Multiple tests for the performance of different investment strategies

Abstract

In the context of modern portfolio theory, we compare the out-of-sample performance of eight investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider short-selling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of the non-trivial strategies, whether the trivial strategy is better than every non-trivial strategy, and which of the non-trivial strategies is significantly outperformed by naive diversification. The empirical part of our study is conducted using US stock returns from the last four decades, obtained via the CRSP database.