Futures and Forwards
Futures and forwards both lock in a price today for settlement or delivery later. The exam tests contract mechanics, margining, fair-value pricing and the basis relationships that show whether a hedge is working.
Contract mechanics
- A futures specification fixes the underlying, contract size, quotation and tick value, delivery month, last trading day and cash or physical settlement.
- Futures are marked to market daily: initial margin is posted at trade, variation margin settles the daily gain or loss, and a maintenance margin breach triggers a top-up.
- Forwards are OTC, bespoke in size and date, settled once at maturity, exposed to bilateral credit risk and typically collateralised under a CSA. They have no active secondary market.
Pricing and basis
Fair forward value is F = S₀ × e^(r − q + c)T, where q is the income yield and c is storage cost net of convenience yield. Basis = spot − futures and converges to zero at expiry. Futures above spot indicate contango; below spot, backwardation.
Worked example
An index stands at 5,000, the risk-free rate is 4%, the dividend yield is 1% and expiry is six months away. F = 5,000 × e^((0.04 − 0.01) × 0.5) = 5,000 × e^0.015 = 5,075.6. If the future trades at 5,100, it is 24.4 points rich: sell the future, buy the index basket financed at 4%, and hold to expiry to capture convergence, ignoring costs. If the dividend yield were 2%, fair value would fall to 5,000 × e^0.01 = 5,050.3.
Hedging and roll
A short hedger sells futures to protect inventory; a long hedger buys to fix an input cost. Positions are closed by an offsetting trade or rolled: close the near contract and open the next. Roll yield depends on curve shape and is positive for a long position in backwardation.
Marks-losing traps
- Adding dividend yield instead of subtracting it.
- Mixing simple and continuous compounding in one calculation.
- Forgetting convergence: futures do not stay at a fixed premium to a moving spot.
- Treating the futures price as a forecast of spot.
- Treating initial margin as a cost rather than returnable collateral.