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

An investor buys a three-year bond with face value 100 and a 5% annual coupon at a price of 100. She sells it after two years. The first coupon is reinvested for one year at 3%, and at the sale date the bond's remaining one-year yield is 4% (annual compounding). What is the annualized realized yield over the two-year holding period (closest figure)?

The realized yield is about 5.41%. The bond sells for 105/1.04 = 100.9615, the first coupon grows to 5.15, and the second coupon is 5, so the terminal value is 111.1115. The two-year root of 1.111115 minus 1 gives 5.41%.

  1. A5.41%Correct
  2. B5.34%
  3. C4.88%
  4. D5.00%

Explanation

Sale price = 105/1.04 = 100.9615. Terminal value = 5(1.03) + 5 + 100.9615 = 111.1115. Realized yield = sqrt(1.111115) − 1 = 5.41%. Omitting interest on the first coupon gives 110.9615 and 5.34%. Using a sale price of 100 gives 110 and 4.88%.

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