Why Hedge a Foreign-Currency Cash Flow?
A business that will receive foreign currency in the future does not yet know how much domestic currency that receipt will buy. Similarly, an obligation payable in foreign currency has an uncertain domestic-currency cost. A currency forward can fix the exchange rate for a specified amount on a specified future date. The central practical questions are which currency to buy or sell and which way the exchange rate is quoted.
This tutorial uses the perspective of a domestic party whose future cash flow is stated in a foreign currency. For example, if the domestic currency is the U.S. dollar and the foreign currency is the euro, a quote of \(1.08\) dollars per euro means that one euro costs \(1.08\) dollars. The direction of the hedge follows the foreign-currency cash flow: a receipt of euros is sold forward, while a payment of euros is bought forward.
Forward Rates and Currency Units
Assume deterministic annual effective interest rates \(i_{\mathrm{dom}}\) in the domestic currency and \(i_{\mathrm{for}}\) in the foreign currency. Under covered interest parity, with the quote defined as domestic currency per foreign unit, the no-arbitrage forward rate for \(T\) years is
The formula assumes that the rates apply over the same period, the currencies can be borrowed and invested at those rates, and there are no transaction costs, taxes, capital controls, or material counterparty constraints. If rates are quoted for a different compounding convention, they must first be expressed consistently with the accumulation factors used in the formula. In this tutorial’s examples, rates are annual effective and maturities are one year.
The exchange-rate units provide a useful check. \(S\) has units of domestic currency per foreign currency, while the interest-rate factors are dimensionless. Therefore, \(F\) retains units of domestic currency per foreign currency. Multiplying \(F\) by a foreign-currency amount gives a domestic-currency amount.
Why Covered Interest Parity Gives This Forward Rate
The rate can be justified by comparing two ways to turn one unit of domestic currency into a domestic amount at time \(T\), with the foreign-currency exposure covered by a forward contract. Investing one domestic unit domestically produces \((1+i_{\mathrm{dom}})^T\) domestic units. Alternatively, convert one domestic unit into \(1/S\) foreign units, invest them to obtain \((1+i_{\mathrm{for}})^T/S\) foreign units, and agree at the outset to convert the result back at \(F\). That route produces \(F(1+i_{\mathrm{for}})^T/S\) domestic units. No-arbitrage requires the two covered outcomes to agree:
This argument explains the no-arbitrage forward rate; it does not say that the forward rate is a forecast of the future spot rate. The purpose of a hedge is to replace an uncertain future conversion rate with the contracted rate, not to predict the market.
Worked Example: Locking the Value of a Euro Receipt
A U.S. exporter expects to receive €500,000 exactly one year from now. The spot rate is $1.08 per euro. The annual effective U.S. dollar interest rate is 4%, and the annual effective euro interest rate is 2%. Find the forward rate and the dollar receipt locked in by a forward hedge. Then compare the hedge with two possible future spot rates.
Method. The company will receive euros, so it should agree to sell €500,000 forward and receive dollars. The quote is dollars per euro, matching the required multiplication of the euro amount by the forward rate.
First calculate the one-year forward rate:
The contracted dollar receipt is
Rounded to the nearest cent, the exporter locks in $550,588.24. If the future spot rate is $1.16 per euro, an unhedged receipt would be worth \(€500{,}000\times \$1.16=\$580{,}000\). If the future spot rate is $1.02 per euro, it would be worth \(€500{,}000\times \$1.02=\$510{,}000\). The forward receipt remains $550,588.24 in either case, assuming the contract is performed as agreed.
Check. The forward quote is in dollars per euro, so multiplying by euros gives dollars. The hedge sells the euros the exporter will receive. The common mistake avoided is multiplying the receipt by the spot rate when the goal is to find its contracted forward value.
Hedging a Foreign-Currency Payment
A future foreign-currency payment creates the opposite transaction. The payer needs foreign currency at the due date, so it agrees to buy the required amount forward. The forward contract fixes the domestic cost of obtaining that currency. If the foreign currency later strengthens against the domestic currency, the hedge prevents the payment from becoming more expensive in domestic terms. If it weakens, the payer does not benefit from the more favorable spot rate because it is still committed to the contracted rate.
Worked Example: Fixing the Cost of a Pound Payment
A U.S. equipment importer must pay £280,000 in one year. The spot rate is $1.24 per pound. The annual effective U.S. dollar interest rate is 5%, and the annual effective pound interest rate is 3%. Determine the required forward position and the dollar cost it locks in. For comparison, calculate the cost at a future spot rate of $1.30 per pound.
Method. The importer owes pounds, so it should buy £280,000 forward and pay dollars. With dollars per pound as the quote, the forward rate is
The dollar cost fixed by the contract is
At a future spot rate of $1.30 per pound, an unhedged payment would cost \(£280{,}000\times \$1.30=\$364{,}000\). The forward hedge instead fixes the cost at $353,941.75.
