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BA543 Financial Markets and Institutions 5/28/2013 Yunyi Zhang

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Cash market and Futures market Needs of Futures Price Models of Pricing Futures Expectations Pricing Theory Arbitrage Pricing Theory Takeaways

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Cash Market A market that commodities are traded for immediate delivery Price is current price (Spot Price - S 0 ) Futures Market A market that commodities are traded for future delivery Delivery date is in the future (Settlement date ) Price is future price at the time of delivery (Futures Price – F T)

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Make money Buy cheap, Sell expensive. Arbitrage Profit Reduce the risk of future price change Price of Raw Material increase lead profit decrease Milk Price Increase cause Ice Cream Makers loss Profits

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Expectations Pricing Theory Arbitrage Pricing Theory

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Futures price should equal the expected spot price at the settlement date F T = S T (Expected) Example 1: Gold Price Consumer: $1300/OZ, 3 Months from Today, Ft=$1300/OZ (Buying price) Seller: $1350/OZ, 3 Months from Today, Ft=$1350/OZ (Selling price)

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Arbitrage the practice of taking advantage of a price difference between futures price and current spot price Example 2: Todays Gold price is $1000/oz 1 Year From Today the Gold Price is $1200/oz Arbitrage Profit : $200

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Two Types Cash and Carry Trade Arbitrage Reverse Cash and Carry Trade Arbitrage Condition: Perfect Market, No tax and Transaction Cost, Lending Rate and Borrowing Rate are the same.

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Cash and Carry Trade Arbitrage Borrow money to buy the commodity today and carry the commodity to the expiration of the futures contract. Then, deliver the commodity for the futures contract and pay off the loan Example 3 (Gold): Current Spot Price: $1000/OZ Future Price (1 year from today): $1200/OZ Interest Rate (1 year): 10%

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Calculation: Today Borrow $1000, buy 1 OZ gold, sell a one-year future contract of gold 1 year from today Sell 1 OZ gold for $1200 Interest cost: $100 Pay loan and interest: $1100 Arbitrage Profit : $100

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Reverse Cash and Carry Trade Arbitrage Sell short the commodity today and buy a future contract, lend the money out for interest income. Then, get the commodity at the expiration date to cover the short position of the commodity, get the loan back Example 4 (Gold): Current Spot Price: $1100/OZ Future Price (1 year from today): $1200/OZ Interest Rate (1 year): 10%

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Calculation: Today Sell 1 OZ gold for $1100 and lend the money out, buy a one-year future contract of gold 1 year from today Get $1100 loan back Interest income: $110 Buy 1 OZ gold for $1200 Arbitrage Profit : $10

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Equilibrium price will not create arbitrage profit Determine the equilibrium (or theoretical ) futures price Formula: F T =S 0 x (1+r f ) T R f is the risk free rate Previous example 3: Equilibrium price: F 1 = S 0 x (1+r f ) 1 F 1 = $1000 x (1+0.1) 1 F 1 = $1100

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About r f In previous example, gold is easy to store and carry, the only cost of carrying the commodity is interest cost In a more realistic setting, the costs of carrying (or storing) may vary 1. Storage costs 2. Insurance costs 3. Transportation costs 4. Financial costs

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Final Formula F T =S 0 x (1+C 0,T ) T F T : Current futures price at time T S 0 : Current spot price T : Carrying Period of the Commodity C 0,T : The percentage cost required to carry the commodity from today until time T

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Expectations Pricing Theory F T = S T (Expected) Arbitrage Pricing Theory Cash and Carry Trade Arbitrage Reverse Cash and Carry Trade Arbitrage F T =S 0 x (1+C 0,T ) T

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Erich Senft, 5/27/2013, 5 Reasons You Should Trade Futures, http://traderkingdom.com/trading-futures-education- topics/trading-futures-basics/2929-5-reasons-you-should- trade-futures Frank J. Fabozzi, Franco P. Modigliani and Frank J. Jones, 2010, Foundations of Financial Markets and Institutions Kevin Bracker, 5/27/2013, Futures Pricing Basic Theory, http://www.youtube.com/watch?v=pXOHyz7XO10 Ronald Moy, 5/27/2013, Futures Pricing, http://www.youtube.com/watch?v=G0lnyzeMtyU Terrence Jalbert, 5/27/2013, CHAPTER 3 Futures Prices, www.blackwellpublishing.com/ufm/chapter3.ppt Wikipedia, http://en.wikipedia.org/wiki/Futures_contract

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