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					              Chapter 8 - Futures
• Over the next few chapters, we will be discussing
  a recent development (over the last 25 years) in
  the financial markets
• Derivatives are a financial instrument that derive
  their value from another asset
• In this chapter, we look at the oldest type of
  derivative called futures
            Chapter 8 - Overview
• What is the difference between forward contracts
  and futures contracts?
• How does one invest in futures?
• What types of futures contracts exist?
• What is a hedge?
• How can futures be used for hedging and for
• How can we price futures contracts?
     Spot vs. Forward contracts

• Spot contracts are immediate transactions
   – The terms are determined at the same time as delivery
     and payment
   – Example: buy a Big Mac at McDonald’s
• Forward contracts are an agreement to transact (in
  fact, an obligation to transact) in the future. The
  terms of the transaction are determined today.
   – Terms to agree on: delivery date, price, type of asset
   – Forward contracts are completely negotiated between
     the contracting parties
   – Example: you agree to buy a house. The closing date,
     purchase price, etc. are all negotiated
• Gains and losses on
                                     Profit and Loss on
  forward contracts are              Forward Contracts
  based on the movement of
  the underlying instrument
• Example: Harry agrees to
  buy wheat in one month at
  a price of $3 per bushel (a
  forward contract)
   – Case 1: If the price of wheat
     at the end of one month is
     $4 per bushel, Harry has a
     $1 gain
   – Case 2: If the price of wheat
     at the end of one month is
     $1 per bushel, Harry has a
     $2 loss
                 Futures Contracts
• A futures contract, in principal, is similar to a
  forward contract
   – It is an agreement, made today, to transact in the future
• However, futures contracts are standardized and
  trade on exchanges
   – Forwards are privately negotiated and a secondary
     market does not exist
• Types include agricultural, metals, oils, financials,
  foreign currencies
             Futures quotes (p.282)
• Contract definition (see soybean example on p.
   – Specifies the terms of the contract such as the delivery
     date, the amount of the asset to be delivered
• Open, hi, lo, settle, change
   – Self-explanatory
• Lifetime hi/lo
• Open interest
   – The number of contracts outstanding on the contract
   – Note that there must be a buyer and a seller for each
     open contract
   – Open interest declines as delivery approaches
                  Trading futures
• Recall the system for trading stocks (NYSE,
• There are various futures markets (e.g. CBOT)
• At the exchange, trades are made in a circular
  shaped “pit”
• Brokers execute trades for their clients
   – Each keep a separate limit book
• Floor traders execute on their own account
• Trades are made by an “open outcry” system
• There are price limits in futures trading (circuit
           Dealing with default risk
• One of the main reasons for the development of
  futures contracts was the default risk in forwards
• Recall our example: wheat prices increase, Harry
  wins. Prices decrease, Harry loses.
• But obligation exists only at maturity or expiration
  of the forward contract
   – Thus, the buyer and seller of forwards are exposed to
   – Default risk or counterparty risk
  Differences between Forwards and
• Features reducing credit risk
   – Daily settlement or mark-to-market
   – Margin account
   – Clearinghouse
• Features promoting liquidity
   – Contract standardization
   – Traded on organized exchanges
                 Daily Settlement

• Recall that forward contracts have no settlement
  until maturity
• Futures contracts settle every day
   – Like a series of one day forward contracts
• At end of trading day, any contract value must be
   – Contract is “marked-to-market”
• Risk is reduced to daily price movement
               Margin Requirements
• To use futures markets,
  party must post collateral
  in cash called margin
   – Daily gains/losses (mark-to-
     market) posted to margin
• Margin guarantees
   – Higher margin for more
     volatile markets
• Initial margin is amount to
  open contract
          Margin Requirements (p.2)
• If account balance drops below maintenance
  margin, customer must deposit more funds (this is
  a margin call)
   – Get back to initial margin (difference from stocks)
   – If not met, customer position is closed out
• The amount in your margin account is the equity
  in your position
   – This can be retrieved at any time if the position is
     closed out
          Margin Account Example
• Instead of a forward contract, Harry buys a futures
  contract on wheat at $3 per bushel
   – One futures contract is for 5,000 bushels
• The following prices represent closing futures
  prices (per bushel) for the next five days: $3.05,
  $2.80, $2.75, $2.60, $2.90
• What is the value of the margin account if the
  initial margin is $5,000 and the maintenance
  margin is $3,500
       Margin Account Example Solution

