Ebenezer Scrooge has invested 40% of his money in share A and the remainder in share...

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Ebenezer Scrooge has invested 40% of his money in share A and the remainder in share B. He assesses their prospects as follow

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Answer 1

Answer #1

weight of A in the portfolio = w_A = 40%

Weight of B in the portfolio = w_B = 60%

Expected return on A = R_A = 18%, Standard deviation of A = σ_A = 21%

Expected return on B = R_B = 21%, Standard deviation of B = σ_B = 28%

Correlation between the returns of A and B = ρ = 0.5

Part a

Expected return of the portfolio is calculated using the formula:

E[R_P] = w_A*R_A + w_B*R_B = 40%*18% + 60%*21% = 19.8%

Varaince of the portfolio is calculated using the formula:

Variance of portfolio = σ_P² = w_A²*σ_A² + w_B²*σ_B² + 2*ρ*w_A*w_B*σ_A*σ_B

σ_P² = (40%)²*(21%)² + (60%)²*(28%)² + 2*0.5*40%*60%*21%*28% = 0.007056 + 0.028224 + 0.014112 = 0.049392

Standard deviation is squareroot of variance

Standard deviation of portfolio = σ_P = (0.049392)^1/2 = 0.222243110129426

Standard deviation of the portfolio = 22.22%

Answer a

Expected Return	19.8	%
Standard Deviation	22.22	%

Part b

Correlation coefficient 0

Correlation between the returns of A and B = ρ = 0

Variance of portfolio = σ_P² = w_A²*σ_A² + w_B²*σ_B² + 2*ρ*w_A*w_B*σ_A*σ_B

σ_P² = (40%)²*(21%)² + (60%)²*(28%)² + 2*0*40%*60%*21%*28% = 0.007056 + 0.028224 + 0 = 0.03528

Standard deviation is squareroot of variance

Standard deviation of portfolio = σ_P = (0.03528)^1/2 = 18.7829710109982%

Standard deviation of the portfolio = 18.78%

Correlation coefficient -0.5

Correlation between the returns of A and B = ρ = -0.5

Variance of portfolio = σ_P² = w_A²*σ_A² + w_B²*σ_B² + 2*ρ*w_A*w_B*σ_A*σ_B

σ_P² = (40%)²*(21%)² + (60%)²*(28%)² + 2*(-0.5)*40%*60%*21%*28% = 0.007056 + 0.028224 + (-0.014112) = 0.021168

Standard deviation is squareroot of variance

Standard deviation of portfolio = σ_P = (0.021168)^1/2 = 14.5492267835786%

Standard deviation of the portfolio = 14.55%

Answer b

Correlation Coefficient 0		Correlation coefficient -0.5
18.78	%	14.55	%

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