Data Analysis and Investment

8/22/2019 Data Analysis and Investment

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DATA ANALYSIS AND INVESTMENT

PURPOSE OF THE STUDY

The purpose of the study is to find out at what percentage of investment should be

invested between the two companies, on the basis of risk and return of each security in

comparison. These percentage help in allocation the funds available for investment based on

portfolios.

IMPLEMENTATION OF STUDY

For implementing the study, ten securities or stock constituting the sensex Market is

selected, comprising of one month opening share price from the Times of India, dated from 1st

March to 31st

March.

In order to know the risk of stock or securities, the formula to be used is given below

Average Returns = Total Return

No. of Days

Standard Deviation () = variance

Variance = 1/n-1 * (Xi-X)]

dx2

= Squares of deviation taken from actual mean.

After that it is required to compare the Stock or Securities of two companies with each other by

using the below formula or Correlation Co-efficient as follows.


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Co-variance (COVab) = (x-x) (y-y)

N-1

(dXdY) =Summation of product of deviation between two companies.

n= Number of observation or samples.

Correlation co-efficient (rab) = COV (ab)

(a)(b)

COVab = Co-Variance between A & B

(a)(b) = product of standard deviation between A & B

This next step is the formation of the optimal portfolio on the basis of what percentage of

should be invested when two securities and stock is combined i.e., calculation of portfolio

weight by using minimum variance equation as follows.

Xa = (b)2rab (a)( b)

(b)2+ (a)

22(rab)( a)( b)

Where,

Xa is the proportion of Security A

Xb is the proportion of Security B

a = standard deviation of Security A

b = standard deviation of Security B

rab= Correlation Co-efficient between A&B


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The final step is to calculate the risk, that portfolio risk, combined shows how much the risk is

reduced by combining two securities or stock by using the given below formula,

p = a2*Wa

2+b

2*Wb

2+2rababWaWb

Where,

p = Portfolio risk.

Wa = Proportion of Investment in security 1.

Wb= Proportion of Investment in security 2

a = Standard deviation of security 1.

b = Standard deviation of security 2.

rab = Correlation co-efficient between Security 1&2.


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APPENDIX

Share price exercised in the month of March 2008

DATE BHEL HDFC BHARATI

TELEVENTURES

ITC ICICI

01-03-08 2176.80 932.60 675.60 171.85 831.90

04-03-08 2172.20 981.10 667.15 172.50 855.35

05-03-08 2099.60 947.70 691.75 166.55 845.85

06-03-08 2010.05 935.00 684.45 162.50 820.70

07-03-08 2026.55 935.65 666.85 162.05 851.60

08-03-08 2015.15 915.65 666.95 158.25 826.60

11-03-08 2175.45 972.30 673.20 159.85 863.40

12-03-08 2175.45 972.30 673.20 159.85 863.40

13-03-08 2103.65 951.25 697.60 140.00 869.70

14-03-08 2117.00 959.65 696.10 149.00 877.35

15-03-08 2030.10 933.65 671.85 142.85 829.70

18-03-08 2007.40 917.75 668.45 147.35 822.00

19-03-08 1955.75 904.20 652.30 145.00 810.65

20-03-08 2079.25 926.60 640.25 142.00 824.00

21-03-08 2045.85 954.15 635.30 140.95 823.90

22-03-08 2103.10 965.95 650.60 144.90 870.35

25-03-08 2230.05 1023.25 681.05 149.30 899.30

26-03-08 2279.50 1011.85 679.65 144.20 894.55

27-03-08 2254.70 975.60 667.95 142.60 876.00

28-03-08 2281.45 955.45 655.95 143.40 857.60

29-03-08 2278.90 933.05 679.70 146.75 855.60

31-03-08 2260.75 949.40 685.15 150.40 853.10


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DATE ONGC RELIANCE SBI TATA

MOTORS

WIPRO

01-03-07 790.60 1354.60 1039.15 783.95 560.85

02-03-07 799.20 1366.75 1052.55 789.25 589.4003-03-07 800.00 1317.35 1008.45 774.50 573.20

06-03-07 773.35 1259.20 962.35 736.30 537.15

07-03-07 770.10 1299.40 991.20 726.30 580.75

08-03-07 765.60 1289.35 964.50 740.60 556.55

09-03-07 780.00 1334.80 1000.30 770.30 576.75

10-03-07 780.00 1334.80 1000.30 770.30 576.75

13-03-07 793.40 1316.00 976.80 764.40 573.00

14-03-07 807.25 1326.90 980.70 773.20 581.90

15-03-07 780.25 1285.05 947.50 745.15 555.25

16-03-07 774.65 1283.75 921.90 725.85 561.15

17-03-07 762.20 1299.80 914.40 749.45 565.90

20-03-07 793.05 1314.00 928.30 770.85 579.05

21-03-07 790.55 1321.05 952.60 769.70 573.30

22-03-07 812.70 1340.05 982.15 776.05 581.65

23-03-07 852.25 1374.25 992.00 780.00 595.15

24-03-07 843.20 1379.20 1027.10 789.00 600.90

27-03-07 853.20 1365.20 1031.60 753.85 586.15

29-03-07 866.30 1348.65 974.20 718.80 558.20

30-03-07 873.45 1356.10 986.45 715.10 565.55

31-03-07 878.15 1368.35 992.90 727.75 558.35


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1. Calculation of standard deviation of BHEL Company

X X-X=d d2

DATE Share price Average Deviation Squared

deviation

01-03-07 2176.00 2130.72 45.28 2050.28

02-03-07 2172.20 2130.72 41.48 1720.59

03-03-07 2099.60 2130.72 -31.12 968.45

06-03-07 2010.05 2130.72 -120.67 14561.25

07-03-07 2026.55 2130.72 -104.17 10851.39

08-03-07 2015.15 2130.72 -115.57 13356.42

09-03-07 2175.45 2130.72 44.73 2000.77

10-03-07 2175.45 2130.72 44.73 2000.77

13-03-07 2103.65 2130.72 -27.07 732.78

14-03-07 2117.00 2130.72 -13.72 188.24

15-03-07 2030.10 2130.72 -100.62 10124.38

16-03-07 2007.40 2130.72 -123.32 15207.82

17-03-07 1955.75 2130.72 -174.97 30614.5020-03-07 2079.25 2130.72 -51.47 2649.16

21-03-07 2043.85 2130.72 -86.87 7546.39

22-03-07 2103.10 2130.72 -27.62 762.86

23-03-07 2230.05 2130.72 99.33 9866.45

24-03-07 2279.50 2130.72 148.78 22135.49

27-03-07 2254.70 2130.72 123.98 15371.04

29-03-07 2281.45 2130.72 150.73 22719.53

30-03-07 2278.90 2130.72 148.18 21957.31

31-03-07 2260.75 2130.72 130.03 16907.80

X=46875.9 d2=224293.67


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Average Return = (TOTAL RETURN)/NO OF DAYS

