ACCA Applied Skills · Financial Management

Hedging techniques for interest rate risk: formula sheet

Full chapter guide

Key formulas

Change in annual interest cost: Change in interest = Exposed amount × Change in rate × (Months ÷ 12); Use only the unhedged amount that reprices, and the time period it is exposed for.
Gap exposure: Gap = Floating-rate liabilities − Floating-rate assets (same repricing period); Here the gap is defined as liabilities minus assets. Net floating liabilities (positive gap) lose if rates rise. Net floating assets (negative gap) lose if rates fall. Gap analysis in banking often uses the opposite sign (assets minus liabilities), so check the definition given in a question.
Fixed rate opportunity cost: Opportunity cost = Debt × (Fixed rate − Current market rate); Applies if market rates fall after you fix. Treat it as a cost relative to the market, not a cash cost increase.
Expectations theory (simple form): Long rate ≈ average of expected future short rates; Liquidity preference adds a premium on top of this for longer maturities.
Net interest exposure: Net exposure = floating-rate liabilities − floating-rate assets; A positive figure means you lose when rates rise. A negative figure means you lose when rates fall.
Change in annual interest cost: Change in cost = net floating exposure × change in rate; Use this to size the effect of a rate move. Apply the change in rate as a decimal.
Matching rule: Floating assets → floating liabilities; fixed assets → fixed liabilities; Aim to match both the rate basis and the period.
Fixed proportion of debt: Fixed % = fixed-rate debt ÷ total debt × 100; A smoothing policy often sets a target for this percentage.
Meaning of the quote: FRA m v n: loan starts in m months and lasts (n − m) months; 3v9 is a 6-month loan starting in 3 months. 6v12 is a 6-month loan starting in 6 months.
Settlement amount: Settlement = Notional × (Market rate − FRA rate) × (months ÷ 12); Use the loan length in months. Ignore the sign for size; the sign tells you who pays.
Who pays (borrower's FRA): Market rate > FRA rate: bank pays you. Market rate < FRA rate: you pay the bank.; The reverse applies to a depositor's FRA.
Which quote to use: Borrower: higher rate. Depositor: lower rate.; The bank always deals at the rate that is worse for you.
Effective rate with an FRA: Net rate ≈ FRA rate; Real loan cost plus or minus the FRA settlement gives about the FRA rate. Exam answers often ignore the timing of the payment.
Futures price: Futures price = 100 − annual interest rate (%); A price of 94.50 implies a rate of 5.50%. Price down means rates up.
Tick value: Tick value = contract size × 0.01% × (contract months ÷ 12); For $1,000,000 and 3 months: 1,000,000 × 0.0001 × 3/12 = $25. Use the contract size given in the question.
Number of contracts: Contracts = (loan or deposit ÷ contract size) × (loan months ÷ contract months); Round to the nearest whole contract. A 6-month loan on a 3-month contract doubles the number.
Which side to take: Borrower: sell futures. Lender or depositor: buy futures.; Close out by doing the opposite deal on the date the rate is fixed.
Futures gain or loss: Gain or loss = price movement in ticks × tick value × number of contracts; Borrower sold at a higher price than the closing price makes a gain.
Basis: Basis = futures price − spot price, where spot price = 100 − spot rate; It falls to zero at expiry.
Basis at close-out: Basis at close-out = current basis × (months left to expiry ÷ months from today to expiry); This is a straight-line estimate. Use it to find the expected futures price on the closing date.
Effective interest rate: Net interest cost = cash interest − futures gain (or + futures loss); effective rate = net cost ÷ loan × 12 ÷ loan months; Always compute it as a check on the answer.
Futures price and rate: Futures price = 100 − interest rate (%); A strike price of 94.50 means a strike rate of 5.50%.
Number of contracts: Contracts = Loan ÷ Contract size × Loan period ÷ Contract period; Round to the nearest whole contract. Use the same time units for both periods.
Tick value: Tick value = Contract size × 0.01% × Contract months ÷ 12; For a 1,000,000 three-month contract, one tick (0.01) is worth 25.
Exchange-traded option exercise rule (borrower): Exercise the put if futures price at expiry < strike price; Gain per contract = (strike price − futures price) ÷ 0.01 × tick value. Dividing the price difference by 0.01 converts points to ticks. For example, 1.50 ÷ 0.01 = 150 ticks × $25 = $3,750.
OTC option premium: Premium = Loan × premium % (not annualised); Payable up front. If the question says so, compound it to the end of the loan at the market rate. That means from the date you pay it, including any months before the loan starts.
Effective rate if exercised: Effective rate = Strike rate + premium cost expressed as an annual rate; For an exchange-traded premium quoted in points, the premium adds that many points to the annual rate.
Effective rate if not exercised: Effective rate = Market rate + premium cost; The option lapses and you borrow at the market rate.
Collar (borrower): Net premium = Cap premium paid − Floor premium received; Rate paid lies between the floor rate and the cap rate, adjusted for net premium.
Net cost with a swap: Net cost = interest paid to lender + swap payment − swap receipt (+ or − any fee); Do this separately for each party, and state the answer as a fixed or floating rate.
Total comparative advantage saving: Saving = |fixed rate gap − floating rate gap|; Fixed rate gap is the difference between the two companies' fixed rates. Floating rate gap is the difference between their floating spreads over the same base. Use the same units.
Saving per party: Share of saving = (total saving − bank fee) × agreed share (often 50% each), unless the question states how the fee is borne; Deduct the bank fee from the total saving first if the question says the fee is paid out of the gains.
Swap saving in money: Annual saving (₹) = rate saving × notional principal; Convert the percentage saving into money only if asked.
Plain vanilla vs basis swap: Plain vanilla = fixed ↔ floating. Basis = floating ↔ floating on different bases.; Learn this as a definition for short written parts.

