comparison
Spot Rate vs Forward Rate
Explain spot rates, forward rates, no-arbitrage relationships, and fixed income exam traps.
TL;DR
A spot rate discounts a cash flow from today to a future date. A forward rate is the implied future period rate that makes investing over different paths equivalent.
Formula Reference
Two-year spot decomposition
(1 + S2)^2 = (1 + S1)(1 + 1f1)1f1 is the one-year forward rate one year from now.
Forward from spot rates
1f1 = [(1 + S2)^2 / (1 + S1)] - 1Annual compounding version.
BA II Plus Keystrokes
- Compute (1 + S2)^2.
- Divide by (1 + S1).
- Subtract 1.
- Convert to percent.
Worked Example
- S1 = 4 percent and S2 = 5 percent.
- 1f1 = (1.05^2 / 1.04) - 1.
- Result: 6.01 percent.
Common Mistakes
- Averaging spot rates to get a forward rate.
- Using annual spot rates without matching compounding.
- Forgetting to square the two-year spot accumulation factor.
Related Guides
- CFA Level I Fixed Income Calculations - Bond pricing, yield, duration, convexity, spot rates, and forward rates for CFA Level I.
- CFA Level I Fixed Income Formula Sheet - Public formula sheet for bond pricing, yield, duration, convexity, spot rates, and forward rates.
- BA II Plus: Bond Price Calculation Step by Step - How to calculate a bond price on the BA II Plus with annual and semiannual coupon inputs.