Suppose you are the money manager of a million dollar investment fund. The fund consists of four stocks with the following investments and betas:

$\backslash$table$[[$Stock$,$Investment,Beta$],[$Alpha$,$$$75,000,-1\mathrm{.}50],[$Bingo$,$$$550,000,-1\mathrm{.}00],[$Charlie$,$$$250,000,0\mathrm{.}50],[$Delta$,$$$125,000,2\mathrm{.}00]]$

a$)$ Calculate the fund's beta.

b$)$ If the market's required rate of return is $10\%$ and the risk$-$free rate is $3\%,$ what is the fund's required rate of return?