Portfolio Selection with Multiple Spectral Risk Constraints

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value-at-risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs; hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient; it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.