Question:
The traditional asset pricing model, known formally as the capital asset pricing model (CAPM)
uses only one variable to explain the returns of a portfolio/stock, and this explanatory variable is
the returns of the market as a whole. And we define the coefficient, β, to describe the systematic
risks that the firm is facing. In particular, β is the coefficient of the following regression equation:
Rit–Rf t = α + β[Rmt − Rf t] + uit
where Rit is the return of the stocks of firm i at time t, Rmt is the return of the market portfolio,
and Rf t is the return of the risk-free rate. uit is the error term.
In contrast, the Fama–French model uses three variables. Fama and French started with the
observation that two classes of stocks have tended to do better than the market as a whole: (i)
small caps and (ii) stocks with a high book-to-market ratio (B/P, customarily called value stocks,
contrasted with growth stocks). They then added two factors to CAPM to reflect a portfolio’s
exposure to these two classes:
Rit–Rf t = α + β1[Rmt − Rf t] + β2SMBt + β3HMLt + uit
where Rit is the return of the portfolio i at time t, Rmt is the return of the market portfolio, and
Rf t is the return of the risk-free rate. SMB stands for “Small [market capitalization] Minus Big”
and HML for “High [book-to-market ratio] Minus Low”; they measure the historic excess returns
of small caps over big caps and of value stocks over growth stocks. uit is the error term.
1. Pick two stocks that you are interested in and download their historical price data from
Yahoo! Finance. Plot the historical prices against time. Compute their monthly returns.
Make sure that your data ranges from January 2018 to December 2022.
2. Assume that you invest 50% each of the stocks that you picked. Compute the monthly
returns of the portfolio over the sample period above.
3. Download the monthly data of the three factors from Ken French’s website
(http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html).
Read the instructions on the website carefully to guarantee that you are downloading the
correct data.
4. Draw the scatter plot the portfolio’s excess return (y-axis) against excess market return
(x-axis) using Eviews.
5. Estimate Fama-French three factor model of your portfolio, and explain the coefficients in
words.
6. Plot the residuals of the regression against time. And conduct the heteroskedasticity tests
using Eviews.
7. Perform the Chow test using Eviews. The breakpoint is March 2020.