A company has borrowed £50 million at LIBOR plus 1%. If rates rise a quarter of a point, interest costs jump by more than a hundred thousand pounds a year. The finance director can fix the rate for a future period with a forward rate agreement, or fix it for years with a swap. Neither involves lending or borrowing new principal: both are bets on a rate, settled in cash.
This topic covers interest rate risk and volatility, money market benchmarks, forward rate agreements (FRAs), how they settle, interest rate swaps, how a swap changes a company’s interest liabilities and the idea of credit arbitrage. The previous topic covered yield curves and credit risk. The next covers forward rates from yield curves, swap pricing and currency swaps.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on FRAs or swaps.
In 30 seconds
Interest rate risk rises with volatility and uncertainty about the direction. A forward rate agreement (FRA) fixes a rate for a future period on a notional amount; buy an FRA to fix a borrowing rate, sell one to fix a deposit rate. A 3v9 FRA covers months 3 to 9. The bank quotes the higher rate to a borrower.
At the start of the period, compare the FRA rate with the benchmark (LIBOR): if LIBOR is higher the buyer is paid, if lower the buyer pays; the amount is discounted to the start. An interest rate swap exchanges fixed for floating interest on a notional principal over several years; there is no exchange of principal and payments are not discounted.
A borrower with a floating loan pays fixed and receives floating to fix its cost. The effective rate: loan rate + fixed paid − floating received. Swaps change liabilities without touching the loan.
Key terms in plain English
| Term | What it means |
|---|---|
| Forward rate agreement (FRA) | A contract that fixes an interest rate for a future period on a notional sum |
| Notional principal | The reference amount on which interest is calculated; it is never actually exchanged |
| Benchmark rate | The market reference rate, such as LIBOR or NIBOR |
| Coupon (plain vanilla) swap | An exchange of fixed-rate and floating-rate interest payments |
| Swap rate | The fixed rate in a swap |
| Credit arbitrage | A gain from differences in the cost of fixed and floating borrowing between companies |
Syllabus check
This topic is in syllabus area E (treasury and advanced risk management). It covers:
- explaining the nature of interest rate risk;
- explaining and using FRAs and interest rate swaps to hedge interest rate risk.
CAMA 2020 and derivatives
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | Derivatives should be used within the company’s powers and for its benefit |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should approve a clear policy for interest rate risk and the instruments used |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
Interest rate risk
A company with variable-rate debt pays more when rates rise and less when they fall. A company with fixed-rate debt is unaffected by rises but loses competitive ground against rivals who borrow at lower rates after a fall. Holders of fixed-rate bonds see prices fall when yields rise. The size matters: on $500 million of variable debt a 0.25% rise costs $1,250,000 a year.
Risk is greatest when rate changes are frequent and large and when the direction is uncertain, which is more likely when inflation is high.
Short-term rates are money market rates; long-term rates are bond yields. A corporate bond’s yield changes with risk-free rates and with the issuer’s perceived credit risk; a downgrade from AA to A+ raises the yield, but that is credit risk, not interest rate risk.
Benchmark rates
Money market loans are priced at a margin over a benchmark, such as LIBOR (London Interbank Offered Rate) for each maturity, with the euro benchmark Euribor, and in Nigeria NIBOR. Loan interest for each period is set from the benchmark at the start of the period, with the margin in basis points (LIBOR + 150 bp means +1.50%). For sterling, interest uses a 365-day year; for dollars, 360.
In the exam, assume months ÷ 12. LIBOR has been replaced by risk-free benchmark rates, such as the Secured Overnight Financing Rate (SOFR) for the dollar and the Sterling Overnight Index Average (SONIA) for sterling. The mechanics below are the same for any benchmark.
Forward rate agreements
An FRA is an over-the-counter contract with a bank that fixes the rate for a future loan or deposit period on a notional amount. A 3v9 (or 3/9) FRA covers a six-month period starting at the end of month 3; a 2v5 covers three months from the end of month 2. Buy an FRA to fix a borrowing cost; sell one to fix a deposit return.
