MATH SL Internal Assessment (IA) 2015 Correlation

The Correlation between IDR Currency and Terms of Trade of Indonesia Research Report

Candidate name: Anggiat Bright Sitorus Candidate number: 001164-0026 Subject: Mathematics Standard Level Date of Submission: 16 January 2015

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INTRODUCTION Exchange rate is commonly understood as the value of one currency in terms of another currency in the floating or fixed exchange market. Floating exchange market refers to the value of one currency determined by the supply and demand of the currency in the foreign exchange market; meanwhile on the fixed exchange market, the currency value is determined by the government ("Fixed and Floating Exchange Rates."). Exchange rates can quote a country’s currency to any other foreign currency; however, the most commonly used foreign currency is the United States Dollar (USD) as it has become the standard currency for most commodities and used in most international transactions. No exception in Indonesia, Indonesia Rupiah (IDR) is commonly paired with USD and directly quoted as USD relative to IDR. An example of this shall be 1 USD = 12,478.55 IDR. Exchange rate is endlessly monitored by people having interests in the economic and financial sectors. Many sources have explained the factors that can influence a country’s exchange rate, including factors such as differentials in inflation, interest rates, current-account deficits, public debt, the terms of trade, and political stability and economic performance (Bergen, Jason. "Factors That Influence Exchange Rates."). Relying on those factors, people have created predictions in the foreign exchange market; some predict with thorough and profound analysis of all factors and some predict by judging the movement of a single or certain factors. Both ways have their advantages and disadvantages. Judging a single factor, instead of creating a complete analysis, helps in making the rapid prediction, but with dubious accuracy. It has become important then to recognize which factor would be the best in predicting the exchange rates. Terms of Trade (TOT) is one of the factors suspected to have a momentous impact of the change in exchange rates. TOT is commonly understood as “the ratio of an index of a country’s export prices to an index of its import prices.” This refers to when a country's TOT is less than 100%; a country experiences fewer exports than imports. On the contrary, when the TOT is more than 100%, a country experiences more exports than imports ("Terms of Trade (TOT)."). The assumption is that export and import values would determine the strength of the currency of a country. When the export values are greater than import values, a country will experience appreciation. Appreciation is commonly understood as an increase in value of one currency against another currency. On the contrary, when the export values are less than import

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values, a country will experience depreciation. Depreciation is commonly understood as a decrease in value of one currency against another currency. Until now, nevertheless, very limited researches are available that observe the correlation between TOT of Indonesia and the currency value of USD relative to IDR. Knowing the significance of understanding their correlation, especially as an observer in the financial sector, it becomes valuable to find out the answer through this report. RATIONALE The rationale of this report is to recognize the correlation between Indonesia’s TOT and the exchange rate of USD relative to IDR, as well as using the Indonesia’s TOT as a predictor of the exchange rate. When there is a potent correlation between the variables, it indicates that when the TOT changes, the strength of IDR value changes as well. Similarly, when there is no potent correlation, the change in terms of TOT does not mean there will be a change in the strength of IDR value. In another way of seeing it, this shall also test the assumption whether the export and import values have any correlation with the value of a country’s currency. Having gained the result, it will be worthwhile for me to provide some advices to my surroundings in determining their investments chiefly into the foreign exchange market. The reason I chose the USD relative to IDR as a variable is because many people actively have transactions in foreign trading between IDR and USD; and the reason I chose to use TOT as a variable is, aside because it is commonly suspected to have a correlation with exchange rates, is because the data are reasonably accessible. My personal reason of choosing this topic is because this will be my early step and valuable experiences in learning more about the financial sector and the foreign exchange market in which I have a profound interest in for the future. AIM The aim of this report is to find the correlation between Indonesia’s TOT and the exchange rate of USD relative to IDR by a building linear regression model between those variables by using available data in reliable sources. This report also interprets and analyzes the model and discusses its implication in real life.

