Principles of Finance with Excel (Основы финансов c Excel)
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PFE, Chapter 23: Introduction to options page 35
23.6. Option strategies—more complicated reasons to buy options
In the previous section we studied the profit and loss from buying and selling calls, puts,
and shares. In this and the following two sections we look at the profit involved in more
complicated option strategies. “Option strategy” refers to the profits which result from holding a
combination of options and shares.
A simple option strategy: buy a stock and buy a put
We begin with a very simple (but useful) strategy: Suppose we decide, on 7 August
2001, to purchase one share of Cisco stock and to purchase a put on the stock with exercise price
20 and expiration date September. The total cost of this strategy is $21.26: $19.26 for the share
of Cisco and $2.00 for each put.
Such a strategy effective insures your stock returns by guaranteeing that on 17 September
2001 you will have at least $20 in hand. Your worst-case net profit will be a loss of $1.65:
Stock price
on 17
September
Strategy Cash in hand Net profit
Less than
$20
Exercise put option and
sell your share of Cisco
for $20.
$20 $20 – ($19.26 + $2)= -$1.65
More than
$20
Let the put option expire
(don’t use it)
Cisco stock
price on 17
September, S
T
S
T
– ($19.26 + $2)=
S
T
- $21.26
In a spreadsheet, here’s the way this strategy looks:
PFE, Chapter 23: Introduction to options page 36
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ABCDEF
Stock price, 7Aug01 19.26
Cost of put option 2
Put exercise price, X 20
Market price of Cisco.
21 September 2001
Exercise
the put
Profit/loss
on the put
Profit/loss
on the stock
Total
profit/loss
0 yes 18 -19.26 -1.26 <-- =C7+D7
5 yes 13 -14.26 -1.26
10 yes 8 -9.26 -1.26
16 yes 2 -3.26 -1.26
18 yes 0 -1.26 -1.26
20 no -2 0.74 -1.26
21 no -2 1.74 -0.26
22 no -2 2.74 0.74
25 no -2 5.74 3.74
28 no -2 8.74 6.74
30 no -2 10.74 8.74
32 no -2 12.74 10.74
34 no -2 14.74 12.74
STOCK + PUT: OPTION STRATEGY PROFITS
Profit/Loss: Stock + Put
-25
-20
-15
-10
-5
0
5
10
15
20
0 5 10 15 20 25 30
Stock price, 21Sept01
Profit
Profit/loss
on the put
Profit/loss
on the stock
Total profit/loss
=IF(A7<$B$4,$B$4-A7,0)-$B$3
=A7-$B$2
Buying a stock or a portfolio and buying a put on the stock or portfolio is often called a
portfolio insurance strategy. Portfolio insurance strategies are very popular among investors.
They guarantee a minimum return on the investment in the shares (at an extra cost, of course:
you have to buy the puts).
PFE, Chapter 23: Introduction to options page 37
ANTICIPATING A BIT—put-call parity
You’ll notice that the graph of the stock+put strategy looks a lot like the graph of
a call (Section 23.2). This may lead you to surmise that the payoffs of the combination
stock+put is somehow equivalent to the payoffs of a call. However, this isn’t quite true,
as you’ll see in the next chapter. There we discuss the put-call parity theorem and show
that—for a put and call written on the same stock and having the same exercise price X:
(
)
stock put call PV X+=+
A more complicated strategy: Stock + 2 puts
Suppose you purchased one share of stock and bought 2 puts, each costing $2 and each
having an exercise price of $20. Here’s what your payoff pattern would look like:
Stock price
on 17
September
Strategy Cash in hand,
17 September
Net profit
S
T
< $20 Exercise both put
options. Give someone
else your share of Cisco
for $20.
Buy an
additional share in the
market and give it to the
put writer for S
T
.
2*20 - S
T
2*20 - S
T
– ($19.26 + $4)=
$16.74 - S
T
More than
$20
Let the put options
expire (don’t use them)
Cisco stock
price on 17
September, S
T
S
T
– ($19.26 + $4)=
S
T
- $23.26
If we make an Excel table, here’s what it looks like:
PFE, Chapter 23: Introduction to options page 38
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ABCDEF
Stock price, 7Aug01 19.26
Cost of put option 2.00
Put exercise price, X 20.00
Market price of Cisco.
