Futures Markets

1

• Futures Markets

2
Futures and Forward Contracts

• Relationship to options
• Options - give the holder the right or option to
  exercise the contract
• Futures Forward Contracts - entail an
  obligation for both parties to honor the contract
  to trade at a specified date at a price agreed
  upon today

3
Futures and Forward Contracts

• Forward - an agreement calling for a future
  delivery of an asset at an agreed-upon price
• Futures - similar to forward but feature
  formalized and standardized characteristics
• Size of contract
• Grade of deliverable asset
• Delivery date
• Delivery location
• Key difference in futures
• Standardization
• Secondary trading - liquidity
• Marked to market
• Clearinghouse warrants performance

4
Futures and Forward Contracts

• Types of Contracts
• Agricultural commodities
• Metals and minerals (including energy contracts)
• Foreign currencies
• Financial futures
• Interest rate futures
• Stock index futures

5
Futures and Forward Contracts

• Long Position agrees to take delivery (buy)
• Short Position agrees to make delivery (sell)
• Profit on positions at maturity
• Profit to Long spot price at maturity -
  original futures price (ST F0)
• Profit to Short original futures price spot
  price at maturity (F0 - ST)
• Zero Sum Game

6
Forward Contracts

• Private agreements between 2 parties to transact
  in the future at terms agreed to today
• Forward contracts can lead to efficiency gains
  for firms by eliminating price uncertainty for
  inputs and/or outputs
• Forward contracts require both parties to have
  essentially opposite needs, at the same time for
  a certain quantity of some good or asset
• Often the contract is backed only by the
  reputation of the firm(s) involved

7
Futures Contract

• Essentially standardized forward contracts which
  are backed by an organized exchange
• Futures contracts exist for commodities ranging
  from lumber to pork bellies, as well as financial
  assets such as currencies, stock indices,
  interest bearing assets, etc.
• For certain commodities, specific details of the
  commodity in question become important, such as
  the quality of the good and the location of
  delivery
• For financial futures the delivery of an actual
  asset rarely occurs and contracts are commonly
  closed out before maturity, or settled in cash at
  maturity

8
Futures Contract

• Exchange determines specific details of the
  contract
• Market forces determine the futures price
• If long, you agree to buy the commodity at the
  futures price on the delivery date
• If short, you agree to sell at the futures price
  on the delivery date
• The Wall Street Journal clippings on the
  following slide illustrate futures prices for
  several commodities, as well as financial futures
• Below the main title of each commodity are the
  details of the contract, such as the exchange on
  which its traded, the size of the contract and
  the denomination

9
(No Transcript)
10
Futures Contract

• For example, Corn futures are traded on the CBT
  (Chicago Board of Trade), with a contract size of
  5000 bushels and a price denominated in cents per
  bushel. In the left most column are the various
  months of delivery which can be contracted for
• The Settle price gives a representative
  trading price for the last few minutes of
  trading. Open interest gives the number of
  contracts outstanding at the end of the trading
  day
• As with options, the clearing house becomes the
  seller of the contract for the long position,
  and the buyer for the short position
• Remember, the cost of entering into the contract
  is 0
• Initial margin of between 5 and 15 of F0 is
  required
• Daily profits and losses accrue via marking the
  market (taxable events)
• If the price moves against you, you may receive
  a margin call

11
Trading Mechanics

• Clearinghouse - acts as a party to all buyers and
  sellers.
• Obligated to deliver or supply delivery
• Closing out positions
• Reversing the trade
• Take or make delivery
• Most trades are reversed and do not involve
  actual delivery

12
Trading With and Without a Clearinghouse
13
Margin and Trading Arrangements

• Initial Margin - funds deposited to provide
  capital to absorb losses
• Marking to Market - each day the profits or
  losses from the new futures price and reflected
  in the account.
• Maintenance or variance margin - an
  established value below which a traders margin
  may not fall.

