Deconstructing Black-Litterman: How to Get the Portfolio You Already Knew You Wanted

Abstract

The Markowitz (1952, 1959) mean-variance (MV) efficient frontier has been the theoretical standard for defining portfolio optimality for more than a half century. However, MV optimized portfolios are highly susceptible to estimation error and difficult to manage in practice (Jobson and Korkie 1980, 1981; Michaud 1989). The Black and Litterman (BL) (1992) proposal to solve MV optimization limitations produces a single maximum Sharpe ratio (MSR) optimal portfolio on the unconstrained MV efficient frontier based on an assumed MSR optimal benchmark portfolio and active views. The BL portfolio is often uninvestable in applications due to large leveraged or short allocations. BL use an input tuning process for computing acceptable sign constrained solutions. We compare constrained BL to MV and Michaud (1998) optimization for a simple data set. We show that constrained BL is identical to Markowitz and that Michaud portfolios are better diversified under identical inputs and optimality criteria. The attractiveness of the BL procedure is due to convenience rather than effective asset management and not recommendable relative to alternatives.