Validity of CAPM by Using Portfolios: Evidence from Indian Capital Market

 

K.M. Yaseer1 & K.P. Shaji2

 

1Department of Commerce, PG Department of Commerce Govt. College Madapally, University of  Calicut , India

2Urban and Rural Development Finance Corporation, Thiruvananthapuram, India

 

Correspondence: K.M. Yaseer, Department of Commerce, PG Department of Commerce Govt. College Madapally, University of  Calicut , India

 

Received: May 20, 2018                                    Accepted: May 28, 2018                       Online Published: July 25, 2018

 

 

 

 

Abstract

This article tests the validity of Capital Asset pricing Model and compares the results of 16 periods including 14 sub periods which comprises 3 years each for the prediction of the expected returns in the Indian capital Market. The tests were conducted on portfolios having different security combinations. By using Black Jenson and Scholes methodology (1972) the study tested the validity of the model for the whole and different sub periods. The study used daily data of the BSE 100 index for the period from January 2001 to December 2010. Empirical results mostly in favor of the standard CAPM model. However, the result does not find conclusive evidence in support of CAPM

 

Keywords: Capital Asset pricing Model, Beta, systematic risk, Security market line.

 

I. Introduction

Globalization and international investments to Indian capital market over the past decade made investment arena tougher and investment decisions complex. Today the market is highly volatile and the investor should be cautious and should identify an appropriate tool to evaluate the risk and return involved in his investment decisions. Normally rational investor will expect high return for bearing risk and the rate of return on the investment should commensurate with the riskiness of the assets. Capital Asset Pricing Model (CAPM) was developed by Sharpe (1964), Lintner (1965), and Mossin (1966) and it has been used widely for determining the risk return relationship in asset management. The core assumption of this model is that contribution of an asset to the variance of the market portfolio is the asset’s systematic risk and beta can explain the asset’s risk. In other words, rate of return and the risk premium, which will be proportional to assets market risk or beta quantifies the amount of risk that cannot be diversified away.

This study has four testable objectives. It checks the empirical validity of the CAPM in Indian stock market and ascertains the relationship between return of securities and market return. It also compared whether expected rate of return is linearly related with systematic risk and the difference in results while using different security combinations. This study is unique in the sense that it is difficult to find a study, which tested the validity of CAPM in Indian capital market by using different portfolio combination. The analysis was conducted for the whole study period and for different sub periods by using two different set of portfolios and failed to find irrefutable evidence in validating CAPM. The size of the sample and the number of companies used to construct the portfolio is one of the important limitations.

2. Review of Literature

CAPM is the widely applauded model to explain the risk return relation. Large number of studies has been carried out to elucidate the relationship between return and factors which affect return and this has been tested with individual security return and portfolio return. Generally portfolio betas are more precise when compared to the individual security beta and researchers like Black and et.al (1972), Friend and Blume (1973) etc, followed portfolio approach to examine CAPM. In1973 Fama and Mac.Beth tested the linearity between expected return and pre ranked historic beta of assets and included squared beta as an additional variable to the basic Capital Asset Pricing Model and found a positive relation between return and risk.

