Expectiles-type risk measures: an alternative to value-at-risk and expected shortfall

Embraced by the international banking standards known as the Basel Accords, value-at-risk (VaR) has long been promoted as the benchmark risk measurement tool in insurance and financial market sectors. Consistently criticised for its lack of subadditivity and its failure to account for the severity of losses in the far tail of the distribution, value-at-risk lost some ground to the tail-sensitive expected shortfall (tail VaR). Its sensitivity to the size of potential losses beyond VaR should be the key incentive for tail VaR to receive the favour of the regulator and prudential risk managers. In that respect, the Basel IV standards, whose implementation is due in January 2023, amended the global bank capital requirements by shifting the quantitative risk metrics system from 99% value-at-risk to 97.5% expected shortfall. Similarly, while capital requirements are determined on the basis of a 99.5% value-at-risk over one year under the EU insurance regulatory regime Solvency II, the Swiss Solvency Test requires the use of a 99% tail VaR. At the same time, the (erroneous) belief that expected shortfall could not be backtested because of its non-elicitability fostered an interest in emerging alternatives, namely expectiles as the sole elicitable law invariant coherent risk measures. In light of this, one may legitimately wonder what the best risk measure might be. Subject to the important caveat that no risk measure can achieve superiority (there is no panacea), the aim of this thesis is to provide a compendium comparison between expectiles and traditional measures (value-at-risk, expected shortfall, and variance) through a number of applications in risk management. In that regard, we will review the commonly accepted desirable properties of risk measures such as coherence, convexity, law-invariance, comonotonic additivity, robustness, and elicitability. While expectiles may address some of the flaws in value-at-risk and expected shortfall, they might fail to detect risk concentrations and difficulties in their interpretation gave rise to criticisms. We also find that the backtesting-related issues and lack of robustness of expected shortfall are indeed not problematic. While non-robustness to outliers might actually enable to foresee future large losses, non-elicitability does not actually preclude backtesting. There is thus no sufficient evidence to justify an all-inclusive replacement of value-at-risk and expected shortfall by expectiles. The main contribution of this work is a paper by J.M. Chen (2018), entitled On exactitude in financial regulation : value at risk, expected shortfall and expectiles.