Tim Olson
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59 lines
3.3 KiB
Markdown
59 lines
3.3 KiB
Markdown
---
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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."
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tags: [indexes, volatility-targeting, risk-management, rebalancing, allocation]
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---
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# Index Volatility Targeting with Risk-Free Asset
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**Section**: 6.5 | **Asset Class**: Indexes | **Type**: Risk Management / Volatility Targeting
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## Overview
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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_*.
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## Construction / Mechanics
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**Risky asset weight** (allocation to the index):
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```
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w = σ_* / σ
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```
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where:
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- σ_*: target volatility (constant, set by the investor)
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- σ: current estimated volatility of the index (e.g., realized or implied)
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**Risk-free asset weight**: 1 - w
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If a maximum leverage constraint L is imposed: w is capped at L.
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**Rebalancing to avoid overtrading**: instead of rebalancing on a fixed schedule (weekly, monthly), rebalance only when the allocation has drifted significantly:
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```
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Rebalance only if |Δw| / w > κ
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```
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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.
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**Net portfolio**: a fraction w in the index + a fraction (1-w) in T-bills.
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## Payoff / Return Profile
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- Targets a constant realized volatility close to σ_*.
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- When market volatility rises, the index allocation is reduced, limiting drawdowns.
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- When market volatility is low, the index allocation increases (potentially with leverage), improving returns.
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- The strategy does not make a directional bet on the market; it is a risk management overlay.
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## Key Parameters / Signals
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- σ_*: volatility target (investor-specified, e.g., 10% annualized)
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- σ: current volatility estimate (realized vol from recent returns, or implied vol from options)
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- w = σ_*/σ: dynamic allocation weight
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- κ: rebalancing threshold (avoids unnecessary turnover)
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- Maximum leverage L: caps w if set
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## Variations
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- Apply to other asset classes (bonds, commodities) using the same framework.
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- Combine volatility targeting with a trend-following signal: only hold the index when its trend is positive, otherwise hold the risk-free asset.
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- Use implied volatility (e.g., VIX) as σ for a forward-looking allocation rather than backward-looking realized vol.
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## Notes
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- 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).
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- The strategy does not protect against sudden gap moves (e.g., flash crashes) where volatility spikes before rebalancing can occur.
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- Transaction costs from rebalancing must be weighed against the volatility-stabilization benefit; the threshold κ controls this trade-off.
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- The choice of σ (historical lookback window vs. implied vol) significantly affects performance and responsiveness.
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