A collar is established by buying a share of stock for $50, buying a 6-month put option with exercise price $45, and writing a 6-month call option with exercise price $55. On the basis of the volatility of the stock, you calculate that for a strike price of $45 and expiration of 6 months, N(d1) = .60, whereas for the exercise price of $55, N(d1) = .35.

a. What will be the gain or loss on the collar if the stock price increases by $1?

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

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