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Uncertainty of Multiple Period Risk Measures

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  • Lönnbark, Carl

    () (Department of Economics, Umeå University)

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 ve day V aR0s for the S&P 500 index. The approaches performed about equally well.

Suggested Citation

  • Lönnbark, Carl, 2009. "Uncertainty of Multiple Period Risk Measures," Umeå Economic Studies 768, Umeå University, Department of Economics.
  • Handle: RePEc:hhs:umnees:0768
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    Keywords

    Asymmetry; Estimation Error; Finance; GJR-GARCH; Prediction; Risk Management;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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