基于CVaR的考虑单个风险的组合证券投资研究
摘要
2008年席卷全球的金融危机让众多的机构和个人投资者损失惨重,世界金融业动荡加剧,一些曾经优质的公司也在劫难逃,特别是一些金融类公司的破产让金融界开始觉醒,进一步深入探讨风险防范和风险管理等问题。此次金融危机对投资者进行了一场深刻的风险教育。本文首先阐述了风险的意义,并对VaR及CVaR的国内外的研究历史、发展历程做了较为细致的回顾。在对组合证券投资理论进行深入分析的基础上,对期望效用理论、组合风险和收益的度量等问题进行了分析讨,着重分析了VaR及CVaR风险度量方法,对二者的优点与缺点进行了比较对比,对CVaR风险度量方法与以前的风险度量方法的优越性有了更清楚的了解,特别是基于CVaR的模型求解问题往往可以转化为线性规划问题,具有良好的操作性。本文从CVaR风险度量方法的理论出发,对模型进行了扩展研究,建立了考虑交易成本、行业(板块)、分散化约束等的组合投资均值—CVaR优化模型,进一步考虑单个资产的剧烈变化对组合投资的影响,建立了考虑单个证券的风险约束的均值—CVaR优化模型,并对模型进行了分析研究,该模型能更好地控制极端风险,防止证券投资组合里某个证券因为破产等原因而引起的巨大损失,更好地达到风险防范的目的。最后选取我国证券市场的实际股票数据,应用遗传算法,对考虑单个证券的风险约束的均值—CVaR组合投资模型进行了实证分析,验证了该模型控制风险的有效性和可操作性,具有一定的理论和应用价值。
The overwhelming financial crisis in 2008 has resulted in tremendous losses on the part of numerous organizational as well as individual investors around the globe. With the aggravation of the international financial turbulence, some enterprises that were once considered high-grade could not escape the curse. And the crash of some financial corporations particularly is bringing the financial field into greater awareness of the situation, as well as the need to further explore issues like risk prevention and risk management. The financial crisis constitutes a profound lesson of risk education. This study/thesis starts with the explanation of the meaning of risk, and gives a general overview of the research history and development of VaR and CVaR both at home and abroad. The theory of utility expect, portfolio risk, and the measure of benefits are discussed on the basis of an in-depth analysis of the theory of portfolio investment, with special focus on the VaR and CVaR risk measurement methods, in which the advantages and disadvantages of the two are analyzed, and the advantages of the CVaR risk measurement method against the past ones is highlighted. The CVaR method is featured by good practicability in that the solution of models based on this method can almost always be transferred into linear programming problems.
This thesis is based on the theory of CVaR risk measurement method, and includes an expanded research of the model, in which an optimized Mean-CVaR portfolio model is built that takes into account transaction cost, industry (modules), and decentralized constraints. Also, an optimized Mean-CVaR model that takes into account the risk constraints of individual securities is built and analyzed, with further considerations on the effects that drastic changes of individual assets exert on portfolio. The optimized model can better control extreme risk, and prevent major losses caused by the crash of some security in the portfolio. At last, an empirical analysis is given to the optimized Mean-CVaR model that takes into account the risk constraints of individual securities, with actual data of Chinese security market adopted and genetic algorithm assumed, so that the effectiveness and practicability of risk control of the model are tested, and its theoretical as well as practical value proved.
The overwhelming financial crisis in 2008 has resulted in tremendous losses on the part of numerous organizational as well as individual investors around the globe. With the aggravation of the international financial turbulence, some enterprises that were once considered high-grade could not escape the curse. And the crash of some financial corporations particularly is bringing the financial field into greater awareness of the situation, as well as the need to further explore issues like risk prevention and risk management. The financial crisis constitutes a profound lesson of risk education. This study/thesis starts with the explanation of the meaning of risk, and gives a general overview of the research history and development of VaR and CVaR both at home and abroad. The theory of utility expect, portfolio risk, and the measure of benefits are discussed on the basis of an in-depth analysis of the theory of portfolio investment, with special focus on the VaR and CVaR risk measurement methods, in which the advantages and disadvantages of the two are analyzed, and the advantages of the CVaR risk measurement method against the past ones is highlighted. The CVaR method is featured by good practicability in that the solution of models based on this method can almost always be transferred into linear programming problems.
