Does a futures trend model's daily return clear the bar?

Question

A trend-following futures model has 225 daily returns. The average daily return is 0.10% and the standard deviation of the daily returns is 0.75%.

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

Accepted Answer

The formula. The t-statistic equals the per-period Sharpe times the square root of the number of periods: t = \frac{\bar{r}}{s}\sqrt{n}. The idea: measure the daily return against its typical daily swing, then scale up by the square root of how many days you observed. Plug in the numbers. The per-day Sharpe is 0.10\%/0.75\% = 0.1333. With n = 225, \sqrt{225} = 15, so t = 0.1333 	imes 15 = 2.0. Verdict. A t of exactly 2.0 sits right on the rough cutoff, and just above the precise two-sided 5% value of 1.96, so the edge is borderline significant. "Borderline" is the honest word: a slightly dif…

Does a futures trend model's daily return clear the bar?

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