Econometrics Modeling

Developing and analyzing an econometric model Business Statistics Satrajit Chakraborty PGP-1 Sec-2 Roll No - 2008247

Analysis of share prices based on macroeconomic factors using Classical Linear Regression Model (CLRM) For the purpose of the study, the general macroeconomic theory has been used, which tries to find out the effect of inflation and foreign portfolio investments (FII) on company’s performance and how these two factors, coupled with market and sector-specific factors affect the share price of a company. Here, share prices of 5 banking stocks have been selected for analysis from April 2003 to March 2008 and the CLRM has been used, which tries to fit a linear least square regression estimate between the dependant and independent variable. The results are then analyzed using EViews. The independent variables are: a) Index values of the BSE BANKEX INDEX over the time period. The base date for BANKEX is 1st January 2002. The base value for BANKEX is 1000 points. BSE has calculated the historical index values of BANKEX since 1st January 2002. b) Inflation rate based on Wholesale Price Index (WPI) of all commodities. WPI Base Year 1993-94 = 100. c) Cash Reserve Ratio, a statutory regulation set by RBI on Indian banks regarding minimum reserves each bank must hold to customer deposits and notes to satisfy withdrawal demands. d) Net FII investments in Indian equity market over the time period to see how major FII contributions towards share price fluctuations in India are. The variables in the model are selected based on the relevance and importance of regulatory and market factors which might affect share prices in banking sector in the long run. The result is then analyzed using Econometric software package to see how much each factor in this model actually influences the share price of each of the companies and what are the limitations of this model and the data used. The 5 companies taken are STATE BANK OF INDIA (SBI), ICICI BANK (ICICI), HDFC BANK (HDFC), AXIS BANK (AXIS) and PUNJAB NATIONAL BANK (PNB).

2

Data used for the analysis WPI

CRR

FII

118.20

BANKE X 1392.79

173.10

4.75

430.30

52.25

179.40

1656.36

173.40

4.75

1220.80

258.95 266.55 275.45 275.15 316.35 302.45 366.65 344.70 374.55 378.35 375.90

48.70 80.15 73.30 71.20 74.75 83.75 135.15 160.35 140.50 146.75 155.15

155.10 169.65 171.90 186.55 202.80 184.70 241.35 257.30 242.95 333.90 375.10

1731.61 1872.26 2020.88 2137.87 2444.47 2379.06 2799.04 2828.55 2805.67 2992.90 3188.07

173.50 173.40 173.70 175.60 176.10 176.90 176.80 178.70 179.80 179.80 180.90

4.75 4.50 4.50 4.50 4.50 4.50 4.50 4.50 4.50 4.50 4.50

230.35

352.55

107.60

261.45

2382.42

182.10

4.50

430.65 441.95 442.85 468.20 447.35 529.70 652.45 642.80 714.40 656.95 584.80

244.40 266.80 269.45 286.05 299.00 340.20 370.75 360.60 380.75 393.00 360.20

369.70 374.80 367.40 402.85 414.35 495.30 518.85 564.40 586.90 544.25 537.20

129.60 127.60 119.05 129.95 152.50 166.50 185.20 206.20 241.05 242.05 230.10

281.95 267.45 265.10 259.45 245.05 348.50 405.20 408.25 457.90 393.30 346.20

2431.33 2539.53 2536.41 2719.17 2736.61 3263.40 3721.97 3670.63 3916.46 3847.96 3504.33

185.20 186.60 188.40 189.40 188.90 190.20 188.80 188.60 188.80 189.40 191.60

4.50 4.50 4.50 4.50 5.00 5.00 5.00 5.00 5.00 5.00 5.00

670.70

392.05

540.05

239.80

381.70

3803.40

192.10

5.00

681.55 800.80 796.65 938.60

421.55 536.00 481.70 600.35

634.10 685.50 640.15 687.55

247.15 259.90 250.00 265.50

379.90 424.65 401.15 450.55

4014.42 4764.91 4468.51 5125.01

193.20 194.60 195.30 197.20

5.00 5.00 5.00 5.00

Oct-05

838.25

497.70

606.00

238.30

404.95

4425.36

197.80

5.00

Nov-05 Dec-05

896.25 907.45

537.15 584.70

687.55 707.45

271.40 286.35

436.10 466.35

4789.72 5081.71

198.20 197.20

5.00 5.00

2581.70 2346.50 2091.30 3851.30 6797.50 3300.50 6161.10 3176.80 2397.50 5604.40 7638.20 3246.90 516.40 913.60 2892.30 2385.60 3263.30 6740.80 6683.80 457.10 8369.00 7502.20 -654.10 1140.10 5328.60 7934.10 5051.20 4646.80 3693.90 4038.70 9335.00

