Discussion Response
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This document was exported from Numbers. Each table was converted to an Excel worksheet. All other objects on each Numbers sheet were placed on separate worksheets. Please be aware that formula calculations may differ in Excel. |
Numbers Sheet Name |
Numbers Table Name |
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| Table 1 |
Sheet1
| Beta |
Table 1 Beta
| R-SQUARED |
Table 1 R-SQUARED
| Lowest
| Risk |
and Optimal Portfol
Table 1 Lowest Risk and Optimal Portfol
Sheet1
A) S&P5
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| 0 |
0 Stocks
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| Sector: |
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| NAME |
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| Recent price |
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| Price 5 year |
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| Price 10 year |
Historic Average |
Geometric Average |
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| 5 Year |
s
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| 10 Year |
s
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| 5 Years |
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| 10 Years |
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| Consumer Dicretionary |
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| Apple |
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| 115.31 |
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| 7
| 0.74 |
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| 80 |
63% |
| 4
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| 4% |
| 8.114 |
2.631 |
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| Information Technology |
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| Adobe |
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| 494.59 |
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| 344.1 |
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| 385.26 |
44%
2
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| 8% |
| 29.298 |
10.033 |
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| Consumer Staples |
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| General mills |
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| 61.41 |
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| 54.95 |
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| 54.7 |
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| 12% |
12%
| 0.492 |
-0.229 |
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| Materials |
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| Applied materials |
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| 64.56 |
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| 51.74 |
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| 52.04 |
25% |
24% |
| 1.764 |
0.352 |
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| Energy |
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| American electric power |
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| 91.61 |
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| 81.39 |
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| 78.43 |
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| 13% |
1
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| 7% |
| 1.244 |
0.418 |
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| Real Estate |
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| Alexandria real estate equities |
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| 158.92 |
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| 149.49 |
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| 146.99 |
6% |
8%
| 1.086 |
| 0.29 |
3
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| Financials |
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| Ameriprise Financial |
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| 172.37 |
| 10
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| 7.48 |
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| 121.98 |
60% |
41% |
| 12.178 |
4.139 |
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| Commercials Services |
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| Accenture |
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| 230.57 |
| 17
| 5.46 |
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| 193.71 |
31% |
1
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| 9% |
| 10.222 |
2.786 |
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| Healthcare |
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| Abbott Laboratories |
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| 114.11 |
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| 94.06 |
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| 89.89 |
21% |
27% |
| 3.21 |
1.522 |
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| Utilities |
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| 3M |
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| 164.78 |
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| 147 |
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| 78.56 |
12%
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| 10% |
| 2.756 |
7.722 |
