Pricing and Valuation of Futures Contracts — MCQs

Northbridge Manufacturing exports specialized equipment to euro-area customers and sponsors a defined-benefit pension plan invested partly in domestic equities. The corporate treasury and pension teams are jointly reviewing derivative hedges, although each team's exposure and objective are evaluated separately. Treasury expects to receive the euro-denominated amount in Exhibit 1 in three months. Northbridge prepares its financial statements in USD, making EUR the base currency and USD the price currency in the quoted exchange rates. A decline in the USD-per-EUR rate would reduce the receivable's USD value. Treasury wants to eliminate this uncertainty with a forward contract and has no desire to speculate on the currency movement. Treasury also holds the existing three-month forward described in Exhibit 1. Under that contract, Northbridge will deliver EUR and receive USD at the contracted rate. The current forward rate represents the USD-per-EUR rate available on a new contract with the same remaining maturity. The existing contract's value must be stated from Northbridge's perspective and discounted from its maturity value using the three-month USD rate. The annual rate is effective, and three months is one-quarter of a year. Separately, the pension plan's equity portfolio closely tracks the equity index underlying its futures contracts. The investment committee wants to reduce, but not eliminate, systematic equity exposure for the next quarter. It will use the beta-adjustment method and assumes the futures have a beta of 1.00 relative to their underlying index. The dollar value of each futures contract is determined by multiplying the quoted futures price by the contract multiplier. Contract quantity should be rounded to the nearest whole contract, although the supplied values produce a whole-number result. A negative calculated quantity represents a short futures position. Treasury additionally considers replacing a full forward hedge with currency options. Management wants to establish a minimum USD conversion value for the euro receivable but retain the benefit if EUR appreciates against USD. Each available currency option treats EUR as the underlying base currency and has a USD-denominated exercise price. The options are European and expire when the receivable is collected. Northbridge will purchase rather than write an option when limited downside exposure is required.

Northbridge Pension Fund reports its assets and liabilities in USD but invests in foreign securities. The investment committee permits the use of deliverable foreign-exchange forwards and exchange-traded currency options solely for hedging. Unless otherwise stated, each derivative's maturity matches the horizon of the exposure, and transaction costs, taxes, and counterparty defaults are ignored. Northbridge expects to receive EUR 20 million in three months from the maturity of a euro-denominated bond. The fund has no offsetting EUR liability and intends to convert the entire receipt into USD at that time. The committee wants to eliminate uncertainty about the USD value of the receipt. The applicable three-month forward rate is quoted in Exhibit 1 as units of USD per EUR. The treasurer must identify both the correct direction of the EUR forward transaction and the USD amount locked in by that transaction. Northbridge also owns a GBP-denominated equity portfolio valued at GBP 30 million. Existing forward contracts hedge 40% of that portfolio's GBP exposure. Following a strategic review, the committee raises the target hedge ratio to 70%. The portfolio's market value is assumed to remain GBP 30 million while the adjustment is executed. Only the incremental forward transaction necessary to reach the new target is required; existing hedges should not be closed and re-established. For a separate EUR-denominated asset allocation, the committee has a moderately favorable view of the euro. It nevertheless wants protection against a material decline in the euro's USD value over the next six months. The committee is willing to pay an upfront premium, requires a minimum effective USD conversion value, and wants to retain the benefit if the euro appreciates. The currency manager considers selling EUR forward, selling EUR calls, and buying EUR puts, with USD as the other currency in each transaction. All foreign-currency asset positions and receivables represent long exposure to the relevant foreign currency from the perspective of the USD-based fund. Accordingly, the manager must distinguish between a forward commitment that fixes the future conversion rate and an option position that provides asymmetric protection.

Helios Pension Reserve is a EUR-based institutional investor holding a diversified portfolio of US equities. The portfolio's investment committee expects the underlying equities to outperform over the next three months but is uncertain about the USD/EUR exchange rate. Unless hedged, the EUR value of the portfolio will decline if the USD depreciates against EUR, even if the US securities' USD prices remain unchanged. Currency quotes are expressed as USD per EUR, so EUR is the base currency and USD is the price currency. The portfolio's USD asset exposure is economically equivalent to a long position in USD and a short position in EUR. To neutralize that exposure with a forward or futures contract, Helios must establish the opposite currency position for the three-month horizon. A full hedge is intended to offset the current market value of the currency exposure rather than the expected value of the portfolio at the end of the horizon. The committee first considers a three-month currency forward. A forward would lock in the EUR value associated with the hedged USD amount, eliminating both unfavorable and favorable currency movements. The committee then considers exchange-traded EUR futures. Because each futures contract is specified in EUR, the number of contracts must be based on the EUR equivalent of the USD portfolio exposure at the current spot exchange rate. The direction of the futures position must match the direction required under the forward hedge. One committee member objects to surrendering all potential gains from USD appreciation. For this alternative objective, the committee evaluates a currency option that provides the right, but not the obligation, to sell USD and buy EUR. Such an option would be exercised following sufficient USD depreciation but allowed to expire if the USD appreciates. The premium is acceptable because retaining favorable currency participation is part of the revised objective. Helios also examines an imperfect cross-hedge using a related currency futures contract. The committee has estimated the correlation and volatilities from returns measured over matching intervals. Because spot and futures price changes are not perfectly correlated and have different volatilities, a one-for-one hedge need not minimize variance. Exhibits 1 and 2 provide the portfolio exposure, contract specifications, and minimum-variance hedge inputs.

