portflolio optimisation 2 - copy

7/29/2019 Portflolio Optimisation 2 - Copy

1/28

Date Coca Cola Disney General El 3M (MMMJohnson a IBM DFT MSFT

3-Jan-12 32.84 38.31 18.08 83.92 63.56 188.62 24.88 28.72

1-Dec-11 34.03 36.93 17.31 79.1 63.24 180.08 23.63 25.25

1-Nov-11 32.7 34.72 15.23 78.43 62.41 184.11 21.87 24.88

3-Oct-11 32.99 33.79 16 75.94 61.52 180.09 20.18 25.7

1-Sep-11 32.62 29.21 14.57 68.99 60.85 170.57 19.01 24.02

1-Aug-11 33.78 32.99 15.47 79.74 62.87 167.68 22.35 25.68

1-Jul-11 32.61 37.41 16.98 83.18 61.36 176.61 24.6 26.28

1-Jun-11 32.27 37.81 17.88 90.54 63 166.6 24.32 24.94

2-May-11 31.81 40.32 18.47 90.09 63.72 164.06 25.11 23.99

1-Apr-11 32.12 41.75 19.23 92.25 61.7 164.92 23.5 24.7

1-Mar-11 31.59 41.74 18.86 88.73 55.63 157.66 23.29 24.19

1-Feb-11 30.21 42.37 19.67 87.52 57.68 156.51 23.34 25.33

3-Jan-11 29.71 37.65 18.81 82.93 55.61 156.01 21.91 26.27

1-Dec-10 31.09 36.33 17.08 81.41 57.55 141.34 20.33 26.44

1-Nov-10 29.86 34.98 14.67 79.22 57.27 136.23 21.47 23.93

1-Oct-10 28.79 34.62 14.85 78.95 58.8 137.68 23.85 25.11

1-Sep-10 27.47 31.71 15.06 81.28 57.16 128.61 23.9 23.06

2-Aug-10 26.03 31.18 13.32 73.63 52.6 118.05 23.37 22.1

1-Jul-10 25.68 32.28 14.83 79.69 53.09 122.5 23.87 24.17

1-Jun-10 23.35 30.18 13.26 73.58 53.97 117.81 23.23 21.55

3-May-10 23.75 32.02 14.95 73.88 53.28 119.5 24.04 24.16

1-Apr-10 24.69 35.3 17.24 82.09 58.23 122.44 20.87 28.47

1-Mar-10 25.41 33.45 16.64 77.36 59.05 121.73 20.32 27.31

1-Feb-10 24.16 29.93 14.68 74.2 57.05 120.7 18.38 26.73

4-Jan-10 24.86 28.31 14.61 74.03 56.5 115.65 15.58 26.151-Dec-09 26.12 30.9 13.74 76.03 57.89 123.69 16.87 28.29

2-Nov-09 26.21 28.62 14.46 71.22 56.48 119.4 14.96 27.29

1-Oct-09 24.26 25.93 12.87 67.22 52.65 113.46 14.08 25.62

1-Sep-09 24.43 26.01 14.82 67.43 54.3 112.52 12.44 23.76

3-Aug-09 22.01 24.67 12.47 65.88 53.89 111.05 12.21 22.77

1-Jul-09 22.49 23.79 12.02 63.97 53.86 110.43 9.99 21.61

1-Jun-09 21.66 22.1 10.52 54.52 50.24 97.78 8.79 21.84

1-May-09 22 22.94 12 51.8 48.79 99.52 8.84 19.19

1-Apr-09 19.27 20.74 11.26 51.8 45.91 96.14 7.93 18.5

2-Mar-09 19.67 17.2 9 44.71 46.12 90.25 6.42 16.77

2-Feb-09 18.09 15.88 7.57 40.88 43.84 85.73 4.97 14.74

2-Jan-09 18.92 19.59 10.49 47.85 50.16 84.91 3.48 15.51

1-Dec-08 20.05 21.49 14.01 51.19 52.03 77.97 1.93 17.63

3-Nov-08 20.75 21.02 14.56 59.54 50.94 75.6 2 18.33

1-Oct-08 19.35 24.18 16.55 56.74 52.9 85.65 5.82 20.11

2-Sep-08 23.22 28.64 21.63 60.28 59.75 107.76 14.24 24.04

1-Aug-08 22.7 30.19 23.52 63.18 60.74 112.15 16.18 24.58

1-Jul-08 22.45 28.32 23.68 61.68 58.67 117.45 15.07 23.07

Adjusted close price


2/28

2-Jun-08 22.66 29.12 22.34 60.98 55.13 108.78 17.18 24.68

1-May-08 24.8 31.36 25.43 67.96 57.18 118.78 18.46 25.4

1-Apr-08 25.5 30.26 27.07 66.95 57.08 110.32 16.42 25.49

3-Mar-08 26.36 29.28 30.64 68.91 55.19 105.24 15.04 25.37

1-Feb-08 25.16 30.25 27.43 68.26 52.72 104.07 15.16 24.31

2-Jan-08 25.39 27.85 29.01 68.91 53.37 97.53 15.54 29.02

3-Dec-07 26.41 30.12 30.41 72.95 56.38 98.43 17.68 31.691-Nov-07 26.73 30.61 31.14 72.03 57.26 95.77 16.79 29.91

