In a recent paper, Marcos Lopez de Prado of Hess Energy Trading Company and David H. Bailey of Lawrence Berkeley National Laboratory, derive closed form approximations for Expected Maximum Drawdown (MaxDD). They also derive formulae for the expected time to reach the Maximum Drawdown (t*) and the expected Maximum Time Under Water (MaxTuW), which under the assumption of IID Normality turns out to be three times the time taken to reach the maximum drawdown. Bailey and de Prado show that this ‘Triple Penance Rule' holds independently of the Sharpe Ratio.

This has important consequences for people who may be using some combination of drawdown and Sharpe Ratio to stop out loss-making funds.

Moreover, Bailey and de Prado show that under the more general case, when first-order serial-auto-correlation is accounted for, the Triple Penance rule may no longer apply as the higher volatility of positively serial auto correlated funds may enable them to recover faster than 3 x the length of time it took the drawdown to occur.

They state,� 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 skilful portfolio mana......................

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This article was published in Opalesque's New Managers a top-down monthly analysis, news and research publication on the global emerging manager space.