FUTURES

1

• FUTURES
• FORWARDS

2
Introduction

• The futures market enables various entities to
  lessen price risk, the risk of loss because of
  uncertainty over the future price of a commodity
  or financial asset
• The two major market participants are the hedger
  and the speculator
• A futures contract is a legally binding agreement
  to buy or sell something in the future
• The person who initially sells the contract
  promises to deliver a quantity of a standardized
  commodity to a designated delivery point during
  the delivery month the other party to the trade
  promises to pay a predetermined price for the
  goods upon delivery

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Forward and Futures

• Forward contract two parties agree to exchange
  an asset on a future date at a price set today.
• no collateral posted
• Tailor-made
• OTC
• Futures Contract a highly liquid version of a
  forward contract.
• margin account settlement price
• Futures commission merchant
• Trading pit
• Exchange clearinghouse

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Forward and Futures Trading Mechanics
5
Trading Mechanics

• Most futures contracts are eliminated before the
  delivery month
• The speculator with a long position would sell a
  contract, thereby canceling the long position
• The hedger with a short position would buy a
  contract, thereby canceling the short position
• Example
• Suppose a speculator purchases a July soybean
  contract at a purchase price of 6.12 per bushel.
  The contract is for 5,000 bushels of No. 2 yellow
  soybeans at an approved delivery point by the
  last business day in July.
• Upon delivery, the purchaser of the contract must
  pay 6.12(5,000) 30,600.
• At the delivery date, the price for soybeans is
  6.16. This equates to a profit of 6.16 - 6.12
  0.04 per bushel, or 200. If the spot price on
  the delivery date were only 6.10, the purchaser
  would lose 6.12 - 6.10 0.02 per bushel, or
  100.

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Ensuring the Promise is Kept

• In 1974, Congress passed the Commodity Exchange
  Act establishing the Commodity Futures Trading
  Commission (CFTC)
• Ensures a fair futures market
• A self-regulatory organization, the National
  Futures Association was formed in 1982
• Enforces financial and membership requirements
  and provides customer protection and grievance
  procedures
• The Clearing Corporation ensures that contracts
  are fulfilled
• Becomes party to every trade
• Ensures the integrity of the futures contract
• Assumes responsibility for those positions when a
  member is in financial distress

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Some contracts size and margin requirements

• Good faith deposits (or performance bonds) are
  required from every member on every contract to
  help ensure that members have the financial
  capacity to meet their obligations

• Selected Good Faith Deposit Requirements
• Data as of January 2, 2004

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Quotations
9
Types of Orders

• A broker in commodity futures is a futures
  commission merchant (not the individual who
  places the order)
• When placing an order, the client should specify
  the type of order
• A market order instructs the broker to execute a
  clients order at the best possible price at the
  earliest opportunity
• With a limit order, the client specifies a time
  and a price
• E.g., sell five December soybeans at 540, good
  until canceled
• A stop order becomes a market order when the stop
  price is touched during trading action
• When executed, stop orders close out existing
  commodity positions
• E.g., a short seller may use a stop order to
  protect himself against rising commodity prices

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Market Participants

• A hedger is someone engaged in a business
  activity where there is an unacceptable level of
  price risk
• A processor earns his living by transforming
  certain commodities into another form? e.g., a
  soybean processor buys soybeans and crushes them
  into soybean meal and oil
• A speculator finds attractive investment
  opportunities in the futures market and takes
  positions in futures in the hope of making a
  profit (rather than protecting one). The
  speculator is willing to bear price risk. For
  example, a position trader is someone who
  routinely maintains futures positions overnight
  and sometimes keep a contract for weeks a day
  trader closes out all his positions before
  trading closes for the day
• Scalpers (or locals) are individuals who trade
  for their own account, making a living by buying
  and selling contracts. Scalpers help keep prices
  continuous and accurate.
• Example Scalping With Treasury Bond Futures
• You just sold 5 T-bond futures to ZZZ for 77
  31/32. Now, a sell order for 5 T-bond futures
  reaches the pit and you buy them for 77 30/32.
  Thus, you just made 1/32 on each of the 5
  contracts, for a dollar profit of
• 1/32 x 100,000/contract x 5 contracts 156.25

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ClearingHouse Matching Trades

• Every trade must be cleared by or through a
  member firm of the Board of Trade Clearing
  Corporation
• Each trader is responsible for making sure his
  deck promptly enters the clearing process
• After the Clearing Corporation receives trading
  cards
• Mismatches (out trades) result in an Unmatched
  Trade Notice being sent to each clearing member
• After resolving all out trades, the computer
  prints a daily Trade Register
• Shows a complete record of each clearing members
  trades for the day
• Contains subsidiary accounts for each customer
  clearing through the firm
• Commodity prices may move so much in a single day
  that good faith deposits for many members are
  seriously eroded before the day ends.
• The president of the Clearing Corporation may
  issue a market variation call for members to
  deposit more funds into their account

