Capturing Tail Risks Beyond VaR
28 Pages Posted: 7 Sep 2008 Last revised: 10 Jul 2009
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: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
How Accurate are Value-at-Risk Models at Commercial Banks
By Jeremy Berkowitz and James M. O'brien
-
The Predictive Ability of Several Models of Exchange Rate Volatility
By Kenneth D. West and Dongchul Cho
-
Bank Capital and Value at Risk
By Patricia Jackson, David Maude, ...
-
Bank Capital Requirements for Market Risk: The Internal Models Approach
By Darryll Hendricks and Beverly Hirtle