Multiple Regression Review
Question 1 (Estimating the CAPM)
Create a new Eviews workfile and import 8 series from Sheet1 of USstocks_monthly which contains monthly data starting in January 1973 and ending in June 2014. The series are:
U_KO: Coca-Cola share price
U_IBM: IBM share price
U_XRX: Xerox share price
U_GE: General Electric share price
RF: the 1 month US Treasury Bill rate
MKT_RF: the excess return on the market, is the value-weight return on all NYSE, AMEX, and NASDAQ stocks (from CRSP) minus the one-month Treasury bill rate (from Ibbotson Associates)
SMB: SMB (Small Minus Big) is the average return on the three small portfolios minus the average return on the three big portfolios.
HML: (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios
(a) Generate excess returns over the RF series for two share prices of interest to you.
(b) Estimate the CAPM (single market factor) model for your selected stocks and interpret the estimated beta coefficient.
(c) How would you answer an analyst who tells you that returns are completely unrelated to the market (have no systematic risk)?
(d) Comment on the explanatory power of the model.
(e) Is the data autocorrelated? Are the errors homoskedastic?
(f) The Newey-West correction is a procedure that adjusts the covariance matrix of the estimators to account for autocorrelation and heteroskedasticity. Using eviews, re-estimate the model using robust (Newey-West) standard errors. What do you observe about the estimated standard errors?
(g) Re-formulate the model so that you can test the hypothesis that beta is unity using the standard t-test, and conduct the hypothesis test.
Question 2 (Testing the APT Model)
(a) Re-estimate the CAPM models using your data, but this time include the unanticipated variables SMB and HML. Report the results.
(b) Are the coefficients on SMB and HML individually significantly different from zero? Interpret the coefficients.
(c) Conduct an F test that the coefficients on SMB and HML are jointly zero. What answer do you get? Is the CAPM regression a good model of the share prices?
(e) If the CAPM model omits relevant variables, what does this imply for the estimated coefficients? What problem might we expect to see in the regression residuals?
(f) What is the F-statistic of the regression? Write down the exact null and alternative hypotheses for the standard F-test testing the significance of the model. What is the number of restrictions for this test? Check the computation of the F-statistic using the R-square of the regression.
Description of Fama/French Factors
Construction: The Fama/French factors are constructed using the 6 value-weight portfolios formed on size and book-to-market. (See the description of the 6 size/book-to-market portfolios.)
SMB (Small Minus Big) is the average return on the three small portfolios minus the average return on the three big portfolios,
SMB = 1/3 (Small Value + Small Neutral + Small Growth)
- 1/3 (Big Value + Big Neutral + Big Growth).
HML (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios,
HML = 1/2 (Small Value + Big Value)
- 1/2 (Small Growth + Big Growth).
Rm-Rf, the excess return on the market, is the value-weight return on all NYSE, AMEX, and NASDAQ stocks (from CRSP) minus the one-month Treasury bill rate (from Ibbotson Associates).
See Fama and French, 1993, "Common Risk Factors in the Returns on Stocks and Bonds," Journal of Financial Economics, for a complete description of the factor returns.
Stocks: Rm-Rf includes all NYSE, AMEX, and NASDAQ firms. SMB and HML for July of year t to June of t+1 include all NYSE, AMEX, and NASDAQ stocks for which we have market equity data for December of t-1 and June of t, and (positive) book equity data for t-1.
Attachment:- stocks_monthly.xls