The aim of the paper is to evaluate six different Capital Asset Pricing Model (CAPM) using stock price of Verizon Communication Inc. Six different models are developed using regression analysis. In each of the regression model excess return on stock is taken as dependent variable. The common independent variable in the six model is return on market portfolio. Under independent variables used in different models are change in risk premium, small minus big and high minus low. The objective is to make a comparative analysis among different CAPM model using different econometric tool. The Durbin-Watson test statistic is used to examine whether the models suffer from serial correlation or not. Coefficient diagnostics test using Wald coefficient restrict has been performed to test whether β values in each of the model is significantly different from zero or not. Finally, in order to test whether there is any specification error in the model “Reset” test has been run for each of the model. To examine the viability of the estimated econometric model, the reported β value of the estimated models are compared to those reported in different financial website (google finance and yahoo finance).
Table 1: Estimated Regression Models
|
|
Model 1 |
Model 2 |
Model 3 |
Model 4 |
Model 5 |
Model 6 |
|
0.00 |
0.00 |
0.12 |
0.00 |
0.16 |
0.20 |
|
|
0.00 |
0.00 |
|||||
|
0.00 |
||||||
|
DW d-Statistic |
2.04 |
2.04 |
2.01 |
2.07 |
2.03 |
2.04 |
|
(1.65, 1.69) |
(1.63, 1.72) |
(1.63, 1.72) |
(1.63, 1.72) |
(1.61, 1.74) |
(1.59, 1.76) |
|
|
Don’t reject |
Don’t reject |
Don’t reject |
Don’t reject |
Don’t reject |
Don’t reject |
|
|
Overall F-Test |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|
RESET Test |
0.65 |
0.51 |
0.01 |
0.63 |
0.00 |
0.00 |
|
0.21 |
0.21 |
0.30 |
0.21 |
0.30 |
0.30 |
Model 1: Simple CAPM
The simple CAPM model include only one dependent variable that is return to market portfolio. The model to be estimated is
Using the regression result the estimated equation is obtained as
In the regression model the value of R square is obtained as 0.21. This implies return on market portfolio can explain only 21 percent variation in excess return to company’s stock. The corresponding coefficient of market portfolio return is 0.65. This implies for unit change in market portfolio return excess return on stocks change by 0.65. The associated p value for the coefficient is 0.0000. As the p value is less than the significant value of 0.05, the null hypothesis of no significant relation between market portfolio return and excess return on stock has been rejected. This can also be examined using t statistics. The computed t statistics is 6.1117. The critical t value is 1.9776. As the computed t exceeds the critical t the, the coefficient of market portfolio return is statistically significant. The overall significance of the model can be tested using the F statistics. The associated p value for F statistics is 0.0000. As the p value is less than significance level, the model is statistically significant.
Model 2: Simple CAPM Plus ‘Change in Risk Premium’ Measure
In the second model another variable called “change in risk premium (CRP)” is added in the model. The model to be estimated is
Using values of the regression analysis the model is estimated as
The value of R bar square in the model is 0.21. That is addition of new variable does not improve the explanatory power of the model. The coefficient corresponding to market portfolio return and change in risk premium are 0.6549 and 0.6980 respectively. Both the coefficients are positive implying both has a positive influence on excess return on stocks. For market portfolio return compute t value is 6.1412. The t value is greater than critical t value of 1.9777, implying rejection of null hypothesis of no significant relation between market portfolio return and excess return on stock. For change in risk premium however the computed t is 0.7078. This is smaller than critical t implying the variable is statistically insignificant. The result of t test is further supported by the p value. The model has overall significance as examined from the significance value of F statistics.
