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Long
Butterfly
The long butterfly spread is
a three-leg strategy that is
appropriate for a neutral
forecast - when you expect
the underlying stock price
(or index level) to change
very little over the life of
the options. A butterfly can
be implemented using either
call or put options. For
simplicity, the following
explanation discusses the
strategy using call options.
A long call butterfly spread
consists of three legs with
a total of four options:
long one call with a lower
strike, short two calls with
a middle strike and long one
call of a higher strike. All
the calls have the same
expiration, and the middle
strike is halfway between
the lower and the higher
strikes. The position is
considered "long" because it
requires a net cash outlay
to initiate.
When a butterfly spread is
implemented properly, the
potential gain is higher
than the potential loss, but
both the potential gain and
loss will be limited.
The total cost of a long
butterfly spread is
calculated by multiplying
the net debit (cost) of the
strategy by the number of
shares each contract
represents. A butterfly will
break-even at expiration if
the price of the underlying
is equal to one of two
values. The first break-even
value is calculated by
adding the net debit to the
lowest strike price. The
second break-even value is
calculated by subtracting
the net debit from the
highest strike price. The
maximum profit potential of
a long butterfly is
calculated by subtracting
the net debit from the
difference between the
middle and lower strike
prices. The maximum risk is
limited to the net debit
paid for the position.
Butterfly spreads achieve
their maxim profit potential
at expiration if the price
of the underlying is equal
to the middle strike price.
The maximum loss is realized
when the price of the
underlying is below the
lowest strike or above the
highest strike at
expiration.
As with all advanced option
strategies, butterfly
spreads can be broken down
into less complex
components. The long call
butterfly spread has two
parts, a bull call spread
and a bear call spread. The
following example, which
uses options on the Dow
Jones Industrial Average (DJX),
illustrates this point.
Long Butterfly - DJX
= $75.28 |
Buy |
**1 DJX 72
Call **@
$6.10 x 100 |
$610 |
(wing) |
Sell |
**2 DJX 75
Call **@
$4.10 x 100 |
($820) |
(butterfly body) |
Buy |
**1 DJX 78
Call **@
$2.60 x 100 |
$260 |
(wing) |
Net Debit from Trade |
$50 |
($870 - $820) |
In this example the total
cost of the butterfly is the
net debit ($.50) x the
number of shares per
contract (100). This equals
$50, not including
commissions. Please note
that this is a three-legged
trade, and there will be a
commission charged for each
leg of the trade.
An expiration profit and
loss graph for this strategy
is displayed below.
*The profit/loss above does
not factor in commissions,
interest, tax, or margin
considerations.
This profit and loss graph
allows us to easily see the
break-even points, maximum
profit and loss potential at
expiration in dollar terms.
The calculations are
presented below.
The two break-even points
occur when the underlying
equals 72.50 and 77.50. On
the graph these two points
turn out to be where the
profit and loss line crosses
the x-axis.
**First
Break-even Point =** |
Lowest Strike (72) +
Net Debit (.50) =
72.50 |
**Second
Break-even Point =** |
Highest Strike (78)
- Net Debit (.50) =
77.50 |
The maximum profit can only
be reached if the
DJX is equal to the
middle strike (75) on
expiration. If the
underlying equals 75 on
expiration, the profit will
be $250 less the commissions
paid.
**Maximum
Profit =** |
Middle Strike (75) -
Lower Strike (72) -
Net Debit (.50) =
2.50 |
$2.50 x Number of
Shares per Contract
(100) = $250 less
commissions |
The maximum loss, in this
example, results if the
DJX is below the lower
strike (72) or above the
higher strike (78) on
expiration. If the
underlying is less than 72
or greater than 78 the loss
will be $50 plus the
commissions paid.
**Maximum Loss
=** |
Net Debit (.50) |
$.50 x Number of
Shares per Contract
(100) = $50 plus
commissions |
By looking at the components
of the total position, it is
easy to see the two spreads
that make up the butterfly.
**Bull call spread**:
Long 1 of the November 72
calls & Short one of the
November 75 calls
**Bear call spread**:
Short one of the November 75
calls & Long 1 on the
November 78 calls
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Summary
A long butterfly spread is
used by investors who
forecast a narrow trading
range for the underlying
security, and who are not
comfortable with the
unlimited risk that is
involved with being short a
straddle. The long butterfly
is a strategy that takes
advantage of the time
premium erosion of an option
contract, but still allows
the investor to have a
limited and known risk. |