IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates
Annual spot rates are s1 = 4% and s2 = 5%. What is the one-year forward rate from time 1 to time 2, f(1,2), to the nearest 0.01%?
The forward rate is 1.05 squared divided by 1.04, minus one, which equals about 6.01%. This follows from no-arbitrage between investing for two years at the spot rate and investing for one year then rolling over at the forward rate.
- A4.50%
- B5.00%
- C5.50%
- D6.01%Correct
- 6.25%
Explanation
(1+f) = (1.05)^2/1.04 = 1.1025/1.04 = 1.06010. So f is about 6.01%. The arithmetic average of 4.5% ignores compounding and is wrong; 5.5% is the simple average of 5 and 6 taken wrongly.
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