. XYZ stock is selling for $100 per share. Call options on XYZ with a strike pri
ID: 2666060 • Letter: #
Question
. XYZ stock is selling for $100 per share. Call options on XYZ with a strike price of $100 are selling at $5 per share. John invests $1,000 by buying 10 shares of XYZ. Pat invests $1,000 by buying 200 call options on XYZ (with a strike price of $100) and holds the options until just before they expire. At the expiration of the options, XYZ stock is selling for $110 per share.a. What is the profit that John’s investment has earned?
b. What is the profit that Pat’s investment has earned?
c. What is the price of XYZ at expiration that would give John and Pat the same amount of profit?
Explanation / Answer
a) John's profit is ($110 - $100) per share x 10 shares he bought = $100 b) I am unsure about the quoted convention here. In the real market - 1 option contract represents 100 shares - if you were to follow the wording in this question it would mean 1 option contract costs 100 shares x $5/share = $500 per option contract - which isn't realistic. I will assume that is $5 per option contract, not share, meaning one option contract represents one share. This makes more sense, since in the question it says Pat bought 200 call options for $1,000. Pat's Profit is = ($110 - $100) x 200 shares less option premium ($5 per option contract)] = ($10 x 200) - 1,000 = 1,000 c) Do this by replacing $110 in the equations above with x, and equating them as follows. Then solve for x (x - 100) 10 = (x-100)200 - 1,000 10x - 1000 = 200x - 20,000 - 1,000 190x = 20,000 x is approx $105.26 there is rounding
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