基于Copula-VaR方法的我国外汇储备币种结构研究
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摘要
近年来我国的外汇储备规模以惊人的速度增长,现在已经超过了2万亿美元,如此大的规模使得外汇储备的保值增值要求日益突出,因此如何对其进行风险管理成为一个重要的研究课题。自布雷顿森林体系瓦解后,汇率波动成为外汇储备风险的一个主要来源,而为了避免这种由于汇率波动所造成的损失,各国都采取了外汇储备币种多元化的措施,力图通过不同外汇币种的选择来降低外汇储备总体的风险。本文把我国的外汇储备看作是一个由美元和欧元两种外汇资产组成的资产组合,使用目前国际上流行的VaR方法来测算不同币种结构下的外汇储备总体的风险,同时为提高VaR值计算的准确性,在计算过程中使用了连接函数Copula这种在金融风险分析领域有广泛应用的数学方法。
本文从美元和欧元两种外汇兑人民币的汇率数据出发建立模型,首先选择出了最适合外汇储备资产组合VaR值测算的一个Archimedean Copula类并估计了其参数,然后通过蒙特卡罗模拟,利用Matlab编程得出了美元和欧元两币种比例相对变化时外汇储备总体的VaR值。结果表明随着外汇储备中美元资产比例的逐步增大,相应地欧元资产的比例逐步减小,外汇储备总体的VaR值越来越小,因此从控制风险的角度考虑我们应该增加外汇储备中美元的比例而降低欧元的比例。
由于我国目前实行人民币主要钉住美元而非完全市场化的汇率制度,美元兑人民币的汇率波动性明显小于其它币种,因而必然造成资产组合中美元越多则风险越小,这一现实正好验证了本文中模型及其计算结果的正确性。同时需要指出的是,外汇储备币种结构的确定还受收益、全球经济环境、一国国际贸易状况甚至是政治外交等多种因素的影响,因此想要确定一个最优的外汇储备币种结构,单由Copula-VaR方法从风险管理角度考虑是不全面的,还要综合其他因素做更深入的研究。
In recent years,China's foreign exchange reserve scale increased at a remarkable rate,which is more than 2 trillion U.S.dollars now. Such a huge scale makes foreign exchange reserve's value increasing and risk avoiding of a great significance,so the risk management of foreign exchange reserve becomes an important research project. After the collapse of the Bretton Woods System,exchange rate fluctuation became the main source of the risks in foreign exchange reserve.In order to avoid such kind of risks,lots of countries have taken measures to diversify their foreign exchange reserve composition,which means they choose different currency structure to reduce the overall risk.This paper considers our foreign exchange reserve as a portfolio composed of two foreign exchange assets—U.S.dollar and Euro and then estimates the overall portfolio risks when the relative proportion of the two currencies changed. In this process,we measures portfolio risks by calculating it's VaR value and at the same time,we use Copula function to improve the accuracy of VaR calculation,which is a mathematical method and widely used in the field of financial risk analysis.
Starting with U.S. dollar and Euro's exchange rate data to RMB,this paper first selected an Archimedean Copula which is the most suitable one to calculate the VaR value of a portfolio composed of two foreign exchange assets,and then we estimated it's parametre.After that, by using Monte Carlo Simulation, we calculated the portfolio's VaR value when the relative proportion of the two currencies changed with the help of Matlab programming. At last we conclude that our foreign exchange reserve's VaR value reduced when the proportion of U.S.dollar increased,whereas the proportion of Euro decreased.So based on the view of risk management, China's foreign exchange reserve should reduce the proportion of Euro and accordingly, increase the proportion of U.S.dollor.
Since China's current exchange system is pegging RMB to U.S.dollar rather than full market-oriented, the exchange rate volatility of U.S.dollar to RMB is obviously less than the other currencies, which equals the larger U.S.dollar's proportion,the smaller the portfolio's risks.So this reality has proved the correctness of the front calculation methods and conclutions.In addition,the determination of one country's foreign exchange reserve composition is also affected by factors such as income,global economic environment,a country's trade condition and even some political and diplomatic factors.So it is imcomplete to determine a specific foreign exchange reserve compsition just by the use of Copula-VaR method,we should do some deeper research with a comprehensive consideration of the other factors.
