Skip to content

FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

Two loans each have standalone unexpected loss of $4 million. The default correlation between them is 0.25. Using the standard formula for the standard deviation of the sum of two loss variables, what is the portfolio unexpected loss, and what is the diversification benefit relative to the simple sum?

Portfolio variance is 16 + 16 + 2 × 0.25 × 16 = 40, so unexpected loss is about $6.32 million. Against the undiversified sum of $8 million, the diversification benefit is about $1.68 million. Assuming zero correlation would overstate the benefit.

  1. AUL of about $6.32 million; benefit of about $1.68 millionCorrect
  2. BUL of $6.00 million; benefit of $2.00 million
  3. CUL of about $7.07 million; benefit of about $0.93 million
  4. DUL of about $5.66 million; benefit of about $2.34 million

Explanation

Variance = 16 + 16 + 2×0.25×16 = 40, so UL = sqrt(40) = 6.325 million. Simple sum is 8, so benefit = 1.675 million. $5.66m uses correlation 0 (sqrt32). $7.07m uses correlation 0.25 incorrectly as 0.5... sqrt(48)=6.93, so it is also wrong, while correlation 1 gives 8. $6.00m is not derived from the formula.

Did you get it right without looking?

One question tells you little. A timed set on Introduction to Credit Risk Modeling and Assessment shows your real accuracy, how long you take and where you lose marks.

Practise Introduction to Credit Risk Modeling and AssessmentFree diagnostic mock

More Introduction to Credit Risk Modeling and Assessment questions