lize option purchases of 1
month, 3 months, and 6 months, preferably each generated by a separate computer
analysis similar to the one described earlier. He will know how much of his total
assets he can place into purchases of each holding period, because he will know his
annualized risk.
Example: Suppose that a very large investor, or pool of investors, has $1 million com
mitted to this T-bill/option strategy. Further, suppose ½ of 1 % of the money is to be
committed to 30-day option purchases with the idea of reinvesting every 30 days.
Similarly, ½ of 1 % is to be placed in 90-day purchases and 1 % in 180-day purchases.
The annualized risk is 10%:
Total annualized risk = ½% x 360 + ½% x 360 + 1 % x 360
30 90 180
= .06 + .02 + .02 = 10%
418 Part IV: Additional Considerations
With asset.s of $1 million, this means that $.5,000 would be committed to 30-day pur
chases; $.5,000 to 90-day purchases; and $10,000 to 180-day purchases. This money
would be reinvested in similar quantities at the end of each holding period.
RISK ADJUSTMENT
The subject of adjusting the ratio to constantly reflect 10% risk must be addressed at
the end of each holding period. Although it is correct for the investor to keep his per
centage commitments constant, he must not be deluded into automatically reinvest
ing the same amount of dollars each time.
Example: At the end of 30 days, the value of the entire portfolio, including potential
option profits and losses, and interest earned, was down to $990,000. Then only ½ of
1 % of that amount should be invested in the next 30-day purchase ($4,9.50).
By operating in this manner - first computing the annualized risk and balanc
ing it through predetermined percentage commitments to holding periods of various
lengths; and second, readjusting the actual dollar commitment at the end of each
holding period - the overall risk/reward ratios v,ill be kept close to the levels
described in the earlier, simple desciiption of this strategy. This may require a rela
tively large amount of work on the part of the strategist, but large portfolios usually
do require work.
The smaller investor does not have the luxury of such complete diversification,
but he also does not have to adjust his total position as often.
Example: An investor decided to commit $.50,000 to this strategy. Since there is a
1,200% annualized risk in 30-day purchases, it does not make much sense to even
consider purchases that are so short-term for assets of this size. Rather, he might
decide to commit 1 % of his assets to a 90-day purchase and 3% to a 180-day pur
chase. In dollar amounts, this would be $.500 in a 90-day option and $1,.500 in 180-
day options. Admittedly, this does not leave much room for diversification, but to risk
more in the short-term purchases would expose the investor to too much risk. In
actual practice, this investor would probably just invest .5% of his assets in 180-day
purchases, also a 10% annualized risk. This would mean that he could operate with
only one option buyer's analysis (the 180-day one) and could place $2,.500 into selec
tions from that list.
His adjustments of the assets committed to option purchases could not be done
as frequently as the large investor, because of the commissions involved. He certain
ly would have to adjust every 180 days, but might prefer to do so more frequently -
perhaps every 90 days - to be able to space his 180-day commitments over different
Chapter 26: Buying Options and Treasury Bills 419
option expiration cycles. It should also be pointed out that T-bills can be bought and
sold only in amounts of at least $10,000 and in increments of $5,000 thereafter. That
is, one could buy or sell $10,000 or $15,000 or $20,000 or $25,000, and so on, but
could not buy or sell $5,000 or $8,000 or $23,000 in T-bills. This is of little concern
to the investor with $1 million, since it takes only a fraction of a percentage of his
assets to be able to round up to the next $5,000 increment for a T-bill sale or pur
chase. However, the medium-sized investor with a $50,000 portfolio might run into
problems. While short-term T-bills do represent the best risk-free investment, the
medium-sized investor might want to utilize one of the no-load, money market funds
for at least part of his income-bearing assets. Such funds have only slightly more risk
than T-bills and offer the ability to deposit and withdraw in any amount.
The truly small investor might be feeling somewhat left out. Could it be possi
ble to operate this strategy with a very small amount of money, such as $5,000? Yes
it could, but there are several disadvantages.
Example: It would be extremely difficult to keep the risk level down to 10% annual
ly with only $5,000. For example, 5% of the money invested every 180 days is only
$250 in each investment period. Since the option selection process that is described
will tend to select at- or slightly out-of-the-money calls, many of these will cost more
than 2½ points for one option. The small investor might decide to raise his risk level
slightly, although the risk level should never exceed 20% annually, no matter how
small the actual dollar investment. To exceed this risk level would be to completely
defeat the purpose of the fixed-income/option purchase strategy. Obviously, this
small investor cannot buy T-bills, for his total investable assets are below the mini
mum $10,000 purchase level. He might consider utilizing one of the money market
funds. Clearly, an investor of this small magnitude is operating at a double disadvan
tage: His small dollar commitment to option purchases may preclude him from buy
ing some of the more attractive items; and his fixed-income portion will be earning a
smaller percentage interest rate than that of the larger investor who is in T-bills or
some other form of relatively risk-free, income-bearing security. Consequently, the
small investor should carefully consider his finan


disadvan
tage: His small dollar commitment to option purchases may preclude him from buy
ing some of the more attractive items; and his fixed-income portion will be earning a
smaller percentage interest rate than that of the larger investor who is in T-bills or
some other form of relatively risk-free, income-bearing security. Consequently, the
small investor should carefully consider his financial capability and willingness to
adhere strictly to the criteria of this strategy before actually committing his dollars.
It may appear to the reader that the actual dollars being placed at risk in each
option purchase are quite small in these examples. In fact, they are rather small, but
they have been shown to represent 10% annualized risk. An assumption was made in
these examples that the risk in each option purchase was 100% for the holding peri
od. This is a fairly restrictive assumption and, if it were lessened, would allow for a
larger dollar commitment in each holding period. It is difficult and dangerous, how-
420 Part IV: Additional Considerations
ever, to assume that the risk in holding a call option is less than 100% in a holding
period as short as 30 days. The strategist may feel that he is disciplined enough to sell
out when losses occur and thereby hold the risk to less than 100%. Alternatively,
mathematical analysis will generally show that the expected loss in a fixed time peri
od is less than 100%. One can also mitigate the probability oflosing all of his money
in an option purchase by buying in-the-money options. While they are more expen
sive, of course, they do have a larger probability of having some residual worth even
if the underlying stock doesn't rise to the trader's expectations. Adhering to any of
these criteria can lead one to become too aggressive and therefore be too heavily
committed to option purchases. It is far safer to stick to the simpler, more restrictive
assumption that one is risking all his money, even over a fairly short holding period,
when he buys an option.
