Drawdown-Based Stop-Outs and the 'Triple Penance' Rule
David H. Bailey
Lawrence Berkeley National Laboratory
Marcos Lopez de Prado
Hess Energy Trading Company; Lawrence Berkeley National Laboratory; RCC at Harvard University
How long does it take for a portfolio manager to recover from a drawdown? We find that, under standard portfolio theory assumptions, the answer is strikingly unequivocal: On average, it takes three times the period elapsed between the high-watermark and the maximum drawdown, a principle we denote 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 drawdown 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.
Number of Pages in PDF File: 40
Keywords: drawdown, time under water, stop-out, triple penance, serial correlation, Sharpe ratio
JEL Classification: G0, G1, G2, G15, G24, E44working papers series
Date posted: January 16, 2013 ; Last revised: November 24, 2013
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