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gateway/knowledge/trading/strategies/stocks/two-moving-averages.md

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+---
+description: "Signals long/short entries when a shorter moving average crosses above or below a longer moving average, optionally augmented with stop-loss rules based on price thresholds."
+tags: [stocks, trend-following, moving-average, technical-analysis]
+---
+
+# Two Moving Averages
+
+**Section**: 3.12 | **Asset Class**: Stocks | **Type**: Trend-Following / Technical Analysis
+
+## Overview
+The two-moving-averages strategy replaces the current stock price in the single-MA signal with a shorter moving average. When the shorter MA crosses above the longer MA, a long position is established (bullish signal); when the shorter MA crosses below, a short position is established (bearish signal). This reduces sensitivity to single-day price noise relative to the single-MA strategy.
+
+## Construction / Signal
+Two MAs with lengths T' < T (e.g., T' = 10 days, T = 30 days):
+
+**Basic signal**:
+```
+Signal = { Establish long / liquidate short if MA(T') > MA(T)
+          { Establish short / liquidate long if MA(T') < MA(T)   (322)
+```
+
+**With stop-loss rules** (Delta is a predefined percentage threshold, e.g., Delta = 2%):
+
+Let P_1 be the previous day's closing price:
+```
+Signal = { Establish long position if MA(T') > MA(T)
+          { Liquidate long position if P < (1 - Delta) * P_1
+          { Establish short position if MA(T') < MA(T)
+          { Liquidate short position if P > (1 + Delta) * P_1     (323)
+```
+
+A long position is liquidated if the current price P falls more than Delta below the previous day's price P_1 (even if the shorter MA has not yet crossed the longer MA). Similarly, a short position is liquidated if P rises more than Delta above P_1.
+
+## Entry / Exit Rules
+- **Long entry**: MA(T') crosses above MA(T).
+- **Long exit**: MA(T') crosses below MA(T), or price falls Delta% below prior day's close (stop-loss).
+- **Short entry**: MA(T') crosses below MA(T).
+- **Short exit**: MA(T') crosses above MA(T), or price rises Delta% above prior day's close (stop-loss).
+
+## Key Parameters
+- **Short MA length T'**: Typically 10–50 trading days
+- **Long MA length T**: Typically 30–200 trading days; T' < T required
+- **MA type**: SMA or EMA for both
+- **Stop-loss threshold Delta**: Typically 1–3% (e.g., 2%)
+- **Example**: T' = 10, T = 30; or classic "golden cross" T' = 50, T = 200
+
+## Variations
+- **No stop-loss**: Use basic signal (Eq. 322) only
+- **EMA crossover**: Use exponential MAs instead of simple MAs for both T' and T
+- **Three moving averages**: See Section 3.13 for additional false-signal filtering
+
+## Notes
+- The two-MA crossover is a classic technical analysis signal (e.g., "golden cross": 50-day MA crosses 200-day MA bullishly).
+- Stop-loss rules protect realized profits but can trigger premature exits if the shorter MA has not yet crossed.
+- Like all single-stock technical analysis strategies, this is considered "unscientific" by many academics but is widely used in practice.
+- Applicable on a single-stock or multi-stock basis.
+- Delta must be calibrated via backtesting; too tight a stop causes excessive whipsaw, too loose provides little protection.