The distribution of out-of-sample returns of estimated optimal portfolios

Abstract

We derive a stochastic representation for the joint distribution of the out-of-sample mean and variance of a large class of portfolio rules that combines the sample optimal mean-variance portfolio with the sample global minimum-variance portfolio. Our results allow the combining coefficients to be either constant or estimated from historical data. Such a representation enables us to obtain the distributions and moments, asymptotically and in finite samples, of three out-of-sample portfolio performance measures, i.e., return, utility, and Sharpe ratio. These results are useful for a variety of applications, and we detail two of them as illustrations. Our paper provides a comprehensive toolkit that researchers can use to evaluate the out-of-sample performance of existing portfolio rules and develop better portfolio rules in the future.

Keywords: portfolio choice, out-of-sample performance, parameter uncertainty, estimation risk, stochastic representation. JEL Classification: G11, G12

JEL Classification: G11, G12