基于偏度的多期组合投资调整模型
摘要
投资组合理论是金融学中的重要研究课题之一,其目的是寻求一个在给定收益水平下使投资风险最小化,或者在给定的投资风险水平下使投资收益最大化的最优投资组合。VaR(Value-at-Risk)是近年来提出的新的风险度量方法,尤其其计算方法,已经引起众多研究学者们的注意,成为金融风险管理领域研究的前沿课题。
本文首先介绍了投资组合理论的现状和风险管理与VaR的历史背景。随后在介绍经典的均值--方差模型的基础上,总结了近年来几种拓展模型;介绍了VaR的定义、性质、计算方法及其应用。在建立模型时,本文创新有以下几个方面:
1.将单一期模型扩展到多期由于不同时期资产收益率以及投资者对风险和收益偏好的变化,加之资金等条件的限制,大多数组合投资问题具有明显的动态特征。本文把单期投资组合拓展到多期,建立了多期投资组合调整模型,并给出实证分析验证模型的有效性,这对投资者的连续投资行为具有一定的指导作用。
2.加入VaR限制条件,研究了偏度下的带有交易费用的组合投资模型迄今为止,对于均值--方差模型,其研究的局限和不足很多,一般都是侧重或者只考虑交易费用、或者只考虑三阶矩,本文同时考虑了交易费用和三阶矩,并在期望收益中减去交易费用得到净收益作为一个约束条件;在投资者具有一定的风险承受能力的假设下,加入了VaR限制条件,提出了基于偏度的多期投资组合模型,讨论了解的矩阵形式。
在最后,总结了本文的研究工作并对进一步的研究方向进行了展望。
Portfolio theory is one of the important research content in Economics. It aims to attain the portfolios of the maximum of investment’s return with the given value of the risk of portfolio or of the minimum of investment’s risk with the given level of the investment’s return. VaR(Value- at-Risk),which are new risk measurement methods, are put forth recently and is given attentions by more and more researchers in particular, and becomes a latest research content in finance’s risk management.
The updated development situation of portfolio and the background of VaR are introduced at first. The latest extension models are discussed on basis of the classic model in portfolio’s theories, which was the mean-variance model; on the foundation of the definition and characters of VaR, the computation methods and application are proposed. On constructing the model, the main innovations in the thesis are as follows.
1. Extending the one-period portfolio model to multi-period. As the variation of the rate of the return and risk, in addition to the limitation of the money, the portfolio has exactly dynamic characteristics. So we construct the adjusting model of multi-period portfolio with transaction costs. And finally, a numerical example is displayed to test the model.
2. Our model considers the factors of VaR limit, transaction costs and skewness simultaneously.
Up to now, researches on avoiding the drawbacks of using MV model are limited on some sections of considering only transaction cost or only third moment. And the net expected return, which is one of the limit of the model, is the expected return subsided by the costs. Our model , which introduces VaR into the limits, considers the two factors above simultaneously under the assumption of investors` stated endurance,then the matrix form of the solution is discussed.
Finally, we get together the paper and mentioned the directions of the further research.
本文首先介绍了投资组合理论的现状和风险管理与VaR的历史背景。随后在介绍经典的均值--方差模型的基础上,总结了近年来几种拓展模型;介绍了VaR的定义、性质、计算方法及其应用。在建立模型时,本文创新有以下几个方面:
1.将单一期模型扩展到多期由于不同时期资产收益率以及投资者对风险和收益偏好的变化,加之资金等条件的限制,大多数组合投资问题具有明显的动态特征。本文把单期投资组合拓展到多期,建立了多期投资组合调整模型,并给出实证分析验证模型的有效性,这对投资者的连续投资行为具有一定的指导作用。
2.加入VaR限制条件,研究了偏度下的带有交易费用的组合投资模型迄今为止,对于均值--方差模型,其研究的局限和不足很多,一般都是侧重或者只考虑交易费用、或者只考虑三阶矩,本文同时考虑了交易费用和三阶矩,并在期望收益中减去交易费用得到净收益作为一个约束条件;在投资者具有一定的风险承受能力的假设下,加入了VaR限制条件,提出了基于偏度的多期投资组合模型,讨论了解的矩阵形式。
在最后,总结了本文的研究工作并对进一步的研究方向进行了展望。
Portfolio theory is one of the important research content in Economics. It aims to attain the portfolios of the maximum of investment’s return with the given value of the risk of portfolio or of the minimum of investment’s risk with the given level of the investment’s return. VaR(Value- at-Risk),which are new risk measurement methods, are put forth recently and is given attentions by more and more researchers in particular, and becomes a latest research content in finance’s risk management.
