Is There a Best SMA Calculation Interval for Long-term Crossing Signals?
Posted in Technical Trading
June 11, 2009
Is a 10-month simple moving average (SMA) the best SMA for long-term crossing signals (to exploit return momentum by capturing part of long uptrends while avoiding part of long downtrends)? If not, is there some other optimum SMA calculation interval? To check, we compare the average monthly returns and return variabilities from SMA crossing signals generated by SMA calculation intervals ranging from 3 to 48 months, as applied to the Dow Jones Industrial Average (DJIA). Using monthly DJIA closes for January 1930 through May 2009 and monthly yields for 3-month Treasury bills (T-bills) for January 1934 through May 2009, we find that:
To calculate average monthly returns and return variabilities, we assume that:
- When DJIA closes above (below) its SMA at the end of a month, funds are in DJIA (cash) at the close for the next month.
- Funds earn the T-bill yield when in cash.
- We can safely ignore dividends, trading frictions (variable and difficult to estimate over the sample period) and tax implications.
The following chart plots average monthly returns derived from these rules for SMA calculation intervals ranging from 3 to 48 months over the entire sample period and three subperiods. The average monthly return for a buy-and-hold strategy over the entire sample period is 0.59%. The chart shows that:
- Over the entire sample period, although there are small maximums for 10-month and 44-month SMAs, average monthly returns differ little for SMAs based on at least 6 months of historical data.
- During the 1934-1979 subperiod, 9-month and 10-month SMAs generate comparatively high average monthly returns, and average monthly returns tend to decline as the SMA calculation interval lengthens.
- During the complementary subperiod since 1980, the 9-month and 10-month SMAs no longer stand out, and there is a slight tendency for average monthly returns to increase as the SMA calculation interval lengthens.
- During the recent subperiod since 1990, SMAs with calculation intervals less than 18 months appear inferior, with little difference in average monthly returns for intervals of 18 months or longer.
The inconsistencies among these results suggest that there may be no optimum SMA calculation interval for crossing signals, or even a preferred range of calculation intervals. Recent data suggests that the calculation interval should be at least 18 months.
Might return variability be decisive in choosing an SMA calculation interval?
The next chart plots the standard deviations of monthly returns for SMA calculation intervals ranging from 3 to 48 months over the entire sample period and three subperiods. The standard deviation of monthly returns for a buy-and-hold strategy over the entire sample period is 4.42%. The chart shows that:
- Over the entire sample period, the standard deviations of monthly returns mostly increase with the SMA calculation interval.
- During the 1934-1979 subperiod, standard deviations of monthly returns vary little with the SMA calculation interval.
- During more recent subperiods since 1980 and since 1990, standard deviations of monthly returns increase substantially with the SMA calculation interval.
The difference in results before and after 1979 weakens any conclusion, but perhaps shorter SMA calculation intervals are preferable to long ones for suppression of return variability.
Does a combination of reward and risk help pick an SMA calculation interval?
The final chart plots ratios of average monthly returns to standard deviations of monthly returns (reward/risk) for SMA calculation intervals ranging from 3 to 48 months over the entire sample period and three subperiods. Reward/risk based on monthly data for a buy-and-hold strategy over the entire sample period is 0.13. The chart shows that:
- While there are some minor peaks and valleys, there is little variation in reward/risk with SMA calculation interval over the entire sample and during the subsample since 1980.
- During the 1934-1979 subsample, 9-month and 10-month SMAs stand out as generating relatively high ratios of reward to risk.
- During the recent subperiod since 1990, SMAs with calculation intervals in the range 18 months to 24 months appear to be advantageous, but 9-month and 10-month SMAs underperform.
Inconsistencies in these results represent conflicting evidence for picking an SMA calculation interval.
In summary, evidence from simple tests does not support a belief that there is a best SMA calculation interval for generating crossing signals to exploit long-term stock market trends.
