The capital asset pricing model (CAPM) is an important model in the field of finance. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio consisting of all publicly traded stocks, which is called the market portfolio. Generally the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk free asset. The resulting difference is called the risk premium, since it is the reward or punishment for making a risky investment. The CAPM says that the risk premium on security j is proportional to the risk premium on the market portfolio. That is,
() mffjj rrrr
where rj and rf are the returns to security j and the risk-free rate, respectively, rm is the return on the market portfolio, and βj is the beta value of security j. A stock’s beta is important to investors since it reveals the stock’s volatility. It measures the sensitivity of security j’s return to variation in the whole stock market. As such, values of beta less than 1 (i.e. β <1) indicate that stock is defensive since its variation is less than the market’s. A beta greater than 1 (i.e. β >1) indicates an aggressive stock. Investors usually want an estimate of a stock’s beta before purchasing it. The “econometric model” of CAPM can be obtained by including an intercept and an error term in the above model, i.e.
The data file capam4.wf1 includes the monthly returns of six firms, Microsoft (ms), GE (ge), GM (gm), IBM (ibm), Disney (disney), and Mobil-Exxon (mex), the rate of return on the market portfolio (mkt), and the rate of return on the risk free asset (riskfree). The data also includes the risk premium on the market portfolio (rp_mkt = mf rr ï€ ) and the risk premiums for Microsoft (rp_ms), GE (rp_ge), GM (rp_gm), IBM (rp_ibm), Disney (rp_disney), and Mobil-Exxon (rp_mex). The 132 observations cover January 1998 to December 2008. The data is available from the LMS.
1. Estimate the regression model (2) using the Microsoft data, and report the result along with the standard errors below the estimated coefficients and R2. [5 marks] Hint: The model is a simple regression model because it can be written as xey 12 , where , jf rry () mf rrx ï€ï€½ using the Microsoft data. Use rp_mkt as the explanatory variable, and rp_ms as the dependant variable for Microsoft.
2. Interpret the estimate of βj from your regression result above. [5 marks]
3. Finance theory suggests that αj = 0 for security j under market efficiency. This is because αj represents the excess profit or loss of security j when the market excess return is zero (rm – rf = 0). That is, if the market is efficient, this profit or loss should disappear rather quickly by arbitrage. Test the null hypothesis that αj = 0 for the Microsoft stock, against an appropriate alternative hypotheses. [5 marks]
4. Perform a hypothesis test that βj = 0 against the alternative that βj ≠ 0 using the Microsoft data. [5 marks]
5. Tech stocks typically have high beta values (β > 1). This statement implies that the Microsoft stock (a Tech stock) is an aggressive stock. Evaluate this claim by conducting an appropriate test on their β values. [5 marks]
6. What is the R2 for the regression? Interpret it. [5 marks]
7. If for January 2009, the risk free rate does not change from December 2008 but the market return increases by 1% point, what is the predicted return for Microsoft? Show your calculations. [5 marks]
8. Repeat Question 1 for each: GE, GM, IBM, Disney, and Mobil-Exxon. [10 marks]
9. Attach your Eviews outputs at the end of your report as a