Stop-Outs Under Serial Correlation and 'The Triple Penance Rule'
David H. Bailey
Lawrence Berkeley National Laboratory; University of California, Davis
Marcos Lopez de Prado
Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; Harvard University - RCC
October 1, 2014
Journal of Risk, 2014, Forthcoming
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: http://ssrn.com/abstract=2511599
Number of Pages in PDF File: 35
Keywords: Downside, time under water, stop-out, triple penance, serial correlation, Sharpe ratio
JEL Classification: G0, G1, G2, G15, G24, E44
Date posted: January 16, 2013 ; Last revised: July 5, 2015
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