Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate

Short selling strategy leads to a portfolio with significantly better risk-return structure compared to the standard approach. Moreover, investors can use risk-neutral interest rate to increase the return of the portfolio. In this paper, we study the cardinality-constrained mean-variance portfolio optimization model with and without short selling and risk-neutral interest rate. First, to avoid negative investment in stocks with no short selling position, the non-negativeness of the product of each stock's return to the proportion of investment on it is added to the model as a constraint. Then, we further present an improved model, where instead of determining the term of the short rebate according to the proportion of the total funds invested, it is determined according to the return. Finally, all models are compared using the data set of the S&P 500 index, Communication Service.