There are three investments, B1, B2 and B3. All of them have the same expected value and each with two possible payoffs. The payoffs from investment B1 are independent from payoffs from B2 and B3. The payoffs from B2 and B3 are perfectly negatively correlated, which means that when B2 has a high payoff, B3 has a low payoff, and vice versa. An investor has only $800 to invest. Find the investment strategy that minimizes the risk. Hint: It may be easier to think of the following situation. Let events F and G be independent. The following is given: Payoff from investing $100 in either B2 or B3 Cases B2 Вз Probability event F happens event F does not happen $140 | $100 $100 $140 0.5 0.5 and Payoff from investing $100 in B1 Cases B1 Probability event G happens event G does not happen $140 $100 0.5 0.5

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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There are three investments, B1, B2 and B3. All of them have the same expected value
and each with two possible payoffs. The payoffs from investment B1 are independent from
payoffs from B2 and B3. The payoffs from B2 and B3 are perfectly negatively correlated,
which means that when B2 has a high payoff, B3 has a low payoff, and vice versa.
An investor has only $800 to invest. Find the investment strategy that minimizes the
risk.
Hint: It may be easier to think of the following situation. Let events F
and G be independent. The following is given:
Payoff from investing $100 in either B2 or B3
В
$100 $140
Cases
B3
Probability
event F happens
event F does not happen $140 $100
0.5
0.5
and
Payoff from investing $100 in BỊ
Cases
В
Probability
$100
event G happens
event G does not happen $140
0.5
0.5
Transcribed Image Text:There are three investments, B1, B2 and B3. All of them have the same expected value and each with two possible payoffs. The payoffs from investment B1 are independent from payoffs from B2 and B3. The payoffs from B2 and B3 are perfectly negatively correlated, which means that when B2 has a high payoff, B3 has a low payoff, and vice versa. An investor has only $800 to invest. Find the investment strategy that minimizes the risk. Hint: It may be easier to think of the following situation. Let events F and G be independent. The following is given: Payoff from investing $100 in either B2 or B3 В $100 $140 Cases B3 Probability event F happens event F does not happen $140 $100 0.5 0.5 and Payoff from investing $100 in BỊ Cases В Probability $100 event G happens event G does not happen $140 0.5 0.5
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