The Black-Litterman Model : A Consistent Estimation of the Parameter Tau

In addition to giving a detailed description and explanation of the Black–Litterman (BL) model, this paper deals with estimation of the parameter tau. This parameter is the most mysterious one in the BL model, as the literature does not provide specific guidance on its calibration. Specifically, I develop an estimation procedure that yields a suitable and consistent estimate of tau, which results in a modification of the original BL model. The approach combines cross-section and time-series regressions, both commonly approach to estimate the capital asset pricing model. The novelty here consists in utilizing random intercepts when estimating the time-series regressions. In addition, a new definition of beta is derived. Within this framework, the parameter tau is obtained from the cross-sectional regression. The approach is able to capture the serial, cross, and cross-lag correlations of the excess returns. To illustrate the new framework, I provide an empirical application and show that it is easily applicable by portfolio managers