危机传染背景下资产组合风险模型测试精度比较研究
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摘要
从1929年的美国股市大崩溃开始,国际金融市场历经了数次危机传染。而美国次贷危机更因在短时间内便震撼国际金融市场,演变成全球性的经济危机且影响深远,而成为金融危机传染的代表性事件。国际金融市场危机传染的频繁发生,使得投资者面临着巨大的风险,同时也对金融风险管理提出了更高的要求。
金融风险管理的基础与核心在于如何正确地度量风险,由于在金融实务中,投资者往往对资产组合进行投资而非单一资产,因而对于资产组合风险的度量更具现实意义。同单一资产的风险评估相比,投资组合的风险评价更为复杂,因为在组合风险的计量过程中,不仅需要考虑组合中单一资产收益的波动率模型,还必须考虑到组合中各个资产间的相依关系。然而金融资产间的相关性错综复杂,所以如何正确地选择和运用风险度量工具就成为组合风险评价中最重要的一个环节。
本文以美国S&P500指数、日本日经225指数、中国上证综指和香港恒生指数作为研究对象,将四类时变Copula-EVT模型作为核心研究方法,以美国次贷危机为代表的金融危机传染作为一条贯穿始终的研究主线,层层推进四个关键问题：
·危机传染是否显著地影响了股市间尾部极值风险传导的强度?
·股市间风险传导的方向是否发生明显的变化?
·危机爆发后,对于二元资产组合及多元资产组合的多头头寸与空头头寸,各类风险模型假定下的VaR风险价值模型和ES预期损失模型的测度精度是否显著改变?其变化状况是否有所不同?
·哪些因素将影响到VaR模型和ES模型的预测准确度?其影响的结果怎样?
为此,本文在各股指收益的标准残差序列的基础上,结合EVT极值理论,构建边缘分布,分别运用四类时变Copula函数构建各个资产组合的联合分布,采用拟合效果相对较好的时变t Copula-GJR-EVT模型,得到危机爆发前后股市间的极值动态相依系数；通过时变SJC-Copula-EVT模型获得股市间的上尾和下尾极值相关系数。运用格兰杰因果检验的方法,分析了金融危机传染对于股市间风险传导方向产生的影响。实证研究结果表明,危机的爆发,对于股市间极值风险传递的强度和风险传导的方向产生了很大的影响。次贷危机发生以后,国际股市间极值风险传染的程度普遍增强,其时变特征也非常明显。从股市风险传导的方向上看：次贷危机爆发以前,股指间的风险主要汇集于纽约股市,而三大亚洲股市,即中国沪市、香港股市和东京股市间不存在风险传导关系。次贷危机爆发后,股市间风险传导的途径和方向发生了明显的变化：不仅美国纽约股市与其他股市间形成了双向风险传导关系,亚洲股市间也显现出密切而复杂的风险传导格局,中国股市与国际股市的极值风险关联度显著增强。
这些鲜明的特点,无疑将影响到投资组合风险模型的测度准确度。在此背景下,本文将四个股指收益进行组合,构造了二元资产组合及多元资产组合,基于四类时变Copula-EVT模型和DCC-GARCH模型,分别针对多头头寸和空头头寸,建立了VaR模型和ES模型,并运用Backtesting方法进行后验分析,对比研究了危机以后各类风险模型测度精度的变化状况。实证结果表明：第一,次贷危机爆发后,金融市场间极值风险正向相关的程度显著增强,分散化投资的作用在一定程度上被削弱,资产组合VaR风险价值模型的测度精度有所降低；然而在某些状况下,预期损失ES模型的测度精度却在危机后有一定程度的提高。第二,无论是VaR模型还是ES模型,基于时变Copula-EVT构建的风险模型,其测度精度在总体上高于DCC-GARCH风险模型。第三,边缘分布模型的选择,对于时变Copula-EVT风险模型的测度效果具有重要影响。第四,由不同类型的时变Copula函数构造的风险模型,对于资产组合风险的预测准确度有所不同。综合来看,危机爆发以后,时变SJC-Copula-EVT-VaR模型与时变tCopula-EVT-ES模型的测度精度均相对较高,这进一步表明,次贷危机对于资产组合风险模型的测度效果产生了巨大冲击,善于刻画变量间非对称性、厚尾性相依特征的模型显现出较强的测度优势。尽管如此,对于资产组合的风险测度,仍需根据资产组合的分布特征以及科学的对比研究来灵活地选择合适的风险模型。
在经济全球化的今天,无论是从时间还是空间的角度,金融危机传染都日趋严重。美国次贷危机爆发以来,金融市场的运行环境更加错综复杂,金融风险极容易在各个市场之间相互传染。在金融危机频发的背景下进行投资组合,应特别注意防范组合投资风险。对于资产组合的风险评估,应尝试构建多个风险模型,选择测度准确度相对较高的模型进行风险评估,并将VaR模型与ES模型结合使用。此外,对投资组合的风险评估还应立足于动态的角度,因为尾部极值风险传导具有时变特性,所以在使用静态类风险评估方法时必须谨慎,以防错误评估资产组合的风险,同时,必须及时有效地采取相应的止损措施,以防范极端金融事件导致股市同时暴跌而对组合资产造成巨额亏损。
Since the Stock Market Crash of1929, the international financial markets have experienced crisis contagion for several times. The subprime mortgage crisis of the United States, once shocked the international financial market in a short period, has evolved into a global economic crisis with far-reaching influence and become the representative event of financial contagion. The frequent occurrence of risk contagion in the international financial markets presents huge risk for investors and places higher requirements for financial risk management.
The basis and the core of financial risk management lie in how to correctly measure the risk. As in the financial practice, investors prefer portfolio rather than a single asset, thus the measurement for the portfolio risk is of greater realistic significance. Compared with the risk assessment of a single asset, that of portfolio is more complicated, for the measurement of portfolio risk considers not only the volatility model of the returns on a single asset of the portfolio, but also the dependence relationship among the assets of the portfolio. However, the correlation among financial assets is perplexing, so how to choose and use the risk measurement tools properly become one of the most important links in the process of portfolio risk assessment.
