Is this 3-year monthly track record's average return real?

Question

A market-neutral equity book has 36 monthly returns. The average monthly return is 0.9% and the standard deviation of the monthly returns is 3.0%.

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

Accepted Answer

What the t-statistic measures. We want to know whether the positive average return is a real edge or just luck. The t-statistic is the average return divided by its own standard error, that is, how many standard errors the sample mean sits above zero: t = \frac{\bar{r}}{s/\sqrt{n}} = \frac{\bar{r}}{s}\sqrt{n}. In words: take the mean return, divide by the return's typical wiggle, and scale up by the square root of the number of observations. The ratio \bar{r}/s is just the per-period Sharpe ratio, so a clean way to remember this is: t-statistic = per-period Sharpe times the square root of the…

Is this 3-year monthly track record's average return real?

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