The Sharpe Ratio Efficient Frontier
David H. Bailey
Lawrence Berkeley National Laboratory
Marcos Lopez de Prado
Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; RCC at Harvard University
July 1, 2012
Journal of Risk, Vol. 15, No. 2, Winter 2012/13
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: 46
Keywords: Sharpe ratio, Efficient frontier, IID, Normal distribution, Skewness, Excess kurtosis, Track record
JEL Classification: C02, G11, G14, D53Accepted Paper Series
Date posted: April 24, 2011 ; Last revised: December 28, 2012
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