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There is a very deep and liquid forward market for crude oil and there is an active spot market. It is also possible to rent storage space in tankers for long periods of time. However it is not possible to rent (borrow) crude oil itself. Suppose spot crude oil (West Texas intermediate grade) is trading for 758/barrel. The one-year riskless rate (r) is 0.25% and the storage cost (u) for a barrel of oil is equal to 3% of its value per year. (These rates are in continuously compounded form.) (a) What one-year forward prices would allow arbitrage opportunities? Suppose one defines the convenience yield to be y ru- log(F/S)]. What values of y does arbitrage rule out? (b) Now suppose you work for a large oil producing company and you hold millions of barrels of crude oil in excess inventory. A hedge fund approaches you and offers to repay you 115 million barrels of oil in one year if you lend him 100 million barrels today. He will fully collateralize the loan by giving you custody of U.S. treasury bills equal to the market value of the oil, so there is no credit risk in the proposed transaction. Why might you not agree to do this? What does your decision imply about your implicit value of y. (c) Does y tell you anything about where the market expects spot prices to be in one year?

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