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

A model has a flat expected short rate of 5% and a short-rate volatility of 1.5% (annualized). Using the approximation that the convexity effect on a T-year zero-coupon yield is about -0.5*sigma^2*T^2/2 within a constant-volatility, no-drift-adjustment framework, which T-year yield reduction is closest to the convexity effect for T=10?

The convexity effect is about 0.56 percentage points. It equals 0.5 times sigma squared times T squared divided by 2, so 0.25 times 0.000225 times 100 gives 0.005625. Dropping one of the one-half factors would double it to 1.13%, which is incorrect.

  1. A0.56%Correct
  2. B1.13%
  3. C2.25%
  4. D0.11%

Explanation

Convexity effect = -0.5*sigma^2*T^2/2 = -0.25*(0.015^2)*100 = -0.25*0.0225*... compute: 0.015^2=0.000225; times 100=0.0225; times 0.25=0.005625, i.e. 0.56%. Option B forgets the extra 1/2 (0.5*0.0225=1.13%); option C omits both factors (2.25%).

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