An intraday scalper's daily edge: how strong is the evidence?

Question

An intraday scalping desk has 144 daily returns. The average daily return is 0.25% and the standard deviation of the daily returns is 1.0%.

Compute the t-statistic for the hypothesis that the true average daily return is zero, and decide 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}. Read it as: the daily return compared with its typical daily swing, scaled up by the square root of the number of days. Plug in the numbers. The per-day Sharpe is 0.25\%/1.0\% = 0.25. With n = 144, \sqrt{144} = 12, so t = 0.25 	imes 12 = 3.0. Verdict. A t of 3.0 is comfortably above 2, so the average return is statistically significant: the probability of a mean this large arising from pure noise is only about 0.3%. This is what a genuinely strong per-day S…

An intraday scalper's daily edge: how strong is the evidence?

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