11.(Commodity Arbitrage of Consumption Commodities)Suppose you are a commodity arbitrageur on the NYMEX. On April 8, 2009, the NYMEX spot crude oil is trading at $52.24 per barrel. . The annualized continuously compounded borrowing interest rates is 1.36% and saving interest rate is 1.34%. The continuously compounded storage cost is 1% per annum.(3 points)(11.1)Find the range of the 3-month forward price that would allow you to arbitrage by buying oil and storing them. Suppose the convenience yield of oil for you is 2% per annum.(3 points) (11.2)You may also arbitrage by borrowing oil. Note that lenders may charge a higher convenience yield than yours. Suppose the current 3-month forward price is $51. Find the maximum continu-ously compounded convenience yield per annum you can pay if you would like to arbitrage by borrowing oil.

12.Two non-dividend-paying stocks ABC and XYZ are both trading at $12 per share.

(12.1)Should the one-year forward price of ABC be lower than the one-year forward price of XYZ? Why?

(12.2)Suppose the one-year forward prices for ABC and XYZ are both $13. Assume that the price of

ABC is expected to be $10 in a year and the price of XYZ is expected to be $20 in a year. What is

your expected payoff in one year if you short one share of ABC forward and long one share of

XYZ forward? Is this an arbitrage strategy?

(12.3)If the one-year forward price of ABC is $9 per share and the one-year forward price of XYZ is $19

per share, find the arbitrage strategy assuming that you may buy or sell only 1 share of ABC in

the spot market. Describe your action now and in one year. Will you ever lose?

13.(Alternative Definitions of Contango) In class, we say that a futures contract is in contango at time 0 if the futures price F(0,T) is higher than the spot price S(0) for T>0. Some people also say that a market is in contango if F(0,T) increases with T for T>0. Are these two definitions equivalent? Why?

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