Foreign Exchange and International Treasury

Introduction

International treasury manages liquidity, funding, investment and financial risk across currencies and jurisdictions. A domestic transaction is normally settled in one currency; an international transaction may expose the firm to exchange-rate movements between contracting, accounting and settlement dates. Currency changes can therefore alter cash flows, reported financial statements, competitiveness and enterprise value.

This chapter adopts the quotation convention domestic currency per unit of foreign currency. Thus, if the US dollar is domestic and the euro is foreign, S_t = 1.1000 USD/EUR means that one euro costs USD 1.10. An increase in this rate represents euro appreciation and dollar depreciation.

Learning Objectives

After studying this chapter, students should be able to:

1. Interpret spot and forward exchange-rate quotations and compute cross-rates.
2. Apply covered interest parity and related international parity conditions.
3. Explain and calculate the cash flows and values of foreign-exchange swaps and cross-currency swaps.
4. Distinguish transaction, translation and economic currency exposures.
5. Design operational and financial hedging strategies using forwards, futures, swaps, money-market hedges and options.
6. Evaluate hedge effectiveness, basis risk, governance requirements and residual exposure.

1. The Foreign-Exchange Market

The foreign-exchange market facilitates the conversion of currencies and the transfer of purchasing power across countries. Major participants include commercial banks, central banks, institutional investors, multinational corporations, brokers, governments and retail intermediaries.

1.1 Spot exchange rates

A spot transaction exchanges currencies at the prevailing spot rate, normally with settlement according to the market convention for the currency pair. Settlement is commonly two business days after trade date, although important exceptions exist.

Let:

• S_t = spot exchange rate at time t, measured as units of domestic currency per unit of foreign currency;
• Q_f = quantity of foreign currency;
• V_d = domestic-currency value.

The domestic value of foreign currency is:

For example, EUR 500,000 at USD 1.10/EUR is worth:

Under this quotation convention, a rise in S_t increases the domestic value of a foreign-currency asset and the domestic cost of a foreign-currency liability.

1.2 Bid–ask spreads

A dealer's bid is the price at which the dealer buys the foreign currency, while the ask is the price at which the dealer sells it. If EUR/USD is quoted as 1.0995–1.1005 USD/EUR, a customer selling euros receives USD 1.0995 per euro, while a customer buying euros pays USD 1.1005.

The proportional spread relative to the midpoint is:

Bid–ask spreads compensate dealers for operating costs, inventory exposure, credit risk and market liquidity risk.

1.3 Direct, inverse and cross-rates

If S_D/F denotes domestic currency per unit of foreign currency, the inverse quotation is:

Cross-rates are obtained only after ensuring that units cancel correctly. If:

• S_USD/EUR = 1.10 USD per EUR;
• S_EUR/GBP = 1.18 EUR per GBP,

then:

In practice, bid and ask cross-rates must be calculated separately; midpoint calculations should not be used to claim an executable arbitrage profit.

2. Forward Foreign Exchange

A forward contract is an agreement made today to exchange specified currency amounts at a future date at a predetermined exchange rate. It is an over-the-counter instrument that can be tailored by amount and maturity.

A firm expecting a foreign-currency receipt can sell the currency forward. A firm expecting a foreign-currency payment can buy it forward. The forward fixes the domestic-currency value but also removes favorable exchange-rate participation.

2.1 Forward premium and discount

Let F_t,T be the forward rate agreed at time t for maturity T. The annualized forward premium on the foreign currency, using a simple proportional convention, is:

Here τ is the fraction of a year to maturity. The measure is positive when the foreign currency is at a forward premium. Market conventions may annualize differently, so treasury systems must use the convention specified in the contract.

Forward points are commonly quoted as F_t,T − S_t. For most major currency pairs, one pip is 0.0001 of the quoted rate, although conventions differ for some currencies.

