The Black-Litterman model: Active risk targeting and the parameter tau

There is apparent persistent confusion over certain aspects of Black-Litterman expected returns, with a number of publications offering various explanations, clarifications, and criticisms as to how the model works in practice. The parameter tau (τ) has proved to be a particularly confounding feature of the model: A wide range of opinions and suggestions on how to interpret and quantify tau has accumulated in the literature and includes some harsh condemnation of Black-Litterman specifically related to tau. This article presents a simple interpretation of tau, shows that it is directly related to the level of active risk implicit in the Black-Litterman model, and is easily calibrated so that Black-Litterman expected returns produce portfolios with targeted levels of active risk. The main contribution is an alternative derivation of Black-Litterman that affords a direct way to target active risk without requiring a specific value for tau. This derivation reveals that portfolio construction using Black-Litterman is equivalent to creating a mean-variance optimal portfolio of active strategies that is then overlaid onto a benchmark portfolio, and by targeting active risk directly, users of the Black-Litterman model do not need to consider tau at all. © 2017 Macmillan Publishers Ltd.