= 46875.9

22

= 2130.72

Variance = 1/n-1* (Xi-X)]

= 1/22-1 (224293.67

= 10680.65

Standard Deviation = Variance

= 10680.65

= 103.34


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2. Calculation of standard deviation of HDFC Company

X X-X=d d2


deviation

01-03-07 932.60 952.43 -19.83 393.23

02-03-07 981.10 952.43 28.67 821.97

03-03-07 947.70 952.43 -4.73 22.37

06-03-07 935.00 952.43 -17.43 303.80

07-03-07 935.65 952.43 -16.78 281.57

08-03-07 915.65 952.43 -36.78 1352.77

09-03-07 972.30 952.43 19.87 394.82

10-03-07 972.30 952.43 19.87 394.82

13-03-07 951.25 952.43 -1.18 1.39

14-03-07 959.65 952.43 7.22 52.13

15-03-07 933.10 952.43 -19.33 373.65

16-03-07 917.75 952.43 -34.68 1202.70

17-03-07 904.20 952.43 -48.23 2326.1320-03-07 926.60 952.43 -25.83 667.19

21-03-07 954.15 952.43 1.72 2.96

22-03-07 965.95 952.43 13.52 182.79

23-03-07 1023.25 952.43 70.82 5015.47

24-03-07 1011.85 952.43 59.42 3530.74

27-03-07 975.60 952.43 23.17 536.85

29-03-07 955.45 952.43 3.02 9.12

30-03-07 933.05 952.43 -19.38 375.58

31-03-07 949.40 952.43 -3.03 9.18

X=20953.55 d2=18251.23


10/63


= 20953.5

22

= 952.43


= 1/22-1 (18251.23)

= 869.106


= 869.106

= 29.48


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3. Calculation of standard deviation of BHARATI TELEVENTURESCompany

X X-X=d d2


deviation

01-03-07 675.60 670.95 4.65 21.62

02-03-07 667.15 670.95 -3.8 14.44

03-03-07 691.75 670.95 20.8 432.6406-03-07 684.45 670.95 13.5 182.25

07-03-07 666.85 670.95 -4.1 16.81

08-03-07 666.95 670.95 -4 16

09-03-07 673.20 670.95 2.25 5.063

10-03-07 673.20 670.95 2.25 5.063

13-03-07 697.60 670.95 26.65 710.22

14-03-07 696.10 670.95 25.15 632.52

15-03-07 671.85 670.95 0.9 0.81

16-03-07 668.45 670.95 -2.5 6.25

17-03-07 652.45 670.95 -18.5 342.25

20-03-07 640.25 670.95 -30.7 942.49

21-03-07 635.30 670.95 -35.65 1270.92

22-03-07 650.60 670.95 -20.35 414.12

23-03-07 681.05 670.95 10.1 102.01

24-03-07 679.65 670.95 8.7 75.69

27-03-07 667.95 670.95 3 9

29-03-07 655.95 670.95 -15 225

30-03-07 679.70 670.95 8.75 76.56


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31-03-07 685.15 670.95 14.2 201.64

X=14761.05 d2=5763.37


= 14761.05

22

= 670.95


= 1/22-1 (5763.37)

= 274.44


= 274.44

= 16.56


13/63

4. Calculation of standard deviation of ITC LTD Company

X X-X=d d2


deviation

01-03-07 171.85 151.91 19.94 397.60

02-03-07 172.50 151.91 20.59 423.95

03-03-07 166.55 151.91 14.64 214.33

06-03-07 162.50 151.91 10.59 112.15

07-03-07 162.05 151.91 10.14 102.82

08-03-07 158.25 151.91 6.34 40.19

09-03-07 159.85 151.91 7.94 63.04

10-03-07 159.85 151.91 7.94 63.04

13-03-07 140.00 151.91 -11.91 141.85

14-03-07 149.00 151.91 -2.91 8.47

15-03-07 142.85 151.91 -9.06 82.08

16-03-07 147.35 151.91 -4.56 20.79

17-03-07 145.00 151.91 -6.91 47.7520-03-07 142.00 151.91 -9.91 98.21

21-03-07 140.95 151.91 -10.96 120.12

22-03-07 144.90 151.91 -7.01 49.14

23-03-07 149.30 151.91 -2.61 6.81

24-03-07 144.20 151.91 -7.71 59.44

27-03-07 142.60 151.91 -9.31 86.68

29-03-07 143.40 151.91 -8.51 72.42

30-03-07 146.75 151.91 -5.16 26.63

31-03-07 150.40 151.91 -1.51 2.28

X=3342.1 d2=2239.79


14/63


= 3342.1

22

= 151.91


= 1/22-1 (2239.79)

= 106.65


= 106.65

= 10.32


15/63

5. Calculation of standard deviation of ICICI LTD Company

X X-X=d d2


deviation

01-03-07 831.90 851.03 -19.13 365.96

02-03-07 855.35 851.03 4.32 18.66

03-03-07 845.85 851.03 -5.18 26.8306-03-07 820.70 851.03 30.33 919.91

07-03-07 851.60 851.03 0.57 0.32

08-03-07 826.60 851.03 -24.43 596.82

09-03-07 863.40 851.03 12.37 153.02

10-03-07 863.40 851.03 12.37 153.02

13-03-07 869.70 851.03 18.67 348.57

14-03-07 877.35 851.03 26.32 692.74

15-03-07 829.70 851.03 -21.33 454.97

16-03-07 822.00 851.03 -29.03 842.74

17-03-07 810.65 851.03 -40.38 1603.54

20-03-07 824.00 851.03 -27.03 730.62

21-03-07 823.90 851.03 -27.13 736.04

22-03-07 870.35 851.03 19.32 373.26

23-03-07 899.30 851.03 48.27 2329.99

24-03-07 894.55 851.03 43.52 1893.99

27-03-07 876.00 851.03 24.97 623.50

29-03-07 875.60 851.03 6.57 43.16

30-03-07 855.60 851.03 4.57 20.88


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31-03-07 853.10 851.03 2.07 4.28

