Currency Futures and Forward Contracts
Although most retail traders involved in forex trading use the spot market, the currency futures market is by far the largest in terms of daily turnover. A futures contract is one of many classes of derivative instruments, which means that its value is tied to or derived from another asset. Because many currency traders use futures contracts, let’s take a closer look at their mechanics.
In simple terms, a futures contract is similar to putting something on layaway. For example, assume you wish to buy a big screen television for your spouse as an anniversary present coming up in three months. You find a great sale on the set you want and wish to buy it. However, there may be very good reasons you do not want to take delivery of it just yet. The first and most common reason is that you may not have the money available today but would like to lock in the sale price. Second, there is obviously a storage problem. It’s not too easy hiding a big screen television in the broom closet for three months. You could rent a storage unit but that adds to the cost and may defeat the sale price altogether.
By using layaway, you have locked in your purchase price, solved the storage problem, and given yourself time to come up with the money. Layaway works by placing a small deposit on the product and agreeing to fully pay for it by some specified date. The store holds the product for you so that you are assured of having it available on that future date. For customers, layaway plans solve the problems of price uncertainty, cash flow, and storage. For the store, layaways are beneficial too because they allow them to lock in future sales today.
If you understand the mechanics of a layaway plan, you have the basic idea of a futures contract. A futures contract is an agreement today to buy or sell something in the future at a predetermined price. Now, some of you familiar with options may think this definition sounds a lot like an option. If you read the definition closely, you’ll see that it is with one exception. If you buy an option, you have the right, not the obligation, to buy or sell an asset in the future. If you buy a futures contract, on the other hand, you have purchased the commodity – you just haven’t taken delivery of it yet. So the main difference between a futures contract and an option is that options provide the right to buy; futures contracts represent an obligation to buy.
If you buy a futures contract, you are “long” the contract and are agreeing to buy some type of commodity. The seller, on the other hand, is “short” the contracts and is agreeing to sell the commodity. Using the layaway plan analogy, if you put something on layaway, you are the “long” position since you will be buying. The store is the “short” position since they are agreeing to sell the item. As with a layaway plan, the buyer deposits a small amount of money as a good faith deposit and agrees to take delivery at the expiration date in the future. Rather than taking delivery today though, each party is agreeing to settle the deal in the future thus creating a futures contract.
However, unlike layaway plans, when you enter into a futures contract you do not necessarily have to take delivery of the commodity. The reason is that you are allowed to sell that contract to someone else. Using our layaway example, assume that you agree to pay $5,000 for the television in three months but shortly thereafter the price shoots up to $6,000. If we also assume that the layaway contract says that it is transferable, you could sell this agreement to somebody else for a fee. Why would somebody buy it? Because the layaway agreement you hold (futures contract) specifies a purchase price of $5,000 but the market price for the set is now $6,000. Anybody in the market for this set would certainly like to have your contract and thus should be willing to pay for it if you put it up for sale. Specifically, buyers should be willing to pay up to $1,000 for the contract since that is how much they will save by using your contract to pay $5,000 rather than the $6,000 current market price. In an active market, your contract would be bid up to a value of $1,000. In fact, most traders who use futures contracts do not ever take delivery of the underlying asset as that is the function of the spot market. Most use futures contracts to hedge future risk or to speculate on future price movement.
When and Why Did Futures Begin Trading?
The earliest futures contract was recorded in 1851, although evidence of forward contracts date back to Biblical times. The roots of the modern day futures contract started in the Midwest in the 1800s. It was there that grain traders faced volatile market conditions, which ultimately led to the creation of a futures exchange.
Chicago, just by coincidence, was strategically located. It was centrally located to the grain farmers and also situated at the base of Lake Michigan – one of the five Great Lakes in North America. Easy access to the Great Lakes made shipping easier and the farmers and grain traders found it convenient to meet in Chicago and exchange commodities through agreements called "to arrive" contracts. In 1848, merchants formed the Chicago Board of Trade (CBOT), the first and still the largest futures exchange in the world today. Today, the CBOT and CME are two of the primary exchanges for many commodity and financial futures.
Although futures contracts may sound intimidating, you’ve probably used many versions of them and been happy with the results. Have you ever purchased a car from a dealer that had to be ordered from the factory? Did you ever sign a contract to purchase a house that wasn't yet built? These examples are, in a sense, nothing more than a futures contract. We agree on the price today but do not pay for it or take delivery until sometime in the future. In most cases, we are required to place a small deposit as a show of good faith, but the real money doesn't change hands until the future date. Magazine subscriptions, C.O.D. packages, and layaways are other forms of "futures" contracts.
Let's take a closer look at the benefits of a futures contract by considering the following example. Assume you want the hottest new convertible car to hit the market but find that your local dealers are sold out. That won't keep a dealer from selling you one though – he can simply enter into a futures contract with you. Although car dealers won't refer to these agreements as futures contracts, that's basically what they are. The salesman may say, "I don't have that car on the lot right now but can order one for you. It will take about three months before we can get it." If you agree, the salesman will require a small deposit, maybe as low as a couple hundred bucks, and have you sign an agreement saying that you will pay the agreed upon purchase price when it arrives in three months. That's essentially a futures contract. You both agreed to buy and sell something today for a predetermined price but will not pay for it and take delivery until a later time.
So while many investors hear that futures contracts are risky that’s really a misconception. They can be used in risky ways but when used to hedge risks they are an invaluable tool. In this example, you wanted the car today but the dealer did not have it. If you wait for three months for the next shipment to arrive, you are running the risk of prices moving higher (after all, the fact that he is sold out suggests that there is excess demand and prices may rise). By signing the contract and placing a small deposit, you are locking in your purchase price and have removed all unwanted risk of higher prices associated with waiting for the new cars to arrive. At the same time, you will not benefit if the car price should fall but that obviously was not a concern of yours, otherwise you would not have signed the contract.
The car dealer, on the other hand, faces the opposite set of risks. The dealer is at risk if prices fall (or that you will go somewhere else to purchase) so wants to guarantee the sale today and lock in his selling price. It is important to understand that the futures contract is made possible because each of you faced opposite risks. You faced the risk of rising prices and the dealer faced the risk of falling prices. Entering into a futures contract with the dealer accomplishes two important things:
For the dealer, the futures contract locked in profits
For you, the futures contract controlled costs
Futures contracts were designed to remove unwanted risks associated with unforeseen future events. They exist for the very reason your car dealer and you are willing to lock in a price today for delivery in the future. If that sounds like a good thing, then maybe futures contracts are not such a bad idea. In fact, as you learn more, you will probably agree that the futures contract is probably the most important and successful financial innovation ever.
