CFA Level I · CFA Level I Exam · The Term Structure of Interest Rates: Spot, Par, and Forward Curves
Spot rates (annual) are 1-year 1.00%, 2-year 2.00% and 3-year 3.00%. The 3-year par rate for an annual-pay bond is closest to:
The par rate is about 2.97%. Using spot-rate discount factors of 0.9901, 0.9612 and 0.9151, their sum is 2.8664, and (1 − 0.9151)/2.8664 gives roughly 2.96–2.97%. On an upward-sloping curve the par rate lies slightly below the final spot rate of 3.00%.
- A2.00%
- B2.97%Correct
- C3.00%
Explanation
Discount factors: 1/1.01=0.990099; 1/1.0404=0.961169; 1/1.092727=0.915142. Sum=2.866410. Par rate=(1-0.915142)/2.866410=0.029605, about 2.96%, closest to 2.97%. The 3.00% option ignores the shape of the curve; 2.00% is the simple average of the spot rates.
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