OSCAR: an asset selection heuristic for cardinality constrained portfolio optimization

Abstract

Markowitz proposed a mean-variance model to select a portfolio that minimizes risk for a given return. To minimize risk, diversifying is known to be a key concept. However, a widely diversified portfolio contains some problems in a practical manner. First, it is hard for a portfolio manager to handle the portfolio due to its “well-diversified” non-zero components. Also, the high transaction cost makes the Markowitz model hard to use intactly in practice. To solve this problem, researchers added a cardinality constraint that restricts the number of assets contained in a portfolio to the original Markowitz model. Unfortunately, the cardinality constraint exacerbates the problem from a simple mean-variance model to a NP-hard problem. Since deriving an exact optimal portfolio in a NP-hard problem takes long time, recent studies focused on developing efficient algorithms. Here, we propose a novel heuristic that solves for a Sharpe ratio maximization problem and derives high-quality solution in a short time. Our heuristic first select assets satisfying the cardinality constraint. With the selected assets, we reoptimize the original Markowitz problem without the cardinality constraint.