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Topic 2 Forwards and Futures. Futures and Forwards. The purpose of this lecture is to develop an understanding of the futures and forwards markets. We will first examine the mechanics of the futures markets. Contract specification Margin account behavior

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Topic 2Forwards and Futures

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Futures and Forwards

  • The purpose of this lecture is to develop an understanding of the futures and forwards markets.

    • We will first examine the mechanics of the futures markets.

      • Contract specification

      • Margin account behavior

    • We will then examine how forward and futures are used for hedging.

    • Finally we examine the pricing of forwards, and to a lesser degree, futures.

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Futures Contract Mechanics

  • Recall what a futures agreement is: it is an agreement between two parties to buy or sell an asset at a fixed price at a fixed date in the future. 

  • Futures are traded on exchanges; forwards are not. The two biggest exchanges are the CBOT and the CME. 

  • What happens when you place an order to buy a corn futures contract at the “current market” price?

    • Your broker passes instructions on to a rep on the floor of the CBOT.

    • Passed via messenger to a trader in the Corn “pit”.

    • The trader looks around to determine what the best price available is, and then uses hand signals to find a party with whom to trade.

    • If they find somebody at the price they are quoting, the deal is done, if not, they offer a higher price. Eventually they will find somebody.

    • You are notified of the trade and the price.

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Futures Contract Mechanics

  • There are two types of traders: commission brokers and locals.

    • Commission brokers - mainly concerned with making money by trading for you.

    • Locals - trading for their own account.

  • Order Types:

    • A limit order says buy at price X or better.

    • Market order says buy at whatever the current price is.

  • Closing Positions

    Most of the time positions are closed out by taking opposite positions in the contract right before the close of the contract. Occasionally, however, a party will take delivery, so it is important that we understand how the delivery mechanism works.

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Specification of Futures Contracts

  • When dealing with a futures contract, there are a number of details that must be iron-clad. Let’s examine these issues.

  • The Asset

    • When dealing with commodities there can be quite a bit of variation in quality. For this reason the contract will state the grade or grades of the commodity that are acceptable. Also, note that they usually use USDA grades plus additional factors when determining these issues for food.

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Specification of Futures Contracts

  • Substitutions: Occasionally the contract will allow for there to be variations in grade, provided that there is a discount in the price charged. This is especially true for assets whose quality depends upon issues like weather.

  • Note that in the financial futures, there is at least one situation where there is choice in the delivery asset: this is in the US Treasury contracts.

    • The US Treasury bond futures contract is any long-term US T-bond that has a maturity of greater than 15 years and is not callable within 15 years.

    • Similarly, the T-note contract is on any US T-bond with a maturity of more that 6.5 years and is not callable within 6.5 years. The bond must not mature in more than 10 years.

    • There is a formula that determines the price which is paid depending on the coupon and maturity of the delivered bond. This also results in some bonds being cheaper to deliver than others. We will discuss this in great detail later in the course, and particularly in FINN 6211.

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Specification of Futures Contracts

  • Contract Size

    • Another issue that is of great importance is the size of the underlying contract. That is, how many bushels or barrels are you contracting to buy? The exchange tries to set these based on the likely users of the contracts.

    • Agricultural contracts are usually designed for relatively small hedgers - i.e. farmers. They will do $10,000 or $20,000 contracts. Financial contracts are usually in the $100,000 range.

  • Delivery Arrangements

    • The delivery arrangements have an important role. This is true even though there may not be many people that are choosing to deliver the contracts. The reason this is important is because the delivery arrangements determine the relationship between the spot and futures prices.

    • The delivery arrangements will determine where, when, and how the delivery must be made. Undoubtedly the when is most important, but the where and how is also important.

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Specification of Futures Contracts

  • Price Quotes

    • The exchange determines the manner in which prices can be quoted on the contract. This is usually tied to the manner in which the underlying contract is traded.

    • Examples: crude oil futures are in dollars and cents per barrel. T-Bond futures are quoted in dollars and 32nds of a dollar. Thus the minimum price movement for an oil futures is $.01 and for a T-bond future it is $1/32 = $.03125.

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Specification of Futures Contracts

  • Daily Price Limits

    • Most price limits are established by the exchange. If the contract moves down to its limit it is said to be “limit down” and trading ceases for the day (although the exchange can make exceptions). If the contract moves up to its limit it is said to be “limit up” and trading ceases for the day (although the exchange can make exceptions).

    • The role of limits is to limit the price volatility based on speculative excess, but they can become an artificial barrier to trading. It is not clear that these are good for the market or the market participants.

