The Impact of Linear Constraints in Mean-Variance Optimization

Industrial Problems Seminar 

Christopher Bemis (X Cubed Capital Management)

Abstract

We study the effect linear constraints have on risk in the context of mean variance optimization (MVO). Jagannathan and Ma (2003) establish an equivalence between certain constrained and unconstrained MVO problems via a modification of the covariance matrix. We extend their results to arbitrary linear constraints and provide alternative interpretations for the effect of constraints on both the input parameters to the problems at hand and why ex-post performance is improved in the constrained setting.  In addition, we present a signal modification strategy similar in approach to that of Black-Litterman.