Inefficiency of Modified VaR and ES

24 Pages Posted: 20 Nov 2015

See all articles by R. Douglas Martin

R. Douglas Martin

University of Washington

Rohit Arora

University of Texas at Austin - Red McCombs School of Business

Date Written: October 29, 2015

Abstract

Modified Value-at-Risk (mVaR) and Modified Expected Shortfall (mES) are risk estimators that can be calculated without modelling the distribution of asset returns. These modified estimators use skewness and kurtosis corrections to normal distribution parametric VaR and ES formulas to reduce bias in risk measurement for non-normal return distributions. However, the use of skewness and kurtosis estimators that are needed to implement mVaR and mES can lead to highly inflated mVaR and mES estimator standard errors. To assess the magnitude of standard error inflation we derive formulas for the large sample standard errors of mVaR and mES using multivariate delta method and compare them against standard errors of parametric VaR and ES estimators, under both normal and t-distributions. Our asymptotic results show that mVaR and mES estimators can have standard errors considerably larger than those of parametric VaR and ES estimators, and small-sample Monte Carlo confirms that the asymptotic results are approximately correct in sample sizes commonly used in practice.

Keywords: Modified VaR, Modified ES, large sample estimator standard error and efficiency, delta-method

JEL Classification: C13, C14, G20

Suggested Citation

Martin, R. Douglas and Arora, Rohit, Inefficiency of Modified VaR and ES (October 29, 2015). Available at SSRN: https://ssrn.com/abstract=2692543 or http://dx.doi.org/10.2139/ssrn.2692543

R. Douglas Martin (Contact Author)

University of Washington ( email )

Applied Mathematics & Statistics
Seattle, WA 98195
United States

Rohit Arora

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX
United States

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