The updated development situation of portfolio and the background of VaR are introduced at first. The latest extension models are discussed on basis of the classic model in portfolio’s theories, which was the mean-variance model; on the foundation of the definition and characters of VaR, the computation methods and application are proposed. On constructing the model, the main innovations in the thesis are as follows.
1. Extending the one-period portfolio model to multi-period. As the variation of the rate of the return and risk, in addition to the limitation of the money, the portfolio has exactly dynamic characteristics. So we construct the adjusting model of multi-period portfolio with transaction costs. And finally, a numerical example is displayed to test the model.
2. Our model considers the factors of VaR limit, transaction costs and skewness simultaneously.
Up to now, researches on avoiding the drawbacks of using MV model are limited on some sections of considering only transaction cost or only third moment. And the net expected return, which is one of the limit of the model, is the expected return subsided by the costs. Our model , which introduces VaR into the limits, considers the two factors above simultaneously under the assumption of investors` stated endurance,then the matrix form of the solution is discussed.
Finally, we get together the paper and mentioned the directions of the further research.
引文
[1] 丁义明,方福康,风险概念分析,系统工程学报,2001(10),16(5):402~406
[2] R A Jarrow,V Maksimovic,W T Ziemba.Finance Handbook in Operations Research and Management Science .Amsterdam:North-Holland,1995:30~69
[3] J B Williams.The Theory of Value.Harvard University Press,1938(3):51~60
[4] J Marchak.Money and the theory of assets.Economitrica,1938,6:311~325
[5] V Neurnann,O Morgenstem.Theory of Games and Economic Behavior. Princeton:Princeton University Press,1947,(6):59~68
[6] Markowitz H.Portfolio selection.Journal of Finance,1952,7(1):77~91
[7] Markowitz H M.Porfolio efficient diversification of investment(Second Edition).New York:John Wile&Sons,1991
[8] J Tobin.Liquidity preference as behavior toward risk.Rev Econ Studies, 1958,(25):65~86
[9] Sharpe,Willim F.Capital asset prices:A theory of market equilibrium under conditions of risk.Journal of finance,1964,19
[10] Linter,John.The valuation of risk assets and the selection of risky investments in stock portfolios and capital budges.Review of economics and stastics,1965,7
[11] 曹国华,黄薇,安全第一的证券组合优化模型与绩效管理,重庆大学学报(自然科学版), 2000,23(3):94~96
[12] 蔡宪唐,戴贞德,徐伟宣,基于收益率倒数损失的投资组合指标,中国管理科学,2001(4),10(2):6~11
[13] 郑锦亚,迟国泰,基于差异系数 μ /σ 的最优投资组合方法,2001(2),9(1):1~5
[14] 詹原瑞,市场风险的度量:VaR的计算与应用,系统工程理论与实践,1999(12)12:1~7
[15] 王春峰,万海晖,张维,融市场风险测量模型-VaR,系统工程学报,2000,15(1):67~75
