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Sample Size Bias and Sharpe's Performance Measure: A Note

Published online by Cambridge University Press:  06 April 2009

Robert E. Miller  and
Adam K. Gehr
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Extract

Several years ago Sharpe suggested a measure for the evaluation of portfolio performance. The measure was conceptually simple, easily calculated, and applicable to an entire investment portfolio, in contrast to the measures of Treynor and Jensen which measure only the undiversifiable risk in a portfolio. Sharpe's measure is still a frequently recommended tool for measuring portfolio performance. The measure is, however, biased. It is the purpose of this note to demonstrate the existence of the bias, indicate its size, and provide a means of correcting it.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 13 , Issue 5 , December 1978 , pp. 943 - 946
Copyright
Copyright © School of Business Administration, University of Washington 1978

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References

1 Sharpe, William F., “Mutual Fund Performance,” Journal of Business, Vol. 39, No. 1, Part II (01 1966), pp. 119–39CrossRefGoogle Scholar.

2 Treynor, Jack L., “How to Rate Management of Investment Funds,” Harvard Business Review, Vol. 43, No. 1 (01–02 1965), pp. 63–76Google Scholar.

3 Jensen, Michael C., Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios,” Journal of Business, Vol. 42, No. 2 (04 1969), pp. 167–247CrossRefGoogle Scholar.

4 See e.g., Sprecker, C. Ronald, Introduction to Investment Management (Houghton Mifflin, 1975), pp. 379–385Google Scholar , or Francis, Jack C., Investments Analysis and Management (McGraw-Hill, 1972), pp. 494–497Google Scholar.