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Dealing with Margins

• Assume you are short 2 December SP 400 futures
  contracts for 924.5 (an SP 400 contract is for
  500 times the index). The total value of the
  position is 2 times 500 times 924.5 or 924,500.
  Let s assume that your initial margin is 5 or
  46,225 and your maintenance margin is 4.5, that
  is 41,602.5. Lets look at when a margin call
  will occur

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Margins
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Some notations

• Futures Price the price, set today, at which
  the asset will be traded in the future
• At Maturity futures price spot price
• Trade agreements
• Buy a futures, you are long in the futures market
  ()
• Sell a futures, you are short in the futures
  market(-)

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Speculating with futures

• Assume that a buyer and seller agree on a futures
  price of 45. At expiration, the underlying
  security is priced at 53.
• Buyer makes 8.00
• Seller loses 8.00
• At t0, Buyer went long on the contract at 45
• At maturity, Buyer bought from seller at 45and
  sold on the spot at 53 to realize the profit of
  8.
• At t0, seller went short on the contract at 45
• At maturity, seller rushed to buy at 53 on the
  spot, and sold at a committed 45 to buyer, to
  lose 8.

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Hedging

• Futures contracts allow buyers and manufacturers
  to lock into prices and costs, respectively
• If a firm wants gold, it buys contracts,
  promising to pay a set price in the future (long
  hedge)
• A gold mining company sells contracts, promising
  to deliver the gold (short hedge)
• Hedge - a trading strategy in which derivative
  securities are used to reduce or completely
  offset a counterparty's risk exposure to an
  underlying asset.
• Long hedge - created by supplementing a short
  spot holding with a long futures position.
• Short hedge - holding a short futures position
  against the long position on the spot.

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Example

• A farmer expects to harvest 40,000 bushels of
  wheat in August. It costs him about 3.05 a
  bushel to plant and harvest the crop. An August
  futures price of 3.45 is available. How can the
  farmer lock the price of his crop?

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Solution

• Build a selling (short) hedge sell 8 of these
  August futures contracts (40,000/5,000).

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An other example

• You are managing a 100,000 (face value)
  portfolio in T-BONDS priced at 98-10 or
  98,312.5. In June, you are concern with a
  forthcoming increase in interest rates (within
  the next 6 months, around Novembermay be). A
  December T-bond futures priced at 97-00 (97,000)
  is available. On November 15th interest rates
  increase and T-bonds drop to 96-08 the December
  futures contract price drops to 95-10.

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Solution

• You enter into a short hedge to lock the value
  of your portfolio for the next seven month.

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Another Example

• you are managing 5 million of common stock
  portfolio. You are concern that the market will
  go down in the next three months. The current
  3-month SP400 index futures is selling at 200.
  The price of 1 contract is 500 per index point
  Assume that the portfolio value falls to 4
  million two months after and that the SP400
  index futures falls simultaneously at 170.

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Solution

• you are long in the cash market to protect
  yourself, you will go short in the futures market
  (short hedge) if the value of one contract is
  100,000 (200 x 500), you need 50
  (5,000,000/100,000) contracts to hedge the
  whole 5,000,000.

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Imperfect hedge

• In practice, a contract on a similar asset may
  not exist----gtuse the closest proxy!
• For bond portfolio, a T-bond futures
• For Stock portfolio, an index futures
• For a combination, treat each asset class
  independently

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Imperfect hedges and bond portfolio

• The objective of hedging is to select a hedge
  ratio (D) such as
• (change in S) hedge ratio X (change in F) 0
• or
• hedge ratio D (change in S) / (change in F)

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Imperfect hedges and bond portfolio(continued)
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Imperfect hedges and bond portfolio(continued)
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Example

• suppose an investment banker underwrites the
  issue of a bond that will be sold in 3 months. He
  has set the indenture and expect to sell the
  animal at par! The total issue amounts to
  10,000,000 (or 10,000 bonds). Yet, he is
  concerned about a rise in interest rates.

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Solution

• He short-hedges the new issue in the T-BOND
  futures market. He knows that the bond is far
  from being a T-BOND, but futures on this bond are
  not traded. Knowing that a T-Bond futures
  contract covers 100,000, he finds that the right
  amount of contracts to be sold to hedge the new
  issue should be 82 contracts

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Solution (continued)
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Example

• You manage a fund you plan to sell 100,000,000
  of a type of bonds in 2 months from now to
  reallocate the assets of the portfolio.