On a technical note, futures contracts are exchange traded and are standardized as to the size and quality of the underlying asset. The car example we just gave is really what's called a forward agreement since it is not a standardized contract traded on an exchange; instead, it was a privately negotiated contract by two independent people. The car dealer and you were completely free to set the delivery date, deposit amounts, and other contract specifications, which is a really nice feature about forward agreements. The bad thing about them is they are often illiquid meaning that if you must get out of your contract, you may have to take a substantially reduced price to get someone to buy it from you, assuming the contract is even transferable. With forwards, you're also at risk of default by the other party and you must make sure you're dealing with someone reputable who can "make good" on the contract – especially if it moves against them.
Futures contracts, on the other hand, are cleared through well-capitalized clearing firms so there is no risk of default by the other party. The clearing firm becomes the buyer to every seller and the seller to every buyer. Futures contracts are standardized as to size, quality, delivery dates and all other contract specifications with one exception – price – which is left for the market to decide.
Whether standardization is good or bad is a matter of debate and there are certainly pros and cons to each side. Standardization is good in that it provides a lot of liquidity but not so good in that it creates inflexible terms. You may hear the terms forwards and futures from time to time and just be aware that they are basically the same thing. Futures contracts are just standardized forward contracts. Let's take the next step and see in detail how a futures contract actually works.
Let's continue with our previous example and assume that you signed a contract to buy the car from the dealer for $40,000 in three months. The risk to the car dealer is that the price falls so he is happy to sign the agreement to lock in this price today. While it is possible he could get a higher price in three months, his concern is that he could get less. That’s the risk to the car dealer and he can guard against this risk by having you sign the contract today.
On the other hand, you are willing to buy the car for $40,000 but there are none available until three months from now. If you wait for three months to buy the car, you face the risk of rising prices. The car dealer is interested in guarding against falling prices while you are interested in guarding against rising prices. The car dealer and you are dealing with opposite sets of risks, which means they can both be guarded with the contract buy and sell in three months.
When one guards against risk with financial assets, it is called a hedge. The car dealer needs a hedge against falling prices and you need a hedge against rising prices. A hedge is an asset whose value will move in the opposite direction as that of the asset you're trying to protect. In other words, if the price of the asset you're trying to protect falls, the price of the hedge will rise. An asset used as a hedge is usually not intended to make money but only offset losses. Insurance on your home is a hedge. If you buy insurance, the value of that policy declines as the year goes on assuming you make no claims. However, if you have $20,000 damage from a hurricane, you're policy (your hedge) now pays you $20,000. Notice how you do not profit from the hedge since you lost $20,000 and gained that same amount. Hedges just offset losses. When you signed the contract at the dealer, both of you hedged your respective risks.
Let’s now assume that three months have passed and it is time to make the deal. Prices, however, have risen and the car now sells for $45,000. While the dealer may not be so happy about selling it, he is under contract to do so.
There are a couple of ways you can settle this. One method is straightforward; the dealer can deliver the car to you worth $45,000 and receive a $40,000 check in exchange. If so, the terms of the contract are satisfied and the contract is executed. The car dealer loses a $45,000 car and gains a $40,000 check. You have the opposite set of transactions and gain the car but lose the cash. Table 3-1 shows the effects on each of you if you take delivery of the car:
Table 3-1
That means, had the dealer not entered the contract with you, he could now sell it for the higher $45,000 price, which would net an additional $5,000 to the dealer. Because you entered the contract though, he must make delivery and sell the $45,000 car for $40,000. He will not realize the additional $5,000 of market value. That lost opportunity to the dealer is transferred to you.
Let’s now take a look at another way to settle the contract. To emphasize the point, we’re going to assume that you have moved hundreds of miles away from the car dealership and the identical car is sitting in the showroom at your local dealer. Wouldn’t it be nice to buy the car around the corner from you rather than having to drive hundreds of miles to the original dealership? Of course, the local car carries the $45,000 price tag. However, couldn’t you and the original dealer call it even if he just sent you a check for $5,000? That way you don’t have to drive all the way back to that dealership to get the car. You buy the car locally for $45,000 but receive a check for $5,000 thus effectively paying $40,000 for the car, which is the price you and the dealer agreed upon three months ago.
But why would the dealer want to send a $5,000 check? The answer is that, doing so, he is effectively out of the contract and can now sell the car for the new going price of $45,000. So he makes an additional $5,000 on the car but must send that amount to you, which is a wash. By sending you a $5,000 check, you have effectively let the dealer out of the contract. The point being that it doesn’t make one bit of difference to the dealer. Of course, this assumes that the original dealer has a new buyer ready to buy the car. But in a very liquid market such as with futures contracts, there are always buyers and sellers at every moment.
Table 3-2 shows the effects of this second method of settlement for each of you:
Table 3-2
Notice the bottom lines in Table 3-2. The dealer can effectively sell the car for $40,000 and you can effectively purchase the car for $40,000, which is exactly how you and the dealer wanted to end up three months ago. The futures contract just allowed you to carry out the same transactions more efficiently even though you were separated by hundreds of miles.
Compare Tables 3-1 and 3-2. In Method #1, the net effect was that the dealer lost $5,000 worth of value but in Method #2 he lost $5,000 cash. You received $5,000 worth of value under Method #1 but received that same amount of cash in Method #2. The bottom line is that either method effectively makes your purchase price $40,000 and the sales price received by the dealer also $40,000. Although the dealer never sells the car to you in Method #2, he effectively transfers that value to you in the form of a check.
We have just seen two methods in fulfilling the contract if prices rise. First, we could take actual delivery of the car. Second, we could settle in cash and buy and sell the car in our local markets. Now let's take a look at how we could complete the contract if, instead, prices fell.
Let’s say that after three months the car is, instead, selling for $38,000 rather than $45,000. When the price falls, you are not so interested in completing the contract for $40,000; however, you are under contractual obligation to do so. The first method of settlement is to take delivery and pay $40,000 for a car worth $38,000. If so, the dealer has an effective gain of $2,000 at your expense.
Table 3-3 shows that taking delivery of the car caused the dealer to lose a $38,000 car but gain a $40,000 check, which is the agreed upon price three months ago. This nets a $2,000 gain to the dealer. Likewise, you are exposed to the opposite set of transactions and receive a $38,000 car in exchange for $40,000 cash for a $2,000 loss.
Table 3-3
But as before, you can save the time and expense of having to drive to the original car dealer’s location by sending him a check for $2,000 and buying the car locally for $38,000. This effectively makes you pay the agreed upon price of $40,000 for the car. The original dealer could then sell the car to another individual for $38,000 but would still net the original $40,000 agreed upon price after counting your $2,000 check. Whether the dealer delivers the car to you or accepts your $2,000 check, you effectively buy and sell the car for $40,000, which is exactly how both of you wanted to end up three months ago.
So our second method of completing this agreement is for him to buy back the contract from you for $2,000 as shown in Table 3-4:
Table 3-4
The most important point to understand is that whether prices rise or fall and regardless of the method chosen to settle the contract, the car dealer receives $40,000 for the car and you spend $40,000 for the car. The fears of rising or falling prices are perfectly hedged by simply entering into an agreement to prearrange these transactions three months earlier. No matter what happens to the price of the car during the three-month interim, you and the dealer both know that the transaction will take place for $40,000.
