基于下偏度最小化贷款组合优化模型
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摘要
贷款组合优化决策是商业银行在综合考虑其贷款风险和贷款收益的前提下,从众多贷款申请企业中选取一组最优贷款对象的过程,它是商业银行信贷管理的核心问题。商业银行通过调整资金的运用,改善其资产配置水平,从而实现资产的流动性、盈利性和安全性。受全球金融危机的影响,各行业生产经营困难加剧,以至于导致商业银行合理协调资金配置实现“三性”平衡的难度增大,商业银行亟待探讨新的资金管理及风险控制手段,因此基于风险控制的贷款组合优化决策模型研究具有重要的现实意义。
本论文共五章进行阐述。第一部分是绪论,主要介绍本文的选题意义及国内外资产负债优化管理理论的研究现状；第二部分是模型原理阐述,为模型构建奠定理论基础；第三部分是模型构建,构建目标函数及大量约束条件；第四部分为应用实例与结果分析,通过实证及对比分析证明该模型的合理性和有效性；第五部分是结论。
本文的主要研究工作如下：
(1)揭示了基于下偏度的损失控制原理。根据偏度原理,运用贷款组合下偏度来衡量收益率的概率密度函数的“左尾”的偏斜方向和偏斜程度。大量研究表明,贷款组合的收益率并非服从正态分布,而是呈现“尖峰厚尾”的形状,而收益率概率分布的“左尾”表示实际收益率低于预期收益率的概率,是真正的贷款组合风险,因此,用下偏度控制风险,更符合投资者的心理,也更符合实际。
(2)构建了基于下偏度最小化的贷款组合优化模型。依据下偏度损失控制原理,结合数学规划方法,以投资者风险厌恶为出发点,以组合风险价值VaR为约束条件,构建基于下偏度最小化的贷款组合优化模型,反映贷款组合的“左尾”风险,减少极值事件发生对银行造成的重大损失。
本文的特色与创新表现为两个方面：一是下偏度不要求贷款收益服从正态分布,能够很好地反映收益率分布的“左尾”,降低商业银行贷款组合发生重大损失的概率；二是下偏度可以真实反映贷款的本质,符合投资者的心理,并且可以反映多笔贷款之间的相关联系,解决现有模型的解析能力不足的问题。
Loan portfolio optimization decision is a process that the commercial banks select a group of optimal loan objects through many loan application enterprises based on the comprehensive consideration of the loan risk and loan earnings. It is the core problem of the commercial bank credit management. The commercial bank improve its asset allocation level by adjusting funds apply, so as to realize the liquidity, profitability and safety of assets ("three properties").The global financial crisis made the business grow difficultily, so that increased the difficulty of keeping "three-properties" for commercial banks. Commercial banks must explore a new method of capital management and risk control immediately. So, Loan optimization model based on risk controlling has important practical significance.
The paper is divided into five chapters. The first part is the introduction, mainly introduces the significance and the development process and research status of portfolio theory. The second part expatiates the basic theory of the model,so can provide the theoretical basis for the model construction. The third part is the construction of optimal model of loan portfolio, including target function and a large number of constraints.The forth part is the practical analysis, proving that the model is reasonable and effective through empirical analysis and comparison. The last part is the conclusion.
The main results of the paper are as follows;
(1) The paper revealed the theory of loss control based on downside skewness. According to the skewness principle, the paper measured the deflection direction and deflection degree of yield's probability density function by using downside skewness of the loan portfolio. A mass of researches indicated that loan portfolios yields was not normal distribution, but the distribution of "peak thick tail".The "left end" of yields probability distribution is the real risk, and shows the probability that the actual yields less than the expected rate. So, controlling the risk with the downside skewness satisfies the investor's psychological and be more actual.
(2) The paper constructed optimization model of downside skewness minimum on loans portfolio. Controlling the risk based on the principle downside skewness, combining with the mathematical programming method, investors'risk aversion as a starting point, value at risk as constraint of assets'risk, then the optimization model of downside skewness minimum on loans portfolio is set up. The model can reflect the "left rail" of the loan's yield primly, and reduce the probability of serious losses of commercial bank.
The contribution of this paper lies on two aspects. Firstly, the downside skewness don't demand that the loan's yield is normal distribution, reflect the "left rail" of the loan's yield primely, and reduce the probability of serious losses of commercial bank. Secondly, Measuring loans risk by the downside skewness could meet the investor's psychology, reflect the relationship among loans and resolve the problem that the existing model analytical ability of existing model is poor.
本论文共五章进行阐述。第一部分是绪论,主要介绍本文的选题意义及国内外资产负债优化管理理论的研究现状；第二部分是模型原理阐述,为模型构建奠定理论基础；第三部分是模型构建,构建目标函数及大量约束条件；第四部分为应用实例与结果分析,通过实证及对比分析证明该模型的合理性和有效性；第五部分是结论。
本文的主要研究工作如下：
(1)揭示了基于下偏度的损失控制原理。根据偏度原理,运用贷款组合下偏度来衡量收益率的概率密度函数的“左尾”的偏斜方向和偏斜程度。大量研究表明,贷款组合的收益率并非服从正态分布,而是呈现“尖峰厚尾”的形状,而收益率概率分布的“左尾”表示实际收益率低于预期收益率的概率,是真正的贷款组合风险,因此,用下偏度控制风险,更符合投资者的心理,也更符合实际。
(2)构建了基于下偏度最小化的贷款组合优化模型。依据下偏度损失控制原理,结合数学规划方法,以投资者风险厌恶为出发点,以组合风险价值VaR为约束条件,构建基于下偏度最小化的贷款组合优化模型,反映贷款组合的“左尾”风险,减少极值事件发生对银行造成的重大损失。
本文的特色与创新表现为两个方面：一是下偏度不要求贷款收益服从正态分布,能够很好地反映收益率分布的“左尾”,降低商业银行贷款组合发生重大损失的概率；二是下偏度可以真实反映贷款的本质,符合投资者的心理,并且可以反映多笔贷款之间的相关联系,解决现有模型的解析能力不足的问题。
Loan portfolio optimization decision is a process that the commercial banks select a group of optimal loan objects through many loan application enterprises based on the comprehensive consideration of the loan risk and loan earnings. It is the core problem of the commercial bank credit management. The commercial bank improve its asset allocation level by adjusting funds apply, so as to realize the liquidity, profitability and safety of assets ("three properties").The global financial crisis made the business grow difficultily, so that increased the difficulty of keeping "three-properties" for commercial banks. Commercial banks must explore a new method of capital management and risk control immediately. So, Loan optimization model based on risk controlling has important practical significance.
