Actively Managed Mean-Variance Portfolios

Abstract

I present closed-form analytical solutions to the active mean-variance portfolio management problem relative to a pre-specified benchmark subject to a budget constraint and a beta constraint. The imposition of the beta constraint makes the benchmark relevant to the portfolio problem. I provide an intuitive interpretation of the optimal active portfolio in the general mean-variance case as well as a detailed expression for the optimal weights when returns follow a single-factor model. I show that the value-added of active portfolio management is simply the incremental certainty equivalent return of the active portfolio relative to the certainty equivalent return of the benchmark. I investigate the out-of-sample performance of the optimal active mean-variance portfolio using industry portfolios as well as individual stocks.

Keywords: active portfolio management, benchmark, mean-variance portfolio, tracking error, replicating portfolio

JEL Classification: G11, G10