Optimal portfolio selection with stochastic maximum downside risk and uncertain implicit transaction costs

Abstract

A multi-stage stochastic optimal portfolio policy that minimizes downside risk in the presence of uncertain implicit transaction costs is proposed. As asset returns in economic recessions and booms are characterised by extreme movements, some individual stocks show an extreme reaction while others exhibit a milder reaction. The study therefore considers a risk-averse and conservative investor who is highly concerned about the performance of his portfolio in an economic recession environment. Maximum negative deviation is taken as the downside risk and stochastic programming is applied with stochastic data given in the form of a scenario tree. A set of discrete scenarios of asset returns is considered, taking the deviation around each return scenario. Thus uncertainties of asset returns and implicit transaction costs are represented by discrete approximations of a multi-variate continuous distribution. The portfolio is rebalanced at discrete time intervals as new information on returns get realised. First-stage optimal-portfolio results show that implicit transaction costs vary from 7.1% to 16.7% of returns on investment.