BSM call value as a leveraged position in the underlying — MCQs

Northbridge Global Fund is a USD-based investor holding publicly traded European equities whose market values are denominated in EUR. The investment committee manages the equity exposure separately from the currency exposure and requires a fixed percentage of the EUR market value to be hedged over the next three months. The fund uses USD per EUR quotations, meaning that EUR is the base currency and USD is the price currency. Currency manager Daniel Cho considers a deliverable forward contract. Because the fund owns EUR assets, an unhedged decline in the USD/EUR rate would reduce the assets' translated USD value. Cho must choose the direction and notional amount of the forward based on the required hedge ratio. Exhibit 1 provides the exposure, policy requirement, forward rate, and the assumed expiration spot rate. Forward payoffs are measured in USD, and transaction costs and taxes are ignored. Cho also reviews an existing short EUR forward with one month remaining. The contract was worth zero at initiation, but the current forward rate for the remaining maturity now differs from the contractual delivery rate. Cho values the position from Northbridge's perspective by comparing the delivery rate on the existing contract with the rate available on a replacement contract and discounting the difference using the USD discount factor. All required inputs appear in Exhibit 2. For another mandate, Cho considers exchange-traded currency futures rather than an OTC forward. He estimates a minimum-variance hedge ratio using the correlation between changes in the spot value of the exposure and changes in the futures price, together with their respective standard deviations. The futures position should offset the fund's long EUR exposure. The calculated number of contracts is rounded to the nearest whole contract. Exhibit 3 supplies the exposure amount, contract size, volatilities, and correlation. Margin requirements do not constrain the mandate, and basis risk is reflected in the estimated hedge ratio.

Ellison Manufacturing is a US-based company that reports in USD and sells specialized equipment to European customers. Its treasury department manages contractual EUR receivables using foreign-exchange derivatives. The chief financial officer requires transaction exposures to be measured in the reporting currency and directs analysts to state exchange rates as units of USD, the price currency, per unit of EUR, the base currency. Treasury analyst David Lin is estimating the fair six-month forward rate using covered interest parity. The applicable spot exchange rate and annualized risk-free rates are shown in Exhibit 1. Both money markets use simple interest for the six-month period, and the rates are borrowing and lending rates available to Ellison. There are no transaction costs, taxes, capital controls, or counterparty credit concerns. Lin must account for the fact that a USD-per-EUR quote increases when EUR appreciates against USD. Ellison also has an existing three-month short EUR forward. The contract requires Ellison to deliver EUR 10 million and receive USD at a delivery rate of 1.1200 USD per EUR. Lin values the contract from Ellison's perspective by comparing its contractual delivery rate with the forward rate on a new offsetting contract having the same remaining maturity. The resulting cash flow difference at settlement is discounted using the stated USD rate because the difference is measured in USD. The company expects another confirmed EUR receivable from a customer. Management's objective is to eliminate uncertainty in the USD value of the receivable rather than retain gains from possible EUR appreciation. The amount and date are contractually fixed, and management is willing to forgo favorable currency movements to obtain a complete exchange-rate lock. Lin considers buying EUR forward, selling EUR forward, and purchasing EUR call options. After Ellison establishes its original hedge, the European customer expands its order. The settlement date does not change, but the expected EUR receipt increases as shown in Exhibit 2. Ellison does not immediately resize its forward position. Lin therefore evaluates the combined exposure from the revised receivable and the existing forward sale. He treats the receivable as a long EUR exposure and the contractual forward delivery obligation as a short EUR exposure. Any mismatch remains exposed to changes in the USD-per-EUR exchange rate.