Results of various empirical tests revealed that there is a mixed feeling on the applicability of CAPM in predicting risk return relationship. Studies conducted by (Fama and Mac Beth 1973), (Gibbons and Ferson, 1985) are generally in favor of CAPM. At the same time there is substantial criticism against the CAPM since the mid of 1975 and many empirical studies uncovered various anomalies that were clearly in conflict with the model’s predictions. (Ross, 1976) introduced the concept of a multi factor model with the theoretical foundation and presented a number of state variables to explain the expected. (Roll, 1977) argued that one cannot empirically test the CAPM because the construction of the market portfolio as per the theory is impossible. (Basu, 1977) found that when stocks are sorted on earnings-price ratios (E/P), the expected returns on high E/P stocks are higher when compared to the return predicted by the Capital Asset Pricing Model. Similarly (Stattman, 1980) tested the effect of book value on stock return, (Banz, 1981) the size effect. (Bhandari, 1988) the effect of leverage and showed the inefficiency of beta to explain the market returns.   In 1992 by using the cross-sectional regression Fama and French examined the validity of CAPM and found that size, book to market, debt equity and earning price should consider in the explanation of expected stock return. Further, Chan et.al (1991) challenged the validity of CAPM. (Bark, 1991) tested the risk-return relationship for assets by using the CAPM with Fama and Macbeths’ two-stage approach and found Sharpe-Linter-Mossin CAPM frame work is not adequate in the Korean stock market. (Yue, 1997) tested CAPM with multivariate testing based on Gibbon’s methodology in Hong Kong market and their results rejected both the Sharpe- Lintner CAPM and Black CAPM at an extremely low level. (Harris et al., 2003), (Fan, 2004), (Malin and et. al, 2004) UK, France and German markets rejected CAPM. (Michailidis et.al, 2006) found that their study do not support the theory’s basic hypothesis of CAPM in Greek securities market but explained the excess returns. Pettengill et. al (1995) found valid relationship between beta and returns by using a modified methodology of Fama and MacBeth (1973). (Rahman et al., 2006) in Bangladesh market, (Andor et al., 1999) Hungarian capital market also found positive relationship between beta and ex-post return, concluded that CAPM valid for these markets. Besides this (Majumdar et al., 2007) neither support nor reject (mixed result) the Capital Asset Pricing Model.  In Indian context few studies were conducted for analyzing risk- return relationship and studies by (Madhusoodanan, 1997), (Srinivasan, 1988) have generally supported CAPM. Studies by (Rao and Bhole, 1990), (Vaidyanathan, 1995), (Sehgal, 1997), (Sehgal, 2003), (Mohanthy, 2002), (Manjunatha, et.al 2006) questioned the validity of CAPM in Indian context.

While examining the literature it is clear that most of the studies in India used monthly or yearly data and only few studies used daily and weekly data to test the validity of Capital Asset Pricing Model. There is dearth of studies in Indian context and is planned to examine the CAPM by using daily data of 70 companies listed in BSE100-index with two different combinations of portfolios.

3. Objectives of the Research

The main objectives of the study is to revisit the empirical validity of CAPM frame work in Indian stock market by using different set of portfolios . The study will use Black et.al (1972) methodology and Fama and Mac Beth (1973) methodology to test the non linearity.

§  To examine the empirical validity of the ‘CAPM’ in Indian stock market.

§  To establish the relationship between return of securities and market return in Indian stock market.

§  To check whether expected rate of return is linearly related with systematic risk.

§  To compare the result of portfolios with different security combinations.

4. Source and Period of Data

The sample for the study covers nine years daily data of 70 companies of BSE 100 stock Index, a broad-based index, launched in 1989 for the period from 01-01-2001 to 31-12-2009   The data used in this study were sourced from of Prowess- a data base of CMIE and the websites Reserve Bank of India (RBI). The study considers 91 day Treasury bill rate as the proxy for the risk free assets, will better reflects the short term changes in the financial market.

5. Methodology for Testing Capital Asset Pricing Model

Black, Jensen and Scholes (1972) introduced a time series test of the CAPM and the relationship between risk and return has been analyzed systematically.  The present study also follows a similar approach will follow portfolio technique and use time series regression of excess portfolio return on excess market return and also cross sectional regression in risk premium form and is expressed by the equation below. In the first step, betas (systematic risk) of individual securities are measured and the beta coefficients of individual securities were calculated for the whole period and for the sub periods. A time series regression between the daily percentage return against the market return is used to get the beta coefficient of each security in the sample and the model is shown below.

                                                Rit- Rft = a i +bi (Rmt –Rft) + eit      ----------------------                           (1)

Where: Rit is the rate of return on asset i (or portfolio) at time t, Rft is the risk-free rate at time t, Rmt is the rate of return on the market portfolio at time t, BSE 30 index is taken as the best proxy for the market portfolio. eit is the beta of stock i, eit is the error term of regression equation at time t. 

In the second stage, for the formation of portfolios individual beta for each stock is arranged on ascending order and stocks were grouped in to portfolios having 10 and 5 stocks each according to their beta value .The first portfolio comprises the first 10/5 securities with lowest beta, the next portfolio with the next 10/5 securities and same method is followed for the formation of other portfolios and there by last portfolio is formed with securities having the highest beta. Then portfolio betas are calculated by using the following model.

rpt = ap + bp rmt + ept                       ----------------------                                            (2)

Where

rpt is the average excess portfolio return on time t, bp is the estimated portfolio beta, and, e pt is the error term in the regression equation at time t.