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Solution

• You build a short hedge by selling 1,111 T-Bond
  futures

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Dealing With Coupon Differences

• To standardize the 100,000 face value T-bond
  contract traded on the Chicago Board of Trade, a
  conversion factor is used to convert all
  deliverable bonds to bonds yielding 6

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Hedging With Interest Rate Futures

• The hedge ratio is
• The number of contracts necessary is given by

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Futures Hedging Example

• A bank portfolio holds 10 million face value in
  government bonds with a market value of 9.7
  million, and an average YTM of 7.8. The weighted
  average duration of the portfolio is 9.0 years.
  The cheapest to deliver bond has a duration of
  11.14 years, a YTM of 7.1, and a CBOT correction
  factor of 1.1529.
• An available futures contract has a market price
  of 90 22/32 of par, or 0.906875. What is the
  hedge ratio? How many futures contracts are
  needed to hedge?

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On the equity side Index futures

• The fastest growing segment of the futures market
  is in financial futures
• Stock index futures are similar in every respect
  to a traditional agricultural contract except for
  the matter of delivery
• Index futures settle in cash rather than by
  delivery of the underlying asset
• There is no actual delivery mechanism at
  expiration of an SP 500 futures contract
• You actually deliver the dollar difference
  between the original trade price and the final
  price of the index at contract termination

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Synthetic Index Portfolios

• Large institutional investors can replicate a
  well-diversified portfolio of common stock by
  holding
• A long position in the stock index futures
  contract and
• Satisfying the margin requirement with T-bills
• The resulting portfolio is a synthetic index
  portfolio
• The futures approach has the following advantages
  over the purchase of individual stocks
• Transaction costs will be much lower on the
  futures contracts
• The portfolio will be much easier to follow and
  manage
• As time passes, the difference between the cash
  index and the futures price will narrow
• At the end of the futures contract, the futures
  price will equal the index (basic convergence)

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Imperfect hedge and equity portfolio
Using Futures Contracts to Hedge Portfolios You
are the manager of an equity portfolio. You are
bullish in the long term, but anticipate a
temporary market decline. How can you use
futures contracts to hedge your stock portfolio?
If you are long stock, you should be short
futures. You need to calculate the number of
contracts necessary to counteract likely changes
in the portfolio value.

• In a perfect hedge
• N portfolio value/contract value
• In reality, there are only index futures and your
  portfolio is not exactly the same as the index!
• Nportfolio value/contract value x ?portfolio

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Example

• Suppose that in mid-December you own a portfolio
  worth 3,243,750 you expect the market to plunge
  within the next 6 months thus, you sell June SP
  500 futures contracts which currently trade at a
  settlement price of 617.00. The value of a single
  contract is 308,500--i.e., 500 x 617-- your
  portfolio has a beta of 1.15 with the SP400
  then, you decide to short 12 contracts, as you
  are long in the equity market

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Hedge Ratio example

• Determining the Factors for A Hedge
• Suppose the manager of a 75 million stock
  portfolio (with a beta of 0.9 and a dividend
  yield of 1.0) wants to hedge using the December
  SP 500 futures.
• On the previous day, the SP 500 closed at
  1,484.43, and the DEC 00 SP 500 futures closed
  at 1,517.20.
• The value of the futures contract is 250 x
  1,517.20 379,300
• And the hedge ratio is 178 contracts

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The Market Falls

• Using the Hedge in A Falling Market
• Assume the SP 500 index falls 5, from 1,484.43
  to 1,410.20 after four months.
• Given beta, the portfolio should have fallen by
  5.0 x 0.9 4.5, which translates to
  3,375,000. However, you receive dividends of 1
  x .333 x 75,000,000 250,000.
• If you sold 178 contracts short at 1,517.20,
  your account will benefit by (1,517.20
  1,410.20) x 250 x 178 4,761,500.
• The combined positions (stock, dividends, and
  futures contracts) result in a gain of 1,636,500.

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The Market Rises

• Using the Hedge in A Rising Market
• Assume the SP 500 index rises from 1,484.43 to
  1,558.70 after four months.
• Given beta, the portfolio should have advanced
  by 5.0 x 0.9 4.5, which translates to
  3,375,000. You still receive dividends of 1 x
  .333 x 75,000,000 250,000.
• If you sold 178 contracts at 1,517.20, your
  account will lose (1,517.20 1,558.70) x 250 x
  178 1,846,750.
• The combined positions (stock, dividends, and
  futures contracts) result in a gain of
  1,778,250.

