1.. Commodity futures provide an opportunity for buyers and suppliers of commodities such as wheat to arrange in advance sales of a commodity, with deliv- ery and payment taking place at a speci?ed time in the future. The price is decided at the time the order is placed, and the buyer is asked to deposit an amount less than the value of the order, but enough to protect the seller from loss in case the buyer should decide not to meet the obligation.

An investor is considering investing $15,000 in wheat futures and believes that there is a 0.10 probability that he will lose $5,000 by the expiration of the contract, a 0.20  probability  that  he  will  make  $2,000,  a  0.25  probability  that he will make $3,000, a 0.15 probability he will make $4,000, a 0.15 probability he will make $5,000, a 0.10 probability he will make $6,000, and a 0.05 probability that he will make $7,000. If the investor should ?nd out that he is going to lose $5,000, he can pull out of his contract, losing $3,500 for certain and an additional $3,000 with probability 0.20 (the latter amount deposited with a brokerage ?rm as a guarantee). Draw the decision tree for this problem, and solve it. What should the investor do?

2. For problem 1, suppose that the investor is considering another invest- ment as an alternative to wheat. He is considering investing his $15,000 in a limited partnership for the same duration of time as the futures contract. This alternative has a 0.50 chance of earning $5,000 and a 0.50 chance of earning nothing. Add this infor- mation to your decision tree of problem 1, and solve it.