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A portfolio is created out of three risky assets with expected returns 7 = 4,7 = 2 and 73 = 5. Moreover assume that

A portfolio is created out of three risky assets with expected returns 7 = 4,7 = 2 and 73 = 5. Moreover assume that their variances are given by o2 = 8, o2 = 0 = 10 and that their covariances are 12 = 2 and 13 = 023 = 0. a) Using the method of Lagrange multipliers, find an equation describing all efficient portfolios that can be created out of these three assets in other words: the efficient frontier. (Assume that shortselling is permitted.) b) Find the minimum variance point. c) Now assume there is a risk-free asset with rf = 1. Find the efficient frontier for this case.

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a Let w1 w2 and w3 be the weights of the three assets in the portfolio respectively The expected return of the portfolio is then given by rp w1 overli... blur-text-image

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