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

In a one-factor model, the short rate has volatility of 1.00% per year, and a bond has a duration of 5 (the bond price falls by 5% for each 1% rise in rate). The market price of risk, lambda, is 0.30 per unit of rate volatility. Using the standard relation where the bond's expected excess return equals duration times lambda times sigma, what is the bond's expected excess return per year?

The expected excess return is duration times the market price of risk times rate volatility: 5 x 0.30 x 1.00% = 1.50% per year. Excess return scales with both interest rate sensitivity and the price of risk.

  1. A0.15%
  2. B1.50%Correct
  3. C5.30%
  4. D6.00%

Explanation

Expected excess return = D x lambda x sigma = 5 x 0.30 x 1.00% = 1.50%. The 0.15% option mistakenly divides by 10 through a scaling slip. The 6.00% option wrongly adds duration and lambda terms inconsistently, and 5.30% adds 5 + 0.30 instead of multiplying.

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