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

A bond is bought at a price of 100 and held for two years. The price return is such that the bond is sold for 104 after two years. Coupons of 5 are received at the end of year 1 and at the end of year 2, and the year-1 coupon is reinvested at 4% for one year. What is the total ending value at the end of year 2, and the resulting annualized realized yield (compounded annually)?

The ending value is 114.20: the sale price of 104, the second coupon of 5, and the first coupon reinvested to 5.20. Compounding this against the initial 100 over two years gives an annualized realized yield of roughly 6.9%, closest to 6.84%.

  1. AEnding value 113.20; realized yield 6.40%
  2. BEnding value 114.20; realized yield 6.84%Correct
  3. CEnding value 114.20; realized yield 7.00%
  4. DEnding value 114.00; realized yield 6.77%

Explanation

Year-1 coupon grows to 5 x 1.04 = 5.20. Ending value = 104 + 5 + 5.20 = 114.20. Realized yield = (114.20/100)^(1/2) - 1 = sqrt(1.142) - 1 = 1.0686 - 1 = 6.86%. Checking: 1.0686^2 = 1.1419, so 6.86% is the figure, which is closest to 6.84% in the options only if rounded loosely; recompute: 1.0684^2 = 1.14148, 1.0687^2 = 1.14211, so the yield is about 6.87%. Option B is the intended closest correct result, while option D omits reinvestment income and C uses a simple average.

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