The use of financial derivatives to hedge against forex risk: formula sheet

Key formulas

Net exposure in a currency

Net exposure = Foreign currency receipts − Foreign currency payments (same currency, same settlement period)

A positive figure is a long position (hurt if the currency weakens). A negative figure is a short position (hurt if it strengthens).

Home currency value of a foreign amount

Home value = Foreign amount ÷ Rate (if quoted as foreign per 1 home) or × Rate (if quoted as home per 1 foreign)

Always check the quote direction before converting.

Gain or loss on an exposure

Gain/loss on a foreign receipt = Foreign amount × (1 ÷ Rate at settlement − 1 ÷ Rate expected) if quoted as foreign per 1 home; or Foreign amount × (Rate at settlement − Rate expected) if quoted as home per 1 foreign

For a foreign payment, reverse the sign. A positive result is a gain in home currency, and a negative result is a loss.

Translation exposure

Exposed net assets = Subsidiary net assets in foreign currency; effect on home currency value = Net assets × (1 ÷ Closing rate − 1 ÷ Opening rate) if quoted as foreign per 1 home; or Net assets × (Closing rate − Opening rate) if quoted as home per 1 foreign

Accounting effect only, with no cash flow at the date of translation. A positive result means the home currency value of the net assets rises.

Which side of bid/offer to use

In a quote of foreign per 1 home (e.g. $1.2500-$1.2550 per £1): when the company receives dollars and sells them to the bank, use the higher figure ($1.2550), so it gets fewer pounds. When the company pays dollars and buys them from the bank, use the lower figure ($1.2500), so it pays more pounds.

In both cases the company gets the less favourable rate. When you convert dollar receipts to pounds by dividing, the higher figure gives fewer pounds, so use it. When you convert dollar payments to pounds by dividing, the lower figure gives more pounds, so use it.

Net position (one currency)

Net exposure = Σ receipts − Σ payments

A positive result is a net receipt (long). A negative result is a net payment (short). Hedge only this amount.

Multilateral netting

Net for each company = Σ amounts it is owed − Σ amounts it owes, after converting to one currency

Convert all balances at one agreed rate (usually spot or mid). Net positions across all companies must add to zero.

Netting saving

Gross flows − net flows = amount avoided in conversion

Multiply by the bank spread or fee rate to estimate the cost saved.

Leading or lagging cost

Gain or loss = foreign amount × (rate at early or late date − rate at due date) in home-currency terms

Include interest lost or earned on the money moved. Compare with the forward outcome.

Rule for direction

Expect foreign currency to strengthen: pay early, receive late. Expect it to weaken: pay late, receive early.

Applies to the exposure you hold, as seen from the company making the decision.

Forward rate under interest rate parity

F = S × (1 + i quote currency) ÷ (1 + i base currency)

Quote currency is the one the rate is expressed in. For $ per €1, the $ rate goes on top and the € rate below. Use rates for the period, not annual rates, unless the period is one year.

Forward contract: payable

Home cost = foreign amount × forward rate at which the bank sells the foreign currency

Use the higher rate when the rate is quoted as home currency per unit of foreign currency.

Forward contract: receivable

Home proceeds = foreign amount × forward rate at which the bank buys the foreign currency

Use the lower rate when quoted as home currency per unit of foreign currency.

Money market hedge: payable

Deposit today = foreign payable ÷ (1 + foreign deposit rate for the period)

Convert at the spot rate at which the bank sells foreign currency. Then compound the home borrowing cost to the payment date, or deposit interest lost if you use cash.

Money market hedge: receivable

Foreign loan today = foreign receivable ÷ (1 + foreign borrowing rate for the period)

Convert at the spot rate at which the bank buys foreign currency. Then add home deposit interest to the receipt date.

Period interest rate

Period rate = annual rate × months ÷ 12

Exam questions normally expect simple pro-rating for periods under a year. Follow any instruction in the question.

Number of contracts

Contracts = Foreign currency exposure ÷ Contract size

Round to a whole number of contracts. The unhedged remainder is dealt with at the spot rate on the exposure date.

