentum or below their MA are dropped (weight set to zero).
|
||||
- **Position cap**: Bounds `w_i <= w_i^max` can be imposed to prevent overweighting of any single volatile ETF.
|
||||
|
||||
## Key Parameters
|
||||
- **Formation period T**: 6–12 months
|
||||
- **MA filter length T'**: 100–200 days (optional; aligns with sector momentum rotation MA filter)
|
||||
- **Weighting scheme**: Equal (Eq. 371), volatility-adjusted (Eq. 372), or variance-adjusted/Sharpe-optimal (Eq. 373)
|
||||
- **Position cap**: Maximum weight per ETF (optional; mitigates concentration risk)
|
||||
- **Holding period**: Monthly rebalancing typical
|
||||
|
||||
## Variations
|
||||
- **No MA filter**: Use only positive cumulative return filter
|
||||
- **With position caps**: Add `w_i <= w_i^max` to prevent overweighting high-momentum volatile ETFs
|
||||
- **Sector rotation overlay**: Combine with sector momentum rotation (Section 4.1) by restricting the universe to top-ranked sectors
|
||||
|
||||
## Notes
|
||||
- Eq. (371) is the simplest weighting; it overweights volatile ETFs since on average `R_i^cum ∝ sigma_i`.
|
||||
- Eq. (372) mitigates volatility overweighting by dividing by sigma_i.
|
||||
- Eq. (373) is the optimal Sharpe ratio solution under the assumption of uncorrelated (diagonal covariance) ETF returns.
|
||||
- The key advantage of ETFs for multi-asset trend following: a small number of instruments (tens of ETFs) can provide exposure to many asset classes, sectors, geographies, and factors simultaneously.
|
||||
- Long-only construction avoids shorting complexity; the MA filter prevents buying ETFs in absolute downtrends even if they have relative momentum.
|
||||
- For some literature on multi-asset portfolios, dynamic asset allocation, and related topics: Bekkers, Doeswijk and Lam (2009), Black and Litterman (1992), Faber (2015, 2016), Mladina (2014).
|
||||
63
gateway/knowledge/trading/strategies/etfs/r-squared.md
Normal file
63
gateway/knowledge/trading/strategies/etfs/r-squared.md
Normal file
@@ -0,0 +1,63 @@
|
||||
---
|
||||
description: "Overweights ETFs with high selectivity (low R-squared against factor model) and high alpha, and underweights ETFs with low selectivity (high R-squared), using a two-dimensional sort on R-squared and alpha."
|
||||
tags: [etfs, r-squared, alpha, selectivity, factor-model]
|
||||
---
|
||||
|
||||
# R-Squared
|
||||
|
||||
**Section**: 4.3 | **Asset Class**: ETFs | **Type**: Factor-Based / Selectivity
|
||||
|
||||
## Overview
|
||||
Empirical studies suggest that augmenting Jensen's alpha with an indicator based on R-squared from a factor model regression adds predictive value for future ETF returns. R-squared measures how much of an ETF's return variance is explained by common factors; low R-squared (high "selectivity") combined with high alpha predicts strong future performance. High R-squared (low selectivity) combined with low alpha predicts weak future performance.
|
||||
|
||||
## Construction / Signal
|
||||
Run a serial regression of ETF returns `R_i(t)` on 4 factors (Fama-French 3 + Carhart momentum):
|
||||
|
||||
```
|
||||
R_i(t) = alpha_i + beta_{1,i} MKT(t) + beta_{2,i} SMB(t) + beta_{3,i} HML(t) + beta_{4,i} MOM(t) + epsilon_i(t) (365)
|
||||
```
|
||||
|
||||
Compute regression R-squared:
|
||||
```
|
||||
R^2 = 1 - SS_res / SS_tot (366)
|
||||
|
||||
SS_res = sum_{i=1}^{N} epsilon_i(t)^2 (367)
|
||||
|
||||
SS_tot = sum_{i=1}^{N} (R_i(t) - R_bar(t))^2 (368)
|
||||
|
||||
R_bar(t) = (1/N) * sum_{i=1}^{N} R_i(t) (369)
|
||||
```
|
||||
|
||||
**Selectivity** = `1 - R^2` [Amihud and Goyenko, 2013]. High selectivity = low R-squared = returns less explained by common factors.
|
||||
|
||||
**Two-dimensional sort strategy**:
|
||||
1. Sort ETFs into quintiles by R-squared (5 groups).
|
||||
2. Within each R-squared quintile, sort ETFs into sub-quintiles by alpha (5 sub-groups).
|
||||
3. This creates 25 groups of ETFs.
|
||||
4. **Buy** ETFs in the group with lowest R-squared quintile and highest alpha sub-quintile.
|
||||
5. **Sell** ETFs in the group with highest R-squared quintile and lowest alpha sub-quintile.
|
||||
|
||||
## Entry / Exit Rules
|
||||
- **Entry**: At rebalance, run regression, compute R-squared and alpha for each ETF, perform 5×5 sort, enter long/short positions.
|
||||
- **Exit**: Hold for estimation period or holding period; rebalance periodically.
|
||||
- **Estimation period**: Same as alpha rotation (typically 1 year); longer estimation periods can be used, especially for monthly returns.
|
||||
|
||||
## Key Parameters
|
||||
- **Factor model**: 4-factor (Fama-French 3 + Carhart MOM); 3-factor also usable
|
||||
- **Estimation period**: Typically 1 year; can be longer for monthly return data
|
||||
- **Sort dimensions**: R-squared quintiles × alpha sub-quintiles (5×5 = 25 groups)
|
||||
- **Holding period**: Similar to alpha rotation strategy (1–3 months)
|
||||
- **Selectivity definition**: `1 - R^2`
|
||||
|
||||
## Variations
|
||||
- **3-factor model**: Use Fama-French 3 factors without momentum factor MOM
|
||||
- **Different quintile splits**: Use deciles instead of quintiles for finer grouping
|
||||
- **R-squared only**: Sort purely by R-squared without the alpha sub-sort
|
||||
- **Estimation period alignment**: Use same estimation period as alpha rotation strategy (Section 4.2) for consistency
|
||||
|
||||
## Notes
|
||||
- R-squared as a measure of active management: in Amihud and Goyenko (2013), R-squared is applied to mutual funds; Garyn-Tal (2014a, 2014b) applies it to actively managed ETFs.
|
||||
- Low R-squared means the ETF has high "active share" — its returns are driven more by the manager's specific bets than by passive factor exposure.
|
||||
- The estimation period and return frequency for R-squared can be the same as for alpha rotation (see Section 4.2 and fn. 77).
|
||||
- Longer estimation periods are particularly appropriate if R_i(t) are monthly returns.
|
||||
- Can be combined with the MA filter (Section 4.1.1) as an additional condition.
|
||||
@@ -0,0 +1,74 @@
|
||||
---
|
||||
description: "Overweights ETFs from outperforming sectors and underweights those from underperforming sectors based on T-month cumulative return momentum, with optional MA filter and dual-momentum variants."
|
||||
tags: [etfs, momentum, sector-rotation]
|
||||
---
|
||||
|
||||
# Sector Momentum Rotation
|
||||
|
||||
**Section**: 4.1 / 4.1.1 / 4.1.2 | **Asset Class**: ETFs | **Type**: Momentum / Sector Rotation
|
||||
|
||||
## Overview
|
||||
Empirical evidence shows that the momentum effect exists not only for individual stocks but also for sectors and industries. The sector momentum rotation strategy overweights ETFs from outperforming sectors and underweights those from underperforming sectors, using ETFs concentrated in specific sectors/industries to implement sector/industry rotation without buying or selling large numbers of underlying stocks.
|
||||
|
||||
## Construction / Signal
|
||||
Similarly to stock price-momentum (Section 3.1), use each sector ETF's cumulative return as the momentum measure. Let `P_i(t)` be the price of ETF labeled by i:
|
||||
|
||||
```
|
||||
R_i^cum(t) = P_i(t) / P_i(t + T) - 1 (361)
|
||||
```
|
||||
|
||||
Here `t + T` is T months in the past w.r.t. t. After time t, buy ETFs in the top decile by `R_i^cum(t)` and hold for a holding period (typically 1–3 months).
|
||||
|
||||
**Dollar-neutral construction**: Buy top-decile ETFs and short bottom-decile ETFs (ETFs can be shorted).
|
||||
|
||||
**Long-only construction**: Buy only top-decile ETFs, equal-weight or volatility-weight.
|
||||
|
||||
## Entry / Exit Rules
|
||||
- **Entry**: At rebalance, rank all sector ETFs by cumulative return `R_i^cum`; buy top-decile, optionally short bottom-decile.
|
||||
- **Exit**: Hold for 1–3 months; rebalance at the next scheduled interval.
|
||||
- **Formation period T**: Typically 6–12 months.
|
||||
|
||||
## Key Parameters
|
||||
- **Formation period T**: 6–12 months
|
||||
- **Holding period**: 1–3 months
|
||||
- **Portfolio construction**: Long-only (top decile) or dollar-neutral (top long, bottom short)
|
||||
- **Weights**: Uniform or volatility-adjusted
|
||||
|
||||
## Variations
|
||||
|
||||
### 4.1.1 — Sector Momentum Rotation with MA Filter
|
||||
|
||||
A refinement that requires an ETF to pass a moving average filter before entering a position, preventing buys in sectors with downward price trends even if they rank high by relative momentum.
|
||||
|
||||
```
|
||||
Rule = { Buy top-decile ETFs only if P > MA(T')
|
||||
{ Short bottom-decile ETFs only if P < MA(T') (362)
|
||||
```
|
||||
|
||||
- `P` = ETF's current price at transaction time
|
||||
- `MA(T')` = moving average of ETF's daily prices over T' days (T' can differ from formation period T; typically T' = 100–200 days)
|
||||
|
||||
This ensures the absolute price level (trend) also supports the trade direction.
|
||||
|
||||
### 4.1.2 — Dual-Momentum Sector Rotation
|
||||
|
||||
In long-only strategies, mitigates the risk of buying sector ETFs when the broad market is trending down. Augments relative (cross-sectional) momentum with absolute (time-series) momentum of a broad market index ETF:
|
||||
|
||||
```
|
||||
Rule = { Buy top-decile ETFs if broad market P > MA(T')
|
||||
{ Buy an uncorrelated ETF (e.g., gold, Treasury) if broad market P <= MA(T') (363)
|
||||
```
|
||||
|
||||
- `P` = broad market index ETF's price at transaction time
|
||||
- `MA(T')` = moving average of the broad market index ETF's price; typically T' = 100–200 days
|
||||
|
||||
If the broad market is below its moving average (downtrend), capital is rotated into an ETF uncorrelated with the broad market (e.g., gold or Treasury ETF) instead of sector ETFs.
|
||||
|
||||
Reference: Antonacci (2014, 2017).
|
||||
|
||||
## Notes
|
||||
- ETF-based sector rotation is simpler to implement than stock-level sector rotation: one ETF trade per sector instead of dozens of stock trades.
|
||||
- The MA filter (4.1.1) reduces the chance of buying momentum in a sector that is in absolute decline.
|
||||
- Dual-momentum (4.1.2) addresses the long-only strategy's vulnerability to broad market drawdowns.
|
||||
- Typical formation period: 6–12 months; typical holding period: 1–3 months.
|
||||
- Dollar-neutral construction removes broad market exposure but requires shorting ETFs (feasible in practice).
|
||||
@@ -0,0 +1,50 @@
|
||||
---
|
||||
description: "A barbell portfolio holds bonds at two extreme maturities (short and long) to achieve a target duration while gaining higher convexity than an equivalent bullet, providing better protection against parallel yield curve shifts."
|
||||
tags: [fixed-income, duration, convexity, barbell, yield-curve]
|
||||
---
|
||||
|
||||
# Barbells
|
||||
|
||||
**Section**: 5.3 | **Asset Class**: Fixed Income | **Type**: Duration / Convexity
|
||||
|
||||
## Overview
|
||||
A barbell concentrates holdings at two maturities: a short maturity T_1 and a long maturity T_2. It is a combination of two bullet strategies. For a given modified duration (matching a bullet at intermediate maturity T_*), the barbell achieves higher convexity, providing better protection against parallel yield shifts at the cost of lower overall yield.
|
||||
|
||||
## Construction / Mechanics
|
||||
For a simple barbell of w_1 dollars in zero-coupon bonds with maturity T_1 and w_2 dollars with maturity T_2 (continuous compounding, constant yield Y), with price-adjusted weights w̃_1 = w_1·exp(-T_1·Y) and w̃_2 = w_2·exp(-T_2·Y):
|
||||
|
||||
**Duration** (equals a bullet at T_*):
|
||||
```
|
||||
D = (w̃_1·T_1 + w̃_2·T_2) / (w̃_1 + w̃_2) (390)
|
||||
T_* = D_* = D (391)
|
||||
```
|
||||
|
||||
**Convexity** (exceeds the equivalent bullet):
|
||||
```
|
||||
C = (w̃_1·T_1² + w̃_2·T_2²) / (w̃_1 + w̃_2) (392)
|
||||
C_* = T_*² (393)
|
||||
```
|
||||
|
||||
The convexity advantage:
|
||||
```
|
||||
C - C_* = (w̃_1·w̃_2 / (w̃_1 + w̃_2)²) · (T_2 - T_1)² > 0 (394)
|
||||
```
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Higher convexity than an equivalent bullet means the barbell outperforms when yields move significantly in either direction (parallel shifts).
|
||||
- The long-maturity bonds benefit from high yields; the short-maturity bonds provide protection if rates rise (proceeds reinvested at higher rates).
|
||||
- Flattening of the yield curve (short-term rates rise relative to long-term) has a positive impact; steepening has a negative impact.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- T_1 (short maturity), T_2 (long maturity): the two maturities defining the barbell
|
||||
- w_1, w_2: dollar allocations to short and long maturities
|
||||
- Target duration D: matched to the equivalent bullet at T_*
|
||||
- Convexity advantage C - C_*: larger the spread T_2 - T_1, the greater the convexity benefit
|
||||
|
||||
## Variations
|
||||
- Combine with duration matching to an intermediate bullet for controlled rate exposure.
|
||||
|
||||
## Notes
|
||||
- Higher convexity comes at the expense of lower overall yield (yield curve typically slopes upward, so the mid-point bullet earns more carry).
|
||||
- Duration scales approximately linearly with maturity; convexity scales quadratically — this is why the barbell's convexity exceeds the equivalent bullet.
|
||||
- The barbell is more complex to manage than a bullet due to two distinct maturity exposures.
|
||||
@@ -0,0 +1,66 @@
|
||||
---
|
||||
description: "Bond immunization constructs a portfolio whose duration matches a future cash obligation's maturity, protecting the portfolio value against parallel yield curve shifts to meet a predetermined liability."
|
||||
tags: [fixed-income, duration, immunization, liability-matching, convexity]
|
||||
---
|
||||
|
||||
# Bond Immunization
|
||||
|
||||
**Section**: 5.5 | **Asset Class**: Fixed Income | **Type**: Duration / Liability Matching
|
||||
|
||||
## Overview
|
||||
Bond immunization is used to ensure a portfolio can meet a predetermined future cash obligation F at time T_*. A portfolio is constructed so that its duration matches T_*, making its value insensitive to parallel shifts in the yield curve. It extends to matching convexity for additional protection with three bonds.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Total investment** P given a future obligation F at time T_*, constant yield Y, periodic compounding with period δ:
|
||||
```
|
||||
P = F / (1 + Yδ)^(T_*/δ) (396)
|
||||
```
|
||||
|
||||
**Two-bond immunization** (matches duration only):
|
||||
|
||||
With two bonds of maturities T_1, T_2 and modified durations D_1, D_2, dollar allocations P_1, P_2:
|
||||
```
|
||||
P_1 + P_2 = P (397)
|
||||
P_1·D_1 + P_2·D_2 = P·D (398)
|
||||
```
|
||||
where the target modified duration:
|
||||
```
|
||||
D = T_* / (1 + Yδ) (399)
|
||||
```
|
||||
|
||||
**Three-bond immunization** (matches duration and convexity):
|
||||
|
||||
With three bonds, durations D_1, D_2, D_3 and convexities C_1, C_2, C_3:
|
||||
```
|
||||
P_1 + P_2 + P_3 = P (400)
|
||||
P_1·D_1 + P_2·D_2 + P_3·D_3 = P·D (401)
|
||||
P_1·C_1 + P_2·C_2 + P_3·C_3 = P·C (402)
|
||||
```
|
||||
where the target convexity:
|
||||
```
|
||||
C = T_*(T_* + δ) / (1 + Yδ)² (403)
|
||||
```
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Immunized portfolio is protected against parallel yield curve shifts: the gain/loss from price changes offsets the loss/gain from reinvestment rate changes.
|
||||
- Matching convexity (three-bond) provides additional protection against larger rate moves.
|
||||
- The portfolio value converges to F at time T_* under parallel shifts.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- T_*: maturity of the future cash obligation (target duration)
|
||||
- F: size of the future obligation
|
||||
- Y: assumed constant yield (all bonds assumed same yield — a simplification)
|
||||
- D, C: target modified duration and convexity
|
||||
|
||||
## Variations
|
||||
- **Zero-coupon immunization**: purchase a single zero-coupon bond with maturity T_* — the simplest solution, but may not be available.
|
||||
- **Two-bond**: matches duration only; sufficient for small parallel shifts.
|
||||
- **Three-bond**: matches both duration and convexity; handles larger shifts.
|
||||
- Extension to non-parallel yield curve changes requires additional sophistication.
|
||||
|
||||
## Notes
|
||||
- The assumption that all bonds have the same yield is a simplification; in practice yields differ across maturities and issuers.
|
||||
- The portfolio must be periodically rebalanced as the yield curve changes, incurring transaction costs.
|
||||
- Immunization protects against parallel shifts only; slope and curvature changes can still cause losses.
|
||||
- Non-parallel shifts, credit spread changes, and transaction costs all introduce complexity in practice.
|
||||
36
gateway/knowledge/trading/strategies/fixed-income/bullets.md
Normal file
36
gateway/knowledge/trading/strategies/fixed-income/bullets.md
Normal file
@@ -0,0 +1,36 @@
|
||||
---
|
||||
description: "A bullet portfolio concentrates all bond holdings at a single target maturity, used to express a directional view on interest rates at a specific point on the yield curve."
|
||||
tags: [fixed-income, duration, bullet, yield-curve]
|
||||
---
|
||||
|
||||
# Bullets
|
||||
|
||||
**Section**: 5.2 | **Asset Class**: Fixed Income | **Type**: Duration / Directional
|
||||
|
||||
## Overview
|
||||
In a bullet portfolio all bonds share the same maturity date T, targeting a specific segment of the yield curve. The strategy expresses a view on the direction of interest rates at that maturity. Bonds are typically purchased over time to mitigate timing risk from rate fluctuations.
|
||||
|
||||
## Construction / Mechanics
|
||||
- Select a target maturity T based on the trader's interest rate outlook.
|
||||
- Purchase bonds of that maturity, potentially accumulating positions over time.
|
||||
- Hold to maturity or until the rate view is realized.
|
||||
|
||||
Purchasing over time mitigates interest rate risk: if rates rise, later purchases capture higher yields; if rates fall, earlier purchases lock in higher yields.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- **Rates expected to fall** (bond prices rise): pick a longer maturity — longer bonds gain more in price from a given yield decline (higher duration).
|
||||
- **Rates expected to rise** (bond prices fall): pick a shorter maturity — shorter bonds lose less.
|
||||
- **Uncertain outlook**: diversify across maturities (barbell or ladder preferred).
|
||||
|
||||
## Key Parameters / Signals
|
||||
- Target maturity T: the single maturity determining duration exposure
|
||||
- Modified duration: scales with T; determines price sensitivity to rate changes
|
||||
- Interest rate forecast: the primary signal driving maturity selection
|
||||
|
||||
## Variations
|
||||
- Building the portfolio gradually over time to average in across different rate environments.
|
||||
|
||||
## Notes
|
||||
- Concentrating at one maturity creates pure duration exposure with no convexity advantage.
|
||||
- Compared to a barbell with the same duration, a bullet has lower convexity, meaning it is more exposed to parallel yield curve shifts.
|
||||
- Suitable when the trader has a strong directional view on a specific maturity segment.
|
||||
@@ -0,0 +1,56 @@
|
||||
---
|
||||
description: "The carry factor strategy buys bonds with the highest carry — the return earned as a bond rolls down the yield curve — combining bond yield income with the roll-down return from the yield curve's slope."
|
||||
tags: [fixed-income, factor, carry, roll-down, yield-curve]
|
||||
---
|
||||
|
||||
# Carry Factor
|
||||
|
||||
**Section**: 5.11 | **Asset Class**: Fixed Income | **Type**: Factor / Carry
|
||||
|
||||
## Overview
|
||||
Carry in fixed income is the return from holding a bond as it "rolls down" the yield curve toward maturity. If the term structure is upward-sloping and stable, a bond's yield declines as its maturity shortens, causing a price appreciation on top of the coupon income. The carry factor strategy buys bonds in the top decile by carry and sells those in the bottom decile.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Carry** over horizon Δt for a bond with current maturity T:
|
||||
|
||||
```
|
||||
C(t, t+Δt, T) = [P(t+Δt, T) - P(t, T)] / P(t, T) (413)
|
||||
```
|
||||
|
||||
Under the assumption that the yield curve shape is constant (R(t,T) = f(T-t) only), the yield at t+Δt is R(t+Δt, T) = R(t, T-Δt), giving:
|
||||
|
||||
```
|
||||
C(t, t+Δt, T) = R(t,T)·Δt + C_roll(t, t+Δt, T) (414)
|
||||
```
|
||||
|
||||
Two components:
|
||||
1. **Yield income**: R(t,T)·Δt — the bond's current yield times the holding period
|
||||
2. **Roll-down return**:
|
||||
```
|
||||
C_roll(t, t+Δt, T) ≈ -ModD(t,T) · [R(t, T-Δt) - R(t, T)] (415)
|
||||
```
|
||||
This is the price appreciation as the bond shortens in maturity by Δt along a static yield curve, estimated using modified duration.
|
||||
|
||||
**Portfolio construction**: rank all bonds by C(t, t+Δt, T); long top decile, short bottom decile (zero-cost version).
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Earns yield income plus roll-down return when the yield curve is upward-sloping and stable.
|
||||
- Roll-down return is greatest in the steepest segments of the yield curve.
|
||||
- Underperforms or loses when the yield curve flattens, inverts, or shifts upward unexpectedly.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- R(t,T): current yield (income component)
|
||||
- ModD(t,T): modified duration (scales the roll-down component)
|
||||
- R(t, T-Δt) - R(t, T): slope of the yield curve at maturity T (steeper = more roll-down)
|
||||
- Δt: carry horizon (e.g., 1 month)
|
||||
|
||||
## Variations
|
||||
- Long-only: buy top decile by carry (no short sales required).
|
||||
- Cross-asset carry: extend the same framework to other fixed income markets (government bonds, credit, etc.).
|
||||
|
||||
## Notes
|
||||
- The static yield curve assumption simplifies computation; actual carry will differ if the curve shifts.
|
||||
- For financed portfolios, R(t,T) is replaced by R(t,T) - r_f (excess yield over the risk-free rate) in the income component, but this does not affect portfolio weights.
|
||||
- High-carry bonds tend to have longer maturities in an upward-sloping curve environment, so the carry factor has implicit duration exposure.
|
||||
- Carry and roll-down are sometimes separated as distinct signals; roll-down alone favors bonds in the steepest curve segments regardless of yield level.
|
||||
@@ -0,0 +1,55 @@
|
||||
---
|
||||
description: "CDS basis arbitrage exploits the mispricing between a bond's credit spread and its CDS spread — when the CDS basis is negative (bond spread too high), buy the bond and buy CDS protection to lock in a risk-free profit."
|
||||
tags: [fixed-income, arbitrage, cds, credit-spread, basis]
|
||||
---
|
||||
|
||||
# CDS Basis Arbitrage
|
||||
|
||||
**Section**: 5.14 | **Asset Class**: Fixed Income | **Type**: Arbitrage / Credit
|
||||
|
||||
## Overview
|
||||
A credit default swap (CDS) provides insurance against default on a bond. In theory, the CDS spread should equal the bond yield spread over the risk-free rate, making the insured bond equivalent to a risk-free instrument. The CDS basis is the difference between these two spreads, and deviations from zero create arbitrage opportunities.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**CDS basis**:
|
||||
```
|
||||
CDS basis = CDS spread - bond spread (417)
|
||||
```
|
||||
|
||||
where bond spread = bond yield - risk-free rate.
|
||||
|
||||
**Arbitrage logic**:
|
||||
- CDS spread should ≈ bond spread (both represent compensation for default risk)
|
||||
- If CDS basis ≠ 0 (and |basis| exceeds transaction costs), an arbitrage opportunity exists
|
||||
|
||||
**Negative basis trade** (most common):
|
||||
- CDS basis < 0: bond spread > CDS spread → bond is relatively cheap
|
||||
- Trade: **buy the bond** (receive the high spread) + **buy CDS protection** (pay the lower CDS spread)
|
||||
- Net P&L per dollar of insured debt: bond spread - CDS spread = -basis > 0
|
||||
- Result: a nearly risk-free positive carry, since the CDS makes the bond effectively risk-free
|
||||
|
||||
**Positive basis trade** (less common in practice):
|
||||
- CDS basis > 0: CDS spread > bond spread → CDS protection is expensive relative to bond
|
||||
- Trade: sell the bond + sell CDS protection (write CDS)
|
||||
- In practice, this often means unwinding an existing position (already owning both the bond and CDS)
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Earns the absolute value of the CDS basis as a near-riskless spread.
|
||||
- Position closed when basis converges back to zero.
|
||||
- The trade is essentially a carry trade: positive carry from the basis for as long as it persists.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- CDS basis = CDS spread - bond spread: the primary signal
|
||||
- Transaction cost threshold: |basis| must exceed bid-ask spreads and financing costs
|
||||
- Sign of basis: negative → buy bond + buy CDS; positive → sell bond + sell CDS
|
||||
|
||||
## Variations
|
||||
- **Synthetic bond replication**: CDS + risk-free bond (e.g., Treasury repo) replicates a corporate bond; mispricing between the two creates the arbitrage.
|
||||
|
||||
## Notes
|
||||
- CDS protection makes the bond synthetically risk-free, but counterparty risk on the CDS remains.
|
||||
- Negative basis arbitrage requires financing the bond purchase (repo market); the repo rate affects net P&L.
|
||||
- The CDS basis can persist or widen during stress periods (e.g., 2008 financial crisis) before eventually converging, creating significant mark-to-market losses in the interim.
|
||||
- Liquidity risk: corporate bonds may be illiquid, making it difficult to close the position at fair value.
|
||||
- In the positive basis case, selling a corporate bond short is operationally challenging.
|
||||
@@ -0,0 +1,44 @@
|
||||
---
|
||||
description: "A dollar-duration-neutral butterfly combines a long barbell (short T_1 and long T_3 maturities) with a short bullet (intermediate T_2) at zero net cost, immunizing against parallel yield curve shifts to profit from yield curve curvature changes."
|
||||
tags: [fixed-income, butterfly, duration-neutral, yield-curve, curvature]
|
||||
---
|
||||
|
||||
# Dollar-Duration-Neutral Butterfly
|
||||
|
||||
**Section**: 5.6 | **Asset Class**: Fixed Income | **Type**: Yield Curve / Curvature
|
||||
|
||||
## Overview
|
||||
The dollar-duration-neutral butterfly is a zero-cost combination of a long barbell (long T_1 and T_3 maturity bonds) and a short bullet (short the T_2 intermediate maturity bond), where T_1 < T_2 < T_3. Both zero cost (dollar neutrality) and dollar-duration neutrality conditions are imposed, immunizing the portfolio against parallel yield curve shifts. The strategy profits from changes in yield curve curvature.
|
||||
|
||||
## Construction / Mechanics
|
||||
Let P_1, P_2, P_3 be the dollar amounts invested in the three bonds, and D_1, D_2, D_3 their modified durations.
|
||||
|
||||
**Zero-cost** (dollar neutrality): the long barbell finances the short bullet position:
|
||||
```
|
||||
P_1 + P_3 = P_2 (404)
|
||||
```
|
||||
|
||||
**Dollar-duration neutrality** (parallel shift immunity):
|
||||
```
|
||||
P_1·D_1 + P_3·D_3 = P_2·D_2 (405)
|
||||
```
|
||||
|
||||
These two equations determine P_1 and P_3 given P_2.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Profits when the yield curve becomes more curved (humped): the intermediate yield rises relative to the wings, or the wings fall relative to the body.
|
||||
- Immune to small parallel shifts in the yield curve (both level and dollar-duration matched).
|
||||
- Exposed to changes in the slope and curvature of the yield curve.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- T_1 (short wing), T_2 (body), T_3 (long wing): the three maturities; T_1 < T_2 < T_3
|
||||
- D_1, D_2, D_3: modified durations of the three bonds
|
||||
- P_2: the reference position size (determines P_1 and P_3 via the two constraints)
|
||||
|
||||
## Variations
|
||||
- See also: fifty-fifty butterfly (5.7) and regression-weighted butterfly (5.8), which relax the zero-cost condition.
|
||||
|
||||
## Notes
|
||||
- Dollar-duration neutrality (Eq. 405) protects against parallel shifts only; non-parallel changes in slope or curvature can still generate losses or gains.
|
||||
- The zero-cost constraint (Eq. 404) means no initial capital is required, making it attractive as an overlay strategy.
|
||||
- In practice, bid-ask spreads, financing costs, and liquidity differences across maturities affect profitability.
