You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your risky portfolio includes the following investments in the given proportions: Stock A 25 % Stock B 32 % Stock C 43 % Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%. a. What is the proportion y?

y = 0.80

Step-by-step explanation:

Given:

- The expected rate of return for risky portfolio E (r_p) = 0.18

- The T-bill rate is r_f = 0.08

Find:

Investing proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%.

What is the proportion y?

Solution:

- The proportion y is a fraction of expected risky portfolio and the left-over for the T-bill compliance. Usually we see a major proportion is for risky portfolio as follows:

E (r_c) = y*E (r_p) + (1 - y) * r_f

y*E (r_p) + (1 - y) * r_f = 0.16

- Re-arrange for proportion y:

y = (0.16 - r_f) / (E (r_p) - r_f)

- Plug in values:

y = (0.16 - 0.08) / (0.18 - 0.08)

y = 0.80

- Hence, we see that 80% of the total investment budget becomes a part of risky portfolio returns.