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

A 5-year zero-coupon bond with face value 100 trades at 74.73, which is a yield of 6.00% per year compounded annually. What is the equivalent yield expressed with semiannual compounding?

The equivalent semiannual yield is 5.91%. Set (1 + y/2) squared equal to 1.06, so y/2 is about 2.956% and y about 5.91%. More frequent compounding requires a lower quoted rate than the 6.00% annual yield for the same effective return.

  1. A5.91%Correct
  2. B6.00%
  3. C5.83%
  4. D6.09%

Explanation

Solve (1 + y/2)^2 = 1.06. Then 1 + y/2 = 1.029563, so y = 5.91%. The 5.83% option is the continuously compounded rate, ln(1.06). The 6.09% option goes the wrong way, converting a semiannual 6% to annual. Semiannual compounding is more frequent, so its quoted rate must be lower than 6.00%.

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