You are considering two assets with the following characteristics:
E(R) = 0.15 E(R2)=0.20
01 = 0.10
sigma2 = 0.2
w1 = 0.5
w2 = 0.5
Compute the mean and standard deviation of two portfolios if r1,2 = 0.40 and -0.60, respectively.
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To compute the mean and standard deviation of the two portfolios, we will use the following formulas:
Portfolio mean:
E(Rp) = w1 * E(R1) + w2 * E(R2)
Portfolio variance:
Var(Rp) = w1^2 * Var(R1) + w2^2 * Var(R2) + 2 * w1 * w2 * Cov(R1, R2)
Portfolio standard deviation:
σp = sqrt(Var(Rp))
Given the following information:
E(R1) = 0.15
E(R2) = 0.20
w1 = 0.5
w2 = 0.5
Var(R1) = 0.10
Var(R2) = 0.20
Cov(R1, R2) = -0.60
Computing the mean of the first portfolio:
E(Rp1) = 0.5 * 0.15 + 0.5 * 0.20
E(Rp1) = 0.075 + 0.100
E(Rp1) = 0.175
Computing the mean of the second portfolio:
E(Rp2) = 0.5 * 0.15 + 0.5 * (-0.60)
E(Rp2) = 0.075 + (-0.300)
E(Rp2) = -0.225
Computing the variance of the first portfolio:
Var(Rp1) = (0.5)^2 * 0.10 + (0.5)^2 * 0.20 + 2 * 0.5 * 0.5 * (-0.60)
Var(Rp1) = 0.025 + 0.050 - 0.150
Var(Rp1) = -0.075
Computing the variance of the second portfolio:
Var(Rp2) = (0.5)^2 * 0.10 + (0.5)^2 * 0.20 + 2 * 0.5 * 0.5 * (-0.60)
Var(Rp2) = 0.025 + 0.050 - 0.150
Var(Rp2) = -0.075
Since the variance cannot be negative, it seems there might be an error in the given information. Please double-check the provided numbers.
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