CAPM

CAPM ASSIGNMENT Manish Singla Roll No. 186 Section C

Single Index Model o

o

Relates returns on each security to the returns on a common index, such as the CNX Nifty or Sensex Stock Index Expressed by the following equation : Ri

o o



 i



 i R M



ei

Divides return return into two components: components: a unique part, i a market-related part, part, i.Rm Beta measures sensitivity of stock to stock market movements.

CAPM Model The capital asset pricing model provides a formula that calculates the expected return on a security based on its level of risk. The formula for the capital asset pricing model is the risk free rate plus beta times the difference of the return on the market and the risk free rate.

Single Index Model o

o

Relates returns on each security to the returns on a common index, such as the CNX Nifty or Sensex Stock Index Expressed by the following equation : Ri

o o



 i



 i R M



ei

Divides return return into two components: components: a unique part, i a market-related part, part, i.Rm Beta measures sensitivity of stock to stock market movements.

CAPM Model The capital asset pricing model provides a formula that calculates the expected return on a security based on its level of risk. The formula for the capital asset pricing model is the risk free rate plus beta times the difference of the return on the market and the risk free rate.

Procedure : 1.) Weekly returns were taken for stocks stocks and S&P BSE 500 500 for the last 1 year from BSE BSE website. 2.) Ex ante Beta calculated for the 103-252 data rows using the returns on equity and market for 1-98 data rows. This was done using SLOPE function in excel. 3.) 364 day T-bils rate was used as the risk free rate . rate . Rf was obtained by dividing this rate by 52 weeks. 4.) Ri-Rf was calculated for the 51-100 data rows. Regression analysis was done using Y values as Ri- Rf and X values as the Beta Following regression was used:

Hypothesis Testing If CAPM holds in general, correlation of equity return with the market return (βi) (β i) alone could provide suﬃcient explanation t o the risk premium, such that αi should be zero. For this reason, a hypothesis testing is performed with null hypothesis α=0 at 5% significance level. H0: α = 0 H1: α ≠ 0

Objective: In these observations, we are trying to analyze whether the CAPM model holds true for the stocks listed on the Bombay Stock Exchange or not.

Financial Technologies Using Regression we get

Intercept X Variable 1

Coefficients -0.02204 0.008861

Standard Error 0.058198 0.03262

t Stat -0.37877 0.271647

P-value 0.705402 0.786272

Regression Statistics Multiple R

0.022324

R Square Adjusted R Square

0.000498

Standard Error

-0.00626 0.08083

Observations

150

Financial Technologies Line Fit Plot 0.5 0 Y

-0.5 -1

0

1

2

3

Y Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.02 and the p-value is 0.705 Since p-value > 0.05 we reject the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Financial Technologies

HCL Technologies Using regression we get,

Coefficients

Standard Error

Intercept

0.006425

0.003523

X Variable 1

-0.00759

0.00563

t Stat

P-value

1.82361 1.34751

0.070229 0.179877


0.110091


0.01212 0.005445

Standard Error

0.019772

Observations

150

HCL Technologies Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 0 -0.1

0.5

1

1.5

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.006 and the p-value is 0.07 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of HCL Technologies

Hexaware Technologies Using regression we get,

Coefficients

Standard Error

t Stat

P-value

Intercept

0.004827

0.004563

1.057901

0.291824

X Variable 1

-0.00261

0.005027

-0.51827

0.605047


0.042563


0.001812

Standard Error

0.021254

-0.00493

Observations

150

Hexaware Technologies Line Fit Plot 0.1

Y

Y

0 0 -0.1

0.5

1

1.5

2

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.004 and the p-value is 0.29 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei InHence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Hexaware Technologies

Infosys Using regression we get,

Coefficients

Standard Error

Intercept

0.000545

X Variable 1

0.001142

t Stat

P-value

0.00649

0.083957

0.933204

0.013606

0.083922

0.933232


0.006898


4.76E-05 -0.00671

Standard Error

0.024303

Observations

150

Infosys Line Fit Plot 0.2 0.1 0 Y

-0.1 0

0.2

0.4

0.8

Y Predicted Y

-0.2 -0.3

0.6

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.005 and the p-value is 0.93 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Infosys

Mindtree Using regression we get,

Coefficients

Standard Error

t Stat

Intercept

0.010443

0.007102

1.470495

0.14355

X Variable 1

-0.02327

0.022019

-1.05685

0.292301

P-value


0.086547


0.00749 0.000784

Standard Error

0.018704

Observations

150

Mindtree Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

0.2

0.4

0.6

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.01 and the p-value is 0.14 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Mindtree

