FRM Part I · FRM Exam Part I · Properties of Interest Rates
The 1-year zero rate is 4.00% with annual compounding. A 2-year bond with a 5% annual coupon and face value 100 trades at 99.00. Using bootstrapping, what is the 2-year zero rate with annual compounding?
The 2-year zero rate is about 5.58%. Strip out the present value of the first coupon at the 4% 1-year zero rate, leaving 94.19 for the final 105 payment, and solve for the rate. The yield to maturity of about 5.54% is different because it is a single blended rate.
- A5.58%Correct
- B5.54%
- C5.10%
- D6.00%
Explanation
The first coupon is worth 5/1.04 = 4.8077. The remaining value is 99 - 4.8077 = 94.1923, which must equal 105/(1+z)^2. So (1+z)^2 = 1.11472 and z = 5.58%. The 5.54% option is the bond's yield to maturity, which uses one rate for both cash flows and is not a zero rate.
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