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 which allows more general view formulations than the original formula. Specifically, the equivalent formula provides more intuitive explanation under the limiting case of deterministic views, and it is also easier to show that 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 also implement the formula in an optimal asset allocation setting using equity analysts' 12-month ahead target price forecasts for the period of 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.

Keywords: Asset allocation, Black-Litterman model, Target price

JEL Classification: G12