Asymptotic Equivalence of Conservative Value-at-Risk- and Expected Shortfall-Based Capital Charges

20 Pages Posted: 8 Jun 2016

See all articles by Giovanni Puccetti

Giovanni Puccetti

University of Florence - Department of Economics and Management

Ludger Rüschendorf

University of Freiburg

Date Written: February 28, 2014

Abstract

We show that the conservative estimate of the value-at-risk (VaR) for the sum of d random losses with given identical marginals and finite mean is equivalent to the corresponding conservative estimate of the expected shortfall in the limit, as the number of risks becomes arbitrarily large. Examples of interest in quantitative risk management show that the equivalence also holds for relatively small and inhomogeneous risk portfolios. When the individual random losses have infinite first moment, we show that VaR can be arbitrarily large with respect to the corresponding VaR estimate for comonotonic risks if the risk portfolio is large enough.

Keywords: value-at-risk, capital charges

Suggested Citation

Puccetti, Giovanni and Rüschendorf, Ludger, Asymptotic Equivalence of Conservative Value-at-Risk- and Expected Shortfall-Based Capital Charges (February 28, 2014). Journal of Risk, Vol. 16, No. 3, 2014. Available at SSRN: https://ssrn.com/abstract=2790918

Giovanni Puccetti (Contact Author)

University of Florence - Department of Economics and Management ( email )

Via delle Pandette, 9
Firenze, Florence 50127
Italy

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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