Econometric Models Using the Eviews - Coursework Example

CAPM & FAMA FRENCH [Pick the Contents Contents 2 Capital Asset Pricing Model 3 Fama & French Model Three Factor Model: 4 2 1Motivation to Test Theory 4 2.1.2Usefulness of Eviews 5 2.1.3Main Assumption of the Theories 5 2.1.5.1Assumptions of CAPM 5 2.1.5.1Assumptions of Fama French Model 5 2.1Hypothesis Testing 5 2.2 The Data 7 2.3Empirical Results 7 Part 2: Determinants of Audit Fee 14 2.1What determines the Cost of an Audit Fee? 14 2.2 Hypothesis 14 3.Conclusion 16 Bibliography 17 Introduction The paper is based on the quantitative analysis and econometric models using the Eviews. A brief explanation of each of these is mentioned below The econometrics referred to as the application of methods such as statistical and mathematical data that represents the economics or the branch of economics to generate more objective and empirical results of economic variables relationships (Brooks, 2002,p 1). The econometric model used to generate and understand the relationships among number of economic indicators. The main objective of econometrics is to conduct quantitative analysis, which refers to defining the opinions in more structured and understandable ways so more reliable facts can be produced from the analysis. The report uses the Eviews for the data analysis and hypothesis testing for CAPM & FAMA French Model (Dougherty, 2011) The paper is bifurcated into two parts. Part 1 is based on the test of Capital Asset Pricing Model and Fama French Model using the factors for US stocks for the period of 1963 to 2013. Part 2 of the report is based on the audit fees to evaluate whether the firm characteristics explain the cost of audit or not. Theory Capital Asset Pricing Model The capital asset pricing model is referred to as the model that describes the relationship between the risk and return, which determines the appropriate required rate of return on assets. (Sharifzadeh, 2010) The formula for capital asset pricing model is as follows E (Ri) = Rf + βi(E(Rm) – Rf) E (Ri) = Expected return on Asset Rf = Risk free returns i.e. interest from Govt Securities such as Tbills and Tbonds Βi = Beta , which refers to as the sensitivity of the risk premium to the expected return. The risk premium is referred to as the excess ret urn of the market over the risk free return .i.e. (E (Rm) – Rf) E(Rm) = Expected Return of market portfolio Fama & French Model Three Factor Model: Fama & French model is referred to as the extension of capital asset pricing model. The model adds the size and value factors in addition to the market risk factor in capital asset pricing model. The model considers the fact that whether the small cap stocks and value stocks outperform markets on regular basis. This is the reason; Fama French model is referred to as the three factor model. (Bodie, et al., 2009) R= Rf + B3(Km – Rf) + bs SMB+ bvHML + α R= Portfolio Expected rate of Return Rf = Risk free returns i.e. interest from Govt Securities such as Tbills and Tbonds Km = Return of the market portfolio (Km – Rf) = Market Risk Premium = Excess return on market over risk free return SMB= Small Market capitalization Minus Big Market Capitalization stocks HML = High Book to Market Value Stocks Minus Low Book to Market Value stocks B3 = Sensitivity of the market risk premium on portfolio expected return bs = Sensitivity of SMB to market return bv = Sensitivity of HML on portfolio expected returns The co-efficient bs and bv can be negative as well. 2.1.1 Motivation to Test Theory The section of the report identifies the fact that why should we test CAPM and Fama French Model? The answer is that the CAPM is used to assess the impact on expected return on asset exclusively by the movement in market risk premium. The CAPM gives an ideal situation of how to price securities that are traded in financial markets to determine the expected return on asset. The major reason to use the CAPM model is that the model gives the objective nature of cost of equity, which the model can yield. (Besley & Brigham, 2007) The Fama French model supplements the CAPM model to further evaluate the cost of equity in terms of return on asset by adding two more factors i.e. Small minus large market capitalization stocks and HMB High minus low book to market values. The reason to test the Fama French model adds the size and value factors in addition to the market risk factor in capital asset pricing model. (Brigham & Ehrhardt, 2013) 2.1.2 Usefulness of Eviews Econometric view is a statistical package for windows. The Eview is used for the time series analysis. It generates the statistical and economic analysis, which may also be referred to as the quantitative analysis. Econometric views is used in combination with other programming languages to support and display the statistical analysis 2.1.3 Main Assumption of the Theories 2.1.5.1 Assumptions of CAPM Following are the main assumptions of CAPM 1. All investors are Rational 2. All investors are risk averse 3. Investors have goals to maximize economic utilities. 