Calculation of the Spearman correlation coefficient
Article 7
1. Institutions shall calculate the Spearman correlation coefficient referred to in Article 6(1) of this Regulation by performing the following steps in the following order: (a) they shall determine the time series of observations of the hypothetical and theoretical changes in the trading desk portfolio’s value for the most recent 250 business days; (b) from the time series of the hypothetical and theoretical changes referred to in point (a), institutions shall produce the corresponding time series of ranks in accordance with paragraph 2, treating the time series of the hypothetical and theoretical changes as the originating time series; (c) they shall calculate the Spearman correlation coefficient in accordance with the following formula: Where: R HPL = the time series of ranks produced from the time series of hypothetical changes referred to in point (b); R RTPL = the time series of ranks produced from the time series of theoretical changes referred to in point (b); = the standard deviation of the time series of ranks R HPL calculated in accordance with paragraph 3, point (a); = the standard deviation of the time series of ranks R RTPL calculated in accordance with paragraph 3, point (b); cov ( R HPL , R RTPL ) = the covariance calculated in accordance with paragraph 3, point (c), between the times series of ranks R HPL and R RTPL . 2. Institutions shall produce the time series of ranks referred to in paragraph 1, point (b), from an originating time series by performing the following steps in the following order: (a) for each observation within the originating time series, institutions shall count the number of observations with a lower value than that observation within that time series; (b) institutions shall label each observation with the number resulting from the calculation set out in point (a) increased by one; (c) where, as a result of the labelling in accordance with point (b), two or more observations are labelled with the same number, institutions shall in addition increase the numbers of those labels with the following fraction: where N equals the quantity of the labels with the same number; (d) institutions shall consider as time series of ranks, the time series of the labels obtained in accordance with points (b) and (c). 3. Institutions shall calculate the standard deviation of the time series of ranks R HPL in accordance with the formula laid down in point (a), the standard deviation of the time series of ranks R RTPL in accordance with the formula laid down in point (b), and the covariance between those time series in accordance with the formula laid down in point (c) as follows: (a) ; (b) ; (c) ; Where: i = the index that denotes the observation in the time series of ranks; = the ‘i-th’ observation of the time series of ranks R HPL ; = the mean of the time series of ranks R HPL ; = the ‘i-th’ observation of the time series of ranks R RTPL ; = the mean of the time series of ranks R RTPL .