基于高阶矩风险控制的贷款组合优化模型

Optimal model of loan portfolio based on the higher central-moment constraints

以银行各项资产组合收益率最大化为目标函数,以VaR来控制贷款组合的风险价值,以偏度约束来控制贷款组合收益率的整体分布向大于均值的方向倾斜、以减少发生总体损失的单侧风险,以峰度来控制贷款组合收益率分布出现极端情况的双侧风险,建立了资产分配的收益率均值-方差-偏度-峰度模型.本模型的创新与特色是通过峰度约束控制了贷款组合收益率向极端损失偏离的程度.在马可维茨均值-方差模型的基础上,增加了偏度和峰度参数,建立了收益率均值-方差-偏度-峰度模型.模型通过方差约束,控制了组合收益率偏离均值的离散程度:通过偏度约束,控制了组合收益率总体分布向损失一侧偏离的程度:通过峰度约束,控制了组合收益率出现极端损失或收益的可能性.模型从多个角度控制了贷款组合的风险,拓展了经典的均值-方差优化组合思路.

By using VaR as risk control of the loans portfolio, using skewness constrain to avoid the distribution of loan portfolio yield toward left of mean to reduce left side risk of general risk, using kurtosis constrain as the control of the distribution＇s fat tail on both sides to reduce the extreme loss, the optimal model of loan portfolio which targets the maximum rate of return on bank loans portfolio based on the higher central-moment constraints is set up. The contribution of this article is we identified the importance of using higher central-moments, especially the kurtosis in bank loans portfolio optimization. Addition to the classic Markowitz model, we build a mean-variance-skewness-kurtosts model which introduced kurtosis constrain to reduce the extreme loss, skewness constrain to avoid general risk and VaR as risk control of the loans portfolio. The model we built controls the portfolio＇s risk from multi-angle and extends the classic mean-variance optimal theory.