In about 95% of the actual futures contracts, investors just offset their obligations by closing the contract out for cash and "offsetting" the contract thus causing it to be closed. Investors and speculators just close out their positions by either paying or receiving money, which mathematically makes it equivalent to their buying and selling prices that they agreed to at the start of the contract. This concept is shown in “Method 2” of the previous two examples. If the car price rises, the car dealer sends you a check; if the price falls, you send the dealer a check. Regardless, of the outcome, you purchase the car locally while the original dealer sells the car locally. The cash sent by one party allows both parties to trade at the originally agreed upon price.
This example also shows the clear potential for performance risk with forward contracts. If the car price rose substantially, there is a chance the dealer backs away from the contract. On the other hand, if price falls, you may decide to not purchase the car. With futures contracts, however, there is no such risk. Both the buyer and seller are subject to maintenance margin to assure the transactions go through as originally agreed.
Also notice how easy it is for an untrained eye to only focus on the dealer’s $5,000 "loss" when the car’s price rose or your $2,000 "loss" when the price fell and thus view this futures contract as a speculative, risky arrangement! But a close examination reveals that's not the case. Three months earlier when you wanted to buy the car, the dealer was concerned with getting less than $40,000. He does not see sending somebody a check for any amount above $40,000 as a loss. Provided the dealer is guaranteed to get $40,000 he is perfectly willing to do that. Likewise, you were concerned with paying more than $40,000 to get the car in three months. You should be perfectly willing to send a check if you’re able to get the car in three months for less money. Your worry about paying more for the car is perfectly hedged by the contract. Futures contracts allow people to hedge risks of rising or falling prices. In most cases, money just changes hands and the underlying assets are never delivered.
Futures Markets Are a Zero-Sum Game
We said that hedges are not intended to provide profits but rather offset losses. Just as with the home insurance example, the homeowner gained a $20,000 check but lost $20,000 in value of the home, which is a net breakeven. Any arrangement that operates where one person's gain is exactly another person's loss is called a zero-sum game. A zero-sum game just means that one person cannot be made better off without making another equally worse off.
Futures contracts are a zero-sum game. This simply means that, in the end, no new money is brought to market such as when new shares of stock are issued. Futures contracts do not provide a means to raise new capital, which is often a criticism. In the car dealer example, when prices rose $5,000, the dealer lost that amount and you gained that amount. Likewise, when prices fell $2,000, the car dealer gained that amount and you lost that amount for a net zero gain or loss in the market. Keep this in mind as you hear about the "devastating" losses created in the futures markets. There is always a party on the other side of the trade that profited by the exact amount. So the futures markets do not create disastrous "holes" in the financial system but rather allow for hedgers and speculators to hedge risks by simply passing money from one to another. Those "holes" are filled by gains of equal size.
In financial lingo, if you own an asset (stock, bond, futures contract etc.) you are long the position. With a long position, you are hoping to profit from an increase in that asset's price. You are attempting to "buy low, sell high." However, it is also possible to profit from a decrease in the asset's price. To do so you must reverse the transactions and sell the asset first and then buy it back later at hopefully a lower price. If you sell first, you are "short" the position. Short sellers attempt to "sell high, buy low." While it may sound complicated, short sales can be accomplished with relatively the same quickness and ease as purchasing a stock. For now, just understand that long positions make money if prices rise and short positions make money if prices fall.
Many people new to futures get easily confused when trying to decide if the hedger or speculator should buy or sell the futures contract. In other words, should they be the long position or the short one? If you are speculating, the answer is easy and is no different from stocks, bonds, options, or other assets. If the think the price will rise, you buy the futures contract. If you think prices will fall, you short the contract. Where it gets tricky for some is when you consider a hedging transaction, such as when you and the car dealer wanted to hedge against rising or falling car prices respectively. It's actually very easy to figure out and there are a couple of ways you may find helpful.
First, the dealer was afraid of falling prices. How can he protect his profit? Obviously he would need an asset that rises in price as prices fall; he needs a short hedge. If he sells (shorts) the contract, he can protect the dealership from falling prices since the short contract will rise in price if the underlying prices fall.
On the other hand, you were fearful of rising prices so you would need a long hedge for price protection. If you buy the contract, that contract will rise in price and offset your cost in the future if the car price should rise.
Because the car dealer needed a short hedge and you needed a long hedge, you were able to match up the needs and create a "futures" contract. You would be the buyer of the contract and the dealer would be the seller.
If you are not comfortable thinking in terms of long and short hedges, you can use another method, possibly more straightforward, to determine who should be long and short the contract.
Since the car dealer would be the seller of the car in the future, he would need to be the seller (short position) of the contract. Similarly, you will be the buyer of the car in the future so would be a buyer (long position) of the contract. Just remember that a buyer is a buyer and a seller is a seller. Buying a futures contract is the same as buying something in the future. Selling a futures contract is the same as selling something in the future. It's not anymore difficult than that.
Refer back to Tables 3-2 and 3-4 for a moment. In Table 3-2 we said that the dealer could close out the contract by paying $5,000 to you. Now this should make more sense as to why that arrangement worked. He was the long position and you were the short position. Because prices rose, the dealer’s short position was hurt by $5,000 (remember, short positions profit if prices fall) so the dealer can pay you that amount and the contract is considered complete. Notice it is the loser that pays the winner.
Likewise in Table 3-4 we assumed that prices fell by $2,000. In that case, you would have to pay the dealer $2,000 to close out the contract. That's because your long position was hurt by the fall in price and the dealer’s short position was strengthened and the loser must pay the winner.
Notice that this contract was closed for equal gains and losses at the same time. In other words, if the dealer wishes to end the contract, he must rely on you to take the opposing side and close it out too. What if you do not wish to do so at that time? In the real world of futures trading, it does not matter what the other person wishes to do. Because futures contracts are standardized, the dealer would only need to buy the contract from another seller.
In effect, the car dealer will have switched places with that person and they are the new short position paired with you. Likewise, if you wish to close out the contract, you do not need the car dealer to agree to it. You simply sell the contract to another buyer. If so, that new buyer is now the new long position and the dealer is still the short position. The ability to swap contracts and allow buyers and sellers a way out at their discretion is perhaps the biggest advantage of standardized contracts.
For every futures contract there must be one buyer (long position) and one seller (short position), which is why futures are a zero-sum game. Any gain in the long positions is canceled out by equal losses in the short positions. This is not true for the stock market. While there are usually some short positions for any given stock, it is not a necessary condition. It is therefore possible for all stockholders to have a profit on a given day. If Intel rises $1 and there are no short positions, then all stockholders have increased their wealth by $1 per share. However, if the underlying rises $1 in the futures markets, then half the positions have a gain and half will have a loss.
This car dealer example captures the very essence of any futures contract. If you understand what took place with the different scenarios of rising and falling prices, you will be able to follow along and understand the rationales behind currency futures contracts. Let's now run through an example and see how they can be used to hedge day-to-day business risks.
