Finance · level 3
Forward rates from spots
The forward is whatever makes rolling short equal to locking long. Approximate it linearly first, then run the exact compounding if you need the decimals.
Worked example: 1-year spot 5%, 2-year spot 6%. Implied 1-year rate, one year forward?
1-yr spot5%
2-yr spot6%
forward7.01%
Step by step
- 1
No-arbitrage
(1 + s₂)² = (1 + s₁)(1 + f)
- 2
Rearrange
f = (1 + 6%)² / (1 + 5%) − 1 = 7.01%
- 3
Mental shortcut
2 × 6 − 5 = 7%
The linear approximation is close enough to sanity-check the exact answer.
1-year spot 5%, 2-year spot 6%. Implied 1-year rate, one year forward? = 7.01
The theory behind it
Intuition
Forwards are the rates that make holding long and rolling short equivalent — no free lunch between maturities.
Common pitfalls
- ×Averaging spot rates instead of compounding them.
- ×Reading the forward rate as a forecast rather than an arbitrage condition.
In the interview
Yield-curve and FX-hedging questions.