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Specification of Futures Contracts

  • Position limits

    • The exchanges limit the size that speculators, not hedgers, can take in the contracts. This is to prevent them from “moving” or unduly influencing the market. For example, the CME limits speculators in the Random Length Lumber contract to a total of 1000 contracts and no more than 300 in a given delivery month.

    • The SEC may also intervene against hedgers. For example, FHLMC was once asked by the SEC to reduce their holdings - they had 10% of the open interest in the T-bond contract. Since they were hedging a mortgage portfolio the exchange did not care, but the SEC did.

    • Let’s look at a couple of actual contract specifications.

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Specifications of Futures Contracts

  • Corn on the Chicago Board of Trade:,1493,14+58+138+14389,00.html

  • US Treasury Bond Chicago Board of Trade,1493,14+58+140+14431,00.html

  • Random Length Lumber on the Chicago Mercantile Exchange

  • Live Cattle on the CME:

  • Platinum on the NYMEX

  • Propane (but not propane accessories) on the NYMEX

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Operation of Margins

  • Marking to Market and margins

    • Marking to market simply means that the contracts are “settled up” at the end of each day. Generally here is how things work. When you enter a futures contract, you owe the exchange nothing (recall it is valueless initially.) Your broker, however, will demand an “initial margin” account from you. You will be required to put some money (usually several thousand dollars) into this account. The account is interest bearing.

    • At the end of each trading day you “settle up” with the broker. If the market has moved for you by X dollars, those many dollars are deposited into your account by the broker; if it has moved against you, X dollars are taken out of the margin account and sent to the exchange.

    • The broker will set a “maintenance” margin for your account. This will be less than the initial margin. If your margin account falls below this amount, you receive a “margin call” and must put deposit enough funds to bring it back to the initial margin level. If you do not do this very quickly (a day or so), the broker closes out the position for you (i.e. takes an offsetting position). Again, this happens prior to you having a chance of defaulting on the contract.

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Operation of Margins

  • Example from page 28 of Hull:

    • You tell your broker to buy on June 5 two December gold futures contracts at $400 per ounce. Each contract is for 100 ounces, so you have just agreed to buy 200 ounces of gold in December for $80,000. Your broker sets your initial margin to $4,000 (5% is typical).

    • If by the end of the day on June 5 the futures price has fallen to $397, you have lost $3 per ounce or $600 total. This will be taken from your account and sent to the exchange. (If it had gone up to $403 you would have made $600 dollars.)

    • Let’s assume the maintenance margin is $1,500 per contract. Looking at table 2.1 on page 28, on June 13 the balance in the margin account falls to $2,660. You receive a margin call for $1,340, which you deposit into the account.

    • Note that the account is closed out (i.e. you take an offsetting short position) on June 24 at a price of $392.30. You have lost (cumulatively) $7.70 per ounce or $1,540.

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Operation of Margins

  • Odds and ends:

    • If allowed to earn competitive interest rates, margin accounts do not necessarily reflect a real cost.

    • Day trades (announced) are usually subject to lower margin requirements.

    • Hedgers typically have lower margin requirements.

    • Finally Spread trades typically have lower margin requirements. A spread is where one trader simultaneously takes a long position in one month and a short position in a second month.

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Operation of Margins

Clearinghouse Margins

  • The clearinghouse is operated by the exchange to be the middleman in the futures transactions. Each member of the clearinghouse is required to maintain a “clearing margin” with the exchange for each contract their clients maintain. These work like normal margins except that the “maintenance margin” is 100% of the initial margin.

  • Clearinghouse margins can be calculated on either a gross or net basis. For example if you had two clients, with one short 50 contracts and the other long 75 contracts, under the gross system the margin would be based on 125 contracts total. Under the net system it would be 25. Net is the most commonly used system today.

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  • The most commonly used newspaper for futures information is the Wall Street Journal. Look on page 32 of Hull for an example

  • Note a couple of patterns that can be seen in the newspaper quotes on pages 32-33

    • Gold prices rise with maturity - this is a normal market.

    • Platinum prices fall with maturity - this is an inverted market.

  • You can also get quotes from a variety of on-line sources:

    • The exchanges

    • Brokers

    • Information providers such as

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  • For example, let’s look at the live cattle contract that trades on the CBOT.

  • First, let’s remember the specifications:

  • Then, let’s look at the current day’s trading results:

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  • Let’s also look at the gold futures contract (as quoted from


  • It is also interesting to see what is happening with the random length lumber contract.

