Changes In Price Per Barrel And The Abu Dhabi Index

Changes in Price Per Barrel and the Abu Dhabi Index

Introduction:

This paper analysis the relationship between the changes in price per barrel and the Abu Dhabi index, changes in oil prices have led to changes in the index which is a combination of indexes from the industrial sector, service sector and the banking center. We retrieve the data regarding oil prices from http://www.economagic.com/em-cgi/data.exe/feddal/oilp+1 and the data regarding Abu Dhabi index is retrieved from www.adx.ae, series data from December 2005 and December 2007 was collected which would aid in this analysis.

Data collected:

Data collected from both websites is as follows starting from December 2005 to December 2007; the following table represents the data:

date

price per barrel

Abu Dhabi index

Dec-05

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Changes in Price Per Barrel and the Abu Dhabi Index

59.43

5,202.95

Jan-06

65.51

4,646.93

Feb-06

61.63

4,503.28

Mar-06

62.87

4,479.46

2/79

Changes in Price Per Barrel and the Abu Dhabi Index

Apr-06

69.69

3,741.40

May-06

70.94

3,600.15

Jun-06

70.96

3,557.00

Jul-06

74.41

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Changes in Price Per Barrel and the Abu Dhabi Index

3,417.62

Aug-06

73.05

3,596.82

Sep-06

63.87

3,544.14

Oct-06

58.89

3,399.12

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Changes in Price Per Barrel and the Abu Dhabi Index

Nov-06

59.15

2,974.76

Dec-06

62.06

2,999.66

Jan-07

54.23

2,980.42

Feb-07

59.26

5/79

Changes in Price Per Barrel and the Abu Dhabi Index

3,090.91

Mar-07

60.56

2,883.67

Apr-07

63.96

3,052.74

May-07

63.46

3,577.52

Jun-07

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Changes in Price Per Barrel and the Abu Dhabi Index

67.48

3,544.65

Jul-07

74.12

3,480.37

Aug-07

72.39

3,436.81

Sep-07

79.93

3,557.74

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Changes in Price Per Barrel and the Abu Dhabi Index

Oct-07

85.93

4,271.51

Nov-07

94.62

4,163.01

Dec-07

91.7

4,551.80

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Changes in Price Per Barrel and the Abu Dhabi Index

The above data will then help us to analyze the changes in oil prices and the index and therefore establish the relationship between the two variables.

Below is a graphical representation of the data:

The chart below shows the Abu Dhabi index from the year December 2005 to December 2007

From the above chart it is evident that there has been a gradual decline in the index over the years until December 2006 where the index starts to rise gradually.

The chart below shows the changes in price over time, it is evident that the prices have risen over the past two years although there has been slight decline and increases in the prices; however the chart shows a gradual increase in price per barrel.

Regression analysis:

We perform regression analysis on the two variables; we investigate whether there is a relationship between the change in oil prices and the performance of Abu Dhabi index performance. We first represent the data in a scatter diagram as follows which includes a line of best fit:

From the above line of best fit in the chart it is clear that as oil prices increase then the index

performance improves and therefore we conclude that an increase in the price per barrel will

improve the performance of the Abu  Dhabi index. We now perform a regression analysis to

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Changes in Price Per Barrel and the Abu Dhabi Index

check the relationship between prices and the index; in this case the prices become the independent variable while the index becomes the dependent variable. The estimation process can be found in index 1.

We are estimating a model of the form Y = a + bx

Where y is the dependent variable which in this case is the index while x is the independent variable which in this case is price of oil per barrel, we us the formula

b = (n∑xy – ∑x∑y)/ ( n ∑x2 – (∑x)2) to estimate the slope and a = mean y – mean x (b) to estimate the autonomous value

After estimating the results of the model is as follows:

Y = 2358.260284 + 19.35813784 X

From the above model we interpret the results for the slope as follows, an increase in the price per barrel by one unit holding all other factors constant will increase the Abu index by 19.35 units, also if the price per barrel declines by one unit and we hold all other factors constant then the Abu index will decline by 19.35 units.

For the constant we interpret the results as follows, if we hold all other factors constant and the price per barrel is zero then the Abu index value will be equal to 2358 units approximately, this shows that the constant value is zero and at the same time the two variables have positive correlation, meaning that an increase in price per barrel of oil will increase the performance of the index.