Choosing S&P500Index of the United States, Nikkei225Index of Japan, Shanghai Composite Index of China and Hang Seng Index of Hongkong as the objects of this study and the four kinds of time-varying Copula-EVT models as the core research method, this paper focuses on financial contagion represented by the subprime mortgage crisis of the United States as the mainline of the study, pushing forward four key problems hierarchically:
· Does the financial contagion significantly affect the intensity of the tail extreme risk conduction among the stock markets?
· Is the direction of risk conduction in the stock market remarkably changed?
· After the outbreak of the crisis, for the long position and the short position of binary portfolio and multi-asset portfolio, is the measurement precision of VaR model and ES model under all kinds of risk model assumptions significantly changed? Are the changes varied?
· What factors will affect the prediction precision of VaR model and ES model? How are the results of effect?
Therefore, based on the standardized residual sequence of each share index returns and combined with the extreme value theory, this paper constructs the marginal distribution, applying four kinds of time-varying Copula functions to construct the joint distribution of the portfolios respectively and applying the time-varying t Copula-GJR-EVT model with better imitative effect to get the dynamic correlation coefficient among the stock markets before and after the breakout of the crisis; by the time-varying SJC-Copula-EVT model, the correlation coefficient of the upper and lower tail among the stock markets is obtained. By using Granger causality test, the influence of financial contagion on the direction of risk conduction has been analyzed. The results of empirical research show that the outbreak of the subprime mortgage crisis has great influence on the intensity and direction of risk contagion. After the outbreak of the crisis, risk contagion has got much more serious among the international stock markets and the time-varying characteristics have got quite obvious. See from the direction of the risk conduction in stock markets:before the outbreak of the subprime mortgage crisis, the risk of stock index is mainly concentrated in the New York stock market and the three major Asian stock markets, namely the Chinese mainland stock market, the Hongkong stock market and the Tokyo stock market does not have risk conduction in between. After the outbreak of the subprime mortgage crisis, the path and direction of risk conduction in the stock markets have been changed remarkably:The U.S. stock market and the others are in a two-way risk conduction relationship. In addition, close and intricate risk relations also exist among the stock markets of Asia, and the correlation of extreme risks between Chinese stock market and the international stock markets is significantly enhanced.
