How Robust Is Robust Covariance? Evidence from International Portfolio Selection

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