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DISCUSSION This report takes several general steps, starting with data collection and calculation continued to mapping the data in the scatter diagram to understand the data spreading. Next is to build the linear regression model using Ms. Excel software which then compared with the model built by hand using mathematical equations. Having the model, it is then continued with drawing a linear line to fit in the data and analyzing the model (including the use of the Pearson correlation to check the strength of the correlation). At the end, the error resulted by the model is then checked to test the reliability of the model. Data Collection and Calculation The data is collected online with BPS (Badan Pusat Statistik) Indonesia as the main source. The data collected range from January 2011 to September 2014, including data as below: 

Indonesia Cumulative Export Values by Month



Indonesia Cumulative Import Values by Month



Average Exchange Rate USD relative to IDR by Month

The reason data range for more than three years because the more data used, the more accurate the result will be in describing the actual condition. Nevertheless, the percentage error will be higher than the fewer data used. The TOT Index is then calculated with the below formula. The TOT index by Month can be seen in Appendix II.

Scatter Diagram From the data collection, there are two sets of data: 1) TOT index by Month and 2) average exchange rate USD relative to IDR by Month. TOT is the independent variable because the change in TOT is suspected to affect the exchange rate. Meanwhile, the exchange rate is the dependent variable because it becomes my interest to have an observation regarding whether TOT affects the exchange rate. These two sets of data are related one to another based on the Month. For instance, in January 2012, the TOT index is: 106.98 and the average exchange rate is: 9049.0065; this is then noted as (106.98, 9049.0065). All data are mapped in the scatter diagram, in this case, this made with Graphmatica as GDC.

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Figure 1. Scatter Diagram TOT vs Exchange Rate (USD-IDR).

Linear Regression Model The data are then inserted into Ms. Excel to calculate the y², x², and xy; where x is the TOT and y is the exchange rate (USD-IDR). The scatter plot and the linear regression line are depicted using the software, which resulted in a linear regression model as the following:

To prove the reliability of the equation that is given by Ms. Excel, a manual calculation is calculated by using the formula below (Stephanie."Find a Linear Regression Equation by Hand."): ; Where a is the intercept and b is the slope of the line

Where

is the sum of TOT

Where

is the sum of the exchange rate (USD-IDR)

n is the total months in the data collection

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From data collection of January 2011 to September 20141, all variables are given in the formula above. Then, the calculation of the linear regression of TOT relative to the exchange rate (USD-IDR) can be revealed. The calculations are below:

The calculation above indicates a very similar linear equation with the one provided by Ms. Excel. Hence, it can be said that the model is correct. For the way forward, the model used is the one resulted from Ms. Excel, that is: y = -56.454x + 15777. The scatter plot with the linear regression line is pictured as in the below figure.

y = -56.454x + 15777

Figure 2. Scatter Diagram with Linear Regression line.

The linear regression model is analyzed for its characteristics such as: directions, strength, outliers, and linearity. Direction - This linear regression line indicates a negative gradient or said a downward trend (Haese, R. C, “Mathematics for the International Student: Mathematics SL.”) , which determines the two variables have a negative or inverse correlation during 2011 until 2014. When the TOT

1

See Appendix III

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index increases, then the exchange rate decreases; in other words, IDR becomes stronger relative to the USD (USD becomes weaker relative to IDR) and vice versa. Strength - Judging from the diagram in Figure 2, the strength of the correlation between the two variables is moderate to weak because the points fall not so close to the linear line, especially the points at the top side of the line. To strengthen the confidence in judging the strength, a Pearson’s correlation coefficient is calculated as well. The formula and calculations are given below2:

The Pearson correlation coefficient is also acquired using Ms. Excel by using a formula which is “= Pearson (data 1, data 2)”. The result from Excel is (-0.446154935) which is similar with the result calculated manually by hand. From this result, the strength of the correlation is weak negative correlation since it is in the between of -0.5 and -0.1 which is the range of weak negative correlation (Haese, R. C. “Mathematics for the International Student: Mathematics SL.”). Outliers – As seen in Figure 2, some outliers appeared especially data located far top of the linear line, but they prove to be an authentic data, not caused by any error. Therefore, they are appropriate to be kept. The curve fit is accurate since the manual calculation and Excel are almost similar which is y= -56.4542x+ 15777.49 and y = -56.454x + 15777. Linearity - Based on the data spreading, it is suggested that the more appropriate result that would fit with the data collections is polynomial instead of linear. Linear regression line method was used to have an easy assumption and more focused into the trend direction. However, it leads to inaccurate results because other factors that affect the two variables are being ignored. Using the polynomial method is supported by the graph with a curve fit line which is made by mathematical software called “Graphmatica”.

2

See Appendix III

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Figure 3. Polynomial line TOT vs Exchange Rate (USD-IDR).