Common mistake and correction. Treating the payment as a foreign-currency receipt would lead to selling pounds forward, which is the wrong contract direction: the importer needs to acquire pounds. The correct position is to buy pounds forward. The quote also matters: since it is dollars per pound, multiplying the pound payment by the forward rate produces dollars. This avoids the separate error of inverting the quote and then multiplying as though it were still dollars per pound.
Netting Cash Flows on the Same Date
When foreign-currency receipts and payments are in the same currency and fall on the same date, they can sometimes be offset before entering into a forward. This can reduce the amount that must be hedged. Netting is appropriate only if the cash flows can in fact be combined: a receipt due on one date cannot automatically offset a payment due on another date, because the forward rates and currency exposures may differ.
Worked Example: Netting a Receipt and Payment
A domestic firm will receive €420,000 and pay €135,000 on the same date one year from now. The spot rate is $1.10 per euro. The annual effective U.S. dollar interest rate is 3%, and the annual effective euro interest rate is 1%. Find the net foreign-currency exposure and the locked domestic-currency amount. Also check the result by hedging the two gross cash flows separately.
Method. Both cash flows are in euros and have the same maturity. The net exposure is a receipt of
Because the net amount is a receipt, the firm should sell €285,000 forward. The one-year forward rate is
The locked net dollar receipt is
To check by hedging gross amounts, selling €420,000 forward gives \(€420{,}000\times 1.1217821782=\$471{,}148.5148\), while buying €135,000 forward costs \(€135{,}000\times 1.1217821782=\$151{,}440.5941\). Their difference is \(\$471{,}148.5148-\$151{,}440.5941=\$319{,}707.9207\), which rounds to the same $319,707.92.
Check. The net position is a euro receipt, so it is sold forward. The gross and net calculations agree because both cash flows use the same forward rate and settlement date. The common mistake avoided is netting amounts with different currencies or different due dates as though one forward rate covered them both.
A Reliable Calculation Process
A disciplined sequence prevents most errors in currency-forward hedge questions. In particular, the quote convention determines whether to multiply or divide, while the direction of the foreign cash flow determines whether to buy or sell the foreign currency.
State explicitly which currency is domestic and which is foreign. Record whether the quote is domestic per foreign or foreign per domestic.
Write the foreign-currency amount and its due date. Decide whether it is a receipt or a payment before choosing the contract direction.
Use covered interest parity with rates and maturity that match the cash flow. If the market quote is the inverse of the domestic-per-foreign quote, invert the rate consistently.
Sell the foreign currency forward for a receipt; buy the foreign currency forward for a payment.
With a domestic-per-foreign quote, multiply the foreign amount by the forward rate. Confirm that the currency units cancel to leave domestic currency.
What the Hedge Does—and Does Not Do
A forward hedge controls the exchange rate for the contracted amount and date. It does not eliminate other risks, such as a customer failing to pay, a business needing to pay earlier than expected, or the amount of the eventual cash flow being different from the amount hedged. If the foreign-currency amount is uncertain, a forward for a fixed amount may leave the firm over-hedged or under-hedged.
A forward also removes the chance to benefit from a favorable exchange-rate movement on the hedged amount. That is not a defect in the calculation: it is the trade-off for fixing the domestic value or cost. A forward rate is determined by the spot rate and the two currencies’ interest rates under covered interest parity; it should not be interpreted as a prediction of the future spot rate.
Check Your Understanding
For each problem, assume annual effective rates, no transaction costs, and the stated forward hedge is available for the exact amount and maturity.
- A Canadian firm will receive US$80,000 in one year. The spot quote is C$1.35 per U.S. dollar; the annual effective Canadian rate is 4% and the U.S. rate is 2%. State the forward position and find the locked Canadian-dollar receipt. (Answer: Sell US$80,000 forward; C$110,117.65.)
- A U.S. company must pay CHF100,000 in one year. The spot quote is $1.10 per franc, the U.S. annual effective rate is 5%, and the Swiss annual effective rate is 3%. Find the forward rate and locked dollar cost. (Answer: Buy CHF100,000 forward; $1.121359 per franc; $112,135.92.)
- A firm will receive €500,000 and pay €150,000 on the same date in one year. The spot rate is $0.90 per euro; the annual effective U.S. rate is 10% and the euro rate is 0%. Find the net exposure and the locked dollar amount. (Answer: Net receipt of €350,000; sell it forward at $0.99 per euro for a $346,500.00 receipt.)
- A U.S. importer owes CAD200,000 in one year. The only quote supplied is C$1.36 per U.S. dollar. The U.S. annual effective rate is 4%, and the Canadian annual effective rate is 2%. Find the forward rate in the supplied quote convention and the importer’s locked U.S.-dollar cost. (Answer: Buy CAD200,000 forward; forward quote C$1.333846 per U.S. dollar; locked cost approximately US$149,942.33.)