本文从美元和欧元两种外汇兑人民币的汇率数据出发建立模型,首先选择出了最适合外汇储备资产组合VaR值测算的一个Archimedean Copula类并估计了其参数,然后通过蒙特卡罗模拟,利用Matlab编程得出了美元和欧元两币种比例相对变化时外汇储备总体的VaR值。结果表明随着外汇储备中美元资产比例的逐步增大,相应地欧元资产的比例逐步减小,外汇储备总体的VaR值越来越小,因此从控制风险的角度考虑我们应该增加外汇储备中美元的比例而降低欧元的比例。
由于我国目前实行人民币主要钉住美元而非完全市场化的汇率制度,美元兑人民币的汇率波动性明显小于其它币种,因而必然造成资产组合中美元越多则风险越小,这一现实正好验证了本文中模型及其计算结果的正确性。同时需要指出的是,外汇储备币种结构的确定还受收益、全球经济环境、一国国际贸易状况甚至是政治外交等多种因素的影响,因此想要确定一个最优的外汇储备币种结构,单由Copula-VaR方法从风险管理角度考虑是不全面的,还要综合其他因素做更深入的研究。
In recent years,China's foreign exchange reserve scale increased at a remarkable rate,which is more than 2 trillion U.S.dollars now. Such a huge scale makes foreign exchange reserve's value increasing and risk avoiding of a great significance,so the risk management of foreign exchange reserve becomes an important research project. After the collapse of the Bretton Woods System,exchange rate fluctuation became the main source of the risks in foreign exchange reserve.In order to avoid such kind of risks,lots of countries have taken measures to diversify their foreign exchange reserve composition,which means they choose different currency structure to reduce the overall risk.This paper considers our foreign exchange reserve as a portfolio composed of two foreign exchange assets—U.S.dollar and Euro and then estimates the overall portfolio risks when the relative proportion of the two currencies changed. In this process,we measures portfolio risks by calculating it's VaR value and at the same time,we use Copula function to improve the accuracy of VaR calculation,which is a mathematical method and widely used in the field of financial risk analysis.
Starting with U.S. dollar and Euro's exchange rate data to RMB,this paper first selected an Archimedean Copula which is the most suitable one to calculate the VaR value of a portfolio composed of two foreign exchange assets,and then we estimated it's parametre.After that, by using Monte Carlo Simulation, we calculated the portfolio's VaR value when the relative proportion of the two currencies changed with the help of Matlab programming. At last we conclude that our foreign exchange reserve's VaR value reduced when the proportion of U.S.dollar increased,whereas the proportion of Euro decreased.So based on the view of risk management, China's foreign exchange reserve should reduce the proportion of Euro and accordingly, increase the proportion of U.S.dollor.
Since China's current exchange system is pegging RMB to U.S.dollar rather than full market-oriented, the exchange rate volatility of U.S.dollar to RMB is obviously less than the other currencies, which equals the larger U.S.dollar's proportion,the smaller the portfolio's risks.So this reality has proved the correctness of the front calculation methods and conclutions.In addition,the determination of one country's foreign exchange reserve composition is also affected by factors such as income,global economic environment,a country's trade condition and even some political and diplomatic factors.So it is imcomplete to determine a specific foreign exchange reserve compsition just by the use of Copula-VaR method,we should do some deeper research with a comprehensive consideration of the other factors.
