The Sharpe Ratio Efficient Frontier

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

36 Pages Posted: 24 Apr 2011 Last revised: 7 May 2020

See all articles by David H. Bailey

David H. Bailey

Lawrence Berkeley National Laboratory; University of California, Davis

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; Abu Dhabi Investment Authority; True Positive Technologies

Date Written: April 1, 2012


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 López de Prado, Marcos and López de Prado, Marcos, The Sharpe Ratio Efficient Frontier (April 1, 2012). Journal of Risk, Vol. 15, No. 2, Winter 2012/13, Available at SSRN: or

David H. Bailey

Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States


University of California, Davis ( email )

One Shields Avenue
Apt 153
Davis, CA 95616
United States


Marcos López de Prado (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States


Abu Dhabi Investment Authority ( email )

211 Corniche Road
Abu Dhabi, Abu Dhabi PO Box3600
United Arab Emirates


True Positive Technologies ( email )

United States


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