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

Continuously compounded rates are as follows. The one-year spot rate is 2.5%. The forward rate from year 1 to year 2 is 3.5%. The forward rate from year 2 to year 3 is 4.5%. What is the price of a three-year zero-coupon bond with face value 100?

The price is about 90.03. Under continuous compounding the three-year spot rate equals the average of the one-year spot and the two forward rates, which is 3.5%. Discounting 100 at that rate for three years, 100 times e to the power of minus 0.105, gives the price.

  1. A90.03Correct
  2. B90.19
  3. C87.37
  4. D92.77

Explanation

With continuous compounding the three-year spot rate is the average of the forward rates: (2.5 + 3.5 + 4.5)/3 = 3.5%. Price = 100·e^(−0.105) = 90.03. Using only the last forward rate gives 87.37. Using 3.5% annual compounding gives 90.19. Using the 2.5% spot rate gives 92.77.

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