price was 40, the stock price was also 40,
and the call price was 3. Thus, the maximum risk = 40 + 2 x 3 - 40 = 6. This con
firms that the maximum risk in the position is 6 points, or $600. The upside break
even point is then 40 + 6, or 46, and the downside break-even point is 40 - 6, or 34.
These also agree with Table 4-2 and Figure 4-2.
Before expiration, profits can be made even closer to the striking price, because
there will be some time value premium left in the purchased calls.
Example: IfXYZ moved to 45 in one month, each call might be worth 6. If this hap
pened, the investor would have a 5-point loss on the stock, but would also have a 3-
point gain on each of the two options, for a net overall gain of 1 point, or $100. Before
expiration, the break-even point is clearly somewhere below 46, because the position
is at a profit at 45.
Ideally, one would like to find relatively underpriced calls on a fairly volatile
stock in order to implement this strategy most effectively. These situations, while not
prevalent, can be found. Normally, call premiums quite accurately reflect the volatil
ity of the underlying stock. Still, this strategy can be quite viable, because nearly
every stock, regardless of its volatility, occasionally experiences a straight-line, fairly
large move. It is during these times that the investor can profit from this strategy.
126 Part II: Call Option Strategies
Generally, the underlying stock selected for the reverse hedge should be
volatile. Even though option premiums are larger on these stocks, they can still be
outdistanced by a straight-line move in a volatile situation. Another advantage of uti
lizing volatile stocks is that they generally pay little or no dividends. This is desirable
for the reverse hedge, because the short seller will not be required to pay out as
much.
The technical pattern of the underlying stock can also be useful when selecting
the position. One generally would like to have little or no technical support and
resistance within the loss area. This pattern would facilitate the stock's ability to make
a fairly quick move either up or down. It is sometimes possible to find a stock that is
in a wide trading range, frequently swinging from one side of the range to the other.
If a reverse hedge can be set up that has its loss area well within this trading range,
the position may also be attractive.
Example: The XYZ stock in the previous example is trading in the range 30 to 50,
perhaps swinging to one end and then the other rather frequently. Now the reverse
hedge example position, which would make profits above 46 or below 34, would
appear more attractive.
FOLLOW-UP ACTION
Since the reverse hedge has a built-in limited loss feature, it is not necessary to take
any follow-up action to avoid losses. The investor could quite easily put the position
on and take no action at all until expiration. This is often the best method of follow
up action in this strategy.
Another follow-up strategy can be applied, although it has some disadvantages
associated with it. This follow-up strategy is sometimes known as trading against the
straddle. When the stock moves far enough in either direction, the profit on that side
can be taken. Then, if the stock swings back in the opposite direction, a profit can
also be made on the other side. Two examples \vill show how this type of follow-up
strategy works.
Example 1: The XYZ stock in the previous example quickly moves down to 32. At
that time, an 8-point profit could be taken on the short sale. This would leave two
long calls. Even if they expired worthless, a 6-point loss is all that would be incurred
on the calls. Thus, the entire strategy would still have produced a profit of 2 points.
However, if the stock should rally above 40, profits could be made on the calls as well.
A slight variation would be to sell one of the calls at the same time the stock profit is
taken. This would result in a slightly larger realized profit; but if the stock rallied back
Cl,apter 4: Other Call Buying Strategies 127
above 40, the resulting profits there would be smaller because the investor would be
long only one call instead of two.
Example 2: XYZ has moved up to a price at which the calls are each worth 8 points.
One of the calls could then be sold, realizing a 5-point profit. The resulting position
would be short 100 shares of stock and long one call, a protected short sale. The pro
tected short sale has a limited risk, above 40, of 3 points (the stock was sold short at
40 and the call was purchased for 3 points). Even if XYZ remains above 40 and the
maximum 3-point loss has to be taken, the overall reverse hedge would still have
made a profit of 2 points because of the 5-point profit taken on the one call.
Conversely, if XYZ drops below 40, the protected short sale position could add to the
profits already taken on the call.
There is a variation of this upside protective action.
Example 3: Instead of selling the one call, one could instead short an additional 100
shares of stock at 48. If this was done, the overall position would be short 200 shares
of stock (100 at 40 and the other 100 at 48) and long two calls - again a protected
short sale. If XYZ remained above 40, there would again be an overall gain of 2
points. To see this, suppose that XYZ was above 40 at expiration and the two calls
were exercised to buy 200 shares of stock at 40. This would result in an 8-point prof
it on the 100 shares sold short at 48, and no gain or loss on the 100 shares sold short
at 40. The initial call cost of 6 points would be lost. Thus, the overall position would
profit by 2 points. This means of follow-up action to the upside is more costly in com
missions, but would provide bigger profits if XYZ fell back below 40, because there
are 200 shares of XYZ short.
In theory, if any of the foregoing types of follow-up action were taken and the
underlying stock did indeed revers


The initial call cost of 6 points would be lost. Thus, the overall position would
profit by 2 points. This means of follow-up action to the upside is more costly in com
missions, but would provide bigger profits if XYZ fell back below 40, because there
are 200 shares of XYZ short.
In theory, if any of the foregoing types of follow-up action were taken and the
underlying stock did indeed reverse direction and cross back through the striking
price, the original position could again be established. Suppose that, after covering
the short stock at 32, XYZ rallied back to 40. Then XYZ could be sold short again,
reestablishing the original position. If the stock moved outside the break-even points
again, further follow-up action could be taken. This process could theoretically be
repeated a number of times. If the stock continued to whipsaw back and forth in a
trading range, the repeated follow-up actions could produce potentially large profits
on a small net change in the stock price. In actual practice, it is unlikely that one
would be fortunate enough to find a stock that moved that far that quickly.
The disadvantage of applying these follow-up strategies is obvious: One can
never make a large profit if he continually cuts his profits off at a small, limited
128 Part II: Call Option Strategies
amount . .. When XYZ falls to 32, the stock can be covered to ensure an overall profit
of 2 points on the transaction. However, if XYZ continued to fall to 20, the investor
who took no follow-up action would make 14 points while the one who did take fol
low-up action would make only 2 points. Recall that it was stated earlier that there is
a high probability of realizing limited losses in the reverse hedge strategy, but that
this is balanced by the potentially large profits available in the remaining cases. If one
takes follow-up action and cuts off these potentially large profits, he is operating at a
distinct disadvantage unless he is an extremely adept trader.
Proponents of using the follow-up strategy often counter with the argument
that it is frustrating to see the stock fall to 32 and then return back to nearly 40 again.
If no follow-up action were taken, the unrealized profit would have dissolved into a
loss when the stock rallied. This is true as far as it goes, but it is not an effective
enough argument to counterbalance the negative effects of cutting off one's profits.
ALTERING THE RATIO OF LONG CALLS
TO SHORT STOCK
Another aspect of this strategy should be discussed. One does not have to buy exact
ly two calls against 100 shares of short stock. More bullish positions could be con
structed by buying three or four calls against 100 shares short. More bearish positions
could be constructed by buying three calls and shorting 200 shares of stock. One
might adopt a ratio other than 2:1, because he is more bullish or bearish. He also
might use a different ratio if the stock is between two striking prices, but he still
wants to create a position that has break-even points spaced equidistant from the cur
rent stock price. A few examples will illustrate these points.
Example: XYZ is at 40 and the investor is slightly bullish on the stock but still wants
to employ the reverse hedge strategy, because he feels there is a chance the stock
could drop sharply. He might then short 100 shares of XYZ at 40 and buy 3 July 40
calls for 3 points apiece. Since he paid 9 points for the calls, his maximum risk is that
9 points if XYZ were to be at 40 at expiration. This means his downside break-even
price is 31, for at 31 he would have a 9-point profit on the short sale to offset the 9-
point loss on the calls. To the upside, his break-even is now 44½. IfXYZ were at 44½
and the calls at 4½ each at expiration, he would lose 4½ points on the short sale, but
would make l ½ on each of the three calls, for a total call profit of 4½.
A more bearish investor might short 200 XYZ at 40 and buy 3 July 40 calls at 3.
His break-even points would be 35½ on the downside and 49 on the upside, and his
maximum risk would be 9 points. There is a general formula that one can always
Cbapter 4: Other Call Buying Strategies 129
apply to calculate the maximum risk and the break-even points, regardless of the
ratios involved.
Maximum risk= (Striking price Stock price) x Round lots shorted
+ Number of calls bought x Call price
U .d b ak S .ki . Maximum risk psi e re -even = tn ng pnce + ( b f all b h Num er o c s oug t -
Number of round lots short)
D .d b k St .ki . Maximum risk owns1 e rea -even = n ng pnce - b f d l h Num er o roun ots s ort
To verify this, use the numbers from the example in which 100 XYZ were shorted at
40 and three July 40 calls were purchased for 3 each.
Maximum risk= (40-40) x 1 + 3 x 3 = 9
Upside break-even = 40 + 9/(3 - 1) = 40 + 4¼ = 44¼
Downside break-even= 40- 9/1 = 31 ·
It was stated earlier that one might use an adjusted ratio in order to space the break
even points evenly around the current stock price.
Example: Suppose XYZ is at 38 and the XYZ July 40 call is at 2. If one wanted to set
up a reverse hedge that would profit if XYZ moved either up or down by the same
distance, he could not use the 2:1 ratio. The 2:1 ratio would have break-even points
of 34 and 46. Thus, the stock would start out much closer to the downside break-even
point - only 4 points away - than to the upside break-even point, which is 8 points
away. By altering the ratio, the investor can set up a reverse hedge that is more neu
tral on the underlying stock. Suppose that the investor shorted 100 shares of XYZ at
38 and bought three July 40 calls at 2 each. Then his break-even points would be 32
on the downside and 44 on the upside. This is a more neutral situation, with the
downside break-even point being 6 points below the current stock price and the
upside break-even point being 6 points away. The formulae above can be used to ver
ify that, in fact, the break-evens are

eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf


shorted 100 shares of XYZ at
38 and bought three July 40 calls at 2 each. Then his break-even points would be 32
on the downside and 44 on the upside. This is a more neutral situation, with the
downside break-even point being 6 points below the current stock price and the
upside break-even point being 6 points away. The formulae above can be used to ver
ify that, in fact, the break-evens are 32 and 44. Note that the 3: 1 ratio has a maximum
risk of 8 points, while the 2:1 ratio only had 6 points maximum risk.
A final adjustment that can be applied to this strategy is to short the stock and
buy two calls, but with the calls having different striking prices. If XYZ were at 37¼ to
start with, one would have to use a ratio other than 2:1 to set up a position with break
even points spaced equidistant from the current stock price. When these higher ratios
are used, the maximum risk is increased and the investor has to adopt a bullish or bear
ish stance. One may be able to create a position with equidistant break-even points and
a smaller maximum risk by utilizing two different striking prices.
130
Example: The following prices exist:
XYZ, 37½;
XYZ July 40 call, 2; and
XYZ July 35 call, 4.
Part II: Call Option Strategies
If one were to short 100 XYZ at 37½ and to buy one July 40 call for 2 and one July
35 call for 4, he would have a position that is similar to a reverse hedge except that
the maximum risk would be realized anywhere between 35 and 40 at expiration.
Although this risk is over a much wider range than in the normal reverse hedge, it is
now much smaller in dimension. Table 4-3 and Figure 4-3 show the results from this
type of position at expiration. The maximum loss is 3½ points ($350), which is a
smaller amount than could be realized using any ratio strictly with the July 35 or the
July 40 call. However, this maximum loss is realizable over the entire range, 35 to 40.
Again, large potential profits are available if the stock moves far enough either to the
upside or to the downside.
This form of the strategy should only be used when the stock is nearly centered
between two strikes and the strategist wants a neutral positioning of the break-even
points. Similar types of follow-up action to those described earlier can be applied to
this form of the reverse hedge strategy as well.
TABLE 4-3.
Reverse hedge using two strikes.
XYZ Price at Stock July 40 Coll July 35 Coll Total
Expiration Profit Profit Profit Profit
25 +$1,250 -$200 -$ 400 +$ 650
30 + 750 - 200 400 + 150
31 1/2 + 600 - 200 400 0
35 + 250 - 200 400 350
371/2 0 - 200 150 350
40 - 250 - 200 + 100 350
431/2 - 600 + 150 + 450 0
45 - 750 + 300 + 600 + 150
50 - 1,250 + 800 + 1,100 + 650
Gapter 4: Other Call Buying Strategies 131
FIGURE 4-3.
Reverse hedge using two strikes (simulated combination purchase).
C:
~ ·5.
in
~
l/l
.3
0
i.l::-$350
e a.
SUMMARY
40
Stock Price at Expiration
The strategies described in this chapter would not normally be used if the underly
ing stock has listed put options. However, if no puts exist, or the puts are very illiq
uid, and the strategist feels that a volatile stock could move a relatively large distance
in either direction during the life of a call option, he should consider using one of the
forms of the reverse hedge strategy - shorting a quantity of stock and buying calls on
more shares than he is short. If the desired movement does develop, potentially large
profits could result. In any case, the loss is limited to a fixed amount, generally
around 20 to 30% of the initial investment. Although it is possible to take follow-up
action to lock in small profits and attempt to gain on a reversal by the stock, it is wiser
to let the position run its course to capitalize on those occasions when the profits
become large. Normally a 2:1 ratio (long 2 calls, short 100 shares of stock) is used in
this strategy, but this ratio can be adjusted if the investor wants to be more bullish or
more bearish. If the stock is initially between two striking prices, a neutral profit
range can be set up by shorting the stock and buying calls at both the next higher
strike and the next lower strike.
CHAPTER 5
Naked Call Writing
The next two chapters will concentrate on various aspects of writing uncovered call
options. These strategies have risk ofloss if the underlying stock should rise in price,
but they offer profits if the underlying stock declines in price. This chapter on
naked, or uncovered, call writing - demonstrates some of the risks and rewards
inherent in this aggressive strategy. Novice option traders often think that selling
naked options is the "best" way to make money, because of time decay. In addition,
they often assume that market-makers and other professionals sell a lot of naked
options. In reality, neither is true. Yes, options do eventually lose their premium if
held all the way until expiration. However, when an option has a good deal of life
remaining, its excess value above intrinsic value what we call "time value premium"
- is, in reality, heavily influenced by the volatility estimate of the stock. This is called
implied volatility and is discussed at length later in the book. For now, though, it is
sufficient to understand that a lot can go wrong when one writes a naked option,
before it eventually expires. As to professionals selling a lot of naked options, the fact
is that most market-makers and other full-time option traders attempt to reduce their
exposure to large stock price movements if possible. Hence, they may sell some
options naked, but they generally try to hedge them by buying other options or by
buying the underlying stock.
Many novice option traders hold these misconceptions, probably because there
is a general belief that most options expire worthless. Occasionally, one will even hear
or see a statement to this effect in the mainstream media, but it is not true that most
options expir


y may sell some
options naked, but they generally try to hedge them by buying other options or by
buying the underlying stock.
Many novice option traders hold these misconceptions, probably because there
is a general belief that most options expire worthless. Occasionally, one will even hear
or see a statement to this effect in the mainstream media, but it is not true that most
options expire worthless. In fact, studies conducted by McMillan Analysis Corp. in
both bull and bear months indicate that about 65% to 70% of all options have some
value (at least half a point) when they expire. This is not to say that all option buyers
make money, either, but it does serve to show that many more options do not expire
worthless than do.
132
Qapter 5: Naked Call Writing 133
THE UNCOVERED (NAKED) CALL OPTION
When one sells a call option without owning the underlying stock or any equivalent
security (convertible stock or bond or another call option), he is considered to have
written an uncovered call option. This strategy has limited profit potential and theo
retically unlimited loss. For this reason, this strategy is unsuitable for some investors.
This fact is not particularly attractive, but since there is no actual cash investment
required to write a naked call ( the position can be financed with collateral loan value
of marginable securities), the strategy can be operated as an adjunct to many other
investment strategies.
A simple example will outline the basic profit and loss potential from naked
writing.
Example: XYZ is selling at 50 and a July 50 call is selling for 5. If one were to sell the
July 50 call naked - that is, without owning XYZ stock, or any security convertible into
XYZ, or another call option on XYZ - he could make, at most, 5 points of profit. This
profit would accrue if XYZ were at or anywhere below 50 at July expiration, as the
call would then expire worthless. If XYZ were to rise, however, the naked writer
could potentially lose large sums of money. Should the stock climb to 100, say, the
call would be at a price of 50. If the writer then covered (bought back) the call for a
price of 50, he would have a loss of 45 points on the transaction. In theory, this loss
is unlimited, although in practice the loss is limited by time. The stock cannot rise an
infinite amount during the life of the call. Clearly, defensive strategies are important
in this approach, as one would never want to let a loss run as far as the one here.
Table 5-1 and Figure 5-1 (solid line) depict the results of this position at July expira
tion. Note that the break-even point in this example is 55. That is, if XYZ rose 10%,
or 5 points, at expiration, the naked writer would break even. He could buy the call
back at parity, 5 points, which is exactly what he sold it for. There is some room for
error to the upside. A naked write will not necessarily lose money if the stock moves
up. It will only lose if the stock advances by more than the amount of the time value
premium that was in the call when it was originally written.
Naked writing is not the same as a short sale of the underlying stock. While both
strategies have large potential risk, the short sale has much higher reward potential,
but the naked write will do better if the underlying stock remains relatively
unchanged. It is possible for the naked writer to make money in situations when the
short seller would have lost money. Using the example above, suppose one investor
had written the July 50 call naked for 5 points while another investor sold the stock
short at 50. If XYZ were at 52 at expiration, the naked writer could buy the call back
at parity, 2 points, for a 3-point profit. The short seller would have a 2-point loss.
134
TABLE 5-1.
Position at July expiration.
XYZ Price at Call Price at
Expiration Expiration
30 0
40 0
50 0
55 5
60 10
70 20
80 30
FIGURE 5-1.
Uncovered (naked) call write.
+$500
C
0
~ ·15..
X
w
cu
(/J
~ ...I
0
lt,
.... ......
", Naked Write
45 SO',
.... .. .... .. .. Short Sale ,,
.. ..
Stock Price at Expiration
..
Part II: Call Option Strategies
Profit on
Naked Write
+$ 500
+ 500
+ 500
0
500
- 1,500
- 2,500
.. .... ..
~
Moreover, the short seller pays out the dividends on the underlying stock, whereas
the naked call writer does not. The naked call will expire, of course, but the short sale
does not. This is a situation in which the naked write outperforms the short sale.
However, ifXYZ were to fall sharply- to 20, say- the naked writer could only make
5 points while the short seller would make 30 points. The dashed line in Figure 5-1
shows how the short sale of XYZ at 50 would compare with the naked write of the
July 50 call. Notice that the two strategies are equal at 45 at expiration; they both
Cl,apter 5: Naked Call Writing 135
make a 5-point profit there. Above 45, the naked write does better; it has larger prof
its and smaller losses. Below 45, the short sale does better, and the farther the stock
falls, the better the short sale becomes in comparison. As will be seen later, one can
more closely simulate a short sale by writing an in-the-money naked call.
INVESTMENT REQUIRED
The margin requirements for writing a naked call are 20% of the stock price plus the
call premium, less the amount by which the stock is below the striking price. If the
stock is below the striking price, the differential is subtracted from the requirement.
However, a minimum of 10% of the stock price is required for each call, even if the
C-'Omputation results in a smaller number. Table 5-2 gives four examples of how the ini
tial margin requirement would be computed for four different stock prices. The 20%
collateral figure is the minimum exchange requirement and may vary somewhat among
different brokerage houses. The call premium may be applied against the requirement.
In the first line of Table 5-2, if the XYZ July 50 call were selling for 7


