A portfolio whith two assets A and B. Expected return of the assets are a= 10% a

Question

A portfolio whith two assets A and B. Expected return of the assets are

a= 10% a=10%

b=10% b=20%

The correlation of A and B is =-0,5

In the portfolio S the weight for A w and for B (1-w)

S=sA+(1-w)B

Furthermore the market M is 30% A and 70%B

a) Find expected return and variance of portfolio M?

b) For what value of w we get min variance of portfolio S?

c) Find expected return and variance in this point(MVP). Now it is given that the covariance between M and S is Cov[M,S] = 0,025-0,029w

d) What is the expected return of portfolio that has no covariance whith M?

e) Prove that the covariance between M and S is Cov [M,S]= 0,025-0,029w

Help have tried this for days :(

Explanation / Answer

a) According to the given information, Weight of asset-A = 30% Weight of asset-B = 70% Expected return on asset-A = 10% Expected return on asset-B = 10% Standard deviation on asset-A = 10% Standard deviation on asset- B = 20% Correlation between A and B = -0.5 The formula for calculating the portfolio expected return is E(Rp) = Wa * E(Ra) + Wb * E(Rb) where E(Rp) is the expected return on portfolio = 0.30 * 0.10 + 0.70 * 0.10 = 0.03 + 0.07 = 0.1 or 10% Therefore, the expected return on portfolio is 10% Calculating the portfolio variance: The formula for calculating the portfolio variance is (Wa)^2 x [SD(A)]^2 + (Wb)^2 x [SD(B)]^2 + 2 x Wa x Wb x SD(A) x SD(B) x Correlation co-efficient Where SD = Standard deviation Substituting the values in the above formula, we get = (0.3)^2 x (0.1)^2 + (0.7)^2 x (0.2)^2 + 2 x 0.3 x 0.7 x 0.1 x 0.2 x (-0.5) = 0.09 x 0.01 + 0.49 x 0.04 - 0.0042 = 0.0009 + 0.0196 - 0.0042 = 0.0163 Therefore, the portfolio variace = 0.0163 But, we know that the standard deviation is the square root of variance. Portfolio Standard deviation = Sqrt(0.0163) = 0.1276 or 12.76% Therefore, the standard deviation of portfolio is 12.76% b) The minimum variance portfolio is calculated using the formula as: For Asset-A = Variance of asset - B / (Variance of asset-A + Variance of asset-B) But , we know that Variance = (Standard deviation)^2 Variance of asset-A = (0.10)^2 = 0.01 Variance of asset-B = (0.20)^2 = 0.04 Therefore, calculting the weight of asset-A Weight of asset-A = 0.04 / (0.01 + 0.04) = 0.8 Weight of asset-B = 1 - Weight of asset-A = 1 - 0.8 = 0.20 Therefore, the weights of asset-A and B are 80% and 20% c) The correlation is calculated by using the formula as: Correlation = Covariance / [SD(A) x SD(B)]

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