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

Under a model with constant volatility sigma = 1% and zero risk premium, the convexity effect on a T-year zero yield is approximately sigma^2 T^2 / 6 subtracted from the expected-rate average. If the expected short rate is flat at 5%, what is the approximate 10-year yield?

Convexity lowers the yield by sigma squared times T squared over six: 0.0001 times 100 divided by 6 is about 0.167%. Subtracting from the flat 5% expected rate gives a 10-year yield of roughly 4.83%.

  1. A4.83%Correct
  2. B4.50%
  3. C4.92%
  4. D5.00%

Explanation

Convexity effect = 0.0001 x 100 / 6 = 0.01/6 = 0.001667 = 0.1667%. Yield = 5.00% - 0.167% = 4.833%, about 4.83%. 4.50% uses sigma^2T^2/2 with a wrong scale, 4.92% is a misscaled effect, and 5.00% ignores convexity.

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