From this graph, not only the linear regression line can be relied on, but also the polynomial regression should be relied on for further analysis. It is reasonable since the exchange rates are affected by other factors that mentioned earlier in the rationale. Therefore, TOT may affect the exchange rates, but other factors may be more influential. Model Reliability Testing Using a percentage error is the best way to look for the reliability of the data collection. It compares the approximate value with the exact value by inserting the x value or TOT into the regression line function, to find the y value, the USD-IDR exchange rate. Consequently, the formula for the percentage error and the calculation is:

Below is the example of the error calculation for the year 2011. The detail calculation for the other years can be seen in Appendix IV: Year - 2011

January February March April

TOT Index (x)

116.303886 122.6846566 112.9758688 111.1901162

Approximate USD/IDR (y) y = -56.454x + 15777 9211.18042 8850.960397 9399.060304 9499.873183

Exact Value USD/IDR (y) 9034.175564 8909.759526 8758.671892 8648.658414

Percentage error (%) 2% 1% 7% 10%

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May June July August September October November December

123.3481554 121.9930352 107.4731605 123.697302 115.6521499 109.1697004 111.9629658 103.6546442

8813.503236 8890.005191 9709.710199 8793.792511 9247.973529 9613.933731 9456.242729 9925.280714

8562.544668 8560.837126 8526.018929 8526.354327 8731.185577 8860.814772 9003.017429 9051.310131

Average Percentage Error for 2011 (%)

3% 4% 14% 3% 6% 8% 5% 10% 6%

Table 1. Average Percentage Error (%) in 2011

The summary of Average Percentage Error for each year is as below. It can be seen that the average percentage error ranges from lowest 6% to highest 13%. The overall average is 9%. There might be possibility that the 13% error of 2014 could be lower considering the data collected

is

not

for

a

complete

year,

but

only

until

September

2014.

Regardless, the percentage error overall is somewhat around 9% is considered at an acceptable level. It is considerably acceptable because it only depends on the level of risk that someone is willing to absorb. If someone is a risk taker, 9 % is acceptable for them. The equation of linear regression closely behaves in real life with only 9% error per year. In addition, with small variations of percentage error between the years, it can also be concluded that the model fit quite good for each of the years. Year 2011 2012 2013 2014 Average overall

Average Percentage Error (%) 6% 9% 8% 13% 9% Table 1. Average Percentage Error (%)

However, it is also worth considering, for a specific month, the percentage error can reach up to 20% percentage error (see Appendix IV). This may also give an indication that the model sometime may not be the best model for predicting, especially considering there are also other factors aside of the TOT or export-import activities that may influence the fluctuation of the exchange rate, such as political factor and economic performance of Indonesia. It can be said that, the appropriateness of using the model depends also on the level of risk someone is willing to take.

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CONCLUSION In conclusion, having tested the correlation between TOT index and exchange rate (USDIDR) using a linear regression model, it can be said that the two variables have a negative correlation with weak to moderate strength. When the TOT index increases, then the exchange rate decreases. Through the Pearson Correlation Coefficient, the weak to moderate strength is confirmed as the r value is in between -0.5 and -0.1. It was also found that linear assumption may not be the best assumption in judging their relationship, as polynomial may fit better. The linear model that is found in this report is y = -56.454x + 15777. This model can be used to predict the value of the exchange rate (USD-IDR) by inputting the value of TOT index. This model has been tested for its percentage error using the data collected from January 2011 to September 2014. The result indicates that the model gives results in a total average of percentage error of 9%. This percentage error is considered acceptable since it depends on someone who is willing to take the risks. Therefore, it can be said that this model represents the actual condition quite well. However, on the other side, one shall be aware that TOT and the exchange rate (USDIDR) is correlated but does not mean both variables have causation. There are still other factors out there that have influences or impacts to the exchange rate (USD-IDR). REFLECTION From this report, I understood that linear regression can be used to build a model and have predictions for exchange rates. Nevertheless, there is a lack of confidence to determine the terms of trade have a huge impact on exchange rates. It is plausible, as the strength of the trend is a weak to moderate negative correlation which means although there is a correlation, it may not potentially affect the exchange rates. Furthermore, the correlation of both variables doesn’t mean they have causation. Consequently, other factors still have more impacts to exchange rates. The equation of the linear equation is reliable because it is found by using Ms. Excel calculation which is trusted as a technology that has a high accuracy. Manual calculation can be said to have an important role to prove the calculation result of Ms. Excel. Eventually, both calculation results are similar which proved that they are correct to be used. The reliability of the data can be seen through at the percentage error. The average percentage error of my data is somewhat around 9%, which indicates it is at an acceptable level. An acceptable level means my percentage error only depends on the level of risk that someone,

