A collar is established by buying a share of stock for $$45,$ buying a $6-$month put option with exercise price $$39,$ and writing a $6-$month

call option with exercise price $$51.$ On the basis of the volatility of the stock, you calculate that for a strike price of $$39$ and expiration

of $6$ months, $N(d_1)=0\mathrm{.}7267,$ whereas for the exercise price of $$51,N(d_1)=0\mathrm{.}6310.$

a$.$ What will be the gain or loss on the collar if the stock price increases by $$1?($Round your answer to $2$ decimal places.$)$

Answer is complete but not entirely correct.

b$.$ What happens to the delta of the portfolio if the stock price becomes very large?

Answer is not complete.

Delta of the portfolio approaches

c$.$ What happens to the delta of the portfolio if the stock price becomes very small?

Delta of the portfolio approaches