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  • As the delivery month approaches, the futures price will converge toward the spot price of the underlying asset. Depending upon actual delivery requirements the two may not exactly converge, but they will be very close by the beginning of the delivery period. If not, an arbitrage opportunity will exist.

  • To see this, go back to the gold contract. Let’s say it is December, and we are in the delivery period. The spot price of gold is $415, but the futures price is $420 (per ounce.) An arbitrageur could simply short the futures price at $420, buy the spot gold at $415, and then deliver the gold for settlement. This would net the arbitrageur $5*100*# of contracts or $500 per contract.

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  • Now if there is a single delivery date, and grade, then you would expect to see a smooth convergence, something like:


Futures price

Spot Price


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  • We can see an example of this in the crude oil market:

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  • In reality, however, most futures contracts do allow a range of delivery dates, which makes it somewhat harder to see convergence in practice.

  • The charts on the following pages show convergence in the gold futures contract for August, 2003.

  • The first chart shows spot gold prices in London for January through December 2003.

  • Gold contracts can be delivered any time between the first day of the delivery month and the third to last business day.

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  • Sometimes the exchange provides alternatives as to when, where, and what will be delivered. When that is the case, the party that is short has the option as to when and what to deliver. They announce this to the exchange via a notice of intention.

  • The exchange then notifies a party (exchange’s choice) that has an outstanding long position to accept delivery. Usually, the price is at the most recent settlement price (since delivery can occur over a range of time.)

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Cash Settlement

  • Some futures, particularly financial futures, are cash settled. Essentially, this means that on the last day of the contract it is marked to market and then declared closed. The closing settlement price is set equal to the closing spot price on that date. An exception to this is in the S&P 500 futures contract. Its closing price is set as the opening price of the spot on the closing date.

    • This is done to prevent the chaos of the “triple witching hour” when the stock index futures, stock index options, and options on stock index futures all expire on the same day. Basically arbitrageurs were able to make money by playing the three against each other. Some claimed this increased volatility; others argued it just enforced efficiency. The big problem was really that some of the exchanges could not handle the volume.

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  • Futures are regulated in by the Commodity Futures Trading Commission (CFTC).

  • Accounting for hedge positions is very difficult. In 2000 a new accounting standard, Financial Accounting Standard 133, was adopted by the Financial Accounting Standards Board. This standard is very difficult to interpret and implement, but we will examine it later in the semester.

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Hedging Using Futures

  • The purpose of hedging is to remove uncertainty, not to improve the average wealth of the hedger. It is like insurance; on average it doesn’t make you wealthier, it just insures that you won’t have massive losses.

    • A company that knows it will sell an asset in the future (i.e. is naturally long the asset, physically has it right now) can hedge by going short a futures contract. Essentially, the natural long position and the short futures position will cancel each other out. If you are a natural short (i.e. must buy in the future), then you want to take a long position in the contract to hedge.

  • Note that roughly 50% of the time you make more money by not hedging.

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Hedging Using Futures

  • There are at least 3 major reasons hedging does not always work perfectly:

    • The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract (heating oil vs. jet fuel).

    • The hedger may be uncertain as to the exact date when the asset will be bought or sold.

    • The hedge may require the futures contract to be closed out before the expiration date.

  • These problems generate what is sometimes known as basis risk.

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Hedging Using Futures

  • For non-financial futures, the basis is defined as:

    basis= spot price of asset to be hedged - futures price of contract used

  • If the spot and the futures are the same asset, the basis should be zero at expiration. If the spot rises by more than the futures price, the basis increases, and this is called strengthening of the basis; the opposite is weakening of the basis.

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Hedging Using Futures

  • Let B1, B2, S1 , S2 , F1 and F2 represent the spot, futures and basis values at time 1 and 2 respectively.

    • S1= $2.5 F1=$2.20

    • S2= $2.0 F1=$1.90

    • So B1 = 2.5 - 2.20 = .30 and B2 = 2.0 - 1.9 = .10

  • Since B1>B2, the basis weakened.

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Hedging Using Futures

  • Let’s assume a couple of positions to see exactly how hedging would work.

    • Begin by assuming that the hedger knows she will sell the asset at time t2 and so takes a short futures position at time t1. What does she get at time 2?

      S2 + (F1 - F2) = 2.0 + (2.20 - 1.90) = $2.30

    • Which equals: F1 + (S2 - F2) = F1 + b2.

    • If t2 were the closing date of the futures contract, b2 would approach 0 and the price would be certain, but it is not, so there is basis risk.

