CASH AND FUTURES BA 543 Financial Markets and

CASH AND FUTURES BA 543 Financial Markets and Institutions 5/28/2013 Yunyi Zhang

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

CASH MARKET AND FUTURES MARKET � 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 – FT)

WHY DO WE NEED A FUTURES PRICE � 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

MODELS OF PRICING FUTURES � Expectations Pricing Theory � Arbitrage Pricing Theory

EXPECTATIONS PRICING THEORY � Futures price should equal the expected spot price at the settlement date � FT = ST (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)

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

ARBITRAGE PRICING THEORY � 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.

ARBITRAGE PRICING THEORY • 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%

ARBITRAGE PRICING THEORY � 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

ARBITRAGE PRICING THEORY • 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%

ARBITRAGE PRICING THEORY � 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

ARBITRAGE PRICING THEORY � Equilibrium price will not create arbitrage profit � Determine the equilibrium (or theoretical ) futures price � Formula: FT=S 0 x (1+rf)T � Rf is the risk free rate � Previous example 3: � Equilibrium price: � � � F 1 = S 0 x (1+rf)1 F 1 = $1000 x (1+0. 1)1 F 1 = $1100

ARBITRAGE PRICING THEORY � About rf � 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. 2. 3. 4. Storage costs Insurance costs Transportation costs Financial costs

ARBITRAGE PRICING THEORY � Final Formula FT=S 0 x (1+C 0, T)T � FT : 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

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

REFERENCE � � � � Erich Senft, 5/27/2013, 5 Reasons You Should Trade Futures, http: //traderkingdom. com/trading-futures-educationtopics/trading-futures-basics/2929 -5 -reasons-you-shouldtrade-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=p. XOHyz 7 XO 10 Ronald Moy, 5/27/2013, Futures Pricing, http: //www. youtube. com/watch? v=G 0 lnyze. Mty. U Terrence Jalbert, 5/27/2013, CHAPTER 3 Futures Prices, www. blackwellpublishing. com/ufm/chapter 3. ppt Wikipedia, http: //en. wikipedia. org/wiki/Futures_contract

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