outcomes at expiration—above or below the strike—this spread has three
possibilities: below both strikes, between the strikes, or above both strikes.
In this example, if Apple is below $395 at expiration, both calls expire
worthless. The rights and obligations of the options are gone, as is the cash
spent on the trade. In this case, the entire debit of $4.40 is lost.
If Apple is between the strikes at expiration, the 405-strike call expires
worthless. The trader is long stock at an effective price of $399.40. This is
the $395-strike price at which the stock would be purchased if the call is
exercised, plus the $4.40 premium spent on the spread. The break-even
price of the trade is $399.40. If Apple is above $399.40 at expiration, the
trade is profitable; below $399.40, it is aloser. The aptly named bull call
spread requires the stock to rise to reach its profit potential. But unlike an
outright long call, profits are capped with the spread.
If Apple is above $405 at expiration, both calls are in-the-money (ITM).
If the 395-strike calls are exercised, the trader buys 100 shares of Apple at
$395 and these shares, in turn, would be sold at $405 when the 405-strike
calls are assigned, for a $10 gain per share. Subtract from that $10 the $4.40
debit spent on the trade and the net profit is $5.60 per share.
There are some other differences between the 395–405 call spread and the
outright purchase of the 395 call. The absolute risk is lower. To buy the
395-strike call costs 14.60, versus 4.40 for the spread—abig difference.
Because the debit is lower, the margin for the spread is lower at most
option-friendly brokers, as well.
If we dig alittle deeper, we find some other differences between the bull
call spread and the outright call. Long options are haunted by the specter of
time. Because the spread involves both along and ashort option, the time-
decay risk is lower than that associated with owning an option outright.
Implied volatility (IV) risk is lower, too. Exhibit 9.2 compares the greeks of
the long 395 call with those of the 395–405 call spread.
EXHIBIT 9.2 Apple call versus bull call spread (Apple @ $391).
395 Call395–405 Call
Delta 0.484 0.100
Gamma0.00970.0001
Theta −0.208−0.014
Vega 0.513 0.020

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The positive deltas indicate that both positions are bullish, but the outright
call has ahigher delta. Some of the 395 call’sdirectional sensitivity is lost
when the 405 call is sold to make aspread. The negative delta of the 405
call somewhat offsets the positive delta of the 395 call. The spread delta is
only about 20 percent of the outright call’sdelta. But for atrader wanting to
focus on trading direction, the smaller delta can be asmall sacrifice for the
benefit of significantly reduced theta and vega. Theta spread’srisk is about
7 percent that of the outright. The spread’svega risk is also less than 4
percent that of the outright 395 call. With the bull call spread, atrader can
spread off much of the exposure to the unwanted risks and maintain adisproportionately higher greeks in the wanted exposure (delta).
These relationships change as the underlying moves higher. Remember,
at-the-money (ATM) options have the greatest sensitivity to theta and vega.
With Apple sitting at around the long strike, gamma and vega have their
greatest positive value, and theta has its most negative value. Exhibit 9.3
shows the spread greeks given other underlying prices.
EXHIBIT 9.3 AAPL 395–405 bull call spread.
As the stock moves higher toward the 405 strike, the 395 call begins to
move away from being at-the-money, and the 405 call moves toward being
at-the-money. The at-the-money is the dominant strike when it comes to the
characteristics of the spread greeks. Note the greeks position when the
underlying is directly between the two strike prices: The long call has
ceased to be the dominant influence on these metrics. Both calls influence
the analytics pretty evenly. The time-decay risk has been entirely spread off.
The volatility risk is mostly spread off. Gamma remains aminimal concern.
When the greeks of the two calls balance each other, the result is adirectional play.

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As AAPL continues to move closer to the 405-strike, it becomes the at-
the-money option, with the dominant greeks. The gamma, theta, and vega
of the 405 call outweigh those of the ITM 395 call. Vega is more negative.
Positive theta now benefits the trade. The net gamma of the spread has
turned negative. Because of the negative gamma, the delta has become
smaller than it was when the stock was at $400. This means that the benefit
of subsequent upward moves in the stock begins to wane. Recall that there
is amaximum profit threshold with avertical spread. As the stock rises
beyond $405, negative gamma makes the delta smaller and time decay
becomes less beneficial. But at this point, the delta has done its work for the
trader who bought this spread when the stock was trading around $395. The
average delta on amove in the stock from $395 to $405 is about 0.10 in this
case.
When the stock is at the 405 strike, the characteristics of the trade are
much different than they are when the stock is at the 395 strike. Instead of
needing movement upward in the direction of the delta to combat the time
decay of the long calls, the position can now sit tight at the short strike and
reap the benefits of option decay. The key with this spread, and with all
vertical spreads, is that the stock needs to move in the direction of the delta
to the short strike.
Strengths and Limitations
There are many instances when abull call spread is superior to other bullish
strategies, such as along call, and there are times when it isn’t. Traders
must consider both price and time.
Abull call spread will always be cheaper than the outright call purchase.
That’sbecause the cost of the long-call portion of the spread is partially
offset by the premium of the higher-strike short call. Spending less for the
same exposure is always abetter choice, but the exposure of the vertical is
not exactly the same as that of the long call. The most obvious trade-off is
the fact that profit is limited. For smaller moves—up to the price of the
short strike—vertical spreads tend to be better trades than outright call
purchases. Beyond the strike? Not so much.
But time is atrade-off, too. There have been countless times that Ihave
talked with new traders who bought acall because they thought the stock

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was going up. They were right and still lost money. As the adage goes,
timing is everything. The more time that passes, the more advantageous the
lower-theta vertical spread becomes. When held until expiration, avertical
spread can be abetter trade than an outright call in terms of percentage
profit.
In the previous example, when Apple is at $391 with 40 days until
expiration, the 395 call is worth 14.60 and the spread is worth 4.40. If
Apple were to rise to be trading at $405 at expiration, the call rises to be
worth 10, for aloss of 4.60 on the 14.60 debit paid. The spread also is worth
10. It yields again of about 127 percent on the initial $4.40 per share debit.
But look at this same trade if the move occurs before expiration. If Apple
rallies to $405 after only acouple weeks, the outcome is much different.
With four weeks still left until expiration, the 395 call is worth 19.85 with
the underlying at $405. That’sa 36 percent gain on the 14.60. The spread is
worth 5.70. That’sa 30 percent gain. The vertical spread must be held until
expiration to reap the full benefits, which it accomplishes through erosion
of the short option.
The long-call-only play (with asignificantly larger negative theta) is
punished severely by time passing. The long call benefits more from aquick move in the underlying. And of course, if the stock were to rise to aprice greater than $405, in ashort amount of time—the best of both worlds
for the outright call—the outright long 395 call would be emphatically
superior to the spread.

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Bear Call Spread
The next type of vertical spread is called abear call spread . Abear call
spread is ashort call combined with along call that has ahigher strike
price. Both calls are on the same underlying and share the same expiration
month. In this case, the call being sold is the option of higher value. This
call spread results in anet credit when the trade is put on and, therefore, is
called acredit spread.
The bull call spread and the bear call spread are two sides of the same
coin. The difference is that with the bull call spread, one is buying the call
spread, and with the bear call spread, one is selling the call spread. An
example of abear call spread can be shown using the same trade used
earlier.
Here we are selling one AAPL February (40-day) 395 call at 14.60 and
buying the 405 call at 10.20. We are selling the 395–405 call at $4.40 per
share, or $440.
Exhibit 9.4 is an at-expiration diagram of the trade.

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EXHIBIT 9.4 Apple bear call spread.
The same three at-expiration outcomes are possible here as with the bull
call spread: the stock can be above both strikes, between both strikes, or
below both strikes. If the stock is below both strikes at expiration, both calls
will expire worthless. The rights and obligations cease to exist. In this case,
the entire credit of $440 is profit.
If AAPL is between the two strike prices at expiration, the 395-strike call
will be in-the-money. The short call will get assigned and result in ashort
stock position at expiration. The break-even price falls at $399.40—the
short strike plus the $4.40 net premium. This is the price at which the stock
will effectively be sold if assignment occurs.
If Apple is above both strikes at expiration, it means both calls are in-the-
money. Stock is sold at $395 because of assignment and bought back at
$405 through exercise. This leads to aloss of $10 per share on the negative
scalp. Factoring in the $4.40-per-share credit makes the net loss only $5.60
per share with AAPL above $405 at February expiration.
Just as the at-expiration diagram is the same but reversed, the greeks for
this call spread will be similar to those in the bull call spread example
except for the positive and negative signs. See Exhibit 9.5 .
EXHIBIT 9.5 Apple 395–405 bear call spread.

