Use the Fama-French 3-Factor model to run the following tests and alternative techniques to account for violations of the classical linear regression assumptions (CLRM) of the monthly returns of a...

Use the Fama-French 3-Factor model to run the following tests and alternative techniques to account for violations of the classical linear regression assumptions (CLRM) of the monthly returns of a portfolio of stocks consisting of an equal weighting of five stocks (Pfizer, Kraft Foods, AT&T, Home Depot, Du Pont). The data file used for this assignment is attached (port.dta). Step 1: Run the following Fama-French 3-Factor regression: . reg exret mktrf smb hml where: exret is the portfolio return minus the return on the risk free rate mktrf is the return of the S&P 500 Index minus the risk free rate smb is the returns of a portfolio of small firms minus returns of big firms hml is the returns of a portfolio of high book-to-market firms minus the returns of low book-to-market firms Interpret the results. Step 2: Check if ( ^) (residuals have a mean = 0). Note: Ordinary Least Squares (OLS) insures this assumption is true so we do not have to check when using the reg command in Stata. Step 3: Check if ( ^) (constant variance of the residuals). . rvfplot , yline(0) . estat imtest, white (White test) . estat hettest (Breusch-Pagan test) If needed, do the following: (1) Rerun the regression using the Huber-White sandwich estimators by adding the “robust” option. (2) Run a robust regression using the rreg command: . rreg exret mktrf smb hml Describe the differences between the results from the original regression, the regression with the robust option, and the robust (rreg) regression and why they are different. Page 2 of 3 Step 4: Check the are non-stochastic (independent variables are uncorrelated with residuals). Note: If the independent variables are measured with certainty (not estimated) this assumption is satisfied. You may run a pair-wise correlation to check, however, this procedure is very sensitive to correlation and may indicate the presence of correlation that will not cause concern when the independent variables are fixed (not estimated). . pwcorr r mktrf smb hml, sig Step 5: Check if ( ) (residuals are normally distributed). Note: Need to rerun regression before running regression post-estimation commands because the previous estimates were erased from memory. . reg exret mktrf smb hml . kdensity r, normal (kernel density estimate of distribution with normal distribution) . sktest r (skewness-kurtosis test) . swilk r (Swilk test) . estat imtest (tests skewness and kurtosis) What should be done if normality assumption is violated? Step 6: Check for outliers and influential observations. . predict rstd, rstandard . list… if abs(rstd)> 2.58 & rstd < .="" .="" predict="" double="" lev,="" leverage="" .="" gsort="" –lev="" .="" list="" …="" in1/5="" .="" predict="" double="" dfits,dfits="" .="" quietly="" gen="" cutoff="abs(dfits)"> 2*sqrt((e(df_m)+1)/e(N)) . list… dfits if cutoff == 1 . reg exret mktrf smb hml . dfbeta . quietly gen dfcut1 = abs(_dfbeta_1) > 2/sqrt(e(N)) . sort _dfbeta_1 . list date exret mktrf smb hml _dfbeta_1 if dfcut1 == 1 repeat above three commands for each _dfbeta_n (where n = 2, 3) What might be done if outliers or influential observations are present? Page 3 of 3 Step 7: Check for multicollinearity between independent continuous regressors (note this is different from testing the are non-stochastic under the CLRM assumptions). Some texts recommend running a pair-wise correlation to check, however, this procedure is very sensitive to correlation and may indicate the presence of correlation between independent variables that will not cause concern. Examining the variance inflation factors are a better procedure. . pwcorr mktrf smb hml, sig (pair-wise correlation) Variance inflation factors: You can use the vif command after the regression to check for multicollinearity. VIF stands for variance inflation factor. As a rule of thumb, a variable whose VIF values are greater than 10 may merit further investigation. Tolerance, defined as 1/VIF, is used by many researchers to check on the degree of collinearity. A tolerance value lower than 0.1 is comparable to a VIF of 10. It means that the variable could be considered as a linear combination of other independent variables. . collin mktrf smb hml (user-written collinearity test, collin must be installed) Note: Need to rerun regression before running the vif command because the previous estimates may have been erased from memory. . reg mktrf smb hml . estat vif What should be done if multicollinearity is present? Step 8: Test the model specification to see if there are any omitted variables. . estat ovtest