Banks can quote because the money market lets them derive a rate. ICAN’s example: a bank borrows $1m for nine months at 5% (interest $37,500) and deposits it for three months at 4.75% (interest $11,875 on $1m, so $1,011,875 at the end). To break even by lending $1,011,875 for months 3 to 9 it needs $25,625, an annual rate of 25,625 ÷ 1,011,875 × 12 ÷ 6 = 5.06%.
How an FRA settles
At the start of the notional period, the FRA rate is compared with the benchmark rate. If the FRA rate is higher, the buyer pays the seller; if the FRA rate is lower, the buyer receives. The amount is (difference) × notional × period, discounted to the start at the reference rate.
ICAN’s example. A company will borrow £5m in three months for six months and buys a 3v9 FRA at 5.40% (the bank’s quote is 5.40 – 5.36; the borrower takes the higher).
- If six-month LIBOR is 6.25%: the bank pays 0.85% × 5m × 6÷12 = £21,250 (discounted: 21,250 ÷ 1.03125 = about £20,606).
- If LIBOR is 4.75%: the company pays 0.65% × 5m × 6÷12 = £16,250 (discounted to about £15,873).
- Either way the effective rate is fixed at 5.4%. The company cannot benefit from a favourable move.
ICAN’s second example. A company needs $20m for three months starting in two months. FRA quotes: 2v5 is 3.67 – 3.63. It borrows at LIBOR + 50 bp; LIBOR at the start is 4.50%.
- A 2v5 FRA; the borrower takes the higher rate, 3.67%.
- FRA receipt.
4.50% − 3.67% = 0.83%. - Effective cost.
5.00% − 0.83% = 4.17% (= 3.67% + 0.50%).
Interest rate swaps
A swap is an agreement, usually for several years, to exchange interest payments on a notional principal at agreed dates. In a coupon (plain vanilla) swap one party pays a fixed rate (the swap rate) and the other a floating rate such as LIBOR. There is no exchange of principal, and payments are settled net at the end of each period, so they are not discounted (unlike an FRA).
ICAN’s example: a four-year, $20m swap, the company pays 4.25% fixed every six months and the bank pays six-month LIBOR. If LIBOR is 5.00% the bank pays the company 0.75% × 20m × 6÷12; if LIBOR is 3.00% the company pays 1.25% × 20m × 6÷12. There are eight exchanges over four years. A swap is like a series of FRAs.
Using swaps
- Floating to fixed. ICAN’s example: a £10m loan at LIBOR + 1% with five years to run. The bank quotes 5.34 – 5.39 for a five-year swap. The company pays the higher rate, 5.39%, receives LIBOR and keeps paying LIBOR + 1% on the loan.
Net = (LIBOR + 1) + 5.39 − LIBOR = 6.39% fixed.
Another example: a loan at LIBOR + 150 bp with the company paying 5.8% fixed and receiving LIBOR gives 7.3% fixed. - Fixed to floating. ICAN’s example: €40m of 5% bonds, ten years left, swap quote 4.22 – 4.25. The company receives the lower rate, 4.22%, and pays floating.
Net = 5% − 4.22% + floating = floating + 0.78%.
Swaps let a company move between fixed and floating without redeeming bonds or renegotiating loans, and follow a policy (for example, between 25% and 75% fixed). They give fixed-rate exposure to a company that can only borrow floating from banks. A swap can be cancelled for a payment equal to its value.
Credit arbitrage exists when two companies face different quality spreads in the fixed and floating markets: the party with the comparative advantage in each market borrows there, then they swap and share the saving. Such opportunities have become rare.
The rules in more depth
Why an FRA is settled at the start
The difference is known when the rate is set, so it is paid then, which means discounting.
Why a borrower buys an FRA
It pays out if rates rise, offsetting the higher borrowing cost.
Why swaps are not discounted
Payments occur at the end of each period when the rate is already known.
Why the bank takes the better side
It quotes the rate more favourable to itself, as in foreign exchange.
Effect on analysis
Identify the exposure, choose buy or sell, find the net rate and state that favourable moves are given up.
