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CMA Final · Risk Management in Banking and Insurance · Credit Risk Management

A bank's loan portfolio has three borrowers with exposures of ₹100 crore each. Each has a one-year PD of 4%, LGD of 50%, and defaults are assumed independent. Management uses expected loss as the provisioning basis, and then lends a fourth identical borrower of ₹100 crore, with every parameter the same. What is the change in the portfolio's expected loss, and what does it show?

The expected loss rises by ₹2 crore, since each borrower contributes 4% × 50% × ₹100 crore. Expected loss is additive across exposures whether or not defaults are correlated; diversification reduces unexpected loss variability, not the expected loss itself.

  1. ARises by ₹2 crore; expected loss is additive across exposures regardless of correlationCorrect
  2. BRises by ₹2 crore; but only because defaults are independent
  3. CRises by ₹0.5 crore; expected loss falls per borrower due to diversification
  4. DRises by ₹4 crore; expected loss equals PD times exposure

Explanation

Each borrower's EL = 0.04 × 0.50 × 100 = ₹2 crore, so the fourth adds ₹2 crore (from ₹6 to ₹8 crore). Expected loss is a mean and therefore additive whatever the correlation; diversification affects unexpected loss, not EL. Ignoring LGD gives ₹4 crore.

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