Global Portfolio Optimization Revisited: A Least Discrimination Alternative to Black-Litterman

Abstract: Global portfolio optimization models rank among the proudest achievements of modern finance theory, but practitioners are still struggling to put them to work. In 1992, Black and Litterman recognized the difficulties portfolio managers have in expanding their personal views about some expected asset returns into full probabilistic forecasts about all asset returns and developed a method to facilitate this task. We propose a more general method based on a least discrimination (LD) principle. It produces a probabilistic forecast that is true to personal views but is otherwise as close as possible to a chosen reference forecast. For this purpose we expand the concept of optimal portfolio to include non-linear pay-offs and derive an economic measure of distance - a generalized relative entropy distance - between probabilistic forecasts. The LD method produces optimal portfolios matching any views, including views on volatility and correlation as well as expected returns, and containing option-like pay-offs, if allowed. It also justifies a simple linear interpolation between reference and personal forecasts, should a compromise need be reached.