FX exposure for importers: exposure, hedge ratio, and the price of the hedge

An importer owes money in a currency it does not earn in. The invoice is in euro, the accounts are in dollars, and between the order and the payment the exchange rate does whatever it does. That gap is the exposure, and it is a number before it is a problem: so many units of foreign currency, falling due on a date, convertible at a rate that is known today and unknown at settlement.

Three quantities price it, and none of them requires a view. The exposure is the foreign-currency amount times the rate, and it is the size of the position. The hedge ratio is the share of that position covered by a forward, and it is a policy parameter the business sets rather than a market judgement. The cost of the hedge is the difference between the forward rate and spot, annualised and set against the size of the move the business is protecting itself from. Compute those three and the decision is exposed rather than made — which is the correct division of labour. Whether to hedge is a question about the business: its margins, its pricing power, its tolerance for a bad quarter. What the hedge costs, and what it pays at every terminal rate, is arithmetic.

What follows is that arithmetic on one payable, worked to the cent: the forward derived from spot and the two interest rates, a table of outcomes across five terminal rates and three hedge ratios where the middle column is the mean of the outer two in every row, the break-even rate, the reconciliation of the hedge’s cost against the interest differential, and the five things the calculation does not contain.

What an exposure is, and what nets it out

Transaction exposure is the foreign-currency amount that will actually be exchanged. For an importer it is the payables book, currency by currency and date by date, and the first mistake in the measurement is to treat the gross payables as the exposure. Three adjustments come before the rate is applied.

Receivables in the same currency offset. A business that buys components in euro and sells finished goods in euro has a natural hedge: the euro it receives pays the euro it owes, and only the net position carries currency risk. The exposure is the net, and for many importers with any export book the net is a fraction of the gross.

The date is part of the position. A payable due in 30 days and a payable due in 180 days are different exposures: the first is nearly a settled fact and the second is a forecast of a shipment. A book of payables is a ladder of dates, and the hedge that matches the ladder costs less than the one that covers the total at one date, because the mismatch has to be rolled and the roll has its own price.

The reporting currency decides the sign. The exposure is not “euro risk” in the abstract; it is the dollar value of a euro liability. A business that reports in euro and owes in euro has no transaction exposure at all on that invoice, however inconvenient the payment is.

There is a fourth, softer adjustment that belongs in the note rather than the arithmetic. An exposure is a forecast of a payment: the goods may be late, the quantity may change, the invoice may be disputed. A hedge of a payment that does not happen is itself a position, and it has to be closed or rolled. The arithmetic below assumes the payment happens on the date stated; the note should say so.

Three numbers, in order

The procedure is a sequence, and the order matters because each number depends on the one before.

Exposure. Foreign-currency amount × spot rate, and the result is the reporting-currency amount at today’s rate — the base against which every outcome is measured.

Hedge ratio. Notional covered by the forward ÷ exposure. It runs from zero to one and it is a business decision, but it is expressed as a number, which is the point: “we hedge most of the book” is not a policy, and 0.75 is.

Cost of the hedge. The forward rate minus spot, in pips and as a percentage of spot, annualised, and expressed in reporting currency on the notional. Two things have to sit beside that figure or it will be misread: the annualised figure is the interest-rate differential between the two currencies, and the break-even terminal rate is the forward itself.

One payable, worked through

Table 1 is the full arithmetic for a single illustrative payable: one million euro due in ninety days, reported in dollars, with the two ninety-day interest rates and the spot. Every figure in the table is computed from the four inputs beside it, and the construction is designed so that a reader with a calculator can reproduce it in one pass.

Table 1. The exposure and hedge arithmetic for an illustrative payable. Day count actual/360, simple interest in both legs. Source: constructed for this piece; illustrative, not a market quotation.