 

to estimate the ex post security market line for each testing period the portfolio return are regressed against portfolio betas. The model is

          rp =  λ0 + λ1 bp + ep                    ----------------------                                 (3)

Where

rp = is the average excess return of the portfolio P, bp is the beta of the portfolio P, and ep is the error term in the regression equation

Further the study will also tested the non- linearity between the total portfolio return and betas by using the following equation. 

           rp =  λ0  +  λ1bp  +  λ2b2p +  ep                                 -------------------             (4)

 

6. CAPM in Different Periods.

To test the validity of CAPM, the study considered whole period data that is (2001-2009) and then the entire test period is divided in to seven different sub periods comprising three years each. The details are shown in Table1 below.

 

Table 1. Different Portfolio Formation Periods and Testing Periods

Period

1

2

3

4

5

6

7

8

Period Range

01-09

01-03

02-04

03-05

04-06

05-07

06-08

07-09

Portfolio Formation

2001

2001

2002

2003

2004

2005

2006

2007

Testing period

2009

2003

2004

2005

2006

2007

2008

2009

 

6.1. CAPM in the Whole Study Period (2001-2009) with Portfolios Having Ten Securities

Port folio

Portfolio Return(rp)

Intercept

Beta

Standard Error

R2

F value

P Value of Beta at 99%

P1

0.11130

0.07971***

0.47233

0.76289

0.54509

2688.93

0.0000

P2

0.11554

0.06680***

0.72892

0.97319

0.63685

3935.33

0.0000

P3

0.12702

0.06868***

0.87242

0.79571

0.78981

8432.46

0.0000

P4

0.13047

0.06646***

0.95720

0.90286

0.77844

7884.51

0.0000

P5

0.19971

0.12924***

1.05378

0.91577

0.80541

9288.38

0.0000

P6

0.16271

0.08401***

1.17683

1.09133

0.78425

8156.95

0.0000

P7

0.18238

0.09388***

1.32345

1.20891

0.78931

8406.92

0.0000

Avg Rf

0.01626

Average    rm = (Rm-Rf)

0.06687

***significant at 99 % level.

The study investigated the applicability of CAPM and the data used in this study consists 5259 days observations of 70 stocks listed in the BSE 100 Index. The results for the whole period by using the model (2) are shown in Table 2 below. Portfolio 1(P1) with lowest beta earned the minimum return of (0.1113) and the portfolio 5 with the beta (1.0538) gives the maximum return (0.1997). During the study period the average risk free return is (0.0163) and the average excess return on the market is (0.0669).The CAPM postulates that higher risk beta is associated with higher

Table 2.Test Results for Whole Study Period (2001 – 2009) (N= 5259) rate of return and the result of the study partially supports this argument since portfolio6 and portfolio7 with highest beta bags less return than portfolio 5.

R-square explains the relative amount of the variance in return of a particular portfolio with the return on index. 

In the case of portfolio 1, the R2 value is (0.54509), which indicates less than adequate correlation with the market index. Were as in portfolio 5, R2 value is (0.80541), which indicates that above 80 per cent of the variation in the scrip has been explained by the relationship with the index. The positive constants suggest that the portfolios have earned higher returns than the CAPM has predicted. Thus from the analysis it is clear that in most of the cases β is a predictor of return in Indian capital market during the study period but there no conclusive evidence in favor of CAPM.

6.1.1 Test of Non-Linearity (2001-2009)

Test for the non-linearity helps one to check whether there exists non-linearity between portfolio return with beta. As per theory, if CAPM holds true λ0 and λ2 will be equal to zero and the λ1 will be equal to the average risk premium. In this work the non-linearity has been tested by using the regression model (4).The results of the estimated values are summarized in the Table 3; it shows that the value of the constant λ0 is not significantly different from zero. Statistically the t - value is (0.8377), which is less than (2.7765) at 5% significant level and thereby it is consistent with the argument of CAPM.

 

Table 3. Test of Non-Linearity for the Whole Period (2001 - 2009)

 

Coefficients

Std error

t- value

p-value

λ0

0.08368  

0.09989 

0.8377   

0.4493

λ1

0.02685   

0.23162    

0.1159   

0.9133

λ 2

0.03990  

0.12751  

0.3130   

0.7699

Critical value for 4-Degrees of freedom (2.7765)

 

In the case of λ1, the t- value is (0.1159) is smaller than (2.7765), and it is not significantly different from zero. As per the CAPM, the λ1 should be equal to the average risk premium; hence the result is inconsistent with the CAPM hypothesis. In the case of λ2, the value (0.3130) and the t-value is less than (2.7765) at 5% significance level and thereby it is consistent with the CAPM hypothesis. Thus, it is clear tha betas are linearly related with expected return. Hence CAPM cannot be clearly rejected during the study period.

