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

In a model with normally distributed rate changes, the short-rate volatility is 1.2% per year and the market price of risk is constant at 0.25. A bond's duration is 6. A risk manager also notes that the bond's 10-year yield includes a convexity effect. Which statement correctly separates the risk premium effect on the bond's expected return from convexity?

The risk premium gives an expected excess return of 6 x 0.25 x 1.2% = 1.80% per year. Convexity is a distinct effect that lowers long-maturity yields and is not part of this premium, so it does not add to or equal it.

  1. AExpected excess return is 1.80% from the risk premium, and convexity lowers the yield, not this premiumCorrect
  2. BExpected excess return is 0.30% from the risk premium, and convexity adds to it
  3. CExpected excess return is 7.20% because duration multiplies volatility and lambda squared
  4. DExpected excess return is 1.80% and convexity raises the yield by the same amount

Explanation

Excess return = 6 x 0.25 x 1.2% = 1.80%. Convexity is a separate effect that lowers long-term yields (the Jensen's inequality term) and does not form part of the risk premium. The 0.30% option uses lambda x sigma only, ignoring duration, and the 7.20% option wrongly squares lambda.

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