sults in a smaller number. Table 5-2 gives four examples of how the ini
tial margin requirement would be computed for four different stock prices. The 20%
collateral figure is the minimum exchange requirement and may vary somewhat among
different brokerage houses. The call premium may be applied against the requirement.
In the first line of Table 5-2, if the XYZ July 50 call were selling for 7 points, the $700
call premium could be applied against the $1,800 margin requirement, reducing the
actual amount that the investor would have to put up as collateral to $1,100.
TABLE 5-2.
Initial collateral requirements for four stock prices.
Coll
Written
XYZ July 50
XYZ July 50
XYZ July 50
XYZ July 50
Stock Price When
Coll Written
55
50
46
40
*Requirement cannot be less than 10%.
Coll
Price
$700
400
200
100
20% of
Stock Price
$1,100
1,000
920
800
Out-of-the
Money
Differential
$ 0
0
400
- 1,000
Total Margin
Requirement
$1,800
1,400
720
400*
In addition to the basic requirements, a brokerage firm may require that for a
customer to participate in uncovered writing, he have a minimum equity in his
account. This equity requirement may range from as low as $2,000 to as high as
$100,000. Since naked call writing is a high-risk strategy, some brokerage firms
require that the customer be able to show both financial wherewithal and option
136 Part II: Call Option Strategies
trading experience before the account can be approved for naked call writing. In
addition, some brokers require that a maintenance requirement be applied against
each option written naked. This requirement, sometimes called a kicker, is usually
less than $250 per call and is generally used by the broker to ensure that, should the
customer fail to respond to an assignment notice against his naked call, the commis
sion costs for buying and selling the underlying stock would be defrayed.
Naked Option Positions Are Marked to the Market Daily. This
means that the collateral requirement for the position is recomputed daily, just as in
the short sale of stock. The same margin formula that was described above is applied
and, if the stock has risen far enough, the customer will be required to deposit addi
tional collateral or close the position. The need for such a mark to market is obvious.
If the underlying stock should rise, the brokerage firm must ensure that the customer
has enough collateral to cover the eventuality of buying the stock in the open market
and selling it at the striking price if an assignment notice should be received against
the naked call. The mark to market works to the customer's favor if the stock falls in
price. Excess collateral is then released back into the customer's margin account, and
may be used for other purposes.
It is important to realize that, in order to write a naked call, collateral is all that
is required. No cash need be "invested" if one owns securities with sufficient collat
eral loan value.
Example: An investor owns 100 shares of a stock selling at $60 per share. This stock
is worth $6,000. If the loan rate on stock is 50% of $6,000, this investor has a collat
eral loan value equal to 50% of $6,000, or $3,000. This investor could write any of the
naked calls in Table 5-2 without adding cash or securities to his account. Moreover,
he would have satisfied a minimum equity requirement of at least $6,000, since his
stock is equity.
This aspect of naked call writing - using collateral value to finance the writing
- is attractive to many investors, since one is able to write calls and bring in premi
ums without disturbing his existing portfolio. Of course, if the stock underlying the
naked call should rise too far in price, additional collateral may be called for by the
broker because of the mark to market. Moreover, there is risk whether cash or col
lateral is used. If one buys in a naked call at a loss, he will then be spending cash, cre
ating a debit in his account.
Regardless of how one finances a naked option position, it is generally a good
idea to allow enough collateral so that the stock can move all the way to the point at
which one would cover the option or take follow-up action. For example, suppose a
136 Part II: Call Option Strategies
trading experience before the account can be approved for naked call writing. In
addition, some brokers require that a maintenance requirement be applied against
each option written naked. This requirement, sometimes called a kicker, is usually
less than $250 per call and is generally used by the broker to ensure that, should the
customer fail to respond to an assignment notice against his naked call, the commis
sion costs for buying and selling the underlying stock would be defrayed.
Naked Option Positions Are Marked to the Market Daily. This
means that the collateral requirement for the position is recomputed daily, just as in
the short sale of stock. The same margin formula that was described above is applied
and, if the stock has risen far enough, the customer will be required to deposit addi
tional collateral or close the position. The need for such a mark to market is obvious.
If the underlying stock should rise, the brokerage firm must ensure that the customer
has enough collateral to cover the eventuality of buying the stock in the open market
and selling it at the striking price if an assignment notice should be received against
the naked call. The mark to market works to the customer's favor if the stock falls in
price. Excess collateral is then released back into the customer's margin account, and
may be used for other purposes.
It is important to realize that, in order to write a naked call, collateral is all that
is required. No cash need be "invested" if one owns securities with sufficient collat
eral loan value.
Example: An investor owns 100 shares of a stock selling at $60 per share. This stock
is worth $6,000. If the loan rate on stock is 50% of $6,0


ustomer's margin account, and
may be used for other purposes.
It is important to realize that, in order to write a naked call, collateral is all that
is required. No cash need be "invested" if one owns securities with sufficient collat
eral loan value.
Example: An investor owns 100 shares of a stock selling at $60 per share. This stock
is worth $6,000. If the loan rate on stock is 50% of $6,000, this investor has a collat
eral loan value equal to 50% of $6,000, or $3,000. This investor could write any of the
naked calls in Table 5-2 without adding cash or securities to his account. Moreover,
he would have satisfied a minimum equity requirement of at least $6,000, since his
stock is equity.
This aspect of naked call writing - using collateral value to finance the writing
- is attractive to many investors, since one is able to write calls and bring in premi
ums without disturbing his existing portfolio. Of course, if the stock underlying the
naked call should rise too far in price, additional collateral may be called for by the
broker because of the mark to market. Moreover, there is risk whether cash or col
lateral is used. If one buys in a naked call at a loss, he will then be spending cash, cre
ating a debit in his account.
Regardless of how one finances a naked option position, it is generally a good
idea to allow enough collateral so that the stock can move all the way to the point at
which one would cover the option or take follow-up action. For example, suppose a
136 Part II: Call Option Strategies
trading experience before the account can be approved for naked call writing. In
addition, some brokers require that a maintenance requirement be applied against
each option written naked. This requirement, sometimes called a kicker, is usually
less than $250 per call and is generally used by the broker to ensure that, should the
customer fail to respond to an assignment notice against his naked call, the commis
sion costs for buying and selling the underlying stock would be defrayed.
Naked Option Positions Are Marked to the Market Daily. This
means that the collateral requirement for the position is recomputed daily, just as in
the short sale of stock. The same margin formula that was described above is applied
and, if the stock has risen far enough, the customer will be required to deposit addi
tional collateral or close the position. The need for such a mark to market is obvious.
If the underlying stock should rise, the brokerage firm must ensure that the customer
has enough collateral to cover the eventuality of buying the stock in the open market
and selling it at the striking price if an assignment notice should be received against
the naked call. The mark to market works to the customer's favor if the stock falls in
price. Excess collateral is then released back into the customer's margin account, and
may be used for other purposes.
It is important to realize that, in order to write a naked call, collateral is all that
is required. No cash need be "invested" if one owns securities with sufficient collat
eral loan value.
Example: An investor owns 100 shares of a stock selling at $60 per share. This stock
is worth $6,000. If the loan rate on stock is 50% of $6,000, this investor has a collat
eral loan value equal to 50% of $6,000, or $3,000. This investor could write any of the
naked calls in Table 5-2 without adding cash or securities to his account. Moreover,
he would have satisfied a minimum equity requirement of at least $6,000, since his
stock is equity.
This aspect of naked call writing - using collateral value to finance the writing
- is attractive to many investors, since one is able to write calls and bring in premi
ums without disturbing his existing portfolio. Of course, if the stock underlying the
naked call should rise too far in price, additional collateral may be called for by the
broker because of the mark to market. Moreover, there is risk whether cash or col
lateral is used. If one buys in a naked call at a loss, he will then be spending cash, cre
ating a debit in his account.
Regardless of how one finances a naked option position, it is generally a good
idea to allow enough collateral so that the stock can move all the way to the point at
which one would cover the option or take follow-up action. For example, suppose a
Gapter 5: Naked Call Writing 137
stock is trading at 50 and one sells an April 60 call naked, figuring that he will cover
the call if the stock rises to 60 ( that is, if the option becomes an in-the-money option).
He should set aside enough collateral to margin the position as if the stock were at
60 (even though the actual margin requirement will be smaller than that). If he
allows that extra collateral, then he will never be forced into a margin call at a stock
price prior to (that is, below) where he wanted to take follow-up action. Simply stat
ed, let the market take you out of a position, not a margin call.
THE PHILOSOPHY OF SELLING NAKED OPTIONS
The first and foremost question one must address when thinking about selling naked
options (or any strategy, for that matter) is: "Can I psychologically handle the thought
of naked options in my account?" Notice that the question does not have anything to
do with whether one has enough collateral or margin to sell calls (although that, too,
is important) nor does it ask how much money he will make. First, one must decide
if he can be comfortable with the risk of the strategy. Selling naked options means
that there is theoretically unlimited risk if the underlying instrument should make a
large, sudden, adverse move. It is one's attitude regarding that fact alone that deter
mines whether he should consider selling naked options. If one feels that he won't be
able to sleep at night, then he should not sell naked options, regardless of any profit
projections that might seem attractive.
If one feels that the psychological suitability aspect is


