Kenji is considering two investment strategies. The first strategy involves putting all of his available funds in Project A. If Project A succeeds, he will
receive a $16,000 return, and if it fails, he will suffer a $8,000 loss. There is a chance of 50% Project A will succeed and a chance of 50% it will fail.
An alternative involves diversification: investing half of his funds in Project A and half of his funds in Project B (which has the same payoff structure as
Project A).
• If both projects succeed, he will receive an $8,000 return from Project A and an $8,000 return from Project B, for a net gain of
$16,000.
• If both projects fail, he will suffer a $4,000 loss on Project A and a $4,000 loss on Project B, for a net loss of $8,000.
• If one project succeeds and one fails, he will receive an $8,000 return from the successful project and will suffer a $4,000 loss on the
failed project, for a net gain of $4,000.
As with Project A, there is a 50% chance that Project B will succeed and a 50% 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 Kenji chooses the second strategy, which is putting half of his funds in Project A and half into Project B. The probability that both projects will
succeed is
the probability that both projects will fail is
?, and the probability that one project will fail and one project will succeed is
The first strategy (investing everything in Project A) offers Kenji an expected payoff that is
the expected payoff from the second
strategy (investing half in each project).
The probability of losing $8,000 is
under the first strategy (invest everything in Project A) than under the second strategy (invest half in
each project).