引文
[1]Harry Markowits.Portfolio Selection[J].Journal of Finance,1952,3(7):77-91
[2]Harry Markowits.Portfolio Selection:efficient diversification of investment (Second Edition)[M].First published by Blackwell Publishing Ltd,1991,72-196
[3]Roger,S.The Management of Foreign Exchange Reserves.BIS Economic Papers, http://www.bis.org/publ/econ38.pdf,1993,9-73
[4]Robert H.Heller, Malcolm A.Knight.Reserve-Currency Preferences of Central Banks.Essays in International Finance.International Finance Section,Princeton University, Princeton,1978,(131):20-35
[5]Michael P. Dooley. An Analysis of the Management of the Currency Composition of Reserve Assets and External Liabilities of Developing Countries [J].The Reconstruction of International Monetary Arrangement,1987, (262): 385-434
[6]Eichengreen, Matheson. The Currency Composition of Foreign Exchange Reserves:Reports and prospect[Z].http://scholar.google.cn/,2001,165-286
[7]王国林.关键货币汇率变动对我国外汇储备规模的影响[J].世界经济与政治论坛,2005,(5)：70-73
[8]宋铁波,陈建国.当前我国外汇储备币种组合分析[J].南方金融,2001,(4)：11-13
[9]杨胜刚,谭卓.基于层次分析法的中国外汇储备货币结构管理研究[J].财经理论与实践,2007,28(3)：2-7
[10]任璐,潘志斌.中国外汇储备币种结构[J].商场现代化,2008,(29)：335-337
[11]刘莉亚.我国外汇储备币种结构与收益率的一个估计[J].财经研究,2008,(7)：121-132
[12]奚君羊.国际储备研究[M].北京：中国金融出版社,2000,96-234
[13]Don Bredin, Stuart Hyde. FOREX Risk:Measurement and Evaluation Using Value-at-Risk[J].Journal of Business Finance and Accounting,2004,31(9-10): 1389-1417
[14]Philippe jorion.Value at Risk:The New Benchmark for Controlling Derivatives Risk[M].The McGraw-Hill Companies,Inc,1997:1-200
[15]Jer-Shiou Chiou,Jui-Cheng Hung and Mei-Maun Hseu.A VaR Investigation of Currency Composition in Foreign Exchange Reserves[J],International Research Journal of Finance and Economics,2008, (21):76-92
[16]S.Pafka and I Kondor. Evaluating the RiskMetrics methodology in measuring volatility and Value-at-Risk in financial markets[J].2001, (299):305-310
[17]I.A.Moosa,B.Bollen.A benchmark for measuring bias in estimated daily value at risk[J].International Review of Finacial Analysis,2002, (11):85-100
[18]郑文通.金融风险管理的VaR方法及其应用[J].国际金融研究,1997,(9)：58-62
[19]姚刚.风险值测定法浅析[J].经济科学,1998,(1)：122-271
[20]王春峰,万海晖.金融市场风险测量模型-VaR[J].系统工程学报,2000,(1)：67-75
[21]李亚静,朱宏泉,何跃.基于VaR的风险分析理论与计算方法[J].预测,2000,(5)：36-46
[22]吴世农,陈斌.风险度量方法与金融资产配置模型的理论和实证研究[J].经济研究,1999,(9)：30-38
[23]马杰,任若恩.VaR方法在外汇风险管理中的应用[J].北京航空航天大学学报：社会科学版,2000,(3)：352-355
[24]吴娓.涉外企业外汇交易风险的测量与套期保值策略研究：[西南财经大学博士论文].成都：西南财经大学会计学院,2007,47-77
[25]戴国强,徐龙炳,陆蓉.VaR方法对我国金融风险管理的借鉴及应用[J].金融研究,2000,(7)：45-51
[26]赵睿,赵陵.VaR方法与资产组合分析[J].数量经济技术经济研究,2002,(11)：44-47
[27]邵欣炜,张屹山.基于VaR的证券投资组合风险评估及管理体系[J].数量经济技术经济研究,2003,(12)：66-70
[28]马超群,李红权等.风险价值的完全参数方法及其在金融市场风险管理中的应用[J].系统工程理论与实践,2001,(4)：74-79
[29]马超群,李红权.VaR方法在金融风险管理中的应用[J].系统工程,2000,(2)：56-59
[30]高铁梅.计量经济分析方法与建模—EViews应用及实例[M].北京：清华大学出版社,2006,441-483
[31]Rober B.Nelsen.An introduction to Copulas(Second Edition)[M].New York: Springer,2006,1-155
[32]Davis Bundi Ntwiga. Copulas in Finance.http://users.aims.ac.za/-bundi/ AIMS-ESSAY.pdf,2004,1-34
[33]Eric Bouye.Copulas for Finance-A Reading Guide and Some Applications. Working Paper,Credit Lyonnais,2000,20-62