X=18722.6 d2=12950.82


= 18722.6

22

= 851.03


= 1/22-1 (12950.82)

= 616.70


= 616.70

= 24.83


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6. Calculation of standard deviation of ONGC Company

X X-X=d d2


deviation

01-03-07 790.60 806.36 -15.76 248.38

02-03-07 799.20 806.36 -7.16 51.26

03-03-07 800.00 806.36 -6.36 40.45

06-03-07 773.35 806.36 -33.01 1089.66

07-03-07 770.10 806.36 -36.26 1314.79

08-03-07 765.60 806.36 -40.76 1661.38

09-03-07 780.00 806.36 -26.36 694.85

10-03-07 780.00 806.36 -26.36 694.85

13-03-07 793.40 806.36 -1.96 3.84

14-03-07 807.25 806.36 0.89 0.79

15-03-07 780.25 806.36 -26.11 681.73

16-03-07 774.65 806.36 -31.71 1005.52

17-03-07 762.20 806.36 -44.16 1950.1120-03-07 793.05 806.36 -13.31 177.16

21-03-07 790.55 806.36 -15.81 249.96

22-03-07 812.70 806.36 6.34 40.19

23-03-07 852.25 806.36 45.89 2105.89

24-03-07 843.20 806.36 36.84 1357.18

27-03-07 853.20 806.36 46.84 2193.98

29-03-07 866.30 806.36 59.94 3592.80

30-03-07 873.45 806.36 67.09 4501.07

31-03-07 878.15 806.36 71.79 5153.80

X=17739.9 d2=30687.99


18/63


= 17739.9

22

= 806.36


= 1/22-1 (30687.99)

= 1461.33


= 1461.33

= 38.22


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7. Calculation of standard deviation of RELIANCE Company

X X-X=d d2


deviation

01-03-07 1354.60 1328.87 25.73 662.03

02-03-07 1366.75 1328.87 37.88 1434.89

03-03-07 1317.35 1328.87 -11.52 132.7106-03-07 1259.20 1328.87 -69.67 4853.91

07-03-07 1299.40 1328.87 -29.47 868.48

08-03-07 1289.35 1328.87 -39.52 1561.83

09-03-07 1334.80 1328.87 5.93 35.16

10-03-07 1334.80 1328.87 5.93 35.16

13-03-07 1316.00 1328.87 -12.87 165.64

14-03-07 1326.90 1328.87 -1.97 3.88

15-03-07 1285.50 1328.87 -43.37 1880.96

16-03-07 1283.75 1328.87 -45.12 2035.81

17-03-07 1299.80 1328.87 -29.07 845.06

20-03-07 1314.00 1328.87 -14.87 221.11

21-03-07 1321.05 1328.87 -7.82 61.15

22-03-07 1340.05 1328.87 11.18 124.99

23-03-07 1374.25 1328.87 45.38 2059.34

24-03-07 1379.20 1328.87 50.33 2533.11

27-03-07 1365.20 1328.87 36.33 1319.87

29-03-07 1348.65 1328.87 19.78 391.25

30-03-07 1356.10 1328.87 27.23 741.47


20/63

31-03-07 1368.35 1328.87 39.48 1558.97

X=29235.05 d2=23556.48


= 29235.05

22

= 1328.87


= 1/22-1 (23556.48)

= 1121.73


= 1121.73

= 33.49


21/63

8. Calculation of standard deviation of STATE BANK Company

X X-X=d d2


deviation

01-03-07 1039.15 983.06 56.09 3146.09

02-03-07 1052.55 983.06 69.49 4828.86

03-03-07 1088.45 983.06 105.39 11107.05

06-03-07 962.35 983.06 -20.71 428.90

07-03-07 991.20 983.06 8.14 66.26

08-03-07 964.50 983.06 -18.56 344.47

09-03-07 1000.30 983.06 17.24 297.21

10-03-07 1000.30 983.06 17.27 297.21

13-03-07 976.80 983.06 -6.26 39.19

14-03-07 980.70 983.06 -2.36 5.57

15-03-07 947.50 983.06 -35.56 1264.51

16-03-07 921.90 983.06 -61.16 3740.54

17-03-07 914.40 983.06 -68.66 4714.1920-03-07 928.30 983.06 -54.76 2998.66

21-03-07 952.60 983.06 -30.46 927.81

22-03-07 982.15 983.06 -0.91 0.83

23-03-07 992.00 983.06 8.94 79.92

24-03-07 1027.10 983.06 44.04 1939.52

27-03-07 1013.60 983.06 48.54 2356.13

29-03-07 974.20 983.06 -8.86 78.49

30-03-07 986.45 983.06 3.39 11.49

31-03-07 992.90 983.06 9.84 96.82

X=21627.4 d2=38769.72


22/63


= 21627.4

22

= 983.06


= 1/22-1 (38769.72)

= 1846.177


= 1846.177

= 42.96


23/63

9. Calculation of standard deviation of TATAMOTORS Company

X X-X=d d2


deviation

01-03-07 783.95 756.87 27.08 733.33

02-03-07 789.25 756.87 32.38 1048.46

03-03-07 774.50 756.87 17.63 310.8206-03-07 736.30 756.87 -20.57 423.12

07-03-07 726.30 756.87 -30.57 934.52

08-03-07 740.60 756.87 -16.27 264.71

09-03-07 770.30 756.87 13.43 180.36

10-03-07 770.30 756.87 13.43 180.36

13-03-07 764.40 756.87 7.53 56.70

14-03-07 773.20 756.87 16.33 266.67

15-03-07 745.15 756.87 -11.72 137.36

16-03-07 725.85 756.87 -31.02 962.24

17-03-07 749.45 756.87 -7.42 55.06

20-03-07 770.85 756.87 13.98 195.44

21-03-07 769.70 756.87 12.83 164.61

22-03-07 776.05 756.87 19.18 367.87

23-03-07 780.00 756.87 23.13 534.99

24-03-07 789.00 756.87 32.13 1032.34

27-03-07 753.85 756.87 -3.02 9.12

29-03-07 718.80 756.87 -38.07 1449.32

30-03-07 715.10 756.87 -41.77 1744.73


24/63

31-03-07 727.75 756.87 -29.12 847.97

X=16651.1 d2=11900.1


= 16651.1

22

= 756.87


= 1/22-1 (11900.1)