AVOIDING EXCESSIVE RISK
One final word of caution must be inserted. The investor should not attempt to
become 'Janey" with the income-bearing portion of his assets. T-bills may appear to
be too "tame" to some investors, and they consider using GNMA's (Government
National Mortgage Association certificates), corporate bonds, convertible bonds, or
municipal bonds for the fixed-income portion. Although the latter securities may
yield a slightly higher return than do T-bills, they may also prove to be less liquid and
they quite clearly involve more risk than a short-term T-bill does. Moreover, some
investors might even consider placing the balance of their funds in other places, such
as high-yield stock or covered call writing. While high-yield stock purchases and cov
ered call writing are conservative investments, as most investments go, they would
have to be considered very speculative in comparison to the purchase of a 90-day T
hill. In this strategy, the profit potential is represented by the option purchases. The
yield on short-term T-bills will quite adequately offset the risks. One should take
great care not to attempt to generate much higher yields on the fixed-income portion
of his investment, for he may find that he has assumed risk with the portion of his
money that was not intended to have any risk at all.
A fair amount of rigorous mathematical work has been done on the evaluation
of this strategy. The theoretical papers are quite favorable. Scholars have generally
considered only the purchase of call options as the risk portion of the strategy.
Obviously, the strategist is quite free to purchase put options without harming the
overall intent of the strategy. When only call options are purchased, both static and
down markets harm the performance. If some puts are included in the option pur
chases, only static markets could produce the worst results.
Chapter 26: Buying Options and Treasury Bills 421
There are trade-offs involved as well. If, after purchasing the options, the mar
ket experiences a substantial rally, that portion of the option purchase money that is
devoted to put option purchases will be lost. Thus, the combination of both put and
call purchases would do better in a down market than a strategy of buying only calls,
but would do worse in an up market. In a broad sense, it makes sense to include some
put purchases if one has the funds to diversify, since the frequency of market rallies
is smaller than the combined frequency of market rallies and declines. The investor
who owns both puts and calls will be able to profit from substantial moves in either
direction, because the profitable options will be able to overcome the limited losses
on the unprofitable ones.
SUMMARY
In summary, the T-bill/option strategy is attractive from several viewpoints. Its true
advantage lies in the fact that it has predefined risk and does not have a limit on
potential profits. Some theorists claim it is the best strategy available, if the options
are "underpriced" when they are purchased. The strategy is also relatively simple to
operate. It is not necessary to have a margin account or to compute collateral require
ments for uncovered options; the strategy can be operated completely from a cash
account. There are no spreads involved, nor is it necessary to worry about details such
as early assignment (because there are no short options in this strategy).
The investor who is going to employ this strategy, however, must not be delud
ed into thinking that it is so simple that it does not take any work at all. The concepts
and application of annualized risk management are very important to the strategy. So
are the mechanics of option buying - particularly a disciplined, rational approach to
the selection of which calls and/or puts to buy. Consequently, this strategy is suitable
only for the investor who has both the time and the discipline to

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


at it is so simple that it does not take any work at all. The concepts
and application of annualized risk management are very important to the strategy. So
are the mechanics of option buying - particularly a disciplined, rational approach to
the selection of which calls and/or puts to buy. Consequently, this strategy is suitable
only for the investor who has both the time and the discipline to operate it correctly.
Arbitrage
Arbitrage in the securities market often connotes that one is buying something in
one marketplace and selling it in another marketplace, for a small profit with little
or no risk. For example, one might buy XYZ at 55 in New York and sell it at 55¼ in
Chicago. Arbitrage, especially option arbitrage, involves a far wider range of tactics
than this simple example. Many of the option arbitrage tactics involve buying one
side of an equivalent position and simultaneously selling the other side. Since there
is a large number of equivalent strategies, many of which have been pointed out in
earlier chapters, a full-time option arbitrageur is able to construct a rather large
number of positions, most of which have little or no risk. The public customer can
not generally operate arbitrage-like strategies because of the commission costs
involved. Arbitrageurs are firm traders or floor traders who are trading through a
seat on the appropriate securities exchange, and therefore have only minimal trans
action costs.
The public customer can benefit from understanding arbitrage techniques, even
ifhe does not personally employ them. The arbitrageurs perform a useful function in
the option marketplace, often making markets where a market might not otherwise
exist (deeply in-the-money options, for example). This chapter is directed at the
strategist who is actually going to be participating in arbitrage. This should not be
confusing to the public customer, for he will better understand the arbitrage strate
gies if he temporarily places himself in the arbitrageur's shoes.
It is virtually impossible to perform pure arbitrage on dually listed options; that
is, to buy an option on the CBOE and sell it on the American exchange in New York
for a profit. Such discrepancies occur so infrequently and in such small size that an
option arbitrageur could never hope to be fully employed in this type of simple arbi
trage. Rather, the more complex forms of arbitrage described here are the ones on
which he would normally concentrate.
422
Chapter 27: Arbitrage 423
BASIC PUT AND CALL ARBITRAGE ("DISCOUNTING")
The basic call and the basic put arbitrages are two of the simpler forms of option arbi
trage. In these situations, the arbitrageur attempts to buy the option at a discount
while simultaneously taking an opposite position in the underlying stock. He can then
exercise his option immediately and make a profit equal to the amount of the discount.
The basic call arbitrage is described first. This was also outlined in Chapter 1,
under the section on anticipating exercise.
Example: XYZ is trading at 58 and the XYZ July 50 call is trading at 7¾. The call is
actually at a discount from parity of ¼ point. Discount options generally either are
quite deeply in-the-money or have only a short time remaining until expiration, or
both. The call arbitrage would be constructed by:
1. buying the call at 7¾;
2. selling the stock at 58;
3. exercising the call to buy the stock at 50.
The arbitrageur would make 8 points of profit from the stock, having sold it at 58 and
bought it back at 50 via the option exercise. He loses the 7¾ points that he paid for
the call option, but this still leaves him with an overall profit of¼ point. Since he is
a member of the exchange, or is trading the seat of an exchange member, the arbi
trageur pays only a small charge to transact the trades.
In reality, the stock is not sold short per se, even though it is sold before it is
bought. Rather, the position is designated, at the time of its inception, as an "irrevo
cable exercise." The arbitrageur is promising to exercise the call. As a result, no
uptick is required to sell the stock.
The main goal in the call arbitrage is to be able to buy the call at a discount from
the price at which the stock is sold. The differential is the profit potential of the arbi
trage. The basic put arbitrage is quite similar to the call arbitrage. Again, the arbi
trageur is looking to buy the put option at a discount from parity. The put arbitrage
is completed with a stock purchase and option exercise.
Example: XYZ is at 58 and the XYZ July 70 put is at 11 ¾. With the put at ¼ discount
from parity, the arbitrageur might take the following action:
1. Buy put at 11 ¾.
2. Buy stock at 58.
3. Exercise put to sell stock at 70.
424 Part IV: Additional Considerations
The stock transaction is a 12-point profit, since the stock was bought at 58 and is sold
at 70 via the put exercise. The cost of the put - 11 ¾ points - is lost, but the arbi
trageur still makes ¼-point profit. Again, this profit is equal to the arrwunt of the dis
count in the option when the position was established. Generally, the arbitrageur
would exercise his put option immediately, because he would not want to tie up his
capital to carry the long stock. An exception to this would be if the stock were about
to go ex-dividend. Dividend arbitrage is discussed in the next section.
