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

An analyst compares two 10-year zero-coupon yield curves built from the same expected short-rate path. Curve A assumes volatility of 1% and curve B assumes volatility of 2%, with no risk premium in either. Which conclusion is correct regarding the 10-year yield and the convexity effect?

Curve B's yield is lower by three times curve A's convexity effect. The effect is proportional to variance, so doubling volatility quadruples it. Curve B has 4c versus curve A's c, and the gap between the two is 3c, with B's yield lower.

  1. ACurve B has a 10-year yield lower than curve A by three times the convexity effect of curve ACorrect
  2. BCurve B has a 10-year yield lower than curve A by twice the convexity effect of curve A
  3. CCurve B has a 10-year yield lower than curve A by four times the convexity effect of curve A
  4. DThe yields are equal because the convexity effect depends only on the expected path

Explanation

The convexity effect scales with sigma^2. Curve A's effect is c; curve B's is 4c. The difference in yields is 4c-c=3c, with B lower. Option C confuses B's total effect with the difference between curves.

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