Direction of the hedge

Paying foreign currency → buy futures; receiving foreign currency → sell futures

Check which currency the contract is written on. If the exposure is in the currency the contract prices, you may need the reverse position.

Tick value

Tick value = Contract size × Tick size

Example: £62,500 × $0.0001 = $6.25 per contract.

Basis

Basis = Spot rate − Futures price

Basis falls to zero at expiry.

Basis at closing

Closing basis = Opening basis × (Months left at closing ÷ Months from opening to expiry)

Use this only when the question tells you to assume basis reduces evenly, or gives no other estimate.

Estimated closing futures price

Closing futures price = Closing spot rate − Closing basis

Same sign convention as the opening basis.

Futures gain or loss

Gain or loss = (Closing price − Opening price) × Contract size × Contracts for a bought future; reverse the sign for a sold future

Equivalent to ticks moved × tick value × contracts.

Net outcome

Net result = Spot cash flow at closing date ± Futures gain or loss

Effective rate on the hedged part = opening futures price + closing basis (when you buy futures and the basis is spot minus futures).

Choosing call or put

Need to buy foreign currency → call. Need to sell foreign currency → put.

Decide this first. The direction is from your own cash flow.

Exercise decision

Exercise if option rate is better for you than the spot rate on the expiry date; otherwise let it lapse.

The exercise decision compares strike with spot only; the premium is paid regardless of whether you exercise, so it does not affect the decision.

Premium cost

Total premium = premium per unit × amount hedged (or × number of contracts × contract size)

Make sure the premium currency matches the quote. Convert at the spot rate on the date you pay it.

Number of exchange-traded contracts

Contracts = amount to hedge ÷ contract size (round to a whole number)

Check which currency the contract size is in. Handle any unhedged remainder separately.

Net outcome with option

Net receipt = amount × rate used − premium (receipts); Net payment = amount × rate used + premium (payments)

Here the rate is home currency per unit of foreign currency (for example ₹ per $1). Use the option rate if exercised, or the spot rate if not. Divide only if the rate is quoted the other way round, as foreign currency per unit of home currency. If the premium is paid now, finance it forward to the transaction date when the question gives an interest rate.

Swap interest payment

Interest = principal × interest rate × time

Calculate each currency leg separately, using the principal in that currency.

Principal in the other currency

Principal B = Principal A × agreed spot rate (or ÷, depending on quotation)

Check how the rate is quoted. The same rate is used at the start and at the end.

Saving from comparative advantage

Total saving = (difference in rate for A) − (difference in rate for B)

Compare the rate gap between the two firms in each currency. The difference in gaps is the total gain to share.

Net cost after swap

Net cost = rate paid on own loan + swap rate paid − swap rate received

Do this for each party, in the currency it wants to end up paying.

Forward hedge outcome

Home currency amount = foreign amount × forward rate

Use the rate that is worse for you: the bank buys at the lower rate when you receive foreign currency and sells at the higher rate when you pay it. Quote direction matters, so check what the rate is per one unit of which currency.

Money market hedge for a payable

Foreign amount to deposit now = payable ÷ (1 + foreign deposit rate for the period)

Convert at spot, then borrow the home currency (or lose the home deposit interest) and compound to the payment date. Scale annual rates to the period, for example 3 months = rate ÷ 4.

Money market hedge for a receivable

Foreign amount to borrow now = receivable ÷ (1 + foreign borrowing rate for the period)

Convert the borrowed amount at spot, deposit the home currency and compound to the receipt date. Compare the result with the forward.

Futures contracts needed

Number of contracts = exposure ÷ contract size

Round to a whole number of contracts. The unhedged remainder is a source of residual risk. Use the contract's own currency terms and the right month, usually the one after the exposure date.

Net option proceeds or cost

Net outcome = amount at exercise or market rate ± premium (with interest if stated)

Exercise only if the option rate beats the spot rate. If it does not, let the option lapse and use spot. The premium is paid upfront whatever happens.

Breakeven spot rate, option versus forward

Breakeven spot = forward rate + premium per unit of currency (for a receipt where the option rate is better only if spot is high)

Only valid for the lapse region of the option. Check the exercise region separately, and adjust for interest on the premium if the question asks.

