FRM Part I · FRM Exam Part I · Properties of Interest Rates
Annually compounded zero rates are 4% for 1 year and 5% for 2 years. What is the 2-year par yield, expressed as an annual coupon rate with annual payments?
The 2-year par yield is about 4.98%. It is the coupon that prices the bond at par when each cash flow is discounted at its zero rate: (1 - d2)/(d1 + d2) = 0.0930/1.8686. It is not equal to the 2-year zero rate of 5%.
- A4.98%Correct
- B5.00%
- C4.50%
- D5.13%
Explanation
Discount factors are d1 = 1/1.04 = 0.961538 and d2 = 1/1.05^2 = 0.907029. The par coupon is c = (1 - d2)/(d1 + d2) = 0.092971/1.868567 = 4.98%. The 5.00% figure is the 2-year zero rate, which is a different concept. The 5.13% figure uses (1-d2)/d2 divided by 2, which wrongly ignores the discounting of the first coupon.
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