|
||||
@@ -0,0 +1,46 @@
|
||||
---
|
||||
description: "A fifty-fifty butterfly sets equal dollar durations on both wings of the barbell, making it approximately neutral to small yield curve steepening and flattening while remaining dollar-duration neutral, trading zero-cost for curve-neutrality."
|
||||
tags: [fixed-income, butterfly, duration-neutral, yield-curve, curvature]
|
||||
---
|
||||
|
||||
# Fifty-Fifty Butterfly
|
||||
|
||||
**Section**: 5.7 | **Asset Class**: Fixed Income | **Type**: Yield Curve / Curvature
|
||||
|
||||
## Overview
|
||||
The fifty-fifty butterfly is a variation of the dollar-duration-neutral butterfly that equalizes the dollar durations of the two wings (short-maturity and long-maturity positions). This makes the strategy approximately neutral to small steepening and flattening of the yield curve (not just parallel shifts), at the cost of no longer being dollar-neutral (it is not zero-cost). It is also known as the "neutral curve butterfly."
|
||||
|
||||
## Construction / Mechanics
|
||||
Using the same notation as the dollar-duration-neutral butterfly (Section 5.6), with modified durations D_1, D_2, D_3 and dollar positions P_1, P_2, P_3:
|
||||
|
||||
**Equal wing dollar durations**:
|
||||
```
|
||||
P_1·D_1 = P_3·D_3 = (1/2)·P_2·D_2 (406)
|
||||
```
|
||||
|
||||
This implies dollar-duration neutrality is preserved:
|
||||
```
|
||||
P_1·D_1 + P_3·D_3 = P_2·D_2
|
||||
```
|
||||
|
||||
But the zero-cost condition P_1 + P_3 = P_2 is generally not satisfied.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Approximately neutral to small steepening and flattening of the yield curve: the spread change between the body (T_2) and the short wing (T_1) equals the spread change between the body and the long wing (T_3).
|
||||
- Still immune to parallel shifts (dollar-duration neutral).
|
||||
- Profits from curvature changes: if the body cheapens relative to both wings, the position gains.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- P_1·D_1 = P_3·D_3 = (1/2)·P_2·D_2: the defining equal-wing constraint
|
||||
- T_1 < T_2 < T_3: the three maturities
|
||||
- Net cost P_2 - P_1 - P_3: non-zero unlike the dollar-duration-neutral butterfly
|
||||
|
||||
## Variations
|
||||
- Dollar-duration-neutral butterfly (Section 5.6): zero-cost but not curve-neutral.
|
||||
- Regression-weighted butterfly (Section 5.8): uses empirical β to account for differential yield volatility across the curve.
|
||||
|
||||
## Notes
|
||||
- The name "fifty-fifty" refers to the equal split of the body's dollar duration between the two wings.
|
||||
- Curve-neutrality is approximate and holds only for small parallel steepening/flattening moves.
|
||||
- The non-zero cost means the trader must finance the net position, which has carry implications.
|
||||
- Short-term rates are empirically more volatile than long-term rates, which limits the curve-neutrality assumption; this motivates the regression-weighted butterfly.
|
||||
@@ -0,0 +1,100 @@
|
||||
---
|
||||
description: "Background concepts for fixed income instruments: zero-coupon bonds, coupon bonds, floating rate bonds, swaps, duration, and convexity — the foundational mechanics underlying all fixed income strategies."
|
||||
tags: [fixed-income, background, duration, convexity, swaps]
|
||||
---
|
||||
|
||||
# Fixed Income Generalities
|
||||
|
||||
**Section**: 5.1 | **Asset Class**: Fixed Income | **Type**: Background / Reference
|
||||
|
||||
## Overview
|
||||
Fixed income instruments are promises to pay cash flows at future dates, priced today as the present value of those flows. The yield of a bond summarizes its return as a single annualized rate. Duration and convexity characterize how bond prices respond to interest rate changes, and are the primary risk-management tools for fixed income portfolios.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### 5.1.1 Zero-Coupon Bonds
|
||||
A zero-coupon (discount) bond with maturity T pays $1 at time T. Its price at time t is P(t,T), with P(T,T) = 1. The continuously compounded yield is:
|
||||
|
||||
```
|
||||
R(t,T) = -ln(P(t,T)) / (T - t) (374)
|
||||
```
|
||||
|
||||
### 5.1.2 Coupon Bonds
|
||||
A coupon bond pays principal $1 at maturity T plus n coupon payments of amount kδ at times T_i = T_0 + iδ (i = 1,...,n), where δ is the payment period. Price at time t:
|
||||
|
||||
```
|
||||
P_c(t,T) = P(t,T) + kδ Σ_{i=I(t)}^n P(t,T_i) (375)
|
||||
```
|
||||
|
||||
where I(t) = min(i : t < T_i). At issuance (t = T_0), the par coupon rate is:
|
||||
|
||||
```
|
||||
k = (1 - P(T_0,T)) / (δ Σ_{i=1}^n P(T_0,T_i)) (377)
|
||||
```
|
||||
|
||||
### 5.1.3 Floating Rate Bonds
|
||||
Coupon payments are based on LIBOR. The LIBOR rate at T_{i-1} for period [T_{i-1}, T_i] is:
|
||||
|
||||
```
|
||||
L(T_{i-1}) = (1/δ) [1/P(T_{i-1},T_i) - 1] (378)
|
||||
```
|
||||
|
||||
The coupon paid at T_i is X_i = L(T_{i-1})δ = 1/P(T_{i-1},T_i) - 1. The total value at T_0:
|
||||
|
||||
```
|
||||
V_0 = 1 - [P(T_0,T_n) - P(T_0,T)] (380)
|
||||
```
|
||||
|
||||
If T = T_n then V_0 = 1 (the bond prices at par).
|
||||
|
||||
### 5.1.4 Swaps
|
||||
An interest rate swap exchanges fixed rate payments for floating (LIBOR) payments. A long swap = long fixed coupon bond + short floating rate bond. The fixed rate giving zero initial value:
|
||||
|
||||
```
|
||||
k = (1 - P(T_0,T_n)) / (δ Σ_{i=1}^n P(T_0,T_i)) (383)
|
||||
```
|
||||
|
||||
### 5.1.5 Duration and Convexity
|
||||
**Macaulay duration** is the present-value-weighted average maturity of cash flows:
|
||||
|
||||
```
|
||||
MacD(t,T) = (1/P_c(t,T)) [(T-t)P(t,T) + kδ Σ_{i=I(t)}^n (T_i-t)P(t,T_i)] (384)
|
||||
```
|
||||
|
||||
**Modified duration** measures relative price sensitivity to parallel yield shifts:
|
||||
|
||||
```
|
||||
ModD(t,T) = -∂ln(P_c(t,T)) / ∂R(t,T) (385)
|
||||
```
|
||||
|
||||
For constant yield Y with periodic compounding: ModD = MacD / (1 + Yδ).
|
||||
Approximate price change: ΔP_c/P_c ≈ -ModD · ΔR
|
||||
|
||||
**Dollar duration** measures absolute price sensitivity:
|
||||
|
||||
```
|
||||
DD(t,T) = -∂P_c(t,T)/∂R(t,T) = ModD(t,T) · P_c(t,T) (387)
|
||||
```
|
||||
|
||||
**Convexity** captures nonlinear (second-order) effects:
|
||||
|
||||
```
|
||||
C(t,T) = -(1/P_c(t,T)) · ∂²P_c(t,T)/∂R(t,T)² (388)
|
||||
```
|
||||
|
||||
Full second-order approximation:
|
||||
|
||||
```
|
||||
ΔP_c/P_c ≈ -ModD·ΔR + (1/2)·C·(ΔR)² (389)
|
||||
```
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Yield R(t,T)**: inverse of price; drives all valuation
|
||||
- **Modified duration**: primary interest rate risk metric; scales approximately linearly with maturity
|
||||
- **Dollar duration**: used for hedging and portfolio construction
|
||||
- **Convexity**: scales approximately quadratically with maturity; higher convexity = better protection against parallel yield shifts at the cost of lower yield
|
||||
|
||||
## Notes
|
||||
- Duration and convexity formulas assume parallel shifts in the yield curve; non-parallel shifts require more sophisticated treatment.
|
||||
- Floating rate bonds priced at par (V_0 = 1) when T = T_n because the variable coupons replicate rolling T-bond investments.
|
||||
- Periodic vs. continuous compounding: MacD and ModD coincide under continuous compounding; differ under periodic compounding by factor (1 + Yδ).
|
||||
43
gateway/knowledge/trading/strategies/fixed-income/ladders.md
Normal file
43
gateway/knowledge/trading/strategies/fixed-income/ladders.md
Normal file
@@ -0,0 +1,43 @@
|
||||
---
|
||||
description: "A ladder portfolio holds bonds spread evenly across n equidistant maturities to diversify interest rate and reinvestment risk while maintaining an approximately constant duration through systematic roll-down."
|
||||
tags: [fixed-income, duration, ladder, diversification, yield-curve]
|
||||
---
|
||||
|
||||
# Ladders
|
||||
|
||||
**Section**: 5.4 | **Asset Class**: Fixed Income | **Type**: Duration-Targeting / Diversification
|
||||
|
||||
## Overview
|
||||
A ladder holds bonds with (roughly) equal capital allocations across n different maturities T_i (i = 1,...,n), where maturities are equidistant: T_{i+1} = T_i + δ. The strategy maintains an approximately constant duration by selling shorter-maturity bonds as they near maturity and replacing them with new longer-maturity bonds. It diversifies both interest rate risk and reinvestment risk.
|
||||
|
||||
## Construction / Mechanics
|
||||
- Allocate roughly equal capital to each rung T_i, i = 1,...,n (n is sizable, e.g., n = 10).
|
||||
- Equidistant maturities: T_{i+1} = T_i + δ.
|
||||
- Average (effective) maturity of the portfolio:
|
||||
|
||||
```
|
||||
T = (1/n) Σ_{i=1}^n T_i (395)
|
||||
```
|
||||
|
||||
- As the shortest rung approaches maturity, sell it and purchase a new bond at the longest maturity, maintaining the ladder structure.
|
||||
- Also generates regular income from coupon payments across all rungs.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Higher average maturity T → higher income (upward-sloping yield curve), but also higher interest rate risk.
|
||||
- Rolling shorter bonds into longer bonds continuously captures roll-down return.
|
||||
- Diversification across maturities smooths the impact of rate moves: if rates rise, maturing short bonds are reinvested at higher rates; if rates fall, longer bonds appreciate.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- n: number of rungs (more rungs = more diversification)
|
||||
- δ: spacing between maturities
|
||||
- T (average maturity): determines the income/risk trade-off
|
||||
- Equal capital allocation per rung: ensures no concentration at any maturity
|
||||
|
||||
## Variations
|
||||
- Unequal allocations tilting toward shorter or longer maturities (incorporating a partial bullet or barbell bias).
|
||||
|
||||
## Notes
|
||||
- The ladder avoids the concentration risk of bullets and barbells, making it suitable for investors uncertain about the rate environment.
|
||||
- The constant-duration property is approximate; exact duration changes as bonds age and are replaced.
|
||||
- Reinvestment risk is diversified: proceeds from maturing bonds are spread across the yield curve over time rather than all reinvested at once.
|
||||
- Transaction costs from regular rolling must be weighed against the diversification and roll-down benefits.
|
||||
@@ -0,0 +1,44 @@
|
||||
---
|
||||
description: "The low-risk factor strategy buys bonds with lower risk (shorter maturity and higher credit rating) within a credit tier, exploiting the empirical anomaly that lower-risk bonds outperform higher-risk bonds on a risk-adjusted basis."
|
||||
tags: [fixed-income, factor, low-risk, credit, anomaly]
|
||||
---
|
||||
|
||||
# Low-Risk Factor
|
||||
|
||||
**Section**: 5.9 | **Asset Class**: Fixed Income | **Type**: Factor / Anomaly
|
||||
|
||||
## Overview
|
||||
Empirical evidence suggests that lower-risk bonds tend to outperform higher-risk bonds on a risk-adjusted basis (the "low-risk anomaly"), mirroring a similar effect in equities. "Riskiness" in fixed income is measured by credit rating and maturity. The strategy builds long portfolios of the lowest-risk bonds within a given credit tier.
|
||||
|
||||
## Construction / Mechanics
|
||||
Portfolio construction uses two risk dimensions:
|
||||
|
||||
1. **Credit rating**: separates the investment universe into quality tiers.
|
||||
- Investment Grade (IG): credit ratings AAA through A-.
|
||||
- High Yield (HY): credit ratings BB+ through B-.
|
||||
|
||||
2. **Maturity (duration)**: within each credit tier, rank bonds by maturity and take the **bottom decile** (shortest maturities = lowest duration risk).
|
||||
|
||||
Example portfolios:
|
||||
- IG low-risk: Investment Grade bonds (AAA–A-), bottom decile by maturity.
|
||||
- HY low-risk: High Yield bonds (BB+–B-), bottom decile by maturity.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Earns a risk-adjusted premium by being long the lowest-risk bonds in each tier.
|
||||
- Outperforms the broad credit market on a Sharpe ratio basis due to the low-risk anomaly.
|
||||
- Returns are driven by credit spread compression and coupon income, with lower sensitivity to interest rate moves (short maturity).
|
||||
|
||||
## Key Parameters / Signals
|
||||
- Credit rating tier: AAA–A- (IG) or BB+–B- (HY)
|
||||
- Maturity rank: bottom decile selects shortest-maturity bonds
|
||||
- Risk-adjusted return (Sharpe ratio): primary evaluation metric
|
||||
|
||||
## Variations
|
||||
- Can be combined with a short position in the top-risk decile (highest maturity within the tier) to create a long-short low-risk factor.
|
||||
- Risk metrics beyond credit rating and maturity (e.g., option-adjusted spread, liquidity) can be incorporated.
|
||||
|
||||
## Notes
|
||||
- The low-risk anomaly in bonds mirrors the similar effect documented in equities but is driven by different mechanisms (credit and duration rather than beta).
|
||||
- Separating IG and HY tiers is important because the risk-return relationship differs significantly between investment grade and speculative grade.
|
||||
- Liquidity may be lower for short-maturity high-yield bonds, increasing transaction costs.
|
||||
- The strategy is typically implemented as a long-only portfolio; short positions in corporate bonds are operationally difficult.
|
||||
@@ -0,0 +1,53 @@
|
||||
---
|
||||
description: "A regression-weighted butterfly uses an empirically estimated β to account for the higher volatility of short-term rates relative to long-term rates, improving yield-curve-neutrality beyond the fifty-fifty butterfly."
|
||||
tags: [fixed-income, butterfly, duration-neutral, yield-curve, curvature, regression]
|
||||
---
|
||||
|
||||
# Regression-Weighted Butterfly
|
||||
|
||||
**Section**: 5.8 | **Asset Class**: Fixed Income | **Type**: Yield Curve / Curvature
|
||||
|
||||
## Overview
|
||||
Empirically, short-term interest rates are significantly more volatile than long-term rates. The regression-weighted butterfly accounts for this by weighting the short wing's dollar duration by a factor β > 1, estimated from historical data via regression. This produces better curve-neutrality than the fifty-fifty butterfly in practice.
|
||||
|
||||
## Construction / Mechanics
|
||||
Using positions P_1, P_2, P_3 with modified durations D_1, D_2, D_3 (T_1 < T_2 < T_3):
|
||||
|
||||
**Dollar-duration neutrality** (parallel shift immunity):
|
||||
```
|
||||
P_1·D_1 + P_3·D_3 = P_2·D_2 (407)
|
||||
```
|
||||
|
||||
**Regression-weighted curve-neutrality**:
|
||||
```
|
||||
P_1·D_1 = β · P_3·D_3 (408)
|
||||
```
|
||||
|
||||
where β > 1 is the regression coefficient from regressing the spread change between the body (T_2) and the short wing (T_1) on the spread change between the body and the long wing (T_3), using historical data.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Immune to both parallel shifts (407) and, approximately, to yield curve slope changes in proportion β.
|
||||
- Profits from yield curve curvature moves: gains when the body yields rise relative to the wings.
|
||||
- More robust curve-neutrality than the fifty-fifty butterfly in practice due to the empirically calibrated β.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- β: regression coefficient (typically β > 1, calibrated from historical spread data)
|
||||
- P_1, P_3: determined by solving (407) and (408) given P_2
|
||||
- T_1, T_2, T_3: the three maturity points on the yield curve
|
||||
|
||||
## Variations
|
||||
|
||||
### 5.8.1 Maturity-Weighted Butterfly
|
||||
Instead of estimating β from historical regressions, it is set analytically from the three bond maturities:
|
||||
|
||||
```
|
||||
β = (T_2 - T_1) / (T_3 - T_2) (409)
|
||||
```
|
||||
|
||||
This is proportional to the ratio of the short-wing maturity distance to the long-wing maturity distance from the body. It is a simpler, model-based alternative that does not require historical calibration.
|
||||
|
||||
## Notes
|
||||
- β is empirically greater than 1 because short-term rates fluctuate more than long-term rates; the short wing therefore needs less dollar duration to hedge the same spread move.
|
||||
- The regression β should be re-estimated periodically as the volatility relationship between short and long rates can change over time.
|
||||
- The maturity-weighted variant (5.8.1) provides a model-based β that requires no estimation but may not capture the true empirical volatility asymmetry.
|
||||
- All butterfly strategies share the exposure to transaction costs, financing costs, and bid-ask spreads that can erode theoretical curve-neutrality profits.
|
||||
@@ -0,0 +1,52 @@
|
||||
---
|
||||
description: "Rolling down the yield curve buys long- or medium-term bonds in the steepest segment of the yield curve and holds them while they appreciate as they shorten in maturity, then reinvests proceeds into new steepest-segment bonds."
|
||||
tags: [fixed-income, roll-down, yield-curve, carry, duration]
|
||||
---
|
||||
|
||||
# Rolling Down the Yield Curve
|
||||
|
||||
**Section**: 5.12 | **Asset Class**: Fixed Income | **Type**: Carry / Roll-Down
|
||||
|
||||
## Overview
|
||||
The rolling down the yield curve strategy captures the roll-down component C_roll of bond returns by purchasing bonds in the steepest segments of the yield curve and holding them while their maturity shortens, causing price appreciation. Bonds are sold before maturity and the proceeds reinvested in new long/medium-term bonds from the same steep segment.
|
||||
|
||||
## Construction / Mechanics
|
||||
The roll-down return over horizon Δt:
|
||||
|
||||
```
|
||||
C_roll(t, t+Δt, T) ≈ -ModD(t,T) · [R(t, T-Δt) - R(t, T)] (415)
|
||||
```
|
||||
|
||||
This is maximized when:
|
||||
- **ModD(t,T)** is large (longer-maturity bonds have higher duration)
|
||||
- **R(t, T-Δt) - R(t, T) < 0** (yield declines as maturity shortens — upward-sloping curve)
|
||||
- The magnitude |R(t, T-Δt) - R(t, T)| is large (steep segment of the curve)
|
||||
|
||||
**Strategy mechanics**:
|
||||
1. Identify the steepest segment(s) of the yield curve.
|
||||
2. Buy long- or medium-term bonds from those segments.
|
||||
3. Hold while they "roll down" the curve (their maturity shrinks and yield declines).
|
||||
4. Sell before maturity approaches (before they enter a flatter/shorter segment).
|
||||
5. Reinvest proceeds into new long/medium-term bonds from the steep segment.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Earns roll-down return C_roll in addition to yield income R(t,T)·Δt.
|
||||
- Total carry C(t, t+Δt, T) = R(t,T)·Δt + C_roll(t, t+Δt, T).
|
||||
- Profits maximized in steeply upward-sloping yield curves.
|
||||
- Loses money when the yield curve flattens, inverts, or when long-end yields rise (parallel upward shift).
|
||||
|
||||
## Key Parameters / Signals
|
||||
- Yield curve slope: identifies which segments offer the most roll-down return
|
||||
- Modified duration: amplifies the roll-down return
|
||||
- Holding horizon Δt: determines how far down the curve the bond rolls before sale
|
||||
- Curve stability: strategy depends on curve shape remaining approximately stable
|
||||
|
||||
## Variations
|
||||
- Pure roll-down: focus exclusively on C_roll, ignoring yield income (selects steepest curve segments regardless of absolute yield level).
|
||||
- Combined carry + roll: as in the carry factor strategy (5.11), which uses total C as the signal.
|
||||
|
||||
## Notes
|
||||
- The yield curve must be upward-sloping for roll-down to be positive; in a flat or inverted curve the roll-down may be zero or negative.
|
||||
- Transaction costs from repeated roll-overs must be weighed against the roll-down income.
|
||||
- The strategy has implicit duration risk: long/medium bonds lose value in a rising rate environment, which can more than offset the roll-down gain.
|
||||
- Steepest curve segments often occur at the short to medium end (e.g., 2-10 year part of the Treasury curve) and can shift over time with monetary policy.
|
||||
@@ -0,0 +1,59 @@
|
||||
---
|
||||
description: "Swap spread arbitrage takes a long (short) position in an interest rate swap versus a short (long) position in a Treasury bond of the same maturity, profiting from the difference between the swap rate, Treasury yield, LIBOR, and the repo rate."
|
||||
tags: [fixed-income, arbitrage, swap, libor, treasury, spread]
|
||||
---
|
||||
|
||||
# Swap Spread Arbitrage
|
||||
|
||||
**Section**: 5.15 | **Asset Class**: Fixed Income | **Type**: Arbitrage / Rates
|
||||
|
||||
## Overview
|
||||
The swap spread arbitrage is a dollar-neutral strategy that combines a long (or short) position in an interest rate swap with an offsetting short (or long) position in a Treasury bond of the same maturity. It profits from the spread between the swap fixed rate and the Treasury yield, net of financing costs (LIBOR vs. repo rate). The strategy is essentially a bet on the direction of LIBOR relative to the repo rate.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Instruments**:
|
||||
- Interest rate swap: receive fixed rate r_swap, pay floating LIBOR L(t)
|
||||
- Treasury bond: short the bond (financed at repo rate r(t))
|
||||
|
||||
**Per-dollar-invested P&L rate**:
|
||||
```
|
||||
C(t) = ±[C_1 - C_2(t)] (418)
|
||||
C_1 = r_swap - Y_Treasury (419)
|
||||
C_2(t) = L(t) - r(t) (420)
|
||||
```
|
||||
|
||||
where:
|
||||
- C_1: constant spread = swap fixed rate minus Treasury yield (the swap spread)
|
||||
- C_2(t): floating spread = LIBOR minus repo rate
|
||||
- Plus sign: long swap strategy (receive fixed, short Treasury)
|
||||
- Minus sign: short swap strategy (pay fixed, long Treasury)
|
||||
|
||||
**Long swap strategy** (plus sign):
|
||||
- Receive r_swap (fixed leg of swap) + short Treasury (financed at repo) → pay Y_Treasury + repo rate
|
||||
- Profitable if C_2(t) = L(t) - r(t) < C_1
|
||||
|
||||
**Short swap strategy** (minus sign):
|
||||
- Pay r_swap (fixed leg) + long Treasury (funded at repo) → receive Y_Treasury
|
||||
- Profitable if C_2(t) = L(t) - r(t) > C_1
|
||||
|
||||
## Payoff / Return Profile
|
||||
- The long swap strategy profits if LIBOR falls (C_2 decreases below C_1).
|
||||
- The short swap strategy profits if LIBOR rises (C_2 increases above C_1).
|
||||
- This is fundamentally a **LIBOR bet**: the trade profits or loses based on the LIBOR-repo spread relative to the constant swap spread C_1.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- C_1 = r_swap - Y_Treasury: the swap spread (constant at trade inception)
|
||||
- C_2(t) = L(t) - r(t): the LIBOR-repo spread (time-varying)
|
||||
- Net P&L driver: ±(C_1 - C_2(t)); direction depends on long vs. short swap position
|
||||
|
||||
## Variations
|
||||
- Adjust maturity of the swap and Treasury bond to target different parts of the yield curve.
|
||||
- Pair with CDS basis trades for multi-leg credit/rates arbitrage.
|
||||
|
||||
## Notes
|
||||
- The strategy is dollar-neutral (the swap and Treasury position offset each other in notional terms).
|
||||
- LIBOR risk is the dominant risk: unexpected changes in LIBOR (e.g., central bank policy shifts, bank credit stress) directly affect P&L.
|
||||
- The repo rate r(t) can vary and introduces additional uncertainty in C_2(t).
|
||||
- With the transition away from LIBOR to SOFR and other risk-free rates, the mechanics of this strategy are evolving.
|
||||
- Counterparty risk on the swap and margin requirements must be accounted for in practice.
|
||||
@@ -0,0 +1,66 @@
|
||||
---
|
||||
description: "The value factor strategy for bonds selects bonds with the highest actual credit spread relative to a theoretically predicted spread from a cross-sectional regression, going long undervalued bonds in the top decile."
|
||||
tags: [fixed-income, factor, value, credit-spread, regression]
|
||||
---
|
||||
|
||||
# Value Factor
|
||||
|
||||
**Section**: 5.10 | **Asset Class**: Fixed Income | **Type**: Factor / Value
|
||||
|
||||
## Overview
|
||||
"Value" in fixed income is defined by comparing a bond's observed credit spread to a theoretically predicted (fair value) credit spread. Bonds trading with a spread significantly above their predicted fair value are cheap (high value); those below are expensive. The strategy buys the top-decile bonds by value score.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Step 1: Estimate fair value spreads** via a cross-sectional linear regression across N bonds (i = 1,...,N):
|
||||
|
||||
```
|
||||
S_i = Σ_{r=1}^K β_r · I_{ir} + γ · T_i + ε_i (410)
|
||||
```
|
||||
|
||||
where:
|
||||
- S_i: observed credit spread of bond i (bond yield minus risk-free rate)
|
||||
- I_{ir}: dummy variable = 1 if bond i has credit rating r, 0 otherwise (K ≤ 21 ratings)
|
||||
- T_i: maturity of bond i
|
||||
- β_r, γ: regression coefficients (note: no separate intercept since Σ_r I_{ir} = 1 for each bond)
|
||||
- ε_i: regression residual
|
||||
|
||||
The constraint:
|
||||
```
|
||||
Σ_{r=1}^K I_{ir} = 1 for all i (412)
|
||||
```
|
||||
(each bond has exactly one credit rating, so the intercept is absorbed into the rating dummies)
|
||||
|
||||
**Step 2: Compute fair value spread**:
|
||||
```
|
||||
S_i* = S_i - ε_i (411)
|
||||
```
|
||||
(the fitted value from the regression)
|
||||
|
||||
**Step 3: Compute value score** — either:
|
||||
- V_i = ln(S_i / S_i*), or
|
||||
- V_i = ε_i / S_i* = S_i / S_i* - 1
|
||||
|
||||
**Step 4: Select portfolio** — long bonds in the top decile by V_i (most undervalued).
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Profits when cheap bonds (high V_i) revert toward fair value, compressing their spreads.
|
||||
- Returns driven by credit spread compression and coupon income.
|
||||
- The strategy assumes mean-reversion in credit spreads around their rating- and maturity-implied fair value.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- S_i: observed credit spread (bond yield minus risk-free rate)
|
||||
- S_i*: fair value credit spread from cross-sectional regression
|
||||
- V_i = ln(S_i/S_i*) or V_i = S_i/S_i* - 1: value score
|
||||
- Top decile by V_i: the portfolio selection criterion
|
||||
|
||||
## Variations
|
||||
- Long-short: long top decile (cheap bonds), short bottom decile (expensive bonds).
|
||||
- Separate regressions for Investment Grade and High Yield universes.
|
||||
- Additional cross-sectional controls (e.g., industry, liquidity) can be added as regressors.
|
||||
|
||||
## Notes
|
||||
- "Value" in fixed income is harder to define than in equities because bonds have finite lifetimes and their spreads are heavily influenced by credit ratings and maturity.
|
||||
- The cross-sectional regression should be run on bonds within a comparable universe (e.g., only IG or only HY) to ensure meaningful comparisons.
|
||||
- Credit spread data may be noisy; outliers from bonds near distress can distort the regression.
|
||||
- Shorting corporate bonds is operationally challenging; the strategy is often implemented long-only.
|
||||
@@ -0,0 +1,56 @@
|
||||
---
|
||||
description: "Yield curve spread strategies (flatteners and steepeners) trade the difference in yields between two maturities of the same issuer, going short the spread when rates are expected to rise and long when rates are expected to fall."
|
||||
tags: [fixed-income, yield-curve, spread, flattener, steepener, duration]
|
||||
---
|
||||
|
||||
# Yield Curve Spread (Flatteners & Steepeners)
|
||||
|
||||
**Section**: 5.13 | **Asset Class**: Fixed Income | **Type**: Yield Curve / Spread
|
||||
|
||||
## Overview
|
||||
Yield curve spread strategies trade the yield spread between two bonds of the same issuer at different maturities. If interest rates are expected to rise, the yield curve is expected to flatten (short end rises more than long end); if rates are expected to fall, the curve steepens. The strategy goes short the spread (flattener) or long the spread (steepener) accordingly.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Yield curve spread**: the difference in yields between a longer-maturity bond (back leg) and a shorter-maturity bond (front leg) of the same issuer:
|
||||
```
|
||||
Spread = Y(back leg, long maturity) - Y(front leg, short maturity)
|
||||
```
|
||||
|
||||
**Trading rule**:
|
||||
```
|
||||
Rule = { Flattener: Short spread if interest rates expected to rise
|
||||
{ Steepener: Buy spread if interest rates expected to fall (416)
|
||||
```
|
||||
|
||||
**Position construction**:
|
||||
- **Short the spread (flattener)**: sell shorter-maturity bonds (front leg) + buy longer-maturity bonds (back leg).
|
||||
- **Buy the spread (steepener)**: buy shorter-maturity bonds (front leg) + sell longer-maturity bonds (back leg).
