An investor has currently all of his wealth in Treasury bills. He is considering to invest $40\%$ of his funds in a stock with a beta of $0\mathrm{.}80,20\%$ in another stock with a beta of $1\mathrm{.}40,$ with the remainder left in Treasury bills. The risk$-$free rate is $5\mathrm{.}0\%$ and the market premium is $5\mathrm{.}6\%.$

Determine the beta and the expected return of the proposed portfolio.