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Value-at-Risk: The Effect of Autoregression in a Quantile Process

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  • Khizar Qureshi

Abstract

Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%. Here we demonstrate Conditional Autoregressive Value at Risk, first introduced by Engle, Manganelli (2001). CAViaR suggests that negative/positive returns are not i.i.d., and that there is significant autocorrelation. The model is tested using data from 1986- 1999 and 1999-2009 for GM, IBM, XOM, SPX, and then validated via the dynamic quantile test. Results suggest that the tails (upper/lower quantile) of a distribution of returns behave differently than the core.

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  • Khizar Qureshi, 2016. "Value-at-Risk: The Effect of Autoregression in a Quantile Process," Papers 1605.04940, arXiv.org.
    • Handle: RePEc:arx:papers:1605.04940
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    1. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    2. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    3. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
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    5. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
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    Cited by:

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