The forward is not a number from a screen; it is the no-arbitrage implication of the two interest rates and the spot. Borrow dollars for ninety days at 4.30, convert at spot, lend euro at 2.10, and at maturity the euro proceeds are known and the dollar repayment is known; the rate at which those two amounts exchange is 1.0909363, and any other rate leaves an arbitrage. That is why the forward premium of 0.547 per cent, annualised to 2.19, sits within one basis point of the 2.20 per cent interest differential: they are the same number seen from two sides. The one basis point is the difference between annualising a 90-day rate by multiplying by four and the exact compounding of the two legs, and it is a rounding artefact rather than a market feature.

The exposure at spot is $1,085,000 and the hedged cost is $1,090,936.33, so the hedge adds $5,936.33 to the invoice — 0.547 per cent of the position, and $0.0059363 for every euro of exposure. That is the price of certainty, and the next table is what it buys.

The outcomes, and the check that they add up

Table 2 sets five terminal rates against three hedge ratios on the same million-euro payable. Each cell is the total dollar cost of the invoice: the uncovered part converted at the terminal rate, plus the covered part converted at the forward. The forward column is constant because the forward is a contract; the unhedged column moves one for one with the rate.

Table 2. The dollar cost of the illustrative €1,000,000 payable at five terminal spot rates and three hedge ratios. The covered portion is bought forward at 1.0909363; the uncovered portion settles at the terminal spot. Source: computed from Table 1.

Two properties of the table are worth checking, because they are what make it arithmetic rather than a scenario exercise.

The middle column is the mean of the outer two in every row. At 1.0400 the half-hedged cost is $1,065,468.17, which is the average of $1,040,000.00 and $1,090,936.33; at 1.1300 it is $1,110,468.17, the average of $1,130,000.00 and $1,090,936.33. That is not a coincidence and it is the definition of a hedge ratio applied to a linear instrument: half the position is fixed, half floats, and the cost is a weighted average. A table in which the middle row is not the average of the outer two has a hedge ratio in the label that is not in the computation — a very common defect, usually a notional that was set on the gross exposure rather than the net.

All three columns meet at the forward. At 1.0909363 the hedged and unhedged costs are identical, because the forward is the terminal rate at which the hedge has cost nothing and saved nothing. Above that rate the hedge is cheaper than the market; below it, the unhedged position is cheaper. This is the break-even, and it is exactly the forward rate — no more, no less. A hedge with a break-even that is not the forward contains a fee, a spread or a mismatched date, and the difference is the price of those.

The whole table also scales one for one with the move. A 1 per cent move in the rate is $10,850 on the exposure — 1,085,000 × 0.01 — and the range in the table, from 1.0400 to 1.1300, is 900 pips of a $1,085,000 position: $90,000 between the best and worst unhedged outcomes, against a hedge cost of $5,936.33. Set the two numbers beside each other and the arithmetic says something modest: the hedge costs 0.55 per cent of the exposure, which is the price of a 0.55 per cent move — $5,936 on either side of the break-even rate. Whether that is cheap is a question about the margin the business earns, and it is answered somewhere other than in the rate.

The hedge ratio is a number, and it can be quoted

The third table makes the ratio quotable, which is worth doing because most hedging conversations fail on the word “some”. Table 3 runs the same payable at five ratios.

Table 3. The notional, the fixed leg and the cost of the hedge at five hedge ratios on the illustrative €1,000,000 payable. The cost is the forward minus spot, applied to the notional, and the fixed leg is the notional multiplied by the unrounded forward of 1.0909363. Source: computed from Table 1.

The columns are linear in the ratio and the costs are proportional: each 25 per cent of cover costs $1,484.08 and fixes a quarter of the position. There is no discontinuity, no threshold and no cheaper point — which is the arithmetic answer to a question usually settled by intuition. What the ratio should be is a question the business answers: a distributor with a 4 per cent gross margin has less room for a 0.55 per cent swing on the cost of goods than an importer with 30, and the same payable at the same rate implies different ratios for the two. The arithmetic prices each rung of the ladder; choosing one is a commercial decision, and this note does not make it.

What the cost of the hedge really is

The most useful thing a table like Table 1 does is dismantle the word “cost”. The 0.547 per cent is not a fee paid to anyone. It is the interest differential, and it is visible from the other side of the transaction.