1-Oct-07 26.44 31.97 33.48 74.28 54.74 105.36 19.24 32.66

4-Sep-07 24.6 31.75 33.67 80.49 55.19 106.88 60.01 26.14

1-Aug-07 22.88 31.02 31.4 78.26 51.9 105.87 60.65 25.49

2-Jul-07 22.17 30.47 31.31 76.06 50.48 100.04 58.26 25.64

1-Jun-07 22.25 31.52 30.93 74.24 51.41 95.16 59.62 26.06

1-May-07 22.39 32.27 30.14 75.24 52.79 96.38 57.89 27.14

2-Apr-07 22.06 31.85 29.57 70.41 53.24 92.05 56.1 26.39

1-Mar-07 20.28 31.35 28.36 65.02 49.95 84.89 56.55 24.57

1-Feb-07 19.59 31.18 28 63.02 52.17 83.7 54.46 24.83

3-Jan-07 20.09 32.02 28.69 62.81 55.05 89.03 53.77 27.11


3/28

PG WMT Coca Cola Disney General El 3M (MMM Johnson a IBM DFT

60.97 59.88 -3.50% 3.74% 4.45% 6.09% 0.51% 4.74% 5.29%

64.01 58.32 4.07% 6.37% 13.66% 0.85% 1.33% -2.19% 8.05%

61.96 57.13 -0.88% 2.75% -4.81% 3.28% 1.45% 2.23% 8.37%

61.4 55.01 1.13% 15.68% 9.81% 10.07% 1.10% 5.58% 6.15%

60.14 50.34 -3.43% -11.46% -5.82% -13.48% -3.21% 1.72% -14.94%

60.61 51.59 3.59% -11.82% -8.89% -4.14% 2.46% -5.06% -9.15%

58.53 50.75 1.05% -1.06% -5.03% -8.13% -2.60% 6.01% 1.15%

60.01 51.17 1.45% -6.23% -3.19% 0.50% -1.13% 1.55% -3.15%

63.25 53.17 -0.97% -3.43% -3.95% -2.34% 3.27% -0.52% 6.85%

61.27 52.59 1.68% 0.02% 1.96% 3.97% 10.91% 4.60% 0.90%

57.68 49.79 4.57% -1.49% -4.12% 1.38% -3.55% 0.73% -0.21%

59.03 49.38 1.68% 12.54% 4.57% 5.53% 3.72% 0.32% 6.53%

59.11 53.26 -4.44% 3.63% 10.13% 1.87% -3.37% 10.38% 7.77%

59.79 51.23 4.12% 3.86% 16.43% 2.76% 0.49% 3.75% -5.31%

56.76 51.1 3.72% 1.04% -1.21% 0.34% -2.60% -1.05% -9.98%

59.08 51.17 4.81% 9.18% -1.39% -2.87% 2.87% 7.05% -0.21%

55.31 50.56 5.53% 1.70% 13.06% 10.39% 8.67% 8.95% 2.27%

55.04 47.37 1.36% -3.41% -10.18% -7.60% -0.92% -3.63% -2.09%

56.41 48.08 9.98% 6.96% 11.84% 8.30% -1.63% 3.98% 2.76%

54.89 45.15 -1.68% -5.75% -11.30% -0.41% 1.30% -1.41% -3.37%

55.91 47.49 -3.81% -9.29% -13.28% -10.00% -8.50% -2.40% 15.19%

56.89 50.09 -2.83% 5.53% 3.61% 6.11% -1.39% 0.58% 2.71%

57.46 51.92 5.17% 11.76% 13.35% 4.26% 3.51% 0.85% 10.55%

57.47 50.21 -2.82% 5.72% 0.48% 0.23% 0.97% 4.37% 17.97%

55.9 49.61 -4.82% -8.38% 6.33% -2.63% -2.40% -6.50% -7.65%54.67 49.63 -0.34% 7.97% -4.98% 6.75% 2.50% 3.59% 12.77%

56.22 50.4 8.04% 10.37% 12.35% 5.95% 7.27% 5.24% 6.25%

52.3 45.9 -0.70% -0.31% -13.16% -0.31% -3.04% 0.84% 13.18%

51.83 45.35 11.00% 5.43% 18.85% 2.35% 0.76% 1.32% 1.88%

48.42 47 -2.13% 3.70% 3.74% 2.99% 0.06% 0.56% 22.22%

49.67 45.83 3.83% 7.65% 14.26% 17.33% 7.21% 12.94% 13.65%

45.37 44.51 -1.55% -3.66% -12.33% 5.25% 2.97% -1.75% -0.57%

46.11 45.7 14.17% 10.61% 6.57% 0.00% 6.27% 3.52% 11.48%

43.89 46.06 -2.03% 20.58% 25.11% 15.86% -0.46% 6.53% 23.52%

41.45 47.62 8.73% 8.31% 18.89% 9.37% 5.20% 5.27% 29.18%

42.4 44.75 -4.39% -18.94% -27.84% -14.57% -12.60% 0.97% 42.82%

47.97 42.82 -5.64% -8.84% -25.12% -6.52% -3.59% 8.90% 80.31%

54.03 50.95 -3.37% 2.24% -3.78% -14.02% 2.14% 3.13% -3.50%

56.25 50.57 7.24% -13.07% -12.02% 4.93% -3.71% -11.73% -65.64%

56.41 50.5 -16.67% -15.57% -23.49% -5.87% -11.46% -20.52% -59.13%

60.53 54.19 2.29% -5.13% -8.04% -4.59% -1.63% -3.91% -11.99%

60.6 53.45 1.11% 6.60% -0.68% 2.43% 3.53% -4.51% 7.37%

56.87 52.83 -0.93% -2.75% 6.00% 1.15% 6.42% 7.97% -12.28%

Simple return


4/28

52.49 50.65 -8.63% -7.14% -12.15% -10.27% -3.59% -8.42% -6.93%

57.01 52.04 -2.75% 3.64% -6.06% 1.51% 0.18% 7.67% 12.42%

57.87 52.04 -3.26% 3.35% -11.65% -2.84% 3.42% 4.83% 9.18%

60.13 47.28 4.77% -3.21% 11.70% 0.95% 4.69% 1.12% -0.79%

56.79 44.29 -0.91% 8.62% -5.45% -0.94% -1.22% 6.71% -2.45%

56.14 45.32 -3.86% -7.54% -4.60% -5.54% -5.34% -0.91% -12.10%

62.69 42.45 -1.20% -1.60% -2.34% 1.28% -1.54% 2.78% 5.30%63.19 42.59 1.10% -4.25% -6.99% -3.03% 4.60% -9.10% -12.73%

