Question

The current price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted at $2 and the price of a one-year European call option on the stock with a strike price of $50 is quoted at $3.

a) Investor A is bullish on the stock and buys 100 shares. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year.

b) Suppose investor A buys the call option on 100 shares instead. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year. Compare buying stock versus buying call option in terms of risk and reward.

c) Investor B is bearish on the stock and shorts 100 shares. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year. Assume that he needs to post 50% cash margin when he initiates the short position (and assume there is no margin call).

d) Suppose investor B buys the put option on 100 shares instead. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year. Compare shorting stocks versus buying put option in terms of risk and reward.

e) Investor C wants to own the shares but worries about the downside. So he buys both the stock and the put option on 100 shares. a. Draw a diagram illustrating how the investor’s profit varies with future share price. What are his max profit and max loss per share? b. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year.

f) Investor D wants to own the shares but wants to reduce his initial investment cost. So he buys the stock and shorts the call option on 100 shares. a. Draw a diagram illustrating how the investor’s profit varies with stock price. What are his max profit and max loss per share? b. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year.

g) Investor E wants to bet on the possible share price fluctuations in the coming year. He buys the put option and the call option on 100 shares. a. Draw a diagram illustrating how the investor’s profit varies with stock price. What are his max profit and max loss per share? b. Compute his dollar profit and return if the share price is $25, $42, or $56 in one year.

Answer 1

	a)
		Investment in stock=100*$40	$4,000
			A	B=A*100	C=B-4000	D=C/4000
				Value of	Profit/	Percentage
			Share Price	100 Shares	(Loss)	gain/(loss)
			$25	$2,500	($1,500)	-37.50%
			$42	$4,200	$200	5.00%
			$56	$5,600	$1,600	40.00%
	b)	Payoff of Call Option with strike $50
		and Price at expiration =S
		Max((S-50),0)
		Cost of Call option per share	$3
		Total Investment	$300
			S	A	B=(A-3)*100	C=B/300
			Price at	Payoff	Profit/	Percentage
			Expiration	per Option	(Loss)	Gain/(Loss)
			$25	$0	($300)	-100%
			$42	$0	($300)	-100%
			$56	$6	$300	100%
		Option has Limited risk and infinite reward
		Stock has infinite risk and infinite reward
	c)	Investment =50%*40*100	$2,000
			A	B=A*100	C=4000-B	D=C/2000
				Value of	Profit/	Percentage
			Share Price	100 Shares	(Loss)	gain/(loss)
			$25	$2,500	$1,500	75.00%
			$42	$4,200	($200)	-10.00%
			$56	$5,600	($1,600)	-80.00%
	d)	Payoff of Put Option with strike $30
		and Price at expiration =S
		Min.((30-S),0)
		Cost of Put option per share	$2
		Total Investment	$200
			S	A	B=(A-2)*100	C=B/200
			Price at	Payoff	Profit/	Percentage
			Expiration	per Option	(Loss)	Gain/(Loss)
			$25	$5	$300	150%
			$42	$0	($200)	-100%
			$56	$0	($200)	-100%
		Option has Limited risk and infinite reward
		Shorting Stock has infinite risk and infinite reward
	e)	BUYS SHARE AND PUT OPTION:
		Investment in Shares	$4,000
		Investment in Put Option	$200
		Total Investment	$4,200
			S	A	B=A-40	C=(A+B-2)*100	D=C/4200
			Price at	Payoff	Payoff	Profit/	Percentage
			Expiration	per Option	Per Shares	(Loss)	Gain/(Loss)
			$15	$15	($25)	($1,200)
			$20	$10	($20)	($1,200)
			$25	$5	($15)	($1,200)	-29%
			$30	$0	($10)	($1,200)
			$42	$0	$2	$0	0%
			$50	$0	$10	$800
			$56	$0	$16	$1,400	33%