Question: Problem 6 (15 points) Consider two securities with expected returns My and My and standard de- viations o, and 02 with correlation of 0. Let

Problem 6 (15 points) Consider two securities with expected returns My and My and standard de- viations o, and 02 with correlation of 0. Let w and 1 - w be the investment weights in the two securities 1 and 2, respectively with the portfolio of the two securities represented as p= (1-] 14,(W) Now let f(w) where o(w) is the variance of portfolio p when w is the weight of the first security and My(w) is the expected return of portfolio p when w is the weight of the first security. Now suppose that you wish to find a portfolio p that minimizes f(w) where you allow short selling. (a) (3 points) Explain BRIEFLY why it makes sense to minimize f(w). (b) (7 points) What conditions do optimal portfolios have to satisfy? (c) (5 points) Under what conditions will the optimal portfolio p that mini- mizes f(w) be a minimum variance portfolio? Problem 6 (15 points) Consider two securities with expected returns My and My and standard de- viations o, and 02 with correlation of 0. Let w and 1 - w be the investment weights in the two securities 1 and 2, respectively with the portfolio of the two securities represented as p= (1-] 14,(W) Now let f(w) where o(w) is the variance of portfolio p when w is the weight of the first security and My(w) is the expected return of portfolio p when w is the weight of the first security. Now suppose that you wish to find a portfolio p that minimizes f(w) where you allow short selling. (a) (3 points) Explain BRIEFLY why it makes sense to minimize f(w). (b) (7 points) What conditions do optimal portfolios have to satisfy? (c) (5 points) Under what conditions will the optimal portfolio p that mini- mizes f(w) be a minimum variance portfolio

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