Suppose that you have just started your first job as a junior investment manager at a

hedge fund. You have the data on the risk levels and the corresponding expected return

$($appreciation$,$ or yield$)$ of the following five securities $($e$.$g$.$ stocks, or bonds$)$:

Table $1$: Risk$-$Return Characteristics of Five Securities

$($a$)(12$ points$)$ Use the OLS formulas provided in class, or from the textbook, to regress

the expected return of a security $(Y_i)$ on the corresponding risk index $(x_i).$ That is$,$

estimate the following regression model:

$Y_i={}_0+{}_1{x}_i+u_i$

Report your estimates hat$({)}_0$ and hat$({)}_1.$ Show your work.

$($b$)(6$ points$)$ Use your estimates hat$({)}_0$ and hat$({)}_1$ to find the expected return to a risk$-$free security,

that is$,$ a security with risk index $x_i=0.$ In other words, find hat$(E)[Y|x_i=0].$

$($c$)(7$ points$)$ Suppose a broker offers you to invest in a security with expected return of

$14\%$ and a risk index of $20.$ Based on your regression estimates and the model in $(1),$

does that represent a good deal? Explain your reasoning.

$($d$)(5$ points$)$ Suppose that you're considering investing in a security with expected return

of $15\%.$ Based on your estimates, what level of risk $($that is$,$ what value of the risk index$)$

would be consistent with such expected return?