2.2 Covered interest parity

Covered interest parity follows from the absence of arbitrage between comparable domestic and foreign investments when exchange risk is fully covered by a forward contract.

Assume:

• borrowing and lending are possible at the stated rates;
• instruments have identical maturity and comparable credit risk;
• taxes, capital controls, transaction costs and bid–ask spreads are absent;
• rates use compatible compounding and day-count conventions.

Investing one unit of domestic currency domestically produces 1 + i_d τ. Alternatively, convert it into foreign currency at S_t, invest abroad and sell the foreign proceeds forward. Equating the maturity values gives:

where:

• i_d = annual domestic interest rate;
• i_f = annual foreign interest rate;
• τ = maturity in years under the applicable convention.

With continuously compounded zero rates, the corresponding relationship is:

These formulas are alternative forms and should not be mixed without adjusting for compounding.

Worked Example 1: A parity-implied forward rate

Suppose:

• spot rate = USD 1.1000/EUR;
• three-month USD rate = 4% per year;
• three-month EUR rate = 2% per year;
• τ = 90/360 = 0.25.

Then:

Because the USD interest rate exceeds the EUR interest rate, the euro trades at a forward premium against the dollar under covered interest parity.

2.3 Valuing an existing forward contract

A forward has approximately zero value at inception when contracted at the market forward rate. Thereafter, its value changes.

For a contract to buy Q_f units of foreign currency at delivery rate K, its domestic-currency value at time t is:

Equivalently, when the current market forward rate for the remaining maturity is F_t,T:

The value of a short foreign-currency forward has the opposite sign. These equations assume compatible simple-compounded zero rates and no default before maturity.

3. International Parity Relationships

Parity relationships connect exchange rates, interest rates and price levels. They are theoretical benchmarks, not guaranteed short-term forecasting rules.

3.1 Purchasing power parity

Absolute purchasing power parity states that identical tradable goods should have the same price after currency conversion, absent transport costs, taxes, trade barriers and market segmentation.

Relative purchasing power parity predicts that exchange-rate changes reflect inflation differences:

where π_d and π_f are domestic and foreign inflation rates over the period. For small rates:

Thus, higher domestic inflation is associated with expected domestic-currency depreciation under the adopted quotation convention.

3.2 International Fisher effect

The Fisher relationship links nominal interest rates, real rates and expected inflation:

If expected real returns are internationally equal, nominal interest differentials mainly reflect expected inflation differentials. The international Fisher effect consequently associates a higher-interest-rate currency with expected depreciation. In practice, risk premiums, monetary policy shocks and capital flows weaken short-run predictions.

3.3 Uncovered interest parity

Uncovered interest parity proposes:

Unlike covered interest parity, the future currency conversion is not locked by a forward contract. The relationship therefore depends on expectations and risk preferences and may fail empirically, especially over short horizons.

4. Foreign-Exchange Swaps

A foreign-exchange swap combines two opposite currency exchanges for different value dates. A party may buy foreign currency spot and simultaneously sell the same amount forward, or perform the reverse transaction. Only the far leg depends on forward points; the transaction does not represent two independent speculative trades.

FX swaps are widely used to manage temporary currency liquidity, roll forward positions and obtain secured-like foreign-currency funding. They generally do not exchange periodic interest payments.

Worked Example 2: FX swap cash flows

A US company needs EUR 2 million for three months but expects the euros to become available at the end of that period. The market quotes:

• spot = USD 1.1000/EUR;
• three-month forward = USD 1.1055/EUR.

The company executes a swap by buying EUR 2 million spot and selling EUR 2 million forward.

The USD 11,000 difference between the legs reflects the forward points and the interest-rate differential. It should not automatically be described as the total economic cost because the two dollar cash flows occur at different dates.

Suppose that one month later the market forward rate for the remaining two months is USD 1.0900/EUR. The company has an existing contract to sell euros at 1.1055. If the two-month USD discount rate is 4.8% per year using simple interest, the value of the short-euro forward is:

The positive value arises because the company can sell euros above the current market forward rate.

