Question

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 30%. The T-bill rate is 10%. Suppose that you have a client that prefers 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 investment proportion

Answer 1

The proportion of the investment is 100%.

Step-by-step explanation:

This can be calculated using the following formula:

Rportfolio = (y * Rrisky) + ((1 - y) * Ttbill) ..................... (1)

Where;

Rportfolio = Overall portfolio expected rate of return = 15%. or 0.15

Rrisky = risky portfolio expected rate of return = 15%, or 0.15

Ttbill = T-bill rate = 10%, or 0.10

Substituting the values into equation (1) and solve for y, we have:

0.15 = (y * 0.15) + ((1 - y) * 0.10)

0.15 = 0.15y + 0.10(1 - y)

0.15 = 0.15y + 0.10 - 0.10y

0.15 - 0.10 = 0.15y - 0.10y

0.05 = 0.05y

y = 0.05 / 0.05

y = 1.00, or 100%

Therefore, the proportion of the investment is 100%.