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Acredit spread is commonly traded as an income-generating strategy. The
idea is simple: sell the option closer-to-the-money and buy the more out-of-
the-money (OTM) option—that is, sell volatility—and profit from
nonmovement (above acertain point). In this example, with Apple at $391,
aneutral to slightly bearish trader would think about selling this spread at
4.40 in hopes that the stock will remain below $395 until expiration. The
best-case scenario is that the stock is below $395 at expiration and both
options expire, resulting in a $4.40-per-share profit.
The strategy profits as long as Apple is under its break-even price,
$399.40, at expiration. But this is not so much abearish strategy as it is anonbullish strategy. The maximum gain with acredit spread is the premium
received, in this case $4.40 per share. Traders who thought AAPL was
going to decline sharply would short it or buy aput. If they thought it would
rise sharply, they’duse another strategy.
From agreek perspective, when the trade is executed it’svery close to its
highest theta price point—the 395 short strike price. This position
theoretically collects $0.90 aday with Apple at around $395. As time
passes, that theta rises. The key is that the stock remains at around $395
until the short option is just about worthless. The name of the game is sit
and wait.
Although the delta is negative, traders trading this spread to generate
income want the spread to expire worthless so they can pocket the $4.40 per
share. If Apple declines, profits will be made on delta, and theta profits will
be foregone later. All that matters is the break-even point. Essentially, the
idea is to sell anaked call with amaximum potential loss. Sell the 395s and
buy the 405s for protection.
If the underlying decreases enough in the short term and significant
profits from delta materialize, it is logical to consider closing the spread
early. But it often makes more sense to close part of the spread. Consider

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that the 405-strike call is farther out-of-the-money and will lose its value
before the 395 call.
Say that after two weeks abig downward move occurs. Apple is trading at
$325 ashare; the 405s are 0.05 bid at 0.10, and the 395s are 0.50 bid at
0.55. At this point, the lion’sshare of the profits can be taken early. Atrader
can do so by closing only the 395 calls. Closing the 395s to eliminate the
risk of negative delta and gamma makes sense. But does it make sense to
close the 405s for 0.05? Usually not. Recouping this residual value
accomplishes little. It makes more sense to leave them in your position in
case the stock rebounds. If the stock proves it can move down $70; it can
certainly move up $70. Because the majority of the profits were taken on
the 395 calls, holding on to the 405s is like getting paid to own calls. In
scenarios where abig move occurs and most of the profits can be taken
early, it’soften best to hold the long calls, just in case. It’sawin-win
situation.

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Credit and Debit Spread Similarities
The credit call spread and the debit call spread appear to be exactly opposite
in every respect. Many novice traders perceive credit spreads to be
fundamentally different from debit spreads. That is not necessarily so.
Closer study reveals that these two are not so different after all.
What if Apple’sstock price was higher when the trade was put on? What
if the stock was at $405? First, the spread would have had more value. The
395 and 405 calls would both be worth more. Atrader could have sold the
spread for a $5.65-per-share credit. The at-expiration diagram would look
almost the same. See Exhibit 9.6 .
EXHIBIT 9.6 Apple bear call spread initiated with Apple at $405.
Because the net premium is much higher in this example, the maximum
gain is more—it is $5.65 per share. The breakeven is $400.65. The price
points on the at-expiration diagram, however, have nothing to do with the
greeks. The analytics from Exhibit 9.5 are the same either way.
The motivation for atrader selling this call spread, which has both
options in-the-money, is different from that for the typical income
generator. When the spread is sold in this context, the trader is buying
volatility. Long gamma, long vega, negative theta. The trader here has a

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Bear Put Spread
There is another way to take abearish stance with vertical spreads: the bear
put spread. Abear put spread is along put plus ashort put that has alower
strike price. Both puts are on the same underlying and share the same
expiration month. This spread, however, is adebit spread because the more
expensive option is being purchased.
Imagine that astock has had agood run-up in price. The chart shows asteady march higher over the past couple of months. Astudy of technical
analysis, though, shows that the run-up may be pausing for breath. An
oscillator, such as slow stochastics, in combination with the relative
strength index (RSI), indicates that the stock is overbought. At the same
time, the average directional movement index (ADX) confirms that the
uptrend is slowing.
For traders looking for asmall pullback, abear put spread can be an
excellent strategy. The goal is to see the stock drift down to the short strike.
So, like the other members of the vertical spread family, strike selection is
important.
Let’slook at an example of ExxonMobil (XOM). After the stock has
rallied over atwo-month period to $80.55, atrader believes there will be ashort-term temporary pullback to $75. Instead of buying the June 80 puts
for 1.75, the trader can buy the 75–80 put spread of the same month for
1.30 because the 75 put can be sold for 0.45. 1
In this example, the June put has 40 days until expiration. Exhibit 9.7
illustrates the payout at expiration.

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EXHIBIT 9.7 ExxonMobil bear put spread.
If the trader is wrong and ExxonMobil is still above 80 at expiry, both
puts expire and the 1.30 premium is lost. If ExxonMobil is between the two
strikes, the 80 puts are ITM, resulting in an exercise, and the 75 puts are
OTM and expire. The net effect is short stock at an effective price of
$78.70. The effective sale price is found by taking the price at which the
short stock is established when the puts are exercised—$80—minus the net
1.30 paid for the spread. This is the spread’sbreakeven at expiration.
If the trader is right and ExxonMobil is below both strikes at expiration,
both puts are ITM, and the result is a 3.70 profit and no position. Why a
3.70 profit? The 80 puts are exercised, making the trader short at $80, and
the 75 puts are assigned, so the short is bought back at $75 for apositive
stock scalp of $5. Including the 1.30 debit for the spread in the profit and
loss (P&(L)), the net profit is $3.70 per share when the stock is below both
strikes at expiration.
This is abearish trade. But is the bear put spread necessarily abetter trade
than buying an outright ATM put? No. The at-expiration diagram makes this
clear. Profits are limited to $3.70 per share. This is an important difference.
But because in this particular example, the trader expects the stock to
retrace only to around $75, the benefits of lower cost and lower theta and
vega risk can be well worth the trade-off of limited profit. The trader’s

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objectives are met more efficiently by buying the spread. The goal is to
profit from the delta move down from $80 to $75. Exhibit 9.8 shows the
differences between the greeks of the outright put and the spread when the
trade is put on with ExxonMobil at $80.55.
EXHIBIT 9.8 ExxonMobil put vs. bear put spread (ExxonMobil @
$80.55).
80 Put75–80 Put
Delta −0.445−0.300
Gamma+0.080+0.041
Theta −0.018−0.006
Vega +0.110+0.046
As in the call-spread examples discussed previously, the spread delta is
smaller than the outright put’s. It appears ironic that the spread with the
smaller delta is abetter trade in this situation, considering that the intent is
to profit from direction. But it is the relative differences in the greeks
besides delta that make the spread worthwhile given the trader’sgoal.
Gamma, theta, and vega are proportionately much smaller than the delta in
the spread than in the outright put. While the spread’sdelta is two thirds
that of the put, its gamma is half, its theta one third, and its vega around 42
percent of the put’s.
Retracements such as the one called for by the trader in this example can
happen fast, sometimes over the course of aweek or two. It’snot
necessarily bad if this move occurs quickly. If ExxonMobil drops by $5
right away, the short delta will make the position profitable. Exhibit 9.9
shows how the spread position changes as the stock declines from $80 to
$75.
EXHIBIT 9.9 75–80 bear put spread as ExxonMobil declines.

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The delta of this trade remains negative throughout the stock’sdescent to
$75. Assuming the $5 drop occurs in one day, adelta averaging around
−0.36 means about a 1.80 profit, or $180 per spread, for the $5 move (0.36
times $5 times 100). This is still afar cry from the spread’s $3.70 potential
profit. Although the stock is at $75, the maximum profit potential has yet to
be reached, and it won’tbe until expiration. How does the rest of the profit
materialize? Time decay.
The price the trader wants the stock to reach is $75, but the assumption
here is that the move happens very fast. The trade went from being along-
volatility play—long gamma and vega—to ashort-vol play: short gamma
and vega. The trader wanted movement when the stock was at $80 and
wants no movement when the stock is at $75. When the trade changes
characteristics by moving from one strike to another, the trader has to
reconsider the stock’soutlook. The question is: if Ididn’thave this position
on, would Iwant it now?
The trader has achoice to make: take the $180 profit—which represents a
138 percent profit on the 1.30 debit—or wait for theta to do its thing. The
trader looking for aretracement would likely be inclined to take aprofit on
the trade. Nobody ever went broke taking aprofit. But if the trader thinks
the stock will sit tight for the remaining time until expiration, he will be
happy with this income-generating position.
Although the trade in the last, overly simplistic example did not reap its
full at-expiration potential, it was by no means abad trade. Holding the
spread until expiration is not likely to be part of atrader’splan. Buying the
80 put outright may be abetter play if the trader is expecting afast move. It
would have abigger delta than the spread. Debit and credit spreads can be
used as either income generators or as delta plays. When they’re used as
delta plays, however, time must be factored in.

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Bull Put Spread
The last of the four vertical spreads is abull put spread. Abull put spread is
ashort put with one strike and along put with alower strike. Both puts are
on the same underlying and in the same expiration cycle. Abull put spread
is acredit spread because the more expensive option is being sold, resulting
in anet credit when the position is established. Using the same options as in
the bear put example:
With ExxonMobil at $80.55, the June 80 puts are sold for 1.75 and the
June 75 puts are bought at 0.45. The trade is done for acredit of 1.30.
Exhibit 9.10 shows the payout of this spread if it is held until expiration.
EXHIBIT 9.10 ExxonMobil bull put spread.
The sale of this spread generates a 1.30 net credit, which is represented by
the maximum profit to the right of the 80 strike. With ExxonMobil above
$80 per share at expiration, both options expire OTM and the premium is
all profit. Between the two strike prices, the 80 put expires in the money. If
the ITM put is still held at expiration, it will be assigned. Upon assignment,

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the put becomes long stock, profiting with each tick higher up to $80, or
losing with each tick lower to $75. If the 80 put is assigned, the effective
price of the long stock will be $78.70. The assignment will “hit your sheets”
as abuy at $80, but the 1.30 credit lowers the effective net cost to $78.70.
If the stock is below $75 at option expiration, both puts will be ITM. This
is the worst case scenario, because the higher-struck put was sold. At
expiration, the 80 puts would be assigned, the 75 puts exercised. That’sanegative scalp of $5 on the resulting stock. The initial credit lessens the pain
by 1.30. The maximum possible loss with ExxonMobil below both strikes
at expiration is $3.70 per spread.
The spread in this example is the flip side of the bear put spread of the
previous example. Instead of buying the spread, as with the bear put, the
spread in this case is sold.
Exhibit 9.11 shows the analytics for the bull put spread.
EXHIBIT 9.11 Greeks for ExxonMobil 75–80 bull put spread.
Instead of having ashort delta, as with the bear spread, the bull spread is
long delta. There is negative theta with positive gamma and vega as XOM
approaches the long strike—the 75s, in this case. There is also positive theta
with negative gamma and vega around the short strike—the 80s.
Exhibit 9.11 shows the characteristics that define the vertical spread. If
one didn’tknow which particular options were being traded here, this could
almost be atable of greeks for either a 75–80 bull put spread or a 75–80
bull call spread.
Like the other three verticals, this spread can be adelta play or atheta
play. Abullish trader may sell the spread if both puts are in-the-money.
Imagine that XOM is trading at around $75. The spread will have apositive

