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Consider an investor who plans to choose a portfolio of four stocks. From market data, the expected returns of these stocks are estimated as #1

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Consider an investor who plans to choose a portfolio of four stocks. From market data, the expected returns of these stocks are estimated as #1 = -0.2, H2 = 0.1, H3 = 0.2, Ha = 0.3. The estimated values of the corresponding standard deviations of the returns are g = 0.2, 02 = 0.1, 03 = 0.2, 04 = 0.3. Based on statistical evidence, it is assumed that the only correlated pairs of stocks are {1,3}, {1,4} and {2,4} with respective correlation coefficients P13 = 0.3, P14 = 0.1, P24 = -0.1 for the returns. a. (4) What is the expected return vector and the covariance matrix of these five stocks? b. (4) What are the weights of the minimum variance portfolio (MVP)? Does the MVP have shortselling? c. (4) What are the expected return and standard deviation of the MVP? d. (4) What are the weights of the portfolio admitting the minimum variance among all portfolios with expected return u = 2? Consider an investor who plans to choose a portfolio of four stocks. From market data, the expected returns of these stocks are estimated as #1 = -0.2, H2 = 0.1, H3 = 0.2, Ha = 0.3. The estimated values of the corresponding standard deviations of the returns are g = 0.2, 02 = 0.1, 03 = 0.2, 04 = 0.3. Based on statistical evidence, it is assumed that the only correlated pairs of stocks are {1,3}, {1,4} and {2,4} with respective correlation coefficients P13 = 0.3, P14 = 0.1, P24 = -0.1 for the returns. a. (4) What is the expected return vector and the covariance matrix of these five stocks? b. (4) What are the weights of the minimum variance portfolio (MVP)? Does the MVP have shortselling? c. (4) What are the expected return and standard deviation of the MVP? d. (4) What are the weights of the portfolio admitting the minimum variance among all portfolios with expected return u = 2

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