use R studio to answer the following:

Consider the Capital Asset Pricing Model $($CAPM$)$ in the lecture and the data set mfunds.csv we

covered in the class, answer the following questions.

$1)$ There are $6$ mutual funds included in the dataset $($tbill is Treasury bill, it is not a mutual

fund$),$ which mutual fund has the largest correlation with the $$market$$ return, valmrkt?

Which mutual fund has the smallest correlation with valmrkt?

$2)$ Fit the CAPM model for the mutual fund which has the largest correlation with valmrkt,

and write it down $($hint: valmrkt is the predictor$).$

$3)$ Fit the CAPM model for the mutual fund which has the smallest correlation with valmrkt,

and write it down $($hint: valmrkt is the predictor$).$

$4)$ Plot the two scatterplots of two mutual funds vs valmrkt along with their respective fitted

line $($use clear labels in the plots$).$

$5)$ Conduct a hypothesis test to examine whether the chosen mutual fund in part $2)$ follows

exactly the market or not $($use $\backslash$alpha $=0\mathrm{.}05).$ Write down the hypothesis, test statistic, p$-$

value, and your conclusion $($hint$,$ refer to Page $71$ in Lecture $1).$

$6)$ Conduct a hypothesis test to examine whether the chosen mutual fund in part $2)$ softens

the market moves $($use $\backslash$alpha $=0\mathrm{.}05).$ Write down the hypothesis, test statistic, p$-$value, and

your conclusion $($hint$,$ refer to Page $71$ in Lecture $1$ again, but softens means the fund

does not follow as much as the market moves$).$

$7)$ Suppose the market return is at $2\%,$ what would you expect the return of the mutual fund

in part $2)$ to be$?$ What is the $95\%$ predictive interval for the mutual fund return? What is

the $90\%$ predictive interval for the mutual fund return? Which one gives you narrower

prediction interval?