Multivariate copulas in financial market risk with particular focus on trading strategies and asset allocation

**Authors:**Stander, Yolanda Sophia**Date:**2012-11-05**Subjects:**Copulas (Mathematical statistics) , Variables (Mathematics) , Asset allocation , Financial risk**Type:**Thesis**Identifier:**uj:7351 , http://hdl.handle.net/10210/8099**Description:**D.Comm. , Copulas provide a useful way to model different types of dependence structures explicitly. Instead of having one correlation number that encapsulates everything known about the dependence between two variables, copulas capture information on the level of dependence as well as whether the two variables exhibit other types of dependence, for example tail dependence. Tail dependence refers to the instance where the variables show higher dependence between their extreme values. A copula is defined as a multivariate distribution function with uniform marginals. A useful class of copulas is known as Archimedean copulas that are constructed from generator functions with very specific properties. The main aim of this thesis is to construct multivariate Archimedean copulas by nesting different bivariate Archimedean copulas using the vine construction approach. A characteristic of the vine construction is that not all combinations of generator functions lead to valid multivariate copulas. Established research is limited in that it presents constraints that lead to valid multivariate copulas that can be used to model positive dependence only. The research in this thesis extends the theory by deriving the necessary constraints to model negative dependence as well. Specifically, it ensures that the multivariate copulas that are constructed from bivariate copulas that capture negative dependence, will be able to capture negative dependence as well. Constraints are successfully derived for trivariate copulas. It is, however, shown that the constraints cannot easily be extended to higher-order copulas. The rules on the types of dependence structures that can be nested are also established. A number of practical applications in the financial markets where copula theory can be utilized to enhance the more established methodologies, are considered. The first application considers trading strategies based on statistical arbitrage where the information in the bivariate copula structure is utilised to identify trading opportunities in the equity market. It is shown that trading costs adversely affect the profits generated. The second application considers the impact of wrong-way risk on counterparty credit exposure. A trivariate copula is used to model the wrong-way risk. The aim of the analysis is to show how the theory developed in this thesis should be applied where negative correlation is present in a trivariate copula structure. Approaches are considered where conditional and unconditional risk driver scenarios are derived by means of the trivariate copula structure. It is argued that by not allowing for wrong-way risk, a financial institution’s credit pricing and regulatory capital calculations may be adversely affected. The final application compares the philosophy behind cointegration and copula asset allocation techniques to test which approach produces the most profitable index-tracking portfolios over time. The copula asset allocation approach performs well over time; however, it is very computationally intensive.**Full Text:**

**Authors:**Stander, Yolanda Sophia**Date:**2012-11-05**Subjects:**Copulas (Mathematical statistics) , Variables (Mathematics) , Asset allocation , Financial risk**Type:**Thesis**Identifier:**uj:7351 , http://hdl.handle.net/10210/8099**Description:**D.Comm. , Copulas provide a useful way to model different types of dependence structures explicitly. Instead of having one correlation number that encapsulates everything known about the dependence between two variables, copulas capture information on the level of dependence as well as whether the two variables exhibit other types of dependence, for example tail dependence. Tail dependence refers to the instance where the variables show higher dependence between their extreme values. A copula is defined as a multivariate distribution function with uniform marginals. A useful class of copulas is known as Archimedean copulas that are constructed from generator functions with very specific properties. The main aim of this thesis is to construct multivariate Archimedean copulas by nesting different bivariate Archimedean copulas using the vine construction approach. A characteristic of the vine construction is that not all combinations of generator functions lead to valid multivariate copulas. Established research is limited in that it presents constraints that lead to valid multivariate copulas that can be used to model positive dependence only. The research in this thesis extends the theory by deriving the necessary constraints to model negative dependence as well. Specifically, it ensures that the multivariate copulas that are constructed from bivariate copulas that capture negative dependence, will be able to capture negative dependence as well. Constraints are successfully derived for trivariate copulas. It is, however, shown that the constraints cannot easily be extended to higher-order copulas. The rules on the types of dependence structures that can be nested are also established. A number of practical applications in the financial markets where copula theory can be utilized to enhance the more established methodologies, are considered. The first application considers trading strategies based on statistical arbitrage where the information in the bivariate copula structure is utilised to identify trading opportunities in the equity market. It is shown that trading costs adversely affect the profits generated. The second application considers the impact of wrong-way risk on counterparty credit exposure. A trivariate copula is used to model the wrong-way risk. The aim of the analysis is to show how the theory developed in this thesis should be applied where negative correlation is present in a trivariate copula structure. Approaches are considered where conditional and unconditional risk driver scenarios are derived by means of the trivariate copula structure. It is argued that by not allowing for wrong-way risk, a financial institution’s credit pricing and regulatory capital calculations may be adversely affected. The final application compares the philosophy behind cointegration and copula asset allocation techniques to test which approach produces the most profitable index-tracking portfolios over time. The copula asset allocation approach performs well over time; however, it is very computationally intensive.**Full Text:**

