ACCA Applied Skills · Financial Management

Hedging techniques for foreign currency risk: formula sheet

Full chapter guide

Key formulas

Transaction risk – receivable: Home currency received = foreign amount ÷ rate (if rate is quoted as foreign per 1 home); Check the quote direction first. A weaker foreign currency means less home currency received.
Transaction risk – payable: Home currency paid = foreign amount ÷ rate at settlement; A stronger foreign currency means you pay more in home currency.
Translation of subsidiary net assets: Net assets in home currency = net assets in foreign currency ÷ closing rate (foreign per 1 home); Quoted as home per 1 foreign, multiply instead. Gain or loss is the difference between the two translated amounts.
Classification rule: Short-term cash flow on a known deal = transaction; consolidation of overseas accounts = translation; long-term competitiveness = economic; Use this to label any scenario quickly.
Bank buys base currency: Bank buys base at the lower rate (bid) of the quote; Use this when your company sells (receives) the base currency, for example an export receipt in the base currency.
Bank sells base currency: Bank sells base at the higher rate (offer) of the quote; Use this when your company buys (pays) the base currency, for example an import payment in the base currency.
Forward rate with a premium: Forward rate = Spot + premium (applied to each side of the spread); Premium means the base currency is worth more in the future, so the forward rate rises. In exams a premium is usually quoted low-high, for example '1.1000 - 1.1200 spot, 0.40 - 0.50 cents premium'. Add 0.0040 to the lower rate and 0.0050 to the higher rate. Then check the forward spread is still low-high.
Forward rate with a discount: Forward rate = Spot − discount (applied to each side of the spread); Discount means the base currency is worth less in the future, so the forward rate falls. In exams a discount is usually quoted high-low, for example 0.80 - 0.60 cents. Subtract 0.0080 from the lower rate and 0.0060 from the higher rate. Then check the forward spread is still low-high.
Converting amounts: Quoted currency amount = Base amount × rate; Base amount = Quoted amount ÷ rate; Multiply to go from base to quoted. Divide to go from quoted to base.
Interest rate parity (forward rate): F₀ = S₀ × (1 + iᶜ) ÷ (1 + iᵇ); S₀ is the spot rate quoted as units of currency c per 1 unit of currency b. iᶜ is the interest rate of the quoted currency c. iᵇ is the interest rate of the base currency b. Use rates for the same period as the forward contract.
Purchasing power parity (future spot rate): S₁ = S₀ × (1 + hᶜ) ÷ (1 + hᵇ); Same layout as IRP but with expected inflation rates h. S₁ is the expected spot rate at the end of the year. Use the inflation rates for the period.
Quick direction rule: Higher rate (interest or inflation) = weaker currency; The currency with the higher rate depreciates against the other. Use this to check your answer is sensible.
Multi-year PPP: S_n = S₀ × [(1 + hᶜ) ÷ (1 + hᵇ)]ⁿ; Use when inflation rates are constant for n years. If rates differ by year, apply each year's ratio in turn.
Change in rate over less than a year: F₀ = S₀ × (1 + iᶜ × m ÷ 12) ÷ (1 + iᵇ × m ÷ 12); Use when the question gives annual rates and a period of m months. Convert annual rates to the period by simple proportion unless told otherwise.
Net exposure: Net exposure = Receivables in currency − Payables in currency; Use the same currency and the same time period. A positive result is a net receipt, and a negative result is a net payment.
Leading and lagging rule for payments: Expect currency to strengthen → lead (pay early). Expect currency to weaken → lag (pay late).; For receipts, reverse it. Expect the currency to weaken: collect early. Expect it to strengthen: delay.
Netting versus matching: Netting = offset amounts due at similar dates. Matching = use a currency inflow or account to cover an outflow in that currency.; Matching may involve a foreign currency bank account, and dates need not be identical.
Forward contract outcome: Home currency amount = foreign amount × forward rate; Use the rate that is worse for you. A customer buying foreign currency uses the bank's selling rate. A customer selling foreign currency uses the bank's buying rate.
