Exchange-Rate Determination and Financial Risk Management

Introduction

International firms exchange currencies to buy inventory, sell products, borrow, invest and consolidate foreign subsidiaries. Exchange-rate movements can therefore change contractual cash flows, reported earnings, asset values, competitive position and firm value. International financial management is concerned not with predicting every currency movement, but with identifying exposures, measuring their sensitivity and selecting economically justified controls.

This chapter develops purchasing power parity (PPP), interest rate parity (IRP), forward-rate relationships and the management of transaction, translation and economic exposure. It also evaluates forwards, futures, options, swaps, money-market hedges, natural hedges and hedge accounting.

Learning objectives

By the end of this chapter, students should be able to:

1. Explain and apply absolute and relative PPP.
2. Use covered and uncovered IRP and distinguish spot, forward and expected future rates.
3. Measure transaction, translation and economic exposure quantitatively.
4. Compare forwards, futures, options, swaps and money-market hedges.
5. Construct natural hedges and evaluate their limitations.
6. Explain the principal accounting and governance issues in hedging.

1. Exchange-rate determination

Let S be quoted as units of home currency per unit of foreign currency. Thus, an increase in S means that the foreign currency appreciates against the home currency. Let P_H and P_F denote comparable price levels in the home and foreign countries.

Purchasing power parity

Absolute PPP states that an identical basket should cost the same after currency conversion:

This is a long-run relationship based on the law of one price. It assumes comparable goods, no transport costs, no tariffs, no taxes, competitive markets and no non-traded goods. These assumptions rarely hold exactly, so absolute PPP is mainly a benchmark.

Relative PPP focuses on rates of change. If π_H and π_F are home and foreign inflation rates, respectively, the exact predicted exchange-rate change is:

For low inflation rates, the approximation is π_H − π_F. If home inflation exceeds foreign inflation, the home currency is expected to depreciate, so S is expected to rise.

Example. Suppose S_0 = 1.20 home currency units per euro, home inflation is 6% and euro-area inflation is 2%. Relative PPP predicts:

S₁ = 1.20 × (1.06 ÷ 1.02) = 1.2471

The predicted depreciation is approximately 3.92%, not 4% exactly. PPP is more reliable over long horizons than over short horizons because capital flows, interest rates, risk premia and market expectations dominate short-run movements.

Interest-rate parity

Covered interest parity (CIP) links the spot rate, forward rate and interest rates when investors can eliminate currency risk with a forward contract. With annual rates and the quotation S as home currency per foreign currency:

where F_0 is the forward rate, i_H is the home interest rate and i_F is the foreign interest rate. For periods other than one year, replace rates by appropriate compounding factors, such as (1 + i_H)^T.

Example. If S_0 = 1.10, i_H = 5%, and i_F = 3%, then:

F₀ = 1.10 × 1.05 ÷ 1.03 = 1.1214

The forward premium on the foreign currency is approximately 1.95%: (1.1214 ÷ 1.10) − 1.

CIP is an arbitrage relationship and generally holds closely in liquid markets, although transaction costs, credit risk, capital controls and funding-market segmentation can create deviations. The forward rate is not necessarily an unbiased forecast of the future spot rate.

Uncovered interest parity (UIP) relates expected future spot rates to interest differentials:

UIP requires investors to remain unhedged and assumes no risk premium. It is an expectation-based proposition and is less consistently supported by evidence than CIP. A forward contract locks in F_0; it does not guarantee that F_0 equals the later spot rate.

Forward quotations and basis

A forward premium or discount can be measured as:

where n is the number of days to maturity. The 360 convention is common in money markets, but the contract convention must be used in practice. A forward quote is a price for future delivery, whereas a forecast is an estimate of a future market price.

2. Foreign-exchange exposure

Exposure is the sensitivity of a home-currency value to exchange-rate changes. It should be distinguished from risk: exposure is the underlying sensitivity, while risk includes uncertainty about the exchange rate and the consequences of that uncertainty.

Transaction exposure

Transaction exposure arises from contracted foreign-currency cash flows, such as receivables, payables, loans and firm commitments. For a foreign-currency receivable R, valued at S home currency units per foreign unit:

and the change caused by a rate movement is:

For a payable P, the home-currency cost is P × S; an increase in S creates a loss.

