The data set

Portfolios

Formed

on

ME

eqW.txt

contained portfolios constructed based on the mar-

ket value of the company (total outstanding number of stock shares times the stock price). Columns

11 is the returns of the portfolio contains (equally weighted) the smallest 10% of the companies in

terms of their market value.

Answer the following questions:

1. Calculate the market returns by taking the weighted average of columns 3 to 5, with weights

0.3, 0.4 and 0.3.

(a) Plot the market return series (

plot(x,type='l')

will do).

(b) Comment on the features you see in the figure

2. Use the data from 1965.01 to 1969.12 (rows 463:522) only to fit a simple linear regression using

Column 11 (the small company portfolio) as the response variable and the market return you

obtained in (1) as explanatory variable. Answer the following questions:

(a) Draw a scatter plot and add the estimated regression line to the plot.

(b) What is the standard error of

b

1

for estimating

1

?

(c) Obtain a 95% confidence interval for

b

1

. What does a confidence interval mean in

general?

(d) What is the

p

-value for testing

H

0

:

0

= 0 vs

H

1

:

0

6

= 0? What is your conclusion?

(e) What is the

p

-value for testing

H

0

:

1

= 0 vs

H

1

:

1

6

= 0? What is your conclusion?

(f) Perform a 5% level test for testing

H

0

:

1

= 1 vs

H

1

:

1

6

= 1? What is your conclusion?

(g) Obtain the

R

2

of this linear regression model. What does it mean? Comment on it.