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who is using this model, is willing to take. That average percentage error is not determined as either low or high degree of reliability. Therefore, someone who is a risk-taker can rely on this model since they need to accept any possible results (either bad or good) that they may have by using this model. This model can be used either in short-term or long-term because it is proven by inputting data range for more than three years which indicate a better accuracy. The model of linear equation may not reveal the best results for showing the impact of exchange rates; instead, the polynomial regression line would be more vigorous with the data. Linear regression line method was used to have a simple assumption and more focused into the trend direction. However, it leads to inaccurate results because other factors that affect the two variables are being ignored. Therefore, other methods of regression are recommended to be further investigated. I have increased awareness regarding the use of correlation in real life context. This application of correlation in real life is based on the math SL syllabus and it is very beneficial in the field of economics and business. Correlation can improve the confidence of every individual to decide decisions as it increases certainty. In real life, investments are significantly vital for every individual since they become as the part of the additional or even main source of incomes. Hence, in order to be thriving in investments, especially in exchange markets, more data collection is required in order to have more certainty and accurate results. Most importantly, using a linear regression might be the basic step to reveal the meaning of the data collection. Even though it is the basic, it requires efforts such as calculating Pearson Correlation Coefficient and finding the regression line. Fortunately, Ms. Excel can be relied on. However, it needs to be proved by using a manual way since it may lead to inaccuracy. Proving can be reliable since it is used by a computer and calculator. Furthermore, proving needs to be thorough since a mistake calculation can lead to a disaster. The data should be calculated multiple times with the formulas that are familiar. From this report, some critical questions may arise such as; What if I used polynomial line best fit instead of linear best fit to analyze further the data collection? What if I used interpolation and extrapolation method for the graph to have more accurate predictions?

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Bibliography Bergen, Jason. "Factors That Influence Exchange Rates." FInvestopedia, 04 May 2004. Web. 05 Jan. 2015. < http://www.investopedia.com/articles/basics/04/050704.asp>. "Converter USD in Terms of IDR Exchange Rate." X-rates.com, n.d. Web. 06 Jan. 2015. . "Fixed and Floating Exchange Rates." Tutor2u, n.d. Web. 06 Jan. 2015. . Haese, R. C. “Mathematics for the International Student: Mathematics SL.”Adelaide Airport, S. Aust.: Haese Mathematics, 2012. Print. "Indonesia Exports-Imports." Badan Pusat Statistik, n.d. Web. 6 Jan. 2015. . Stephanie. "Find a Linear Regression Equation by Hand." StatisticsHowTo, n.d. Web. 09 Jan. 2015. . "Terms of Trade (TOT)." Investopedia, 24 Feb. 2010. Web. 06 Jan. 2015. .

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APPENDIX: I: DATA OF INDONESIA CUMMULATIVE EXPORT AND IMPORT IN 2011-2014 AND IDR EXCHANGE RATE No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Year

2011

2012

2013

2014

Month January February March April May June July August September October November December January February March April May June July August September October November December January February March April May June July August September October November

Value of Export (US$) 14,606,249,454 14,415,278,398 16,365,953,469 16,554,240,767 18,287,435,825 18,386,855,403 17,418,472,565 18,647,825,151 17,543,408,243 16,957,743,283 17,235,463,273 17,077,694,229 15,570,069,320 15,695,443,242 17,251,519,437 16,173,190,978 16,829,545,550 15,441,457,938 16,090,595,299 14,047,007,385 15,898,115,717 15,324,042,715 16,316,911,273 15,393,946,390 15,375,487,902 15,015,627,735 15,024,577,683 14,760,892,129 16,133,358,194 14,758,819,151 15,087,863,565 13,083,707,039 14,706,775,080 15,698,330,394 15,938,557,641