All these distinctive features will undoubtedly affect the measurement precision of portfolio risk model. In this context, this paper combines the four stock index returns to construct binary portfolio and multi-asset portfolio. Based on the four time-varying Copula-EVT models and DCC-GARCH model, this paper targets to the long position and short position respectively, establishes VaR model and ES model and does experimental analysis by using the Backtesting method, so as to compare the changes of measurement precision of various risk models after the crisis. The empirical results show that:firstly, the subprime mortgage crisis has enhanced the positive correlation between the extreme risks among financial markets significantly, weakens the function of multi-asset investment to some degree and decreases the measurement precision of the VaR model of portfolio; however, in some cases, the measurement precision of ES model is improved to a certain extent after the crisis. Secondly, no matter the VaR model or ES model, the risk models constructed based on the time-varying Copula-EVT will have a higher measurement than that of the DCC-GARCH risk model. Thirdly, the selection of marginal distribution model has important influence on the measurement precision of time-varying Copula-EVT risk model. Fourthly, time-varying Copula functions of different types have different prediction precision on portfolio risk model. In general, after the outbreak of the crisis, the measurement precision of time-varying SJC-Copula-EVT-VaR model and that of Copula-EVT-ES model are both relatively high, which further indicates that the subprime mortgage crisis has a huge impact on the measurement precision of portfolio risk model and the models that do better in portraying the asymmetry, the fat tail and the dependency of the variables present stronger advantages in measurement. Nonetheless, for the risk measurement of portfolio, it is still in great need to flexibly choose proper risk model based on the distribution characteristics of portfolio and scientific comparative study.
In the economic globalization of the day, from both the perspectives of time and space, the contagion of financial crisis is becoming increasingly serious. Since the outbreak of the subprime mortgage crisis, the environment of financial market is more perplexing than ever before and the financial risk tends to transfer among different markets. In a background that financial crisis frequently occurs, top priority should be given to preventing the investment risk in portfolio. For the risk assessment of portfolio, different risk models should be established for selection. As one risk model with better measurement precision is selected, VaR model and ES model should be applied jointly. In addition, risk assessment on the portfolio should also be based on a dynamic perspective, for the tail extreme risk conduction has time-varying characteristics, risk assessors must be cautious in using static risk assessment methods, so as to prevent the improper assessment on portfolio risk. At the same time, corresponding measures should be taken effectively to prevent investors from loss, so as to keep away from the huge losses on portfolio brought by the joint crash of stock markets which may be caused by extreme financial events.
金融风险管理的基础与核心在于如何正确地度量风险,由于在金融实务中,投资者往往对资产组合进行投资而非单一资产,因而对于资产组合风险的度量更具现实意义。同单一资产的风险评估相比,投资组合的风险评价更为复杂,因为在组合风险的计量过程中,不仅需要考虑组合中单一资产收益的波动率模型,还必须考虑到组合中各个资产间的相依关系。然而金融资产间的相关性错综复杂,所以如何正确地选择和运用风险度量工具就成为组合风险评价中最重要的一个环节。
本文以美国S&P500指数、日本日经225指数、中国上证综指和香港恒生指数作为研究对象,将四类时变Copula-EVT模型作为核心研究方法,以美国次贷危机为代表的金融危机传染作为一条贯穿始终的研究主线,层层推进四个关键问题：
·危机传染是否显著地影响了股市间尾部极值风险传导的强度?
·股市间风险传导的方向是否发生明显的变化?
·危机爆发后,对于二元资产组合及多元资产组合的多头头寸与空头头寸,各类风险模型假定下的VaR风险价值模型和ES预期损失模型的测度精度是否显著改变?其变化状况是否有所不同?
·哪些因素将影响到VaR模型和ES模型的预测准确度?其影响的结果怎样?