[34]Mario R.Melchiori.Which Archimedean Copula is the right one?.Published in the YieldCurve.com e-Journal(www.YieldCurve.com),2003,(10):4-17
[35]Rosenberg J,Schuermann T. A general approach to integrated risk management with skewed fat-tailed risks.Working Paper of Federal Reserve Bank of New York,2004,3-27
[36]Christian Genest,Michel Gendron and Michael Bourdeau-Brien.The Advent of Copulas in Finance[J],The European Journal of Finance,2009,1-10
[37]Paul Embrechts,Filip Lindskog and Alexander McNeil.Modelling Dependence with Copulas and Applications to Risk Management[J].Department of Mathematics,ETHZ,CH-8092 Zurich,Switzerland,2001,(9):1-41
[38]S.G Coles.An Introduction to statistical modelling of Extreme Values[M]. Springer,2001,122-231
[39]Schwettzer B,Wolff E.On nonparametric measures of dependence for random variables[J].Annals of Statistics,1981, (9):879-885
[40]R. de Matteis, Fitting copulas to data:[Diploma thesis, University Zurich]. Mathematics Department of the Federal Institute of Technology Zurich,2001, 25-39
[41]张尧庭.连接函数(Copula)技术与金融风险分析[J].统计研究,2002,(4)：41-44
[42]张尧庭.我们应该选用什么样的相关性指标[J].统计研究,2002,(9)：41-44
[43]吴振翔,叶五一,谬柏其.基于Copula的外汇投资组合风险分析[J].中国管理科学,2004,(4)：1-5
[44]史道济,姚庆祝.改进Copula对数据拟合的方法[J].系统工程理论与实践,2004,(4)：49-55
[45]欧阳资生,王非.基于Copula方法的国债市场相依风险度量[J].统计研究,2008,(7)：82-85
[46]杨湘豫,夏宇.基于Copula方法的开放式基金投资组合的VaR研究[J].系统工程,2008,(12)：40-44
[47]郝礼祥,程希骏.基于Copula-VaR方法对上证和深证的研究[J].中国科学院研究生院学报,2008,(5)：682-686
[48]杜江,陈希镇,于波.Archimedean Copula函数的参数估计[J].科学技术与工程,2009,(3)：637-640
[49]阮敬.SAS统计分析从入门到精通[M].北京：人民邮电出版社,2009,123-139
[50]王苏斌,郑海涛,邵谦谦等.SPSS统计分析[M].北京：机械工业出版社,2003, 230-278
[51]张威.Matlab基础与编程入门[M].西安：西安电子科技大学出版社,2004,110-150
[2]Harry Markowits.Portfolio Selection:efficient diversification of investment (Second Edition)[M].First published by Blackwell Publishing Ltd,1991,72-196
[3]Roger,S.The Management of Foreign Exchange Reserves.BIS Economic Papers, http://www.bis.org/publ/econ38.pdf,1993,9-73
[4]Robert H.Heller, Malcolm A.Knight.Reserve-Currency Preferences of Central Banks.Essays in International Finance.International Finance Section,Princeton University, Princeton,1978,(131):20-35
[5]Michael P. Dooley. An Analysis of the Management of the Currency Composition of Reserve Assets and External Liabilities of Developing Countries [J].The Reconstruction of International Monetary Arrangement,1987, (262): 385-434
[6]Eichengreen, Matheson. The Currency Composition of Foreign Exchange Reserves:Reports and prospect[Z].http://scholar.google.cn/,2001,165-286
[7]王国林.关键货币汇率变动对我国外汇储备规模的影响[J].世界经济与政治论坛,2005,(5)：70-73
[8]宋铁波,陈建国.当前我国外汇储备币种组合分析[J].南方金融,2001,(4)：11-13
[9]杨胜刚,谭卓.基于层次分析法的中国外汇储备货币结构管理研究[J].财经理论与实践,2007,28(3)：2-7
[10]任璐,潘志斌.中国外汇储备币种结构[J].商场现代化,2008,(29)：335-337
[11]刘莉亚.我国外汇储备币种结构与收益率的一个估计[J].财经研究,2008,(7)：121-132
[12]奚君羊.国际储备研究[M].北京：中国金融出版社,2000,96-234
[13]Don Bredin, Stuart Hyde. FOREX Risk:Measurement and Evaluation Using Value-at-Risk[J].Journal of Business Finance and Accounting,2004,31(9-10): 1389-1417
[14]Philippe jorion.Value at Risk:The New Benchmark for Controlling Derivatives Risk[M].The McGraw-Hill Companies,Inc,1997:1-200
[15]Jer-Shiou Chiou,Jui-Cheng Hung and Mei-Maun Hseu.A VaR Investigation of Currency Composition in Foreign Exchange Reserves[J],International Research Journal of Finance and Economics,2008, (21):76-92
