Answer:
A. Expected return on the portfolio = 15.25%
B. Standard deviation of the portfolio = 51.44%
Explanation:
A. What is the expected return on a portfolio composed of 25% of Security F and 75% of Security G?
This can be calculated as follows:
Expected return on the portfolio = (PF * EF) + (PG * EG) ...................... (1)
Where;
PF = Proportion invested in security F = 25%
EF = Expected return of security F = 11.5%
PG = Proportion invested in security F = 75%
EG = Expected return of security G = 16.5%
Substituting the values into equation (1), we have:
Expected return on the portfolio = (25% * 11.5%) + (75% * 16.5%) = 15.25%
B. If the correlation between the returns of security F and security G is 0.24, what is the standard deviation of the portfolio described in part (a)?
This can be calculated as follows:
Standard deviation of the portfolio = ((PF^2 * FSD^2) + (PG^2 * GSD^2) + (2 * PF * PG * FSD * GSD * Corab))^(1/2) ................... (2)
Where;
PF = Proportion invested in security F = 25%
FSD = Standard deviation of security F = 44.5%
PG = Proportion invested in security F = 75%
GSD = Standard deviation of security G = 63.5%
Corab = correlation between the returns of security F and security G = 0.24
Substituting the values into equation (2), we have:
Standard deviation of the portfolio = ((25%^2 * 44.5%^2) + (75%^2 * 63.5%^2) + (2 * 25% * 75% * 44.5% * 63.5% * 0.24))^(1/2) = 51.44%
