The Impact of Constraints on Minimum Variance Portfolios

Abstract

Minimum variance strategies are a proven approach to profiting from the low volatility effect, but if taken directly from an optimizer they tend to have disadvantageous attributes such as low liquidity, high turnover, high tracking error, and concentrated positions in stocks, economic sectors, and countries or regions. Minimum variance index providers and portfolio managers typically mitigate these implementation problems by imposing constraints. In this study, we construct minimum variance portfolios for the U.S., global developed, and emerging markets, and we apply commonly used constraints to determine their individual and collective impact on simulated portfolio characteristics, investment performance, and implicit trading costs. The constraints we tested succeed in improving investability, but they shift minimum variance portfolio characteristics toward those of the capitalization-weighted benchmark. In particular, each additional constraint increases volatility. Notwithstanding this tendency, the simulated performance advantage of minimum variance indices over market-cap-weighted indices is strong enough to make it a valid choice for investors interested in risk-managed strategies.

Keywords: low volatility, minimum variance, smart beta, constrained optimization

JEL Classification: F21, G11, G14, G20