There are many types of futures contracts and currency futures are certainly one of the more popular contracts for businesses involved in importing and exporting. These firms face exchange rate risk, which can be a serious threat to firms in this industry. If a U.S. exporter is going to accept payment in a foreign currency in the future, they must exchange that foreign currency for U.S. dollars at some time. The risk to the firm lies in the fact that the exchange rate at that time may be unfavorable and large losses could develop. Similarly, a U.S. firm may import goods and be required to pay for them in units of the foreign currency. As with the exports, the risk lies in the exchange rate at the time payment is due.
These firms can hedge the risk of exchange rate fluctuations by using currency futures contracts. When you buy a futures contract, you are in effect, signing an agreement to pay a fixed amount of US Dollars for a fixed amount of foreign currency. You are just locking in your purchase price of foreign currency. For example, you may buy a three-month futures contract for USD/JPY = 117, or JPY/USD = .008547. On a technical note, the Japanese yen futures are quoted in points with one point being equal to one millionth of a dollar, which is $.000001 or $1/1,000,000 per Japanese yen. A quote of 8547 points is equal to 8547/1,000,000, which equals $.008547 per yen. Whenever you see a futures quote on the Japanese yen, you simply divide that quote by one million and that's how many dollars you're agreeing to pay per yen. The Japanese Yen contract just happens to control a fixed amount of 12,500,000 yen. If you were to buy this contract at 8547 then you’re agreeing to pay $.008547 per yen, or a total of $.008547 * 12,500,000 = $106,837.50 for the entire contract. Now, just because you bought the contract for 8547 does not mean that its value will remain at 8547; that is up to the market to decide. As things change so will the price per yen of the contract. One thing is for sure: As the expiration date nears the price of the yen will approach the current spot price.
We just said that the futures price at expiration would converge to the spot price since the futures price is essentially the spot price near expiration. Now it's time to find out why the two prices are forced to converge. If the futures contract is not trading for (or at least very close to) the spot price then arbitrage is possible.
For example, if the yen were trading for 8537 in the spot market near expiration but the futures contract was trading for 8547, arbitrageurs would buy the currency in the spot market for 8537 and immediately sell the futures contract for 8547 for a guaranteed profit. By selling the futures contract, the arbitrageurs must make delivery at 8547 but are assured of doing so since they already purchased the currency in the spot market at 8537. This activity puts buying pressure on the spot market and selling pressure on the futures price and will eventually bring the two prices together.
Likewise, if yen were trading for 8557 in the spot market but the futures contract was trading for 8547, arbitrageurs would buy the futures contract and sell short the currency in the open market for a guaranteed profit. By purchasing the futures contract, the arbitrageur is accepting the obligation to buy yen at expiration. That’s okay since they must do this at sometime anyway to cover the short position at 8557. The arbitrageur has guaranteed a "sell high, buy low" trade. This activity puts buying pressure on the futures contract and selling pressure on the spot market and again will eventually bring the two prices together.
The only way to prevent arbitrage then is for the futures contract price to converge to the spot price at expiration. After all, the concept of a futures contract is to aid the market in determining the spot price in the future. If that future point (expiration) has arrived, obviously the spot price is the same as futures price. Figure 3-5 demonstrates how the individual futures and spot markets are allowed to fluctuate somewhat independently but must meet at expiration:
Figure 3-5
Now that you have a better idea of the mechanics of a futures contract, let's stick with our car dealer example and see how he could use a real futures contract to hedge the considerable risk of currency fluctuations.
Assume that the U.S. car dealer is going to order 12 of the convertible cars we talked about in the previous section. The cars will be built in Japan and shipped to the U.S. in three months. At that time, the car dealer must pay 49,842,000 yen (¥49,842,000) for delivery. That’s the price that the Japanese car manufacturer wants and it remains fixed. The problem for the U.S. car dealer is that he must buy the yen and there’s no telling how much they will cost at the time of delivery.
How much are 49,842,000 yen worth in U.S. dollars? That depends on the exchange rate between the two currencies and we’ll assume USD/JPY = 117. If the car dealer needed to buy the cars today, he would need to pay 49,842,000 /117 = $426,000 for the shipment. In other words, $426,000 will purchase 49,842,000 yen, which is the current amount needed to fulfill the contract price.
The risk to the car dealer is that the value of the yen rises against the dollar thus making his order far more costly. In order to hedge the risk of rising yen prices, there are several things the dealer could do. First, the dealer could buy the yen today. However, as with any payment, he would prefer to not pay for something that is not due immediately so that the dealership may earn interest on those dollars. While it is possible the dealer could hold the yen in a Japanese bank to earn interest but that would require opening a Japanese bank account, which may be more trouble than it’s worth.
Second, rather than buying the yen today, the dealer could wait for three months and buy them at that time. Of course, the risk of waiting for three months to pass before buying the Japanese yen is that the currency may be much more expensive at that time, which means the cars would cost significantly more than $426,000. Taking this chance is certainly not a smart way to manage expenses and run a business.
So what can the car dealer do? Just as you could hedge against the rising price of a single car by signing an agreement to take delivery of it in three months, the car dealer can guard against rising yen prices in the same way. He can use the same principles on a much bigger scale to guard against the risk of rising prices of Japanese yen. To do this, the car dealer simply needs to prearrange the purchase of yen three months in the future, which he can easily do with a futures contract.
How did we determine that the dealer must purchase the contracts? Remember what we learned earlier regarding long and short hedges. Our car dealer is afraid of rising yen prices so will need a long contract in order to hedge that fear; he will need to buy a Japanese yen futures contract thus locking in today his future purchase price of yen. We can come to the same conclusion using our alternative method; that is, the car dealer is a buyer of yen in the future so will be a buyer of the yen futures contract.
The car dealer has a guaranteed delivery of 12 cars in three months with a fixed payment of 49,842,000 yen, which is anticipated to be valued at $426,000 since the current exchange rate is USD/JPY = 117 (or $.008547 per yen). It is the uncertainty of the value of the yen in the future that he wishes to hedge. As we said before, if the price of yen rises then the dealer may end up with a much larger than anticipated expense. It is in the dealer’s best interest to lock in a yen price today. What price will he pay for the yen by purchasing a three-month futures contract? That depends on a number of factors, which we’ll talk about in a later section. For now, just realize that the exchange rate for the yen will be slightly higher or lower than the current exchange rate. In other words, if the current exchange rate is USD/JPY = 117 (or JPY/USD = .008547) then a three-month futures contract will probably be quoting something higher or lower than 8547. To make the example easier though, we’re going to assume that the dealer can get this same exchange rate.
Because futures contracts are standardized, they control a fixed amount of currency. As we said earlier, the Japanese Yen contract controls 12,500,000 yen. The car dealer needs to control 49,842,000 yen so he will need to buy 49,842,000/12,500,000 = 3.98 futures contracts on the yen. However, another drawback with standardized contracts is that you cannot buy fractional contracts so the dealer would either need to under hedge and buy three contracts or slightly over hedge and buy four.
