Futures and forward contracts
Domain focus
This domain tests forward and futures pricing, convergence, margin mechanics and delivery. You should be able to compute a fair forward price with carry costs or income, explain marking to market, and distinguish initial from variation margin.
Core rules
- Fair forward price for an investment asset with no income: F0 = S0(1 + rT) using simple rates, or S0e^{rT} with continuous compounding. With income or storage: F0 = (S0 − PV(income) + PV(storage))(1 + rT).
- At expiry, futures and forwards converge to spot; otherwise cash-and-carry arbitrage exists.
- Futures are marked to market daily. Initial margin is collateral posted at inception; variation margin settles daily gains/losses. Maintenance margin triggers a top-up.
- Contango: futures price above spot, often due to carry. Backwardation: futures below spot, often due to convenience yield or shortage.
- Delivery may be physical or cash-settled. Futures are standardised and usually closed out before delivery; forwards are private contracts.
Worked example
Spot gold is $1,900/oz. Six-month simple rate is 5% p.a. Storage costs $12/oz payable at maturity. Fair six-month futures = S0(1 + rT) + storage = 1,900(1 + 0.05 × 0.5) + 12 = 1,900 × 1.025 + 12 = 1,947.50 + 12 = $1,959.50. If the futures price is $1,975, arbitrage: borrow $1,900, buy spot, store, sell futures. At expiry repay 1,947.50, pay storage 12, deliver gold, receive 1,975, profit $15.50 per oz before transaction costs.
Traps that cost marks
- Applying an annual rate without prorating for the contract period.
- Forgetting storage costs, dividends or convenience yield.
- Confusing initial margin with variation margin, or assuming margin is a cost rather than collateral.
- Assuming the futures price is a forecast of spot; it is a carry-based price.
- Ignoring daily settlement funding risk and margin calls.