Value of Import (US$) 12,558,694,259 11,749,862,451 14,486,238,209 14,888,230,483 14,825,868,915 15,072,053,394 16,207,276,766 15,075,369,345 15,169,115,540 15,533,378,964 15,393,896,679 16,475,570,731 14,554,618,780 14,866,785,109 16,325,662,478 16,937,875,721 17,036,735,320 16,727,521,763 16,354,450,283 13,813,875,810 15,348,557,469 17,207,931,360 16,935,009,726 15,581,977,290 15,450,235,320 15,313,286,233 14,887,075,645 16,463,468,844 16,660,559,292 15,636,019,963 17,416,991,671 13,012,045,835 15,509,774,940 15,674,021,743 15,149,325,413

USD/IDR 9034.1756 8909.7595 8758.6719 8648.6584 8562.5447 8560.8371 8526.0189 8526.3543 8731.1856 8860.8148 9003.0174 9051.3101 9049.0065 9008.1915 9140.8020 9158.9418 9268.8984 9415.9986 9433.9247 9488.2893 9548.5414 9597.6121 9617.1683 9642.3812 9656.7843 9682.5440 9706.4351 9722.8320 9752.2900 9875.2500 10087.4700 10601.1300 11309.2400 11141.3600 11473.0700

December January February March April May June

16,967,798,188 14,472,285,648 14,634,090,390 15,192,634,701 14,292,472,554 14,823,602,661 15,409,451,765

15,455,864,981 14,916,227,693 13,790,661,990 14,523,719,412 16,254,976,317 14,770,336,777 15,697,742,441

12020.9700 12044.6281 11832.5100 11420.1139 11433.3900 11523.6116 11888.9032

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July August September

14,124,129,298 14,481,642,319 15,275,846,089

14,081,710,235 14,793,236,965 15,546,096,309

11687.5300 11721.2600 11918.3900

II: TERMS OF TRADE (EXPORT PRICES/IMPORT PRICES) X 100 No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Year

2011

2012

2013

2014

Month January February March April May June July August September October November December January February March April May June July August September October November December January February March April May June July August September October November December January February March April May

Terms of Trade Index 116.30 122.68 112.98 111.19 123.35 121.99 107.47 123.70 115.65 109.17 111.96 103.65 106.98 105.57 105.67 95.49 98.78 92.31 98.39 101.69 103.58 89.05 96.35 98.79 99.52 98.06 100.92 89.66 96.84 94.39 86.63 100.55 94.82 100.16 105.21 109.78 97.02 106.12 104.61 87.93 100.36

42 43 44 45

June July August September

98.16 100.30 97.89 98.26

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III: SUM, AVERAGE, PEARSONS VALUE OF TOT AND EXCHANGE RATE (USD-IDR) IN 2011-2014 No

Year 1

Terms of Trade Index (x)

USD/IDR (y)

