Estimated study time: 45 minutes
Content:
A forward contract is a private, customized agreement between two parties to buy or sell an asset at a specified future date (delivery date) at a price agreed upon today (the forward price). The party obligated to buy the asset holds the long position; the party obligated to sell holds the short position. Forward contracts are OTC (over-the-counter) instruments: flexible, customized, but carrying counterparty risk (the risk that the other party defaults before settlement). At expiration, the payoff to the long is: ST – F0, where ST is the spot price at expiration and F0 is the forward price agreed at initiation. If the underlying's price has risen above F0, the long profits; if below F0, the short profits. No cash is exchanged at initiation — the contract has zero value initially.
The no-arbitrage forward price for an asset with no income and no storage costs is: F0 = S0 × (1 + r)^T, where S0 is the current spot price, r is the risk-free rate, and T is the time to expiration in years. This formula reflects the cost of carry: the forward price must equal what it would cost to buy and hold the asset today until delivery. If F0 > S0 × (1 + r)^T, arbitrageurs sell the forward and buy the asset (financing at r), locking in a riskless profit. For assets with continuous income yield (dividends or foreign interest), the forward price is: F0 = S0 × e^((r–q)T) in continuous compounding notation. For commodity forwards, storage costs and convenience yield affect pricing: F0 = S0 × e^((r + storage cost – convenience yield)T). These formulas are applications of the cost of carry model.
Futures contracts are exchange-traded forward contracts with standardized terms: the underlying asset, contract size, delivery date, and settlement procedure are specified by the exchange. Futures are marked to market daily — gains and losses are settled in cash through a margin account at the end of each trading day. Initial margin must be deposited when entering a futures position; if the account falls below the maintenance margin, a margin call requires a deposit to restore the account to initial margin. Daily marking to market virtually eliminates counterparty risk (unlike OTC forwards) because losses are collected daily before they can accumulate into large defaults. Exchange clearinghouses serve as central counterparties for all futures contracts.
Futures prices and expected future spot prices are related through the concept of basis: basis = spot price – futures price. As delivery approaches, the basis converges to zero (the basis narrows to zero at expiration). The difference between forward and futures prices arises from the daily marking to market: if an asset's price is positively correlated with interest rates, futures prices will be slightly lower than forward prices (because futures gains are reinvested at higher rates when the asset performs well, but this effect is washed out for most non-interest-rate assets). For interest rate futures (like Eurodollar or Treasury futures), the relationship between futures prices and interest rates is explicitly inverted: when rates rise, bond prices (and Treasury futures prices) fall.
Key Terms:
Quiz Questions:
Q1. The spot price of crude oil is $80 per barrel. The risk-free rate is 5% per year. Storage costs are $2 per barrel per year. What is the fair value 1-year forward price?
A) $80.00 B) $86.00 C) $84.00 D) $82.00
Answer: B — F0 = S0 × (1 + r) + Storage = $80 × 1.05 + $2 = $84 + $2 = $86. The forward price must equal the spot price plus all carry costs. If F0 > $86, arbitrageurs could buy oil at spot and sell forward, earning a riskless profit above borrowing costs and storage. If F0 < $86, they sell spot and buy forward, again locking in riskless profit.
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Q2. An investor enters a long position in a forward contract to buy 1,000 shares of stock at $50 per share in 6 months. At expiration, the stock price is $58. What is the investor's profit/loss on the forward contract?
A) Loss of $8,000 B) Profit of $8,000 C) Profit of $50,000 D) No profit or loss, since forward contracts are cash-settled
Answer: B — Payoff to long = (ST – F0) × quantity = ($58 – $50) × 1,000 = $8 × 1,000 = $8,000 profit. The long benefits when the underlying price rises above the forward price. If the price had fallen to $42, the long would suffer a $8,000 loss. Forward contracts create linear, symmetric exposure — equal magnitude gain/loss for equal magnitude price moves.
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Q3. A futures trader holds a long position in 10 gold futures contracts (each contract = 100 troy ounces). The initial margin is $5,000 per contract and the maintenance margin is $3,500 per contract. If gold futures fall by $20 per ounce in one day, what happens?
A) The trader loses $20,000 and receives a margin call if account value falls below $35,000 B) The trader gains $20,000 since gold fell in price C) No margin call is possible on the first day of trading D) The trader's loss is limited to the initial margin of $50,000
Answer: A — Daily loss = $20/oz × 100 oz/contract × 10 contracts = $20,000. Initial margin = $5,000 × 10 = $50,000. After loss: account value = $50,000 – $20,000 = $30,000. Maintenance margin = $3,500 × 10 = $35,000. Since $30,000 < $35,000, the trader receives a margin call requiring the account to be restored to initial margin ($50,000) — requiring a deposit of $20,000.
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Q4. Which of the following is a key advantage of futures contracts over forward contracts?
A) Futures contracts can be customized to any size, date, or underlying asset B) Futures contracts virtually eliminate counterparty risk through daily marking to market and exchange clearing C) Futures contracts require no collateral, making them cheaper to initiate D) Futures contracts can be exercised early, before the expiration date
Answer: B — Futures contracts virtually eliminate counterparty risk because gains and losses are settled daily through a central clearinghouse. Even if one party to a futures contract defaults, the maximum loss is one day's price movement (the margin between daily settlements). Forward contracts lack this protection — if a counterparty defaults just before a large settlement date, the loss can be enormous. The tradeoff is that futures are less customizable than OTC forwards.
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Q5. The current S&P 500 index level is 5,000. The 1-year risk-free rate is 5% and the dividend yield on the index is 1.5%. Using the no-arbitrage cost of carry model, what is the fair value of the 1-year S&P 500 futures contract?
A) 5,250 B) 5,175 C) 5,325 D) 5,000
Answer: B — F0 = S0 × (1 + r – q) = 5,000 × (1 + 0.05 – 0.015) = 5,000 × 1.035 = 5,175. The dividend yield (q) reduces the forward price below what it would be for a non-dividend-paying asset, because futures buyers do not receive dividends during the life of the contract — the spot price embeds the present value of upcoming dividends, which are "extracted" and must be subtracted from the financing cost.
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