6.2. CAPM in Different Sub Periods

6.2.1 Consolidated Test Results for Different Sub –Periods (Ten Securities)

CAPM is tested for different study period by using portfolios having 10 securities. The results for different study periods are summarized below in Tables 4 to 7. The findings are mostly supportive in different test periods to the hypothesis of Capital Asset Pricing Model, which says that higher beta provides higher return to the investor. Study reveals that while using percentage return and portfolios with equal weight, in most of the case beta explain the variation in portfolio returns, in few periods lower beta earned more return than higher beta portfolios, which is clear from table. 4.

Table 4. Consolidated Results for Different Sub Periods by Using 10 Securities

 

Port folio

Sub period 1 (20001-2003)

Sub period 2 (2002-2004)

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

Portfolio return

Constant

Beta

F  Value

R2

P value Beta

P1

0.1358

0.1189***

0.34760

0.2715

279.90

0.0000

0.18812

0.1456***

0.40544

390.38

0.3402

0.0000

P2

0.1988

0.1709***

0.57192

0.3664

434.37

0.0000

0.13299

0.0651***

0.64687

1315.22

0.6347

0.0000

P3

0.1438

0.1084***

0.72707

0.5547

935.38

0.0000

0.27030

0.1820***

0.84115

1378.53

0.6455

0.0000

P4

0.1821

0.1415***

0.83370

0.5541

933.16

0.0000

0.20948

0.1071***

0.97486

1317.89

0.6352

0.0000

P5

0.2164

0.1702***

0.94681

0.5903

1081.92

0.0000

0.23339

0.1177***

1.10212

2776.67

0.7858

0.0000

P6

0.2196

0.1668***

1.08355

0.5961

1108.22

0.0000

0.27087

0.1415***

1.23187

2449.39

0.7639

0.0000

P7

0.1284

0.0514

1.57857

0.7688

2496.59

0.0000

0.27020

0.1172***

1.45715

2179.65

0.7422

0.0000

Avg Rf

0.01681

Average   rm = (Rm-Rf)

0.04881

Avg Rf

0.0142

Average rm = (Rm-Rf)

0.10498

*** significant at 99%

 

 

Table  5. Consolidated Results for Different Sub Periods by Using 10 Securities

Port folio

Sub period 3( 2003-2005)

Sub period 4 (2004-2006)

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

P1

0.19576

0.1312***

0.46072

0.39166

487.370

0.0000

0.19367

0.13865***

0.56299

0.53150

854.283

0.0000

P2

0.23213

0.1359***

0.69667

0.64385

1368.55

0.0000

0.13098

0.04788**

0.81057

0.77784

2636.53

0.0000

P3

0.19582

0.0762***

0.84995

0.73712

2122.70

0.0000

0.18110

0.09071***

0.89768

0.78512

2751.36

0.0000

P4

0.24712

0.1152***

0.94406

0.70782

1833.88

0.0000

0.16977

0.07077***

0.97381

0.81428

3301.59

0.0000

P5

0.24341

0.0943***

1.06785

0.84625

4166.87

0.0000

0.13713

0.02389

1.1060

0.81169

3245.86

0.0000

P6

0.23194

0.0589**

1.24122

0.74919

2261.24

0.0000

0.17221

0.04885*

1.20218

0.84072

3974.74

0.0000

P7

0.27509

0.0690**

1.47422

0.79990

3026.13

0.0000

0.17639

0.02408

1.48129

0.84064

3972.28

0.0000

Avg Rf

0.01366

Average   rm = (Rm-Rf)

0.13860

Avg Rf

0.0142

Average rm = (Rm-Rf)

0.10505

*** Significant at99%,** Significant at 95%,* Significant at90%

 

Table  6. Consolidated Results for Different Sub Periods by Using 10 Securities

Port folio

Sub period 5 (2005-2007)

Sub period 6  (2006-2008)

 

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

 

