Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3.4% + 1.15RM + eA RB = -1.5% +…

1. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:   

RA = 3.4% + 1.15RM + eA

RB = –1.5% + 1.30RM + eB

σM = 15.0%; R-squareA = 0.26; R-squareB = 0.16   

What is the covariance between each stock and the market index?

1. STOCK A

2. STOCK B

2. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:

RA = 3% + 1.00RM + eA

RB = –1.0% + 1.30RM + eB

σM = 18%; R-squareA = 0.27; R-squareB = 0.13

What are the covariance and correlation coefficient between the two stocks?

3.Consider the two (excess return) index model regression results for A and B:

RA = 1.5% + 1.7RM R-square = 0.622

Residual standard deviation = 12%

RB = –2.4% + 1.3RM R-square = 0.468 Residual standard deviation = 9.8%

a. Which stock has more firm-specific risk? Stock A Stock B

b. Which stock has greater market risk? Stock A Stock B

c. For which stock does market movement has a greater fraction of return variability? Stock A Stock B

d. If rf were constant at 5.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A?

4. A portfolio management organization analyzes 54 stocks and constructs a mean-variance efficient portfolio using only these 54 securities.   

a. How many estimates of expected returns, variances, and covariances are needed to optimize this portfolio?      Estimates of expected returns   Estimates of variances   Estimates of covariances   Total estimates

b. If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed?   Estimates