Multiple-Period Market Risk Prediction under Long Memory: When VaR is Higher than Expected

Journal of Risk Finance (2014), Vol. 15, pp. 4-32

60 Pages Posted: 15 Mar 2009 Last revised: 16 Jan 2014

Date Written: January 16, 2014

Abstract

Several authors, including Andersen and Bollerslev (1998), stress the importance of long-term volatility dependence for value-at-risk (VaR) prediction. The present paper addresses multiple-period market risk forecasts under long memory persistence in market volatility. To this aim, we propose volatility forecasts based on a combination of the GARCH(1,1)-model with potentially fat-tailed and skewed innovations and a long memory specification of the slowly declining influence of past volatility shocks. As the square-root-of-time rule is known to be mis-specified, we use the GARCH setting of Drost and Nijman (1993) as the benchmark forecasting model. Our empirical study of equity market risk is based on daily index returns during the period January 1975 to December 2010. We study the out-of-sample accuracy of VaR predictions for five, ten, 20 and 60 trading days and document that our approach remarkably improves VaR forecasts for the longer horizons. The result is only in part due to higher predicted risk levels. Ex-post calibration to equal unconditional risk levels illustrates that our approach also enhances efficiency in allocating VaR capital through time.

Keywords: multiple-period value-at-risk, volatility scaling, long memory, GARCH, Hurst exponent, square-root-of-time rule

JEL Classification: C22

Suggested Citation

Kinateder, Harald and Wagner, Niklas F., Multiple-Period Market Risk Prediction under Long Memory: When VaR is Higher than Expected (January 16, 2014). Journal of Risk Finance (2014), Vol. 15, pp. 4-32, Available at SSRN: https://ssrn.com/abstract=1359620 or http://dx.doi.org/10.2139/ssrn.1359620

Harald Kinateder

University of Passau ( email )

Innstrasse 27
Passau, 94032
Germany

HOME PAGE: http://sites.google.com/view/harald-kinateder

Niklas F. Wagner (Contact Author)

Passau University ( email )

Innstrasse 27
Passau, 94030
Germany

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