P1

0.27919

  0.0613

1.4924

0.8002

2997.27  

0.0000

0.05494

0.05317*

0.4755

0.59363

1085.4

0.0000

 

P2

0.28746

  0.0672

1.5099

0.7860  

2748.69  

0.0000

0.00965

 0.00700

0.7117

0.77526

2563.1

0.0000

 

P3

0.30661

0.0858 **  

1.5166  

0.7784  

2628.29  

0.0000

0.03012

 0.02690

0.8655

0.81634

3302.5

0.0000

 

P4

0.31259

0.0911**

1.5203    

0.7617 

2391.5

0.0000

   -0.01330

 0.01678

0.9389

0.86496

4759.4

0.0000

 

P5

0.30497

  0.0842 *

1.5222    

0.7771 

2608.02  

0.0000

0.05991

0.05603**

1.0439

0.90513

7088.8

0.0000

 

P6

0.30914

 0.0865  ** 

1.52323     

0.7822  

2686.45  

0.0000

0.06231

0.05787

1.1944

0.86683

4836.6

0.0000

 

P7

0.31722

0.0972**

1.52382     

0.7717  

2529.03  

0.0000

0.12303

0.11767***

1.4412

0.87329

5120.82

0.0000

 

Avg Rf

0.01724

Average   rm = (Rm-Rf)

 0.14487

Avg Rf

0.01939

Average  rm = (Rm-Rf)

0.00372

 

 

 

*** Significant at99%,  ** Significant at95%, Note: The Values of Constant, F, Pand R2 are adjusted to 4 digits.

 

Table 7. Consolidated Results for Different Sub Periods by Using 10 Securities

Port folio

Sub period 7 (2007-2009)

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

P1

0.08502

0.06672  **

0.393851

0.53903

860.651

0.0000

P2

0.04054

0.00929

0.67844

0.73441

2035.23

0.0000

P3

0.08185

0.04320

0.82771

0.79910

2927.60

0.0000

P4

0.08081

0.03690

0.93784

0.83494

3723.10

0.0000

P5

0.11927

0.06948 **

1.04698

0.84949

5719.99

0.0000

P6

0.16448

   0.10719***

1.23770

0.87192

5010.55

0.0000

P7

0.12786

      0.05648

1.47794

0.88429

5624.87

0.0000

Avg Rf

0.04611

Average        rm = (Rm-Rf)

0.04611

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.2.2 Test of Non –Linearity

The test for the non- linearity (Table 8-10) reveals that, for whole and adjusted period result support CAPM hypothesis. In addition high value of estimated correlation coefficient between the intercept and the slope indicates that the model explains excess returns

 

 

Table 8.Consolidated Results for Different Study Periods by Using 10 Securities

Coefficient

Whole Period (2001-2009)

Sub Period 1(2001-2003)

Sub Period 2(2002-2004)

Constant

t -value

P value

Constant

t- value

P value

Constant

t-  value

P value

l0

0.0837

0.8377

 0.4493

0.03810   

 0.5678  

 0.6005

0.12757

1.0150

0.3674

l1

0.0269

0.1159

0.9133

0.33520    

  2.252   

  0.0874 

0.0991

0.3444

0.7479

l2

0.0399

0.3130

0.7699

−0.1736   

−2.326   

  0.0806 

0.0030

0.0201

0.9849

*** Significant at 99 %level,        **   Significant at 95% level

 

Table 9. Consolidated Results for Different Study Periods by Using 10 Securities

 

 Coefficient

Sub Period 3(2003-2005)

Sub Period 4(2004-2006)

Sub Period 5 (2005-2007)

Constant

t- value

P value

Constant

t-  value

P value

Constant

t-  value

P value

l0

0.1839

2.6050

0.0597

  0.2984

  2.766   

 0.0505 

  60.2641     

  1.055   

0.3509

l1

0.0298

0.1946

0.8552

−0.2699

−1.244   

0.2815

−80.6609     

−1.065   

0.3469

l2

0.0186

0.2389

0.8229

  0.12792

 1.224   

 0.2881  

  27.1154     

  1.080   

 0.3410  

 

Table 10. Consolidated Results for Different Study Periods by Using 10 Securities

Coefficient

Sub Period 6 (2006-2008)

Sub Period 7(2007-2009)

