Question

The current price of a stock is $40, and two-month European call options with a strike price of $43 currently sell for $5. An investor who feels that the price of the stock will increase is trying to decide between two strategies: buying 100 shares or buying 800 call options (8 contracts). Both strategies involve an investment of $4,000.
a. Which strategy will earn more profits if the stock increases to $42?
b. How high does the stock price have to rise for the option strategy to be more profitable?

Please choose all correct answers. Please note that each incorrect answer will reduce the score by 10%.

	1.	If the stock closes at $42, buying100 shares will have a profit 0f $200 and buying 800 calls will have a loss of $4,000. So buying stocks will be better than buying options.
	2.	If the stock closes at $42, buying100 shares will have a profit 0f $200 and buying 8000 calls will have a profit of $2000. So buying call options will be better than buying stocks.
	3.	If the stock closes at $42, buying100 shares will have a profit 0f $200 and buying 800 calls will have a loss of $2,000. So buying stocks will be better than buying options.
	4.	The option strategy is more profitable if the stock price goes below $47.94
	5.	The option strategy is more profitable if the stock price rises above $49.14.
	6.	If the stock closes at $42, buying100 shares will have a profit 0f $200 and buying 800 calls will have a loss of $3,000. So buying stocks will be better than buying options.
	7.	The option strategy is more profitable if the stock price rises above $43.45.
	8.	The option strategy is more profitable if the stock price rises above $45.78

Answer 1

lets take,

current price of the stock = s1 = 40

closing price of the stock = s2

strike price = k = 43

price of call option = c= 5

cost of buying 100 shares now = 100*s1 = 100*40 = 4000

cost of buying 800 options= 800*c = 800*5 = 4000

1) correct,

profit@shares = (s2-s1)*100 = (42-40)*100 = 200

since s2<k,call option will not be exercised and he will loose premium he paid to buy options

loss@options = 4000

2) wrong

3) wrong

4) wrong

if s2=47.94,call option will be exercised at 43

profit@options = (47.94-43)*800 = 3952

but he already paid 4000 to buy the option, so his total profit should cross 4000 to earn positive gains

5) Correct

if s2=49.14,call option will be exercised at 43

profit@options = (49.14-43)*800 = 4912

but he already paid 4000 to buy the option, so his total profit will be 4912-4000= 912, this strategy is profitable

6) Wrong

7) Wrong,

since at 47.94, he is earing losses, he cannot earn profits at 43.45

7) Wrong,

since at 47.94, he is earing losses, he cannot earn profits at 45.78

so, 1,5 optons are correct