This thesis is based on the theory of CVaR risk measurement method, and includes an expanded research of the model, in which an optimized Mean-CVaR portfolio model is built that takes into account transaction cost, industry (modules), and decentralized constraints. Also, an optimized Mean-CVaR model that takes into account the risk constraints of individual securities is built and analyzed, with further considerations on the effects that drastic changes of individual assets exert on portfolio. The optimized model can better control extreme risk, and prevent major losses caused by the crash of some security in the portfolio. At last, an empirical analysis is given to the optimized Mean-CVaR model that takes into account the risk constraints of individual securities, with actual data of Chinese security market adopted and genetic algorithm assumed, so that the effectiveness and practicability of risk control of the model are tested, and its theoretical as well as practical value proved.
引文
[1]吴晓求.证券投资学[M].北京:中国人民大学出版社.2004
[2] Markowitz H, Portfolio Selection [J].Journal of Finance, 1952.7:77-91
[3] Tobin J, Liquidity preference as behavior toward risk [J].Rev Econ Studies, 1958.25:239-346
[4] Sharpe W F, A Simplified model for Portfolio Analysis [J].Management Science, 1963.9:277~293
[5] Sharpe W F, Capital asset pricess: a theory of market equilibrium under condition of risk [J].Journal of Finance, 1964.19:425-442
[6] Sharpe W F, Portfolio Theory and Capital Markets [M].New York: McGraw-Hill, 1970
[7] Sharp W, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance, 1964, 19(3): 425-442
[8] Linter J, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets [J]. Review of Economics and Statistics, 1965.47(1): 13-37
[9] Linter J, Security Prices, Risk, and Maximal Gains from Diversification [J].Finance, 1965, 20(4): 587-615.
[10] Jan Mossin, Equilibrium in a Capital Asset Market [J]. Econometrica, 1966, 34(4): 768-783
[11] Ross S, An empirical Investigation of Arbitrage Pricing Theory [J]. Finance, 1980.5:1073-1103
[12] Perold A F, Large-Scale Portfolio Optimization [J]. Management Science, 1984.30:1143-1160
[13] Konno H, Suzuki K, A fast algorithm for solving large scale Mean- variance models by compact factorization of covariance matrices [J]. Journal of the Operations Research Society of Japan, 1992, 35:93-104
[14] Jacobs B I, Levy K N, Markowitz H. Portfolio Optimization with Factors, Scenarios and Realistic Short Posotions [J]. Operations Research, 2005.53(4):1377-1386
[15] Roll R, An Empirical Investigation of Arbitrage Pricing Theory [J]. J Finance,1980.5:1073-1103
[16] Mao J, Models of capital budgeting, E-V versus E-S [J]. Journal of Finance and Quantitative Analysis,1970.5:657-675
[17] Pyle D,Turnovsky S,Safty-first and expected utility maximization in mean-stardard deviation portfolio analysis[J],Rev of Econ,1970,1:75-81
[18] Dantzig G B, Infanger G, Multi-stage stochastic liner programs for portfolio optimization [J]. Ammals of Operations Research, 1993.45:59-76
[19] Watada J, Fuzzy portfolio selection and its applications to decision making [J].Tatra Mountains Mathematical Publication, 1997.13:219-248
[20]吴如海,宋逢明,基金分离下中国股市交易量模型的实证研究[J].管理科学学报,1999,14(1):267-271
[21]马永开,唐小我,不允许卖空的多因素证券组合投资决策模型[J].系统工程理论与实践,2000,20(2):37-43
[22]荣喜民,张喜彬,张世英,组合证券投资模型研究[J].系统工程学报,1998,13(1):81-88
[23]王春峰,效用函数意义下投资组合有效选择问题的研究[J].中国管理科学,2002,10(2):15-19
[24]陈收,汪寿阳,利率随资本结构变化条件下的模型比较分析[J].系统工程理论与实践,2002,(4):39-44
[25]史本山,文忠平,β约束条件下的证券组合风险决策[J].预测,1996,15(5):34-40
[26]陈伟忠,在证券品种可变情况下M-V有效集的漂移分析[J].西安交通大学学报,1997,31(12):106-110
[27]韩其恒,唐万生,机会约束下的投资组合问题[J].系统工程学报,2002,17(1):87-92
[28]徐大江,国际证券投资最大风险极小化的多目标决策模型分析[J].系统工程,1998,16(1):23-26
[29]郑立辉,证券选择的极大极小设计问题分析[J].系统工程理论与实践,2000,20(2):48-51
[30]刘海龙,郑立辉,证券投资决策的微分对策方法[J].系统工程学报,1999,14(21):69-72
[31] Li Z F, Li Z X, Optimal portfolio selection of assets with transaction costs and no short sales [J]. International Journal of Systems Science, 2001.32(2)
[32] Xia Y S, Wang S Y, A new modelfor portfolio selection with order of expected Returns [J]. Computers and Operations Research, 2000.27:409-422
[33]张世英,王东,基金投资行为及其监管的模糊随机理论研究[J].管理科学学报,2000,3(1):58-65
[34]梁建峰,唐万生,有交易费用的组合证券投资的概率准则模型[J].系统工程,2000,19(2):5-10
[35]刘海龙,樊治平,带有风险规避的证券投资最优策略[J].系统工程理论与实践,2000,20(2):44-47
[36]吴冲锋,何勇,期货价格及其模型初探[J].系统工程理论与方法应用,1994,3(4):70-75
[37]李化想,基于CVaR的衍生投资组合优化模型:[硕士学位论文].武汉:武汉理工大学,2008,3.
