Implementing Black-Litterman Using an Equivalent Formula and Equity Analyst Target Prices

Abstract

We examine an alternative and equivalent Black and Litterman [1992] formula using classical multivariate analysis, which is easier to interpret and allows more general view formulations than the original formula. Specifically, the equivalent formula provides a more intuitive explanation under the limiting case of deterministic views, and makes it easier to show the resulting optimal portfolio as a combination of the market portfolio and a long–short view portfolio. The equivalent formula also allows for more convenient empirical implementations when views and expected return priors are correlated. We then use a numerical example to illustrate the equivalent formula, and we also implement the formula in an optimal asset-allocation setting, using equity analysts’ 12-month-ahead target price forecasts for the period 1999–2010. We show that the optimal portfolio outperforms the market (S&P 500) and this result is robust across different time periods and model parameter choices.