|
||||
|
||||
**Dollar-duration matching**: to immunize against small parallel shifts, match the dollar durations of the front and back legs:
|
||||
```
|
||||
P_front · D_front = P_back · D_back
|
||||
```
|
||||
|
||||
Without duration matching, a parallel shift in the yield curve can generate significant losses.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- **Flattener profits** when the curve flattens: short-end yields rise more than long-end yields (or long-end falls more than short-end).
|
||||
- **Steepener profits** when the curve steepens: long-end yields rise more than short-end (or short-end falls more than long-end).
|
||||
- Dollar-duration-neutral construction limits losses from parallel yield curve moves.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- Yield curve slope: R(long maturity) - R(short maturity) — the key signal
|
||||
- Front leg maturity T_1, back leg maturity T_2: define the segment being traded
|
||||
- Modified durations D_1, D_2: used for dollar-duration matching
|
||||
- Interest rate outlook: the primary driver of direction (flattener vs. steepener)
|
||||
|
||||
## Variations
|
||||
- **Curve trades across issuers**: trading the slope difference between two issuers (adds credit spread risk).
|
||||
- **Butterfly trades**: extend the two-leg spread to a three-leg position to trade curvature rather than slope (see Sections 5.6–5.8).
|
||||
|
||||
## Notes
|
||||
- Parallel yield curve shifts can cause losses if dollar durations are not matched; duration-matching is essential for a pure slope bet.
|
||||
- Even with duration matching, large parallel moves (exceeding the immunization approximation) can generate losses due to convexity differences between legs.
|
||||
- The strategy is exposed to idiosyncratic supply-and-demand effects at specific maturities (e.g., Treasury auction effects, central bank purchases).
|
||||
- Financing costs (repo rates for the short leg) affect the net P&L of the strategy.
|
||||
@@ -0,0 +1,48 @@
|
||||
---
|
||||
description: "Futures calendar spread strategy that takes simultaneous long/short positions in near-month and deferred-month contracts to bet on supply/demand fundamentals while reducing overall market volatility exposure."
|
||||
tags: [futures, calendar-spread, term-structure, spread-trading]
|
||||
---
|
||||
|
||||
# Calendar Spread
|
||||
|
||||
**Section**: 10.2 | **Asset Class**: Futures | **Type**: Spread Trading / Relative Value
|
||||
|
||||
## Overview
|
||||
A calendar spread (also called a time spread or intra-commodity spread) involves simultaneously buying and selling futures contracts on the same underlying commodity or asset but with different delivery months. By taking offsetting positions, the trader reduces exposure to outright price moves and focuses on the relative pricing of near versus deferred contracts, which reflects supply-and-demand fundamentals and storage costs.
|
||||
|
||||
## Construction / Mechanics
|
||||
**Bull spread**: Buy a near-month futures contract, sell a deferred-month futures contract.
|
||||
- P&L = price change of near-month - price change of deferred-month
|
||||
- Benefits when near-month appreciates relative to deferred (supply tightening, demand surge)
|
||||
|
||||
**Bear spread**: Sell a near-month futures contract, buy a deferred-month futures contract.
|
||||
- P&L = price change of deferred-month - price change of near-month
|
||||
- Benefits when deferred-month appreciates relative to near-month (supply glut, weak demand)
|
||||
|
||||
**Economic rationale**: For commodity futures, near-month contracts react more strongly to current supply and demand imbalances than deferred contracts. Therefore:
|
||||
- Expect low supply + high demand → use a **bull spread**
|
||||
- Expect high supply + low demand → use a **bear spread**
|
||||
|
||||
## Return Profile
|
||||
Profits from changes in the spread between near and deferred contract prices. The outright directional market risk is substantially reduced (though not fully eliminated) relative to an outright futures position. The strategy is driven by term structure dynamics, convenience yield changes, storage cost changes, and short-term supply/demand imbalances.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| Near-month contract | The shorter-dated futures leg |
|
||||
| Deferred-month contract | The longer-dated futures leg |
|
||||
| Spread = near - deferred | Positive → backwardation; negative → contango |
|
||||
| Bull signal | Expected low supply and high demand (buy spread) |
|
||||
| Bear signal | Expected high supply and low demand (sell spread) |
|
||||
|
||||
## Variations
|
||||
- **Skip-month spread**: skip one contract month between the two legs to amplify the spread move.
|
||||
- **Butterfly spread**: three legs (buy near, sell middle, buy far) to isolate curvature of the term structure.
|
||||
- **Crack spread** (energy): spread between crude oil and refined product futures (captures refining margin rather than a pure calendar spread).
|
||||
- **Inter-commodity spread**: similar mechanics but between related but different commodities (e.g., corn vs. wheat).
|
||||
|
||||
## Notes
|
||||
- While market exposure is reduced relative to outright futures, calendar spreads are not market-neutral; correlation between legs can break down during stress events.
|
||||
- Margin requirements for calendar spreads are typically lower than for outright futures because exchanges recognise the reduced directional risk.
|
||||
- Liquidity in deferred contracts is typically lower than in near-month contracts; wide bid-ask spreads on the deferred leg can erode profits.
|
||||
- For financial futures (equity index, interest rate), the spread is primarily driven by carry (financing cost and dividend/coupon income) rather than physical supply and demand.
|
||||
@@ -0,0 +1,79 @@
|
||||
---
|
||||
description: "Futures mean-reversion strategy that buys recent underperformers and sells recent outperformers relative to an equally-weighted futures market index, with an extension using volume and open interest filters."
|
||||
tags: [futures, mean-reversion, contrarian, market-index, dollar-neutral]
|
||||
---
|
||||
|
||||
# Contrarian Trading (Mean-Reversion)
|
||||
|
||||
**Section**: 10.3 | **Asset Class**: Futures | **Type**: Mean-Reversion / Contrarian
|
||||
|
||||
## Overview
|
||||
Analogous to the equity mean-reversion strategy (Section 3.9), this futures strategy bets that recent losers will rebound and recent winners will give back gains. Returns of individual futures are measured relative to an equally-weighted market index, and capital is allocated inversely to the deviation from that index. The result is a dollar-neutral, automatically constructed contrarian portfolio rebalanced weekly.
|
||||
|
||||
## Construction / Mechanics
|
||||
Within a universe of N futures labeled i = 1,...,N, define the "market index" return as the equally-weighted average:
|
||||
|
||||
```
|
||||
R_m = (1/N) Σ R_i (469)
|
||||
```
|
||||
|
||||
where R_i are individual futures returns, typically measured over the last one week.
|
||||
|
||||
The capital allocation weights are:
|
||||
|
||||
```
|
||||
w_i = -γ [R_i - R_m] (470)
|
||||
```
|
||||
|
||||
where γ > 0 is fixed via the dollar-neutral normalization condition:
|
||||
|
||||
```
|
||||
Σ |w_i| = 1 (471)
|
||||
```
|
||||
|
||||
- Futures below the market index (R_i < R_m): positive weight (long)
|
||||
- Futures above the market index (R_i > R_m): negative weight (short)
|
||||
- The portfolio is automatically dollar-neutral (Σ w_i = 0)
|
||||
- The strategy buys losers and sells winners relative to the market index
|
||||
|
||||
**Volatility adjustment**: To mitigate overinvestment in volatile futures, suppress w_i by 1/σ_i or 1/σ_i², where σ_i are the historical volatilities.
|
||||
|
||||
## Return Profile
|
||||
Profits when futures returns mean-revert toward the market index over a one-week horizon. Returns are driven by short-term overreaction and subsequent correction. The strategy is market-neutral at the index level.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| R_i | Individual futures return over the last week |
|
||||
| R_m | Equally-weighted market index return (Eq. 469) |
|
||||
| w_i = -γ[R_i - R_m] | Allocation weight; negative for winners, positive for losers |
|
||||
| γ | Scaling parameter fixed by Eq. (471) |
|
||||
| σ_i | Historical volatility; used to suppress w_i optionally |
|
||||
| Rebalancing | Weekly |
|
||||
|
||||
## Variations
|
||||
|
||||
### 10.3.1 Contrarian Trading — Market Activity
|
||||
Volume and open interest filters can improve the basic mean-reversion signal. Define:
|
||||
|
||||
```
|
||||
v_i = ln(V_i / V_i') (472)
|
||||
u_i = ln(U_i / U_i') (473)
|
||||
```
|
||||
|
||||
where V_i is total volume for futures i over the last week, V_i' is total volume over the prior week, and U_i, U_i' are the analogous open interest quantities.
|
||||
|
||||
**Construction:**
|
||||
1. Take the upper half of futures by volume factor v_i (higher recent volume relative to prior week).
|
||||
2. Within that subset, take the lower half by open interest factor u_i.
|
||||
3. Apply the contrarian weights from Eq. (470) to this filtered subset.
|
||||
|
||||
**Rationale:**
|
||||
- Larger volume changes indicate greater overreaction (a stronger snap-back is expected).
|
||||
- A decrease in open interest (low u_i) signals hedger withdrawal and suggests a deeper market for the mean-reversion to work.
|
||||
|
||||
## Notes
|
||||
- The simple weighting scheme (Eq. 470) can overinvest in highly volatile futures; volatility scaling (1/σ_i or 1/σ_i²) is recommended in practice.
|
||||
- Weekly rebalancing incurs transaction costs; the net alpha must exceed round-trip costs across all positions.
|
||||
- Contrarian strategies can suffer sustained losses during trending regimes; combining with a trend-following overlay (Section 10.4) may reduce drawdowns.
|
||||
- The market-index return R_m links this strategy to the broader futures universe; changing the universe composition changes the benchmark and alters all weights.
|
||||
80
gateway/knowledge/trading/strategies/futures/hedging-risk.md
Normal file
80
gateway/knowledge/trading/strategies/futures/hedging-risk.md
Normal file
@@ -0,0 +1,80 @@
|
||||
---
|
||||
description: "Futures hedging strategy that uses futures contracts to offset price or interest-rate risk on an underlying asset position, with variants for cross-hedging and duration-based interest-rate risk hedging."
|
||||
tags: [futures, hedging, risk-management, interest-rate, cross-hedge]
|
||||
---
|
||||
|
||||
# Hedging Risk with Futures
|
||||
|
||||
**Section**: 10.1 | **Asset Class**: Futures | **Type**: Hedging / Risk Management
|
||||
|
||||
## Overview
|
||||
Futures contracts allow traders to mitigate exposure to price risk on an underlying asset. A trader who anticipates needing to buy (sell) an asset at a future date can lock in a price today by buying (selling) a futures contract. The strategy eliminates directional price exposure at the cost of potentially missing favourable price moves. Variants address situations where no exact futures contract exists (cross-hedging) and interest-rate risk on fixed-income assets.
|
||||
|
||||
## Construction / Mechanics
|
||||
**Basic hedge**: A trader expects to buy (sell) X units of an asset at time T.
|
||||
- To hedge rising prices: buy futures contracts at time t for delivery at T.
|
||||
- To hedge falling prices: sell futures contracts at time t for delivery at T.
|
||||
|
||||
The futures position offsets the P&L on the underlying physical exposure.
|
||||
|
||||
## Return Profile
|
||||
The hedge eliminates (or substantially reduces) the P&L variability due to the hedged risk factor. The net position approximates a risk-free return when the hedge ratio is well-calibrated. Basis risk (see cross-hedging) is the residual risk that remains.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| Hedge ratio | Number of futures contracts per unit of underlying exposure |
|
||||
| Delivery date T | Futures expiry chosen to match or exceed the hedging horizon |
|
||||
| Basis risk | Residual risk when futures price and spot price do not move in perfect lockstep |
|
||||
|
||||
## Variations
|
||||
|
||||
### 10.1.1 Cross-Hedging
|
||||
When a futures contract for the exact asset to be hedged does not exist, a futures contract on a correlated asset can be used. The payoff at maturity T of the cross-hedged position (short futures, unit hedge ratio) is:
|
||||
|
||||
```
|
||||
S(T) - F(t,T) + F(t,T)
|
||||
= [S*(T) - F(t,T)] + [S(T) - S*(T)] + F(t,T) (463)
|
||||
```
|
||||
|
||||
where the subscript * denotes the underlying of the futures contract (different from the hedged asset), S(T) is the spot price of the hedged asset, and F(t,T) is the futures price.
|
||||
|
||||
- First term [S*(T) - F(t,T)]: basis risk from the difference between futures price and the futures' underlying spot at delivery.
|
||||
- Second term [S(T) - S*(T)]: risk from the difference between the two underlying assets.
|
||||
|
||||
In practice the optimal hedge ratio h ≠ 1 and can be estimated via serial regression of the hedged asset's spot return on the futures return, or by other methods.
|
||||
|
||||
### 10.1.2 Interest Rate Risk Hedging
|
||||
Fixed-income assets are sensitive to interest rate changes. Futures on interest rate instruments (e.g., T-bond futures) can be used to hedge this risk.
|
||||
|
||||
- Long hedge (buy futures): protects against rising asset prices (falling rates)
|
||||
- Short hedge (sell futures): protects against falling asset prices (rising rates)
|
||||
|
||||
P&L for the long hedge established at t=0 with unit hedge ratio and maturity T:
|
||||
```
|
||||
P_L(t,T) = B(0,T) - B(t,T) (464)
|
||||
P_S(t,T) = B(t,T) - B(0,T) (465)
|
||||
```
|
||||
where the futures basis is:
|
||||
```
|
||||
B(t,T) = S(t) - F(t,T) (466)
|
||||
```
|
||||
|
||||
**Conversion factor model** (for bonds in a futures delivery basket):
|
||||
```
|
||||
h_C = C × (M_B / M_F) (467)
|
||||
```
|
||||
where M_B is bond notional, M_F is futures notional, C is the conversion factor.
|
||||
|
||||
**Modified duration hedge ratio** (applicable to both deliverable and non-deliverable bonds):
|
||||
```
|
||||
h_D = β × (D_B / D_F) (468)
|
||||
```
|
||||
where D_B is the dollar duration of the bond, D_F is the dollar duration of the futures, and β is the sensitivity of bond yield changes to futures yield changes (often set to 1).
|
||||
|
||||
## Notes
|
||||
- Basis risk is the primary residual risk in any futures hedge; it arises from imperfect correlation between futures and spot prices.
|
||||
- The conversion factor model applies only to T-bond and T-note futures; the duration model is more general.
|
||||
- β in Eq. (468) can be estimated from historical regression of bond yield changes on futures yield changes.
|
||||
- Cross-hedges with dissimilar underlying assets carry additional residual risk that simple regression-based hedge ratios may not fully capture.
|
||||
- Hedging eliminates upside as well as downside; traders should consider whether they need a full hedge or a partial one.
|
||||
@@ -0,0 +1,83 @@
|
||||
---
|
||||
description: "Futures momentum strategy that weights positions proportionally to the sign of recent returns scaled by historical volatility, equivalent to a diagonal-covariance mean-variance optimisation."
|
||||
tags: [futures, momentum, trend-following, time-series, volatility-scaled]
|
||||
---
|
||||
|
||||
# Trend Following (Momentum)
|
||||
|
||||
**Section**: 10.4 | **Asset Class**: Futures | **Type**: Momentum / Trend-Following
|
||||
|
||||
## Overview
|
||||
Trend-following constructs a futures portfolio by going long instruments with positive recent returns and short those with negative returns, with position sizes inversely proportional to volatility. This is equivalent to a mean-variance optimisation using a diagonal covariance matrix (ignoring cross-futures correlations) and expected returns proportional to the sign of recent performance. It is one of the most widely used and robust strategies in futures markets.
|
||||
|
||||
## Construction / Mechanics
|
||||
Let R_i be the return of futures i (i = 1,...,N) over a look-back period T. Define the trend signal:
|
||||
|
||||
```
|
||||
η_i = sign(R_i) (475)
|
||||
```
|
||||
|
||||
The portfolio weights are:
|
||||
|
||||
```
|
||||
w_i = γ × (η_i / σ_i) (474)
|
||||
```
|
||||
|
||||
where σ_i are the historical volatilities (computed over T or another window) and γ > 0 is fixed via:
|
||||
|
||||
```
|
||||
Σ |w_i| = 1 (476)
|
||||
```
|
||||
|
||||
**Dollar-neutral version**: demeaning the weights to achieve Σ w_i = 0:
|
||||
|
||||
```
|
||||
w_i = γ [η_i/σ_i - (1/N) Σ η_j/σ_j] (477)
|
||||
```
|
||||
|
||||
**Balanced long/short version**: when the number of long positions N+ ≈ number of short positions N- (i.e., N+ = |H+| ≈ N- = |H-|), use separate normalisation constants γ+ and γ-:
|
||||
|
||||
```
|
||||
w_i = γ+ × η_i/σ_i, i ∈ H+ (η_i > 0) (478)
|
||||
w_i = γ- × η_i/σ_i, i ∈ H- (η_i < 0) (479)
|
||||
```
|
||||
|
||||
satisfying Eq. (476) and the dollar-neutrality condition:
|
||||
|
||||
```
|
||||
Σ w_i = 0 (480)
|
||||
```
|
||||
|
||||
**Demeaned returns variant**: replace R_i with R̃_i = R_i - R_m (market-adjusted returns, where R_m is Eq. (469)) to remove the common market factor and prevent skewed η_i distribution.
|
||||
|
||||
**Signal smoothing**: to avoid instability when |R_i| is small relative to σ_i (causing η_i to flip on minor changes), replace sign(R_i) with:
|
||||
|
||||
```
|
||||
η_i = tanh(R_i / κ)
|
||||
```
|
||||
|
||||
where κ is a smoothing parameter (e.g., the cross-sectional standard deviation of R_i).
|
||||
|
||||
## Return Profile
|
||||
Profits when futures trend: long positions appreciate as upward trends continue, short positions benefit from sustained downward trends. The volatility scaling ensures that each position contributes roughly equal risk regardless of individual futures volatility. The strategy does not profit from mean-reversion.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| T | Look-back period for R_i and σ_i (days, weeks, or months) |
|
||||
| η_i = sign(R_i) | Trend signal; +1 for uptrend, -1 for downtrend |
|
||||
| σ_i | Historical volatility; normalises position size |
|
||||
| γ | Scaling constant fixed by normalisation condition |
|
||||
| κ | Smoothing parameter for tanh signal variant |
|
||||
|
||||
## Variations
|
||||
- **Cumulative return signal**: use E_i = R_i directly (rather than sign) for expected returns; more continuous but potentially noisy.
|
||||
- **Non-diagonal covariance**: use a full covariance matrix C_ij for more accurate portfolio optimisation (see Section 3.18, Eq. 350).
|
||||
- **Multiple time horizons**: combine short-term (days), medium-term (weeks), and long-term (months) trend signals to diversify across time scales.
|
||||
- **Exponential moving averages / HP filter**: apply to returns to suppress noise before computing η_i (Sections 3, 8.1).
|
||||
|
||||
## Notes
|
||||
- The simple sign-based weights are not dollar-neutral by default; demeaning (Eq. 477) or the balanced variant (Eqs. 478-479) is required for dollar neutrality.
|
||||
- Signal instability: for small |R_i| (compared to σ_i), η_i can flip on minor return changes; tanh smoothing mitigates this.
|
||||
- Transaction costs are a meaningful drag because the strategy trades weekly or monthly and may have high turnover in trending markets that reverse.
|
||||
- The strategy is broadly equivalent to standard managed futures / CTA approaches and has shown positive long-run performance across many asset classes and time periods.
|
||||
74
gateway/knowledge/trading/strategies/fx/carry-trade.md
Normal file
74
gateway/knowledge/trading/strategies/fx/carry-trade.md
Normal file
@@ -0,0 +1,74 @@
|
||||
---
|
||||
description: "FX carry trade that exploits the empirical failure of Uncovered Interest Rate Parity by buying high-interest-rate currencies and selling low-interest-rate currencies via forward contracts."
|
||||
tags: [fx, carry, interest-rate-differential, uirp]
|
||||
---
|
||||
|
||||
# Carry Trade
|
||||
|
||||
**Section**: 8.2 | **Asset Class**: FX | **Type**: Carry
|
||||
|
||||
## Overview
|
||||
Uncovered Interest Rate Parity (UIRP) predicts that the excess return from investing in a high-interest-rate currency should be exactly offset by that currency's depreciation. Empirically the opposite tends to hold: high-interest-rate currencies appreciate on average. The carry trade exploits this "forward premium/discount anomaly" (Fama puzzle) by writing (selling) forwards on currencies at a forward premium and buying forwards on currencies at a forward discount.
|
||||
|
||||
## Construction / Mechanics
|
||||
The UIRP condition (which does not reliably hold) is:
|
||||
|
||||
```
|
||||
(1 + r_d) = [E_t(S(t+T)) / S(t)] × (1 + r_f) (440)
|
||||
```
|
||||
|
||||
The no-arbitrage forward FX rate is given by Covered Interest Rate Parity (CIRP):
|
||||
|
||||
```
|
||||
F(t,T) = S(t) × (1 + r_d) / (1 + r_f) (441)
|
||||
```
|
||||
|
||||
- r_d: domestic risk-free interest rate
|
||||
- r_f: foreign risk-free interest rate
|
||||
- S(t): spot FX rate at time t (units of domestic currency per 1 unit of foreign)
|
||||
- F(t,T): forward FX rate for delivery at T
|
||||
- E_t(S(t+T)): expected future spot rate at time t
|
||||
|
||||
**Trade logic:**
|
||||
- If F(t,T) > S(t) (forward premium, i.e., r_d > r_f): **sell** the forward (borrow foreign, invest domestic)
|
||||
- If F(t,T) < S(t) (forward discount, i.e., r_f > r_d): **buy** the forward (borrow domestic, invest foreign)
|
||||
|
||||
## Return Profile
|
||||
Profits when the carry differential is not fully offset by spot rate moves — i.e., when UIRP fails (the typical empirical finding). Losses occur if the borrowed currency suddenly appreciates sharply against the invested currency ("carry unwind" or "crash risk").
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Signal | Description |
|
||||
|--------|-------------|
|
||||
| F(t,T) > S(t) | Sell the forward (currency at forward premium) |
|
||||
| F(t,T) < S(t) | Buy the forward (currency at forward discount) |
|
||||
| Typical horizon T | 1 month |
|
||||
|
||||
## Variations
|
||||
|
||||
### 8.2.1 High-Minus-Low (HML) Carry
|
||||
The carry trade can be applied cross-sectionally across a universe of N foreign currencies. Define the log forward discount for currency i:
|
||||
|
||||
```
|
||||
D(t,T) = s(t) - f(t,T) (442)
|
||||
```
|
||||
|
||||
where s(t) = ln(S(t)) and f(t,T) = ln(F(t,T)). By CIRP:
|
||||
|
||||
```
|
||||
D(t,T) = ln((1 + r_f) / (1 + r_d)) ≈ r_f - r_d (443)
|
||||
```
|
||||
|
||||
**Portfolio construction:**
|
||||
- Positive D(t,T): buy a forward on that currency (higher foreign rate)
|
||||
- Negative D(t,T): sell a forward on that currency (lower foreign rate)
|
||||
- Sort all N currencies by D(t,T); go long the top quantile, short the bottom quantile
|
||||
- Dollar-neutral (zero-cost) implementation by construction
|
||||
- Forwards are typically one-month tenors; portfolio rebalanced monthly
|
||||
|
||||
The cross-sectional spread captures the "high-minus-low" carry factor, analogous to HML in equity factor models.
|
||||
|
||||
## Notes
|
||||
- The single-pair carry trade is exposed to large drawdowns during "carry unwind" episodes (e.g., 2008), when risk-off flows reverse the trade sharply.
|
||||
- Cross-sectional (HML) implementation diversifies idiosyncratic currency risk but retains systematic crash risk.
|
||||
- Transaction costs (bid-ask spreads on forwards) are a meaningful drag, particularly for less-liquid currency pairs.
|
||||
- The trade is equivalent to borrowing the low-rate currency and lending the high-rate currency when transaction costs and FX hedging costs are ignored.
|
||||
@@ -0,0 +1,45 @@
|
||||
---
|
||||
description: "Dollar carry trade that goes long or short all foreign currency forwards simultaneously based on the average cross-sectional forward discount relative to the USD."
|
||||
tags: [fx, carry, dollar-risk, cross-sectional]
|
||||
---
|
||||
|
||||
# Dollar Carry Trade
|
||||
|
||||
**Section**: 8.3 | **Asset Class**: FX | **Type**: Carry / Macro
|
||||
|
||||
## Overview
|
||||
Rather than sorting currencies into long and short buckets based on individual forward discounts, the dollar carry trade takes a uniform long or short position in a basket of N foreign currencies relative to the USD. The signal is the average forward discount across all currencies. When this average is positive, the dollar is expensive on a carry basis and all foreign currency forwards are bought; when negative, all are sold. This trade is related to the broad strength or weakness of the U.S. economy.
|
||||
|
||||
## Construction / Mechanics
|
||||
Compute the average cross-sectional forward discount for a basket of N currencies:
|
||||
|
||||
```
|
||||
D_bar(t,T) = (1/N) Σ D_i(t,T) (444)
|
||||
```
|
||||
|
||||
where D_i(t,T) is the forward discount for currency i (see Eq. 442 in carry-trade.md).
|
||||
|
||||
**Trade logic:**
|
||||
- D_bar(t,T) > 0: go **long** all N foreign currency forwards with equal weights
|
||||
- D_bar(t,T) < 0: go **short** all N foreign currency forwards with equal weights
|
||||
- T can be 1, 2, 3, 6, or 12 months
|
||||
|
||||
## Return Profile
|
||||
Profits when the average forward discount correctly predicts the net direction of the USD against the foreign currency basket. Empirical evidence links positive average forward discounts to weak U.S. economic conditions, so the strategy also provides indirect macro exposure.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| N | Number of foreign currencies in the basket |
|
||||
| T | Forward contract tenor (1, 2, 3, 6, or 12 months) |
|
||||
| D_bar(t,T) | Average forward discount; positive = go long all forwards, negative = go short |
|
||||
|
||||
## Variations
|
||||
- The equal-weight long/short rule can be replaced by a weight proportional to each currency's individual D_i to incorporate cross-sectional dispersion.
|
||||
- The basket can be restricted to G10 currencies or expanded to include EM currencies.
|
||||
|
||||
## Notes
|
||||
- The strategy is not dollar-neutral; it is an explicit bet on the direction of the USD versus a broad basket.
|
||||
- Unlike the HML carry trade (Section 8.2.1), this strategy does not hedge out the common dollar factor and thus carries more systemic risk.
|
||||
- Performance is empirically linked to U.S. business cycle conditions: when the U.S. economy is weak, the average forward discount tends to be positive, making the trade profitable in a carry sense.
|
||||
- Correlations across currencies in the basket can be high during crisis periods, reducing the diversification benefit.
|
||||
@@ -0,0 +1,57 @@
|
||||
---
|
||||
description: "FX combined strategy that blends the HP-filter moving-average momentum signal with the carry trade using minimum-variance portfolio weights to reduce overall volatility."
|
||||
tags: [fx, carry, momentum, combination, minimum-variance]
|
||||
---
|
||||
|
||||
# Momentum & Carry Combo
|
||||
|
||||
**Section**: 8.4 | **Asset Class**: FX | **Type**: Combination (Momentum + Carry)
|
||||
|
||||
## Overview
|
||||
Both the FX momentum strategy (Section 8.1) and the carry trade (Section 8.2) capture distinct but complementary sources of FX returns. Combining them in an optimally weighted portfolio can reduce overall variance relative to either strategy alone. The weights are derived by minimising the historical variance of the combined return given the sample variances and correlation of the two strategy return series.
|
||||
|
||||
## Construction / Mechanics
|
||||
Let R₁(t_s) and R₂(t_s) be the historical return series of the momentum and carry strategies respectively. Define their sample statistics:
|
||||
|
||||
```
|
||||
σ₁² = Var(R₁(t_s)) (445)
|
||||
σ₂² = Var(R₂(t_s)) (446)
|
||||
ρ = Cor(R₁(t_s), R₂(t_s)) (447)
|
||||
```
|
||||
|
||||
The combined portfolio return is:
|
||||
|
||||
```
|
||||
R(t_s) = w₁ R₁(t_s) + w₂ R₂(t_s) (448)
|
||||
w₁ + w₂ = 1 (449)
|
||||
Var(R(t_s)) → min (450)
|
||||
```
|
||||
|
||||
Solving the constrained minimisation yields the minimum-variance weights:
|
||||
|
||||
```
|
||||
w₁ = (σ₂² - σ₁σ₂ρ) / (σ₁² + σ₂² - 2σ₁σ₂ρ) (451)
|
||||
w₂ = (σ₁² - σ₁σ₂ρ) / (σ₁² + σ₂² - 2σ₁σ₂ρ) (452)
|
||||
```
|
||||
|
||||
## Return Profile
|
||||
Profits from both the trend-following component (momentum captures trending FX moves) and the carry component (interest rate differential). The minimum-variance weighting reduces drawdowns when one strategy temporarily underperforms, particularly during carry unwinds when momentum may be positive.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| σ₁, σ₂ | Historical volatilities of momentum and carry strategy returns |
|
||||
| ρ | Historical correlation between the two strategy returns |
|
||||
| w₁, w₂ | Optimal weights (sum to 1); derived from sample covariance matrix |
|
||||
| Estimation window | Rolling historical window for σ₁, σ₂, ρ |
|
||||
|
||||
## Variations
|
||||
- **Equal-weighted combo**: w₁ = w₂ = 0.5; simpler but ignores relative volatilities.
|
||||
- **Risk-parity combo**: weight each strategy inversely to its volatility (σ₂/(σ₁+σ₂) and σ₁/(σ₁+σ₂)).
|
||||
- **Extended combo**: include additional FX strategies (e.g., dollar carry, value) using the full sample covariance matrix (see Sections 3.6 and 4.6 for the general multi-strategy framework).
