Answer:
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:
[tex]E(r_{c}) - r_{r} = y[E(r_{p} ) - r_{r} ][/tex]
Here,
Risk-premium of client's overall portfolio is [tex]E(r_{c})-r_{r}[/tex]
Risk-premium of client's risky portfolio is [tex]E(r_{p})-r_{r}[/tex]
Expected return on client's overall portfolio is [tex]E(r_{c})[/tex]
Expected return on client's risky portfolio is [tex]E(r_{p})[/tex]
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:
[tex]E(r_{c}) - r_{r} = y[E(r_{p} ) - r_{r} ][/tex]
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%
