Case study: Application of goal programming in portfolio selection

Abstract

A classic problem in operational research and finance is the selection of a portfolio of shares, investments, or financial products. The set of shares chosen and their percentage of the total portfolio are the decision variables of this model. The classic models tend to consider the minimisation or some measure of risk and the maximisation of return, with an ‘efficient frontier’ of possible portfolios being considered in the resulting bi-objective space. Markowitz (1952) introduced the mean-variance model for portfolio selection. In this model, the mean represents average return and variance represents a measure of risk. It can be seen that this problem is a multiple objective one by definition. It can also be expanded to contain further objectives related to issues such as liquidity, portfolio size or composition, social responsibility, or size of dividends (Steuer et al., 2007). If the decision makers (i.e. the portfolio manager or owners) have set goals for levels of return and risk or other measures of portfolio performance then the goal programming framework is a natural choice for modelling and solving this problem.