Mixture Distribution Scenarios for Investment Decisions with Downside Risk

31 Pages Posted: 29 Aug 2008 Last revised: 16 Jul 2009

See all articles by Leela R. Mitra

Leela R. Mitra

CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications; OptiRisk Systems; Brunel University

Xiaochen (Michael) Sun

HSBC Global Asset Management

Diana Roman

Brunel University London - School of Information Systems, Computing and Mathematics

Gautam Mitra

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

Keming Yu

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

Date Written: August 28, 2008

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.

Keywords: Scenario generation, downside risk, investment choice

JEL Classification: G11

Suggested Citation

Mitra, Leela R. and Sun, Xiaochen (Michael) and Roman, Diana and Mitra, Gautam and Yu, Keming, Mixture Distribution Scenarios for Investment Decisions with Downside Risk (August 28, 2008). Available at SSRN: https://ssrn.com/abstract=1260228 or http://dx.doi.org/10.2139/ssrn.1260228

Leela R. Mitra (Contact Author)

CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications ( email )

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

OptiRisk Systems ( email )

UNICOM R&D House
One Oxford Road
Uxbridge, UB9 4DA
United Kingdom

Brunel University ( email )

United Kingdom

Xiaochen (Michael) Sun

HSBC Global Asset Management ( email )

78 St. James's Street
London, London SW1A 1EJ
United Kingdom

Diana Roman

Brunel University London - School of Information Systems, Computing and Mathematics ( email )

United Kingdom

Gautam Mitra

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications ( email )

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

Keming Yu

Brunel University London - CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications

John Crank Building
Brunel University
Uxbridge, UB8 3PH
United Kingdom

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