A parametric bootstrap to evaluate portfolio allocation models

Abstract

If the asset returns are multivariate normal and the investor knows the moments, the Mean–Variance (MV) solution provides the portfolio with the highest Sharpe ratio. However, estimation errors of the moments misalign the allocation weights, and the out-of-sample Sharpe ratio falls. The paper introduces a parametric bootstrap to estimate the predictive Sharpe ratio, the most likely Sharpe ratio that the investor would see out of sample. This Sharpe ratio is advantageous because it includes the distortions from estimation errors and the investor can see the most likely results before investing capital. The approach is quite general and one can use the approach for any portfolio allocation model that uses the moments in some way. The ex ante feature of the test is key, as the test allows the investor to see which model works best before the investors commits capital.