2. Justin has $1 million dollars. He comes to you for advice on how to invest...

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2. Justin has $1 million dollars. He comes to you for advice on how to invest the money. You do some research and find that there are three ways he can invest. He can invest in stocks, bonds or hold cash. Let the proportion of wealth he invests in stocks be x while the proportion of wealth he invests in bonds be y. You research the potential returns from investment and decide there are 5 different scenarios that could occur. In each of these scenarios, the return to cash is zero. In scenario 1, the value of stocks and bonds remain unchanged. This occurs with probability 0.4 In scenario 2, the value of stocks double and bonds increase in value by 50%. This occurs with probability 0.2 In scenario 3, stocks lose half their value and bonds decrease by 25%. This occurs with probability 0.2 In scenario 4, stocks double but bonds decrease by 25%. This occurs with probability 0.1 In scenario 5, stocks lose half their value but bonds increase by 50%. a. (5 points) Calculate what Justin's final wealth is in each of the five scenarios, as a function of x and y. Let W1, W2, W3, W4 and Wg indicate his wealth in each of the respective scenarios. b. (10 points) Suppose that Justin's utility is given by U(W) = W –w². (The unit for W is millions of dollars). What values of x and y will maximize Justin's expected 1 4 utility? Present your final answer in fractions rather than decimals. 2. Justin has $1 million dollars. He comes to you for advice on how to invest the money. You do some research and find that there are three ways he can invest. He can invest in stocks, bonds or hold cash. Let the proportion of wealth he invests in stocks be x while the proportion of wealth he invests in bonds be y. You research the potential returns from investment and decide there are 5 different scenarios that could occur. In each of these scenarios, the return to cash is zero. In scenario 1, the value of stocks and bonds remain unchanged. This occurs with probability 0.4 In scenario 2, the value of stocks double and bonds increase in value by 50%. This occurs with probability 0.2 In scenario 3, stocks lose half their value and bonds decrease by 25%. This occurs with probability 0.2 In scenario 4, stocks double but bonds decrease by 25%. This occurs with probability 0.1 In scenario 5, stocks lose half their value but bonds increase by 50%. a. (5 points) Calculate what Justin's final wealth is in each of the five scenarios, as a function of x and y. Let W1, W2, W3, W4 and Wg indicate his wealth in each of the respective scenarios. b. (10 points) Suppose that Justin's utility is given by U(W) = W –w². (The unit for W is millions of dollars). What values of x and y will maximize Justin's expected 1 4 utility? Present your final answer in fractions rather than decimals.

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