Mphasis Using regression we get,

Coefficients

Standard Error

t Stat

P-value

Intercept

0.002744

0.007419

0.369821

0.712044

X Variable 1

-0.00287

0.011899

-0.24106

0.809845


0.019811


0.000392

Standard Error

0.022582

Observations

-0.00636 150

Mphasis Line Fit Plot 0.15 0.1 0.05 Y

Y

0 -0.05 0 -0.1

0.5

1

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.002 and the p-value is 0.71 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Mphasis

Oracle Financial Using regression we get,

Coefficients

Standard Error

Intercept

0.004644

X Variable 1

-0.00903

t Stat

P-value

0.00271

1.713715

0.088675

0.005707

-1.58308

0.115537


0.129041


0.016652 0.010007

Standard Error

0.016516

Observations

150

Oracle Financial Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

0.5

1

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.004 and the p-value is 0.08 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Oracle Financial

TCS Using regression we get, Standard Error

t Stat

P-value

-0.00767

0.004114

1.86356

0.064365

0.02559

0.010528

2.43067

0.016267

Coefficients Intercept X Variable 1


0.195927


0.038388

Standard Error

0.016943

0.03189

Observations

150

TCS Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

0.2

0.4

0.6

0.8

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.007 and the p-value is 0.06 Since p-value > 0.05 we do not accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of TCS

Tech Mahindra Using regression we get,

Coefficients

Standard Error

Intercept

0.010979

0.005309

X Variable 1

-0.02201

0.012742

t Stat

P-value

2.06784 1.72696

0.040396 0.086261


0.140546


0.019753 0.01313

Standard Error

0.01939

Observations

150

Tech Mahindra Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

0.2

0.4

0.6

0.8

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.01 and the p-value is 0.04 Since p-value <0.05 we accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model holds true in Indian Equity Market taking the example of Tech Mahindra

Wipro Technologies Using regression we get,

Coefficients

Standard Error

t Stat

P-value

Intercept

0.008529

0.003757

2.269852

0.024661

X Variable 1

-0.01845

0.007963

-2.31651

0.021903


0.187055


0.03499 0.028469

Standard Error

0.020979

Observations

150

Wipro Ltd. Line Fit Plot 0.1 0 0

Y

0.5

-0.1 -0.2

1

Y Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.008 and the p-value is 0.02 Since p-value < 0.05 we accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model holds true in Indian Equity Market taking the example of Wipro Ltd.

CAIRN Using Regression we get Coefficient s Intercept X Variable 1

-0.00373

Standard Error 0.00888 3

0.006023

0.01255 7

-0.41975

P-value 0.67527 5

0.02128

Upper 95% 0.01382 5

0.47967 9

0.63216 4

0.01879

0.03083 8

t Stat

Lower 95%

Lower 95.0% 0.02128

Upper 95.0% 0.01382 5

0.01879

0.03083 8


0.039399


0.001552

Standard Error

0.017245

-0.00519

Observations

150

BPCL Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

0.5

1

1.5

2

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.00373 and the p-value (intercept) and p-value(x-variable) is 0.67527 and 0.632164 Since p-value (x-variable)> 0.05 we reject the null hypothesis that α = 0 and β=0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Cairn

GAIL Using Regression we get Coefficient s Intercept X Variable 1

0.024692

Standard Error 0.01574 1

-0.02911

0.01863 6

Lower 95%

t Stat 1.56861 3

P-value 0.11887 4

0.00641

Upper 95% 0.05579 8

-1.56221

0.12037 5

0.06594

0.00771 4

Lower 95.0% 0.00641

Upper 95.0% 0.05579 8

0.06594

0.00771 4


0.127367


0.016222 0.009575

Standard Error

0.01795

Observations

150


Y

0 -0.05 -0.1

0

0.5

1

1.5

2

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.024692 and the p-value (intercept) and p-value(x-variable) is 0.118874 and 0.120375 Since p-value (x-variable)> 0.05 we reject the null hypothesis that α = 0 and β=0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of GAIL