Choosing the side of a bid-offer quote: Quoted as home per 1 foreign (e.g. $/€ 1.2000 – 1.2100): customer receiving foreign currency uses the lower rate; customer paying foreign currency uses the higher rate; If the quote is foreign per 1 home, the logic reverses: divide, and use the rate that gives you less. Always check how the quote is written.
Periodic interest rate: Rate for the period = annual rate × (months ÷ 12); Exam questions usually use simple interest for periods under a year unless told otherwise.
Money market hedge for a payable: Foreign deposit now = foreign payable ÷ (1 + foreign deposit rate for period). Home cost now = deposit × spot (selling rate). Future home cost = home cost now × (1 + home borrowing rate for period); If the company already has spare cash, use the home deposit rate as the lost interest instead of the borrowing rate, and say so.
Money market hedge for a receivable: Foreign loan now = foreign receivable ÷ (1 + foreign borrowing rate for period). Home proceeds now = loan × spot (buying rate). Future home receipt = proceeds × (1 + home deposit rate for period); If the company has an overdraft, the proceeds can instead reduce the overdraft, saving the home borrowing rate.
Tick value: Tick value = contract size × tick size; For example, a £62,500 contract with a $0.0001 tick gives $6.25 per tick. The exam normally supplies the contract size and tick size.
Number of contracts: Number of contracts = exposure in contract currency ÷ contract size; Round to the nearest whole number. Say that the hedge is then slightly over or under the exposure.
Basis: Basis = spot rate − futures price; Use the same definition throughout. Basis converges to zero at the expiry date. Always check which sign convention the question uses.
Estimated basis at closure: Basis at closure = basis today × (months left at closure ÷ months left today); This assumes straight-line convergence. Count months to the expiry date of the contract, not to the transaction date.
Closing futures price: Closing futures price = spot rate at closure − basis at closure; Rearranged from the basis formula. Use it when the question gives the spot rate at closure and not the futures price.
Futures gain or loss: Gain or loss = ticks moved × tick value × number of contracts; Sold futures gain when the price falls. Bought futures gain when the price rises.
Net outcome: Net outcome = spot amount at closure ± futures gain or loss; Add a gain to a receipt or subtract it from a payment. Do the reverse for a loss.
Hedge direction: Receiving the contract currency: sell futures. Paying the contract currency: buy futures; Close out with the opposite trade at the transaction date.
Which option to buy: Paying foreign currency → buy a call on the foreign currency. Receiving foreign currency → buy a put on the foreign currency.; Think about what you need to do with the foreign currency. Pay it means you buy it (call). Receive it means you sell it (put).
Exercise decision: Call: exercise if spot > strike. Put: exercise if spot < strike.; Spot and strike are both quoted as home currency per unit of foreign currency. If they are equal, you are indifferent.
Premium cost: Premium = foreign currency amount × premium per unit; Premium is paid at the start and is non-refundable. Ignore interest on it unless the question tells you to include it.
Total cost of a call hedge (paying foreign currency): Total cost = amount × lower of (strike, spot) + premium; Worst-case effective rate is the strike plus premium per unit.
Total receipt of a put hedge (receiving foreign currency): Total receipt = amount × higher of (strike, spot) − premium; Worst-case effective rate is the strike minus premium per unit.
Break-even against a forward (call, paying foreign currency): Break-even spot = forward rate − premium per unit (valid only when this is below the strike); The option is cheaper than the forward if spot at expiry is below the break-even spot. The forward is cheaper if spot is above it.
Currency swap mechanics: Start: swap principals at spot. Term: each party pays interest on the principal it received, in that currency. End: re-swap principals at the same spot rate.; The end exchange is at the original rate, which is why the exchange rate risk is removed.