= 566.67


= 566.67

= 23.80


25/63

10. Calculation of standard deviation of WIPRO Company

X X-X=d d2


deviation

01-03-07 560.85 572.13 -11.28 127.24

02-03-07 589.40 572.13 17.27 298.25

03-03-07 573.20 572.13 1.07 1.14

06-03-07 537.15 572.13 -34.98 1223.60

07-03-07 580.75 572.13 8.62 74.30

08-03-07 556.55 572.13 -15.58 242.74

09-03-07 576.75 572.13 4.62 21.34

10-03-07 576.75 572.13 4.62 21.34

13-03-07 573.00 572.13 0.87 0.76

14-03-07 581.90 572.13 9.77 95.45

15-03-07 555.25 572.13 -16.88 284.93

16-03-07 561.15 572.13 -10.98 120.56

17-03-07 565.90 572.13 -6.23 38.8120-03-07 579.05 572.13 6.92 47.89

21-03-07 573.30 572.13 1.17 1.37

22-03-07 581.65 572.13 9.52 90.63

23-03-07 595.15 572.13 23.02 529.92

24-03-07 600.90 572.13 28.77 827.71

27-03-07 586.15 572.13 14.02 196.56

29-03-07 558.20 572.13 -13.93 194.04

30-03-07 565.55 572.13 -6.58 43.29

31-03-07 558.35 572.13 -13.78 189.89

X=12586.9 d2=4671.76


26/63


= 12586.9

22

= 572.13


= 1/22-1 (4671.76)

= 222.46


= 222.46

= 14.91


27/63

1.Correlation between BHEL and HDFC

DATE Deviation of BHEL Deviation of HDFC Production

deviation

01-03-07 45.28 -19.83 -897.90

02-03-07 41.48 28.67 1189.23

03-03-07 -31.12 -4.73 147.19

06-03-07 -120.67 -17.43 2103.2807-03-07 -104.17 -16.78 1747.97

08-03-07 -115.57 -36.78 4250.66

09-03-07 44.73 19.87 888.79

10-03-07 44.73 19.87 888.79

13-03-07 -27.07 -1.18 31.94

14-03-07 -13.72 7.22 -99.06

15-03-07 -100.62 -19.33 1944.98

16-03-07 -123.32 -34.68 4276.74

17-03-07 -174.97 -48.23 8438.80

20-03-07 -51.47 -25.83 1329.47

21-03-07 -86.87 1.72 -149.42

22-03-07 -27.62 13.52 -373.42

23-03-07 99.33 70.82 7034.55

24-03-07 148.78 59.42 8840.51

27-03-07 123.98 23.17 2872.62

29-03-07 150.73 3.02 455.20

30-03-07 148.16 -19.38 -2871.34

31-03-07 130.03 -3.03 -393.99


28/63

dxdy=41655.59

Covariance = (x-x) (y-y)

N-1

= 41655.59/22-1

= 1983.59

Correlation Coefficient rab = COV (ab)

(a)(b)

= 1983.59

(103.34) (29.48)

= 0.65


29/63

2. Correlation between HDFC & BHARATI TELEVENTURESLTD

DATE Deviation of HDFC Deviation of BHARATI

TELEVENTURES

Production

deviation

01-03-07 -19.83 4.65 -92.20

02-03-07 28.67 -3.8 108.95

03-03-07 -4.73 20.8 -98.38

06-03-07 -17.43 13.5 -235.31

07-03-07 -16.78 -4.1 68.79

08-03-07 -36.78 -4 147.12

09-03-07 19.87 2.25 44.71

10-03-07 19.87 2.25 44.71

13-03-07 -1.18 26.65 -31.45

14-03-07 7.22 25.15 181.58

15-03-07 -19.33 0.9 -17.39

16-03-07 -34.68 -2.5 86.7

17-03-07 -48.23 -18.5 892.26

20-03-07 -25.83 -30.7 792.9821-03-07 1.72 -35.65 -61.32

22-03-07 13.52 -20.35 -275.13

23-03-07 70.82 10.1 715.28

24-03-07 59.42 8.7 516.95

27-03-07 23.17 3 69.51

29-03-07 3.02 -15 -45.3

30-03-07 -19.38 8.75 -169.58

31-03-07 -3.03 14.2 -43.03

dxdy=2600.45


30/63


N-1

= 2600.45/22-1

= 123.83


(a)(b)

= 123.83

(29.48)(16.56)

= 0.25


31/63

3. Correlation between BHARATI TELEVENTURESand ITC LTD

DATE Deviation of

BHARATI

TELEVENTURES

Deviation of ITC

LTD

Production

deviation

01-03-07 4.65 19.94 92.72

02-03-07 -3.8 20.59 -78.24

03-03-07 20.8 14.64 304.51

06-03-07 13.5 10.59 142.96

07-03-07 -4.1 10.14 -41.57

08-03-07 -4 6.34 -25.36

09-03-07 2.25 7.94 17.86

10-03-07 2.25 7.94 17.86

13-03-07 26.65 -11.91 -317.40

14-03-07 25.15 -2.91 -73.19

15-03-07 0.9 -9.06 -8.15

16-03-07 -2.5 -4.56 11.4

17-03-07 -18.5 -6.91 127.83

20-03-07 -30.7 -9.91 304.24

21-03-07 -35.65 -10.96 390.72

22-03-07 -20.35 -7.01 142.65

23-03-07 10.1 -2.61 -26.36

24-03-07 8.7 -7.71 -62.38

27-03-07 3 -9.31 -27.93

29-03-07 -15 -8.51 127.65

30-03-07 8.75 -5.16 -45.115

31-03-07 14.2 -1.51 -21.44

dxdy=953.23


32/63


N-1

= 953.23/22-1

= 45.39


(a)(b)

