An empirical comparison between nonlinear programming optimization and simulated annealing (SA) algorithm under a higher moments Bayesian portfolio selection framework

The optimal portfolio selection problem has long been of interest to both academics and practitioners. A higher moments Bayesian portfolio optimization model can overcome the shortcomings of the traditional Markowitz approach and take into consideration the skewness of asset returns and parameter uncertainty. This paper presents a comparison between the simulated annealing and the nonlinear programming methods of optimization for the Bayesian portfolio selection problem in which the objective function includes the portfolio mean, variance and skewness. We make the comparison for a utility function that is easily optimized using both methods. In particular we maximize a cubic utility function, and our results show that to achieve the same level of accuracy, the CPU time for the nonlinear programming optimization will be shorter than for the simulated annealing algorithm. Though it is slower, the simulated annealing algorithm is still a viable option for this utility function.