If the dealer could find another party to take the other side of the trade, he could enter into a forward agreement for exactly 49,842,000 yen and be perfectly hedged. However, finding this person can be difficult to say the least since he would need to find someone willing to sell 49,842,000 yen on that same date. Futures contracts can be executed in seconds and the clearing corporation guarantees its fulfillment. The simplicity that futures contracts provide come at the expense of having to be a little under or over hedged at times but it is usually a good tradeoff. Because 3.98 contracts is much closer to four, let’s assume the dealer decides to slightly over hedge his risk and buy four yen futures contracts and see how they help to manage his risk under different scenarios.
Let's assume that the yen falls relative to the dollar to an exchange rate of JPY/USD = $.008333 in three months. (The price of the yen is now cheaper since it used to cost .008547 so its dollar price has fallen.)
We know that three months ago the dealer was expecting a cash payment of 49,842,000 yen * $.008547 = $426,000 so let’s see what he could do under this scenario. With the yen trading lower at $.008333, the dealer has two choices: 1) He can use the futures contract and pay .008547 per yen or 2) He can close out the futures contract and buy yen in the open market. Just as with our simplified example between you and the dealer, we will soon see that it doesn't really matter which choice the dealer makes; both result in the same outcome. We'll step through both choices to show why it does not matter which choice he makes.
Because the yen has fallen, the dealer may decide to not use the futures contract and will prefer to just purchase the 49,842,000 yen in the open market for the cheaper price of $.008333 or a total purchase price of $415,333. The dealer was locked into a purchase price, though, of $426,000 so appears to be ahead by $426,000 - $415,333 = $10,666 by not using the futures contract. However, that is only part of the story because in order to get out of his futures contract, he must enter an offsetting position, which means he will have to sell the same contract as the one he is long. Remember that the futures contract does not represent a right; it is an obligation. The only way to escape your obligation is to enter an offsetting position in the open market. If you originally bought (sold) the contract then you can offset your obligation by selling (purchasing) the same contract.
Because the car dealer must sell the contract, he is at the mercy of the market to determine the price. What is the dollar price of yen worth on the futures contract now? Even though the dealer locked in a rate of 8547 three months ago there will be nobody willing to lock in that same rate for that contract. The reason is that the contract will be expired shortly so hedgers and speculators will only be willing to lock in at the current spot rate of 8333. This is due to the arbitrage restriction that forces the futures contract price to converge to the spot price near expiration.
This means that the contract can be sold for the spot price of 8333. Because he agreed to pay 8547, this results in a loss of (.008547-.008333) * 12,500,000 = $2,675 per contract, or $10,700 for the four contracts. By choosing to not use the futures contract, the dealer saves $10,666 by purchasing yen in the spot market; however, he loses $10,700 by selling the futures contract. The net effect is that the dealer is at only a slight loss of $10,666 - $10,700 = $34. This slight loss is due to being ever-so-slightly over hedged with four contracts. The net effect is that he is actually net long a few yen and since the yen fell against the dollar, he ended up with a slight loss.
Three months earlier when he bought the contract, if he had been able to buy a contract covering exactly 49,842,000 yen then he would have gained and lost an equal amount of money thus leaving him no better or worse off. In other words, he would have been perfectly hedged and every dollar gained would be matched by one dollar lost. The dealer’s fear, however, is of rising prices; in this scenario, we assumed the yen fell against the dollar so the futures contract will not come to his rescue here. Remember, the dealer bought the futures contract as a long hedge, which will only help if the price of yen rises against the dollar. Because he was slightly over hedged, he ended up with a slight loss of $34. This loss is certainly negligible especially when viewed in light of the costs that face car dealers.
Had the dealer not entered the futures market three months prior, he would have been able to buy yen in the open market and save $10,666. But because he entered the futures contract, he will now lose $10,700 to get out of the contract by selling it. Therefore, using the futures contract to an unsuspecting eye resulted in a unnecessary and reckless loss of $10,700. What the unsuspecting eye does not see is that the dealer is also ahead by $10,666 by using the spot market or that the dealer would be ahead had the yen risen against the dollar, which was his main reason for entering into the futures contract.
We just found out that the dealer would end up with a slight loss of $34 by not using his futures contract. What would happen if the dealer, instead, used the futures contract to buy the yen? The dealer could elect to use the futures contract and take delivery of 12,500,000 yen * 4 contracts = 50,000,000 yen for a total cost of $.008547 per yen, or $427,350. But since he needs to deliver 49,842,000 yen he can then sell the remaining 158,000 which he can do at the current spot rate of .008333 for a total price of $1,316. His total cost for the yen is $427,350 - $1,316 = $426,034. Because he planned for a payment of $426,000, he has a slight loss of $426,034 - $426,034 = $34 by using the futures contract.
We can see that it makes no difference, mathematically, whether the dealer uses the futures contract or not to purchase the yen. This is exactly why most futures contracts are just closed in the open market and then buy or sell the actual underlying asset in the spot market at expiration. Although an investor can certainly take delivery of the yen (or whatever the underlying asset), the futures contract is usually used as a hedge and is never used to take actual delivery.
The purpose of the futures contract is to hedge his risk of the yen rising against the dollar. While the futures contract appears to have created a loss in this instance, you have to remember that the dealer would have paid $426,000 three months ago to insure (hedge) his delivery price. The dealer hardly sees the loss from the contract (whether from selling or using the contract) as a loss if he can pay less money for the yen at time of delivery than he originally planned for. He's more than happy to pay $10,700 to close out the futures contract at a "loss" in order to save $10,666 in the spot market. Remember, these "gains" and "losses" in the futures contracts just mathematically ensure that both the buyer and seller are locked into their original agreed upon prices.
We’ve just seen how the dealer would have a slight loss of $34 if the yen price falls to 8333 at expiration of the contract. Let's assume now that the yen rises to an exchange rate of 8772 (USD/JPY = 114) at expiration. If so, the Japanese Yen contract will be trading for the spot price of 8772. Once again, the car dealer again has two choices with either choice, as before, resulting in the same outcome.
Choice 1: Yen rises - Dealer does not use his futures contract:
With the yen trading at $.008772, the dealer can buy yen in the market for a total payment of 49,842,000 * .008772 = $437,214. However, in order to not use his futures contract he must close it out in the open market by selling the equivalent contract, which will be trading for the spot price of 8772. He was under contract to pay 8547 but can sell that same contract for 8772, which is a gain of (.008772 - .008547) * 50,000,000 yen per four contracts = $11,250. In effect, the dealer pays $437,214 for the yen in the spot market but also receives a gain of $11,250 from the sale of the futures for a net payment of $425,964, which is much closer to the $426,000 price he expected to pay when he initiated the futures position three months ago. Had the dealer not entered the futures contract, he would be exposed to an unexpected expense at expiration of $437,214 - $426,000 = 11,214. By entering the futures contract, the dealer has controlled costs and is actually slightly ahead by $426,000 - $425,964 = $36. The reason the dealer is up with the yen rising is because he chose to slightly over hedge the position and purchase four contracts when only 3.96 were mathematically necessary (but also unattainable).
