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