5. Cross-Currency Swaps

A cross-currency swap normally exchanges principal in two currencies at inception, exchanges periodic interest payments, and re-exchanges principal at maturity. Interest legs may be fixed or floating. Such swaps can transform the currency composition of assets or liabilities and are usually longer-term than FX swaps.

5.1 Cash-flow structure

Consider a three-year swap based on USD 11 million and EUR 10 million, implying an initial exchange rate of USD 1.10/EUR. One party receives 5% annual USD interest and pays 3% annual EUR interest.

Its annual flows are:

• receive USD 550,000;
• pay EUR 300,000;
• at maturity, additionally receive USD 11 million and return EUR 10 million.

In actual markets, quoted spreads may incorporate cross-currency basis, collateral terms and credit considerations.

Worked Example 3: Valuation of a cross-currency swap

After the first annual payment, two years remain. Assume annual discount rates of 4% in USD and 2% in EUR, flat zero curves, no default and spot S_t = 1.08 USD/EUR.

The present value of the remaining USD receipts is:

Amounts are in millions. The present value of the remaining EUR payments is:

Convert the EUR leg at the current spot rate:

Therefore, the approximate value to the party receiving dollars and paying euros is:

This method values each currency leg using its own discount curve and then converts one present value into the reporting currency. More sophisticated valuation may require collateral-specific discounting, forward curves and cross-currency basis adjustments.

6. Types of Foreign-Exchange Exposure

Currency risk is not a single accounting number. Treasury must distinguish contractual exposure from financial-statement exposure and long-term business exposure.

6.1 Transaction exposure

Transaction exposure arises from contracted or highly probable foreign-currency cash flows, including receivables, payables, debt service and dividends. It measures the effect of exchange-rate changes on domestic-currency cash flows between commitment and settlement.

For a foreign-currency amount Q_f, the change in domestic value is:

A foreign-currency receivable benefits from foreign-currency appreciation, while a payable is harmed by it.

6.2 Translation exposure

Translation exposure arises when foreign subsidiaries' financial statements are converted into the parent's reporting currency for consolidation. Exchange-rate changes can affect translated assets, liabilities, income and equity even when no immediate cash flow occurs.

The amount depends on the applicable accounting standard, functional-currency determination and translation method. Under a current-rate approach, many balance-sheet items are translated at the closing rate, while income-statement items may use transaction-date or appropriate average rates. Translation differences may be reported in other comprehensive income, subject to the relevant accounting framework.

Translation exposure should not automatically be hedged. A hedge may reduce reported equity volatility while creating real cash costs, liquidity requirements and tax consequences.

6.3 Economic exposure

Economic, or operating, exposure is the sensitivity of future operating cash flows and enterprise value to unexpected exchange-rate changes. It includes effects on prices, volumes, input costs and competitive behavior.

A simplified empirical model is:

where:

• ΔCF_t = change in operating cash flow;
• ΔS_t = exchange-rate change;
• β = estimated cash-flow sensitivity;
• ε_t = other influences.

The estimate may be unstable because exchange rates interact with inflation, demand, interest rates and competitor responses. Scenario analysis often complements regression.

7. Financial Currency-Hedging Instruments

7.1 Forward hedge

A forward hedge is direct and customizable. If a US firm will receive EUR 1 million in 90 days and sells it forward at USD 1.1200/EUR, it locks in USD 1.12 million. If the maturity spot rate is 1.0600, the unhedged receipt would have been USD 1.06 million, so the forward improves the outcome by USD 60,000. If the spot rate instead rises above 1.1200, the firm forgoes the favorable movement.

7.2 Money-market hedge

A money-market hedge synthetically fixes a future exchange rate through borrowing, spot conversion and investment.

For a foreign-currency receivable Q_f, the firm can:

1. borrow the present value of the foreign receivable;
2. convert the borrowed foreign currency into domestic currency at spot;
3. invest the domestic proceeds;
4. use the eventual receivable to repay the foreign loan.

