Forward Contracts and Futures: Basics for Exam FM

Forward Contracts

A forward contract is an agreement to buy or sell an asset at a specified future date for a price agreed upon today (the forward price). No money changes hands at inception. At maturity, the buyer pays the forward price F and receives the asset. The payoff to the long position is S_T - F, where S_T is the spot price at maturity. The payoff to the short position is F - S_T.

The forward price for a non-dividend-paying asset is F = S_0 * (1+i)^T, where S_0 is the current spot price and i is the risk-free rate. This ensures no arbitrage.

Forward Price with Income

If the underlying asset pays dividends or provides income, the forward price is reduced. For discrete dividends with present value D: F = (S_0 - D) * (1+i)^T. For continuous dividend yield delta: F = S_0 * e^((r - delta)*T) in continuous compounding notation, or F = S_0 * ((1+i)/(1+delta))^T in discrete notation.

On Exam FM, the most common setup involves stocks with known dividends or continuous dividend yields.

Futures vs. Forwards

Futures contracts are standardized and traded on exchanges, while forwards are customized over-the-counter agreements. Futures are marked to market daily, meaning gains and losses are settled each day. This daily settlement introduces reinvestment considerations. However, for Exam FM purposes, the key pricing relationships are the same. The no-arbitrage forward price formula is the central result. Exam FM problems typically ask you to compute the forward price, determine the profit from a forward position, or construct arbitrage strategies when the market price deviates from the theoretical forward price.