Report on CAPM Model

  • Category:
    Business
  • Document type:
    Coursework
  • Level:
    Masters
  • Page:
    6
  • Words:
    3826

26Capital Pricing Model

Report on CAPM Model

The Name of the School

Q1. Assumption and the implication of CAPM

The introduction of capital asset pricing model (CAPM) was set apart by the disclosure of William Sharpe (1964) and John Lintner (1965) where Sharpe was honored Nobel Prize in 1990 (Barberis, Greenwood & Shleifer 2015). Before their discovery, there exist nothing like (CAPM) which was built on the initial principles concerning the nature of taste and the investment opportunities which was able to give clear and straightforward and testable predictions concerning the return and risk. The major assumption and implication of the CAPM model include:-

CAPM assumes that all the asset markets are perfectly competitive with very many investors and the implication of this is that the many investors that exist are the price takers in the market. The model further assumes that the market is frictionless with no taxes and zero cost of transaction (Barberis, Greenwood & Shleifer 2015). The model assumes the economic behaviour of an individual in the market where they draw conclusion about the overall market prices returns and quantities. The implication of the equilibrium assumption is that of the expected asset return which cannot be observed directly in the market (Zabarankin, Pavlikov & Uryasev 2014). Furthermore if every person believes in this particular theory, at that point it is conceivable that there is a focal part of the business sector portfolio which would rearrange the portfolio choice and gives a method of reasoning to a business sector indexing speculation examination (Zabarankin, Pavlikov & Uryasev 2014).

The model moreover expect that the lot of financial specialists that exist in the business sector are appearing to be identical time of arranging skyline. Al the financial specialists in the business sector have measure up to access to every one of the securities with no duties and commissions (Barberis, Greenwood & Shleifer 2015). Financial specialists can obtain and loan at the one risk free rate and ultimately speculators are capable at any offered point to short any advantage, furthermore hold any part of a benefit which exist in the business sector. Another critical ramifications is that there is an unequivocal risk return exchange off for each individual stocks (Zabarankin, Pavlikov & Uryasev 2014). The CAPM show ordinarily determines anticipated that profits would be utilized as a part of the capital planning assessment and direction. Also, the risk premium on an individual security is typically a component of its deliberate risk, measured by the covariance with the business sector.

Q2. Validity and the effect of violation of the CAPM assumption

To a larger extent, we can argue that CAPM is very valid subject to very many arguments. In most cases, investors hold well diversified portfolio and this is done to ensure that the investors has shed out some risk arising from the firm (Fama and French 2015). Therefore, we can conclude that those given portfolio are having high chances of correlating with the CAPM model. In his study, Brennan showed that even if the investors had distinct individual tax rate, still the new version of CAPM will be held constant. In another study, Mayer’s showed that a new version of CAPM will be held in situations where investors were allowed to trade in non-traded assets such as human capital (Zabarankin, Pavlikov & Uryasev 2014). In his case, he derived the CAPM, where high beta securities could have higher than anticipated risk premium and low beta securities lower than anticipated risk premiums.

Fischer and Black proved that even if there is no risk-free rate asset in the market, one is capable of deriving a zero beta version of CAPM, where the intercept might be higher than expected under the normal CAPM model (Dempsey 2013). This further validates the assumption and the expected results of its violation. Lastly, the consumption based CAPM normally allows for the fact that investors horizon are longer than one period and therefore when they choose portfolios they are also thinking of how the present portfolios will hedge risk in future time of assets (Barberis, Greenwood & Shleifer 2015).

Q3: Empirical test of the CAPM

In analyzing the empirical test of CAPM, we uses the data from two industries that is from technology industry and manufacturing industry. Eight regression were done using the excess asset return model

Report on CAPM Model

Testing the null hypothesis which is

Test: Report on CAPM Model 1

The first case we run the regression for the two industries separately using the 30 year time period. The results are shown in the appendix I below. For the first industry which is the technology,

We have Report on CAPM Model 2= 148372

While Report on CAPM Model 3

Report on CAPM Model 4

For technology industry, it proves the CAPM theory which states that the assets cannot be fully diversified from the risk. With industry beta of Report on CAPM Model 5>0 it shows that the asset is exposed to market risk for the entire market (Scott 2014).

