Sixteen quarters of returns: is the average significant?

Question

A discretionary commodity strategy has 16 quarterly returns spanning four years. The average quarterly return is 2.0% and the standard deviation of the quarterly returns is 5.0%.

Compute the t-statistic for the hypothesis that the true average quarterly return is zero, and decide whether it is significant at the 5% level (t of about 2).

Accepted Answer

The formula. The t-statistic is the per-period Sharpe times the square root of the number of periods: t = \frac{\bar{r}}{s}\sqrt{n}. In words: the average quarterly return relative to its typical quarterly swing, scaled by the square root of the number of quarters. Plug in the numbers. The per-quarter Sharpe is 2.0\%/5.0\% = 0.40. With n = 16, \sqrt{16} = 4, so t = 0.40 	imes 4 = 1.6. Verdict. A t of 1.6 is below 2, so the average return is not statistically significant. Notice the trap: the per-quarter Sharpe of 0.40 is actually respectable, but with only 16 data points there simply are not…

Sixteen quarters of returns: is the average significant?

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