A hedge fund wants to purchase $100$ shares of company TXT$.$ The bid $=$ $$70,$ offer $=$ $$80.$ They also want to purchase $200$ shares of company ZZTOP. The bid $=$ $$15,$ offer $=$ $$25.$

$1)$ What is the proportional bid$$offer spread of each company?

$2)$ What is the midmarket total value of each position?

$3)$ What is the cost to the hedge fund to unwind the portfolio?

$4)$ If the bid$$offer spreads are normally distributed with mean $$10$ and standard deviation $$3,$ what is the $99\%$ worst$-$case cost of unwinding the position in the future?