4. The investors are broadly diversified across the range of investments 5. Investors can lend and borrow unlimited amount at risk free rate. 6. All investors execute trade without transaction or taxation cost. 7. All investors have the expectations that are homogeneous 8. Market is informational efficient and all investors have the access to the information at the same time (Focardi & Fabozzi, 2004) 2.1.5.1 Assumptions of Fama French Model Fama French model covers the limitations of the capital asset pricing model, which arises from the assumptions of CAPM. The Fama French model assumes that in addition to market portfolio there are additional risk factors due to market capitalization and size of the stocks (Lam, 2005) 2.1 Hypothesis Testing Capital Asset Pricing Model The Null and Alternate Hypothesis are as follows H0= α=0 H1= α ≠0 Alpha represents the constant co-efficient,which is the risk free rate and the null hypothesis states that the remaining market risk premium zero, constant has no significance impact on asset returns. Alternate hypothesis states that constant has significant impact on monthly retruns on mines industry. H0= β=0 H1= β ≠0 The null hypothesis represents the expected risk premium has no significant impact on return on assets and alternate hypothesis states that the value of the beta has significant impact on the monthly returns on mines industry. There are six different portfolios are used with respect to book to market value and size. The analysis of result of each of the portfolio is then compared with the base portfolio of Mines Industry. Fama French Model Fama French model includes three factors i.e. market risk premium, SMB and HML. The null and alternate hypothesis are as follows α represents constant, which is risk free rate in this case β1 represents market risk premium β2 represents the sensitivity of SMB on return on asset  β3 represents the sensitivity of SMB on return on asset 2.2 The Data The data consists of monthly return of mines industry and the time period ranges from January 1963 to July 2013. The CAPM model uses the size and book to market value of equity and determines how book to market and size affects the output. In addition to this, the Fama French model uses 2 more variables i.e. SMB and HML. To test Fama French three factor model monthly returns of 6 portfolios sorted by size and book to market ratios is also used. 2.3 Empirical Results Significance level is 5% Table 1 Summary of main results obtained by simple regression Portfolio No Coefficient/ p-value Coefficients and p-value Mean R² DW F-stat (Prob) Constant β Mines Coefficient 0.06854 0.94746 0.95545 0.26554 1.95052 273.96630 p-value 0.79070 0.00000 1 (B-H) Coefficient 0.24777 0,914016 1.11811 0.76391 1.85385 1957.58000 p-value 0.00800 0,0000 2(B-M) Coefficient 0.07871 0,903427 0.94379 0.86808 1.81764 3980.99200 p-value 0.22330 0,0000     3(B-L) Coefficient (-0.035790) 1.00932 0.88180 0.94038 1.78370 9542.21200 p-value 0.44270 0.00000 4(S-H) Coefficient 0.53482 1.05580 1.47545 0.71279 1.80073 1501.45200 p-value 0.00000 0.00000 5(S-M) Coefficient 0.35907 1.06893 1.30621 0.77394 1.97071 2071.27200 p-value 0.00070 0.00000 6(S-L) Coefficient (-0.163510) 1.34295 0.91949 0.76513 1.94247 1970.92300 p-value 0.23110 0,0000 P-value refers to as the alternative to rejection point. It represents the smallest level of significance. If p Fcrit, reject the null hypothesis. The F-statistic is greater that Fcritical value in case of CAPM but in case of 3 factor FF model F statistic is lower. Therefore, reject the null hypothesis in case of CAPM but not in case of FF Model. Heteroskedasticity test white CAPM F-statistic 1.557242     Prob. F(9,597) 0.1247 Obs*R-squared 13.92308     Prob. Chi-Square(9) 0.1251 Scaled explained SS 19.91112     Prob. Chi-Square(9) 0.0185 Heteroskedasticity test white FF Heteroskedasticity Test: White F-statistic 1.557242     Prob. F(9,597) 0.1247 Obs*R-squared 13.92308     Prob. Chi-Square(9) 0.1251 Scaled explained SS 19.91112     Prob. Chi-Square(9) 0.0185 Corrected output Dependent Variable: ERMINESHASAN Method: Least Squares Date: 01/02/15 Time: 16:55 Sample: 1963M01 2013M07 Included observations: 607 White heteroskedasticity-consistent standard errors & covariance Variable Coefficient Std. Error t-Statistic Prob.   C -0.147195 0.265079 -0.555286 0.5789 MKT_RF 0.930494 0.072719 12.79582 0.0000 SMB 0.373052 0.092338 4.040088 0.0001 HML 0.327999 0.103232 3.177306 0.0016 R-squared 0.341558     Mean dependent var 0.538287 Adjusted R-squared 0.338282     S.D. dependent var 7.611953 S.E. of regression 6.192023     Akaike info criterion 6.490969 Sum squared resid 23119.71     Schwarz criterion 6.520020 Log likelihood -1966.009     Hannan-Quinn criter. 6.502272 F-statistic 104.2660     Durbin-Watson stat 1.943733 Prob(F-statistic) 0.000000 The corrected output removes the assumptions of homogeneous variance among all observations. The change in standard deviation means different variables have different variances. Test for autocorrelation HAC standard errors & covariance (Bartlett kernel, Newey-West fixed bandwidth = 6.0000) Variable Coefficient Std. Error t-Statistic Prob.   C -0.147195 0.266906 -0.551485 0.5815 MKT_RF 0.930494 0.068441 13.59548 0.0000 SMB 0.373052 0.108934 3.424564 0.0007 HML 0.327999 0.109261 3.001986 0.0028 The histogram of the regression model for CAPM The histogram of the regression model for FF 3-factor: In case of CAPM and FF model, the data is positively skewed. The kurtosis is positive, which indicate the peaked distribution. The JB also indicate the positive skewness. 