[38]刘俊山,基于风险测度理论的证券投资组合优化模型:[博士学位论文].上海:复旦大学,2007,4.
[39]刘小茂,田立,VaR与CVaR的对比研究及实证分析[J].华中科技大学学报,2005,10,Vol.33:112-114.
[40]荣喜民,夏江山,基于CVaR约束的指数组合优化模型及实证分析[J].数理统计与管理,2007,Vol.26:621-625.
[41]彭正宇,VaR及其改进模型CVaR[J].科技情报开发与经济,2008,Vol.18.
[42]陈金龙,张维,CVaR与投资组合优化统一模型[J].系统工程理论方法应用,2002,3:68-71.
[43]李朋根,肖春来,基于条件风险价值的投资组合优化模型[J].北方工业大学学报,2007, Vol.19:70-74.
[44]荣喜民,张奎庭,李践,有交易成本的组合投资[J].天津大学学报,2002,35(2),196-198.
[45]蒋敏等,基于多目标CVaR模型的证券组合投资的风险度量和策略[J],经济数学,2007,Vol.12:386-390.
[46]李金华,基于加权CVaR模型的投资组合研究:[硕士学位论文].武汉:武汉理工大学,2007,12.
[47]王雨飞,基于遗传算法的CVaR模型研究:[硕士学位论文].西安:西安电子科技大学,2007,1.
[2] Markowitz H, Portfolio Selection [J].Journal of Finance, 1952.7:77-91
[3] Tobin J, Liquidity preference as behavior toward risk [J].Rev Econ Studies, 1958.25:239-346
[4] Sharpe W F, A Simplified model for Portfolio Analysis [J].Management Science, 1963.9:277~293
[5] Sharpe W F, Capital asset pricess: a theory of market equilibrium under condition of risk [J].Journal of Finance, 1964.19:425-442
[6] Sharpe W F, Portfolio Theory and Capital Markets [M].New York: McGraw-Hill, 1970
[7] Sharp W, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance, 1964, 19(3): 425-442
[8] Linter J, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets [J]. Review of Economics and Statistics, 1965.47(1): 13-37
[9] Linter J, Security Prices, Risk, and Maximal Gains from Diversification [J].Finance, 1965, 20(4): 587-615.