IOC Using Regression we get


-0.00259

-0.0002

Standard Error

t Stat

0.016025

0.16174

0.013592

0.01505

P-value

Lower 95%

0.871729

0.03426

0.988015

0.02706

Upper 95%

Lower 95.0%

Upper 95.0%

0.029076

0.03426

0.029076

0.026654

0.02706

0.026654


0.001237


1.53E-06 -0.00676

Standard Error

0.021958

Observations

150


Y

0 -0.05 -0.1

0

0.5

1

1.5

2

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.00259 and the p-value (intercept) and p-value(x-variable) is 0.871729 and 0.988015 Since p-value (x-variable)> 0.05 we reject the null hypothesis that α = 0 and β=0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not holds true in Indian Equity Market taking the example of IOC

ONGC Using Regression we get


-0.00037

-0.00603

Standard Error

t Stat

0.001651

0.22455

0.006432

0.93678

P-value

Lower 95%

0.82264

0.00363

0.3504

0.01874

Upper 95%

Lower 95.0%

Upper 95.0%

0.002891

0.00363

0.002891

0.006685

0.01874

0.006685


0.076775


0.005894

Standard Error

0.017041

-0.00082

Observations

150


Y

0 -0.05 -0.1

0

0.5

1

1.5

2

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.00037 and the p-value (intercept) and p-value(x-variable) is 0.82264 and 0.3504 Since p-value (x-variable)> 0.05 we reject the null hypothesis that α = 0 and β=0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not holds true in Indian Equity Market taking the example of ONGC

DLF Using Regression we get


Standard Error

t Stat

P-value

-0.03236

0.058207

-0.55589

0.579124

0.014539

0.029245

0.497145

0.619825

Lower 95% 0.14738 0.04325

Upper 95% 0.082668 0.07233

Lower 95.0%

Upper 95.0%

0.14738 0.04325


0.040831


0.001667

Standard Error

0.036237

-0.00508

Observations

150

DLF Line Fit Plot 0.1 0 0

Y

1

2

-0.1 -0.2

3

Y Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.03236and the p-(intercept) is 0.579124 and p value (X variable) is 0.619825 Since p-value (X variable) > 0.05 we reject the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true for DLF

0.082668 0.07233

HDIL Coefficients Intercept X Variable 1

Standard Error

t Stat

P-value

0.0359

0.025375

1.414799

0.159228

-0.01233

0.008124

-1.51756

0.131258

Lower 95% 0.01424 0.02838

Upper 95% 0.086043 0.003726

Lower 95.0%

Upper 95.0%

0.01424 0.02838


0.123783


0.015322 0.008669

Standard Error

0.044403

Observations

150

HDIL Line Fit Plot 0.2 0.1 0 Y

-0.1 0

2

4

Y Predicted Y

-0.2 -0.3

6

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.0359 and the p-(intercept) is 0.159228 and p value (X variable) is 0.131258 Since p value (X variable) > 0.05 we reject the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true for HDIL

0.086043 0.003726

Peninsula Land Standard Error


t Stat

P-value

0.00017

0.015537

0.010927

0.991296

-0.00128

0.0069

-0.18484

0.853604

Lower 95% 0.03053 0.01491

Upper 95% 0.030874 0.01236

Lower 95.0% 0.03053 0.01491

Upper 95.0% 0.030874


0.015192


0.000231

Standard Error

0.035975

-0.00652

Observations

150

Peninsula Land Line Fit Plot 0.2 0.1 Y

Y

0

Predicted Y 0

-0.1

1

2

3

4

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.00017 and the p-(intercept) is 0.991296 and p value (X variable) is 0.853604 Since p value (X variable) > 0.05 we reject the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei ] Hence we can conclude that the CAPM model does not hold true for Peninsula Land

0.01236

Sobha Developers Coefficients Intercept X Variable 1

Standard Error

t Stat

P-value

-0.00197

0.00681

-0.28936

0.772708

0.000373

0.005548

0.067168

0.946539

Lower 95% 0.01543 0.01059

Upper 95% 0.011487 0.011337

Lower 95.0% 0.01543 0.01059

Upper 95.0% 0.011487 0.011337


0.005521


3.05E-05 -0.00673

Standard Error

0.027306

Observations

150

Sobha Developer Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

1

2

3

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.00197 and the p-(intercept) is 0.772708 and p value (X variable) is 0.946539 Since p value (X variable) > 0.05 we reject the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true for Sobha Developer

Colgate Palmolive India Using Regression we get Coefficients 0.000885

Standard Error 0.00547

t Stat 0.16183

P-value 0.87166

-0.00213

0.009829

-0.21624

0.829099



0.017772

R Square

0.000316

Adjusted R Square

-0.00644

Standard Error

0.017143

Observations

150

X Variable 1 Line Fit Plot 0.1 0.05 Y

Y

0

Predicted Y 0

-0.05

0.5

1

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.0008 and the p-value is 0.87 Since x variable p-value > 0.05 we cannot accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market taking the example of Colgate Palmolive

