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:
- 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.
- 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.
- 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.
- 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”
Frequently Asked Questions
What is trend following and how do momentum and moving average rules differ?
Trend following is a trading approach that buys when an asset's price trend is up and sells when it is down. Intrinsic (time series) momentum buys when the latest closing price exceeds the closing price at the start of a lookback interval, while simple, linear, and exponential moving average rules buy when the latest close exceeds an equally, linearly, or exponentially weighted average close over the interval.
Are moving averages better than momentum for trend following?
Moving average rules are theoretically more reliable than the intrinsic momentum rule for trend following, according to Zakamulin and Giner's November 2018 paper. Both behave very similarly, especially in strong trends, but moving averages are more robust to perturbations of the trend model and to changes in the lookback interval. This conclusion comes from a theoretical analysis, not an empirical test.
How do you test trend following rules theoretically using an autoregressive return model?
Zakamulin and Giner converted four price-based trend rules (intrinsic momentum, simple, linear, and exponential moving averages) into return-based versions. They modeled the trend as an autoregressive return process and examined how each trading rule interacts with that model. They then assessed robustness by perturbing the trend model and changing the lookback interval.
Is a moving average less sensitive to model uncertainty than a momentum rule?
Yes, in the theoretical analysis, moving average rules are less sensitive to model uncertainty than a comparable momentum rule because they are more robust to trend model perturbations and lookback interval changes. The difference is smaller for strong price trends, where the two rule types behave very similarly. Weaker trends show more divergence between them.
What are the limitations of theoretical comparisons of momentum and moving average trend rules?
The theoretical results are gross, not net, so they ignore trade execution costs and differences in trading frequency across rules. The study also assumes no lag between signal and execution, so conclusions depend on a market timer slightly anticipating signals, which may be problematic for relatively complicated strategies and older data. Empirical tests that account for trading frequencies and frictions produce somewhat different results.