𝐴𝑅𝑊 𝑖 = 𝛽 ∗ ( 𝛼 𝛽 ) ( 𝐴𝑅𝑆 𝑖 )

In this method, the ARW associated to the ARS is growing exponentially, with an upper boundary ‘ 𝛼 ’ and a lower boundary ‘ 𝛽 ’ . For a given institution where the ARS is 100 (the riskiest score), the corresponding risk weight will be ‘ α ’ , which is the highest risk weight. Similarly, if the ARS is 0, the corresponding risk weight will be ‘ 𝛽 ’ , which is the lowest risk weight.

Where the distribution of the ARS of member institutions of a DGS covers only a partial range of the possible ARS, instead of the full range from 0 to 100, the DGS may reflect that situation by deciding to apply a threshold ‘ γ ’ of the ARS higher than 0 and a threshold ‘ 𝛿 ’ lower than 100. In this case, an ARS smaller or equal to ‘ γ ’ should be assigned an ARW of ‘ 𝛽 ’ and an ARS higher or equal to ‘ 𝛿 ’ should be assigned an ARW of ‘ 𝛼 ’ . The corresponding enhanced formula is:

𝐴𝑅𝑊 𝑖 = 𝛽 ∗ ( 𝛼 𝛽 ) ( 𝐴𝑅𝑆 (𝛿−𝛾) 𝑖 −𝛾 )

Where:

0 < 𝛾 < 𝛿 < 100 ;

γ is the lower threshold of the ARS translating to the lowest ARW β ; and

𝛿 is the actual upper threshold of the ARS translating to the highest ARW α .

The DGS should set the thresholds ‘ γ ’ and ‘ 𝛿 ’ so that no member institution ’s ARS exceeds ‘ 𝛿 ’ or falls below ‘ 𝛾 ’ at the time of the calibration.