The Capital Asset Pricing Model
The proposed econometric application focuses on the dynamic analysis of stock prices of several
companies. The raw series are taken from the Yahoo! Finance website and are collected
in the Gretl data file capm.gdt. They are of weekly frequency and cover the period January
2000 – December 2016, for a total of 887 observations. The data are the adjusted closing
prices of dividends and divisions, which are used to calculate returns. Raw data includes the
• CAC40 : weekly value of the French stock market index
• LIVRETA : annual risk-free investment rate (“Livret A”)
: weekly share value of several firms
At first, you need to select 4 firms among the following: BNP, Carrefour, Volkswagen,
Total, Engie, Michelin, Sodexo, l’Oréal, LVMH, Société Générale, Danone, Vinci, Axa and
Bouygues. Then, you must send me an email with your choice. Before you start to work
with the series, you need to receive a confirmation email from me. Everybody should have
a different set of data. Write your report as if it were addressed to a boss or to a friend. It
should be understandable by a non-specialist.
I. Data Analysis
1. Plot the evolution of the French stock market index over the period. Comment on this
graph, trying to find links with past events, whether historical, economic, or otherwise.
2. Plot the evolution of the annual risk-free investment rate over the period. Comment on
3. For each selected firm, plot the evolution of the share value. Comment on these graphics,
trying to explain specific observed changes (look at the history and past events of the firm).
4. The return rate of firm i at period t is defined as the growth rate of the share value (including
dividends and divisions) between t and t−1, denoted ri
, which can be approximated
by log difference:
rFIRM,t = log FIRMt − log FIRMt−1 (1)
For each firm, calculate the return rate (ri), then the excess returns (ri−rf ), or risk premium.
Be careful, the risk-free investment rate is annual in the data file, so convert it to a weekly
rate beforehand (dividing it by 52).
Calculate the rate of return of CAC40 (rm) and the excess market return (rm − rf ).
1You can use any statistical software. The homework can be written in English or in French. It must be
saved in a Pdf file and uploaded on the platform’s course Ametice before the deadline. For any question,
you can contact me by email, firstname.lastname@example.org
2The file contains the shares of companies belonging to different industrial sectors: banking, goods and
services, oil, automobile.
For each company, draw on the same graph the excess return (ri − rf ), against the excess
market return (rm − rf ). Comment on these graphs.
II. Econometric Analysis
From the equilibrium relationship of the Capital Asset Pricing Model (CAPM), we can derive
the following linear regression model:
ri − rf = αi + βi(rm − rf ) + ε (2)
where rf is the weekly risk-free investment rate, ri
is the return rate of the firm i and rm is
return rate of the market (CAC 40).
5. What interpretation can be made of the coefficients αi and βi? Give an understandable
interpretation by a non-specialist. (Help: look at the theory of CAPM)
6. For each firm, estimate by OLS the regression model (2). Summarize the results for all
firms in a single Table, including values of the coefficients, standard errors, t-ratio and R2
7. What are the classical assumptions made on the regression model to estimate it by OLS.
Under these assumptions, why is the OLS estimation always preferred in practice?
8. For each firm, test the null hypothesis that each coefficient is equal to zero, αi then βi
Interpret the results. Do firms have abnormal returns relative to the market?
9. For each firm, test the null hypothesis that the slope coefficient is equal to one,
H0 : βi = 1. According to the estimation results, which firms are, on average, more risky
than the market? Which are, on average, less risky than the market?
10. If the risk-free investment rate is unchanged and you anticipate an increase in the
CAC40, which is the firm with the highest expected excess return increase? The one whose
expected excess return increase is the lowest? Same question if you anticipate a drop in the
CAC40. Justify your answers.
11. Rank the companies, from the most risky to the least risky. If you were to compose
a stock portfolio, what would be your personal choice among the shares of the companies
studied previously? Explain why.
12. For the least risky company, ranked last, are the results of the regression consistent
with the figure obtained in question 4 (excess return of the title vs. the market)? Explain
why. What do you conclude about the reliability of the CAPM, especially when the R2
low (if this is the case)?