Multicriteria portfolio selection problem: robust assets allocation

Abstract

The paper shows how to overcome practical difficulties of using the results of modern portfolio theory linked with high dimensions and the insufficient amount of information available about the input parameters, the factors that make the optimal solution unrobust. The modified mean-variance optimisation model shows that Markowitz's portfolio can be improved. The generalised optimal portfolio problem is formulated as a multicriteria problem. The performance index that presents linear convolution of the chosen criteria is considered. The closed-form solution is given under assumption that net short sales are allowed. In contrast to several known pure mathematical regularisation approaches applied to the portfolio selection problem, the considered portfolio model includes the average trading volume of shares of the portfolio's security for a specified period of time measured as a percentage of its total float number of shares, which is used to quantify the portfolio's components based on their potential price increase. The offered additional criterion, which has a clear economic interpretation allows investors to build portfolios that are more robust compared to mean-variance portfolios.