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

Which statement about the relationship between convexity and the shape of the term structure is correct when interest rate volatility increases, holding expected short rates and risk premia fixed?

Higher volatility increases the convexity benefit: bond prices rise relative to the price at expected rates, so long-term yields fall relative to short ones. The effect grows with maturity and volatility squared, and it is separate from the risk premium.

  1. ALong-term spot rates fall relative to short rates, because convexity raises bond pricesCorrect
  2. BLong-term spot rates rise because convexity lowers bond prices
  3. CThe term structure is unaffected because convexity is a risk premium
  4. DShort rates fall to offset volatility, leaving long rates unchanged

Explanation

Convexity makes bond prices a convex function of rates, so expected price exceeds the price at expected rates (Jensen's inequality). Higher prices mean lower yields, and the effect grows with maturity and volatility. So the long end is pulled down, which causes a downward effect on the curve.

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