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A Note on Optimal Estimation from a Risk-Management Perspective under Possibly Misspecified Tail Behavior

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  • Lucas, Andre

Abstract

Many financial time series show leptokurtic behavior--that is, fat tails. Such tail behavior is important for risk management. In this article I focus on the calculation of Value-at-Risk (VaR) as a downside-risk measure for optimal asset portfolios. Using a framework centered on 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 overestimation or underestimation 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--that is, a least squares type of estimator. The maximum likelihood estimator has 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.

Suggested Citation

  • Lucas, Andre, 2000. "A Note on Optimal Estimation from a Risk-Management Perspective under Possibly Misspecified Tail Behavior," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 31-39, January.
    • Handle: RePEc:bes:jnlbes:v:18:y:2000:i:1:p:31-39
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    3. Franses, Philip Hans & Lucas, André, 1997. "Outlier robust cointegration analysis," Serie Research Memoranda 0045, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Nikola Radivojevic & Milena Cvjetkovic & Saša Stepanov, 2016. "The new hybrid value at risk approach based on the extreme value theory," Estudios de Economia, University of Chile, Department of Economics, vol. 43(1 Year 20), pages 29-52, June.
    2. Alejandro Bernales & Diether W. Beuermann & Gonzalo Cortazar, 2014. "Thinly traded securities and risk management," Estudios de Economia, University of Chile, Department of Economics, vol. 41(1 Year 20), pages 5-48, June.
    3. Gong, Xu & Wen, Fenghua & Xia, X.H. & Huang, Jianbai & Pan, Bin, 2017. "Investigating the risk-return trade-off for crude oil futures using high-frequency data," Applied Energy, Elsevier, vol. 196(C), pages 152-161.
    4. Cortazar, Gonzalo & Beuermann, Diether & Bernales, Alejandro, 2013. "Risk Management with Thinly Traded Securities: Methodology and Implementation," IDB Publications (Working Papers) 4647, Inter-American Development Bank.

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    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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