Robust portfolio allocation under discrete asset choice constraints

The mean-variance portfolio allocation model is very sensitive to estimation errors in the model parameters. Robust optimization is a technique used to incorporate the uncertainty introduced by estimation errors directly into portfolio allocation. Practitioners are often faced with complex constraints on the portfolio structure such as limits on the number of securities in the portfolio, which are modelled with discrete variables, and introduce discontinuities in the efficient frontier. This article investigates the size of discontinuities in the efficient frontiers obtained by the classical and robust mean-variance models under such discrete asset choice constraints, as well as the impact of portfolio size on the discontinuity being considered. In addition, we analyse the effects of applying discrete asset choice restrictions to the portfolio selection problem, as well as using estimated and true parameters in the computation of the classical and robust mean-variance investment strategies under discrete asset choice constraints. Computational experiments reveal reduction of the size of discontinuity when using robust optimization mean-variance models. © 2011 Macmillan Publishers Ltd.