Question

# Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .098,...

 Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .098, E(RB) = .158, σA = .368, and σB = .628.

 a-1. Calculate the expected return of a portfolio that is composed of 43 percent Stock A and 57 percent Stock B when the correlation between the returns on A and B is .58. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
 a-2. Calculate the standard deviation of a portfolio that is composed of 43 percent Stock A and 57 percent Stock B when the correlation between the returns on A and B is .58. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
 b. 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 −.58. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Formulae used are:

E(p) = E(rA) * W(A) + E(rB) * W(B)

SD(p) = sqrt(W(A)^2 * SD(A)^2 + W(B)^2 * SD(B)^2 + 2* W(A) * SD(A) * W(B) * SD(B) * corr(A,B))

a1 and a2

 E(rA) 9.80% E(rB) 15.80% SD(A) 36.80% SD(B) 62.80% Corr 0.58
 W(A) W(B) E(p) Var(p) SD(p) 0.43 0.57 13.22% 21.89% 46.78%

b.

 E(rA) 9.80% E(rB) 15.80% SD(A) 36.80% SD(B) 62.80% Corr -0.58
 W(A) W(B) E(p) Var(p) SD(p) 0.43 0.57 13.22% 8.75% 29.58%

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