Black-Litterman Model

The Black-Litterman model is an asset allocation model that was developed by Fischer Black and Robert Litterman of Goldman Sachs. The Black-Litterman model is essentially a combination of two main theories of modern portfolio theory, the capital asset pricing model (CAPM) and Harry Markowitz's mean-variance optimization theory.

The main benefit of the Black-Litterman model is that it allows the portfolio manager to use it as a tool for producing a set of expected returns within the mean-variance optimization framework. This can allow the manager to avoid certain problems or issues inherent in Markowitz's mean-variance optimization framework, such as the concentration of portfolio assets in only a handful of the assets under optimization.

Black and Litterman’s approach was developed as a quantitative approach to managing the issue of model estimation error, which is problematic when generating expected return outcomes. There are two versions of the Black-Litterman approach:

• Unconstrained Black-Litterman (UBL) model: Taking the weights of asset classes in a global benchmark such as MSCI World as a neutral starting point, asset weights are adjusted to reflect an investor’s views on the expected returns of asset classes according to a Bayesian procedure that considers the strength of the investor’s beliefs. This produces an unconstrained Black-Litterman model or UBL model since the model does not prohibit constraints on asset-class weights.
• Black-Litterman (BL) model: This approach reverse engineers the expected returns implicit in a diversified market portfolio (a process called reverse optimization) and combines them with an investor’s personal views on expected returns in a systematic way that takes factors in the investor’s confidence in such views. The view-adjusted expected return forecast is then used in a mean-variance optimization with a constraint against short sales or possibly other model constraints.

Because the UBL model is unconstrained, resulting model allocation outputs can be unpractical for many investment applications. For instance, the model may call for shorting one asset to purchase another. Many managers may find it difficult to sell an investor on a strategy where one asset is shorted 30%, so it generates funds to purchase another, creating an asset-weighted 130% of the overall portfolio.

The BL approach overcomes these practical limitations by often implementing short sale constraints. By adjusting a model’s allocation to an investor’s views, two desirables model qualities surface: (1) resulting asset allocations which are well diversified; and, (2) resulting asset allocations the factor in an investor’s views on asset-class returns, if any, as well as the strength of those views.

The practical goal of the BL approach is to create stable, mean-variance-efficient portfolios that overcome the problem of expected return sensitivity. Resulting sets of expected asset-class returns used by the BL model blends equilibrium returns and an investor’s views, should they have one.