FRM Part I · FRM Exam Part I · Interest Rates
The 1-year spot rate is 2% and the 2-year spot rate is 3%, both annually compounded. What is the 2-year par rate for an annual-coupon bond, closest to which value?
The 2-year par rate is about 2.99%. It equals one minus the 2-year discount factor, divided by the sum of the 1- and 2-year discount factors: 0.057404/1.922988 = 2.985%. It is slightly below the 3% two-year spot rate on an upward-sloping curve.
- A2.99%Correct
- B2.50%
- C3.00%
- D3.50%
Explanation
Discount factors are d1 = 1/1.02 = 0.980392 and d2 = 1/1.0609 = 0.942596. The par rate is (1 − d2)/(d1 + d2) = 0.057404/1.922988 = 2.985%, or about 2.99%. The 3.00% option is just the 2-year spot rate, and 2.50% is the simple average of the spots. Neither is the par coupon.
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