14
Margin and Trading Arrangements

• Margin call - when the maintenance margin is
  reached, broker will ask for additional margin
  funds
• Convergence of Price - as maturity approaches
  the spot and futures price converge (FT ST 0)
• Delivery - Actual commodity of a certain grade
  with a delivery location or for some contracts
  cash settlement

15
Trading Strategies

• Speculation -
• short - believe price will fall
• long - believe price will rise
• Hedging -
• long hedge - protecting against a rise in price
• short hedge - protecting against a fall in price

16
Basis and Basis Risk

• Basis - the difference between the futures price
  and the spot price
• F - S
• over time the basis will likely change and will
  eventually converge (FT ST 0)
• Basis Risk - the variability in the basis that
  will affect profits and/or hedging performance

17
Valuation of Futures and Forwards Contracts

• Most forward and futures contracts can be valued
  using simple arbitrage arguments
• Spot-futures parity theorem - two ways to acquire
  an asset for some date in the future
• Strategy 1 Purchase it now and store it
• Strategy 2 Take a long position in futures
• These two strategies must have the same market
  determined costs

18
Parity Example Using Gold

• Strategy 1 Buy gold now at the spot price
  (S0) and hold it until time T when it will be
  worth ST
• Strategy 2 Enter a long position in gold
  futures today and invest enough funds in T-bills
  (risk-free) so that it will cover the futures
  price

19
Parity Example Outcomes

• Action Initial flows Flows at T
• Strategy A Buy gold - S0 ST
• Strategy B (1) Long futures 0 ST F0
• (2) Invest in Bill
• F0/(1rf)T - F0/(1rf)T F0
• Total for B - F0/(1rf)T
  ST
• Since the strategies have the same flows at time
  T
• F0 / (1 rf)T S0
• F0 S0 (1 rf)T
• The futures price has to equal the carrying cost
  of the gold.

20
Spot-Futures Parity Theorem

• Without service or payment case
• The spot-futures parity relationship states that
  the equilibrium futures price on an asset
  providing no service or payment (such as
  dividends) is

21
Spot-Futures Parity Theorem

• 2. With service or payment case
• If the asset provides services or payments (such
  as dividends) with yield d, the parity
  relationship becomes
• Let I represent the present value of cash income
  stream, which can be 1 or more payments at known
  dates in the future, discounted to the present at
  the rate rf. The relationship between the spot
  and futures price in this case is

22
Spot-Futures Parity Theorem

• Suppose the spot price of a 5-year bond is
  currently 900, and the bond is expected to make
  coupon payments of 60 6 months from now, and
  another 60 payment 12 months from now. If the
  annual risk free rate is 9, what will the
  forward price on this bond be, if delivery is to
  take place 1 year from now?
• First we need to calculate the present value of
  the coupon payments
• Now, using I, calculate the forward price of, so
  as to rule out arbitrage

23
Spot-Futures Parity Theorem

• In Class Exercise
• Assume there is a one-year forward contract
  traded on a stock that pays a dividend of 3
  after 9 months. The current price of the stock
  is 100, the annual risk-free rate is 10, F0 is
  108, and the consensus forecast of analysts is
  that the end-of-year price will be 118.
• What is the forward price consistent with absence
  of arbitrage?
• Is there an arbitrage? If so, indicate how you
  would exploit it below.
• Forward contract (long or short)
• Risk-free rate (borrow or lend) and amount
  _______.
• Stock (buy or sell short)
• Cash flow today__________.
• Cash flow one year from now__________.

24
Gold Futures Prices October 2004
25
Stock Index Contracts

• Available on both domestic and international
  stocks
• Advantages over direct stock purchase
• lower transaction costs
• better for timing or allocation strategies
• takes less time to acquire the portfolio

26
Stock Index Futures
27
Correlations Among Major US Stock Market Indexes
28
Index Arbitrage

• Exploiting mispricing between underlying
  stocks and the futures index contract
• Futures Price too high - short the future and
  buy the underlying stocks
• Futures price too low - long the future and
  short sell the underlying stocks
• Difficult to do in practice
• Transactions costs are often too large
• Trades cannot be done simultaneously

29
Additional Financial Futures Contracts

• Foreign Currency
• Forwards versus futures
• Interest Rate Futures

30
Spot and Forward Prices in Foreign Exchange
31
Swaps

• Large component of derivatives market
• Over 100 trillion outstanding
• Interest Rate Swaps
• Currency Swaps
• Interest rate swaps are based on LIBOR

32
Interest Rate Swap