underlying instrument should make a
large, sudden, adverse move. It is one's attitude regarding that fact alone that deter
mines whether he should consider selling naked options. If one feels that he won't be
able to sleep at night, then he should not sell naked options, regardless of any profit
projections that might seem attractive.
If one feels that the psychological suitability aspect is not a roadblock, then he
can consider whether he has the financial wherewithal to write naked options. On the
surface, naked option margin requirements are not large (although in equity and
index options, they are larger than they were prior to the crash of 1987).
In general, one would prefer to let the naked options expire worthless, if at all
possible, without disturbing them, unless the underlying instrument makes a signifi
cant adverse move. So, out-of-the-money options are the usual choice for naked sell
ing. Then, in order to reduce ( or almost eliminate) the chance of a margin call, one
should set aside the margin requirement as if the underlying had already rrwved to
the strike price of the option sold. By allowing margin as if the underlying were
already at the strike, one will almost never experience a margin call before the under
lying price trades up to the strike price, at which time it is best to close the position
or to roll the call to another strike.
Thus, for naked equity call options, allow as collateral 20% of the highest naked
strike price. In this author's opinion, the biggest mistake a trader can make is to ini
tiate trades because of margin or taxes. Thus, by allowing the "maximum" margin,
one can make trading decisions based on what's happening in the market, as opposed
to reacting to a margin call from his broker.
138 Part II: Call Option Strategies
"Suitability" also means not risking nwre nwney than one can afford to lose. If
one allows the "maximum" margin, then he won't be risking a large portion of his
equity unless he is unable to cover when the underlying trades through the strike
price of his naked option. Gaps in trading prices would be the culprits that could pre
vent one from covering. Gaps are common in stocks, less common in futures, and
almost nonexistent in indices. Hence, index options are the options of choice when it
comes to naked writing. Index options are discussed later in the book.
Finally, there is one more "rule" that a naked option writer must follow:
Someone has to be watching the position at all times. Disasters could occur if one
were to go on vacation and not pay attention to his naked options. Usually, one's bro
ker can watch the position, even if the trader has to call him from his vacation site.
In sum, then, to write naked options, one needs to be prepared psychological
ly, have sufficient funds, be willing to accept the risk, be able to monitor the position
every day, sell options whose implied volatility is extremely high, and cover any naked
options that become in-the-money options.
RISK AND REWARD
One can adjust the apparent risks and rewards from naked call writing by his selec
tion of an in-the-money or out-of-the-money call. Writing an out-of-the-money call
naked, especially one quite deeply out-of-the-money, offers a high probability of
achieving a small profit. Writing an in-the-money call naked has the most profit
potential, but it also has higher risks.
Example: XYZ is selling at 40 and the July 50 is selling for½. This call could be sold
naked. The probability that XYZ could rise to 50 by expiration has to be considered
small, especially if there is not a large amount of time remaining in the life of the call.
In fact, the stock could rise 25%, or 10 points, by expiration to a price of 50, and the
call would still expire worthless. Thus, this naked writer has a good chance of realiz
ing a $50 profit, less commissions. There could, of course, be substantial risk in terms
of potential profit versus potential loss if the stock rises substantially in price by expi
ration. Still, this apparent possibility of achieving additional limited income with a
high probability of success has led many investors to use the collateral value of their
portfolios to sell deeply out-of-the-money naked calls.
For those employing this technique, a favored position is to have a stock at or
just about 15 and then sell the near-term option with striking price 20 naked. This
option would sell for one-eighth or one-quarter, perhaps, although at times there
might not be any bid at all. At this price, the stock would have to rally nearly one-
C.,,er 5: Naked Call Writing 139
third, or 33%, for the writer to lose money. Although there are not usually many
optionable stocks selling at or just above $10 per share, these same out-of-the-money
writers would also be attracted to selling a call with a striking price 15 when the stock
is at 10, because a 50% upward move by the stock would be required for a loss to be
realized.
This strategy of selling deeply out-of-the-money calls has its apparent attraction
in that the writer is assured of a profit unless the underlying stock can rally rather
substantially before the call expires. The danger in this strategy is that one or two
losses, perhaps amounting to only a couple of points each, could wipe out many peri
ods of profits. The stock market does occasionally rally heavily in a short period, as
witnessed repeatedly throughout history. Thus, the writer who is adopting this strat
egy cannot regard it as a sure thing and certainly cannot afford to establish the writes
and forget them. Close monitoring is required in case the market begins to rally, and
by no means should losses be allowed to accumulate.
The opposite end of the spectrum in naked call writing is the writing of fairly
deeply in-the-money calls. Since an in-the-money call would not have much time
value premium in it, this writer does not have much leeway to the upside. If the
stock rallies at a


nd forget them. Close monitoring is required in case the market begins to rally, and
by no means should losses be allowed to accumulate.
The opposite end of the spectrum in naked call writing is the writing of fairly
deeply in-the-money calls. Since an in-the-money call would not have much time
value premium in it, this writer does not have much leeway to the upside. If the
stock rallies at all, the writer of the deeply in-the-money naked call will normally
experience a loss. However, should the stock drop in price, this writer will make
larger dollar profits than will the writer of the out-of-the-money call. The sale of the
deeply in-the-money call simulates the profits that a short seller could make, at least
until the stock drops close to the striking price, since the delta of a deeply in-the
money call is close to 1.
Example: XYZ is selling at 60 and the July 50 call is selling for 10½. IfXYZ rises, the
naked writer will lose money, because there is only ½ of a point of time value pre
mium in the call. If XYZ falls, the writer will make profits on a point-for-point basis
until the stock falls much closer to 50. That is, if XYZ dropped from 60 to 57, the call
price would fall by almost 3 points as well. Thus, for quick declines by the stock, the
deeply in-the-money write can provide profits nearly equal to those that the short
seller could accumulate. Notice that if XYZ falls all the way to 50, the profits on the
written call will be large, but will be accumulating at a slower rate as the time value
premium builds up with the stock near the striking price.
If one is looking to trade a stock on the short side for just a few points of nwve
ment, he might use a deeply in-the-nwney naked write instead of shorting the stock.
His investment will be smaller - 20% of the stock price for the write as compared to
50% of the stock price for the short sale - and his return will thus be larger. (The
requirement for the in-the-money amount is offset by applying the call's premium.)
140 Part II: Call Option Strategies
The writer should take great caution in ascertaining that the call does have some time
premium in it. He does not want to receive an assignment notice on the written call.
It is easiest to find time premium in the more distant expiration series, so the writer
would normally be safest from assignment by writing the longest-term deep in-the
money call if he wants to make a bearish trade in the stock.
Example: An investor thinks that XYZ could fall 3 or 4 points from its current price
of 60 in a quick downward move, and wants to capitalize on that move by writing a
naked call. If the April 40 were the near-term call, he might have the choice of sell
ing the April 40 at 20, the July 40 at 20¼, or the October 40 at 20½. Since all three
calls will drop nearly point for point with the stock in a move to 56 or 57, he should
write the October 40, as it has the least risk of being assigned. A trader utilizing this
strategy should limit his losses in much the same way a short seller would, by cover
ing if the stock rallies, perhaps breaking through overhead technical resistance.
ROLLING FOR CREDITS
Most writers of naked calls prefer to use one of the two strategies described above.
The strategy of writing at-the-money calls, when the stock price is initially close to the
striking price of the written call, is not widely utilized. This is because the writer who
wants to limit risk will write an out-of-the-money call, whereas the writer who wants
to make larger, quick trading profits will write an in-the-money call. There is, how
ever, a strategy that is designed to utilize the at-the-money call. This strategy offers a
high degree of eventual success, although there may be an accumulation of losses
before the success point is reached. It is a strategy that requires large collateral back
ing, and is therefore only for the largest investors. We call this strategy "rolling for
credits." The strategy is described here in full, although it can, at times, resemble a
Martingale strategy; that is, one that requires "doubling up" to succeed, and one that
can produce ruin if certain physical limits are reached. The classic Martingale strat
egy is this: Begin by betting one unit; if you lose, double your bet; if you win that bet,
you'll have netted a profit of one unit (you lost one, but won two); if you lost the sec
ond bet, double your bet again. No matter how many times you lose, keep doubling
your bet each time. When you eventually win, you will profit by the amount of your
original bet (one unit). Unfortunately, such a strategy cannot be employed in real life.
For example, in a gambling casino, after enough losses, one would bump up against
the table limit and would no longer be able to double his bet. Consequently, the strat
egy would be ruined just when it was at its worst point. While "rolling for credits"
doesn't exactly call for one to double the number of written calls each time, it does
require that one keep increasing his risk exposure in order to profit by the amount of
that original credit sold. In general, Martingale strategies should be avoided.
Cl,apter 5: Naked Call Writing 141
In essence, the writer who is rollingf or credits sells the most time premium that
he can at any point in time. This would generally be the longest-term, at-the-money
call. If the stock declines, the writer makes the time premium that he sold. However,
if the stock rises in price, the writer rolls up for a credit. That is, when the stock
reaches the next higher striking price, the writer buys back the calls that were origi
nally sold and sells enough long-term calls at the higher strike to generate a credit.
In this way, no debits are incurred, although a realized loss is taken on the rolling up.
If the stock persists and rises to the next striking price, the process is repeated.
Eventually, the stock will stop rising - they always do - and the last set of w


