A plain vanilla swap looks like a strip of forwards, but it charges ONE fixed rate across every settlement date. That single tension is the whole reading.
A pay-fixed, receive-floating interest rate swap with eight quarterly settlements exchanges (floating − fixed) × notional on each date. Stacked end-to-end, that looks identical to eight FRAs.
The similarity is real but incomplete, which is exactly what the exam wants you to describe: how a swap lines up with a series of forward contracts, then where it breaks away. In a strip of FRAs, each forward uses its OWN implied forward rate (period 1's differs from period 2's). Every FRA has zero value at initiation because it locks in its own equilibrium rate.
A swap charges ONE fixed rate across all settlements. That single rate sits above some implied forwards and below others. In an upward-sloping curve, early-period implied forwards typically sit below the swap rate (negative value to the fixed-payer), later ones sit above (positive).
Common mistakes
- Treating a swap as a strip of at-market forwards. Each implied forward in the strip is OFF-market when the single swap rate is applied. Their values sum to zero at inception, but individually they are non-zero. Trap: "each forward in the equivalent strip has zero value at initiation."
- Forgetting that the floating leg prices to par at reset. This shortcut is what makes the pricing formula work. Trap: trying to forecast every floating coupon when a reset just occurred.
- Confusing price with value. Price is the contractual fixed rate. Value is the dollar mark-to-market. Trap: answering "value at initiation" with the swap rate (e.g., 3.94%) when the correct answer is zero.
Bottom line
- A swap is a portfolio of OFF-market forwards sharing one fixed rate (not a strip of at-market forwards); their values net to zero at initiation.
- Swap price (the fixed rate) is set at initiation so PV(fixed leg) = PV(floating leg), making value zero on day one.
- The swap rate solves .
- Swap value after initiation = PV(fixed leg) − PV(floating leg) from the fixed-receiver's view, computed with the current discount factors.
Exam shortcut
For pricing, memorize the words: "one minus last discount factor, over sum of discount factors." For valuing after initiation, treat the fixed leg like a bond (include notional in the final period) and the floating leg as par at the most recent reset, then subtract. For sign discipline, ask "did rates move TOWARD or AWAY from the locked rate?" The side locked in at the now-unfavorable rate loses.
The full lesson (about 1,535 words, 10 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- pricing and valuation of swaps
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