On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles
66 Pages Posted: 8 Mar 2018
Date Written: March 8, 2018
This article reviews two leading measures of financial risk and an emerging alternative. Thanks to their adoption by the Basel accords, VaR and expected shortfall are the leading risk measures in financial regulation. Expectiles complement VaR and expected shortfall by offsetting those competing measures’ known weaknesses. Indeed, expectiles are the only elicitable law-invariant coherent risk measures. After reviewing these theoretical properties and practical concerns involving backtesting and robustness, this article more closely examines the potential use of expectiles as a regulatory measure of financial risk.
Expectiles are most readily understood if they are evaluated as a special class of quantiles. For ease of regulatory implementation, expectiles can be defined exclusively in terms of VaR, expected shortfall, and the thresholds at which those competing risk measures are enforced. Those concepts are well understood, if vigorously debated, in financial regulation. Moreover, expectiles are in harmony with other applications of partial moments and gain/loss ratios to financial risk management. Expectiles may address some of the flaws in VaR and expected shortfall — subject to the inescapable reservation that no risk measure can achieve exactitude in regulation.
Keywords: Expectiles, Market Risk, Risk Measures, Expected Shortfall, VaR, Basel Accords, Elicitability, Coherent Risk Measures, Backtesting, Robustness, Gain/Loss Ratios
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