|
||||
|
||||
## Notes
|
||||
- The minimum-variance weights are sensitive to the estimation window; rolling windows introduce parameter instability.
|
||||
- If ρ is close to 1, both strategies move together and diversification benefits are limited; if ρ is close to -1, the combo can nearly eliminate variance but requires large offsetting positions.
|
||||
- The combo does not necessarily improve the Sharpe ratio compared with each individual strategy; it primarily targets variance reduction.
|
||||
- Constraints (e.g., w₁, w₂ ≥ 0) may be applied to avoid short-selling a strategy that has negative expected return.
|
||||
@@ -0,0 +1,51 @@
|
||||
---
|
||||
description: "FX moving-average crossover strategy that first applies the Hodrick-Prescott filter to remove high-frequency noise from spot rates before computing the MA signals."
|
||||
tags: [fx, momentum, moving-averages, trend-following]
|
||||
---
|
||||
|
||||
# Moving Averages with HP Filter
|
||||
|
||||
**Section**: 8.1 | **Asset Class**: FX | **Type**: Momentum / Trend-Following
|
||||
|
||||
## Overview
|
||||
FX spot rate time series are noisier than equity prices, which leads to false signals when raw rates are used in standard moving-average crossover strategies. The Hodrick-Prescott (HP) filter first decomposes the spot rate into a smooth lower-frequency trend component S*(t) and a higher-frequency noise component ν(t). Moving averages are then computed on S*(t) rather than the raw rate, substantially reducing whipsaws.
|
||||
|
||||
## Construction / Mechanics
|
||||
The HP filter minimises a penalised objective that trades off fit against smoothness:
|
||||
|
||||
```
|
||||
S(t) = S*(t) + ν(t) (437)
|
||||
|
||||
g = Σ[S(t) - S*(t)]² + λ Σ[S*(t+1) - 2S*(t) + S*(t-1)]² (438)
|
||||
g → min (439)
|
||||
```
|
||||
|
||||
- S(t): raw FX spot rate at time t
|
||||
- S*(t): smooth ("regular") lower-frequency component
|
||||
- ν(t): higher-frequency ("irregular") noise, treated as noise
|
||||
- λ: smoothing parameter (penalises variation in the second discrete derivative of S*(t))
|
||||
- Common convention: λ = 100 × n², where n is the data frequency in years (e.g., n = 12 for monthly data gives λ = 14,400)
|
||||
|
||||
Once S*(t) is obtained, two moving averages MA(T₁) and MA(T₂) with T₁ < T₂ are calculated on S*(t):
|
||||
- MA(T₁) > MA(T₂): **buy signal** (go long the foreign currency)
|
||||
- MA(T₁) < MA(T₂): **sell signal** (go short the foreign currency)
|
||||
|
||||
## Return Profile
|
||||
Profits when FX trends persist long enough for the shorter MA to remain above (below) the longer MA. The HP filter reduces false crossovers caused by transient noise, improving the signal-to-noise ratio versus raw-rate MAs.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Typical Value | Description |
|
||||
|-----------|--------------|-------------|
|
||||
| λ | 100 × n² | Smoothing parameter; n = data frequency in years |
|
||||
| T₁ | shorter window | Fast MA period (computed on S*(t)) |
|
||||
| T₂ | longer window | Slow MA period (computed on S*(t)); T₁ < T₂ |
|
||||
| Estimation period | Several years of monthly data | Used to fit S*(t) |
|
||||
|
||||
## Variations
|
||||
- The HP filter can be replaced by other smoothing techniques (Kalman filter, exponential moving averages) to extract the trend component before computing MAs.
|
||||
- The underlying MA crossover logic is identical to the equity version (Section 3.12); only the input series differs.
|
||||
|
||||
## Notes
|
||||
- λ has no universally optimal value; the common heuristic λ = 100n² may not be best for all currency pairs or market regimes.
|
||||
- The HP filter is backward-looking and non-causal in real time (two-sided filter); practitioners often use the one-sided (real-time) variant to avoid look-ahead bias.
|
||||
- FX markets are highly liquid but subject to central-bank interventions that can abruptly break trends.
|
||||
@@ -0,0 +1,52 @@
|
||||
---
|
||||
description: "FX triangular arbitrage that exploits momentary mispricing across three currency pairs by executing a circular chain of exchanges to lock in a riskless profit."
|
||||
tags: [fx, arbitrage, triangular, market-microstructure]
|
||||
---
|
||||
|
||||
# FX Triangular Arbitrage
|
||||
|
||||
**Section**: 8.5 | **Asset Class**: FX | **Type**: Arbitrage
|
||||
|
||||
## Overview
|
||||
Triangular arbitrage involves three currencies (A, B, C) and three currency pairs. If the cross-rate implied by trading A→B→C→A differs from the direct rate, a riskless profit exists. Such mispricings are extremely short-lived and require fast market data feeds and execution systems.
|
||||
|
||||
## Construction / Mechanics
|
||||
Given three currencies A, B, C and their bid/ask prices, there are two chains:
|
||||
1. A → B → C → A
|
||||
2. A → C → B → A (equivalent to swapping B and C in chain 1)
|
||||
|
||||
Focus on chain 1. The relevant rates are:
|
||||
- Bid(A→B): rate at which A is exchanged into B
|
||||
- Bid(B→C): rate at which B is exchanged into C
|
||||
- Ask(C→A): rate at which C is exchanged back into A (cost = 1/Ask(C→A))
|
||||
|
||||
Note: Bid(B→A) = 1/Ask(B→A) and Ask(A→B) = 1/Bid(A→B).
|
||||
|
||||
The overall round-trip exchange rate for chain 1 is:
|
||||
|
||||
```
|
||||
R(A→B→C→A) = Bid(A→B) × Bid(B→C) × (1 / Ask(C→A)) (453)
|
||||
```
|
||||
|
||||
**Profit condition:** If R(A→B→C→A) > 1, the trader profits by executing all three legs simultaneously. Starting with 1 unit of A, the trader ends with R > 1 units of A.
|
||||
|
||||
## Return Profile
|
||||
The P&L per unit of A is R - 1 when R > 1. Profits are typically very small per trade (fractions of a pip) but can be accumulated at high frequency. The strategy is notionally riskless if all three legs are executed simultaneously; execution lag introduces market risk.
|
||||
|
||||
## Key Parameters / Signals
|
||||
| Parameter | Description |
|
||||
|-----------|-------------|
|
||||
| R(A→B→C→A) | Round-trip rate; > 1 signals a profitable arbitrage |
|
||||
| Bid(A→B), Bid(B→C) | Bid rates for the two intermediate legs |
|
||||
| Ask(C→A) | Ask rate for the closing leg |
|
||||
| Execution speed | Critical: mispricings disappear in milliseconds |
|
||||
|
||||
## Variations
|
||||
- **Multi-currency arbitrage**: extend to more than 3 currency pairs (N-currency chains); computational complexity increases but can uncover deeper mispricings.
|
||||
- **Chain 2** (A→C→B→A): identical logic with B and C swapped; both chains should be monitored simultaneously.
|
||||
|
||||
## Notes
|
||||
- Opportunities are ephemeral; the strategy is effectively a latency arbitrage and is dominated by high-frequency traders with co-located infrastructure.
|
||||
- Bid-ask spreads are the primary cost; even small spreads can eliminate the theoretical profit, so only very tight markets are viable.
|
||||
- Unlike statistical arbitrage, this is a near-deterministic arbitrage: no model risk, but significant execution/technology risk.
|
||||
- Applicable to crypto exchanges where cross-exchange and cross-pair mispricings can be larger and more persistent than in professional FX markets.
|
||||
@@ -0,0 +1,62 @@
|
||||
---
|
||||
description: "A macro strategy that holds equities exclusively on important economic announcement days (FOMC, etc.) and switches to risk-free assets on all other days, exploiting the empirical announcement premium."
|
||||
tags: [global-macro, event-driven, fomc, announcement, equities]
|
||||
---
|
||||
|
||||
# Trading on Economic Announcements
|
||||
|
||||
**Section**: 19.5 | **Asset Class**: Global Macro | **Type**: Event-driven / Calendar-based
|
||||
|
||||
## Overview
|
||||
|
||||
Empirical evidence suggests that stocks tend to yield higher returns on important announcement dates — such as Federal Open Market Committee (FOMC) announcement days — than on other trading days. A simple macro trading strategy exploits this "announcement premium" by holding equities (via ETFs or futures) only on announcement days (ADs) and switching to risk-free assets (e.g., Treasuries) during all non-announcement days (NDAs). The strategy rotates 100% between equity exposure and Treasury exposure based solely on the calendar of scheduled announcements.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Signal Construction
|
||||
|
||||
1. Identify a set of important economic announcement dates (ADs). The primary example is FOMC announcement days, but other relevant announcements may include:
|
||||
- Non-Farm Payrolls (NFP)
|
||||
- CPI/inflation releases
|
||||
- GDP advance estimates
|
||||
- Other major central bank decisions (ECB, BoE, etc.)
|
||||
|
||||
2. For each trading day `t`:
|
||||
- If `t` is an announcement day (AD): hold equity ETFs/futures
|
||||
- If `t` is a non-announcement day (NDA): hold risk-free assets (e.g., T-bills or short-term Treasuries)
|
||||
|
||||
### Execution
|
||||
|
||||
- Implemented via ETFs (e.g., SPY for U.S. equities, SHY/BIL for short-term Treasuries) or futures (e.g., E-mini S&P 500 futures + T-bond futures)
|
||||
- Positions are switched at the open or close on the day before/day of each announcement
|
||||
- The strategy moves from 100% equities on ADs to 100% Treasuries on NDAs (binary switching)
|
||||
- Individual stocks are not used — the strategy operates at the index/ETF level
|
||||
|
||||
### Optional Technical Filters
|
||||
|
||||
The basic binary strategy can be augmented with various technical filters (e.g., momentum filters on the equity index) to further refine the signal and potentially improve the risk-adjusted return profile.
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The strategy captures the empirically documented "announcement premium" — the excess return accruing to equity holders on announcement days relative to non-announcement days. By being fully invested in equities only on ADs and earning the risk-free rate otherwise, the strategy aims to achieve equity-like returns with substantially reduced time-in-market and potentially lower overall risk. Returns are driven by the persistence of the announcement premium rather than by market direction.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Announcement calendar**: the set of ADs used (FOMC dates are the primary source; typically 8 per year for FOMC)
|
||||
- **Equity instrument**: broad index ETF or futures (e.g., S&P 500)
|
||||
- **Risk-free instrument**: T-bills, overnight repo, or short-term Treasury ETF
|
||||
- **Switching timing**: day-before close vs. announcement-day open; affects transaction costs
|
||||
- **Technical filter (optional)**: momentum or trend filter applied to the equity index to gate the switch
|
||||
- **Announcement types included**: FOMC only vs. broader macro announcement set
|
||||
|
||||
## Variations
|
||||
|
||||
- **Multi-announcement strategy**: include NFP, CPI, GDP, and other macro releases in addition to FOMC
|
||||
- **International extension**: apply to other central bank announcements (ECB, BoJ, BoE) for non-U.S. equity indexes
|
||||
- **Sector rotation on announcements**: hold rate-sensitive sectors on specific announcement types
|
||||
- **Options-based implementation**: use straddles around announcement dates to capture realized volatility premium
|
||||
- **Partial allocation**: hold a fixed fraction (e.g., 50%) in equities always, and increase to 100% only on ADs
|
||||
|
||||
## Notes
|
||||
|
||||
The existence and persistence of the FOMC announcement premium is well-documented in the academic literature (Savor and Wilson, 2013; Lucca and Moench, 2012). The premium is thought to reflect compensation for macroeconomic uncertainty resolved at announcement events. Transaction costs are relatively low given the infrequent switching (8 FOMC dates per year). The strategy's main risk is that the announcement premium may attenuate or disappear if it becomes widely exploited. Technical filters can help adapt to changing regimes. Because the strategy uses ETFs rather than individual stocks, execution is straightforward and liquidity is not a constraint for most portfolio sizes.
|
||||
@@ -0,0 +1,59 @@
|
||||
---
|
||||
description: "A systematic macro momentum strategy that buys assets favored by incoming macroeconomic trends and sells adversely affected assets, using four state variables to rank global equity indexes, currencies, and bonds."
|
||||
tags: [global-macro, momentum, systematic, multi-asset]
|
||||
---
|
||||
|
||||
# Fundamental Macro Momentum
|
||||
|
||||
**Section**: 19.2 | **Asset Class**: Global Macro | **Type**: Systematic momentum / Cross-sectional ranking
|
||||
|
||||
## Overview
|
||||
|
||||
This strategy aims to capture returns from the market's underreaction to changes in macroeconomic trends by buying assets favored by incoming macroeconomic trends and selling (shorting) assets adversely affected by them. It is a systematic (non-discretionary) strategy that can be applied across different asset classes — global equity indexes, currencies, government bonds, commodities, etc. — and exploits the tendency of prices to lag macroeconomic fundamentals.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### State Variables
|
||||
|
||||
Four macroeconomic state variables are used to characterize conditions in each country:
|
||||
|
||||
1. **Business cycle trend**: estimated using 1-year changes in real GDP growth and CPI inflation forecast, each contributing with a 50% weight
|
||||
2. **International trade trend**: estimated using 1-year changes in spot FX rates against an export-weighted basket
|
||||
3. **Monetary policy trend**: estimated using 1-year changes in short-term interest rates
|
||||
4. **Risk sentiment trend**: estimated using 1-year equity market excess returns
|
||||
|
||||
Note: different asset classes are affected by macroeconomic trends differently. For example, increasing growth is positive for equities and currencies but negative for bonds.
|
||||
|
||||
### Portfolio Construction
|
||||
|
||||
1. For a given asset class (e.g., global equity indexes), rank each country's asset using the values of the four state variables
|
||||
2. Construct a zero-cost long-short portfolio by going long the assets in the top decile and shorting those in the bottom decile
|
||||
3. Portfolios for various asset classes can be combined, e.g., with equal weights
|
||||
4. Holding period typically ranges from three to six months
|
||||
|
||||
Multiple ranking and portfolio construction methods are available (see also Subsection 3.6 for multifactor portfolio construction approaches).
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
Returns are driven by the market's systematic underreaction to macroeconomic trends: as trends gradually become recognized by market participants, prices adjust and the long positions appreciate while short positions decline. The strategy is fundamentally a momentum strategy but grounded in macroeconomic state variables rather than pure price momentum. Typical holding periods of 3–6 months mean lower turnover and transaction costs compared to short-term momentum.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Business cycle signal**: 1-year change in real GDP growth + CPI inflation forecast (50/50 weight)
|
||||
- **International trade signal**: 1-year change in spot FX rate vs. export-weighted basket
|
||||
- **Monetary policy signal**: 1-year change in short-term rates
|
||||
- **Risk sentiment signal**: 1-year equity market excess return
|
||||
- **Decile cutoffs**: top/bottom decile thresholds for portfolio construction
|
||||
- **Asset class weighting**: equal weight across combined asset class portfolios
|
||||
- **Holding period**: 3–6 months typical
|
||||
|
||||
## Variations
|
||||
|
||||
- **Single asset class**: apply the strategy only to equity indexes, only to currencies, or only to government bonds
|
||||
- **Broader factor set**: add additional state variables (e.g., current account balance, credit conditions)
|
||||
- **Discretionary overlay**: combine the systematic signal with analyst judgment
|
||||
- **CTA/managed futures extension**: apply the framework to futures contracts on equity indexes, bonds, and currencies
|
||||
|
||||
## Notes
|
||||
|
||||
Macro trading strategies constitute an investment style, not an asset class — they are not limited to any particular asset class or geographic region. The strategy can be classified as directional, long-short, or relative value depending on implementation. The three broad categories of macro strategies are discretionary macro, systematic macro, and CTA/managed futures. This strategy falls in the systematic macro category. Transaction costs are relatively modest given the 3–6 month holding period, but liquidity varies significantly across country assets. Care must be taken when applying this strategy to emerging markets where data quality and market access can be constraints.
|
||||
@@ -0,0 +1,63 @@
|
||||
---
|
||||
description: "A systematic macro strategy that ranks government bonds from multiple countries using fundamental factors (GDP, inflation, sovereign risk, real interest rate, momentum, term spread, Cochrane-Piazzesi) to construct a zero-cost long-short bond portfolio."
|
||||
tags: [global-macro, fixed-income, bonds, systematic, factor-investing]
|
||||
---
|
||||
|
||||
# Global Fixed-Income Strategy
|
||||
|
||||
**Section**: 19.4 | **Asset Class**: Global Macro | **Type**: Systematic / Cross-sectional factor investing
|
||||
|
||||
## Overview
|
||||
|
||||
This systematic macro trading strategy is based on a cross-sectional analysis of government bonds from various countries. Bonds are ranked using a set of fundamental and quantitative factors, and a zero-cost long-short portfolio is constructed by buying top-ranked bonds and selling bottom-ranked bonds. Country-bond ETFs are typically used as the investment vehicle.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Factor Set
|
||||
|
||||
Government bonds are evaluated and ranked using the following variables:
|
||||
|
||||
1. **GDP**: economic growth expectations; stronger GDP growth typically is negative for bonds (higher rates expected)
|
||||
2. **Inflation**: higher inflation erodes bond values; used as a negative signal for bonds
|
||||
3. **Sovereign risk**: credit quality of the government issuer; higher sovereign risk is negative for bonds
|
||||
4. **Real interest rate**: nominal rate minus inflation; higher real rates may indicate better bond valuations
|
||||
5. **Output gap**: difference between actual and potential GDP; affects future inflation and monetary policy expectations
|
||||
6. **Value**: valuation metric for bonds (e.g., yield relative to historical norms)
|
||||
7. **Momentum**: recent price/return trend of the bond
|
||||
8. **Term spread**: difference between long-term and short-term yields; an indicator of the yield curve shape and expected monetary policy
|
||||
9. **Cochrane-Piazzesi predictor**: a combination of forward rates that predicts excess bond returns (from Cochrane and Piazzesi, 2005)
|
||||
|
||||
### Portfolio Construction
|
||||
|
||||
1. For each country, compute the factor scores for its government bond
|
||||
2. Rank bonds across all countries based on the combined factor scores
|
||||
3. Construct a zero-cost portfolio: buy bonds in the top quantile, sell bonds in the bottom quantile
|
||||
4. Multifactor portfolios can also be constructed (analogous to Subsection 3.6)
|
||||
5. Investment vehicle: typically country-bond ETFs
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
Returns are driven by systematic differences in bond valuations and expected returns across countries, as captured by the factor set. The strategy captures value, momentum, carry, and macro-fundamental signals simultaneously. Because it is long-short and zero-cost, returns are driven purely by relative differences rather than by the overall level of bond markets. The Cochrane-Piazzesi predictor specifically targets excess return predictability from the term structure of interest rates.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **GDP growth**: typically 1-year change; positive for equities, negative for bonds
|
||||
- **Inflation**: YoY CPI; negative for nominal bonds
|
||||
- **Sovereign risk**: credit rating or CDS spread; negative signal for bonds
|
||||
- **Real interest rate**: nominal yield minus breakeven inflation
|
||||
- **Output gap**: estimated as deviation of GDP from potential (HP filter or similar)
|
||||
- **Value**: yield spread vs. historical average or fair-value model
|
||||
- **Momentum**: 12-month (or other lookback) return of the bond/ETF
|
||||
- **Term spread**: 10Y-2Y yield spread or similar
|
||||
- **Cochrane-Piazzesi (CP) predictor**: `cp_t = a + b * (y^5_t - (1/5)*sum_{n=1}^{5} f^n_t)` — a linear combination of forward rates that predicts excess returns on bonds
|
||||
|
||||
## Variations
|
||||
|
||||
- **Single-factor strategies**: pure momentum, pure value, or pure carry in government bonds
|
||||
- **Equity + bond combined macro**: extend the fundamental macro momentum framework (Section 19.2) to include bond rankings alongside equity index rankings
|
||||
- **Emerging market bonds**: apply the framework to EM sovereign debt, with additional currency risk considerations
|
||||
- **Corporate bond extension**: apply analogous factors to cross-sectional corporate bond strategies
|
||||
|
||||
## Notes
|
||||
|
||||
Cross-sectional government bond strategies require careful attention to currency risk — unless currency-hedged, returns are affected by both bond prices and exchange rate movements. Country-bond ETFs provide liquid access but may introduce tracking error relative to the underlying bond indexes. The Cochrane-Piazzesi predictor has been widely studied and validated in the academic literature for predicting U.S. Treasury excess returns, and has been extended internationally. Factor construction requires consistent data across countries, which can be challenging for some emerging market sovereign bonds.
|
||||
@@ -0,0 +1,77 @@
|
||||
---
|
||||
description: "A global macro inflation hedging strategy that allocates to commodities based on the spread between headline and core inflation, using ETFs or futures to execute the hedge."
|
||||
tags: [global-macro, inflation, commodities, hedging]
|
||||
---
|
||||
|
||||
# Global Macro Inflation Hedge
|
||||
|
||||
**Section**: 19.3 | **Asset Class**: Global Macro | **Type**: Inflation hedging / Commodity allocation
|
||||
|
||||
## Overview
|
||||
|
||||
Exogenous shocks — such as political or geopolitical events — can cause commodity prices (e.g., oil) to rise, leading to increased prices in oil-dependent economies. This strategy uses the spread between headline inflation (HI) and core inflation (CI) as a signal to determine the appropriate commodity allocation within a portfolio as an inflation hedge. The hedge is executed via ETFs, futures, or direct commodity exposure.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Inflation Pass-Through Mechanism
|
||||
|
||||
There are two steps in the inflation transmission process:
|
||||
|
||||
1. **Pass-through from commodity prices to headline inflation (HI)**: commodity price shocks quickly reflect in the headline Consumer Price Index (CPI), which covers a broad basket of goods and services
|
||||
2. **Pass-through from HI to core inflation (CI)**: core inflation excludes commodities (and other volatile components like food) and adjusts more slowly
|
||||
|
||||
**HI** is the raw inflation measured by indices such as the Consumer Price Index (CPI) based on prices of goods and services in a broad basket.
|
||||
**CI** excludes some products such as commodities, which are highly volatile and add noise to the index.
|
||||
|
||||
HI quickly reflects exogenous shocks around the world, while CI lags.
|
||||
|
||||
### Commodity Allocation Formula
|
||||
|
||||
The commodity allocation percentage (CA) within the portfolio is:
|
||||
|
||||
```
|
||||
CA = max(0, min(HI_YoY - CI_YoY / HI_YoY, 1)) (547)
|
||||
```
|
||||
|
||||
More precisely:
|
||||
```
|
||||
CA = max(0, min((HI_YoY - CI_YoY) / HI_YoY, 1))
|
||||
```
|
||||
|
||||
Where "YoY" stands for "year-on-year" change in the respective inflation measure.
|
||||
|
||||
**Interpretation:**
|
||||
- When `HI_YoY > CI_YoY`: the commodity-driven component of inflation is elevated; increase commodity allocation
|
||||
- When `HI_YoY <= CI_YoY`: no commodity-driven inflation premium; commodity allocation goes to zero
|
||||
- The formula is capped at 1 (100%) to prevent over-allocation
|
||||
- The floor at 0 prevents negative (short) commodity allocation
|
||||
|
||||
### Execution
|
||||
|
||||
The commodity exposure can be implemented by buying a basket of various commodities through:
|
||||
- ETFs (e.g., broad commodity ETFs, energy ETFs)
|
||||
- Futures contracts on commodity indexes or individual commodities
|
||||
- Direct commodity positions
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
The strategy profits when commodity prices rise and the portfolio's commodity allocation benefits from this appreciation, offsetting inflationary erosion of the rest of the portfolio. The return profile is asymmetric: the allocation increases when the inflation signal is elevated and goes to zero when it is absent. This is a hedging strategy, so the primary objective is inflation protection rather than alpha generation.
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **HI_YoY**: year-on-year headline inflation rate (e.g., CPI)
|
||||
- **CI_YoY**: year-on-year core inflation rate (CPI excluding volatile components)
|
||||
- **Spread (HI - CI)**: the commodity-driven inflation component; the hedge signal
|
||||
- **CA**: resulting commodity allocation percentage, bounded in [0, 1]
|
||||
- **Commodity basket composition**: choice of ETFs or futures instruments used to implement the allocation
|
||||
|
||||
## Variations
|
||||
|
||||
- **Sector-specific commodity hedge**: allocate specifically to energy, metals, or agricultural commodities depending on the shock source
|
||||
- **Gold-only hedge**: use gold as the sole inflation hedge instrument (simpler but less diversified)
|
||||
- **TIPS overlay**: complement commodity allocation with Treasury Inflation-Protected Securities (TIPS)
|
||||
- **Dynamic basket rebalancing**: adjust the commodity basket weights based on which commodity categories are driving HI above CI
|
||||
|
||||
## Notes
|
||||
|
||||
Infrastructure assets (Chapter 20) can also serve as an inflation hedge, albeit with some heterogeneity. The two-step pass-through mechanism (commodity prices → HI → CI) means CI is a lagging indicator, providing a systematic signal with some temporal stability. The strategy is inherently defensive — it reduces underperformance during inflationary episodes without requiring a directional forecast on commodity prices per se. The formula naturally results in zero allocation during stable, non-commodity-driven inflation environments, which is appropriate since unneeded commodity exposure introduces unnecessary volatility.
|
||||
301
gateway/knowledge/trading/strategies/index.md
Normal file
301
gateway/knowledge/trading/strategies/index.md
Normal file
@@ -0,0 +1,301 @@
|
||||
---
|
||||
description: "Master catalog of 150+ trading strategies organized by asset class. Load this page first, then use MemoryLookup with a specific page name to drill into any strategy's full details, formulas, and mechanics."
|
||||
tags: [trading, strategies, index, catalog]
|
||||
---
|
||||
|
||||
# Trading Strategies — Master Index
|
||||
|
||||
Source: *151 Trading Strategies* (Kakushadze & Serur, 2018). Each strategy has a dedicated knowledge page.