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| Industrials |
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| A.O Smith |
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| 53.28 |
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| 40.39 |
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| 42.22 |
32% |
26% |
| 1.778 |
0.206 |
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| Variance |
is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of numbers is spread out from their average while standard deviation is a measure of the amount of variation or dispersion of a set of values (Sharma, Sharma and Singh, 2018).
Sector: NAME Recent price
Price 5 Year |
Price 10 year Variance
| Standard Deviation |
5 Years 10 Years 5 Years 10 Years
Consumer Dicretionary Apple 115.31 70.74 80
3
| 7.21 |
| 26.605 |
| 6.10 |
5.16 |
Information Technology Adobe 494.59 344.1 385.26
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| 167.738 |
| 122.395 |
| 12.95 |
11.06 |
Consumer Staples General mills 61.41 54.95 54.7
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| 23.272 |
| 17.106 |
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| 4.82 |
4.14 |
Materials Applied materials 64.56 51.74 52.04
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| 23.26 |
| 16.834 |
4.82
4.10 |
Energy American electric power 91.61 81.39 78.43
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| 34.6 |
| 25.143 |
| 5.88 |
5.01 |
Real Estate Alexandria real estate equities 158.92 149.49 146.99
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| 61.682 |
| 45.54 |
| 7.85 |
6.75 |
Financials Ameriprise Financial 172.37
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| 107.48 |
121.98
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| 55.97 |
| 40.183 |
7.48
6.34 |
Commercials Services Accenture 230.57
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| 175.46 |
193.71
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| 81.206 |
| 59.974 |
| 9.01 |
7.74 |
Healthcare Abbott Laboratories 114.11 94.06 89.89
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| 41.634 |
| 29.806 |
| 6.45 |
5.46
Utilities 3M 164.78 147 78.56
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| 62.356 |
| 39.034 |
| 7.90 |
6.25 |
Industrials A.O Smith 53.28 40.39 42.22
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| 18.734 |
| 13.589 |
| 4.33 |
3.69 |
Sector: NAME Recent price Price 5 year Price 10 year
Maximum Value |
Minimum Value |
Range |
Consumer Dicretionary Apple 115.31 70.74 80 115.31 70.74
44.57 |
Information Technology Adobe 494.59 344.1 385.26 494.59 344.1
150.49 |
Consumer Staples General mills 61.41 54.95 54.7 61.41 54.7
6.71 |
Materials Applied materials 64.56 51.74 52.04 64.56 51.74
12.82 |
Energy American electric power 91.61 81.39 78.43 91.61 78.43
13.18 |
Real Estate Alexandria real estate equities 158.92 149.49 146.99 158.92 149.49
9.43 |
Financials Ameriprise Financial 172.37 107.48 121.98 172.37 107.48
64.89 |
Commercials Services Accenture 230.57 175.46 193.71 230.57 175.46
55.11 |
Healthcare Abbott Laboratories 114.11 94.06 89.89 114.11 89.89
24.22 |
Utilities 3M 164.78 147 78.56 164.78 78.56
86.22 |
Industrials A.O Smith 53.28 40.39 42.22 53.28 40.39
12.89 |
Sector: NAME Recent price Price 5 year Price 10 year Standard Deviation
Coefficient of Variation |
5 Years 10 Years 5 Years 10 Years
Consumer Dicretionary Apple 115.31 70.74 80
8.41 |
8.94 |
9% 9%
Information Technology Adobe 494.59 344.1 385.26
18.55 |
19.63 |
4% 4%
Consumer Staples General mills 61.41 54.95 54.7
7.41 |
7.40 |
13% 13%
Materials Applied materials 64.56 51.74 52.04
7.19 |
7.21 12% 12%
Energy American electric power 91.61 81.39 78.43
9.02 |
| 8.86 |
10% 10%
Real Estate Alexandria real estate equities 158.92 149.49 146.99
12.23 |
| 12.12 |
8% 8%
Financials Ameriprise Financial 172.37 107.48 121.98
10.37 |
11.04 |
7% 8%
Commercials Services Accenture 230.57 175.46 193.71
13.25 |
13.92 |
7% 7%
Healthcare Abbott Laboratories 114.11 94.06 89.89
9.70 |
9.48 |
9% 9%
Utilities 3M 164.78 147 78.56 12.12 8.86 8% 7%
Industrials A.O Smith 53.28 40.39 42.22
6.36 |
6.50 |
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| 14% |
14%
C) Correlation matrice |
Sector: NAME Recent price Price 5 year Price 10 year
| Correlation Matrices |
5 Years 10 Years
Consumer Dicretionary Apple 115.31 70.74 80
| 0.9835298733 |
| 0.9816744048 |
Information Technology Adobe 494.59 344.1 385.26
| 0.9863421979 |
| 0.9817452885 |
Consumer Staples General mills 61.41 54.95 54.7
| 0.9519710971 |
| 0.9104779822 |
Materials Applied materials 64.56 51.74 52.04
| 0.9450912401 |
| 0.9019260928 |
Energy American electric power 91.61 81.39 78.43
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| 0.93 |
13671278
| 0.8840075567 |
Real Estate Alexandria real estate equities 158.92 149.49 146.99
| 0.925099551 |
| 0.8795087951 |
Financials Ameriprise Financial 172.37 107.48 121.98
| 0.9490497407 |
| 0.903087365 |
Commercials Services Accenture 230.57 175.46 193.71
| 0.9855464502 |
| 0.9007444387 |
Healthcare Abbott Laboratories 114.11 94.06 89.89
| 0.9988189122 |
| 0.7645093521 |
Utilities 3M 164.78 147 78.56 1 1
Industrials A.O Smith 53.28 40.39 42.22 0 0
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Beta