For the manufacturing industry the results are shown in the appendix II and it shows that

We have Report on CAPM Model 6= 0.189993

While Report on CAPM Model 7

WithReport on CAPM Model 8 it further proves the CAPM theory for the manufacturing industry is highly volatile. Report on CAPM Model 9= 0.189993 which shows presence of volatile market. However, technology industry is more volatile than manufacturing industry with higher beta. Therefore, we can conclude that, regardless of the amount we enhance our speculations, it’s difficult to dispose of all the risk (Scott 2014)

From a nearer investigation of different models, unmistakably the beta and alpha coefficients are more noteworthy than 1 supporting the discoveries from the underlying relapse from index 1 and 2. At the point when the information is assembled into 10 years for each industry it further uncovers that riskless economic situation can’t be achieved supporting the capital resource estimating model found by Fama and French (1992). Despite the fact that present day approach shows that specific risk can be expelled through improvement. The drawback is that expanding still doesn’t deal with the issue of productive risk; even a course of action of all the shares in the offer exchanging framework can’t execute that hazard (Fama and French 2015). Henceforth, while figuring a justified return, proficient risk is the thing that diseases money related experts most. CAPM, along these lines, progressed as a way to deal with measure this efficient risk (Dempsey 2013).

Q4: Background and characteristics of Fama and French three factor model

As a result of numerous issues experienced while utilizing CAPM amid the examination if the acknowledged returns and the impact of other risk elements has put the CAPM model under constant feedback. The value of the model is to a great extent constrained with numerous suspicions of single risk element (Fama and French 2015). Numerous researchers utilizes the CAPM model, the covariance of return portfolio with the business sector portfolio come back to clarify the minor departure from the excess portfolio return. All things considered, in an observational study embraced by Fama and French (1992) demonstrates that the covariance of the arrival portfolio and the business sector return is not ready to completely clarify the progressions on the portfolio over excess returns. They discovered that the covariance have extremely negligible or no force at all as far as clarifying the cross-sectional variety in resource/value return (Ai, Croce & Li 2013).

As a result of poor execution of CAPM, Fama and French created three variable model to help in filling the crevice left by CAPM (Fama and French 2015). They contended in their study that the abnormalities which are identifying with CAPM are caught by the three element model. The three component model were created on the premise of the way that normal excess portfolio returns are ordinarily sensible to the three variable model in particular;

Q5: Excess market portfolio return

The difference between Excess return on the course of action of little stocks and over excess return on a game plan of gigantic stocks (SMB). The difference between the Excess return on a course of action of high-book to market stocks and the over excess return on a game plan of low book to market stock (Ai, Croce & Li 2013). The thought about the going with formula to clear up the model. Another important three factor model characteristics is the regression equation which is stated as:

Report on CAPM Model 10

Report on CAPM Model 11

Report on CAPM Model 12

Empirical test

Using the excess return model:

Report on CAPM Model 13

Test the following hypotheses:

Report on CAPM Model 14 , Report on CAPM Model 15 ,Report on CAPM Model 16 ,Report on CAPM Model 17

In this study, it covers the period from January 1980 to 2009 which is a thirty year period having 12 months each giving a total of 360 months. The study tested CAPM using two industry which includes manufacturing and technology industry. Furthermore, we included Small minus big and high minus low in the model. Since the main aim of this exercise was to test the prediction of CAPM, we used the Black et al (1972). We start with the first portfolio to estimate beta of the industry which was technology then we moved to second industry which was manufacturing industry (Ai, Croce & Li 2013).

From the result of the analysis in Appendix 6, the fit of the model was tested using R-square, the results shows that R-square is 0.828339 indicating that a total of 82.83% of the total variables in the models were tested and is the model is fit for making conclusion. For the three variables used in the model, SMB, HML and Mkt-Rf, the P-value which is 3.2E-57, 5.55E-10 ad 2.5E-81 respectively is less than 0.05 critical value hence they are statistically significance at significance level of 95%. The coefficient beta for SMB is 1.256517 indicating high volatility hence high risk. For the HML the beta >0 and is -0.43791 indicating risk free portfolio while Mkt-Rf 1.161159 showing high risk market portfolio (Fama &French 2015).