Example. A Canadian importer must pay €500,000 in 90 days. If the spot rate rises from C$1.45/€ to C$1.52/€, the unhedged cost rises from C$725,000 to C$760,000, a C$35,000 loss relative to the original rate.

Translation exposure

Translation exposure results when a foreign subsidiary’s financial statements are converted into the parent’s presentation currency. It is an accounting measurement exposure, not necessarily a cash-flow exposure.

Assume a subsidiary has foreign-currency assets of €10 million and liabilities of €6 million. Its net assets are €4 million. If the closing rate changes from C$1.40/€ to C$1.50/€, the translated net assets increase from C$5.6 million to C$6.0 million. The translation adjustment is therefore C$400,000, subject to the applicable accounting standard and translation method.

A simplified sensitivity measure is:

If net foreign assets are positive, foreign-currency appreciation increases the translated net-asset amount; if net foreign liabilities are positive, it decreases it. The exact financial-statement treatment depends on the functional currency, presentation currency and applicable standard, such as IAS 21 or the relevant national GAAP. Translation adjustments commonly enter other comprehensive income rather than current profit, but exceptions and recycling rules must be assessed carefully.

Economic exposure

Economic exposure is the effect of exchange-rate changes on the present value of future operating cash flows. It includes both recognized and unrecognized transactions and affects revenues, costs, prices, demand and competition.

A simple one-period operating model is:

where Q is quantity sold, P_H is the home-currency selling price, C_H is home-currency cost and C_F is foreign-currency cost. The economic exposure over a small exchange-rate change is approximately:

If cash flows occur in several periods:

where k is the appropriate discount rate. The derivative dPV/dS captures the combined effect on foreign revenues, foreign costs, volumes and prices.

Worked calculation. A manufacturer expects annual sales of 100,000 units to foreign customers. The foreign-currency price is €50, foreign variable cost is €30 per unit, and home-currency variable cost is $12 per unit. At S = $1.10/€, operating cash flow before fixed costs is:

100,000 × (50 − 30) × 1.10 − 100,000 × 12 = $1,000,000.

If the euro falls to $1.00 and volume and prices remain unchanged, cash flow becomes $800,000. The estimated exposure for this movement is a $200,000 decline. In reality, demand, prices, sourcing and competitors may respond, so economic exposure cannot be measured from accounting balances alone. Scenario analysis, sensitivity analysis and cash-flow-at-risk models are useful supplements.

3. Hedging instruments and methods

Forward contracts

A forward is an over-the-counter agreement to exchange a specified currency amount at a specified rate on a specified date. A receivable is hedged by selling the foreign currency forward; a payable is hedged by buying it forward.

For the importer owing €500,000, a 90-day forward rate of $1.48/€ fixes the dollar payment at $740,000, eliminating uncertainty but also eliminating gains if the euro weakens. Credit exposure to the dealer, customization and possible early termination are important considerations.

Futures contracts

Currency futures are standardized, exchange-traded contracts. They require initial margin and daily marking to market. A payable is generally hedged by taking a long futures position in the foreign currency; a receivable is generally hedged by taking a short position.

The effective locked rate is affected by the futures price change and the basis. Define basis as:

A hedge is imperfect when the exposure date, currency, amount or contract maturity does not match the futures contract.

Worked comparison. A firm needs €1,000,000 in three months. It buys futures at $1.095/€ and deposits margin. At maturity, the spot rate is $1.12 and the futures price is $1.118. The currency purchase costs $1,120,000. The long futures gain is:

(1.118 − 1.095) × 1,000,000 = $23,000.

Ignoring margin interest and fees, the effective cost is $1,097,000, or $1.097/€. It is not exactly the initial futures price because basis and daily settlement matter.

Currency options

A currency option gives its holder the right, but not the obligation, to trade currency at the strike price K. A call on foreign currency protects a payable; a put on foreign currency protects a receivable. Let S_T be the spot rate at maturity and q the foreign-currency amount.

For a call on foreign currency, the payoff to the holder is:

For a put on foreign currency:

If the premium is p home-currency units per foreign unit, the net cost of a call hedge for a payable, ignoring financing, is:

This formula assumes the firm buys the currency in the market when S_T ≤ K and exercises when S_T > K. The option provides protection while retaining favorable movements, but the premium must be paid.

