Forwards

What are Forwards?

A forward is a general term that describes a contract (i.e. a derivative) where one party buys and another one sells a fixed quantity of a specific asset at a price fixed today for delivery and payment at a future date. The party to the contract that agrees to buy is called the long side of the contract while the seller is short. A future is a standardized forward contract.

Basic Pricing of Forwards

As a forward is an agreement, it is a derivative instrument. When the trade is agreed upon, this derivative, unlike an option, has no value to either the long or the short. However, if the underlier is moving up, the long will benefit and the short will lose and vice versa.

Because there is no value in the contract at the time of trade there can be no gain or loss made by either party just by entering the trade. Therefore, the agreed price must be such that the above conditions are fulfilled. This is known as an arbitrage free price. To see what this arbitrage free price might be, let us consider the following equity forward:

A trader has sold a stock forward (i.e. is short), for delivery in one year. The trader borrows USD100 to buy a share for USD100 and holds it until delivery. Interest on the borrowed money is USD5 (5%) and the stock pays a dividend in one year of USD2 (for simplicity let us assume the dividend is paid just before expiry of the contract).

In one year, the investor will collect the agreed forward price from the long, pay the interest (USD5 outflow) and loan (USD100 outflow) and receive the dividend (USD2 onflow). The net of these transactions is an outflow of USD103. This means that the minimum agreed forward price at the time of trade must be 103. Else there would be an immediate gain or loss to the seller.

The above describes the general idea of an arbitrage free price for forwards and futures. It can also be described with the following formula:

Fair forward/futures price = Spot price (USD100) – Dividends (USD2) + Interest Cost (USD5) = USD103

At delivery, the stock price might well have changed, which creates a gain for the long if the stock is up and a gain for the short if the stock is down. In other words, the long will benefit price increases from when the trade was agreed. However, and this is important, unlike a cash buyer, the forward long does not benefit from dividend payments before delivery, on the contrary, dividend payments bring the value of the share down. In other words, the long gets the price return on the stock, not the total return.

Described differently, buying a stock under a forward agreement is like borrowing money to get exposed to the price appreciation of the stock. Buying a future is therefore a way to create leverage on your investment.

The pricing example above is simplified. In reality, the timing of a dividend will matter, the size of the dividend might be unknown or uncertain and the funding costs (interest) might differ between market participants.