FUTURES

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FUTURES
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Definition

• Futures are marketable forward contracts.
• Forward Contracts are agreements to buy or sell
  a specified asset (commodities, indices, debt
  securities, currencies, etc.) at an agreed-upon
  price (f) for purchase or delivery on a specified
  date (delivery date T).

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Futures Exchanges

• Futures are traded on organized exchanges
• CBOT
• CME
• NYFE
• The exchanges provide marketability
• Listings
• Standardization
• Position Traders
• Clearinghouse

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Futures Positions

• Long Position Agreement to buy.
• Short Position Agreement to sell.
• Long Hedge Taking a long position in futures to
  protect against a price increase.
• Short Hedge Taking a short position in a futures
  to protect against a price decrease.

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Clearinghouse

• Like the OCC, the futures clearinghouse
  guarantees each contract (both long and short
  positions) and acts as an intermediary, breaking
  up each contract after it has been established.

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Example

• Suppose A buys a September Wheat Futures contract
  (5,000 bu.) from B for fo 2.50/bu.
• A is long B is Short
• After the contract is established, the CH steps
  in and breaks up the contract.

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CH Records

• A agrees to buy at 2.50.
• B agrees to sell at 2.50.

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Example Continued

• Suppose the price of wheat increases, causing the
  September futures price to increase to ft
  3.00.
• Suppose A decides to close by going short.
• New Contract A agrees to sell September Wheat
  futures at 3.00 to C.
• A is short C is long.
• After the contract is established, the CH breaks
  it up.

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CH Records

• A agrees to buy at 2.50.
• B agrees to sell at 2.50.
• A agrees to sell at 3.00.
• C agrees to buy at 3.00.

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At Expiration

• In the absence of arbitrage, the price on an
  expiring futures contract must be equal to the
  spot price.

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Example Continued

• At the September expiration, suppose the spot
  price of wheat is at 3.50/bu.
• B is short and needs to close by going long (B is
  not a farmer).
• C is long and needs to close by going short (C
  does not need 5000 bu of wheat).
• New Contract B agrees to buy September Wheat
  (that is expiring) from C for 3.50.
• CH breaks up the contract.

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CH Records

• B agrees to sell at 2.50.
• C agrees to buy at 3.00.
• B agrees to buy at 3.50.
• C agrees to sell at 3.50.

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Long Futures Hedge

• Take long position in futures to protect against
  an increase in the spot price.
• EXAMPLE
• OJ distributor plans to buy 15,000 lbs of frozen
  OJ in September. To protect against an increase
  in the spot price of OJ, the distributor goes
  long in one OJ futures contract (size 15,000
  lbs) at fo 0.96/lb.
• At delivery, the distributor buys OJ on the spot
  market at the spot price and closes the futures
  position by going short in the expiring futures
  at a futures price equal to the spot price.

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Cost at T
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Short Futures Hedge

• Take short position in futures to protect against
  a decrease in the spot price.
• EXAMPLE
• Wheat farmer plans to sell 5000 bu. of wheat in
  September. To protect against a decrease in the
  spot price, the farmer goes short in a September
  wheat futures at fo 2.40
• At delivery, the farmer sells wheat on the spot
  market at the spot price and closes the futures
  position by going long in the expiring futures at
  a futures price equal to the spot price.

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Revenue at T
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Hedging Risk

• Quantity Risk
• Quality Risk
• 
  Timing Risk

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Speculative Positions

• Pure Outright Position
• Long Position (Bullish)
• Short Position (bearish)
• Spread
• Intracommodity Spread long and short in futures
  on the same underlying asset but with different
  expirations.
• Intercommodity Spread Long and short in futures
  with different underlying assets but the same
  expiration.

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Initial Margin Requirements

• Initial Margin Cash or RF securities that must
  be deposited with the broker to secure the
  position. Initial margin (Mo) is equal to a
  porportion (m) times the contract value.
• Example September wheat contract at fo 2.40
  (long or short) with m .10

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Maintenance Margin Requirements

• Maintenance Margin Keep the equity value of the
  commodity account (Eq) equal to a proportion (90
  to 100) of initial margin.

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Example

• September wheat prices increase from 2.40 to
  2.42. With a 100 maintenance margin
  requirement, a long position would be
  overmargined and a short position would be
  undermargined

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Undermargined Positions

• If an account is undermargined, the investor must
  deposit additional funds to satisfy the
  maintenance margin requirement. If the investor
  does not do this, then she will receive a margin
  call from the broker instructing her that her
  account will be closed unless she deposits the
  requisite funds.
• When the equity value of the account meets the
  maintenance margin requirement, the account is
  said to be marked to market.

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Other Points

• Equity accounts are adjusted daily.
• Futures Funds are often set up where the funds of
  investors are used to buy RF securities which the
  fund uses to satisfy the margin requirements for
  the futures. Such funds can be viewed as
  overmargined futures positions.

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Futures Pricing

• Basis (B)
• Carrying Cost Model Equilibrium futures price is
  equal to the net cost of carrying the underlying
  asset to expiration. This relation is governed
  by arbitrage.

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Pricing Futures on PDB

• Let So spot price of PDB with maturity of 91
  days T Rf RF rate or repo rate with maturity
  of T fo price of PDB futures expiring at T.