In Appendix 7, the fit of the model was tested using R-square, the results shows that R-square is 0.819812 indicating that a total of 81.9812% of the total variables in the models were tested and is the model is fit for making conclusion (Fama &French 2015). For the three variables used in the model, SMB, HML and Mkt-Rf, the P-value which is 5.63E-48, 7.4E-21 and 4.6E-112 respectively is less than 0.05 critical value hence they are statistically significance at significance level of 95%. The coefficient beta for SMB is 0.762542 indicating high volatility hence high risk. For the HML the beta and is 0.47099 indicating low risk portfolio while Mkt-Rf 1.058549 showing high risk market portfolio. Along these lines, we can contends that specific theories can be tried independent of whether one trusts in the legitimacy of the basic CAPM or in some other adaptation of the hypothesis (Scott 2014). Firstly, the hypothesis focuses that higher deliberate risk (beta) is connected with a larger amount of return and in this study, we can verification that both the assembling division and the innovation part have higher return that is why it is associated with high risk giving beta > 1(Scott 2014). It can also be noticed that the findings of this study is a proof of CAPM model that explains that risk free portfolio does not exist in real life hence all the two industries post high risk asset portfolio.

Part B: Wage Data

Descriptive statistics

From the study, there are seven variables which was under study, they include Wage, Education, Experience, Gender, Age, Marital status and Union. The researcher carried out descriptive analysis in SPSS and the results are shown in Appendix 1 below. From the analysis, age is having the highest mean of 36.811 followed by experience with 17.8221 union has the lowest mean of 0.179775. The analysis also gives standard deviation of the variables with experience the highest with 12.37971 followed by age 11.72657 with 11.72657 then wage with 7.708645. Union on the other hand gives the smallest standard deviation of 0.38436. This is an indication on low effect of union on wage and salary. Minimum ranges from 0 and maximum is 66.75. The result of descriptive analysis is presented in appendix 1 below.

The study further investigated the effect of education on an employee wage using the equation;

Report on CAPM Model 18 …………………………………………… (1)

The regression output is in the appendix 2 below.

XX states that an R-squared in the range of 0.10 to 0.15 is reasonable for making decision and indicates that the model is fit, from the analysis, R-squares is 0.14586446 indicating that the model is fit and conclusion on the relationship of the variables can be reached. This can be represented in the graph below

Report on CAPM Model 19

Furthermore, P-value is 5.47E-20 < 0.05 meaning the result is statistically significance at the significant level of 95%. From the study, the coefficient is of education is 1.125691 implying that one more year of education increases an individual salary by 1.125691 and also there is positively relationship between education and individual salary. From the result we can right the predictive equation as

Wages I = -1.11897 +1.125691educ +Ɛ

Adding experience to the first model, the researcher intended to know how education and experience influences an individual wages. The model two is written as:

Report on CAPM Model 20 …………………………… (2)

The regression result are in the appendix 3 below. From the appendix two, it can be noticed that the model is perfectly fit since its R-squared is 0.202025 indicating that of 20% of the variables were analyzed in the regression analysis. The fit model line can be represented in the figure below;

Report on CAPM Model 21

On the significance level of the study, education has p-value of 5.56E-27 while experience p-value is 1.89E-09 the p-value is < 0.05 therefore at significance level of 95%, the analysis is statistically significant. The coefficient of the study gives 1.388 and 0.1576 for education and experience respectively. This indicate that 1 year of education increases salary by 1.388 and 1 more year for experience increases wages by 0.1576

Therefore the predictive equation can be given as

Wage= -7.35672 +1.388 education + 0.1576 experience

To investigate more on factors influencing an individual wage, the third model which includes gender was developed. The model equation is given by,

Report on CAPM Model 22

From this regression was done and the regression output was placed in appendix 4 below.

The model gives R-squared of 0.253158 indicating that the model is fit since over 25% of the variables were included in the study. This is shown in the graph below

Report on CAPM Model 23

The p-values of education, experience and gender is gives as 3.28E-29, 3.19E-11 and 3.19E-09 respectively. The p-value of the three variables are < 0.05 meaning the variables are statistically significance at significance level of 95%. The relationship of the three variables are also shown at the appendix 4 with education, experience and gender coefficients as 1.41076, 0.169951 and -3.50645 respectively. Both experience and education positively influence individual wage while gender negatively influence.