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0.364 delta, positive gamma, and negative theta. The spread as awhole is adecaying asset. It needs the underlying to rally to combat time decay.
Abullish trader may also sell this spread if XOM is between the two
strikes. In this case, with XOM at, say, $77, the delta is +0.388, and all
other greeks are negligible. At this particular price point in the underlying,
the trader has almost pure leveraged delta exposure. But this trade would be
positioned for only asmall move, not much above $80. Aspeculator
wanting to trade direction for asmall move while eliminating theta and
vega risks achieves her objectives very well with avertical spread.
Abullish-to-neutral trader would be inclined to sell this spread if
ExxonMobil were around $80 or higher. Day by day, the 1.30 premium
would start to come in. With 40 days until expiration, theta would be small,
only 0.004. But if the stock remained at $80, this ATM put would begin
decaying faster and faster. The objective of trading this spread for aneutral
trader is selling future realized volatility—selling gamma to earn theta. Atrader can also trade avertical spread to profit from IV.

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Verticals and Volatility
The IV component of avertical spread, although small compared with that
of an outright call or put, is still important—especially for large traders with
low margin and low commissions who can capitalize on small price
changes efficiently. Whether it’sacall spread or aput spread, acredit
spread or adebit spread, if the underlying is at the short option’sstrike, the
spread will have anet negative vega. If the underlying is at the long
option’sstrike, the spread will have positive vega. Because of this
characteristic, there are three possible volatility plays with vertical spreads:
speculating on IV changes when the underlying remains constant, profiting
from IV changes resulting from movement of the underlying, and special
volatility situations.
Vertical spreads offer alimited-risk way to speculate on volatility changes
when the underlying remains fairly constant. But when the intent of avertical spread is to benefit from vega, one must always consider the delta
—it’sthe bigger risk. Chapter 13 discusses ways to manage this risk by
hedging with stock, astrategy called delta-neutral trading.
Non-delta-neutral traders may speculate on vol with vertical spreads by
assuming some delta risk. Traders whose forecast is vega bearish will sell
the option with the strike closest to where the underlying is trading—that is,
the ATM option—and buy an OTM strike. Traders would lean with their
directional bias by choosing either acall spread or aput spread. As risk
managers, the traders balance the volatility stance being taken against the
additional risk of delta. Again, in this scenario, delta can hurt much more
than help.
In the ExxonMobil bull put spread example, the trader would sell the 80-
strike put if ExxonMobil were around $80 ashare. In this case, if the stock
didn’tmove as time passed, theta would benefit from historical volatility
being’slow—that is, from little stock movement. At first, the benefit would
be only 0.004 per day, speeding up as expiration nears. And if implied
volatility decreased, the trader would profit 0.04 for every 1 percent decline
in IV. Small directional moves upward help alittle. But in the long run,

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those profits are leveled off by the fact that theta gets smaller as the stock
moves higher above $80—more profit on direction, less on time.
For the delta player, bull call spreads and bull put spreads have apotential
added benefit that stems from the fact that IV tends to decrease as stocks
rise and increase when stocks fall. This offers additional opportunity to the
bull spread player. With the bull call spread or the bull put spread, the trader
gains on positive delta with arally. Once the underlying comes close to the
short option’sstrike, vega is negative. If IV declines, as might be
anticipated, there is afurther benefit of vega profits on top of delta profits.
If the underlying declines, the trader loses on delta. But the pain can
potentially be slightly lessened by vega profits. Vega will get positive as the
underlying approaches the long strike, which will benefit from the firming
of IV that often occurs when the stock drops. But this dual benefit is paid
for in the volatility skew. In most stocks or indexes, the lower strikes—the
ones being bought in abull spread—have higher IVs than the higher strikes,
which are being sold.
Then there are special market situations in which vertical spreads that
benefit from volatility changes can be traded. Traders can trade vertical
spreads to strategically position themselves for an expected volatility
change. One example of such asituation is when astock is rumored to be atakeover target. Anatural instinct is to consider buying calls as an
inexpensive speculation on ajump in price if the takeover is announced.
Unfortunately, the IV of the call is often already bid up by others with the
same idea who were quicker on the draw. Buying acall spread consisting of
along ITM call and ashort OTM call can eliminate immediate vega risk
and still provide wanted directional exposure.
Certainly, with this type of trade, the trader risks being wrong in terms of
direction, time, and volatility. If and when atakeover bid is announced, it
will likely be for aspecific price. In this event, the stock price is unlikely to
rise above the announced takeover price until either the deal is
consummated or asecond suitor steps in and offers ahigher price to buy the
company. If the takeover is a “cash deal,” meaning the acquiring company
is tendering cash to buy the shares, the stock will usually sit in avery tight
range below the takeover price for along time. In this event, implied
volatility will often drop to very low levels. Being short an ATM call when

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The Interrelations of Credit
Spreads and Debit Spreads
Many traders Iknow specialize in certain niches. Sometimes this is because
they find something they know well and are really good at. Sometimes it’sbecause they have become comfortable and don’thave the desire to try
anything new. I’ve seen this strategy specialization sometimes with traders
trading credit spreads and debit spreads. I’ve had serial credit spread traders
tell me credit spreads are the best trades in the world, much better than debit
spreads. Habitual debit spread traders have likewise said their chosen
spread is the best. But credit spreads and debit spreads are not so different.
In fact, one could argue that they are really the same thing.
Conventionally, credit-spread traders have the goal of generating income.
The short option is usually ATM or OTM. The long option is more OTM.
The traders profit from nonmovement via time decay. Debit-spread traders
conventionally are delta-bet traders. They buy the ATM or just out-of-the-
money option and look for movement away from or through the long strike
to the short strike. The common themes between the two are that the
underlying needs to end up around the short strike price and that time has to
pass to get the most out of either spread.
With either spread, movement in the underlying may be required,
depending on the relationship of the underlying price to the strike prices of
the options. And certainly, with acredit spread or debit spread, if the
underlying is at the short strike, that option will have the most premium.
For the trade to reach the maximum profit, it will need to decay.
For many retail traders, debit spreads and credit spreads begin to look
even more similar when margin is considered. Margin requirements can
vary from firm to firm, but verticals in retail accounts at option-friendly
brokerage firms are usually margined in such away that the maximum loss
is required to be deposited to hold the position (this assumes Regulation Tmargining). For all intents and purposes, this can turn the trader’scash
position from acredit into adebit. From acash perspective, all vertical
spreads are spreads that require adebit under these margin requirements.

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Building a Box
Two traders, Sam and Isabel, share ajoint account. They have each been
studying Johnson & Johnson (JNJ), which is trading at around $63.35 per
share. Sam and Isabel, however, cannot agree on direction. Sam thinks
Johnson & Johnson will rise over the next five weeks, and Isabel believes it
will decline during that period.
Sam decides to buy the January 62.50 −65 call spread (January has 38
days until expiration in this example). Sam can buy this spread for 1.28. His
maximum risk is 1.28. This loss occurs if Johnson & Johnson is below
$62.50 at expiration, leaving both calls OTM. His maximum gain is 1.22,
realized if Johnson & Johnson is above $65 (65–62.50–1.28). With Johnson
& Johnson at $63.35, Sam’sdelta is long 0.29 and his other greeks are
about flat.
Isabel decides to buy the January 62.50–65 put spread for adebit of 1.22.
Isabel’sbiggest potential loss is 1.22, incurred if Johnson & Johnson is
above $65 ashare at expiration, leaving both puts OTM. Her maximum
possible profit is 1.28, realized if the stock is below $62.50 at option
expiration. With Johnson & Johnson at $63.35, Isabel has adelta that is
short around 0.27 and is nearly flat gamma, theta, and vega.
Collectively, if both Sam and Isabel hold their trades until expiration, it’sazero-sum game. With Johnson & Johnson below $62.50, Sam loses his
investment of 1.28, but Isabel profits. She cancels out Sam’sloss by making
1.28. Above $65, Sam makes 1.22 while Isabel loses the same amount,
canceling out Sam’sgains. Between the two strikes, Sam has gains on his
62.50 call and Isabel has gains on her 65 put. The gains on the two options
will total 2.50, the combined total spent on the spreads—another draw.
EXHIBIT 9.12 Sam’slong call spread in Johnson & Johnson.
62.50–65 Call Spread
Delta +0.290
Gamma+0.001
Theta −0.004
Vega +0.006