GSK Using Regression we get Coefficients 0.003521


t Stat 0.635368

P-value 0.52617

-0.00488

0.00903

-0.54092

0.589373



0.04442

R Square

0.001973

Adjusted R Square

-0.00477

Standard Error

0.032683

Observations

150


Y

0 -0.1 -0.2

0

0.5

1

1.5

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is0.0035 and the p-value is 0.52 Since x variable p-value > 0.05 we cannot accept the null hypothesis that α = 0 Hence we understand that the value of alpha is not statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market

HUL Using Regression we get Coefficients 0.001571


t Stat 0.190156

P-value 0.849448

0.000799

0.014219

0.056226

0.955238



0.004622

R Square

2.14E-05

Adjusted R Square

-0.00674

Standard Error

0.023103

Observations

150


Y

0

Predicted Y 0

-0.1

0.5

1

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.0015 and the p-value is 0.84 Since x variable p-value > 0.05 we cannot accept the null hypothesis that α = 0 Hence we understand that the value of alpha is not statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market

Jubilant Foodworks Using Regression we get Coefficients 0.00522548


t Stat 1.398876

P-value 0.163942

-0.00836651

0.00474343

-1.76381

0.079828



0.143483993

R Square

0.020587656

Adjusted R Square

0.013970005

Standard Error

0.01926696

Observations

150


Y

0 -0.05 -0.1

0

0.5

1

1.5

Predicted Y

X Variable 1


Tata Global Beverages Using Regression we get Coefficients 0.000973


t Stat 0.139126

P-value 0.88954

0.000112

0.006081

0.018388

0.985354



0.001511

R Square

2.28E-06

Adjusted R Square

-0.00675

Standard Error

0.020339

Observations

150


Y

0 -0.05 -0.1

0

0.5

1

1.5

2

Predicted Y

X Variable 1


United Spirits Using Regression we get Coefficients -0.00144


t Stat -0.15063

P-value 0.88047428

0.004354

0.010899

0.39945

0.69013778



0.032817

R Square

0.001077

Adjusted R Square

-0.00567

Standard Error

0.027376

Observations

150


Y

0

Predicted Y 0

-0.1

0.5

1

1.5

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.0014 and the p-value is 0.88

Since x variable p-value > 0.05 we cannot accept the null hypothesis that α = 0 Hence we understand that the value of alpha is not statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true in Indian Equity Market

Bajaj Auto Using Regression we get

Coefficients

Standard Error

t Stat

P-value

0.001625

0.001583

1.026628

0.306271

0.023401

0.011797

1.983659

0.049144


Lower 95% -0.0015 8.89E05

Upper 95% 0.004754 0.046714

Lower 95.0% -0.0015 8.89E05

Upper 95.0% 0.004754 0.046714


0.16093


0.025899 0.019317

Standard Error

0.015358

Observations

150

Bajaj Auto Line Fit Plot 0.1 0.05

-0.4

Y

0

Y

-0.2

-0.05

0

0.2

Predicted Y

-0.1 X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is 0.001 and the p-(intercept) is is 0.306 and p value (X variable) is 0.049 Since all conditions are met and p value (X variable) is 0.049< 0.05 we accept the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model holds true for Bajaj Auto

Exide Coefficients Intercept X Variable 1

Standard Error

t Stat

P-value

-0.00717

0.017078

-0.41994

0.675135

0.009402

0.022921

0.410194

0.682257

Lower 95% 0.04092 0.03589

Upper 95% 0.026577 0.054698

Lower 95.0% 0.04092 0.03589

Upper 95.0% 0.026577 0.054698


0.033699


0.001136

Standard Error

0.019316

-0.00561

Observations

150

Exide Line Fit Plot 0.1 0.05 Y

Y

0 -0.05 -0.1

0

0.5

1

Predicted Y

X Variable 1

Observation and Inferences: From the regression analysis, we can see the value of intercept is -0.007 and the p-(intercept) is is 0.675 and p value (X variable) is 0.682 Since p value (X variable) > 0.05 we reject the null hypothesis that α = 0 Hence we understand that the value of alpha is statistically zero in the regression Ri-Rf =αi + βi (Rm-Rf) + ei Hence we can conclude that the CAPM model does not hold true for Exide

CAPM

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