g price, the writer buys back the calls that were origi
nally sold and sells enough long-term calls at the higher strike to generate a credit.
In this way, no debits are incurred, although a realized loss is taken on the rolling up.
If the stock persists and rises to the next striking price, the process is repeated.
Eventually, the stock will stop rising - they always do - and the last set of written
options will expire worthless. At that time, the writer would make an overall profit
consisting of an amount equal to all the credits that he had taken in so far. In reality,
most of that credit will simply be the initial credit received. The "rolls" are done for
even money or a small credit. In essence, the increased risk generated by continual
ly rolling up is all geared toward eventually capturing that initial credit. The similar
ity to the Martingale strategy is strongest in this regard: One continually increases his
risk, knowing that when he eventually wins (i.e., the last set of options expires worth
less), he profits by the amount of his original "bet."
There are really only two requirements for success in this strategy. The first is
that the underlying stock eventually fall back, that it does not rise indefinitely. This is
hardly a requirement; it is axiomatic that all stocks will eventually undergo a correc
tion, so this is a simple requirement to satisfy. The second requirement is that the
investor have enough collateral backing to stay with the strategy even if the stock runs
up heavily against him.
This is a much harder requirement to satisfy, and may in fact tum out to be
nearly impossible to satisfy. If the stock were to experience a straight-line upward
move, the number of calls written might grow so substantially that they would
require an unrealistically large amount of collateral (margin). At a minimum, this
strategy is applicable only for the largest investors. For such well-collateralized
investors, this strategy can be thought of as a way to add income to a portfolio. That
is, a large stock portfolio's equity may be used to finance this strategy through its loan
value. There would be no margin interest charges, because all transactions are cred
it transactions. (No debits are created, as long as the Martingale "limits" are not
reached.) The securities portfolio would not have to be touched unless the strategy
were terminated before the last set of calls expired worthless.
This is where the danger comes in: If the stock upon which the calls are written
rises so fast that one completely uses up all of his collateral value to finance the naked
calls, and then one is required to roll again, the strategy could result in large losses.
For a while, one could simply continue to roll the same number of calls up for deb
its, but eventually those debits would mount in size if the stock persisted in rising. At
142 Part II: Call Option Strategies
this point, even if the stock did finally decline enough for the last set of calls to expire
worthless, the overall strategy might still have been operated at a loss.
Example: The basic strategy in the case of rising stock is shown in Table 5-3. Note
that each transaction is a credit and that all ( except the last) involve taking a realized
loss.
This example assumes that the stock rose so quickly that a longer-term call was
never available to roll into. That is, the October calls were always utilized. If there
were a longer-term call available (the January series, for example), the writer should
roll up and out as well. In this way, larger credits could be generated. The number of
calls written increased from 5 to 15 and the collateral required as backing for the
writing of the naked calls also increased heavily. Recall that the collateral require
ment is equal to 20% of the stock price plus the call premium, less the amount by
which the call is out-of-the-money. The premium may be used against the collateral
requirements. Using the stock and call prices of the example above, the investment
is computed in Table 5-4. While the number of written calls has tripled from 5 to 15,
the collateral requirement has more than quadrupled from $5,000 to $21,000. This is
why the investor must have ample collateral backing to utilize this strategy. The gen
eral philosophy of the large investors who do apply this strategy is that they hope to
eventually make a profit and, since they are using the collateral value of large securi
ty positions already held, they are not investing any more money. The strategy does
not really "cost" these investors anything. All profits represent additional income and
do not in any way disturb the underlying security portfolio. Unfortunately, losses
taken due to aborting the strategy could seriously affect the portfolio. This is why the
investor must have sufficient collateral to carry through to completion.
The sophisticated strategist who implements this strategy will generally do
more rolling than that discussed in the simple example above. First, if the stock
drops, the calls will be rolled down to the next strike - for a credit - in order to con
stantly be selling the most time premium, which is always found in the longest-term
at-the-money call. Furthermore, the strategist may want to roll out to a more distant
expiration series whenever the opportunity presents itself. This rolling out, or for
ward, action is only taken when the stock is relatively unchanged from the initial
price and there is no need to roll up or down.
This strategy seems ve:ry attractive as long as one has enough collateral backing.
Should one use up all of his available collateral, the strategy could collapse, causing
substantial losses. It may not necessarily generate large rates of return in rising mar
kets, but in stable or declining markets the generation of additional income can be
quite substantial. Since the investor is not putting up any additional cash but is uti-
Cl,apter 5: Naked


has enough collateral backing.
Should one use up all of his available collateral, the strategy could collapse, causing
substantial losses. It may not necessarily generate large rates of return in rising mar
kets, but in stable or declining markets the generation of additional income can be
quite substantial. Since the investor is not putting up any additional cash but is uti-
Cl,apter 5: Naked Call Writing
TABLE 5-3.
Rolling for credits when stock is rising.
Initially: XYZ = 50
Sell 5 XYZ October 50's at 7
later: XYZ rises to 60
Buy 5 XYZ October 50's at 11 and
sell 8 XYZ October 60's at 7
Later: XYZ rises further to 70
Buy 8 XYZ October 60's at 11 and
sell 15 XYZ October 70's at 6
Finally: XYZ falls and the October 70's expire worthless
TABLE 5-4.
Increase in collateral requirement.
Initially: XYZ = 50
Sell 5 XYZ October 50's at 7
($3,500 net credit)
Later: . XYZ = 60
Sell 8 XYZ October 60's at 7
Buy 5 October 50's at 11
($3,600 net credit to date)
Later: XYZ = 70
Sell 15 XYZ October 70's at 6
Buy 8 XYZ October 60' s at 1 1
($3,800 net credit to date)
143
+$3,500 credit
- 5,500 debit
+ 5,600 credit
- 8,800 debit
+ 9,000 credit
Net gain = +$3,800
$ 5,000 collateral required
$ 9,600 collateral required
$21,000 collateral required
lizing the collateral power of his present securities, his "investment" is actually zero.
Any profits represent additional income. The investor must be aware of one other
factor that can upset the strategy. If a stock should rise so far as to require the num
ber of calls to exceed the position limits set by the OCC, the strategy is ruined. In the
example above, XYZ would probably have to rise to about a price of over 200, with
out a correction, before the sale of"' 1,000 calls would be required. If the strategist
originally started with too many naked calls, he could potentially exceed the limit in
a short time period. Rather than attempting to sell too many calls initially in any one
"Position limits are higher now.
144 Part II: Call Option Strategies
security, the strategist should diversify several moderately sized positions throughout
a variety of underlying stocks. If he does this, he will probably never have to exceed
the position limit of contracts short in any one security.
Even with as many precautions as one might take, there is no guarantee that
one would have the collateral available to withstand a gain of 1000% or more, such
as is occasionally seen with high-flying tech stocks or new IPOs. One would probably
be best served, if he really wants to operate this strategy, to stick with stocks that are
well capitalized (some of the biggest in the industry), so that they are less suscepti
ble to such violent upside moves. Even then, though, there is no guarantee that one
will not run out of collateral in a sharply rising market, because it is impossible to esti
mate with complete certainty just how far any one stock might advance in a particu
lar period of time.
TIME VALUE PREMIUM IS A MISNOMER
Once again, the topic of time value premium is discussed, as it was in Chapter 3.
Many novice option traders think that if they sell an out-of-the-money option
(whether covered or naked), all they have to do is sit back and wait to collect the pre
mium as time wears it away. However, a lot of things can happen between the time
an option is sold and its expiration date. The stock can move a great deal, or implied
volatility can skyrocket. Both are bad for the option seller and both completely coun
teract any benefit that time decay might be imparting. The option seller must con
sider what might happen during the life of the option, and not simply view it as a
strategy to hold the option until expiration. Naked call writers, especially, should
operate with that thought in mind, but so should covered call writers, even though
most don't. What the covered writer gives away is the upside; and if he constantly
sells options without regard to the possibilities of volatility or stock price increases,
he will be doing himself a disservice.
So, while it is still proper to refer to the part of an option's price that is not
intrinsic value as "time value premium," the knowledgeable option trader under
stands that it is also more heavily influenced by volatility and stock price movement
than by time.
SUMMARY
In a majority of cases, naked call writing is applied as a deeply out-of-the-money
strategy in which the investor uses the collateral value of his security holdings to par
ticipate in a strategy that offers a large probability of making a very limited profit. It
is a poor strategy, because one loss may wipe out many profits. The trader who
Oapter 5: Naked Call Wdting 145
desires an alternative to a short sale may use the sale of an in-the-money naked call
in order to attempt to make a quick profit on a smaller investment than the short sell
er would have to make. Both of these strategies could entail large risk if one does not
have sufficient capital backing.
An alternative strategy, but one that is available only to very large investors, is
to sell at-the-money calls naked, rolling up and forward for credits if the underlying
stock rises in price. This strategy, however, can become disastrous if it takes on
Martingale-like qualities during a rocketing rise by the underlying stock.
Ratio Call Writing
Two basic types of call writing have been described in previous chapters: covered call
writing, in which one owns the underlying stock and sells a call; and naked call writ
ing. Ratio writing is a combination of these two types of positions.
THE RATIO WRITE
Simply stated, ratio call writing is the strategy in which one owns a certain number
of shares of the underlying stock and sells calls against more shares than he owns.
Thus, there is a ratio of calls written to stock owned. The most common ratio is the
2:1 ratio, whereby one owns 100 shares of the underlying stock and sells 2 calls. Note


