FNGB 7460 Portfolio Management Fordham University

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FORDHAM UNIVERSITY G raduate School of Business Portfolio Management Prof. Christopher Blake FN GB 7460 Spring 201 3 Problem Set 2 Consider the following data for assets 1 through 5 (i = 1, ..., 5): Asset i i R i  1 7% 4% 2 12% 6% 3 18% 12% 4 20% 10% 5 22% 13% Also, 12  = − 0.15, 13  = 0.45, 14  = 0.3, 15  = 0.4, 23  = 0.4, 24  = 0.15, 25  = 0.3, 34  = 0.8, 35  = 0.5, and 45  = 0.2. Answer questions 1, 2 and 3 using the above data. Show all work involved on separate sheets of paper attached to this page. 1a) (3 0 points) Using the formulas introduced in class, what are the investment weights, the expected return ( R ) and the total risk (  ) of the l east risky two - asset portfolio constructed from assets 1 and 5? (Assume short sales are allowed.) We want to find the weights that minimize the standard deviation, i.e. for an optimal risky portfolio. The following formula is used : 𝑤 1 = 𝑅 1 ∗ 𝜎 5 2 − 𝑅 5 ∗ 𝜎 15 𝑅 1 ∗ 𝜎 5 2 + 𝑅 5 ∗ 𝜎 1 2 − ( 𝑅 1 + 𝑅 5 ) ∗ 𝜎 15 Where 𝜎 15 is the covariance of the assets 1 and 5 :
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