Drawdown-Based Stop-Outs and the 'Triple Penance' Rule

Abstract:     
We develop a framework for informing the decision of stopping a portfolio manager or investment strategy once it has reached the drawdown or time under water limit associated with a certain confidence level. Under standard portfolio theory assumptions, we show that it takes three times longer to recover from the maximum drawdown than the time it took to produce it, with the same confidence level ('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-formula 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 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, E44

working papers series