---
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.