a$.$ You have $$100,000$ to invest in a portfolio containing Stock $x,$ Stock $Y,$ and a risk$-$free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of $13$ percent and that has only $70$ percent of the risk of the overall market. If $x$ has an expected return of $35$ percent and a beta of $1\mathrm{.}6,Y$ has an expected return of $20$ percent and a beta of $1\mathrm{.}3,$ and the risk$-$free rate is $7$ percent, how much money will you invest in Stock $Y?$

b$.$ How do you explain your answer? $($Hint: Do the results indicate taking a short position in one of the Stocks?$)$