Question

Suppose the expected returns and standard deviations of Stocks A and B are E(R_A) = .100, E(R_B) = .160, σ_A = .370, and σ_B = .630.

  

a-1.	Calculate the expected return of a portfolio that is composed of 45 percent Stock A and 55 percent Stock B when the correlation between the returns on A and B is .60. (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 45 percent Stock A and 55 percent Stock B when the correlation between the returns on A and B is .60. (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 −.60. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a-1 Expected Return = Weights * Respective Returns

Expected Return = 0.45 * 0.10 + 0.55 * 0.16

Expected Return = 13.30%

a-2 Standard Deviation = Sqrt (Weight of A^2 * SD of A^2 + Weight of B^2 * SD of B^2 + 2 * Weight A * Weight B * SD of A * SD of B * Correlation)

Standard Deviation = Sqrt (0.45^2 * 0.37^2 + 0.55^2 * 0.63^2 + 2 * 0.45 * 0.55 * 0.37 * 0.63 * 0.60)

Standard Deviation = Sqrt (0.027722 + 0.120062 + 0.069231)

Standard Deviation = 46.58%

b.

Standard Deviation = Sqrt (Weight of A^2 * SD of A^2 + Weight of B^2 * SD of B^2 + 2 * Weight A * Weight B * SD of A * SD of B * Correlation)

Standard Deviation = Sqrt (0.45^2 * 0.37^2 + 0.55^2 * 0.63^2 + 2 * 0.45 * 0.55 * 0.37 * 0.63 * -0.60)

Standard Deviation = Sqrt (0.027722 + 0.120062 - 0.069231)

Standard Deviation = 28.03%

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