The Statistics of Sharpe Ratios

Posted: 14 Feb 2003  

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

Abstract

The building blocks of the Sharpe ratio--expected returns and volatilities--are unknown quantities that must be estimated statistically and are, therefore, subject to estimation error. This raises the natural question: How accurately are Sharpe ratios measured? To address this question, I derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic theory under several sets of assumptions for the return-generating process--independently and identically distributed returns, stationary returns, and with time aggregation. I show that monthly Sharpe ratios cannot be annualized by multiplying by the square root of 12 except under very special circumstances, and I derive the correct method of conversion in the general case of stationary returns. In an illustrative empirical example of mutual funds and hedge funds, I find that the annual Sharpe ratio for a hedge fund can be overstated by as much as 65 percent because of the presence of serial correlation in monthly returns, and once this serial correlation is properly taken into account, the rankings of hedge funds based on Sharpe ratios can change dramatically.

Keywords: Performance Measurement and Evaluation, Performance Measurement

Suggested Citation

Lo, Andrew W., The Statistics of Sharpe Ratios. Financial Analysts Journal, Vol. 58, No. 4, July/August 2002. Available at SSRN: https://ssrn.com/abstract=377260

Andrew W. Lo (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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National Bureau of Economic Research (NBER) ( email )

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Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

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Cambridge, MA 02142
United States

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