Question

Consider the following information about a risky portfolio that you manage and a risk-free asset: E(rP) = 16%, σP = 20%, rf = 4%. a. Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 5%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset? (Do not round intermediate calculations. Round your answer to 2 decimal place.)

b. What will be the standard deviation of the rate of return on her portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse? First client Second client

Answer 1

The return on the portfolio is given by the below formula,

Return on the portfolio = w1*Er1 + w2*Er2

where w1 and w2 are the weights and Er1 and Er2 are the returns

5 = w1 * 16 + (1 - w1) * 4

5 = 16w1 + 4 - 4w1

1 = 12w1

w1 = 1 / 12 = 8.33%

w2 = 1 - 0.0833 = 91.67%

Standard deviation of the portfolio = std deviation on risky portfolio * proportion into risky asset = 0.0833*20 = 1.67%

Second client is more risk averse as he is setting a limit to the risk he can take. He is not ready to take higher risks for higher returns.