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

In a one-factor model of the term structure, a risk manager decomposes the 10-year spot rate into the average of expected future short rates, a risk premium, and a convexity term. Assuming investors demand a positive risk premium for holding longer bonds and rate volatility is non-zero, which statement about the net effect of these components on the shape of the curve is most accurate?

Convexity lowers long-maturity spot rates relative to expected short rates, because rate volatility raises expected bond prices through convexity. This pushes yields down and partly offsets the positive risk premium, which pushes yields up. The effect grows with maturity and volatility.

  1. AConvexity raises long-term spot rates relative to expected short rates, so it reinforces the risk premium
  2. BConvexity lowers long-term spot rates relative to expected short rates, so it offsets part of the risk premiumCorrect
  3. CConvexity affects only the short end of the curve, leaving long maturities unaffected
  4. DConvexity has no effect when volatility is constant across maturities

Explanation

Because bond prices are convex in yields, volatility raises expected bond prices, which lowers the yield required today. The convexity term therefore reduces long-term spot rates and offsets part of the positive risk premium. It grows with maturity and volatility, so it is not confined to the short end and does not vanish with constant volatility.

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