Annualize a quarterly Sharpe of 0.50

Question

A strategy's quarterly returns give a Sharpe ratio of 0.50 per quarter. Assume 4 quarters per year and independent quarterly returns. What is the annualized Sharpe ratio?

Accepted Answer

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 = 4. Why the square root. Over 4 independent quarters the average return grows by a factor of 4 while the volatility grows only by \sqrt{4} = 2, so the Sharpe scales by 2. Plug in the numbers. SR{	ext{annual}} = 0.50 	imes \sqrt{4} = 0.50 	imes 2 = 1.0. Interpretation. A quarterly Sharpe of 0.50 annualizes to exactly 1.0. Because \sqrt{4} is a clean 2, quarterly-to-annual is the easiest case: just double the quarterly Sharpe.…

Annualize a quarterly Sharpe of 0.50

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