FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift
In Model 1 with r_0 = 3.00% and σ = 80 bps per year, a risk manager wants the 5%-tail (one-sided) short-rate level in 1 year, using a z-value of 1.645 for 95% confidence. Which value is closest to the rate that is exceeded on the upside only 5% of the time?
The 95th percentile short rate is about 4.32%. With zero drift the mean stays at 3.00%, the one-year standard deviation is 0.80%, and adding 1.645 times 0.80% gives roughly 1.32% above the mean.
- A4.32%Correct
- B3.80%
- C4.80%
- D1.68%
Explanation
Mean is 3.00% (zero drift), sd = 0.80% × √1 = 0.80%. Upper 95th percentile = 3.00% + 1.645 × 0.80% = 3.00% + 1.316% = 4.316% ≈ 4.32%. The 1.68% option is the lower tail (wrong sign).
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