$(15$ Percent$)$ Assume that you are the portfolio manager of the YTT Fund, a $$5$ million hedge fund that contains the following stocks. The required rate of return on the market is $12\mathrm{.}00\%$ and the risk$-$free rate is $4\mathrm{.}50\%.$

$\backslash$table$[[$Stock$,$Amount,Beta$],[$A$,$$$850,000,1\mathrm{.}5],[$B$,$$$650,000,0\mathrm{.}8],[$C$,$$$1,500,000,1\mathrm{.}3],[$D$,$$$800,000,0\mathrm{.}6],[$E$,$$$1,200,000,1\mathrm{.}2],[,$$$5,000,000,]]$

a$.$ What rate of return should investors expect $($and require$)$ on this fund and what is the beta of this fund?

b$.$ The investors require you to reduce the risk of the fund and thus you plan to cut the investment in Stock C by $$500,000$ and add $$500,000$ to stock B$.$ What will the fund's required rate of return be after this change?