You have a $$1,000$ portfolio which is invested in stocks A$,$ B$,$ and a risk$-$free asset. $$400$ is invested in stock A$.$ Stock A has a beta of $1\mathrm{.}31$ and stock B has a beta of $0\mathrm{.}71.$ How much needs to be invested in stock B if you want a portfolio beta of $0\mathrm{.}90?$

Multiple Choice

$657$

$1414$

$503$

$249$

$530$