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Problem 11-06 As the chief investment officer for a money management firm specializing in taxable individual investors, you are trying to establish a strategic asset allocation for two different clients. You have established that Ms. A has a risk-tolerance factor of 8, while Mr. B has a risk-tolerance factor of 25. The characteristics for four model portfolios follow: ASSET MIX Portfolio Stock Bond ER σ2 1 10 % 90 % 8 % 5 % 2 21 79 9 11 3 64 36 10 14 4 85 15 11 24 Calculate the expected utility of each prospective portfolio for each of the two clients. Do not round intermediate calculations. Round your answers to two decimal places. Portfolio Ms. A Mr. B 1 2 3 4 Which portfolio represents the optimal strategic allocation for Ms. A? Which portfolio is optimal for Mr. B? Portfolio -Select- represents the optimal strategic allocation for Ms. A. Portfolio -Select- is the optimal allocation for Mr. B. For Ms. A, what level of risk tolerance would leave her indifferent between having Portfolio 1 or Portfolio 2 as her strategic allocation? Round your answer to the nearest whole number.

Question

Problem 11-06

As the chief investment officer for a money management firm specializing in taxable individual investors, you are trying to establish a strategic asset allocation for two different clients. You have established that Ms. A has a risk-tolerance factor of 8, while Mr. B has a risk-tolerance factor of 25. The characteristics for four model portfolios follow:

ASSET MIX Portfolio Stock Bond ER σ2 1 10 % 90 % 8 % 5 % 2 21 79 9 11 3 64 36 10 14 4 85 15 11 24 Calculate the expected utility of each prospective portfolio for each of the two clients. Do not round intermediate calculations. Round your answers to two decimal places.

Portfolio Ms. A Mr. B 1

2

3

4

Which portfolio represents the optimal strategic allocation for Ms. A? Which portfolio is optimal for Mr. B?

Portfolio -Select- represents the optimal strategic allocation for Ms. A. Portfolio -Select- is the optimal allocation for Mr. B.

For Ms. A, what level of risk tolerance would leave her indifferent between having Portfolio 1 or Portfolio 2 as her strategic allocation? Round your answer to the nearest whole number.

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Solution

To solve this problem, we need to calculate the expected utility of each portfolio for each client. The formula for expected utility is:

Expected Utility = Expected Return - 0.005 * Risk Tolerance Factor * Variance

Let's calculate the expected utility for each portfolio and each client:

For Ms. A (Risk-Tolerance Factor = 8):

Portfolio 1: Expected Utility = 8 - 0.005 * 8 * 5 = 8 - 0.2 = 7.8 Portfolio 2: Expected Utility = 9 - 0.005 * 8 * 11 = 9 - 0.44 = 8.56 Portfolio 3: Expected Utility = 10 - 0.005 * 8 * 14 = 10 - 0.56 = 9.44 Portfolio 4: Expected Utility = 11 - 0.005 * 8 * 24 = 11 - 0.96 = 10.04

For Mr. B (Risk-Tolerance Factor = 25):

Portfolio 1: Expected Utility = 8 - 0.005 * 25 * 5 = 8 - 0.625 = 7.375 Portfolio 2: Expected Utility = 9 - 0.005 * 25 * 11 = 9 - 1.375 = 7.625 Portfolio 3: Expected Utility = 10 - 0.005 * 25 * 14 = 10 - 1.75 = 8.25 Portfolio 4: Expected Utility = 11 - 0.005 * 25 * 24 = 11 - 3 = 8

The optimal portfolio for each client is the one with the highest expected utility. Therefore, the optimal portfolio for Ms. A is Portfolio 4 and for Mr. B is Portfolio 3.

To find the level of risk tolerance that would leave Ms. A indifferent between Portfolio 1 and Portfolio 2, we set the expected utilities of the two portfolios equal to each other and solve for the risk tolerance factor:

8 - 0.005 * Risk Tolerance * 5 = 9 - 0.005 * Risk Tolerance * 11

Solving this equation gives a risk tolerance factor of approximately 20. Therefore, a risk tolerance factor of 20 would leave Ms. A indifferent between Portfolio 1 and Portfolio 2.

This problem has been solved

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