Suppose the expected returns and standard deviations of Stoc

Suppose the expected returns and standard deviations of Stocks A and B are E(R_A) = .096, E(R_B) = .156, _A = .366, and _B = .626.

Calculate the expected return of a portfolio that is composed of 41 percent Stock A and 59 percent Stock B when the correlation between the returns on A and B is .56. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Calculate the standard deviation of a portfolio that is composed of 41 percent Stock A and 59 percent Stock B when the correlation between the returns on A and B is .56. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Calculate the standard deviation of a portfolio with the same portfolio weights as in part (a) when the correlation coefficient between the returns on Stocks A and B is .56. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Solution

SD of 2 stocks portfolio (_p²) = (X_A²)×(_A²)+(X_B²)×(_B²)+2×X_A×X_B×r_AB×_A×_B

Here, X is weighs of respective portfolios and is standard deviation of respective stocks

When stocks are correlated with 0.56:

= (0.41)^2×(0.366)^2+(0.156)^2×(0.626)^2+2×0.41×0.59×0.56×0.366×0.626

= 0.0941 or 9.41%

When stocks are correlated with -0.56:

= (0.41)^2×(0.366)^2+(0.156)^2×(0.626)^2+2×0.41×0.59×-0.56×0.366×0.626

= -0.03 or -3%