FRM Part I · FRM Exam Part I · Measuring Credit Risk
Two borrowers each have a one-year default probability of 10%. The default correlation between them is 0.20. What is the probability that both default within the year?
The joint default probability is 2.8%. It is the independent joint probability of 1% plus the correlation contribution of 0.20 times 0.09, which is 1.8%. Ignoring correlation gives 1.0%, which understates the risk.
- A1.0%
- B1.8%
- C2.8%Correct
- D3.8%
Explanation
Joint default probability = p1·p2 + ρ·sqrt[p1(1−p1)p2(1−p2)] = 0.01 + 0.20 × 0.09 = 0.01 + 0.018 = 0.028. The 1.0% figure assumes independence, and 1.8% only counts the correlation term.
Did you get it right without looking?
One question tells you little. A timed set on Measuring Credit Risk shows your real accuracy, how long you take and where you lose marks.
More Measuring Credit Risk questions
- Holding all other Merton model inputs constant, the volatility of a firm's assets increases. Which outcome is correct?
- A bank has a USD 20 million loan to a firm. A guarantor, independent of the firm, guarantees the loan fully. The firm has a one-year PD of 5…
- Which statement about the Markov assumption in rating transition matrices is correct?
- A bank's one-year rating transition matrix shows that a BB-rated obligor has a 4% probability of moving to B, 88% of staying at BB, 6% of up…
- A one-year transition matrix gives the following for a BBB obligor: 90% stay BBB, 6% move to BB, 4% default. A BB obligor has 85% stay BB, 5…
- In a Merton framework, a firm's assets are worth 200 million. It has zero-coupon debt of face value 150 million due in one year, and the con…