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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

Annually compounded spot rates are 3% for 1 year, 4% for 2 years and 5% for 3 years. A 3-year bond with face value 100 pays a 5% annual coupon. What is its price using these spot rates?

The price is 100.18. Each cash flow is discounted at its own spot rate: 5 at 3%, 5 at 4% squared, and 105 at 5% cubed. The result is 100.18. Discounting everything at a single 5% rate would give par, which ignores the term structure.

  1. A100.18Correct
  2. B100.00
  3. C102.78
  4. D103.50

Explanation

Price = 5/1.03 + 5/1.04^2 + 105/1.05^3 = 4.8544 + 4.6228 + 90.7030 = 100.18. Using the flat 5% yield gives 100.00, which ignores the term structure. Discounting every flow at 4% gives 102.78.

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