Meridian Pension Plan reports its assets and liabilities in USD but allocates part of its portfolio to euro-denominated securities. The investment committee permits currency overlays when they reduce uncompensated currency risk or create a clearly specified exposure. The committee requires every recommendation to state the base and price currencies, hedge direction, notional amount, and maturity. All quotes in this case are expressed as USD per EUR, so EUR is the base currency and USD is the price currency. Meridian currently owns a diversified portfolio of euro-area securities with the market value shown in Exhibit 1. The portfolio manager wants to hedge 75% of the EUR exposure for six months because the manager is concerned that EUR may depreciate against USD. The physical securities will remain in the portfolio. The manager can enter a deliverable forward under which Meridian either buys or sells EUR for USD at the quoted six-month rate. The forward will be sized using the current EUR market value; no rebalancing occurs before maturity. Taxes, transaction costs, and changes in the local-currency value of the securities are ignored for purposes of calculating the currency hedge. The committee is also considering three prospective overlay mandates summarized in Exhibit 2. Mandate I concerns the existing EUR assets and seeks to remove the effect of EUR depreciation over a known six-month horizon. Mandate II concerns a separate, contractually fixed EUR payment that Meridian must make in six months. The committee wants protection against an increase in the USD cost of that payment but wants to benefit if EUR becomes cheaper. Mandate III seeks symmetric participation in either direction of EUR movement and does not permit payment of an upfront option premium. The committee recognizes that a forward commitment imposes obligations on both parties, whereas an option gives its buyer a right but not an obligation. Separately, the committee reviews the relationship between the spot and forward quotations in Exhibit 1 to understand what the forward premium implies about relative interest rates in the two currencies, consistent with covered interest rate parity. Each question is independent. The hedge-ratio calculations use only Exhibit 1, the instrument-selection question uses the relevant mandate in Exhibit 2, and the interest rate parity question relies solely on the spot and forward quotations in Exhibit 1.

Ardent Medical Systems, a US-based manufacturer whose functional currency is USD, has sold diagnostic equipment to a customer in the eurozone. The customer will pay a fixed EUR amount in three months. Because Ardent reports and budgets in USD, a depreciation of the EUR against the USD before collection would reduce the receivable's USD value. All exchange rates in the case are quoted as USD per EUR, making EUR the base currency and USD the price currency. Treasurer Samuel Lee evaluates three alternatives: leaving the receivable unhedged, selling EUR under a three-month forward contract, or purchasing a three-month European put on EUR. The forward has no initial premium and requires physical delivery of EUR at maturity. The put permits Ardent to sell EUR at the exercise price but does not require exercise. The quoted option premium is paid today in USD per EUR of notional. For the requested option comparison, financing on the premium is explicitly ignored. Lee expects the expiration spot rate to be below the put's exercise price. He nevertheless distinguishes the expected outcome from the guaranteed minimum outcome. The unhedged strategy provides neither a floor nor a fixed conversion rate. The forward fixes Ardent's conversion rate but eliminates participation in any appreciation of the EUR. The put provides a floor after deducting its premium while allowing Ardent to benefit if the expiration spot rate exceeds the exercise price. Management states that, for one decision, its sole objective is to obtain the highest certain minimum USD proceeds; it assigns no value to retaining favorable currency upside. Ardent also has access to exchange-traded EUR futures and asks Lee to calculate a minimum-variance hedge. The futures and the receivable have the same three-month horizon, and futures contracts are available only in whole numbers. The hedge ratio must be calculated as the correlation between spot and futures price changes multiplied by the ratio of their standard deviations. Because Ardent will receive EUR, a hedge should gain value when the EUR depreciates. Margin liquidity and basis risk are acceptable within Ardent's risk policy. The exposure, quotations, option terms, contract size, and statistical inputs are provided in Exhibits 1 and 2.

Westhaven Global Equity Fund reports returns in USD but invests in securities denominated in several foreign currencies. Currency manager Daniel Cho is evaluating transaction and portfolio exposures. Exchange rates are quoted as units of USD, the price currency, per one unit of the foreign base currency. Interest rates in Exhibit 1 are effective rates for the six-month period, not annualized rates. A portfolio company is scheduled to pay Westhaven EUR 12 million in six months. The amount and payment date are contractually fixed. Cho is concerned that EUR may depreciate against USD before the receipt is converted, and he wants to eliminate the USD value uncertainty using a forward contract. Counterparty credit risk and transaction costs are assumed to be negligible. Cho also calculates the no-arbitrage six-month forward exchange rate from the spot exchange rate and the USD and EUR interest rates. Because the quote is USD per EUR, USD is the price currency and EUR is the base currency. Covered interest rate parity applies, and the two interest rates correspond to the same six-month horizon as the forward. A separate EUR 10 million receivable was previously hedged by selling EUR forward at USD 1.1150 per EUR. On the scheduled settlement date, Westhaven learns that the receipt will be delayed. The counterparty requires settlement of the original forward, so Westhaven must offset the EUR sale at the current spot rate before establishing a replacement hedge. Cho measures the close-out result from Westhaven's perspective and excludes the value of any new forward. Finally, Westhaven owns a GBP-denominated equity portfolio worth GBP 20 million. The investment committee wants protection against GBP depreciation over the next year but wishes to retain any USD return resulting from GBP appreciation. The committee accepts an upfront option premium in exchange for this asymmetric outcome. Cho's proposed hedge directions are summarized in Exhibit 2.