Statistics 2000, Section 001, Midterm 1 (185 Points) Part ...
Business Statistics: Midterm...
Transcript of Business Statistics: Midterm...
Business Statistics:Midterm Solutions
N Vera ChauThe University of Chicago: Booth
November 9, 2017
1 True False(2 points each)
1. F
2. T
3. F
4. F
5. T
6. F
7. T
8. F
9. T
10. F
2 Multiple Choice(2 points each)
1. c
2. d
3. d
4. 3,4,1,2
3 Long Answer Questions3.1
a. (2 pts)
P (ri+1 = −0.1) = 0.35
P (ri+1 = 0) = 0.3
P (ri+1 = 0.1) = 0.35
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Business Stats Midterm Solutions N Vera Chau
b. (4 pts)
E [ri=1] = −0.1× 0.35 + 0.1× 0.35 = 0
V ar(ri+1) = 0.35× (−0.1− 0)2 + 0.35× (0.1− 0)2 = 0.007
c. (3 pts)
yes. You can verify that P (ri = x) = P (ri+1 = x) for every x.
d. (3 pts)
No.
P (r + i = 0, ri+1 = 0) = 0.15
P (ri = 0)P (ri+1 = 0) = 0.35× 0.35
e. (2 pts)
P (ri+1 = −0.1|ri = 0) =0.95
0.3= 0.1667
P (ri+1 = 0|ri = 0) =0.2
0.3= 0.667
P (ri+1 = 0.1|ri = 0) =0.05
0.3= 0.1667
f. (2 pts)
P (ri+1 = −0.1|ri = 0.1) =0.15
0.35= 0.4286
P (ri+1 = 0|ri = 0.1) =0.05
0.35= 0.1429
P (ri+1 = 0.1|ri = 0.1) =0.15
0.35= 0.4286
g. (2 pts)
P (ri+1 = −0.1|ri = −0.1) =0.15
0.35= 0.4286
P (ri+1 = 0|ri = −0.1) =0.05
0.35= 0.1429
P (ri+1 = 0.1|ri = −0.1) =0.15
0.35= 0.4286
h. (3 pts)
E [ri+1|ri = −0.1] = −0.1× 0.4286 + 0.1× 0.4286 = 0
E [ri+1|ri = 0] = −0.1× 0.1667 + 0.1× 0.1667 = 0
E [ri=1|ri = 0.1] = −0.1× 0.4286 + 0.1× 0.4286 = 0
i. (3 pts)
V ar(ri+1|ri = 0) = 0.1667× (−0.1)2 + 0.1667× (−0.1)2 = 0.0033
V ar(ri+1|ri = 0.1) = 0.4286× (−0.1)2 + 0.4286× (0.1)2 = 0.00857
November 9, 2017 Prof. Russell Fall, 2017
Business Stats Midterm Solutions N Vera Chau
j. (4 pts)
Variance is higher if the return moves in the previous period. In particular, when ri = 0, the variancein the next period is lower than when ri either decreases or increases.
k. (3 pts)
P (0.01)P (−.01|.01)P (.01| − .01)P (.01|.01)= 0.35× 0.42863 = 0.0276
l. (3 pts)
P (0)P (0|0)3 = 0.3× 0.6673 = 0.089
3.2a. (6 pts)
E [0.75 ∗A+ 0.25H] = 0.75(0.00016) + 0.25(0.00009) = 0.0001425
V ar(0.75A+ 0.25H) = 0.752(0.0018) + 0.252(0.0027) + 2(0.25 ∗ 0.75).0018 = 0.001856
b. (6 pts)
E [1.5A− 0.5H] = 1.5(0.00016)− 0.5(0.00009) = 0.000195
V ar(1.5A− 0.5H) = 1.52(0.0018) + (−0.5)2(0.0027)− 2(1.5 ∗ 0.5).0018 = 0.002025
c. (6 pts)
U1 = 0.0001425− 7(0.001856) = −0.01284
U2 = 0.000195− 7(0.002025) = −0.01398
Portfolio 1 is preferred.
3.3(3 points each)
a. 0.2875
b. 1− 0.8057 = 0.1943
c. 0.8057− 0.2827 = 0.523
d. Notice that 0.0049 ≈ 0.005 so ≈ −0.035
November 9, 2017 Prof. Russell Fall, 2017