The Black-Litterman Model: Extensions and Asset Allocation

Abstract

The Black-Litterman Model (BLM), created by Fischer Black and Robert Litterman, is a sophisticated portfolio construction method that overcomes the problem of unintuitive, highly-concentrated portfolios, input-sensitivity, and estimation error maximization. The BLM uses a Bayesian approach to combine the subjective views of an investor regarding the expected returns of one or more assets with the market equilibrium vector of expected returns (the prior distribution) to form a new, mixed estimate of expected returns. The resulting new vector of returns (the posterior distribution), leads to intuitive portfolios with sensible portfolio weights. (Idzorek, 2004). BLM was first introduced in Black and Litterman (1990) and further explained in Black and Litterman (1991) and Black and Litterman (1992) It is an asset allocation model which has its roots in mean-variance (MV) optimization model and capital asset pricing model (CAPM). Model builds on MV optimization and CAPM by using a Bayesian framework that allows investors to incorporate their views on markets effectively into asset allocation process. Main contribution of BLM is that it enables investors to construct sensible portfolios without using unnecessary constraints which also reflect their views on markets. It is well known to both academics and practitioners that standard MV optimization is very sensitive to expected returns and often generates extreme portfolios (concentration in very few assets, large long and short positions). BLM overcomes these issues by choosing a neutral reference point, CAPM equilibrium. It also allows investors to express their views with varying confidence levels and integrate these views into CAPM prior by using a Bayesian framework. As a result, since its introduction BLM has been increasingly used among practitioners and allowed asset allocation decisions to be in more of a quantitative nature rather than qualitative because of the apparent shortcomings of MV optimization model.