Question

Create a portfolio using the two stocks and information below:

	Expected Return	Standard Deviation	Weight in Portfolio
Stock A	8.00%	11.00%	42.00%
Stock B	9.00%	32.00%	58.00%
----------------------	----------------------	----------------------	----------------------
Correlation (A,B)	0.1300	----------------------	----------------------

(Do not round intermediate calculations. Record your answers in decimal form and round your answers to 4 decimal places. Ex. x.xxxx)

What is the variance of A?

What is the variance of B?

What is the Correlation (A,A)?

What is the Correlation (B,B)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the expected return on the portfolio above?

What is the variance on the portfolio above?

What is the standard deviation on the portfolio above?

make sure the answers are correct please

Answer 1

Variance is the square of the standard deviation

Standard Deviation of A = σ_A = 11%

Variance of A = (11%)² = σ_A² = 0.0.0121

The variance of B = (32%)² = σ_B² = 0.1024

Correlation (A,A) = ρ(A, A) = 1

Correlation (B,B) = ρ(B, B) = 1

The formula to calculate the covarinace between two variables X and Y = Cov(X, Y) = ρ(X,Y) * σ_X * σ_Y

Covariance (A,A) = ρ(A, A)*σ_A*σ_A = 1*σ_A*σ_A = Variance of A = 0.0121

Covariance (A,B) = ρ(A, B)*σ_A*σ_B= 0.13*0.11*0.32 = 0.004576 = 0.0046

Covariance (B,A) = ρ(A, B)*σ_B*σ_A = 0.13*0.32*0.11 = 0.004576 = 0.0046

Covariance (B,B) = ρ(B, B)*σ_B*σ_B = 1*σ_B*σ_B = Variance of B = 0.1024

Weight of portfolio: W_A = 0.42, W_B = 0.58

Expected Return: E[R_A] = 8%, E[R_B] = 9%

Correlation of A, B = ρ(A, B) = 0.1300

Expected Return on the portfolio = E[R_P] = W_A*E[R_A] + W_B*E[R_B] = 0.42*8% + 0.58*9% = 0.0858

Variance of the Portfolio = σ_p² = W_A²*σ_A²+W_A²*σ_A²+2*Cov(A,B)*W_A*W_B = 0.42²*0.0121+(0.58²*0.1024)+2*0.004576*0.42*0.58 = 0.00213444+ 0.03444736+0.0022294272 = 0.03881122720 = 0.0388

Standard Deviation of the portfolio = σ_p = (0.03881122720)^1/2 = 0.1970056527108 = 0.1970