FRM Part II · FRM Exam Part II · Estimating Default Probabilities
An analyst estimates the average annual hazard rate from historical data. A rating class has a seven-year cumulative default probability of 12.0%. Assuming a constant hazard rate, which is closest to the average annual hazard rate? (ln 0.88 = -0.1278)
The average hazard rate is about 1.83%. With constant hazard, survival over seven years equals exp(-7λ) = 0.88, so λ = 0.1278/7 ≈ 1.83%. Simply dividing 12% by seven gives 1.71% and ignores the exponential survival relationship.
- A1.83%Correct
- B1.71%
- C1.50%
- D12.0%
Explanation
Survival = exp(-7λ) = 0.88, so 7λ = 0.1278 and λ = 1.826%, about 1.83%. Dividing 12% by 7 gives 1.71%, which ignores compounding. 1.50% and 12.0% are not derived from the formula.
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