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Example

• Price on spot PDB maturing in 161 days is So
  97.5844 70-day RF rate is 6.38.
• Equilibrium price of PDB futures with expiration
  of 70 days (or T 70/365)

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Arbitrage

• Overpriced
• If the market price of PDB futures is at 99, an
  arbitrageur could earn a riskless profit of
  99-.98.74875 0.25125 (times 1M) by
• Borrowing 97.5844 at Rf 6.38 , then buying
  161-day SPOT PDB at So 97.5844
• taking short position in a PDB futures expiring
  in 70 days at fm 99.
• At T, the arbitrageur would sell the spot PDB on
  the futures (it would now have a maturity of 91
  days) and pay off her loan.

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Arbitrage

• Underpriced
• If the market price of PDB futures is at 98, an
  investor holding 161-day spot PDB could earn a
  riskless profit of 98.74875-98 0.74875 (times
  1M) by
• Selling the PDBs for 97.5844, then investing
  the proceeds in RF security for 91 days at Rf
  6.38
• taking long position in a PDB futures expiring
  in 70 days at fm 98.
• At T, the arbitrageur would buy the spot PDB on
  the futures (it would now have a maturity of 91
  days) for 98 and receive 98.74875 from her
  investment.

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Pricing Futures on Stock Portfolio

• Carrying Cost Model

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Pricing Commodity Futures

• Carrying Cost Model

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Example Pricing Commodity Futures

• In June, the spot price of a bushel of wheat is
  2.00, the annual storage cost is 0.30/Bu, Rf
  8, and transportation cost of transporting wheat
  from the destination point on the futures
  contract to a grain elevator is 0.01/bu. The
  equilibrium price of a September wheat futures (T
  .25) is 2.124/bu

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Pricing Relation Between Futures with Different
Expirations

• Carrying Cost Model

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Financial Futures

• Stock Index Futures
• Foreign Currency Futures
• Debt Securities

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Stock Index Futures

• Types
• SP 500 (CME, Multiplier 500)
• MMI (CBT, Multiplier 250)
• SP OTC (CME, Multiplier 500)
• Cash Settlement Feature
• Multiplier
• Use Speculation, hedging, and portfolio
  management.

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Hedging Portfolio Future Value

• Example
• Portfolio manager plans to liquidate a 50M
  portfolio in September. The portfolio is
  well-diversified with a beta of 1.25. The
  current SP 500 is at 1250 and there is a
  September SP 500 futures index trading at fo
  1250. (Note futures and spot prices are usually
  not equal.)
• Hedging Strategy Go short in 100 September index
  futures contracts

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Hedged Value at T
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Portfolio Uses

• Speculating on Unsystematic Risk
• Market Timing
• Dynamic Portfolio Insurance

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Pricing Stock Index Futures

• Let So spot price of stock index (SP 500) Rf
  RF rate or repo rate with maturity of T D
  dividend per share on portfolio underlying the
  index which can be estimated from a proxy
  portfolio fo price of index future expiring at
  T.

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Proxy Portfolio

• Stock Index futures are often priced in terms of
  a proxy portfolio. A Proxy portfolio is a
  portfolio which is highly correlated with the
  index (could be 30-stock portfolio or a MF). This
  portfolio can be viewed as equivalent to holding
  hypothetical shares in the index.
• For example, if the SP 500 is at 1200, a 10M
  well-diversified portfolio with a beta of 1 and
  expected dividends at T worth 250,000 could be
  viewed as owning 8333.333 hypothetical index
  shares that are selling at 1200 per share and
  paying a dividend per share of 30.

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Example

• Spot index (SP 500) is at 1200 and RF rate is 8
  for RF securities maturing in 180 days.
• Using the proxy portfolio, the equilibrium price
  SP 500 futures with expiration of 180 days (or
  T .5 per year

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Index Arbitrage

• Overpriced
• If the futures were priced at fm 1245, an
  arbitrageur could earn a riskless profit by going
  long in the proxy portfolio and short in the
  futures
• Borrow 10M and buy portfolio.
• Go short in 8333.333/500 16.6667 futures.

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CF at T
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Foreign Currency Futures

• Traded on the IMM.
• Futures on major currencies
• DM (125,000)
• BP (25,000)
• FF (250,000)
• Use Hedging and speculation.

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Pricing Currency Futures

• Carrying cost for currency futures is the
  interest rate parity model discussed in many
  international text

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Pricing Currency Futures
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Pricing Currency Futures

• Covered Interest Arbitrage

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IRPT and Cutoff Exchange Rate

• Use the IRPT to determine the cutoff expected
  exchange rate for determining whether to invest
  in domestic or foreign RF security.

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IRPT and Cutoff Exchange Rate

• Example

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IRPT and Cutoff Exchange Rate

• Use Ef from IRPT as curtoff rate

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Cross Exchange Rate Relation

• Cross Rates

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Cross Exchange Rate Relation

• Triangular Arbitrage

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Speculation

• Expect Exchange rate to decrease -- appreciation
  of the dollar.

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Hedging Example

• Expecting a receipt of 625,000 DM in September.
• September DM futures is trading at
• fo 0.40/DM.
• Hedging Strategy Go short in 5 September DM
  futures
• nf 625000DM/125000DM

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Hedged Dollar Revenue at T
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Hedging Example

• Hedging with money market