Because the yen is trading higher than his contract price of 8547, the car dealer could decide to use the contract to purchase the yen. If so, his payment will be $.008547 * 50,000,000 = $427,350. Because he must deliver 49,842,000 yen, he can sell the remaining 158,000 yen at the spot price of .008772 for a total of $1,385. His total payments for the yen are then $427,350 - $1,386 = $425,964 thus providing him with a slight gain of $36 and is exactly what we came up with in the previous section where we assumed the dealer did not use the futures contract.
As stated before, because it doesn't make any difference to the dealer whether he uses the contract or not most people who hedge with futures will just close out the futures contract at either a gain or loss and then purchase or sell the underlying asset in the spot market. The advantages and disadvantages along with the net gains or losses to the car dealer are zero. These are summarized in Table 3-6:
Table 3-6
Was The Car Dealer Speculating In The Futures Markets?
Now you can see why the financial press is often so critical of futures markets. It is because they do not understand why someone would use them in the first place. For our car dealer, the use of a futures contract meant he was locked into a known expense of $426,000 three months into the future. That's it. Locking in an expense makes perfectly good business sense – especially if the dealer already has the cars sold! However, if the yen rises against the dollar, there will be missed profit opportunities that show up in the form of losses on the futures contracts. But risk is never defined as missing out on some of the rewards and “losses” on futures contracts, used for hedging, are simply the reflection of missed opportunities. Losses from hedging should therefore not be viewed as a reckless, speculative use of futures contracts.
Anybody who is perfectly hedged with a long futures contract, just like our car dealer, will have a loss on that contract if the underlying price falls. What the financial press fails to see (or possibly, conveniently leaves out) is that this loss is mirrored by an equally large gain in the spot market. So was our car dealer speculating in the market by using futures contracts? Were his losses the result of reckless gambling in the futures market? Hopefully you now understand that it isn't but certainly could be misconstrued as one if one does not understand the whole story.
Should the Car Dealer Hedge?
One of the toughest decisions faced by businesses dealing in foreign goods is whether to hedge or not. As we have seen, any business dealing in foreign assets exposes it to currency price fluctuation and therefore an uncertainty about the profitability of the deal. In other words, foreign currency fluctuation presents a large element of risk for the business. In the past, businesses were often negligent in their classification of exchange rate risk. Many would just calculate the returns based on the spot and forward rates.
For instance, assume that USD/JPY = 117 and the forward rate is USD/JPY = 120. Business would often consider the “currency effect” to be a 2.6% increase since the dollar is expected to strengthen by (120-117)/117 = 2.6%. However, what if the spot rate in the future is not 120 but is instead 122? Had we known this value at the beginning, we would calculate the currency effect as (122-117)/117 = 4.3%, which is a difference of 4.3% - 2.6% = 1.7% from the previous calculation. This difference is often called the “surprise effect,” which is just due to noise. We can calculate the surprise effect as 122-120/117 = 1.7%.
The currency surprise is therefore the additional movement in the spot rate relative to what was predicted by the forward rate. This implies that if you have an unhedged foreign currency transaction that your return is actually comprised of two parts. The first is the amount you could hedge with the forward contract and the second is the surprise effect. It is up to the business to decide whether to accept the surprise effect or not since the other can be hedged away through the forward or futures markets. The decision to hedge depends on the impact that losses could have versus the costs associated with hedging.
Futures Contracts are Settled Daily
In the previous examples, we assumed that the profits or losses were realized at expiration of the contract, which we did to make the examples easier to follow. In the real world of futures trading, contracts are settled daily with cash. This is done to ensure that those with losses do not let them mount to levels where they must default. The process of settling daily is called marking to market. This just means that the profits or losses are all “marked” according to the current “market” prices.
Let’s run through some examples to understand how this works. In the examples, we assumed the car dealer purchased four contracts at an agreed upon price of 8547. If the price of the yen were to rise the next day by three pips to 8550, then the dealer’s account would be credited with cash. This is because the dealer is long the contract and the long position makes money as prices rise. Because he was long four contracts, his account would be credited 4 contracts * 12,500,000 yen per contract * (.008550- .008547) gain = $150 cash. The person who was short the contract would be debited for the same amount. The process of marking to market effectively moved cash from the person who was short the contract to the dealer who was long.
On the other hand, if the yen fell by three pips to 8544 then the dealer’s account would be debited $150 cash. Recall that futures are a zero-sum game and that means that all of the debits must equal all of the credits.
For any market price movement, there must be an equal amount of debits and credits since there must be a buyer for every seller. If the market moves in favor of the buyer then it must have moved an equal amount against the seller and vice versa. The debits from those accounts adversely affected are simply transferred as credits to the accounts positively affected. So if you are in a futures contract, you will likely see cash debited from or credited to your account daily. The only time this will not happen is if the underlying price closes at exactly the same price as the previous day. While debits may seem unsettling, remember that you are gaining that same value back from the spot market. You will be able to buy the goods cheaper in the open market, which is a gain to you. The gain to you from the cheaper market price is exactly equal to the debits to your account.
On the other hand, if you account is credited with cash, it’s because the spot market is becoming more costly to you. That increased cost is perfectly hedged by the credits. At expiration of the contract, all debits and credits to your account just ensure that your originally agreed upon price is realized.
Hedgers and Speculators
The car dealer in this example was using the futures contract to hedge his risk of rising yen prices. People who use futures contracts for hedging are usually manufacturers, farmers, importers and exporters or any business where price fluctuations of the underlying asset can severely impact their profitability. Hedgers use futures contracts to secure the delivery price of the asset at a future date.
If you buy a futures contract, you’re trying to secure a low price (you’re hedging the risk of rising prices. On the other hand, if you sell a futures contract, you’re trying to lock in a high price (and hedging the risk of falling prices). Any business that buys commodities as an input will usually be the buyer of a futures contract. For example, Kellogg Company may use futures contracts to lock in the price of wheat or other grains. Ford Motor Company may use futures to secure the price of steel.
Any business that produces commodities as a final product will sell futures contracts to secure a high price. A farmer, for example, may sell futures contracts to secure a selling price for wheat while Exxon-Mobil may sell futures to secure their selling price for gasoline. Whether locking in low or high prices, hedgers are trying to avoid price uncertainty or volatility.
On the other hand, speculators are not trying to avoid price volatility but, instead, are seeking it. They wish to speculate on price movement and either buy or sell futures contracts accordingly to profit from the outlook. Speculators wish to profit from the same price swings that hedgers are trying to avoid. Hedgers seek to minimize risk while speculators seek to increase risk in search of profits.