[16] Black F,Jenson M,Scholes M.The capital asset pricing model:some Empirical test studies in the theory of capital markets.New York,1972:110~120
[17] 何宜庆,王浣尘,王芸,龚薇, E--Sh风险下的证券组合投资多目标决策模型,系统工程学报,2001(2),16(1):66~71
[18] 张喜彬,荣喜民,张世英,E--SV风险侧度组合证券投资模型及代数解法,系统工程与电子技术,1999,21(12):23~25
[19] 荣喜民,张喜彬,张世英,组合证券投资模型研究,系统工程学报,1998,13(1):81~88
[20] 欧阳光中,李敬湖,证券组合与投资分析,北京:高等教育出版社,1997
[21] 王春峰,屠新曙,厉斌,效用函数意义下投资组合有效选择问题的研究,中国管理科学,2002,10(2):15~19
[22] 王春峰,金融市场风险管理,天津:天津大学出版社,2001
[23] 覃森,VaR 与 CvaR 风险控制下 Log-最优资产组合模型的研究:[硕士学位论文],西安;西北工业大学,2004
[24] 杨晓光,马超群,文风华,VaR 之下后尾分布的最优资产组合的收敛性,管理科学学报,2002(2),5(1):65~69
[25] 景乃权,陈姝,VaR模型及其在投资组合中的应用,财贸经济,2003,2
[26] 叶五一,缪柏其,吴振翔,基于Bootstrap方法的VaR计算,系统工程学报,2004,19(5):528~531
[27] Li.D,Ng.WL.Optimal dynamic Portfolio selection:multi-period mean-variance formulation.Mathematical Finance,2000,10(3):387~406
[28] 牟太勇,周宗放,多期组合投资权序列矩阵及其应用,中国管理科学,2003,11(专辑):181~183
[29] 杨德权,胡运权等,考虑交易费用的多时期证券投资策略研究,哈尔滨工业大学学报,1999,31(5):37~40
[30] Arditti, F.D, H.Levy.Portfolio Efficient Analysis in Three Monents: The Multi-period case.Journal of Finance,1975,(30):797~809
[31] 丁元耀,贾让成,均值--极差型组合投资优化选择模型,预测,1999,18(4):64~65
[32] Giorgio Consigli.Tail estimation and mean-VaR portfolio selection in market subject to financial instability.Journal of Bank & Finance,2002,26(7):1355~1382
[33] 刘善存,证券组合投资的风险决策模型及其应用研究:[博士毕业论文],北京;北京航空航天大学,2002
[34] Gustavo M.de Athayde,Renato G.Flóres Jr.Finding a maximum skewness portfolio-a general solution to three-moments portfolio choice. Journal of Economic Dynamics & Control,2004,28:1335~1352
[35] Perold A F.Llarge-scale portfolio optimization.Maniagement Sciece,1984,30:1143~1160
[36] Dantgitz G B,Infanger G.Multistage stochastic linear prograns for portfolio optimiazation.Annals of Operations Research,1993,45:59~76
[37] Gennotte G,Jung A.Investment strategies under transaction costs:the finite horizon case.Management Sciece,1994,40:385~404
[38] Mark.T Leang,Hazen Daouk,An-Sing Chen.Using investment portfolio return to combine forecast: A multiobjective approach.European Journal of Operation Research,2001,134(1):41~102
[39] 肖柳青,周石鹏,实用最优化方法,上海:上海交通大学出版社,2000
[2] R A Jarrow,V Maksimovic,W T Ziemba.Finance Handbook in Operations Research and Management Science .Amsterdam:North-Holland,1995:30~69
[3] J B Williams.The Theory of Value.Harvard University Press,1938(3):51~60
[4] J Marchak.Money and the theory of assets.Economitrica,1938,6:311~325
[5] V Neurnann,O Morgenstem.Theory of Games and Economic Behavior. Princeton:Princeton University Press,1947,(6):59~68
[6] Markowitz H.Portfolio selection.Journal of Finance,1952,7(1):77~91
[7] Markowitz H M.Porfolio efficient diversification of investment(Second Edition).New York:John Wile&Sons,1991
