Asymptotically Efficient Estimation of the Conditional Expected Shortfall
This paper proposes a procedure for efficient estimation of the trimmed mean of a random variable conditional on a set of covariates. For concreteness, the paper focuses on a financial application where the trimmed mean of interest corresponds to the conditional expected shortfall, which is known to be a coherent risk measure. The proposed class of estimators is based on representing the estimand as an integral of the conditional quantile function. Relative to the simple analog estimator that weights all conditional quantiles equally, asymptotic efficiency gains may be attained by giving different weights to the different conditional quantiles while penalizing excessive departures from uniform weighting. The approach presented here allows for either parametric or nonparametric modeling of the conditional quantiles and the weights, but is essentially nonparametric in spirit. The paper establishes the asymptotic properties of the proposed class of estimators. Their finite sample properties are illustrated through a set of Monte Carlo experiments and an empirical application.
|Date of creation:||2010|
|Date of revision:||Dec 2010|
|Contact details of provider:|| Postal: Via Sallustiana, 62 - 00187 Roma|
Phone: +39 066790013
Fax: +39 0647924872
Web page: http://www.eief.it/repec
More information through EDIRC
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.:
- McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
- Giuseppe De Luca, 2008. "SNP and SML estimation of univariate and bivariate binary-choice models," Stata Journal, StataCorp LP, vol. 8(2), pages 190-220, June.
- Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006.
"Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure,"
Econometric Society, vol. 74(2), pages 539-563, 03.
- Joshua Angrist & Victor Chernozhukov & Ivan Fernandez-Val, 2004. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," NBER Working Papers 10428, National Bureau of Economic Research, Inc.
- Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275, june. pag.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Moller, Jan Kloppenborg & Nielsen, Henrik Aalborg & Madsen, Henrik, 2008. "Time-adaptive quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1292-1303, January.
- Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
- Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007.
"Quantile and probability curves without crossing,"
CeMMAP working papers
CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile And Probability Curves Without Crossing," Boston University - Department of Economics - Working Papers Series WP2007-011, Boston University - Department of Economics.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Post-Print hal-01052958, HAL.
- Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
- Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
- Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
- Franco Peracchi & Andrei V. Tanase, 2008. "On estimating the conditional expected shortfall," CEIS Research Paper 122, Tor Vergata University, CEIS, revised 14 Jul 2008.
- Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Huixia Judy Wang & Xiao-Hua Zhou, 2010. "Estimation of the retransformed conditional mean in health care cost studies," Biometrika, Biometrika Trust, vol. 97(1), pages 147-158.
- Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers 92-49, C.V. Starr Center for Applied Economics, New York University.
- Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 459-470, September.
- Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
When requesting a correction, please mention this item's handle: RePEc:eie:wpaper:1013. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Facundo Piguillem)
If references are entirely missing, you can add them using this form.