Journal of Risk

Long–short portfolio optimization in the presence of discrete asset choice constraints and two risk measures

Ritesh Kumar, Gautam Mitra, Diana Roman


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 regarding buying and selling and holding thresholds, and cardinality restrictions on the number of stocks to be held in the portfolio. The mean- variance-CVaR model is based on the mean-variance approach but has an additional constraint on CVaR. Our empirical investigations show that short-selling strategies lead to a superior choice of portfolios, with higher expected return and much lower risk exposures. In particular, the downside risk can be considerably reduced by introducing short selling. Our long-short extension to the mean-variance-CVaR model incorporates the practice of many financial institutions with regard to "short" decisions. Numerical experiments with the resulting model, which is a quadratic mixed integer program, are conducted on real data drawn from the FTSE 100 index.

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