Benchmark Tracking Portfolio Problems with Stochastic Ordering Constraints

This work debates several approaches to solve the benchmark tracking problems and introduces different orders of stochastic dominance constraints in the decisional process. Portfolio managers usually address with the problem to compare their performance with a given benchmark. In this work, we propose different solutions for index tracking, enhanced indexation and active managing strategies. Firstly, we introduce a linear measure to deal with the passive strategy problem analyzing its impact in the index tracking formulation. This measure results to be not only theoretically suitable but also it empirically improves the solution the results. Then, proposing realistic enhanced indexation strategies, we show how to solve this problem minimizing a linear dispersion measure. Secondly, we generalize the idea to consider a functional in the tracking error problem considering the class of dilation, expected bounded risk measures and LP compound metric. We formulate different metrics for the benchmark tracking problem and we introduce linear formulation constraints to construct portfolio which maximizes the preference of non-satiable risk averse investors with positive skewness developing the concept of stochastic investment chain. Thirdly, active strategies are proposed to maximize the performances of portfolio managers according with different investor's preferences. Thus, we introduce linear programming portfolio selection models maximizing four performance measures and evaluate the impact of the stochastic dominance constraints in the ex-post final wealth

Portfolio selection with options

We describe an optimization model to evaluate the portfolio performance in the option’s market. Hedgers, managers and investors, in agreement with Markovitz’s theory, aimed at creating a portfolio made up by assets with negative correlation, so as to have a portfolio not linked to the economic cycle. The optimization portfolio problem with contingent claims allows to create wealth also in financial crisis without using short selling, since option returns show a strong negative correlation. The basic idea of this work is using only trading price options, in particular those written on principal stock Indexes, in order to create a diversified portfolio. Thus we propose an ex post analysis over a two-years period using different international portfolio strategies on the derivative market