59.36 40.2 7.48% 0.69% -0.56% -7.72% -0.82% -1.42% -67.94%

59.76 38.81 7.52% 2.35% 7.23% 2.85% 6.34% 0.95% -1.06%

55.49 38.8 3.20% 1.81% 0.29% 2.89% 2.81% 5.83% 4.10%

52.56 40.65 -0.36% -3.33% 1.23% 2.45% -1.81% 5.13% -2.28%

51.7 42.56 -0.63% -2.32% 2.62% -1.33% -2.61% -1.27% 2.99%

53.69 42.11 1.50% 1.32% 1.93% 6.86% -0.85% 4.70% 3.19%

54.41 42.2 8.78% 1.59% 4.27% 8.29% 6.59% 8.43% -0.80%

53.07 41.35 3.52% 0.55% 1.29% 3.17% -4.26% 1.42% 3.84%

53.35 42.34 -2.49% -2.62% -2.41% 0.33% -5.23% -5.99% 1.28%

54.51 41.8 0.95% 0.59% -0.18% 0.70% 0.34% 1.42% 1.55%


5/28

MSFT PG WMT

13.74% -4.75% 2.67% vcv matrix

1.49% 3.31% 2.08% 0.95% Coca Cola

-3.19% 0.91% 3.85% 0.59% Disney

6.99% 2.10% 9.28% -0.18% General El

-6.46% -0.78% -2.42% 0.70% 3M (MMM

-2.28% 3.55% 1.66% 0.34% Johnson an

5.37% -2.47% -0.82% 1.42% IBM

3.96% -5.12% -3.76% 1.55% DFT

-2.87% 3.23% 1.10% 0.41% MSFT

2.11% 6.22% 5.62% 0.30% PG

-4.50% -2.29% 0.83% 0.70% WMT

-3.58% -0.14% -7.29%

-0.64% -1.14% 3.96% P1 P2

10.49% 5.34% 0.25% -0.14934 -0.00208

-4.70% -3.93% -0.14% -0.1937 -0.0979

8.89% 6.82% 1.21% -0.0572 -0.14189

4.34% 0.49% 6.73% 0.063277 0.111637

-8.56% -2.43% -1.48% 0.418131 0.232387

12.16% 2.77% 6.49% -0.13772 0.020108

-10.80% -1.82% -4.93% 0.060665 0.03793

-15.14% -1.72% -5.19% 0.204337 0.113706

4.25% -0.99% -3.52% 0.525323 0.428285

2.17% -0.02% 3.41% 0.266219 0.297811

2.22% 2.81% 1.21% 1 1

-7.56% 2.25% -0.04% 0.002682 0.0059573.66% -2.76% -1.53% 0.038909 0.032049

6.52% 7.50% 9.80% 0.15% 0.10%

7.83% 0.91% 1.21%

4.35% 7.04% -3.51% Risk-free rate 0.001

5.37% -2.52% 2.55% Theta 0.399

-1.05% 9.48% 2.97%

13.81% -1.60% -2.60% Super Portfolio of P1 and RFA

3.73% 5.06% -0.78% Weight of RFA 0

10.32% 5.89% -3.28% 0.015868

13.77% -2.24% 6.41% 0.001389

-4.96% -11.61% 4.51% 0.037263

-12.02% -11.22% -15.96%

-3.82% -3.95% 0.75%

-8.85% -0.28% 0.14%

-16.35% -6.81% -6.81%

-2.20% -0.12% 1.38%

6.55% 6.56% 1.17%

-6.52% 8.34% 4.30%

Expected return

Variance

St. Deviation

returnstandard deviation

variance

IBM

DFT

MSFT

PG

WMT

Total weight

WMT

Coca Cola

Disney

General Electric

3M (MMM)

Johnson and Johnson

3M (MMM)

Johnson and Johnson

IBM

DFT

MSFT

PG

Mean

Coca Cola

Disney

General Electric


6/28

-2.83% -7.93% -2.67%

-0.35% -1.49% 0.00%

0.47% -3.76% 10.07%

4.36% 5.88% 6.75%

-16.23% 1.16% -2.27%

-8.43% -10.45% 6.76%

5.95% -0.79% -0.33%-8.42% 6.45% 5.95%

24.94% -0.67% 3.58%

2.55% 7.70% 0.03%

-0.59% 5.57% -4.55%

-1.61% 1.66% -4.49%

-3.98% -3.71% 1.07%

2.84% -1.32% -0.21%

7.41% 2.52% 2.06%

-1.05% -0.52% -2.34%

-8.41% -2.13% 1.29%

0.41% 0.30% 0.70%

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.00% 0.50% 1.00% 1.50% 2.00% 2.5


7/28

Coca Cola Disney General El 3M (MMM Johnson anIBM DFT MSFT PG

0.002618 0.001672 0.003092 0.001402 0.001269 0.000891 -0.00048 0.002063 0.001316

0.001672 0.005806 0.005888 0.003206 0.001826 0.0023 0.004233 0.003088 0.001759

0.003092 0.005888 0.011543 0.004679 0.002604 0.002603 0.001394 0.004326 0.003199

0.001402 0.003206 0.004679 0.004234 0.001497 0.001446 0.001818 0.002116 0.00153

0.001269 0.001826 0.002604 0.001497 0.002037 0.001114 0.000874 0.001417 0.001449

0.000891 0.0023 0.002603 0.001446 0.001114 0.003224 0.006547 0.001558 0.000665

-0.00048 0.004233 0.001394 0.001818 0.000874 0.006547 0.04364 0.000281 -0.0011

0.002063 0.003088 0.004326 0.002116 0.001417 0.001558 0.000281 0.006133 0.001194

0.001316 0.001759 0.003199 0.00153 0.001449 0.000665 -0.0011 0.001194 0.00226

0.000734 0.000776 0.001724 0.000597 0.000754 0.000414 -0.00121 0.001246 0.000585

Optimal risky portfolio

0 St. Deviatio

0.005957 3.20%

0.001195 -0.4 3.03%

0.001027 -0.2 3.11%

0.032049 0 3.20%

0.2 3.32%

0.4 3.44%

0.6 3.58%

0.8 3.73%

1 3.89%

1.2 4.06%

1.4 4.23%

P1 St. Deviatio

0.443549 3.73%

0.191986 -0.4 5.22%

-0.39815 -0.2 4.47%

0.257949 0 3.73%

-0.32971 0.2 2.98%

0.497718 0.4 2.24%

-0.03087 0.6 1.49%

-0.16055 0.8 0.75%

0.134663 1 0.00%

0.393418 1.2 0.75%

1.000001 1.4 1.49%

0.015868

0.037263

0.001389

return

standard deviation

variance

IBM

DFT

MSFT

PG

WMT

sum

Coca Cola

Disney

General Electric

3M (MMM)

Johnson and Johnson

expected return of portfolio

Weight of P1

covariance

variance

standard deviation


8/28

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0.00% 1.00% 2.00% 3.00% 3.00% 3.50% 4.00% 4.50%

Series1


9/28

WMT

0.000734

0.000776

0.001724

0.000597

0.000754

0.000414

-0.00121

0.001246

0.000585

0.00205

Exp. Return

0.60%

0.73%

0.66%

0.60%

0.53%

0.46%

0.40%

0.33%

0.27%

0.20%

0.14%

Exp. Return

1.59%

2.18%

1.88%

1.59%

1.29%

0.99%

0.69%

0.40%

0.10%

-0.20%

-0.49%


10/28

0% 4.00% 5.00% 6.00%

Series1


11/28

Date Coca Cola Disney General El 3M (MMMJohnson a IBM DFT MSFT

3-Jan-12 32.84 38.31 18.08 83.92 63.56 188.62 24.88 28.72

1-Dec-11 34.03 36.93 17.31 79.1 63.24 180.08 23.63 25.25

1-Nov-11 32.7 34.72 15.23 78.43 62.41 184.11 21.87 24.88

3-Oct-11 32.99 33.79 16 75.94 61.52 180.09 20.18 25.7

1-Sep-11 32.62 29.21 14.57 68.99 60.85 170.57 19.01 24.021-Aug-11 33.78 32.99 15.47 79.74 62.87 167.68 22.35 25.68

