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

A portfolio manager observes that the yield curve is downward sloping at very long maturities even though she believes expected short rates are flat and risk premia are zero. Which explanation is most consistent with term structure theory?

The downward slope at the long end is explained by the convexity effect from Jensen's inequality. Bond prices are convex in rates, so volatility pushes long-maturity yields below the average expected short rate. This effect grows with volatility and maturity, and liquidity preference would push the opposite way.

  1. AJensen's inequality: convexity of bond prices reduces long-term yields below expected short rates, and the effect increases with volatilityCorrect
  2. BLiquidity preference: investors demand extra yield for long bonds
  3. CMarket segmentation: pension demand pushes up long yields
  4. DThe pure expectations hypothesis: long rates equal the average expected short rate

Explanation

With flat expected rates and zero risk premium, the pure expectations hypothesis predicts a flat curve. A downward slope at the long end comes from convexity, which lowers long yields and rises with volatility and maturity. Liquidity preference would produce an upward slope.

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