Protective put: structure, payoff, max profit, max loss, breakeven — MCQs

Meridian Asset Management uses equity and commodity derivatives to obtain market exposure without immediately trading the underlying assets. A portfolio manager asks analyst Elena Varga to price a new equity index forward and to value an existing long forward. Both contracts are based on indexes for which dividend income is represented by a continuously compounded yield. The contracts have no interim cash settlement, and their values are considered from the perspective of the long party. Varga explains that the delivery price of a newly initiated forward is selected so the contract has zero value at inception. After initiation, however, changes in the underlying index, interest rates, dividend yield, and remaining maturity can cause the existing contract to have a positive or negative value. She therefore plans to calculate a current forward price for the remaining term and discount the difference between that price and the contractual delivery price. The firm's risk committee is also comparing a customized OTC forward with an exchange-traded futures contract. Both alternatives would provide similar underlying exposure. The committee's principal concern is not liquidity or transparency; it is the possibility that a large unsecured receivable could accumulate before the contract expires. Varga notes that futures gains and losses are settled through variation margin, whereas the proposed forward uses less frequent collateral transfers. Finally, Meridian is considering a commodity forward. The commodity is held for operational reasons and provides a measurable convenience yield. Storage costs are proportional to the spot price and are paid continuously. Varga states that financing and storage increase the forward price, whereas benefits received from holding the physical commodity reduce it. All rates in the exhibits are annual continuously compounded rates, transaction costs and taxes are zero, and borrowing and lending occur at the stated risk-free rates.

Apex Derivatives Fund uses forwards, futures, and swaps to alter market exposures without liquidating underlying securities. Portfolio manager Helena Ortiz asks an analyst to review several positions under no-arbitrage assumptions. All contracts are free of default risk, transaction costs, and taxes, and borrowing and lending are available at the stated risk-free rates. The fund entered a long equity index forward three months ago. The contract originally had a six-month maturity and requires the fund to buy one unit of the index at the contractual delivery price. The analyst must distinguish the forward price that would apply to a new contract today from the value of the fund's existing contract. The index pays dividends continuously, and the risk-free rate and dividend yield are expressed using continuous compounding. Apex is also considering an arbitrage involving a storable commodity. Storage must be paid in full when the commodity is acquired, and the storage provider assumes all physical storage obligations through the forward expiration date. The commodity provides no monetary income or nonmonetary convenience yield. Ortiz instructs the analyst to determine the trade direction from the quoted forward price rather than merely calculate a theoretical price. The fund's exchange-traded equity index futures are marked to market daily through its margin account. No contracts are closed during the day described in Exhibit 1. Thus, any change in settlement price produces an immediate variation-margin cash flow rather than an accumulated payment deferred to expiration. Finally, Apex holds a plain-vanilla interest rate swap with two remaining semiannual settlement dates. The swap's floating leg has just reset to the current market reference rate and the related net settlement has just occurred. For valuation, the analyst represents the receive-fixed swap as a long fixed-rate bond and a short floating-rate bond. The fixed rate applies to notional principal but the notional itself is not exchanged. Immediately after a reset, the floating-rate bond is valued at par. Exhibit 1 provides the forward and futures information, and Exhibit 2 provides the swap terms and relevant discount factors.

Northbridge Asset Management uses equity-index derivatives for tactical positioning and risk control. Maya Ortiz, a derivatives analyst, is asked to review several proposed transactions. All contracts are assumed free of counterparty default risk, transaction costs, taxes, and bid–ask spreads. Interest rates are deterministic, and the index underlying the contracts generates no income during the relevant periods. Ortiz first estimates the no-arbitrage delivery price on a new six-month equity-index forward. The contract will be initiated at zero value and settled through a single cash payment at maturity. Northbridge can borrow or lend at the annual risk-free rate shown in Exhibit 1, with simple interest applied over fractional years. She then values an existing long equity-index forward that was entered into three months ago. The contract has three months remaining and requires Northbridge to purchase one index unit for the contractual delivery price. A newly initiated three-month forward on the same index has the current delivery price reported in Exhibit 1. Ortiz notes that the difference between the current forward price and the contractual delivery price is payable only at maturity and therefore must be discounted when determining the contract's current value. A junior analyst argues that forward and futures prices must be identical whenever they reference the same underlying asset and have the same maturity. Ortiz responds that futures contracts are marked to market through daily variation margin. Consequently, when interest rates vary unpredictably and futures gains or losses are correlated with rates, the timing of interim cash flows can cause futures and forward prices to differ. Finally, Northbridge wants to reduce the systematic equity exposure of a USD 30 million portfolio without selling its underlying securities. The portfolio manager specifies a target beta of 0.70 and authorizes the use of the equity-index futures contract in Exhibit 1. Each futures contract has an exposure equal to the futures price multiplied by the contract multiplier. Ortiz will determine the signed number of contracts using the change in beta, with a negative result implemented by selling futures. Ortiz separately considers a related but distinct scenario in which the objective is a complete hedge of systematic risk rather than a partial adjustment to the target beta.

