Uncertainty in the Black-Litterman model : a practical perspective

Deriving an optimal asset allocation hinges crucially on the quality of inputs used in the optimization. If the vector of expected returns and the covariance matrix are known with certainty, mean-variance optimization produces optimal portfolios. If, however, these parameters are estimated with uncertainty, mean-variance optimization maximizes estimation error. We provide a literature review of procedures developed in academia to incorporate parameter uncertainty in the asset allocation process, focusing on common heuristics and Bayesian methods. The Black-Litterman model, an application of the Bayesian framework, has practical appeal for investors as it permits the specification of subjective views. Calibration of the model is, however, not trivial and induces rigidity. In Fuhrer and Hock (2023), a generalization of the Black-Litterman model was introduced and a fully quantitative, objective parameterization was derived. Here, we start with the same generalization, but present a qualitative, more intuitive approach for setting parameters. This gives the investor more control over the mixing of views and equilibrium returns, while lending intuition to the parameter choice in the classical setting.