Question

A portfolio has 20% of its funds invested in Security A, 75% of its funds invested in Security B, and 5% invested in the risk free asset. The risk-free asset earns 4%. Security A has an expected return of 8% and a standard deviation of 18%. Security B has an expected return of 10% and a standard deviation of 22%. Securities A and B have a coefficient of correlation of 0.60.

This single question has two parts (below)

I am overwhelmed with this 2 part question please provide detailed instruction. typed out formulas are preferred, and if you have to use excel, please explain the excel process. No financial calculator please.

What is the standard deviation of the portfolio?

What is the expected return of the portfolio?

Answer 1

Security	Weights	Expected Return	Standard Deviation
A	20%	8%	18%
B	75%	10%	22%
Risk-free	5%	4%	0

Weight of security A = W_A = 20%, Weight of security B = W_B = 75%, Weight of risk-free asset = W_F = 5%

Return on security A = R_A = 8%, Return on security B = R_B = 10%, Return on risk-free asset = R_F = 4%

Risk-free asset carry zero risk, so its standard deviation is 0

Standard Deviation of A = σ_A = 18%, Standard Deviation of B = σ_B = 22%, Standard Deviation of risk-free asset = σ_F = 0

Variance and Standard Deviation of the portfolio

Variance of the portfolio is caclculated using the below formula:

Variance of the portfolio = σ_P² = W_A²*σ_A² + W_B²*σ_B² + W_F²*σ_F² + 2*W_A*W_B*ρ_A,B*σ_A*σ_B + 2*W_A*W_B*ρ_A,F*σ_A*σ_F + 2*W_B*W_F*ρ_B,F*σ_B*σ_F​​​​​​​

ρ_A,B = Correlation coefficient between A and B = 0.6

Now, σ_F = 0

σ_P² = (20%)²*(18%)² + (75%)²*(22%)² + 0 + 2*20%*75%*0.6*18%*22% + 0​​​​​​​ + 0

σ_P² = 0.001296 + 0.0272250 + 0.00713 = 0.035649

Standard deviation is square root of Variance

Standard Deviation of the portfolio = σ_P = 0.035649^1/2 = 0.188809427730715 = 18.8809427730715%

Answer part 1 -> Standard deviation of the portfolio = 18.8809427730715%

Expected return of the portfolio

Expected Return of the portfolio is calculated using the below formula:

E[R_P] = W_A*R_A + W_B*R_B + W_F*R_F​​​​​​​ = 20%*8% + 75%*10% + 5%*4% = 9.3%

Answer part 2 -> Expected return of the portfolio = 9.3%