How Robust Is Robust Covariance? Evidence from International Portfolio Selection

Abstract

This paper investigates whether the use of robust covariance improves portfolio performance and, in the presence of uncertainty, whether the 1/N strategy is as good as you think. In addition to sample covariance, we use a battery of robust covariance matrix. Our empirical evidence has two findings: First, the range of in-sample estimation horizon and out-of-sample holding period matter the most; secondly, generally, assets selected by robust covariance does not matter, the only exception is covariance estimated by multivariate t distribution Although the 1/N strategy is as optimal as the literature suggests, it does not cover all assets, yet n assets selected out of N by certain strategy perform better. Whether the out-of-sample holding period is set to be 1 and 3 months, our empirical illustration shows that: n assets selected from 90-day estimation window performs best, portfolio with 1/n weight consistently outperforms that with pre-optimized weights. As a result, robust investment strategy matters the most, rather than robust covariance. The factors that affect covariance estimator is not outliers, but the one that balance information.

Keywords: international portfolio, robust covariance, rolling, estimation errors

JEL Classification: C13; C51; G11