Being Naive about Naive Diversification: Can Investment Theory be Consistently Useful

Abstract

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and taught in MBA texts. DeMiguel, Garlappi and Uppal (2007), however, show that, due to estimation errors, existing theory-based portfolio strategies are not as good as we once thought, and the estimation window needed for them to beat the naive $1/N$ strategy (that invests equally across N risky assets) is 'around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets.' In this paper, we modify the modern portfolio theory to account for estimation errors, so that the theory becomes more relevant in practice to yield positive gains over the naive 1/N strategy under realistic estimation windows. In particular, we provide new portfolio strategies that not only perform as well as the 1/N strategy in an exact one-factor model that favors the 1/N, but also outperform it substantially in a one-factor model with mispricing, in multi-factor models with and without mispricing, and in models calibrated from real data without any factor structures. We also find that the usual maximum likelihood (ML) estimator of the true portfolio rule can have Sharpe ratios higher than the 1/N in many cases, and hence, if one is concerned only about Sharpe ratios, the ML estimator is not as bad as one might have once believed.