A collar is established by buying a share of stock for $50, buying a six-month put option with exercise price $45, and writing a six-month call option with exercise price $55. Based on the volatility of the stock, you calculate that for an exercise price of $45 and maturity of six months, N(d1) = 0.60, whereas for the exercise price of $55, N(d1) = 0.35. Required:
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? Very small?