Abstracts

Within a traditional context of myopic discrete-time mean-variance portfolio optimisation, the problem of conditioned optimisation, in which predictive information about returns contained in a signal is used to inform the choice of portfolio weights, was first expressed and solved in concrete terms by Ferson and Siegel. An optimal control formulation of conditioned portfolio problems was proposed and justified by Boissaux and Schiltz. This opens up the possibility of solving variants of the basic problem that do not allow for closed-form solutions through the use of standard numerical algorithms used for the discretisation of optimal control problems.
The present paper contributes to the empirical literature on this topic. We compare the performance of strategies resulting from conditioned optimisation and using several possible indicators for signalling purposes, to that obtained using standard approaches to portfolio investment. In particular, we report on both ex ante improvements to the accessible efficient frontier as measured through the typical associated metrics such as the Sharpe ratio, and ex post results affected, most notably, by specification errors regarding the relationship between signal and returns. We then discuss different problem parameters, examine their impact on performance and check whether significant ex post improvements may be achieved through optimal parameter selection.
This analysis implies the solving of optimal control problems involving a multidimensional objective function integral. To that effect, we propose a very simple direct collocation discretisation scheme suitable for the numerical solution of problems of this type. A convergence result is established to show that the scheme is consistent with multidimensional Pontryagin Principle relations in several important respects. Whilst the discussion focuses on the two-dimensional case, the simplicity of the scheme allows for easy generalisation. We carry out a backtest using real-world data and confirm that its results validate our proposed numerical scheme.