3. An investor buys 500 shares of ABC stock at S17 a share. He sells 5 call cont

Question

3. An investor buys 500 shares of ABC stock at S17 a share. He sells 5 call contracts (100 shares each) with a striking price of $17.50 and premium of $2 a share. Assume interest r = 0% annual effective. (a) Draw a time diagram. What is the investor's initial investment? (b) What will be the investor's profit at expiration if the spot price of the stock is S17? (c) What will be the investor's profit at expiration if the spot price of the stock is $18 if the calls are exercised? (d) What will be the investor's profit at expiration if the spot price of the stock is 816 and the investor sells his

Explanation / Answer

a) The investor purchased 500 shares at $ 17 a share, that means he made an investment of 500*17 = $8,500.

The investor also sold 5 call contracts of 100 shares each at $2 a share, which means the investor will receive 5*100*2 = $1000 today and he needs to make payment at a later point of time if the share price crosses 17.5 which is the strike price.

So, at time t=0, the investor investment is = 8,500-1000 = $7,500. This is what time diagram will also show, an outflow of 7,500 at t=0.

b) If the stock price remains 17, he wont make any profit in the shares he purchased, however since the strike price of call was 17.5, the call wont happen and the investor will make profit of $1000 which he received initially as call writing premium.

c) If the spot price of stock goes to 18, he will make $1 profit on 500 shares he is holding i.e. $500, but he also needs to make payment on call option since the price crossed the strike price of $17.5, so the investor will make payment of $0.5 per share but he had collecter $2 initially which means he makes profit of $1.5 per share on call option i.e. 5*100*1.5 = $750.

So, total profit = 500+750 = 1,250.

d) If the stock price falls to $16, the investor will incur loss of $500 on investment and will make profit of $1,000 on call option which means he will make $500 profit on net basis.

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