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

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+---
+description: "Uses three moving averages of ascending length to filter false signals, requiring full alignment of all three MAs before establishing or liquidating long or short positions."
+tags: [stocks, trend-following, moving-average, technical-analysis]
+---
+
+# Three Moving Averages
+
+**Section**: 3.13 | **Asset Class**: Stocks | **Type**: Trend-Following / Technical Analysis
+
+## Overview
+Adding a third moving average helps filter false signals that arise in the two-MA strategy. A long position is established only when all three MAs are in descending order by length (shortest on top), confirming a strong uptrend. Liquidation occurs as soon as the shortest MA drops below the middle MA — an earlier warning than waiting for a full cross of the two outer MAs.
+
+## Construction / Signal
+Three MAs with lengths T_1 < T_2 < T_3 (e.g., T_1 = 3, T_2 = 10, T_3 = 21):
+
+```
+Signal = { Establish long position if MA(T_1) > MA(T_2) > MA(T_3)
+          { Liquidate long position if MA(T_1) <= MA(T_2)
+          { Establish short position if MA(T_1) < MA(T_2) < MA(T_3)
+          { Liquidate short position if MA(T_1) >= MA(T_2)             (324)
+```
+
+- **Long trigger**: All three MAs are in bullish alignment (T_1 > T_2 > T_3 in value).
+- **Long liquidation**: Early warning — the short MA drops back below the middle MA (even if still above the long MA).
+- **Short trigger**: All three MAs are in bearish alignment (T_1 < T_2 < T_3 in value).
+- **Short liquidation**: Early warning — the short MA rises back above the middle MA.
+
+## Entry / Exit Rules
+- **Long entry**: MA(T_1) > MA(T_2) > MA(T_3)
+- **Long exit**: MA(T_1) <= MA(T_2)
+- **Short entry**: MA(T_1) < MA(T_2) < MA(T_3)
+- **Short exit**: MA(T_1) >= MA(T_2)
+
+## Key Parameters
+- **Short MA length T_1**: Typically 3–10 trading days
+- **Middle MA length T_2**: Typically 10–21 trading days
+- **Long MA length T_3**: Typically 21–50 trading days; must have T_1 < T_2 < T_3
+- **Example**: T_1 = 3, T_2 = 10, T_3 = 21
+- **MA type**: SMA or EMA
+
+## Variations
+- **Different exit rule**: Liquidate when T_1 falls below T_3 (slower exit) instead of T_2
+- **Combined with stop-loss**: Add price-based stop-loss as in the two-MA strategy (Section 3.12)
+- **Four or more MAs**: Further extension possible but increases complexity and reduces signal frequency
+
+## Notes
+- The three-MA strategy generates fewer signals than the two-MA strategy, filtering out some false crossovers.
+- The early liquidation rule (based on T_1 vs T_2 only) provides faster exit than waiting for full reversal.
+- Like all MA-based strategies, considered "unscientific" by academics but widely used by practitioners.
+- Best applied in trending markets; whipsaw losses occur in range-bound (mean-reverting) markets.
+- Applicable single-stock or across a universe; parameter selection should be done via backtesting.