Heuristic approaches to realistic portfolio optimisation

Abstract

Previous research in portfolio optimisation has incorporated some real-world aspects but, to the best of our knowledge, none has incorporated all of them in a model applicable to actual real-world portfolios. We therefore develop a realistic model, investigate the efficiency of its solution by two heuristic methods, genetic algorithms and tabu search, and then examine the insights provided by the optimisation of real portfolios. Our model is based on the classical mean-variance approach, enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs that include a substantial illiquidity premium, and is applied to a large 100-stock portfolio. We find that for large portfolios the performance of genetic algorithms is three orders of magnitude better than that of tabu search. The results confirm that both floor and ceiling constraints have a substantial negative impact on real portfolio performance. Optimal portfolios with nonlinear costs and cardinality constraints often contain a large number of stocks with very low weightings. Their function is to diversify risk, and floor constraints hamper this, damaging portfolio performance. In addition, nonlinear transaction costs that are comparable in magnitude to forecast returns tend to diversify portfolios materially.