Which moving average rules and measurement (lookback) intervals work best? In the March 2015 version of his paper entitled “Market Timing with Moving Averages: Anatomy and Performance of Trading Rules” Valeriy Zakamulin compares market timing rules based on different kinds of moving averages, including simple momentum. He first compares the mathematics of these rules to identify similarities and differences. He then conducts very long run out-of-sample tests of a few trading rules with distinct weighting schemes to measure their market timing effectiveness. He tries both an expanding window (inception-to-date) and rolling windows to discover optimal lookback intervals. He uses Sharpe ratio as his principal performance metric. He estimates one-way trading friction as a constant 0.25%. Using monthly returns for the S&P Composite Index and for the risk-free asset during January 1860 through December 2009, he finds that:
- The only logical differences among moving average rules derive from the weighting schemes applied according to the age of price changes.
- The optimal lookback interval for each rule varies over time and perhaps depends on market conditions. Using a 20-year rolling window over the entire sample period to determine optimality:
- The average (median) optimal lookback interval for a simple momentum rule is 7 (5) months.
- The average (median) optimal lookback interval for a simple moving average rule is 10 (11) months.
- There is support for the belief that market timing based on moving averages works.
- Over the entire sample period, all market timing rules tested are significantly less risky than a buy-and-hold approach (because they are in cash about a third of the time).
- And, while the mean returns of the timing rules are less than that of buy-and-hold, their Sharpe ratios are generally higher.
- Results suggest that equal weighting of monthly price changes is optimal. Specifically, the simple momentum rule (for which price changes are equally weighted) generates the best out-of-sample performance.
- Rolling windows mostly (four out of six rules) outperform an expanding window for determining the optimal lookback interval.
- However, the probability of beating buy-and-hold (higher Sharpe ratio) depends on investment horizon. Over horizons of five or ten years, market timing rules are about equally likely to outperform and underperform (but average outperformance is greater than the average underperformance). In general, lengthening the investment horizon increases the odds that market timing rules beat the market.
In summary, evidence from long run tests of moving average timing rules on the U.S. stock market are mixed, with outperformance more likely for long investment horizons, equal weighting of past returns and a dynamic lookback interval.
Cautions regarding findings include:
- The Sharpe ratio may not be the decisive performance metric for some investors.
- The assumed level of trading friction (0.25% one-way) may be very low for large parts of the long sample period (see “Trading Frictions Over the Long Run”), to the advantage of market timing rules.
- Testing many different rules and optimization methods on the same set of data introduces data snooping bias, such that results for the best rule likely overstate its expected performance.
- Findings are for the U.S. equity market and may not apply to other equity markets and other asset classes.
Frequently Asked Questions
What is a moving average market timing rule?
A moving average market timing rule is a trading strategy that holds stocks or moves to cash based on a signal from average past prices over a chosen lookback interval. Variants such as simple momentum and the simple moving average differ only in how they weight price changes by age. In the article's tests on the S&P Composite Index (January 1860–December 2009), the strategies were in cash about a third of the time.
Do moving average timing rules beat buy-and-hold?
Moving average timing rules generally produced higher Sharpe ratios than buy-and-hold on the S&P Composite Index from January 1860 to December 2009, even though their mean returns were lower. Evidence is mixed overall: over 5- or 10-year horizons the rules were about equally likely to outperform or underperform, though average outperformance exceeded average underperformance. Longer investment horizons raised the odds of beating buy-and-hold.
How are the best lookback periods for moving average trading rules determined?
The optimal lookback interval for moving average rules was determined out-of-sample using either an expanding (inception-to-date) window or rolling windows, with the Sharpe ratio as the main performance metric. Using a 20-year rolling window, the average (median) optimal lookback was 7 (5) months for simple momentum and 10 (11) months for a simple moving average. Rolling windows beat the expanding window for four of six rules, and one-way trading friction was assumed at 0.25%.
Is simple momentum better than a simple moving average for market timing?
Simple momentum, which weights monthly price changes equally, generated the best out-of-sample performance among the moving average timing rules tested on the S&P Composite Index (1860–2009). The article finds the only logical differences among such rules are the weights applied to price changes by age, and results suggest equal weighting is optimal. Simple momentum's optimal lookback averaged 7 months versus 10 months for the simple moving average.
What are the limitations of moving average market timing backtests?
Moving average timing backtests have several caveats: the Sharpe ratio may not be the decisive metric for some investors, and the assumed 0.25% one-way trading friction is probably too low for much of the long sample, which favors timing rules. Testing many rules and optimization methods on the same data introduces data snooping bias, so the best rule's results likely overstate expected performance. Findings are for the U.S. equity market (1860–2009) and may not apply to other markets or asset classes.