Uncertainty of Multiple Period Risk Measures

University of Umea Economic Studies Paper No. 768

Posted: 18 Oct 2009

Date Written: October 17, 2009

Abstract

In general, the properties of the conditional distribution of multiple period returns do not follow easily from the one-period data generating process. This renders computation of Value-at-Risk and Expected Shortfall for multiple period returns a non-trivial task. In this paper we consider some approximation approaches to computing these measures. Based on the results of a simulation experiment we conclude that among the studied analytical approaches the one based on approximating the distribution of the multiple period shocks by a skew-t was the best. It was almost as good as the simulation based alternative. We also found that the uncertainty due to the estimation risk can be quite accurately estimated employing the delta method. In an empirical illustration we computed five day VaR's for the S&P 500 index. The approaches performed about equally well.

Keywords: Asymmetry, Estimation Error, Finance, GJR-GARCH, Prediction, Risk Management

JEL Classification: C16, C46, C52, C53, C63, G10

Suggested Citation

Lönnbark, Carl and Lönnbark, Carl, Uncertainty of Multiple Period Risk Measures (October 17, 2009). University of Umea Economic Studies Paper No. 768 , Available at SSRN: https://ssrn.com/abstract=1490292

Carl Lönnbark (Contact Author)

Umeå University ( email )

Samhallsvetarhuset, Plan 2
Umea University
Umeå, SE 901 87
Sweden

Swedbank ( email )

SE-105 34 Stockholm
Sweden

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