It is this interplay between hedgers and speculators that make the futures market work. A speculator attempting to buy low and sell high is probably buying that contract from a hedger selling a contract high to protect him from declining prices. Table 3-7 outlines the respective roles of the hedger and speculator:
Table 3-7
Pricing a Futures Contract - What’s it Worth?
One of the complications with derivatives is their pricing. If we have no way to determine what a fair price is to pay for a contract then you can be pretty sure the market will react to the uncertainty and bid low and offer high, leading to wide bid-ask spreads, which can result in the market breaking down. However, in the real world of trading we see that’s not true. The reason is that we do have a very sound way of figuring out how much someone should pay for a futures contract. This very idea is confusing to new traders; after all, if we have no idea what the exchange rate will be in the future, how can we determine a fair price?
On an intuitive level, a futures price should reflect the expectations of the future spot price no matter how much uncertainty there may be in the market. It should always be an unbiased predictor of the future spot rate (we’ll find out more about this in a later section “How Exchange Rates are Determined”). As expectations change so too will the futures price.
In the 1930s, two famous economists, John Maynard Keynes and John Hicks, proposed that futures price was actually a biased predictor of the future spot price. They claimed that while it does reflect the future spot price it also contained a risk premium.
Hicks and Keynes supposed that some markets are dominated by long hedgers. These are markets where certain manufacturers wish to buy the underlying commodities in the future. In other words, they wish to lock in their future purchase price today. If these people wish to protect their purchase prices, they must persuade another person – usually a speculator – to take the short side of the futures contract. How do you persuade someone to hold a short futures contract? The long hedgers must bid it up above its expected spot price in the future (this difference is the risk premium they referred to).
If hedgers bid up the price, then the price of the futures contract will fall as it nears expiration, leaving the speculator with a positive expected return. In a market dominated by long hedgers, we would expect the prices to continuously rise as time to maturity is increased. The theory that says hedgers hold long contracts on a net balance is called contango theory. Similarly futures contracts that exhibit rising prices as time is increased are said to be in a contango market.
Contango Theory:
Hedgers hold long contracts on a net balance thus creating a normal market.
Contango Market:
Futures markets that exhibit rising prices as time to maturity increases.
While prices rise from month to month in a contango market, the price of the contract is expected to fall as expirations approaches. This may seem contradictory but think about what is happening. The hedgers must bid the contracts higher than their expected prices at expiration so that the short sellers can expect a profit. So while the futures contract prices rise from month to month, the individual contract prices are expected to fall as expiration gets closer. Their prices fall because the futures price will converge to the spot price.
Figure 3-8 shows the mechanics of a contango market. The futures price is bid up higher than the current spot price and is also bid up higher than the expected spot price that will prevail in the future. Once that future spot price emerges, the futures price will fall to meet that price.
Figure 3-8
Please keep in mind that this is a theory that explains the price pattern of rising futures prices that are expected to fall near expiration. It does not necessarily mean that it must turn out this way. Nonetheless, we should expect to see an overall positive return for short sellers of futures contracts in a contango market.
There is a theory opposite that of the contango theory that states that some markets will be dominated by short hedgers – those wishing to sell the asset in the future. These people are usually the producers of the commodity who wish to protect their selling price and therefore need a short hedge. In order to persuade a speculator to hold a long futures contract in this market, they must sell it below the expected future spot price so that the speculator can expect a positive return.
As an analogy of this effect, imagine that you are trading in your existing car for that new convertible and that it has a market value of $10,000. That's the price it can be sold for quickly at a retail dealership. If that is the case, you can’t expect the dealer to give you $10,000 for it. If they did, they would pay $10,000 for the car and then sell it for the same amount, which leaves them with no profit. In order to persuade the dealer to take your car (take the long position), you must be willing to take less than the market value for it. You may, for example, take $8,500 for it meaning the car dealer is "long" at $8,500 and can sell it for the expected $10,000 market value, which leaves them an expected profit.
In the same sense, short hedgers must be willing to take less than the expected future spot price to get a speculator to hold the long side of the futures contract. The theory that supports this argument is called normal backwardation and, just for the record, I had nothing to do with the selection of that name. At any rate, normal backwardation theory states that hedgers are primarily short the futures contracts and speculators are long. The short hedgers compete in the market and push the price below the expected future spot price in order to get a speculator to purchase the contract.
Hedgers hold short contracts on a net balance thus creating inverted markets.
Futures markets that exhibit falling prices as time to maturity increases.
Figure 3-9 shows how the dominant short hedgers push the futures prices below the expected future spot price. This below-expected price allows the speculators to expect a positive gain. Again, please do not think that if you hold long futures contracts that you must have a gain. This theory suggests that the overall price is below what it is expected so that the long speculators have some incentive to hold the contract. Market conditions can change quickly, leaving the long positions with large losses. So the theory suggests that one can expect a positive gain over time and not that gains must occur on each contract.
Figure 3-9
So while contango markets rise in price with the more distant months, those prices are expected to fall as expiration nears to compensate the short speculators. The reverse is true for normal backwardated markets. Normal backwardated markets fall in price with the more distant months; however, those prices are expected to rise as expiration nears to compensate the long speculators. Figure 3-10 shows how contango markets are expected to fall and normal backwardated markets are expected to rise as expiration nears:
Figure 3-10
Empirical studies have shown that futures prices do not contain any significant risk premium. We should therefore not expect to always see rising or falling futures prices as we check the quotes for longer maturities. In fact, many markets exhibit both characteristics and are subsequently called mixed markets. In a mixed market, you will find futures prices rising through certain ranges and falling through others.
The rational for the mixed markets is basically a mixture of the contango and normal backwardation theories. Depending on supply and demand conditions, sometimes the markets are dominated by long hedgers and other times by short hedgers. Keynes and Hicks based their propositions in agricultural markets where the producers were most likely the hedgers. Today, there are numerous players including producers, consumers, and arbitrageurs (a group the Keynes and Hicks didn’t allow for) that use futures for hedging.
Cost-of-Carry Model
As discussed in the previous section, empirical studies have shown that there is no basis to expect the quotes for distant futures expirations to be more or less expensive than the current spot market price. Because of this, researchers were led to the cost-of-carry model, which is the standard for pricing futures contracts today. The term “cost-of-carry” refers to the fact that there is a cost of holding or “carrying” a position for periods of time. That cost is the risk-free rate of interest. For example, assume the risk-free interest rate is 5% and I ask you to buy $100 worth of yen and hold them for one year at which point I will pay you $100 for them. That’s effectively a forward contract.
However, just because you will receive $100 at the end of the year – exactly the amount you used to buy the yen – does not mean there is no cost to you. Had you not used the $100 to buy the yen you could have left it in the bank to earn interest and had $105 at the end of one year. In other words, there is a $5 cost “to carry” the position for one year. If you are guaranteed to sell the yen in one year and interest rates are 5% then you should be willing to sell the forward contract to me for $105. This is the basic idea behind the cost-of-carry model as applied to futures contracts although it is slightly more complex since we’re dealing with two currencies and two risk-free rates.
