Part I describes the calculation of VaR in its conventional form. For illustrative purposes, Part I will describe parametric VaR on a Gaussian distribution. Part II summarizes known weaknesses in VaR, from inherent model and estimation risk to VaR’s failure to perform under extreme economic stress and VaR’s failure to satisfy the theoretical constraints on “coherent” measurements of risk. Part Ill describes how to calculate expected shortfall as an extension of conditional VaR.
It further describes how expected shortfall, but not VaR, provides a coherent measure of risk.
Part Ill then reverses field. It explains how VaR, but not expected shortfall (or, for that matter, nearly every other general spectral measure of risk), satisfies the mathematical requirement of “elicitability. ” Mathematical limitations on measures of risk therefore force regulators and bankers to choose between coherence and elicitability, between theoretically sound consolidation of diverse risks (on one hand) and reliable backtesting of risk forecasts against historical observations.
Justin Smith Morrill Professor of Law, Michigan State University (effective July 1, 2013).
This paper summarizes a presentation made on April 17, 2013, at Georgetown Law Center’s colloquium on international financial regulation, conducted by Professor Christopher J. drummer. I appreciate comments by Adam Candeub and Jeffrey Sexton. Special thanks to Heather Elaine Worland Chen. Jim Chen Page 1 Electronic copy available
Conventional VaR Like modern portfolio theory and the entire edifice of quantitative finance derived from those beginnings,l conventional value-at-risk analysis assumes that risk is rguably represents the most important tool for evaluating market risk as one of several threats to the global financial system.
Basel II identifies a version ofVaR analysis as that accord’s preferred tool for assessing banks’ exposure to market risk. 4 Authorities around the world have endorsed VaR, either as a regulator standard or as a best practice. Even absent regulatory compulsion, private firms routinely use VaR as an internal risk management tool, often directing traders to reduce exposure below the level prescribed by those firms’ own VaR limits.