The basic call and put arbitrages may exist at any time, although they will be
more frequent when there is an abundance of deeply in-the-money options or when
there is a very short time remaining until expiration. After market rallies, the call
arbitrage may be easier to establish; after market declines, the put arbitrage will be
easier to find. As an expiration date draws near, an option that is even slightly in-the
money on the last day or two of trading could be a candidate for discount arbitrage.
The reason that this is true is that public buying interest


very short time remaining until expiration. After market rallies, the call
arbitrage may be easier to establish; after market declines, the put arbitrage will be
easier to find. As an expiration date draws near, an option that is even slightly in-the
money on the last day or two of trading could be a candidate for discount arbitrage.
The reason that this is true is that public buying interest in the option will normally
wane. The only public buyers would be those who are short and want to cover. Many
covered writers will elect to let the stock be called away, so that will reduce even fur
ther the buying potential of the public. This leaves it to the arbitrageurs to supply the
buying interest.
The arbitrageur obviously wants to establish these positions in as large a size as
possible, since there is no risk in the position if it is established at a discount. Usually,
there will be a larger market for the stock than there will be for the options, so the
arbitrageur spends more of his time on the option position. However, there may be
occasions when the option markets are larger than the corresponding stock quotes.
When this happens, the arbitrageur has an alternative available to him: He might sell
an in-the-money option at parity rather than take a stock position.
Example: XYZ is at 58 and the XYZ July 50 call is at 7¾. These are the same figures
as in the previous example. Furthermore, suppose that the trader is able to buy more
options at 7¾ than he is able to sell stock at 58. If there were another in-the-money
call that could be sold at parity, it could be used in place of the stock sale. For exam
ple, if the XYZ July 40 call could be sold at 18 (parity), the arbitrage could still be
established. Ifhe is assigned on the July 40 that he is short, he will then be short stock
at a net price of 58 - the striking price of 40, plus the 18 points that were brought in
from the sale of the July 40 call. Thus, the sale of the in-the-money call at parity is
equivalent to shorting the stock for the arbitrage purpose.
In a similar manner, an in-the-money put can be used in the basic put arbitrage.
Example: With XYZ at 58 and the July 70 put at 11¾, the arbitrage could be estab
lished. However, if the trader is having trouble buying enough stock at 58, he might
Chapter 27: Arbitrage 425
be able to use another in-the-money put. Suppose the XYZ July 80 put could be sold
at 22. This would be the same as buying the stock at 58, because if the put were
assigned, the arbitrageur would be forced to buy stock at 80 - the striking price - but
his net cost would be 80 minus the 22 points he received from the sale of the put, for
a net cost of 58. Again, the arbitrageur is able to use the sale of a deeply in-the-money
option as a substitute for the stock trade.
The examples above assumed that the arbitrageur sold a deeper in-the-money
option at parity. In actual practice, if an in-the-money option is at a discount, an even
deeper in-the-money option will generally be at a discount as well. The arbitrageur
would normally try to sell, at parity, an option that was less deeply in-the-money than
the one he is discounting.
In a broader sense, this technique is applicable to any arbitrage that involves a
stock trade as part of the arbitrage, except when the dividend in the stock itself is
important. Thus, if the arbitrageur is having trouble buying or selling stock as part of
his arbitrage, he can always check whether there is an in-the-money option that could
be sold to produce a position equivalent to the stock position.
DIVIDEND ARBITRAGE
Dividend arbitrage is actually quite similar to the basic put arbitrage. The trader can
lock in profits by buying both the stock and the put, then waiting to collect the divi
dend on the underlying stock before exercising his put. In theory, on the day before
a stock goes ex-dividend, all puts should have a time value premium at least as large
as the dividend amount. This is true even for deeply in-the-money puts.
Example: XYZ closes at 45 and is going to go ex-dividend by $1 tomorrow. Then a
put with striking price of 50 should sell for at least 6 points ( the in-the-money amount
plus the amount of the dividend), because the stock will go ex-dividend and is expect
ed to open at 44, six points in-the-money.
If, however, the put' s time value premium should be less than the amount of the
dividend, the arbitrageur can take a riskless position. Suppose the XYZ July 50 put is
selling for 5¾, with the stock at 45 and about to go ex-dividend by $1. The arbi
trageur can take the following steps:
1. Buy the put at 5¼.
2. Buy the stock at 45.
3. Hold the put and stock until the stock goes ex-dividend (1 point in this case).
4. Exercise the put to sell the stock at 50.
426 Part IV: Additional Considerations
The trader makes 5 points from the stock trade, buying it at 45 and selling it at 50 via
the put exercise, and also collects the I-point dividend, for a total inflow of 6 points.
Since he loses the 5¾ points he paid for the put, his net profit is ¼ point.
Far in advance of the ex-dividend date, a deeply in-the-money put may trade
very close to parity. Thus, it would seem that the arbitrageur could "load up" on these
types of positions and merely sit back and wait for the stock to go ex-dividend. There
is a flaw in this line of thinking, however, because the arbitrageur has a carrying cost
for the rrwney that he must tie up in the long stock. This carrying cost fluctuates with
short-term interest rates.
Example: If the current rate of carrying charges were 6% annually, this would be
equivalent to 1 % every 2 months. If the arbitrageur were to establish this example
position 2 months prior to expiration, he would have a carrying cost of .5075 point.
(His total outlay is 50¾ points, 45 for the stock and 5¾ for the options, and he would
pay 1 % to carry that stock and option for the two months until the ex-dividend dat


rate of carrying charges were 6% annually, this would be
equivalent to 1 % every 2 months. If the arbitrageur were to establish this example
position 2 months prior to expiration, he would have a carrying cost of .5075 point.
(His total outlay is 50¾ points, 45 for the stock and 5¾ for the options, and he would
pay 1 % to carry that stock and option for the two months until the ex-dividend date.)
This is more than ½ point in costs - clearly more than the ¼-point potential profit.
Consequently, the arbitrageur must be aware of his carrying costs if he attempts to
establish a dividend arbitrage well in advance of the ex-dividend date. Of course, if
the ex-dividend date is only a short time away, the carrying cost has little effect, and
the arbitrageur can gauge the profitability of his position mostly by the amount of the
dividend and the time value premium in the put option.
The arbitrageur should note that this strategy of buying the put and buying the
stock to pick up the dividend might have a residual, rather profitable side effect. If
the underlying stock should rally up to or above the striking price of the put, there
could be rather large profits in this position. Although it is not likely that such a rally
could occur, it would be an added benefit if it did. Even a rather small rally might
cause the put to pick up some time premium, allowing the arbitrageur to trade out
his position for a profit larger than he could have made by the arbitrage discount.