= 45.39

(16.56) (10.32)

= 0.26


33/63

4. Correlation between ITC & ICICI LTD

DATE Deviation of ITC

LTD

Deviation of ICICI Production

deviation

01-03-07 19.94 -19.13 -381.45

02-03-07 20.59 4.32 88.95

03-03-07 14.64 -5.18 -75.84

06-03-07 10.59 30.33 321.19

07-03-07 10.14 0.57 5.78

08-03-07 6.34 -24.43 -154.89

09-03-07 7.94 12.37 98.23

10-03-07 7.94 12.37 98.23

13-03-07 -11.91 18.67 -222.36

14-03-07 -2.91 26.32 -76.59

15-03-07 -9.06 -21.33 193.25

16-03-07 -4.56 -29.03 132.38

17-03-07 -6.91 -40.38 279.03

20-03-07 -9.91 -27.03 267.8621-03-07 -10.96 -27.13 297.34

22-03-07 -7.01 19.32 -135.43

23-03-07 -2.61 48.27 -125.98

24-03-07 -7.71 43.52 -335.54

27-03-07 -9.31 24.97 -232.47

29-03-07 -8.51 6.57 -55.91

30-03-07 -5.16 4.57 -23.58

31-03-07 -1.51 2.07 -3.13

dxdy=40.93


34/63


N-1

= 40.93 /22-1

= 1.949


(a)(b)

= 1.949

(10.32) (24.83)

= 0.007


35/63

5. Correlation between ICICI and ONGC LTD

DATE Deviation of ICICI Deviation of ONGC

LTD

Production

deviation

01-03-07 -19.13 -15.76 301.49

02-03-07 4.32 -7.16 -30.93

03-03-07 -5.18 -6.36 32.94

06-03-07 30.33 -33.01 1001.19

07-03-07 0.57 -36.26 -36.83

08-03-07 -24.43 -40.76 995.77

09-03-07 12.37 -26.36 -326.07

10-03-07 12.37 -26.36 -326.07

13-03-07 18.67 -1.96 -36.59

14-03-07 26.32 0.89 23.42

15-03-07 -21.33 -26.11 556.93

16-03-07 -29.03 -31.71 920.54

17-03-07 -40.38 -44.16 1783.18

20-03-07 -27.03 -13.31 359.7721-03-07 -27.13 -15.81 428.93

22-03-07 19.32 6.34 122.49

23-03-07 48.27 45.89 2215.11

24-03-07 43.52 36.84 1603.27

27-03-07 24.97 46.84 1169.59

29-03-07 6.57 59.94 393.81

30-03-07 4.57 67.09 306.60

31-03-07 2.07 71.79 148.61

dxdy=11607.67


36/63


N-1

= 11607.67/22-1

= 552.74


(a)(b)

= 552.74/ (24.83) (38.22)

= 0.58


37/63

6. Correlation between ONGC & RELIANCELTD

DATE Deviation of ONGC

LTD

Deviation of

RELIANCE

Production

deviation

01-03-07 -15.76 25.73 -405.50

02-03-07 -7.16 37.88 -271.22

03-03-07 -6.36 -11.52 73.27

06-03-07 -33.01 -69.67 2299.81

07-03-07 -36.26 -29.47 1068.58

08-03-07 -40.76 -39.52 1610.84

09-03-07 -26.36 5.93 -156.31

10-03-07 -26.36 5.93 -156.31

13-03-07 -1.96 -12.87 25.23

14-03-07 0.89 -1.97 -1.75

15-03-07 -26.11 -43.37 1132.39

16-03-07 -31.71 -45.12 1430.75

17-03-07 -44.16 -29.07 1283.73

20-03-07 -13.31 -14.87 197.9221-03-07 -15.81 -7.82 123.63

22-03-07 6.34 11.18 70.88

23-03-07 45.89 45.38 2082.49

24-03-07 36.84 50.33 1854.16

27-03-07 46.84 36.33 1701.69

29-03-07 59.94 19.78 1185.61

30-03-07 67.09 27.23 1826.86

31-03-07 71.79 39.48 2834.27

dxdy=19811.02


38/63


N-1

= 19811.02 /22-1

= 943.38


(a)(b)

= 943.38

(38.22) (33.49)

= 0.74


39/63

7. Correlation between RELIANCE and SBI LTD

DATE Deviation of

RELIANCE

Deviation of SBI Production

deviation

01-03-07 25.73 56.09 1443.19

02-03-07 37.88 69.49 2623.28

03-03-07 -11.52 105.39 -1214.09

06-03-07 -69.67 -20.71 1442.87

07-03-07 -29.47 8.14 -239.89

08-03-07 -39.52 -18.56 733.49

09-03-07 5.93 17.24 102.23

10-03-07 5.93 17.27 102.23

13-03-07 -12.87 -6.26 80.57

14-03-07 -1.97 -2.36 4.65

15-03-07 -43.37 -35.56 1542.24

16-03-07 -45.12 -61.16 2759.54

17-03-07 -29.07 -68.66 1995.95

20-03-07 -14.87 -54.76 814.2821-03-07 -7.82 -30.46 238.19

22-03-07 11.18 -0.91 -10.17

23-03-07 45.38 8.94 405.69

24-03-07 50.33 44.04 2216.53

27-03-07 36.33 48.54 1763.46

29-03-07 19.78 -8.86 -175.25

30-03-07 27.23 3.39 92.51

31-03-07 39.48 9.84 390.46

dxdy=17120.96


40/63


N-1

= 17120.96/22-1

= 815.28


(a)(b)

= 815.28

(33.49) (42.96)

