证券投资风险度量方法及其应用研究
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摘要
证券市场上的投资者都希望选择最适合自己资产或者资产组合进行投资,以获得最大的效用,即最大的满意程度。众所周知,证券市场上的投资收益往往是不确定的,因而投资者从中产生的效用也是不确定的,也就是存在风险,因此投资者也只能在资产的期望收益和风险这两个投资效用的主要影响因素中进行权衡取舍,以达到最大的期望效用。本文主要关心的问题是,证券的投资风险该如何度量并控制,以及投资者的效用具体是怎样去度量的。
本论文在已有的证券投资风险度量的基础上,讨论了信息熵这种风险度量方法的基本性质以及它与方差这种传统的风险度量方法的联系和区别。然后本论文简单介绍了行为投资组合理论以及非理性投资者的认知风险怎么度量。接下来,本论文重点讨论了假设各项资产收益率的联合分布分别为多元正态分布、多元t分布、多元(分段)均匀分布时投资组合收益率的信息熵怎么计算以及对应的优化模型,并利用多元分段均匀分布去逼近一般的多元连续型分布,从而得出当各项资产的收益率相互独立多元连续型时的近似最优投资组合比例。最后,本论文引入了模糊环境,讨论了模糊环境下怎样选择投资组合比例使得不同风险态度的投资者对投资组合收益率的期望值和风险的综合效用最大化,并进行实证分析。
All the investors in the security market hope to find the best assets or portfolio so as to get the highest utility, or the largest extent of satisfaction. As is known to all, almost every asset has an uncertain return, which results in an uncertain utility to the investors, and that is where the risk comes from. So the investors have to weigh between the two most significant factors which influence the utility of the asset---the expected return and the risk in order to gain the highest utility. The focus of the thesis is how to measure and control the risk of the security risk and how to measure the utility investors gain from the assets.
On the basis of the traditional methods to measure the risk of security investment, we discuss information entropy--- another method to measure the risk of security investment as well as its properties and its relations and differences to variance---the classical method to measure the risk of security investment. Then, we introduce behavioral portfolio theory and how to measure the perceptional risk of irrational investors。Furthermore, we focus on the information entropy of the return of the portfolio on condition that the joint distribution of the return of each asset is a multivariate normal distribution, a multivariate t distribution and a multivariate (piecewise) uniform distribution and the respective optimization model, and we use the multivariate (piecewise) uniform distribution to approximate a multivariate continuous distribution in order to get the approximate optimal portfolio weight on condition that the returns of the assets are independent to each other and the distribution of each asset is a multivariate continuous distribution. Finally, we introduce the fuzzy environment and discuss how to select the portfolio weight so as to maximize the integrated utility of the expectation and risk of the return of the portfolio for investors with different attitudes to the risk on the fuzzy environment and use the models in empirical analysis.
本论文在已有的证券投资风险度量的基础上,讨论了信息熵这种风险度量方法的基本性质以及它与方差这种传统的风险度量方法的联系和区别。然后本论文简单介绍了行为投资组合理论以及非理性投资者的认知风险怎么度量。接下来,本论文重点讨论了假设各项资产收益率的联合分布分别为多元正态分布、多元t分布、多元(分段)均匀分布时投资组合收益率的信息熵怎么计算以及对应的优化模型,并利用多元分段均匀分布去逼近一般的多元连续型分布,从而得出当各项资产的收益率相互独立多元连续型时的近似最优投资组合比例。最后,本论文引入了模糊环境,讨论了模糊环境下怎样选择投资组合比例使得不同风险态度的投资者对投资组合收益率的期望值和风险的综合效用最大化,并进行实证分析。
All the investors in the security market hope to find the best assets or portfolio so as to get the highest utility, or the largest extent of satisfaction. As is known to all, almost every asset has an uncertain return, which results in an uncertain utility to the investors, and that is where the risk comes from. So the investors have to weigh between the two most significant factors which influence the utility of the asset---the expected return and the risk in order to gain the highest utility. The focus of the thesis is how to measure and control the risk of the security risk and how to measure the utility investors gain from the assets.
