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

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