DATE

SBI

ICICI

HDFC

AXIS

PNB

Apr-03 May03 Jun-03 Jul-03 Aug-03 Sep-03 Oct-03 Nov-03 Dec-03 Jan-04 Feb-04 Mar-04 Apr-04 May04 Jun-04 Jul-04 Aug-04 Sep-04 Oct-04 Nov-04 Dec-04 Jan-05 Feb-05 Mar-05 Apr-05 May05 Jun-05 Jul-05 Aug-05 Sep-05

278.55

121.40

246.35

44.35

352.30

137.65

245.05

384.20 421.85 439.25 451.60 484.20 470.75 538.50 595.80 585.30 605.70 642.60

150.20 158.60 179.50 204.35 248.10 249.90 295.70 295.25 271.80 295.90 315.20

465.00

3

Jan-06 Feb-06 Mar-06 Apr-06 May06 Jun-06 Jul-06 Aug-06 Sep-06 Oct-06 Nov-06 Dec-06 Jan-07 Feb-07 Mar-07 Apr-07 May07 Jun-07 Jul-07 Aug-07 Sep-07 Oct-07 Nov-07 Dec-07 Jan-08 Feb-08 Mar-08

886.80 877.20 968.05 913.65

609.15 615.10 589.25 590.25

762.55 736.05 773.50 826.60

337.15 328.35 356.35 347.05

465.55 441.30 471.20 433.05

5254.89 5204.69 5265.24 5245.79

196.30 196.40 196.80 199.00

5.00 5.00 5.00 5.00

831.00

536.05

740.20

285.80

405.40

4769.87

201.30

5.00

727.40 810.05 930.00 1028.3 0 1095.5 0 1314.0 0 1245.9 0 1138.0 5 1039.1 5

487.40 554.05 596.50

791.15 795.05 853.15

266.75 297.85 342.90

325.55 380.20 469.75

4348.79 4781.14 5308.01

203.10 204.00 205.30

5.00 5.00 5.00

3677.60 7204.00 6688.80 521.90 7354.20 479.50 1145.20 4643.10

699.05

926.00

379.20

526.20

6038.87

207.80

5.00

5424.70

433.75

518.45

6484.06

208.70

5.00

8013.10

474.05

544.75

7179.71

209.10

5.00

9380.10

469.05

506.95

7085.73

208.40

5.00

3667.40

534.00

508.15

7260.09

208.80

5.50

492.10

992.90 1105.2 5 1352.4 0 1525.3 0 1624.5 0 1599.5 0 1950.7 0 2068.1 5 2300.3 0 2371.0 0 2162.2 5 2109.7 0 1598.8 5

776.85 871.45 890.40 940.50

1004.0 5 1118.4 0 1069.7 5 1078.1 5

831.90

932.60

460.00

424.25

6408.01

208.90

5.50

7655.30

853.10

949.40

490.15

471.65

6542.01

209.80

6.00

1082.00

467.85

503.40

6882.89

211.50

6.00

6679.20

579.55

536.35

7607.35

212.30

6.50

3959.70

605.00

539.80

8009.94

212.30

6.50

1643.10

626.70

514.75

8148.68

213.60

6.50

634.10

484.30

7858.79

213.80

7.00

764.40

542.70

9469.26

215.10

7.00

918.80

525.70

10655.33

215.20

7.00

931.25

601.85

10870.88

215.90

7.50

967.10

664.35

11418.00

216.40

7.50

5579.10

648.60

10713.91

218.10

7.50

-611.40

604.15

10113.73

219.90

7.50

2262.60

508.15

7717.61

225.50

7.50

-130.40

865.90 918.90 955.30 927.05 884.65 1063.1 5 1257.0 0 1184.6 5 1232.4 0 1145.6 5 1090.9 5 770.10

1026.1 5 1139.7 5 1144.1 0 1198.6 5 1171.3 0 1439.0 5 1653.1 0 1719.0 0 1727.8 0 1568.0 0 1453.4 5 1319.9 5

1110.8 0 1018.7 5 781.15

4

23872.4 0 7770.50 16132.6 0 20590.9 0 5849.90

The share prices taken are the monthly closing price of the company and the BANKEX. The WPI values are also monthly closing data. The FII values are the net FII in Equity market only for the months specified. The CRR values are percentage of statutory bank deposits with RBI.