An importer that buys euro forward for dollars is, in economic substance, borrowing dollars for ninety days and lending euro for ninety days. The forward rate is the rate at which that pair of loans is fair, and the premium is the difference between the two interest rates. A business that instead bought the euro today would pay spot, hold the euro, and earn 2.10 per cent on it for the quarter while forgoing 4.30 per cent on the dollars — a net cost of 2.20 per cent annualised, which is the same 0.547 per cent over the quarter. The hedge does not create that cost; it fixes it. The alternative has the same cost and an unknown return, because the alternative is a position in the currency.

Two consequences follow, and both are arithmetic. A forward quoted at worse than parity is a different product: if a bank quotes 1.0925 against a parity forward of 1.0909363, the extra 0.0016 — $1,600 on a million euro — is the bank’s spread and is not in the interest differential. And the cost of the hedge is not comparable across horizons: 0.547 per cent for ninety days is 2.19 per cent a year, while the same rate differential applied to a 30-day payable is 0.18 per cent for the month and still 2.19 per cent a year. Comparing a monthly hedge cost with an annual one, or with a margin, is the second most common error after quoting a ratio without a notional.

What the arithmetic leaves out

Five things, and the note should name them because each one can be larger than the number the table produces.

The credit line. A forward is a bank commitment, not a purchase. It consumes a line, may require a margin or a CSA, and its availability depends on the counterparty relationship rather than on the exposure. A hedge that cannot be executed for credit reasons is not a hedge, and the arithmetic says nothing about whether the line exists.

The counterparty spread. The table uses a parity forward. A bank’s quote includes a bid-offer, and on an exotic or a thin date the spread can equal a substantial share of the premium — 0.0016 in the example above is 27 per cent of the 0.005936 total premium.

The timing mismatch. The payment date is an assumption. A shipment delayed by three weeks leaves a forward that matures before the cash does, and rolling it is a second transaction at a second price. On a book of payables the roll costs are frequently larger than the premium, and they never appear in a single-invoice calculation.

The basis, where the pair is a cross. A business that pays in a currency with no liquid forward market hedges through dollars, in two legs, and the second leg carries its own spread and its own correlation. The arithmetic assumed a liquid pair with a quoted forward; where there is none, the forward has to be constructed and the construction is a model.

The exposure behind the exposure. The hedge fixes the dollar cost of the euro invoice. It does not fix the euro invoice: if the supplier reprices, or the quantity changes, or the goods are rejected, the hedge covers a payment that is no longer the right size. That is not a flaw in the arithmetic; it is the boundary of what a currency hedge is for, and the commonest way a well-hedged book still loses money is a commercial change the hedge did not anticipate.

One further limitation is worth stating plainly, because it is the one the table cannot address at all. A hedge ratio is a choice under uncertainty, and the table prices the choice rather than evaluating it. At 1.0400 the unhedged importer is $50,936.33 better off than the hedged one; at 1.1300 it is $39,063.67 worse off. Neither column is a forecast and neither is a recommendation. The importer who hedges 100 per cent has bought certainty at 0.547 per cent; the one who hedges nothing has taken the position that the rate will not move against them by more than that. Both are defensible, both are decisions, and the arithmetic’s job is to make sure the person making one knows what it costs.

What the calculation costs

Three engine calls: fx for the move against a prior spot and the annualised carry from the rate differential, rates_math for the forward and the day-count factors, and validate to cross-check the spot against a second observation within 0.1 per cent — a rate that is stale by an hour at a fixing is a different exposure. At $0.006125 on Base that is $0.018375.

Two drafting calls at DeepSeek’s measured $0.00700 is $0.01400, so one exposure review is $0.032375. Ten a month, on a book of significant invoices, is 30 engine calls ($0.183750) and 20 model calls ($0.14000): $0.323750, or $0.032375 a review. At the long-prompt rate of $0.00955 the model line rises to $0.19100 and the month to $0.374750, 16 per cent more; on Qwen at a flat $0.00875 the model line is $0.17500 and the month $0.358750. The 0.50 USDC opening balance is 71 calls at $0.00700, which is fifteen reviews at these counts. The document parts that render the schedule carry no published per-call price and sit outside every total.

