You are presented with the results from regression analysis

You are presented with the results from regression analysis, where the excess returns on a company A are regressed on the excess returns on the S&P 500 portfolio.  (Returns are monthly, from Oct 2010 to Oct 2015)

Regression Statistics

R Square 0.04

Total number of observations 60

(a) Based on the above analysis, what is the beta of company A?

(b) Given beta, what is the required excess return of company A according to CAPM, if the expected excess return on the market portfolio is 5%?

(c) What is the alpha of company A? Is it (statistically) significantly different than zero? Based on this alpha what buy/sell recommendation would you make for investors in company A?

(d) Company A, as any other company, has both systematic and unsystematic risk. The sum of the two is the total risk of company A. What portion of the risk that company A carries is systematic?

(e) In March 2015 the return on the market is 0.3%. The return on company A for the samemonth is -0.6%. Based on the regression analysis, what was the predicted return for company A in March 2015? What is the magnitude of the error in this prediction?

Hint: The regression equation that Excel estimates for you is (rA-rf)i=+*(rM-rf)i+I, where i is the number of the month, months go from 1 to 60.          CAPM requires that alpha be zero—for part (b).

Solution

a)

beta = 0.5

b)

(b) Given beta, what is the required excess return of company A according to CAPM, if the expected excess return on the market portfolio is 5%?

0.15

(c) What is the alpha of company A? Is it (statistically) significantly different than zero? Based on this alpha what buy/sell recommendation would you make for investors in company A?

0.05

(d) Company A, as any other company, has both systematic and unsystematic risk. The sum of the two is the total risk of company A. What portion of the risk that company A carries is systematic?

3.33/6 = 0.555