Conditioned Higher-Moment Portfolio: Optimization Using Optimal Control

Abstract

The present chapter contributes to two strains of portfolio optimization literature. The first is conditioned portfolio optimization, which discusses the mathematically correct treatment of information external to the investment assets themselves within what is otherwise a classical portfolio optimization context. The second is portfolio optimization involving higher moments of returns, which attempts to optimize for expected levels of portfolio returns moments beyond mean and variance. The optimal control formulation of conditioned portfolio problems introduced in Boissaux and Schiltz (2010) allows for generic numerical solution methods to be applied in the context of conditioned optimization if single signal series are used, and was applied to obtain constrained-weight solutions to the basic conditioned mean-variance problem in Boissaux and Schiltz (2011). In this chapter, the approach is applied to the higher-moment problem context. We formulate and backtest two constrained-weight higher-moment problem variants which avoid non-convex objective functions. In both cases, the use of conditioning information significantly improves observed strategy performance with respect to all metrics optimized by each problem formulation. We also briefly discuss and give results for the full four-moment problem using quartic polynomial utility functions, and find that results provide evidence that the full problem can be worked in practice even though its potentially non-convex objective function may cause numerical issues.