A decision rule

The purpose of the arithmetic is to leave the business with three numbers per currency and per date, and one schedule that holds them together.

Publish the exposure as a number, netted and dated. Currency, amount, due date, reporting currency, and the rate used. Gross payables are not the exposure, and an exposure without a date cannot be hedged without a mismatch.

Publish the hedge ratio as a number, with its notional. The ratio is the policy and the notional is the instruction. A ratio without a notional is a sentiment; a notional without a ratio cannot be checked against the book.

Publish the cost in three forms. Pips against spot, per cent of exposure, and annualised — because the first is what the dealer quotes, the second is what the margin absorbs, and the third is what the board compares with the interest differential it is really paying. Add the break-even rate, which is the forward, and the reader can see at a glance where the hedge stops paying for itself.

Publish what the number excludes. The credit line, the spread, the roll risk and the commercial assumptions behind the payment date. A hedge schedule that reports 0.547 per cent and does not say that a bank’s quote may carry a spread worth a quarter of it is understating the cost, and a cost estimate that is understated is the one that gets approved.

The decision that follows is not whether to hedge — that is a commercial judgement about margins and tolerance, and this note does not make it. The decision is what to put in front of the person who does: an exposure, a ratio, a cost and a break-even, computed from four inputs, adding up in every row, with the excluded items named. That is a smaller deliverable than a view on the currency, and it is the one an importer can actually use.

Method note

The payable, the spot, the two ninety-day rates, the terminal rates in Table 2 and the hedge ratios in Table 3 are constructed for this piece and labelled illustrative; they are not a market quotation and should not be used as one. The forward is computed as spot × (1 + r USD × 90/360) ÷ (1 + r EUR × 90/360) = 1.0850 × 1.010750 ÷ 1.005250 = 1.0909363, with simple interest on an actual/360 basis. Every cell of Table 2 is 1,000,000 × ((1 − h) × terminal spot + h × 1.0909363) with h the hedge ratio, and the arithmetic has been checked for the linearity property stated in the text: the 50 per cent column is the mean of the 0 and 100 per cent columns in all six rows, and all three columns meet at 1.0909363. The hedge cost of $5,936.33 is 1,000,000 × (1.0909363 − 1.0850); the $50,936.33 and $39,063.67 comparisons are the same difference measured against the 1.0400 and 1.1300 terminal rates; the 1 per cent sensitivity is 1,085,000 × 0.01 = $10,850. Engine prices are the published $0.006125 per basic operation on Base, from catalog.json, read 31 October 2026; the analyst services are pending review and return no 402 quote, so that price is published rather than measured. Model prices are measured from the live 402 handshake on 31 October 2026: $0.00700 for deepseek-v4-flash on Base at a short prompt and max_tokens: 1000, $0.00955 at about 3,000 tokens, and $0.00875 for qwen3.8-flash at both lengths. Monthly counts are planning assumptions. Nothing here is a forecast of any exchange rate, a recommendation to hedge or not to hedge, or investment, legal or tax advice.

The pillar is Finance and markets on x402 — three engines, four jobs, one price. The role that produces this schedule is trade_analyst, which measures a series into indicators and a signal and states the level at which a view fails — the same discipline as naming a break-even rate, applied to a different instrument — and which will not produce a forward-looking return. The compute is bought at x402.press/services/deepseek/ with a second model at x402.press/services/qwen/; the measured handshake is reviewed at DeepSeek: per-call chat completions over x402, and the two endpoints against each other at Inference endpoints compared. An exposure schedule is read beside the accounts it will land in, where Financial statement red flags tests the working-capital and currency lines, and beside the entity it belongs to, where How to value a private company has to absorb the same currency into its cash-flow forecast.

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