1. Institutions shall calculate the estimate of the left-tail expected shortfall of a time series X in accordance with the following formula:
\mathrm{ES}_{\mathrm{Left}}(X) = \frac{-1}{\alpha \times N} \times \left\{ \sum_{i=1}^{[\alpha \times N]} X_{(i)} + (\alpha \times N - [\alpha \times N]) \times X_{([\alpha \times N] + 1)} \right\}
where:
— | N is the number of observations in the time series; |
— | α = 2,5 %; |
— | [\alpha \times N] denotes the integer part of the product α ×N; |
— | X_{(i)} denotes the i-th smallest observation in the time series X. |
2. Institutions shall calculate the estimate of the right-tail expected shortfall of a time series X in accordance with the following formula:
\mathrm{ES}_{\mathrm{Right}}(X) = \mathrm{ES}_{\mathrm{Left}}(-X)
where:
— | [IMAGE_1] ([IMAGE_2]) is the estimate of left-tail expected shortfall for the time series [IMAGE_3] calculated in accordance with paragraph 1. |