The paper is divided into five chapters. The first part is the introduction, mainly introduces the significance and the development process and research status of portfolio theory. The second part expatiates the basic theory of the model,so can provide the theoretical basis for the model construction. The third part is the construction of optimal model of loan portfolio, including target function and a large number of constraints.The forth part is the practical analysis, proving that the model is reasonable and effective through empirical analysis and comparison. The last part is the conclusion.
The main results of the paper are as follows;
(1) The paper revealed the theory of loss control based on downside skewness. According to the skewness principle, the paper measured the deflection direction and deflection degree of yield's probability density function by using downside skewness of the loan portfolio. A mass of researches indicated that loan portfolios yields was not normal distribution, but the distribution of "peak thick tail".The "left end" of yields probability distribution is the real risk, and shows the probability that the actual yields less than the expected rate. So, controlling the risk with the downside skewness satisfies the investor's psychological and be more actual.
(2) The paper constructed optimization model of downside skewness minimum on loans portfolio. Controlling the risk based on the principle downside skewness, combining with the mathematical programming method, investors'risk aversion as a starting point, value at risk as constraint of assets'risk, then the optimization model of downside skewness minimum on loans portfolio is set up. The model can reflect the "left rail" of the loan's yield primly, and reduce the probability of serious losses of commercial bank.
The contribution of this paper lies on two aspects. Firstly, the downside skewness don't demand that the loan's yield is normal distribution, reflect the "left rail" of the loan's yield primely, and reduce the probability of serious losses of commercial bank. Secondly, Measuring loans risk by the downside skewness could meet the investor's psychology, reflect the relationship among loans and resolve the problem that the existing model analytical ability of existing model is poor.
引文
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[2]中国金融稳定报告(2011)[EB].[2011,06,14].http://www.pbc.gov.cn/publish/jinrongwendingju/370/2011/2011061417173485084674 1/20110614171734850846741_.html
[3]Markos A. Katsoulakis, Andrew J. Majda, Dionisio G. Vlachos. Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. Journal of Computational Physics,2003,186:250-178.
[4]陈鹏,吴冲锋,李为冰.信用风险度量和管理方法研究[J].管理工程学报,2002,6(6)485-490.
[5]Markowitz, H. Portfolio Selection:Efficient Diversification of Investments. New York:John Wiley&Son, Inc.1959.
[6]Gordon Alexander and Alexander Baptista. A VaR-Constrained Mean-Variance Model: Implications for Portfolio Selection and the Basle Capital Accord. Working paper, University of Minnesota.2001(7).
[7]Kaplanski, Guy. Traditional beta,downside risk beta and market risk premiums.The Quarterly Review of Economics and Finance Volume:44, Issue:5,2004(12):636-653.
[8]W. F. Sharpe. A Simiplified Modei for Portfolio Analysis. Management Science,1963, 10(2):277-292.
[9]Jensen M C. Risk:the Pricing of Capital Assets and the Evaluation of Investment Portfolio. Journal of Business.1969.4
[10]Ross S A. The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory. 1976(12):343-346.
[11]Jarrow, R, D. Lando and S. Turnbull. A Markov Model for the Term Structure of Credit Risk Spreads. Review of Finanical Studies,1997,10:481-523.
[12]Merton,R. On the pricing of corporate debt:The risk structure of interest rates. Journal of Finance,1974, (28):449-470.
[13]Merton, R. On the Pricing of Corporate debt:the Risk Structure of Interest Rates [J]. Journal of Financial Economics.1977(5):241-249.
[14]Michael B. Gordy. a Compatative Anatomy of Credit Risk Models. Journal of Banking &Finance 2000(24):119-149.
[15]Wilson, T. Portfolio Credit Risk I.Risk 10(9),1987,9.
[16]Markowitz, H. Portfolio Selection[J]. Journal of Finance.1952,7(1):77-91.
[17]Li Duan, Ng Wan-Lung. Optimal Dynamic Portfolio Selection:Multiperiod Mean-VaRiance Formulation[J]. Mathematical Finance.2000,10(3):387-406.
[18]姜灵敏.基于综合风险收益的贷款组合优化决策[J].数理统计与理.2006,24(6)：84-88.
[19]迟国泰,洪忠诚,赵志宏.基于行业组合的贷款总体风险优化决策模型[J].管理学报.2007,4(4)：398-403.
[20]Monica B, Loriana P.Value-at-Risk:a Multivariate Switching Regime Approach[J]. Journal of Emprical Finance.2000,7(5):531-554.
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