This form of arbitrage occasionally lends itself to a limited form of risk arbi
trage. Risk arbitrage is a strategy that is designed to lock in a profit if a certain event
occurs. If that event does not occur, there could be a loss (usually quite limited);
hence, the position has risk. This risk element differentiates a risk arbitrage from a
standard, no-risk arbitrage. Risk arbitrage is described more fully in a later section,
but the following example concerning a special dividend is one form of risk arbitrage.
Example: XYZ has been known to declare extra, or special, dividends with a fair
amount of regularity. There are several stocks that do so - Eastman Kodak and
General Motors, for example. In this case, assume that a hypothetical stock, XYZ, has
Chapter 27: Arbitrage 427
generally declared a special dividend in the fourth quarter of each year, but that its
normal quarterly rate is $1.00 per share. Suppose the special dividend in the fourth
quarter has ranged from an extra $1.00 to $3.00 over the past five years. If the arbi
trageur were willing to speculate on the size of the upcoming dividend, he might be
able to make a nice profit. Even if he overestimates the size of the special dividend,
he has a limited loss. Suppose XYZ is trading at 55 about two weeks before the com
pany is going to announce the dividend for the fourth quarter. There is no guarantee
that there will, in fact, be a special dividend, but assume that XYZ is having a rela
tively good year profitwise, and that some special dividend seems forthcoming.
Furthermore, suppose the January 60 put is trading at 7½. This put has 2½ points of
time value premium. If the arbitrageur buys XYZ at 55 and also buys the January 60
put at 7½, he is setting up a risk arbitrage. He will profit regardless of how far the
stock falls or how much time value premium the put loses, if the special dividend is
larger than $1.50. A special dividend of $1.50 plus the regular dividend of $1.00
would add up to $2.50, or 2½ points, thus covering his risk in the position. Note that
$1.50 is in the low end of the $1.00 to $3.00 recent historical range for the special
dividends, so the arbitrageur might be tempted to speculate a little by establishing
this dividend risk arbitrage. Even if the company unexpectedly decided to declare no
special dividend at all, it would most likely still pay out the $1.00 regular dividend.
Thus, the most that the arbitrageur would lose would be 1 ½ points (his 2½-point ini
tial time value premium cost, less the 1-point dividend). In actual practice, the stock
would probably not change in price by a great deal over the next two weeks (it is a
high-yield stock), and therefore the January 60 put would probably have some time
value premium left in it after the stock goes ex-dividend. Thus, the practical risk is
even less than 1 ½ points.
While these types of dividend risk arbitrage are not frequently available, the
arbitrageur who is willing to do some homework and also take some risk may find that
he is able to put on a position with a small risk and a profitability quite a bit larger
than the normal discount dividend arbitrage.
There is really not a direct form of dividend arbitrage involving call options. If
a relatively high-yield stock is about to go ex-dividend, holders of the calls will
attempt to sell. They do so because the stock will drop in price, thereby generally
forcing the call to drop in price as well, because of the dividend. However, the hold
er of a call does not receive cash dividends and therefore is not willing to hold the
call if the stock is going to drop by a relatively large amount (perhaps ¾ point or
more). The effect of these call holders attempting to sell their calls may often pro
duce a discount option, and therefore a basic call arbitrage may be possible. The arbi
trageur should be careful, however, if he is attempting to arbitrage a stock that is
428 Part IV: Additional Considerations
going ex-dividend on the following day. Since he must sell the stock to set up the arbi
trage, he cannot afford to wind up the day being short any stock, for he will then have
to pay out the dividend the following day (the ex-dividend date). Furthermore, his
records must be accurate, so that he exercises all his long options on the day before
the ex-dividend date. If the arbitrageur is careless and is still short some stock on the
ex-date, he may find that the dividend he has to pay out wipes


not afford to wind up the day being short any stock, for he will then have
to pay out the dividend the following day (the ex-dividend date). Furthermore, his
records must be accurate, so that he exercises all his long options on the day before
the ex-dividend date. If the arbitrageur is careless and is still short some stock on the
ex-date, he may find that the dividend he has to pay out wipes out a large portion of
the discount profits he has established.
CONVERSIONS AND REVERSALS
In the introductory material on puts, it was shown that put and call prices are relat
ed through a process known as conversion. This is an arbitrage process whereby a
trader may sometimes be able to lock in a profit at absolutely no risk. A conversion
consists of buying the underlying stock, and also buying a put option and selling a
call option such that both options have the same terms. This position will have a
locked-in profit if the total cost of the position is less than the striking price of the
options.
Example: The following prices exist:
XYZ common, 55;
XYZ January 50 call, 6½; and
XYZ January 50 put, 1.
The total cost of this conversion is 49½ - 55 for the stock, plus 1 for the put, less 6½
for the call. Since 49½ is less than the striking price of 50, there is a locked-in profit
on this position. To see that such a profit exists, suppose the stock is somewhere
above 50 at expiration. It makes no difference how far above 50 the stock might be;
the result will be the same. With the stock above 50, the call will be assigned and the
stock will be sold at a price of 50. The put will expire worthless. Thus, the profit is½
point, since the initial cost of the position was 49½ and it can eventually be liquidat
ed for a price of 50 at expiration. A similar result occurs if XYZ is below 50 at expi
ration. In this case, the trader would exercise his put to sell his stock at 50, and the
call would expire worthless. Again, the position is liquidated for a price of 50 and,
since it only cost 49½ to establish, the same ½-point profit can be made. No matter
where the stock is at expiration, this position has a locked-in-profit of½ point.
This example is rather simplistic because it does not include two very important
factors: the possible dividend paid by the stock and the cost of carrying the position
Chapter 27: Arbitrage 429
until expiration. The inclusion of these factors complicates things somewhat, and its
discussion is deferred momentarily while the companion strategy, the reversal, is
explained.
A reversal (or reverse conversion, as it is sometimes called) is exactly the oppo
site of a conversion. In a reversal, the trader sells stock short, sells a put, and buys a
call. Again, the put and call have the same terms. A reversal will be profitable if the
initial credit ( sale price) is greater than the striking price of the options.
Example: A different set of prices will be used to describe a reversal:
XYZ common, 55;
XYZ January 60 call, 2; and
XYZ January 60 put, 7½.
The total credit of the reversal is 60½ - 55 from the stock sale, plus 7½ from the put
sale, less the 2-point cost of the call. Since 60½ is greater than the striking price of
the options, 60, there is a locked-in profit equal to the differential of½ point. To ver
ify this, first assume that XYZ is anywhere below 60 at January expiration. The put
will be assigned - stock is bought at 60 - and the call will expire worthless. Thus, the
reversal position is liquidated for a cost of 60. A ½-point profit results since the orig
inal sale value ( credit) of the position was 60½. On the other hand, if XYZ were above
60 at expiration, the trader would exercise his call, thus buying stock at 60, and the
put would expire worthless. Again, he would liquidate the position at a cost of 60 and
would make a ½-point profit.