Using EUR 1 million, a 90-day EUR rate of 2%, a USD rate of 4%, spot 1.1000 USD/EUR and a 360-day basis:

Convert at spot:

Investing for 90 days gives:

The synthetic forward rate is therefore 1.10547 USD/EUR, equal to the covered-interest-parity rate under the stated assumptions.

7.3 Currency futures

Currency futures are standardized, exchange-traded contracts with daily marking to market and margin requirements. They reduce bilateral counterparty risk but create potential basis risk because contract sizes and maturities may not match the exposure.

Let:

• ΔV_E = change in the domestic value of the unhedged exposure;
• ΔV_C = gain on one futures contract held in a specified reference orientation, such as one long contract;
• N = signed number of contracts in that reference orientation.

The hedged change is ΔV_E + NΔV_C. Minimizing its variance gives:

A negative N^* means taking the direction opposite to the specified reference orientation. For example, if ΔV_C is the gain on one long euro futures contract, a euro receivable usually has positive covariance with that gain; the optimal hedge therefore involves a short futures position.

If the estimated covariance is 1.8 × 10⁹ USD² and the variance of one long contract's gain is 4.5 × 10⁶ USD², then:

The estimated minimum-variance position is 400 short contracts. Estimates depend on historical data, hedge horizon and contract specification and should not be treated as permanently stable.

7.4 Currency options

A currency option provides the right, but not the obligation, to exchange currency at a strike rate. The buyer pays a premium.

For a call option on foreign currency with strike K, maturity spot S_T and foreign amount Q_f, the gross domestic-currency payoff is:

For a put option on foreign currency:

A foreign-currency payable can be protected with a call, while a receivable can be protected with a put. Options are particularly suitable for uncertain tenders, forecast sales and other contingent exposures because the holder can allow the option to expire if the underlying transaction does not occur.

8. Operational Hedging

Financial contracts usually address a defined exposure horizon. Economic exposure often requires changes to operations and strategy.

Operational methods include:

• matching foreign-currency revenues and costs;
• borrowing in the currency of long-term cash inflows;
• diversifying suppliers, production sites and markets;
• invoicing in the firm's functional currency where commercially feasible;
• including currency-adjustment clauses in contracts;
• leading or lagging intercompany payments, subject to law and transfer-pricing policy;
• netting reciprocal group obligations;
• adjusting product design, sourcing and pricing flexibility.

A natural hedge reduces net exposure without a standalone derivative, but it may conflict with procurement efficiency, customer preferences or strategic objectives. Treasury should not sacrifice a profitable operating model merely to minimize accounting volatility.

9. Designing a Currency-Risk Program

A sound hedge program begins with the exposure, not the instrument.

Figure: Integrated foreign-exchange risk management process.

The process should specify:

1. Exposure scope: committed, forecast, accounting or economic exposure.
2. Risk objective: cash-flow certainty, earnings stability, covenant protection or value preservation.
3. Risk appetite: acceptable unhedged amount and adverse-rate tolerance.
4. Hedge ratio: the proportion hedged, possibly varying with forecast confidence and maturity.
5. Instrument choice: cost, liquidity, flexibility, accounting treatment and counterparty risk.
6. Performance measurement: compare the combined exposure-and-hedge result with the approved benchmark.

Hedge effectiveness should not be judged from the derivative's standalone gain or loss. A derivative loss may indicate that the underlying exposure gained value.

10. Illustrative Case: Aster Appliances

Background

Aster Appliances is a fictional US-based manufacturer with the US dollar as its functional currency. It has:

• a EUR 4 million receivable due in 90 days;
• a JPY 300 million payable due in 90 days;
• forecast EUR sales of EUR 2 million in six months, with only 70% confidence.

