Lest we forget: learn from out-of-sample errors when optimizing portfolios

Portfolio optimization often struggles in realistic out-of-sample contexts. We de-construct this stylized fact, comparing historical forecasts of portfolio optimization inputs with subsequent out of sample values. We confirm that historical forecasts are imprecise guides of subsequent values but also find the resulting forecast errors are not entirely random. They have predictable patterns and can be partially reduced using their own history. Learning from past forecast errors to calibrate inputs (akin to empirical Bayesian learning) results in portfolio performance that reinforces the case for optimization. Furthermore, the portfolios achieve performance that meets expectations, a desirable yet elusive feature of optimization methods.