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EXHIBIT 9.13 Isabel’slong put spread in Johnson & Johnson.
62.50–65 Put Spread
Delta −0.273
Gamma−0.001
Theta +0.005
Vega −0.006
These two spreads were bought for acombined total of 2.50. The
collective position, composed of the four legs of these two spreads, forms anew strategy altogether.
The two traders together have created abox. This box, which is empty of
both profit and loss, is represented by greeks that almost entirely offset each
other. Sam’spositive delta of 0.29 is mostly offset by Isabel’s −0.273 delta.
Gamma, theta, and vega will mostly offset each other, too.
Chapter 6 described abox as long synthetic stock combined with short
synthetic stock having adifferent strike price but the same expiration
month. It can also be defined, however, as two vertical spreads: abull (bear)
call spread plus abear (bull) put spread with the same strike prices and
expiration month.
The value of abox equals the present value of the distance between the
two strike prices (American-option models will also account for early
exercise potential in the box’svalue). This 2.50 box, with 38 days until
expiration at a 1 percent interest rate, has less than apenny of interest
affecting its value. Boxes with more time until expiration will have ahigher
interest rate component. If there was one year until expiration, the
combined value of the two verticals would equal 2.475. This is simply the
distance between the strikes minus interest (2.50–[2.50 × 0.01]).
Credit spreads are often made up of OTM options. Traders betting against
astock rising through acertain price tend to sell OTM call spreads. For astock at $50 per share, they might sell the 55 calls and buy the 60 calls. But
because of the synthetic relationship that verticals have with one another,
the traders could buy an ITM put spread for the same exposure, after

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Condors and Butterflies
The “wing spread” family is aset of option strategies that is very popular,
particularly among experienced traders. These strategies make it possible
for speculators to accomplish something they could not possibly do by just
trading stocks: They provide ameans to profit from atruly neutral market
in asecurity. Stocks that don’tmove one iota can earn profits month after
month for income-generating traders who trade these strategies.
These types of spreads have alot of moving parts and can be intimidating
to newcomers. At their heart, though, they are rather straightforward break-
even analysis trades that require little complex math to maintain. Asimple
at-expiration diagram reveals in black and white the range in which the
underlying stock must remain in order to have aprofitable position.
However, applying the greeks and some of the mathematics discussed in
previous chapters can help atrader understand these strategies on adeeper
level and maximize the chance of success. This chapter will discuss condors
and butterflies and how to put them into action most effectively.

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Condor
Acondor is afour-legged option strategy that enables atrader to capitalize
on volatility—increased or decreased. Traders can trade long or short iron
condors.
Long Condor
Long one call (put) with strike A; short one call (put) with ahigher strike,
B; short one call (put) at strike C, which is higher than B; and long one call
(put) at strike D, which is higher than C. The distance between strike price
Aand Bis equal to the distance between strike Cand strike D. The options
are all on the same security, in the same expiration cycle, and either all calls
or all puts.
Long Condor Example
Buy 1 XYZ November 70 call (A)
Sell 1 XYZ November 75 call (B)
Sell 1 XYZ November 90 call (C)
Buy 1 XYZ November 95 call (D)
Short Condor
Short one call (put) with strike A; long one call (put) with ahigher strike, B;
long one call (put) with astrike, C, that is higher than B; and short one call
(put) with astrike, D, that is higher than C. The options must be on the
same security, in the same expiration cycle, and either all calls or all puts.
The differences in strike price between the vertical spread of strike prices Aand Band the strike prices of the vertical spread of strikes Cand Dare
equal.
Short Condor Example
Sell 1 XYZ November 70 call (A)
Buy 1 XYZ November 75 call (B)
Buy 1 XYZ November 90 call (C)
Sell 1 XYZ November 95 call (D)

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Iron Condor
An iron condor is similar to acondor, but with amix of both calls and puts.
Essentially, the condor and iron condor are synthetically the same.
Short Iron Condor
Long one put with strike A; short one put with ahigher strike, B; short one
call with an even higher strike, C; and long one call with astill higher
strike, D. The options are on the same security and in the same expiration
cycle. The put credit spread has the same distance between the strike prices
as the call credit spread.
Short Iron Condor Example
Buy 1 XYZ November 70 put (A)
Sell 1 XYZ November 75 put (B)
Sell 1 XYZ November 90 call (C)
Buy 1 XYZ November 95 call (D)
Long Iron Condor
Short one put with strike A; long one put with ahigher strike, B; long one
call with an even higher strike, C; and short one call with astill higher
strike, D. The options are on the same security and in the same expiration
cycle. The put debit spread (strikes Aand B) has the same distance between
the strike prices as the call debit spread (strikes Cand D).
Long Iron Condor Example
Sell 1 XYZ November 70 put (A)
Buy 1 XYZ November 75 put (B)
Buy 1 XYZ November 90 call (C)
Sell 1 XYZ November 95 call (D)

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Butterflies
Butterflies are wing spreads similar to condors, but there are only three
strikes involved in the trade—not four.
Long Butterfly
Long one call (put) with strike A; short two calls (puts) with ahigher strike,
B; and long one call (put) with an even higher strike, C. The options are on
the same security, in the same expiration cycle, and are either all calls or all
puts. The difference in price between strikes Aand Bequals that between
strikes Band C.
Long Butterfly Example
Buy 1 XYZ December 50 call (A)
Sell 2 XYZ December 60 call (B)
Buy 1 XYZ December 70 call (C)
Short Butterfly
Short one call (put) with strike A; long two calls (puts) with ahigher strike,
B; and short one call (put) with an even higher strike, C. The options are on
the same security, in the same expiration cycle, and are either all calls or all
puts. The vertical spread made up of the options with strike Aand strike Bhas the same distance between the strike prices of the vertical spread made
up of the options with strike Band strike C.
Short Butterfly Example
Sell 1 XYZ December 50 call
Buy 2 XYZ December 60 call
Sell 1 XYZ December 70 call

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Iron Butterflies
Much like the relationship of the condor to the iron condor, abutterfly has
its synthetic equal as well: the iron butterfly.
Short Iron Butterfly
Long one put with strike A; short one put with ahigher strike, B; short one
call with strike B; long one call with astrike higher than B, C. The options
are on the same security and in the same expiration cycle. The distances
between the strikes of the put spread and between the strikes of the call
spread are equal.
Short Iron Butterfly Example
Buy 1 XYZ December 50 put (A)
Sell 1 XYZ December 60 put (B)
Sell 1 XYZ December 60 call (B)
Buy 1 XYZ December 70 call (C)
Long Iron Butterfly
Short one put with strike A; long one put with ahigher strike, B; long one
call with strike B; short one call with astrike higher than B, C. The options
are on the same security and in the same expiration cycle. The distances
between the strikes of the put spread and between the strikes of the call
spread are equal. The put debit spread has the same distance between the
strike prices as the call debit spread.
Long Iron Butterfly Example
Sell 1 XYZ December 50 put
Buy 1 XYZ December 60 put
Buy 1 XYZ December 60 call
Sell 1 XYZ December 70 call
These spreads were defined in terms of both long and short for each
strategy. Whether the spread is classified as long or short depends on
whether it was established at acredit or adebit. Debit condors or butterflies

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are considered long spreads. And credit condors or butterflies are
considered short spreads.
The words long and short mean little, though in terms of the spread as awhole. The important thing is which strikes have long options and which
have short options. Acall debit spread is synthetically equal to aput credit
spread on the same security, with the same expiration month and strike
prices. That means along condor is synthetically equal to ashort iron
condor, and along butterfly is synthetically equal to ashort iron butterfly,
when the same strikes are used. Whichever position is constructed, the best-
case scenario is to have debit spreads expire with both options in-the-money
(ITM) and credit spreads expire with both options out-of-the-money
(OTM).
Many retail traders prefer trading these spreads for the purpose of
generating income. In this case, atrader would sell the guts, or middle
strikes, and buy the wings, or outer strikes. When atrader is short the guts,
low realized volatility is usually the objective. For long butterflies and short
iron butterflies, the stock needs to be right at the middle strike for the
maximum payout. For long condors and short iron condors, the stock needs
to be between the short strikes at expiration for maximum payout. In both
instances, the wings are bought to limit potential losses of the otherwise
naked options.

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Long Butterfly Example
Atrader, Kathleen, has been studying United Parcel Service (UPS), which
is trading at around $70.65. She believes UPS will trade sideways until July
expiration. Kathleen buys the July 65–70–75 butterfly for 2.00. She
executes the following legs:
Kathleen looks at her trade as two vertical spreads, the 65–70 bull (debit)
call spread and the 70–75 bear (credit) call spread. Intuitively, she would
want UPS to be at or above $70 at expiration for her bull call spread to have
maximum value. But she has the seemingly conflicting goal of also wanting
UPS to be at or below $70 to get the most from her 70–75 bear call spread.
The ideal price for the stock to be trading at expiration in this example is
right at $70 per share—the best of both worlds. The at-expiration diagram,
Exhibit 10.1 , shows the profit or loss of all possible outcomes at expiration.
EXHIBIT 10.1 UPS 65–70–75 butterfly.
If the price of UPS shares declines below $65 at expiration, all these calls
will expire. The entire 2.00 spent on the trade will be lost. If UPS is above
$65 at expiration, the 65 call will be ITM and will be exercised. The call

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will profit like along position in 100 shares of the underlying. The
maximum profit is reached if UPS is at $70 at expiration. Kathleen makes a
5.00 profit from $65 to $70 on her 65 calls. But because she paid 2.00
initially for the spread, her net profit at $70 is just 3.00. If UPS is above $70
ashare at expiration in this example, the two 70 calls will be assigned. The
assignment of one call will offset the long stock acquired by the 65 calls
being exercised. Assignment of the other call will create ashort position in
the underlying. That short position loses as UPS moves higher up to $75 ashare, eating away at the 3.00 profit. If UPS is above $75 at expiration, the
75 call can be exercised to buy back the short stock position that resulted
from the 70’sbeing assigned. The loss on the short stock between $70 and
$75 will cost Kathleen 5.00, stripping her of her 3.00 profit and giving her anet loss of 2.00 to boot. End result? Above $75 at expiration, she has no
position in the underlying and loses 2.00.
Abutterfly is abreak-even analysis trade . This name refers to the idea
that the most important considerations in this strategy are the breakeven
points. The at-expiration diagram, Exhibit 10.2 , shows the break-even
prices for this trade.
EXHIBIT 10.2 UPS 65–70–75 butterfly breakevens.
If the position is held until expiration and UPS is between $65 and $70 at
that time, the 65 calls are exercised, resulting in long stock. The effective
purchase price of that stock is $67. That’sthe strike price plus the cost of