Market rates are:

• three-month EUR forward: USD 1.095/EUR;
• three-month JPY forward: USD 0.00674/JPY;
• six-month EUR put strike: USD 1.08/EUR;
• put premium: USD 0.025/EUR.

Problem

Management wants to protect near-term liquidity while retaining flexibility over uncertain sales. It is also concerned that hedging every forecast mechanically could create speculative positions if sales do not occur.

Analysis and solution

Aster adopts the following strategy:

1. Sell 75% of the EUR receivable—EUR 3 million—forward.
2. Buy the full JPY payable forward because the amount and date are contractually fixed.
3. Buy a put on EUR 1 million of forecast sales rather than using a forward.
4. Leave the remaining exposures unhedged within approved risk limits and develop more euro-denominated sourcing as an operational hedge.

The EUR forward locks in:

The JPY forward fixes the payable at:

The option premium is:

Outcome

After 90 days, assume spot rates are USD 1.04/EUR and USD 0.00695/JPY. The euro receipt produces:

An entirely unhedged receipt would have produced USD 4,160,000. The partial forward hedge therefore adds USD 165,000 relative to that outcome.

The JPY forward costs USD 2,022,000, compared with an unhedged spot cost of:

The hedge reduces the payable's dollar cost by USD 63,000 in this scenario.

After six months, assume the forecast sale occurs and spot is USD 1.02/EUR. Aster exercises its EUR put. On the EUR 1 million hedged amount, it receives USD 1.08 million before premium, or USD 1.055 million after deducting the USD 25,000 premium without time-value adjustment. This is USD 35,000 more than conversion at spot after considering the premium. If the sale had not occurred, the option could expire; the maximum direct loss would have been the premium, whereas an unconditional forward might have created an unwanted short-euro position.

Learning points

• Firm commitments and uncertain forecasts may require different instruments.
• Hedge ratios should reflect risk appetite and forecast reliability.
• Hedge performance must be evaluated jointly with the underlying exposure.
• Options protect contingent transactions without imposing an obligation to deliver currency.
• Operational measures can supplement rather than replace financial hedges.

11. Governance, Regulation and Technology

Foreign-exchange derivatives can reduce risk but can also create leverage, liquidity needs and operational complexity. Effective governance generally includes board-approved policies, authorized instruments, counterparty limits, segregation of dealing and settlement, independent valuation, confirmation matching and exception reporting.

Treasury should document the economic relationship between exposure and hedge, including currency, amount, maturity and risk being hedged. Where hedge accounting is sought, the entity must satisfy the applicable accounting standard's designation, documentation and effectiveness requirements. Hedge accounting changes the timing or presentation of gains and losses; it does not change the derivative's economics.

International operations must also consider derivatives reporting, capital controls, sanctions, anti-money-laundering obligations, tax rules and transfer-pricing requirements. Ethical treasury practice prohibits disguising speculation as hedging, manipulating valuations or using inappropriate rates for internal transactions.

Modern treasury-management systems aggregate exposures, obtain electronic quotes, monitor limits and automate settlement instructions. Payment-versus-payment arrangements can reduce principal settlement risk. Artificial intelligence may improve cash-flow forecasting and anomaly detection, but models can inherit biased data, understate regime changes or generate false confidence. Human approval, model validation, cybersecurity and audit trails remain necessary.

Contemporary market developments include increased electronic trading, greater collateralization, cross-currency basis effects, faster payment infrastructure and experiments with tokenized deposits and central-bank digital currencies. These developments may alter settlement processes, but they do not eliminate market, legal, liquidity or counterparty risk.

12. Challenges and Limitations

No hedge is perfect. Important limitations include:

• Basis risk: the hedging instrument may not move exactly with the exposure.
• Forecast risk: expected transactions may be delayed, reduced or cancelled.
• Liquidity risk: margin calls and collateral requirements may create cash demands.
• Counterparty risk: an over-the-counter counterparty may default.
• Rollover risk: short-term hedges may become expensive or unavailable when renewed.
• Model risk: correlations, volatilities and cash-flow forecasts may be incorrectly estimated.
• Accounting mismatch: derivative gains and exposure losses may be reported in different periods.
• Overhedging: hedging more than the actual exposure creates a net speculative position.
• Strategic limitation: financial hedges cannot permanently offset an uncompetitive cost structure.