[16]S.Pafka and I Kondor. Evaluating the RiskMetrics methodology in measuring volatility and Value-at-Risk in financial markets[J].2001, (299):305-310
[17]I.A.Moosa,B.Bollen.A benchmark for measuring bias in estimated daily value at risk[J].International Review of Finacial Analysis,2002, (11):85-100
[18]郑文通.金融风险管理的VaR方法及其应用[J].国际金融研究,1997,(9)：58-62
[19]姚刚.风险值测定法浅析[J].经济科学,1998,(1)：122-271
[20]王春峰,万海晖.金融市场风险测量模型-VaR[J].系统工程学报,2000,(1)：67-75
[21]李亚静,朱宏泉,何跃.基于VaR的风险分析理论与计算方法[J].预测,2000,(5)：36-46
[22]吴世农,陈斌.风险度量方法与金融资产配置模型的理论和实证研究[J].经济研究,1999,(9)：30-38
[23]马杰,任若恩.VaR方法在外汇风险管理中的应用[J].北京航空航天大学学报：社会科学版,2000,(3)：352-355
[24]吴娓.涉外企业外汇交易风险的测量与套期保值策略研究：[西南财经大学博士论文].成都：西南财经大学会计学院,2007,47-77
[25]戴国强,徐龙炳,陆蓉.VaR方法对我国金融风险管理的借鉴及应用[J].金融研究,2000,(7)：45-51
[26]赵睿,赵陵.VaR方法与资产组合分析[J].数量经济技术经济研究,2002,(11)：44-47
[27]邵欣炜,张屹山.基于VaR的证券投资组合风险评估及管理体系[J].数量经济技术经济研究,2003,(12)：66-70
[28]马超群,李红权等.风险价值的完全参数方法及其在金融市场风险管理中的应用[J].系统工程理论与实践,2001,(4)：74-79
[29]马超群,李红权.VaR方法在金融风险管理中的应用[J].系统工程,2000,(2)：56-59
[30]高铁梅.计量经济分析方法与建模—EViews应用及实例[M].北京：清华大学出版社,2006,441-483
[31]Rober B.Nelsen.An introduction to Copulas(Second Edition)[M].New York: Springer,2006,1-155
[32]Davis Bundi Ntwiga. Copulas in Finance.http://users.aims.ac.za/-bundi/ AIMS-ESSAY.pdf,2004,1-34
[33]Eric Bouye.Copulas for Finance-A Reading Guide and Some Applications. Working Paper,Credit Lyonnais,2000,20-62
[34]Mario R.Melchiori.Which Archimedean Copula is the right one?.Published in the YieldCurve.com e-Journal(www.YieldCurve.com),2003,(10):4-17
[35]Rosenberg J,Schuermann T. A general approach to integrated risk management with skewed fat-tailed risks.Working Paper of Federal Reserve Bank of New York,2004,3-27
[36]Christian Genest,Michel Gendron and Michael Bourdeau-Brien.The Advent of Copulas in Finance[J],The European Journal of Finance,2009,1-10
[37]Paul Embrechts,Filip Lindskog and Alexander McNeil.Modelling Dependence with Copulas and Applications to Risk Management[J].Department of Mathematics,ETHZ,CH-8092 Zurich,Switzerland,2001,(9):1-41
[38]S.G Coles.An Introduction to statistical modelling of Extreme Values[M]. Springer,2001,122-231
[39]Schwettzer B,Wolff E.On nonparametric measures of dependence for random variables[J].Annals of Statistics,1981, (9):879-885
[40]R. de Matteis, Fitting copulas to data:[Diploma thesis, University Zurich]. Mathematics Department of the Federal Institute of Technology Zurich,2001, 25-39
[41]张尧庭.连接函数(Copula)技术与金融风险分析[J].统计研究,2002,(4)：41-44
[42]张尧庭.我们应该选用什么样的相关性指标[J].统计研究,2002,(9)：41-44
[43]吴振翔,叶五一,谬柏其.基于Copula的外汇投资组合风险分析[J].中国管理科学,2004,(4)：1-5
[44]史道济,姚庆祝.改进Copula对数据拟合的方法[J].系统工程理论与实践,2004,(4)：49-55
[45]欧阳资生,王非.基于Copula方法的国债市场相依风险度量[J].统计研究,2008,(7)：82-85
[46]杨湘豫,夏宇.基于Copula方法的开放式基金投资组合的VaR研究[J].系统工程,2008,(12)：40-44
[47]郝礼祥,程希骏.基于Copula-VaR方法对上证和深证的研究[J].中国科学院研究生院学报,2008,(5)：682-686
[48]杜江,陈希镇,于波.Archimedean Copula函数的参数估计[J].科学技术与工程,2009,(3)：637-640
[49]阮敬.SAS统计分析从入门到精通[M].北京：人民邮电出版社,2009,123-139
[50]王苏斌,郑海涛,邵谦谦等.SPSS统计分析[M].北京：机械工业出版社,2003, 230-278
[51]张威.Matlab基础与编程入门[M].西安：西安电子科技大学出版社,2004,110-150
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