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A note on optimal estimation from a risk management perspective under possibly mis-specified tail behavior

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  • Lucas, Andr‚

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

Abstract

Many financial time-series show leptokurtic behavior, i.e., fat tails. Such tail behavior is important for risk management. In this paper I focus on the calculation of Value-at-Risk (VaR) as a downside-risk measure for optimal asset portfolios. Using a framework centered around the Student t distribution, I explicitly allow for a discrepancy between the fat-tailedness of the true distribution of asset returns and that of the distribution used by the investment manager. As a result, numbers for the over-estimation or under-estimation of the true VaR of a given portfolio can be computed. These numbers are used to rank several well-known estimation methods for determining the unknown parameters of the distribution of asset returns. Minimizing the absolute (percentage) mismatch between the nominal and actual or true VaR leads to the choice of a Gaussian maximum quasi-likelihood estimator, i.e., a least-squares type estimator. The maximum likelihood estimator has a less satisfactory behavior. Outlier robust estimators perform even worse if the required confidence level for the VaR is high. An explanation for these results is provided.

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File URL: ftp://zappa.ubvu.vu.nl/19970056.pdf
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Bibliographic Info

Paper provided by VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics in its series Serie Research Memoranda with number 0056.

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Date of creation: 1997
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Handle: RePEc:dgr:vuarem:1997-56

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Web page: http://www.feweb.vu.nl

Related research

Keywords: Value-at-Risk; leptokurtosis; downside-risk; optimal asset allocation; model mis-specification; minimax optimality; robustness; risk managment; quasi-likelihood;

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  1. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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