Explicit coupling of informative prior and likelihood functions in a Bayesian multivariate framework and application to a new non-orthogonal formulation of the Black–Litterman model

Under an assumption of normality, we explore a non-orthogonal Bayesian technique in which redundant information can in principle be filtered out of the posterior distribution by the explicit coupling of the prior and likelihood functions. The Black–Litterman forecasting model widely used by investment practitioners in various forms is revisited in the light cast by the new technique, and implications for the posterior mean and overall posterior density are examined. A numerical backtest experiment conducted on a portfolio of MSCI sector indices invested using a total return acceleration strategy over the 2003–2007 period sheds some light on the possible benefits of the non-orthogonal approach. Non-orthogonal coupling is found to improve both the future expected returns and the risk model. The resulting competitive advantage to an investor applying the technique to portfolio construction is then investigated in terms of relative performance within the mean-variance framework. With the present simplified backtest settings, the annual outperformance ranges from 13 to 98 basis points after 36 rebalancing periods, depending on the accuracy of the original forecasts.