The Black–Litterman model: A risk budgeting perspective

The Black–Litterman model of expected returns is well-known throughout the investment management industry. Despite the model's familiarity, elucidating exactly what it does in a straightforward manner has proved to be a challenge, as evidenced by a number of publications aimed at intuiting, explaining or demystifying the model. Part of the lack of clarity is likely due to the fact that the model is derived with an emphasis on Bayesian statistics, and as a result, key concepts and equations are expressed in terms that may obfuscate the practical workings of the model for many prospective users. This article shows that Black–Litterman expected returns can also be derived in the context of a widely used mean-variance optimization approach to active investing known as risk budgeting. The risk budgeting derivation clearly illustrates the mean-variance mechanics of the model, and offers a simple framework for understanding how Black–Litterman expected returns generate portfolio weights that accurately reflect underlying investment views when used in unconstrained optimization. Viewing Black–Litterman from a risk budgeting perspective helps clarify the practicalities of the model in a way that may be more familiar and insightful to a wider audience, and should be helpful in promoting Black–Litterman as a useful tool for investment managers.