Worked option comparison. A firm must buy €1,000,000. It buys a call with K = $1.10/€ and premium p = $0.025/€. If S_T = $1.18, the option is exercised. Net cost is:

1,000,000 × (1.10 + 0.025) = $1,125,000.

If S_T = $1.04, it is not exercised and net cost is 1,000,000 × (1.04 + 0.025) = $1,065,000. An unhedged purchase would cost $1,180,000 in the first case and $1,040,000 in the second. The option costs $25,000 but preserves the benefit of a weaker euro.

A collar combines a purchased option with a sold option, reducing premium but limiting favorable outcomes. The sold option creates an obligation and must be understood under stress scenarios.

Money-market hedges

A money-market hedge uses borrowing and lending to create a synthetic forward. The direction is crucial.

Foreign-currency payable. To hedge a payable of P foreign units due in T years:

1. Borrow the present value of the required home-currency amount.
2. Convert the borrowed home currency into foreign currency at the spot rate.
3. Invest the foreign currency until maturity.
4. Use the foreign investment to settle the payable.
5. Repay the home-currency borrowing.

If i_F and i_H are annual effective rates, the foreign amount to invest today is P ÷ (1 + i_F)^T. Its home-currency cost today is S_0P ÷ (1 + i_F)^T. The home repayment is:

The borrowing is in home currency, not foreign currency. This is the correct sequence for a foreign-currency payable.

Example. A firm owes €500,000 in one year. S_0 = $1.10/€, i_H = 6%, and i_F = 3%. It invests €500,000 ÷ 1.03 = €485,436.89, requiring $533,980.58 today. It borrows that dollar amount and repays:

$533,980.58 × 1.06 = $566,019.42.

The synthetic locked cost is $566,019.42, or $1.1320/€. This equals the covered-parity forward calculation: 1.10 × 1.06 ÷ 1.03 = 1.1320.

For a foreign-currency receivable, the sequence is reversed in economic direction: borrow the present value of the foreign receivable, convert it to home currency and invest the home proceeds; use the foreign-currency receipt at maturity to repay the foreign borrowing.

Currency swaps

A currency swap exchanges principal and interest cash flows in different currencies. It is useful for longer-term funding, especially when counterparties have comparative borrowing advantages or need to transform existing debt exposure.

Suppose a firm borrows €10 million at 4% and swaps the obligation into dollars at an agreed notional exchange rate of $1.10/€. The dollar notional is $11 million. Annual euro interest of €400,000 is exchanged for dollar interest at 5%, or $550,000. At maturity, principal exchanges are reversed according to the contract. The economic benefit depends on comparative funding costs, fees, credit valuation adjustments and the exchange-rate basis. A swap is not automatically cheaper than direct borrowing.

4. Natural hedges and hedge design

A natural hedge offsets currency inflows and outflows without a derivative. Examples include sourcing components in the same currency as sales, borrowing in the currency of foreign assets, matching receivable and payable maturities, and locating production near customers.

Natural hedges can reduce transaction exposure and economic exposure, but they may increase operating complexity, reduce supplier choice or create concentration risk. A good hedge policy identifies the exposure, currency, amount, timing, confidence level and acceptable residual risk before selecting an instrument.

A practical decision framework is:

5. Hedge accounting, governance and technology

Hedge accounting seeks to represent economically related hedging instruments and exposures in the same reporting periods. Under IFRS 9 and comparable frameworks, formal designation, documentation, an eligible hedging relationship, an identified risk and continuing effectiveness assessment are normally required. Cash-flow hedge accounting may defer the effective portion of a derivative gain or loss in other comprehensive income until the hedged cash flow affects profit or loss. Rules differ by jurisdiction and instrument, so professional advice and current standards are essential.

Governance controls should include approved counterparties, authority limits, segregation of dealing and confirmation, independent valuation, collateral monitoring, documentation of forecasts and regular stress testing. A hedge should not be judged only by whether it makes a profit: a derivative loss may accompany a larger gain on the underlying exposure.

Treasury-management systems can aggregate exposures, automate confirmations, calculate value-at-risk and monitor hedge ratios. Machine-learning forecasts may support scenario generation, but they do not remove model risk, structural breaks or management responsibility. Explainability, data quality, cybersecurity and human approval remain essential.

