Exchange rates and monetary constraints

Convert a payment without confusing the two currencies

Keep the unit beside every amount before multiplying. Consider an additional paper example in which a domestic importer must pay a foreign supplier 80 foreign units next month. At a quote of 4 domestic units per foreign unit, the importer needs 320 domestic units. Multiplying 80 by 4 cancels the foreign unit in the conversion and leaves domestic units. If the quote becomes 5 before payment, the requirement becomes 400 domestic units. The supplier still receives 80 foreign units. The extra 80 domestic units reflect a changed conversion price, not another delivery or an increase in the foreign invoice.

Suppose the importer has a domestic deposit of 350 and no other liquid assets. At the first quote it could exchange 320 and retain 30. At the second quote it is short of 50 because 400 exceeds 350 by 50. Its domestic bank balance did not shrink when the exchange rate moved. Its ability to meet this particular foreign obligation did shrink. This is a payment shortage caused by currency mismatch. Whether the firm is insolvent requires valuing its other assets and obligations too. One unpaid invoice does not supply a complete balance sheet.

To continue this payment sequence, assume the importer obtains a separate domestic bank loan of 50. Its domestic deposit rises from 350 to 400, and it takes on a loan liability of 50. The bank adds a loan asset and a deposit liability of 50. Approval is an assumption, not a consequence of the currency shortage. This funding transaction supplies the missing domestic balance before the exchange; finding a currency dealer alone would not do so.

To trace the exchange itself, assume one dealer holds deposits in both currencies at the same banks as the importer. Ignore fees. The importer gives up a domestic deposit of 400 and receives a foreign deposit of 80. The dealer receives the domestic deposit of 400 and gives up its foreign deposit of 80. Each bank transfers a liability between its customers. Neither bank needs to erase 400 domestic units and manufacture 80 foreign units. These are exchanges of existing claims. If the customers use different banks, the banks must also settle the relevant obligations in each currency through the appropriate payment arrangements.

The importer then pays the supplier from its foreign deposit. Its foreign deposit falls by 80, and the supplier's rises by 80. Payment extinguishes the importer's invoice liability and the supplier's receivable, meaning the supplier's claim for payment. The supplier already recorded the sale separately from collecting the money. This distinction prevents counting a sale twice as income. The dealer's exchange and the supplier's receipt are separate transactions with separate counterparties. Commercial banks may use correspondent banks, which hold accounts and make payments for other banks, rather than holding direct central-bank accounts in every currency. After conversion and payment, the importer has no deposits left in this example. Its invoice is settled, but the new domestic loan of 50 remains due.

The inverse quotation describes the same exchange with a different unit. At 4 domestic units per foreign unit, one domestic unit buys 0.25 foreign units. At 5, it buys 0.20. The first quote rises by 1 divided by 4, or 25%. The inverse falls by 0.05 divided by 0.25, or 20%. There is no disagreement between the two calculations. Each percentage uses its own starting denominator. Whenever someone says the currency moved by a percentage, ask which currency is in the numerator and what dates the comparison uses. Otherwise the sign and size can both mislead.

What defending a fixed rate requires

A peg is an institutional commitment to a conversion price, not an arithmetic consequence of choosing a unit of account. Take another paper example with a parity of 4 domestic units per foreign unit. Assume the central bank sells foreign deposits directly to an eligible domestic bank at that parity. The bank requests 10 foreign units and pays 40 domestic reserve units. The central bank's foreign assets fall by 10 foreign units, valued at 40 domestic units at the peg. Its domestic reserve liabilities fall by 40. Both sides of its balance sheet decline by the same domestic value.

On the commercial bank's books, domestic reserves fall by 40 and foreign deposit assets rise by 10 foreign units. Its customers' deposits need not change at this stage because the bank bought foreign currency for itself. A later customer purchase requires another entry. If the central bank began with usable foreign assets of 30 foreign units, this sale leaves 20. At unchanged transaction sizes it could make two more such sales before exhausting that specified stock. This calculation assumes those assets can actually be sold or transferred immediately. It does not count inaccessible, pledged, or otherwise unusable claims as ready payment funds.

Creating additional domestic reserves cannot directly restore those foreign assets. A foreign lender might provide 15 foreign units, but the central bank then gains a foreign asset and a foreign borrowing obligation together. It must inspect maturity, interest, and repayment terms rather than call the loan free reserve replenishment. Agreements with other central banks can also provide access under particular terms. None follows automatically from the balance-sheet identity. Our paper case therefore establishes a finite intervention capacity under its assumptions, not the date on which a real peg must fail or the measures authorities should choose.

Interest-rate comparisons explain one source of pressure without predicting an exchange rate. Suppose a saver can invest 400 domestic units for a year at 2%, receiving 408. Alternatively, at a credible unchanged parity, 400 converts to 100 foreign units. A 5% foreign return produces 105 foreign units, convertible back into 420 domestic units. Under equal risk, no fees, and unrestricted conversion, the second option pays 12 more domestic units. Those conditions explain why a persistent rate difference can encourage transactions that put pressure on the peg. They do not establish that every saver can or will make this trade.

Now remove the assumption of a known future conversion price. If the end-year quote is 3.8 domestic units per foreign unit, the 105 foreign units convert into only 399 domestic units. Domestic appreciation has reversed the comparison. Taxes, credit risk, and restrictions can also change it. The impossible trinity concerns the constraints created by maintaining a fixed rate alongside capital mobility and independent monetary policy. It does not say every temporary interest-rate gap is impossible. A currency union removes national exchange rates within the union, but also removes each national government's ability to set its own common-currency reserve supply and policy rate.