Quick revision

Transaction risk is on settlement of individual deals; translation risk is on consolidation; economic risk is on long-term competitiveness.
When you deal with a bank on a bid/offer quote, you deal at the rate less favourable to you (more favourable to the bank). This does not apply to exchange-traded futures, which settle at the exchange price.
Check the quote direction first: a quote of X per 1 unit of the base currency tells you whether to multiply or divide.
Forward rate from interest rate parity: for a rate quoted as A per 1 B, F = S × (1 + rate of A) ÷ (1 + rate of B), with rates for the period of the contract. If the quote is home currency per 1 foreign unit, A is the home currency.
Expected future spot from purchasing power parity uses inflation rates in the same way, with the same quote convention.
A forward contract fixes the rate and removes both downside and upside.
A money market hedge for a foreign payable: deposit the present value of the payable (discounted at the foreign deposit rate for the period), buying that foreign currency at spot with home borrowing or cash. The deposit grows to the payable amount and pays it at maturity. If you borrowed, repay the home loan with interest. If you used home cash instead, the cost is that cash plus the interest it could have earned, or you can compare the cash at its future value. For a receivable: borrow abroad now, convert to home currency and invest at home.
Futures are standard contracts, so you round to a whole number of contracts and a small residual exposure stays open.
Futures hedging: the final outcome is the spot result plus the gain or loss on the futures, and basis risk means the hedge is not perfect.
An option gives the right but not the obligation to deal; you pay the premium, and you exercise only if the option rate beats the spot rate.
A swap exchanges currency flows or interest streams and is mainly useful for longer-term exposures.
Always end a hedging answer with a comparison table in words and a clear recommendation.

Common mistakes

Calling a loss on consolidating an overseas subsidiary a transaction loss. Fix: Transaction risk needs a cash flow on a specific deal. Consolidation effects are translation risk and are not cash flows.
Saying translation risk should always be hedged with forwards. Fix: Translation gains and losses are unrealised. Many firms do not hedge them. Where they do, it is usually to protect ratios or covenants, for example by borrowing in the foreign currency.
Using the offer rate when the company receives base currency Fix: Always think from the bank's side first. If the company receives base currency from a customer, the bank buys it, so the lower rate applies.
Subtracting a premium instead of adding it Fix: Remember that a premium on the base currency means it is worth more in the future, so the forward rate rises. Add premiums, subtract discounts.
Putting the rates upside down. Fix: Always put the quoted currency's rate on top. Then check that the higher-rate currency is weaker.
Using inflation rates for a forward rate, or interest rates for a future spot rate. Fix: Remember: IRP = interest = forward rate. PPP = prices (inflation) = future spot rate.
Calling a forward contract or option an internal technique. Fix: Internal methods use the company's own operations. If a bank or market product is involved, it is external.
Netting amounts in different currencies without converting. Fix: Net only within one currency. Different currencies are offset only if you treat them separately or if they are closely linked.
Using the wrong side of the bid-offer spread. Fix: Remember the bank always gives you the worse rate. Write 'bank buys' or 'bank sells' beside the rate before using it.
Using the annual interest rate for a three- or six-month period. Fix: Multiply the annual rate by months ÷ 12 as your first step. Write the period rate down.

Exam tips

Always label the risk type in the first line of your answer. Markers award marks for the correct classification before the explanation.
In Section B cases, look for keywords: 'invoice', 'payable in three months' point to transaction; 'consolidated' points to translation; 'competitors', 'long-term' and 'market share' point to economic.
Objective questions are all or nothing, so check the rate direction and whether the effect is a gain or a loss before you choose.
In written answers, link the hedge to the risk type. Say that translation risk is non-cash and economic risk needs operational responses.
If asked to compare types, use a short structure: what it affects, time horizon, cash or non-cash, how it is managed.
In objective questions, the wrong rate is usually one of the answer options. Decide buy or sell from the bank's side before you look at the options.
Always apply a premium or discount to both sides of the spread and check the lower number still comes first.
In Section C, write down the rate you chose and the reason in one line. Method marks are available even if the arithmetic slips.