FRM Part I · FRM Exam Part I · Interest Rates
A 2-year zero-coupon bond with a face value of 100 is priced at 90.25. What is its yield to maturity expressed as a semiannually compounded (bond-equivalent) annual rate, to two decimals?
The semiannual bond-equivalent yield is 5.21%. Take the fourth root of 100/90.25 to get a half-year yield of about 2.605%, then double it. The 5.26% figure is the annually compounded yield, which uses a different compounding convention.
- A5.21%Correct
- B5.26%
- C4.88%
- D5.00%
Explanation
Over 4 half-years, (100/90.25)^(1/4) - 1 = 1.052632^0.25 - 1 = 2.6054% per half-year. Doubling gives 5.21%. The 5.26% option is the annually compounded yield, since 90.25 equals 100/1.0526^2. The 4.88% option divides the 9.75% total gain by 2 years, which is a simple-interest error.
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