The forward contract is the most basic form of derivative. It is an agreement between two parties (the “counterparties”) to make a trade at some future date. One party is S, the seller who agrees to deliver the underlying. The other party is B, the buyer, who agrees to take delivery of the underlying. The seller is also called “short” the contract and the buyer is “long” the contract. The agreement is binding on both parties since a contract is drawn up and executed upon entering the contract. Forward contracts are traded over the counter. The counterparties determine the nature and quality of the asset to be delivered, when delivery will take place (the expiration date of the forward), where delivery will take place and how pricing will be carried out. The OTC contract is custom-tailored to meet the needs of the counterparties.
Forward contracts enable market participants such as farmers to hedge their price risk. If a farmer has corn in the ground in May that he anticipates selling next July, he may worry that the price will fall before he can get the corn to the market. To hedge away this undesirable price risk, he can arrange to lock in a forward price today. The forward price he locks in may or may not be the price that actually prevails in July, but he has locked in a guaranteed price. On the other hand, the counterparty is speculating that the ultimate price for corn in July will be higher than the contracted price. The counterparty does not own the asset and so is not subject to the same price risk as the farmer. The forward contract establishes a shifting of price risk from the farmer, who does not wish to bear it, to the speculator, who does wish to take this risk on.
Entering a forward contract can help the farmer eliminate the unknown, but will not guarantee a profit. Because a forward contract is essentially a private transaction between two individuals, the creditworthiness of each party is a big factor. A forward transaction is a zero-sum game: one party’s loss is the other’s gain, so if the losing party decides to default on the contract, the other party is subject to loss. Usually, the contracts are non-transferable, which greatly reduces liquidity. No money changes hands at contract initiation. The payoff occurs only at expiration.
An example of such a contract is when you sell an item on eBay. If someone bids on the item, assuming they have met all of the conditions you have set (such as reserve price), you are bound to deliver the item at the end of the auction, and they are bound to pay for it at the ending price. The “contract” specifies what will be delivered, where it will be delivered and how delivery is to take place, in addition to how payment should be made. In a way, the buyer is agreeing on a forward price for your item. If the buyer defaults, you have some recourse through eBay, and if you default by refusing to deliver the item, the buyer can get recourse through eBay. The items are unique so that if you change your mind, the buyer can’t go to another seller to get the identical item at the identical price. And if the buyer changes their mind, you can’t easily transfer their contract to another. (You could contact the next bidder on the list, but probably wouldn’t get as high a price.)
An example of short selling is if you decide to sell books on Amazon.com. Suppose that you notice that a particular Adobe Photoshop book is selling on the site for $31. You decide to offer one for sale at $29 even though you don’t own the book, because coincidentally, you recently saw a street vendor selling the books for $20. If you sell the book, you plan to get one from the street vendor to deliver. In theory, this is a smart strategy because the vendor has to hold the inventory, and you get cash first to purchase the asset. In practice, though, what if the street vendor is not there on the day you wish to purchase the book? Or the vendor raises the price on the book? Or, even, is out of the book? You still have to deliver the book and thus will have to go to a bookstore to purchase it, possibly just breaking even, or even suffering a loss. Forwards are traded on a diverse array of underlying assets including financial assets such as stocks, stock indices, interest rates and currencies; grains and oils including coconut, corn and soybean oil;
Valuing forward contracts
Suppose the spot price (the present price in the market) of corn today is $1.82 per bushel and Mr. McDonald the farmer can lock in a July forward price of $2.05 per bushel. Entering into the contract, the farmer is guaranteed -- no matter what -- a price of $2.05 per bushel in July, say, after he harvests his corn. (The contract size for corn is 5,000 bushels.) If the July spot price turns out to be $2.50 per bushel, the farmer will be disappointed, because he could have received $2.50 per bushel but has agreed to accept $2.05. Locking into this forward price causes him to lose out on the potential excess profit over the forward price (per contract size) of $(2.50 – 2.05)*5,000 = $2,250. He will, though, have the $2.05*5,000 = $10,250 per contract size realized from the sale of his corn. (This is the meaning of the statement, “Forward contracts don’t guarantee a profit; they just guarantee a price.”)
On the other hand, what if corn prices fall to $1.70/bushel by July? The farmer gets a bad price for his corn, $1.70*5,000 = $8,500 but has a gain from his forward position of $(2.05-1.7)*5,000 =$1,750. Total value of his portfolio of corn and forward contract is $10,250. Either way, he has received a net per-bushel price of $2.05, as guaranteed by the forward contract.