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the spread; that’sthe lower break-even price. The other break-even is at
$73. The net short position of 100 shares resulting from assignment of the
70 call loses more as the stock rises between $70 and $75. The entire 3.00
profit realized at the $70 share price is eroded when the stock reaches $73.
Above $73, the trade produces aloss.
Kathleen’strading objective is to profit from UPS trading between $67
and $73 at expiration. The best-case scenario is that it declines only slightly
from its price of $70.65 when the trade is established, to $70 per share.
Alternatives
Kathleen had other alternative positions she could have traded to meet her
goals. An iron butterfly with the same strike prices would have shown about
the same risk/reward picture, because the two positions are synthetically
equivalent. But there may, in some cases, be aslight advantage to trading
the iron butterfly over the long butterfly. The iron butterfly uses OTM put
options instead of ITM calls, meaning the bid-ask spreads may be tighter.
This means giving up less edge to the liquidity providers.
She could have also bought acondor or sold an iron condor. With condor-
family spreads, there is alower maximum profit potential but awider range
in which that maximum payout takes place. For example, Kathleen could
have executed the following legs to establish an iron condor:
Essentially, Kathleen would be selling two credit spreads: the July 60–65
put spread for 0.30 and the July 75–80 call spread for 0.35. Exhibit 10.3
shows the payout at expiration of the UPS July 60–65–75–80 iron condor.

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EXHIBIT 10.3 UPS 60–65–75–80 iron condor.
Although the forecast and trading objectives may be similar to those for
the butterfly, the payout diagram reveals some important differences. First,
the maximum loss is significantly higher with acondor or iron condor. In
this case, the maximum loss is 4.35. This unfortunate situation would occur
if UPS were to drop to below $60 or rise above $80 by expiration. Below
$60, the call spread expires, netting 0.35. But the put spread is ITM.
Kathleen would lose anet of 4.70 on the put spread. The gain on the call
spread combined with the loss on the put spread makes the trade aloser of
4.35 if the stock is below $60 at expiration. Above $80, the put spread is
worthless, earning 0.30, but the call spread is aloser by 4.65. The gain on
the put spread plus the loss on the call spread is anet loser of 4.35. Between
$65 and $75, all options expire and the 0.65 credit is all profit.
So far, this looks like apretty lousy alternative to the butterfly. You can
lose 4.35 but only make 0.65! Could there be any good reason for making
this trade? Maybe. The difference is wiggle room. The breakevens are 2.65
wider in each direction with the iron condor. Exhibit 10.4 shows these
prices on the graph.

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Keys to Success
No matter which trade is more suitable to Kathleen’srisk tolerance, the
overall concept is the same: profit from little directional movement. Before
Kathleen found astock on which to trade her spread, she will have sifted
through myriad stocks to find those that she expects to trade in arange. She
has afew tools in her trading toolbox to help her find good butterfly and
condor candidates.
First, Kathleen can use technical analysis as aguide. This is arather
straightforward litmus test: does the stock chart show atrending, volatile
stock or aflat, nonvolatile stock? For the condor, aquick glance at the past
few months will reveal whether the stock traded between $65 and $75. If it
did, it might be agood iron condor candidate. Although this very simplistic
approach is often enough for many traders, those who like lots of graphs
and numbers can use their favorite analyses to confirm that the stock is
trading in arange. Drawing trendlines can help traders to visualize the
channel in which astock has been trading. Knowing support and resistance
is also beneficial. The average directional movement index (ADX) or
moving average converging/diverging (MACD) indicator can help to show
if there is atrend present. If there is, the stock may not be agood candidate.
Second, Kathleen can use fundamentals. Kathleen wants stocks with
nothing on their agendas. She wants to avoid stocks that have pending
events that could cause their share price to move too much. Events to avoid
are earnings releases and other major announcements that could have an
impact on the stock price. For example, adrug stock that has been trading
in arange because it is awaiting Food and Drug Administration (FDA)
approval, which is expected to occur over the next month, is not agood
candidate for this sort of trade.
The last thing to consider is whether the numbers make sense. Kathleen’siron condor risks 4.35 to make 0.65. Whether this sounds like agood trade
depends on Kathleen’srisk tolerance and the general environment of UPS,
the industry, and the market as awhole. In some environments, the
0.65/4.35 payout-to-risk ratio makes alot of sense. For other people, other
stocks, and other environments, it doesn’t.

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Greeks and Wing Spreads
Much of this chapter has been spent on how wing spreads perform if held
until expiration, and little has been said of option greeks and their role in
wing spreads. Greeks do come into play with butterflies and condors but not
necessarily the same way they do with other types of option trades.
The vegas on these types of spreads are smaller than they are on many
other types of strategies. For atypical nonprofessional trader, it’shard to
trade implied volatility with condors or butterflies. The collective
commissions on the four legs, as well as margin and capital considerations,
put these out of reach for active trading. Professional traders and retail
traders subject to portfolio margining are better equipped for volatility
trading with these spreads.
The true strength of wing spreads, however, is in looking at them as
break-even analysis trades much like vertical spreads. The trade is awinner
if it is on the correct side of the break-even price. Wing spreads, however,
are acombination of two vertical spreads, so there are two break-even
prices. One of the verticals is guaranteed to be awinner. The stock can be
either higher or lower at expiration—not both. In some cases, both verticals
can be winners.
Consider an iron condor. Instead of reaping one premium from selling one
OTM call credit spread, iron condor sellers double dip by additionally
selling an OTM put credit spread. They collect adouble credit, but only one
of the credit spreads can be aloser at expiration. The trader, however, does
have to worry about both directions independently.
There are two ways for greeks and volatility analysis to help traders trade
wing spreads. One of them involves using delta and theta as tools to trade adirectional spread. The other uses implied volatility in strike selection
decisions.

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Directional Butterflies
Trading abutterfly can be an excellent way to establish alow-cost,
relatively low-risk directional trade when atrader has aspecific price target
in mind. For example, atrader, Ross, has been studying Walgreen Co.
(WAG) and believes it will rise from its current level of $33.50 to $36 per
share over the next month. Ross buys abutterfly consisting of all OTM
January calls with 31 days until expiration.
He executes the following legs:
As adirectional trade alternative, Ross could have bought just the January
35 call for 1.15. As acheaper alternative, he could have also bought the 35–
36 bull call spread for 0.35. In fact, Ross actually does buy the 35–36
spread, but he also sells the January 36–37 call spread at 0.25 to reduce the
cost of the bull call spread, investing only adime. The benefit of lower cost,
however, comes with trade-offs. Exhibit 10.5 compares the bull call spread
with abullish butterfly.
EXHIBIT 10.5 Bull call spread vs. bull butterfly (Walgreen Co. at $33.50).

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The butterfly has lower nominal risk—only 0.10 compared with 0.35 for
the call spread. The maximum reward is higher in nominal terms, too—0.90
versus 0.65. The trade-off is what is given up. With both strategies, the goal
is to have Walgreen Co. at $36 around expiration. But the bull call spread
has more room for error to the upside. If the stock trades alot higher than
expected, the butterfly can end up being alosing trade.
Given Ross’sexpectations in this example, this might be arisk he is
willing to take. He doesn’texpect Walgreen Co. to close right at $36 on the
expiration date. It could happen, but it’sunlikely. However, he’dhave to be
wildly wrong to have the trade be aloser on the upside. It would be amuch
larger move than expected for the stock to rise significantly above $36. If
Ross strongly believes Walgreen Co. can be around $36 at expiration, the
cost benefit of 0.10 vs. 0.35 may offset the upside risk above $37. As ageneral rule, directional butterflies work well in trending, low-volatility
stocks.
When Ross monitors his butterfly, he will want to see the greeks for this
position as well. Exhibit 10.6 shows the trade’sanalytics with Walgreen Co.
at $33.50.
EXHIBIT 10.6 Walgreen Co. 35–36–37 butterfly greeks (stock at $33.50,
31 days to expiration).
Delta +0.008
Gamma−0.004
Theta +0.001
Vega −0.001
When the trade is first put on, the delta is small—only +0.008. Gamma is
slightly negative and theta is very slightly positive. This is important
information if Walgreen Co.’sascent happens sooner than Ross planned.
The trade will show just asmall profit if the stock jumps to $36 per share
right away. Ross’stheoretical gain will be almost unnoticeable. At $36 per
share, the position will have its highest theta, which will increase as
expiration approaches. Ross will have to wait for time to pass to see the
trade reach its full potential.
This example shows the interrelation between delta and theta. We know
from an at-expiration analysis that if Walgreen Co. moves from $33.50 to
$36, the butterfly’sprofit will be 0.90 (the spread of $1 minus the 0.10

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Three Looks at the Condor
Strike selection is essential for asuccessful condor. If strikes are too close
together or two far apart, the trade can become much less attractive.
Strikes Too Close
The QQQs are options on the ETFs that track the Nasdaq 100 (QQQ). They
have strikes in $1 increments, giving traders alot to choose from. With
QQQ trading at around $55.95, consider the 54–55–57–58 iron condor. In
this example, with 31 days until expiration, the following legs can be
executed:
In this trade, the maximum profit is 0.63. The maximum risk is 0.37. This
isn’tabad profit-to-loss ratio. The break-even price on the downside is
$54.37 and on the upside is $57.63. That’sa $3.26 range—atight space for
amover like the QQQ to occupy in amonth. The ETF can drop about only
2.8 percent or rise 3 percent before the trade becomes aloser. No one needs
any fancy math to show that this is likely alosing proposition in the long
run. While choosing closer strikes can lead to higher premiums, the range
can be so constricting that it asphyxiates the possibility of profit.
Strikes Too Far
Strikes too far apart can make for impractical trades as well. Exhibit 10.7
shows an options chain for the Dow Jones Industrial Average Index (DJX).
These prices are from around 2007 when implied volatility (IV) was
historically low, making the OTM options fairly low priced. In this
example, DJX is around $135.20 and there are 51 days until expiration.
EXHIBIT 10.7 Options chain for DJIA.

