Constrained mean-risk portfolio optimisation: an application of multiobjective simulated annealing

We solve different constrained mean-risk portfolio optimisation models using a recently developed simulated annealing-based multiobjective optimisation algorithm. We consider practical and widely used constraints in portfolio modelling, i.e., the cardinality constraint which imposes a limit on the number of assets in the portfolio and the quantity constraints which restrict the proportion of each asset in the portfolio to lie between lower and upper bounds. Various risk measures are employed – the classical variance and three risk measures that form the so called downside-risk family, i.e., expected shortfall, value-at-risk and semivariance. The experimental results demonstrate that the algorithm generates a number of efficient portfolios capturing a great range of the trade-offs between mean and risk independently of the risk function used. Comparison with benchmark (when possible) efficient frontiers provides strong evidence that the algorithm effectively solves the discrete constrained mean-risk problems. Furthermore, a computational comparison with a population-based evolutionary algorithm, namely SPEA2, shows that the simulated annealing-based multiobjective optimisation technique achieves almost as good performance in a timely manner.