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
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