13

Butterflies and condors: combining call spreads and put spreads 145
T
able 13.5 Marks and Spencer long April 320–330–340–350 put condor
M&S
310.00 320.00 322.25 330.00 340.00 347.75 350.00 360.00
Spread debit
–2.25

Value of long
350–340 put
spread at
expiry
10.00 10.00 10.00 10 .00 10.00 2.25 0.00 0.00
Value of short
330–320 put
spread at
expiration
–10.00 –10.00 –7.75 0.00 0.00 0.00 0.00 0.00
Profit/loss
–2.25 –2.25 0.00 7.75 7.75 0.00 –2.25 –2.25
*Long at-the-money put condor
For stationary markets
Put condors, like call condors, can be placed at many different strikes,
depending on your near-term outlook for the underlying. If your out-
look calls for a stationary market, but you wish to leave room for error
on the downside, you can substitute the long at-
the-money put condor for the at-the-money put
butterfly. You might, for example, buy the above

–––––
Total debit: –3.50
Maximum profit: difference between highest two strikes minus spread
debit: (360 – 350) – 3.5 = 6.5
Range of maximum profit: 350 – 340
Upper break-even level: highest strike minus spread debit:
360 – 3.5 = 356.5
Lower break-even level: lowest strike plus spread debit:
330 + 3.5 = 333.5
Profit range: 356.5 – 333.5 = 23
Maximum loss: cost of spread: 3.5
The risk/return ratio is again favourable at 3.5/6.5 = 0.54 for 1, or 1/1.85.
By now you should be an expert at tabulating and graphing the expiration
profit/loss levels of condors and butterflies.
* Short at-the-money put condor
For volatile markets
Like the butterfly, the condor can be sold in order to profit from a vola-
tile or trending market. Although this is more of a market-maker’s trade,
you might consider trading it during volatile mar-
kets. For example, you could sell the above April
360–350–340–330 put condor at 3.5. If Marks and
Spencer closes above 360 or below 330 at expira-
tion, you earn the credit from the spread. In this
case you are taking a slightly bullish position.
The profit/loss figures are exactly the opposite of the above long put
condor.
Like the butterfly, the
condor can be sold in
order to profit
from a volatile or

strikes
Butterflies are flexible spreads which can profit from a variety of trading
ranges. You can extend the profit range of a butterfly by extending the
distance of the strikes. If XYZ is at 100, and you
expect it to rally into a range of between 105 and
115, then you can buy the 100–110–120 call but-
terfly. This spread costs more than the adjacent
strike, 105–110–115 call butterfly, but it has a
greater profit range.
Butterflies are flexible
spreads which can
profit from a variety of
trading ranges

148 Part 2

Options spreads
Using the set of Marks and Spencer April options, you could pay 11.25 for
the 350 call, sell two 370 calls at 3.75, and pay 1 for the 390 call, for a net
debit of 4.75. Your profit range is then 354.75 to 385.25, or 30.5 points, or
8.7 per cent of the share’s value.
Condors can also increase their profit ranges by increasing the distance
of the strikes. This is especially feasible while that stock indexes and, as
a result, options premiums, are at high levels. Consider the set of FTSE
options below.
June FTSE-100 options
June Future at 6250
4
106 days until expiry
ATM implied at 26 per cent


Butterflies and condors: combining call spreads and put spreads 149
Volatility, days until expiration, and butterflies
and condors
Likewise when volatilities are high, you can often find inexpensive adja-
cent strike butterflies and condors, such as in the above FTSE example.
This is because the underlying is trading in a wide range, and the prob-
ability of it settling near a particular strike at expiration is small. The same
factors apply to these spreads when there are many days until expiration.
At times like these, it is preferable to trade butterflies and condors with
non-adjacent strikes.
The advantages
In this chapter we have covered butterflies and condors in depth. The rea-
sons for this are twofold: when purchased, these spreads have low risk/
return ratios; also, they can easily be opened and closed in one transac-
tion. They are therefore justifiable trading strategies under many market
conditions. It is worth learning how to use them.14
The covered write, the calendar
spread and the diagonal spread
The diagonal spread for trending markets
There are two additional spreads that profit from stationary markets. The
covered write involves selling a call against a long underlying position,
and the calendar or time spread involves selling a near-term at-the-
money option, usually a call, and buying a further-term at-the-money
option, again usually a call. Both spreads profit from time decay.
The covered write or the buy-write
If an investor owns or is long an underlying con-

