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

A three-year bond with face value 100 and a 6% annual coupon is bought at par and held to maturity. Each coupon is reinvested at 4% until maturity. What is the annualized realized (horizon) yield, compounded annually?

The realized yield is 5.89%. The coupons grow at 4% to 18.7296 in total, giving a terminal value of 118.7296 on a 100 investment. Taking the three-year root gives 5.89%, which is below 6% because reinvestment is at a lower rate than the coupon.

  1. A5.89%Correct
  2. B6.00%
  3. C5.66%
  4. D5.00%

Explanation

Terminal value = 6(1.04)^2 + 6(1.04) + 6 + 100 = 6.4896 + 6.24 + 6 + 100 = 118.7296. Realized yield = (118.7296/100)^(1/3) − 1 = 5.89%. The 6.00% figure assumes reinvestment at the yield itself. The 5.66% figure comes from 118 with no interest on the coupons.

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