Dividends and carrying costs are important in reversals, too; these factors are
addressed here. The conversion involves buying stock, and the trader will thus
receive any dividends paid by the stock during the life of the arbitrage. However, the
converter also has to pay out a rather large sum of money to set up his arbitrage, and
must therefore deduct the cost of carrying the position from his potential profits. In
the example above, the conversion position cost 49½ points to establish. If the trad
er's cost of money were 6% annually, he would thus lose .06/12 x 49½, or .2475 point
per month for each month that he holds the position. This is nearly ¼ of a point per
month. Recall that the potential profit in the example is ½ point, so that if one held
the position for more than two months, his carrying costs would wipe out his profit.
It is extremely important that the arbitrageur compute his carrying costs accurately
prior to establishing any conversion arbitrage.
If one prefers formulae, the profit potentials of a conversion or a reversal can
be stated as:
430 l'art IV: Additional Considerations
Conversion profit = Striking price + Call price - Stock price - Put price +
Dividends to be received - Carrying cost of position
Reversal profit = Stock + Put - Strike - Call + Carrying cost - Dividends
Note that during any one trading day, the only items in the formulae that can change
are the prices of the securities involved. The other items, dividends and carrying cost,
are fixed for the day. Thus, one could have a small computer program prepared that
listed the fixed charges on a particular stock for all the strikes on that stock.
Example: It is assumed that XYZ stock is going to pay a ½-point dividend during the
life of the position, and that the position will have to be held for three months at a
carrying cost of 6% per year. If the arbitrageur were interested in a conversion with
a striking price of 50, his fixed cost would be:
Conversion fixed cost = Carrying rate x Time held x Striking price -
Dividend to be received
= .06 X 3/12 X 50 - ½
= .75- ½ = .25, or¼ point


y a ½-point dividend during the
life of the position, and that the position will have to be held for three months at a
carrying cost of 6% per year. If the arbitrageur were interested in a conversion with
a striking price of 50, his fixed cost would be:
Conversion fixed cost = Carrying rate x Time held x Striking price -
Dividend to be received
= .06 X 3/12 X 50 - ½
= .75- ½ = .25, or¼ point
The arbitrageur would know that if the profit potential, computed in the simplistic
manner using only the prices of the securities involved, was greater than ¼ point, he
could establish the conversion for an eventual profit, including all costs. Of course,
the carrying costs would be different if the striking price were 40 or 60, so a com
puter printout of all the possible striking prices on each stock would be useful in
order for the trader to be able to refer quickly to a table of his fixed costs each day.
MORE ON CARRYING COSTS
The computation of carrying costs can be made more involved than the simple
method used above. Simplistically, the carrying cost is computed by multiplying the
debit of the position by the interest rate charged and the time that the position will
be held. That is, it could be formulated as:
Carrying cost = Strike x r x t
where r is the interest rate and t is the time that the position will be held. Relating
this formula for the carrying cost to the conversion profit formula given above, one
would get:
Conversion profit = Call - Stock - Put + Dividend + Strike - Carrying cost
= Call - Stock - Put + Dividend + Strike ( 1 - rt)
Chapter 27: Arbitrage 431
In an actuarial sense, the carrying cost could be expressed in a slightly more complex
manner. The simple formula (strike x r x t) ignores two things: the compounding
effect of interest rates and the "present value" concept ( the present value of a future
amount). The absolutely correct formula to include both present value and the com
pounding effect would necessitate replacing the factor strike (1- rt) in the profit for
mula by the factor
Strike
(1 + r)f
Is this effect large? No, not when rand tare small, as they would be for most option
calculations. The interest rate per month would normally be less than 1 %, and the
time would be less than 9 months. Thus, it is generally acceptable, and is the com
mon practice among many arbitrageurs, to use the simple formula for carrying costs.
In fact, this is often a matter of convenience for the arbitrageur if he is computing
the carrying costs on a hand calculator that does not perform exponentiation.
However, in periods of high interest rates when longer-term options are being ana
lyzed, the arbitrageur who is using the simple formula should double-check his cal
culations with the correct formula to assure that his error is not too large.
For purposes of simplicity, the remaining examples use the simple formula for
carrying-cost computations. The reader should remember, however, that it is only a
convenient approximation that works best when the interest rate and the holding
period are small. This discussion of the compounding effect of interest rates also rais
es another interesting point: Any investor using margin should, in theory, calculate
his potential interest charge using the compounding formula. However, as a matter
of practicality, extremely few investors do. An example of this compounding effect on
a covered call write is presented in Chapter 2.
BACK TO CONVERSIONS AND REVERSALS
Profit calculation similar to the conversion profit formula is necessary for the rever
sal arbitrage. Since the reversal necessitates sho1ting stock, the trader must pay out
any dividends on the stock during the time in which the position is held. However,
he is now bringing in a credit when the position is established, and this money can
be put to work to earn interest. In a reversal, then, the dividend is a cost and the
interest earned is a profit.
432 Part IV: Additional Considerations
Example: Use the same XYZ details described above: The stock is going to pay a ½
point dividend, the position will be held for three months, and the money will earn
interest at a rate of ½ of 1 % per month. If the trader were contemplating an arbi
trage with a striking price of 30, the fixed cost would be:
Reversal fixed cost = Dividend to be paid - Interest rate per month x
Months held x Striking price
= .50 - .005 X 3 X 30
= ½ - .045 = .005 point
The fixed cost in this reversal is extremely small. In fact, the reader should be able to
see that it is often possible - even probable - that there will be a fixed credit, not a
frxed cost, in a reversal arbitrage. To verify this, rework the example with a striking
price of 50 or 60. As in a conversion, the frxed cost (or profit) in a reversal is a num
ber that can be used for the entire trading day. It will not change.
BORROWING STOCK TO SELL SHORT
The above example assumes that the arbitrageur earns the full carrying rate on the
short stock. Only certain arbitrageurs are actually able to earn that rate. When one
sells stock short, he must actually borrow the stock from someone who owns it, and
then the seller goes into the market to sell the stock. When customers of brokerage
firms keep stock in a margin account, they agree to let the brokerage firm loan their
stock out without the customer's specific approval. Thus, if an arbitrageur working for
that brokerage firm wanted to establish a reversal, and if the stock to be sold short in
the reversal were available in one of the margin accounts, the arbitrageur could bor
row that stock and earn the full carrying rate on it. This is called "using box stock,"
since stock held in margin accounts is generally referred to as being in the "box."
There are other times, however, when an arbitrageur wants to do a reversal but
does not have access to "box" stock. He must then find someone else from whom to
borrow the stock. Obviously, there are people who own


could bor
row that stock and earn the full carrying rate on it. This is called "using box stock,"
since stock held in margin accounts is generally referred to as being in the "box."