On the basis of the traditional methods to measure the risk of security investment, we discuss information entropy--- another method to measure the risk of security investment as well as its properties and its relations and differences to variance---the classical method to measure the risk of security investment. Then, we introduce behavioral portfolio theory and how to measure the perceptional risk of irrational investors。Furthermore, we focus on the information entropy of the return of the portfolio on condition that the joint distribution of the return of each asset is a multivariate normal distribution, a multivariate t distribution and a multivariate (piecewise) uniform distribution and the respective optimization model, and we use the multivariate (piecewise) uniform distribution to approximate a multivariate continuous distribution in order to get the approximate optimal portfolio weight on condition that the returns of the assets are independent to each other and the distribution of each asset is a multivariate continuous distribution. Finally, we introduce the fuzzy environment and discuss how to select the portfolio weight so as to maximize the integrated utility of the expectation and risk of the return of the portfolio for investors with different attitudes to the risk on the fuzzy environment and use the models in empirical analysis.
引文
[1] Markowitz H. Portfolio Selection[J]. Journal of Finance,1952(7).
[2] Roy,A. Safety—first and the Holding of Assets[J]. Econometrica,1952(20).
[3] Tobin,J. Liquidity Preference as Behavior Towards Risk[J]. Review of Economic Studies,1958(2).
[4] William,F.Sharpe. A Simplified Model of Portfolio Analysis[J]. Management Science,1963(9).
[5]徐丽梅.现代投资组合理论及其分支的发展综述[J].首都经济贸易大学学报,2006(4):75-79.
[6]徐少君.投资组合理论发展综述[J].浙江社会科学,2004(4):198-202.
[7]蒲玮.证券投资组合理论综述[J].科学与管理,2008(1):12-14.
[8]欧阳光中,李敬湖.证券组合与投资分析[M].高等教育出版社,1996:27-30.
[9]何信《金融风险度量及其应用研究》,天津大学博士学位论文,2004年6月;
[10] Huang J C, Chiu C L, Lee M C. Hedging with zero value at risk hedge ratio [J]. Applied Financial Economics,2006,16(3):259-269.
[11] Richard D F H, Shen J. Hedging and value at risk [J]. Journal of Futures Markets,2006,26(4):369—390.
[12] Gordon J A, Alexandre M B. A comparison of VaR and CVaR constraints on portfolio selection with the Mean—Variance model [J]. Management Science,2004,50(9):1261-1273.
[13]百度百科. http://baike.baidu.com/view/936.html?wtp=tt.
[14]薛春光.风险度量与证券投资组合模型的研究[D].新疆:新疆大学运筹学与控制论专业,2007: 8-13,25-26.
[15]鲁晨光.投资组合的熵理论和信息价值[M].合肥:中国科学技术大学出社,1997:187-188.
[16]龚光鲁,钱敏平.应用随机过程教程及在算法和智能计算中的随机模型[M].北京:清华大学出版社,2004:243-245.
[17]杨丽娟《基于最小叉熵计算VaR的模型》,“商场现代化”2008年12月(上旬刊)总第559期;
[18]杨春鹏、姜伟、吕学梁《Shannon’s Entropy and Risk Perception》,“青岛大学学报”2007年6月第2期;
[19]杨春鹏、姜伟、吕学梁《投资心理与基于信息熵的认知风险》,“青岛大学学报”2007年9月第3期
[20]李华,李兴斯.证券投资组合中的熵优化模型研究[J].大连理工大学报,2005(1):153-156.
[21]范进.熵理论在信息源选择和信息识别中的应用[J].华东经济管理,2006(7):57-61.
[22]曾建华,汪寿阳.一个基于模糊决策理论的投资组合模型[J].系统工程理论与实践, 2003(1):99-103.
[23]宋喜民,苏丽.有交易成本的模糊最优化投资[J].数学的实践与认识,2003(11):27-29.
[24] Bem Daryl J.,An Experimental Analysis of Self-Persuasion[J].Journal of Experimental Social Psychology,1965,(1):199—218.
[25] Shiller R. Measuring Bubble Expectations and Investor Confidence[J].Journal of Psychology and Financial Markets,2000,(1):49—60.
[26] Danie1 K.,Hirshleifer D,Subrahmanyam A.Invest Psychology and Security Market Under—and Overreactions[J].Journal of Finance,1998,53(6):1839—1885.
[27]薛春光.风险度量与证券投资组合模型的研究[D].新疆:新疆大学运筹学与控制论专业,2007: 8-13,25-26.
[28]董杰.多元t分布线性模型的统计推断问题,同济大学理学院硕士学位论文,2006年11月。
[29]邵宇,刁羽.微观金融学及其数学基础[M].清华大学出版社,2008:48-50.
[30] XING Xiusan.Physical entropy, information entropy and their evolution eqiatopms [M].SCIENCE IN CHINA(Series A), October 2001.
[31] WANG Wu-xiang,LIU Bing, ZHANG Chen-li.Corporation Strategic Investment on Behavioral Finance [M].Chinese Business Review , Feb 2007.
