Question

Consider the following options portfolio: You write a January 2012 expiration calloption on IBM with exercise price \(170. You also write a January expiration IBM putoption with exercise price \)165.

a. Graph the payoff of this portfolio at option expiration as a function of IBM’s stockprice at that time.

b. What will be the profit/loss on this position if IBM is selling at \(167 on the optionexpiration date? What if IBM is selling at \)175? Use The Wall Street Journal listingfrom Figure 15.1 to answer this question.

c. At what two stock prices will you just break even on your investment?

d. What kind of “bet” is this investor making; that is, what must this investor believeabout IBM’s stock price in order to justify this position?

Short answer

a. As below

b. $6.61

c. $6.61

d. low volatility

Step-by-step solution

Graphical representation of Payoff

Position	ST< 75	75< ST< 80	ST> 80
Short call	0	0	-(ST - 80)
Short put	-(75 -ST)	0	0
Total	ST - 75	0	80 - ST

Calculation of profit / loss ‘b’

From the given figure (15.1):

Proceeds from writing option = Call + Put = $2.64 + $3.97 = $6.61

Calculation of break even ‘c’

The break even would happen if the short position in the put or call results in a cash outflow of $6.61

Explanation on investors bet

The investor is betting on the low volatility of IBM’s stock price. The investor expects a low stock movement and sells the put and call option. So, the stock price would experience an effect indirectly causing its volatility to be low. So, the investor bets on the basis of low volatility.