1-Jul-11 32.61 37.41 16.98 83.18 61.36 176.61 24.6 26.28

1-Jun-11 32.27 37.81 17.88 90.54 63 166.6 24.32 24.94

2-May-11 31.81 40.32 18.47 90.09 63.72 164.06 25.11 23.99

1-Apr-11 32.12 41.75 19.23 92.25 61.7 164.92 23.5 24.7

1-Mar-11 31.59 41.74 18.86 88.73 55.63 157.66 23.29 24.19

1-Feb-11 30.21 42.37 19.67 87.52 57.68 156.51 23.34 25.33

3-Jan-11 29.71 37.65 18.81 82.93 55.61 156.01 21.91 26.27

1-Dec-10 31.09 36.33 17.08 81.41 57.55 141.34 20.33 26.44

1-Nov-10 29.86 34.98 14.67 79.22 57.27 136.23 21.47 23.93

1-Oct-10 28.79 34.62 14.85 78.95 58.8 137.68 23.85 25.11

1-Sep-10 27.47 31.71 15.06 81.28 57.16 128.61 23.9 23.06

2-Aug-10 26.03 31.18 13.32 73.63 52.6 118.05 23.37 22.1

1-Jul-10 25.68 32.28 14.83 79.69 53.09 122.5 23.87 24.17

1-Jun-10 23.35 30.18 13.26 73.58 53.97 117.81 23.23 21.55

3-May-10 23.75 32.02 14.95 73.88 53.28 119.5 24.04 24.16

1-Apr-10 24.69 35.3 17.24 82.09 58.23 122.44 20.87 28.47

1-Mar-10 25.41 33.45 16.64 77.36 59.05 121.73 20.32 27.31

1-Feb-10 24.16 29.93 14.68 74.2 57.05 120.7 18.38 26.73

4-Jan-10 24.86 28.31 14.61 74.03 56.5 115.65 15.58 26.15

1-Dec-09 26.12 30.9 13.74 76.03 57.89 123.69 16.87 28.292-Nov-09 26.21 28.62 14.46 71.22 56.48 119.4 14.96 27.29

1-Oct-09 24.26 25.93 12.87 67.22 52.65 113.46 14.08 25.62

1-Sep-09 24.43 26.01 14.82 67.43 54.3 112.52 12.44 23.76

3-Aug-09 22.01 24.67 12.47 65.88 53.89 111.05 12.21 22.77

1-Jul-09 22.49 23.79 12.02 63.97 53.86 110.43 9.99 21.61

1-Jun-09 21.66 22.1 10.52 54.52 50.24 97.78 8.79 21.84

1-May-09 22 22.94 12 51.8 48.79 99.52 8.84 19.19

1-Apr-09 19.27 20.74 11.26 51.8 45.91 96.14 7.93 18.5

2-Mar-09 19.67 17.2 9 44.71 46.12 90.25 6.42 16.77

2-Feb-09 18.09 15.88 7.57 40.88 43.84 85.73 4.97 14.74

2-Jan-09 18.92 19.59 10.49 47.85 50.16 84.91 3.48 15.51

1-Dec-08 20.05 21.49 14.01 51.19 52.03 77.97 1.93 17.63

3-Nov-08 20.75 21.02 14.56 59.54 50.94 75.6 2 18.33

1-Oct-08 19.35 24.18 16.55 56.74 52.9 85.65 5.82 20.11

2-Sep-08 23.22 28.64 21.63 60.28 59.75 107.76 14.24 24.04

1-Aug-08 22.7 30.19 23.52 63.18 60.74 112.15 16.18 24.58

1-Jul-08 22.45 28.32 23.68 61.68 58.67 117.45 15.07 23.07

2-Jun-08 22.66 29.12 22.34 60.98 55.13 108.78 17.18 24.68

1-May-08 24.8 31.36 25.43 67.96 57.18 118.78 18.46 25.4

Adjusted close price


12/28

1-Apr-08 25.5 30.26 27.07 66.95 57.08 110.32 16.42 25.49

3-Mar-08 26.36 29.28 30.64 68.91 55.19 105.24 15.04 25.37

1-Feb-08 25.16 30.25 27.43 68.26 52.72 104.07 15.16 24.31

2-Jan-08 25.39 27.85 29.01 68.91 53.37 97.53 15.54 29.02

3-Dec-07 26.41 30.12 30.41 72.95 56.38 98.43 17.68 31.69

1-Nov-07 26.73 30.61 31.14 72.03 57.26 95.77 16.79 29.91

1-Oct-07 26.44 31.97 33.48 74.28 54.74 105.36 19.24 32.664-Sep-07 24.6 31.75 33.67 80.49 55.19 106.88 60.01 26.14

1-Aug-07 22.88 31.02 31.4 78.26 51.9 105.87 60.65 25.49

2-Jul-07 22.17 30.47 31.31 76.06 50.48 100.04 58.26 25.64

1-Jun-07 22.25 31.52 30.93 74.24 51.41 95.16 59.62 26.06

1-May-07 22.39 32.27 30.14 75.24 52.79 96.38 57.89 27.14

2-Apr-07 22.06 31.85 29.57 70.41 53.24 92.05 56.1 26.39

1-Mar-07 20.28 31.35 28.36 65.02 49.95 84.89 56.55 24.57

1-Feb-07 19.59 31.18 28 63.02 52.17 83.7 54.46 24.83

3-Jan-07 20.09 32.02 28.69 62.81 55.05 89.03 53.77 27.11


13/28

PG WMT DJW Coca Cola Disney General El 3M (MMM Johnson a IBM

60.97 59.88 12,632.91 -3.50% 3.74% 4.45% 6.09% 0.51% 4.74%

64.01 58.32 12,217.56 4.07% 6.37% 13.66% 0.85% 1.33% -2.19%

61.96 57.13 12,045.68 -0.88% 2.75% -4.81% 3.28% 1.45% 2.23%

61.4 55.01 11,955.01 1.13% 15.68% 9.81% 10.07% 1.10% 5.58%

60.14 50.34 10,913.38 -3.43% -11.46% -5.82% -13.48% -3.21% 1.72%60.61 51.59 11,613.53 3.59% -11.82% -8.89% -4.14% 2.46% -5.06%

58.53 50.75 12,143.24 1.05% -1.06% -5.03% -8.13% -2.60% 6.01%

60.01 51.17 12,414.34 1.45% -6.23% -3.19% 0.50% -1.13% 1.55%

63.25 53.17 12,569.79 -0.97% -3.43% -3.95% -2.34% 3.27% -0.52%

61.27 52.59 12,810.54 1.68% 0.02% 1.96% 3.97% 10.91% 4.60%

57.68 49.79 12,319.73 4.57% -1.49% -4.12% 1.38% -3.55% 0.73%

59.03 49.38 12,226.34 1.68% 12.54% 4.57% 5.53% 3.72% 0.32%

59.11 53.26 11,891.93 -4.44% 3.63% 10.13% 1.87% -3.37% 10.38%

59.79 51.23 11,577.51 4.12% 3.86% 16.43% 2.76% 0.49% 3.75%

56.76 51.1 11,006.02 3.72% 1.04% -1.21% 0.34% -2.60% -1.05%

59.08 51.17 11,118.49 4.81% 9.18% -1.39% -2.87% 2.87% 7.05%

55.31 50.56 10,788.05 5.53% 1.70% 13.06% 10.39% 8.67% 8.95%

55.04 47.37 10,014.72 1.36% -3.41% -10.18% -7.60% -0.92% -3.63%

56.41 48.08 10,465.94 9.98% 6.96% 11.84% 8.30% -1.63% 3.98%

54.89 45.15 9,774.02 -1.68% -5.75% -11.30% -0.41% 1.30% -1.41%

55.91 47.49 10,136.63 -3.81% -9.29% -13.28% -10.00% -8.50% -2.40%

56.89 50.09 11,008.61 -2.83% 5.53% 3.61% 6.11% -1.39% 0.58%

57.46 51.92 10,856.63 5.17% 11.76% 13.35% 4.26% 3.51% 0.85%

57.47 50.21 10,325.26 -2.82% 5.72% 0.48% 0.23% 0.97% 4.37%

55.9 49.61 10,067.33 -4.82% -8.38% 6.33% -2.63% -2.40% -6.50%

54.67 49.6310,428.05

-0.34% 7.97% -4.98% 6.75% 2.50% 3.59%56.22 50.4 10,344.84 8.04% 10.37% 12.35% 5.95% 7.27% 5.24%

