A Sharper Ratio: A General Measure for Correctly Ranking Non-Normal Investment Risks

39 Pages Posted: 5 Oct 2013

See all articles by Kent A. Smetters

Kent A. Smetters

University of Pennsylvania - Business & Public Policy Department; National Bureau of Economic Research (NBER)

Xingtan Zhang

University of Pennsylvania - The Wharton School

Date Written: October 2013

Abstract

While the Sharpe ratio is still the dominant measure for ranking risky assets, a substantial effort has been made over the past three decades to find a way to account for non-Normally distributed risks. This paper derives a generalized ranking measure which, under a regularity condition, correctly ranks risks relative to the original investor problem for a broad probability space. Moreover, like the Sharpe ratio, the generalized measure maintains wealth separation for the broad HARA utility class. Besides being effective in the presence of "fat tails," the generalized measure is also a foundation for multi-asset class portfolio optimization due to its ability to pairwise rank two risks following two different probability distributions. This paper also explores the theoretical foundations of risk ranking, including proving a key impossibility theorem: any ranking measure that is valid for non-Normal distributions cannot generically be free from investor preferences. Finally, this paper shows that the generalized ratio provides substantially more ranking power than simpler approximation measures that have sometimes been used in the past to account for non-Normal higher moments, even if those approximations are extended to include an infinite number of higher moments.

Suggested Citation

Smetters, Kent and Zhang, Xingtan, A Sharper Ratio: A General Measure for Correctly Ranking Non-Normal Investment Risks (October 2013). NBER Working Paper No. w19500, Available at SSRN: https://ssrn.com/abstract=2336365

Kent Smetters (Contact Author)

University of Pennsylvania - Business & Public Policy Department ( email )

3641 Locust Walk
Philadelphia, PA 19104-6372
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Xingtan Zhang

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

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