Beta Values |
Variance |
Coefficient of variation |
| Beta |
|
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| Stock |
5 Year 10 Year 5 Year 10 Year
| 5-Year |
10 Year
Apple
| 37.21 |
26.605 9% 9%
| 0.0024 |
| 0.0034 |
Adobe 167.738 122.395 4% 4%
| 0.0003 |
| 0.0004 |
General mills 23.272 17.106 13% 13%
| 0.0055 |
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| 0.0074 |
Applied materials 23.26 16.834 12% 12%
| 0.0053 |
0.0074
American electric power 34.6 25.143 10% 10%
| 0.0030 |
| 0.0041 |
Alexandria real estate equities 61.682 45.54 8% 8%
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| 0.0013 |
| 0.0017 |
Ameriprise Financial 55.97 40.183 7% 8% 0.0013
|
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| 0.0019 |
Accenture 81.206 59.974 7% 7%
| 0.0008 |
| 0.0011 |
Abbott Laboratories 41.634 29.806 9% 9%
| 0.0022 |
| 0.0031 |
3M 62.356 39.034 8% 7%
| 0.0012 |
0.0019
A.O Smith 18.734 13.589 14% 14%
| 0.0072 |
| 0.0100 |
Beta = covariance of stock/ variance of stock |
Beta
Stock 5-Year 10 Year
Apple 0.0024 0.0034
Adobe 0.0003 0.0004
General mills 0.0055 0.0074
Applied materials 0.0053 0.0074
American electric power 0.0030 0.0041
Alexandria real estate equities 0.0013 0.0017
Ameriprise Financial 0.0013 0.0019
Accenture 0.0008 0.0011
Abbott Laboratories 0.0022 0.0031
3M 0.0012 0.0019
A.O Smith 0.0072 0.0100
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Beta Values
10 Year
A.O Smith 3M Abbott Laboratories Accenture Ameriprise Financial Alexandria real estate equities American electric power Applied materials General mills Adobe Apple 0.010014 0.001866 0.003119 0.001094 0.001868 0.001741 0.004143 0.007350 0.007447 0.000365 0.003443 5-Year
A.O Smith 3M Abbott Laboratories Accenture Ameriprise Financial Alexandria real estate equities American electric power Applied materials General mills Adobe Apple 0.007243 0.001247 0.002238 0.000803 0.001324 0.001285 0.003014 0.005318 0.005475 0.000264 0.002430
R-SQUARED
R-Squared
Values
Correlation Matrices
| R-Squared |
Stock 5 Years 10 Years 5 Years 10 Years
Apple 0.9835298733 0.9816744048
| 0.9673310117 |
| 0.9636846371 |
Adobe 0.9863421979 0.9817452885
| 0.9728709314 |
| 0.9638238115 |
General mills 0.9519710971 0.9104779822
| 0.9062489697 |
| 0.8289701561 |
Applied materials 0.9450912401 0.9019260928
| 0.8931974521 |
| 0.8134706769 |
American electric power 0.9313671278 0.8840075567
| 0.8674447267 |
| 0.7814693602 |
Alexandria real estate equities 0.925099551 0.8795087951
| 0.8558091793 |
| 0.7735357206 |
Ameriprise Financial 0.9490497407 0.903087365
| 0.9006954104 |
| 0.8155667888 |
Accenture 0.9855464502 0.9007444387
| 0.9713018055 |
| 0.8113405438 |
Abbott Laboratories 0.9988189122 0.7645093521
| 0.9976392194 |
| 0.5844745495 |
3M 1 1 1 1
A.O Smith 0 0 0 0
R-Squared = Correlation squared |
R-Squared
Stock 5 Years 10 Years
Apple 0.9673310117 0.9636846371
Adobe 0.9728709314 0.9638238115
General mills 0.9062489697 0.8289701561
Applied materials 0.8931974521 0.8134706769
American electric power 0.8674447267 0.7814693602
Alexandria real estate equities 0.8558091793 0.7735357206
Ameriprise Financial 0.9006954104 0.8155667888
Accenture 0.9713018055 0.8113405438
Abbott Laboratories 0.9976392194 0.5844745495
3M 1 1
A.O Smith 0 0
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R-Squared
10 Years
A.O Smith 3M Abbott Laboratories Accenture Ameriprise Financial Alexandria real estate equities American electric power Applied materials General mills Adobe Apple 0.000000
1.000 |
000 0.584475 0.811341 0.815567 0.773536 0.781469 0.813471 0.828970 0.963824 0.963685 5 Years
A.O Smith 3M Abbott Laboratories Accenture Ameriprise Financial Alexandria real estate equities American electric power Applied materials General mills Adobe Apple 0.000000 1.000000 0.997639 0.971302 0.900695 0.855809 0.867445 0.893197 0.906249 0.972871 0.967331
Lowest Risk and Optimal Portfol
Lowest Risk over the Previous 5 Years |
NAME Recent price Price 5 year Variance Risk
Apple 115.31 70.74 37.21 6.10
Adobe 494.59 344.1 167.738 12.95
General mills 61.41 54.95 23.272 4.82
Applied materials 64.56 51.74 23.26 4.82
American electric power 91.61 81.39 34.6 5.88
Alexandria real estate equities 158.92 149.49 61.682 7.85
Ameriprise Financial 172.37 107.48 55.97 7.48
Accenture 230.57 175.46 81.206 9.01
Abbott Laboratories 114.11 94.06 41.634 6.45
3M 164.78 147 62.356 7.90
A.O Smith 53.28 40.39 18.734 4.33
7.05 |
Risk = Square root of variance |
Optimal portfolio |
Risk free return = 7.05 |
NAME
Mean Returns |
Portfolio Allocation |
Covariance |
Expected Returns |
Apple 8.114
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| 0.09 |
09
0.09 0.74
Adobe 29.298
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| 0.0909 |
| 0.04 |
2.66 |
General mills 0.492 0.0909
0.13 |
0.04
Optimal Portfolio |
-0.49 |
Applied materials 1.764 0.0909
0.12 |
| 0.16 |
American electric power 1.244 0.0909
| 0.10 |
0.11 |
Alexandria real estate equities 1.086 0.0909
| 0.08 |
0.10
Ameriprise Financial 12.178 0.0909
| 0.07 |
1.11 |
Accenture 10.222 0.0909 0.07 0.93
Abbott Laboratories 3.21 0.0909 0.09 0.29
3M 2.756 0.0909 0.08
0.25 |
A.O Smith 1.778 0.0909
0.14 |
0.16
Total |
1.000
1.01 |
6.56 |
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