A survey of computational approaches to portfolio optimization by genetic algorithms

The portfolio optimization problem has become a standard financial engineering problem since the pioneering work of Markowitz on Modern Portfolio Theory. It aims to find an optimal allocation of capital among a set of assets by simultaneously minimizing the risk and maximizing the return of the investment. In the theoretical case of linear constraints, this problem is basically solved by quadratic programming. However, real-life financial market imposes some nonlinear constraints such as cardinality constraints, which limit the number of assets held in the portfolio, minimum transaction lots constraints, which require holding discrete units in assets, multiples of minimum lots, e.g., 100 or 200 shares, or transaction costs, which tend to eliminate small holdings. If we take into account these constraints, our problem becomes computationally intractable in theoretical sense, e.g., NPhard. GA, genetic algorithm, is a collective term describing family of stochastic algorithms based on the natural selection principle – survival of the fittest, and is widely adopted in many fields. In fact, many empirical studies have reported that GA can find good approximate solutions for NP-hard problems. Already various GA-based approaches have been proposed to solve portfolio optimization problems. We survey more than 10 state-of-the-art approaches on the topic, categorize them, compare their computational results and provide brief descriptions of the techniques involved. The aim of this paper is to provide a good guide to the application of GA to portfolio optimization.