Capturing Tail Risks Beyond VaR

28 Pages Posted: 7 Sep 2008 Last revised: 10 Jul 2009

See all articles by Woon K. Wong

Woon K. Wong

IMRU, Cardiff Business School

Guobin Fan

School of Management and Economics, The University of Electronic Science and Technology of China

Yong Zeng

University of Electronic Science and Technology of China (UESTC)

Date Written: May 1, 2009

Abstract

Since Value-at-Risk (VaR) disregards tail losses beyond the VaR boundary, the expected shortfall (ES), which measures the average loss when a VaR is exceeded, and the tail-risk-of-VaR (TR), which sums the sizes of tail losses, are used to investigate risks at the tails of distributions for major stock markets. As VaR exceptions are rare, we employ the saddlepoint or small sample asymptotic technique to backtest ES and TR. Because the two risk measures are complementary to each other and hence provide more powerful backtests, we are able to show that (a) the correct specification of distribution tail, rather than heteroscedastic process, plays a key role to accurate risk forecasts; and (b) it is best to model the tails separately from the central part of distribution using the generalized Pareto distribution. To sum up, we provide empirical evidence that financial markets behave differently during crises, and extreme risks cannot be modeled effectively under normal market conditions or based on a short data history.

Keywords: Value-at-Risk, expected shortfall, tail risk, backtesting, saddlepoint technique

JEL Classification: G11, G32

Suggested Citation

Wong, Woon K. and Fan, Guobin and Zeng, Yong, Capturing Tail Risks Beyond VaR (May 1, 2009). Available at SSRN: https://ssrn.com/abstract=1263949 or http://dx.doi.org/10.2139/ssrn.1263949

Woon K. Wong (Contact Author)

IMRU, Cardiff Business School ( email )

Cardiff CF10 3EU
United Kingdom

Guobin Fan

School of Management and Economics, The University of Electronic Science and Technology of China ( email )

No.4, Section 2, North Jianshe Road
Chengdu, Chengdu
China

Yong Zeng

University of Electronic Science and Technology of China (UESTC) ( email )

No.4, Section 2, North Jianshe Road
Chengdu, Chengdu
China

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