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

In a model with normally distributed rate changes, a risk manager compares the term structure of a zero-coupon bond yield with the expected future short rate path when rate volatility is 1.2% per year and the short rate is expected to be flat at 4%. Which statement best describes the effect of convexity on the shape of the curve?

Convexity lowers long-maturity yields below the expected short-rate path, because volatility raises expected bond prices through Jensen's inequality. The effect grows with maturity and volatility squared, so it bends the curve downward at long maturities even when expected rates are flat.

  1. AConvexity raises long-maturity yields above the expected rate path, steepening the curve
  2. BConvexity lowers long-maturity yields below the expected rate path, causing the curve to bend downward at long maturitiesCorrect
  3. CConvexity has no effect when expected rates are flat
  4. DConvexity shifts the curve in parallel at all maturities

Explanation

Bond prices are convex in yield, so volatility raises expected bond prices (Jensen's inequality), which lowers yields relative to the expected rate path. The effect grows with maturity (roughly proportional to sigma squared times T squared), so it bends the curve down at long maturities. It is not zero when rates are flat and not parallel.

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