Model 3: Simple CAPM Plus ‘Small Minus Big’ Size Premium Measure
The third model of CAPM include an additional variable called small minus big in the simple CAPM model. The model is given as
Using the stock data of Verizon Communication Inc’s the estimated model is
The value of R bar square increased slightly in the model with the value being 0.30. That is addition of new variable increases the explanatory power of the model. The coefficient corresponding to market portfolio return and small minus big are 0.8282 and -0.8338 respectively. The market portfolio return thus has a positive influence on excess return while the difference in average return between small and big portfolios has a negative influence on excess stock return. For market portfolio return compute t value is 7.6456 and that for SMB is -4.2787. Both the t values are greater than critical t value of 1.9777, implying rejection of null hypothesis of no significant relation between the concerned variables. The result of t test is further supported by the p value. The model has overall significance as examined from the significance value of F statistics.
Model 4: Simple CAPM Plus ‘High Minus Low’ Value Premium Measure
This version of CAPM model include difference between two value portfolio and two growth portfolio in the simple CAPM model. The designed model is
Using regression output, the estimated model is
The value of R bar square is same as the previous model. That is the two explanatory variables now can explain 30 percent variation in excess return of stocks. The coefficient corresponding to market portfolio return and high minus low are 0.6706 and -0.2980 respectively. The market portfolio return thus has a positive influence on excess return while the difference in average return between two value and growth portfolios has a negative influence on excess stock return. For market portfolio return compute t value is 7.6456 and that for SMB is -4.2787. The variable HML however is not statistically significant as the p value is greater than the significant value. The market portfolio return is statistically significant (p value lower than significance value). The model has overall significance.
Model 5: Fama and French Three-Factor Model
The three factor include SMB and HML in the simple CAPM model. The model to be estimated is
Putting the values of estimated coefficient from regression result, the model is obtained as
In the three factor model, value of R bar square increased only slightly to 0.31. This shows a slightly higher explanatory power of the model. The coefficient of market portfolio increased to 0.8484. The effect of market portfolio return on excess stock return is positive while that of SMB and HML have an adverse effect on excess stock return. All the coefficient except HML is statistically significant. The overall model is statistically significant.
Model 6: Combined Model
The combined model evaluates impact of all the independent variables on excess stock return. The model is given as
Using the regression result the estimated model is obtained as
In the combined model, the value of R bar square is 0.30. Inclusion of additional variables does not improve the explanatory power of the model. Market portfolio return and CRP have a positive effect on excess return on stock. SMB and HML have an adverse effect on excess stock return. In the model only significant variables are market portfolio return and SMB. The model is overall statistically significant as the five previous models.
The Durbin Watson test is used to examine whether the error terms in the model has serial correlation or not. The null hypothesis is no positive serial correlation. The alternative hypothesis is the present of positive serial autocorrelation. In all the five models the Durbin Watson test statistic is greater than the upper critical value. Each of the model thus fail to reject null hypothesis of no positive serial autocorrelation. The error terms in the model are thus free from any positive serial autocorrelation.
Hypothesis I
H0: α = 0 against HA: α ≠ 0
In all the six model the coefficient, the p value is greater than the significant level of 0.05. This implies non-rejection of null hypothesis stating α = 0.
Hypothesis II
H0: βM = 0 against HA: βM ≠ 0
The p value associated with the coefficient of βM is less than the significance level in all the six models of CAPM. In this case, the null hypothesis of βM = 0 is rejected. The market portfolio return thus is statistically significant in all the models.
Hypothesis III
H0: βM = 1 against HA: βM ≠ 1
In model 1, 2 and 4, the p value associated with the coefficient is less than the significant value of 0.05. The null hypothesis thus is rejected in these three models implying value of βM is significantly different from 1. In model 3, 5 and 6 the p value is greater than significance level implying acceptance of null hypothesis. The coefficient of market portfolio return thus is equivalent to 1 in these three model.
Hypothesis IV
H0: βc = 0 against HA: βc ≠ 0
The variable named change in risk premium (CRP) is included only in model 2 and model 6. In both the model p value is greater than 5% significance level indicating acceptance of null hypothesis of βc = 0. The CRP thus is not statistically significant in either of the model.
