Problem 1. You are presented with the results from regression analysis, where th

Question

Problem 1.
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)

(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 same

month 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).

Explanation / Answer

a)Beta is the Coefficient of market returns=1.2

b) required excess return of company A by CAPM=Beta*expected excess return on the market portfolio

required excess return of company A by CAPM=1.2*5%=6%

c)The intercept is the alpha=.5

t-stat=3.333 is high enough to conclude that it is (statistically) significantly different than zero.

According to CAPM the alpha should eventually turns to 0, the required return from stock are higher than expected ,this should lower to restore alpha to 0 in process increasing the price of security therefore the stock is undervalued and should be buy.

d)variance of unsystematic risk=.15^2=.0225

variance of systematic risk=(1.2*.2)^2=.0576

portion of the risk that company A carries is systematic=.0576/(.0576+.0225)=0.72 or 72%

e)predicted return for company A in March 2015=.5+1.2*.3=.86%

magnitude of the error in this prediction=.86%-(­0.6%)=1.46%

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