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This would be agreat trade if it weren’tfor the prices one would have to
accept to put it on. First, the 120 puts are offered at 0.25 and the 123 puts
are 0.25 bid. This means that the put spread would be sold at zero! The
maximum risk is 3.00, and the maximum gain is zero. Not areally good
risk/reward. The 142–145 call spread isn’tmuch better: it can be sold for adime.
At the time, again alow-volatility period, many traders probably felt it
was unlikely that the DJX will rise 5 percent in a 51-day period. Some
traders may have considered trading asimilarly priced iron condor (though
of course they’dhave to require some small credit for the risk). Alittle over
ayear later the DJX was trading around 50 percent lower. Traders must
always be vigilant of the possibility of volatility, even unexpected volatility
and structure their risk/reward accordingly. Most traders would say the
risk/reward of this trade isn’tworth it. Strikes too far apart have agreater
chance of success, but the payoff just isn’tthere.
Strikes with High Probabilities of Success
So how does atrader find the happy medium of strikes close enough
together to provide rich premiums but far enough apart to have agood
chance of success? Certainly, there is something to be said for looking at
the prices at which atrade can be done and having asubjective feel for
whether the underlying is likely to move outside the range of the break-
even prices. Alittle math, however, can help quantify this likelihood and aid
in the decision-making process.
Recall that IV is read by many traders to be the market’sconsensus
estimate of future realized volatility in terms of annualized standard
deviation. While that is amouthful to say—or in this case, rather, an eyeful
to read—when broken down it is not quite as intimidating as it sounds.
Consider asimplified example in which an underlying security is trading at
$100 ashare and the implied volatility of the at-the-money (ATM) options
is 10 percent. That means, from astatistical perspective, that if the expected
return for the stock is unchanged, the one-year standard deviations are at
$90 and $110. 1 In this case, there is about a 68 percent chance of the stock
trading between $90 and $110 one year from now. IV then is useful
information to atrader who wants to quantify the chances of an iron

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condor’sexpiring profitable, but there are afew adjustments that need to be
made.
First, because with an iron condor the idea is to profit from net short
option premium, it usually makes more sense to sell shorter-term options to
profit from higher rates of time decay. This entails trading condors
composed of one- or two-month options. The IV needs to be deannualized
and converted to represent the standard deviation of the underlying at
expiration.
The first step is to compute the one-day standard deviation. This is found
by dividing the implied volatility by the square root of the number of
trading days in ayear, then multiplying by the square root of the number of
trading days until expiration. The result is the standard deviation (σ) at the
time of expiration stated as apercent. Next, multiply that percentage by the
price of the underlying to get the standard deviation in absolute terms.
The formula 2 for calculating the shorter-term standard deviation is as
follows:
This value will be added to or subtracted from the price of the underlying
to get the price points at which the approximate standard deviations fall.
Consider an example using options on the Standard & Poor’s 500 Index
(SPX). With 50 days until expiration, the SPX is at 1241 and the implied
volatility is 23.2 percent. To find strike prices that are one standard
deviation away from the current index price, we need to enter the values
into the equation. We first need to know how many actual trading days are
in the 50-day period. There are 35 business days during this particular 50-
day period (there is one holiday and seven weekend days). We now have all
the data we need to calculate which strikes to sell.
The lower standard deviation is 1134.55 (1241 − 106.45) and the upper is
1347.45 (1241 + 106.45). This means there would be about a 68 percent
chance of SPX ending up between 1134.55 and 1347.45 at expiration. In
this example, to have about atwo-thirds chance of success, one would sell
the 1135 puts and the 1350 calls as part of the iron condor.

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Being Selective
There is about atwo-thirds chance of the underlying staying between the
upper and lower standard deviation points and about aone-third chance it
won’t. Reasonably good odds. But the maximum loss of an iron condor will
be more than the maximum profit potential. In fact, the max-profit-to-max-
loss ratio is usually less than 1 to 3. For every $1 that can be made, often $4
or $5 will be at risk.
The pricing model determines fair value of an option based on the implied
volatility set by the market. Again, many traders consider IV to be the
market’sconsensus estimate of future realized volatility. Assuming the
market is generally right and options are efficiently priced, in the long run,
future stock volatility should be about the same as the implied volatility
from options prices. That means that if all of your options trades are
executed at fair value, you are likely to break even in the long run. The
caveat is that whether the options market is efficient or not, retail or
institutional traders cannot generally execute trades at fair value. They have
to sell the bid (sell below theoretical value) and buy the offer (buy above
theoretical value). This gives the trade astatistical disadvantage, called
giving up the edge, from an expected return perspective.
Even though you are more likely to win than to lose with each individual
trade when strikes are sold at the one-standard-deviation point, the edge
given up to the market in conjunction with the higher price tag on losers
makes the trade astatistical loser in the long run. While this means for
certain that the non-market-making trader is at aconstant disadvantage,
trading condors and butterflies is no different from any other strategy.
Giving up the edge is the plight of retail and institutional traders. To profit
in the long run, atrader needs to beat the market, which requires careful
planning, selectivity, and risk management.
Savvy traders trade iron condors with strikes one standard deviation away
from the current stock price only when they think there is more than atwo-
thirds chance of market neutrality. In other words, if you think the market
will be less volatile than the prices in the options market imply, sell the iron
condor or trade another such premium-selling strategy. As discussed above,
this opinion should reflect sound judgment based on some combination of

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technical analysis, fundamental analysis, volatility analysis, feel, and
subjectivity.
A Safe Landing for an Iron Condor
Although traders can’tcontrol what the market does, they can control how
they react to the market. Assume atrader has done due diligence in studying
astock and feels it is aqualified candidate for aneutral strategy. With the
stock at $90, a 16.5 percent implied volatility, and 41 days until expiration,
the standard deviation is about 5. The trader sells the following iron condor:
With the stock at $90, directly between the two short strikes, the trade is
direction neutral. The maximum profit is equal to the total premium taken
in, which in this case is $800. The maximum loss is $4,200. There is about
atwo-thirds chance of retaining the $800 at expiration.
After one week, the overall market begins trending higher on unexpected
bullish economic news. This stock follows suit and is now trading at $93,
and concern is mounting that the rally will continue. The value of the spread
now is about 1.10 per contract (we ignore slippage from trading on the bid-
ask spreads of the four legs of the spread). This means the trade has lost
$300 because it would cost $1,100 to buy back what the trader sold for atotal of $800.
One strategy for managing this trade looking forward is inaction. The
philosophy is that sometimes these trades just don’twork out and you take
your lumps. The philosophy is that the winners should outweigh the losers
over the long term. For some of the more talented and successful traders
with aproven track record, this may be aviable strategy, but there are more
active options as well. Atrader can either close the spread or adjust it.
The two sets of data that must be considered in this decision are the prices
of the individual options and the greeks for the trade. Exhibit 10.8 shows
the new data with the stock at $93.
EXHIBIT 10.8 Greeks for iron condor with stock at $93.

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The trade is no longer neutral, as it was when the underlying was at $90.
It now has adelta of −2.54, which is like being short 254 shares of the
underlying. Although the more time that passes the better—as indicated by
the +0.230 theta—delta is of the utmost concern. The trader has now found
himself short amarket that he thinks may rally.
Closing the entire position is one alternative. To be sure, if you don’thave
an opinion on the underlying, you shouldn’thave aposition. It’slike
making abet on asporting event when you don’treally know who you
think will win. The spread can also be dismantled piecemeal. First, the 85
puts are valued at $0.07 each. Buying these back is ano-brainer. In the
event the stock does retrace, why have the positive delta of that leg working
against you when you can eliminate the risk inexpensively now?
The 80 puts are worthless, offered at 0.05, presumably. There is no point
in trying to sell these. If the market does turn around, they may benefit,
resulting in an unexpected profit.
The 80 and 85 puts are the least of his worries, though. The concern is acontinuing rally. Clearly, the greater risk is in the 95–100 call spread.
Closing the call spread for aloss eliminates the possibility of future losses
and may be awise choice, especially if there is great uncertainty. Taking asmall loss now of only around $300 is abetter trade than risking atotal loss
of $4,200 when you think there is astrong chance of that total loss
occurring.
But if the trader is not merely concerned that the stock will rally but truly
believes that there is agood chance it will, the most logical action is to
position himself for that expected move. Although there are many ways to
accomplish this, the simplest way is to buy to close the 95 calls to eliminate
the position at that strike. This eliminates the short delta from the 95 calls,

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The Retail Trader versus the Pro
Iron condors are very popular trades among retail traders. These days one
can hardly go to acocktail party and mention the word options without
hearing someone tell astory about an iron condor on which he’smade abundle of money trading. Strangely, no one ever tells stories about trades in
which he has lost abundle of money.
Two of the strengths of this strategy that attract retail traders are its
limited risk and high probability of success. Another draw of this type of
strategy is that the iron condor and the other wing spreads offer something
truly unique to the retail trader: away to profit from stocks that don’tmove.
In the stock-trading world, the only thing that can be traded is direction—
that is, delta. The iron condor is an approachable way for anonprofessional
to dabble in nonlinear trading. The iron condor does agood job in
eliminating delta—unless, of course, the stock moves and gamma kicks in.
It is efficient in helping income-generating retail traders accomplish their
goals. And when aloss occurs, although it can be bigger than the potential
profits, it is finite.
But professional option traders, who have access to lots of capital and
have very low commissions and margin requirements, tend to focus their
efforts in other directions: they tend to trade volatility. Although iron
condors are well equipped for profiting from theta when the stock
cooperates, it is also possible to trade implied volatility with this strategy.
The examples of iron condors, condors, iron butterflies, and butterflies
presented in this chapter so far have for the most part been from the
perspective of the neutral trader: selling the guts and buying the wings. Atrader focusing on vega in any of these strategies may do just the opposite
—buy the guts and sell the wings—depending on whether the trader is
bullish or bearish on volatility.
Say atrader, Joe, had abullish outlook on volatility in Salesforce.com
(CRM). Joe could sell the following condor 100 times.

