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Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets

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An Erratum to this article was published on 18 April 2012

Abstract

A traditional Monte Carlo simulation using linear correlations induces estimation bias in measuring portfolio value-at-risk (VaR), due to the well-documented existence of fat-tail, skewness, truncations, and non-linear relations in return distributions. In this paper, we consider the above issues in modeling VaR and evaluate the effectiveness of using copula-extreme-value-based semiparametric approaches. To assess portfolio risk in six Asian markets, we incorporate a combination of extreme value theory (EVT) and various copulas to build joint distributions of returns. A backtesting analysis using a Monte Carlo VaR simulation suggests that the Clayton copula-EVT evinces the best performance regardless of the shapes of the return distributions, and that in general the copulas with the EVT provide better estimations of VaRs than the copulas with conventionally employed empirical distributions. These findings still hold in conditional-coverage-based backtesting. These findings indicate the economic significance of incorporating the down-side shock in risk management.

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Notes

  1. To prevent unreasonably large price movements on the market, several emerging markets impose limitations on daily stock price movements, meaning that the change in an individual stock in each trading day cannot exceed a certain fixed percentage point in comparison with the previous day’s closing price. For instance, in Taiwan, the change in a stock price cannot exceed 7%, and the ceiling in Korea is 15%. With this sort of imposed narrow price range on its stock market, a country’s stock return distribution is easily truncated so as to have no distribution tail.

  2. According to Yang and Lim (2004) capital flows to the East Asian economics have steadily increased in 1990s. Although the capital flows turned to weak in 1998 due to the financial crisis, the flows resumed and remain strong since 1999.

  3. Lee and Tan (1999) pointed out that during the early stage of the currency turmoil, most central banks tend to opt for market interventions in support of the sudden depreciation of the local currency value.

  4. See Nelsen (2006) for a detailed derivation.

  5. See Embrechts et al. (2005) for a detailed derivation.

  6. See Coles (2001) and Beirlant et al. (2004) for detailed treatments of EVT.

  7. Since the six countries have their own business days, the number of observations varied for each country. Indonesia had 1,957 observations, Korea had 1,968 observations, Malaysia had 1,967 observations, Singapore had 2,004 observations, Taiwan had 1,997 observations, and Thailand had 1,961 observations.

  8. In general there are 250 business days in a year. As explained in the previous footnote, the length of the data in each country is from 1957 to 2004 days; therefore, each model generates from 1707 to 1754 dynamic VaRs.

  9. To present the results in their corresponding p values, we applied a one-tail hypothesis. Thus, if the observed number of violations is lower than the expected number, we test whether the observed number is higher than the lower bound of the 95% confidence interval, while if the observed number of violations is higher than the expected number, we test whether the observed number of violations is lower than the upper bound of the 95% confidence interval.

  10. See Christoffersen (1998) and Jorion (2007) for a detailed derivation.

  11. The situation of Korea is not applicable to the IND and CC tests, because in the results for Korea there exists no π11.

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Acknowledgments

The authors thank Cheng-Few Lee (Editor-in-Chief) and an anonymous referee for their comments and suggestions. We are also grateful for comments and suggestions from Raj Aggarwal, Peter Chow, Harry Rosen, and seminar participants at The Graduate Center of City University of New York and at the EFA and the PBFEAM meetings. All remaining errors are our own.

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Authors and Affiliations

  1. Department of Accounting and Finance, York College, The City University of New York, 94-20 Guy R. Brewer Blvd, Jamaica, NY, 11451, USA

    Chun-Pin Hsu

  2. Finance Department, Western Connecticut State University, Danbury, CT, USA

    Chin-Wen Huang

  3. Department of Finance and Supply Chain Management, Shippensburg University of Pennsylvania, Shippensburg, PA, USA

    Wan-Jiun Paul Chiou

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  1. Chun-Pin Hsu
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Correspondence to Chun-Pin Hsu.

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Hsu, CP., Huang, CW. & Chiou, WJ.P. Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets. Rev Quant Finan Acc 39, 447–468 (2012). https://doi.org/10.1007/s11156-011-0261-0

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