Investment Opportunities, Uncertain Implicit Transaction Costs and Maximum Downside Risk in Dynamic Stochastic Financial Optimization

Abstract

A dynamic stochastic methodology in optimal portfolio selection that maximizes investment opportunities and minimizes maximum downside risk while taking into account implicit transaction costs incurred in initial trading and in subsequent rebalancing of the portfolio is proposed. The famous mean-variance model (Markowitz, 1952) and the mean absolute deviation model (Konno and Yamazaki, 1991) both penalize gains (upside deviations) and losses (downside deviations) in the same way. However, investors are concerned about downside deviations and are happy of upside deviations. Hence the proposed model penalizes only downside deviations and, instead, maximizes upside deviations. The methodology maintains transaction cost at the investor's prescribed level. Dynamic stochastic programming is employed with stochastic data given in the form of a scenario tree. Consideration a set of discrete scenarios of asset returns and implicit transaction costs is given, taking deviation around each return scenario. Model validation is done by comparing its performance with those of the mean-variance, mean absolute deviation and minimax models. The results show that the proposed model generates optimal portfolios with least risk, highest portfolio wealth and minimum implicit transaction costs.Keywords: Investment opportunities; downside risk; uncertain implicit transaction costs.JEL Classifications: C01; C58; D81; G11