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

Bond A has duration 2 and bond B has duration 8 in a one-factor model with a single constant market price of risk. Bond A has an expected excess return over the short rate of 0.40% per year. What should bond B's expected excess return be if there is no arbitrage?

Bond B should earn 1.60%. With one factor and one price of risk, excess return per unit of duration is constant, so 0.40% divided by 2 gives 0.20% per unit, and multiplying by duration 8 gives 1.60% per year.

  1. A0.10%
  2. B0.80%
  3. C1.60%Correct
  4. D3.20%

Explanation

No arbitrage means excess return divided by duration is the same for all bonds: 0.40%/2 = 0.20% per unit of duration. Bond B gets 8 x 0.20% = 1.60%. The 0.80% option scales by 2 rather than the duration ratio of 4, and 0.10% inverts the ratio.

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