Uncertainty in the Black-Litterman model: Empirical estimation of the equilibrium

The Black-Litterman model is a widely used and well established application of the Bayesian framework to asset allocation problems. It is, however, difficult to calibrate, as it requires the specification of abstract uncertainty parameters. We propose a new, more flexible model that allows the empirical estimation of the equilibrium, alleviating the need for parametrization. In an empirical application, we illustrate the sensitivity of the classical Black-Litterman model to the choice of the uncertainty parameter. We then demonstrate that the flexible model successfully exploits information in the cross-section of index constituents' returns to find an optimal trade-off in calibration of the uncertainty.