You manage a risky portfolio with an expected rate of return of 17% and a standard...

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 28%. The T-bill rate is 7%. Your client’s degree of risk aversion is A = 2.0, assuming a utility function U = E(r) − ½Aσ².

a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What are the expected value and standard deviation of the rate of return on your client’s optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Solutions

Expert Solution

a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Proportion of y = (Expected return of risky portfolio - risk free rate) / (Risk Aversion * variance)

Proportion of y = (17% - 7%) / (2.0 * 0.28^2)

Proportion of y = 10% / (2.0 * 0.0784)

Proportion of y = 63.78%

b. What are the expected value and standard deviation of the rate of return on your client’s optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected Value = risk free rate + Proportion of Y * (Expected return of Risky portfolio - risk free rate)

Expected Value = 7% + 63.78% * 10%

Expected Value = 13.38%

Standard Deviation = proportion of Y * standard deviation

Standard Deviation = 63.78% * 28%

Standard Deviation = 17.86%

jeff jeffy answered 1 year ago

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