Meridian Global Fund is a USD-based institutional portfolio with equity, currency, and interest-rate exposures. Its investment committee permits derivatives for hedging and tactical risk adjustment but prohibits uncovered speculative option writing. The fund has sufficient liquidity for margin and option premiums, and all proposed contracts have maturities aligned with the related exposures. The fund will receive EUR 8 million from the sale of a European holding in three months. Its reporting currency is USD, and the committee wants to eliminate uncertainty about the receivable's USD value. The relevant forward quotation is expressed as USD per EUR, so EUR is the base currency and USD is the price currency. The portfolio manager proposes using a deliverable currency forward for the full receivable amount. Meridian also expects to pay GBP 5 million for a planned acquisition in six months. The transaction is highly likely but has not yet closed. The committee wants to establish a maximum USD acquisition cost while retaining the benefit if GBP depreciates against USD. The committee is willing to pay an option premium for this asymmetric protection. Options are quoted on GBP against USD, and physical exercise would deliver the GBP required for the acquisition. The fixed-income segment contains a receive-floating, pay-fixed interest-rate swap with a notional amount of USD 20 million and a fixed rate of 4.50%, established at the then-current par swap rate. At the upcoming reset date, the floating reference rate for the next settlement period is set at 3.80%, and the settlement period is calculated on a 90/360-day basis. The counterparty remains creditworthy, and the contractual fixed rate does not reset, whereas floating receipts adjust to the prevailing reference rate at each reset. The portfolio manager must determine the net cash flow to Meridian at the upcoming reset. Finally, Meridian holds a USD 25 million diversified equity portfolio with a beta of 1.20. The committee expects elevated short-term volatility and directs the manager to reduce beta to 0.80 without selling the underlying securities. An equity index futures contract has a current notional value of USD 250,000 and a beta of 1.00 relative to the portfolio's benchmark. The futures position will be closed when the tactical view expires. Taxes, transaction costs, tracking error, and changes in contract notional value can be ignored for the hedge calculation.

Westridge Pension Trust is a USD-based institutional investor. Its investment committee asks risk manager Samuel Ortiz to make two temporary adjustments without selling the underlying assets. First, the committee wants to reduce the systematic equity exposure of a USD 50 million US equity portfolio from its current beta to a lower target beta for the next three months. The selected equity index futures contract has a price and multiplier shown in Exhibit 1. The portfolio's dividends are already reflected in its market value, and Ortiz should use the standard beta-adjustment formula based on the change from current beta to target beta. Second, Westridge owns an unhedged euro-denominated asset currently worth EUR 10 million. The investment itself will be retained for one year, but the committee wants to eliminate, as nearly as possible, the effect of changes in the USD value of the euro over that period. The amount of the euro exposure is expected to remain EUR 10 million, and the proposed currency forward will mature at the same time as the hedge horizon. The exchange-rate quote is USD per EUR, making EUR the base currency and USD the price currency. The committee is not seeking additional currency return. Ortiz also checks whether the quoted one-year currency forward is consistent with covered interest parity. The relevant spot rate and annually compounded one-year USD and EUR risk-free rates are provided in Exhibit 2. There are no taxes, transaction costs, capital controls, or credit constraints. Borrowing and lending are available at the stated rates in both currencies. The committee is deciding whether to use exchange-traded futures or OTC forwards for future temporary hedges. Futures positions are centrally cleared and marked to market daily. Adverse price changes can therefore require variation-margin payments before the final hedge date, even when the ultimate hedge performs as intended. OTC forwards settle at maturity and can be customized to the exposure, but they create direct counterparty exposure unless collateral or other credit mitigation is used. Neither instrument necessarily eliminates basis risk when its underlying asset, contract size, or maturity differs from the exposure being hedged. Ortiz assesses each implementation decision independently rather than assuming that the instrument used for one exposure must also be used for the other.