FRM Part I · FRM Exam Part I · External and Internal Credit Ratings
A bank estimates a constant annualized hazard rate for a BB-rated issuer from a cumulative five-year default probability of 18.0%. Using the continuous-time relationship, which annual hazard rate is closest to the implied value?
The implied hazard rate is about 3.97% per year. Five-year survival is 82%, so the hazard equals the negative natural log of 0.82 divided by five, roughly 0.0397. Simply dividing 18% by five gives 3.6%, which ignores the compounding of survival.
- A3.6%
- B3.97%Correct
- C3.31%
- D4.12%
Explanation
Survival over five years is 1 − 0.18 = 0.82. Hazard λ = −ln(0.82)/5 = 0.19845/5 = 0.03969, about 3.97%. Dividing 18% by 5 gives 3.6%, which ignores compounding of survival. The 3.31% figure uses 1−0.82^(1/5)? That is 3.9%, so it is wrong.
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