Question

Consider the following information about a risky portfolio that you manage and a risk-free asset: E(rp) = 13%, Op = 17%, If=5%.

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 7%. 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.)

Answer 1

To achieve an expected rate of return of 7%, the client should invest approximately 29% in the risky portfolio and 71% in the risk-free asset, based on the given expected returns and risk rates.

Step-by-step explanation:

The question concerns the calculation of the proportion of funds to allocate to a risky portfolio and a risk-free asset in order to achieve a desired expected rate of return on an overall investment portfolio. Given the information E(rp) = 13%, which is the expected return of the portfolio, σp = 17%, the standard deviation (risk) of the portfolio, and If=5%, the risk-free rate, we can use the formula for the expected return on a complete portfolio:

E(rc) = w * E(rp) + (1 - w) * If

where E(rc) is the expected return on the complete portfolio, w is the proportion of the investment in the risky portfolio, E(rp) is the expected return on the risky portfolio, and If is the risk-free rate. The client wants an expected return (E(rc)) of 7%, so we set up the equation:

0.07 = w * 0.13 + (1 - w) * 0.05

Solving for w, we obtain the proportion to invest in the risky portfolio, which is approximately w = 0.29 or 29%, and consequently (1 - w) = 0.71 or 71% in the risk-free asset.