Best practice is therefore to combine accurate exposure data, proportionate financial hedges, operational flexibility, scenario analysis, governance and periodic reassessment.

Chapter Summary

Foreign-exchange treasury begins with consistent quotation conventions and accurate measurement of currency cash flows. Spot rates determine immediate conversion values, while forward rates fix future exchange values. Covered interest parity establishes the no-arbitrage relationship among spot rates, forward rates and comparable interest rates. Purchasing power parity, the Fisher effect and uncovered interest parity provide broader, but less reliable, expectations-based relationships.

FX swaps combine opposite exchanges at two dates and are important for short-term currency liquidity. Cross-currency swaps exchange principal and interest in different currencies and can transform long-term funding. Their valuation requires discounting each currency leg using the appropriate curve and converting the resulting present values consistently.

Transaction exposure affects contracted cash flows, translation exposure affects consolidated reporting, and economic exposure affects long-term operating value. Forwards, futures, money-market hedges, swaps and options address different exposure characteristics. Operational hedges alter the underlying pattern of revenues, costs and financing. A defensible risk program aligns hedge instruments and ratios with exposure certainty, risk appetite, liquidity, accounting and governance requirements.

Key Terms

Spot rate: Exchange rate for currency delivery under the applicable spot settlement convention.

Bid rate: Rate at which a dealer buys the quoted foreign currency.

Ask rate: Rate at which a dealer sells the quoted foreign currency.

Cross-rate: Exchange rate between two currencies derived through a third currency.

Forward contract: Agreement to exchange currencies at a future date at a predetermined rate.

Forward points: Difference between a forward rate and the corresponding spot rate.

Covered interest parity: No-arbitrage relationship connecting spot rates, forward rates and interest rates.

Purchasing power parity: Relationship connecting exchange rates with relative national price levels or inflation.

FX swap: Simultaneous purchase and sale of the same currency amount for different value dates.

Cross-currency swap: Contract exchanging principal and interest cash flows in different currencies.

Transaction exposure: Currency sensitivity of contracted or highly probable cash flows.

Translation exposure: Currency effect arising from converting foreign operations into a reporting currency.

Economic exposure: Sensitivity of future operating cash flows and firm value to exchange-rate changes.

Money-market hedge: Hedge constructed through borrowing, spot conversion and investment.

Currency future: Standardized exchange-traded contract for future currency delivery or cash settlement.

Currency option: Right, but not obligation, to exchange currency at a specified strike rate.

Basis risk: Risk that a hedge and its underlying exposure do not change by equal and opposite amounts.

Natural hedge: Reduction of net currency exposure through offsetting operating or financing cash flows.

Hedge ratio: Proportion of an exposure covered by hedging instruments.

Cross-currency basis: Market spread reflecting deviations from a simple interest-parity relationship in cross-currency funding markets.

Review Questions

Short Answer Questions

1. What does an increase in a domestic-currency-per-foreign-currency quotation signify?
2. Distinguish an FX swap from a cross-currency swap.
3. Why is covered interest parity considered a no-arbitrage condition?
4. What is basis risk in a currency futures hedge?
5. Why may an option be preferable to a forward for a forecast transaction?

Long Answer Questions

1. Explain and compare transaction, translation and economic exposure.
2. Derive covered interest parity using domestic and foreign investment strategies.
3. Discuss the advantages and limitations of forwards, futures, options and money-market hedges.
4. Explain how operational hedging can reduce a multinational firm's long-term economic exposure.
5. Describe the governance and control framework required for an international treasury function.

