A daily Sharpe of 0.05: what is it annualized?

Question

A strategy's daily returns give a Sharpe ratio of 0.05 per day. Assume 252 trading days per year and independent daily returns. What is the annualized Sharpe ratio?

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The scaling rule. Multiply the per-period Sharpe by the square root of the number of periods per year: SR{	ext{annual}} = SR{	ext{period}} 	imes \sqrt{k}, \qquad k = 252. Why the square root. Average return adds up across days (a factor of k), volatility grows only by \sqrt{k}, and the ratio scales by \sqrt{k}. Plug in the numbers. SR{	ext{annual}} = 0.05 	imes \sqrt{252} = 0.05 	imes 15.87 \approx 0.79. Interpretation. A daily Sharpe of 0.05 annualizes to about 0.79, a middling figure. Compare with a daily Sharpe of 0.10, which annualizes to about 1.59: doubling the per-day Sharpe doub…

A daily Sharpe of 0.05: what is it annualized?

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