Let’s run through an example to see how the cost-of-carry model works. Assume the following:
USUSD/JPY = 117
Risk-free interest rate for U.S. = 5%
Risk-free interest rate for Japan = 10%
With this information, what should the one-year futures contract be trading for? Although we have no way of knowing what the future spot rate will be, we can show the fair price of the contract through the process of arbitrage. This price is called the “fair value” of the contract. To understand the fair value, assume a U.S. investor has $100 to invest at the risk-free rate. He can do one of two things. First, he can invest it in the U.S. and get $105 in a year. Second, he can convert the $100 to yen and invest in Japan to get the higher interest rate. However, if he chooses to invest in Japan then he faces exchange rate risk once converts the yen back to dollars at the end of the year. How much should he be willing to pay for a futures contract that guarantees the sale of the yen in one year?
Figure 3-11 shows how the investor would come up with such a price. If he invests in the U.S. then he will have $105 at the end of the year. That’s his benchmark. Alternatively, he could take the $100 and convert them to yen, which he does by multiplying by the USD/JPY exchange rate of 117. This gives him 11,700 yen which earns 10% thus leaving him with 12,870 yen at the end of the year.
Figure 3-11
If the USD/JPY exchange rate is still 117 at that time, the investor can covert his yen to 12,870/117 = $110 thus giving him the Japanese interest rate of 10% on his money. Therefore, the investor should certainly be willing to lock in a rate of 117. However, so will a lot of other investors and that starts the bidding war on the contract. At what point will the bidding stop? It will stop once there is no difference between the two choices. We can figure that out by mathematically solving for 12,870/x = $105.
In other words, 12,870 yen divided by some exchange rate (x) must equal $105. That exchange rate turns out to be USD/JPY = 122.57. The cost-of-carry model tells us that the one-year futures contract will be trading for 122.57. If the investor can lock in his selling price for yen at 122.57 then he’ll end up with 12,870/122.57 = $105 and there no longer is a difference between investing in the U.S. or Japan and that means the price of the futures contract is fair.
What would happen if the one-year contract was not trading for this amount? If it is trading for any other price then arbitrage is possible. For example, assume that the one-year futures contract is trading for 120. An arbitrageur could borrow $100 from a bank thus owing $105 in one year. He could then convert the $100 to 11,700 yen and invest it in Japan. At the same time, he would buy the futures contract thus guaranteeing him the sale of yen and the purchase of dollars at 120 at the end of the year.
After a year has passed, the arbitrageur will have earned 12,870 yen and will then use the futures contract to convert them back to 12,870/120 = $107.25. Out of this money, he pays back $105 to the bank and is left with an arbitrage profit of $2.25. Arbitrageurs would obviously take these steps with much larger amounts than $100 but this figure was used to make the example easier to follow. Arbitrage profits are risk-free profits for no out-of-pocket expense so the incentive is very strong for these steps to take place. As arbitrageurs buy the futures contract, they will bid its price higher than the current price of 120.
So we just found out that if the USD/JPY exchange rate is 117 and the interest rates are 5% and 10% in the U.S. and Japan respectively that the one-year futures contract must trade for more than 120.
What happens if the market bids the futures contract higher to, say 125? Now there is an arbitrage opportunity in the reverse direction. Arbitrageurs would borrow the Japanese yen and invest in the United States. For example, an arbitrageur may borrow 11,700 yen and therefore owe 11,700 * 10% = 12,870 yen in one year. He will take the 11,700 yen and exchange them for $100, which will be invested at 5% and grow to a value of $105 by year end.
At the same time, the arbitrageur will sell the one-year futures contract at 125. At the end of a year, the arbitrageur will have $105 in the U.S., which can be converted back to $105 * 125 = 13,125 yen by using his futures contract. After paying back the loan, the arbitrageur is left with a profit of 13,125 – 12,870 = 255 yen, or $2.04 after exchanging it back at the current spot rate of 125. This shows that if the futures contract is priced at 125 (or higher) then arbitrageurs will sell the contract to lock in risk-free guaranteed profits. Its price will therefore start to fall below 125. The first example showed that the contract must trade for more than 120 while the second example showed that it must trade for less than 125. The only time the arbitrage stops is when the one-year USD/JPY contract is trading for exactly 122.57, which is the fair value of the contract.
The fair value for any futures contract can immediately be determined by understanding the steps outlined in Figure 3-11. In that diagram, the arbitrageur took $100 and multiplied it by the spot exchange rate of 117 and then invested that amount at 10% interest (which is the same as multiplying by 1.10). Next, we figured out which future rate would be necessary to divide by so that it equaled the home interest rate multiplier of 1.05. Mathematically, we took the following steps:
We can rearrange this to solve for the futures price and find that it is:
This shows that the fair value for the futures contract is simply the spot rate multiplied by the interest rate differential between the two countries. Notice that the foreign interest rate (1.10) is in the numerator of the interest rate differential while the home interest rate (1.05) is in the denominator. The reason for this is that we assumed the exchange rate was given in American terms; that is, we used USD/JPY. When given this way, the foreign interest rate will be in the numerator. Had we used an exchange rate in foreign terms and used JPY/USD then we’d find that the home interest rate would be in the numerator.
If the contract is for a different time period other than one year, we must modify the formula so that we can account for the time differences:
where:
rf is the foreign interest rate expressed as a decimal (i.e., 10% = 0.10)
rd is the home interest rate expressed as a decimal (i.e., 5% = 0.05)
n is the number of periods that you’re dividing the year into. For example, if you’re calculating the six-month forward rate then n = 2 since you’re dividing the year into two parts.
t is the number of years
Using this formula, how much would the six-month futures contract be trading for? We can see that it would be trading for 119.93:
We mentioned earlier that futures contracts are nothing more than standardized forward contracts. Are the prices of futures and forwards therefore going to be equal? We can show through the process of arbitrage that if the risk-free interest rate remains the same for all maturities then the forward price will be the same as the futures contract price.
However, because of the daily settlement procedures with futures contracts, if the spot asset is positively correlated with interest rates (i.e., its price tends to rise when interest rates rise and vice versa) then the futures holder will receive immediate cash that can be invested at the higher rates. This means that the futures trader will receive a higher than average interest rate for the investment when compared to someone trading a forward contract. On the other hand, if interest rates fall, the spot price of the asset falls and the futures trader is earning less than the average interest rate.
This means that if the spot asset is positively correlated with interest rates that you will most likely see the futures contract trading for a higher price than the forward contract. The reason is that the futures contract holder receives a higher than average interest rate so that contract is more desirable to own and it will therefore command a higher price in the market.
However, if the spot price is negatively correlated with interest rates (i.e., its price tends to rise when interest rates fall and vice versa) then you’ll see the futures contract trading for a lower price than the forward contract. In the real world, these differences are usually negligible but the effect is important for traders to understand.