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Changes in Price Per Barrel and the Abu Dhabi Index

Hypothesis testing:

We now check the validity of the statement that the change in oil prices per barrel is greater than the change in the Abu index, to test this hypothesis we have to get the changes for each series of data and then get their mean change and also the standard deviation that will help in hypothesis testing:

After calculation of the mean changes and the standard deviation the following were the results:

mean

standard deviation

variance

change in price (p)

1.344583

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Changes in Price Per Barrel and the Abu Dhabi Index

4.799689

23.03702

change in index(I)

-27.1313

308.4973

95170.61

We test the following hypothesis:

Null hypothesis

H0:P=I

Alternative hypothesis:

Ha: P > I

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Changes in Price Per Barrel and the Abu Dhabi Index

We test the hypothesis at 5% level of test,

The T statistics calculated is equal to:

Tc = (p – I)/[(Sp/n)+(Si/n)]½

Where sp is the variance of change in price and si is the variance of change in index and n is the sample size, the results are as follows

Tc = (1.344583 – -27.1313)/[( 23.03702/24)+( 95170.61/24)]½

Tc = 0.452145

From the Z tables at 5% level of test the value is less than the calculated value, because the critical value is less than the calculated value 0.452145 we reject the null hypothesis that changes in price of oil is equal to changes in the Abu index.

Following the rejection of our null hypothesis we conclude that an increase in the level of prices per barrel is greater than the increase in the index performance of Abu Dhabi, for this reason therefore we also find out that the correlation of determination value is 0.106522; this shows that 10.65% of deviations in Abu index are explained by the changes in prices, this also means that 89% of deviations in the Abu index are explained by other variables.

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Changes in Price Per Barrel and the Abu Dhabi Index

Conclusion:

From the above analysis it is evident that a change in the price per barrel will improve the performance of the Index, however it is evident from the R squared value that only 10% of changes in the Index are attributed to changes in the price per barrel.

Further analysis show that the change in prices per barrel is greater than the change in Index performance, using this I recommend that oil selling countries and companies should not increase oil prices for the reason of improving their Index performance in other industry, this is evident from the above analysis that when an increase in price of oil occurs then the index only improves by a small portion.

References:

Abu Dhabi website, price index for abu Dhabi from the year December 2005 to December 2007, this page is available at www.adx.ae

Economic magic website, oil prices from the year December 2005 to December 2007, this page is available at www.economagic.com/em-cgi/data.exe/feddal/oilp+1

Index 1

x

y

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Changes in Price Per Barrel and the Abu Dhabi Index

date

price per barrel

Abu Dhabi index

y2

x2

xy

Dec-05

59.43

15/79

Changes in Price Per Barrel and the Abu Dhabi Index

5,202.95

27070689

3531.925

309211.3

Jan-06

65.51

4,646.93

21593958

4291.56

304420.4

Feb-06

16/79

Changes in Price Per Barrel and the Abu Dhabi Index

61.63

4,503.28

20279531

3798.257

277537.1

Mar-06

62.87

4,479.46

20065562

3952.637

281623.7

17/79

Changes in Price Per Barrel and the Abu Dhabi Index

Apr-06

69.69

3,741.40

13998074

4856.696

260738.2

May-06

70.94

3,600.15

12961080

5032.484

255394.6

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Changes in Price Per Barrel and the Abu Dhabi Index

Jun-06

70.96

3,557.00

12652249

5035.322

252404.7

Jul-06

74.41

3,417.62

11680126

5536.848

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Changes in Price Per Barrel and the Abu Dhabi Index

254305.1

Aug-06

73.05

3,596.82

12937114

5336.303

262747.7

Sep-06

63.87

3,544.14

12560928

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Changes in Price Per Barrel and the Abu Dhabi Index

4079.377

226364.2

Oct-06

58.89

3,399.12

11554017

3468.032

200174.2

Nov-06

59.15

2,974.76

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Changes in Price Per Barrel and the Abu Dhabi Index

8849197

3498.723

175957.1

Dec-06

62.06

2,999.66

8997960

3851.444

186158.9

Jan-07

54.23

22/79

Changes in Price Per Barrel and the Abu Dhabi Index

2,980.42

8882903

2940.893

161628.2

Feb-07

59.26

3,090.91

9553725

3511.748

183167.3

Mar-07

23/79

Changes in Price Per Barrel and the Abu Dhabi Index

60.56

2,883.67

8315553

3667.514

174635.1

Apr-07

63.96

3,052.74

9319222

4090.882

195253.3

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Changes in Price Per Barrel and the Abu Dhabi Index

