Monetary and Economic Studies Vol.20, No.1 / January 2002

Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization

Yasuhiro Yamai, Toshinao Yoshiba

We compare expected shortfall with value-at-risk (VaR) in three aspects: estimation errors, decomposition into risk factors, and optimization.
We describe the advantages and the disadvantages of expected shortfall over VaR. We show that expected shortfall is easily decomposed and optimized while VaR is not. We also show that expected shortfall needs a larger size of sample than VaR for the same level of accuracy.

Keywords: Expected shortfall; Value-at-risk; Optimization

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2002 Bank of Japan All Rights Reserved.

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