|
||||
|
||||
**Usage:** `MemoryLookup({page: "trading/strategies/<dir>/<file>"})` — e.g. `MemoryLookup({page: "trading/strategies/options/covered-call"})`
|
||||
|
||||
---
|
||||
|
||||
## Options (Chapter 2)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 2.2 | Covered call | Buy stock + sell call; income strategy capping upside | `options/covered-call` |
|
||||
| 2.3 | Covered put | Short stock + sell put; income with neutral-to-bearish bias | `options/covered-put` |
|
||||
| 2.4 | Protective put | Long stock + long put; hedges downside, preserves upside | `options/protective-put` |
|
||||
| 2.5 | Protective call | Short stock + long call; hedges upside risk on short position | `options/protective-call` |
|
||||
| 2.6 | Bull call spread | Buy near-ATM call, sell OTM call; capped bullish bet | `options/bull-call-spread` |
|
||||
| 2.7 | Bull put spread | Sell higher put, buy lower put; credit-based bullish bet | `options/bull-put-spread` |
|
||||
| 2.8 | Bear call spread | Sell lower call, buy higher call; credit-based bearish bet | `options/bear-call-spread` |
|
||||
| 2.9 | Bear put spread | Buy near-ATM put, sell OTM put; capped bearish bet | `options/bear-put-spread` |
|
||||
| 2.10 | Long synthetic forward | Long call + short put at same strike; replicates long forward | `options/long-synthetic-forward` |
|
||||
| 2.11 | Short synthetic forward | Long put + short call at same strike; replicates short forward | `options/short-synthetic-forward` |
|
||||
| 2.12 | Long combo | Buy OTM call + sell OTM put; bullish risk reversal | `options/long-combo` |
|
||||
| 2.13 | Short combo | Buy OTM put + sell OTM call; bearish risk reversal | `options/short-combo` |
|
||||
| 2.14 | Bull call ladder | Bull call spread + sell higher OTM call; limited upside, unlimited risk above K3 | `options/bull-call-ladder` |
|
||||
| 2.15 | Bull put ladder | Short near-ATM put + buy two lower OTM puts; bearish adjustment | `options/bull-put-ladder` |
|
||||
| 2.16 | Bear call ladder | Short near-ATM call + buy two higher OTM calls; bullish adjustment | `options/bear-call-ladder` |
|
||||
| 2.17 | Bear put ladder | Bear put spread + sell lower OTM put; unlimited downside risk | `options/bear-put-ladder` |
|
||||
| 2.18 | Calendar call spread | Long far-dated call, short near-dated call at same strike; exploits time decay | `options/calendar-call-spread` |
|
||||
| 2.19 | Calendar put spread | Long far-dated put, short near-dated put at same strike; exploits time decay | `options/calendar-put-spread` |
|
||||
| 2.20 | Diagonal call spread | Long deep ITM far-dated call, short OTM near-dated call; combines direction + decay | `options/diagonal-call-spread` |
|
||||
| 2.21 | Diagonal put spread | Long deep ITM far-dated put, short OTM near-dated put; combines direction + decay | `options/diagonal-put-spread` |
|
||||
| 2.22 | Long straddle | Buy ATM call + put; profits from large move either direction | `options/long-straddle` |
|
||||
| 2.23 | Long strangle | Buy OTM call + OTM put; cheaper volatility play than straddle | `options/long-strangle` |
|
||||
| 2.24 | Long guts | Buy ITM call + ITM put; pricier volatility play than straddle | `options/long-guts` |
|
||||
| 2.25 | Short straddle | Sell ATM call + put; income when stock stays near strike | `options/short-straddle` |
|
||||
| 2.26 | Short strangle | Sell OTM call + OTM put; wider profit zone than short straddle | `options/short-strangle` |
|
||||
| 2.27 | Short guts | Sell ITM call + ITM put; higher credit, narrower profit zone | `options/short-guts` |
|
||||
| 2.28 | Long call synthetic straddle | Short stock + buy 2 ATM calls; replicates long straddle | `options/long-call-synthetic-straddle` |
|
||||
| 2.29 | Long put synthetic straddle | Long stock + buy 2 ATM puts; replicates long straddle | `options/long-put-synthetic-straddle` |
|
||||
| 2.30 | Short call synthetic straddle | Long stock + sell 2 ATM calls; replicates short straddle | `options/short-call-synthetic-straddle` |
|
||||
| 2.31 | Short put synthetic straddle | Short stock + sell 2 ATM puts; replicates short straddle | `options/short-put-synthetic-straddle` |
|
||||
| 2.32 | Covered short straddle | Covered call + short ATM put; higher income, more downside risk | `options/covered-short-straddle` |
|
||||
| 2.33 | Covered short strangle | Covered call + short OTM put; wider profit zone | `options/covered-short-strangle` |
|
||||
| 2.34 | Strap | Buy 2 ATM calls + 1 ATM put; bullish volatility bias | `options/strap` |
|
||||
| 2.35 | Strip | Buy 1 ATM call + 2 ATM puts; bearish volatility bias | `options/strip` |
|
||||
| 2.36 | Call ratio backspread | Sell fewer near-ATM calls, buy more OTM calls; strongly bullish | `options/call-ratio-backspread` |
|
||||
| 2.37 | Put ratio backspread | Sell fewer near-ATM puts, buy more OTM puts; strongly bearish | `options/put-ratio-backspread` |
|
||||
| 2.38 | Ratio call spread | Buy fewer ITM calls, sell more near-ATM calls; income with unlimited upside risk | `options/ratio-call-spread` |
|
||||
| 2.39 | Ratio put spread | Buy fewer ITM puts, sell more near-ATM puts; income with unlimited downside risk | `options/ratio-put-spread` |
|
||||
| 2.40 | Long call butterfly | Buy ITM + OTM calls, sell 2 ATM calls; profits if stock stays near middle strike | `options/long-call-butterfly` |
|
||||
| 2.41 | Long put butterfly | Buy ITM + OTM puts, sell 2 ATM puts; profits if stock stays near middle strike | `options/long-put-butterfly` |
|
||||
| 2.42 | Short call butterfly | Sell ITM + OTM calls, buy 2 ATM calls; profits from large move | `options/short-call-butterfly` |
|
||||
| 2.43 | Short put butterfly | Sell ITM + OTM puts, buy 2 ATM puts; profits from large move | `options/short-put-butterfly` |
|
||||
| 2.44 | Long iron butterfly | Bull put spread + bear call spread around ATM; income near center | `options/long-iron-butterfly` |
|
||||
| 2.45 | Short iron butterfly | Bear put spread + bull call spread around ATM; profits from large move | `options/short-iron-butterfly` |
|
||||
| 2.46 | Long call condor | 4-leg call spread; profits if stock stays between inner strikes | `options/long-call-condor` |
|
||||
| 2.47 | Long put condor | 4-leg put spread; profits if stock stays between inner strikes | `options/long-put-condor` |
|
||||
| 2.48 | Short call condor | Inverse 4-leg call spread; profits from large move | `options/short-call-condor` |
|
||||
| 2.49 | Short put condor | Inverse 4-leg put spread; profits from large move | `options/short-put-condor` |
|
||||
| 2.50 | Long iron condor | OTM bull put spread + OTM bear call spread; income in wide range | `options/long-iron-condor` |
|
||||
| 2.51 | Short iron condor | OTM bear put spread + OTM bull call spread; profits from large move | `options/short-iron-condor` |
|
||||
| 2.52 | Long box | Long + short synthetic forward at different strikes; locks in fixed arbitrage payoff | `options/long-box` |
|
||||
| 2.53 | Collar | Long stock + long OTM put + short OTM call; defined risk/reward range | `options/collar` |
|
||||
| 2.54 | Bullish short seagull spread | Bull call spread financed by short OTM put; zero-cost bullish structure | `options/bullish-short-seagull-spread` |
|
||||
| 2.55 | Bearish long seagull spread | Short combo hedged by long OTM call; zero-cost bearish structure | `options/bearish-long-seagull-spread` |
|
||||
| 2.56 | Bearish short seagull spread | Bear put spread financed by short OTM call; zero-cost bearish structure | `options/bearish-short-seagull-spread` |
|
||||
| 2.57 | Bullish long seagull spread | Long combo hedged by long OTM put; zero-cost bullish structure | `options/bullish-long-seagull-spread` |
|
||||
|
||||
---
|
||||
|
||||
## Stocks (Chapter 3)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 3.1 | Price-momentum | Buy past winners, short past losers based on 12-month cumulative return | `stocks/price-momentum` |
|
||||
| 3.2 | Earnings-momentum | Buy high-SUE stocks, short low-SUE; captures post-earnings drift | `stocks/earnings-momentum` |
|
||||
| 3.3 | Value | Buy high Book-to-Price stocks, short low B/P; exploits value premium | `stocks/value` |
|
||||
| 3.4 | Low-volatility anomaly | Buy low-vol stocks, short high-vol; low risk = higher risk-adjusted return | `stocks/low-volatility-anomaly` |
|
||||
| 3.5 | Implied volatility | Buy stocks with rising call IV, short those with rising put IV | `stocks/implied-volatility` |
|
||||
| 3.6 | Multifactor portfolio | Blend multiple ranking factors (value + momentum etc.) by averaging ranks | `stocks/multifactor-portfolio` |
|
||||
| 3.7 | Residual momentum | Momentum on Fama-French regression residuals, stripping common factors | `stocks/residual-momentum` |
|
||||
| 3.8 | Pairs trading | Long cheap stock, short rich stock in correlated pair when spread deviates | `stocks/pairs-trading` |
|
||||
| 3.9 | Mean-reversion – cluster | Generalize pairs to N-stock cluster; buy underperformers, short outperformers | `stocks/mean-reversion-cluster` |
|
||||
| 3.10 | Mean-reversion – weighted regression | Continuous loadings matrix extension of cluster mean-reversion | `stocks/mean-reversion-weighted-regression` |
|
||||
| 3.11 | Single moving average | Long/short when price crosses a single MA | `stocks/single-moving-average` |
|
||||
| 3.12 | Two moving averages | Long/short on MA crossover (short vs. long window) | `stocks/two-moving-averages` |
|
||||
| 3.13 | Three moving averages | Require all three MAs to align before entering | `stocks/three-moving-averages` |
|
||||
| 3.14 | Support and resistance | Trade pivot-point-derived support/resistance levels | `stocks/support-and-resistance` |
|
||||
| 3.15 | Channel | Donchian channel mean-reversion or breakout | `stocks/channel` |
|
||||
| 3.16 | Event-driven – M&A | Merger arbitrage: long target, short acquirer in stock deals | `stocks/event-driven-ma` |
|
||||
| 3.17 | Machine learning – KNN | KNN regression on price/volume features to predict forward returns | `stocks/ml-knn` |
|
||||
| 3.18 | Statistical arbitrage – optimization | Maximize Sharpe via covariance matrix optimization; dollar-neutral variant | `stocks/statistical-arbitrage-optimization` |
|
||||
| 3.19 | Market-making | Earn bid-ask spread via passive limit orders with directional signal filter | `stocks/market-making` |
|
||||
| 3.20 | Alpha combos | Combine many weak alpha signals into a mega-alpha via structured optimization | `stocks/alpha-combos` |
|
||||
|
||||
---
|
||||
|
||||
## ETFs (Chapter 4)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 4.1 | Sector momentum rotation | Overweight top-momentum sector ETFs; with MA filter and dual-momentum variants | `etfs/sector-momentum-rotation` |
|
||||
| 4.2 | Alpha rotation | Rotate into sector ETFs with highest Jensen's alpha from factor regression | `etfs/alpha-rotation` |
|
||||
| 4.3 | R-squared | Overweight low-R² (high selectivity) high-alpha ETFs | `etfs/r-squared` |
|
||||
| 4.4 | Mean-reversion | Long low-IBS ETFs, short high-IBS ETFs (daily mean-reversion) | `etfs/mean-reversion` |
|
||||
| 4.5 | Leveraged ETFs | Short both leveraged ETF and its inverse to harvest daily decay | `etfs/leveraged-etfs` |
|
||||
| 4.6 | Multi-asset trend following | Long-only momentum across asset-class ETFs, volatility-weighted | `etfs/multi-asset-trend-following` |
|
||||
|
||||
---
|
||||
|
||||
## Fixed Income (Chapter 5)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 5.1 | Generalities | Bond mechanics: zero-coupon, coupon, floaters, swaps, duration, convexity | `fixed-income/generalities` |
|
||||
| 5.2 | Bullets | Hold bonds at a single target maturity to express a rate view | `fixed-income/bullets` |
|
||||
| 5.3 | Barbells | Hold two maturity extremes; higher convexity than equivalent bullet | `fixed-income/barbells` |
|
||||
| 5.4 | Ladders | Equal-capital allocation across n equidistant maturities | `fixed-income/ladders` |
|
||||
| 5.5 | Bond immunization | Match portfolio duration to liability maturity to hedge rate risk | `fixed-income/bond-immunization` |
|
||||
| 5.6 | Dollar-duration-neutral butterfly | Long barbell + short bullet; neutral to parallel shifts, bets on curvature | `fixed-income/dollar-duration-neutral-butterfly` |
|
||||
| 5.7 | Fifty-fifty butterfly | Butterfly with equal wing dollar durations | `fixed-income/fifty-fifty-butterfly` |
|
||||
| 5.8 | Regression-weighted butterfly | Butterfly with empirically estimated wing weights; maturity-weighted variant | `fixed-income/regression-weighted-butterfly` |
|
||||
| 5.9 | Low-risk factor | Buy lowest-maturity bonds within IG/HY tier; exploits low-risk anomaly | `fixed-income/low-risk-factor` |
|
||||
| 5.10 | Value factor | Buy bonds with spread above regression-implied fair value | `fixed-income/value-factor` |
|
||||
| 5.11 | Carry factor | Long top-decile bonds by total carry (yield + roll-down) | `fixed-income/carry-factor` |
|
||||
| 5.12 | Rolling down the yield curve | Buy bonds in steepest curve segments and hold through roll-down appreciation | `fixed-income/rolling-down-yield-curve` |
|
||||
| 5.13 | Yield curve spread | Flattener or steepener trade between two maturities, duration-matched | `fixed-income/yield-curve-spread` |
|
||||
| 5.14 | CDS basis arbitrage | Buy bond + buy CDS protection when negative basis creates near-riskless carry | `fixed-income/cds-basis-arbitrage` |
|
||||
| 5.15 | Swap-spread arbitrage | Long/short IRS vs. Treasury at same maturity; captures LIBOR-repo spread | `fixed-income/swap-spread-arbitrage` |
|
||||
|
||||
---
|
||||
|
||||
## Indexes (Chapter 6)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 6.1 | Generalities | Index construction, futures/ETF vehicles, spot-futures pricing, basis | `indexes/generalities` |
|
||||
| 6.2 | Cash-and-carry arbitrage | Trade basis when index futures deviate from fair value F* = (S-D)·exp(r·T) | `indexes/cash-and-carry-arbitrage` |
|
||||
| 6.3 | Dispersion trading | Long single-stock straddles, short index straddle; exploits IV correlation premium | `indexes/dispersion-trading` |
|
||||
| 6.4 | Intraday ETF arbitrage | Exploit short-lived bid-ask mispricings between two ETFs on same index | `indexes/intraday-etf-arbitrage` |
|
||||
| 6.5 | Index volatility targeting | Dynamically allocate w = σ*/σ to index and (1-w) to T-bills | `indexes/volatility-targeting` |
|
||||
|
||||
---
|
||||
|
||||
## Volatility (Chapter 7)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 7.1 | Generalities | Historical vs. implied vol, VIX, volatility instruments (futures, ETNs, swaps) | `volatility/generalities` |
|
||||
| 7.2 | VIX futures basis trading | Short VIX futures in contango, long in backwardation based on basis threshold | `volatility/vix-futures-basis-trading` |
|
||||
| 7.3 | Volatility carry | Short VXX + long VXZ; harvest contango roll differential between maturities | `volatility/volatility-carry` |
|
||||
| 7.4 | Volatility risk premium | Sell ATM straddles when implied > realized vol; gamma-hedged variant | `volatility/volatility-risk-premium` |
|
||||
| 7.5 | Volatility skew – long risk reversal | Buy OTM call + sell OTM put; exploit put IV > call IV skew | `volatility/volatility-skew-risk-reversal` |
|
||||
| 7.6 | Variance swaps | Trade realized vs. implied variance directly; no delta-hedging needed | `volatility/variance-swaps` |
|
||||
|
||||
---
|
||||
|
||||
## Foreign Exchange (Chapter 8)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 8.1 | Moving averages with HP filter | HP-filter FX series, then apply MA crossover signals | `fx/moving-averages-hp-filter` |
|
||||
| 8.2 | Carry trade | Buy high-rate currencies, sell low-rate currencies via forwards | `fx/carry-trade` |
|
||||
| 8.3 | Dollar carry trade | Long/short all currencies vs. USD based on average forward discount | `fx/dollar-carry-trade` |
|
||||
| 8.4 | Momentum & carry combo | Blend HP-MA momentum with carry using minimum-variance weights | `fx/momentum-carry-combo` |
|
||||
| 8.5 | FX triangular arbitrage | Exploit circular mispricing across three currency pairs for riskless profit | `fx/triangular-arbitrage` |
|
||||
|
||||
---
|
||||
|
||||
## Commodities (Chapter 9)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 9.1 | Roll yields | Long backwardated, short contangoed futures based on front/second-month ratio | `commodities/roll-yields` |
|
||||
| 9.2 | Hedging pressure | Use COT positioning data to identify long/short commodity opportunities | `commodities/hedging-pressure` |
|
||||
| 9.3 | Portfolio diversification | Add commodities to equity portfolio for low cross-asset correlation benefit | `commodities/portfolio-diversification` |
|
||||
| 9.4 | Value | Buy commodities cheap vs. 5-year-ago spot; sell those expensive | `commodities/value` |
|
||||
| 9.5 | Skewness premium | Buy low-skewness, sell high-skewness commodity futures | `commodities/skewness-premium` |
|
||||
| 9.6 | Trading with pricing models | Fit stochastic term-structure model; trade rich/cheap vs. model fair value | `commodities/pricing-models` |
|
||||
|
||||
---
|
||||
|
||||
## Futures (Chapter 10)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 10.1 | Hedging risk | Offset price/rate risk with futures; cross-hedging and IR hedging variants | `futures/hedging-risk` |
|
||||
| 10.2 | Calendar spread | Long near-month, short deferred-month (or vice versa); bet on supply/demand | `futures/calendar-spread` |
|
||||
| 10.3 | Contrarian trading | Buy recent underperforming futures, short outperforming; volume/OI filter variant | `futures/contrarian-trading` |
|
||||
| 10.4 | Trend following | Weight positions by sign of recent returns scaled by historical volatility | `futures/trend-following` |
|
||||
|
||||
---
|
||||
|
||||
## Structured Assets (Chapter 11)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 11.1 | CDO generalities | CDO mechanics, tranche structure, valuation, spread pricing, risky duration | `structured-assets/cdo-generalities` |
|
||||
| 11.2 | Carry – equity tranche | Buy equity tranche + delta-hedge with CDS index; earn tranche/index spread diff | `structured-assets/carry-equity-tranche` |
|
||||
| 11.3 | Carry – senior/mezzanine | Sell senior/mezz tranche + buy CDS index; earn index premium over tranche | `structured-assets/carry-senior-mezzanine` |
|
||||
| 11.4 | Carry – tranche hedging | Buy low-quality tranche + sell high-quality tranche; earn spread differential | `structured-assets/carry-tranche-hedging` |
|
||||
| 11.5 | Carry – CDS hedging | Buy low-quality tranche + hedge with single-name CDS | `structured-assets/carry-cds-hedging` |
|
||||
| 11.6 | CDOs – curve trades | Long/short CDO tranches of different maturities; bet on spread curve shape | `structured-assets/cdo-curve-trades` |
|
||||
| 11.7 | MBS trading | Buy MBS passthrough + hedge duration with IRS; primary exposure = prepayment risk | `structured-assets/mbs-trading` |
|
||||
|
||||
---
|
||||
|
||||
## Convertibles (Chapter 12)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 12.1 | Convertible arbitrage | Buy convertible bond + short underlying stock via delta hedge ratio h = Δ·C | `convertibles/convertible-arbitrage` |
|
||||
| 12.2 | Convertible OAS | Long high-OAS convertible, short low-OAS from same issuer; profit on convergence | `convertibles/convertible-oas` |
|
||||
|
||||
---
|
||||
|
||||
## Tax Arbitrage (Chapter 13)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 13.1 | Municipal bond tax arbitrage | Borrow at taxable rates, invest in tax-exempt munis; capture after-tax spread | `tax-arbitrage/muni-bond-tax-arbitrage` |
|
||||
| 13.2 | Cross-border tax arbitrage | Exploit dividend imputation tax credits via stock loan or deep ITM puts | `tax-arbitrage/cross-border-tax-arbitrage` |
|
||||
|
||||
---
|
||||
|
||||
## Miscellaneous Assets (Chapter 14)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 14.1 | Inflation hedging – inflation swaps | Buy/sell zero-coupon or year-on-year CPI swaps to hedge or trade inflation | `miscellaneous/inflation-hedging-swaps` |
|
||||
| 14.2 | TIPS-Treasury arbitrage | Short Treasury, replicate with TIPS + inflation swaps + STRIPS; lock in spread | `miscellaneous/tips-treasury-arbitrage` |
|
||||
| 14.3 | Weather risk – demand hedging | Hedge weather-driven demand using CDD/HDD futures/options | `miscellaneous/weather-risk-hedging` |
|
||||
| 14.4 | Energy – spark spread | Trade power plant gross margin via electricity/gas futures ratio hedge | `miscellaneous/energy-spark-spread` |
|
||||
|
||||
---
|
||||
|
||||
## Distressed Assets (Chapter 15)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 15.1 | Buy and hold distressed debt | Passively hold diversified distressed debt portfolio through reorganization | `distressed-assets/buy-and-hold-distressed-debt` |
|
||||
| 15.2 | Active distressed investing | Acquire control; three sub-strategies: court reorganization, debt purchase, loan-to-own | `distressed-assets/active-distressed-investing` |
|
||||
| 15.3 | Distress risk puzzle | Long healthy stocks, short distressed stocks (HMD portfolio) with vol-scaling | `distressed-assets/distress-risk-puzzle` |
|
||||
|
||||
---
|
||||
|
||||
## Real Estate (Chapter 16)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 16.2 | Mixed-asset diversification | Add real estate to stock/bond portfolio via MVO; low correlation benefit | `real-estate/mixed-asset-diversification` |
|
||||
| 16.3 | Intra-asset diversification | Diversify within real estate: property type, economic region, and combined | `real-estate/intra-asset-diversification` |
|
||||
| 16.4 | Real estate momentum | Buy high-momentum MSAs, short low-momentum MSAs via REITs/housing futures | `real-estate/momentum-regional` |
|
||||
| 16.5 | Inflation hedging | Hold commercial real estate as inflation hedge (strong empirical relationship) | `real-estate/inflation-hedging` |
|
||||
| 16.6 | Fix-and-flip | Buy distressed property, renovate, resell; short-term value-add strategy | `real-estate/fix-and-flip` |
|
||||
|
||||
---
|
||||
|
||||
## Cash (Chapter 17)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 17.2 | Money laundering (dark side) | Three-stage illegal process; documented for AML/educational awareness only | `cash/money-laundering-dark-side` |
|
||||
| 17.3 | Liquidity management | Optimize cash holdings to meet liquidity demands while minimizing drag | `cash/liquidity-management` |
|
||||
| 17.4 | REPO | Borrow/lend cash at preset rate using securities as collateral | `cash/repo` |
|
||||
| 17.5 | Pawnbroking | Secured short-term lending against physical collateral with right of sale | `cash/pawnbroking` |
|
||||
| 17.6 | Loan sharking | Illegal high-rate uncollateralized lending; documented for educational awareness only | `cash/loan-sharking` |
|
||||
|
||||
---
|
||||
|
||||
## Cryptocurrencies (Chapter 18)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 18.2 | ANN strategy | EMA/EMSD/RSI features → softmax classifier → BTC buy/sell signals | `crypto/ann-strategy` |
|
||||
| 18.3 | Sentiment – naïve Bayes | Twitter keyword features → Bernoulli naïve Bayes → BTC direction forecast | `crypto/sentiment-naive-bayes` |
|
||||
|
||||
---
|
||||
|
||||
## Global Macro (Chapter 19)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 19.2 | Fundamental macro momentum | Rank assets on 4 state variables (business cycle, trade, monetary, risk sentiment) | `global-macro/fundamental-macro-momentum` |
|
||||
| 19.3 | Global macro inflation hedge | Commodity allocation driven by headline vs. core inflation spread | `global-macro/inflation-hedge` |
|
||||
| 19.4 | Global fixed-income strategy | Rank government bonds on 9 macro/value/momentum factors; long-short | `global-macro/global-fixed-income` |
|
||||
| 19.5 | Trading on economic announcements | Hold equities on FOMC/announcement days only; T-bills otherwise | `global-macro/economic-announcements` |
|
||||
|
||||
---
|
||||
|
||||
## Infrastructure (Chapter 20)
|
||||
|
||||
| # | Strategy | Summary | Page |
|
||||
|---|---|---|---|
|
||||
| 20 | Infrastructure overview | Asset class overview: transport, utilities, energy; ETFs, listed/unlisted funds, munis | `infrastructure/infrastructure-overview` |
|
||||
@@ -0,0 +1,60 @@
|
||||
---
|
||||
description: "Cash-and-carry (index) arbitrage exploits price inefficiencies between an index spot price and its futures price, trading the basis when futures are mispriced relative to their theoretical fair value."
|
||||
tags: [indexes, arbitrage, futures, basis, cash-and-carry]
|
||||
---
|
||||
|
||||
# Cash-and-Carry Arbitrage
|
||||
|
||||
**Section**: 6.2 | **Asset Class**: Indexes | **Type**: Arbitrage
|
||||
|
||||
## Overview
|
||||
Cash-and-carry arbitrage (also called "index arbitrage") exploits discrepancies between the spot value of an index and the price of index futures. Theoretically, the futures price must equal the spot price compounded at the risk-free rate minus the present value of dividends. When the actual futures price deviates from this fair value beyond transaction costs, an arbitrage trade exists.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Theoretical (fair) futures price**:
|
||||
```
|
||||
F*(t,T) = [S(t) - D(t,T)] · exp(r(T-t)) (421)
|
||||
```
|
||||
|
||||
where:
|
||||
- F*(t,T): theoretical futures price with delivery T at time t
|
||||
- S(t): current spot value of the index
|
||||
- D(t,T): present value (as of t) of dividends paid by index constituents between t and T
|
||||
- r: risk-free rate (assumed constant)
|
||||
|
||||
**Basis** (normalized deviation from fair value):
|
||||
```
|
||||
B(t,T) = [F(t,T) - F*(t,T)] / S(t) (422)
|
||||
```
|
||||
|
||||
where F(t,T) is the actual futures price.
|
||||
|
||||
**Trading rule**:
|
||||
- If B(t,T) > 0 (futures rich relative to spot): **sell futures + buy cash** (index basket)
|
||||
- If B(t,T) < 0 (futures cheap relative to spot): **buy futures + sell cash** (index basket)
|
||||
- Only trade when |B(t,T)| exceeds pertinent transaction costs
|
||||
- Close the position when the basis converges to zero (futures price converges to fair value at delivery)
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Earns the basis B(t,T) as a riskless profit (if perfectly hedged) when the position is held to delivery.
|
||||
- The basis converges to zero at expiry: futures price → spot price at delivery.
|
||||
- Return per dollar of notional ≈ |B(t,T)| minus transaction costs.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- B(t,T): the basis — primary signal; trade when |B| > transaction cost threshold
|
||||
- S(t): index spot level
|
||||
- D(t,T): expected dividends over the futures lifetime
|
||||
- r: risk-free rate
|
||||
- Transaction cost threshold: determines minimum |B| required to trade profitably
|
||||
|
||||
## Variations
|
||||
- **Incomplete basket**: use a subset of index constituents to reduce transaction costs; introduces tracking error.
|
||||
- **ETF arbitrage**: similar logic applied to ETF mispricing (see Section 6.4).
|
||||
|
||||
## Notes
|
||||
- Arbitrage opportunities are short-lived and require extremely fast execution; this is a domain of high-frequency trading.
|
||||
- Selling the cash index (short-selling constituent stocks) is operationally complex: hard-to-borrow stocks, short-sale restrictions, etc.
|
||||
- Dollar-neutral long cash / short futures book helps manage execution but requires continuous monitoring.
|
||||
- Slippage from large orders moving the market can be prohibitive.
|
||||
- Incomplete baskets (omitting illiquid or low-cap stocks) reduce transaction costs but introduce residual tracking risk.
|
||||
@@ -0,0 +1,79 @@
|
||||
---
|
||||
description: "Dispersion trading goes long single-stock option straddles on index constituents and short the index option straddle, exploiting the empirical tendency for index implied volatility to exceed the theoretical volatility implied by constituent volatilities and correlations."
|
||||
tags: [indexes, volatility, dispersion, options, straddle, correlation]
|
||||
---
|
||||
|
||||
# Dispersion Trading in Equity Indexes
|
||||
|
||||
**Section**: 6.3 | **Asset Class**: Indexes | **Type**: Volatility / Arbitrage
|
||||
|
||||
## Overview
|
||||
Dispersion trading exploits the empirical observation that the implied volatility of index options is typically higher than the theoretical index volatility implied by constituent implied volatilities and their correlations. The strategy goes long single-stock volatility (via straddles on each constituent) and short index volatility (via a short index straddle), profiting when realized correlations are lower than the correlation implied by index options pricing.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Theoretical index variance** from constituent volatilities and correlation matrix:
|
||||
```
|
||||
σ_I² = Σ_{i,j=1}^N w_i·w_j·σ_i·σ_j·ρ_ij (423)
|
||||
```
|
||||
|
||||
where:
|
||||
- w_i: index weights (assumed market-cap weighted)
|
||||
- σ_i: implied volatility of stock i (from single-stock options)
|
||||
- ρ_ij: sample (historical) correlation matrix (ρ_ii = 1)
|
||||
|
||||
Empirically, the implied index volatility ̃σ_I > σ_I, i.e., index options are priced at a premium to theoretical constituent volatility.
|
||||
|
||||
**Position construction** (near-ATM straddles, ~1 month to expiry):
|
||||
- For each stock i in the index: **long n_i straddles** on stock i (near-ATM)
|
||||
- **Short 1 index straddle** (near-ATM, index level P_I)
|
||||
|
||||
**Sizing** n_i (for market-cap-weighted index):
|
||||
```
|
||||
n_i = S_i · P_I / Σ_{k=1}^N S_k·P_k (424)
|
||||
```
|
||||
|
||||
where S_i is shares outstanding for stock i. With this sizing, P_I = Σ_i n_i·P_i, so the index straddle payoff matches the sum of individual straddle payoffs as closely as possible.
|
||||
|
||||
All positions held until expiry (~1 month).