52.3 45.9 9,712.73 -0.70% -0.31% -13.16% -0.31% -3.04% 0.84%

51.83 45.35 9,712.28 11.00% 5.43% 18.85% 2.35% 0.76% 1.32%

48.42 47 9,496.28 -2.13% 3.70% 3.74% 2.99% 0.06% 0.56%

49.67 45.83 9,171.61 3.83% 7.65% 14.26% 17.33% 7.21% 12.94%

45.37 44.51 8,447.00 -1.55% -3.66% -12.33% 5.25% 2.97% -1.75%

46.11 45.7 8,500.33 14.17% 10.61% 6.57% 0.00% 6.27% 3.52%

43.89 46.06 8,168.12 -2.03% 20.58% 25.11% 15.86% -0.46% 6.53%

41.45 47.62 7,608.92 8.73% 8.31% 18.89% 9.37% 5.20% 5.27%

42.4 44.75 7,062.93 -4.39% -18.94% -27.84% -14.57% -12.60% 0.97%

47.97 42.82 8,000.86 -5.64% -8.84% -25.12% -6.52% -3.59% 8.90%

54.03 50.95 8,776.39 -3.37% 2.24% -3.78% -14.02% 2.14% 3.13%

56.25 50.57 8,829.04 7.24% -13.07% -12.02% 4.93% -3.71% -11.73%

56.41 50.5 9,325.01 -16.67% -15.57% -23.49% -5.87% -11.46% -20.52%

60.53 54.19 10,850.66 2.29% -5.13% -8.04% -4.59% -1.63% -3.91%

60.6 53.45 11,543.96 1.11% 6.60% -0.68% 2.43% 3.53% -4.51%

56.87 52.83 11,378.02 -0.93% -2.75% 6.00% 1.15% 6.42% 7.97%

52.49 50.65 11,350.01 -8.63% -7.14% -12.15% -10.27% -3.59% -8.42%

57.01 52.04 12,638.32 -2.75% 3.64% -6.06% 1.51% 0.18% 7.67%

Simple return


14/28

57.87 52.04 12,820.13 -3.26% 3.35% -11.65% -2.84% 3.42% 4.83%

60.13 47.28 12,262.89 4.77% -3.21% 11.70% 0.95% 4.69% 1.12%

56.79 44.29 12,266.39 -0.91% 8.62% -5.45% -0.94% -1.22% 6.71%

56.14 45.32 12,650.36 -3.86% -7.54% -4.60% -5.54% -5.34% -0.91%

62.69 42.45 13,264.82 -1.20% -1.60% -2.34% 1.28% -1.54% 2.78%

63.19 42.59 13,371.72 1.10% -4.25% -6.99% -3.03% 4.60% -9.10%

59.36 40.2 13,930.01 7.48% 0.69% -0.56% -7.72% -0.82% -1.42%59.76 38.81 13,895.63 7.52% 2.35% 7.23% 2.85% 6.34% 0.95%

55.49 38.8 13,357.74 3.20% 1.81% 0.29% 2.89% 2.81% 5.83%

52.56 40.65 13,211.99 -0.36% -3.33% 1.23% 2.45% -1.81% 5.13%

51.7 42.56 13,408.62 -0.63% -2.32% 2.62% -1.33% -2.61% -1.27%

53.69 42.11 13,627.64 1.50% 1.32% 1.93% 6.86% -0.85% 4.70%

54.41 42.2 13,062.91 8.78% 1.59% 4.27% 8.29% 6.59% 8.43%

53.07 41.35 12,354.35 3.52% 0.55% 1.29% 3.17% -4.26% 1.42%

53.35 42.34 12,268.63 -2.49% -2.62% -2.41% 0.33% -5.23% -5.99%

54.51 41.8 12,621.69 1.03% 0.53% -0.26% 0.60% 0.34% 1.37%


15/28

DFT MSFT PG WMT DJW Risk Free rat Coca Cola Disney General El

5.29% 13.74% -4.75% 2.67% 3.40% 0.0001 -3.51% 3.73% 4.44%

8.05% 1.49% 3.31% 2.08% 1.43% 0.0001 4.06% 6.36% 13.65%

8.37% -3.19% 0.91% 3.85% 0.76% 0.0001 -0.89% 2.74% -4.82%

6.15% 6.99% 2.10% 9.28% 9.54% 0.0001 1.13% 15.67% 9.81%

-14.94% -6.46% -0.78% -2.42% -6.03% 0.0001 -3.44% -11.47% -5.83%-9.15% -2.28% 3.55% 1.66% -4.36% 0.0001 3.58% -11.82% -8.90%

1.15% 5.37% -2.47% -0.82% -2.18% 0.0001 1.05% -1.07% -5.04%

-3.15% 3.96% -5.12% -3.76% -1.24% 0.0001 1.44% -6.23% -3.20%

6.85% -2.87% 3.23% 1.10% -1.88% 0.0001 -0.97% -3.43% -3.96%

0.90% 2.11% 6.22% 5.62% 3.98% 0.0001 1.67% 0.02% 1.95%

-0.21% -4.50% -2.29% 0.83% 0.76% 0.0001 4.56% -1.50% -4.13%

6.53% -3.58% -0.14% -7.29% 2.81% 0.0001 1.67% 12.53% 4.56%

7.77% -0.64% -1.14% 3.96% 2.72% 0.0001 -4.45% 3.63% 10.12%

-5.31% 10.49% 5.34% 0.25% 5.19% 0.0001 4.11% 3.85% 16.42%

-9.98% -4.70% -3.93% -0.14% -1.01% 0.0001 3.71% 1.03% -1.22%

-0.21% 8.89% 6.82% 1.21% 3.06% 0.0001 4.80% 9.17% -1.40%

2.27% 4.34% 0.49% 6.73% 7.72% 0.0001 5.52% 1.69% 13.05%

-2.09% -8.56% -2.43% -1.48% -4.31% 0.0001 1.35% -3.42% -10.19%

2.76% 12.16% 2.77% 6.49% 7.08% 0.0001 9.97% 6.95% 11.83%

-3.37% -10.80% -1.82% -4.93% -3.58% 0.0001 -1.69% -5.75% -11.31%

15.19% -15.14% -1.72% -5.19% -7.92% 0.0001 -3.82% -9.30% -13.29%

2.71% 4.25% -0.99% -3.52% 1.40% 0.0001 -2.84% 5.52% 3.60%

10.55% 2.17% -0.02% 3.41% 5.15% 0.0001 5.17% 11.75% 13.34%

17.97% 2.22% 2.81% 1.21% 2.56% 0.0001 -2.82% 5.71% 0.47%

-7.65% -7.56% 2.25% -0.04% -3.46% 0.0001 -4.83% -8.39% 6.32%

12.77% 3.66% -2.76% -1.53% 0.80% 0.0001 -0.35% 7.96% -4.99%6.25% 6.52% 7.50% 9.80% 6.51% 0.0001 8.03% 10.37% 12.35%

