4. Diversification Aa Aa Rosa is considering two investment strategies. The firs

Question

4. Diversification Aa Aa Rosa 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 $2,000 loss. There is a 70% chance Project A will succeed and a 30% 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 $1,000 loss on Project A and a $1,000 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 $2,000 suffer a $1,000 loss on the failed project, for a net gain of $4,000. As with Project A, there is a 70% chance that Project B will succeed and a 30% chance that it will fall. 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 Rosa 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 Rosa 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 $2,000 is the first strategy (invest everything in Project A)

Explanation / Answer

The expected payoff from the first strategy (investing everything in project A) is = 70% x 10000 + 30% x - 2000 = $6400

Second strategy:

The probability that both projects will succeed = 70% x 70% = 49%

The probability that both projects will fail = 30% x 30% = 9%

The probability that one project will fail and one project will succeed = 30% x 70% + 70% x 30% = 42%

Payoff = 49% x 10000 + 42% x 4000 + 9% x - 2000 = $6400

The first strategy offers Rosa an expected payoff that is equal to the expected payoff from the second strategy.

The probability of losing $2000 is lower (=9%) under the second strategy than under the first strategy.(=30%)

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