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Profits when constituent volatilities are high relative to index volatility (low realized correlation).
|
||||
- Loses when correlation spikes (e.g., broad market selloff where all stocks fall together), causing the index to move as much as the constituents.
|
||||
- The strategy can also be viewed as short the average pairwise correlation ρ_ij.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- ̃σ_I: implied index volatility (from index options)
|
||||
- σ_I: theoretical index volatility from Eq. (423) using constituent implied vols + historical correlations
|
||||
- Spread ̃σ_I - σ_I: the basis to be monetized
|
||||
- Realized vs. implied correlation: the key P&L driver
|
||||
|
||||
## Variations
|
||||
|
||||
### 6.3.1 Dispersion Trading — Subset Portfolio
|
||||
For large indexes (e.g., S&P 500), some constituent stocks may lack liquid single-stock options (typically smaller-cap stocks). These must be excluded from the bought portfolio. Additional reasons to use a subset:
|
||||
- Reducing the number of single-stock positions lowers transaction costs.
|
||||
- The sample correlation matrix ρ_ij is singular for typical lookback periods (e.g., 1 year of daily returns with N=500 stocks), making Eq. (423) unreliable.
|
||||
|
||||
**Stabilized correlation matrix** using a statistical risk model (PCA-based):
|
||||
```
|
||||
ψ_ij = ξ_i²·δ_ij + Σ_{A=1}^K λ^(A)·V_i^(A)·V_j^(A) (425)
|
||||
ξ_i² = 1 - Σ_{A=1}^K λ^(A)·[V_i^(A)]² (426)
|
||||
```
|
||||
|
||||
where K < r (r = rank of ρ_ij) principal components explain systematic risk; ξ_i is the idiosyncratic (specific) risk of stock i. K is chosen via eRank.
|
||||
|
||||
Using ψ_ij instead of ρ_ij, the theoretical variance becomes:
|
||||
```
|
||||
σ_I² = Σ_{i,j=1}^N w_i·w_j·σ_i·σ_j·ψ_ij
|
||||
= Σ_i w_i²σ_i²ξ_i² + Σ_{A=1}^K λ^(A)·[Σ_i λ^(A)·V_i^(A)·w_i·σ_i]² (427)
|
||||
```
|
||||
|
||||
The subset long portfolio contains only the N_* stocks with the lowest w_i²σ_i²ξ_i² values (e.g., N_* = 100 for S&P 500), which are the stocks contributing least specific risk to the index.
|
||||
|
||||
## Notes
|
||||
- This strategy sits at the boundary of index and volatility strategies; it can also be viewed as correlation trading.
|
||||
- The strategy loses badly during market crises when correlations spike toward 1 (e.g., 2008), as the index moves almost as much as the individual stocks.
|
||||
- The pairwise correlations ρ_ij are unstable out-of-sample; using a PCA-based risk model (subset variation) mitigates this.
|
||||
- ATM options may not be available for all stocks; OTM options close to ATM can substitute.
|
||||
- The strategy is typically implemented with options expiring in about 1 month, and all positions held to expiration.
|
||||
35
gateway/knowledge/trading/strategies/indexes/generalities.md
Normal file
35
gateway/knowledge/trading/strategies/indexes/generalities.md
Normal file
@@ -0,0 +1,35 @@
|
||||
---
|
||||
description: "Background on index investing: an index is a diversified portfolio of assets with defined weights, and investment vehicles such as futures and ETFs allow efficient, single-trade exposure to broad indexes."
|
||||
tags: [indexes, background, etf, futures, index-arbitrage]
|
||||
---
|
||||
|
||||
# Index Generalities
|
||||
|
||||
**Section**: 6.1 | **Asset Class**: Indexes | **Type**: Background / Reference
|
||||
|
||||
## Overview
|
||||
An index is a diversified portfolio of assets combined according to specified weights. The underlying assets are typically stocks (e.g., DJIA, S&P 500, Russell 3000). Index weights are determined by price (DJIA) or market capitalization (S&P 500, Russell 3000). Investment vehicles such as index futures and index-based ETFs allow a trader to gain broad market exposure through a single trade.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Index types by weighting scheme**:
|
||||
- **Price-weighted**: DJIA — each stock's weight proportional to its price; a high-priced stock has disproportionate influence.
|
||||
- **Market-cap-weighted**: S&P 500, Russell 3000 — each stock's weight proportional to its market capitalization (shares × price); larger companies dominate.
|
||||
- **Equal-weighted**: each constituent receives the same weight; requires frequent rebalancing.
|
||||
|
||||
**Investment vehicles**:
|
||||
- **Index futures**: standardized contracts to buy/sell the index at a future date; require no upfront payment of the full notional (margin only); settled in cash.
|
||||
- **Index ETFs**: exchange-traded funds that hold (or replicate) the index constituents; trade intraday like stocks; e.g., SPY (S&P 500), IVV (iShares S&P 500).
|
||||
- Both instruments allow leveraged or hedged exposure to the index.
|
||||
|
||||
## Key Concepts
|
||||
- **Spot price S(t)**: current value of the index based on constituent prices.
|
||||
- **Futures price F(t,T)**: price of the futures contract with delivery at T; theoretically F*(t,T) = [S(t) - D(t,T)] · exp(r(T-t)) where D(t,T) is the present value of dividends and r is the risk-free rate.
|
||||
- **Basis B(t,T)**: normalized difference between futures price and theoretical fair value; basis trading exploits deviations of B from zero.
|
||||
- **Tracking error**: difference between an ETF's NAV return and the index return; minimizing tracking error is a key ETF management objective.
|
||||
|
||||
## Notes
|
||||
- Index futures and ETFs are highly liquid, making index strategies generally easier to implement than single-stock strategies.
|
||||
- Market-cap-weighted indexes concentrate exposure in the largest stocks; this can create significant single-name risk.
|
||||
- ETF arbitrage (Section 6.4) exploits intraday mispricings between different ETFs tracking the same index.
|
||||
- Dispersion trading (Section 6.3) exploits the difference between index implied volatility and constituent implied volatilities.
|
||||
@@ -0,0 +1,49 @@
|
||||
---
|
||||
description: "Intraday ETF arbitrage exploits short-term mispricings between two ETFs tracking the same underlying index by buying the cheaper ETF and shorting the more expensive one when their bid-ask prices diverge beyond a threshold."
|
||||
tags: [indexes, arbitrage, etf, intraday, high-frequency]
|
||||
---
|
||||
|
||||
# Intraday Arbitrage Between Index ETFs
|
||||
|
||||
**Section**: 6.4 | **Asset Class**: Indexes | **Type**: Arbitrage / High-Frequency
|
||||
|
||||
## Overview
|
||||
When two ETFs track the same underlying index, their prices should be nearly identical. Short-lived intraday mispricings arise due to order flow imbalances, liquidity differences, or market microstructure effects. The strategy exploits these mispricings by simultaneously buying the cheaper ETF and shorting the more expensive one, closing the position when prices converge.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
Let ETF1 and ETF2 track the same index. Let P_1^Bid, P_1^Ask be the bid and ask prices for ETF1, and P_2^Bid, P_2^Ask for ETF2. Let κ be a predefined price threshold (κ close to 1, e.g., κ = 1.002).
|
||||
|
||||
**Trading rule**:
|
||||
```
|
||||
Rule = { Buy ETF2, short ETF1 if P_1^Bid ≥ P_2^Ask × κ
|
||||
{ Liquidate position if P_2^Bid ≥ P_1^Ask
|
||||
{ Buy ETF1, short ETF2 if P_2^Bid ≥ P_1^Ask × κ
|
||||
{ Liquidate position if P_1^Bid ≥ P_2^Ask (428)
|
||||
```
|
||||
|
||||
- **Enter**: when one ETF's bid exceeds the other's ask by at least factor κ (i.e., the spread exceeds transaction costs by a sufficient margin).
|
||||
- **Exit**: when the spread collapses (the two bid-ask ranges overlap), meaning convergence has occurred.
|
||||
- Orders are placed as marketable **"fill or kill"** limit orders to ensure immediate execution.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Earns the price differential (P_1^Bid - P_2^Ask or P_2^Bid - P_1^Ask) when the ETFs revert to parity.
|
||||
- Profit per trade ≈ (P_i^Bid/P_j^Ask - 1) - transaction costs, which is small (basis points level) but high frequency.
|
||||
- Cumulative return from many small, fast trades.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- κ: minimum price threshold to trigger trade (e.g., 1.002 = 0.2% premium)
|
||||
- P_i^Bid, P_i^Ask: real-time bid and ask prices for each ETF
|
||||
- Entry condition: P_1^Bid ≥ P_2^Ask × κ (or vice versa)
|
||||
- Exit condition: bid-ask ranges overlap (spread collapses to zero)
|
||||
|
||||
## Variations
|
||||
- Apply the same logic to an ETF and its underlying index futures (similar to cash-and-carry arbitrage, Section 6.2).
|
||||
- Multi-ETF: trade mispricings across three or more ETFs on related (but not identical) indexes.
|
||||
|
||||
## Notes
|
||||
- Arbitrage opportunities are ephemeral and require a fast order execution system; slippage will eat away profits at slow execution speeds.
|
||||
- "Fill or kill" limit orders are critical: partial fills create unhedged residual risk.
|
||||
- The threshold κ must exceed the effective transaction cost (bid-ask spread + commissions + market impact) to ensure profitability.
|
||||
- E.g., for S&P 500 ETFs: SPY (SPDR Trust) and IVV (iShares) are the main candidates.
|
||||
- This strategy is firmly in the domain of high-frequency / algorithmic trading.
|
||||
@@ -0,0 +1,58 @@
|
||||
---
|
||||
description: "Index volatility targeting maintains a constant portfolio volatility level by dynamically rebalancing between a risky index and a risk-free asset, scaling the index allocation inversely with current volatility."
|
||||
tags: [indexes, volatility-targeting, risk-management, rebalancing, allocation]
|
||||
---
|
||||
|
||||
# Index Volatility Targeting with Risk-Free Asset
|
||||
|
||||
**Section**: 6.5 | **Asset Class**: Indexes | **Type**: Risk Management / Volatility Targeting
|
||||
|
||||
## Overview
|
||||
A volatility targeting strategy maintains a constant target volatility σ_* for a portfolio by periodically rebalancing between a risky asset (an index) and a riskless asset (e.g., U.S. Treasury bills). The allocation to the risky asset is scaled inversely with the current (estimated) volatility of the index, so the portfolio's realized volatility stays close to σ_*.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Risky asset weight** (allocation to the index):
|
||||
```
|
||||
w = σ_* / σ
|
||||
```
|
||||
|
||||
where:
|
||||
- σ_*: target volatility (constant, set by the investor)
|
||||
- σ: current estimated volatility of the index (e.g., realized or implied)
|
||||
|
||||
**Risk-free asset weight**: 1 - w
|
||||
|
||||
If a maximum leverage constraint L is imposed: w is capped at L.
|
||||
|
||||
**Rebalancing to avoid overtrading**: instead of rebalancing on a fixed schedule (weekly, monthly), rebalance only when the allocation has drifted significantly:
|
||||
```
|
||||
Rebalance only if |Δw| / w > κ
|
||||
```
|
||||
where Δw is the change in w since the last rebalance and κ is a preset threshold (e.g., 5–10%). This reduces transaction costs while maintaining approximately constant volatility.
|
||||
|
||||
**Net portfolio**: a fraction w in the index + a fraction (1-w) in T-bills.
|
||||
|
||||
## Payoff / Return Profile
|
||||
- Targets a constant realized volatility close to σ_*.
|
||||
- When market volatility rises, the index allocation is reduced, limiting drawdowns.
|
||||
- When market volatility is low, the index allocation increases (potentially with leverage), improving returns.
|
||||
- The strategy does not make a directional bet on the market; it is a risk management overlay.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- σ_*: volatility target (investor-specified, e.g., 10% annualized)
|
||||
- σ: current volatility estimate (realized vol from recent returns, or implied vol from options)
|
||||
- w = σ_*/σ: dynamic allocation weight
|
||||
- κ: rebalancing threshold (avoids unnecessary turnover)
|
||||
- Maximum leverage L: caps w if set
|
||||
|
||||
## Variations
|
||||
- Apply to other asset classes (bonds, commodities) using the same framework.
|
||||
- Combine volatility targeting with a trend-following signal: only hold the index when its trend is positive, otherwise hold the risk-free asset.
|
||||
- Use implied volatility (e.g., VIX) as σ for a forward-looking allocation rather than backward-looking realized vol.
|
||||
|
||||
## Notes
|
||||
- Volatility targeting implicitly creates momentum-like behavior: reduces risk when volatility spikes (which often accompanies market selloffs) and adds risk when volatility is low (often in trending markets).
|
||||
- The strategy does not protect against sudden gap moves (e.g., flash crashes) where volatility spikes before rebalancing can occur.
|
||||
- Transaction costs from rebalancing must be weighed against the volatility-stabilization benefit; the threshold κ controls this trade-off.
|
||||
- The choice of σ (historical lookback window vs. implied vol) significantly affects performance and responsiveness.
|
||||
@@ -0,0 +1,80 @@
|
||||
---
|
||||
description: "An overview of infrastructure as an asset class, covering direct and indirect investment vehicles, and three core strategies: portfolio diversification, inflation hedging, and stable cash flow generation from brownfield projects."
|
||||
tags: [infrastructure, real-assets, inflation-hedge, diversification, long-term]
|
||||
---
|
||||
|
||||
# Infrastructure — Investment Overview
|
||||
|
||||
**Section**: 20 | **Asset Class**: Infrastructure | **Type**: Real assets / Long-term buy-and-hold
|
||||
|
||||
## Overview
|
||||
|
||||
Infrastructure investing encompasses long-term investments in essential physical assets and systems that underpin economic activity. It is a distinct asset class characterized by long-lived assets, predictable (often inflation-linked) cash flows, and low correlation with traditional financial assets. Infrastructure is inherently a long-term, buy-and-hold asset class, and the three main investment strategies are: improving risk-adjusted portfolio returns through diversification, hedging inflation, and generating stable cash flows — with brownfield projects being best suited for the latter.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Infrastructure Asset Categories
|
||||
|
||||
Infrastructure spans a wide range of asset types:
|
||||
|
||||
- **Transportation**: roads, bridges, tunnels, railways, ports, airports
|
||||
- **Telecommunications**: transmission cables, satellites, towers
|
||||
- **Utilities**: electricity generation, gas or electricity transmission/distribution, water supply, sewage, waste management
|
||||
- **Energy**: conventional and renewable energy infrastructure (pipelines, wind farms, solar facilities)
|
||||
- **Healthcare**: hospitals, clinics, senior homes
|
||||
- **Education**: schools, universities, research institutes
|
||||
- **Social infrastructure**: various government-mandated facilities
|
||||
|
||||
### Investment Vehicles
|
||||
|
||||
Investors can gain exposure to infrastructure assets through:
|
||||
|
||||
1. **Private equity-type investments**: unlisted/private infrastructure funds (direct ownership stakes in infrastructure projects or companies)
|
||||
2. **Listed infrastructure funds**: closed-end or open-end funds traded on exchanges
|
||||
3. **Publicly traded infrastructure companies**: stocks of companies that own and operate infrastructure assets
|
||||
4. **Municipal bonds**: bonds earmarked to fund infrastructure projects
|
||||
5. **Tracking ETFs**: ETFs that track global infrastructure fund indexes
|
||||
6. **Unlisted infrastructure funds**: provide direct economic exposure without exchange listing
|
||||
|
||||
### Project Types
|
||||
|
||||
- **Brownfield projects**: associated with established, existing assets in need of improvement or maintenance. More appropriate for stable cash flow generation because assets are already operational with known revenue streams.
|
||||
- **Greenfield projects**: associated with assets yet to be constructed. Higher risk during construction phase; revenue streams are uncertain until operational.
|
||||
|
||||
## Return Profile / Objective
|
||||
|
||||
Infrastructure investments pursue three primary objectives:
|
||||
|
||||
### 1. Portfolio Diversification (Risk-Adjusted Return Enhancement)
|
||||
Infrastructure assets typically have low correlation with equities and bonds, providing diversification benefits. Exposure via tracking ETFs, global infrastructure funds, or unlisted funds improves the risk-adjusted return of a well-diversified portfolio.
|
||||
|
||||
### 2. Inflation Hedging
|
||||
Infrastructure assets, like real estate, can be inflation-hedging investments. Many infrastructure contracts include explicit inflation escalators (e.g., toll road revenues linked to CPI). The inflation-hedging properties can be heterogeneous across infrastructure sub-sectors — regulated utilities and toll roads tend to have stronger inflation linkage than, e.g., merchant power plants. Related strategy: the Global Macro Inflation Hedge (Section 19.3) uses a similar concept applied to commodities.
|
||||
|
||||
### 3. Stable Cash Flow Generation
|
||||
Infrastructure investments can generate predictable, stable cash flows from long-term concession agreements, regulated rate structures, or monopoly-like market positions. For this objective:
|
||||
- **Brownfield projects are preferred** over greenfield because existing operational assets have known revenues, established customer bases, and lower execution risk
|
||||
- **Sector diversification** across transportation, utilities, energy, and social infrastructure can smooth cash flow volatility
|
||||
|
||||
## Key Parameters / Signals
|
||||
|
||||
- **Asset type**: transportation vs. utilities vs. energy vs. social — affects inflation linkage, regulatory environment, and cash flow stability
|
||||
- **Project stage**: brownfield (operational) vs. greenfield (development) — determines risk/return profile and suitability for cash flow strategies
|
||||
- **Investment vehicle**: listed (liquid, mark-to-market) vs. unlisted (illiquid, appraisal-based) — affects portfolio construction and liquidity management
|
||||
- **Regulatory framework**: regulated vs. merchant — regulated assets have more predictable revenue; merchant assets have commodity/market price exposure
|
||||
- **Concession length**: duration of operating rights; longer concessions provide longer cash flow visibility
|
||||
- **Inflation linkage**: explicit CPI escalators vs. implicit pass-through
|
||||
|
||||
## Variations
|
||||
|
||||
- **Core infrastructure**: large, stabilized brownfield assets (airports, toll roads, regulated utilities) with the most predictable cash flows and lowest risk
|
||||
- **Core-plus infrastructure**: slightly higher risk, some development or operational improvement component
|
||||
- **Value-add / opportunistic infrastructure**: significant operational improvements or greenfield development; higher risk/return
|
||||
- **Infrastructure debt**: senior secured lending to infrastructure projects; lower return but higher in the capital structure
|
||||
- **Renewable energy infrastructure**: wind, solar, storage projects; inflation-linked revenues (often via power purchase agreements) with greenfield construction risk
|
||||
|
||||
## Notes
|
||||
|
||||
Infrastructure as an asset class has grown substantially in institutional portfolios (pension funds, sovereign wealth funds, endowments) due to its long-duration, inflation-linked cash flow characteristics that match long-dated liabilities. The illiquidity premium in unlisted infrastructure can be significant, but requires patient capital and robust governance. Diversification across sectors mitigates the risk that any single regulatory regime or commodity market adversely impacts the portfolio. Key risks include regulatory/political risk (government changes to concession terms or rate structures), construction risk (greenfield), and interest rate risk (infrastructure assets are long-duration and sensitive to discount rate changes).
|
||||
|
||||
**Source**: Kakushadze and Serur, "151 Trading Strategies" (2018), Chapter 20.
|
||||
@@ -0,0 +1,61 @@
|
||||
---
|
||||
description: "Capture or hedge the gross margin of a gas-fired power plant by trading the spread between wholesale electricity prices and natural gas fuel costs, using electricity and gas futures in the ratio determined by the plant's heat rate."
|
||||
tags: [miscellaneous, energy, spread-trading, hedging, commodities]
|
||||
---
|
||||
|
||||
# Energy — Spark Spread
|
||||
|
||||
**Section**: 14.4 | **Asset Class**: Miscellaneous (Energy Commodities) | **Type**: Spread Trading / Hedging
|
||||
|
||||
## Overview
|
||||
The spark spread is the difference between the wholesale price of electricity and the price of natural gas required to produce it. It measures the gross margin of a gas-fired power plant (excluding all other costs: operation, maintenance, capital, etc.). A spark spread position is built by taking a short position in electricity futures and a long position in natural gas futures, in the ratio determined by the plant's heat rate.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Heat rate** (fuel efficiency of the power plant):
|
||||
```
|
||||
H = Q_F / Q_E (516)
|
||||
```
|
||||
- `Q_F` = amount of fuel (natural gas) used, measured in MMBtu
|
||||
- `Q_E` = electricity produced, measured in MWh
|
||||
- `H` measured in MMBtu/MWh
|
||||
- MMBtu = 1,000,000 Btu; Btu ≈ 1,055 Joules
|
||||
|
||||
**Spark spread** (in $/MWh):
|
||||
```
|
||||
S = P_E - H × P_F (517)
|
||||
```
|
||||
- `P_E` = price of electricity ($/MWh)
|
||||
- `P_F` = price of natural gas ($/MMBtu)
|
||||
|
||||
**Hedge ratio** for futures contracts:
|
||||
```
|
||||
h = H × F_E / F_F (518)
|
||||
```
|
||||
- `F_E = 736 MWh` (standard electricity futures contract size)
|
||||
- `F_F = 10,000 MMBtu` (standard natural gas futures contract size)
|
||||
|
||||
Since `h` is generally not a whole number, it is approximated as the ratio `h ≈ N_F / N_E` with the lowest possible whole-number denominator `N_E`. The hedge consists of buying `N_F` gas futures contracts for every `N_E` sold electricity futures contracts.
|
||||
|
||||
## Return Profile
|
||||
- **Electricity producer (natural hedge)**: short electricity futures + long gas futures locks in a fixed spark spread, hedging against a compression of the gross margin
|
||||
- **Speculator / spread trader**: profits if the spark spread widens (electricity prices rise relative to gas prices) on a long spread position, or if it narrows on a short spread position
|
||||
- The strategy has no directional energy price exposure — only exposure to the relative price of electricity vs. natural gas
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Heat rate `H`**: plant-specific efficiency; lower `H` = more efficient plant = higher spark spread for the same fuel cost
|
||||
- **Spark spread `S`**: core signal; compare to historical average or fair value based on plant operating costs
|
||||
- **Contract sizes `F_E`, `F_F`**: determine the achievable hedge ratio granularity
|
||||
- **Seasonal patterns**: electricity demand (and spark spread) exhibits strong seasonality driven by heating/cooling demand
|
||||
|
||||
## Variations
|
||||
- **Dark spread**: same concept for coal-fired power plants (replaces natural gas with coal prices)
|
||||
- **Quark spread**: same concept for nuclear power plants
|
||||
- **Clean spark spread**: adjusts for carbon emission costs (CO2 allowance prices) in addition to fuel costs
|
||||
|
||||
## Notes
|
||||
- The spark spread measures gross margin only; it does not account for fixed operating costs, maintenance, or capital expenditures
|
||||
- Basis risk exists between the price indexes referenced in futures contracts and the actual spot prices at the delivery location
|
||||
- Liquidity is concentrated in front-month contracts; longer-dated spark spread trades may have wide bid-ask spreads
|
||||
- Heat rates vary with plant load and ambient temperature; a single fixed `H` is an approximation
|
||||
- Regulatory risk: electricity markets are often heavily regulated; price caps and dispatch rules can affect realized spreads
|
||||
@@ -0,0 +1,56 @@
|
||||
---
|
||||
description: "Buy or sell inflation swaps to exchange fixed and floating (CPI-linked) cash flows, hedging against unexpected inflation or speculating on inflation relative to the breakeven rate."
|
||||
tags: [miscellaneous, inflation, derivatives, swaps, fixed-income]
|
||||
---
|
||||
|
||||
# Inflation Hedging — Inflation Swaps
|
||||
|
||||
**Section**: 14.1 | **Asset Class**: Miscellaneous (Inflation Derivatives) | **Type**: Hedging / Macro
|
||||
|
||||
## Overview
|
||||
Inflation swaps allow parties to exchange a fixed rate of inflation for a floating (CPI-linked) rate, analogous to interest rate swaps. A buyer of an inflation swap is long inflation: they receive the floating CPI-linked rate and pay the fixed rate ("breakeven rate"). The buyer profits if realized inflation exceeds expected inflation (i.e., the fixed swap rate). The fixed rate is typically calculated as the spread between Treasury notes/bonds and TIPS with the same maturity.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
### Zero-Coupon Inflation Swap (ZC)
|
||||
The most common type. Only one cash flow at maturity `T` (in years). Cash flows per $1 notional:
|
||||
|
||||
```
|
||||
C_fixed = (1 + K)^T - 1 (500)
|
||||
C_floating = I(T)/I(0) - 1 (501)
|
||||
```
|
||||
|
||||
- `K` = fixed rate (the "breakeven rate")
|
||||
- `I(t)` = CPI value at time `t`; `t = 0` is when the swap is entered into
|
||||
|
||||
### Year-on-Year Inflation Swap (YoY)
|
||||
References annual inflation rather than cumulative. Assuming annual payments (`t = 1, ..., T`):
|
||||
|
||||
```
|
||||
C_fixed(t) = K (502)
|
||||
C_floating(t) = I(t)/I(t-1) - 1 (503)
|
||||
```
|
||||
|
||||
The buyer pays `C_fixed` and receives `C_floating` at each period.
|
||||
|
||||
## Return Profile
|
||||
- **Buyer (long inflation)**: profits when realized CPI exceeds the breakeven rate `K`; losses when inflation is lower than expected
|
||||
- **Seller (short inflation)**: profits when realized inflation is below `K`
|
||||
- Returns are driven by the difference between realized inflation and the fixed swap rate; there is no equity or credit risk in a plain vanilla inflation swap
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **Breakeven rate** `K`: the fixed rate embedded in the swap; derived from the Treasury/TIPS spread for the same maturity
|
||||
- **CPI index** `I(t)`: typically the Consumer Price Index; contract specifies which index and lag
|
||||
- **Maturity** `T`: ZC swaps concentrate all cash flow at maturity; YoY swaps distribute annual payments
|
||||
- **Notional**: scales all cash flows linearly
|
||||
|
||||
## Variations
|
||||
- **Zero-Coupon vs. Year-on-Year**: ZC is simpler with one cash flow; YoY resets annually and is less sensitive to base-period CPI distortions
|
||||
- **Real rate swaps**: swap fixed real rate for floating real rate; related but distinct instrument
|
||||
- **Inflation caps/floors**: options on inflation; cap protects buyer if inflation exceeds a ceiling rate
|
||||
|
||||
## Notes
|
||||
- Liquidity in inflation swap markets is concentrated in major currencies (USD, EUR, GBP)
|
||||
- Counterparty risk: OTC instruments; cleared versions available on some CCPs
|
||||
- Basis risk between the CPI index in the swap and the actual inflation exposure being hedged
|
||||
- The fixed rate `K` is model-independent (observed from market), but fair value of the floating leg requires CPI forecasting
|
||||
@@ -0,0 +1,65 @@
|
||||
---
|
||||
description: "Short an overvalued Treasury bond and offset it with a synthetic replicating portfolio of TIPS plus zero-coupon inflation swaps, capturing the empirically persistent positive cash flow at inception."
|
||||
tags: [miscellaneous, arbitrage, fixed-income, TIPS, Treasuries]
|
||||
---
|
||||
|
||||
# TIPS-Treasury Arbitrage
|
||||
|
||||
**Section**: 14.2 | **Asset Class**: Miscellaneous (Fixed Income) | **Type**: Arbitrage
|
||||
|
||||
## Overview
|
||||
Based on the empirical observation that Treasury bonds are almost persistently overvalued relative to TIPS (Treasury Inflation-Protected Securities). The strategy shorts a Treasury bond and offsets the position with a synthetic portfolio that precisely replicates all Treasury bond cash flows using TIPS and zero-coupon inflation swaps. Because the synthetic portfolio costs less than the Treasury bond, the net cash flow at inception is positive, representing the arbitrage profit.
|
||||
|
||||
## Construction / Mechanics
|
||||
**Short leg**: Sell Treasury bond with price `P_Treasury`, fixed coupon rate `r_Treasury`, maturity `T`.
|
||||
|
||||
**Synthetic replicating portfolio** (long legs):
|
||||
- Buy TIPS with price `P_TIPS`, maturity `T`, fixed coupon rate `r`, and `n` coupon payments at times `t_i` (`i = 1, ..., n`, with `t_n = T`)
|
||||
- Simultaneously sell `n` zero-coupon inflation swaps with maturities `t_i`, fixed rate `K`, and notionals:
|
||||
```
|
||||
N_i = r + δ_{t_i, T} per $1 of TIPS principal
|
||||
```
|
||||
where `δ_{t_i, T} = 1` if `i = n` (maturity), 0 otherwise (to match principal repayment)
|
||||
|
||||
**TIPS cash flows** (per $1 notional; `I(t)` = CPI at time `t`):
|
||||
```
|
||||
C_TIPS(t_i) = N_i × I(t_i)/I(0) (504)
|
||||
C_swap(t_i) = N_i × [(1 + K)^t_i - I(t_i)/I(0)] (505)
|
||||
C_total(t_i) = C_swap(t_i) + C_TIPS(t_i) = N_i(1 + K)^t_i (506)
|
||||
```
|
||||
|
||||
The total cash flow replicates fixed coupon payments with effective coupon rates `r_eff(t_i) = r(1 + K)^t_i`.
|
||||
|
||||
**STRIPS positions** to match Treasury coupons exactly (small long or short positions in zero-coupon discount bonds):
|
||||
```
|
||||
S(t_i) = D(t_i) × {[r_Treasury - r_eff(t_i)] + δ_{t_i,T} × [1 - (1+K)^t_i]} (507)
|
||||
```
|
||||
where `D(τ)` is the discount factor (STRIPS value) with maturity `τ`.
|
||||
|
||||
**Net cash flow at inception**:
|
||||
```
|
||||
C(0) = P_Treasury - P_TIPS - Σ S(t_i) (508)
|
||||
i=1
|
||||
```
|
||||
|
||||
Empirically, `C(0) > 0` even after transaction costs — hence arbitrage.
|
||||
|
||||
## Return Profile
|
||||
The profit is locked in at trade inception as a positive `C(0)`. All subsequent cash flows net to zero by construction (the synthetic portfolio precisely replicates the Treasury). Returns are model-independent and driven purely by the persistent Treasury overvaluation relative to TIPS.
