SMAs for Measurement Intervals of Longer Than a Month

Referring to “10-month Versus 40-week Versus 200-day SMA”, a reader inquired whether using measurement intervals of longer than a month to calculate simple moving averages (SMA) would generate fewer trades than monthly intervals and therefore lower trading frictions and better performance. To check we compare the performance of moving averages based on 12 months (12M), six bi-months (6Bi-M) and four quarters (4Q). Using monthly dividend-adjusted closes for SPDR S&P 500 (SPY) from inception in January 1993 through January 2012, along with the contemporaneous monthly 3-month Treasury bill (T-bill) yield (19 years), 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).
• Test cumulative/terminal values of $100,000 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 (switching between SPY and T-bills) frictions ranging from 0.0% to 2.0%, with focus on a baseline 0.2%.

The following chart compares cumulative values of $100,000 initial investments in the three SMA rules and buy-and-hold SPY over the available sample period starting in January 1994. The interval for calculation of cumulative values is six months, allowing synchronization across SMA rules. The 4Q SMA is the winner, but the 6Bi-M SMA does not beat the 12M SMA. All three SMAs easily beat buy-and-hold SPY.

The 12M, 6Bi-M and 4Q SMA rules are in SPY 72%, 74% and 75% of the time, respectively.

For a different perspective, we look at six-month return statistics.

The next chart summarizes average six-month net return statistics for the three SMA rules and buy-and-hold SPY over the available sample period. The three SMA rules all increase average return and substantially reduce volatility compared to buy-and-hold. The 4Q SMA generates the best return enhancement. However, as noted above, there is no progression in improvement across 12M to 6Bi-M to 4Q SMAs.

What happens when we vary the switching friction?

The next chart shows how terminal values of the three SMA rules vary with level of switching friction. The numbers of switches between SPY and T-bills are 15, 9 and 7, respectively, for the 12M, 6Bi-M and 4Q SMA rules over the available sample period. The 4Q SMA rule wins at all levels of friction. Because these numbers are small, trading frictions have limited affect on comparative performance.

Are results robust to starting point?

As a robustness test, we delay the start of the sample by one month and by two months, generating different sets of data for the 4Q SMA rule.

The final two charts compare cumulative values of $100,000 initial investments in the three SMA rules and buy-and-hold SPY over the available sample period starting in February 1994 (upper chart) and March 1994 (lower chart). The interval for calculation of cumulative values is again six months, allowing synchronization across SMA rules.

For both alternatives, while the SMA rules mostly beat buy-and-hold, the 4Q SMA rule performs poorly compared to the other two rules. Apparently, the initial case above is lucky for the 4Q SMA rule.

The 4Q SMA rule is in SPY 69% (68%) of the time for the February (March) 1994 starting point, compared to 75% above.

In summary, evidence from simple tests does not support belief that an SMA based on quarterly measurements outperforms rules based on monthly or bi-monthly measurements for the broad value-weighted U.S. equity market over the past 19 years. The decisive factor in this contest is luck, not trading friction.

Cautions regarding findings include:

• The sample period is very short in terms of number of bear markets, which drives SMA performance. Instability of 4Q SMA rule performance emphasizes this caution.
• See the discussion at the end of “10-month Versus 40-week Versus 200-day SMA”.

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