Suppose you held a diversified portfolio consisting of a $$1,000$ investment in each of $10$ different common stocks. The portfolio's beta is $1\mathrm{.}60.$ Now suppose you decided to sell one of the stocks in your portfolio with a beta of $4\mathrm{.}70$ for $$1,000$ and use the proceeds to buy another stock with a beta of $1\mathrm{.}00.$ What would your portfolio's new beta be$?$

$-2\mathrm{.}1000$

$1\mathrm{.}9700$

$1\mathrm{.}2300$

$1\mathrm{.}0000$