Suppose the expected returns and standard deviations of Stocks A and B are E( R

Question

Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .083, E(RB) = .143, A = .353, and B = .613.

Calculate the expected return of a portfolio that is composed of 28 percent A and 72 percent B when the correlation between the returns on A and B is .43. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Calculate the standard deviation of a portfolio that is composed of 28 percent A and 72 percent Bwhen the correlation between the returns on A and B is .43. (Do not round intermediate calculations and round your final answer 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 A and B is .43. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .083, E(RB) = .143, A = .353, and B = .613.

Explanation / Answer

Answer:

a-1) Expected return of a portfolio = E(RA) *W(A) + E(RB) *W(B)

= (0.083 * 28%) + (0.143*72%)

= 0.1262

=12.62%

a-2) Portfolio Variance = w2 (A) *2(A) + w2 B *2(B) + 2*(wA)*(wB)* (A) *(B)* correlation

= (0.28)^2 *(0.353)^2 + (0.72)^2 *(0.613)^2 + (2*0.28*0.72*0.353*0.613*0.43)

= 0.2421

=24.21%

b) Portfolio Variance = w2 (A) *2(A) + w2 B *2(B) + 2*(wA)*(wB)* (A) *(B)* correlation

= (0.28)^2 *(0.353)^2 + (0.72)^2 *(0.613)^2 + (2*0.28*0.72*0.353*0.613*-0.43)

= 0.1671

=16.71%

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