Illustrative case: Northstar Medical Devices

Background. Northstar, a Canadian company, will pay €2 million for equipment in six months and expects €1.5 million of sales receipts over the following year. It also owns a German subsidiary with net assets of €8 million.

Problem. Management is concerned about a euro appreciation, but sales receipts are uncertain and the equipment payment is firm.

Analysis. The equipment is a transaction exposure. The German net assets create translation exposure: a $0.10 increase in the euro rate changes the translated net assets by approximately C$800,000. The expected sales create economic and transaction exposure, but their uncertain timing makes a rigid hedge potentially excessive.

Approach. Northstar purchases euros forward for part of the equipment payment and uses euro calls for the uncertain portion. It matches expected euro receipts against euro costs where timing permits. It considers euro debt as a partial natural hedge of the subsidiary investment, while monitoring leverage and interest-rate risk. Treasury documents the hedge relationship and tests effectiveness under the applicable accounting standard.

Outcome. The firm obtains a known maximum cost for the committed payment while retaining some benefit if the euro weakens. It does not hedge the full uncertain sales forecast, reducing the risk of over-hedging. Translation volatility is reported separately from operating cash-flow risk.

Learning points. Exposure classification must precede instrument choice; certainty of cash flow determines hedge firmness; and accounting presentation, liquidity and governance are part of the economic decision.

Limitations and critical evaluation

PPP and UIP are useful theoretical benchmarks, not mechanical short-term forecasting tools. Forward rates can contain risk premia and liquidity effects. Derivatives introduce counterparty, basis, liquidity, rollover, model and operational risks. Options require premium valuation and may be expensive when volatility is high. Futures require margin and can generate cash-flow pressure through daily settlement. Swaps create long-term counterparty and funding exposure. Natural hedges may change the business itself and are not costless.

A robust policy therefore combines contractual hedging, operating flexibility, diversified funding, scenario analysis and independent oversight. The objective is not to eliminate every fluctuation, but to protect cash flows and strategic capacity at an acceptable cost.

Chapter Summary

PPP links exchange rates to relative price levels and predicts long-run currency adjustment, while CIP links spot and forward rates through interest-rate differentials. UIP concerns expected future spot rates and is less certain because it includes expectations and risk premia. Transaction exposure concerns contracted foreign-currency cash flows; translation exposure concerns conversion of foreign financial statements; and economic exposure concerns the present value of future operating cash flows.

Forwards lock rates, futures provide standardized and margined hedges, options provide asymmetric protection, swaps transform longer-term currency funding, and money-market hedges synthesize forward positions through borrowing and investing. For a foreign-currency payable, the correct money-market sequence is to borrow home currency, buy and invest the present value of the foreign amount, and use the foreign investment to settle the payable. Natural hedges, careful measurement, hedge accounting, controls and technology complement—but do not replace—professional judgment.

Key Terms

Purchasing power parity: The proposition that exchange rates reflect relative price levels.

Relative PPP: The relationship between inflation differentials and exchange-rate changes.

Covered interest parity: The no-arbitrage relationship among spot, forward and interest rates.

Uncovered interest parity: An expectation-based relationship between interest differentials and future spot rates.

Spot rate: The current exchange rate for near-immediate delivery.

Forward rate: The contracted exchange rate for future delivery.

Transaction exposure: Sensitivity of contracted foreign-currency cash flows.

Translation exposure: Accounting sensitivity arising from converting foreign statements.

Economic exposure: Sensitivity of future operating cash-flow value to exchange rates.

Forward contract: An OTC agreement to exchange currency at a future date.

Currency futures: Standardized exchange-traded currency contracts.

Currency option: A right, but not an obligation, to exchange currency.

Strike price: The exchange rate specified in an option.

Currency swap: An agreement to exchange currencies and related interest payments.

Money-market hedge: A hedge created through borrowing, conversion and investment.

Natural hedge: An operational offset between foreign-currency inflows and outflows.

Basis risk: Risk that the hedge price and exposure price do not move identically.

Hedge accounting: Accounting treatment aligning hedging results with the hedged exposure.

Over-hedging: Hedging more currency than the underlying exposure ultimately requires.

