Cardinality Constrained Portfolio Optimization on an Ising Machine

In this paper, we propose an Ising-machine based method for solving the cardinality constrained mean-variance portfolio optimization problem (CCMVPOP), which is an NP-hard problem and often solved using metaheuristics. Firstly, we formulate this problem as a binary quadratic program (BQP) to be solved by an Ising machine-software system. Namely, we propose formulations for each objective and constraint using binary variables exclusively. Furthermore, we evaluate and compare well known integer to binary variable encoding as well as propose a new encoding for the CCMVPOP. The evaluation is done by studying which encoding converges the fastest to the highest return over risk collection of assets for a given data set which represent stocks involved in a capital market index. Used data range from capital market index composed of 31 assets for the smallest and up to 225 for the largest. The experimental results confirm that the proposed formulations to the CCMVPOP for an Ising machine-software system are effective.