FRM Part II · FRM Exam Part II · Credit Risk Management
A portfolio has 100 equal loans of USD 1 million each. A second portfolio has 10 equal loans of USD 10 million each. Total exposure is USD 100 million in both. Using the Herfindahl-Hirschman Index (sum of squared exposure shares), what are the HHI values of the first and second portfolios respectively?
The HHI is 0.01 for the 100-loan portfolio and 0.10 for the 10-loan portfolio. For n equal exposures the index equals 1/n, so fewer, larger loans produce a ten times higher concentration measure even though total exposure is identical.
- A0.01 and 0.10Correct
- B0.10 and 0.01
- C0.0001 and 0.001
- D0.01 and 0.01
Explanation
Portfolio 1: 100 × (0.01)^2 = 0.01. Portfolio 2: 10 × (0.10)^2 = 0.10. Check: HHI for n equal names is 1/n, giving 1/100 and 1/10. Swapping them confuses the direction, since fewer names means higher concentration.
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