Problem $1$

You are given the following information about stock $x$ and the market portfolio, $M$ :

You are not given the expected return of stock $x.$ The correlation of the returns on the stock $x$ and

the market portfolio is equal to $0\mathrm{.}4.$

a$)$ What is the beta $()$ of stock $x?$

b$)$ Assuming the CAPM holds, what is the expected return on stock $x?$

c$)$ You have $$1,000$ to invest in some combination of the risk$-$free asset, stock $x,$ and the market

portfolio. You are thinking of investing $$300$ in the risk free asset, $$400$ in stock $x,$ and $$300$

in the market portfolio. What is the overall expected return, standard deviation and beta of

this portfolio?