Backtesting Expectile: Disentangling Unconditional Coverage and Independence Properties

Under current regulations, financial institutions are required to estimate the daily Value-at-Risk (VaR) or Expected Shortfall (ES) of their trading positions. Despite being widely studied and adopted, both risk measures have theoretical limitations: VaR is not coherent and ES is not elicitable. Expectile, the only law-invariant risk measure that is both coherent and elicitable, has gained considerable interest in both risk management and statistics recently. However, the backtesting of expectile has not yet received adequate attention, and existing backtests tend to suffer from size distortion or low test power. This paper proposes novel unconditional and conditional backtests for expectile. Simulation studies show that the proposed tests exhibit promising finite sample size performance. In addition, in an empirical study, we apply the proposed tests to S&P 500 data.