2. You have a portfolio of the following options right now: 1) 1 long call optio

Question

2. You have a portfolio of the following options right now: 1) 1 long call option with X=50; 2) 2 short calloptions with X=55; and 3) 1 long call with X=62. The current stock price is $55. Although you didn’t recordthem 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 deltaneutral (that is, you would like to have a portfolio with zero delta). What stock position should youadd 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 stockprice doubles?

Explanation / Answer

a. Delta of your Portfolio: 100(0.62 + 0.15 - 2(0.51)) = -25

b. To have a portfolio with zero delta yo have to add 25 shares .

c.When the stock price doubles the delta of new position in the above is 25, because the delta on each of the options would be about 1,0 so the two short options would cancel the two long options.

Assumption: The underlying for each option is 100 shares

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