为此,本文在各股指收益的标准残差序列的基础上,结合EVT极值理论,构建边缘分布,分别运用四类时变Copula函数构建各个资产组合的联合分布,采用拟合效果相对较好的时变t Copula-GJR-EVT模型,得到危机爆发前后股市间的极值动态相依系数；通过时变SJC-Copula-EVT模型获得股市间的上尾和下尾极值相关系数。运用格兰杰因果检验的方法,分析了金融危机传染对于股市间风险传导方向产生的影响。实证研究结果表明,危机的爆发,对于股市间极值风险传递的强度和风险传导的方向产生了很大的影响。次贷危机发生以后,国际股市间极值风险传染的程度普遍增强,其时变特征也非常明显。从股市风险传导的方向上看：次贷危机爆发以前,股指间的风险主要汇集于纽约股市,而三大亚洲股市,即中国沪市、香港股市和东京股市间不存在风险传导关系。次贷危机爆发后,股市间风险传导的途径和方向发生了明显的变化：不仅美国纽约股市与其他股市间形成了双向风险传导关系,亚洲股市间也显现出密切而复杂的风险传导格局,中国股市与国际股市的极值风险关联度显著增强。
这些鲜明的特点,无疑将影响到投资组合风险模型的测度准确度。在此背景下,本文将四个股指收益进行组合,构造了二元资产组合及多元资产组合,基于四类时变Copula-EVT模型和DCC-GARCH模型,分别针对多头头寸和空头头寸,建立了VaR模型和ES模型,并运用Backtesting方法进行后验分析,对比研究了危机以后各类风险模型测度精度的变化状况。实证结果表明：第一,次贷危机爆发后,金融市场间极值风险正向相关的程度显著增强,分散化投资的作用在一定程度上被削弱,资产组合VaR风险价值模型的测度精度有所降低；然而在某些状况下,预期损失ES模型的测度精度却在危机后有一定程度的提高。第二,无论是VaR模型还是ES模型,基于时变Copula-EVT构建的风险模型,其测度精度在总体上高于DCC-GARCH风险模型。第三,边缘分布模型的选择,对于时变Copula-EVT风险模型的测度效果具有重要影响。第四,由不同类型的时变Copula函数构造的风险模型,对于资产组合风险的预测准确度有所不同。综合来看,危机爆发以后,时变SJC-Copula-EVT-VaR模型与时变tCopula-EVT-ES模型的测度精度均相对较高,这进一步表明,次贷危机对于资产组合风险模型的测度效果产生了巨大冲击,善于刻画变量间非对称性、厚尾性相依特征的模型显现出较强的测度优势。尽管如此,对于资产组合的风险测度,仍需根据资产组合的分布特征以及科学的对比研究来灵活地选择合适的风险模型。
在经济全球化的今天,无论是从时间还是空间的角度,金融危机传染都日趋严重。美国次贷危机爆发以来,金融市场的运行环境更加错综复杂,金融风险极容易在各个市场之间相互传染。在金融危机频发的背景下进行投资组合,应特别注意防范组合投资风险。对于资产组合的风险评估,应尝试构建多个风险模型,选择测度准确度相对较高的模型进行风险评估,并将VaR模型与ES模型结合使用。此外,对投资组合的风险评估还应立足于动态的角度,因为尾部极值风险传导具有时变特性,所以在使用静态类风险评估方法时必须谨慎,以防错误评估资产组合的风险,同时,必须及时有效地采取相应的止损措施,以防范极端金融事件导致股市同时暴跌而对组合资产造成巨额亏损。
Since the Stock Market Crash of1929, the international financial markets have experienced crisis contagion for several times. The subprime mortgage crisis of the United States, once shocked the international financial market in a short period, has evolved into a global economic crisis with far-reaching influence and become the representative event of financial contagion. The frequent occurrence of risk contagion in the international financial markets presents huge risk for investors and places higher requirements for financial risk management.
The basis and the core of financial risk management lie in how to correctly measure the risk. As in the financial practice, investors prefer portfolio rather than a single asset, thus the measurement for the portfolio risk is of greater realistic significance. Compared with the risk assessment of a single asset, that of portfolio is more complicated, for the measurement of portfolio risk considers not only the volatility model of the returns on a single asset of the portfolio, but also the dependence relationship among the assets of the portfolio. However, the correlation among financial assets is perplexing, so how to choose and use the risk measurement tools properly become one of the most important links in the process of portfolio risk assessment.
Choosing S&P500Index of the United States, Nikkei225Index of Japan, Shanghai Composite Index of China and Hang Seng Index of Hongkong as the objects of this study and the four kinds of time-varying Copula-EVT models as the core research method, this paper focuses on financial contagion represented by the subprime mortgage crisis of the United States as the mainline of the study, pushing forward four key problems hierarchically:
· Does the financial contagion significantly affect the intensity of the tail extreme risk conduction among the stock markets?
