We will derive a two$-$state put option value in this problem. Data: S$0=$ $$260$; X $=$ $$270$; $1+$ r $=1\mathrm{.}10.$ The two possibilities for ST are $$300$ and $$180.$

Required:

a$.$ The range of S is $$120$ while that of P is $$90$ across the two states. What is the hedge ratio of the put? $($Negative value should be indicated by a minus sign. Round your answer to $2$ decimal places.$)$

b$.$ Form a portfolio of three shares of stock and four puts. What is the $($nonrandom$)$ payoff to this portfolio? $($Round your answer to $2$ decimal places.$)$

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 $$260,$ calculate the put value. $($