Build a confidence interval for a mean return

Question

You have 64 days of a strategy's returns: sample mean 0.10\% per day, sample standard deviation 1.5\% per day. Build a 95\% confidence interval for the true mean daily return. Is the mean significantly positive, and which quantity, standard deviation or standard error, belongs in the interval?

Accepted Answer

The confidence interval for the mean is built from the standard error, the precision of the average, not the standard deviation, the spread of individual days: \operatorname{SE}(\bar X) = \frac{\sigma}{\sqrt{n}} = \frac{1.5\%}{\sqrt{64}} = \frac{1.5\%}{8} = 0.1875\%. The 95\% interval is \bar X \pm 1.96 	imes \operatorname{SE}: 0.10\% \pm 1.96 	imes 0.1875\% = 0.10\% \pm 0.3675\% = (-0.27\%,\ 0.47\%). Is the mean significantly positive? No. The interval comfortably includes 0, so at the 95\% level you cannot reject a true mean of zero; the 0.10\% average is well within one noise band of not…

Build a confidence interval for a mean return

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