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

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. Specifically, 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. JEL Classification: G12 ∗We thank Ravi Jagannathan for extensive discussions and helpful comments. We gratefully acknowledge financial support from the Financial Institutions and Markets Research Center at the Kellogg School of Management. † [email protected], College of Business, Minnesota State University Mankato. ‡ [email protected], Mendoza College of Business, University of Notre Dame. ♦ [email protected], Federal Reserve Bank of New York. The views expressed are those of the authors and do not reflect the views of the Federal Reserve Bank of New York or the Federal Reserve System.