IDEAS home Printed from https://ideas.repec.org/p/vua/wpaper/1997-56.html
   My bibliography  Save this paper

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

Author

Listed:
  • Lucas, André

    (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.

Suggested Citation

  • Lucas, André, 1997. "A note on optimal estimation from a risk management perspective under possibly mis-specified tail behavior," Serie Research Memoranda 0056, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  • Handle: RePEc:vua:wpaper:1997-56
    as

    Download full text from publisher

    File URL: http://degree.ubvu.vu.nl/repec/vua/wpaper/pdf/19970056.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, 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. 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.
    5. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    2. Tang, Niansheng & Wang, Wenjun, 2019. "Robust estimation of generalized estimating equations with finite mixture correlation matrices and missing covariates at random for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 640-655.
    3. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    4. Anatolyev, Stanislav, 2009. "Dynamic modeling under linear-exponential loss," Economic Modelling, Elsevier, vol. 26(1), pages 82-89, January.
    5. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    6. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
    7. Schwiebert, Jörg & Wagner, Joachim, 2015. "A Generalized Two-Part Model for Fractional Response Variables with Excess Zeros," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113059, Verein für Socialpolitik / German Economic Association.
    8. Michael R. Baye & J. Rupert J. Gatti & Paul Kattuman & John Morgan, 2009. "Clicks, Discontinuities, and Firm Demand Online," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 18(4), pages 935-975, December.
    9. Gannon, Gerard L. & Choi, Daniel F. S., 1998. "Structural models: Intra/Inter-day volatility transmission and spillover persistence of the HSI, HSIF and S&P500 futures," International Review of Financial Analysis, Elsevier, vol. 7(1), pages 19-36.
    10. Antoine, Bertille & Dovonon, Prosper, 2021. "Robust estimation with exponentially tilted Hellinger distance," Journal of Econometrics, Elsevier, vol. 224(2), pages 330-344.
    11. José M. R. Murteira & Joaquim J. S. Ramalho, 2016. "Regression Analysis of Multivariate Fractional Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 515-552, April.
    12. Piotr Borkowski & Jan Mielniczuk, 2010. "Postmodel selection estimators of variance function for nonlinear autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 50-63, January.
    13. C. Gouriéroux & A. Monfort & J.‐M. Zakoïan, 2019. "Consistent Pseudo‐Maximum Likelihood Estimators and Groups of Transformations," Econometrica, Econometric Society, vol. 87(1), pages 327-345, January.
    14. DOLADO , Juan J. & RODRIGUEZ-POO, Juan & VEREDAS, David, 2004. "Testing weak exogeneity in the exponential family : an application to financial point processes," LIDAM Discussion Papers CORE 2004049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. von Haefen, Roger H. & Phaneuf, Daniel J., 2003. "Estimating preferences for outdoor recreation:: a comparison of continuous and count data demand system frameworks," Journal of Environmental Economics and Management, Elsevier, vol. 45(3), pages 612-630, May.
    16. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2021. "Generalized aggregation of misspecified models: With an application to asset pricing," Journal of Econometrics, Elsevier, vol. 222(1), pages 451-467.
    17. Alessandra Cretarola & Gianna Fig`a-Talamanca & Marco Patacca, 2017. "A sentiment-based model for the BitCoin: theory, estimation and option pricing," Papers 1709.08621, arXiv.org.
    18. Wooldridge, Jeffrey M., 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 182(1), pages 226-234.
    19. Chen, Willa W. & Deo, Rohit S., 2006. "Estimation of mis-specified long memory models," Journal of Econometrics, Elsevier, vol. 134(1), pages 257-281, September.
    20. Baye, Michael & GATTI, RUPERT J & Kattuman, Paul & Morgan, John, 2004. "Estimating Firm-Level Demand at a Price Comparison Site: Accounting for Shoppers and the Number of Competitors," Competition Policy Center, Working Paper Series qt923692d1, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.

    More about this item

    Keywords

    Value-at-Risk; leptokurtosis; downside-risk; optimal asset allocation; model mis-specification; minimax optimality; robustness; risk managment; quasi-likelihood;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vua:wpaper:1997-56. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: R. Dam (email available below). General contact details of provider: https://edirc.repec.org/data/fewvunl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.