Illustrate transaction, translation and economic risks with examples and explain how to hedge each one.
The idea
Each currency risk has its own hedge. A foreign-currency receivable is a long position, so the transaction hedge is to sell the currency forward. A money market hedge does the same job. The firm borrows the present value of the receivable in the foreign currency, converts it at spot and invests the proceeds at home. For a payable the steps are reversed. If the exposure is contingent, as when a bid may be lost, a put or call option is better than a forward, which would leave a naked position if the contract does not materialise. Translation exposure is reduced with a balance sheet hedge, which finances foreign assets with local-currency liabilities, or by hedging the net investment with forwards. Economic risk is long-term, so the answer is operational. Match the currency of costs and revenues, diversify markets and suppliers, or finance in the foreign currency. Short-dated forwards only postpone economic risk.
Formulas
Money market hedge of a foreign-currency payable: home currency paid today
cost today = payable ÷ (1 + iF × t) × S0
- payable
- the foreign-currency amount due
- iF
- the foreign deposit rate, per year, simple interest
- t
- the fraction of a year until payment
- S0
- the spot rate, home currency per unit of foreign currency
Deposit just enough foreign currency now to grow into the payable. For a receivable reverse it: borrow the present value in the foreign currency, convert at spot and invest at home. Use the period fraction, not the annual rate.
A practice question
A US exporter will receive EUR 2 million in three months. Which forward position hedges the transaction exposure?
- Sell EUR 2 million forward for delivery in three months - correct
- Buy EUR 2 million forward for delivery in three monthsWhy not: Adds to the long EUR exposure instead of offsetting it.
- Take no action, since gains and losses on foreign receivables average out over timeWhy not: Averaging out is not guaranteed for a single known receivable; the exposure is real and can be hedged.
- Buy EUR 2 million spot now and hold the cash until the receivable is paidWhy not: Increases the net long EUR position and ties up funds; it does not offset the receivable.
A foreign-currency receivable is a long exposure to the currency, so the hedge is a short position: sell the currency forward and lock in the USD proceeds.
A harder one
A US company owes EUR 5 million in six months. Spot EUR/USD is 1.0850 and the six-month EUR deposit rate is 2.0% per year (simple interest). It uses a money market hedge: buy EUR now and deposit them. How much USD must it pay today, closest to?
- USD 5,425,000Why not: Converts the full EUR 5 million at spot without discounting for the interest the deposit will earn.
- USD 5,318,627Why not: Discounts at the annual 2% rather than the six-month 1%; the deposit only earns half a year of interest.
- USD 5,371,287 - correct
- USD 5,479,250Why not: Compounds instead of discounting, buying too many euros.
The deposit must grow to EUR 5 million: PV = 5,000,000 / (1 + 0.02 x 0.5) = EUR 4,950,495. Buying that at spot costs 4,950,495 x 1.0850 = USD 5,371,287 today.
The hardest tier
A US firm will receive GBP 8 million in 90 days. Spot GBP/USD is 1.2650 and the 90-day forward is 1.2590. The 90-day rates are 4.0% per year in GBP and 5.0% per year in USD (simple interest, quarter-year period). Which hedge gives more USD at day 90, and by how much?
- The money market hedge, by about USD 73,000 - correct
- The forward hedge, by about USD 73,000Why not: Reverses the comparison; the money market hedge proceeds are USD 10.145 million against USD 10.072 million from the forward.
- The forward hedge, by about USD 52,000Why not: Omits the interest earned on the USD proceeds in the money market hedge, which makes it look worse than the forward.
- The money market hedge, by about USD 145,000Why not: Uses annual instead of quarterly rates, over-discounting the GBP and over-compounding the USD.
Money market hedge: borrow 8,000,000/1.01 = GBP 7,920,792, convert at 1.2650 = USD 10,019,802, invest at 1.25% to get USD 10,145,050. Forward: 8,000,000 x 1.2590 = USD 10,072,000. Difference = USD 73,050 in favour of the money market hedge.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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