[32] Rockenbach, B. The Behavioral Relevance of Mental Accounting for the Pricing of Fianacial Options. Journal of Economic Behavioral & Organizaion,2004,53:513-527.
[33] Daniel,K.D.,Hirshfeiler,D,Subrahmanyam A. Overconfidence,Arbitrage and Equilibrium Assets Pricing[J]. The Journal of Finance, 2001,6(3).
[34] Kapur,J.N, Kesavan,H.K. Entropy Optimization Principle With application,San Diego: Academic Press,1992.
[35] Yulmetyev, R.M., Gafarov, F.M. Dynamics of the information entropy in random processes, Physica A, 1999, 273(3-4):416-438.
[36]张光远《关于多元t分布的一些讨论》,新疆大学学报,1996年8月第13卷第3期.
[37]李潇潇、杨春鹏《基于投资者情绪的认知风险和认知收益》,“青岛大学学报”2009年6月第2期.
[38]林玉蕊《期望效用函数理论及其应用》,“大学数学”2008年4月第2期.
[39] Huawang Shi Wanqing Li Wenqing Meng. A New Approach to Construction Project Risk Assesment Based on Rough Set, 2008 International Conference on Information Management, Innovation Management and Industrial Engineering.
[40] Jiang Rong, Liao Hongzhi, Yu Jiankun, Sun Yafei, Li Junlin, Chen Lihua. An Approach to Measuring Software Development Risk Based on Information Entropy, 2009 International Conference on Computational Intelligence and Natural Computing.
[41] Victor Richmond R. Jose, Robert F. Nau, Robert L. Winkler. Scoring rules, generalized entropy, and utility maximization. 2009 International Conference on Computational Intelligence and Natural Computing. OPERATIONS RESEARCH Vol. 56, No. 5, September–October 2008
[42] LEE Sang—Hyuk, LEE Sang.Min, SOHN Gyo—Yong, KIM Jaeh—Yung. Fuzzy entropy design for non convex fuzzy set and application to mutual information. J.Cent. South Univ. Techno1.(2011) 18:184—189.
[43] Ole Jakob Bergfjord. Risk perception and risk management in Norwegian aquaculture. Journal of Risk Research. 2009, 12(1).
[44]Ellen Ter Huurne, Jan Gutteling. Information needs and risk perception as predictors of risk information seeking. Journal of Risk Research. 2008, 11(7)
[45] Juite Wang ,W.-L. Hwang. A fuzzy set approach for R&D portfolio selection using a real options valuation model. Omega. 2007, 35(3)
[2] Roy,A. Safety—first and the Holding of Assets[J]. Econometrica,1952(20).
[3] Tobin,J. Liquidity Preference as Behavior Towards Risk[J]. Review of Economic Studies,1958(2).
[4] William,F.Sharpe. A Simplified Model of Portfolio Analysis[J]. Management Science,1963(9).
[5]徐丽梅.现代投资组合理论及其分支的发展综述[J].首都经济贸易大学学报,2006(4):75-79.
[6]徐少君.投资组合理论发展综述[J].浙江社会科学,2004(4):198-202.
[7]蒲玮.证券投资组合理论综述[J].科学与管理,2008(1):12-14.
[8]欧阳光中,李敬湖.证券组合与投资分析[M].高等教育出版社,1996:27-30.
[9]何信《金融风险度量及其应用研究》,天津大学博士学位论文,2004年6月;
[10] Huang J C, Chiu C L, Lee M C. Hedging with zero value at risk hedge ratio [J]. Applied Financial Economics,2006,16(3):259-269.
[11] Richard D F H, Shen J. Hedging and value at risk [J]. Journal of Futures Markets,2006,26(4):369—390.
[12] Gordon J A, Alexandre M B. A comparison of VaR and CVaR constraints on portfolio selection with the Mean—Variance model [J]. Management Science,2004,50(9):1261-1273.
[13]百度百科. http://baike.baidu.com/view/936.html?wtp=tt.
[14]薛春光.风险度量与证券投资组合模型的研究[D].新疆:新疆大学运筹学与控制论专业,2007: 8-13,25-26.
[15]鲁晨光.投资组合的熵理论和信息价值[M].合肥:中国科学技术大学出社,1997:187-188.
[16]龚光鲁,钱敏平.应用随机过程教程及在算法和智能计算中的随机模型[M].北京:清华大学出版社,2004:243-245.
