We will derive a two$-$state put option value in this problem. Data: S$0=$ $$300$; X $=$ $$310$; $1+$ r $=1\mathrm{.}10.$ The two possibilities for ST are $$350$ and $$150.$

Required:

a$.$ The range of S is $$200$ while that of P is $$160$ 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 four shares of stock and five 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 $$300,$ calculate the put value. $($Do not round intermediate calculations and round your answer to $2$ decimal places.$)$

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