2001, to lower the risk weights and make the risk weighting function less steep for
the IRB Foundation Approach only. Moreover, the potential modifications (if incor-
porated into the BIS II proposals) would make the correlation coefficient a function
of the PD, such that the correlation coefficient between assets decreases as the PD in-
creases. Finally, the confidence level built into the risk weighting function would be
increased from 99.5% to 99.9%.
The potential modifications to equations (1) and (2) corporate loan risk weight
curves are as follows:
(3)where
(4)(5)and
(6)where for a subordinated loan, for an unsecured loan, for a
loan fully secured by physical, non–real estate collateral, and for a loan fully
secured by receivables. In equations (3) through (6), stands for the natural expo-
nential function, stands for the standard normal cumulative distribution function
and stands for the inverse standard normal cumulative distribution function.
Equation (4) denotes the maturity factor M. This is reportedly unchanged from the
BIS II proposals shown in equation (2) in that it is still benchmarked to a fixed three-
year Weighted Average Life of the loan.^43 The correlation coefficient is computed
in equation (5). The correlation ranges from 0.20 for the lowest PD value to 0.10 for
the highest PD value. This inverse relationship appears to be somewhat counterintu-
itive in that empirically asset correlations increase during systemic crises when PDs
also tend to increase, thereby implying a direct positive (rather than inverse) rela-
tionship between correlation and PD.
Using the potential modifications of November 2001, the BRW is calculated from
equations (3) through (5). The actual risk weight (RW) is then calculated in equation
(6) where and the stipulated fixed LGD for each type of
loan. For example, under the potential modifications of November 2001, the LGD
takes on a value of either 40% (if the loan is fully secured by receivables), 45% (if
fully secured by physical, non–real estate collateral), 50% (if unsecured but senior)
or 75% (if subordinated). Risk-weighted assets are then computed by multiplying the
risk weight times the exposure at default. Finally, the minimum capital requirement
is computed by multiplying the risk-weighted assets times 8%; that is, the minimum
capital requirement on the individual loan RWEAD 8%.
RW 1 X> 502 x BRW XRG 1. 2N 1. 2expX 40X 75 X 50 X 45RW 1 X> 502 BRW 31 11 exp50PD2>1 1 exp^5024R 0.10 311 exp50PD2>1 1 exp^5024 0.20M 1 0.047 111 PD2>PD0.44 2 1 R>1 1 R 22 0.5G 1 0.999 24BRW 12.5 LGD M N 311 R 2 0.5 G 1 PD 23.4 INTERNAL RATINGS-BASED MODELS FOR CREDIT RISK 3 • 13(^43) In contrast to the Advanced IRB Approach, the Foundation IRB Approach does not input the loan’s
actual maturity into the risk weight calculation.