Read the conversion table as a balance-sheet change

The formula and table above hold the foreign principal at 100. There is no exchange-rate slider or payment simulation here. Compare the two rows as alternative valuations of the same obligation, not as two debts added together. Before depreciation, multiply 100 foreign units by 4 to obtain a domestic equivalent of 400. After depreciation, multiply 100 by 5 to obtain 500. The difference is 100 domestic units. This is a valuation change before any repayment. It becomes a larger domestic cash requirement if the debtor must buy foreign currency at the new quote when payment falls due.

Extend that table on paper with a firm holding domestic assets worth 700 and owing only this foreign principal. At the first quote its domestic-valued equity is 300 because 700 less 400 is 300. At the second quote its equity is 200 because 700 less 500 is 200. The asset total has not changed, and the foreign lender has not increased the principal. Revaluing the foreign liability raises its domestic equivalent by 100 and reduces the firm's residual net worth by 100. These entries use one consistent domestic valuation basis and assume no other price changes or accrued interest.

Contrast a second firm with domestic assets of 300 plus a foreign deposit of 100 foreign units, and the same foreign debt. Initially the foreign asset and debt each translate into 400, leaving equity of 300. After depreciation they each translate into 500. Total assets become 800 and liabilities 500, so equity remains 300. The foreign asset gain offsets the liability increase. Matching currency alone is not a complete liquidity plan, however. A deposit available today differs from an uncertain foreign sale expected next year. Payment dates and the ability to use the asset when needed still matter.

A hedge is a contract intended to offset a specified exposure. In an additional paper case, a firm arranges today to buy 100 foreign units next month for 410 domestic units. This forward contract fixes its conversion payment for that transaction if both parties perform. If the market quote next month is 5, an otherwise identical spot purchase costs 500. The contracted purchase therefore costs 90 less than that spot alternative. If the quote instead becomes 3.8, spot would cost 380, and the contracted purchase costs 30 more. The hedge removes this specified price uncertainty rather than guaranteeing the cheapest eventual purchase.

The forward seller must deliver the foreign units and may itself hedge with another party or hold matching assets. The firm's reduced exposure has a contractual counterparty, not a disappearance of currency risk throughout the world. Fees, collateral demands, and failure to perform can introduce other risks. A contract covering 100 foreign units also leaves an extra invoice of 20 uncovered. To explore the table, write asset, debt, and payment-date columns before changing the quote. Recalculate both foreign assets and foreign liabilities. This reveals whether the example concerns a net currency exposure, a gross funding requirement, or both.

Separate competitiveness, inflation, and debt service

A change in the exchange rate reaches different contracts differently. Consider a paper exporter selling one machine for a fixed 100 foreign units. Its domestic revenue rises from 400 to 500 when the quote rises from 4 to 5. Suppose making that machine requires imported components costing 60 foreign units plus domestic labor costing 120 domestic units. The components rise from 240 to 300 domestic units. Before depreciation, revenue less these costs is 40. Afterward it is 80. The revenue gain is 100, but the cost gain is 60. Ignoring the imported inputs would exaggerate the improvement in this simplified margin.

If the export price instead stays fixed at 400 domestic units, the foreign buyer's cost falls from 100 foreign units to 80. The exporter's domestic revenue does not rise just because the currency weakened. Whether buyers order more depends on their preferences, competing products, capacity, and delivery terms. Meanwhile, the same imported components still become costlier in domestic money. Thus an exchange-rate movement alone does not determine either the exporter's profit or the country's export volume. The currency in which the invoice is fixed must appear in the explanation before any claim about competitiveness.

For a consumer-price illustration, assume a fixed basket initially costs 200 domestic units. Imported goods account for 50 and domestically supplied items for 150. If depreciation raises the imported component by 20% and the domestic component stays unchanged, imports cost 60 and the basket costs 210. The basket increase is 10 divided by 200, or 5%. This result assumes complete pass-through to that imported component. If sellers absorb half the conversion increase in margins, the component rises by only 10%, to 55, and the basket rises by 2.5%. Neither assumption is an estimated response for an actual economy.

A higher basket level and a continuing inflation rate are different outcomes. If the basket rises to 210 and remains there next year, inflation over that next year is zero, not another 5%. Continued depreciation, changing margins, or wage and price adjustments would require additional assumptions. Domestic debt service also differs from purchasing power. A fixed domestic principal of 400 remains 400 after depreciation. Its holder may buy fewer imports with the payment, but the debtor does not automatically owe 500. A foreign principal creates the conversion exposure illustrated above. Indexation clauses can alter either example and must be read separately.

Compare governments by listing obligations and institutions rather than assigning safety from one ratio. An own-currency treasury with a floating exchange rate does not need foreign units to discharge an ordinary domestic-currency bond, but it still faces legal payment procedures and real-resource constraints. A foreign-currency borrower must obtain the promised foreign payment asset. A currency-union member cannot individually create the shared settlement asset merely by authorizing a budget. For each, record maturities and revenues as well as currency denomination. The resulting comparison identifies which constraint is relevant without pretending that accounting supplies a default forecast or a policy recommendation.