[8] J Tobin.Liquidity preference as behavior toward risk.Rev Econ Studies, 1958,(25):65~86
[9] Sharpe,Willim F.Capital asset prices:A theory of market equilibrium under conditions of risk.Journal of finance,1964,19
[10] Linter,John.The valuation of risk assets and the selection of risky investments in stock portfolios and capital budges.Review of economics and stastics,1965,7
[11] 曹国华,黄薇,安全第一的证券组合优化模型与绩效管理,重庆大学学报(自然科学版), 2000,23(3):94~96
[12] 蔡宪唐,戴贞德,徐伟宣,基于收益率倒数损失的投资组合指标,中国管理科学,2001(4),10(2):6~11
[13] 郑锦亚,迟国泰,基于差异系数 μ /σ 的最优投资组合方法,2001(2),9(1):1~5
[14] 詹原瑞,市场风险的度量:VaR的计算与应用,系统工程理论与实践,1999(12)12:1~7
[15] 王春峰,万海晖,张维,融市场风险测量模型-VaR,系统工程学报,2000,15(1):67~75
[16] Black F,Jenson M,Scholes M.The capital asset pricing model:some Empirical test studies in the theory of capital markets.New York,1972:110~120
[17] 何宜庆,王浣尘,王芸,龚薇, E--Sh风险下的证券组合投资多目标决策模型,系统工程学报,2001(2),16(1):66~71
[18] 张喜彬,荣喜民,张世英,E--SV风险侧度组合证券投资模型及代数解法,系统工程与电子技术,1999,21(12):23~25
[19] 荣喜民,张喜彬,张世英,组合证券投资模型研究,系统工程学报,1998,13(1):81~88
[20] 欧阳光中,李敬湖,证券组合与投资分析,北京:高等教育出版社,1997
[21] 王春峰,屠新曙,厉斌,效用函数意义下投资组合有效选择问题的研究,中国管理科学,2002,10(2):15~19
[22] 王春峰,金融市场风险管理,天津:天津大学出版社,2001
[23] 覃森,VaR 与 CvaR 风险控制下 Log-最优资产组合模型的研究:[硕士学位论文],西安;西北工业大学,2004
[24] 杨晓光,马超群,文风华,VaR 之下后尾分布的最优资产组合的收敛性,管理科学学报,2002(2),5(1):65~69
[25] 景乃权,陈姝,VaR模型及其在投资组合中的应用,财贸经济,2003,2
[26] 叶五一,缪柏其,吴振翔,基于Bootstrap方法的VaR计算,系统工程学报,2004,19(5):528~531
[27] Li.D,Ng.WL.Optimal dynamic Portfolio selection:multi-period mean-variance formulation.Mathematical Finance,2000,10(3):387~406
[28] 牟太勇,周宗放,多期组合投资权序列矩阵及其应用,中国管理科学,2003,11(专辑):181~183
[29] 杨德权,胡运权等,考虑交易费用的多时期证券投资策略研究,哈尔滨工业大学学报,1999,31(5):37~40
[30] Arditti, F.D, H.Levy.Portfolio Efficient Analysis in Three Monents: The Multi-period case.Journal of Finance,1975,(30):797~809
[31] 丁元耀,贾让成,均值--极差型组合投资优化选择模型,预测,1999,18(4):64~65
[32] Giorgio Consigli.Tail estimation and mean-VaR portfolio selection in market subject to financial instability.Journal of Bank & Finance,2002,26(7):1355~1382
[33] 刘善存,证券组合投资的风险决策模型及其应用研究:[博士毕业论文],北京;北京航空航天大学,2002
[34] Gustavo M.de Athayde,Renato G.Flóres Jr.Finding a maximum skewness portfolio-a general solution to three-moments portfolio choice. Journal of Economic Dynamics & Control,2004,28:1335~1352
[35] Perold A F.Llarge-scale portfolio optimization.Maniagement Sciece,1984,30:1143~1160
[36] Dantgitz G B,Infanger G.Multistage stochastic linear prograns for portfolio optimiazation.Annals of Operations Research,1993,45:59~76
[37] Gennotte G,Jung A.Investment strategies under transaction costs:the finite horizon case.Management Sciece,1994,40:385~404
[38] Mark.T Leang,Hazen Daouk,An-Sing Chen.Using investment portfolio return to combine forecast: A multiobjective approach.European Journal of Operation Research,2001,134(1):41~102
[39] 肖柳青,周石鹏,实用最优化方法,上海:上海交通大学出版社,2000