13.18% 7.83% 0.91% 1.21% 0.00% 0.0001 -0.70% -0.32% -13.17%

1.88% 4.35% 7.04% -3.51% 2.27% 0.0001 10.99% 5.42% 18.84%

22.22% 5.37% -2.52% 2.55% 3.54% 0.0001 -2.14% 3.69% 3.74%

13.65% -1.05% 9.48% 2.97% 8.58% 0.0001 3.82% 7.64% 14.25%

-0.57% 13.81% -1.60% -2.60% -0.63% 0.0001 -1.55% -3.67% -12.34%

11.48% 3.73% 5.06% -0.78% 4.07% 0.0001 14.16% 10.60% 6.56%

23.52% 10.32% 5.89% -3.28% 7.35% 0.0001 -2.04% 20.57% 25.10%

29.18% 13.77% -2.24% 6.41% 7.73% 0.0001 8.73% 8.30% 18.88%

42.82% -4.96% -11.61% 4.51% -11.72% 0.0001 -4.40% -18.95% -27.84%

80.31% -12.02% -11.22% -15.96% -8.84% 0.0001 -5.64% -8.85% -25.13%

-3.50% -3.82% -3.95% 0.75% -0.60% 0.0001 -3.38% 2.23% -3.79%

-65.64% -8.85% -0.28% 0.14% -5.32% 0.0001 7.23% -13.08% -12.03%

-59.13% -16.35% -6.81% -6.81% -14.06% 0.0001 -16.68% -15.58% -23.49%

-11.99% -2.20% -0.12% 1.38% -6.01% 0.0001 2.28% -5.14% -8.04%

7.37% 6.55% 6.56% 1.17% 1.46% 0.0001 1.11% 6.59% -0.68%

-12.28% -6.52% 8.34% 4.30% 0.25% 0.0001 -0.94% -2.76% 5.99%

-6.93% -2.83% -7.93% -2.67% -10.19% 0.0001 -8.64% -7.15% -12.16%

12.42% -0.35% -1.49% 0.00% -1.42% 0.0001 -2.75% 3.63% -6.07%


16/28

9.18% 0.47% -3.76% 10.07% 4.54% 0.0001 -3.27% 3.34% -11.66%

-0.79% 4.36% 5.88% 6.75% -0.03% 0.0001 4.76% -3.21% 11.69%

-2.45% -16.23% 1.16% -2.27% -3.04% 0.0001 -0.91% 8.61% -5.45%

-12.10% -8.43% -10.45% 6.76% -4.63% 0.0001 -3.87% -7.54% -4.61%

5.30% 5.95% -0.79% -0.33% -0.80% 0.0001 -1.21% -1.61% -2.35%

-12.73% -8.42% 6.45% 5.95% -4.01% 0.0001 1.09% -4.26% -7.00%

-67.94% 24.94% -0.67% 3.58% 0.25% 0.0001 7.47% 0.68% -0.57%-1.06% 2.55% 7.70% 0.03% 4.03% 0.0001 7.51% 2.34% 7.22%

4.10% -0.59% 5.57% -4.55% 1.10% 0.0001 3.19% 1.80% 0.28%

-2.28% -1.61% 1.66% -4.49% -1.47% 0.0001 -0.37% -3.34% 1.22%

2.99% -3.98% -3.71% 1.07% -1.61% 0.0001 -0.63% -2.33% 2.61%

3.19% 2.84% -1.32% -0.21% 4.32% 0.0001 1.49% 1.31% 1.92%

-0.80% 7.41% 2.52% 2.06% 5.74% 0.0001 8.77% 1.59% 4.26%

3.84% -1.05% -0.52% -2.34% 0.70% 0.0001 3.51% 0.54% 1.28%

1.28% -8.41% -2.13% 1.29% -2.80% 0.0001 -2.50% -2.63% -2.41%

1.49% 0.18% 0.39% 0.67% 0.07% Mean 11.34% 6.95% -2.27%

Standard de 17.84% 26.43% 37.28%

variance 3.18% 6.99% 13.90%


17/28

3M (MMMJohnson a IBM DFT MSFT PG WMT DJW

6.09% 0.50% 4.73% 5.28% 13.73% -4.76% 2.67% 3.39%

0.85% 1.32% -2.20% 8.04% 1.48% 3.30% 2.07% 1.42%

3.27% 1.44% 2.22% 8.37% -3.20% 0.90% 3.85% 0.75%

10.07% 1.09% 5.57% 6.15% 6.99% 2.09% 9.27% 9.54%

-13.49% -3.22% 1.72% -14.95% -6.47% -0.78% -2.43% -6.04%-4.14% 2.45% -5.06% -9.15% -2.29% 3.55% 1.65% -4.37%

-8.14% -2.61% 6.00% 1.14% 5.36% -2.47% -0.83% -2.19%

0.49% -1.14% 1.54% -3.15% 3.95% -5.13% -3.77% -1.25%

-2.35% 3.27% -0.53% 6.84% -2.88% 3.22% 1.09% -1.89%

3.96% 10.90% 4.60% 0.89% 2.10% 6.22% 5.62% 3.98%

1.37% -3.56% 0.73% -0.22% -4.51% -2.30% 0.82% 0.76%

5.53% 3.71% 0.31% 6.52% -3.59% -0.14% -7.29% 2.80%

1.86% -3.38% 10.37% 7.76% -0.65% -1.15% 3.95% 2.71%

2.76% 0.48% 3.74% -5.32% 10.48% 5.33% 0.25% 5.18%

0.33% -2.61% -1.06% -9.99% -4.71% -3.94% -0.15% -1.02%

-2.87% 2.86% 7.04% -0.22% 8.88% 6.81% 1.20% 3.05%

10.38% 8.66% 8.94% 2.26% 4.34% 0.48% 6.73% 7.71%

-7.61% -0.93% -3.64% -2.10% -8.57% -2.44% -1.49% -4.32%

8.30% -1.64% 3.97% 2.75% 12.15% 2.76% 6.48% 7.07%

-0.41% 1.29% -1.42% -3.38% -10.81% -1.83% -4.94% -3.59%

-10.01% -8.51% -2.41% 15.18% -15.15% -1.73% -5.20% -7.93%

6.11% -1.40% 0.57% 2.70% 4.24% -1.00% -3.53% 1.39%

4.25% 3.50% 0.85% 10.55% 2.16% -0.03% 3.40% 5.14%

0.22% 0.97% 4.36% 17.96% 2.21% 2.80% 1.20% 2.55%

-2.64% -2.41% -6.51% -7.66% -7.57% 2.24% -0.05% -3.47%

6.75% 2.49% 3.58% 12.76% 3.66% -2.77% -1.54% 0.80%5.94% 7.27% 5.23% 6.24% 6.51% 7.49% 9.80% 6.50%

