Journal of Economic Theory and Econometrics: Journal of the Korean Econometric Society
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Journal of Economic Theory and Econometrics
JETEM/계량경제학보/計量經濟學報/JKES
Journal of the Korean Econometric Society

Modeling Non-Normally Distributed Stock Portfolio Returns and Applications to Risk Management

Vol.26, No.3, September , 35–62



  •   (Department of Business Administration, Myongji University)

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Abstract  

We utilize the copula function methodology to separate out the components which describe the marginal behavior of the return processes and the dependence structure between the random variables from the joint density. In order to reflect the non-ellipticity of the joint distribution and heavy tails in the extreme quantile of the marginal distributions of asset returns, we use the generalized Pareto distribution (GPD) as the margins and a variety of parametric copula functions along with a nonparametric copula function in the analysis. We select the optimal copulas from a variety of non-nested copulas based on the model selection criteria. In calculating the risk measures, we assume that the returns are jointly distributed to the parametric copulas as well as to the empirical copula. We then compare the result with that from the bivariate normal distribution. The results show that the VaR and ES computed from the copula function which takes the complicated and possibly nonlinear dependence structure into account performs better than the one based on the linear correlation-based normality assumption.


Keywords
   fat-tail behavior, Value-at-Risk, expected shortfall, generalized Pareto distribution, extreme value theory, copula function

JEL classification codes
   G10
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