Question

Suppose the same client in the previous problem decides to invest in your risky portfolio a proportion (y) of his total investment budget 1 1 1 1 1 a. b. c. 4. a. b. 5. a. b. 6. a. b. 7. 8. so that his overall portfolio will have an expected rate of return of 15%. (LO 5-3) What is the proportion y?

Answer 1

An investor is going to invest some amount of total investment in a risky portfolio which has the expected return of 17% and standard deviation of 27%. The remaining amount will be invested in the T-bills which has the expected return on 7%.

The risky portfolio includes stock A, stock B, and stock C.

By investing in risky portfolio and T-bills, the expected return on the portfolio will be 15%.

Proportion of risky portfolio in investors investment budget can be calculated by using the following equation:

`E(r_(c)) - r_(r) = y[E(r_(p) ) - r_(r) ]`

Here,

Risk-premium of client's overall portfolio is
`E(r_(c))-r_(r)`

Risk-premium of client's risky portfolio is
`E(r_(p))-r_(r)`

Expected return on client's overall portfolio is
`E(r_(c))`

Expected return on client's risky portfolio is
`E(r_(p))`

Proportion of risky portfolio in client's overall portfolio is y.

Risk-free rate on Treasury bill is

This equation represents the relationship between risk-premium of risky portfolio, risk-premium of investor's overall portfolio and the proportion of risky portfolio in investor's overall portfolio.

Calculate the proportion of risky portfolio as follows:

`E(r_(c)) - r_(r) = y[E(r_(p) ) - r_(r) ]`

0.15 - 0.07 = y (0.17 - 0.07)

0.08 = y (0.10)

y = 0.08/0.10

Y = 0.80 (or) 80%

Hence, the proportion of risky portfolio in investor's overall portfolio (y) is 80%