= 0.56


41/63

8. Correlation between SBI & TATAMOTORS LTD

DATE Deviation of SBI Deviation of TATA

MOTOR

Production

deviation

01-03-07 56.09 27.08 1518.92

02-03-07 69.49 32.38 2250.09

03-03-07 105.39 17.63 1858.03

06-03-07 -20.71 -20.57 426.00

07-03-07 8.14 -30.57 -248.84

08-03-07 -18.56 -16.27 301.97

09-03-07 17.24 13.43 231.53

10-03-07 17.27 13.43 231.94

13-03-07 -6.26 7.53 -47.14

14-03-07 -2.36 16.33 -38.54

15-03-07 -35.56 -11.72 416.76

16-03-07 -61.16 -31.02 1897.18

17-03-07 -68.66 -7.42 509.46

20-03-07 -54.76 13.98 -765.5421-03-07 -30.46 12.83 -390.80

22-03-07 -0.91 19.18 -17.45

23-03-07 8.94 23.13 206.78

24-03-07 44.04 32.13 1415.01

27-03-07 48.54 -3.02 -146.59

29-03-07 -8.86 -38.07 337.30

30-03-07 3.39 -41.77 -141.60

31-03-07 9.84 -29.12 -286.54

dxdy=9517.93


42/63


N-1

= 9517.93 /22-1

= 453.23


(a)(b)

= 453.23

(42.96) (23.80)

= 0.44


43/63

9. Correlation between TATA MOTORS and WIPRO

DATE Deviation of TATA

MOTOR

Deviation of WIPRO Production

deviation

01-03-07 27.08 -11.28 -305.46

02-03-07 32.38 17.27 559.20

03-03-07 17.63 1.07 18.86

06-03-07 -20.57 -34.98 719.54

07-03-07 -30.57 8.62 -263.51

08-03-07 -16.27 -15.58 253.49

09-03-07 13.43 4.62 62.05

10-03-07 13.43 4.62 62.05

13-03-07 7.53 0.87 6.55

14-03-07 16.33 9.77 159.54

15-03-07 -11.72 -16.88 197.83

16-03-07 -31.02 -10.98 340.59

17-03-07 -7.42 -6.23 46.23

20-03-07 13.98 6.92 96.7421-03-07 12.83 1.17 15.01

22-03-07 19.18 9.52 182.59

23-03-07 23.13 23.02 532.45

24-03-07 32.13 28.77 924.38

27-03-07 -3.02 14.02 -472.34

29-03-07 -38.07 -13.93 530.32

30-03-07 -41.77 -6.58 291.55

31-03-07 -29.12 -13.78 401.27

dxdy=4788.93


44/63

Covariance

= (x-x) (y-y)

N-1

= 4788.93/22-1

= 228.04


(a)(b)= 228.04

(23.80) (14.91)

= 0.64


45/63

Calculation of Portfolio Weight

Deriving the Minimum risk portfolio the following formula is used

(b)2

rab (a) (b)Wa =

(a)2 + (b)2 2(rab)(a)(b)Where Xa is proportion of 1

stsecurity

Xb is proportion of 2nd

security

a is standard deviation of 1st

security

b is standard deviation of 2nd

security


46/63

1. Portfolio Weight BHEL AND HDFC

Calculation of portfolio weight between two companies

a = 103.34; b= 29.48; rab=0.65

(29.48)2 (0.65) (103.34) (29.48)

Wa =

(103.34)2

+ (29.48)2 2(0.65) (103.34) (29.48)

= -1111.13

7587.82

Wa = -0.15

Wb = 1 Wa

Wb = 1 (- 0.15)

Wb = 1.15

2. Portfolio Weight HDFC AND BHARATI TELEVENTURES


a = 29.48; b =16.56; rab = 0.25

(16.56)

2

(0.25) (29.48) (16.56)Wa =

(29.48)2

+ (16.56)2 2(0.25) (29.48) (16.56)

152.18

=

899.2

Wa = 0.17

Wb = 1 WaWb = 1 0.17

Wb = 0.83


47/63

3. Portfolio Weight BHARATI TELEVENTURESAND ITC


a = 16.56; b= 10.32; rab = 0.26

(10.32)2 (0.26)(16.56)(10.32)

Wa =

(16.56)2

+ (10.32)2 2(0.26)(16.56)(10.32)

= 62.07

291.87

Wa = 0.21

Wb = 1 Wa

Wb = 1 (0.21)

Wb = 0.79

4. Portfolio Weight ITC AND ICICI


a = 10.32;

b = 24.83; rab= 0.007(24.83)

2 (0.007) (10.32) (24.83)

Wa =

(10.32)2

+ (24.83)2 2(0.007) (10.32) (24.83)

614.74

=

719.44

Wa = 0.85Wb = 1 Wa

Wb = 1 (0.85)

Wb = 0.15


48/63

5. Portfolio Weight ICICI AND ONGC


a = 24.83; b=38.22; rab = 0.58

(38.22)2 (0.58) (24.83) (38.22)

Wa =

(24.83)2

+ (38.22)2 2(0.58) (24.83) (38.22)

910.34

=

976.44

Wa = 0.93

Wb = 1 Wa

Wb = 1 (0.93)

Wb = 0.07

6. Portfolio Weight ONGC AND RELIANCE


a = 38.2;

b = 33.49; rab = 0.74(33.49)

2 (0.74) (38.22) (33.49)

Wa =

(38.22)2

+ (33.49)2 2(0.74) (38.22) (33.49)

174.39

=

687.97

Wa = 0.25Wb = 1 Wa

Wb = 1 (0.25)

Wb = 0.75


49/63

7. Portfolio Weight RELIANCE AND SBI


a = 33.49; b = 42.96; rab = 0.56

(42.96)2 (0.56) (33.49) (42.96)

Wa =

(33.49)2

+ (42.96)2 2(0.56) (33.49) (42.96)

1039.88

=

1355.77

Wa = 0.76

Wb = 1 Wa

Wb = 1 (0.76)

Wb = 0.24

8. Portfolio Weight SBI AND TATAMOTOR


a = 42.96;

b = 23.80; rab = 0.44(23.80)

2 (0.44) (42.96) (23.80)

Wa =

(4.96)2

+ (23.80)2 2(0.44) (42.96) (23.80)

116.56

=

1512.25

Wa = 0.08Wb = 1 Wa

Wb = 1 (0.08)

Wb = 0.92


50/63

9. Portfolio Weight TATAMOTOR AND WIPRO


a = 23.80; b = 14.91; rab = 0.64

(14.91)2 (0.64) (23.80) (14.91)

Wa =

(23.80)2

+ (14.91)2 2(0.64) (23.80) (14.91)