21 September 2001
Exercise
the put
Profit/loss
on the puts
Profit/loss
on the stock
Total
profit/loss
0 yes 36 -19.26 16.74 <-- =C7+D7
5 yes 26 -14.26 11.74
10 yes 16 -9.26 6.74
16 yes 4 -3.26 0.74
18 yes 0 -1.26 -1.26
20 no -4 0.74 -3.26
21 no -4 1.74 -2.26
22 no -4 2.74 -1.26
25 no -4 5.74 1.74
28 no -4 8.74 4.74
30 no -4 10.74 6.74
32 no -4 12.74 8.74
34 no -4 14.74 10.74
36
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STOCK + 2 PUTS PUT: OPTION STRATEGY PROFITS
Stock + 2 Puts
-5
0
5
10
15
20
0 5 10 15 20 25 30
Stock price, 21Sept01
Profit
=2*(IF(A7<$B$4,$B$4-A7,0)-$B$3)
=A7-$B$2
Comparing strategies
What’s better as a strategy: buying a share of Cisco and buying 1 put, or buying a share
of Cisco and buying 2 puts? Look at the graphs of the two strategies:
PFE, Chapter 23: Introduction to options page 39
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ABC D
Stock price, 7Aug01 19.26
Cost of put option 2.00
Put exercise price, X 20.00
Market price of Cisco.
21 September 2001 Stock + Put Stock + 2 Puts
0 -1.26 16.74 <-- =2*IF(A7<=$B$4,$B$4-A7,0)+A7-($B$2+2*$B$3)
5 -1.26 11.74
10 -1.26 6.74
16 -1.26 0.74
18 -1.26 -1.26
20 -1.26 -3.26
21 -0.26 -2.26
22 0.74 -1.26
25 3.74 1.74
28 6.74 4.74
30 8.74 6.74
32 10.74 8.74
34 12.74 10.74
STOCK + PUT COMPARED TO STOCK + 2 PUTS
Comparing Stock + Put to Stock + 2 Puts
-5.00
0.00
5.00
10.00
15.00
20.00
0 5 10 15 20 25 30 35
Cisco price, 21Sept01
Profit
Stock + Put Stock + 2 Puts
=IF(A7<=$B$4,$B$4-A7,0)+A7-($B$2+$B$3)
The choice between the two strategies involves tradeoffs (that’s the nature of market
efficiency: in an efficient market no asset ever completely dominates another asset).
•
The stock+put strategy has higher profit when the Cisco September stock price > 20,
but it has a negative profit for Cisco S
T
< 20
•
The stock + 2 put strategy costs more (you can see this by noting that its payoff when
S
T
= 20 is less than that of the stock + put strategy). On the other hand, it has positive
profits both for very low and for high S
T
.
PFE, Chapter 23: Introduction to options page 40
Which strategy should you choose? It depends on your prediction of the future: If you
think that Cisco is going to make a big move, up or down, then stock + 2 puts is for you, since
this strategy makes profits on “big moves” of the stock price (whether up or down). If you think,
on the other hand, that Cisco might go up, but you want protection when and if its price goes
down (that is, no bets for you), then stock + put is your choice.
Another strategy: One share of stock + 1, 2, 3, or 4 puts
There’s almost nothing to say here, except to show you the graphs:
PFE, Chapter 23: Introduction to options page 41
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ABCDEFGH
Stock price, 7Aug01 19.26
Cost of put option 2
Put exercise price, X 20
Number of puts purchased 2
Market price of Cisco.
21 September 2001
Exercise
the put
Profit/loss
on single put
Profit/loss
on the stock
Total profit:
1 put
Total profit:
2 puts
Total profit:
3 puts
Total profit:
4 puts
0 yes 18 -19.26 -1.26 16.74 34.74 52.74
5 yes 13 -14.26 -1.26 11.74 24.74 37.74
10 yes 8 -9.26 -1.26 6.74 14.74 22.74
16 yes 2 -3.26 -1.26 0.74 2.74 4.74
18 yes 0 -1.26 -1.26 -1.26 -1.26 -1.26
20 no -2 0.74 -1.26 -3.26 -5.26 -7.26
21 no -2 1.74 -0.26 -2.26 -4.26 -6.26
22 no -2 2.74 0.74 -1.26 -3.26 -5.26
25 no -2 5.74 3.74 1.74 -0.26 -2.26
28 no -2 8.74 6.74 4.74 2.74 0.74
30 no -2 10.74 8.74 6.74 4.74 2.74
32 no -2 12.74 10.74 8.74 6.74 4.74
34 no -2 14.74 12.74 10.74 8.74 6.74
STOCK + SEVERAL PUTS PUT: OPTION STRATEGY PROFITS
Total Profits: 1 Share of Stock + (1,2,3,4) Puts
-20
-10
0
10
20
30
40
50
60
0 5 10 15 20 25 30 35
Stock price, 21Sep01
Profit
Total profit:
1 put
Total profit:
2 puts
Total profit:
3 puts
Total profit:
4 puts
A
ll the lines cross when stock price
= 18. At this point the net put profit
= 0 and the strategy produces a
loss of $2.
