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

a. Plot the payoff of this collar as a function of the stock price at the option expiration date.

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

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

d. If the costs of the put and the call position used in the construction of the collar were $3 and $5, respectively, what will be the total return to this position if at maturity the stock price is $55.