For all the values, log transformations have been taken, except the CRR value which is in percentage. This was done as the Sum Squared Residual value was coming abnormally high, by taking ordinary values, because of variations in the base of each variable.

Results and Analysis Methodology and Assumptions 1) Used White’s heteroskedasticity consistent standard error estimates. The effect of using White’s correction is that in general the standard errors for the slope coefficients are increased relative to the usual OLS standard errors. This makes us more “conservative” in hypothesis testing, so that we would need more evidence against the null hypothesis before we would reject it and the estimates are close to Best Linear Unbiased Estimate 2) 90% confidence level is taken for analysis purpose. 3) The normality of the data has been tested, as the CLRM is most useful for data with normal distribution. 4) The results are analyzed after estimating the regression equation. 5) Discrepancies, if any, are noted and causes for the same are analyzed (like heteroskedasticity, autocorrelation etc). 6) Finally the overall comparative analysis for each company is done

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Analysis for SBI Histogram-Normality Test 12 Series: Residuals Sample 2003M05 2007M10 Observations 39

10 8

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

6 4

1.03e-17 -0.001633 0.096412 -0.098298 0.046059 0.195208 2.537333

2 0 -0.10

Jarque-Bera Probability -0.05

-0.00

0.05

0.595540 0.742472

0.10

Since the Skewness is almost zero and Kurtosis is less than 3, the data is normal. Dependent Variable: DLOG(SBI) Method: Least Squares Date: 02/03/09 Time: 11:47 Sample (adjusted): 2003M05 2007M10 Included observations: 39 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Variable

Coefficient

Std. Error

t-Statistic

Prob.

C DLOG(BANKEX) DLOG(FII) DLOG(WPI) CRR

-0.083331 0.975892 0.004483 0.349935 0.017782

0.092132 0.105067 0.005199 1.947027 0.018411

-0.904477 9.288257 0.862299 0.179728 0.965834

0.3721 0.0000 0.3946 0.8584 0.3409

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.688807 0.652196 0.048674 0.080551 65.21864 1.677151

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

6

0.065167 0.082533 -3.088136 -2.874858 18.81421 0.000000

From this result, the conclusions are a) There is significant relationship between the share price of SBI and the BANKEX index. There seem to be no significant relationship between the dependant variable and FII, WPI, CRR. b) Around 65% variations in dependant variable are explained by variations in independent variables. c) The model is sound in explaining the overall significance of the independent variables on the dependant variable as Prob (F-Statistic) is zero. d) The Durbin-Watson test statistic is around 1.68, which shows that there is no significant positive serial correlation in the model. e) The linear regression equation is DLOG(SBI)

=

-0.083

+

0.976DLOG(BANKEX)

+

0.004DLOG(FII)

+

0.349DLOG(WPI) + 0.017CRR

Analysis for ICICI Histogram-Normality Test 6 Series: Residuals Sample 2003M05 2007M10 Observations 39

5 4

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

3 2

9.96e-18 0.004317 0.063255 -0.084386 0.038659 -0.286813 2.127258

1 Jarque-Bera Probability

0 -0.05

0.00

1.772431 0.412213

0.05

Since the Skewness is almost zero and Kurtosis is less than 3, the data follows normal distribution.

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Dependent Variable: DLOG(ICICI) Method: Least Squares Date: 02/03/09 Time: 12:18 Sample (adjusted): 2003M05 2007M10 Included observations: 39 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Variable

Coefficient

Std. Error

t-Statistic

Prob.

