  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.
