week 4

• Forward contract


  A commitment to purchase at a future date a given amount of a commodity or an asset at a price agreed on today
• Forward price


  The price fixed now for future exchange
• Long position


  The party that has agreed to buy
• Short position


  The party that has agreed to sell
• Spot price


  The price for immediate delivery
• Forward contracts


  • Customized
  • Non-standard and traded over the counter (not on exchanges)
  • No money changes hands until maturity
  • Non-trivial counterparty risk
  • Illiquidity
• Forward contract example


  • Current price of oil is $100/barrel
  • Oil buyer needs 1,000 barrels in 6 months
  • 6-month forward contract for 1,000 barrels of oil at $110/barrel
• Futures contract


  An exchange-traded, standardized, forward-like contract that is marked to market daily
• Mark to market


  Settling the contract every day since day 1 by paying the price difference
• Mark to market eliminates counterparty risk
• Futures contracts


  • Standardized contracts (underlying, quantity, maturity)
  • Exchange traded
  • Guaranteed by the clearinghouse—no counter-party risk
  • Gains/losses settled daily (marked to market)
  • Margin required as collateral to cover losses
• Margin


  Cash or marketable securities deposited by an investor with their broker
• Margins minimize the possibility of a loss through a default on a contract
• Futures contracts have zero NPV
• If the price of the futures contract is not zero

  One party will sell it to a third party and make a profit, which will drive the new price of the contract to zero
• Futures contract example


  • NYMEX heating-oil futures with delivery in Dec. 2007 at a price of $75 / bbl. on July 27, 2007 with 51,475 contracts traded
• Futures contract example continued


  • Arctic Fuels buys 10 of the Dec. heating-oil futures contracts at a futures price of $75 / bbl.
  • Northern Refineries sells 10 of the Dec. heating-oil futures contracts at a futures price of $75 / bbl.
• The next day the price of the December contract increases to $77/bbl.

  • The clearinghouse pays $2 x 10,000 = $20,000 to AF's margin account.
  • NR must pay $2 x 10,000 = $20,000 into the clearinghouse.
• If the price then drop back to $76/bbl. on the day after


  • AF must pay $1 x 10,000 = $10,000 to the clearing house.
  • The clearinghouse will put $1x 10,000 = $10,000 into NR's margin account.
• No counterparty risk in futures contracts
• Futures contract example continued


  • Suppose the spot price of heating oil in Dec up to $77/bbl. Then the futures price at the end of the contract will be $77/bbl.
  • For Arctic Fuels: It gets a cumulative profit of ($77-$75)x10,000 = $20,000
  • For Northern Refineries: It suffers a cumulative loss of $20,000
• Forward contracts vs Futures contracts


  Forward contracts: Usually closed out, private contract between 2 parties, non-standard contract, 1 specified delivery date, settled at end of contract, some credit risk

  Futures contracts: Exchange traded, standard contract, range of delivery dates, settled daily, virtually no credit risk
• Forward/futures prices ultimately linked to future spot prices
• B


  The contract becomes more valuable as the price of the asset rises
• C


  The contract is worth zero if the price of the asset declines after the contract has been entered into
• D


  The contract is worth zero if the price of the asset rises after the contract has been entered into
• Trader enters into a short cotton futures contract


  1. Futures price is 50 cents per pound

  2. Contract is for the delivery of 50,000 pounds
• Cotton price at the end of the contract

  • 48.20 cents per pound
  • 51.30 cents per pound
• The trader sells for 50 cents per pound something that is worth 48.20 cents per pound. Gain = ($0.5 - $0.482)x50,000 = $900
• The trader sells for 50 cents per pound something that is worth 51.30 cents per pound. Loss = ($0.513-$0.5)x50,000=$650
• Forward/futures prices


  Ultimately linked to future spot prices
• Two ways to buy the underlying asset for date-T delivery


  • Buy a forward or futures contract with maturity date T
  • Buy the underlying asset now and store it until T
• Difference between the two methods


  • Costs (storage for commodities, not financials)
  • Benefits (convenience for commodities, dividends for financials)
• By no arbitrage, these two methods must cost the same
• Easy to store (negligible costs of storage)

  No dividends or benefits
• No-arbitrage requires that the forward price of gold equals the spot price of gold compounded at the risk-free rate
• Arbitrage profit is $30 if the spot price of gold is $1,400, the 1-year forward price of gold is $1,500, and the 1-year US$ interest rate is 5% per annum
• Arbitrage profit is $70 if the spot price of gold is $1,400, the 1-year forward price of gold is $1,400, and the 1-year US$ interest rate is 5% per annum
• Forward price of gold


  F = S (1+r )T, where S is the spot price, r is the 1-year risk-free rate, and T is the time to maturity
• Storage costs


  Costs of holding commodities in storage