There are other times, however, when an arbitrageur wants to do a reversal but
does not have access to "box" stock. He must then find someone else from whom to
borrow the stock. Obviously, there are people who own stock and would loan it to
arbitrageurs for a fee. There are people who specialize in matching up investors with
stock to loan and arbitrageurs who want to borrow stock. These people are said to be
in the "stock loan" business. Generally, the fee for borrowing stock in this manner is
anywhere from 10 to 20% of the prevailing carrying cost rate. For example, if the cur
rent carrying rate were 10% annually, then one would expect to pay 1 or 2% to the
lender to borrow his stock. This reduces the profitability of the reversal slightly. Since
small margins are being worked with, this cost to borrow the stock may make a sig
nificant difference to the arbitrageur.
These variations in the rates that an arbitrageur can earn on the credit balances
in his account affect the marketplace. For example, a particular reversal might be
Chapter 27: Arbitrage 433
available in the marketplace at a net profit of ½ point, or 50 cents. Such a reversal
may not be equally attractive to all arbitrageurs. Those who have "box" stock may be
willing to do the reversal for 50 cents; those who have to pay 1 % to borrow stock may
want 0.55 for the reversal; and those who pay 2% to borrow stock may need 0.65 for
the reversal. Thus, arbitrageurs who do conversions and reversals are in competition
with each other not only in the marketplace, but in the stock loan arena as well.
Reversals are generally easier positions for the arbitrageur to locate than are
conversions. This is because the fixed cost of the conversion has a rather burdensome
effect. Only if the stock pays a rather large dividend that outweighs the carrying cost
could the fixed portion of the conversion formula ever be a profit as opposed to a
cost. In practice, the interest rate paid to carry stock is probably higher than the
interest earned from being short stock, but any reasonable computer program should
be able to handle two different interest rates.
The novice trader may find the term "conversion" somewhat illogical. In the
over-the-counter option markets, the dealers create a position similar to the one
shown here as a result of actually converting a put to a call.
Example: When someone owns a conventional put on XYZ with a striking price of
60 and the stock falls to 50, there is often little chance of being able to sell the put
profitably in the secondary market. The over-the-counter option dealer might offer
to convert the put into a call. To do this, he would buy the put from the holder, then
buy the stock itself, and then offer a call at the original striking price of 60 to the
holder of the put. Thus, the dealer would be long the stock, long the put, and short
the call - a conversion. The customer would then own a call on XYZ with a striking
price of 60, due to expire on the same date that the put was destined to. The put
that the customer owned has been converted into a call. To effect this conversion,
the dealer pays out to the customer the difference between the current stock price,
50, and the striking price, 60. Thus, the customer receives $1,000 for this conver
sion. Also, the dealer would charge the customer for costs to carry the stock, so that
the dealer had no risk. If the stock rallied back above 60, the customer could make
more money, because he owns the call. The dealer has no risk, as he has an arbitrage
position to begin with. In a similar manner, the dealer can effect a reverse conver
sion - converting a call to a put - but will charge the dividends to the customer for
doing so.
RISKS IN CONVERSIONS AND REVERSALS
Conversions and reversals are generally considered to be riskless arbitrage. That is,
the profit in the arbitrage is fixed from the start and the subsequent movement of the
434 Part IV: Additional Considerations
underlying stock makes no difference in the eventual outcome. This is generally a
true statement. However, there are some risks, and they are great enough that one
can actually lose money in conversions and reversals if he does not take care. The
risks are fourfold in reversal arbitrage: An extra dividend is declared, the interest rate
falls while the reversal is in place, an early assignment is received, or the stock is
exactly at the striking price at expiration. Converters have similar risks: a dividend
cut, an increase in the interest rate, early assignment, or the stock closing at the strike
at expiration.
These risks are first explored from the viewpoint of the reversal trader. If the
company declares an extra dividend, it is highly likely that the reversal will become
unprofitable. This is so because most extra dividends are rather large - more than the
profit of a reversal. There is little the arbitrageur can do to avoid being caught by the
declaration of a truly extra dividend. However, some companies have a track record
of declaring extras with annual regularity. The arbitrageur should be aware of which
companies these are and of the timing of these extra dividends. A clue sometimes
exists in the marketplace. If the reversal appears overly profitable when the arbi
trageur is first examining it (before he actually establishes it), he should be somewhat
skeptical. Perhaps there is a reason why the reversal looks so tempting. An extra div
idend that is being factored into the opinion of the marketplace may be the answer.
The second risk is that of variation in interest rates while the reversal is in
progress. Obviously, rates can change over the life of a reversal, normally 3 to 6
months. There are two ways to compensate for this. The simplest way is


al. Perhaps there is a reason why the reversal looks so tempting. An extra div
idend that is being factored into the opinion of the marketplace may be the answer.
The second risk is that of variation in interest rates while the reversal is in
progress. Obviously, rates can change over the life of a reversal, normally 3 to 6
months. There are two ways to compensate for this. The simplest way is to leave
some room for rates to move. For example, if rates are currently at 12% annually, one
might allow for a movement of 2 to 3% in rates, depending on the length of time the
reversal is expected to be in place. In order to allow for a 2% move, the arbitrageur
would calculate his initial profit based on a rate of 10%, 2% less than the currently
prevailing 12%. He would not establish any reversal that did not at least break even
with a 10% rate. The rate at which a reversal breaks even is often called the "effec
tive rate" - 10% in this case. Obviously, if rates average higher than 10% during the
life of the reversal, it will make money. Normally, when one has an entire portfolio of
reversals in place, he should know the effective rate of each set of reversals expiring
at the same time. Thus, he would have an effective rate for his 2-month reversals, his
3-month ones, and so forth.
Allowing this room for rates to move does not necessarily mean that there will
not be an adverse affect if rates do indeed fall. For example, rates could fall farther
than the room allowed. Thus, a further measure is necessary in order to completely
protect against a drop in rates: One should invest his credit balances generated by the
reversals in interest-bearing paper that expires at approximately the same time the
reversals do, and that bears interest at a rate that locks in a profit for the reversal
Chapter 27: Arbitrage 435
account. For example, suppose that an arbitrageur has $5 million in 3-month rever
sals at an effective rate of 10%. If he can buy $5 million worth of 3-month Certificates
of Deposit with a rate of 11 ½%, then he would lock in a profit of 1 ½% on his $5 mil
lion. This method of using paper to hedge rate fluctuations is not practiced by all
arbitrageurs; some think it is not worth it. They believe that by leaving the credit bal
ances to fluctuate at prevailing rates, they can make more if rates go up, and that will
cushion the effect when rates decline.
