Suboptimality in portfolio conditional value-at-risk optimization

In this paper, we consider the portfolio optimization problem, with conditional value-at-risk as the objective. We summarize commonly used methods of solution and note that the linear programming (LP) approximation is the most generally applicable and easiest to use (the LP uses a Monte Carlo sample from the true asset returns distribution). The suboptimality of the obtained approximate portfolios is then analyzed using a numerical example, with up to 101 assets and Student t-distributed returns, ranging from light to heavy tails. The results can be used as an estimate of the portfolio suboptimality for more general asset returns distributions, based on the number of assets, tail heaviness and fineness of the discretization. Computation times using the different techniques available in the literature are also analyzed.