Question

A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 − $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 − $1.00 = $2.50 per share. The point of purchasing a European option is to limit the risk of a decrease in the per-share price of the stock. Suppose you purchased 200 shares of the stock at $28 per share and 70 six-month European put options with an exercise price of $26. Each put option costs $1.

(a)

Using data tables, construct a model that shows the value of the portfolio with options and without options for a share price in six months between $20 and $29 per share in increments of $1.00. What is the benefit of the put options on the portfolio value for the different share prices? For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300). If you answer is zero, enter “0”.

Share Price Benefit of Options $20 $_______ $21 $_______ $22 $_______ $23 $_______ $24 $_______ $25 $_______ $26 $_______ $27 $_______ $28 $_______ $29 $_______

Answer 1

Cost of stocks purchased = 200*28 = $560

Cost of put options purchased = 70*1 = $70

Total money spent = 560+70 = $630

Exercise Price of put option purchased = $26

The option will be worthless if at expiry share price of the stock is greater than $26 (since it is a put option with exercise @ $26).

Writing the portfolio value in each case:

Stock price (at expiry)	Value of shares held (A)	Value of put options held (B)	Value of portfolio (A+B)	Profit (A+B-$630)
20	200*20 = $400	70*6 = $420	$400+$420 = $820	$820-$630= 190
21	200*21= $420	70*5 = $350	$420+$350 = $770	$770-$630= 140
22	200*22 = $440	70*4 = $280	$440+$280 = $720	$720-$630= 90
23	200*23 = $460	70*3 = $210	$460+$210 = $670	$670-$630= 40
24	200*24 = $480	70*2 = $140	$480+$140 = $620	$620-$630= -10
25	200*25 = $500	70*1 = $70	$500+$70 = $570	$570-$630= -60
26	200*26 = $520	70*0 = $0	$520+$0 = $520	$520-$630= -110
27	200*27 = $540	70*0 = $0	$540+$0 = $540	$540-$630= -90
28	200*28 = $560	70*0 = $0	$560+$0 = $560	$560-$630= -70
29	200*29 = $580	70*0 = $0	$580+$0 = $580	$580-$630= -50