# 10-month Versus 40-week Versus 200-day SMA

July 11, 2013 • **Posted in** Technical Trading

A reader asked: “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.

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.

The final chart compares terminal values of initial investments of $10,000 for rules applying 10-month, 40-week and 200-day SMA rules to the S&P 500 Index for one-way trading frictions ranging from 0.0% to 0.25% and no return on cash over the period November 1950 through June 2013. The rules based on the 10-month, 40-week and 200-day SMAs are in the market 69%, 68% and 69% of the time, respectively. This contest involves about 76 completely independent signaling intervals.

Only the 200-day SMA rule beats buy-and-hold for low trading friction (less than 0.02%).

The trade-off between loss of dividends and return on cash while out of the market may be decisive for SMA rules versus buy-and-hold.

The S&P 500 Index is not directly tradable, and replicating it in the older part of the sample may have been costly. The right-hand side of the chart may be realistic (or even optimistic) for the early part of the sample period.

In summary, *evidence from simple tests indicates that a 10-month SMA outperforms 40-week and 200-day SMAs under reasonably realistic trading assumptions for the broad value-weighted U.S. equity market over the past 20 years, but the source of outperformance may be luck.*

Cautions regarding findings include:

- Lagging trades after signals may materially affect results.
- Actual trading frictions would vary with account size. In general, the smaller the account, the bigger the advantage of the 10-month SMA rule over the 40-week and 200-day SMA rules for trading SPY.
- As described in “Trading Frictions Over the Long Run”, trading friction varies over time. More precise modeling of trading friction over time may materially affect results.
- Realistic accounting for dividend reinvestment timing and costs may materially affect results.
- Per “Is There a Best SMA Calculation Interval for Long-term Crossing Signals?”, the selection of a 10-month SMA may be an artifact of pre-1980 data. Other month-based intervals may work as well.
- Per “Pure Versus Buffered SMA Crossing Signals”, buffering 200-day SMA signals to reduce trading costs may not help much.

Several readers suggested looking at: long-run combination SMAs; optimized confirmation days/weeks after 200-day/40-week SMA signals; and, exponential moving averages instead of SMAs. Testing of additional and more complex rules elevates data snooping bias, both direct and inherited from prior studies. Also, as noted above, credible modeling of variations in trading friction over the long run is problematic. Uncertainties argue for priority on seeking incremental edges elsewhere.

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