1) Conclusion and Summary The analysis is based on monthly returns on Mines industry using the CAPM and Fama French Model. The Fama French model overcomes the limitations of CAPM model and identifies that with the additions of size and value factors, the evaluation of regression results are more accurate and F-test indicate that the independent variables are not significant. . Part 2: Determinants of Audit Fee 1. Introduction Auditing is considered to be a very significant activity for organization evaluation. It is sort of an assessment that a company has to undergo in order to evaluate effectiveness of organization’s internal operations and control. There are two different methods of auditing, one is internal evaluation that is called as internal audit and the other one is evaluation from an external person that is called as external audit. Annual audit is a mandatory activity that every organization has to conduct on annual basis. Therefore, in order to conduct external audit an organization has to pay fee to external auditor which is called as audit fee. Audit fees depend upon the terms and conditions mentioned in the contract which is created from mutual consent between the auditor and auditee (Clatworthy & Peel, 2007). The fee also depends upon the type of services rendered and the number of staff that will be involved in the audit process. Furthermore, the determinants of audit fee are classified into two major subgroup; client (auditee) attributes and auditor attribute. Size, complexity, risk and profitability are the characteristics for measuring client attributes which will in turn help in assisting the audit fee for the company. Audit fee is usually mentioned in the annual report of the company. (El-Gammal , 2011). 2. Theoretical Background: 2.1 What determines the Cost of an Audit Fee? Following are the major determinants of Audit Fee a) Size refers big versus small firms in terms of business structure. Time frame for audit of big firm is longer than that of smaller firm. Size of firm is measured using Log of Total Assets b) Complexity refers to the un-standardized presentation of information. Complexity is measure by the number of subsidies c) Risk refers to the risk of errors in detecting fraud. Its measurement method include total liabilities to total assets d) Reputation refers to the reputation of the auditor. More reputable auditor is more costly. A dummy variable of one equals to one of the big four and 0 if other auditor. 2.2 Hypothesis The model summarized regarding the audit fee by considering the determinants of audit Audit model is described as follows; Log( Audit fee)=  Big4 Dummy= Reputation Log(TA)= log of Total Assets Nsubs= Complexity Tilta= Risk One can expect the positive linear relationship between size, complexity and risk variables and the cost of the audit. In addition, firms with higher return on assets (retta) are expected to have lower audit fees, since this indicate the auditee’s profitability. The Null Hypotheses can be written as: 2.3 The data consist of a random sample of a cross section of 5,000 UK firms. Audit fee The co-efficient are significantly different than zero because the f-stat is significantly greater. The R2 represents that the 79 % of the audit fee determination is explained by the all the independent variables mentioned above. The DW test indicates that there is no autocorrelation because the value is equal to 2. Heteroskedasticity Test: White F-statistic 11.72809     Prob. F(34,4965) 0.0000 Obs*R-squared 371.7126     Prob. Chi-Square(34) 0.0000 Scaled explained SS 566.3773     Prob. Chi-Square(34) 0.0000 The data is negatively skewed with positive kurtosis that indicates the peaked distribution. As the Jarque-Bera value represents significantly greater value than the values in chi square table so it indicates the rejection of null hypothesis that the residuals are normally distributed. 3. Conclusion The audit fee is significantly affected by the major determinants of audit fee such as size, reputation, complexity and risks along with some other factors such as return on assets etc. using the data of 5000 UK firms, the data shows no autocorrelation but slightly negatively skewed and peaked. Therefore, the assumption of normal distribution is wrong. Bibliography 1. Brooks, C., 2002. Introductory Econometrics for Finance. New York: Cambridge University Press. 2. Besley, S., & Brigham, E. (2007). Essentials of Managerial Finance. Cengage Learning. 3. Bodie, Z., Kane, A., Marcus, A. J., & Mohanty, P. (2009). Investments. Tata McGraw-Hill Education. 4. Brigham, E., & Ehrhardt, M. (2013). Financial Management: Theory & Practice. Cengage Learning. 5. Clatworthy, M. A. and Peel, M. J. (2007). The effect of corporate status on external audit fees: Evidence from the UK. Journal of Business Finance and Accounting, 34, 169-201. 6. Dougherty, C., 2011. Introduction to Econometrics. New York: Oxford University Press. 7. El-Gammal , W., 2011. Determinants of Audit Fees: Evidence from Lebanon. Internation Business Research, 5(11), pp. 136-145. 8. Focardi, S. M., & Fabozzi, F. J. (2004). The Mathematics of Financial Modeling and Investment Management. John Wiley & Sons. 9. Lam, K. (2005). Is Farma French model Three factor model better than the CAPM? Simon Fraser University. 10. Sharifzadeh, M. (2010). An Empirical and Theoretical Analysis of Capital Asset Pricing Model. Universal Publisher. Read More