Turn a daily Sharpe of 0.10 into an annual Sharpe

Question

A strategy's daily returns give a Sharpe ratio of 0.10 per day. Assume 252 trading days per year and independent daily returns. What is the annualized Sharpe ratio?

Accepted Answer

The scaling rule. To annualize a Sharpe ratio, multiply the per-period Sharpe by the square root of the number of periods in a year: SR{	ext{annual}} = SR{	ext{period}} 	imes \sqrt{k}, where k is the number of periods per year. Here k = 252 trading days. Why the square root. Over k independent days, the average return simply adds up, growing by a factor of k, but the volatility grows only by \sqrt{k} (independent wiggles partly cancel). The Sharpe is return divided by volatility, so it scales by k/\sqrt{k} = \sqrt{k}. Plug in the numbers. SR{	ext{annual}} = 0.10 	imes \sqrt{252} = 0.10 \…

Turn a daily Sharpe of 0.10 into an annual Sharpe

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