upside profit from the underlying.
This spread is best used by investors who have purchased the underlying
at significantly lower levels, who think that there is little or no upside
potential, and who can tolerate short-term declines in the underlying.
Consider Coca-Cola at 52.67; August options with 60 days until expiration:
Strike
40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00
August calls
4.04 2.52 1.45 0.79 0.34
August puts
0.34 0.47 0.82 1.30 2.05 2.90
For example, Coca-Cola is currently trading at 52.67, and the August 60
calls, with 60 days until expiration, are priced at 0.34. You may sell one
call on each 100 Coca-Cola shares that you own. Alternatively, you may
pay 52.67 for 100 shares, while selling the call, as a spread.
At expiration, the maximum profit for your spread occurs at the strike
price of the call. There, you gain the price appreciation of the stock plus
the full income from the call. The maximum profit is calculated as the
strike price minus the purchase price of the stock plus the income from
the call, or (60 – 52.67) + 0.34 = 7.67.
Above the call strike price, the profit from the stock is offset by the loss on
the call, on a point for point basis. The maxium profit is earned, no more,
no less. The stock will be called away from you at expiration.
The lower break-even level for your position is the price at which the
call income equals the decline in the stock price. This is calculated as the
price of the stock minus the income from the call, or 52.67 – 0.34 = 52.33.
Below this level the spread loses point for point with the stock.
The expiration profit/loss for this covered write is summarised as follows.
Maximum profit: strike price minus stock price, plus income from call:
(60 – 52.67) + 0.34 = 7.67

8
10
0
–2
–4
–6
–8
–10
–12
42.5
45 47.5 50 52.5 55 57.5 60 62.5 65
Figure 14.1
Expiration profit/loss for Coca-Cola

154 Part 2

Options spreads
Two comments
First, if this chart looks like a naked short put, then you’re absolutely right.
The buy write is no more than a synthetic short put. (Refer to Chapter 21
on synthetics.)
So why bother with the complications? Make it simple: if you want to
buy stock and write the call, and if there are no dividends involved, and if
you’re a short-term investor, then just sell the in the money put and save
yourself commissions. You’ll have the same risk profile. (Obviously, I’m
not a fan of selling naked puts.)
Second, and more importantly, there is currently a lot of common advice
which tells you to initiate buy-writes for tempting yields. Well-meaning
advisers usually tell you that you could pay 52.67 for Coca-Cola and sell
the August 55 call at 1.45. Your annualised return would be 1.45/52.67 ×

How to manage the risk of the covered write
The covered write is best suited to long-term stock-holders who can toler-
ate a decline in the stock price below the current price.
There are two solutions to the upside risk. Using the above spread, first
note that with Coca-Cola at 52.67, the August 55 calls are priced at 1.45.
Let’s assume that Coca-Cola immediately rallies $5, to 57.67. At this point,
your short 60 calls will be worth approximately 1.45, and you may simply
buy them back. Your profit/loss is as follows:
Sale of 60 call: 0.34 credit
Purchase of 60 call: 1.45 debit
Profit on stock: 5 credit
––––––––––
Profit/loss: 3.89 credit
With this solution you have revised your outlook. You have concluded
that there is significant upside potential for Coca-Cola.
The second solution is to maintain your outlook. You conclude that you
have erred in your estimate for Coca-Cola’s upside potential, but that the
stock’s new level is the top for the time being. Your strategy is to write
calls for the next two expirations, and you expect to profit in the end.
With Coca-Cola at 57.67, the value of the 60 call will be, as we said,
approximately 1.45. The 65 call will then be approximately 0.34. The
60–65 call spread will be approximately 1.45 – 0.34 = 1.11. You can then
buy this spread, and by doing so, roll your short call to the 65 strike.
The options summary is as follows:
Sale of 60 call: 0.34
Purchase of 60 call: –1.45
Sale of 65 call: 0.34
–––––
Total options debit: –0.77
Here, the profit equals the five points appreciation on the stock minus the

Stock
profit/
loss at
expiration
(–full amt) –7.67 –5.17 –2.67 0.00 0.77 7.33 9.83 12.33
Total
profit/loss
(–full amt) –8.44 –5.94 –3.44 –0.77 0.00 6.56 9.06 11.56
A story and a bit of advice
With the covered write, it is important not to think in terms of the short call
as ‘downside protection’. Remember ’portfolio insurance’? A form of this

14

The covered write, the calendar spread and the diagonal spread 157
now discredited strategy was a variation of the covered write. During the
1980s portfolio insurance was sold to investors as a means of ‘downside pro-
tection’, in other words, calls were written against a stock portfolio in order
to compensate for a price decline, and in the meantime, to earn income.
Have you ever heard of an insurance policy that paid you to be insured?
On 19 October 1987, no amount of calls sold protected stockholders from
the enormous loss of their assets’ values. With options, the only form of
full downside protection is the purchase of a put.
The long calendar spread or long time spread
Calendar spreads in particular can be complicated, and their return poten-
tials can in many cases be duplicated by other stationary market spreads.
However, learning about them is an excellent way to improve your under-
standing of options, and to improve your risk awareness.
Because an option’s decay accelerates with time it is possible to sell a near-
term option and buy a further-term option at the same strike in order to

