On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles

Abstract

This article reviews two leading measures of financial risk and an emerging alternative. Embraced by the Basel accords, value-at-risk and expected shortfall are the leading measures of financial risk. Expectiles offset the weaknesses of value-at-risk (VaR) and expected shortfall. Indeed, expectiles are the only elicitable law-invariant coherent risk measures. After reviewing practical concerns involving backtesting and robustness, this article more closely examines regulatory applications of expectiles. Expectiles are most readily 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. Moreover, expectiles are in harmony with gain/loss ratios in financial risk management. Expectiles may address some of the flaws in VaR and expected shortfall—subject to the reservation that no risk measure can achieve exactitude in regulation.

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