C DLOG(BANKEX) DLOG(FII) DLOG(WPI) CRR

0.041186 1.070291 0.000381 1.132593 -0.008379

0.061617 0.106202 0.003767 1.333488 0.011999

0.668423 10.07784 0.101012 0.849347 -0.698336

0.5084 0.0000 0.9201 0.4016 0.4897

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.784890 0.759583 0.040869 0.056791 72.03437 2.089395

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

0.065925 0.083352 -3.437660 -3.224383 31.01473 0.000000

From this result, the conclusions are a) There is significant relationship between the share price of ICICI and the BANKEX index. There seem to be no significant relationship between the dependant variable and FII, WPI and CRR. b) Around 76% variations in dependant variable are explained by variations in independent variables. c) The model is sound in explaining the overall significance of the independent variables on the dependant variable as Prob (F-Statistic) is zero. d) The Durbin-Watson test statistic is around 2.08, which shows that there is no serial correlation in the model. e) The linear regression equation is DLOG(ICICI) = 0.041 + 1.070DLOG(BANKEX) + 0.0003DLOG(FII) + 1.136 DLOG(WPI) - 0.008CRR

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Analysis for HDFC Histogram-Normality Test 9 Series: Residuals Sample 2003M05 2007M10 Observations 39

8 7 6

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

5 4 3 2

-5.60e-18 -0.001380 0.092150 -0.115055 0.046486 -0.164158 2.610191

Jarque-Bera Probability

1 0 -0.10

-0.05

-0.00

0.05

0.422083 0.809741

0.10

Since the Skewness is almost zero and Kurtosis is less than 3, the data follows normal distribution. Dependent Variable: DLOG(HDFC) Method: Least Squares Date: 02/03/09 Time: 12:30 Sample (adjusted): 2003M05 2007M10 Included observations: 39 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Variable

Coefficient

Std. Error

t-Statistic

Prob.

C DLOG(BANKEX) DLOG(FII) DLOG(WPI) CRR

-0.068374 0.727538 -0.014716 -0.623383 0.014415

0.064753 0.136101 0.006504 1.571663 0.012859

-1.055905 5.345596 -2.262608 -0.396639 1.120994

0.2985 0.0000 0.0302 0.6941 0.2701

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.551686 0.498944 0.049145 0.082116 64.84341 2.830740

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

From this result, the conclusions are

9

0.040246 0.069428 -3.068893 -2.855615 10.45995 0.000012

a) There is significant relationship between the share price of HDFC and the BANKEX index and FII. There is no significant relationship between the dependant variable and WPI and CRR. b) Around 50% variations in dependant variable are explained by variations in independent variables. c) The model is sound in explaining the overall significance of the independent variables on the dependant variable as Prob (F-Statistic) is zero. d) The Durbin-Watson test statistic is around 2.83, which shows that there is no serial correlation in the model. e) The linear regression equation is DLOG(HDFC)

=

-0.068

+

0.728DLOG(BANKEX)

–

0.015DLOG(FII)

–

0.623DLOG(WPI) + 0.014CRR

Analysis for AXIS Histogram-Normality Test 12 Series: Residuals Sample 2003M05 2007M10 Observations 39

10 8

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

6 4

1.49e-17 -0.012771 0.363968 -0.204073 0.108238 1.225139 5.520367

2 Jarque-Bera Probability

0 -0.2

-0.1

-0.0

0.1

0.2

0.3

20.07868 0.000044

0.4

Since the Skewness greater than zero and Kurtosis is greater than 5, the data does not normal distribution and hence the CRLM seems not the best fit for analyzing AXIS Bank data. So, the data analysis has not been shown. But the probable cause, as obtained from the Stability Test of the model by Ramsey-Reset Test shows that some non-linear combinations of the explanatory variables explains the exogenous variable, that is the CRLM is mis-specified. 10

Ramsey RESET Test: F-statistic Log likelihood ratio

0.031718 0.077237

Probability Probability

0.968810 0.962118

So the null-hypothesis that all regression coefficients of the non-linear terms are zero is rejected, that is the model suffers from mis-specification or lack of stability.