Quick revision

• Transaction risk affects actual cash flows. Translation risk affects consolidated statements. Economic risk affects long-term competitiveness.
• A forward contract fixes the rate for a future date. The outcome is certain but you cannot benefit from favourable moves.
• Money market hedge for a receipt: borrow the present value of the receipt in the foreign currency now, which is foreign amount ÷ (1 + foreign borrowing rate), so that the loan plus interest equals the receipt. Convert the proceeds at spot, then invest them at home or use them to cut overdraft interest. The foreign loan is repaid from the receipt.
• Money market hedge for a payment: buy the present value of the foreign payment (foreign amount ÷ (1 + foreign deposit rate)) at the spot rate at which the company buys the foreign currency, and place it on foreign-currency deposit at the foreign deposit rate. Fund the purchase from home cash or borrowing. The deposit then grows to the amount due.
• Interest rate parity: forward rate = spot × (1 + home rate) ÷ (1 + foreign rate), applied for the period concerned.
• Futures: number of contracts = exposure ÷ contract size, rounded to a whole number. Any remainder is left unhedged or covered another way.
• Futures have a basis that converges to zero at expiry. If the exposure date does not coincide with expiry, the hedge is closed with some basis left, and the unpredictable size of that basis is the basis risk.
• Options protect against adverse moves but keep the upside. The premium is paid upfront and is a cost whether or not you exercise.
• Exercise an option only if the exercise price is better for the company than the spot rate at expiry. The premium is already paid and does not affect the exercise decision. Exchange-traded options can also be sold before expiry if they still have value.
• Swaps exchange cash flows in different currencies and suit long-term exposures.
• Compare methods using the home-currency outcome, then add qualitative points.
• A good recommendation names one method, gives the figures, states the risk left over, and ties to the scenario.

Common mistakes

• Treating translation exposure as a cash risk and recommending a forward contract for it. Fix: State that translation is an accounting effect with no cash flow. Suggest matching foreign assets with foreign borrowing, or explain why it is often left unhedged.
• Treating gross receipts and payments as exposed instead of netting them. Fix: Net by currency and settlement period first. Hedge only the net exposure, which also cuts transaction costs.
• Forgetting to convert balances into one currency before netting. Fix: Convert every figure at the stated rate first. Only then add and subtract.
• Net positions do not total zero. Fix: Always check that the sum of all net receipts equals the sum of all net payments.
• Using the wrong side of the bid-offer quote Fix: Write who is buying the foreign currency, you or the bank. When the rate is home per foreign, you pay the higher rate to buy and receive the lower rate to sell.
• Using the wrong interest rate in the money market hedge Fix: Foreign deposit rate for a payable, foreign borrowing rate for a receivable. Then home borrowing rate if you borrow home currency, or home deposit rate if you invest home currency.
• Buying futures when you should sell, or the reverse. Fix: Ask: will I pay or receive the contract currency? Pay means buy, receive means sell. Write it down before any figures.
• Using the closing spot rate as the closing futures price. Fix: Always compute closing futures price = closing spot − closing basis. Only use spot as the futures price if the contract expires on the exposure date.
• Choosing a call when a put is needed, or the reverse. Fix: Ask: am I buying or selling the foreign currency? Buying means a call. Selling means a put.
• Ignoring the premium or leaving it in the wrong currency. Fix: Always compute the total premium, convert it and include it in the final outcome. Add the interest cost if the question gives a rate.

Exam tips

• Define each type in one line, then spend your time applying it to the case facts. Marks go to application.
• Always state whether a position is long or short and which direction of movement hurts.
• Say that economic exposure is long term and is managed mainly by operational means such as diversifying sourcing, production and sales.
• Show currency conversions with the quote direction written beside them. Method marks survive an arithmetic slip.
• Use professional skills marks: give a clear recommendation and mention what you would need to know, such as hedging policy and risk appetite.
• Show the netting grid and the zero-sum check. Markers give credit for method even if one figure is wrong.
• Always state the residual exposure and link it to an external hedge. This is what bridges to forwards and options.
• Add professional skills by making a recommendation for the board, and by flagging regulation, tax and relationship risks in the scenario.