The Out-of-Sample Predictability of Asymmetric Dependence of Portfolio Returns - The Multivariate Copula Distribution Function Approach
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Armed with the copula distribution function that describes the asymmetric tail dependence, and the marginal distributions that capture the fat-tailed behavior, we estimate risk measures such as the Value-at-Risk and expected shortfall and evaluate whether those from the Gaussian copula function underestimate or overestimate true risk measures. We also investigate the impact of asymmetric tail dependence between the portfolio returns on the out-of-sample predictability of the returns. We fit the GPD as the two margins and a variety of copula functions in the extant literature in evaluating the risk measures. We compute the VaR and ES from the benchmark Gaussian copula model and the competing copula models and confirm that the benchmark model underestimate the levels of risk regardless of the measures of dependence. We use the out-of-sample predictability test to evaluate the performance of the competing copula models. We compare the out-of-sample predictability of the three copula-based competing models by calculating the out-of-sample log-likelihood. The Gaussian and the Student’s t copula models are the representative symmetric copulas, while the Clayton copula is selected as the representative asymmetric copula model. According to the test statistics, the out-of-sample predictability of the Clayton and the Student’s t copula models are superior to that of the Gaussian copula model. Overall, the Clayton copula model turns out to be the best out-of-sample forecasting copula model.
Abstract
Armed with the copula distribution function that describes the asymmetric tail dependence, and the marginal distributions that capture the fat-tailed behavior, we estimate risk measures such as the Value-at-Risk and expected shortfall and evaluate whether those from the Gaussian copula function underestimate or overestimate true risk measures. We also investigate the impact of asymmetric tail dependence between the portfolio returns on the out-of-sample predictability of the returns. We fit the GPD as the two margins and a variety of copula functions in the extant literature in evaluating the risk measures. We compute the VaR and ES from the benchmark Gaussian copula model and the competing copula models and confirm that the benchmark model underestimate the levels of risk regardless of the measures of dependence. We use the out-of-sample predictability test to evaluate the performance of the competing copula models. We compare the out-of-sample predictability of the three copula-based competing models by calculating the out-of-sample log-likelihood. The Gaussian and the Student’s t copula models are the representative symmetric copulas, while the Clayton copula is selected as the representative asymmetric copula model. According to the test statistics, the out-of-sample predictability of the Clayton and the Student’s t copula models are superior to that of the Gaussian copula model. Overall, the Clayton copula model turns out to be the best out-of-sample forecasting copula model.
참고문헌 (23)
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