Principles of Finance with Excel (Основы финансов c Excel)
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PFE, Chapter 22: Introduction to options page 30
22.7. Spread
A spread strategy involves buying one option on a stock and writing another option. In
the example below on August 7, 2001:
•
We buy one X=15 September call on Cisco. This option costs $4.50.
•
We write one X=20 September call on Cisco. This option costs 1.35; since we’re
writing the option, this is income on August 7.
In the spreadsheet below we examine this strategy’s payoffs and graph them:
PFE, Chapter 22: Introduction to options page 31
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ABCDEF
Cost of September, X=15 call 4.5
Number of X=15 calls purchased 1
Cost of Sept. X=20 call 1.35
Number of X=20 calls purchased -1
Market price of Cisco.
21 September 2001
Exercise
X=15
call?
Profit/loss
on X=15 call
Exercise
X=20
call?
Profit
/
loss
on X=20
call
Total
profit
0 no -4.5 no 1.35 -3.15
5 no -4.5 no 1.35 -3.15
10 no -4.5 no 1.35 -3.15
15 no -4.5 no 1.35 -3.15
18 yes -1.5 no 1.35 -0.15
20 yes 0.5 no 1.35 1.85
21 yes 1.5 yes 0.35 1.85
22 yes 2.5 yes -0.65 1.85
25 yes 5.5 yes -3.65 1.85
28 yes 8.5 yes -6.65 1.85
30 yes 10.5 yes -8.65 1.85
32 yes 12.5 yes -10.65 1.85
34 yes 14.5 yes -12.65 1.85
SPREAD: BUY ONE OPTION, SELL ANOTHER
Spread Strategy Profits
-4
-3
-2
-1
0
1
2
3
0 5 10 15 20 25 30 35
Stock price, 21Sep01
There’s another way to think about the strategy profits: On September 21, 2001 (the
option expiration date) we will have:
PFE, Chapter 22: Introduction to options page 32
,21 01 ,21 01
This is the option payoff on 21Sep01
from buying a call with X=15
This is the profit from buying
the X=15 option
4.50 15,0 1.35 20,0
CSCO Sep CSCO Sep
Max S Max S
↑↑
↑
−+ − +− −
Writing an option means
taking a loss if Cisco's stock
price is > 20
This is the profit from writing the X=20 option
,21 01
,21 01 ,21 01
015
3.15 15 15 20
5
CSCO Sep
CSCO Sep CSCO Sep
C
S
SS
S
↑
<
=− + − ≤ ≤
,21 01
20
SCO Sep
>
In column G we’ve put this equation as an Excel formula. Notice the two
If functions,
one within the other:
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ABCDEFG H
Cost of September, X=15 call 4.5
Number of X=15 calls purchased 1
Cost of Sept. X=20 call 1.35
Number of X=20 calls purchased -1
Market price of Cisco.
21 September 2001
Exercise
X=15
call?
Profit/loss
on X=15 call
Exercise
X=20
call?
Profit
/
loss
on X=20
call
Total
profit Equation
0 no -4.5 no 1.35 -3.15 -3.15 <-- =-3.15+IF(A10<15,0,IF(A10>20,5,A10-15))
5 no -4.5 no 1.35 -3.15 -3.15 <-- =-3.15+IF(A11<15,0,IF(A11>20,5,A11-15))
10 no -4.5 no 1.35 -3.15 -3.15
15 no -4.5 no 1.35 -3.15 -3.15
18 yes -1.5 no 1.35 -0.15 -0.15
20 yes 0.5 no 1.35 1.85 1.85
21 yes 1.5 yes 0.35 1.85 1.85
22 yes 2.5 yes -0.65 1.85 1.85
25 yes 5.5 yes -3.65 1.85 1.85
28 yes 8.5 yes -6.65 1.85 1.85
30 yes 10.5 yes -8.65 1.85 1.85
32 yes 12.5 yes -10.65 1.85 1.85
34 yes 14.5 yes -12.65 1.85 1.85
SPREAD: BUY ONE OPTION, SELL ANOTHER
Why buy a spread? In this case the spread is a not-too-risky bet on the stock price going
up. If it goes up, you profit (moderately); if the stock price goes down, your loss is limited to
$3.15. This kind of a spread is called a bull spread—you’re bullish on the stock (meaning that
you think the stock price will go up).
