Abstract

http://ssrn.com/abstract=1821643
 
 

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The Sharpe Ratio Efficient Frontier


David H. Bailey


Lawrence Berkeley National Laboratory; University of California, Davis

Marcos Lopez de Prado


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

April 2012

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

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.

Number of Pages in PDF File: 36

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

JEL Classification: C02, G11, G14, D53

Accepted Paper Series


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Date posted: April 24, 2011 ; Last revised: April 23, 2014

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: http://ssrn.com/abstract=1821643 or http://dx.doi.org/10.2139/ssrn.1821643

Contact Information

David H. Bailey
Lawrence Berkeley National Laboratory ( email )
One 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.info
Lawrence Berkeley National Laboratory ( email )
One Cyclotron Road
Berkeley, CA 94720
United States
HOME PAGE: http://www.lbl.gov
RCC at Harvard University ( email )
26 Trowbridge Street
Cambridge, MA 02138
United States
HOME PAGE: http://www.rcc.harvard.edu
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