The study further investigated the correlation between the factors influencing the individual wage. This is shown below

EDUCATION

EXPERIENCE

EDUCATION

0.381922

EXPERIENCE

-0.35268

-0.20537

0.002031

0.176967

-0.15002

0.977961

0.079179

0.100579

-0.03552

0.011225

0.278947

0.161766

-0.02389

0.117926

-0.15703

0.119466

0.093164

The researcher intended to investigate the correlation matrix of all of the variables and use the matrix to discuss the importance of each variable for wages as well as the relationships between the variables. From the above table the relationship between wage and the other variables can be seen clearly with all variables positively related with wage except gender which is negatively related. All variables that is experience, Age, married and union are negatively related with education except gender which is positively related. Experience on the other hand is positively correlated with gender, age, married and union. From the correlation matrix above, gender is positively correlated with age and marital status while negatively related with union. Age on the other hand is positively correlated with marital status and union and lastly married is positively related with being in union. All these factors in one way or the other influence the wage of an individual the difference is that the magnitude which they influence vary from one variable to another.

The researcher lastly formulated the model including all the variables and the model is given as

Report on CAPM Model 24(4)

The regression results are shown in appendix 5 below

From the regression result in appendix 5, the R-square is 0.266 indicating that the model is perfect fit and over 26% of the total variables were included in the analysis. The p value of the variables include education which is 0.2190 > 0.05 hence education is not statistically significance in explaining the effect of the wage in this model, furthermore, experience gives a p-value of 0.625681> 0.05 hence is not statistically significance. Gender on the other hand gives a p-value of 5.88E-08< 0.05 hence is statistically significance at 95% significance level, age p-value is 0.691697 which is >0.05, not statistically significance, marital status gives a p-value of 0.259017 >0.05 indicating that it is not statistically significance and lastly union which gives P-value of 0.005088 <0.005 indicating that it is statistically significance at 95% significance level.

Following this outcome, the model 4 can be re-written as

Wage = α +βgender +βUnion +Ɛ

Therefore, the new regression output can be given as

Coefficients

Standard Error

Intercept

14.36573

0.484336

29.66065

9.4E-115

-2.85181

0.658662

1.79E-05

0.854716

3.115935

0.001933

Therefore, we can conclude that change in gender influences age by -2.85181 while union increase wage by 2.66324.

In conclusion we can state that all the above five variables influences wages and change in one variables can either increase wage an individual earn or reduce the age.

Bibliography

Ai, H., Croce, M.M. and Li, K., 2013. Toward a quantitative general equilibrium asset pricing model with intangible capital. Review of Financial Studies, 26(2), pp.491-530.

Barberis, N., Greenwood, R., Jin, L. and Shleifer, A., 2015. X-CAPM: An extrapolative capital asset pricing model. Journal of Financial Economics, 115(1), pp.1-24.

Dempsey, M., 2013. The capital asset pricing model (CAPM): the history of a failed revolutionary idea in finance? Abacus, 49(S1), pp.7-23.

Fama, E.F. and French, K.R., 2015. A five-factor asset pricing model. Journal of Financial Economics, 116(1), pp.1-22.

Fama, E.F. and French, K.R., 2015. International Tests of a Five-Factor Asset Pricing Model. Fama-Miller Working Paper.

Scott, W.R., 2014. Financial accounting theory. Pearson Education Canada.

Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure. European Journal of Operational Research, 234(2), pp.508-517.

