Stock Market Portfolio Optimization

Abstract

Taking decisions when optimizing results of some problem is a very crucial task. Optimizing a stock market portfolio is a multi-objective optimization problem. While optimizing a stock market portfolio, investors try to get maximum pro t (return) on the capital invested in a bunch of stocks, at the same time they try to minimize the chances of loss (risk). The decision taken by investors are selecting a bunch of stock for investment and distributing investment amount between them. Markowitz mean-variance model optimize portfolio for desired return at minimum possible risk. But, it not possi- ble to employ cardinlity constraint in Markowitz model. When cardinality constraint is added to Markowitz model, it turned into Mixed Integer Quadratic Programming prob- lem, which is an NP-Hard problem. This research work optimize a cardinality constrained portfolio using genetic algorithm and proposes a new fitness function that consider in- vestors desired return for optimization. This research work is a carried out in two steps, first identifying k stocks (cardinality constraint) for investment using genetic algorithms, and then distributing the investment amount among them using quadratic programming. This research work is carried out on 5 benchmark datasets HangSeng 31, DAX 100, FTSE 100, S&P 100, and Nikkei 225. The experimental results shows that this approach is as good as standard Markowitz model.