(CAPM; regression analysis; hypothesis testing; confidence interval) The capital asset price model (CAPM) is an important model in the field of finance. It explains variations in the rate of return of a security "j" as a function of the rate of return on a portfolio consisting of all publicly traded stocks, which is called the market portfolio ("m"). Generally, the rate of return on any investment is measured in comparison to its opportunity cost, which is the return on a risk-free asset ("f"). The resulting difference is called the risk premium associated with that investment, because it is the reward or punishment for making a risky (i.e., non-risk-free) investment. The CAPM says that the risk premium on security j (labeled "rj - rf") is proportional to the risk premium on the market portfolio (labeled "rm - rf"). That is:
rj - rf = βj (rm - rf)
In other words, the ratio between the two risk premia is:
βj = (rj - rf) / (rm - rf )
Where rj is the return on security j, rf is the return on the risk-free asset, and rm is the return on the market portfolio. βj is typically called the beta value of security j. A stock's beta is important to investors because it reveals the stock's volatility. It measures the sensitivity of security j's return to variation in the entire stock market. As such, values of beta less than 1 indicate that the stock is "defensive" because its variation is less than the market's. A beta greater than 1 indicates an "aggressive" stock. Investors usually want to know an estimate of a stock's beta before investing in the stock.
The model shown in the first equation above is the "economic (theoretic) CAPM model." The "econometric (empirical) CAPM model" is obtained by adding an intercept (β0) in the economic model (even though theory says it should be zero) and an error term ( uj ):
rj - rf = β0 +βj (rm - rf) + uj
The Excel file "CAPM" contains data on the monthly rate of return (rj) of three firms (Microsoft, GM, and Mobil-Exxon), the monthly rate of return on the market portfolio (rm ), and the rate of return on U.S. 3-month Treasury Bills, which is the risk-free asset (rf). The 120 monthly observations cover the period January 1999 to December 2008. There is a "data dictionary" (in pdf format) that accompanies the dataset.
(a) Construct the variable "rm - rf". Next, construct the variable "rj - rf" for each of the three companies in your sample.
(b) Construct a table of descriptive statistics that effectively summarize all the variables (except for the variable date). Please make sure your table is nicely formatted.
Provide brief, to-the-point, and meaningful comments on your results.
(c) Create a histogram for the variable "rj - rf" for the Microsoft stock. Make sure to properly label the histogram with titles, legends, labels, notes, etc. And, make sure that this histogram looks "readable" and "visually pleasant." (Imagine that you are planning to present this histogram to a potential business client.)
Provide brief, to-the-point, and meaningful comments on your results.
(d) Use OLS regression to estimate the ("econometric") CAPM model for each firm (separately), and comment on their estimated beta values. Which firm appears most aggressive? Which firm appears most defensive?
(e) Based on your results from part (d), for each stock, test at the 5% significance level the null hypothesis that the stock's beta value is 1 against the two-sided alternative hypothesis that it is not 1.
(Note: You should complete this part "by hand" using the results from part (d); or, you may type up your answers if you prefer.)
Attachment:- CAPM_and_Regression_Analysis.xlsx