Sam is considering two investment strategies. The first strategy involves puttin

Question

Sam is considering two investment strategies. The first strategy involves putting all of his available funds in Project X. If Project X succeeds, he will receive a $30,000 return, and if it fails, he will suffer a $20,000 loss. There is a 90% chance Project X will succeed and a 10% chance it will fail. The second strategy involves diversification: investing half of his funds in Project X and half of his funds in Project Y (which has the same payoff structure as Project If both projects succeed, he will receive a $15,000 return from Project X and a $15,000 return fronm Project Y, for a net gain of $30,000. If both projects fail, he will suffer a $10,000 loss on Project X and a $10,000 loss on Project Y, for a net loss of $20,000. If one project succeeds and one fails, he will receive a $15,000 return from the successful project and will suffer a $10,000 loss on the failed project, for a net gain of $5,000 As with Project X, there is a 90% chance that Project Y will succeed and a 10% chance that it will fail. Assume that the outcomes of Project X and Project Y are independent. That is, the success or failure of Project X has nothing to do with the success or failure of Project Y The expected payoff from the first strategy (investing everything in Project X) is Suppose Sam chooses the second strategy, which is putting half of his funds in Project X and half into Project Y. The probability that both projects will succeed is and the probability that one project will fail and one project will succeed is , the probability that both projects will fail is

Explanation / Answer

Expected payoff from first strategy = (Prob. of Success)*Payoff under success+(Prob. of failure)*Payoff under failure

1) Expected payoff from first strategy = 0.9*30000 + 0.1*(-20000) = 27000 -2000 = $25000.

2) Probability that both will succeed = (Prob. Of X’s success)*(Prob. of Y’s success) = 0.9*0.9 =0.81

3) Probability that both will fail = (Prob. Of X’s failure)*(Prob. of Y’s failure) = 0.1*0.1 =0.01

4) Probability that one project fail and one project will succeed = (Prob. Of X’s success)*(Prob. of Y’s failure) + (Prob. Of X’s failure)*(Prob. of Y’s success) = 0.9*0.1 +0.1*0.9 = 0.18

Expected payoff under second strategy = 0.81*30000 + 0.01*(-20000)+0.18*(5000) = 25000

5) Payoff from both strategy are equal.

6) Higher

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