Question

Suppose the assets of a bank consist of $500 million of loans to BBB-rated corporations. The PD for the corporations is estimated as 0.3%. The average maturity is three years and the LGD is 60%. a. What is the total risk-weighted assets (RWA) for credit risk under the Basel II advanced IRB approach? Assume 99.9% confidence. b. How much Tier 1 is required? c. How does this compare with the capital required under Basel I?

Answer 1

Under the Basel II advanced IRB approach Risk weighted average asset (RWA)

WCDR = N [{N^-1(PD) + √p N^-1 (x)}/ √1-p]

WCDR = N [{N^-1(0.003) + √0.2233 N^-1 (0.999)}/ √1-0.2233]

WCDR = 0.0720

Where ,

p = 0.12[1 + e ^{− 50×0.003} ] = 0.2233

b = [0.11852 − 0.05478 × ln (0.003)] ² = 0.1907

MA = [1+ (3.0 – 2.5) * 0.1907] / 1- 1.5*0.1907

MA = 1.53

So,

RWA = 500 × 0.6 × (0.0720 − 0.003) × 1.53 × 12.5 = 397.13

The total capital is 8% of this or $31.77 million. Half of this must be Tier I. Under both the Basel II standardized approach and under Basel I the risk weight is 100% and the total capital required is 8% of $500 or $40 million.