A least discrimination method for portfolio optimization: an alternative to the Black–Litterman approach

Jacques Pézier

Abstract

ABSTRACT

Black and Litterman recommend that portfolio optimization start with a reference portfolio (eg, a performance benchmark) and inferring the returns forecast that makes this portfolio optimal. Personal views on some asset returns may then be expressed as deviations from the inferred forecast that justify adding an active portfolio to the reference portfolio. We support this approach but, instead of using the Black-Litterman methodology for blending personal views with the market inferred forecast, we propose a less artificial and more general methodology based on the least discrimination principle: the personal forecast for all asset returns should be true to personal views and lead to the optimal active portfolio offering the lowest potential gain in certainty equivalent excess return over the reference portfolio. The least discrimination method can be applied to a variety of views, and leads to optimal nonlinear payoffs (options) when views are expressed on volatilities and correlations.