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Hedging Using Futures

  • Financial Instruments

    For financial futures, basis risk tends to be small. This has to do with arbitrage being relatively easy to implement, and so prices are kept “in check”. The basis risk that does exist is largely due to the unknown future risk-free interest rate and its effect on the price.

  • Asset Mismatch

    If the asset to be hedged is not the one on which the futures contract is based, there is additional basis risk. Define S*2 as the price of the asset underlying the futures at time 2, and S2 be the price of the asset actually being hedged.

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Hedging Using Futures

  • Once again, the price being received at time 2 is:

    • S2 + (F1-F2), but now we have to deal with S*2 also:

    • F1 + (S*2-F2) + (S2 - S*2) (This is just adding and subtracting S*2!)

    • S*2-F2 is the basis risk arising from the hedge and S2 - S*2 is the basis risk arising from the mismatch.

  • Choice of Contract

    Frequently a potential hedger will have two choices of which contract they will use.

    • Choice of asset underlying the futures contract.

    • Choice of the delivery month.

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Hedging Using Futures

  • Rules of thumb:

    • Choose contract that most closely matches your asset (in terms of price movements).

    • Basis risk increases as the time difference between the hedge expiration and the delivery month increases. A common rule of thumb is “choose a delivery month that is as close as possible to, but no later than, the expiration of the hedge.”

  • Size of the Hedge

    An important issue is how many contracts to use to create the hedge. The hedge ratio is the ratio of the size of the position taken in futures contracts divided by the size of the exposure:

    HR = (size of futures position)/(size of exposure)

  • It is not always the case that the optimal ratio is 1.

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Hedging Using Futures

  • Define the following:

    • ΔS - change in spot price during hedge

    • ΔF - change in futures price during hedge

    • σs - standard deviation of ΔS

    • σF - standard deviation of ΔF

    • ρ - correlation coefficient between ΔF and ΔS

    • h - hedge ratio.

  • For a short hedge (i.e. long asset, short futures), the change in the value of the hedge during the life of the hedge is: ΔS - h ΔF

  • for a long hedge it is h ΔF - ΔS

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Hedging Using Futures

  • Recalling from your stats days, the variance of two assets is given by:

    • va,b = X2aσ2a + X2bσ2b + 2ρ XaσaXbσb

  • Applying this here: vS,F = σ2s + h2 σ2h + 2ρhσsσh

  • Taking the first partial with respect to h yields:

    • δV/δh = 2hσ2h + 2ρσsσh

  • At the variance minimizing level this will be equal to 0, and so

    δV/δh = 2hσ2h + 2ρσsσh = 0

    2hσ2h = -2ρσsσh or hσh = -ρσs

    • So h= -(ρσs)/ σh or -ρ (σs/ σh )

    • if ρ=1, h=1.

    • Note that in appendix 3 Hull assumes that you are shorting to hedge.

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Hedging Using Futures

  • The difficulty with the hedge ratio is that it simply tells you how many units of the hedge instrument to use for each unit of the primary instrument. It does not take into account that with a futures contract you have to buy in integral units of the contract, so you cannot buy the exact number of hedge instruments that you might want to use.

    • To determine the optimal number of contracts to purchase, you just multiply the hedge ratio by the ratio of the size of the position being hedged (NA) with the size of one unit of the futures contract you are using.

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Hedging Using Futures

  • So let’s look at the example 3.3 from Hull (page 59.)

  • An airline is going to purchase two million gallons of jet fuel in one month. There is no jet fuel futures contract (why would this be?), but there is a home heating oil contract.

  • In table 3.3 Hull provides us with monthly changes in the price of both fuel prices and the HHO futures price.

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Hedging Using Futures

  • Hull calculates the following parameters for us:

    σF= 0.0313 (st. deviation of change in HHO futures price)

    σS= 0.0263 (st. deviation of change in spot jet fuel price)

    ρ = 0.928 (correlation coefficient between the two)

    The optimal hedge ratio, therefore is:

    Note that Hull shows this as 0.78, because he assumes you realize that since you are hedging against increases in prices, you would be taking a short position in the futures contract.

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Hedging Using Futures

  • It turns out that Home Heating Oil futures contracts are for 42,000 gallons of heating oil (they trade on the NYMEX).

  • Recall that we want to hedge 2,000,000 gallons of heating oil. Therefore, the optimal number of contracts to use is:

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Hedging Using Futures

  • Before we can really do anything else with hedging, we need to have a background in the pricing of futures and forwards contracts.

  • This will be the main topic of lecture #3, although we will return to some hedging issues.