Minimum-Variance Portfolios in the U.S. Equity Market

Abstract

In the minimum-variance portfolio, far to the left on the efficient frontier, security weights are independent of expected security returns. Portfolios can be constructed using only the estimated security covariance matrix, without reference to equilibrium expected or actively forecasted returns. Empirical results illustrate the practical value of large-scale numerical optimizations using return-based covariance matrix estimation methodologies, providing new perspective on the factor characteristics of low-volatility portfolios. Optimizations that go back to 1968 reveal that the long-only minimum-variance portfolio has about three-fourths the realized risk of the capitalization-weighted market portfolio, with higher average returns. TOPICS:Portfolio construction, statistical methods, analysis of individual factors/risk premia