May-07

63.46

3,577.52

12798649

4027.172

227029.4

Jun-07

67.48

3,544.65

12564544

4553.55

25/79

Changes in Price Per Barrel and the Abu Dhabi Index

239193

Jul-07

74.12

3,480.37

12112975

5493.774

257965

Aug-07

72.39

3,436.81

11811663

26/79

Changes in Price Per Barrel and the Abu Dhabi Index

5240.312

248790.7

Sep-07

79.93

3,557.74

12657514

6388.805

284370.2

Oct-07

85.93

4,271.51

27/79

Changes in Price Per Barrel and the Abu Dhabi Index

18245798

7383.965

367050.9

Nov-07

94.62

4,163.01

17330652

8952.944

393904

Dec-07

91.7

28/79

Changes in Price Per Barrel and the Abu Dhabi Index

4,551.80

20718883

8408.89

417400.1

total

1720.1

92,254.44

3.5E+08

120930.1

6397424

mean

29/79

Changes in Price Per Barrel and the Abu Dhabi Index

68.804

3690.1776

30/79

Changes in Price Per Barrel and the Abu Dhabi Index

b = (n∑xy – ∑x∑y)/ ( n ∑x2 –  (∑x)2)

31/79

Changes in Price Per Barrel and the Abu Dhabi Index

n

25

32/79

Changes in Price Per Barrel and the Abu Dhabi Index

∑x

1720.1

∑y

92,254.44

33/79

Changes in Price Per Barrel and the Abu Dhabi Index

∑xy

6397424.173

∑x2

120930.0542

34/79

Changes in Price Per Barrel and the Abu Dhabi Index

∑y2

349512566.2

35/79

Changes in Price Per Barrel and the Abu Dhabi Index

mean x

68.804

mean y

3690.1776

36/79

Changes in Price Per Barrel and the Abu Dhabi Index

n∑xy – ∑x∑y

1248742.076

37/79

Changes in Price Per Barrel and the Abu Dhabi Index

n ∑x2 – (∑x)2

38/79

Changes in Price Per Barrel and the Abu Dhabi Index

64507.345

39/79

Changes in Price Per Barrel and the Abu Dhabi Index

b

19.35813784

40/79

Changes in Price Per Barrel and the Abu Dhabi Index

a = mean y – mean x (b)

41/79

Changes in Price Per Barrel and the Abu Dhabi Index

2358.260284

Index 2

x

y

42/79

Changes in Price Per Barrel and the Abu Dhabi Index

date

price per barrel

Abu Dhabi index

x’

y’

