Portfolio Optimization: Scenario Generation, Models and Algorithms

In single-period portfolio optimization several facets of the problem may influence the goodness of the portfolios. In this thesis, we aim at investigating the impact of some of these facets on the performances of the portfolios. Firstly, we consider the problem of generating scenarios. We survey different techniques to generate scenarios for the rates of return. We also compare these techniques by providing in-sample and out-of-sample analysis of the portfolios. As reference model we use the Conditional Value-at-Risk (CVaR) model with transaction costs. Extensive computational results are presented. Secondly, we analyze portfolio optimization when data uncertainty is taken into consideration. In deterministic mathematical optimization, it is assumed that all the input data are equal to some nominal values. Nevertheless, the solution can be sub-optimal or even infeasible when some of the data take values different from the nominal ones. Several techniques that are immune to data uncertainty, called robust, are known. We investigate the effectiveness of two robust techniques when applied to a portfolio selection problem. The reference model assumes the CVaR as performance measure. We carried out extensive computational experiments under different market behaviors. Thirdly, we study portfolio optimization in a rebalancing framework, considering transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model with transaction costs, based on the CVaR as performance measure, to introduce portfolio rebalancing. We suggest a procedure to use the proposed optimization model in a rebalancing framework. Extensive computational results are presented. Finally, we study the index tracking and the enhanced index tracking problems. We present two mixed-integer linear programming formulations. We introduce a heuristic framework, called Enhanced Kernel Search, to solve the index tracking problem. We show its effectiveness comparing the performances of several heuristics with those of a general-purpose solver using benchmark instances.