The third risk of reversal arbitrage is reception of an early assignment on the
short puts. This forces the arbitrageur to buy stock and incur a debit. Thus, the posi
tion does not earn as much interest as was originally assumed. If the assignment is
received early enough in the life of the reversal (recall that in-the-money puts can
be assigned very far in advance of expiration), the reversal could actually incur an
overall loss. Such early assignments normally occur during bearish markets. The only
advantage of this early assignment is that one is left with unhedged long calls; these
calls are well out-of-the-money and normally quite low-priced (¼ or less). If the
market should reverse and turn bullish before the expiration of the calls, the arbi
trageur may make money on them. There is no way to hedge completely against a
market decline, but it does help if the arbitrageur tries to establish reversals with the
call in-the-money and the put out-of-the-money. That, plus demanding a better
overall return for reversals near the strike, should help cushion the effects of the
bear market.
The final risk is the most common one, that of the stock closing exactly at the
strike at expiration. This presents the arbitrageur with a decision to make regarding
exercise of his long calls. Since the stock is exactly at the strike, he is not sure whether
he will be assigned on his short puts at expiration. The outcome is that he may end
up with an unhedged stock position on Monday morning after expiration. If the stock
should open on a gap, he could have a substantial loss that wipes out the profits of
many reversals. This risk of stock closing at the strike may seem minute, but it is not.
In the absence of any real buying or selling in the stock on expiration day, the process
of discounting will force a stock that is near the strike virtually right onto the strike.
Once it is near the strike, this risk materializes.
There are two basic scenarios that could occur to produce this unhedged stock
position. First, suppose one decides that he will not get put and he exercises his calls.
However, he was wrong and he does get put. He has bought double the amount of
stock - once via call exercise and again via put assignment. Thus, he will be long on
Monday morning. The other scenario produces the opposite effect. Suppose one
decides that he will get put and he decides not to exercise his calls. If he is wrong in
this case, he does not buy any stock - he didn't exercise nor did he get put.
Consequently, he will be short stock on Monday morning.
436 Part IV: Additional Considerations
If one is truly undecided about whether he will be assigned on his short puts,
he might look at several clues. First, has any late news come out on Friday evening
that might affect the market's opening or the stock's opening on Monday morning? If
so, that should be factored into the decision regarding exercising the calls. Another
clue arises from the price at which the stock was trading during the Friday expiration
day, prior to the close. If the stock was below the strike for most of the day before
closing at the strike, then there is a greater chance that the puts will be assigned. This
is so because other arbitrageurs (discounters) have probably bought puts and bought
stock during the day and will exercise to clean out their positions.
If there is still doubt, it may be wisest to exercise only half of the calls, hoping
for a partial assignment on the puts (always a possibility). This halfway measure will
normally result


a greater chance that the puts will be assigned. This
is so because other arbitrageurs (discounters) have probably bought puts and bought
stock during the day and will exercise to clean out their positions.
If there is still doubt, it may be wisest to exercise only half of the calls, hoping
for a partial assignment on the puts (always a possibility). This halfway measure will
normally result in some sort of unhedged stock position on Monday morning, but it
will be smaller than the maximum exposure by at least half.
Another approach that the arbitrageur can take if the stock is near the strike of
the reversal during the late trading of the options' life - during the last few days - is
to roll the reversal to a later expiration or, failing that, to roll to another strike in the
same expiration. First, let us consider rolling to another expiration. The arbitrageur
knows the dollar price that equals his effective rate for a 3-month reversal. If the cur
rent options can be closed out and new options opened at the next expiration for at
least the effective rate, then the reversal should be rolled. This is not a likely event,
mostly due to the fact that the spread between the bid and asked prices on four sep
arate options makes it difficult to attain the desired price. Note: This entire four-way
order can be entered as a spread order; it is not necessary to attempt to "leg" the
spread.
The second action - rolling to another strike in the same expiration month -
may be more available. Suppose that one has the July 45 reversal in place (long July
45 call and short July 45 put). If the underlying stock is near 45, he might place an
order to the exchange floor as a three-way spread: Sell the July 45 call (closing), buy
the July 45 put (closing), and sell the July 40 call ( opening) for a net credit of 5 points.
This action costs the arbitrageur nothing except a small transaction charge, since he
is receiving a 5-point credit for moving the strike by 5 points. Once this is accom
plished, he will have moved the strike approximately 5 points away and will thus have
avoided the problem of the stock closing at the strike.
Overall, these four risks are significant, and reversal arbitrageurs should take
care that they do not fall prey to them. The careless arbitrageur uses effective rates
too close to current market rates, establishes reversals with puts in-the-money, and
routinely accepts the risk of acquiring an unhedged stock position on the morning
after expiration. He will probably sustain a large loss at some time. Since many rever
sal arbitrageurs work with small capital and/or have convinced their backers that it is
Chapter 27: Arbitrage 437
a riskless strategy, such a loss may have the effect of putting them out of business.
That is an unnecessary risk to take. There are countermeasures, as described above,
that can reduce the effects of the four risks.
Let us consider the risks for conversion traders more briefly. The risk of stock
closing near the strike is just as bad for the conversion as it is for the reversal. The
same techniques for handling those risks apply equally well to conversions as to
reversals. The other risks are similar to reversal risks, but there are slight nuances.
The conversion arbitrage suffers if there is a dividend cut. There is little the
arbitrageur can do to predict this except to be aware of the fundamentals of the com
pany before entering into the conversion. Alternatively, he might avoid conversions
in which the dividend makes up a major part of the profit of the arbitrage.
Another risk occurs if there is an early assignment on the calls before the ex-div
idend date and the dividend is not received. Moreover, an early assignment leaves the
arbitrageur with long puts, albeit fractional ones since they are surely deeply out-of
the-money. Again, the policy of establishing conversions in which the dividend is not
a major factor would help to ease the consequences of early assignment.
The final risk is that interest rates increase during the time the conversion is in
place. This makes the carrying costs larger than anticipated and might cause a loss.
The best way to hedge this initially is to allow a margin for error. Thus, if the pre
vailing interest rate is 12%, one might only establish reversals that would break even
if rates rose to 14%. If rates do not rise that far on average, a profit will result. The
arbitrageur can attempt to hedge this risk by shorting interest-bearing paper that
matures at approximately the same time as the conversions. For example, if one has
$5 million worth of 3-month conversions established at an effective rate of 14% and
he shorts 3-month paper at 12½%, he locks in a profit of 1 ½%. This is not common
practice for conversion arbitrageurs, but it does hedge the effect of rising interest
rates.
