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

An analyst observes that the term structure is downward sloping at long maturities even though expected future short rates are flat. Which explanation is most consistent with the convexity effect rather than expectations or risk premium?

Convexity explains it: greater rate volatility increases the value of convexity in long bonds, so their yields are pushed below the expected path of short rates. This is separate from expectations of falling rates and from risk premia, which would tend to raise long yields.

  1. AInvestors require extra compensation for duration risk, making long yields lower
  2. BHigher rate volatility raises the value of convexity, lowering long-maturity yields relative to expected short ratesCorrect
  3. CCentral bank guidance implies future short rates will fall
  4. DDemand for short-term bills has dropped, raising short yields

Explanation

With flat expected short rates and no other changes, the downward slope at long maturities arises from convexity: volatility increases bond prices on average, lowering yields, increasingly with maturity. A duration risk premium would raise long yields, and guidance of falling rates is an expectations effect.

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