Is there a link between the forward price and the spot price? Market participants will want to understand this relationship so they can decide whether to enter into a forward contract.
Because the forward contract is derived from an underlying asset, it can be priced by appealing to the no- arbitrage agreement. We classify our underlying assets as those that can be stored, those that cannot be stored, and those that make cash payments such as coupons and dividend payments. Define spot price as the current price of the underlying. What is the relationship of the forward price to the underlying spot price?
t = time 0 ≤ t ≤ T
T = expiration or maturity date of contract St = spot price of underlying at time t
Ft,T = forward price at time t for maturity T
r = risk-free interest rate
We can use no-arbitrage arguments to form a relationship between St and Ft,T. Suppose that an arbitrageur
(“arb” for short) can take either side of the contract. The arb (say, a large investment bank) can borrow and
lend money at the risk-free rate r and has no transaction costs. The spot price of the asset today is St. The
arb’s counterparty (a grain elevator, say) quotes a forward price Ft,T. If the arb thinks that the forward price
is too low, that is, the arb believes the actual spot price in July will be higher than Ft,T, how could the arb
profit? (This type of question is always answered by remembering the mantra, “Buy low, sell high.”) The
arb could short 5,000 bushels of corn in the spot market today receiving St, and take the income and put it
in the bank, earning a rate r for the period. At the same time, the arb goes long on one forward corn contract, agreeing to purchase the corn in July for Ft,T. Let’s make a chart of the arb’s cash flows.
Comments
Transaction t T
Sell corn in spot market St -ST purchase spot for delivery
Invest proceeds in bank -St er(T-t)St interest on deposity
Long forward contract 0 ST - Ft,T profit/(loss) on forward leg of transaction
Total 0 -Ft,T+er(T-t)St
time
The above shows that we require the following relationship to hold:
Ft,T = Ster(T-t)
It doesn’t matter what the ultimate spot price at maturity (ST) is: the arb is hedged no matter what. This
parity relationship must hold in order to preclude any arbitrage. Although the spot and forward price will vary over time, at maturity, they must converge.
Now what if the arb anticipates that the ultimate spot price will be lower than the forward price? How can the arb profit in this case? The answer is to execute a cash and carry arbitrage.
As a numerical example, suppose that the risk-free rate is 5% and time to expiry (time to expiration date)
is one year. The current spot and forward prices are S0 = $1.985/bushel, F0,1 = $2.34/bushel. The arb sees
an arbitrage opportunity when comparing the current futures price F0,1 with the expected spot S0e0.05(1-0).
Since S0e0.05(1-0) = $1.985 e0.05(1-0) =$2.0868 < F0,1 = $2.34, profit could be made by entering into a forward
agreement to deliver corn in one year at the forward price of $2.34/bushel. In order to be hedged, the arb
borrows money at the rate r to finance the purchase of corn in the spot market at S0. This corn will be sold
at maturity for price ST. The chart of the arb’s cash flows appears below.
Comments
Transaction t T
Buy corn in spot market -St ST purchase spot for delivery
Borrow money at rate r St -er(T-t)St for purchase of spot, has to be paid back at T
Short forward contract 0 Ft,T-ST profit/(loss) on forward leg of transaction
Total 0 Ft,T-er(T-t)St
Cash and Carry Arbitrage time
t=0 t=T
Spot St
Settlement of contract
At maturity, the contract is usually settled by delivery of the agreed upon underlying, if the underlying is some physical asset such as corn, oil or gold. For financial assets such as an exchange rate or forward on the S&P 500, it is not feasible to deliver the actual index, so such contracts are settled in cash. This will be discussed further in the section on futures.
Payoff graphs
Ignoring any transactions costs, let’s examine the profit and loss for the corn contract with a July strike of $2.05.
The payoff received will be ST – K. This idea and payoff diagram are important because they will be built
upon to develop more complex derivatives.
Valuing forward contracts with additional cash flows
The formula developed to price forward contracts Ft,T = Ster(T-t) can be extended to include contracts on
underlyings that involve storage costs, require insurance, or pay dividends. The combination of all costs (storage, insurance, etc.) is called the cost of carry.
For example, if you sell a forward contract to deliver 100 ounces of gold three months from now, you will have to store the gold until delivery. The contract specifications will probably require insurance as well. If
s is the total annual cost to store the gold, we can create a cash flow table just as we did before to develop
the theoretical price of the forward. You will purchase gold at current spot price St by borrowing money at
the rate r, as before, but this time you will also need to borrow enough to finance the annualized cost of carry s.