Mixture Distribution Scenarios for Investment Decisions with Downside Risk

Abstract

Recently considerable attention has been given to downside risk control in the context of portfolio choice; see Sortino and Satchell (2005). We propose an integrated model for portfolio choice in which downside risk is considered explicitly at the stage of the scenario generation which describes asset price behaviour and in the subsequent step of portfolio construction. The scenario generation method is deliberately chosen to create a mixture discrete distribution for future asset returns. The behaviour and dependence of asset returns in the lower tails are captured using a discrete approximation to a multivariate copula model. The upside returns are modelled using a discrete approximation to a multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model. The asset allocation problem is based on an extension of the mean-variance approach, with an additional conditional value at risk (CVaR) constraint. The implementation of the model is that of a long short portfolio of exchange traded funds (ETF) of equity indices. Computational results of validating the model and backtesting are presented.