Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

TL;DR

This paper analyzes the estimation risk in high-dimensional mean-variance portfolios using Bayesian and shrinkage methods, providing deterministic equivalents for out-of-sample performance and bias corrections to improve investment decisions.

Contribution

It offers a theoretical framework using random matrix theory to quantify estimation risk and develop bias corrections for high-dimensional portfolio optimization.

Findings

Deterministic equivalents for out-of-sample performance

Quantification of risk underestimation and return overestimation

Bias corrections improve portfolio performance

Abstract

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings.