4. Diversification Aa Aa Bette is considering two investment strategies. The fir

Question

4. Diversification Aa Aa Bette is considering two investment strategies. The first strategy involves putting all of her available funds in Project A. If Project A succeeds, she will receive a $10,000 return, and if it fails, she will suffer a $4,000 loss. There is a 80% chance Project A will succeed and a 20% chance it will fail. The second strategy involves diversification: investing half of her funds in Project A and half of her funds in Project B (which has the same payoff structure as Project A) If both projects succeed, she will receive a $5,000 return from Project A and a $5,000 return from Project If both projects fail, she will suffer a $2,000 loss on Project A and a $2,000 loss on Project B, for a net loss · If one project succeeds and one fails, she will receive a $5,000 return from the successful project and will B, for a net gain of $10,000. of $4,000 suffer a $2,000 loss on the failed project, for a net gain of $3,000 As with Project A, there is a 80% chance that Project B will succeed and a 20% chance that it will fail. Assume that the outcomes of Project A and Project B are independent. That is, the success or failure of Project A has nothing to do with the success or failure of Project B The expected payoff from the first strategy (investing everything in Project A) is Suppose Bette chooses the second strategy, which is putting half of her funds in Project A and half into Project B. 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 the The first strategy (investing everything in Project A) offers Bette an expected payoff that is expected payoff from the second strategy (investing half in each project) under the second strategy (invest half in each project) than under The probability of losing $4,000 is the first strategy (invest everything in Project A).

Explanation / Answer

=> Expected Pay off for first alternative = 10000*80% + (-4000)*20% = 7200

=> The probability that:

Both will succeed = 0.8*0.8 = 0.64

Both will fail = 0.2*0.2 = 0.04

one will fail and one will succeed = (0.8*0.2) + (0.8*0.2) = 0.32

=> Pay off in second strategy = (10000*0.64) + (-4000*0.04) + (3000*0.32) = 7200

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

=> Probability of loosing 4000 in:

1st strategy = 0.2

2nd strategy = 0.04

Therefore, the probability of loosing 4000 is lesser under 2nd strategy than under 1st strategy.

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