The book by Carmona refers to “Statistical Analysis of Financial Data in R” by Ren´e A. Carmona, 2nd edition; Accessible at
https://lbdiscover.ust.hk/bib/991003455739703412
I. Problem 4.8 on page 273 of the book by Carmona (In both questions 1 and 5, whenconducting LS regressions, check whether the predictors are statistically significant at 5% significance level; as to the residuals, compute the studentized residuals instead of the raw residuals.) The data hills.csv can be downloaded from Canvas.
II. Download the dataset “Google” from the course website. The dataset contains:• First and second column (rGoog): Date and Alphabet Inc. (GOOG)’s monthly return from 2010.01 to 2021.08.
• Third column(rf): Monthly risk free rate of the same period.
• Fourth to sixth column (rMex, rSmB, rHmL): Fama-French Three-factor monthly returns of the same period.
Conduct the following analysis parallel to what we did in class for Berkeshire Hathaway Inc. (BRK-A). Set the significance level to be 5%.
1. Fit a single factor model for the excess return of GOOG with one predictor “rMex” using LS regression. Report the summary of the fit. (cf. Lect 8 p.5)
2. Based on the single factor model result, for GOOG stock data during the period tested (cf.Lect 8 p.9-17),
(i). Is the market (excess) return significant in explaining the variation in the return of
GOOG?
(ii). Is α significantly different from 0? If so, in which direction? (iii). Is β significantly different from 1? If so, in which direction?
(iv). Use the standardized/studentized residuals to conduct model diagnostics and comment.
3. Fit the Fama-French Three-factor model for GOOG using LS regression. Report the summaryof the fit.(cf. Lect 8 p.21)
4. Are the three factors as a whole statistically significant? Is any single one of the factorsstatistically significant?(cf. Lect 8 p.22)
5. How much can the single factor explain the variation in the GOOG returns? How much canthe three factors explain the variation in the GOOG returns? (cf. Lect 8 p.13)
6. Does the 3-factor model explain statistically significantly more variation than the single factormodel (cf. Lect 8 p.24)?
