CMA Final · Strategic Financial Management · Swaps
A 2-year annual-pay swap has spot zero rates of 6% for year 1 and 7% for year 2. What is the fair fixed swap rate, using discount factors from these zero rates (annual compounding)?
The fair fixed rate is about 6.98%. It equals one minus the final discount factor divided by the sum of the discount factors, which is 0.1266 divided by 1.8168, giving roughly 6.97 to 6.98%, higher than the simple average of 6.5%.
- A6.50%
- B6.98%Correct
- C7.00%
- D6.51%
Explanation
DF1 = 1/1.06 = 0.943396; DF2 = 1/1.07² = 1/1.1449 = 0.873439. Sum = 1.816835. Swap rate = (1 - 0.873439)/1.816835 = 0.126561/1.816835 = 6.966%, about 6.97%, so the closest option is 6.98%. Simple average 6.50% ignores discount weighting, and 7.00% is just the 2-year zero rate.
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