Show all steps please. Portfolio Standard Deviation Suppose the expected returns
ID: 2735991 • Letter: S
Question
Show all steps please.
Portfolio Standard Deviation Suppose the expected returns and standard deviations of Stocks A and B are E(R_A) = 11. E(R_B) = .13, sigma_A = .39, and sigma_b = .76. Calculate the expected return and standard deviation of a portfolio that is composed of 35 percent A and 65 percent B when the correlation between the returns on A and B is .5. Calculate the standard deviation of a portfolio with the same portfolio weights as in t then the correlation coefficient between the returns on A and B is - .5. How does the correlation between the returns on A and B affect the standard deviation of the portfolio?Explanation / Answer
Expected Return = [WA x E(R)A] + [WB x E(R)B]
Standard Deviation of the Portfolio:
P = [2AW2A + 2BW2B + 2WAWB A B CORAB]1/2
Expected Return = [0.35 x 0.11] + [0.65 x 0.13] = 0.123
Standard Deviation of the Portfolio:
P = [(0.392 x 0.352)+(0.762x0.652) + (2x0.35x0.65x0.39x0.76x0.5)]1/2 = 0.574543
Standard Deviation of the Portfolio when correlation coefficient is -.5:
P = [(0.392 x 0.352)+(0.762x0.652) + (2x0.35x0.65x0.39x0.76x-0.5)]1/2 = 0.441857
Correlation coefficient of stocks measures the proportional move of one stock, when the other moves. When two stocks are positively correlated, they will move in the same direction by the degree of their correlation, while when they are negatively correlated, they will move in opposite directions. So, if the correlation is positive, it will increase the standard deviation of portfolio and if it’s negative, it will decrease the standard deviation of portfolio. Same is the case here.