Trend Following: Momentum or Moving Average?

Are moving averages or intrinsic (time series) momentum theoretically better for following trends in asset prices? In their November 2018 paper entitled “Trend Following with Momentum Versus Moving Average: A Tale of Differences”, Valeriy Zakamulin and Javier Giner compare from a theoretical perspective effectiveness of four popular trend following rules:

1. Intrinsic Momentum – buy (sell) when the closing price at the end of a specified lookback interval is greater (less) than the closing price at the beginning of the lookback interval.
2. Simple Moving Average – buy (sell) when the closing price at the end of a specified lookback interval is greater (less) than the equally weighted average closing price during the lookback interval.
3. Linear Moving Average – buy (sell) when the closing price at the end of a specified lookback interval is greater (less) than the linearly weighted (weights linearly increasing to the most recent) average closing price during the lookback interval.
4. Exponential Moving Average – buy (sell) when the closing price at the end of a specified lookback interval is greater (less) than the exponentially weighted (weights exponentially increasing to the most recent) average closing price during the lookback interval.

They transform these price rules into return-based versions and create a trend model as an autoregressive return process. They then explore interactions of the trading rules with the trend model. Based on this theoretical approach, they conclude that:

• Momentum and moving average rules behave very similarly, more so for strong than weak price trends.
• However, moving average rules are more robust than the momentum rule with respect to perturbing the trend model and changing the lookback interval. Moving average rules are therefore less sensitive to model uncertainty in real world use.

In summary, theory suggests that moving average rules are more reliable trend following metrics than is a comparable momentum rule.

Cautions regarding conclusions include:

• Theoretical analyses summarized above are gross, not net. They do not account for costs of executing signals and do not address differences in trading frequencies across trend following rules. See “Intrinsic Momentum or SMA for Avoiding Crashes?” and “Optimal Intrinsic Momentum and SMA Intervals Across Asset Classes” for empirical contests between momentum and simple moving averages that consider trading frequencies and account for associated frictions (results are somewhat different).
• The study assumes no lag between signal and execution, so conclusions depend on a market timer slightly anticipating signals. For relatively complicated strategies, and for older data, this assumption may be problematic.

See also:

• “Long-run Moving Average Horse Race for Timing the U.S. Stock Market”
• “Net Performance of SMA and Intrinsic Momentum Timing Strategies”
• “Intrinsic Momentum Versus SMAs for Size Portfolios”