cent (Feb–Nov = 89 days)
May options with 188 days until expiry, May implied at 44 per cent
(May–Feb = 90 days)
Strike
180.0 (CS) 220.0 (CS) 260.0 (CS)
November calls
44.0 8.5 Cab
(7) (17) (10.5)
February calls
51.0 25.5 10.5
(5) (7) (6.5)
May calls
56.0 32.5 17.0
The values of the calendar spreads are given in parentheses (CS). Note that
the calendar spread with the most value is the February–November 220
call calendar spread. There the characteristic of at-the-money, accelerated
time decay is most in evidence. By comparing the February–November 220
call calendar spread to the February–November 180 and 260 call calendar
spreads it can be seen that as the underlying moves away from the strikes,
the calendar spreads have less value.
Because of this latter fact, many traders buy calendar spreads that are out
of the money. Their outlook calls for the underlying to approach the strike
of the spread as the front month option reaches 30 or fewer days until
expiration. For example, you could pay 6.5 for the May–February 260 call
calendar, and if the stock rises to 260 at the point when February has nine
days until expiration, then the spread will be worth approximately 17, or
the present value of the February–November 220 call calendar.
To get an accurate profit/loss assessment at expiration requires simulation
by computer, which can determine the value of the calendar at various
points in time and at various price levels of the underlying. The above set

between the two options contracts.
Short-term interest rate and other interest rate contracts have their own
risks. A central bank may unexpectedly announce a change in interest
rates, or the change may be greater or less than expected. Economic indi-
cators may change the market’s assessment of the interest rate outlook.
This will cause the spreads between the underlying futures contracts, and
consequently the options spreads, to change. Caution must be exercised
when spreading options between contracts with different delivery months.
There is significant risk in spreading agricultural commodities from old
crop to new crop. For example, with CBOT corn early in the growing
season you should avoid selling September calls against December calls.
This is because a shortage may develop in September which will cause
its underlying futures contract to rally while the December underlying
remains practically unchanged. Many commodities have seasonal volatil-
ity trends which should be studied.
Calendar spreads must
often be evaluated as
two separate positions,
a proper risk/return
profile can only be
obtained with a risk
analysis program

160 Part 2

Options spreads
Most calendars traded are call calendars, but there is no reason not to
trade put calendars. The profit/loss characteristics are practically identical,
except in the OEX and other American styled contracts, where the calls
and puts have different behaviour due to early exercise. Puts on stocks are

Introduction
Part 3 describes the finesse of options. There’s a lot involved here and it
takes you way past 1×1s.
This part guides you through advanced topics such as how the Greeks
interact. Bear in mind that the Greeks have non-linear variables, and so
you need to read about them and work with them. In other words, reading
this part will give you a head start on experience.
Part 3 also discusses volatility skews. It talks about why a 10 per cent out-
of-the-money put costs more that a 10 per cent OTM call in the financials.
It discusses common problems in trading options, such as leverage (gear-
ing), as well as practical issues such as liquidity.
One of these days you’ll ask youself why such and such happened, and it
will probably be because of a topic covered in Part 3. So, read or skim this
part once each year I do.15
The interaction of the Greeks
The Greeks, the time until expiration and the implied volatility interact
with each other in ways that work together and in ways that trade off.
They work differently for each options position. By knowing how they
interact you can test your position for market scenarios. You can antici-
pate what may happen under the best, or return, scenario, or under the
worst, or risk, scenario. You can know what to expect.
This chapter summarises what you have previously learned about the
Greeks. It places them all into perspective and describes their interaction.
Comparing options 1: the Greeks and time
Let’s look again at December Corn options. Tables 15.1 and 15.2 show two
sets of options with different days until expiration, and with the corre-
sponding deltas, gammas, thetas and vegas. The price of the underlying is

($ per
implied
volatility
point)
320 63.00 0.90 3
1
/
4
0.10 0.003 2.75 22.5
340 47.00 0.80 7.00 0.20 0.005 4.50 23.0
360 33
7
/
8
0.67 14.00 0.33 0.007 5.50 35.5
380
a
22.00 0.53 22.00 0.47 0.008 6.65 37.5
400 15.00 0.40 35.00 0.60 0.007 6.00 36.5
420 8
5
/
8
0.27 48
1
/
2
0.73 0.006 5.50 25.0
440
b

per
Corn
point
Theta
($ per
day)
Vega ($
per ivol
point)
320 60
1
/
8
0.99
1
/
8
0.01 0.001 1.0 1.4
340 41
1
/
8
0.92 1
1
/
4
0.08 0.005 4.0 9
360 24
5
/

/
8
0.87 0.006 5.2 15
440
5
/
8
0.04 60
1
/
2
0.96 0.003 2.25 6.5

15

The interaction of the Greeks 167
December Corn at $3.80 × 5,000 bushels; 30 days until expiration; implied
volatility at 30 per cent; no volatility skews; interest rate at 3 per cent;
options multiplier at $50
Table 15.3 is a generalised summary of the effect of time on the Greeks.
Again, the underlying is held constant. The terms ‘in-the- money’ (ITM),
‘at-the-money’ (ATM) and ‘out-of-the-money’ (OTM) are used in abbrevi-
ated form.
Table 15.3 The effect of time passing on the Greeks
Delta Gamma Theta Vega
Time forward: OTM call down up up down
put down up up down
ATM call unch’d up up down
put unch’d up up down
ITM call up up up down