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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 notes that the observed yield curve is humped: yields rise to a peak at about 5 years and then decline. Assuming expected short rates are flat, which factor best explains the downward slope at long maturities?

With flat expected short rates, the convexity effect explains the declining long end because it grows with the square of maturity and pushes long-term rates down. Risk premia would normally raise long yields, and mean reversion to a higher level would also steepen the curve upward.

  1. AThe convexity effect, which grows with maturity and lowers long-term ratesCorrect
  2. BThe liquidity premium, which grows with maturity and lowers long-term rates
  3. CMean reversion of the short rate to a higher long-run level
  4. DSegmented-market demand for short-term bonds

Explanation

With flat expected short rates, the only factor that pushes long rates down increasingly with maturity is convexity, since its effect grows with the square of maturity. A positive liquidity or risk premium would raise long rates, and higher mean reversion would raise them too.

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