43/79

Changes in Price Per Barrel and the Abu Dhabi Index

x’2

y’2

change in price

change in index

Dec-05

59.43

5,202.95

-9.374

1,512.77

87.87188

2288480

44/79

Changes in Price Per Barrel and the Abu Dhabi Index

Jan-06

65.51

4,646.93

-3.294

956.75

10.85044

915375.2

6.08

-556.02

Feb-06

45/79

Changes in Price Per Barrel and the Abu Dhabi Index

61.63

4,503.28

-7.174

813.10

51.46628

661135.5

-3.88

-143.65

Mar-06

62.87

4,479.46

46/79

Changes in Price Per Barrel and the Abu Dhabi Index

-5.934

789.28

35.21236

622966.7

1.24

-23.82

Apr-06

69.69

3,741.40

0.886

51.22

0.784996

47/79

Changes in Price Per Barrel and the Abu Dhabi Index

2623.734

6.82

-738.06

May-06

70.94

3,600.15

2.136

-90.03

4.562496

8104.969

1.25

48/79

Changes in Price Per Barrel and the Abu Dhabi Index

-141.25

Jun-06

70.96

3,557.00

2.156

-133.18

4.648336

17736.27

0.02

-43.15

Jul-06

49/79

Changes in Price Per Barrel and the Abu Dhabi Index

74.41

3,417.62

5.606

-272.56

31.42724

74287.65

3.45

-139.38

Aug-06

73.05

3,596.82

4.246

50/79

Changes in Price Per Barrel and the Abu Dhabi Index

-93.36

18.02852

8715.641

-1.36

179.20

Sep-06

63.87

3,544.14

-4.934

-146.04

24.34436

51/79

Changes in Price Per Barrel and the Abu Dhabi Index

21326.98

-9.18

-52.68

Oct-06

58.89

3,399.12

-9.914

-291.06

98.2874

84714.53

-4.98

-145.02

52/79

Changes in Price Per Barrel and the Abu Dhabi Index

Nov-06

59.15

2,974.76

-9.654

-715.42

93.19972

511822.3

0.26

-424.36

Dec-06

62.06

53/79

Changes in Price Per Barrel and the Abu Dhabi Index

2,999.66

-6.744

-690.52

45.48154

476814.6

2.91

24.90

Jan-07

54.23

2,980.42

-14.574

54/79

Changes in Price Per Barrel and the Abu Dhabi Index

-709.76

212.4015

503755.9

-7.83

-19.24

Feb-07

59.26

3,090.91

-9.544

-599.27

91.08794

359121.7

55/79

Changes in Price Per Barrel and the Abu Dhabi Index

5.03

110.49

Mar-07

60.56

2,883.67

-8.244

-806.51

67.96354

650454.5

1.3

-207.24

56/79

Changes in Price Per Barrel and the Abu Dhabi Index

Apr-07

63.96

3,052.74

-4.844

-637.44

23.46434

406326.7

3.4

169.07

May-07

63.46

57/79

Changes in Price Per Barrel and the Abu Dhabi Index

3,577.52

-5.344

-112.66

28.55834

12691.73

-0.5

524.78

Jun-07

67.48

3,544.65

-1.324

-145.53

58/79

Changes in Price Per Barrel and the Abu Dhabi Index

1.752976

21178.28

4.02

-32.87

Jul-07

74.12

3,480.37

5.316

-209.81

28.25986

44019.23

59/79

Changes in Price Per Barrel and the Abu Dhabi Index

6.64

-64.28

Aug-07

72.39

3,436.81

3.586

-253.37

12.8594

64195.14

-1.73

-43.56

60/79

Changes in Price Per Barrel and the Abu Dhabi Index

Sep-07

79.93

3,557.74

11.126

-132.44

123.7879

17539.72

7.54

120.93

Oct-07

85.93

4,271.51

61/79

Changes in Price Per Barrel and the Abu Dhabi Index

17.126

581.33

293.2999

337947.4

6

713.77

Nov-07

94.62

4,163.01

25.816

472.83

62/79

Changes in Price Per Barrel and the Abu Dhabi Index

666.4659

223570.5

8.69

-108.50

Dec-07

91.7

4,551.80

22.896

861.62

524.2268

742393.2

-2.92

63/79

Changes in Price Per Barrel and the Abu Dhabi Index

388.79

total

1720.1

92,254.44

2580.294

9077298

32.27

-651.15

mean

64/79

Changes in Price Per Barrel and the Abu Dhabi Index

68.804

3690.178

1.344583

-27.1313

std devation

65/79

Changes in Price Per Barrel and the Abu Dhabi Index

4.799689

308.4973

66/79

Changes in Price Per Barrel and the Abu Dhabi Index

r2 = (b2∑x’2)/ ∑y’2

67/79

Changes in Price Per Barrel and the Abu Dhabi Index

68/79

Changes in Price Per Barrel and the Abu Dhabi Index

mean

stad deviation

variance

b

19.35814

69/79

Changes in Price Per Barrel and the Abu Dhabi Index

change in price

1.344583

4.799689

23.03702

b2

374.7375

change in index

70/79

Changes in Price Per Barrel and the Abu Dhabi Index

-27.1313

308.4973

95170.61

∑x’2

2580.294

71/79

Changes in Price Per Barrel and the Abu Dhabi Index

∑y’2

9077298

Tc = (p –  I)/[(Sp/n)+(Si/n)]½

72/79

Changes in Price Per Barrel and the Abu Dhabi Index

0.959876

73/79

Changes in Price Per Barrel and the Abu Dhabi Index

r2

0.106522

3965.442

74/79

Changes in Price Per Barrel and the Abu Dhabi Index

3966.402

62.97938

75/79

Changes in Price Per Barrel and the Abu Dhabi Index

76/79

Changes in Price Per Barrel and the Abu Dhabi Index

28.47583

77/79

Changes in Price Per Barrel and the Abu Dhabi Index

0.452145

78/79

Changes in Price Per Barrel and the Abu Dhabi Index

79/79