Question

Suppose that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your client chooses to invest 70% of a portfolio in your fund and 30% in the T-bills. Suppose the same client in the previous problem decides to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. What is the proportion y

Answer 1

Proportion y = 80%

Step-by-step explanation:

E(rc) - r(f) = y[E(rp) - r(f)]. Where E(rc) - r(f) is Risk premium of clients overall portfolio and y[E(rp) - r(f)] is Risk premium of clients risky portfolio

0.15 - 0.07 = y[0.17 - 0.07]

0.08 = y(0.10)

y = 0.08/0.10

y = 0.80

y = 80%

So, the proportion of risky portfolio(y) is 80%. So, to achieve overall return of 15% on portfolio, investors needs to invest 80% investment in risky portfolio.