FRM Part II · FRM Exam Part II · Estimating Default Probabilities
A risk analyst at a bank reviews a rating agency's cumulative default table. For a bond rated Ba, the cumulative default probabilities are 1.2% at one year and 2.9% at two years. Assuming the table is accurate, what is the unconditional probability that the bond defaults during the second year only?
The unconditional probability of defaulting only in the second year is 1.7%. Cumulative default probability to year two (2.9%) includes first-year defaults (1.2%), so subtracting the first-year figure isolates the incremental second-year default probability.
- A1.7%Correct
- B1.2%
- C2.9%
- D4.1%
Explanation
Cumulative default probability to year 2 includes defaults in year 1 and year 2. The probability of defaulting in year 2 only is 2.9% - 1.2% = 1.7%. Adding the figures (4.1%) double counts, and 1.2% is only the first-year figure.
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