In this short note we propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realized cash-flow separately, one could bind them into the secured position, for which the risk measurement process is much easier. Using this simple concept combined with monotonicity of Expected Shortfall with respect to its target confidence level , one can provide an unconditional coverage backtesting framework for Expected Shortfall that is a natural extension of the current Value-at-Risk regulatory traffic-light approach  .
We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of Expected Shortfall with respect to its target confidence level we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realisations for the secured position that add up to a negative total. Surprisingly, this simple quantity could be used to construct an efficient backtesting framework for unconditional coverage of Expected Shortfall in a natural extension of the regulatory traffic-light approach for Value-at-Risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures .
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In this short note we
We
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realized
realised
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the risk measurement process
risk measurement
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, one can provide an unconditional coverage
we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realisations for the secured position that add up to a negative total. Surprisingly, this simple quantity could be used to construct an efficient
R
Expected Shortfall that is
unconditional coverage of Expected Shortfall in
D
current Value-at-Risk
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for Value-at-Risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures