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Lesson 1 of 6 · 12 min
Swaps versus a series of forward rate agreements
An interest rate swap is like a strip of FRAs on consecutive periods, except that every period uses one constant fixed rate instead of a different implied forward rate for each period.
In short
- A swap exchanges a series of future cash flows; a forward (including an FRA) is a single exchange on one future date.
- Both settle the net difference between a fixed rate agreed at inception and a market reference rate (MRR) set later, on a notional amount for a stated period.
- Shared features: firm commitment, symmetric payoff, no cash exchanged upfront, value of zero at inception, and counterparty credit risk.
- Differences: an FRA settles once, usually at the start of its interest period; a standard swap settles periodically, at the end of each period.
- A series of FRAs has a different fixed rate per period (each one's implied forward rate); a swap has one constant fixed swap rate for all periods.
One exchange or many
A forward commits two parties to one exchange of value at a future date. A swap commits them to a whole series of exchanges on scheduled dates. The rest of this module uses interest rate swaps, but the same ideas apply to any swap that exchanges a series of cash flows on some underlying.
Recall that a forward rate agreement (FRA) fixes today the rate on a notional deposit for one future period. At the fixing date, the fixed-rate payer gains if MRR sets above the agreed fixed rate and receives the net difference from the floating-rate payer. That single cash flow is exactly what one period of a swap looks like.
So a one-period swap and an FRA on the same period are economically the same contract. A multi-period swap looks like several FRAs lined up back to back, one for each interest period.
| Feature | Series of FRAs | Interest rate swap |
|---|---|---|
| Net settlement on notional | Yes, fixed vs MRR | Yes, fixed vs MRR |
| Payoff profile | Symmetric | Symmetric |
| Cash upfront / value at t = 0 | None / zero | None / zero |
| Counterparty credit risk | Yes | Yes |
| Contracts | One per period | One for all periods |
| Fixed rate | Different per period: each IFR | One constant swap rate |
| Settlement timing | Once, at start of the period | Each period, at the end |
Where they are the same
In both contracts the cash flow is the net difference between the fixed rate and MRR, times the notional, times the accrual period. The notional itself is never exchanged. The fixed payer gains when MRR sets above the fixed rate; the floating payer gains when it sets below.
Both have a symmetric payoff: each basis point that MRR moves above the fixed rate is a gain to one side and the same loss to the other. Both start with no cash exchanged and, at the no-arbitrage fixed rate, a value of zero to each party (ignoring transaction and credit costs).
Because each side may later owe the other money, both are exposed to counterparty credit risk: the risk that the party who owes a net payment fails to make it.
Where they differ: one fixed rate, not many
Interest rates have a term structure. The no-arbitrage fixed rate of an FRA is the implied forward rate for its period, , and implied forward rates usually differ from period to period. A strip of FRAs therefore has a different fixed rate for each period.
A standard swap uses a single fixed swap rate for every period. Take an upward-sloping zero curve of 2.00%, 2.80% and 3.40% for one, two and three years. The FRA rates for years 1, 2 and 3 are 2.0000%, 3.6063% and 4.6105%, while the three-year swap rate is a constant 3.3709% (the next lesson shows how it is solved).
Timing differs too. An FRA settles once, usually at the start of its interest period with the net amount discounted. A standard swap sets MRR at the start of each period and pays the net difference at the end of that period.
Think of the swap rate as an average of the forward rates that is weighted by discount factors. One constant rate is what makes swaps convenient for issuers and investors, who usually have level fixed-rate cash flows such as bond coupons.
Formulas
- Implied forward rate from zero rates
z_A, z_B = zero rates to A and B. The IFR is the no-arbitrage FRA fixed rate for the period from A to B.
- Net payment to the fixed-rate payer for one period
For an FRA the fixed rate is that period's IFR; for a swap it is the constant swap rate. Reverse the sign for the fixed-rate receiver.
Worked examples
Example 1 The FRA strip behind a three-year swap
Annual zero rates are 2.00% (one year), 2.80% (two years) and 3.40% (three years). What fixed rates would a strip of one-year FRAs covering years 1, 2 and 3 carry?
Example 2 Expected net flows of a receive-fixed swap
Using the same curve, a fund receives the 3.3709% swap rate on EUR 50 million for three years, annual payments, and pays MRR. If MRR sets at the implied forward rates, what net amount does the fund expect each year?
Example 3 Which instrument fits?
A corporate treasurer wants to fix the rate on a four-year quarterly floating-rate loan. A colleague suggests entering 16 separate FRAs instead of one swap. What are the main drawbacks?
On the exam
Expect matching items (FRA only, swap only, or both) on features such as constant fixed rate, zero value at inception, symmetric payoff and credit risk, plus a quick implied forward rate calculation.
- Saying a swap has no counterparty credit risk. Both swaps and FRAs do.
- Thinking a swap's fixed rate changes each period like an FRA strip. A standard swap's fixed rate is constant.
- Mixing up timing: FRAs usually settle at the start of the interest period, swaps at the end of each period.
Check yourself
Q1One-year and two-year annual zero rates are 3.0% and 3.5%. The no-arbitrage fixed rate on a one-year FRA starting in one year is closest to:
Q2Which feature is shared by an interest rate swap and a series of FRAs?
Q3A standard interest rate swap most likely differs from a series of FRAs covering the same periods because the swap:
Q4With an upward-sloping zero curve, the fixed rates on a strip of consecutive one-year FRAs are most likely:
Q5On a swap or an FRA, MRR sets above the agreed fixed rate. The fixed-rate payer:
Answer the 5 questions: +10 XP for each one you get right first time.
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