Long-Short Portfolio Optimisation in the Presence of Discrete Asset Choice Constraints and Two Risk Measures

36 Pages Posted: 12 Mar 2008

See all articles by Ritesh Kumar

Ritesh Kumar

Indian Institute of Management (IIM), Calcutta

Gautam Mitra

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

Diana Roman

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

Abstract

This paper considers long-short portfolio optimization in the presence of two risk measures: variance and Conditional Value at Risk (CVaR) and asset choice constraints of (i) buy, sell and holding thresholds (ii) cardinality restrictions on the number of stocks to be held in the portfolio. The mean-variance-CVaR model improves upon the classical mean-variance model by controlling both the variance and CVaR of the resulting return distribution. Our long-short extension to the mean-variance-CVaR model incorporates many financial institutions' practices in respect of the short decisions. We highlight that introducing short selling leads to superior choice of portfolios, with higher expected return and much lower risk exposures, as characterized by CVaR and variance. We further analyze the effects of applying buy and sell thresholds and cardinality restrictions on the number of stocks. Such constraints are of practical importance but make the efficient frontier discontinuous. When stocks' returns are represented as discrete random variables, the formulation leads to a Quadratic Mixed Integer Program (QMIP). We conclude that the long-short model with cardinality constraint is superior to the long only model even without cardinality constraint. The models are tested on real data drawn from the FTSE 100 index.

Keywords: investment, portfolio, risk, short-selling

JEL Classification: D81, G11, C60

Suggested Citation

Kumar, Ritesh and Mitra, Gautam and Roman, Diana, Long-Short Portfolio Optimisation in the Presence of Discrete Asset Choice Constraints and Two Risk Measures. Available at SSRN: https://ssrn.com/abstract=1099926 or http://dx.doi.org/10.2139/ssrn.1099926

Ritesh Kumar (Contact Author)

Indian Institute of Management (IIM), Calcutta ( email )

IIM Calcutta
Joka, Diamond Harbour Road
Calcutta 700104, West Bengal
India

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

Diana Roman

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

United Kingdom

Register to save articles to
your library

Register

Paper statistics

Downloads
453
Abstract Views
2,281
rank
61,877
PlumX Metrics