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In this example, February is 59 days from expiration. Exhibit 10.10 shows
the analytics for this trade with CRM at $104.32.
EXHIBIT 10.10 Salesforce.com condor ( Salesforce.com at $104.32).
As expected with the underlying centered between the two middle strikes,
delta and gamma are about flat. As Salesforce.com moves higher or lower,
though, gamma and, consequently, delta will change. As the stock moves
closer to either of the long strikes, gamma will become more positive,
causing the delta to change favorably for Joe. Theta, however, is working
against him with Salesforce.com at $104.32, costing $150 aday. In this
instance, movement is good. Joe benefits from increased realized volatility.
The best-case scenario would be if Salesforce.com moves through either of
the long strikes to, or through, either of the short strikes.
The prime objective in this example, though, is to profit from arise in IV.
The position has apositive vega. The position makes or loses $400 with
every point change in implied volatility. Because of the proportion of theta
risk to vega risk, this should be ashort-term play.
If Joe were looking for asmall rise in IV, say five points, the move would
have to happen within 13 calendar days, given the vega and theta figures.
The vega gain on arise of five vol points would be $2,000, and the theta
loss over 13 calendar days would be $1,950. If there were stock movement
associated with the IV increase, that delta/gamma gain would offset some of
the havoc that theta wreaked on the option premiums. However, if Joe
traded astrategy like acondor as avol play, he would likely expect abigger

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Buying the Calendar
The calendar spread and all its variations are commonly associated with
income-generating spreads. Using calendar spreads as income generators is
popular among retail and professional traders alike. The process involves
buying alonger-term at-the-money option and selling ashorter-term at-the-
money (ATM) option. The options must be either both calls or both puts.
Because this transaction results in anet debit—the longer-term option being
purchased has ahigher premium than the shorter-term option being sold—
this is referred to as buying the calendar.
The main intent of buying acalendar spread for income is to profit from
the positive net theta of the position. Because the shorter-term ATM option
decays at afaster rate than the longer-term ATM option, the net theta is
positive. As for most income spreads, the ideal outcome occurs when the
underlying is at the short strike (in this case, shared strike) when the
shorter-term option expires. At this strike price, the long option has its
highest value, while the short option expires without the trader’sgetting
assigned. As long as the underlying remains close to the strike price, the
value of the spread rises as time passes, because the short option decreases
in value faster than the long option.
For example, atrader, Richard, watches Bed Bath & Beyond Inc. (BBBY)
on aregular basis. Richard believes that Bed Bath & Beyond will trade in arange around $57.50 ashare (where it is trading now) over the next month.
Richard buys the January–February 57.50 call calendar for 0.80. Assuming
January has 25 days until expiration and February has 53 days, Richard will
execute the following trade:
Richard’sbest-case scenario occurs when the January calls expire at
expiration and the February calls retain much of their value.
If Richard created an at-expiration P&(L) diagram for his position, he’dhave trouble because of the staggered expiration months. Ageneral
representation would look something like Exhibit 11.1 .

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EXHIBIT 11.1 Bed Bath & Beyond January–February 57.50 calendar.
The only point on the diagram that is drawn with definitive accuracy is
the maximum loss to the downside at expiration of the January call. The
maximum loss if Bed Bath & Beyond falls low enough is 0.80—the debit
paid for the spread. If Bed Bath & Beyond is below $57.50 at January
expiration, the January 57.50 call expires worthless, and the February 57.50
call may or may not have residual value. If Bed Bath & Beyond declines
enough, the February 57.50 call can lose all of its value, even with residual
time until expiration. If the stock falls enough, the entire 0.80 debit would
be aloss.
If Bed Bath & Beyond is above $57.50 at January expiration, the January
57.50 call will be trading at parity. It will be anegative-100-delta option,
imitating short stock. If Bed Bath & Beyond is trading high enough, the
February 57.50 call will become apositive-100-delta option trading at
parity plus the interest calculated on the strike. The February deep-in-the-
money option would imitate long stock. At a 2 percent interest rate, interest
on the 57.50 strike is about 0.17. Therefore, Richard would essentially have
ashort stock position from $57.50 from the January 57.50 call and would
be essentially long stock from $57.50 plus 0.28 from the February call. The
maximum loss to the upside is about 0.63 (0.80 − 0.17).
The maximum loss if Bed Bath & Beyond is trading over $57.50 at
expiration is only an estimate that assumes there is no time value and that

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interest and dividends remain constant. Ultimately, the maximum loss will
be 0.80, the premium paid, if there is no time value or carry considerations.
The maximum profit is gained if Bed Bath & Beyond is at $57.50 at
expiration. At this price, the February 57.50 call is worth the most it can be
worth without having the January 57.50 call assigned and creating negative
deltas to the upside. But how much precisely is the maximum profit?
Richard would have to know what the February 57.50 call would be worth
with Bed Bath & Beyond stock trading at $57.50 at February expiration
before he can know the maximum profit potential. Although Richard can’tknow for sure at what price the calls will be trading, he can use apricing
model to estimate the call’svalue. Exhibit 11.2 shows analytics at January
expiration.
EXHIBIT 11.2 Bed Bath & Beyond January–February 57.50 call calendar
greeks at January expiration.
With an unchanged implied volatility of 23 percent, an interest rate of two
percent, and no dividend payable before February expiration, the February
57.50 calls would be valued at 1.53 at January expiration. In this best-case
scenario, therefore, the spread would go from 0.80, where Richard
purchased it, to 1.53, for again of 91 percent. At January expiration, with
Bed Bath & Beyond at $57.50, the January call would expire; thus, the
spread is composed of just the February 57.50 call.
Let’snow go back in time and see how Richard figured this trade. Exhibit
11.3 shows the position when the trade is established.

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EXHIBIT 11.3 Bed Bath & Beyond January–February 57.50 call calendar.
Asmall and steady rise in the stock price with enough time to collect
theta is the recipe for success in this trade. As time passes, delta will flatten
out if Bed Bath & Beyond is still right at-the-money. The delta of the
January call that Richard is short will move closer to exactly −0.50. The
February call delta moves toward exactly +0.50.
Gamma and theta will both rise if Bed Bath & Beyond stays around the
strike. As expiration approaches, there is greater risk if there is movement
and greater reward if there is not.
Vega is positive because the long-term option with the higher vega is the
long leg of the spread. When trading calendars for income, implied
volatility (IV) must be considered as apossible threat. Because it is
Richard’sobjective to profit from Bed Bath & Beyond being at $57.50 at
expiration, he will try to avoid vega risk by checking that the implied
volatility of the February call is in the lower third of the 12-month range.
He will also determine if there are any impending events that could cause
IV to change. The less likely IV is to drop, the better.
If there is an increase in IV, that may benefit the profitability of the trade.
But arise in IV is not really adesired outcome for two reasons. First, arise
in IV is often more pronounced in the front month than in the months
farther out. If this happens, Richard can lose more on the short call than he
makes on the long call. Second, arise in IV can indicate anxiety and
therefore agreater possibility for movement in the underlying stock.
Richard doesn’twant IV to rock the boat. “Buy low, stay low” is his credo.
Rho is positive also. Arise in interest rates benefits the position because
the long-term call is helped by the rise more than the short call is hurt. With

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only aone-month difference between the two options, rho is very small.
Overall, rho is inconsequential to this trade.
There is something curious to note about this trade: the gamma and the
vega. Calendar spreads are the one type of trade where gamma can be
negative while vega is positive, and vice versa. While it appears—at least
on the surface—that Richard wants higher IV, he certainly wants low
realized volatility.
Bed Bath & Beyond January–February 57.50 Put
Calendar
Richard’sposition would be similar if he traded the January–February 57.50
put calendar rather than the call calendar. Exhibit 11.4 shows the put
calendar.
EXHIBIT 11.4 Bed Bath & Beyond January–February 57.50 put calendar.
The premium paid for the put spread is 0.75. Ahuge move in either
direction means aloss. It is about the same gamma/theta trade as the 57.50
call calendar. At expiration, with Bed Bath & Beyond at $57.50 and IV
unchanged, the value of the February put would be 1.45—a 93 percent gain.
The position is almost exactly the same as the call calendar. The biggest
difference is that the rho is negative, but that is immaterial to the trade. As
with the call spread, being short the front-month option means negative
gamma and positive theta; being long the back month means positive vega.

