winter2010_notes_part2

winter2010_notes_part2 - Introduction to Commodity Forwards...

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1-1 Introduction to Commodity Forwards Commodity forward prices can be described by the same formula as that for financial forward prices F 0, T = S 0 e ( r −δ ) T
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1-2 Introduction to Commodity Forwards (cont’d) For financial assets, δ i s the dividend yield For commodities, δ i s the commodity lease rate The lease rate is the return that makes an investor willing to buy and then lend a commodity The lease rate for a commodity can typically be estimated only by observing the forward prices
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1-3 Introduction to Commodity Forwards (cont’d) The set of prices for different expiration dates for a given commodity is called the forward curve (or the forward strip ) for that date If on a given date the forward curve is upward- sloping, then the market is in contango . If the forward curve is downward sloping, the market is in backwardation Note that forward curves can have portions in backwardation and portions in contango
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1-4 Equilibrium Pricing of Commodity Forwards A long commodity forward contract at the price F 0,T . + 0 S T F 0,T A zero-coupon bond that pays F 0,T at time T . e rT F 0,T F 0,T Total e rT F 0,T S T = the value of a unit of the commodity at time T. A synthetic commodity can be created by combining a forward contract with a zero-coupon bond Investment strategy: Cost at time 0: Payoff at time T :
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1-5 F 0, t = E 0 ( S T ) e ( r −α ) T Equilibrium Pricing of Commodity Forwards (cont’d) As with financial forwards, the commodity forward price is a biased estimate of the expected spot price, E 0 (S T ), with the bias due to the risk premium on the commodity, r– α
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1-6 Equilibrium Pricing of Commodity Forwards (cont’d) Different commodities have their distinct forward curves, reflecting different properties of Storability Storage costs Production Demand
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1-7 Nonstorability: Electricity Electricity has the following characteristics It cannot be easily stored. Therefore, it is not possible to engage in arbitrage At any point in time, the maximum supply of electricity is fixed Demand for electricity varies substantially by season, by day of week, and by time of day Given these characteristics, electricity forwards have large price swings over the day. Price swings reflect changes in the expected spot price, which in turn reflects changes in demand over the day
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1-8 Pricing Commodity Forward by Arbitrage: An Example Suppose that pencils cost $0.20 today and, for certainty, will cost $0.20 in 1 year Suppose that the continuously compounded interest rate is 10%. Since a lender of the pencil has invested $0.20 in a pencil, he will require a borrower to pay interest. Therefore, the pencil has a lease rate of 10% It can be demonstrated that the pencil forward price must be $0.20
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1-9 Pricing Commodity Forward by Arbitrage: An Example (cont’d) Any forward price less than $0.20 results in arbitrage profits Any forward price greater than $0.20 results in arbitrage profits
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1-10 Pricing Commodity Forward by Arbitrage: An Example (cont’d)
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This note was uploaded on 04/13/2010 for the course FIN 823 taught by Professor Keweiho during the Spring '10 term at Ohio State.

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winter2010_notes_part2 - Introduction to Commodity Forwards...

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