[10] Jan Mossin, Equilibrium in a Capital Asset Market [J]. Econometrica, 1966, 34(4): 768-783
[11] Ross S, An empirical Investigation of Arbitrage Pricing Theory [J]. Finance, 1980.5:1073-1103
[12] Perold A F, Large-Scale Portfolio Optimization [J]. Management Science, 1984.30:1143-1160
[13] Konno H, Suzuki K, A fast algorithm for solving large scale Mean- variance models by compact factorization of covariance matrices [J]. Journal of the Operations Research Society of Japan, 1992, 35:93-104
[14] Jacobs B I, Levy K N, Markowitz H. Portfolio Optimization with Factors, Scenarios and Realistic Short Posotions [J]. Operations Research, 2005.53(4):1377-1386
[15] Roll R, An Empirical Investigation of Arbitrage Pricing Theory [J]. J Finance,1980.5:1073-1103
[16] Mao J, Models of capital budgeting, E-V versus E-S [J]. Journal of Finance and Quantitative Analysis,1970.5:657-675
[17] Pyle D,Turnovsky S,Safty-first and expected utility maximization in mean-stardard deviation portfolio analysis[J],Rev of Econ,1970,1:75-81
[18] Dantzig G B, Infanger G, Multi-stage stochastic liner programs for portfolio optimization [J]. Ammals of Operations Research, 1993.45:59-76
[19] Watada J, Fuzzy portfolio selection and its applications to decision making [J].Tatra Mountains Mathematical Publication, 1997.13:219-248
[20]吴如海,宋逢明,基金分离下中国股市交易量模型的实证研究[J].管理科学学报,1999,14(1):267-271
[21]马永开,唐小我,不允许卖空的多因素证券组合投资决策模型[J].系统工程理论与实践,2000,20(2):37-43
[22]荣喜民,张喜彬,张世英,组合证券投资模型研究[J].系统工程学报,1998,13(1):81-88
[23]王春峰,效用函数意义下投资组合有效选择问题的研究[J].中国管理科学,2002,10(2):15-19
[24]陈收,汪寿阳,利率随资本结构变化条件下的模型比较分析[J].系统工程理论与实践,2002,(4):39-44
[25]史本山,文忠平,β约束条件下的证券组合风险决策[J].预测,1996,15(5):34-40
[26]陈伟忠,在证券品种可变情况下M-V有效集的漂移分析[J].西安交通大学学报,1997,31(12):106-110
[27]韩其恒,唐万生,机会约束下的投资组合问题[J].系统工程学报,2002,17(1):87-92
[28]徐大江,国际证券投资最大风险极小化的多目标决策模型分析[J].系统工程,1998,16(1):23-26
[29]郑立辉,证券选择的极大极小设计问题分析[J].系统工程理论与实践,2000,20(2):48-51
[30]刘海龙,郑立辉,证券投资决策的微分对策方法[J].系统工程学报,1999,14(21):69-72
[31] Li Z F, Li Z X, Optimal portfolio selection of assets with transaction costs and no short sales [J]. International Journal of Systems Science, 2001.32(2)
[32] Xia Y S, Wang S Y, A new modelfor portfolio selection with order of expected Returns [J]. Computers and Operations Research, 2000.27:409-422
[33]张世英,王东,基金投资行为及其监管的模糊随机理论研究[J].管理科学学报,2000,3(1):58-65
[34]梁建峰,唐万生,有交易费用的组合证券投资的概率准则模型[J].系统工程,2000,19(2):5-10
[35]刘海龙,樊治平,带有风险规避的证券投资最优策略[J].系统工程理论与实践,2000,20(2):44-47
[36]吴冲锋,何勇,期货价格及其模型初探[J].系统工程理论与方法应用,1994,3(4):70-75
[37]李化想,基于CVaR的衍生投资组合优化模型:[硕士学位论文].武汉:武汉理工大学,2008,3.
[38]刘俊山,基于风险测度理论的证券投资组合优化模型:[博士学位论文].上海:复旦大学,2007,4.
[39]刘小茂,田立,VaR与CVaR的对比研究及实证分析[J].华中科技大学学报,2005,10,Vol.33:112-114.
[40]荣喜民,夏江山,基于CVaR约束的指数组合优化模型及实证分析[J].数理统计与管理,2007,Vol.26:621-625.
[41]彭正宇,VaR及其改进模型CVaR[J].科技情报开发与经济,2008,Vol.18.
[42]陈金龙,张维,CVaR与投资组合优化统一模型[J].系统工程理论方法应用,2002,3:68-71.
[43]李朋根,肖春来,基于条件风险价值的投资组合优化模型[J].北方工业大学学报,2007, Vol.19:70-74.
[44]荣喜民,张奎庭,李践,有交易成本的组合投资[J].天津大学学报,2002,35(2),196-198.
[45]蒋敏等,基于多目标CVaR模型的证券组合投资的风险度量和策略[J],经济数学,2007,Vol.12:386-390.
[46]李金华,基于加权CVaR模型的投资组合研究:[硕士学位论文].武汉:武汉理工大学,2007,12.
[47]王雨飞,基于遗传算法的CVaR模型研究:[硕士学位论文].西安:西安电子科技大学,2007,1.