Here’s a bear spread: In this case we write the X = 15 call and buy the X=20 call.
PFE, Chapter 22: Introduction to options page 33
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ABCDEFG H
Cost of September, X=15 call 4.5
Number of X=15 calls purchased -1
Cost of Sept. X=20 call 1.35
Number of X=20 calls purchased 1
Market price of Cisco.
21 September 2001
Exercise
X=15
call?
Profit/loss
on X=15 call
Exercise
X=20
call?
Profit
/
loss
on X=20
call
Total
profit Equation
0 no 4.5 no -1.35 3.15 3.15 <-- =3.15-IF(A10<15,0,IF(A10>20,5,A10-15))
5 no 4.5 no -1.35 3.15 3.15 <-- =3.15-IF(A11<15,0,IF(A11>20,5,A11-15))
10 no 4.5 no -1.35 3.15 3.15
15 no 4.5 no -1.35 3.15 3.15
18 yes 1.5 no -1.35 0.15 0.15
20 yes -0.5 no -1.35 -1.85 -1.85
21 yes -1.5 yes -0.35 -1.85 -1.85
22 yes -2.5 yes 0.65 -1.85 -1.85
25 yes -5.5 yes 3.65 -1.85 -1.85
28 yes -8.5 yes 6.65 -1.85 -1.85
30 yes -10.5 yes 8.65 -1.85 -1.85
32 yes -12.5 yes 10.65 -1.85 -1.85
34 yes -14.5 yes 12.65 -1.85 -1.85
BULL SPREAD: A MODERATE BET ON STOCK DECLINE
Spread Strategy Profits
-3
-2
-1
0
1
2
3
4
0 5 10 15 20 25 30 35
Stock price, 21Sep01
22.8. Butterfly
A butterfly is a combination of 3 options. In the butterfly illustrated below:
•
We buy one Cisco October X=15 call for $5
•
We write two Cisco October X=20 calls for $1.80 each
•
We buy one Cisco October X=25 call for $0.45
Here’s the resulting profit pattern:
PFE, Chapter 22: Introduction to options page 34
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ABCDEFGH
GRAPHING THE PROFIT FROM A BUTTERFLY IN CISCO OPTIONS
Strategy: Buy 1 October 15 Call, Write 2 October 20 Calls, Buy 1 October 25 Call
Call prices
XPrice
15 5.00
20 1.80
25 0.45
Payoff and profits
October Cisco
stock price
Payoff on
October X=15
call
Payoff on
October
X=20
call
Payoff on
October X=25
call
Total
profit
0 -5 3.6 -0.45 -1.85
5 -5 3.6 -0.45 -1.85
10 -5 3.6 -0.45 -1.85
15 -5 3.6 -0.45 -1.85
16 -4 3.6 -0.45 -0.85
17 -3 3.6 -0.45 0.15
18 -2 3.6 -0.45 1.15
19 -1 3.6 -0.45 2.15
20 0 3.6 -0.45 3.15
21 1 1.6 -0.45 2.15
22 2 -0.4 -0.45 1.15
23 3 -2.4 -0.45 0.15
24 4 -4.4 -0.45 -0.85
25 5 -6.4 -0.45 -1.85
26 6 -8.4 0.55 -1.85
30 10 -16.4 4.55 -1.85
35 15 -26.4 9.55 -1.85
40 20 -36.4 14.55 -1.85
Butterfly: Profit Pattern
1 X=15 Call bought, 1 X=25 Call bought, 2 X=20 Calls written
-3
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-1
0
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0 5 10 15 20 25 30 35 40
Cisco stock price, October
Total profit
=MAX(A12-15,0)-$C$6
=-2*(MAX(A12-20,0)-$C$7)
=MAX(A12-25,0)-$C$8
PFE, Chapter 22: Introduction to options page 35
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.
In Section ??? of the Chapter 22 we’ll return to butterflies and use them to derive a
remarkable fact about option prices.
Summary
In this section 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.
