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Stop-Outs Under Serial Correlation and 'The Triple Penance Rule'

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

October 1, 2014

Journal of Risk, 2014

At what loss should a portfolio manager be stopped-out? What is an acceptable time under water? We demonstrate that, under standard portfolio theory assumptions, the answer to the latter question is strikingly unequivocal: On average, the recovery spans three times the period involved in accumulating the maximum quantile loss for a given confidence level. We denote this principle the “triple penance rule”.

We provide a theoretical justification to why investment firms typically set less strict stop-out rules to portfolio managers with higher Sharpe ratios, despite the fact that they should be expected to deliver superior performance. We generalize this framework to the case of first-order auto-correlated investment outcomes, and conclude that ignoring the effect of serial correlation leads to a gross underestimation of the downside potential of hedge fund strategies, by as much as 70%. We also estimate that some hedge funds may be firing more than three times the number of skillful portfolio managers, compared to the number that they were willing to accept, as a result of evaluating their performance through traditional metrics, such as the Sharpe ratio.

We believe that our closed-form compact expression for the estimation of downside potential, without having to assume IID cashflows, will open new practical applications in risk management, portfolio optimization and capital allocation. The Python code included confirms the accuracy of our analytical solution.

The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2511599

Number of Pages in PDF File: 35

Keywords: Downside, time under water, stop-out, triple penance, serial correlation, Sharpe ratio

JEL Classification: G0, G1, G2, G15, G24, E44

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Date posted: January 16, 2013 ; Last revised: June 10, 2016

Suggested Citation

Bailey, David H. and Lopez de Prado, Marcos, Stop-Outs Under Serial Correlation and 'The Triple Penance Rule' (October 1, 2014). Journal of Risk, 2014. Available at SSRN: https://ssrn.com/abstract=2201302 or http://dx.doi.org/10.2139/ssrn.2201302

Contact Information

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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References:  19
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