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

35 Pages Posted: 16 Jan 2013 Last revised: 10 Jun 2016

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: October 1, 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:

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

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

Suggested Citation

Bailey, David H. and López de Prado, Marcos and López de Prado, Marcos, Stop-Outs Under Serial Correlation and 'The Triple Penance Rule' (October 1, 2014). Journal of Risk, 2014, 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 )

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Apt 153
Davis, CA 95616
United States


Marcos López de Prado (Contact Author)

Abu Dhabi Investment Authority ( email )

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


Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States


True Positive Technologies ( email )

United States


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