Analysis for PNB Histogram-Normality Test 8 Series: Residuals Sample 2003M05 2007M10 Observations 39

7 6

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

5 4 3 2 1

3.06e-17 -0.006095 0.222010 -0.198445 0.083014 0.342269 3.503667

Jarque-Bera Probability

0 -0.2

-0.1

-0.0

0.1

1.173693 0.556078

0.2

Since the Skewness is almost zero and Kurtosis is almost 3, it can be safely assumed the data approximates normal distribution. Dependent Variable: DLOG(PNB) Method: Least Squares Date: 02/03/09 Time: 12:57 Sample (adjusted): 2003M05 2007M10 Included observations: 39 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.196965

0.107624

1.830120

0.0760

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DLOG(BANKEX) DLOG(FII) DLOG(WPI) CRR

1.449289 0.014258 -1.616152 -0.045938

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.615604 0.570381 0.087761 0.261869 42.22908 2.369202

0.199477 0.008949 2.191599 0.019881

7.265449 1.593236 -0.737431 -2.310652

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

0.0000 0.1204 0.4659 0.0270 0.050667 0.133894 -1.909184 -1.695907 13.61260 0.000001

From this result, the conclusions are a) There is significant relationship between the share price of PNB and the BANKEX index, FII and CRR but no significant relationship with WPI. b) Around 58% variations in dependant variable are explained by variations in independent variables. c) The model is sound in explaining the overall significance of the independent variables on the dependant variable as Prob (F-Statistic) is zero. d) The Durbin-Watson test statistic is around 2.37, which shows that there is no serial correlation in the model. e) The linear regression equation is DLOG(PNB)

=

0.197

+

1.449DLOG(BANKEX)

1.616DLOG(WPI) - 0.046CRR

Comparative analysis Model Selection Schwarz criterion Adjusted R-squared Kurtosis SBI

-2.875

65%

2.53

ICICI

-3.224

76%

2.12

HDFC

-2.856

50%

2.61

AXIS

NA

NA

5.52

PNB

-1.696

57%

3.50

12

+

0.014DLOG(FII)

–

This shows that the CRLM as developed here best fits ICICI Bank share price and is not well applicable for explaining AXIS Bank share price variations over the time period April 2003 – March 2008. Except for Axis Bank, which includes non-linear terms as per the Stability test, the model quite well explains the share price fluctuations of the other 4 bank stocks, with no heteroskedasticity or autocorrelation.

Impact of each variable chosen on the dependent variable at 90% confidence level INDEX

FII

WPI

CRR

SBI

Significant Insignificant Insignificant Insignificant

ICICI

Significant Insignificant Insignificant Insignificant

HDFC Significant PNB

Significant

Significant

Insignificant Insignificant

Significant

Insignificant

Significant

This shows that the suitability of the individual parameter selection for the model is best for PNB, whose prices have been affected significantly by 3 of the 4 parameters selected. Obviously, the Index values are highly influencing the share prices of all the stocks. The WPI Inflation parameter and CRR are not too significant. The Foreign Institutional Investment has significant relationship in determining HDFC and PNB share prices, but surprisingly it is not having much affect on SBI and ICICI share prices. This may be attributed to the seasonality affect, as SBI and ICICI have a stable FII portfolio being major stocks and prior to October 2008, the FIIs did not offload much of their investments in these 2 stocks. This analysis is up to March 2008.

General Conclusion This study concludes that using CAPM model do not always serve the purpose in estimating share price fluctuations, as other macroeconomic variables also influence them. But as seen, the greater is the weightages of the stock in the Index or in other words, for stocks with high market capitalizations, other factors tend to become more and more insignificant (viz. SBI and ICICI) and the CAPM model becomes more relevant and accurate. This study is a sincere attempt to study the complexity of stock price estimation and shows that regression estimation models can be evolved with addition of new parameters and their effects on the stock prices. 13

References For data collection, macroeconomic factor studies and strategy for building econometric model, following sources have been referred 1. ‘Introductory Econometrics for Finance’ © Chris Brooks 2008. 2. Macroeconomics – 9th Edition, Tata McGraw Hill by Rudiger Dornbusch, Stanley Fischer, Richard Startz. 3. Working Paper on India’s Macroeconomic Performance and Policies since 2000 by Shankar Acharya, October 2008, ICRIER. 4. Following websites


http://eaindustry.nic.in




http://www.rbi.org.in




http://www.indiastat.com/




http://www.bseindia.com




http://www.sebi.gov.in




http://finmin.nic.in




http://en.wikipedia.org

5. Prowess Database - http://www.cmie.com/database

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