Principles of Finance with Excel (Основы финансов c Excel)
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PFE, Chapter 23: Introduction to options page 45
• We write two Cisco, October X=20, calls for $1.80 each
•
We buy one Cisco, October X=25, call for $0.45
Here’s the resulting profit pattern:
PFE, Chapter 23: Introduction to options page 46
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ABCDEFGH
Call prices
XPrice
15 5.00
20 1.80
25 0.45
Payoff and profits
October Cisco
stock price
Payoff on
October X=15
call
Payo
ff
on
October
X=20
call
Payoff on
October X=25
call
Total
profit
0 -5 3.6 -0.45 -1.85
5 -5 3.6 -0.45 -1.85
10 -5 3.6 -0.45 -1.85
15 -5 3.6 -0.45 -1.85
16 -4 3.6 -0.45 -0.85
17 -3 3.6 -0.45 0.15
18 -2 3.6 -0.45 1.15
19 -1 3.6 -0.45 2.15
20 0 3.6 -0.45 3.15
21 1 1.6 -0.45 2.15
22 2 -0.4 -0.45 1.15
23 3 -2.4 -0.45 0.15
24 4 -4.4 -0.45 -0.85
25 5 -6.4 -0.45 -1.85
26 6 -8.4 0.55 -1.85
30 10 -16.4 4.55 -1.85
35 15 -26.4 9.55 -1.85
40 20 -36.4 14.55 -1.85
GRAPHING THE PROFIT FROM A BUTTERFLY IN CISCO OPTIONS
Strategy: Buy 1 October 15 Call,
Write 2 October 20 Calls, Buy 1 October 25 Call
Butterfly: Profit Pattern
1 X=15 Call bought, 1 X=25 Call bought, 2 X=20 Calls written
-3
-2
-1
0
1
2
3
4
0 5 10 15 20 25 30 35 40
Cisco stock price, October
Total profit
=MAX(A10-15,0)-$C$4
=-2*(MAX(A10-20,0)-$C$5)
=MAX(A10-25,0)-$C$6
PFE, Chapter 23: Introduction to options page 47
Why buy a butterfly? Looking at the graph you can see that it’s a bet on the stock price
not moving very much. If Cisco’s October stock price is close to $20, we’ll make money from
our butterfly. If it deviates (up or down) by a lot, we’ll lose money, but only moderately.
Of course, if we reverse the option positions in the butterfly, we’ll get a bet on the stock
price moving a lot (big movements either up or down will lead to profits, small movements in the
stock price will lead to losses):
PFE, Chapter 23: Introduction to options page 48
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ABCDEFGH
Call prices
XPrice
15 5.00
20 1.80
25 0.45
Payoff and profits
October Cisco
stock price
Payoff on
October X=15
call
Payo
ff
on
October
X=20
call
Payoff on
October X=25
call
Total
profit
05.00-3.60.451.85
55.00-3.60.451.85
10 5.00 -3.6 0.45 1.85
15 5.00 -3.6 0.45 1.85
16 4.00 -3.6 0.45 0.85
17 3.00 -3.6 0.45 -0.15
18 2.00 -3.6 0.45 -1.15
19 1.00 -3.6 0.45 -2.15
20 0.00 -3.6 0.45 -3.15
21 -1.00 -1.6 0.45 -2.15
22 -2.00 0.4 0.45 -1.15
23 -3.00 2.4 0.45 -0.15
24 -4.00 4.4 0.45 0.85
25 -5.00 6.4 0.45 1.85
26 -6.00 8.4 -0.55 1.85
30 -10.00 16.4 -4.55 1.85
35 -15.00 26.4 -9.55 1.85
40 -20.00 36.4 -14.55 1.85
THE OPPOSITE BUTTERFLY--
A
BET ON LARGE STOCK PRICE
MOVEMENTS
Strategy: Write 1 October 15 Call,
Buy 2 October 20 Calls, Write 1 October 25 Call
Butterfly: Profit Pattern
1 X=15 Call written, 1 X=25 Call written, 2 X=20 Calls bought
-4
-3
-2
-1
0
1
2
3
0 5 10 15 20 25 30 35 40
Cisco stock price, October
Total profit
=$C$4-MAX(A10-15,0)
=2*(MAX(A10-20,0)-$C$5)
=$C$6-MAX(A10-25,0)
PFE, Chapter 23: Introduction to options page 49
Summary
Stock options are securities which make it possible to bet on an increase in the stock price
(calls) or a decrease in the price (puts). In this chapter we’ve looked at the basics of option
markets. We’ve discussed definitions (calls, puts, American versus European options) and profit
patterns of both individual options and combinations of options.
In the next chapter we discuss some facts about stock option prices.
PFE, Chapter 23: Introduction to options page 50
Exercises
Note: Templates for many of these problems are on the CD-ROM which comes with this book.
1. On 2 September 2004 Kellogg stock closed at $41.78. For $2.60 you can buy a call option on
Kellogg with an exercise price of $40. The option expires 17 December 2004.