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **`C(0)`**: the net cash flow at inception; must be positive (and cover transaction costs) for the trade to be worthwhile
|
||||
- **STRIPS prices** `D(t_i)`: discount factors; observable from market
|
||||
- **Fixed rate** `K` on inflation swaps: the breakeven inflation rate
|
||||
- **TIPS coupon rate** `r` and Treasury coupon rate `r_Treasury`: the gap drives the size of STRIPS adjustments
|
||||
|
||||
## Variations
|
||||
- **Duration-neutral overlay**: combine with duration hedges to isolate the mispricing from interest rate directionality
|
||||
- **Partial replication**: use a subset of STRIPS to approximately replicate, reducing transaction costs at the expense of perfect replication
|
||||
|
||||
## Notes
|
||||
- Transaction costs (bid-ask spreads on TIPS, inflation swaps, STRIPS) can erode `C(0)`; the trade is only viable when mispricing is large enough
|
||||
- STRIPS = "Separate Trading of Registered Interest and Principal of Securities" — zero-coupon discount bonds
|
||||
- The persistent Treasury overvaluation has been documented empirically but can narrow or temporarily reverse
|
||||
- Short selling Treasuries requires repo market access; repo rates affect the total cost of carry
|
||||
- Regulatory constraints on short positions in government securities may limit implementation
|
||||
@@ -0,0 +1,70 @@
|
||||
---
|
||||
description: "Hedge weather-driven demand risk using weather derivatives (futures or options on temperature indices) with hedge ratios calibrated to the covariance between demand and the relevant temperature index."
|
||||
tags: [miscellaneous, hedging, weather-derivatives, energy]
|
||||
---
|
||||
|
||||
# Weather Risk — Demand Hedging
|
||||
|
||||
**Section**: 14.3 | **Asset Class**: Miscellaneous (Weather Derivatives) | **Type**: Hedging
|
||||
|
||||
## Overview
|
||||
Many businesses and economic sectors are affected by weather conditions both directly (e.g., energy consumption) and indirectly. Weather risk is hedged using weather derivatives, which reference synthetic temperature indexes since no tradable weather indexes exist. The two most common indexes are based on temperature: Cooling-Degree-Days (CDD) for extreme heat and Heating-Degree-Days (HDD) for extreme cold.
|
||||
|
||||
## Construction / Mechanics
|
||||
|
||||
**Temperature indexes** (over a contract life of `n` days):
|
||||
```
|
||||
I_CDD = Σ max(0, T_i - T_base) (509)
|
||||
i=1
|
||||
|
||||
I_HDD = Σ max(0, T_base - T_i) (510)
|
||||
i=1
|
||||
|
||||
T_i = (T_i^min + T_i^max) / 2 (511)
|
||||
```
|
||||
|
||||
- `T_i` = average daily temperature on day `i`
|
||||
- `T_i^min`, `T_i^max` = minimum and maximum temperatures on day `i`
|
||||
- `T_base = 65°F`
|
||||
|
||||
**Hedging demand risk for heating (HDD)**:
|
||||
|
||||
Using a short futures position or a long put option:
|
||||
```
|
||||
h_futures^HDD = Cov(q_w, I_HDD) / Var(I_HDD) (512)
|
||||
h_put^HDD = -Cov(q_w, max(K - I_HDD, 0)) / Var(max(K - I_HDD, 0)) (513)
|
||||
```
|
||||
|
||||
**Hedging demand risk for cooling (CDD)**:
|
||||
|
||||
Using a long futures position or a long call option:
|
||||
```
|
||||
h_futures^CDD = Cov(q_w, I_CDD) / Var(I_CDD) (514)
|
||||
h_call^CDD = Cov(q_w, max(I_CDD - K, 0)) / Var(max(I_CDD - K, 0)) (515)
|
||||
```
|
||||
|
||||
- `q_w` = the portion of demand affected by weather conditions (excluding other exogenous, non-weather components)
|
||||
- `K` = strike price of the option
|
||||
- Cov and Var are serial (co)variances
|
||||
|
||||
## Return Profile
|
||||
The hedge reduces weather-driven demand volatility. The futures hedge provides linear protection against temperature deviations from average; the options hedge provides asymmetric protection (puts for heating risk, calls for cooling risk). In non-extreme weather years the hedge has negative carry (cost of options, or futures mark-to-market losses when weather is mild).
|
||||
|
||||
## Key Parameters / Signals
|
||||
- **`q_w`**: weather-sensitive component of demand; must be isolated from non-weather demand drivers
|
||||
- **Hedge ratios** `h_futures` and `h_put/h_call`: computed from historical Cov/Var of demand vs. temperature index
|
||||
- **Contract life `n`**: weekly, monthly, or seasonal contracts available
|
||||
- **Base temperature `T_base = 65°F`**: standard for U.S. CME weather contracts
|
||||
- **Strike `K`**: for option-based hedges; determines payoff profile
|
||||
|
||||
## Variations
|
||||
- **Futures-only hedge**: simpler, linear; appropriate when demand has approximately linear sensitivity to temperature
|
||||
- **Options hedge**: asymmetric protection; appropriate when the cost of extreme weather is highly nonlinear
|
||||
- **Combination**: futures for expected temperature deviation plus options for tail risk
|
||||
|
||||
## Notes
|
||||
- No "tradable" weather indexes exist; all weather derivatives reference synthetic indexes based on temperature data from specified weather stations
|
||||
- Basis risk between the specific weather station used in the contract and the firm's actual geographic exposure
|
||||
- Liquidity is concentrated in CME weather futures for major U.S. cities; OTC markets cover more locations but with less liquidity
|
||||
- Weather derivatives are used primarily by energy companies, agriculture, retail, and travel industries
|
||||
- Historical Cov/Var estimates may not be stable across climate regimes; model recalibration is needed periodically
|
||||
@@ -0,0 +1,34 @@
|
||||
---
|
||||
description: "A bullish-adjusted strategy selling a near-ATM call at K1 and buying two higher OTM calls at K2 and K3, arising when a bear call spread is adjusted for a stock that trades higher."
|
||||
tags: [options, hedging, bullish, ladder]
|
||||
---
|
||||
|
||||
# Bear Call Ladder
|
||||
|
||||
**Section**: 2.16 | **Asset Class**: Options | **Type**: Hedging
|
||||
|
||||
## Overview
|
||||
The bear call ladder is a vertical spread consisting of a short call at K1 (near ATM), a long call at K2 (OTM), and a long call at K3 (further OTM, K3 > K2 > K1). A bear call ladder typically arises when a bear call spread goes wrong (the stock trades higher), so the trader buys another OTM call at K3 to adjust the position to bullish.
|
||||
|
||||
## Construction
|
||||
- Sell 1 call option at strike K1 (near ATM)
|
||||
- Buy 1 call option at strike K2 (OTM, K2 > K1)
|
||||
- Buy 1 call option at strike K3 (further OTM, K3 > K2), same expiry
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K3)+ + (S_T - K2)+ - (S_T - K1)+ - H
|
||||
|
||||
- Lower breakeven: S*_down = K1 - H (if H < 0, net credit)
|
||||
- Upper breakeven: S*_up = K3 + K2 - K1 + H
|
||||
- Max profit: P_max = unlimited (above S*_up)
|
||||
- Max loss: L_max = K2 - K1 + H (in zone [K1, K2])
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish adjustment to a bear call spread that has moved against the trader
|
||||
- Profits if the stock continues to rise significantly above K3
|
||||
- Low volatility near K1 environment after adjustment is undesirable
|
||||
|
||||
## Notes
|
||||
The bear call ladder converts a bearish income strategy into a bullish capital gain strategy. The additional long call at K3 limits the maximum loss zone and creates profit on a sharp rally.
|
||||
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A bearish vertical spread selling a lower-strike OTM call at K2 and buying a higher-strike OTM call at K1 for a net credit, profiting if the stock stays below K2."
|
||||
tags: [options, income, bearish, vertical-spread]
|
||||
---
|
||||
|
||||
# Bear Call Spread
|
||||
|
||||
**Section**: 2.8 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The bear call spread is a vertical spread consisting of a long position in an OTM call option with strike K1, and a short position in another OTM call option with a lower strike K2 (K2 < K1). This is a net credit trade. The trader's outlook is bearish. This is an income strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 call option at strike K1 (higher OTM), same expiry
|
||||
- Sell 1 call option at strike K2 (lower OTM, K2 < K1)
|
||||
|
||||
Net credit: C = premium received for K2 call - premium paid for K1 call
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ - (S_T - K2)+ + C
|
||||
|
||||
- Breakeven: S* = K2 + C
|
||||
- Max profit: P_max = C (if S_T <= K2 at expiry; both calls expire worthless)
|
||||
- Max loss: L_max = K1 - K2 - C (if S_T >= K1 at expiry)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bearish to neutral outlook; expects stock to remain below K2 by expiry
|
||||
- Prefer when implied volatility is elevated (larger credit received)
|
||||
- Income generation with defined upside risk
|
||||
|
||||
## Notes
|
||||
The bear call spread is a credit spread. Maximum profit is limited to the net credit received. Maximum loss is the spread width minus the credit. The long call at K1 caps the loss relative to a naked short call.
|
||||
@@ -0,0 +1,34 @@
|
||||
---
|
||||
description: "A bear put spread extended by selling an additional lower OTM put at K3, financing the spread while capping downside profit and creating unlimited risk below K3."
|
||||
tags: [options, income, bearish, ladder]
|
||||
---
|
||||
|
||||
# Bear Put Ladder
|
||||
|
||||
**Section**: 2.17 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The bear put ladder is a vertical spread consisting of a long put at K1 (near ATM), a short put at K2 (OTM, K2 < K1), and a short put at K3 (further OTM, K3 < K2). It is a bear put spread financed by selling an additional OTM put at K3. This adjusts the outlook from bearish (bear put spread) to conservatively bearish or even non-directional with an expectation of low volatility.
|
||||
|
||||
## Construction
|
||||
- Buy 1 put option at strike K1 (near ATM)
|
||||
- Sell 1 put option at strike K2 (OTM, K2 < K1)
|
||||
- Sell 1 put option at strike K3 (further OTM, K3 < K2), same expiry
|
||||
|
||||
Net debit or credit H (assuming K3 + K2 - K1 + H > max(H, 0))
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (K2 - S_T)+ - (K3 - S_T)+ - H
|
||||
|
||||
- Upper breakeven: S*_up = K1 - H (if H > 0)
|
||||
- Lower breakeven: S*_down = K3 + K2 - K1 + H
|
||||
- Max profit: P_max = K1 - K2 - H (achieved in zone [K3, K2])
|
||||
- Max loss: L_max = K3 + K2 - K1 + H (unlimited as S_T -> 0)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Conservatively bearish; expects stock to fall toward K2 but not collapse through K3
|
||||
- Low implied volatility environment expected after entry
|
||||
- The additional short put at K3 reduces cost but creates unlimited downside risk
|
||||
|
||||
## Notes
|
||||
This is an income strategy in the sense that selling the K3 put finances the spread. However, unlimited loss exposure arises if the stock collapses well below K3. Risk management requires a stop-loss below K3.
|
||||
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A bearish vertical spread buying a near-ATM put at K1 and selling a lower-strike OTM put at K2 < K1 for a net debit, profiting if the stock falls toward K2."
|
||||
tags: [options, speculation, bearish, vertical-spread]
|
||||
---
|
||||
|
||||
# Bear Put Spread
|
||||
|
||||
**Section**: 2.9 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The bear put spread is a vertical spread consisting of a long position in a close to ATM put option with strike K1, and a short position in an OTM put option with a lower strike K2 (K2 < K1). This is a net debit trade. The trader's outlook is bearish: the strategy profits if the stock price falls. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 put option at strike K1 (near ATM), paying debit D
|
||||
- Sell 1 put option at strike K2 (OTM lower, K2 < K1), same expiry
|
||||
|
||||
Net debit: D = premium paid for K1 put - premium received for K2 put
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (K2 - S_T)+ - D
|
||||
|
||||
- Breakeven: S* = K1 - D
|
||||
- Max profit: P_max = K1 - K2 - D (achieved when S_T <= K2)
|
||||
- Max loss: L_max = D (if S_T >= K1 at expiry)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Moderately bearish outlook; expects stock to fall toward or below K2 by expiry
|
||||
- Prefer when implied volatility is low (cheaper debit to enter)
|
||||
- Lower cost and lower risk than buying a naked put; downside profit is capped at K2
|
||||
|
||||
## Notes
|
||||
Both profit and loss are limited. The maximum gain equals the spread width minus the net debit. Appropriate when the trader has a bearish view but wants to reduce the premium outlay compared to a simple long put.
|
||||
@@ -0,0 +1,38 @@
|
||||
---
|
||||
description: "A bearish capital-gain strategy (short combo hedged by a long OTM call) buying an OTM put at K1, selling an ATM call at K2, and buying an OTM call at K3, ideally structured at zero cost."
|
||||
tags: [options, speculation, bearish, seagull]
|
||||
---
|
||||
|
||||
# Bearish Long Seagull Spread
|
||||
|
||||
**Section**: 2.55 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The bearish long seagull spread is a short combo (short risk reversal) hedged against the stock price rising by buying an OTM call option. It amounts to a long position in an OTM put at K1, a short position in an ATM call at K2, and a long position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bearish. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 OTM put option at strike K1 (lowest)
|
||||
- Sell 1 ATM call option at strike K2 (middle)
|
||||
- Buy 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
|
||||
- All same expiry; ideally zero net premium (H = 0)
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (S_T - K2)+ + (S_T - K3)+ - H
|
||||
|
||||
Breakeven depends on sign of H:
|
||||
- S* = K1 - H (if H > 0)
|
||||
- S* = K2 - H (if H < 0)
|
||||
- K1 <= S* <= K2 (if H = 0)
|
||||
|
||||
- Max profit: P_max = K1 - H (if stock goes to zero; long put at full value)
|
||||
- Max loss: L_max = K3 - K2 + H (if stock rises above K3; net short call capped at K3)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bearish outlook; expects stock to fall below K1
|
||||
- Ideally zero-cost (H = 0): the short call premium finances the long put
|
||||
- Long call at K3 caps the upside loss from the short call at K2
|
||||
|
||||
## Notes
|
||||
The bearish long seagull is the mirror of the bullish short seagull spread. The long call at K3 hedges the unlimited upside risk of the short call at K2, capping maximum loss at K3 - K2 + H. The maximum profit is limited to K1 - H (stock to zero).
|
||||
@@ -0,0 +1,38 @@
|
||||
---
|
||||
description: "A bearish capital-gain strategy (bear put spread financed by a short OTM call) selling an OTM call at K3, buying an ATM put at K2, and selling an OTM put at K1, ideally structured at zero cost."
|
||||
tags: [options, speculation, bearish, seagull]
|
||||
---
|
||||
|
||||
# Bearish Short Seagull Spread
|
||||
|
||||
**Section**: 2.56 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The bearish short seagull spread is a bear put spread financed with a sale of an OTM call option. It amounts to a short position in an OTM put at K1, a long position in an ATM put at K2, and a short position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bearish. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Sell 1 OTM put option at strike K1 (lowest)
|
||||
- Buy 1 ATM put option at strike K2 (middle)
|
||||
- Sell 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
|
||||
- All same expiry; ideally zero net premium (H = 0)
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = -(K1 - S_T)+ + (K2 - S_T)+ - (S_T - K3)+ - H
|
||||
|
||||
Breakeven depends on sign of H:
|
||||
- S* = K2 - H (if H > 0)
|
||||
- S* = K3 - H (if H < 0)
|
||||
- K2 <= S* <= K3 (if H = 0)
|
||||
|
||||
- Max profit: P_max = K2 - K1 - H (if S_T <= K1; bear put spread at max, put not needed)
|
||||
- Max loss: L_max = unlimited (stock rises without bound above K3; short call exposed)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bearish outlook; expects stock to fall below K2 toward K1
|
||||
- Ideally zero-cost (H = 0): the short call premium finances the bear put spread
|
||||
- Short call at K3 creates unlimited upside risk above K3
|
||||
|
||||
## Notes
|
||||
Unlike the bearish long seagull (which buys a call to cap upside), the bearish short seagull sells a call at K3 to finance the bear put spread, resulting in unlimited upside loss. The short put at K1 caps the downside profit. Requires careful stop-loss management above K3.
|
||||
@@ -0,0 +1,34 @@
|
||||
---
|
||||
description: "A bullish vertical spread extended by selling a second OTM call at K3 > K2, financing a bull call spread while capping upside and creating unlimited risk above K3."
|
||||
tags: [options, income, bullish, ladder]
|
||||
---
|
||||
|
||||
# Bull Call Ladder
|
||||
|
||||
**Section**: 2.14 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The bull call ladder is a vertical spread consisting of a long call at K1 (near ATM), a short call at K2 (OTM), and a short call at K3 (further OTM, K3 > K2 > K1). It is a bull call spread financed by selling an additional OTM call at K3. This adjusts the outlook from bullish (bull call spread) to conservatively bullish or even non-directional with an expectation of low volatility.
|
||||
|
||||
## Construction
|
||||
- Buy 1 call option at strike K1 (near ATM)
|
||||
- Sell 1 call option at strike K2 (OTM)
|
||||
- Sell 1 call option at strike K3 (further OTM, K3 > K2 > K1), same expiry
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ - (S_T - K2)+ - (S_T - K3)+ - H
|
||||
|
||||
- Lower breakeven: S*_down = K1 + H (if H > 0)
|
||||
- Upper breakeven: S*_up = K3 + K2 - K1 - H
|
||||
- Max profit: P_max = K2 - K1 - H (achieved in zone [K2, K3])
|
||||
- Max loss: L_max = unlimited (if S_T >> K3)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Conservatively bullish; expects stock to rise to around K2 but not blow through K3
|
||||
- Low implied volatility environment expected after entry
|
||||
- The additional short call at K3 reduces cost but creates unlimited upside risk
|
||||
|
||||
## Notes
|
||||
This is an income strategy in the sense that selling the K3 call finances the spread. However, unlimited loss exposure arises if the stock surges well above K3. Risk management requires a stop-loss above K3.
|
||||
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A bullish vertical spread buying a near-ATM call at K1 and selling an OTM call at K2 > K1 for a net debit, capping both profit and loss."
|
||||
tags: [options, speculation, bullish, vertical-spread]
|
||||
---
|
||||
|
||||
# Bull Call Spread
|
||||
|
||||
**Section**: 2.6 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The bull call spread is a vertical spread consisting of a long position in a close to ATM call option with strike K1, and a short position in an OTM call option with a higher strike K2. This is a net debit trade. The trader's outlook is bullish: the strategy profits if the stock price rises. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 call option at strike K1 (near ATM), paying debit D
|
||||
- Sell 1 call option at strike K2 (OTM, K2 > K1), same expiry
|
||||
|
||||
Net debit: D = premium paid for K1 call - premium received for K2 call
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ - (S_T - K2)+ - D
|
||||
|
||||
- Breakeven: S* = K1 + D
|
||||
- Max profit: P_max = K2 - K1 - D (achieved when S_T >= K2)
|
||||
- Max loss: L_max = D (if S_T <= K1 at expiry)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Moderately bullish outlook; expects stock to rise toward or above K2 by expiry
|
||||
- Prefer when implied volatility is low (cheaper debit to enter)
|
||||
- Lower cost and lower risk than buying a naked call; upside is capped at K2
|
||||
|
||||
## Notes
|
||||
Both profit and loss are limited. The maximum gain equals the spread width minus the net debit. This strategy is appropriate when the trader has a directional view but wants to reduce the premium outlay compared to a simple long call.
|
||||
@@ -0,0 +1,34 @@
|
||||
---
|
||||
description: "A bearish-adjusted strategy selling a near-ATM put at K1 and buying two lower OTM puts at K2 and K3, arising when a bull put spread is adjusted for a stock that trades lower."
|
||||
tags: [options, hedging, bearish, ladder]
|
||||
---
|
||||
|
||||
# Bull Put Ladder
|
||||
|
||||
**Section**: 2.15 | **Asset Class**: Options | **Type**: Hedging
|
||||
|
||||
## Overview
|
||||
The bull put ladder is a vertical spread consisting of a short put at K1 (near ATM), a long put at K2 (OTM), and a long put at K3 (further OTM, K3 < K2 < K1). A bull put ladder typically arises when a bull put spread goes wrong (the stock trades lower), so the trader buys another OTM put at K3 to adjust the position to bearish.
|
||||
|
||||
## Construction
|
||||
- Sell 1 put option at strike K1 (near ATM)
|
||||
- Buy 1 put option at strike K2 (OTM, K2 < K1)
|
||||
- Buy 1 put option at strike K3 (further OTM, K3 < K2), same expiry
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K3 - S_T)+ + (K2 - S_T)+ - (K1 - S_T)+ - H
|
||||
|
||||
- Upper breakeven: S*_up = K1 + H (if H < 0, net credit)
|
||||
- Lower breakeven: S*_down = K3 + K2 - K1 - H
|
||||
- Max profit: P_max = K3 + K2 - K1 - H (if S_T -> 0)
|
||||
- Max loss: L_max = K1 - K2 + H (in zone [K2, K1])
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bearish adjustment to a bull put spread that has moved against the trader
|
||||
- Profits if the stock continues to fall significantly below K3
|
||||
- Low volatility near K1 environment after adjustment is undesirable
|
||||
|
||||
## Notes
|
||||
The bull put ladder converts a bullish income strategy into a bearish capital gain strategy. The additional long put at K3 limits the maximum loss zone and creates profit on a sharp decline.
|
||||
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A bullish vertical spread selling a higher-strike OTM put at K2 and buying a lower-strike OTM put at K1 for a net credit, profiting if the stock stays above K2."
|
||||
tags: [options, income, bullish, vertical-spread]
|
||||
---
|
||||
|
||||
# Bull Put Spread
|
||||
|
||||
**Section**: 2.7 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The bull put spread is a vertical spread consisting of a long position in an OTM put option with strike K1, and a short position in another OTM put option with a higher strike K2 (K2 > K1). This is a net credit trade. The trader's outlook is bullish. This is an income strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 put option at strike K1 (lower OTM), same expiry
|
||||
- Sell 1 put option at strike K2 (higher OTM, K2 > K1)
|
||||
|
||||
Net credit: C = premium received for K2 put - premium paid for K1 put
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (K2 - S_T)+ + C
|
||||
|
||||
- Breakeven: S* = K2 - C
|
||||
- Max profit: P_max = C (if S_T >= K2 at expiry; both puts expire worthless)
|
||||
- Max loss: L_max = K2 - K1 - C (if S_T <= K1 at expiry)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish to neutral outlook; expects stock to remain above K2 by expiry
|
||||
- Prefer when implied volatility is elevated (larger credit received)
|
||||
- Income generation with defined downside risk
|
||||
|
||||
## Notes
|
||||
The bull put spread is a credit spread. Maximum profit is limited to the net credit received. Maximum loss is the spread width minus the credit. The long put at K1 provides downside protection relative to a naked short put.
|
||||
@@ -0,0 +1,38 @@
|
||||
---
|
||||
description: "A bullish capital-gain strategy (long combo hedged by a long OTM put) buying an OTM put at K1, selling an ATM put at K2, and buying an OTM call at K3, ideally structured at zero cost."
|
||||
tags: [options, speculation, bullish, seagull]
|
||||
---
|
||||
|
||||
# Bullish Long Seagull Spread
|
||||
|
||||
**Section**: 2.57 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The bullish long seagull spread is a long combo (long risk reversal) hedged against the stock price falling by buying an OTM put option. It amounts to a long position in an OTM put at K1, a short position in an ATM put at K2, and a long position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bullish. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 OTM put option at strike K1 (lowest)
|
||||
- Sell 1 ATM put option at strike K2 (middle)
|
||||
- Buy 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
|
||||
- All same expiry; ideally zero net premium (H = 0)
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (K2 - S_T)+ + (S_T - K3)+ - H
|
||||
|
||||
Breakeven depends on sign of H:
|
||||
- S* = K3 + H (if H > 0)
|
||||
- S* = K2 + H (if H < 0)
|
||||
- K2 <= S* <= K3 (if H = 0)
|
||||
|
||||
- Max profit: P_max = unlimited (stock rises above K3; long call gains without bound)
|
||||
- Max loss: L_max = K2 - K1 + H (if stock falls below K1; bear put spread at max loss)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish outlook; expects stock to rise above K3
|
||||
- Ideally zero-cost (H = 0): the short put premium finances the long call
|
||||
- Long put at K1 caps the downside loss from the short put at K2
|
||||
|
||||
## Notes
|
||||
The bullish long seagull is the mirror of the bearish short seagull spread. The long put at K1 hedges the downside risk of the short put at K2, capping maximum loss at K2 - K1 + H. The maximum profit is unlimited on the upside via the long call at K3.
|
||||
@@ -0,0 +1,38 @@
|
||||
---
|
||||
description: "A bullish capital-gain strategy (bull call spread financed by a short OTM put) selling an OTM put at K1, buying an ATM call at K2, and selling an OTM call at K3, ideally structured at zero cost."
|
||||
tags: [options, speculation, bullish, seagull]
|
||||
---
|
||||
|
||||
# Bullish Short Seagull Spread
|
||||
|
||||
**Section**: 2.54 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The bullish short seagull spread is a bull call spread financed with a sale of an OTM put option. It amounts to a short position in an OTM put at K1, a long position in an ATM call at K2, and a short position in an OTM call at K3 (K1 < K2 < K3). Ideally, the trade is structured to have zero cost. The trader's outlook is bullish. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Sell 1 OTM put option at strike K1 (lowest)
|
||||
- Buy 1 ATM call option at strike K2 (middle)
|
||||
- Sell 1 OTM call option at strike K3 (highest, K3 > K2 > K1)
|
||||
- All same expiry; ideally zero net premium (H = 0)
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = -(K1 - S_T)+ + (S_T - K2)+ - (S_T - K3)+ - H
|
||||
|
||||
Breakeven depends on sign of H:
|
||||
- S* = K2 + H (if H > 0)
|
||||
- S* = K1 + H (if H < 0)
|
||||
- K1 <= S* <= K2 (if H = 0)
|
||||
|
||||
- Max profit: P_max = K3 - K2 - H (if S_T >= K3; bull call spread at max)
|
||||
- Max loss: L_max = K1 + H (if stock goes to zero; full loss on short put)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish outlook; expects stock to rise above K2 toward K3
|
||||
- Ideally zero-cost (H = 0): the short put premium finances the bull call spread
|
||||
- Short put at K1 creates downside exposure below K1
|
||||
|
||||
## Notes
|
||||
The seagull spread's name comes from its payoff diagram shape. The upside is capped at K3 - K2 - H. The short put at K1 adds risk if the stock falls sharply, but at zero cost it provides a funded bullish position. Unlike the long combo, there is a defined maximum profit.
|
||||
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A horizontal spread buying a longer-dated ATM call at TTM T' and selling a shorter-dated ATM call at the same strike K with TTM T < T', profiting from time decay when stock stays near K."
|
||||
tags: [options, income, neutral, calendar-spread]
|
||||
---
|
||||
|
||||
# Calendar Call Spread
|
||||
|
||||
**Section**: 2.18 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The calendar call spread (horizontal spread) consists of a long position in a near-ATM call option with TTM T' and a short position in a call option with the same strike K but shorter TTM T < T'. This is a net debit trade. The trader's outlook is neutral to bullish. The best case at expiration of the short call (t = T) is if the stock price is right at the strike (S_T = K), maximizing the remaining value V of the long call.
|
||||
|
||||
## Construction
|
||||
- Buy 1 call option at strike K, TTM T' (longer expiry)
|
||||
- Sell 1 call option at strike K, TTM T < T' (shorter expiry), same strike
|
||||
|
||||
Net debit: D
|
||||
|
||||
## Payoff Profile
|
||||
At t = T (expiry of short call), let V = value of the long call (expiring at T') assuming S_T = K:
|
||||
|
||||
- P_max = V - D (if S_T = K at short expiry)
|
||||
- L_max = D (net debit paid)
|
||||
|
||||
If S_stop-loss <= S_T <= K, the trader can roll by writing another call with strike K and TTM T1 < T'.
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral to mildly bullish; expects stock to remain near K through T
|
||||
- Low volatility environment after entry is ideal (long vega on net position)
|
||||
- Best suited for income generation by repeatedly selling shorter-dated calls against the long call
|
||||
|
||||
## Notes
|
||||
This strategy resembles the covered call strategy in structure. While maintaining the long call, the trader can generate income by periodically selling call options with shorter maturities. The stop-loss price S_stop-loss defines the level below which the entire position is unwound.
|
||||
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A horizontal spread buying a longer-dated ATM put at TTM T' and selling a shorter-dated ATM put at the same strike K with TTM T < T', profiting from time decay when stock stays near K."
|
||||
tags: [options, income, neutral, calendar-spread]
|
||||
---
|
||||
|
||||
# Calendar Put Spread
|
||||
|
||||
**Section**: 2.19 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The calendar put spread (horizontal spread) consists of a long position in a near-ATM put option with TTM T' and a short position in a put option with the same strike K but shorter TTM T < T'. This is a net debit trade. The trader's outlook is neutral to bearish. The best case at expiration of the short put (t = T) is if the stock price is right at the strike (S_T = K), maximizing the remaining value V of the long put.
|
||||
|
||||
## Construction
|
||||
- Buy 1 put option at strike K, TTM T' (longer expiry)
|
||||
- Sell 1 put option at strike K, TTM T < T' (shorter expiry), same strike
|
||||
|
||||
Net debit: D
|
||||
|
||||
## Payoff Profile
|
||||
At t = T (expiry of short put), let V = value of the long put (expiring at T') assuming S_T = K:
|
||||
|
||||
- P_max = V - D (if S_T = K at short expiry)
|
||||
- L_max = D (net debit paid)
|
||||
|
||||
If K <= S_T <= S_stop-loss, the trader can roll by writing another put with strike K and TTM T1 < T'.