222.308-227.10

=

566.44+222.30-454.22

-4.792

=

334.53

Wa = -0.01

Wb = 1 Wa

Wb = 1 (-0.01)

Wb = 1.01


51/63

PORTFOLIO RISK

It is calculated with the help of following formula,

p = a2*Wa2 + b2*Wb2 + 2rab*a*b*WA*Wb

Where, p = Portfolio risk

Wa= Proportion of Investment in security 1

Wb = Proportion of Investment in security 2

a = Standard deviation of security 1

b = Standard deviation of security 2

rab= Correlation Co-efficient between security 1&2

PORTFOLIO RETURN

It is calculated with the help of following formula

PR= (Xa*Wa) + (Xb*Wb)

Where

Xa= Average return of 1st

security

Wa= Weight of 1st

security

Xb= Average return of 2nd security

Wb= Weight of 2nd security


52/63

1. Portfolio Risk and Return between BHEL AND HDFC

a =103.34; b =29.48; Wa =-0.15; Wb =1.15; rab =0.65;

Xa=2130.72; Xb=952.43

p = (103.34)2*(-0.15)

2+ (29.48)

2*(1.15)

2+2(0.65) (103.34)

(29.48) (-0.15) (1.15)

= 677.58 = 26.03

Return = (2130.72*-0.15) + (952.43*1.15)

= 775.7

CONCLUSUION OF BHEL AND HDFC

As per the calculation the BHEL bears a proportion of -0.15 and where as HDFC bears a

proportion of 1.15. The expected returns of the BHEL are 2130.72and HDFC is 952.43. The

variance of the BHEL is 10680.65 and HDFC is 869.106. The standard deviation between the

companies is 103.34% for BHEL and 29.48% for HDFC.

In the combination the risk of the HDFC is less than the BHEL comparisons, therefore

investor can invest combined money or fund in HDFC where as the portfolio risk, combined risk

between two is 26.03% which is less than BHEL and HDFC. Portfolio returns between two

companies is 775.7%


53/63


54/63

2. Portfolio Risk and Return between HDFC AND BHARATI TELEVENTURES

a =29.48; b =16.56; Wa=0.17; Wb =0.83; rab =0.25;

Xa=952.43; Xb=670.95

p = (29.48)2*(0.17)

2+ (16.56)

2*(0.82)

2+2(0.25) (29.48) (16.56)

(0.17)(0.83)

= 248.86 = 15.77

Return = (952.43*0.17) + (670.95*0.83)

= 718.80

CONCLUSUION OF HDFC AND BHARATI TELEVENTURES

As per the calculation the HDFC bears a proportion of 0.17 and where as HEROHONDA

bears a proportion of 0.83. The expected returns of the HDFC are 952.43 and HEROHONDA is

670.95. The variance of the HDFC is 869.106 and HEROHONDA is 274.44. The standard

deviation between the companies is 29.48% for HDFC and 16.56% for HEROHONDA.

In the combination the risk of the HDFC is less than the BHEL comparisons, therefore

investor can invest combined money or fund in HDFC where as the portfolio risk, combined risk

between two is 15.77% which is less than HDFC and HEROHONDA. Portfolio returns between

two companies is 718.8%


55/63

3. Portfolio Risk and Return between BHARATI TELEVENTURESAND ITC

a =16.56; b =10.32; Wa =0.21; Wb =0.79; rab =0.26;

Xa=670.95; Xb=151.91

p = (16.56)2*(0.21)

2+ (10.32)

2*(0.79)

2+2(0.26) (16.56) (10.32)

(0.21)(0.79)

= 91.73 = 9.57

Return = (670.95* 0.21) + (151.91* 0.79)

= 260.8

CONCLUSUION OF BHARATI TELEVENTURESAND ITC LTD

As per the calculation the HERO HONDA bears a proportion of 0.21 and where as ITC LTD

bears a proportion of 0.79. The expected returns of the HERO HONDA are 670.95and ITC is

151.91. The variance of the HERO HONDA is 274.44 and ITC LTD is 106.65 the standard

deviation between the companies is 16.56% for HERO HONDA and 10.32% for ITC LTD.

In the combination the risk of the ITC LTD is less than the HERO HONDA comparisons,

therefore investor can invest combined money or fund in ITC LTD where as the portfolio risk,

combined risk between two is 9.57% which is less than HERO HONDA and ITC LTD. Portfolio

returns between two companies is 260.8%


56/63

4. Portfolio Risk and Return between ITC AND ICICI

a =10.32; b =24.83; Wa=0.85; Wb =0.15; rab =0.007; Xa=151.91

Xb=851.03

p = (10.32)2*(0.85)

2+ (24.83)

2*(0.15)

2+2(0.007)(10.32)(24.83)

(0.85)(0.15)

= 89.47 = 9.47

Return = (151.91*0.85) + (851.03*0.15)

= 256.77

CONCLUSUION OF ITC AND ICICI LTD

As per the calculation the ITC LTD bears a proportion of 0.85 and where as ICICI bears a

proportion of 0.15. The expected returns of the ITC LTD are 151.91and ICICI is 851.03. The

variance of the ITC LTD is 106.65 and ICICI is 616.70 the standard deviation between the

companies is 10.32% for ITC LTD and 24.83% for ICICI LTD.

In the combination the risk of the ITC LTD is less than the ICICI comparisons, therefore

investor can invest combined money or fund in ITC LTD where as the portfolio risk, combined

risk between two is 9.47% which is less than ITC LTD AND ICICI. Portfolio returns between two

companies is 256.77%


57/63

5. Portfolio Risk and Return between ICICI AND ONGC

a =24.83; b =38.22; Wa=0.93; Wb =0.07; rab =0.58;

Xa=951.03; Xb=806.36

p = (24.83)2*(0.93)

2+ (38.22)

2*(0.07)

2+2(0.58) (24.83)

(38.22)(0.93)(0.07)

= 7759.64 = 88.08

Return = (851.03*0.93) + (806.36*0.07)

= 847.8

CONCLUSUION OF ICICI AND ONGC

As per the calculation the ICICI bears a proportion of 0.93 and where as ONGC bears a

proportion of 0.07. The expected returns of the ICICI are 851.03 and ONGC is 806.36. The

variance of the ICICI is 616.70 and ONGC is 1461.33. The standard deviation between the

companies is 24.83% for ICICI and 38.22% for ONGC.