Constant

t-  value

P value

Constant

t-  value

P value

l0

  0.2037

 2.393   

0.0750 

 0.0647

  0.7213

0.5106

l1

−0.4595

             −2.485   

0.0678 

−0.0185

−0.0924

0.9308

l2

  0.2826

     2.975**    

 0.0410 

 0.0529

  0.5030

0.6414

*** Significant at 99 %level,        **   Significant at 95% level

 

6.3 CAPM Frame Work in Indian Capital Market (Portfolios with Five Securities)

In this section an attempt is made to test the empirical validity of the CAPM by using portfolios having five securities. The theory says that through diversification one can strategically reduce the risk by allocating available funds in many securities by forming balanced portfolios. Further, this test will also help us to compare the results with our studies with same set of data and also to check whether number of securities in a portfolio has any influence on measuring the efficiency and validity of CAPM.

While analyzing table 11, it is clear that out of the14 portfolios, with the increase in beta we cannot see any increasing trend in the average portfolio excess return; rather it comes up and down. Results also supplement that, all portfolios including portfolio with lowest beta earned more than the average excess market return and the risk free return. Further the positive constants suggest that, the portfolios earned higher returns than the CAPM has predicted. Further from the Table11, it can be noted that the all constants   has positive values. Thus the result indicates that, the alpha coefficients are significantly different from zero and hence we reject the null hypothesis. Further all estimated betas are found to be statistically significant at 99% level; thereby we reject the null hypothesis that the portfolio beta is not a significant determinant of portfolio return. Thus   β is a predictor of return during the whole study period (2001-2009).

 

Table 11.Results of the Whole Study Period (2001 – 2009)

Port folio

Portfolio Return(rp)

Constant

Beta

Standard Error

R2

F value

P  Value

99%

P1

0.08861

0.06414

0.36583

0.92121

0.33020

1106.26

0.0000

P2

0.13393

0.09521

0.57899

1.09383

0.46691

1965.43

0.0000

P3

0.12553

0.07899

0.69593

1.38381

0.44153

1774.18

0.0000

P4

0.10556

0.05461

0.76191

1.05857

0.61823

3633.93

0.0000

P5

0.13207

0.07543

0.84704

1.06828

0.66276

4410.18

0.0000

P6

0.12198

0.06193

0.89781

1.09352

0.67816

4728.54

0.0000

P7

0.13557

0.07309

0.93429

1.14146

0.67682

4699.57

0.0000

P8

0.12536

0.05982

0.98011

1.22015

0.66855

4526.25

0.0000

P9

0.18670

0.11754

1.03411

1.11044

0.73053

6083.59

0.0000

P10

0.21272

0.14094

1.07345

1.30458

0.67912

4749.29

0.0000

P11

0.18653

0.10890

1.16086

1.68331

0.59786

3336.14

0.0000

P12

0.13889

0.05912

1.19280

1.29372

0.72657

5962.97

0.0000

P13

0.18345

0.10019

1.24502

1.51927

0.67734

4710.72

0.0000

P14

0.18131

0.08756

1.40188

1.44521

0.74628

6600.44

0.0000

Avg Rf

0.01626

Average

rm =(Rm-Rf)

0.06687

significant at 99% level

 

6.4 Consolidated result for the sub periods (Five securities)

In the second Phase test is repeated with five securities by using same methodology and procedure by constructing 14 portfolios for different sub periods and results for different study periods are summarized below in Table 12 to 15. 

6.5 Through Portfolios having five securities each.

Table 12. Consolidated Results for Different Sub Periods by Using 5 Securities

Port folio

Sub period 1 (20001-2003)

Sub period 2 (2002-2004)