Worked examples
Example 1: an FRA payout. A company borrowing $10m for three months in three months buys a 3v6 FRA at 4.0%. LIBOR is 5.0% at the start.
- Difference = 1.0%
amount = 1.0% × 10m × 3÷12 = $25,000. - Discount at 5% × 3÷12 = 1.25%: 25,000 ÷ 1.0125.
- Receipt = $24,691.
Example 2: effective rate. The company in Example 1 pays LIBOR + 1% on its loan.
- Loan cost.
5.0% + 1.0% = 6.0%. - FRA gain = 1.0%.
- Effective rate.
5.0% (= 4.0% + 1.0%).
Example 3: a swap. A loan costs LIBOR + 2%. The company pays 5% fixed and receives LIBOR in a swap.
- Net = LIBOR + 2% + 5% − LIBOR.
- Net = 7%.
- The liability is fixed at 7%.
Example 4: credit arbitrage. X pays 8.0% fixed or LIBOR + 1.5%; Y pays 6.5% fixed or LIBOR + 0.5%.
- Fixed gap = 1.5%; floating gap = 1.0%.
- Y has the comparative advantage in fixed, X in floating.
- Total saving = 0.5%, which they can share through a swap.
How to score full marks
- State the exposure and the direction of the risk.
- Choose buy (borrower) or sell (depositor).
- Pick the right side of the bank’s two-way quote.
- Show the settlement and, for an FRA, discount it.
- Compute the effective rate with the margin.
- Note that fixing the rate forgoes gains.
Common mistakes in the exam
- Selling an FRA when borrowing.
- Forgetting the borrowing margin in the effective rate.
- Not discounting FRA settlements when asked.
- Believing that principal is exchanged in an interest rate swap.
- Using the wrong side of the swap quote.
- Ignoring that the hedge removes favourable moves too.
Quick revision
- Risk rises with volatility; floating debt pays more when rates rise.
- FRA: notional, buy to fix borrowing, sell to fix a deposit; discounted at the start.
- Swap: fixed against floating, several years, no principal, not discounted.
- Pay fixed and receive floating to fix a floating loan.
- Net rate = loan rate + paid − received.
- CAMA 2020: ss. 305, 308, 377(1), 378, 385.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.
Recall check: multiple choice
Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.
Question 1. A company with variable-rate debt is hurt when interest rates:
- Rise
- Fall
- Stay the same
- Are negative
Show the answer
A. Interest costs go up.
Question 2. To fix a future borrowing rate, a company should:
- Buy an FRA
- Sell an FRA
- Buy a put
- Sell a swap fixed rate only
Show the answer
A. Buying fixes the borrowing cost.
Question 3. A 3v9 FRA covers:
- Months 3 to 9
- Months 0 to 3
- Months 9 to 12
- Nine months from now
Show the answer
A. A six-month period.
Question 4. If LIBOR at settlement is above the FRA rate, the FRA buyer:
- Receives a payment
- Pays
- Is cancelled
- Borrows more
Show the answer
A. The FRA compensates the higher cost.
Question 5. FRA settlements are discounted because they are paid:
- At the start of the notional period
- At the end
- Never
- After a year
Show the answer
A. The interest is for a later period.
Question 6. In an interest rate swap, principal is:
- Not exchanged
- Exchanged at the start
- Exchanged at the end only
- Doubled
Show the answer
A. It is notional.
Question 7. A company with a floating loan wanting a fixed cost should:
- Pay fixed and receive floating
- Pay floating and receive fixed
- Do nothing
- Sell the loan
Show the answer
A. The floating receipt offsets the loan.
Question 8. A loan at LIBOR + 1% with a swap paying 5.39% and receiving LIBOR costs:
- 6.39%
- 5.39%
- 4.39%
- LIBOR
Show the answer
A. 1% + 5.39%.
Question 9. Hedging with an FRA means the company:
- Cannot benefit from favourable moves
- Gains from all moves
- Has no cost
- Needs to lend principal
Show the answer
A. The rate is fixed.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Explain the nature of interest rate risk. (4 marks) (b) Explain how an FRA works and who buys or sells it. (6 marks)
Question 12 (20 marks). A company will borrow £8m in three months for six months at LIBOR + 1%. A bank quotes a 3v9 FRA at 4.90 – 4.85. (a) State the FRA the company should use and its rate. (2 marks) (b) Calculate the settlement and the effective borrowing rate if LIBOR is 6.00% at the start. (6 marks) (c) Do the same if LIBOR is 3.50%.
