Question

Compute the expected return and risk on your portfolio using the following information: you invest 20%, 40%, and 40% in assets A, B, and C, respectively: Expected returns on assets A, B, and C: 10%, 5%, and 2%, respectively. Standard deviations of A, B, and C are 10%, 6%, and 1%, respectively. The Covariances between the assets are all zero but the covariance between B and C which is 1.

Answer 1

The following data is provided:

Assets	Weights	Expected Return	Standard Deviation
A	20%	10%	10%
B	40%	5%	6%
C	40%	2%	1%

Weight of A in the portfolio = w_A = 20%, Weight of B in the portfolio = w_B = 40%, Weight of C in the portfolio = w_C = 40%

Expected return on A = R_A = 10%, Expected return on B = R_B = 5%, Expected return on C = R_C = 2%

Standard deviation of A = σ_A = 10%, Standard deviation of B = σ_B = 6%, Standard deviation of C = σ_C = 1%

Correlation between A and B = ρ(A, B) = 0, Correlation between A and C = ρ(A, C) = 0,

Correlation between B and C = ρ(B, C) = 1

Expected Return on portfolio is calculated using the below formula:

E[R_P] = w_A*R_A + w_B*R_B + w_C*R_C = 20%*10% + 40%*5% + 40%*2% = 4.8%

Variance of the portfolio is calculated using the formula:

σ²_P= w_A²*σ_A² + w_B²*σ_B² + w_C²*σ_C² + 2*ρ(A,B)*w_A*w_B*σ_A*σ_B + 2*ρ(B,C)*w_B*w_C*σ_B*σ_C + 2*ρ(A,C)*w_A*w_C*σ_A*σ_C

σ²_P = 20%²*10%² + 40%²*6%² + 40%²*1%² + 0 + 2*1*40%*40%*6%*1% + 0 = 0.0004+0.000576+0.000016+0.000192 = 0.001184

Standard deviation is the square-root of varianceStandard deviation of the portfolio = σ_P = 0.001184^1/2 = 0.0344093

Please note that in the question it is wrongly mentioned as Covariance. It should be correlation coefficient

Answer

Expected Return on Portfolio = 4.8%

Standard deviation or risk of portfolio = 3.44093%