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

In a Ho-Lee-type model with normally distributed rates, a 10-year zero has a duration of 10 and annual rate volatility of 1.00%. The market price of risk (λ) is 0.30 per unit of volatility. Approximately, what is the annualized expected excess return of the 10-year zero over the short rate, if the expected excess return is λ × duration × σ?

The expected excess return equals the market price of risk times duration times rate volatility: 0.30 × 10 × 1.00% = 3.00% per year. Each unit of duration earns compensation proportional to volatility and the price of risk.

  1. A3.00%Correct
  2. B0.30%
  3. C1.00%
  4. D10.00%

Explanation

Expected excess return ≈ λ × D × σ = 0.30 × 10 × 1.00% = 3.00%. 0.30% omits duration, 1.00% omits λ and duration, and 10.00% ignores λ and treats volatility as 1.

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