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Managing an Income-Generating
Calendar
Let’ssay that instead of trading aone-lot calendar, Richard trades it 20
times. His trade in this case is
His total cash outlay is $1,600 ($80 times 20). The greeks for this trade,
listed in Exhibit 11.5 , are also 20 times the size of those in Exhibit 11.3 .
EXHIBIT 11.5 20-Lot Bed Bath & Beyond January–February 57.50 call
calendar.
Note that Richard has a +0.18 delta. This means he’slong the equivalent
of about 18 shares of stock—still pretty flat. Agamma of −0.72 means that
if Bed Bath & Beyond moves $1 higher, his delta will be starting to get
short; and if it moves $1 lower he will be longer, long 90 deltas.
Richard can use the greeks to get afeel for how much the stock can move
before negative gamma causes aloss. If Bed Bath & Beyond starts trending
in either direction, Richard may need to react. His plan is to cover his deltas
to continue the position.
Say that after one week Bed Bath & Beyond has dropped $1 to $56.50.
Richard will have collected seven days of theta, which will have increased
slightly from $18 per day to $20 per day. His average theta during that time
is about $19, so Richard’sprofit attributed to theta is about $133.
With abig-enough move in either direction, Richard’sdelta will start
working against him. Since he started with adelta of +0.18 on this 20-lot

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spread and agamma of −0.72, one might think that his delta would increase
to 0.90 with Bed Bath & Beyond adollar lower (18 − [−0.072 × 1.00]). But
because aweek has passed, his delta would actually get somewhat more
positive. The shorter-term call’sdelta will get smaller (closer to zero) at afaster rate compared to the longer-term call because it has less time to
expiration. Thus, the positive delta of the long-term option begins to
outweigh the negative delta of the short-term option as time passes.
In this scenario, Richard would have almost broken even because what
would be lost on stock price movement, is made up for by theta gains.
Richard can sell about 100 shares of Bed Bath & Beyond to eliminate his
immediate directional risk and stem further delta losses. The good news is
that if Bed Bath & Beyond declines more after this hedge, the profit from
the short stock offsets losses from the long delta. The bad news is that if
BBBY rebounds, losses from the short stock offset gains from the long
delta.
After Richard’shedge trade is executed, his delta would be zero. His
other greeks remain unchanged. The idea is that if Bed Bath & Beyond
stays at its new price level of $56.50, he reaps the benefits of theta
increasing with time from $18 per day. Richard is accepting the new price
level and any profits or losses that have occurred so far. He simply adjusts
his directional exposure to azero delta.

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Rolling and Earning a “Free” Call
Many traders who trade income-generating strategies are conservative.
They are happy to sell low IV for the benefits afforded by low realized
volatility. This is the problem-avoidance philosophy of trading. Due to risk
aversion, it’scommon to trade calendar spreads by buying the two-month
option and selling the one-month option. This can allow traders to avoid
buying the calendar in earnings months, and it also means ashorter time
horizon, signifying less time for something unwanted to happen.
But there’sanother school of thought among time-spread traders. There
are some traders who prefer to buy alonger-term option—six months to ayear—while selling aone-month option. Why? Because month after month,
the trader can roll the short option to the next month. This is asimple tactic
that is used by market makers and other professional traders as well as
savvy retail traders. Here’show it works.
XYZ stock is trading at $60 per share. Atrader has aneutral outlook over
the next six months and decides to buy acalendar. Assuming that July has
29 days until expiration and December has 180, the trader will take the
following position:
The initial debit here is 2.55. The goal is basically the same as for any
time spread: collect theta without negative gamma spoiling the party. There
is another goal in these trades as well: to roll the spread.
At the end of month one, if the best-case scenario occurs and XYZ is
sitting at $60 at July expiration, the July 60 call expires. The December 60
call will then be worth 3.60, assuming all else is held constant. The positive
theta of the short July call gives full benefits as the option goes from 1.45 to
zero. The lower negative theta of the December call doesn’tbite into profits
quite as much as the theta of ashort-term call would.
The profit after month one is 1.05. Profit is derived from the December
call, worth 3.60 at July expiry, minus the 2.55 initial spread debit. This
works out to about a 41 percent return. The profit is hardly as good as it

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would have been if ashort-term, less expensive August 60 call were the
long leg of this spread.
Rolling the Spread
The July–December spread is different from short-term spreads, however.
When the Julys expire, the August options will have 29 days until
expiration. If volatility is still the same, XYZ is still at $60, and the trader’sforecast is still neutral, the 29-day August 60 calls can be sold for 1.45. The
trader can either wait until the Monday after July expiration and then sell
the August 60s, or when the Julys are offered at 0.05 or 0.10, he can buy the
Julys and sell the Augusts as aspread. In either case, it is called rolling the
spread. When the August expires, he can sell the Septembers, and so on.
The goal is to get acredit month after month. At some point, the
aggregate credit from the call sales each month is greater than the price
initially paid for the long leg of the spread, thus eliminating the original net
debit. Exhibit 11.6 shows how the monthly credits from selling the one-
month calls aggregate over time.
EXHIBIT 11.6 A “free” call.
After July has expired, 1.45 of premium is earned. After August
expiration, the aggregate increases to 2.90. When the September calls,
which have 36 days until expiration, are sold, another 1.60 is added to the
total premium collected. Over three months—assuming the stock price,
volatility, and the other inputs don’tchange—this trader collects atotal of
4.50. That’s 0.50 more than the price originally paid for the December 60
call leg of the spread.
At this point, he effectively owns the December call for free. Of course,
this call isn’treally free; it’searned. It’spaid for with risk and maybe afew
sleepless nights. At this point, even if the stock and, consequently, the

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December call go to zero, the position is still aprofitable trade because of
the continued month-to-month rolling. This is now ano-lose situation.
When the long call of the spread has been paid for by rolling, there are
three choices moving forward: sell it, hold it, or continue writing calls
against it. If the trader’sopinion calls for the stock to decline, it’slogical to
sell the December call and take the residual value as profit. In this case,
over three months the trade will have produced 4.50 in premium from the
sale of three consecutive one-month calls, which is more than the initial
purchase price of the December call. At September expiration, the premium
that will be received for selling the December call is all profit, plus 0.50,
which is the aggregate premium minus the initial cost of the December call.
If the outlook is for the underlying to rise, it makes sense to hold the call.
Any appreciation in the value of the call resulting from delta gains as the
underlying moves higher is good—$0.50 plus whatever the call can be sold
for.
If the forecast is for XYZ to remain neutral, it’slogical to continue selling
the one-month call. Because the December call has been financed by the
aggregate short call premiums already, additional premiums earned by
writing calls are profit with “free” protection. As long as the short is closed
at its expiration, the risk of loss is eliminated.
This is the general nature of rolling calls in acalendar spread. It’sabeautiful plan when it works! The problem is that it is incredibly unlikely
that the stock will stay right at $60 per share for five months. It’salmost
inevitable that it will move at some point. It’slike agame of Russian
roulette. At some point it’sgoing to be alosing proposition—you just don’tknow when. The benefit of rolling is that if the trade works out for afew
months in arow, the long call is paid for and the risk of loss is covered by
aggregate profits.
If we step outside this best-case theoretical world and consider what is
really happening on aday-to-day basis, we can gain insight on how to
manage this type of trade when things go wrong. Effectively, along
calendar is atypical gamma/theta trade. Negative gamma hurts. Positive
theta helps.
If we knew which way the stock was going, we would simply buy or sell
stock to adjust to get long or short deltas. But, unfortunately, we don’t. Our

eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:320


Selling the Front, Buying the Back
If for aparticular stock, the February ATM calls are trading at 50 volatility
and the May ATM calls are trading at 35 volatility, avol-calendar trader
would buy the Mays and sell the Februarys. Sounds simple, right? The devil
is in the details. We’ll look at an example and then discuss some common
pitfalls with vol-trading calendars.
George has been studying the implied volatility of a $164.15 stock.
George notices that front-month volatility has been higher than that of the
other months for acouple of weeks. There is nothing in the news to indicate
immediate risk of extraordinary movement occurring in this example.
George sees that he can sell the 22-day July 165 calls at a 45 percent IV
and buy the 85-day September 165 calls at a 38 percent IV. George would
like to buy the calendar spread, because he believes the July ATM volatility
will drop down to around 38, where the September is trading. If he puts on
this trade, he will establish the following position:
What are George’srisks? Because he would be selling the short-term
ATM option, negative gamma could be aproblem. The greeks for this trade,
shown in Exhibit 11.7 , confirm this. The negative gamma means each
dollar of stock price movement causes an adverse change of about 0.09 to
delta. The spread’sdelta becomes shorter when the stock rises and longer
when the stock falls. Because the position’sdelta is long 0.369 from the
start, some price appreciation may be welcomed in the short term. The stock
advance will yield profits but at adiminishing rate, as negative gamma
reduces the delta.

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EXHIBIT 11.7 10-lot July–September 165 call calendar.
But just looking at the net position greeks doesn’ttell the whole story. It
is important to appreciate the fact that long calendar spreads such as this
have long vegas. In this case, the vega is +1.522. But what does this number
really mean? This vega figure means that if IV rises or falls in both the July
and the September calls by the same amount, the spread makes or loses
$152 per vol point.
George’splan, however, is to see the July’svolatility decline to converge
with the September’s. He hopes the volatilities of the two months will move
independently of each other. To better gauge his risk, he needs to look at the
vega of each option. With the stock at $164.15 the vegas are as follows:
If George is right and July volatility declines 8 points, from 46 to 38, he
will make $1,283 ($1.604 × 100 × 8).
There are acouple of things that can go awry. First, instead of the
volatilities converging, they can diverge further. Implied volatility is aslave
to the whims of the market. If the July IV continues to rise while the
September IV stays the same, George loses $160 per vol point.
The second thing that can go wrong is the September IV declining along
with the July IV. This can lead George into trouble, too. It depends the
extent to which the September volatility declines. In this example, the vega
of the September leg is about twice that of the July leg. That means that if
the July volatility loses eight points while the September volatility declines
four points, profits from the July calls will be negated by losses from the
September calls. If the September volatility falls even more, the trade is aloser.

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