Bill Johnson manages a diversified portfolio consisting of a $$5,362$ investment in each of $16$ different common stocks. The portfolio's beta is $1\mathrm{.}02.$ Now suppose Bill decided to sell one of the stocks in the portfolio with a beta or $1\mathrm{.}4$ for $$5,362$ and use the proceeds to buy another stock with a beta of $0\mathrm{.}6.$ What would the portfolio's new beta be$?$