Investments in individual stocks and stock portfolios (combination stock) take a
ID: 3134811 • Letter: I
Question
Investments in individual stocks and stock portfolios (combination stock) take a lot of risk and required details studies on the return rate trend. The objective of investor is to gain higher return and less risky.
The lesser the variation in returns, the investor will be more confident in investing in the portfolios. Based on the following table that consist the return rate of 3 investments, A, B and C; answer the following questions.
a) Use systematic sampling for each investment to collect 5th sample to obtain 10 samples for each investment
Returns of Investments
Investment A
Investment B
Investment C
30.00
13.09
30.33
-32.17
6.80
-26.90
-2.13
13.77
-30.37
30.31
64.26
35.58
4.30
22.42
-5.61
6.06
-18.74
-27.96
25.00
34.40
29.00
14.73
24.37
12.71
12.89
49.87
-26.01
36.13
-15.46
-1.81
-20.24
22.92
0.46
1.53
-16.25
6.11
1.20
20.95
2.07
17.61
-17.33
6.04
-2.59
43.71
29.44
1.20
7.60
40.45
33.00
-12.83
11.00
9.94
57.41
-30.72
14.26
0.52
-25.93
-33.39
65.97
-36.68
-15.83
61.00
8.29
58.67
-26.24
27.93
0.63
-11.96
61.00
0.25
57.01
-28.17
38.00
1.94
-20.44
5.23
61.24
-34.75
6.93
28.45
-34.75
66.00
58.28
9.66
-13.24
-8.55
54.19
24.30
-28.54
63.37
-18.95
-5.29
44.00
-10.01
19.84
-4.15
9.43
-7.04
-20.23
35.24
13.73
23.46
1.21
-12.11
4.16
40.70
8.80
-11.53
31.76
12.89
10.03
22.18
62.64
3.19
11.07
63.00
10.51
3.24
28.23
24.34
8.47
-19.27
39.04
25.10
7.05
22.87
36.08
-9.22
24.76
-24.24
-28.51
45.21
-21.95
-17.00
15.28
-38.47
64.88
-18.09
10.33
17.30
34.21
13.44
47.27
-9.59
12.68
52.00
52.00
68.00
22.70
-26.10
Returns of Investments
Investment A
Investment B
Investment C
30.00
13.09
30.33
-32.17
6.80
-26.90
-2.13
13.77
-30.37
30.31
64.26
35.58
4.30
22.42
-5.61
6.06
-18.74
-27.96
25.00
34.40
29.00
14.73
24.37
12.71
12.89
49.87
-26.01
36.13
-15.46
-1.81
-20.24
22.92
0.46
1.53
-16.25
6.11
1.20
20.95
2.07
17.61
-17.33
6.04
-2.59
43.71
29.44
1.20
7.60
40.45
33.00
-12.83
11.00
9.94
57.41
-30.72
14.26
0.52
-25.93
-33.39
65.97
-36.68
-15.83
61.00
8.29
58.67
-26.24
27.93
0.63
-11.96
61.00
0.25
57.01
-28.17
38.00
1.94
-20.44
5.23
61.24
-34.75
6.93
28.45
-34.75
66.00
58.28
9.66
-13.24
-8.55
54.19
24.30
-28.54
63.37
-18.95
-5.29
44.00
-10.01
19.84
-4.15
9.43
-7.04
-20.23
35.24
13.73
23.46
1.21
-12.11
4.16
40.70
8.80
-11.53
31.76
12.89
10.03
22.18
62.64
3.19
11.07
63.00
10.51
3.24
28.23
24.34
8.47
-19.27
39.04
25.10
7.05
22.87
36.08
-9.22
24.76
-24.24
-28.51
45.21
-21.95
-17.00
15.28
-38.47
64.88
-18.09
10.33
17.30
34.21
13.44
47.27
-9.59
12.68
52.00
52.00
68.00
22.70
-26.10
Explanation / Answer
Here we have to obtain 10 samples from each investment using systematic sampling technique of interval 5 unit.
We will pick one random number of one digit between 1-5 from Fisher-Yates random no. table and corresponding to that random no. we will selelect that sample from the particular investment and after that at every 5 unit interval we will select the sample.In this way we will have 10 samples from each investment.
Investment A
From Fisher-Yates table,Pg-134,3rd row & 6th column we get '2'.
So the 2nd sample is -2.13.
Now the 10 samples are respectively: {-2.13,1.20,0.63,9.43,36.08,13.77,20.95,-11.96,-7.04,-9.22}.
Investment B
From Fisher-Yates table,Pg-134,1st row & 8th column we get '3'.
So the 3rd sample is -5.61.
Now the 10 samples are respectively: {-5.61,29.44,-20.44,4.16,15.28,6.06,1.20,5.23,40.70,-38.47}.
Investment C
From Fisher-Yates table,Pg-135,1st row & 1st column we get '5'.
So the 5th sample is -15.46.
Now the 10 samples are respectively: {-15.46,65.97,-28.54,28.23,22.70,-1.81,-36.68,63.37,24.34,-26.10}.
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