Jason is considering two investment strategies. The first strategy involves putt

Question

Jason 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 $20,000 return, and if it fails, he will suffer a $8,000 loss. There is a 55% chance Project X will succeed and a 45% 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 X). If both projects succeed, he will receive a $10,000 return from Project X and a $10,000 return from Project Y, for a net gain of $20,000 If both projects fail, he will suffer a $4,000 loss on Project X and a $4,000 loss on Project Y, for a net loss of $8,000 .If one project succeeds and one fails, he will receive a $10,000 return from the successful project and wil suffer a $4,000 loss on the failed project, for a net gain of $6,000. As with Project X, there is a 55% chance that Project Y will succeed and a 45% 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 Jason 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 55% , the probability that both projects will fail is -- 45% , and the probability that one project will fail and one project will succeed is 49.5% lower than the The first strategy (investing everything in Project X) offers Jason an expected payoff that is expected payoff from the second strategy (investing half in each project). The probability of losing $8,000 is higher under the second strategy (invest half in each project) than under the first strategy (invest everything in Project X),

Explanation / Answer

=> Expected Pay off for first alternative = 20000*55% + (-8000)*45% = 7400

=> The probability that:

Both will succeed = 0.55*0.55 = 0.3025

Both will fail = 0.45*0.45 = 0.2025

one will fail and one will succeed = (0.55*0.45) + (0.55*0.45) = 0.495

=> Pay off in second strategy = (20000*0.3025) + (-8000*0.2025) + (6000*0.495) = 7400

Therefore, first strategy offers Bette an expected payoff that is equal to the expected pay off from 2nd strategy.

=> Probability of loosing 8000 in:

1st strategy = 0.45

2nd strategy = 0.2025

Therefore, the probability of loosing 8000 is lesser under 2nd strategy than under 1st strategy.

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