The Fama-French three-factor model has become a popular APT model. However, another model called the Carhart four-factor model has also been proposed (Mark Carhart, 1997, "On Persistence in Mutual Fund Performance," Journal of Finance 52, 57-82). In the four-factor model, the first three factors are the same as in the Fama-French three-factor model. The fourth factor is momentum. The momentum factor is constructed by the monthly return difference between the returns on the high and low prior return portfolios.

The factors for the four-factor model are available on Kenneth French's website ( mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html). There is a file for the three-factor model as well as a separate file for the momentum factor.

The data files are zipped. You will need to open the Zip file, save the text file, and then open the text file in Excel. Make sure you download the monthly factors. The Text Import Wizard in Excel will walk you through the steps necessary to import the text files into columns. When you get the data table set up, estimate the four-factor model and answer the following questions for the stock and mutual fund you selected in the previous chapter.

a. Would you expect the explanatory power of the four-factor regression to be higher or lower than the market model regression from the previous chapter? Why?

b. Are the alpha and betas for each regression statistically different from zero?

c. How do you interpret the betas for each independent variable for the stock and the mutual fund?

d. Which of the two regression estimates has the highest R squared? Is this what you would have expected? Why?