A forward contract is an agreement between two parties to buy or sell a given quantity of an asset for an agreed upon price (delivery price) and date in the future. As discussed in the introduction blog, a forward contract allows the future price of an asset to be locked in. This removes the uncertainty regarding the future asset price for a party that is looking to mitigate the risk associated with the asset price.
The counter party that is buying the asset in the forward contract is said to have long forward position, whereas the counter party that is selling the asset is said to have short forward position. The counter party that is long, hopes that the price of the asset goes up. The value of the contract for long position at any point in time is the difference between the spot (current market price of the asset) and forward price of the asset. On the other hand, the counter party with short forward position (selling counter party in the contract) hopes that the asset price goes down. For short counter party, the value of the contract is positive if the selling price (forward price) is higher than the spot price.
Regardless of being long or short, holding a forward contract position implies that a party is either making money on the contract or is loosing money. This is due to the fact that the current asset price (also known as the spot price) fluctuates, whereas the delivery price of the contract remains fixed. If a party is long on the forward contract (i.e. is buying the underlying asset), then an increase in the spot price would result in positive P&L for the party. The positive P&L is derived from the fact that the forward contract enables the contract holder to buy the asset at a price that is lower than the spot price. This of course is based on the current spot price, that may be different at the time of delivery. Every time the spot price changes, the value of the contract changes as well. A contract holder of a contract with positive value does not have to hold the contract until the delivery date and can also sell the contract in the market locking in the profit.
The P&L profile of a forward contract is linear with respect to the underlying asset. This means that one dollar change in the underlying asset would change the value of the contract by one dollar (either plus $1 or minus $1 depending on the contract position and the asset price change).
P&L profile for a long forward position (a $20 increase in underlying asset increases the value of the contract by $20, and vice-versa):
P&L profile for a short forward position (a $20 increase in the asset decreases the value of the contract by $20, and vice-versa):
For short forward position (selling of the underlying), an increase in the underlying asset price means that the party will have to sell the asset at a lower price (delivery price) compared to the spot. Hence the negative correlation between the asset price and P&L.
A forward contract is an example of a linear contract. As the name suggests, the value of the contract is linearly related to the underlying asset. One unit change in the underlying asset price changes the value of the contract by the same amount. Most derivative contracts are non-linear and a unit change in the price of the underlying asset is not matched by a unit change in the value of the contract. Options are one example of non-linear contracts.
Valuation of forward contracts