The bias of IID resampled backtests for rolling window mean-variance portfolios

Abstract

Backtests on historical data are fundamental for evaluating portfolio selection rules, but their reliability is often limited by reliance on a single sample path. This reliance can lead to high estimation variance. IID resampling offers a potential solution by increasing the effective sample size but can disrupt the temporal structure financial data and introduce bias. This paper investigates the drivers and magnitude of this bias for Sharpe Ratio estimates of the rolling-window mean-variance portfolio rule. Analytically, we demonstrate that the bias is driven by the disruption of the return autocorrelation structure. We identify an offsetting mechanism between the component biases in the mean and variance that often renders the final Sharpe Ratio bias a modest fraction of a standard backtest's estimation noise. To help practitioners gauge the potential bias, we derive analytical bounds based on first-lag autocorrelation, providing a simple tool to assess when the bias may be significant.