Essays on naive diversification

Abstract

The mean-variance model pioneered by Nobel laureate Harry Markowitz is the foundation of modern portfolio theory, and is widely applied in asset allocation and active portfolio management. However, the naive 1/N diversification rule (the equal-weight portfolio rule) has received much academic attention because of its superior performance relative to mean-variance portfolio rules. This thesis consists of two essays with respect to the naive 1/N diversification rule.

The first essay examines the sample selection bias in portfolio horse races with the 1/N rule. Numerous studies have developed mean-variance portfolio rules to outperform the naive 1/N rule. However, the outperformance is often justified with a small number of pre-selected datasets. Using a novel performance test based on a large number of datasets, I compare various ``1/N outperformers" with the naive rule. The results show that although some ``1/N outperformers" outperform the 1/N rule on an average basis, a sample selection problem generally exists in claiming significant outperformance over the naive benchmark. To further understand portfolio performance, I explore the theoretical relations between assets' return moments and the performance of optimal versus naive diversification. These relations not only imply strong performance predictability, but also can be exploited to deliver out-of-sample portfolio benefits.

The second essay studies how January seasonality affects the relative performance of the mean-variance and 1/N rules. I find that the good performance of the 1/N rule does not depend on the January seasonality when value-weighted indexes are used for portfolio construction. However, when individual stocks are formed into portfolios, a large proportion of the empirical success of the 1/N rule is attributed to enormous January returns. Mean-variance portfolio rules fail to outperform the naive rule on a risk-adjusted basis; however, the relative performance reverses when January returns are excluded. The results are robust with and without transaction costs, for various mean-variance rules, and across different industries and characteristics.