ation of these two types of positions.
THE RATIO WRITE
Simply stated, ratio call writing is the strategy in which one owns a certain number
of shares of the underlying stock and sells calls against more shares than he owns.
Thus, there is a ratio of calls written to stock owned. The most common ratio is the
2:1 ratio, whereby one owns 100 shares of the underlying stock and sells 2 calls. Note
that this type of position involves writing a number of naked call options as well as a
number of covered options. This resulting position has both downside risk, as does a
covered write, and unlimited upside risk, as does a naked write. The ratio write gen
erally wilI provide much larger profits than either covered writing or naked writing if
the underlying stock remains relatively unchanged during the life of the calls.
However, the ratio write has two-sided risk, a quality absent from either covered or
naked writing.
Generally, when an investor establishes a ratio write, he attempts to be neutral
in outlook regarding the underlying stock. This means that he writes the calls with
striking prices closest to the current stock price.
Example: A ratio write is established by buying 100 shares of XYZ at 49 and selling
two XYZ October 50 calls at 6 points each. If XYZ should decline in price and be
anywhere below 50 at October expiration, the calls will expire worthless and the
writer will make 12 points from the sale of the calls. Thus, even if XYZ drops 12
points to a price of 37, the ratio writer will break even. The stock loss of 12 points
146
Otapter 6: Ratio Call Writing 147
would be offset by a 12-point gain on the calls. As with any strategy in which calls are
sold, the maximum profit occurs at the striking price of the written calls at expiration.
In this example, if XYZ were at 50 at expiration, the calls would still expire worthless
for a 12-point gain and the writer would have a 1-point profit on his stock, which has
moved up from 49 to 50, for a total gain of 13 points. This position therefore has
ample downside protection and a relatively large potential profit. Should XYZ rise
above 50 by expiration, the profit will decrease and eventually become a loss if the
stock rises too far. To see this, suppose XYZ is at 63 at October expiration. The calls
will be at 13 points each, representing a 7-point loss on each call, because they were
originally sold for 6 points apiece. However, there would be a 14-poirit gain on the
stock, which has risen from 49 to 63. The overall net is a break-even situation at 63 -
a 14-point gain on the stock offset by 14 points ofloss on the options (7 points each).
Table 6-1 and Figure 6-1 summarize the profit and loss potential of this example at
October expiration. The shape of the graph resembles a roof with its peak located at
the striking price of the written calls, or 50. It is obvious that the position has both
large upside risk above 63 and large downside risk below 37. Therefore, it is imper
ative that the ratio writer plan to take follow-up action if the stock should move out
side these prices. Follow-up action is discussed later. If the stock remains within the
range 37 to 63, some profit will result before commission charges. This range
between the downside break-even point and the upside break-even point is called the
profit range.
This example represents essentially a neutral position, because the ratio writer
will make some profit unless the stock falls by more than 12 points or rises by more
than 14 points before the expiration of the calls in October. This is frequently an
attractive type of strategy to adopt because, normally, stocks do not move very far in
TABLE 6-1.
Profit and loss at October expiration.
XYZ Price at Stock Call Profit Total
Expiration Profit Price on Calls Profit
30 -$1,900 0 +$1,200 -$ 700
37 - 1,200 0 + 1,200 0
45 400 0 + 1,200 + 800
50 + 100 0 + 1,200 + 1,300
55 + 600 5 + 200 + 800
63 + 1,400 13 - 1,400 0
70 + 2,100 20 - 2,800 - 700
148
FIGURE 6-1.
Ratio write (2: 1 ).
+$1,300
C
0
e ·5.
X
LU
al
rn rn
.3
0
-e a.
Part II: Call Option Strategies
Stock Price at Expiration
a 3- or 6-month time period. Consequently, this strategy has a rather high probabili
ty of making a limited profit. The profit in this example would, of course, be reduced
by commission costs and margin interest charges if the stock is bought on margin.
Before discussing the specifics of ratio writing, such as investment required,
selection criteria, and follow-up action, it may be beneficial to counter two fairly
common objections to this strategy. The first objection, although not heard as fre
quently today as when listed options first began trading, is "Why bother to buy 100
shares of stock and sell 2 calls? You will be naked one call. Why not just sell one
naked call?" The ratio writing strategy and the naked writing strategy have very little
in common except that both have upside risk. The profit graph for naked writing
(Figure 5-1) bears no resemblance to the roof-shaped profit graph for a ratio write
(Figure 6-1). Clearly, the two strategies are quite different in profit potential and in
many other respects as well.
The second objection to ratio writing for the conservative investor is slightly
more valid. The conservative investor may not feel comfortable with a position that
has risk if the underlying stock moves up in price. This can be a psychological detri
ment to ratio writing: When stock prices are rising and everyone who owns stocks is
happy and making profits, the ratio writer is in danger of losing money. However, in
a purely strategic sense, one should be willing to assume some upside risk in
exchange for larger profits if the underlying stock does not rise heavily in price. The
Chapter 6: Ratio Call Writing 149
covered writer has upside protection all the way to infinity; that is, he has no upside
risk at all. This cannot be the mathematically optimum situ


riter is in danger of losing money. However, in
a purely strategic sense, one should be willing to assume some upside risk in
exchange for larger profits if the underlying stock does not rise heavily in price. The
Chapter 6: Ratio Call Writing 149
covered writer has upside protection all the way to infinity; that is, he has no upside
risk at all. This cannot be the mathematically optimum situation, because stocks
never rise to infinity. Rather, the ratio writer is engaged in a strategy that makes its
profits in a price range more in line with the way stocks actually behave. In fact, if
one were to try to set up the optimum strategy, he would want it to make its most
profits in line with the most probable outcomes for a stock's movement. Ratio writ
ing is such a strategy.
Figure 6-2 shows a simple probability curve for a stock's movement. It is most
likely that a stock will remain relatively unchanged and there is very little chance that
it will rise or fall a great distance. Now compare the results of the ratio writing strat
egy with the graph of probable stock outcomes. Notice that the ratio write and the
probability curve have their "peaks" in the same area; that is, the ratio write makes
its profits in the range of most likely stock prices, because there is only a small chance
that any stock will increase or decrease by a large amount in a fixed period of time.
The large losses are at the edges of the graph, where the probability curve gets very
low, approaching zero probability. It should be noted that these graphs show the prof
it and probability at expiration. Prior to expiration, the break-even points are closer
to the original purchase price of the stock because there will still be some time value
premium remaining on the options that were sold.
FIGURE 6-2.
Stock price probability curve overlaid on profit graph of ratio
write.
+$1,300 Probability
Curve
Stock Price
150 Part II: Call Option Strategies
INVESTMENT REQUIRED
The ratio writer has a combination of covered writes and naked writes. The margin
requirements for each of these strategies have been described previously, and the
requirements for a ratio writing strategy are the sum of the requirements for a naked
write and a covered write. Ratio writing is normally done in a margin account,
although one could technically keep the stock in a cash account.
Example: Ignoring commissions, the investment required can be computed as fol
lows: Buy 100 XYZ at 49 on 50% margin and sell 2 XYZ October 50 calls at 6 points
each (Table 6-2). The commissions for buying the stock and selling the calls would be
added to these requirements. A shorter formula (Table 6-3) is actually more desirable
to use. It is merely a combination of the investment requirements listed in Table 6-2.
In addition to the basic requirement, there may be minimum equity require
ments and maintenance requirements, since naked calls are involved. As these vary
from one brokerage firm to another, it is best for the ratio writer to check with his
broker to determine the equity and maintenance requirements. Again, since naked
calls are involved in ratio writing, there will be a mark to market of the position. If
the stock should rise in price, the investor will have to put up more collateral.
It is conceivable that the ratio writer would want to stay with his original posi
tion as long as the stock did not penetrate the upside break-even point of 63.
TABLE 6-2.
Investment required.
Covered writing portion (buy 100 XYZ and sell 1 call)
50% of stock price
Less premium received
Requirement for covered portion
Naked writing portion (sell 1 XYZ call)
20% of stock price
Less out-of-the-money amount
Plus call premium
Less premium received
Requirement for naked portion
Total requirement for ratio write
$2,450
600
$1,850
$ 980
100
+ 600
600
$ 880
$2,730
Cl,apter 6: Ratio Call Writing
TABLE 6-3.
Initial investment required for a ratio write.
70% of stock cost (XYZ = 49)
Plus naked call premiums
Less total premiums received
Plus or minus striking price differential
on naked calls
$3,430
+ 600
- 1,200
100
151
Total requirement $2,730 (plus commissions)
TABLE 6-4.
Collateral required with stock at upside break-even point of 63.
Covered writing requirement $1,850 (see Table 6-2)
20% of stock price (XYZ = 63) 1,260
Plus call premium
Less initial call premium received
Total requirement with XYZ at 63
1,400
600
$3,910
Therefore, he should allow for enough collateral to cover the eventuality of a move
to 63. Assuming the October 50 call is at 14 in this case, he would need $3,910 (see
Table 6-4). This is the requirement that the ratio writer should be concerned with,
not the initial collateral requirement, and he should therefore plan to invest $3,910
in this position, not $2,730 ( the initial requirement). Obviously, he only has to put up
$2,730, but from a strategic point of view, he should allow $3,910 for the position. If
the ratio writer does this with all his positions, he would not receive a margin call
even if all the stocks in his portfolio climbed to their upside break-even points.
SELECTION CRITERIA
To decide whether a ratio write is a desirable position, the writer must first determine
the break-even points of the position. Once the break-even points are known, the
writer can then decide if the position has a wide enough profit range to allow for
defensive action if it should become necessary. One simple way to determine if the
profit range is wide enough is to require that the next higher and lower striking prices
be within the profit range.
152 Part II: Call Option Strategies
Example: The writer is buying 100 XYZ at 49 and selling 2 October 50 calls at 6
points apiece. It was seen, by inspection, that the break-even points in the position
are 37 on the downside and 63 on the upside. A mathematical formula allows one to
quickly compute the break-even points for a 2:1 ratio