Meridian Global Fund is a USD-based investment fund that holds European securities and uses forward and futures contracts to manage currency and commodity exposures. Portfolio manager Elena Morris asks a derivatives analyst to review several proposed transactions using no-arbitrage principles. Unless otherwise stated, transaction costs, bid–ask spreads, taxes, and default risk are ignored. The fund entered a six-month currency forward three months ago. Under the contract, the fund is long EUR5,000,000 and must pay USD1.1200 per EUR at maturity. Morris wants the analyst to determine whether the position currently has positive or negative value. The appropriate valuation method is to compare the contractual delivery price with the current forward price for the remaining three-month term and discount the difference using the USD risk-free rate. All currency rates in Exhibit 1 are quoted as USD per EUR, so EUR is the base currency and USD is the price currency. Morris also advises a US exporter that will receive a fixed EUR amount from a customer in three months. The exporter reports its results in USD and is concerned that EUR may depreciate against USD before payment. The exporter wants to remove the currency uncertainty rather than retain favorable exchange-rate participation and is considering a deliverable forward with a maturity matching the receipt date. For a separate commodity allocation, the fund is considering a one-year forward on a storable investment commodity. The commodity generates no cash income and has no convenience yield. Storage is available at a known fixed cost that is payable only when the forward expires. The analyst is instructed to apply the cost-of-carry model while respecting the actual timing of this storage payment. Finally, the fund uses exchange-traded currency futures for tactical hedges. These contracts are standardized and settled through a clearinghouse. Gains and losses are credited or debited daily through variation margin. Morris notes that daily settlement generally limits the buildup of counterparty credit exposure relative to an otherwise comparable bilateral forward, although adverse daily settlements can create liquidity demands before the hedge reaches its intended horizon.

Bellweather Capital manages a market-neutral portfolio that uses forwards and options to obtain equity exposure without immediately purchasing or selling the underlying shares. The portfolio's derivatives analyst, Maya Singh, is reviewing a one-year forward on a non-index equity. The forward is initiated at market value zero, has no interim settlement, and requires the long party to purchase one share at expiration. The equity is expected to pay a single known cash dividend during the contract's life. All rates in Exhibit 1 are continuously compounded, and there are no transaction costs, taxes, stock-borrowing constraints, or default concerns. Three months after initiation, Singh revalues the existing long forward using the then-current equity price, interest rate, and remaining dividend. The original delivery price remains contractually fixed at USD 102.05. Singh reminds a junior analyst that the current forward price for a new contract is not itself the value of the existing contract. The junior analyst proposes measuring value by taking the difference between the current forward price and the original delivery price without discounting that difference. Singh also examines European call and put options written on the same equity. The options have identical exercise prices and expiration dates. The option data in Exhibit 1 satisfy put–call parity at initiation. Singh considers using combinations of the options to produce linear exposure to the equity's terminal price without an initial investment in the underlying equity. She specifies that the desired synthetic position must have the same terminal payoff as a long forward, including losses when the terminal equity price is below the delivery price. Finally, Bellweather's risk committee is considering replacing some customized bilateral forwards with exchange-traded, centrally cleared futures. The committee expects central clearing and daily marking to market to affect both counterparty risk and liquidity management. Bellweather maintains sufficient unencumbered cash, but the committee recognizes that adverse daily price movements could create variation-margin calls before the ultimate hedge benefit is realized. The committee does not assume that central clearing eliminates every form of derivatives risk.

A portfolio manager replaces a customized bilateral forward with a standardized exchange-traded futures contract on the same underlying. Central clearing most directly reduces:

A share is priced at USD 60.00, the present value of dividends over nine months is USD 1.50, and the effective annual risk-free rate is 6%. The calculated value of the nine-month forward price is closest to:

A treasurer enters a customized OTC contract requiring both parties to exchange currencies at a specified future date. The contract is best described as: