CFA Level II ExamFixed IncomeMedium
A bond trader is analyzing the relationship between spot rates and forward rates. Given a 1-year spot rate (S1) of 3.00% and a 2-year spot rate (S2) of 3.50%, what is the implied 1-year forward rate one year from now (1f1)?
- A3.50%
- B3.00%
- C4.00%
- D4.01%
Show answer & explanationAnswer & explanation
Correct answer: D. 4.01%
The relationship between spot rates and forward rates is given by (1 + S2)^2 = (1 + S1) * (1 + 1f1). (1 + 0.035)^2 = (1 + 0.03) * (1 + 1f1) 1.071225 = 1.03 * (1 + 1f1) (1 + 1f1) = 1.071225 / 1.03 = 1.039999 1f1 = 0.039999 or approximately 4.00%. More precisely, 4.01% if rounded.
Why the other options are wrong
- A. Incorrect. This is S2, not the forward rate.
- B. Incorrect. This is S1, not the forward rate.
- C. Incorrect. This is a common rounding error. The precise calculation yields slightly more than 4.00%.
Spot and Forward Rate Relationship
Forward rates are implied future spot rates derived from the current term structure of spot rates, reflecting the market's expectation of future interest rates.
- The formula is (1 + Sn)^n = (1 + Sk)^k * (1 + kfn-k)^(n-k).
- Investors should be indifferent between investing for 'n' periods at the 'n'-period spot rate or for 'k' periods at the 'k'-period spot rate and then for 'n-k' periods at the 'kfn-k' forward rate.
- Forward rates are not necessarily predictors of future spot rates, but rather reflect breakeven rates.
Memory trick: Spot rates 'stack' up to imply 'future' forward rates.