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.
Highlights
Quantifying market risk represents the first step toward cogent financial management and regulation
Expectiles combine the elicitability of VaR with the coherence of expected shortfall
The tradeoff between expected shortfall’s subadditivity, coherence, and sensitivity and VaR’s elicitability and robustness injects model risk during the very periods that Basel addressed through stressed VaR (Basel Committee on Banking Supervision 2011a)
Summary
Quantifying market risk represents the first step toward cogent financial management and regulation. Since its adoption by Basel II in 1996, value-at-risk (VaR) has become the most widely used measure of financial risk. An “external risk model” robust “with respect to underlying models and data” ensures that “different judges will reach similar conclusions when they implement. These deficiencies have heightened interest in a third approach. Reliance on “internal models and private data” can mislead financial regulation in two class of law-invariant, coherent, and elicitable risk measures.
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