Multi-objective Differential Evolution Based Optimization of Risk Budgeted Global Asset Allocation Portfolios

The Risk Budgeted Global Asset Allocation Portfolio problem strives to obtain an optimal portfolio of assets across global markets, with the objective of maximizing its Sharpe Ratio, subject to the constraints of risk budgets and other specific conditions imposed by the investors on the various asset classes comprising the portfolio. The mathematical formulation of the optimization problem turns out to be a Single objective Non linear Constrained Fractional Programming model, with the risk budgets contributing to the non linearity of the problem and Sharpe Ratio objective, to the Fractional Programming aspect of the problem. In the absence of analytical methods to solve an unexplored problem of such a nature, an attempt was made earlier to solve the problem using conventional Differential Evolution by employing Joines and Houcke´s Dynamic Penalty Function Strategy. However, with the increasing popularity of employing multi-objective optimization concepts to tackle non linear constraints in single objective optimization problems, this work attempts to solve the problem concerned using a Multi-objective Differential Evolution algorithm and compare the same with its predecessor. The performance analysis of the two competing methods over the characteristics of consistency of performance and convergence, have been experimented over a realistic global asset allocation portfolio.