Analytical / Application Questions

1. A company will receive CAD 5 million in four months. Design and compare a forward hedge, money-market hedge and option hedge, stating the additional market data required.
2. A firm's foreign-currency receivable has positive covariance with the gain on one long currency futures contract. Derive the sign of the minimum-variance contract position and explain its economic meaning.
3. Construct a two-currency cash-flow schedule for a cross-currency swap and explain how it should be valued after inception.

Multiple Choice Questions with Answers

Question 1

A US firm quotes the euro at 1.12 USD/EUR. If the rate rises to 1.16 USD/EUR, what has occurred under this quotation convention?

A. The euro has appreciated against the dollar

B. The euro has depreciated against the dollar

C. Both currencies have appreciated

D. The exchange rate is unchanged in economic terms

Correct Answer: A. The euro has appreciated against the dollar

Question 2

Given spot S = 1.2000 USD/EUR, a one-year USD rate of 5% and EUR rate of 2%, what is the parity-implied one-year forward rate using annual simple compounding?

A. 1.1657 USD/EUR

B. 1.2000 USD/EUR

C. 1.2353 USD/EUR

D. 1.2600 USD/EUR

Correct Answer: C. 1.2353 USD/EUR

Question 3

Which exposure arises when a foreign subsidiary's statements are converted into the parent's reporting currency?

A. Transaction exposure

B. Translation exposure

C. Settlement exposure

D. Inventory exposure

Correct Answer: B. Translation exposure

Question 4

A company will receive foreign currency in three months and wants to fix its domestic-currency value. Which forward position is appropriate?

A. Buy the foreign currency forward

B. Sell the foreign currency forward

C. Buy domestic currency spot and leave the receipt unhedged

D. Enter two long foreign-currency forwards

Correct Answer: B. Sell the foreign currency forward

Question 5

An FX swap most commonly consists of:

A. An option and an interest-rate future

B. Two purchases of the same currency for the same date

C. Opposite exchanges of the same currencies for different value dates

D. Only periodic interest payments with no currency exchange

Correct Answer: C. Opposite exchanges of the same currencies for different value dates

Question 6

A firm buys EUR 500,000 spot at 1.10 USD/EUR and simultaneously sells it forward at 1.1060 USD/EUR. How many dollars does it receive on the forward leg?

A. USD 500,000

B. USD 550,000

C. USD 553,000

D. USD 603,000

Correct Answer: C. USD 553,000

Question 7

If ΔV_C is the gain on one long currency futures contract, the minimum-variance signed contract number is:

A. Cov(ΔV_E,ΔV_C) ÷ Var(ΔV_C)

B. −Cov(ΔV_E,ΔV_C) ÷ Var(ΔV_C)

C. Var(ΔV_E) ÷ Cov(ΔV_E,ΔV_C)

D. −Var(ΔV_C) ÷ Var(ΔV_E)

Correct Answer: B. −Cov(ΔV_E,ΔV_C) ÷ Var(ΔV_C)

Question 8

A EUR put has a strike of 1.10 USD/EUR. At maturity, spot is 1.04 USD/EUR. What is the gross payoff on EUR 200,000?

A. USD 0

B. USD 6,000

C. USD 12,000

D. USD 220,000

Correct Answer: C. USD 12,000

Question 9

Which action is an operational rather than a purely financial currency hedge?

A. Selling a receivable forward

B. Buying a currency option

C. Matching foreign-currency input costs with sales revenue

D. Taking a currency futures position

Correct Answer: C. Matching foreign-currency input costs with sales revenue

Question 10

In valuing a cross-currency swap, the academically appropriate basic approach is to:

A. Discount all cash flows using only the reporting-currency rate

B. Ignore principal exchanges after inception

C. Discount each currency leg using its appropriate curve and convert one present value consistently

D. Value the swap only from the original exchange rate

Correct Answer: C. Discount each currency leg using its appropriate curve and convert one present value consistently