EXERCISES
Put butterflies and put convexity
PFE, Chapter 23: Introduction to options page 1
CHAPTER 23: INTRODUCTION TO OPTIONS
*
this version: November 20, 2004
Chapter contents
Overview..............................................................................................................................2
23.1. What’s an option?......................................................................................................9
23.2. Why buy a call option?............................................................................................17
23.3. Why buy a put option?.............................................................................................20
23.4. General properties of option prices..........................................................................22
23.5. Writing options, shorting stock................................................................................26
23.6. Option strategies—more complicated reasons to buy options.................................35
23.7. Another option strategy: Spread .............................................................................41
23.8. The butterfly option strategy.....................................................................................44
Summary............................................................................................................................49
Exercises............................................................................................................................50
*
This is a preliminary draft of a chapter of Principles of Finance with Excel. © 2001 – 2004 Simon Benninga
(benninga@wharton.upenn.edu
).
PFE, Chapter 23: Introduction to options page 2
Overview
The financial assets we have discussed so far in this book are stocks (Chapter 000) and
bonds (Chapter 000). In Chapters 23-26 we discuss another kind of financial asset—options. As
you will see in these chapters, an option is different in many respects from a stock or a bond:
• The value of an option is derived from the value of another asset, usually a stock. For
this reason options are sometimes called derivative assets.
• The buyer of an option buys upside gains but has only limited downside losses.
• Options are more complicated than bonds or stocks. In order to understand options we
will have to introduce you to some new terminology and some new ways of thinking
about financial assets.
A simple example of an option
In order to give some meaning to these somewhat mysterious statements, we start with a
simple example.
1
It is 1 January 2006, and the price of an ounce of gold is $400. You have a
very strong hunch that the price of gold will be $500 in three months. Your hunches have never
failed you, so this must be a sure-fire way to make some money. Taking your total savings of
$400, you go to your local jewelry mart to buy some gold. But with your paltry savings you can
buy only one ounce of gold, and you can make a maximum of only $100—only a 25% return on
your initial investment.
However, the jeweler has another offer for you: For $50, he is willing to sell you a
contract which gives you the right to buy one ounce of gold in three months for $400. You
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Even this simple example is non-trivial. Options are like that!
PFE, Chapter 23: Introduction to options page 3
realize that this contract—a call option on gold—gives you the opportunity of making much
more money that actually buying gold.
Here’s your calculation:
• Using your $400 savings, you can buy eight call options.
• In three months you can use the call options to buy eight ounces of gold for $400 per
ounce. If your hunch is correct, the gold price in three months will be $500 per ounce, so
that you can make $100 per ounce of gold purchased.
• Your total profit using the gold call options will be $800—a profit of 200% on your
initial investment. This compares to the profit of 25% you will make if you use your
$400 savings to buy one ounce of physical gold.
Downside: Suppose your hunch is wrong, and the price of gold in three months is $300.
Now compare the profits of buying one ounce of physical gold to the profits of buying eight call
options:
• If you bought one ounce of physical gold, you would have lost 25% of your initial $400
investment.
• If you bought eight options and the price of gold on 31 March 2006 is $300 per ounce,
the options will be worthless. In this case you would have lost 100% of your initial $400
investment.
PFE, Chapter 23: Introduction to options page 4
CALL OPTION ON ONE OUNCE OF GOLD
Price on 1 January 2006: $50
If presented at Asheville Jewelry Mart on or before 31
March 2006, this piece of paper gives you the right to buy
one ounce of gold for $400. After 31 March 2006, this
piece of paper is worthless.
The owner of this piece of paper can sell it to anyone
else at any time.
Figure 23.1. The gold call option certificates sold by the Asheville Jewelry Mart.
Peacemount stock options—an example
Our gold example should convince you that options are an interesting way to make
money. In this subsection we give an example of a stock option. Stock options give their
holders the right to either buy or sell a stock in the future for a predetermined price. Stock
options come in two flavors: A call option on a stock allows you to make money if the stock
price goes up without losing too much if the stock price goes down. A put option on a stock
allows you to make money if the stock’s price goes down without losing too much if the stock’s
price goes up.
Take a look at Figure 23.2, which shows a call option (the right to buy a share of stock)
on one share of a fictional company called Peacemount. On 26 November 2003 it would cost