A study on optimal share pledge rate based on bilateral risk-CVaR of pledgee

Abstract

This paper proposes the optimal pledge rate model based on the pledgee's bilateral risk-CVaR and dual-objective planning. First, a bilateral risk-CVaR model is constructed, for which a nonparametric kernel estimation method is presented, with a comparative analysis of the efficient frontier for “mean-variance”, “mean-CVaR”, and “mean-bilateral risk CVaR”. Second, it establishes a dual-objective planning model by the objectives of bilateral risk-CVaR and expected return of the pledgee, and accordingly develops an optimal pledge rate model combined with objective deviation, priority factor, and entropy method. Finally, the relationships between the pledge rate, the number of pledged shares, and the expected return are explored through simulation. The results illustrate that: (i) There are sequential inclusion relationships between the “mean-bilateral risk CVaR”, the “mean-CVaR” considering only the downside risk, and the “mean-variance” efficient sets of share pledge rate. (ii) As the number of shares increases, the pledgee's expected return also rises, and its sensitivity to the pledge rate grows. (iii) When the pledgee's expected return fixes, the number of pledged shares and the pledge rate have a U-shaped relationship. As it increases, the number of pledged shares rises, but the variation range of the pledge rate gradually decreases, and the pledgor's default risk declines.