Data: S$0=101$; X $=114$; $1+$ r $=1\mathrm{.}12.$ The two possibilities for ST are $143$ and $85.$

a$.$ The range of S is $58$ while that of P is $29$ across the two states. What is the hedge ratio of the put? $($Round your answer to $2$ decimal places. Negative value should be indicated by parentheses.$)$

b$.$ Form a portfolio of one share of stock and two puts. What is the $($nonrandom$)$ payoff to this portfolio?

c$.$ What is the present value of the portfolio? $($Round your answer to $2$ decimal places.$)$

d$.$ Given that the stock currently is selling at $101,$ calculate the put value. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$