y^2

x^2

x*y

January

116.303886

9034.175564

81616328.12

13526.59

1050709.72

2

February

122.6846566

8909.759526

79383814.81

15051.52

1093090.79

3

March

112.9758688

8758.671892

76714333.31

12763.55

989518.566

4

April

111.1901162

8648.658414

74799292.36

12363.24

961645.334

5

May

123.3481554

8562.544668

73317171.19

15214.77

1056174.09

6

June

121.9930352

8560.837126

73287932.3

14882.3

1044362.5

7

July

107.4731605

8526.018929

72692998.78

11550.48

916318.2

8

August

123.697302

8526.354327

72698718.11

15301.02

1054687.03

9

September

115.6521499

8731.185577

76233601.58

13375.42

1009780.38

10

October

109.1697004

8860.814772

78514038.42

11918.02

967332.494

11

November

111.9629658

9003.017429

81054322.83

12535.71

1008004.53

12

December

103.6546442

9051.310131

81926215.09

10744.29

938210.332

January

106.9768268

9049.006473

81884518.15

11444.04

968033.998

14

February

105.5738892

9008.191501

81147514.12

11145.85

951029.812

15

March

105.6711754

9140.802029

83554261.73

11166.4

965919.295

16

April

95.48535628

9158.941819

83886215.24

9117.453

874544.823

17

May

98.7838646

9268.898428

85912478.07

9758.252

915617.607

18

June

92.31168942

9415.998636

88661030.31

8521.448

869206.742

19

July

98.38664719

9433.924691

88998935.08

9679.932

928172.22

20

August

101.6876623

9488.289321

90027634.24

10340.38

964841.96

21

September

103.5805205

9548.541376

91174642.41

10728.92

989042.886

22

October

89.05220735

9597.612058

92114157.22

7930.296

854688.539

23

November

96.35017362

9617.168279

92489925.71

9283.356

926615.833

24

December

98.79327959

9642.381192

92975515.05

9760.112

952602.461

January

99.51620531

9656.784295

93253482.92

9903.475

961006.529

26

February

98.05620757

9682.543998

93751658.27

9615.02

949433.544

27

March

100.9236336

9706.4351

94214882.35

10185.58

979608.7

28

April

89.65845697

9722.832019

94533462.47

8038.639

871734.116

29

May

96.83563385

9752.29

95107160.24

9377.14

944369.184

30

June

94.3898715

9875.25

97520562.56

8909.448

932123.579

31

July

86.6272652

10087.47

101757051

7504.283

873849.939

32

August

100.5507297

10601.13

112383957.3

10110.45

1065951.36

33

September

94.82262081

11309.24

127898909.4

8991.329

1072371.78

34

October

100.1550888

11141.36

124129902.6

10031.04

1115863.9

13

25

2011

Month

2012

2013

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35

November

105.2096856

11473.07

131631335.2

11069.08

1207078.09

36

December

109.782262

12020.97

144503719.7

12052.15

1319689.28

January

97.02376463

12044.62807

145073065.2

9413.611

1168615.16

38

February

106.1159385

11832.51

140008292.9

11260.59

1255617.9

39

March

104.6056748

11420.11391

130419001.7

10942.35

1194608.72

40

April

87.92675102

11433.39

130722406.9

7731.114

1005300.84

41

May

100.3606274

11523.61156

132793623.5

10072.26

1156516.89

42

June

98.16348958

11888.90322

141346019.7

9636.071

1167056.23

43

July

100.3012352

11687.53

136598357.5

10060.34

1172273.7

44

August

97.89366826

11721.26

137387936

9583.17

1147437.14

45

September

98.26162006

11918.39

142048020.2

9655.346

1171120.31

Sum

4639.939364

448042.8163

4522148402

482245.8

45981777

Average

103.1097636

9956.507029

Pearson

-0.446154935

37

2014

IV. Percentage Error in 2012-2014 y = -56.454x + 15777 2012

2013

Terms of Trade Index (x)

Approximate USD/IDR (y)

Exact Value USD/IDR (y)

Percentage error (%)

January

106.9768268

9737.730221

9049.006473

8%

February

105.5738892

9816.931658

9008.191501

9%

March

105.6711754

9811.439462

9140.802029

7%

April

95.48535628

10386.4697

9158.941819

13%

May

98.7838646

10200.25571

9268.898428

10%

June

92.31168942

10565.63589

9415.998636

12%

July

98.38664719

10222.68022

9433.924691

8%

August

101.6876623

10036.32471

9488.289321

6%

September

103.5805205

9929.465295

9548.541376

4%

October

89.05220735

10749.64669

9597.612058

12%

November

96.35017362

10337.6473

9617.168279

7%

December

98.79327959

10199.72419

9642.381192

6%

Average

99.38777436

10166.16259

9364.146317

9%

January

99.51620531

10158.91215

9656.784295

5%

February

98.05620757

10241.33486

9682.543998

6%

March

100.9236336

10079.45719

9706.4351

4%

April

89.65845697

10715.42147

9722.832019

10%

May

96.83563385

10310.24113

9752.29

6%

June

94.3898715

10448.31419

9875.25

6%

July

86.6272652

10886.54437

10087.47

8%

Sitorus 17

2014

August

100.5507297

10100.5091

10601.13

5%

September

94.82262081

10423.88376

11309.24

8%

October

100.1550888

10122.84462

11141.36

9%

November

105.2096856

9837.492408

11473.07

14%

December

109.782262

9579.352181

12020.97

20%

Average

98.04397175

10242.02562

10419.11462

8%

January

97.02376463

10299.62039

12044.62807

14%

February

106.1159385

9786.33081

11832.51

17%

March

104.6056748

9871.591233

11420.11391

14%

April

87.92675102

10813.1832

11433.39

5%

May

100.3606274

10111.24114

11523.61156

12%

June

98.16348958

10235.27836

11888.90322

14%

July

100.3012352

10114.59407

11687.53

13%

August

97.89366826

10250.51085

11721.26

13%

September

98.26162006

10229.7385

11918.39

14%

Average

98.96141882

10190.23206

11718.92631

13%