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The Market is Unchanged

• Using the Hedge in An Unchanged Market
• Assume the SP 500 index remains at 1,484.43
  after three months.
• There is no gain on the stock portfolio.
  However, you still receive dividends of 1 x .333
  x 75,000,000 250,000.
• If you sold 178 contracts short at 1,517.20,
  your account will benefit by (1,517.20
  1,484.50) x 250 x 178 1,455,150.
• The combined positions (stock, dividends, and
  futures contracts) result in a gain of
  1,705,150.

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Speculation Active bond portfolio management
Increasing Duration With Futures

• Extending duration may be appropriate if active
  managers believe interest rates are going to fall
• Adding long futures positions to a bond portfolio
  will increase duration

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Example

• A portfolio has a market value of 10 million,
  an average yield to maturity of 8.5, and
  duration of 4.85. A forecast of declining
  interest rates causes a bond manager to decide to
  double the portfolios duration. The cheapest to
  deliver Treasury bond sells for 98 of par, has a
  yield to maturity of 7.22, duration of 9.7, and
  a conversion factor of 1.1223. Determine the
  number of futures contracts needed to double the
  portfolio duration.

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Speculation Active management-- Adjust Portfolio
Beta
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Example

• You have a 25 million equity portfolio
  consisting of 22.5M in stocks and 2.5M in
  T-bills. Current beta of equity portion is 0.95.
  You want to increase it to 1.10. An SP400
  futures contract is quoted at 476.6. Thus, You
  need to be long 26 contracts
• N1.1-(22.5/25) X .95 X 25,000,000/(500 X
  476.6)25.7
• It is positive thus buy 26 contracts (you cannot
  buy 25.7 contracts).

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Adjusting Market Risk Example

• Determining the Number of Contracts Needed to
  Increase Market Exposure
• Suppose the manager of a 75 million stock
  portfolio with a beta of 0.9 would like to
  increase market exposure by increasing beta to
  1.5. Yesterday, DEC 00 SP 500 futures closed at
  1517.20
• How can the manager use futures to accomplish
  this goal, assuming the composition of the stock
  portfolio remains unchanged?
• The manager should go long futures and hold them
  with the stock portfolio. Specifically, he should
  purchase 119 SP 500 futures contracts

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Speculation Tactical Changes using Futures

• Investment policy statements may give the
  portfolio manager some latitude in how to split
  the portfolio between equities and fixed income
  securities
• The portfolio manager can mix both T-bonds and
  SP 500 futures into the portfolio to adjust
  asset allocation without disturbing existing
  portfolio components

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Example Initial Situation

• Portfolio market value 175 million
• Invested 82 in stock (average beta 1.10) and
  18 in bonds (average duration 8.7 average YTM
  8.00)
• The portfolio manager wants to reduce the equity
  exposure to 60 stock
• Determine
• How many contracts will remove 100 of each
  market and interest rate risk
• What percentage of this 100 hedge matches the
  proportion of the risk we wish to retain
• Some data
• Stock Index Futures ?September settlement
  1020.0
• Treasury Bond Futures? September settlement
  91.05
• Cheapest to deliver bond
• Price 95
• Maturity 18 years
• Coupon 9
• Duration 8.60
• Conversion factor 1.3275

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Initial Situation
51
Bond Adjustment
Thus, the manager should buy 521 T-bond futures
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Stock Adjustment

• For this portfolio, the hedge ratio is

53
In sum

• The portfolio manager can change the asset
  allocation from 82 stock, 18 bonds to 60
  stock, 40 bonds by
• Buying 521 T-bond futures and
• Selling 166 stock index futures

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Neutralizing Cash

• It is harder to beat the market with the
  downward bias in relative fund performance due to
  cash
• Cash can be neutralized by offsetting it with
  long positions in stock index futures
• Cash can be neutralized by offsetting it with
  long positions in interest rate futures

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Example

• An all-equity fund has a benchmark that follows
  the SP500.
• Fund size500M
• SP500 futures1200
• Beta1
• SP500 return11.5 (long run return)
• Cash return2.5 (long run return)
• Allocation 95 Equity, 5 cash
• Cash need to be on hand in case of investors
  redemptions.
• The fund receives periodic contributions. They
  have a problem cash does return less than equity
  and over long period of time, large cash
  positions biases the performance of a portfolio.
• ?E(Rp)95 x 11.55 x 2.511.05versus 11.5
• One can offset this 45 BP loss by being long on
  SP500 futures?increase the beta of the portfolio
  by neutralizing the cash portionI.e.,
• N(Cash Portfolio size)/(futures size) x beta
  (5 x 500M)/(1200 x 250) x183
• By buying 83 SPX futures, the 95 equity and 5
  cash portfolio will behave exactly like a 100
  equity portfolio
• 475M in stock25M in cash 83 in stock futures
  500M in stocks