Fort part a of the question assume instead of 5 stocks, just 4 stocks given in the question.

Consider an investor who plans to choose a portfolio of four stocks. From market data, the expected returns of these stocks are estimated as p1 = -0.2, H2 = 0.1, f3 = 0.2, H4 = 0.3. The estimated values of the corresponding standard deviations of the returns are 01 = 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. (5) What is the expected return vector and the covariance matrix of these five stocks? b. (5) What are the weights of the minimum variance portfolio (MVP)? Does the MVP have shortselling assuming positive initial wealth? c. (5) What are the expected return and standard deviation of the MVP? d. (5) What are the weights of the portfolio admitting the minimum variance among all portfolios with expected return u = 2? e. (5) What are the weights of the portfolio admitting the minimum variance among all portfolios with expected return u = -3? f. (5) Using two-fund theorem, describe the minimum variance line in terms of the two portfolios computed in parts d and e. g. (5) Describe the risk-expected return curve of the portfolios on the minimum vari- ance line. Draw the curve. Now, in addition to these stocks, a riskless bond is available in the market with return r= 0.05. h. (5) Why does there exist a market portfolio? Consider an investor who plans to choose a portfolio of four stocks. From market data, the expected returns of these stocks are estimated as p1 = -0.2, H2 = 0.1, f3 = 0.2, H4 = 0.3. The estimated values of the corresponding standard deviations of the returns are 01 = 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. (5) What is the expected return vector and the covariance matrix of these five stocks? b. (5) What are the weights of the minimum variance portfolio (MVP)? Does the MVP have shortselling assuming positive initial wealth? c. (5) What are the expected return and standard deviation of the MVP? d. (5) What are the weights of the portfolio admitting the minimum variance among all portfolios with expected return u = 2? e. (5) What are the weights of the portfolio admitting the minimum variance among all portfolios with expected return u = -3? f. (5) Using two-fund theorem, describe the minimum variance line in terms of the two portfolios computed in parts d and e. g. (5) Describe the risk-expected return curve of the portfolios on the minimum vari- ance line. Draw the curve. Now, in addition to these stocks, a riskless bond is available in the market with return r= 0.05. h. (5) Why does there exist a market portfolio