APPENDICES

Part A: Appendix

APPENDIX I

SUMMARY OUTPUT TECHNOLOGY INDUSTRY

Regression Statistics

Multiple R

0.759223

0.576419

Adjusted R Square

0.575236

Standard Error

5.775994

Observations

Significance F

Regression

16253.18

16253.18

487.1749

9.23E-69

Residual

11943.64

33.36211

28196.82

Coefficients

Standard Error

Lower 95%

Upper 95%

Intercept

0.148372

0.306539

0.484022

0.628666

-0.45447

0.751215

1.464847

0.066367

22.07204

9.23E-69

1.334329

1.595364

APPENDIX II

SUMMARY OUTPUT MANUFACTURING INDUSTRY

Regression Statistics

Multiple R

0.811292

0.658195

Adjusted R Square

Standard Error

Observations

Significance F

Regression

8349.018

8349.018

1.82E-85

Residual

4335.699

12.11089

12684.72

Coefficients

Standard Error

Lower 95%

Upper 95%

Intercept

0.189993

0.184692

1.028703

0.304314

-0.17322

1.049882

0.039986

26.25607

1.82E-85

0.971245

Appendix III 1980-1989

SUMMARY OUTPUT TECHNOLOGY

Regression Statistics

Multiple R

0.842065

0.709073

Adjusted R Square

0.706607

Standard Error

4.012555

Observations

Significance F

Regression

4630.531

4630.531

287.5999

Residual

1899.871

6530.402

Coefficients

Standard Error

Lower 95%

Intercept

-0.57413

0.370171

-1.30717

1.278496

0.075389

16.95877

1.129207

SUMMARY OUTPUT MANUFACTURING

Regression Statistics

Multiple R

0.823697

0.678477

Adjusted R Square

0.675753

Standard Error

3.423918

Observations

Significance F

Regression

2919.123

2919.123

249.0036

7.47E-31

Residual

1383.339

11.72321

4302.463

Coefficients

Standard Error

Lower 95%

Intercept

0.069462

0.315867

0.219909

0.826322

-0.55604

1.015103

0.064329

15.77985

7.47E-31

0.887714

Appendix IV: 1990-1999

SUMMARY OUTPUT: TECHNOLOGY

Regression Statistics

Multiple R

0.462999

Adjusted R Square

0.458448

Standard Error

5.558591

Observations

Significance F

Regression

3143.522

3143.522

101.7389

1.25E-17

Residual

3645.956

30.89793

6789.478

Coefficients

Standard Error

Lower 95%

Intercept

0.525283

0.291922

-0.48411

1.287678

0.127663

10.08657

1.25E-17

1.034871

SUMMARY OUTPUT: MANUFACTURING

Regression Statistics

Multiple R

0.523799

Adjusted R Square

0.519764

Standard Error

3.266003

Observations

Significance F

Regression

129.7946

9.81E-21

Residual

10.66678

Coefficients

Standard Error

Lower 95%

Intercept

0.308635

-0.64252

0.521784

-0.80948

0.854563

0.075009

11.39274

9.81E-21

0.706024

Technology

APPENDIX V

SUMMARY OUTPUT TECHNOLOGY

Regression Statistics

Multiple R

0.778492

Adjusted R Square

0.602712

Standard Error

7.005355

Observations

Significance F

Regression

8908.616

8908.616

181.5307

1.27E-25

Residual

5790.849

49.07499

14699.47

Coefficients

Standard Error

Lower 95%

Intercept

0.832625

0.639798

1.301388

0.195661

-0.43435

1.798919

0.133517

13.47333

1.27E-25

1.534519

SUMMARY OUTPUT MANUFACTURING

Regression Statistics

Multiple R

0.870638

Adjusted R Square

0.755959

Standard Error

3.430541

Observations

Significance F

Regression

369.6239

Residual

1388.696

11.76861

5738.655

Coefficients

Standard Error

Lower 95%

Intercept

0.961573

0.313311

3.069073

0.002664

0.341133

0.065384

19.22561

1.127562

APPENDIX 6

SUMMARY OUTPUT: TECHNOLOGY INDUSTRY

Regression Statistics

Multiple R

0.910132

0.828339

Adjusted R Square

0.826893

Standard Error

3.687316

Observations

Significance F

Regression

23356.53326

7785.511

572.6197

8.1E-136

Residual

4840.283668

28196.81693

Coefficients

Standard Error

Lower 95%

Upper 95%

Intercept

0.198929773

1.539335

0.124611

-0.08501

0.697445

1.256517

0.065177073

19.27851

1.128336

1.384697

-0.43791

0.068651483