Empirical evidence of a systematic tail risk premium in the Johannesburg Stock Exchange

**Authors:**Kouadio, Jean Joel Arnaud**Date:**2020**Subjects:**Johannesburg Stock Exchange , Copulas (Mathematical statistics) , Extreme value theory , Financial risk**Language:**English**Type:**Masters (Thesis)**Identifier:**http://hdl.handle.net/10210/451433 , uj:39777**Description:**Abstract: This study defines systematic tail risk as a stock’s exposure to market tail events and assesses the impact of it on the cross section of returns from the Johannesburg Stock Exchange (JSE). To determine the extent to which systematic tail risk explains the cross section of returns in the JSE, the study estimates systematic tail risk by combining the statistical concepts of extreme value theory (EVT) and copula. Specifically, the study first characterizes stocks and market tail events under the Block model and subsequently proxies a stock’s systematic tail risk with parameter estimates of an extreme value copula fitted to the bivariate Generalized Extreme Value (GEV) distribution of stock and market tail events. Based on data on JSE All Share Index companies, provided by the JSE for the period of January 2002 through June 2018, results of the traditional asset pricing portfolios formation and crosssectional regressions show that the extreme value copula parameter adequately captures systematic tail risk in the JSE. More importantly, the results support the existence of a systematic tail risk premium in the JSE. Interestingly, the effect of systematic tail risk on the cross section of returns is time-varying and independent from that of risk measures such as beta and downside beta and firm characteristics such as book-to-market (BTM) ratio, size and past returns. In addition, the results provide evidence on the negative impact of the 2008 Global Financial Crisis on crash aversion in the JSE. The practical relevance of these results is of an utmost importance for both academics and finance professionals. The findings implicitly provide support for the downside risk framework as a legitimate perspective on investors’ perception of risk in equity markets and reveal a need to reconsider somehow disfavoured portfolio theories such as the safety-first criterion for asset pricing endeavours. , M.Com. (Financial Economics)**Full Text:**

**Authors:**Kouadio, Jean Joel Arnaud**Date:**2020**Subjects:**Johannesburg Stock Exchange , Copulas (Mathematical statistics) , Extreme value theory , Financial risk**Language:**English**Type:**Masters (Thesis)**Identifier:**http://hdl.handle.net/10210/451433 , uj:39777**Description:**Abstract: This study defines systematic tail risk as a stock’s exposure to market tail events and assesses the impact of it on the cross section of returns from the Johannesburg Stock Exchange (JSE). To determine the extent to which systematic tail risk explains the cross section of returns in the JSE, the study estimates systematic tail risk by combining the statistical concepts of extreme value theory (EVT) and copula. Specifically, the study first characterizes stocks and market tail events under the Block model and subsequently proxies a stock’s systematic tail risk with parameter estimates of an extreme value copula fitted to the bivariate Generalized Extreme Value (GEV) distribution of stock and market tail events. Based on data on JSE All Share Index companies, provided by the JSE for the period of January 2002 through June 2018, results of the traditional asset pricing portfolios formation and crosssectional regressions show that the extreme value copula parameter adequately captures systematic tail risk in the JSE. More importantly, the results support the existence of a systematic tail risk premium in the JSE. Interestingly, the effect of systematic tail risk on the cross section of returns is time-varying and independent from that of risk measures such as beta and downside beta and firm characteristics such as book-to-market (BTM) ratio, size and past returns. In addition, the results provide evidence on the negative impact of the 2008 Global Financial Crisis on crash aversion in the JSE. The practical relevance of these results is of an utmost importance for both academics and finance professionals. The findings implicitly provide support for the downside risk framework as a legitimate perspective on investors’ perception of risk in equity markets and reveal a need to reconsider somehow disfavoured portfolio theories such as the safety-first criterion for asset pricing endeavours. , M.Com. (Financial Economics)**Full Text:**

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