Investigating the effectiveness of robust portfolio optimization techniques

Data uncertainty is a common feature in most of the real-life optimization problems. Despite that, the usual approach in mathematical optimization is to assume that all the input data are known deterministically and equal to some nominal values. Nevertheless, the optimal solution of the nominal problem can reveal itself suboptimal or even infeasible. An area where data uncertainty is a natural concern is portfolio optimization. As a matter of fact, in portfolio selection every optimization model deals with the estimate of the portfolio rate of return, and of either a risk or a safety measure. In the literature several techniques that are immune to data uncertainty have been proposed. These techniques are called robust. In this article we investigate two well-known robust techniques when applied to a specific portfolio selection problem, and compare the portfolios selected by the respective robust counterparts. Both the approaches allow the modeler to adjust the level of conservatism of the solution. We carried out extensive computational results based on real-life data from London Stock Exchange Market under different market behaviors.