Multi-objective evolutionary methods for time-changing portfolio optimization problems

Abstract

This thesis is focused on the discovery of efficient asset allocations with the use of evolutionary algorithms. The portfolio optimization problem is a multi-objective optimization problem for the conflicting criteria of risk and expected return. Furthermore the nonstationary nature of the market makes it a time-changing problem in which the optimal solution is likely to change as time advances. Hence the portfolio optimization problem naturally lends itself to an exploration with multi-objective evolutionary algorithms for time-changing environments. Two different risk objectives are treated in this work: the established measure of standard deviation, and the Value-at-Risk. While standard deviation is convex as an objective function, historical Value-at-Risk is non-convex and often discontinuous, making it difficult to approach with most conventional optimization techniques. The value of evolutionary algorithms is demonstrated in this case by their ability to handle the Value-at-Risk objective, since they do not have any convexity or differentiability requirements. The D-QMOO time-changing evolutionary algorithm is applied to the portfolio optimization problem. Part of the philosophy behind D-QMOO is the exploitation of predictability in the optimal solution's motion. This problem however is characterized by minimal or non-existent predictability, since asset prices are hard to forecast. This encourages the development of new time-changing optimization heuristics for the efficient solution of this problem. Both the static and time-changing forms of the problem are treated and characteristic results are presented. The methodologies proposed are verified through comparison with established methods and through the performance of the produced portfolios as compared to the overall market. In general, this work demonstrates the potential for the use of evolutionary algorithms in time-changing portfolio optimization as a tool for portfolio managers and financial engineers.