In the combination the risk of the ICICI is less than the ONGC comparisons, therefore

investor can invest combined money or fund in ICICI where as the portfolio risk, combined risk

between two is 88.08% which is less than ICICI and ONGC. Portfolio returns between two

companies is 847.8%


58/63

6. Portfolio Risk and Return between ONGC AND RELIANCE

a =38.22; b =33.49; Wa=0.25; Wb =0.75; rab =0.74;

Xa=806.36; Xb=1328.87

p = (38.22)2*(0.25)

2+ (33.49)

2*(0.75)

2+2(0.74) (38.22)

(33.49)(0.25)(0.75)

= 1075.3 = 32.79

Return = (806.36*0.25) + (1328.87*0.75)

= 1198.24

CONCLUSUION OF ONGC AND RELIANCE

As per the calculation the ONGC bears a proportion of 0.25 and where as RELIANCE bears

a proportion of 0.75. The expected returns of the ONGC are 806.36 and RELIANCE is 1328.87.

The variance of the ONGC is 1461.33 and RELIANCE is 1121.73. The standard deviation between

the companies is 38.22% for ONGC and 33.49% for RELIANCE.

In the combination the risk of the ONGC is less than the RELIANCE comparisons, therefore

investor can invest combined money or fund in ONGC where as the portfolio risk, combined risk

between two is 32.79% which is less than ONGC and RELIANCE. Portfolio returns between two



59/63

7. Portfolio Risk and Return between RELIANCE AND SBI

a =33.49; b =42.96; Wa=0.76; Wb =0.24; rab =0.56;

Xa=1328.87; Xb=983.06

p = (33.49)2*(0.76)

2+ (42.96)

2*(0.24)

2+2(0.56) (33.49)

(42.96)(0.76)(0.24)

= 1025.5 = 32.02

Return = (1328.87*0.76) + (983.06*0.24)

= 1245.8

CONCLUSUION OF RELIANCE AND SBI

As per the calculation the RELIANCE bears a proportion of 0.76 and where as SBI bears a

proportion of 0.24. The expected returns of the RELIANCE are 1328.87 and SBI is 983.06. The

variance of the RELIANCE is 1121.73 and SBI is 1846.177. The standard deviation between the

companies is 33.49% for RELIANCE and 42.96% for SBI.

In the combination the risk of the RELIANCE is less than the SBI comparisons, therefore

investor can invest combined money or fund in RELIANCE where as the portfolio risk, combined

risk between two is 32.02% which is less than RELIANCE and SBI. Portfolio returns between two



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8. Portfolio Risk and Return between SBI AND TATAMOTORS

a =42.96; b =23.80; Wa=0.08; Wb =0.92; rab =0.44;

Xa=983.06; Xb=756.8

p = (42.96)2*(0.08)

2+ (23.80)

2*(0.92)

2+2(0.44) (42.96)

(23.80)(0.08)(0.92)

= 559.5 = 23.65

Return = (983.06*0.08) + (756.87*0.92)

= 774.96

CONCLUSUION OF SBI AND TATAMOTORS

As per the calculation the SBI bears a proportion of 0.08 and where as TATAMOTORS

bears a proportion of 0.92. The expected returns of the SBI are 983.06 and TATAMOTORS is

756.87. The variance of the SBI is 1846.177 and TATAMOTORS is 566.67. The standard deviation

between the companies is 42.96% for SBI and 23.80% for TATAMOTORS.

In the combination the risk of the SBI is less than the TATAMOTORS comparisons,

therefore investor can invest combined money or fund in SBI where as the portfolio risk,

combined risk between two is 23.65% which is less than SBI and TATAMOTORS. Portfolio

returns between two companies is 774.96%


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9. Portfolio Risk and Return between TATA MOTORS AND WIPRO

a =23.80; b =14.91; Wa= -0.01; Wb =1.01; rab =0.64;

Xa=756.87; Xb=572.13

p = (23.80)2*(-0.01)

2+ (14.91)

2*(1.01)

2+2(0.64) (23.80)

(14.91)(-0.01)(1.01)

= 788.61 = 28.08

Return = (756.87*-0.01) + (572.13*1.01)

= 570.29

CONCLUSUION OF TATA MOTORS AND WIPRO

As per the calculation the TATA MOTORS bears a proportion of -0.01 and where as WIPRO

bears a proportion of 1.01. The expected returns of the TATA MOTORS are 756.87 and WIPRO is

572.13. The variance of the TATA MOTORS is 566.67 and WIPRO is 222.46. The standard

deviation between the companies is 23.26% for TATA MOTORS and 14.91% for WIPRO.

In the combination the risk of the WIPRO is less than the TATA MOTORS comparisons,

therefore investor can invest combined money or fund in WIPRO where as the portfolio risk,

combined risk between two is 28.08% which is less than TATA MOTORS and WIPRO. Portfolio

returns between two companies is 570.29%.


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PORTFOLIO RISK AND RETURNS

PORTFOLIO RISK RETURNS

BHEL & HDFC 26.03 775.7

HDFC & BHARATI TELEVENTURES 15.77 718.80

BHARATI TELEVENTURES& ITC 9.59 260.8

ITC & ICICI 9.46 256.77

ICICI & ONGC 88.08 847.8

ONGC & RELIANCE 32.79 1198.24

RELIANCE & SBI 32.02 1245.8

SBI & TATAMOTORS 23.65 774.96

TATAMOTORS & WIPRO 28.08 570.29

INTERPRETATION

The above table explains you about portfolio risk and return. Every company is related

with risk and return. If we watch these companies risk and returns, here RELIANCE and SBI

company has 32.02 risk but with high returns 1245.8. In the same way if compare ICICI and

ONGC has 88.08 risks with less return of 847.8, as a result it has more risk with less return. If we

watch another company as ITC and ICICI 9.46 risk with 256.77 returns. The middle class investor

wants low risk with high return. Because he cannot take more risk so here more investors can

prefer to ITC and ICICI Company with low risk. This portfolio risk and return table is helpful to

the investors to choose which company is better to them and how much it may be security to

their investment money.


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Date post:	08-Aug-2018
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