The Sharpe Ratio Efficient Frontier

Journal of Risk, Vol. 15, No. 2, Winter 2012/13

36 Pages Posted: 24 Apr 2011 Last revised: 23 Apr 2014

David H. Bailey

Lawrence Berkeley National Laboratory; University of California, Davis

Marcos Lopez de Prado

Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; Harvard University - RCC

Date Written: April 2012

Abstract

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is below a certain threshold with a given confidence level. Second, it models the trade-off between track record length and undesirable statistical features (e.g., negative skewness with positive excess kurtosis). Third, it explains why track records with those undesirable traits would benefit from reporting performance with the highest sampling frequency such that the IID assumption is not violated. Fourth, it permits the computation of what we call the Sharpe ratio Efficient Frontier (SEF), which lets us optimize a portfolio under non-Normal, leveraged returns while incorporating the uncertainty derived from track record length. Results can be validated using the Python code in the Appendix.

Keywords: Sharpe ratio, Efficient frontier, IID, Normal distribution, Skewness, Excess kurtosis, Track record

JEL Classification: C02, G11, G14, D53

Suggested Citation

Bailey, David H. and Lopez de Prado, Marcos, The Sharpe Ratio Efficient Frontier (April 2012). Journal of Risk, Vol. 15, No. 2, Winter 2012/13. Available at SSRN: https://ssrn.com/abstract=1821643 or http://dx.doi.org/10.2139/ssrn.1821643

David H. Bailey

Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

HOME PAGE: http://www.davidhbailey.com

University of California, Davis ( email )

One Shields Avenue
Davis, CA 95616
United States

HOME PAGE: http://www.davidhbailey.com

Marcos Lopez de Prado (Contact Author)

Guggenheim Partners, LLC ( email )

330 Madison Avenue
New York, NY 10017
United States

HOME PAGE: http://www.QuantResearch.org

Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

HOME PAGE: http://www.lbl.gov

Harvard University - RCC ( email )

26 Trowbridge Street
Cambridge, MA 02138
United States

HOME PAGE: http://www.rcc.harvard.edu

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