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

TL;DR

This paper examines how distributional deviations from normality affect the performance of shrinkage methods in mean-variance portfolio optimization, revealing that standard comparisons may be misleading in dynamic markets.

Contribution

It analyzes the impact of distributional misspecification on efficient frontiers and challenges prevailing assumptions about estimator performance in portfolio selection.

Findings

Shrinkage methods rescale the sample efficient frontier based on distributional perturbations.

Comparing decision rules at fixed risk levels can be misleading due to frontier rescaling.

Improving covariance prediction is more crucial than mean estimation under distributional misspecification.

Abstract

Mean-variance portfolio decisions that combine prediction and optimisation have been shown to have poor empirical performance. Here, we consider the performance of various shrinkage methods by their efficient frontiers under different distributional assumptions to study the impact of reasonable departures from Normality. Namely, we investigate the impact of first-order auto-correlation, second-order auto-correlation, skewness, and excess kurtosis. We show that the shrinkage methods tend to re-scale the sample efficient frontier, which can change based on the nature of local perturbations from Normality. This re-scaling implies that the standard approach of comparing decision rules for a fixed level of risk aversion is problematic, 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.