A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems

In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty. To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed

Metaheuristic approaches to realistic portfolio optimisation

In this thesis we investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which include a substantial illiquidity premium, and is then applied to a large I 00-stock portfolio. It is shown that genetic algorithms can optimise such portfolios effectively and within reasonable times, without extensive tailoring or fine-tuning of the algorithm. This approach is also flexible in not relying on any assumed or restrictive properties of the model and can easily cope with extensive modifications such as the addition of complex new constraints, discontinuous variables and changes in the objective function. The results indicate that that both floor and ceiling constraints have a substantial negative impact on portfolio performance and their necessity should be examined critically relative to their associated administration and monitoring costs. Another insight is that nonlinear transaction costs which are comparable in magnitude to forecast returns will tend to diversify portfolios; the effect of these costs on portfolio risk is, however, ambiguous, depending on the degree of diversification required for cost reduction. Generally, the number of assets in a portfolio invariably increases as a result of constraints, costs and their combination. The implementation of cardinality constraints is essential for finding the bestperforming portfolio. The ability of the heuristic method to deal with cardinality constraints is one of its most powerful features.Decision SciencesM. Sc. (Operations Research