Time Aggregation of Sharpe Ratio A Better Extrapolation Rule

Vol. 16 No.4, 2018
Ziemowit Bednarek, Pratish Patel and Cyrus Ramezani

The √T rule extrapolates a one-period Sharpe Ratio to T periods. But the rule ignores compounding. By considering compounding, Levy (1972) and others show that the Sharpe Ratio changes non-monotonically with horizon. We also theoretically and empirically show that the Sharpe Ratio term structure is hump-shaped and not upward sloping as the √T rule suggests. We offer a better extrapolation rule. Using bootstrapped Generalized method of Moments (GMM), we provide robust Sharpe Ratio estimates of several popular test assets. The empirical results reject the √T rule over a long horizon.

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