The efficient frontiers of mean-variance portfolio rules under distribution misspecification

Mean-variance portfolio decisions that combine pre-diction and optimisation have been shown to have poor empirical performance. Here, we consider the performance of various shrinkage predictors by their efficient frontiers under different distributional assumptions to study the impact of reasonable departures from Gaussianity. Namely, we investigate the im-pact of first-order autocorrelation, second-order autocorrelation, skewness, and excess kurtosis. We show that the shrinkage predictors tend to rescale the sample efficient frontier, which can change based on the nature of local perturbations from Gaussianity. This rescaling implies that the standard approach of evaluating decision rules for a fixed level of risk aversion can give a misleading impression of comparative performance, and more so in a dynamic market setting. Our results suggest that comparing efficient frontiers has serious implications which oppose the prevailing thinking in the literature. Namely, that sample estimators out-perform Stein type estimators of the mean, and that improving the prediction of the covariance has greater importance than improving that of the means.