-0.32% -3.05% 0.83% 13.17% 7.82% 0.90% 1.20% 0.00%

2.34% 0.75% 1.32% 1.88% 4.34% 7.03% -3.52% 2.27%

2.98% 0.05% 0.55% 22.21% 5.36% -2.52% 2.54% 3.53%

17.32% 7.20% 12.93% 13.64% -1.06% 9.47% 2.96% 8.57%

5.24% 2.96% -1.76% -0.57% 13.80% -1.61% -2.61% -0.64%

-0.01% 6.26% 3.51% 11.47% 3.72% 5.05% -0.79% 4.06%

15.85% -0.46% 6.52% 23.51% 10.31% 5.88% -3.28% 7.34%

9.36% 5.19% 5.26% 29.17% 13.76% -2.25% 6.41% 7.72%

-14.57% -12.61% 0.96% 42.81% -4.97% -11.62% 4.50% -11.73%

-6.53% -3.60% 8.89% 80.30% -12.03% -11.22% -15.97% -8.84%

-14.03% 2.13% 3.13% -3.51% -3.83% -3.96% 0.74% -0.60%

4.93% -3.71% -11.74% -65.64% -8.86% -0.29% 0.13% -5.33%

-5.88% -11.47% -20.53% -59.14% -16.36% -6.81% -6.82% -14.07%

-4.60% -1.64% -3.92% -12.00% -2.21% -0.12% 1.38% -6.01%

2.42% 3.52% -4.52% 7.36% 6.54% 6.55% 1.17% 1.45%

1.14% 6.41% 7.96% -12.29% -6.53% 8.34% 4.30% 0.24%

-10.28% -3.59% -8.43% -6.94% -2.84% -7.94% -2.68% -10.20%

1.50% 0.17% 7.66% 12.42% -0.36% -1.49% -0.01% -1.43%

Excess return


18/28

-2.85% 3.42% 4.82% 9.17% 0.46% -3.77% 10.06% 4.54%

0.94% 4.68% 1.12% -0.80% 4.35% 5.87% 6.74% -0.04%

-0.95% -1.23% 6.70% -2.45% -16.24% 1.15% -2.28% -3.04%

-5.55% -5.35% -0.92% -12.11% -8.43% -10.46% 6.75% -4.64%

1.27% -1.55% 2.77% 5.29% 5.94% -0.80% -0.34% -0.81%

-3.04% 4.60% -9.11% -12.74% -8.43% 6.44% 5.94% -4.02%

-7.72% -0.82% -1.43% -67.95% 24.93% -0.68% 3.57% 0.24%2.84% 6.33% 0.95% -1.06% 2.54% 7.69% 0.02% 4.02%

2.88% 2.80% 5.82% 4.09% -0.59% 5.57% -4.56% 1.09%

2.44% -1.82% 5.12% -2.29% -1.62% 1.66% -4.50% -1.47%

-1.34% -2.62% -1.27% 2.98% -3.99% -3.71% 1.06% -1.62%

6.85% -0.85% 4.70% 3.18% 2.83% -1.33% -0.22% 4.31%

8.28% 6.58% 8.43% -0.80% 7.40% 2.52% 2.05% 5.73%

3.17% -4.26% 1.41% 3.83% -1.06% -0.53% -2.35% 0.69%

0.33% -5.24% -6.00% 1.27% -8.42% -2.14% 1.28% -2.81%

8.25% 3.99% 16.99% 18.54% 4.82% 3.51% 8.34% 1.44%

22.67% 15.63% 19.73% 72.39% 27.79% 16.63% 15.71% 17.41%

5.14% 2.44% 3.89% 52.40% 7.72% 2.76% 2.47% 3.03%


19/28

Table 1: Risk parameter (annualized)SD of excess Beta SD of SD of residuals correlation return

DJW 0.174119 1.000000 0.174119 0.000000 1.000000 0.000726

Coca Cola 0.178364 0.623829 0.111269 0.144608 0.610698 0.010284

Disney 0.264334 1.267653 0.335084 0.147284 0.833185 0.005342

General Electric 0.372762 1.747238 0.651304 0.217850 0.814459 -0.0025913M (MMM) 0.226714 1.007914 0.228508 0.143746 0.775821 0.006045

Johnson and Jo 0.156344 0.621609 0.097185 0.114489 0.689755 0.003381

IBM 0.197273 0.709920 0.140048 0.154748 0.626140 0.013679

DFT 0.723854 0.827465 0.598964 0.715377 0.198369 0.014900

MSFT 0.277876 1.024980 0.284817 0.211477 0.655712 0.001844

PG 0.166264 0.549072 0.091291 0.139043 0.578455 0.003867

WMT 0.157103 0.420442 0.066053 0.140073 0.465035 0.006700

The index model covariance matrixDJW Coca Cola Disney General Electri 3M (MMM)

BETA 1.000000 0.623829 1.267653 1.747238 1.007914

DJW 1.000000 0.030317 0.018913 0.038432 0.052972 0.030557

Coca Cola 0.623829 0.018913 0.032710 0.023975 0.033045 0.019063

Disney 1.267653 0.038432 0.023975 0.070411 0.067150 0.038736

General Electric 1.747238 0.052972 0.033045 0.067150 0.140013 0.053391

3M (MMM) 1.007914 0.030557 0.019063 0.038736 0.053391 0.051462

Johnson and Jo 0.621609 0.018846 0.011756 0.023890 0.032928 0.018995

IBM 0.709920 0.021523 0.013427 0.027284 0.037606 0.021693

DFT 0.827465 0.025087 0.015650 0.031801 0.043832 0.025285

MSFT 1.024980 0.031075 0.019385 0.039392 0.054295 0.031321PG 0.549072 0.016646 0.010385 0.021102 0.029085 0.016778

WMT 0.420442 0.012747 0.007952 0.016158 0.022272 0.012848

Risk-free rate 0.001 P1

Theta 0.052524186 0.309153653

0.095803949

Super Portfolio of P1 and RFA -0.447529987

Weight of RFA 0 0.071469117

0.019050915 0.015457208

0.118108121 0.41470736

0.343668621 0.437570031

-0.184903344

0.023489161

0.264783829

1.000000978

0.019050915

0.343668621

0.118108121

WMT

sum

return

standard deviation

variance

Variance IBM

St. Deviation DFT

MSFT

PG

Coca Cola

Disney

General Electric

3M (MMM)

