Question

Suppose the expected returns and standard deviations of Stocks A and B are E(R_A) = .098, E(R_B) = .158, σ_A = .368, and σ_B = .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.)

  
    

Answer 1

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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