Review Questions

Short Answer Questions

1. Distinguish absolute PPP from relative PPP.
2. Why is a forward rate not necessarily an unbiased forecast of the future spot rate?
3. Define transaction, translation and economic exposure.
4. Why does a currency option preserve favorable exchange-rate movements?
5. State the correct money-market hedge sequence for a foreign-currency payable.

Long Answer Questions

1. Explain CIP and UIP, including their assumptions and practical limitations.
2. Compare forwards, futures and options for hedging a known foreign-currency payable.
3. Explain how translation exposure is measured and why it may not equal cash-flow exposure.
4. Develop a quantitative approach to measuring economic exposure for a multinational manufacturer.
5. Discuss hedge accounting, governance and the risks of relying excessively on derivatives.

Analytical / Application Questions

1. A firm owes €800,000 in one year. The spot rate is $1.08/€, the home interest rate is 5% and the euro interest rate is 3%. Calculate the money-market hedge cost at maturity and compare it with the one-year CIP forward rate.
2. A company must buy £600,000 and can buy a call with strike $1.25/£ and premium $0.03/£. Calculate the net cost if the maturity spot rate is $1.34 and if it is $1.18. Explain the decision in each scenario.
3. A subsidiary has foreign assets of €15 million and liabilities of €9 million. Calculate the translation sensitivity to a $0.07/€ appreciation and discuss two reasons why the economic exposure may differ from this amount.

Multiple Choice Questions with Answers

Question 1

Using S as home currency per foreign currency, which expression represents covered interest parity for one year?

A. F₀ = S₀ × (1 + i_F) ÷ (1 + i_H)

B. F₀ = S₀ × (1 + i_H) ÷ (1 + i_F)

C. F₀ = S₀ + i_H − i_F

D. F₀ = S₀ × i_H × i_F

Correct Answer: B. F₀ = S₀ × (1 + i_H) ÷ (1 + i_F)

Question 2

A firm owes €500,000. If the spot rate rises from $1.45/€ to $1.52/€, what is the increase in the unhedged dollar cost?

A. $35,000

B. $70,000

C. $725,000

D. $760,000

Correct Answer: A. $35,000

Question 3

Which action correctly begins a money-market hedge for a foreign-currency payable?

A. Borrow foreign currency and invest home currency

B. Borrow home currency and purchase the present value of the foreign currency

C. Sell the foreign currency forward and borrow foreign currency

D. Invest the full payable in foreign currency without borrowing

Correct Answer: B. Borrow home currency and purchase the present value of the foreign currency

Question 4

A firm buys a foreign-currency call with strike K. What is its payoff at maturity for amount q when the spot rate is S_T?

A. q × max(K − S_T, 0)

B. q × (S_T + K)

C. q × max(S_T − K, 0)

D. q × K ÷ S_T

Correct Answer: C. q × max(S_T − K, 0)

Question 5

A €1,000,000 call has a strike of $1.10/€ and premium of $0.025/€. If the maturity spot rate is $1.18/€, what is the net cost?

A. $1,100,000

B. $1,118,000

C. $1,125,000

D. $1,205,000

Correct Answer: C. $1,125,000

Question 6

A long currency futures hedge buys at $1.095/€ and closes at $1.118/€ on €1,000,000. What is the futures gain?

A. $2,300

B. $23,000

C. $1,095,000

D. $1,118,000

Correct Answer: B. $23,000

Question 7

A subsidiary has foreign assets of €10 million and liabilities of €6 million. If the exchange rate rises by $0.10/€, the simplified translation sensitivity is:

A. $400,000 decrease

B. $600,000 increase

C. $1,000,000 increase

D. $400,000 increase

Correct Answer: D. $400,000 increase

Question 8

Which exposure primarily concerns the present value of future operating cash flows, including effects on demand and competition?

A. Transaction exposure

B. Translation exposure

C. Economic exposure

D. Settlement exposure

Correct Answer: C. Economic exposure

Question 9

Which instrument is generally standardized, exchange-traded and subject to daily marking to market?

A. Forward contract

B. Currency futures contract

C. Currency swap

D. Natural hedge

Correct Answer: B. Currency futures contract

Question 10

A Canadian firm receives euros from customers and pays euros to suppliers with similar timing. This is primarily an example of:

A. A natural hedge

B. Uncovered interest parity

C. Translation accounting

D. A currency option premium

Correct Answer: A. A natural hedge