[17]杨丽娟《基于最小叉熵计算VaR的模型》,“商场现代化”2008年12月(上旬刊)总第559期;
[18]杨春鹏、姜伟、吕学梁《Shannon’s Entropy and Risk Perception》,“青岛大学学报”2007年6月第2期;
[19]杨春鹏、姜伟、吕学梁《投资心理与基于信息熵的认知风险》,“青岛大学学报”2007年9月第3期
[20]李华,李兴斯.证券投资组合中的熵优化模型研究[J].大连理工大学报,2005(1):153-156.
[21]范进.熵理论在信息源选择和信息识别中的应用[J].华东经济管理,2006(7):57-61.
[22]曾建华,汪寿阳.一个基于模糊决策理论的投资组合模型[J].系统工程理论与实践, 2003(1):99-103.
[23]宋喜民,苏丽.有交易成本的模糊最优化投资[J].数学的实践与认识,2003(11):27-29.
[24] Bem Daryl J.,An Experimental Analysis of Self-Persuasion[J].Journal of Experimental Social Psychology,1965,(1):199—218.
[25] Shiller R. Measuring Bubble Expectations and Investor Confidence[J].Journal of Psychology and Financial Markets,2000,(1):49—60.
[26] Danie1 K.,Hirshleifer D,Subrahmanyam A.Invest Psychology and Security Market Under—and Overreactions[J].Journal of Finance,1998,53(6):1839—1885.
[27]薛春光.风险度量与证券投资组合模型的研究[D].新疆:新疆大学运筹学与控制论专业,2007: 8-13,25-26.
[28]董杰.多元t分布线性模型的统计推断问题,同济大学理学院硕士学位论文,2006年11月。
[29]邵宇,刁羽.微观金融学及其数学基础[M].清华大学出版社,2008:48-50.
[30] XING Xiusan.Physical entropy, information entropy and their evolution eqiatopms [M].SCIENCE IN CHINA(Series A), October 2001.
[31] WANG Wu-xiang,LIU Bing, ZHANG Chen-li.Corporation Strategic Investment on Behavioral Finance [M].Chinese Business Review , Feb 2007.
[32] Rockenbach, B. The Behavioral Relevance of Mental Accounting for the Pricing of Fianacial Options. Journal of Economic Behavioral & Organizaion,2004,53:513-527.
[33] Daniel,K.D.,Hirshfeiler,D,Subrahmanyam A. Overconfidence,Arbitrage and Equilibrium Assets Pricing[J]. The Journal of Finance, 2001,6(3).
[34] Kapur,J.N, Kesavan,H.K. Entropy Optimization Principle With application,San Diego: Academic Press,1992.
[35] Yulmetyev, R.M., Gafarov, F.M. Dynamics of the information entropy in random processes, Physica A, 1999, 273(3-4):416-438.
[36]张光远《关于多元t分布的一些讨论》,新疆大学学报,1996年8月第13卷第3期.
[37]李潇潇、杨春鹏《基于投资者情绪的认知风险和认知收益》,“青岛大学学报”2009年6月第2期.
[38]林玉蕊《期望效用函数理论及其应用》,“大学数学”2008年4月第2期.
[39] Huawang Shi Wanqing Li Wenqing Meng. A New Approach to Construction Project Risk Assesment Based on Rough Set, 2008 International Conference on Information Management, Innovation Management and Industrial Engineering.
[40] Jiang Rong, Liao Hongzhi, Yu Jiankun, Sun Yafei, Li Junlin, Chen Lihua. An Approach to Measuring Software Development Risk Based on Information Entropy, 2009 International Conference on Computational Intelligence and Natural Computing.
[41] Victor Richmond R. Jose, Robert F. Nau, Robert L. Winkler. Scoring rules, generalized entropy, and utility maximization. 2009 International Conference on Computational Intelligence and Natural Computing. OPERATIONS RESEARCH Vol. 56, No. 5, September–October 2008
[42] LEE Sang—Hyuk, LEE Sang.Min, SOHN Gyo—Yong, KIM Jaeh—Yung. Fuzzy entropy design for non convex fuzzy set and application to mutual information. J.Cent. South Univ. Techno1.(2011) 18:184—189.
[43] Ole Jakob Bergfjord. Risk perception and risk management in Norwegian aquaculture. Journal of Risk Research. 2009, 12(1).
[44]Ellen Ter Huurne, Jan Gutteling. Information needs and risk perception as predictors of risk information seeking. Journal of Risk Research. 2008, 11(7)
[45] Juite Wang ,W.-L. Hwang. A fuzzy set approach for R&D portfolio selection using a real options valuation model. Omega. 2007, 35(3)
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