Meb Faber 10-month Versus 40-week Versus 200-day SMA

“I would love to see a backtest pitting a 10-month simple moving average (SMA) against a 200-day SMA for SPY. I assume trading costs would go through the roof on the latter, but do performance gains offset the additional costs?” Other readers asked about a 40-week SMA. Using monthly, weekly and daily dividend-adjusted closes for SPDR S&P 500 (SPY) from inception on 1/29/93 through June 2013, along with the contemporaneous daily 13-week Treasury bill (T-bill) yield, we find that:

For this contest, we make the following rules/assumptions:

Buy (sell) SPY at the close when it crosses above (below) its SMA, anticipating crossing signals such that trades occur at the close on the day of the signal (calculations occur just before the close).
The 10-month SMA rule uses (and trades) only monthly closes, the 40-week SMA rule uses (and trades) only weekly closes, and the 200-day SMA rule uses (and trades) daily closes.
Test cumulative/terminal values of $10,000 initial investments made on the first day that the sample enables calculation of all three SMA rules, with dividends reinvested frictionlessly. Use the T-bill yield for the return on cash (ignoring settlement delays). Test sensitivity to one-way trading frictions ranging from 0.0% to 0.5%.  The following chart compares terminal values of initial investments of$10,000 at the close on 11/11/93 for buying and holding SPY and for applying 10-month, 40-week and 200-day SMA rules to SPY with one-way trading frictions ranging from 0.0% to 0.5% over the entire sample period. The 10-month, 40-week and 200-day SMA rules are in the market 73%, 72% and 73% of the time, respectively. The respective number of switches between SPY and cash are 20, 76 and 148.

The 10-month SMA rule beats both 40-week and 200-day SMA rules due not only to lower cumulative trading friction (fewer trades) but also to better timing (winning for zero trading friction). The 10-month SMA rule beats buying and holding SPY for all levels of trading friction. The 40-week and 200-day SMA do not beat buying and holding SPY for any levels of trading friction.

Since this contest involves only about 25 completely independent observations (25 10-month signaling intervals), differences among the SMAs could be due to luck.

Daily data offer insight regarding why the 10-month and 200-day SMA rules perform differently.

The next chart plots the cumulative returns by trading day for \$10,000 initial investments at the close on 11/11/93 for buying and holding SPY, a 10-month SMA rule, a 40-week SMA rule and a 200-day SMA rule with 0.2% one-way trading friction. The 10-month SMA rule mostly leads the other two SMA rules. Notable points are:

The average daily returns for the 10-month, 40-week and 200-day SMA rules are 0.042%, 0.026% and 0.026%, respectively, compared to 0.040% for buying and holding SPY.
The standard deviations of daily returns for the 10-month, 40-week and 200-day SMA rules are 0.82%, 0.78% and 0.79%, respectively, compared to 1.25% for buying and holding SPY.
The average daily return for SPY for the 202 trading days when the 10-month SMA rule is in stocks but the 200-day SMA rule is out of stocks is 0.21%.
The average daily return for SPY for the 158 trading days when the 10-month SMA rule is out of stocks but the 200-day SMA rule is in stocks is -0.10%.


Relative performance of the rules may derive in large part from major stock market turning points, in which case sample size is much smaller than the 25 independent signaling intervals.

Visualization of the returns on days for which rules disagree may be instructive.

SPY-10m-40w-200d-SMA-rules-cumulatives

The following scatter plot shows SPY returns for days when the 10-month and 200-day SMA rules disagree on whether to be in or out of stocks. As calculated above, it appears that the days when the 10-month SMA rule is disagreeably in stocks tend to have higher returns than the days when the 200-day SMA rule is disagreeably in stocks. The number of clusters (about a dozen) rather than the number of days arguably better characterizes disagreement sample size.

As a robustness test, we perform a simpler test on all three SMA rules using the longer sample available for the S&P 500 Index.