CFA Level II ExamFixed IncomeMedium
An investor is considering a 5-year, 6% annual coupon bond currently trading at par. The current 1-year spot rate is 4%, and the 2-year spot rate is 4.5%. According to the pure expectations theory, what is the implied 1-year forward rate for the second year (f1,1)?
- A4.00%
- B4.50%
- C5.00%
- D5.01%
Show answer & explanationAnswer & explanation
Correct answer: D. 5.01%
According to the pure expectations theory, the long-term spot rate is a geometric average of current and expected future short-term rates. We can calculate the implied forward rate using the formula: (1 + S2)^2 = (1 + S1) * (1 + f1,1). (1 + 0.045)^2 = (1 + 0.04) * (1 + f1,1). 1.092025 = 1.04 * (1 + f1,1). (1 + f1,1) = 1.092025 / 1.04 = 1.050024. f1,1 = 0.050024 or 5.0024%, which is approximately 5.01%.
Why the other options are wrong
- A. This is the current 1-year spot rate, not the forward rate.
- B. This is the current 2-year spot rate, not the forward rate.
- C. This is close but slightly off due to rounding or incorrect calculation, missing the compounding effect.
Pure Expectations Theory (Forward Rates)
The pure expectations theory states that forward rates exclusively represent expected future spot rates, and the yield curve shape is determined by these expectations.
- No liquidity premium or risk premium is assumed.
- Long-term rates are geometric averages of expected short-term rates.
- Implied forward rates can be derived from existing spot rates.
Memory trick: Expect pure future spots, geometrically averaged.