Oil Prices And Index

Oil Prices and 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

1/79

Oil Prices and 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

Oil Prices and 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

3/79

Oil Prices and 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

4/79

Oil Prices and 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

Oil Prices and 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

6/79

Oil Prices and 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

7/79

Oil Prices and Index

Oct-07

85.93

4,271.51

Nov-07

94.62

4,163.01

Dec-07

91.7

4,551.80

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.

8/79

Oil Prices and Index

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 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.

9/79

Oil Prices and Index

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.

Hypothesis testing:

10/79

Oil Prices and Index

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

4.799689

23.03702

11/79

Oil Prices and Index

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

We test the hypothesis at 5% level of test,

The T statistics calculated is equal to:

12/79

Oil Prices and Index

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.

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.

13/79

Oil Prices and Index

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

14/79

Oil Prices and Index

date

price per barrel

Abu Dhabi index

y2

x2

xy

Dec-05

59.43

5,202.95

15/79

Oil Prices and Index

27070689

3531.925

309211.3

Jan-06

65.51

4,646.93

21593958

4291.56

304420.4

Feb-06

61.63

16/79

Oil Prices and Index

4,503.28

20279531

3798.257

277537.1

Mar-06

62.87

4,479.46

20065562

3952.637

281623.7

Apr-06

17/79

Oil Prices and Index

69.69

3,741.40

13998074

4856.696

260738.2

May-06

70.94

3,600.15

12961080

5032.484

255394.6

18/79

Oil Prices and Index

Jun-06

70.96

3,557.00

12652249

5035.322

252404.7

Jul-06

74.41

3,417.62

11680126

5536.848

19/79

Oil Prices and Index

254305.1

Aug-06

73.05

3,596.82

12937114

5336.303

262747.7

Sep-06

63.87

3,544.14

12560928

20/79

Oil Prices and Index

4079.377

226364.2

Oct-06

58.89

3,399.12

11554017

3468.032

200174.2

Nov-06

59.15

2,974.76

21/79

Oil Prices and Index

8849197

3498.723

175957.1

Dec-06

62.06

2,999.66

8997960

3851.444

186158.9

Jan-07

54.23

22/79

Oil Prices and 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

Oil Prices and Index

60.56

2,883.67

8315553

3667.514

174635.1

Apr-07

63.96

3,052.74

9319222

4090.882

195253.3

24/79

Oil Prices and Index

May-07

63.46

3,577.52

12798649

4027.172

227029.4

Jun-07

67.48

3,544.65

12564544

4553.55

239193

25/79

Oil Prices and Index

Jul-07

74.12

3,480.37

12112975

5493.774

257965

Aug-07

72.39

3,436.81

11811663

5240.312

26/79

Oil Prices and Index

248790.7

Sep-07

79.93

3,557.74

12657514

6388.805

284370.2

Oct-07

85.93

4,271.51

18245798

27/79

Oil Prices and Index

7383.965

367050.9

Nov-07

94.62

4,163.01

17330652

8952.944

393904

Dec-07

91.7

4,551.80

28/79

Oil Prices and Index

20718883

8408.89

417400.1

total

1720.1

92,254.44

3.5E+08

120930.1

6397424

mean

68.804

29/79

Oil Prices and Index

3690.1776

30/79

Oil Prices and Index

b = (n∑xy – ∑x∑y)/ ( n ∑x2 –  (∑x)2)

31/79

Oil Prices and Index

n

25

∑x

32/79

Oil Prices and Index

1720.1

∑y

92,254.44

33/79

Oil Prices and Index

∑xy

6397424.173

∑x2

120930.0542

34/79

Oil Prices and Index

∑y2

349512566.2

35/79

Oil Prices and Index

mean x

68.804

mean y

3690.1776

36/79

Oil Prices and Index

n∑xy – ∑x∑y

1248742.076

37/79

Oil Prices and Index

n ∑x2 – (∑x)2

38/79

Oil Prices and Index

64507.345

39/79

Oil Prices and Index

b

19.35813784

40/79

Oil Prices and Index

a = mean y – mean x (b)

41/79

Oil Prices and Index

2358.260284

Index 2

x

y

42/79

Oil Prices and Index

date

price per barrel

Abu Dhabi index

x’

y’

x’2

43/79

Oil Prices and Index

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

Oil Prices and Index

Jan-06

65.51

4,646.93

-3.294

956.75

10.85044

915375.2

6.08

-556.02

Feb-06

45/79

Oil Prices and 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

-5.934

46/79

Oil Prices and Index

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

Oil Prices and Index

2623.734

6.82

-738.06

May-06

70.94

3,600.15

2.136

-90.03

4.562496

8104.969

1.25

-141.25

48/79

Oil Prices and Index

Jun-06

70.96

3,557.00

2.156

-133.18

4.648336

17736.27

0.02

-43.15

Jul-06

74.41

49/79

Oil Prices and Index

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

Oil Prices and Index

-93.36

18.02852

8715.641

-1.36

179.20

Sep-06

63.87

3,544.14

-4.934

-146.04

24.34436

21326.98

51/79

Oil Prices and Index

-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

Oil Prices and 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

Oil Prices and 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

-709.76

54/79

Oil Prices and Index

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

Oil Prices and 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

Oil Prices and Index

Apr-07

63.96

3,052.74

-4.844

-637.44

23.46434

406326.7

3.4

169.07

May-07

63.46

3,577.52

57/79

Oil Prices and Index

-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

Oil Prices and Index

1.752976

21178.28

4.02

-32.87

Jul-07

74.12

3,480.37

5.316

-209.81

28.25986

44019.23

6.64

59/79

Oil Prices and Index

-64.28

Aug-07

72.39

3,436.81

3.586

-253.37

12.8594

64195.14

-1.73

-43.56

Sep-07

60/79

Oil Prices and Index

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

Oil Prices and Index

17.126

581.33

293.2999

337947.4

6

713.77

Nov-07

94.62

4,163.01

25.816

472.83

666.4659

62/79

Oil Prices and Index

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

Oil Prices and Index

388.79

total

1720.1

92,254.44

2580.294

9077298

32.27

-651.15

mean

64/79

Oil Prices and Index

68.804

3690.178

1.344583

-27.1313

std devation

65/79

Oil Prices and Index

4.799689

308.4973

66/79

Oil Prices and Index

r2 = (b2∑x’2)/ ∑y’2

67/79

Oil Prices and Index

68/79

Oil Prices and Index

mean

stad deviation

variance

b

19.35814

69/79

Oil Prices and Index

change in price

1.344583

4.799689

23.03702

b2

374.7375

change in index

-27.1313

70/79

Oil Prices and Index

308.4973

95170.61

∑x’2

2580.294

71/79

Oil Prices and Index

∑y’2

9077298

Tc = (p –  I)/[(Sp/n)+(Si/n)]½

72/79

Oil Prices and Index

0.959876

73/79

Oil Prices and Index

r2

0.106522

3965.442

74/79

Oil Prices and Index

3966.402

62.97938

75/79

Oil Prices and Index

76/79

Oil Prices and Index

28.47583

77/79

Oil Prices and Index

0.452145

78/79

Oil Prices and Index

79/79