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Asymptotically Efficient Estimation of the Conditional Expected Shortfall

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  • Samantha Leorato

    (Tor Vergata University)

  • Franco Peracchi

    (Tor Vergata University and EIEF)

  • Andrei V. Tanase

    (National Bank of Romania)

Abstract

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.

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Bibliographic Info

Paper provided by Einaudi Institute for Economics and Finance (EIEF) in its series EIEF Working Papers Series with number 1013.

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Length: 28 pages
Date of creation: 2010
Date of revision: Dec 2010
Handle: RePEc:eie:wpaper:1013

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  1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521845731.
  2. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  3. Moller, Jan Kloppenborg & Nielsen, Henrik Aalborg & Madsen, Henrik, 2008. "Time-adaptive quantile regression," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(3), pages 1292-1303, January.
  4. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 38(4), pages 433-447, February.
  5. Franco Peracchi & Andrei V. Tanase, 2008. "On estimating the conditional expected shortfall," CEIS Research Paper, Tor Vergata University, CEIS 122, Tor Vergata University, CEIS, revised 14 Jul 2008.
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  15. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
  16. Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6631, London School of Economics and Political Science, LSE Library.
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  20. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 52(3), pages 459-470, September.
  21. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1505-1518, July.
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Citations

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Cited by:
  1. Chun, So Yeon & Shapiro, Alexander & Uryasev, Stan, 2011. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," MPRA Paper 30132, University Library of Munich, Germany.
  2. Rockafellar, R.T. & Royset, J.O. & Miranda, S.I., 2014. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk," European Journal of Operational Research, Elsevier, Elsevier, vol. 234(1), pages 140-154.
  3. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2013. "Pair Copula Construction based Expected Shortfall estimation," Economics Bulletin, AccessEcon, vol. 33(2), pages 1067-1072.

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