Topic 2 Forwards and Futures

1
Topic 2Forwards and Futures
2
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.

3
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.

4
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.

5
Specification of Futures Contracts

• When dealing with a futures contract, there are a
  number of details that must be iron-clad. Lets
  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.

6
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.

7
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.

8
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.

9
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.

10
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.
• Lets look at a couple of actual contract
  specifications.

11
Specifications of Futures Contracts

• Corn on the Chicago Board of Trade
• http//www.cbot.com/cbot/www/cont_detail/0,1493,
  145813814389,00.html
• US Treasury Bond Chicago Board of Trade
• http//www.cbot.com/cbot/www/cont_detail/0,1493,14
  5814014431,00.html
• Random Length Lumber on the Chicago Mercantile
  Exchange
• http//www.cme.com/prd/overview_LB661.html
• Live Cattle on the CME
• http//www.cme.com/prd/overview_LC654.html
• Platinum on the NYMEX
• http//www.nymex.com/jsp/markets/pla_fut_specif.
  jsp
• Propane (but not propane accessories) on the
  NYMEX
• http//www.nymex.com/jsp/markets/pro_fut_specif.
  jsp

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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.

13
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.)
• Lets 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.

14
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.

15
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.

16
Quotes

• 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 www.BarChart.com

17
Quotes

• For example, lets look at the live cattle
  contract that trades on the CBOT.
• First, lets remember the specifications
• http//www.cme.com/clearing/clr/spec/contract_spe
  cifications_cl.html?productLC
• Then, lets look at the current days trading
  results
• http//www.cme.com/trading/dta/del/delayed_quote.
  html?ProductSymbolLCProductFoiTypeFUTProductVe
  nueRProductTypecom

18
Quotes

• Lets also look at the gold futures contract (as
  quoted from Barchart.com)
• http//www2.barchart.com/dfutpage.asp?symGCcode
  BSTK
• It is also interesting to see what is happening
  with the random length lumber contract.

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Convergence

• 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. Lets
  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 5100 of contracts or 500 per
  contract.

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Convergence

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

Price
Futures price
Spot Price
Date
21
Convergence

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

22
Convergence

• 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.

23
Convergence
24
Convergence
25
Convergence
26
Settlement

• 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 (exchanges
  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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Settlement

• 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 SP 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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Regulation

• 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.

29
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 doesnt make
  you wealthier, it just insures that you wont
  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.

32
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 F12.20
• S2 2.0 F11.90
• So B1 2.5 - 2.20 .30 and B2 2.0 - 1.9
  .10
• Since B1gtB2, the basis weakened.

33
Hedging Using Futures

• Lets 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.

34
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 S2 as the price
  of the asset underlying the futures at time 2,
  and S2 be the price of the asset actually being
  hedged.

35
Hedging Using Futures

• Once again, the price being received at time 2
  is
• S2 (F1-F2), but now we have to deal with S2
  also
• F1 (S2-F2) (S2 - S2) (This is just adding
  and subtracting S2!)
• S2-F2 is the basis risk arising from the hedge
  and S2 - S2 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
• ?S - change in spot price during hedge
• ?F - change in futures price during hedge
• ss - standard deviation of ?S
• sF - standard deviation of ?F
• ? - correlation coefficient between ?F and ?S
• 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 ?S - h ?F
• for a long hedge it is h ?F - ?S

38
Hedging Using Futures

• Recalling from your stats days, the variance of
  two assets is given by
• va,b X2 as2a X2 bs2b 2? XasaXbsb
• Applying this here vS,F s2s h2 s2h
  2?hsssh
• Taking the first partial with respect to h
  yields
• dV/dh 2hs2h 2?sssh
• At the variance minimizing level this will be
  equal to 0, and so
• dV/dh 2hs2h 2?sssh 0
• 2hs2h -2?sssh or hsh -?ss
• So h -(?ss)/ sh or -? (ss/ sh )
• if ?1, h1.
• Note that in appendix 3 Hull assumes that you are
  shorting to hedge.

39
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.

40
Hedging Using Futures

• So lets 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.

41
Hedging Using Futures

• Hull calculates the following parameters for us
• sF 0.0313 (st. deviation of change in HHO
  futures price)
• sS 0.0263 (st. deviation of change in spot jet
  fuel price)
• ? 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.

42
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

43
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.