Forwards: Obligation, Payoff, Price
A forward contractIn finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into.Read on Wikipedia → is an agreement to buy or sell something on a future date at a price fixed today. Both parties must complete the trade, even if the market price later makes the agreement unattractive to one of them.
This differs from a spot tradeIn finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement on the spot date, which is normally two business days after the trade date. The settlement price is called spot price. A spot contract is in contrast with a forward contract or futures contract where contract terms are agreed now but delivery and payment will occur at a future date.Read on Wikipedia →, where delivery and payment happen soon after the agreement. Forwards are arranged in the over-the-counter (OTCOver-the-counter (OTC) or off-exchange trading or pink sheet trading is done directly between two parties, without the supervision of an exchange. It is contrasted with exchange trading, which occurs via exchanges. A stock exchange has the benefit of facilitating liquidity, providing transparency, and maintaining the current market price. In an OTC trade, the price is not necessarily publicly disclosed.Read on Wikipedia →) market, where the parties can agree on an amount and date that suit them.
Agreeing on the cost of a currency payment
Suppose a US company must pay £1 million in six months. It earns dollars, so it needs to know how many dollars that payment will require.
In Hull’s historical example, dated 21 May 2020, a bank offers to sell pounds six months forward at $1.2230 per pound. The company accepts and fixes the dollar payment:
£1,000,000 × $1.2230 per pound = $1,223,000The company has a long forward positionIn finance, a long position in a financial instrument means the holder of the position owns a positive amount of the instrument. The holder of the position has the expectation that the financial instrument will increase in value. This is known as a bullish position. The term "long position" is often used in context of buying options contracts.Read on Wikipedia →: it has agreed to buy the pounds. The bank has the short positionIn finance, a position is the amount of a particular security, commodity or currency held or owned by a person or entity.Read on Wikipedia →: it has agreed to sell them. The agreed rate is the delivery price, and the six-month payment date is the contract’s maturityIn finance, maturity or maturity date is the date on which the final payment is due on a loan or other financial instrument, such as a bond or term deposit, at which point the principal is due to be paid.Read on Wikipedia →.
If pounds become more expensive, the company benefits from its fixed rate. If they become cheaper, it must still buy at that rate.
| Market rate in six months | Cost without the forward | Cost under the forward | Result of the long forward |
|---|---|---|---|
| $1.3000 per pound | $1,300,000 | $1,223,000 | +$77,000 |
| $1.2000 per pound | $1,200,000 | $1,223,000 | −$23,000 |
The second outcome does not mean the contract failed to protect the company. It fixed the bill at $1,223,000. The $23,000 loss measures how much more the company pays than it would at the lower market rate. Predictability means giving up that possible saving as well as avoiding a possible increase.
Calculating the contract’s result
Let K be the agreed delivery price and S_T the market price when the
contract ends. For one unit of the asset:
Long forward payoff = S_T − K
Short forward payoff = K − S_TMultiply by the number of units for the whole position. The payoffIn finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into.Read on Wikipedia → is the contract’s result at maturity, measured against the market price. Before costs, one side’s gain is the other’s loss.
For a contract settled by delivery, the company pays the agreed amount and receives the pounds. The calculated payoff need not arrive as a separate payment. It expresses the benefit or cost of that exchange relative to the market.
An ordinary forward agreed at the current market rate usually has no initial purchase price. This does not mean trading is free or that losses are impossible. Fees, the bank’s buying and selling prices, and any collateralIn lending agreements, collateral is a borrower's pledge of specific property to a lender, to secure repayment of a loan. The collateral serves as a lender's protection against a borrower's default and so can be used to offset the loan if the borrower fails to pay the principal and interest satisfactorily under the terms of the lending agreement.Read on Wikipedia → requirements still matter.
What connects a forward price to today’s price
A forward price is not simply a prediction of the future market price. The cost of buying and financing the asset can constrain it.
Consider a separate pricing example from the chapter. A share costs $60, pays no dividends, and can be financed for one year at 5%. Assume there are no trading costs and the required trades are available. Buying the share with borrowed money produces a debt of $63 after a year.
If someone offers to buy it forward for $67, a trader can borrow $60, buy the share, and agree to sell it for $67 in a year. Delivery provides $67; repaying the debt costs $63. The remaining $4 is fixed by those agreements.
If the forward price is $58, an existing shareholder can sell the share for $60, invest that money at 5%, and agree to buy the share back for $58. A year later, the investment provides $63, leaving the shareholder with the share and $5 more than simply holding it would have produced.
These opportunities explain why the fair price in this simplified example is $63. Different assets involve different financing, income, or storage costs, so the calculation does not apply unchanged to every forward.
The market price for a new forward can change. The delivery price in an existing contract stays fixed, which is why that contract can gain or lose value after it is agreed.
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