er and lower striking prices
be within the profit range.
152 Part II: Call Option Strategies
Example: The writer is buying 100 XYZ at 49 and selling 2 October 50 calls at 6
points apiece. It was seen, by inspection, that the break-even points in the position
are 37 on the downside and 63 on the upside. A mathematical formula allows one to
quickly compute the break-even points for a 2:1 ratio write.
Points of maximum profit = Strike price - Stock price + 2 x Call price
Downside break-even point = Strike price - Points of maximum profit
= Stock price - 2 x Call price
Upside break-even point = Strike price + Points of maximum profit
In this example, the points of maximum profit are 50 - 49 + 2 x 6, or 13. Thus,
the downside break-even point would be 37 (50 - 13) and the upside break-even
point would be 63 (50 + 13). These numbers agree with the figures determined ear
lier by analyzing the position.
This profit range is quite clearly wide enough to allow for defensive action
should the underlying stock rise to the next highest strikes of 55 or 60, or fall to the
next two lower strikes, at 45 and 40. In practice, a ratio write is not automatically a
good position merely because the profit range extends far enough. Theoretically,
one would want the profit range to be wide in relation to the volatility of the under
lying stock. If the range is wide in relation to the volatility and the break-even
points encompass the next higher and lower striking prices, a desirable position is
available. Volatile stocks are the best candidates for ratio writing, since their pre
miums will more easily satisfy both these conditions. A nonvolatile stock may, at
times, have relatively large premiums in its calls, but the resulting profit range may
still not be wide enough numerically to ensure that follow-up action could be taken.
Specific measures for determining volatility may be obtained from many data serv
ices and brokerage firms. Moreover, methods of computing volatility are present
ed later in the chapter on mathematical applications, and probabilities are further
addressed in the chapters on volatility trading.
Technical support and resistance levels are also important in establishing the
position. If both support and resistance lie within the profit range, there is a better
chance that the stock will remain within the range. A position should not necessarily
be rejected if there is not support and resistance within the profit range, but the
writer is then subjecting himself to a possible undeterred move by the stock in one
direction or the other.
The ratio writer is generally a neutral strategist. He tries to take in the most
time premium that he can to earn the premium erosion while the stock remains rel
atively unchanged. If one is more bullish on a particular stock, he can set up a 2:1
ratio write with out-of~the-money calls. This allows more room to the upside than to
the downside, and therefore makes the position slightly more bullish. Conversely, if
Cl,apter 6: Ratio Call Writing 153
one is more bearish on the underlying stock, he can write in-the-money calls in a 2:1
ratio.
There is another way to produce a slightly more bullish or bearish ratio write.
This is to change the ratio of calls written to stock purchased. This method is also
used to construct a neutral profit range when the stock is not close to a striking price.
Example: An investor is slightly bearishly inclined in his outlook for the underlying
stock, so he might write more than two calls for each 100 shares of stock purchased.
His position might be to buy 100 XYZ at 49 and sell 3 XYZ October 50 calls at 6 points
each. This position breaks even at 31 on the downside, because if the stock dropped
by 18 points at expiration, the call profits would amount to 18 points and would pro
duce a break-even situation. To the upside, the break-even point lies at 59½ for the
stock at expiration. Each call would be worth 9½ at expiration with the stock at 59½,
and each call would thus lose 3½ points, for a total loss of 10½ points on the three
calls. However, XYZ would have risen from 49 to 59½ - a 10½-point gain - therefore
producing a break-even situation. Again, a formula is available to aid in determining
the break-even point for any ratio.
Maximum profit= (Striking price - Stock price) x Round lots
purchased+ Number of calls written x Call price
D •d b ak Striking Maximum profit owns1 e re -even = - ------~~----price Number of round lots purchased
U .d b ak Striking Maximum profit psi e re -even = + price ( Calls written - Round lots purchased)
Note that in the case of a 2:1 ratio write, where the number of round lots purchased
equals 1 and the number of calls written equals 2, these formulae reduce to the ones
given earlier for the more common 2:1 ratio write. To verify that the formulae above
are correct, insert the numbers from the most recent example.
Example: Three XYZ October 50 calls at a price of 6 were sold against the purchase
of 100 XYZ at 49. The number of round lots purchased is 1.
Maximum profit = (50 - 49) x 1 + 3 x 6 = 19
Downside break-even= 50-19/1 = 31
Upside break-even= 50 + 19/(3 1) = 59½
In the 2:1 ratio writing example given earlier, the break-even points were 37 and 63.
The 3:1 write has lower break-even points of 31 and 59½, reflecting the more bear
ish posture on the underlying stock.
154 Part II: Call Option Strategies
A more bullish write is constructed by buying 200 shares of the underlying stock
and writing three calls. To quickly verify that this ratio (3:2) is more bullish, again use
49 for the stock price and 6 for the call price, and now assume that two round lots
were purchased.
Maximum profit= (50-49) x 2 + 3 x 6 = 20
Downside break-even = 50 - 20/2 = 40
Upside break-even= 50 + 20/(3 - 2) = 70
Thus, this ratio of 3 calls against 200 shares of stock has break-even points of 40 and
70, reflecting a more bullish posture on the underlyin


(3:2) is more bullish, again use
49 for the stock price and 6 for the call price, and now assume that two round lots
were purchased.
Maximum profit= (50-49) x 2 + 3 x 6 = 20
Downside break-even = 50 - 20/2 = 40
Upside break-even= 50 + 20/(3 - 2) = 70
Thus, this ratio of 3 calls against 200 shares of stock has break-even points of 40 and
70, reflecting a more bullish posture on the underlying stock.
A 2: 1 ratio may not necessarily be neutral. There is, in fact, a mathematically
correct way of determining exactly what a neutral ratio should be. The neutral ratio
is determined by dividing the delta of the written call into 1. Assume that the delta of
the XYZ October 50 call in the previous example is .60. Then the neutral ratio is
1.0/.60, or 5 to 3. This means that one might buy 300 shares and sell 5 calls. Using
the formulae above, the details of this position can be observed:
Maximum profit= (50 -49) x 3 + 5 x 6 = 33
Downside break-even = 50 - 33/3 = 39
Upside break-even = 50 + 33/(5 --3) = 66½
According to the mathematics of the situation, then, this would be a neutral position
initially. It is often the case that a 5:3 ratio is approximately neutral for an at-the
money call.
By now, the reader should have recognized a similarity between the ratio writ
ing strategy and the reverse hedge (or simulated straddle) strategy presented in
Chapter 4. The two strategies are the reverse of each other; in fact, this is how the
reverse hedge strategy acquired its name. The ratio write has a profit graph that looks
like a roof, while the reverse hedge has a profit graph that looks like a trough - the
roof upside down. In one strategy the investor buys stock and sells calls, while the
other strategy is just the opposite - the investor shorts stock and buys calls. Which
one is better? The answer depends on whether the calls are "cheap" or "expensive."
Even though ratio writing has limited profits and potentially large losses, the strate
gy will result in a profit in a large majority of cases, if held to expiration. However,
one may be forced to make adjustments to stock moves that occur prior to expiration.
The reverse hedge strategy, with its limited losses and potentially large profits, pro
vides profits only on large stock moves - a less frequent event. Thus, in stable mar
kets, the ratio writing strategy is generally superior. However, in times of depressed
option premiums, the reverse hedge strategy gains a distinct advantage. If calls are
Chapter 6: Ratio Call Writing 155
underpriced, the advantage lies with the buyer of calls, and that situation is inherent
in the reverse hedge strategy.
The summaries stated in the above paragraph are rather simplistic ones, refer
ring mostly to what one can expect from the strategies if they are held until expira
tion, without adjustment. In actual trading situations, it is much more likely that one
would have to make adjustments to the ratio write along the way, thus disturbing or
perhaps even eliminating the profit range. Such travails do not befall the reverse
hedge (simulated straddle buy). Consequently, when one takes into consideration the
stock movements that can take place prior to expiration, the ratio write loses some of
its attractiveness and the reverse hedge gains some.
THE VARIABLE RATIO WRITE
In ratio writing, one generally likes to establish the position when the stock is trading
relatively close to the striking price of the written calls. However, it is sometimes the
case that the stock is nearly exactly between two striking prices and neither the in
the-money nor the out-of-the-money call offers a neutral profit range. If this is the
case, and one still wants to be in a 2:1 ratio of calls written to stock owned, he can
sometimes write one in-the-money call and one out-of-the-money call against each
100 shares of common. This strategy, often termed a variable ratio write or trape
zoidal hedge, serves to establish a more neutral profit range.
Example: Given the following prices: XYZ common, 65; XYZ October 60 call, 8; and
XYZ October 70 call, 3.
If one were to establish a 2:1 ratio write with only the October 60's, he would
have a somewhat bearish position. His profit range would be 49 to 71 at expiration.
Since the stock is already at 65, this means that he would be allowing room for 16
points of downside movement and only 6 points on the upside. This is certainly not
neutral. On the other hand, if he were to attempt to utilize only the October 70 calls
in his ratio write, he would have a bullish position. This profit range for the October
70 ratio write would be 59 to 81 at expiration. In this case, the stock at 65 is too close
to the downside break-even point in comparison to its distance from the upside
break-even point.
A more neutral position can be established by buying 100 XYZ and selling one
October 60 and one October 70. This position has a profit range that is centered
about the current stock price. Moreover, the new position has both an upside and a
downside risk, as does a more normal ratio write. However, now the maximum prof
it can be obtained anywhere between the two strikes at expiration. To see this, note
156 Part II: Call Option Strategies
that if XYZ is anywhere between 60 and 70 at expiration, the stock will be called away
at 60 against the sale of the October 60 call, and the October 70 call will expire worth
less. It makes no difference whether the stock is at 61 or at 69; the same result will
occur. Table 6-5 and Figure 6-3 depict the results from this variable hedge at expira
tion. In the table, it is assumed that the option is bought back at parity to close the
position, but if the stock were called away, the results would be the same.
Note that the shape of Figure 6-3 is something like a trapezoid. This is the
source of the name "trapezoidal hedge," although the strategy is more commonly
known as a variable hedge or variable ratio write. The reader s


