Portfolio risks of bivariate financial returns using copula-VaR approach

A case study on Malaysia and U.S. stock markets

Ruzanna Ab Razak, Noriszura Ismail

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The recent financial turmoil which causes the financial markets to react in a nonlinear way has led to a renewed interest in the modeling of portfolio dependence and risk. Risk can be measured by the traditional VaR measures such as normal VaR and historical simulation. However, it is challenging to estimate the portfolio VaR via parametric methods because of the complexity of modeling the joint multivariate distribution of the assets in the portfolio. Copula model is an alternative method that is able to account for the joint multivariate distribution. The purpose of this study is to evaluate the risks of equally and mixed weighted portfolios of the SP500 and KLCI returns using the VaR based copula (copula-VaR) approach. Comparisons between the copula-VaR estimates with the traditionalVaR measures were also conducted. This study reveals that the marginal distribution of the SP500 and KLCI return series can be modeled by the ARMA-GARCH models, while the dependence structure between both indices can be described by the Clayton copula. The backtesting results indicate that the copula-VaR provide better estimates of the portfolio risks compared to the normal VaR and historical simulation. Our study also found that theVaR models produce a more accurate risk estimates when a less volatile asset has a higher investment fraction in the portfolio.

Original languageEnglish
Pages (from-to)1947-1964
Number of pages18
JournalGlobal Journal of Pure and Applied Mathematics
Volume12
Issue number3
Publication statusPublished - 2016

Fingerprint

Malaysia
Copula
Stock Market
Multivariate Distribution
Joint Distribution
Estimate
Copula Models
ARMA Model
GARCH Model
Dependence Structure
Volatiles
Financial Markets
Marginal Distribution
Modeling
Simulation
Financial markets
Series
Evaluate
Alternatives

Keywords

  • Backtesting
  • Copula
  • Value-at-risk

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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AB - The recent financial turmoil which causes the financial markets to react in a nonlinear way has led to a renewed interest in the modeling of portfolio dependence and risk. Risk can be measured by the traditional VaR measures such as normal VaR and historical simulation. However, it is challenging to estimate the portfolio VaR via parametric methods because of the complexity of modeling the joint multivariate distribution of the assets in the portfolio. Copula model is an alternative method that is able to account for the joint multivariate distribution. The purpose of this study is to evaluate the risks of equally and mixed weighted portfolios of the SP500 and KLCI returns using the VaR based copula (copula-VaR) approach. Comparisons between the copula-VaR estimates with the traditionalVaR measures were also conducted. This study reveals that the marginal distribution of the SP500 and KLCI return series can be modeled by the ARMA-GARCH models, while the dependence structure between both indices can be described by the Clayton copula. The backtesting results indicate that the copula-VaR provide better estimates of the portfolio risks compared to the normal VaR and historical simulation. Our study also found that theVaR models produce a more accurate risk estimates when a less volatile asset has a higher investment fraction in the portfolio.

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