-6.37867

5.55E-10

-0.57292

-0.30289

1.161159

0.045994987

25.24533

1.070703

1.251615

APPENDIX 7

MANUFACTURING INDUSTRY

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.905434

0.819812

Adjusted R Square

0.818293

Standard Error

2.533838

Observations

Significance F

Regression

10399.07801

3466.359

539.9033

4.5E-132

Residual

2285.638633

6.420333

12684.71664

Coefficients

Standard Error

Lower 95%

Upper 95%

Intercept

0.13669989

-0.63277

0.527293

-0.35534

0.182342

0.762542

0.044788161

17.02554

5.63E-48

0.850625

0.047175694

9.983735

0.378212

0.563768

1.058549

0.03160668

4.6E-112

1.120708

Part B: Appendix

Appendix 1: Descriptive statistic

Descriptive

Education 

Experience 

Gender 

Married 

13.01872659

0.458801

36.83333

0.655431

0.179775

Standard Error

0.333586

0.113178243

0.535722

0.021584

0.507458

0.020584

0.016633

0

0

0

0

Standard Deviation

7.708645

2.615372628

12.37971

0.498767

11.72657

0.475673

Sample Variance

59.42321

6.840173985

153.2572

0.248769

137.5125

0.226265

0.147733

Kurtosis

4.991768

0.840774992

-0.38095

-1.97993

-0.58079

-1.57561

0.800367

Skewness

1.697286

-0.203677595

0.687758

0.165822

0.548297

-0.65598

1.672538

0

0

0

0

7228.275

Confidence Level (95.0%)

0.655304

0.222330138

1.052386

0.996864

0.040436

0.032674

Appendix 2: Model 1

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.381922

0.145864

Adjusted R Square

0.144259

Standard Error

Observations

Significance F

Regression

4619.903

4619.902851

90.85197

5.47E-20

Residual

27052.67

50.85088192

31672.57

Coefficients

Standard Error

Lower 95%

Intercept

-1.11897

1.568181

-0.713546101

0.475821

-4.19956

EDUCATION

1.125691

0.118101

9.53163003

5.47E-20

APPENDIX 3: MODEL 2

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.449472

0.202025

Adjusted R Square

0.199019

Standard Error

6.899047

Observations

Significance F

Regression

6398.644

3199.322

67.21709

9.51E-27

Residual

25273.93

47.59685

31672.57

Coefficients

Standard Error

Lower 95%

Intercept

-7.35672

1.828386

-4.02362

6.56E-05

-10.9485

EDUCATION

1.388947

0.122105

5.56E-27

1.149078

EXPERIENCE

0.157697

0.025796

1.89E-09

0.107022

Appendix 4: Model 3

Regression Statistics

Multiple R

0.503148

0.253158

Adjusted R Square

Standard Error

6.680641

Observations

Significance F

Regression

8018.161

59.88489

2.37E-33

Residual

23654.41

44.63096

31672.57

Coefficients

Standard Error

Lower 95%

Intercept

-6.25031

1.780005

0.000484

-9.74704

EDUCATION

0.118295

11.92577

3.28E-29

1.178375

EXPERIENCE

0.169951

0.025062

6.781113

3.19E-11

0.120717

-3.50645

0.582094

-6.02386

3.19E-09

-4.64994

APPENDIX 4: CORRELATION ANALYSIS

EDUCATION

EXPERIENCE

EDUCATION

0.381922

EXPERIENCE

-0.35268

-0.20537

0.002031

0.176967

-0.15002

0.977961

0.079179

0.100579

-0.03552

0.011225

0.278947

0.161766

-0.02389

0.117926

-0.15703

0.119466

0.093164

APPENDIX 5: MODEL 4

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.516426

0.266696

Adjusted R Square

0.258347

Standard Error

Observations

Significance F

Regression

8446.938

1407.823

31.94413

8.11E-33

Residual

23225.63

44.07141

31672.57

Coefficients

Standard Error

Lower 95%

Upper 95%

Intercept

-2.72132

10.18339

-0.26723

0.789396

-22.7263

17.28371

EDUCATION

2.054653

1.669659

1.230582

0.219028

-1.22535

5.334658

EXPERIENCE

1.670308

0.488102

0.625681

4.096559

-3.23235

0.587519

5.88E-08

-4.38652

-2.07819

-0.66227

1.669139

-0.39677

0.691697

-3.94125

2.616717

0.713341

1.129937

0.259017

-0.52685

1.953535

2.154617

0.765886

2.813234

0.005088

0.650052

3.659181