CFA Level II ExamFixed IncomeMedium
A portfolio manager is using the yield curve to forecast future interest rates. If the current 1-year spot rate is 2.0% and the 2-year spot rate is 2.5%, what does the market implicitly expect the 1-year interest rate to be one year from now, assuming the expectations theory holds?
- A3.01%
- B2.0%
- C2.5%
- D3.0%
Show answer & explanationAnswer & explanation
Correct answer: A. 3.01%
According to the pure expectations theory, forward rates are unbiased predictors of future spot rates. The implied 1-year forward rate one year from now (1f1) is calculated using the formula: (1 + S2)^2 = (1 + S1) * (1 + 1f1). (1 + 0.025)^2 = (1 + 0.02) * (1 + 1f1) 1.050625 = 1.02 * (1 + 1f1) (1 + 1f1) = 1.050625 / 1.02 = 1.0300245 1f1 = 0.0300245 or approximately 3.01%.
Why the other options are wrong
- B. Incorrect. This is the 1-year spot rate, not the implied forward rate.
- C. Incorrect. This is the 2-year spot rate, not the implied forward rate.
- D. Incorrect. This is a common rounding error. The precise calculation yields slightly more than 3.00%.
Pure Expectations Theory
The pure expectations theory posits that forward rates are unbiased predictors of future spot rates, implying that the expected return for holding a long-term bond is the same as rolling over short-term bonds.
- Long-term rates are an average of current and expected future short-term rates.
- Assumes investors are risk-neutral and have no preference for liquidity.
- Implies that the shape of the yield curve is determined solely by expectations of future spot rates.
- Forward rate = expected future spot rate.
Memory trick: Expectations 'predict' the future, making forward rates 'reflect' the spot.