Day   Price Contract Price   Change Margin    Margin Call
 0    $3.00    $15,000          $0   $5,000
 1    $3.05    $15,250         $250  $5,250
 2    $2.80    $14,000       -$1,250 $4,000
 3    $2.75    $13,750        -$250  $3,750
 4    $2.60    $13,000        -$750  $3,000    + $2,000
 5    $2.90    $14,500        $1,500 $6,500
• Even with daily settlement and margin accounts,
  there are default risk costs
   – Margin may not be enough if prices move a lot
• Clearinghouse becomes counterparty to every
   – Individual counterparty credit analysis is not needed
• Default risk is spread across the entire market
• With the clearinghouse, positions can be easily
  closed out prior to expiration
   – Closing out a position is also called making a reverse
     trade or unwinding the position
           Speculators and hedgers
• First, buying a future is taking a long position and
  selling a future is taking a short position
• There are two types of players in the futures
• Hedgers use futures to lock in future prices
   – They desire to shed risk
   – Hedgers can be long or short
• Speculators use futures to try to make money on
  price movements
   – They desire to assume risk
             Examples of hedging
• Short hedge
  – It is the spring and a farmer planting her corn is worried
    that when the harvest comes, the price of corn will be
    very low.
  – She can reduce the uncertainty in future prices by
    selling corn futures
• Long hedge
  – A snack company uses corn in the production of tortilla
    chips. It is worried that the price of corn will increase.
  – It can reduce the uncertainty in future prices by buying
    corn futures
Closing out a position
           • Speculators do not really
             want to buy or sell the
             actual asset
              – They close out their
                position before maturity
           • It is not necessary that
             hedgers actually go
             through with the contract
              – It is only important that the
                futures gain/loss offsets (or
                hedges) their other position
• Basis is difference between spot price and futures
  price: F - P
• Risk exposure may be change in basis
   – Hedging reduces risk of changing prices but introduces basis
• Sometimes the hedger cannot match a futures contract
  with the exact underlying instrument. Instead, they use
  a closely related futures contract to hedge
   – This is called a “cross hedge”
   – Example: an apple orchard uses corn futures to hedge the
     volatility of apple prices
            Pricing futures contracts
• Arbitrage is the ability to make a riskless profit by
  simultaneously trading related securities
   – Different stock markets that trade the same stock
• Using arbitrage arguments, we can see that the
  futures price will be equal to the spot price plus
  the “cost of carrying” the underlying asset
   – Cost of carry reflects charges for holding asset now vs.
     buying in the future
             Example in book p.296
• Suppose that a futures contract on gold expires in
  one year, the spot price is $370 per ounce, the risk
  free interest rate is 5%, and storage costs are $1.20
  per ounce
• Gold futures are on 100 oz. and the initial margin
  is $1,800
• If we hold an inventory (buy spot) we must pay all
  costs associated with holding the inventory
   – Here, the costs of carry are storage costs and financing
• Let’s see if any arbitrage exists
                    Case 1: Sell futures
• Suppose futures price is at $400
• We can cover the obligation to deliver gold by
  purchasing gold today and storing it
     – Instead of using our own money, let’s borrow
     – All cash flows become fixed
     – There is an arbitrage
• If arbitrage is not to exist, then the futures price
  must not compensate the futures seller for more
  than the cost of carry
Pfuture  Pspot  cost of carry  370  1.20  (370  18  1.20 )  5%  390 .66
                Case 2: Buy futures
• Suppose futures price is $360
   – We receive gold in one year
• Let’s also sell gold today and invest the proceeds
   – We borrow someone’s gold and pay a borrowing fee
   – There is an arbitrage
• If arbitrage is not to exist, then the futures price
  must not be too low
      Pfuture  Pspot  cost of carry
             Pspot  borrowing fee  interest on sale
             370  20  (370  20  18)  5%  366.60
             Futures price bounds
• Combining the two inequalities, we can determine
  what the futures price should be if there is no
  arbitrage opportunities

           366 .60  Pfutures  390 .66

• If prices are outside this range, arbitrageurs will
  go through the above transactions and earn profit
                  Financial futures
• Financial futures are when the underlying asset is
  a financial asset, index, or interest rate
   – Futures exist for stock indices, T-bills, T-bonds
• As in the case of the farmer and tortilla company,
  investors can hedge their financial assets with
  financial futures
       Hedging with financial futures
• NOTE: T-bonds futures assume that the
  underlying contract is a $100,000, 20-year, 8%
  bond at delivery
   – They recently change this to a 6% bond
• If you want to protect your T-bond against interest
  rate increases, you should use a short hedge
   – Sell T-bond futures
• Can you think of a reason why you would want to
  protect against interest rate declines?
   Speculating with
• Futures can be an attractive alternative to buying
  the underlying asset if you have views on the
  movement of the asset
• Example: Buy T-bond futures if you expect
  interest rates to decline instead of buying T-bonds
   – Only have to pay the margin, not the whole cost
   – Due to the margin, you leverage results (good and bad)
   – Futures are more liquid, easier to unload
• See T-bond spot vs. future comparison on p.302
               Stock index futures
• When the underlying asset is a stock index
   – S&P 500, NASDAQ, foreign market indices
• The index is impractical and expensive to deliver
• When delivery is difficult, futures can be cash
  settled instead of physical delivery
   – S&P 500 stock index futures delivers at $250 times the
     index value
• Diversification is cheap – just use index futures
• Example p.305
                  Index arbitrage
• Large institutional investors monitor the
  relationship between stock index futures and the
  underlying index component stocks
• If there is an arbitrage opportunity, computers
  automatically route orders to take advantage of the
   – These orders are grouped and are called program trades
   – Remember DOT system in stock markets?
             Review of Chapter 8
• Differences between forwards and futures
• Mark-to-market example
• Trading futures contracts
   – Hedging and speculation
• Basic futures pricing
• Examples of financial futures

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