Benchmark Tracking Portfolio Problems with Stochastic Ordering Constraints

Abstract

This work debates several approaches to solve the benchmark tracking problems and introduces dierent 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 dierent 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 dierent 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 dierent 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 nal wealth.

This work debates several approaches to solve the benchmark tracking problems and introduces dierent 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 dierent 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 dierent 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 dierent 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 nal wealth.