A Note on Optimal Estimation from a Risk-Management Perspective under Possibly Misspecified Tail Behavior
AbstractMany 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.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 18 (2000)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main
Other versions of this item:
- Lucas, Andr‚, 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.
- 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.:
- White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
- 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.
- Jose A. Lopez & Christian A. Walter, 2000. "Evaluating covariance matrix forecasts in a value-at-risk framework," Working Papers in Applied Economic Theory 2000-21, Federal Reserve Bank of San Francisco.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.