ge at expira
tion. In the table, it is assumed that the option is bought back at parity to close the
position, but if the stock were called away, the results would be the same.
Note that the shape of Figure 6-3 is something like a trapezoid. This is the
source of the name "trapezoidal hedge," although the strategy is more commonly
known as a variable hedge or variable ratio write. The reader should observe that the
maximum profit is indeed obtained if the stock is anywhere between the two strikes
at eiqJiration. The maximum profit potential in this position, $600, is smaller than the
maximum profit potential available from writing only the October 60's or only the
October 70's. However, there is a vastly greater probability of realizing the maximum
profit in a variable ratio write than there is of realizing the maximum profit in a nor
mal ratio write.
The break-even points for a variable ratio write can be computed most quickly
by first computing the maximum profit potential, which is equal to the time value
that the writer takes in. The break-even points are then computed directly by sub
tracting the points of maximum profit from the lower striking price to get the down
side break-even point and adding the points of maximum profit to the upper striking
price to arrive at the upside break-even point. This is a similar procedure to that fol
lowed for a normal ratio write:
TABLE 6-5.
Results at expiration of variable hedge.
XYZ Price at XYZ October 60 October 70 Total
Expiration Profit Profit Profit Profit
45 -$2,000 +$ 800 +$ 300 -$900
50 - 1,500 + 800 + 300 - 400
54 - 1,100 + 800 + 300 0
60 500 + 800 + 300 + 600
65 0 + 300 + 300 + 600
70 + 500 - 200 + 300 + 600
76 + 1,100 - 800 300 0
80 + 1,500 -$1,200 700 - 400
85 + 2,000 -1,700 - 1,200 - 900
Gopter 6: Ratio Call Writing
FIGURE 6-3.
Variable ratio write (trapezoidal hedge).
+$600
C:
i $
al
"' "' .3
5
;t:
e
0.
$0
Stock Price at Expiration
Points of maximum profit = Total option premiums + Lower
striking price - Stock price
Downside break-even point = Lower striking price - Points of
maximum profit
Upside break-even point = Higher striking price + Points of
maximum profit
157
Substituting the numbers from the example above will help to verify the formula.
The total points of option premium brought in were 11 (8 for the October 60 and 3
for the October 70). The stock price was 65, and the striking prices involved were 60
and 70.
Points of maximum profit = 11 + 60 - 65 = 6
Downside break-even point= 60- 6 = 54
Upside break-even point= 70 + 6 = 76
Thus, the break-even points as computed by the formula agree with Table 6-5 and
Figure 6-3. Nate that the formula applies only if the stock is initially between the two
striking prices and the ratio is 2:1. If the stock is above both striking prices, the for
mula is not correct. However, the writer should not be attempting to establish a vari
able ratio write with two in-the-money calls.
158 Part II: Call Option Strategies
FOLLOW-UP ACTION
Aside from closing the position completely, there are three reasonable approaches to
follow-up action in a ratio writing situation. The first, and most popular, is to roll the
written calls up if the stock rises too far, or to roll down if the stock drops too far. A
second method uses the delta of the written calls. The third follow-up method is to
utilize stops on the underlying stock to alter the ratio of the position as the stock
moves either up or down. In addition to these types of defensive follow-up action, the
investor must also have a plan in mind for taking profits as the written calls approach
expiration. These types of follow-up action are discussed separately.
ROLLING UP OR DOWN AS A DEFENSIVE ACTION
The reader should already be familiar with the definition of a rolling action: The cur
rently written calls are bought back and calls at a different striking price are written.
The ratio writer can use rolling actions to his advantage to readjust his position if the
underlying stock moves to the edges of his profit range.
The reason one of the selection criteria for a ratio write was the availability of
both the next higher and next lower striking prices was to facilitate the rolling actions
that might become necessary as a follow-up measure. Since an option has its great
est time premium when the stock price and the striking price are the same, one
would normally want to roll exactly at a striking price.
Example: A ratio writer bought 100 XYZ at 49 and sold two October 50 calls at 6
points each. Subsequently, the stock drops in price and the following prices exist:
XYZ, 40; XYZ October 50, l; and XYZ October 40, 4.
One would roll down to the October 40 calls by buying back the 2 October
50's that he is short and selling 2 October 40's. In so doing, he would reestablish a
somewhat neutral position. His profit on the buy-back of the October 50 calls
would be 5 points each - they were originally sold for 6 - and he would realize a
10-point gain on the two calls. This 10-point gain effectively reduces his stock cost
from 49 to 39, so that he now has the equivalent of the following position: long 100
XYZ at 39 and short 2 XYZ October 40 calls at 4. This adjusted ratio write has a
profit range of 31 to 49 and is thus a new, neutral position with the stock currently
at 40. The investor is now in a position to make profits if XYZ remains near this
level, or to take further defensive action if the stock experiences a relatively large
change in price again.
Defensive action to the upside - rolling up -works in much the same manner.
Chapter 6: Ratio Call Writing 159
Example: The initial position again consists of buying 100 XYZ at 49 and selling two
October 50 calls at 6. If XYZ then rose to 60, the following prices might exist: XYZ,
60; XYZ October 50, 11; and XYZ October 60, 6.
The ratio writer could thus roll this position up to reestablish a neutral profit
range. If


pside - rolling up -works in much the same manner.
Chapter 6: Ratio Call Writing 159
Example: The initial position again consists of buying 100 XYZ at 49 and selling two
October 50 calls at 6. If XYZ then rose to 60, the following prices might exist: XYZ,
60; XYZ October 50, 11; and XYZ October 60, 6.
The ratio writer could thus roll this position up to reestablish a neutral profit
range. If he bought back the two October 50 calls, he would take a 5-point loss on
each one for a net loss on the calls of 10 points. This would effectively raise his stock
cost by 10 points, to a price of 59. The rolled-up position would then be long 100 XYZ
at 59 and short 2 October 60 calls at 6. This new, neutral position has a profit range
of 47 to 73 at October expiration.
In both of the examples above, the writer could have closed out the ratio write
at a very small profit of about 1 point before commissions. This would not be advis
able, because of the relatively large stock commissions, unless he expects the stock to
continue to move dramatically. Either rolling up or rolling down gives the writer a
fairly wide new profit range to work with, and he could easily expect to make more
than 1 point of profit if the underlying stock stabilizes at all.
Having to take rolling defensive action immediately after the position is estab
lished is the most detrimental case. If the stock moves very quickly after having set
up the position, there will not be much time for time value premium erosion in the
written calls, and this will make for smaller profit ranges after the roll is done. It may
be useful to use technical support and resistance levels as keys for when to take
rolling action if these levels are near the break-even points and/or striking prices.
It should be noted that this method of defensive action - rolling at or near strik
ing prices - automatically means that one is buying back little or no time premium
and is selling the greatest amount of time premium currently available. That is, if the
stock rises, the call's premium will consist mostly of intrinsic value and very little of
time premium value, since it is substantially in-the-money. Thus, the writer who rolls
up by buying back this in-the-money call is buying back mostly intrinsic value and is
selling a call at the next strike. This newly sold call consists mostly of time value. By
continually buying back "real" or intrinsic value and by selling "thin air" or time value,
the writer is taking the optimum neutral action at any given time.
If a stock undergoes a dramatic move in one direction or the other, the ratio
writer will not be able to keep pace with the dramatic movement by remaining in the
same ratio.
Example: If XYZ was originally at 49, but then undergoes a fairly straight-line move
to 80 or 90, the ratio writer who maintains a 2:1 ratio will find himself in a deplorable
situation. He will have accumulated rather substantial losses on the calls and will not
be able to compensate for these losses by the gain in the underlying stock. A similar
160 Part II: Call Option Strategies
situation could arise to the downside. If:X'YZ were to plunge from 49 to 20, the ratio
writer would make a good deal of profit from the calls by rolling down, but may still
have a larger loss in the stock itself than the call profits can compensate for.
Many ratio writers who are large enough to diversify their positions into a num
ber of stocks will continue to maintain 2:1 ratios on all their positions and will simply
close out a position that has gotten out of hand by running dramatically to the upside
or to the downside. These traders believe that the chances of such a dramatic move
occurring are small, and that they will take the infrequent losses in such cases in
order to be basically neutral on the other stocks in their portfolios.
There is, however, a way to combat this sort of dramatic move. This is done by
altering the ratio of the covered write as the stock moves either up or down. For
example, as the underlying stock moves up dramatically in price, the ratio writer can
decrease the number of calls outstanding against his long stock each time he rolls.
Eventually, the ratio might decrease as far as 1:1, which is nothing more than a cov
ered writing situation. As long as the stock continues to move in the same upward
direction, the ratio writer who is decreasing his ratio of calls outstanding will be giv
ing more and more weight to the stock gains in the ratio write and less and less weight
to the call losses. It is interesting to note that this decreasing ratio effect can also be
produced by buying extra shares of stock at each new striking price as the stock
moves up, and simultaneously keeping the number of outstanding calls written con
stant. In either case, the ratio of calls outstanding to stock owned is reduced.
When the stock moves down dramatically, a similar action can be taken to
increase the number of calls written to stock owned. Normally, as the stock falls, one
would sell out some of his long stock and roll the calls down. Eventually, after the
stock falls far enough, he would be in a naked writing position. The idea is the same
here: As the stock falls, more weight is given to the call profits and less weight is given
to the stock losses that are accumulating.
This sort of strategy is more oriented to extremely large investors or to firm
traders, market-makers, and the like. Commissions will be exorbitant if frequent rolls
are to be made, and only those investors who pay very small commissions or who have
such a large holding that their commissions are quite small on a percentage basis will
be able to profit substantially from such a strategy.
ADJUSTING WITH THE DELTA
The delta of the written calls can be used to determine the correct ratio to be used in
this ratio-adjusting defensive strategy. The basic idea is to use the call's delta to
remain as neutral as possible at