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

Portfolio return

Constant

Beta

F  Value

R2

P value Beta

P1

0.19742

0.18649***

0.224016

0.05953

47.543

0.0000

0.17171

0.13756***

0.32533

0.15175

135.43

0.000

P2

0.07307

0.05011***

0.47042

0.32234

357.22

0.0000

0.20452

0.15354***

0.48554

0.28184

297.09

0.000

P3

0.11733

0.09139***

0.53131

0.35932

421.19

0.0000

0.09170

 0.02911

0.59613

0.46562

659.59

0.000

P4

0.28033

0.25043***

0.61253

0.19548

182.48

0.0000

0.17428

 0.10105***

0.69761

0.52564

838.85

0.000

P5

0.14339

0.11568***

0.56765

0.67610

1567.61

0.0000

0.23518

 0.15026***

0.80884

0.54483

906.11

0.000

P6

0.17951

0.14242***

0.75989

0.43036

567.39

0.0000

0.30542

 0.21372***

0.87345

0.48309

707.48

0.000

P7

0.17044

0.13072***

0.81355

0.43529

578.89

0.0000

0.29151

 0.19444***

0.92460

0.42010

548.40

0.000

P8

0.19392

0.15224***

0.85385

0.48513

707.62

0.0000

0.12744

 0.01982

1.02513

0.54577

909.55

0.000

P9

0.20621

0.16085***

0.92927

0.49174

726.60

0.0000

0.21617

 0.10394***

1.06901

0.67917

1602.54

0.000

P10

0.22664

0.17956***

0.96435

0.45395

624.35

0.0000

0.25062

 0.13144***

1.13524

0.64087

1350.90

0.000

P11

0.23548

0.18411***

1.05245

0.44146

593.58

0.0000

0.29870

 0.17431***

1.18485

0.59285

1102.28

0.000

P12

0.20380

0.14939***

1.11465

0.54388

895.50

0.0000

0.24304

0.10877**

1.27889

0.69318

1710.29

0.000

P13

0.20038

 0.13433

1.35309

0.57866

1031.42

0.0000

0.24396

 0.10043***

1.36722

0.66184

1481.60

0.000

P14

0.05651

−0.0315

1.80405

0.60889

1169.21

0.0000

0.29643

0.13401**

1.54707

0.63798

1334.06

0.000

Avg Rf

0.01681

Average   rm = (Rm-Rf)

0.04881

Avg Rf

  0.0142

Average rm = (Rm-Rf)

0.10498

*** Significant at 99%, ** Significant at 95%  .

 

Table 13. Consolidated Results for Different Sub Periods by Using 5 Securities

Port folio

Sub period 3 (20003-2005)

Sub period 4 (2004-2006)

Portfolio return

Constant

Beta

R2

F  Value

P value Beta

Portfolio return

Constant

Beta

F  Value

R2

P value Beta

P1

0.24929

0.20095***

0.34627

0.05431

43.47

0.0000

0.28197

    0.23574***

0.44003

0.24059

238.56

0.0000

P2

0.20172

0.12413***

0.55581

0.33865

387.63

0.0000

0.10538

0.03384

0.68098

0.54276

893.85

0.0000

P3

0.20792

0.11751***

0.64766

0.52264

828.82

0.0000

0.14888

0.06619

0.78709

0.59590

1110.41

0.0000

P4

0.25831

0.15440***

0.74439

0.45755

638.53

0.0000

0.11308

0.02567

0.83205

0.68855

1664.72

0.0000

P5

0.23397

0.12034***

0.81396

0.57012

1003.95

0.0000

0.17716

   0.08494**

0.87792

0.65463

1427.33

0.0000

P6

0.15640

0.03245

0.88791

0.60786

1173.46

0.0000

0.18503

   0.08919**

0.91237

0.67145

1538.93

0.0000

P7

0.18686

0.05801

0.92303

0.61339

1201.05

0.0000

0.20167

     0.10168***

0.95182

0.63368

1302.60

0.0000

P8

0.30750

0.17265***

0.96590

0.54568

909.245

0.0000

0.13786

 0.03367

0.99184

0.74699

2223.26

0.0000

P9

0.21573

0.07267**

1.02480

0.67206

1551.36

0.0000

0.12929

 0.01800

1.05944

0.81215

3255.66

0.0000

P10

0.27128

0.11611***

1.11157

0.70056

1771.07

0.0000

0.14496

 0.02424

1.14913

0.63506

1310.39

0.0000

P11

0.23793

0.06852*

1.21355

0.72147

1960.87

0.0000

0.09773

−0.0250

1.16838

0.79510

2922.04

0.0000

P12

0.22874

0.05149

1.26967

0.60091

1139.83

0.0000

0.24669

     0.11720***

1.23260

0.70469

1796.91

0.0000

P13

0.30853

0.11609***

1.37849

0.64444

1372.07

0.0000

0.12800

−0.01909

1.40033

0.77133

2539.94

0.0000

P14

0.24079

0.02146***

1.57112

0.72060

1952.39

0.0000

0.22479

 0.06110

1.55817

0.76394

2436.99

0.0000

Avg Rf