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

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.