Question

Q12. Suppose you think AppX stock is going to appreciate substantially in value in the next year. Say the stock’s current price, So, is $100, and the call option expiring in one year has an exercise price, X, of $100 and is selling at price, C, of $10. With $10,000 to invest, you are considering three alternatives:
a) Invest all $10,000 in the stock, buying 100 shares.
b) Invest all $10,000 in 1,000 options (10 contracts).
c) Buy 100 options (one contract) for $1,000 and invest the remaining $9,000 in a money market fund paying 4% interest annually.
What is your rate of return for each alternative for four stock prices one year from now?

Answer 1

Ans. Let the four stock prices be $80,$100,$110,$120

	$80	$100	$110	$120
All stocks (see WN)	-20%	0%	10%	20%
All options (see WN)	-100%	-100%	0%	100%
Bills+100 options (see WN)	-6.4%	-6.4%	3.6%	13.6%

Working Notes (WN)

1.Stock price = $80

option 1 : All stocks:

Original Investment = 100 x 100 = 10,000

Return = (80 x 100 – 10,000)/10,000 = -0.2 or – 20%

Option 2 :All options

Original investment = 10 x 1000 = 10,000

When stock price = $80, payoff = 0 since it’s not profitable to exercise. Therefore, the options portfolio has zero value at the end of the year.

Return = (0 – 10,000)/10,000 = 0 or -100%

Option 3 :Money market fund options

Money market investment = 9000 x (1.04) = 9360.Payoff is 0 since it’s not profitable to exercise. Therefore, the options have zero value.

Return = (9360 – 10000)/10000 = or -6.4%

2.Stock price = $100

option 1 : All stocks:

Original Investment = 100 x 100 = 10,000

Return = (100 x 100 – 10,000)/10,000 = 0%

Option 2 :All options

Original investment = 10 x 1000 = 10,000

When stock price = $100, payoff = 0 since it’s not profitable to exercise. Therefore, the options portfolio has zero value at the end of the year.

Return = (0 – 10,000)/10,000 = -100%

Option 3 :Money market fund options

Money market investment = 9000 x (1.04) = 9360.Payoff is 0 since it’s not profitable to exercise. Therefore, the options have zero value.

Return = (9360 – 10000)/10000 = or -6.4%

3.Stock price = $110

option 1 : Return = (110 x 100 – 10,000)/10,000 = 0.1 or 10%

Option 2:When stock price = $110, payoff = 110 – 100 = 10 since it’s profitable to exercise.

Therefore, the options portfolio value at year’s end = 10 x 1000 = 10,000.

Return = (10,000 – 10,000)/10,000 = 0

Option 3:Payoff = 110 – 100 = 10. Therefore, the options’ value =10 x 100 = 1000

Return = ((9360+1000) – 10000)/10000 =0.036 or 3.6%

4.Stock price = $120

option 1 : Return = (120 x 100 – 10,000)/10,000 = 0.2 or 20%

Option 2:When stock price = $120, payoff = 120 – 100 = 20 since it’s profitable to exercise.

Therefore, the options portfolio value at year’s end = 20 x 1000 = 20,000.

Return = (20,000 – 10,000)/10,000 = 1 or 100%

Option 3:Payoff = 120 – 100 = 20. Therefore, the options’ value =20 x 100 = 2000

Return = ((9360+2000) – 10000)/10000 =0.136 or 13.6%