基于VaR收益率约束的贷款组合优化决策模型

本文以贷款的收益率为金融资产的收益,以贷款收益率的波动为标准反映贷款风险,在VaR约束下,以拉格朗日乘子法为工具求二次规划,建立了在既定组合收益范围内,组合风险最小的贷款组合优化决策模型。该模型的特点一是以收益率最大损失的形式、而不是收益额的形式来反应VaR,使组合决策分析更为方便。二是考虑了风险之间的相关性,用组合VaR的收益率最大损失来控制贷款收益率的风险限额;使贷款的分配直接反映了商业银行的风险承受能力。三是在合理的目标收益范围内,给定任意一个决策者期望的收益率,总能找到对应的风险最小的贷款组合,由此模型求出的有效边界,为组合贷款的优化决策提供了科学的方法。

Decision-making Model of Loan's Portfolio Optimization Based on the Yield of VaR

Taking the loan’s yields as the profit of financial asset,taking the volatility of loan’s yields as reflection of loan’s risk,under the constraint of Value at Risk(VaR),based on the solution of quadratic programming,a decision-making model of loan-risk portfolio optimization is set up with the minimum risk within the feasible range of definite portfolio yield.There are three characteristics of the model:Using yield rate of maximum loss but yield amount reflects VaR,so it becomes convenient to the decision analysis.Taking risk correlation into account,it controls risk limitation with the maximum loss on yield rate of VaR,so the ability for risk tolerance of commercial bank is reflected by loan’s distribution or allocation.If given the objective in the feasible range,and given the yield rate as decision-maker expected,the loan’s portfolio to the minimum risk always can be found.The efficient boundary which was given by this model provides a scientific method for the decision-making of the loan’s portfolio.