Stop-outs under serial correlation and the triple penance rule

David H. Bailey and Marcos López de Prado

Abstract

ABSTRACT

At what loss should a portfolio manager (PM) 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 as to why investment firms typically set less strict stop-out rules for PMs with higher Sharpe ratios, despite the fact that they should be expected to deliver a superior performance. We generalize this framework to the case of first-order
autocorrelated investment outcomes, and we 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 as many skillful PMs as they are 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 independent and identically distributed cashflows, will open new practical applications in risk management, portfolio optimization and capital allocation. The Python code included in the online appendix confirms the accuracy of our analytical solution.