Hypothesis V
H0: βs = 0 against HA: βs ≠ 0
The variable SMB is present in the three of six model namely model 3, 5 and 6. In all the model p value is less than 5% significance level indicating rejection of null hypothesis of βs = 0. The variable SMB thus is statistically significant in all the three models.
Hypothesis VI
H0: βh = 0 against HA: βh ≠ 0
The model 4, 5 and 6 include HML as an independent variable in the CAPM. In all the three models p value is greater than significance value of 0.05 implying acceptance of null hypothesis of βh = 0. The HML thus is not statistically significant in either of the model.
Hypothesis VII
H0: βh = βs = 0 against HA: βh = βs ≠ 0
The additional hypothesis test has been performed for model 5 and 6. In both the model the p value associated with the F statistics is less than significance value of 0.05. The null hypothesis thus is rejected for both the model suggesting at least one of these variables is significantly different from 0.
Hypothesis VIII
H0: βc = βh = βs = 0 against HA: βc = βh = βs ≠ 0
This hypothesis test has been performed only for model 6. The p value of F statistics is 0.0002. As the p value is less than 5% significance level, the null hypothesis that coefficients of CRP, SMB and HML are equal to zero is rejected. This in turn implies at least only of coefficient in the model is statistically significant.
The RESET test is used to examine whether the estimated model has any specification error.
Null hypothesis (H0): The model does not have any specification errors.
Alternative Hypothesis (H1): The model suffers from specification errors.
In model 1, 2 and 4 p value associated with the F statistics are 0.6494, 0.5115 and 0.6376. In these three model the p value us greater than significance value of 0.05 implying acceptance of null hypothesis of no specification errors. These three model thus is free from specification errors. In model 3, 5 and 6 on the other hand p value exceeds the significance value indicating rejection of null hypothesis stating no specification errors.
|
Model 1 |
Model 2 |
Model 4 |
Google Finance |
Reuters |
|
0.60 |
0.56 |
The above table mainly compares the beta value of Verizon Communications Inc under google finance, reutters, model 1, model 2 and model 4. The relevant calculation used in deriving the beta is mainly at the levels of 0.60 for Google Finance, and 0.56 in Reuters. The beta of the company is mainly at higher levels, which can be detected from the above table. Hence, from the evaluation it can be detected that the beta derived under different method are relevantly different, which can have negative impact on performance of the company. However, the values of the beta is mainly at he similar levels, which directly indicates that the model is more close to the method, which is being used by Google finance.
|
Model 1 |
Model 2 |
Model 4 |
Yahoo Finance |
|
0.50 |
From the relevant evaluation it can be detected that the beta values of yahoo finance are mainly at the relevant when comparing with the different models. The calculations have mainly indicated that model 1, 2, and 4 does not comply with the yahoo finance measure, which can be used for detecting the beta of the company. hence, it can be detected that the yahoo finance model for calculating beta does not comply with the overall models (Finance.yahoo.com, 2018).
|
Model 3 |
Model 5 |
Yahoo Finance |
|
0.50 |
The model 3 and model 5 does not have any kind of linkage between the overall yahoo finance beta and other models. This mainly helps in detecting that the overall beta derived from the two model is not adequate, which does not allow the investors to derive the adequate risk attributes of the investment.
The above figure relevantly depicts the relation between Verizon Communication Inc’s stock return and each of the independent variable. From the evaluation it can be detected that overall excess return on market portfolio is positively related with stock return. No significant relation however is seen between rest three independent variable and excess stock return.
Conclusion
The overall above assessment aims in evaluating the method, which can be used by the investors in detecting possible return that might be generated from an investment. The analysis suggests that model 1, 2 and 4 are superior compared to other 3. The three models have no specification errors compared to other three. In all the three model beta values are different from 1 meaning stock returns are either more or less volatile market portfolio return. More specifically, the beta values for model 1, 2 and 4 are 0.6469, 0.6549 and 0.6707 respectively. The beta values less than 1 implies than the stock return is less volatile compared to volatility in market return. From the perspective of risk averse individual, the first model that is simple CAPM model is best to analyze the stock return.
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