Forward Contracts

A forward contract is a handshake made today about a trade that happens later: you and I agree now that in six months I'll buy your barrel of oil for exactly $80, whatever the market price turns out to be that day. No money changes hands up front. We've simply locked the price. That's the whole idea, and it's the simplest derivative there is, every futures contract, swap, and option builds on top of it.

The everyday version is a farmer and a bread maker. The farmer worries wheat prices will fall before harvest; the baker worries they'll rise. They agree on a price now, and both stop worrying. Notice the key difference from an option: both sides are obligated. There's no "right, but not the obligation" here. When the delivery date comes, the trade happens no matter what, so unlike an option there's no premium to pay for the privilege.

The payoff

Call the agreed price the delivery price $K$, and let $S_T$ be the market price of the underlying on the delivery date. If you're the buyer (the "long" side), your payoff is

$$\text{long forward payoff} = S_T - K.$$

In words: you're contracted to pay $K$ for something now worth $S_T$, so you gain whenever the market ends up above the price you locked. If it ends below, you overpaid and you lose, dollar for dollar. The seller (the "short") gets the exact mirror, $K - S_T$. There's no floor and no cap on either side, which is what makes the line straight.

What's the fair delivery price?

Here's the clever part. Even though no one knows where the price will end up, the fair delivery price is pinned down exactly, and the forecast doesn't enter at all. For an asset that costs nothing to store and pays no income, the fair forward price is just today's spot price grown at the risk-free rate:

$$F_0 = S_0\, e^{rT}.$$

Here $S_0$ is today's spot price, $r$ is the risk-free interest rate, and $T$ is the time to delivery. The logic is cash and carry: instead of agreeing to buy later, I could borrow $S_0$ today, buy the asset now, and hold it. At delivery I'd owe $S_0 e^{rT}$ on the loan and I'd have the asset. Since that reproduces the forward exactly, the forward must cost the same, or there's free money. This is the cost of carry idea, and it's why the forward price sits above spot when rates are positive. (If the asset pays income like a dividend or coupon $y$, that income offsets the carry, so $F_0 = S_0 e^{(r-y)T}$.)

Worked example

Gold trades at $S_0 = 2000$ per ounce, the one-year rate is $r = 5\%$, and delivery is in $T = 1$ year. The fair forward price is

$$F_0 = 2000 \times e^{0.05} = 2000 \times 1.0513 = 2102.6.$$

So a fair one-year forward locks in about $2,103. Suppose a dealer instead quotes a forward at $2,150. That's $47 too rich. You sell the forward at $2,150, borrow $2,000 today at 5%, and buy the ounce. In a year you deliver the gold, collect $2,150, repay $2000 e^{0.05} = 2102.6$ on the loan, and pocket $2150 - 2102.6 = 47.4$ with no market risk.

Now the payoff side. You entered a long forward at $K = 2103$. If gold ends the year at $S_T = 2300$, you gain $2300 - 2103 = 197$ per ounce. If it ends at $S_T = 1900$, you're contractually forced to pay $2,103 for something worth $1,900, a loss of $203. Same size swings both ways, that's the straight-line payoff.

Where it misleads

• The forward price is not a forecast. $F_0 = S_0 e^{rT}$ comes from arbitrage, not from anyone's view of where the price is headed. It's not the market's "expected" future spot; it's just spot plus carry.
• Both sides are locked in. A forward has no walk-away option. If the market moves hard against you, you can't just abandon it like an out-of-the-money option, you owe the full loss.
• Counterparty risk is real. Forwards are private (over-the-counter) deals. If the far side goes bust before delivery, your hedge evaporates. This single weakness is the reason exchanges invented futures, which settle up daily to keep credit risk tiny.
• Carry can flip the sign. For assets with high storage cost or big income yields, the forward can sit below spot. Always fold storage, dividends, and convenience yield into $r$ before assuming the forward is above spot.

Forwards are the atom of derivatives. Chain a series of them together on interest payments and you get an interest rate swap; standardise and exchange-trade one and you get a future; and the combination of a call minus a put reduces to a forward, which is exactly what Put-Call Parity says.