You have $1000$ dollars to invest and need to construct a portfolio with a beta of $1.$ You decided to invest $400$ dollars in Stock X$,$ which has a beta of $1\mathrm{.}5.$ There is another stock, Stock Y$,$ that has a beta of $0\mathrm{.}8$ and a risk$-$free asset. How much will you invest in Stock Y and will you need to borrow or lend with the risk$-$free rate?

A$.$ There isn't enough information

B$.$ Invest $562\mathrm{.}5$ dollars in Stock Y and borrow $37\mathrm{.}5$ dollars at the risk$-$free rate

C$.$ Investment $562\mathrm{.}5$ dollars in Stock Y and lend $37\mathrm{.}5$ dollars at the risk$-$free rate

D$.$ Invest $600$ dollars in Stock Y and there is no need to borrow or lend at the risk$-$free rate