Portfolio based VaR model: a combination of extreme value theory (EVT) and dynamic conditional correlation (DCC) model

Abstract

This thesis fills a gap in the risk management literature and expands the understanding of the portfolio value at risk (VaR) by providing a theoretical market risk measurement of a portfolio (called “GEV-DCC model”), which combines the tail dynamic conditional correlation (tail-DCC) and extreme value theory. According to the spirit of VaR, the tail distribution is more important than the entire distribution, as well as the correlation in the tail area between various assets. The main advantage of this approach is the increase of accuracy in the parameter estimation of the tail distribution and more consistent correlation measurement for VaR. The results from this method are compared with four other conventional VaR approaches; GARCH model, RiskMetrics, stochastic volatility, and historical simulation. Furthermore, three quality measures are applied to evaluate the suitability, conservativeness, and magnitude of loss of the forecasted VaR, which offer more information from the forecasted VaR pattern.

Applying 16 major equity index returns from developed and emerging markets, this study finds that the GEV-DCC model offers a more accurate coverage across the blocks in the three hypothetical portfolios (the developed equity markets, Asian and Latin American equity markets) compared with the four competing models. The uncovered rates of the GEV-DCC model with the 5-day block approach are generally close to the given probability (α) set in the VaR calculation.

These consistent results can also be found in the robustness test with the shorter forecasting period. In the quality checks, the GEV-DCC presents a relatively stable pattern in the daily and 10-day VaR results. In addition, the GEV-DCC model also provides satisfactory results in the conservativeness and potential loss tests although no direct evidence indicates that it delivers the best result in these two checks. We also find significant differences between the original DCC and the tail-DCC. This evidence shows that the correlations between equity markets in the left tail are significantly higher than the ones in the right tail, and there are significant changes (generally rising) in the tail-DCC patterns around the period of financial crisis in the third quarter of 2008.

The results from this study could potentially provide a critical reference for investors in measuring or managing the market risk.

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Identifiers

ORCID for Taufiq Choudhry: orcid.org/0000-0002-0463-0662

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