23.7. Another option strategy: 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 $4.50.
PFE, Chapter 23: Introduction to options page 42
• We write one X=20 September call on Cisco. This option costs 1.35; since we’re
writing the option, this is income on August 7.
In the spreadsheet below we examine this strategy’s payoffs and graph them:
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ABCDEFG
Cost of September, X=15 call 4.5
Number of X=15 calls purchased 1
Cost of Sept. X=20 call 1.35
Number of X=20 calls purchased -1
Market price of Cisco.
21 September 2001
Exercise
X=15
call?
Profit/loss
on X=15 call
Exercise
X=20
call?
Profit
/
loss
on X=20
call
Total
profit
0 no -4.50 no 1.35 -3.15
5 no -4.50 no 1.35 -3.15
10 no -4.50 no 1.35 -3.15
15 no -4.50 no 1.35 -3.15
18 yes -1.50 no 1.35 -0.15
20 yes 0.50 no 1.35 1.85
21 yes 1.50 yes 0.35 1.85
22 yes 2.50 yes -0.65 1.85
25 yes 5.50 yes -3.65 1.85
28 yes 8.50 yes -6.65 1.85
30 yes 10.50 yes -8.65 1.85
32 yes 12.50 yes -10.65 1.85
34 yes 14.50 yes -12.65 1.85
BULL SPREAD: A MODERATE BET ON STOCK PRICE INCREASE
Spread Strategy Profits
-4
-3
-2
-1
0
1
2
3
0 5 10 15 20 25 30 35
Stock price, 21Sep01
=$B$3*(MAX(A9-15,0)-$B$2)
=$B$6*(MAX(A9-20,0)-$B$5)
=C9+E9
There’s another way to think about the strategy profits: On September 21, 2001 (the
option expiration date) we will have:
PFE, Chapter 23: Introduction to options page 43
,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 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 $3.15. This kind of
a spread is called a bull spread—you’re bullish on the stock (meaning that you think the stock
price will go up).
Here’s a bear spread: In this case we write the X = 15 call and buy the X=20 call. As
you can see from the graph below, the bear spread is a bet that the stock price will decline.
PFE, Chapter 23: Introduction to options page 44
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ABCDEFG
Cost of September, X=15 call 4.5
Number of X=15 calls purchased -1
Cost of Sept. X=20 call 1.35
Number of X=20 calls purchased 1
Market price of Cisco.
21 September 2001
Exercise
X=15
call?
Profit/loss
on X=15 call
Exercise
X=20
call?
Profit
/
loss
on X=20
call
Total
profit
0 no 4.50 no -1.35 3.15
5 no 4.50 no -1.35 3.15
10 no 4.50 no -1.35 3.15
15 no 4.50 no -1.35 3.15
18 yes 1.50 no -1.35 0.15
20 yes -0.50 no -1.35 -1.85
21 yes -1.50 yes -0.35 -1.85
22 yes -2.50 yes 0.65 -1.85
25 yes -5.50 yes 3.65 -1.85
28 yes -8.50 yes 6.65 -1.85
30 yes -10.50 yes 8.65 -1.85
32 yes -12.50 yes 10.65 -1.85
34 yes -14.50 yes 12.65 -1.85
BEAR SPREAD: A MODERATE BET ON STOCK PRICE DECLINE
Spread Strategy Profits
-3
-2
-1
0
1
2
3
4
0 5 10 15 20 25 30 35
Stock price, 21Sep01
=$B$3*(MAX(A9-15,0)-$B$2)
=$B$6*(MAX(A9-20,0)-$B$5)
=C9+E9
23.8. The butterfly option strategy
The last option strategy we consider in this chapter is a butterfly, the combination of three
options. In the butterfly illustrated below:
•
We buy one Cisco, October X=15, call for $5