A note on optimal estimation from a risk management perspective under possibly mis-specified tail behavior
AbstractMany 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics in its series Serie Research Memoranda with number 0056.
Date of creation: 1997
Date of revision:
Contact details of provider:
Web page: http://www.feweb.vu.nl
Value-at-Risk; leptokurtosis; downside-risk; optimal asset allocation; model mis-specification; minimax optimality; robustness; risk managment; quasi-likelihood;
Other versions of this item:
- 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.
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (R. Dam).
If references are entirely missing, you can add them using this form.