Composing local and global behaviors: Higher performance of spin glass based portfolio selection

The basic challenge in optimization is how to navigate through the many non-optimal and mediocre solutions toward the few globally optimal solutions, amidst the growing problem size and computation complexity. If the proximity to an optimal solution could be measured, a desirable technique could be one that navigates speedily, even if crudely, when an optimal solution is not likely to be next; and accurately, even if slowly, otherwise. In this paper, we propose a technique based on spin glass paradigm that uses the above heuristic to solve the classic portfolio selection problem. Study of spin glass paradigm reveals that limiting each spin's interactions to its local neighborhood increases the computational speed of the algorithm, but also introduces an error in performance measure. In contrast, extending each spin's reach globally provides an accurate measure of performance, but slows down the glass computations. Theoretical analysis reveals a decision threshold by which speedy versus accurate navigation, i.e. local versus global glass behavior, can be alternated. The resulting algorithm is then applied to five different world stock market portfolio selection problems consisting of Hang Seng, DAX 100, FTSE 100, S&P 100, and Nikkei. These results demonstrate utility of the hybrid local–global behavior and appropriateness of the proposed decision threshold. Specifically, the results of experiments show faster convergence without a significant loss of accuracy in reaching globally optimal solutions.

► This paper presents a new algorithm that uses local behavior for increasing rate of convergence and uses global behavior for increasing the accuracy to achieve global optimums with regard to spin glass paradigm. ► Our method is applied on NP-complete problem: “portfolio selection”. ► The resulting algorithm is applied to five different world stock market portfolio selection problems consisting of Hang Seng, DAX 100, FTSE 100, S&P 100, and Nikkei. ► A test of reliability, study of Pareto frontier and comparison with other heuristic methods confirm the theoretical analysis and the utility of composing behavior for faster convergence while reaching desirable solutions.