The probability of backtest overfitting

David H. Bailey, Jonathan M. Borwein, Marcos López de Prado and Qiji Jim Zhu

Journal of Computational Finance

Abstract: ABSTRACT Many investment firms and portfolio managers rely on backtests (ie, simulations of;performance based on historical market data) to select investment strategies and allocate;capital. Standard statistical techniques designed to prevent regression overfitting,;such as hold-out, tend to be unreliable and inaccurate in the context of investment;backtests. We propose a general framework to assess the probability of backtest overfitting;(PBO). We illustrate this framework with specific generic, model-free and nonparametric;implementations in the context of investment simulations; we call these;implementations combinatorially symmetric cross-validation (CSCV). We show that;CSCV produces reasonable estimates of PBO for several useful examples.

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