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral to mildly bearish; expects stock to remain near K through T
|
||||
- Low volatility environment after entry is ideal
|
||||
- Best suited for income generation by repeatedly selling shorter-dated puts against the long put
|
||||
|
||||
## Notes
|
||||
This strategy resembles the covered put strategy in structure. While maintaining the long put, the trader can generate income by periodically selling put options with shorter maturities. The stop-loss price S_stop-loss defines the level above which the entire position is unwound.
|
||||
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A strongly bullish volatility strategy selling fewer near-ATM calls at K1 and buying more OTM calls at K2, with unlimited profit on a strong rally and limited loss in between."
|
||||
tags: [options, volatility, bullish, backspread]
|
||||
---
|
||||
|
||||
# Call Ratio Backspread
|
||||
|
||||
**Section**: 2.36 | **Asset Class**: Options | **Type**: Volatility
|
||||
|
||||
## Overview
|
||||
The call ratio backspread consists of a short position in N_S close to ATM call options with strike K1, and a long position in N_L OTM call options with strike K2 (K2 > K1), where N_L > N_S. Typically N_L = 2, N_S = 1 or N_L = 3, N_S = 2. The trader's outlook is strongly bullish. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Sell N_S call options at strike K1 (near ATM)
|
||||
- Buy N_L call options at strike K2 (OTM, K2 > K1, N_L > N_S), same expiry
|
||||
|
||||
Net debit or credit H
|
||||
|
||||
## Payoff Profile
|
||||
f_T = N_L × (S_T - K2)+ - N_S × (S_T - K1)+ - H
|
||||
|
||||
- Lower breakeven (if H < 0, net credit): S*_down = K1 - H/N_S
|
||||
- Upper breakeven: S*_up = (N_L × K2 - N_S × K1 + H) / (N_L - N_S)
|
||||
- Max profit: P_max = unlimited (above the upper breakeven)
|
||||
- Max loss: L_max = N_S × (K2 - K1) + H (in the zone near K2 where long calls are OTM but short calls are ITM)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Strongly bullish; expects a significant rally above K2
|
||||
- Ideally entered as a credit (H < 0) so that profit is also made if stock stays below K1
|
||||
- Loss zone is bounded between the two breakevens
|
||||
|
||||
## Notes
|
||||
The difference between call ratio backspread and ratio call spread: here N_L > N_S (more longs than shorts). The maximum loss occurs near K2 at expiry. If H < 0, the position profits if the stock stays well below K1 or surges well above the upper breakeven.
|
||||
33
gateway/knowledge/trading/strategies/options/collar.md
Normal file
33
gateway/knowledge/trading/strategies/options/collar.md
Normal file
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A hedging strategy (fence) buying stock, buying an OTM put at K1, and selling an OTM call at K2 > K1, capping both upside and downside within a defined range."
|
||||
tags: [options, hedging, bullish, collar]
|
||||
---
|
||||
|
||||
# Collar
|
||||
|
||||
**Section**: 2.53 | **Asset Class**: Options | **Type**: Hedging
|
||||
|
||||
## Overview
|
||||
The collar (a.k.a. "fence") is a covered call augmented by a long put option as insurance against the stock price falling. It amounts to buying stock, buying an OTM put at K1, and selling an OTM call at K2 (K2 > K1). The trader's outlook is moderately bullish. This is a capital gain strategy. Note: a short collar is a covered put augmented by a long call option.
|
||||
|
||||
## Construction
|
||||
- Buy 1 share of stock at S0
|
||||
- Buy 1 OTM put option at strike K1 (K1 < S0), paying put premium
|
||||
- Sell 1 OTM call option at strike K2 (K2 > S0 > K1), receiving call premium
|
||||
|
||||
Net debit or credit H (= D if net debit, = -C if net credit)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = S_T - S0 + (K1 - S_T)+ - (S_T - K2)+ - H
|
||||
|
||||
- Breakeven: S* = S0 + H
|
||||
- Max profit: P_max = K2 - S0 - H (if S_T >= K2; upside capped by short call)
|
||||
- Max loss: L_max = S0 - K1 + H (if S_T <= K1; downside protected by long put)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Moderately bullish; willing to cap upside in exchange for downside protection
|
||||
- Ideal when trader has existing long stock position and wants to protect gains
|
||||
- Often structured as zero-cost (H = 0) by choosing K1 and K2 such that premiums offset
|
||||
|
||||
## Notes
|
||||
The collar sacrifices unlimited upside potential (capped at K2) in exchange for limiting downside loss (floored at K1). It is one of the most common hedging strategies for long equity holders. A zero-cost collar is popular for protecting unrealized gains.
|
||||
32
gateway/knowledge/trading/strategies/options/covered-call.md
Normal file
32
gateway/knowledge/trading/strategies/options/covered-call.md
Normal file
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A buy-write strategy combining long stock with a short call at strike K, generating income by capping upside in exchange for premium collected."
|
||||
tags: [options, income, covered, bullish]
|
||||
---
|
||||
|
||||
# Covered Call
|
||||
|
||||
**Section**: 2.2 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The covered call (a.k.a. "buy-write") strategy amounts to buying stock and writing a call option with strike K against the long stock position. The trader's outlook is neutral to bullish. It has the same payoff as writing a naked put and allows the trader to generate income by periodically selling OTM call options while maintaining the long stock position.
|
||||
|
||||
## Construction
|
||||
- Buy 1 share of stock at price S0
|
||||
- Sell 1 call option at strike K, receiving net credit C
|
||||
|
||||
Net position: long stock + short call
|
||||
|
||||
## Payoff Profile
|
||||
f_T = S_T - S_0 - (S_T - K)+ + C = K - S_0 - (K - S_T)+ + C
|
||||
|
||||
- Breakeven: S* = S0 - C
|
||||
- Max profit: P_max = K - S0 + C (achieved when S_T >= K)
|
||||
- Max loss: L_max = S0 - C (if stock goes to zero)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral to mildly bullish outlook on the underlying
|
||||
- Elevated implied volatility makes collected premium more attractive
|
||||
- Suitable for income generation when the trader is comfortable capping upside at K
|
||||
|
||||
## Notes
|
||||
The covered call strategy is equivalent to writing a put option (short/naked put) in terms of payoff. Upside is capped at K; downside risk is the full cost of the stock minus premium received.
|
||||
32
gateway/knowledge/trading/strategies/options/covered-put.md
Normal file
32
gateway/knowledge/trading/strategies/options/covered-put.md
Normal file
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A sell-write strategy combining short stock with a short put at strike K, generating income while maintaining a neutral-to-bearish position."
|
||||
tags: [options, income, covered, bearish]
|
||||
---
|
||||
|
||||
# Covered Put
|
||||
|
||||
**Section**: 2.3 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The covered put (a.k.a. "sell-write") strategy amounts to shorting stock and writing a put option with strike K against the short stock position. The trader's outlook is neutral to bearish. It has the same payoff as writing a naked call and allows the trader to generate income by periodically selling OTM put options while maintaining the short stock position.
|
||||
|
||||
## Construction
|
||||
- Short 1 share of stock at price S0
|
||||
- Sell 1 put option at strike K, receiving net credit C
|
||||
|
||||
Net position: short stock + short put
|
||||
|
||||
## Payoff Profile
|
||||
f_T = S0 - S_T - (K - S_T)+ + C = S0 - K - (S_T - K)+ + C
|
||||
|
||||
- Breakeven: S* = S0 + C
|
||||
- Max profit: P_max = S0 - K + C (achieved when S_T <= K)
|
||||
- Max loss: L_max = unlimited (stock can rise without bound)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral to mildly bearish outlook on the underlying
|
||||
- Elevated implied volatility makes collected premium more attractive
|
||||
- Suitable for income generation when the trader is comfortable with unlimited upside risk
|
||||
|
||||
## Notes
|
||||
The covered put strategy is symmetrical to the covered call strategy. The short stock position carries unlimited loss potential if the stock rises; the collected put premium provides only limited cushion.
|
||||
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A bullish income strategy augmenting a covered call by also writing an ATM put at the same strike K, increasing income at the cost of additional downside exposure."
|
||||
tags: [options, income, bullish, covered, straddle]
|
||||
---
|
||||
|
||||
# Covered Short Straddle
|
||||
|
||||
**Section**: 2.32 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The covered short straddle amounts to augmenting a covered call by writing a put option with the same strike K and TTM as the sold call option, thereby increasing the income. The trader's outlook is bullish. This is a combination of: long stock + short call at K + short put at K.
|
||||
|
||||
## Construction
|
||||
- Buy 1 share of stock at S0
|
||||
- Sell 1 call option at strike K, receiving credit
|
||||
- Sell 1 put option at strike K (same strike and expiry), receiving additional credit
|
||||
|
||||
Net credit: C (total premium from both short options)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = S_T - S0 - (S_T - K)+ - (K - S_T)+ + C
|
||||
|
||||
- Breakeven: S* = (1/2)(S0 + K - C)
|
||||
- Max profit: P_max = K - S0 + C (if S_T = K at expiry)
|
||||
- Max loss: L_max = S0 + K - C (if stock goes to zero; put assignment + stock loss)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish to neutral; expects stock to remain near or above K
|
||||
- High implied volatility; writing both options collects more premium
|
||||
- The additional short put increases income but also increases downside risk significantly
|
||||
|
||||
## Notes
|
||||
The downside risk is substantially higher than a plain covered call because the short put adds to the loss if the stock falls below K. The maximum loss occurs if the stock goes to zero (stock loss + put assignment at K).
|
||||
@@ -0,0 +1,32 @@
|
||||
---
|
||||
description: "A bullish income strategy augmenting a covered call (short call at K) by also writing an OTM put at strike K' < K, increasing income with a wider profit zone than a covered short straddle."
|
||||
tags: [options, income, bullish, covered, strangle]
|
||||
---
|
||||
|
||||
# Covered Short Strangle
|
||||
|
||||
**Section**: 2.33 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The covered short strangle amounts to augmenting a covered call by writing an OTM put option with strike K' (K' < K) and the same TTM as the sold call option (whose strike is K), thereby increasing the income. The trader's outlook is bullish.
|
||||
|
||||
## Construction
|
||||
- Buy 1 share of stock at S0
|
||||
- Sell 1 call option at strike K
|
||||
- Sell 1 OTM put option at strike K' (K' < K, same expiry)
|
||||
|
||||
Net credit: C (total premium from both short options)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = S_T - S0 - (S_T - K)+ - (K' - S_T)+ + C
|
||||
|
||||
- Max profit: P_max = K - S0 + C (if S_T >= K at expiry; call in money, put expires worthless)
|
||||
- Max loss: L_max = S0 + K' - C (if stock goes to zero; put assigned at K', full stock loss)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish to neutral; expects stock to remain above K' and ideally above K
|
||||
- Lower downside risk than covered short straddle (OTM put vs. ATM put)
|
||||
- The OTM put provides a wider profit zone on the downside at the cost of lower premium collected
|
||||
|
||||
## Notes
|
||||
The short OTM put at K' creates downside risk below K', but less immediate than in the covered short straddle (where the put is ATM). The maximum loss is reduced compared to the covered short straddle because K' < K.
|
||||
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A diagonal spread buying a deep ITM call at K1 with TTM T' and selling an OTM call at K2 with shorter TTM T < T', combining directional and time decay benefits."
|
||||
tags: [options, income, bullish, diagonal-spread]
|
||||
---
|
||||
|
||||
# Diagonal Call Spread
|
||||
|
||||
**Section**: 2.20 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The diagonal call spread consists of a long position in a deep ITM call option with strike K1 and TTM T', and a short position in an OTM call option with strike K2 and shorter TTM T < T' (K2 > K1). This is a net debit trade. The trader's outlook is bullish. At t = T let V be the value of the long call (expiring at T') assuming S_T = K2.
|
||||
|
||||
## Construction
|
||||
- Buy 1 deep ITM call option at strike K1, TTM T' (longer expiry)
|
||||
- Sell 1 OTM call option at strike K2, TTM T < T' (shorter expiry, K2 > K1)
|
||||
|
||||
Net debit: D
|
||||
|
||||
## Payoff Profile
|
||||
At t = T (expiry of short call), let V = value of the long call (expiring at T') assuming S_T = K2:
|
||||
|
||||
- P_max = V - D (if S_T = K2 at short expiry)
|
||||
- L_max = D (net debit paid)
|
||||
|
||||
If S_stop-loss <= S_T <= K2, the trader can write another OTM call with TTM T1 < T'.
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bullish outlook; expects stock to rise toward K2 by the short expiry
|
||||
- Low volatility environment after entry is ideal for maximizing time decay income
|
||||
- The deep ITM long call more closely mimics the underlying stock than an ATM call
|
||||
|
||||
## Notes
|
||||
Similar to the calendar call spread but the deep ITM long call (unlike the close to ATM call in the calendar spread) more closely mimics the underlying stock, providing better protection against a sharp rise in the stock price. The trader can generate income by periodically selling OTM call options with shorter maturities.
|
||||
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A diagonal spread buying a deep ITM put at K1 with TTM T' and selling an OTM put at K2 with shorter TTM T < T', combining directional and time decay benefits."
|
||||
tags: [options, income, bearish, diagonal-spread]
|
||||
---
|
||||
|
||||
# Diagonal Put Spread
|
||||
|
||||
**Section**: 2.21 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The diagonal put spread consists of a long position in a deep ITM put option with strike K1 and TTM T', and a short position in an OTM put option with strike K2 and shorter TTM T < T' (K2 < K1). This is a net debit trade. The trader's outlook is bearish. At t = T let V be the value of the long put (expiring at T') assuming S_T = K2.
|
||||
|
||||
## Construction
|
||||
- Buy 1 deep ITM put option at strike K1, TTM T' (longer expiry)
|
||||
- Sell 1 OTM put option at strike K2, TTM T < T' (shorter expiry, K2 < K1)
|
||||
|
||||
Net debit: D
|
||||
|
||||
## Payoff Profile
|
||||
At t = T (expiry of short put), let V = value of the long put (expiring at T') assuming S_T = K2:
|
||||
|
||||
- P_max = V - D (if S_T = K2 at short expiry)
|
||||
- L_max = D (net debit paid)
|
||||
|
||||
If K2 <= S_T <= S_stop-loss, the trader can write another OTM put with TTM T1 < T'.
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Bearish outlook; expects stock to fall toward K2 by the short expiry
|
||||
- Low volatility environment after entry is ideal for maximizing time decay income
|
||||
- The deep ITM long put more closely mimics the underlying short stock than an ATM put
|
||||
|
||||
## Notes
|
||||
Similar to the calendar put spread but the deep ITM long put (unlike the close to ATM put in the calendar spread) more closely mimics the underlying stock, providing better protection against a sharp drop in the stock price. The trader can generate income by periodically selling OTM put options with shorter maturities.
|
||||
34
gateway/knowledge/trading/strategies/options/long-box.md
Normal file
34
gateway/knowledge/trading/strategies/options/long-box.md
Normal file
@@ -0,0 +1,34 @@
|
||||
---
|
||||
description: "An arbitrage/volatility strategy combining a long synthetic forward and a short synthetic forward (or bull call spread and bear put spread) at two strikes, locking in a fixed payoff of K1 - K2."
|
||||
tags: [options, arbitrage, neutral, box]
|
||||
---
|
||||
|
||||
# Long Box
|
||||
|
||||
**Section**: 2.52 | **Asset Class**: Options | **Type**: Arbitrage
|
||||
|
||||
## Overview
|
||||
The long box strategy can be viewed as a combination of a long synthetic forward and a short synthetic forward, or as a combination of a bull call spread and a bear put spread. It consists of: a long ITM put at K1, a short OTM put at K2 (lower), a long ITM call at K2, and a short OTM call at K1. The trader's outlook is neutral. This is a capital gain strategy. We assume K1 >= K2 + D.
|
||||
|
||||
## Construction
|
||||
- Buy 1 ITM put option at strike K1 (higher)
|
||||
- Sell 1 OTM put option at strike K2 (lower, K2 < K1)
|
||||
- Buy 1 ITM call option at strike K2 (same as short put strike)
|
||||
- Sell 1 OTM call option at strike K1 (same as long put strike)
|
||||
- All same expiry
|
||||
|
||||
Net debit: D (assumed K1 >= K2 + D)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (K2 - S_T)+ + (S_T - K2)+ - (S_T - K1)+ - D
|
||||
= K1 - K2 - D (constant, regardless of S_T)
|
||||
|
||||
- P_max = (K1 - K2) - D (fixed payoff at all stock prices)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Used primarily as an arbitrage strategy when the market price of the box (D) is less than the theoretical value (K1 - K2)
|
||||
- Also used as a tax strategy in some jurisdictions (see footnote 31 in the source)
|
||||
- No directional risk: the payoff is fixed regardless of stock price at expiry
|
||||
|
||||
## Notes
|
||||
The long box has a deterministic payoff of K1 - K2 - D at expiry. If D < K1 - K2 (mispricing), this is a risk-free profit. In practice, transaction costs and bid-ask spreads must be considered. Can also be used as a synthetic loan.
|
||||
@@ -0,0 +1,46 @@
|
||||
---
|
||||
description: "A neutral low-cost debit strategy buying an OTM call at K1, selling two ATM calls at K2, and buying an ITM call at K3 with equidistant strikes, profiting if stock stays near K2."
|
||||
tags: [options, income, neutral, butterfly]
|
||||
---
|
||||
|
||||
# Long Call Butterfly
|
||||
|
||||
**Section**: 2.40 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The long call butterfly is a sideways strategy consisting of a long OTM call at K1, a short position in two ATM calls at K2, and a long ITM call at K3. The strikes are equidistant: K2 - K3 = K1 - K2 = kappa. This is a relatively low cost net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 call option at strike K1 (OTM, upper wing)
|
||||
- Sell 2 call options at strike K2 (ATM, body)
|
||||
- Buy 1 call option at strike K3 (ITM, lower wing, K3 < K2 < K1)
|
||||
- All same expiry; K2 - K3 = K1 - K2 = kappa (equidistant)
|
||||
|
||||
Net debit: D
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ + (S_T - K3)+ - 2 × (S_T - K2)+ - D
|
||||
|
||||
- Lower breakeven: S*_down = K3 + D
|
||||
- Upper breakeven: S*_up = K1 - D
|
||||
- Max profit: P_max = kappa - D (achieved at S_T = K2)
|
||||
- Max loss: L_max = D (if S_T <= K3 or S_T >= K1)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral; expects stock to pin near K2 at expiry
|
||||
- Low implied volatility after entry reduces theta bleed on short options
|
||||
- Low cost structure makes it an efficient way to bet on stability
|
||||
|
||||
## Variations
|
||||
|
||||
### 2.40.1 Modified Call Butterfly
|
||||
A variation where the strikes are no longer equidistant; instead K1 - K2 < K2 - K3. This results in a sideways strategy with a bullish bias. We have:
|
||||
|
||||
f_T = (S_T - K1)+ + (S_T - K3)+ - 2 × (S_T - K2)+ - D
|
||||
|
||||
- Breakeven: S* = K3 + D (single breakeven on the lower side)
|
||||
- Max profit: P_max = K2 - K3 - D (at S_T = K2)
|
||||
- Max loss: L_max = D
|
||||
|
||||
## Notes
|
||||
The equidistant butterfly has two breakevens symmetric around K2. The maximum profit is the wing width kappa minus the debit. Low-cost entry makes the risk/reward ratio attractive for neutral views.
|
||||
@@ -0,0 +1,36 @@
|
||||
---
|
||||
description: "A neutral low-cost debit strategy using four calls with equidistant strikes K1 < K2 < K3 < K4, profiting if the stock stays between K2 and K3 at expiry."
|
||||
tags: [options, income, neutral, condor]
|
||||
---
|
||||
|
||||
# Long Call Condor
|
||||
|
||||
**Section**: 2.46 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The long call condor is a sideways strategy consisting of a long ITM call at K1, a short ITM call at K2 (higher), a short OTM call at K3, and a long OTM call at K4 (higher). All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a relatively low cost net debit trade. The trader's outlook is neutral. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 call option at strike K1 (ITM, lowest)
|
||||
- Sell 1 call option at strike K2 (ITM, K2 > K1)
|
||||
- Sell 1 call option at strike K3 (OTM, K3 > K2)
|
||||
- Buy 1 call option at strike K4 (OTM, highest, K4 > K3)
|
||||
- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
|
||||
|
||||
Net debit: D
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ - (S_T - K2)+ - (S_T - K3)+ + (S_T - K4)+ - D
|
||||
|
||||
- Upper breakeven: S*_up = K4 - D
|
||||
- Lower breakeven: S*_down = K1 + D
|
||||
- Max profit: P_max = kappa - D (if K2 <= S_T <= K3 at expiry)
|
||||
- Max loss: L_max = D (if S_T <= K1 or S_T >= K4)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral; expects stock to remain in the middle zone [K2, K3] at expiry
|
||||
- Low implied volatility after entry; wider profit zone than a butterfly
|
||||
- Low cost entry makes it efficient for betting on a range-bound stock
|
||||
|
||||
## Notes
|
||||
The condor is a wider version of the butterfly: it has a flat profit plateau between K2 and K3 instead of a single peak. The tradeoff is that the maximum profit (kappa - D) is the same as the butterfly but requires K2 != K3 (four distinct strikes).
|
||||
@@ -0,0 +1,34 @@
|
||||
---
|
||||
description: "A volatility strategy shorting stock and buying two ATM calls at strike K, replicating a long straddle by replacing the long put with a synthetic put."
|
||||
tags: [options, volatility, neutral, synthetic, straddle]
|
||||
---
|
||||
|
||||
# Long Call Synthetic Straddle
|
||||
|
||||
**Section**: 2.28 | **Asset Class**: Options | **Type**: Volatility
|
||||
|
||||
## Overview
|
||||
The long call synthetic straddle (the same as a long straddle with the put replaced by a synthetic put) amounts to shorting stock and buying two ATM (or nearest ITM) call options with strike K. The trader's outlook is neutral. This is a capital gain strategy. We assume S0 >= K and D > S0 - K.
|
||||
|
||||
## Construction
|
||||
- Short 1 share of stock at S0
|
||||
- Buy 2 ATM call options at strike K, same expiry
|
||||
|
||||
Net debit: D (assumed D > S0 - K)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = S0 - S_T + 2 × (S_T - K)+ - D
|
||||
|
||||
- Upper breakeven: S*_up = 2K - S0 + D
|
||||
- Lower breakeven: S*_down = S0 - D
|
||||
- Max profit: P_max = unlimited (large move in either direction)
|
||||
- Max loss: L_max = D - (S0 - K) (at S_T = K; intrinsic offset reduces loss)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral view; expects a large move in either direction
|
||||
- S0 >= K (stock at or above the call strike)
|
||||
- D > S0 - K prevents arbitrage
|
||||
- Useful when puts are expensive relative to calls (use calls to synthesize the straddle)
|
||||
|
||||
## Notes
|
||||
The short stock position combined with two long calls replicates a straddle by put-call parity. The maximum loss is reduced by the amount S0 - K (intrinsic value of the synthetic put component).
|
||||
36
gateway/knowledge/trading/strategies/options/long-combo.md
Normal file
36
gateway/knowledge/trading/strategies/options/long-combo.md
Normal file
@@ -0,0 +1,36 @@
|
||||
---
|
||||
description: "A bullish capital-gain strategy (long risk reversal) buying an OTM call at K1 and selling an OTM put at K2 < K1, profiting from a strong upward move."
|
||||
tags: [options, speculation, bullish, risk-reversal]
|
||||
---
|
||||
|
||||
# Long Combo
|
||||
|
||||
**Section**: 2.12 | **Asset Class**: Options | **Type**: Speculation
|
||||
|
||||
## Overview
|
||||
The long combo (a.k.a. "long risk reversal") amounts to buying an OTM call option with strike K1 and selling an OTM put option with strike K2, where K1 > K2. The trader's outlook is bullish. This is a capital gain strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 OTM call option at strike K1
|
||||
- Sell 1 OTM put option at strike K2 (K2 < K1), same expiry
|
||||
|
||||
Net debit or credit H (H = D if net debit, H = -C if net credit; K1 > K2)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ - (K2 - S_T)+ - H
|
||||
|
||||
Breakeven depends on sign of H:
|
||||
- S* = K1 + H (if H > 0, net debit)
|
||||
- S* = K2 + H (if H < 0, net credit)
|
||||
- K2 <= S* <= K1 (if H = 0, zero-cost)
|
||||
|
||||
- Max profit: P_max = unlimited
|
||||
- Max loss: L_max = K2 + H
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Strongly bullish outlook
|
||||
- Traders often structure as zero-cost (H = 0) by selecting K1 and K2 such that premiums offset
|
||||
- Profits from a large upward move; loses if stock falls below K2
|
||||
|
||||
## Notes
|
||||
Unlike the long synthetic forward (where K1 = K2 = S0), the long combo uses out-of-the-money strikes on both legs, creating a gap zone [K2, K1] where the payoff is flat (equal to -H). Downside is limited to K2 + H if S_T goes to zero.
|
||||
33
gateway/knowledge/trading/strategies/options/long-guts.md
Normal file
33
gateway/knowledge/trading/strategies/options/long-guts.md
Normal file
@@ -0,0 +1,33 @@
|
||||
---
|
||||
description: "A volatility strategy buying an ITM call at K1 and an ITM put at K2 > K1, profiting from a large move in either direction at higher cost than a straddle."
|
||||
tags: [options, volatility, neutral, guts]
|
||||
---
|
||||
|
||||
# Long Guts
|
||||
|
||||
**Section**: 2.24 | **Asset Class**: Options | **Type**: Volatility
|
||||
|
||||
## Overview
|
||||
The long guts is a volatility strategy consisting of a long position in an ITM call option with strike K1 and a long position in an ITM put option with strike K2 (K2 > K1). This is a net debit trade. Because both options are ITM, this strategy is more costly to establish than a long straddle position. The trader's outlook is neutral. This is a capital gain strategy. We assume D > K2 - K1.
|
||||
|
||||
## Construction
|
||||
- Buy 1 ITM call option at strike K1
|
||||
- Buy 1 ITM put option at strike K2 (K2 > K1), same expiry
|
||||
|
||||
Net debit: D (assumed D > K2 - K1)
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (S_T - K1)+ + (K2 - S_T)+ - D
|
||||
|
||||
- Upper breakeven: S*_up = K1 + D
|
||||
- Lower breakeven: S*_down = K2 - D
|
||||
- Max profit: P_max = unlimited (stock can move far in either direction)
|
||||
- Max loss: L_max = D - (K2 - K1) (if K1 <= S_T <= K2; intrinsic value offsets some debit)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral directional view; expects a very large move but uncertain of direction
|
||||
- More expensive than a straddle but the ITM options provide intrinsic value floor
|
||||
- Max loss is reduced by the intrinsic spread K2 - K1 relative to the full debit
|
||||
|
||||
## Notes
|
||||
The assumption D > K2 - K1 prevents risk-free arbitrage. The intrinsic value of the ITM options (K2 - K1) offsets part of the debit, making the maximum loss smaller than for a straddle with the same debit D. Both options have positive delta at entry.
|
||||
@@ -0,0 +1,36 @@
|
||||
---
|
||||
description: "A neutral income strategy combining a bull put spread and a bear call spread around a central ATM strike K2, collecting net credit when stock stays near K2."
|
||||
tags: [options, income, neutral, butterfly, iron]
|
||||
---
|
||||
|
||||
# Long Iron Butterfly
|
||||
|
||||
**Section**: 2.44 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The "long" iron butterfly is a sideways strategy combining a bull put spread and a bear call spread. It consists of a long OTM put at K1, short ATM put and ATM call at K2, and long OTM call at K3. The strikes are equidistant: K2 - K1 = K3 - K2 = kappa. This is a net credit trade. The trader's outlook is neutral. This is an income strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 OTM put option at strike K1 (lower wing)
|
||||
- Sell 1 ATM put option at strike K2 (body)
|
||||
- Sell 1 ATM call option at strike K2 (body, same strike as put)
|
||||
- Buy 1 OTM call option at strike K3 (upper wing)
|
||||
- All same expiry; K2 - K1 = K3 - K2 = kappa (equidistant)
|
||||
|
||||
Net credit: C
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ - (K2 - S_T)+ - (S_T - K2)+ + (S_T - K3)+ + C
|
||||
|
||||
- Upper breakeven: S*_up = K2 + C
|
||||
- Lower breakeven: S*_down = K2 - C
|
||||
- Max profit: P_max = C (if K1 <= S_T <= K3; both spreads expire worthless)
|
||||
- Max loss: L_max = kappa - C (if S_T <= K1 or S_T >= K3)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral; expects stock to remain close to K2 through expiry
|
||||
- High implied volatility environment makes the collected credit larger
|
||||
- Defined risk on both sides unlike a short straddle
|
||||
|
||||
## Notes
|
||||
The long iron butterfly achieves the same payoff as the short call butterfly or short put butterfly but is constructed using four legs across two spreads. The maximum loss is limited (kappa - C) unlike in a naked short straddle.
|
||||
@@ -0,0 +1,36 @@
|
||||
---
|
||||
description: "A neutral income strategy combining a bull put spread and a bear call spread with four equidistant OTM/ITM strikes, collecting net credit when stock stays between the inner strikes."
|
||||
tags: [options, income, neutral, condor, iron]
|
||||
---
|
||||
|
||||
# Long Iron Condor
|
||||
|
||||
**Section**: 2.50 | **Asset Class**: Options | **Type**: Income
|
||||
|
||||
## Overview
|
||||
The long iron condor is a sideways strategy combining a bull put spread and a bear call spread. It consists of a long OTM put at K1, a short OTM put at K2, a short OTM call at K3, and a long OTM call at K4. All strikes are equidistant: K4 - K3 = K3 - K2 = K2 - K1 = kappa. This is a net credit trade. The trader's outlook is neutral. This is an income strategy.
|
||||
|
||||
## Construction
|
||||
- Buy 1 OTM put option at strike K1 (lowest)
|
||||
- Sell 1 OTM put option at strike K2 (K2 > K1)
|
||||
- Sell 1 OTM call option at strike K3 (K3 > K2)
|
||||
- Buy 1 OTM call option at strike K4 (highest, K4 > K3)
|
||||
- All same expiry; K2 - K1 = K3 - K2 = K4 - K3 = kappa (equidistant)
|
||||
|
||||
Net credit: C
|
||||
|
||||
## Payoff Profile
|
||||
f_T = (K1 - S_T)+ + (S_T - K4)+ - (K2 - S_T)+ - (S_T - K3)+ + C
|
||||
|
||||
- Upper breakeven: S*_up = K3 + C
|
||||
- Lower breakeven: S*_down = K2 - C
|
||||
- Max profit: P_max = C (if K2 <= S_T <= K3 at expiry; all options expire worthless)
|
||||
- Max loss: L_max = kappa - C (if S_T <= K1 or S_T >= K4)
|
||||
|
||||
## Key Conditions / Signals
|
||||
- Neutral; expects stock to remain between K2 and K3 through expiry
|
||||
- High implied volatility makes the collected credit larger
|
||||
- Defined risk on both sides; popular for structured income trading
|
||||
|
||||
## Notes
|
||||
The long iron condor is the most widely traded condor variant. It provides a wider profit zone than the iron butterfly (K2 to K3 instead of a single point) with the same defined-risk structure. Maximum loss is limited to kappa - C on either side.
|
||||
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Reference in New Issue
Block a user