Chapter 10 Forwards and Futures Road Map Part A Introduction to nance Part B Valuation of assets given discount rates Part C Determination of risk adjusted discount rate Part D Introduction to derivatives Forwards and futures Options Real options Main issues Forwards and Futures Forward and Futures Prices Hedging Financial Risks Using Forwards Futures Chapter 10 Forwards and Futures 10 1 1 Forward Contracts De nition A forward contract is a commitment to purchase at a future date a given amount of a commodity or an asset at a price agreed on today agreement 0 settlement T cid 2 time The price xed now for future exchange is the forward price The buyer obtains a long position in the asset commodity Features of forward contracts traded over the counter not on exchanges custom tailored no money changes hands until maturity non trivial counter party risk Example Consider a 3 month forward contract for 10 000 bushels of soybean at a forward price of 3 5 bushel The long side is committed to buy 10 000 bushels of soybean from the short side three months from now at the price of 3 50 bushel Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 10 2 Forwards and Futures Chapter 10 2 Futures Contracts Forward contracts have two limitations a illiquidity b counter party risk Futures contracts are designed to address these limitations De nition A futures contract is an exchange traded standard ized forward like contract that is marked to the market daily Futures contract can be used to establish a long or short posi tion in the underlying commodity asset Features of futures contracts Standardized contracts 1 underlying commodity or asset 2 quantity 3 maturity Traded on exchanges Guaranteed by the clearing house little counter party risk Gains losses settled daily marked to market Margin account required as collateral to cover losses 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 10 Forwards and Futures 10 3 A Forward Contract A Futures Contract Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 10 4 Forwards and Futures Chapter 10 Example Yesterday you bought 10 December live cattle con tracts at CME at the closing price of 0 7455 lb Contract size 40 000 lbs Agreed to buy 400 000 pounds of live cattle in December Value of position yesterday 0 7455 10 40 000 298 200 No money changed hands Initial margin required 5 20 of contract value Today the futures price closes at 0 7435 lb 0 20 cents lower The value of your position is 0 7435 10 40 000 297 400 a loss of 800 Forward and futures contracts are derivative securities because payo s determined by prices of the underlying asset zero net supply 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 10 Forwards and Futures 10 5 3 Forward and Futures Prices Question What determines forward and futures prices Answer Forward futures prices are linked to spot prices Contract Spot at t Forward Futures Price St H F Ignoring di erences between forwards and futures we have F cid 2 H Two ways to buy the underlying for date T 1 Buy forward or futures contract of maturity T 2 Buy the underlying now and store it until T Di erence between buy and store from forward futures a Cost of storing for commodities b Bene ts from storing Convenience yield for commodities Dividends interests for nancials By arbitrage the costs of these two approaches must equal F cid 2 H 1 rF S0 FV net cost of storing Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 10 6 Forwards and Futures Chapter 10 3 1 Commodities 1 Gold Easy to store negligible cost of storage No dividends or bene ts Two ways to buy gold for T Buy now for S0 and hold until T Buy forward pay F and take delivery at T No arbitrage requires that F S0 1 rF T cid 2 H Example Gold quotes on 2006 08 21 are Spot price 625 70 oz 2007 February futures CMX 641 40 oz The implied 6 month interest rate is rF 5 08 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 10 Forwards and Futures 10 7 2 Oil Costly to store Additional bene ts convenience yield for holding physical commodity over holding futures Not held for long term investment unlike gold but mostly held for future use Let the percentage holding cost be c and convenience yield be y We have F S0 1 rF y c T S0 1 rF cid 2 y T cid 2 H where cid 2 y y c is the net convenience yield Example Prices on 2006 08 21 are Spot oil price 72 45 barrel light sweet Nov 06 oil futures price 74 22 barrel NYM 3 month interest rate is 5 40 LIBOR Annualized net convenience yield is cid 2 y 4 74 Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 10 8 Forwards and Futures Chapter 10 For commodity futures 1 Contango means a spot prices are lower than futures prices and or b prices for near maturities are lower than for distant 2 Backwardation means a spot prices are higher than futures prices and or b prices for near maturities are higher than for distant Backwardation occurs if net convenience yield exceeds interest rate cid 2 y rF y c rF 0 Crude oil forward price curves for selected dates 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 10 Forwards and Futures 10 9 3 2 Financials For nancial futures the underlying are nancial assets Financials have the following features No cost to store the underlying asset Dividend or interest on the underlying 1 Stock index futures Underlying are bundles of stocks S P Nikkei etc Futures settled in cash no delivery Let the dividend yield be d then there is the following relation between the forward futures price and spot price F S0 1 rF d T cid 2 H Deviations from this relation triggers index arbitrage Example Prices on 2006 08 21 are S P 500 closed at 1 279 52 S P futures maturing in December closed at 1 313 60 4 month interest rate is 5 42 The annual dividend yield is d 2 78 Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 10 10 Forwards and Futures Chapter 10 Note Since the underlying asset is a portfolio in the case of index futures trading in the futures market is easier than trading in cash market Thus futures prices may react quicker to macro economic news than the index itself Index futures are very useful to market makers investment bankers stock portfolio managers hedging market risk in block purchases underwriting creating synthetic index fund portfolio insurance 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 10 Forwards and Futures 10 11 Example You have 1 million to invest in the stock market and you have decided to invest in a diversi ed portfolio S P …