Assume that you manage a risky portfolio with an expected rate of return of 18%

Question

Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 31%. The T-bill rate is 4%. Your client’s degree of risk aversion is A = 2.4, assuming a utility function U = E(r) - ½A².

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. Omit the "%" sign in your response.)

Investment proportion % :

b. What is 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. Omit the "%" sign in your response.)

Expected return %:

Standard deviation %:

Explanation / Answer

Ans:

Expected rate of return = 18%

Standard deviation = 31%

T-bill = 4%

Step-1:

Investment proportion = 0.60

= 0.60* 100 = 60%

Step-2:

Calculate expected rate of return:

= 0.60 * 18% + 0.40 * 4%

= 8.4 + 1.6

= 10 %

Calculate standard deviation:

= 0.6 * 0.31 / ½

= 0.3384

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