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Assignment 2 Answers

Assignment 2 Answers - ECON 425 1 Key for ASSIGNMENT 2 Dr...

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ECON 425 Key for ASSIGNMENT 2 Dr. AHN 1. 1) 100 101 100 Pr Pr( 1.52) 0.9357 43/100 43/100 X Z . 2) 101 100 100 103 100 Pr Pr(1.96 5.88) 1 0.975 0.025 43/165 43/165 43/165 X Z . Or = 0.9986-0.025 = 0.9736 2. Strategy I: E(0.5x+0.5y) = 0.5×μ X + 0.5×μ Y = 0.5×0.5 + 0.5×0.5 = 0.5. Var(0.5x+0.5y) = 2 2 2 2 (0.5 0.5 ) (0.5) 2 (0.5) (0.5) (0.5) 0.25 4 0 0.25 4 2 X XY X Y Y Var x y   Strategy II: E(0.2x+0.8y) = 0.2×μ X + 0.8×μ Y = 0.2×0.5 + 0.8×0.5 = 0.5. Var(0.5x+0.5y) = 2 2 2 2 (0.2 0.8 ) (0.2) 2 (0.2) (0.8) (0.8) 0.04 4 0 0.64 4 0.68 4 2.72 X XY X Y Y Var x y   The two strategies give us the same expected returns, but the Strategy I has the returns with smaller variances. It means that Strategy I is less risky while it earns the same returns as Strategy II. So, Strategy I is preferred. 3. 1) 2 700/100 7; 8100/99 81.818; ( ) 81.818/100 0.9045 Y Y s SE Y . 2) (7 5) /0.9045 2.21 t . P-Val = 2 Pr( | |) 2 (1 Pr( | |)) 2 (1 Pr( 2.21)) 0.027 Z t Z t Z . P-Val < 10%. Reject H o . 3) c 2.33. Since t < c, do not reject H o . 4. 1110; 123; 1000 Y Y s
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