Rates · R7 · 9 min
Interest rate swaps
Explain who pays what in a swap, choose the right side for a hedge or a view, and value a swap after rates move.
In the news: “Swap rates jumped and companies rushed to fix their borrowing costs”: the contract behind most interest rate hedging.
The essentials
- Interest rate swap
- An exchange of fixed payments for floating ones, usually compounded or , on a notional that never changes hands. Each period only the difference is paid: 0.5% on £100m is £500,000.
- Payer and receiver
- The pays fixed and gains when rates rise; a company with a floating-rate loan pays fixed to lock in its cost. The gains when rates fall, as a bondholder does.
- Swap rate
- The fixed rate that makes both legs worth the same at the start, so a new swap costs nothing to enter and is worth zero to both sides.
- Value after rates move
- A swap gains or loses value as the market rate for its remaining term moves away from its fixed rate. Paying 3.80% for five years on £50m when the five-year rate is 4.10% is worth about £666,000 to the payer.
- Swap spread
- The swap rate minus the government bond of the same maturity. A negative spread usually means bonds are cheap after heavy supply, not that the government is riskier than a bank.
Value of a swap after rates move
Payer’s value ≈ (S − K) × A × N
- S
- today’s swap rate for the remaining years
- K
- the fixed rate in your swap
- A
- annuity factor: today’s value of 1 a year for the remaining years
- N
- notional. The receiver’s value is the same with the sign flipped
How it works
1. Swapping floating for fixed
A company has a £100m loan whose interest rises and falls with , and it wants certainty. It agrees with a bank: the company pays 4% fixed, and the bank pays it the floating rate, which covers the loan’s interest. Its cost is now fixed. That agreement is an .
2. Only the difference is paid
The £100m, the notional, never changes hands: it only sets the size of the payments. The floating rate is usually in sterling, or in dollars, compounded over the period. Each period the two sides net off: with 4% fixed and SONIA compounding to 4.5% over a year, the bank pays the company 0.5% of £100m, which is £500,000.
3. Payer and receiver
The side that pays fixed is the : it gains when rates rise, because the floating rate it receives goes up. The side that receives fixed is the : it gains when rates fall, just as a bondholder does.
4. Who uses swaps
A company with a floating-rate loan pays fixed to lock in its cost. A company that has issued a fixed-rate bond but would rather pay floating receives fixed. A pension fund that wants to gain when rates fall, to match long pension promises, receives fixed too.
5. A new swap is worth zero
When a swap starts, its fixed rate is set so that both sides expect to pay the same in today’s money. That fixed rate is the for that length. So nobody pays anything up front: a new swap is worth zero to both sides.
6. Then rates move
You pay 3.80% fixed for five years. A week later the five-year swap rate is 4.10%. New payers must pay 4.10%, but you pay only 3.80%: you are 0.30% a year better off for five years. Your swap is now an asset, and the receiver’s side is a liability of the same size.
7. Putting a value on it
Value = the rate gap × the × the notional. The annuity factor is what £1 a year for the remaining years is worth today, a little less than the number of years. Five years at 4.1% gives 4.44, so 0.30% × 4.44 × £50m = about £666,000.
8. Swap spreads
The is the swap rate minus the government bond yield of the same length. A 30-year swap at 4.35% against a 30-year at 5.20% is −85. A negative spread means government bonds look cheap next to swaps, usually because there are a lot of them to absorb, not because the government is riskier than a bank.
Worked example
A company pays 3.80% fixed on a £50m sterling swap with five years left and yearly payments. The five-year swap rate is now 4.10%.
- Rate gap: 4.10% − 3.80% = 0.30% a year in the company’s favour.
- Annuity factor for five yearly payments at 4.10%: (1 − 1.041⁻⁵) ÷ 0.041 = 4.44.
- Value: 0.0030 × 4.44 = 0.01332 of the notional.
- In money: 0.01332 × £50,000,000 = about £666,000 to the company; the receiver is down the same.
About +£666,000 for the payer: 30bp a year for five years, in today’s money.
Check yourself
8 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
A company with floating-rate debt fears rate rises. What swap does it do?
Why is a new swap worth zero, and what makes it worth something later?
What do negative swap spreads tell you?
Remember
Payer’s value ≈ (S − K) × annuity × notional
A swap starts at zero; after that the payer gains when rates rise above the fixed rate and the receiver when they fall below it.
Sources
- Bank for International Settlements — An explanation of negative swap spreads: demand for duration from underfunded pension plans (Working Paper 705)
- Bank for International Settlements — Recent dislocations in fixed income derivatives markets (Quarterly Review, December 2015)
Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.