Construction of a Basket of Diversified Portfolios, via Quantum Annealing, to Aid in Cardinality Constratined Portfolio Optimization

In this project, we propose and investigate a new approach for solving portfolio optimization problems (POP) with cardinality constraints using an evolutionary algorithm based on the distribution of diversified baskets (EADDB).The Diversified basket is the basket of portfolios each of which obtains one of the lowest risks. The distribution of the diversified basket indicates the probability of having each asset in the diversified basket. Finding the diversified basket is an NP-hard problem, and we exploit quantum annealing in order to approximate the diversified basket.In particular, POP is mapped into D-Wave Two™, the first commercially available quantum computer, using one of two methods: discretization, and market graph. Each approach creates several instances of the problem of finding diversified baskets. D-Wave Two’s output is an approximation to this diversified basket, and subsequently the distribution of diversified basket can be determined. Distribution of the diversified basket forms the basis of EADDB. The performance of the proposed EADDB has been evaluated on the Hang-Seng in Hong Kong with 31 assets, one of the benchmark datasets in the OR Library, and has been compared with heuristic algorithms.