1.a. What right does this call option give you?
1.b. Suppose you buy the call option and hold it until the expiration date. If the price of
Kellogg on 17 December 2004, is $52, will you exercise the option? What will be your
profit?
1.c. If the price of Kellogg on 17 December 2004, is $38, will you exercise the option?
What will be your profit?
2. It is mid-July 2008. Intel stock is currently trading at $30, and you think that the price of the
stock will go down by 22 October 2008. For $3 you can buy a put on Intel stock that expires in
October and that has an exercise price of $25.
2.a. What right does this put option give you?
2.b. What happens if the stock does not go below $25 by the time your option expires?
2.c. Suppose you buy the option and hold it until the expiration date. If the price of Intel
on 22 October 2008 is $20, what will be your profit from the option? What if the price is
$38?
PFE, Chapter 23: Introduction to options page 51
3. It is 18 July 2006 and you’ve just bought one call option on ForeverYours stock. The option
cost you $6, expires on 18 September 2004, and has an exercise price of $20.
3.a. Complete the following Excel table.
3.b. Make a graph which shows the Profit (column C) on the y-axis and the Stock Price
on 18Sep04 (column A) on the x-axis.
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12
13
ABC
ForeverYours
stock price,
18sep04--S
T
Exercise
the call
option?
Profit
0
5
10
15
20
25
30
35
40
45
50
4. It is 31 December 2007 and you’ve just bought one put option on ItStinks stock. The option
cost you $3, expires on 13 March 2008, and has an exercise price of $35.
4.a. Complete the following Excel table.
4.b. Make a graph which shows the Profit (column C) on the y-axis and the Stock Price
on 13Mar08 (column A) on the x-axis.
PFE, Chapter 23: Introduction to options page 52
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12
13
ABC
ItStinks
stock price,
13mar08--S
T
Exercise
the put
option?
Profit
0
5
10
15
20
25
30
35
40
45
50
5.
5.a. On 1 September 2004 Ford’s stock price was $13.90 per share. Call options on Ford
expiring on 17 September 2004 with an exercise price of $12.50 sold for $1.50. Should a
call with an exercise price of $12.50 expiring on the 21 January 2005 sell for more that
$1.50? Explain.
5.b. Look at the following table. Is there an option which is clearly mispriced?
Exercise
price X
Call option
price
2.50$
$ 12.80
5.00$
$ 9.00
7.50$
$ 7.90
10.00$
$ 5.20
12.50$
$ 3.00
15.00$
$ 3.30
17.50$
$ 0.60
20.00$
$ 0.15
22.50$
$ 0.10
25.00$
$ 0.05
Ford Call Options
Expiring 21jan05
6.
PFE, Chapter 23: Introduction to options page 53
6.a. On 1 September 2004 GM’s stock price was $41.21 per share. Put options on GM
expiring on 17 September 2004 with an exercise price of $40 sold for $1.80. Should a
call with an exercise price of $40 expiring on the 21 January 2005 sell for more that
$1.80? Explain.
6.b. Look at the following table. Is there an option which is clearly mispriced?
Exercise
price X
Put option
price
5.00$
$ 37.00
10.00$
$ 33.60
15.00$
$ 29.20
20.00$
$ 24.20
30.00$
$ 14.30
35.00$
$ 9.70
40.00$
$ 6.00
45.00$
$ 2.70
50.00$
$ 0.95
55.00$
$ 0.35
60.00$
$ 0.09
65.00$
$ 0.05
70.00$
$ 0.25
GM Put Options
Expiring 21jan05
7. The price of IBM stock on 1 June 2004 was $88.00.
7.a. If you purchased the stock on 1 June and sold it on 1 September 2004 for $84.05,
what would have been your profit?
7.b. If you shorted IBM stock on 1 June and closed out your short position on 1
September 2004, what would have been your profit?
8. It is 15 December 2006, and John is considering buying 100 shares of GoodLuck stock (the
stock price is currently $40 per share). On the same date Mary is considering shorting 100
PFE, Chapter 23: Introduction to options page 54
shares of GoodLuck stock. If both John and Mary intend to close out their positions on 1 April
2007, fill in the following table and graph their profits.
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ABC
GoodLuck stock
price, 15dec06
50.00$
GoodLuck stock
price on 1apr07
John's profit from
buying 100 shares
Mary's profit
from shorting
100 shares
$0.00
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
$80.00
$90.00
$100.00
9. You’ve decided to add 100 shares of ABC Corp. to your portfolio. ABC stock is currently
trading at $50 a share. As an alternative to buying the shares now, you’re considering buying
1000 call options on ABC. Each option has an exercise price of $50 and expires in 3 months.
The options cost $5 each.
9a. Compare the two strategies by filling in the following table and graphing the
percentage profits of each strategy against the stock price S
T
in three months.
9.b. Which strategy is riskier?