Quick revision

A borrower on floating rates loses if rates rise; a depositor loses if rates fall.
Smoothing mixes fixed and floating debt to reduce the effect of rate moves.
Matching offsets assets and liabilities that have similar rate exposure.
Netting uses a position's gains to offset losses before external hedging.
An FRA fixes the rate on a future loan or deposit for a set period and settles only the difference.
With an FRA you cannot gain if rates move in your favour.
Futures are standardised contracts; close out by doing the opposite trade.
Futures prices rise when expected interest rates fall.
Options protect against bad moves and let you keep good ones, but you pay a premium.
A cap sets a maximum rate, a floor sets a minimum, and a collar combines them to cut cost.
A swap exchanges interest payments, not the principal.
Always check the period, the principal and whether the question wants the rate or the cash amount.

Common mistakes

Saying fixed rate debt has no interest rate risk. Fix: State that fixed debt removes cash flow risk but creates opportunity cost if market rates fall, and its market value changes.
Treating gap exposure and basis risk as the same thing. Fix: Gap is a mismatch of amounts or repricing dates. Basis risk is a mismatch of benchmarks even when amounts match.
Including fixed-rate balances in the exposure calculation. Fix: Only floating-rate items change cost when rates move. Exclude fixed items from the change calculation.
Confusing matching with smoothing. Fix: Matching pairs assets with liabilities on the same basis. Smoothing blends fixed and floating debt or spreads maturities.
Using the second number of the quote as the loan length, for example treating 3v9 as a 9-month loan. Fix: Always subtract. 3v9 is 9 − 3 = 6 months, starting in 3 months.
Using the wrong side of the two-way quote. Fix: Borrowers take the higher rate. Depositors take the lower rate. Write 'borrow = high' beside the question.
Buying futures when you should sell, or the reverse. Fix: Write: rates up means price down. A borrower wants a gain when rates rise, so must sell first and buy back lower.
Forgetting the loan period when working out the number of contracts. Fix: Multiply by loan months ÷ contract months. A 6-month loan on a 3-month contract needs twice as many contracts.
Buying a call on futures when you are a borrower Fix: Futures prices fall when rates rise. A borrower needs the price to be able to fall, so buy a put. Say it as: rates up, price down, put.
Forgetting the premium in the net cost Fix: Always add the premium to the cost, even when the option lapses. The premium is paid in every scenario.

Exam tips

In objective tests, write the gap first. Many wrong options use the gross borrowing instead of the net amount.
Read the question for the time period. A six-month exposure is half the annual effect.
In written answers, state both the direction and the reason, for example: floating borrower, rates rise, cost rises.
When asked to explain yield curve shape, name the theory and tie it to the shape described. Do not just list all three.
Link causes to the situation: inflation expectations and central bank policy are the usual drivers in scenarios.
Read the requirement for the words internal, non-derivative or without derivatives. Then do not answer with FRAs or swaps.
In Section A, compute the net floating position first. Most calculations follow from it.
In Section C, use short headed points: method, how it works, limits. Always apply it to the company in the scenario.