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Unformatted text preview: Forwards and Futures Forwards Comm374 March 2011 Ali Lazrak •Forward •Pricing forward •Futures Textbook readings Textbook Chapter 20. 20.1, 20.2, 20.4, 20.5, 20.1, I. Forwards I. Forward contracts Forward A forward contract is an agreement to forward buy or sell an asset at a certain time in the future for a predetermined price F Seller (buyer) is obligated to deliver Seller (pay) on the delivery date (pay) No money changes hands when the No contract is entered contract Traded OTC Forward Buyers and Call Buyers Buyers
Profit Forward Buyer Call Buyer 0 F Price Forward Sellers and Put Buyers Buyers
Profits Forward Seller 0 F Price Put Buyer Forward and hedging Forward A hotel chain buys hotels in Switzerland, financed hotel with a loan in US$: exposure to shortfall in Swisswith Franc Sell Swiss Franc forward contract (short hedge) A wheat farmer has risk exposure to the price wheat she’ll receive for the wheat she produces she’ll Sell wheat forward (short hedge) If the price of wheat ↓, she’ll receive less for the If harvest, but will have an offsetting gain on the forward position II. Pricing Forwards II. Pricing Forwards Pricing
(The case of a security without income) S0 : Spot price of the underlying at time 0 F: forward price, T=1 year: settlement date If T=0, F= S0 Suppose I need an asset 1 year from now: Buy the asset forward: I will have to pay F in one year Borrow the spot price S0 at interest rate r, in order to buy the asset in the spot market: I will have to pay S0(1+r) in one yearT. asset Market price should be set so that I am indifferent: Market F= S0(1+r) Synthetic Forwards Banks sell forward to clients Banks They hedge the position with a short synthetic They forward forward Example: Example: A bank sold forward a non dividend paying stock in 1 bank years to a client at the price F. years To hedge this position, they will borrow S to buy the To stock immediately and store it. At maturity they will receive F from the client an pay At the lenders S(1+r) and make a profit of F-S(1+r). Pricing Forwards Pricing
Dividend The payoff timeline on a long forward is
Date 0 Buy Forward 0 Date T=1 ST - F The payoff timeline on the portfolio: long The dividend paying asset (payout D)+ borrowing PV(F) is Date 0 Date T=1
Buy asset Borrow Portfolio -S0 +(F+D) /(1+r) (F+D) /(1+r)- S0 ST + D -F-D ST - F Law of one price: Law Pricing Forwards Pricing
Dividend yield, continuous compounding, T periods The payoff timeline on a long forward is
Date 0 Buy Forward 0 Date T ST - F The payoff timeline on the portfolio: long The dividend paying asset (dividend yield d)+ borrowing PV(F) is Date 0 Date T
Buy asset Borrow Portfolio -S0e -dT +Fe –rT Fe –rT - S0e –dT ST -F ST - F Law of one price: Law
-rT Fe -rT= S0 e –dT → F= F= (r-d)T S0 e (r-d)T Forwards on commodities Forwards
(Storage costs and convenience yield) Holding commodities requires storage costs Security (gold) Physical storage (grain) Possibility of damage (insurance)
• Summarized as cost of carry, usually written as constant Summarized annual percentage c of initial value annual Holding commodities provide benefits Holding Demand fluctuation Supply shortage (oil)
• Summarized as convenience yield, usually written as Summarized constant annual percentage y of initial value. Pricing commodities Forwards Pricing Storage costs (c) are “negative dividend” Convenience yield (y) is “positive dividend” The payoff timeline on a long forward is The
Date 0 Buy Forward 0 Date T ST - F The payoff timeline on the portfolio: long The commodity+ borrowing PV(F) is
Date 0 Buy commodity Borrow Portfolio -S0e (c-y)T +Fe –rT Fe –rT - S0e –(cy)T Date T ST -F ST - F Law of one price: Law (r+c-y)T F= S0 e (r+c-y)T F= III. Futures III. Futures Futures Like forwards, settlement is differed Standardized (underlying, maturity, size) Future contracts are traded on exchanges Future Prices are reported in real time until the Prices last trading day (convergence) last Credit risk managed by clearing Credit corporations, daily resettlement (Marking to market) to Futures Futures Hedging and speculation Exchanges: Chicago Board of Trade (CBT):corn, wheat, Chicago rice,DIJA, Treasuries bonds rice,DIJA, Chicago Mercantile Exchange (CME): Cattle, hogs, Chicago S&P, T-bills S&P, New York Mercantile Exchange (NYMEX/COMEX): New Electricity, gas, oil, gold Electricity, Montreal (Canadian derivatives exchange): Montreal S&P/TSX60, Canada bonds S&P/TSX60, Winnipeg Commodity Exchange: wheat, canola The NYMEX gold future contract contract Underlying is 100 ounces of gold (price is quoted in Underlying $/ounce) $/ounce) Upon delivery, gold must contain a serial number and Upon an identification stamp of a refiner approved and listed by the exchange by Trading terminates at the close of business on the Trading third to last business day of the maturing month To go long (or short) this futures contract, NYMEX To requires an initial margin of $6,751 requires Profit/losses are taken on a daily basis and the Profit/losses account balance must not fall below the maintenance margin: $5,000 margin: NYMEX Gold Future Source: cmegroup.com Total value of gold underlying the April contract: 1395.7/oz * 100 oz=$139,500 Credit risk in the future market How do we now the other side wont How default? default?
Clearing house Margins Marking to market (daily resettlement) Margins Margins Long 8 Future Gold May (2011) contracts Long Initial margin held as a collateral by the Initial broker: broker: 6,751*8 =$54,008 Margin call when the account balance Margin falls below the maintenance margin falls 5,000*8 =$40,000 It forces both sides of the contract to It take their profits/losses on a daily basis. take Trading Futures Trading Go long on 8 Future Gold contracts May (2011) Go at $1395 today at noon. at At the end of the day, the contract is priced At $1400 (settlement price) $1400 Change in my brokerage account balance is Change (1400 – 1395)*100*8 = +4,000US$ (1400 The new balance is
54,008 +4,000=$58,008 The Future price of the contract is set to The $1,400. $1,400. What happens to my position at day+1? What The position can be liquidated at 11am (say) The with an offsetting (short) order when the future price is $1,401 price
• Net worth (1,401-1,400)*100*8 + 58,008=58,800 The position can be left open in which case it The is marked to market at the settlement price of day+1: day+1:
• If Price = 1,420: Net worth (1,420-1,400)*100*8 + 58,008= If 74,008 74,008 • If Price = 1,375: Net worth (1,375-1,400)*100*8 + 58,008= If 38,008, in which case a margin call is received and additional cash must be ($1,992) injected to keep the position open. must Questions Questions 26 ...
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This note was uploaded on 04/17/2011 for the course COMM 374 taught by Professor Lazrak during the Spring '08 term at UBC.
- Spring '08