The risk$-$free interest rate is zero and the mutual funds claim to deliver the following gross returns:

rtpassive fund before fees $=$ rtstock index $=6\%+$ ut

rtactive fund before fees $=1\mathrm{.}80\%+1\mathrm{.}1*$ rtstock index $+\backslash$epsi t

where the error terms ut and $\backslash$epsi t are independent over time and of each other, have zero means E$($ut$)=$ E$(\backslash$epsi t$)=0,$ and volatilities of $$var$($ut$)=15\%$ and $($var$(\backslash$epsi t$)=4\%.$ The hedge fund uses the same strategy as the active mutual fund, but implements the strategy as a long$-$short hedge fund, applying $4$ times leverage, generating the following return before fees:

rthedge fund before fees $=4*($rtactive fund before fees $$ rtstock index$)$

Question $2$

What is the hedge fund$$s beta?