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FRM Part II · FRM Exam Part II · Expectations, Risk Premium, Convexity and the Shape of the Term Structure

A model with no risk premium has constant normal volatility of 1.2% per year (sigma = 0.012) and expected short rate path flat at 5%. Using the convexity approximation that lowers the T-year spot rate by sigma²T²/6, what is the approximate 10-year spot rate?

The 10-year spot rate is about 4.76%. The convexity adjustment is sigma squared times T squared divided by 6, which is 0.000144 times 100 divided by 6, or 0.24%. Subtracting this from the flat expected 5% short rate gives 4.76%.

  1. A4.76%Correct
  2. B4.88%
  3. C5.00%
  4. D4.99%

Explanation

sigma² = 0.000144. T² = 100. Product = 0.0144; divided by 6 = 0.0024 = 0.24%. Spot = 5.00% - 0.24% = 4.76%. The 4.88% option divides by 12 (wrong factor); 4.99% uses T instead of T² roughly; 5.00% ignores convexity.

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