(6 marks) (d) A £20m loan at LIBOR + 1.5% is swapped, the bank quoting 5.00 – 5.05; state the net rate. (3 marks) (e) State two advantages of a swap. (3 marks)
Question 13 (10 marks). (a) A bank borrows $1m for nine months at 5% and deposits it for three months at 4.75%. Calculate the annual rate it must earn for months 3 to 9 to break even. (4 marks) (b) A company has €40m of 5% bonds and receives 4.22% fixed and pays floating in a swap. State the net cost. (3 marks) (c) Distinguish a swap from an FRA. (3 marks)
Model answers
Show the model answer to Question 11
(a) Risk (4 marks). Variable-rate borrowers pay more when rates rise. (1) Fixed-rate borrowers lose out to rivals who borrow after a fall. (1) Holders of fixed-rate bonds lose when yields rise. (1) Risk is greater when rate changes are frequent, large and uncertain in direction. (1)
(b) FRA (6 marks). An FRA fixes a rate now for a future period on a notional amount, arranged over the counter with a bank. (2) A borrower buys one and a depositor sells one. (1) At the start of the period the FRA rate is compared with the benchmark: if the benchmark is higher the buyer receives, if lower the buyer pays. (2) The payment is discounted to the start. (1)
Show the model answer to Question 12
(a) FRA (2 marks). A 3v9 FRA bought, since the company is borrowing; the bank quotes the higher rate, 4.90%. (2)
(b) LIBOR 6.00% (6 marks).
- The bank pays (6.00 − 4.90)% = 1.10% × 8m × 6÷12 = £44,000, discounted: 44,000 ÷ 1.03 = £42,718. (4)
- Effective rate.
loan 7.00% − 1.10% = 5.90% (= 4.90% + 1%). (2)
(c) LIBOR 3.50% (6 marks).
- The company pays (4.90 − 3.50)% = 1.40% × 8m × 6÷12 = £56,000, discounted: 56,000 ÷ 1.0175 = £55,037. (4)
- Effective rate.
loan 4.50% + 1.40% = 5.90%. (2)
(d) Swap (3 marks).
- The company pays the higher rate, 5.05%, receives LIBOR and pays LIBOR + 1.5% on the loan. (1.5)
- Net = 6.55% fixed. (1.5)
(e) Advantages (3 marks). A company can switch between fixed and floating without changing the underlying loan; it can obtain fixed-rate liabilities when only floating bank loans are available; it follows a policy on the mix. Any two. (1.5 each)
Show the model answer to Question 13
(a) Break-even (4 marks).
- Interest paid.
1m × 5% × 9÷12 = $37,500; deposit grows to $1,011,875, interest $11,875. (2) - Needed = 37,500 − 11,875 = $25,625
- rate = 25,625 ÷ 1,011,875 × 12 ÷ 6 = 5.06%. (2)
(b) Net cost (3 marks).
- Bond cost 5% less 4.22% received plus floating paid. (1.5)
- Net = floating + 0.78%. (1.5)
(c) Difference (3 marks). An FRA fixes a rate for one future period and is settled at the start, discounted. (1.5) A swap covers several periods, with net payments at the end of each, not discounted. (1.5)
Pathfinder on Interest rate risk, FRA settlement, coupon swaps and effective rates
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Neither the May 2014 nor the November 2014 Pathfinder sets a stand-alone question on FRAs or swaps. Practise the settlement and the effective rate in the worked examples.
Revise first: Forward rate agreements
Questions ask for the net rate after a swap. See the section on interest rate swaps.
Revise first: Interest rate swaps
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: No stand-alone question in the May 2014 or November 2014 Pathfinder.
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