CFA Level IFixed IncomeHard
The current one-year spot rate is 3.00% and the current two-year spot rate is 4.00% (both annual compounding). The implied one-year forward rate, one year from today (the '1y1y' forward rate), is closest to:
- A5.50%
- B5.01%
- C4.00%
- D4.50%
Show answer & explanationAnswer & explanation
Correct answer: B. 5.01%
The forward rate satisfies (1+S2)^2 = (1+S1) × (1+1y1y). Solving: (1.04)^2 / 1.03 − 1 = 1.0816/1.03 − 1 = 1.0501 − 1 = 5.01%.
Why the other options are wrong
- A. Overstates the forward rate beyond what the spot curve implies.
- C. Equals the two-year spot rate, ignoring the compounding relationship.
- D. A simple average of the two spot rates, which is not how forward rates are derived.
Implied Forward Rate
A future interest rate implied by the current spot rate curve under no-arbitrage, calculated by comparing compounded returns over different horizons.
- (1+S_long)^n = (1+S_short)^m × (1+forward)^(n-m)
- Used to back out market-implied future short rates
- Basis of bootstrapping and relative value trades
Memory trick: 'Long rate compounds short rate plus the forward gap'