A Practical Approach to the Black and Litterman Model: An Example on European Sectors

In the classical mean-variance approach, an investor is required to provide estimates of the expected returns and covariances of all the securities in the investment universe considered. Obviously, this is a humongous task: typically, portfolio managers focus on a small segment of the investment universe and they pick those stocks in which they believe to achieve superior performances. The unsatisfactory use of mean-variance approach among practitioners as well as the need to consider the peculiarities of investment industry motivated Black and Litterman (1990-2) to formalize a model for combining subjective views with market equilibrium returns. In particular, Black and Litterman focus on portfolios that behave badly in the sense that unrealistic and no-intuitive weights may occur when a mean-variance model is utilized in the asset allocation. The Black and Litterman’s approach allows investors to combine market information with subjective views in a consistent way. The model relies on the use of implied equilibrium returns obtained from reverse optimization as reference model that is “tilted away” in the direction of the assets most favoured by investor’s views. An average investor without particular information on specific assets should invest according to the equilibrium weighting scheme. Portfolio manager may have different expectations about future returns; the model allows investor to incorporate subjective (tactical) views and to combine them with neutral (equilibrium, strategic) views in a consistent way. Moreover, investor indicates the degree of confidence in his views in such a way that higher confidence produces revised expected returns more tilted towards investor’s views. Then, the vector of revised expected returns is utilized as input of an optimizer to obtain optimal portfolio weights. The work reflects upon the analysis on the intuition behind the model presenting details of Bayesian portfolio selection. Furthermore, each input is described in detail explaining some of the most important approaches used. Finally, we analyze how to use the model in practice introducing a factor model to compute views: an example on European sectors will help us to describe the growing importance of the model in the asset allocation.