3. You have a portfolio of the following options right now: 1) 1 long call option with X=50; 2) 2 short call options with X=55; and 3) 1 long call with X=62. The current stock price is $55. Although you didnt record them in the right order, the deltas of the options are 0.15, 0.62, and 0.51.

(a) What is the delta of your portfolio?

(b) You are worried about stock price fluctuations and would like to make your portfolio delta neutral (that is, you would like to have a portfolio with zero delta). What stock position should you add to your portfolio (are you going long or short and how many shares do you need)?

(c) What is the delta (approximately) of the new position you established in part (b) when the stock price doubles?