· Is the direction of risk conduction in the stock market remarkably changed?
· After the outbreak of the crisis, for the long position and the short position of binary portfolio and multi-asset portfolio, is the measurement precision of VaR model and ES model under all kinds of risk model assumptions significantly changed? Are the changes varied?
· What factors will affect the prediction precision of VaR model and ES model? How are the results of effect?
Therefore, based on the standardized residual sequence of each share index returns and combined with the extreme value theory, this paper constructs the marginal distribution, applying four kinds of time-varying Copula functions to construct the joint distribution of the portfolios respectively and applying the time-varying t Copula-GJR-EVT model with better imitative effect to get the dynamic correlation coefficient among the stock markets before and after the breakout of the crisis; by the time-varying SJC-Copula-EVT model, the correlation coefficient of the upper and lower tail among the stock markets is obtained. By using Granger causality test, the influence of financial contagion on the direction of risk conduction has been analyzed. The results of empirical research show that the outbreak of the subprime mortgage crisis has great influence on the intensity and direction of risk contagion. After the outbreak of the crisis, risk contagion has got much more serious among the international stock markets and the time-varying characteristics have got quite obvious. See from the direction of the risk conduction in stock markets:before the outbreak of the subprime mortgage crisis, the risk of stock index is mainly concentrated in the New York stock market and the three major Asian stock markets, namely the Chinese mainland stock market, the Hongkong stock market and the Tokyo stock market does not have risk conduction in between. After the outbreak of the subprime mortgage crisis, the path and direction of risk conduction in the stock markets have been changed remarkably:The U.S. stock market and the others are in a two-way risk conduction relationship. In addition, close and intricate risk relations also exist among the stock markets of Asia, and the correlation of extreme risks between Chinese stock market and the international stock markets is significantly enhanced.
All these distinctive features will undoubtedly affect the measurement precision of portfolio risk model. In this context, this paper combines the four stock index returns to construct binary portfolio and multi-asset portfolio. Based on the four time-varying Copula-EVT models and DCC-GARCH model, this paper targets to the long position and short position respectively, establishes VaR model and ES model and does experimental analysis by using the Backtesting method, so as to compare the changes of measurement precision of various risk models after the crisis. The empirical results show that:firstly, the subprime mortgage crisis has enhanced the positive correlation between the extreme risks among financial markets significantly, weakens the function of multi-asset investment to some degree and decreases the measurement precision of the VaR model of portfolio; however, in some cases, the measurement precision of ES model is improved to a certain extent after the crisis. Secondly, no matter the VaR model or ES model, the risk models constructed based on the time-varying Copula-EVT will have a higher measurement than that of the DCC-GARCH risk model. Thirdly, the selection of marginal distribution model has important influence on the measurement precision of time-varying Copula-EVT risk model. Fourthly, time-varying Copula functions of different types have different prediction precision on portfolio risk model. In general, after the outbreak of the crisis, the measurement precision of time-varying SJC-Copula-EVT-VaR model and that of Copula-EVT-ES model are both relatively high, which further indicates that the subprime mortgage crisis has a huge impact on the measurement precision of portfolio risk model and the models that do better in portraying the asymmetry, the fat tail and the dependency of the variables present stronger advantages in measurement. Nonetheless, for the risk measurement of portfolio, it is still in great need to flexibly choose proper risk model based on the distribution characteristics of portfolio and scientific comparative study.
In the economic globalization of the day, from both the perspectives of time and space, the contagion of financial crisis is becoming increasingly serious. Since the outbreak of the subprime mortgage crisis, the environment of financial market is more perplexing than ever before and the financial risk tends to transfer among different markets. In a background that financial crisis frequently occurs, top priority should be given to preventing the investment risk in portfolio. For the risk assessment of portfolio, different risk models should be established for selection. As one risk model with better measurement precision is selected, VaR model and ES model should be applied jointly. In addition, risk assessment on the portfolio should also be based on a dynamic perspective, for the tail extreme risk conduction has time-varying characteristics, risk assessors must be cautious in using static risk assessment methods, so as to prevent the improper assessment on portfolio risk. At the same time, corresponding measures should be taken effectively to prevent investors from loss, so as to keep away from the huge losses on portfolio brought by the joint crash of stock markets which may be caused by extreme financial events.
引文
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