FRM Part I · FRM Exam Part I · Interest Rates
Annually compounded spot rates are 3.0% for 1 year, 3.5% for 2 years and 4.0% for 3 years. What is the 3-year par yield for an annual-coupon bond, to two decimals?
The 3-year par yield is about 3.97%. Convert each spot rate into a discount factor, then divide one minus the 3-year factor (0.1110) by the sum of the three factors (2.7934). It is below the 4% spot rate because the coupons are paid earlier at lower spot rates.
- A3.97%Correct
- B4.00%
- C3.50%
- D3.70%
Explanation
Discount factors: d1 = 1/1.03 = 0.970874, d2 = 1/1.071225 = 0.933511, d3 = 1/1.124864 = 0.888996. Par yield = (1 - d3)/(d1+d2+d3) = 0.111004/2.793381 = 3.97%. 4.00% is the 3-year spot rate, not the par rate. 3.70% results from dividing 1-d3 by 3, ignoring the differing discount factors.
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