A hedge fund has $\backslash (\backslash$$ $100\backslash$mathrm$\{$~m$\}\backslash )$ AUM $($assets under management$)$ with a high$-$water mark clause and performance fees that are paid quarterly.

In Q$1$ the fund is worth $90$ m $,$ and in Q$2$ the fund is worth $105$ m $.$

Finally, in Q$3,$ the fund is worth $104$ m $.$ Which of the following statements is correct?

The hedge fund will charge a performance fee in Q$3.$

The high$-$water mark is $104$ m in Q$3.$

The hedge fund will not charge a performance fee in Q$2.$

The high$-$water mark is $\backslash (\backslash$$ $100\backslash$mathrm$\{$~m$\}\backslash )$ in Q $1.$