WARNING: CONTAINS MATHS
In financial markets a forward is a type of binding contract in which two parties will agree to the price and quality of an asset to be delivered to a defined place at a given date and time. Payment, for this price agreed to within the contract, is due upon delivery at the expiration, or maturity, of the contract. All forwards are a type of future contract, although not all futures are forwards. A forward may be entered by either party for the purposes of managing risk, reducing costs, or to speculate on the asset (be it a stock, commodity, or currency). A forward may be signed in person, purchased from a financial institution, or purchased from an exchange.
Why would a party take a position on a forward? Simply: for profit. Because both parties are "gambling" on the outcome of the asset (at the expiration of the contract, will the current spot price be greater than, less than, or equal to the future price agreed to in the past. If the spot price at expiration (or time=T) is greater than the price in the contract, then the buyer, who owns the long position on the forward, has won a positive cashflow as their payoff. Since there are no other costs with this type of contract, the profit is equal to the payoff. If the spot price at t=T is less than the price in the contract, then the seller, who owns the short position on the forward, has won a positive cashflow as their payoff. This payoff is equal to the seller's profit. A forward is a zero sum game: whatever the buyer gains is lost by the seller, and vice-versa.
t = time, generally noted in years, or fractions thereof
F0 = Value of asset at t=T, agreed upon at t=0
Q = Quantity of asset to be delivered at t=T, agreed to at t=0
S0 = Price of the asset at t=0
St = Price of the asset at t=t
| Forward Position |
Payoff |
Profit |
| Long |
(St - F0) * Q |
(St - F0) * Q |
| Short |
(F0 - St) * Q |
(F0 - St) * Q |
We now know why a forward contract is written (each party is trying to make a profit), and to what extent they will be successful on the execution date (the payoff/profit table above). The final mystery to answer concerns the setting of the future price. To answer this, we must return to the first definition of a forward: we wish to assign a price today to an asset which will be delivered and paid for at the expiration of the contract, say in one year's time. This price, referred to as F0 is NOT an evaluation nor speculation on what the spot price of the asset will be at the expiration of the contract, such math is included in the current spot price of the asset! Keeping this in mind, we find that we are simply trying to perform a financial valuation on the asset, as available today, if paid for at the expiration of the contract. Most notably, the valuation is calculated under an assumption of no arbitrage, or more plainly, the valuation is calculated as such that any profit gained by the long or short position will be due to the change in value over time by the asset itself, and no other financial engineering of the other variables.
t = time, generally noted in years, or fractions thereof
F0 = Value of asset at t=T, agreed upon at t=0
S0 = Price of the asset at t=0
e = The natural number, e
r = The interest rate for the contract period specified at t=0
s = The cost of storage, expressed as a percentage of the S0 at t=0
c = The convienience factor, economized, expressed as a percentage of the S0 at t=0
d = Any dividend, or leasing rate, expressed as a percentage of the S0 at t=0
| Forward Position |
Valuation of F0 |
| Long and Short |
F0 = S0 * e(r + s + c - d)*t |