Expected return Johnson and Johnson


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0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

0.00% 10.00% 20.00% 30.00% 40.00%


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50.00% 60.00%

Series1


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0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.0000000.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000

0.02395 0.000000 0.000000 0.000000 0.000000

0.000000 0.51176 0.000000 0.000000 0.000000

0.000000 0.000000 0.04472 0.000000 0.000000

0.000000 0.000000 0.000000 0.01933 0.000000

0.000000 0.000000 0.000000 0.000000 0.01962


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Table 1: Risk parameter (annualized)SD of excess Beta SD of SD of residuals correlation return

DJW 0.174119 1.000000 0.174119 0.000000 1.000000 0.000726

Coca Cola 0.178364 0.623829 0.111269 0.144608 0.610698 0.010284

Disney 0.264334 1.267653 0.335084 0.147284 0.833185 0.005342

General Electric 0.372762 1.747238 0.651304 0.217850 0.814459 -0.002591Hershey Food 0.226714 1.007914 0.228508 0.143746 0.775821 0.006045

FedEx 0.156344 0.621609 0.097185 0.114489 0.689755 0.003381

IBM 0.197273 0.709920 0.140048 0.154748 0.626140 0.013679

NOC 0.723854 0.827465 0.598964 0.715377 0.198369 0.014900

UNH 0.277876 1.024980 0.284817 0.211477 0.655712 0.001844

SYY 0.166264 0.549072 0.091291 0.139043 0.578455 0.003867

TGT 0.157103 0.420442 0.066053 0.140073 0.465035 0.006700

The index model covariance matrixDJW Coca Cola Disney General Electri 3M (MMM)

BETA 1.000000 0.623829 1.267653 1.747238 1.007914

DJW 1.000000 0.030317 0.018913 0.038432 0.052972 0.030557

Coca Cola 0.623829 0.018913 0.032710 0.023975 0.033045 0.019063

Disney 1.267653 0.038432 0.023975 0.070411 0.067150 0.038736

General Electric 1.747238 0.052972 0.033045 0.067150 0.140013 0.053391

3M (MMM) 1.007914 0.030557 0.019063 0.038736 0.053391 0.051462

Johnson and Jo 0.621609 0.018846 0.011756 0.023890 0.032928 0.018995

IBM 0.709920 0.021523 0.013427 0.027284 0.037606 0.021693

DFT 0.827465 0.025087 0.015650 0.031801 0.043832 0.025285MSFT 1.024980 0.031075 0.019385 0.039392 0.054295 0.031321

PG 0.549072 0.016646 0.010385 0.021102 0.029085 0.016778

WMT 0.420442 0.012747 0.007952 0.016158 0.022272 0.012848

Macro forecast and forecast of anpha valueDJW Coca Cola Disney General Electric 3M (MMM) Johnson and Jo

Anpha 0.000000 0.009799 0.004444 -0.003798 0.005313 0.002898

Risk premium 0.000593 0.010169 0.010550 0.010834 0.010396 0.010167

Computation of Optimal PorfolioDJW Portfolio 1 Coca Cola Disney General Electri 3M (MMM)

variance of 0.020911 0.021693 0.047459 0.020663

anpha/varianc 2.173788 0.468605 0.204856 -0.080020 0.257126

weight of each 1.000000 0.215571 0.094239 -0.036811 0.118285

weight^2 0.046471 0.008881 0.001355 0.013991


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anpha of 0.008331 0.002112 0.000419 0.000140 0.000628

residue 0.003832 0.000972 0.000193 0.000064 0.000289

initial position 111.225840

Adjusted -2.047751 3.047751

beta 1.000000 0.680880 0.134479 0.058789 -0.022964 0.073789

Risk premium 0.000593 0.008734 0.002192 0.002274 0.002336 0.002241

SD 0.174119 0.133744Sharpe ratio 0.003403 0.065305

weight of Standard Return

18.87% 2.55%

-0.400000 10.95% 11.67%

-0.200000 9.38% 10.02%

0.000000 7.82% 8.37%

0.200000 6.26% 6.71%

0.400000 4.69% 5.06%0.600000 3.13% 3.41%

0.800000 1.56% 1.75%

1.000000 0.00% 0.10%

1.200000 -1.56% -1.55%

1.400000 -3.13% -3.21%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

-4.00% -2.00% 0.00% 2.00% 4.


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0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.020911 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.021693 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.047459 0.000000 0.0000000.000000 0.000000 0.000000 0.000000 0.020663 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000 0.013108

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

Johnson and Jo IBM DFT MSFT PG WMT

0.621609 0.709920 0.827465 1.024980 0.549072 0.420442

0.018846 0.021523 0.025087 0.031075 0.016646 0.012747

0.011756 0.013427 0.015650 0.019385 0.010385 0.007952

0.023890 0.027284 0.031801 0.039392 0.021102 0.016158

0.032928 0.037606 0.043832 0.054295 0.029085 0.022272

0.018995 0.021693 0.025285 0.031321 0.016778 0.012848

0.024822 0.013379 0.015594 0.019316 0.010348 0.007923

0.013379 0.039227 0.017810 0.022061 0.011818 0.009049

0.015594 0.017810 0.532523 0.025713 0.013774 0.0105470.019316 0.022061 0.025713 0.076574 0.017062 0.013065

0.010348 0.011818 0.013774 0.017062 0.028473 0.006999

0.007923 0.009049 0.010547 0.013065 0.006999 0.024980

IBM DFT MSFT PG WMT

0.013139 0.014284 0.001102 0.003431 0.006346

0.010220 0.010289 0.010406 0.010125 0.010048

Johnson and Jo IBM DFT MSFT PG WMT Overall Pf

0.013108 0.023947 0.511765 0.044723 0.019333 0.019621

0.221093 0.548672 0.027912 0.024639 0.177469 0.323438

0.101709 0.252404 0.012840 0.011334 0.081640 0.148790

0.010345 0.063708 0.000165 0.000128 0.006665 0.022138


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0.000295 0.003316 0.000183 0.000012 0.000280 0.000944

0.000136 0.001526 0.000084 0.000006 0.000129 0.000434

0.063449 0.157457 0.008010 0.007071 0.050930 0.092819 0.027401

0.002192 0.002203 0.002218 0.002243 0.002183 0.002166 0.025406

0.1887350.134614

00% 6.00% 8.00% 10.00% 12.00%

Series1


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0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.0000000.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000

0.023947 0.000000 0.000000 0.000000 0.000000

0.000000 0.511765 0.000000 0.000000 0.000000

0.000000 0.000000 0.044723 0.000000 0.000000

0.000000 0.000000 0.000000 0.019333 0.000000

0.000000 0.000000 0.000000 0.000000 0.019621

portflolio optimisation 2 - copy

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