SUMMARY OF CONVERSION ARBITRAGE
The practice of conversion and reversal arbitrage in the listed option markets helps
to keep put and call prices in line. If arbitrageurs are active in a particular option, the
prices of the put and call will relate to the stock price in line with the formulae given
earlier. Note that this is also a valid reason why puts tend to sell at a lower price than
calls do. The cost of money is the determining factor in the difference between put
and call prices. In essence, the "cost" (although it may sometimes be a credit) is sub
tracted from the theoretical put price. Refer again to the formula given above for the
profit potential of a conversion. Assume that things are in perfect alignment. Then
the formula would read:
438 Part IV: Additional Considerations
Put price = Striking price + Call price - Stock price - Fixed cost
Furthermore, if the stock is at the striking price, the formula reduces to:
Put price = Call price - Fixed cost
So, whenever the fixed cost, which is equal to the carrying charge less the dividends,
is greater than zero (and it usually is


perfect alignment. Then
the formula would read:
438 Part IV: Additional Considerations
Put price = Striking price + Call price - Stock price - Fixed cost
Furthermore, if the stock is at the striking price, the formula reduces to:
Put price = Call price - Fixed cost
So, whenever the fixed cost, which is equal to the carrying charge less the dividends,
is greater than zero (and it usually is), the put will sell for less than the call if a stock
is at the striking price. Only in the case of a large-dividend-paying stock, when the
fixed cost becomes negative (that is, it is not a cost, but a credit), does the reverse
hold true. This is supportive evidence for statements made earlier that at-the-money
calls sell for more than at-the-money puts, all other things being equal. The reader
can see quite clearly that it has nothing to do with supply and demand for the puts
and calls, a fallacy that is sometimes proffered. This same sort of analysis can be used
to prove the broader statement that calls have a greater time value premium than
puts do, except in the case of a large-dividend-paying stock.
One final word of advice should be offered to the public customer. He may
sometimes be able to find conversions or reversals, by using the simplistic formula,
that appear to have profit potentials that exceed commission costs. Such positions do
exist from time to time, but the rate of return to the public customer will almost
assuredly be less than the short-term cost of money. If it were not, arbitrageurs would
be onto the position very quickly. The public option trader may not actually be think
ing in terms of comparing the profit potential of a position with what he could get by
placing the money into a bank, but he must do so to convince himself that he cannot
feasibly attempt conversion or reversal arbitrages.
THE "INTEREST PLAY"
In the preceding discussion of reversal arbitrage, it is apparent that a substantial por
tion of the arbitrageur's profits may be due to the interest earned on the credit of the
position. Another type of position is used by many arbitrageurs to take advantage of
this interest earned. The arbitrageur sells the underlying stock short and simultane
ously buys an in-the-money call that is trading slightly over parity. The actual amount
over parity that the arbitrageur can afford to pay for the call is determined by the
interest that he will earn from his short sale and the dividend payout before expira
tion. He does not use a put in this type of position. In fact, this "interest play" strat
egy is merely a reversal arbitrage without the short put. This slight variation has a
residual benefit for the arbitrageur: If the underlying stock should drop dramatically
in price, he could make large profits because he is short the underlying stock. In any
case, he will make his interest credit less the amount of time value premium paid for
the call less any dividends lost.
Chapter 27: Arbitrage 439
Example 1: XYZ is sold short at 60, and a January 50 call is bought for 10¼ points.
Assume that the prevailing interest rate is 1 % per month and that the position is
established one month prior to expiration. XYZ pays no dividend. The total credit
brought in from the trades is $4,975, so the arbitrageur will earn $49.75 in interest
over the course of 1 month. If the stock is above 50 at expiration, he will exercise his
call to buy stock at 50 and close the position. His loss on the security trades will be
$25 the amount of time value premium paid for the call option. (He makes 10
points by selling stock at 60 and buying at 50, but loses 10¼ points on the exercised
call.) His overall profit is thus $24.75.
Example 2: A real-life example may point out the effect of interest rates even more
dramatically. In early 1979, IBM April 240 calls with about six weeks of life remain
ing were over 60 points in-the-money. IBM was not going to be ex-dividend in that
time. Normally, such a deeply in-the-money option would be trading at parity or even
a discount when the time remaining to expiration is so short. However, these calls
were trading 3½ points over parity because of the prevailing high interest rates at the
time. IBM was at 300, the April 240 calls were trading at 63½, and the prevailing
interest rate was approximately 1 % per month. The credit from selling the stock and
buying the call was $23,700, so the arbitrageur earned $365.50 in interest for 1 ½
months, and lost $350 - the 3½ points of time value premium that he paid for the
call. This still left enough room for a profit.
In Chapter 1, it was stated that interest rates affect option prices. The above
examples of the "interest play" strategy quite clearly show why. As interest rates rise,
the arbitrageur can afford to pay more for the long call in this strategy, thus causing
the call price to increase in times of high interest rates. If call prices are higher, so
will put prices be, as the relationships necessary for conversion and reversal arbitrage
are preserved. Similarly, if interest rates decline, the arbitrageur will make lower
bids, and call and put prices will be lower. They are active enough to give truth to the
theory that option prices are directly related to interest rates.
THE BOX SPREAD
An arbitrage consists of simultaneously buying and selling the same security or equiv
alent securities at different prices. For example, the reversal consists of selling a put
and simultaneously shorting stock and buying a call. The reader will recall that the
short stock/long call position was called a synthetic put. That is, shorting the stock
and buying a call is equivalent to buying a put. The reversal arbitrage therefore con
sists of selling a (listed) put and simultaneously buying a (synthetic) put. In a similar
440 Part IV: Additional Considerations
manner, the conversion is merely the purchase of a (listed) put and the simultaneous
sale of a (synthetic) put. Many equ


tion was called a synthetic put. That is, shorting the stock
and buying a call is equivalent to buying a put. The reversal arbitrage therefore con
sists of selling a (listed) put and simultaneously buying a (synthetic) put. In a similar
440 Part IV: Additional Considerations
manner, the conversion is merely the purchase of a (listed) put and the simultaneous
sale of a (synthetic) put. Many equivalent strategies can be combined for arbitrage
purposes. One of the more common ones is the box spread.
Recall that it was shown that a bull spread or a bear spread could be construct
ed with either puts or calls. Thus, if one were to simultaneously buy a (call) bull
spread and buy a (put) bear spread, he could have an arbitrage. In essence, he is
merely buying and selling equivalent spreads. If the price differentials work out cor
rectly, a risk-free arbitrage may be possible.
Example: The following prices exist:
XYZ common, 55
XYZ January 50 call, 7
XYZ January 50 put, 1
XYZ January 60 call, 2
XYZ January 60 put, 5½
The arbitrageur could establish the box spread in this example by executing the
following transactions:
Buy a call bull spread:
Buy XYZ January 50 call
Sell XYZ January 60 call
Net call cost
Buy a put bear spread:
Buy XYZ January 60 put
Sell XYZ January 50 put
Net put cost
Total cost of position
7 debit
2 credit
51/2 debit
1 credit
5 debit
No matter where XYZ is at January expiration, this position will be worth 10 points.
The arbitrageur has locked in a risk-free profit of½ point, since he "bought" the box
spread for 9½ points and will be able to "sell" it for 10 points at expiration. To verify
this, evaluate the position at expiration, first with XYZ above 60, then with XYZ
between 50 and 60, and finally with XYZ below 50. If XYZ is above 60 at expiration,
the puts will expire worthless and the call bull spread will be at its maximum poten
tial of 10 points, the difference between the striking prices. Thus, the position can be
liquidated for 10 points if XYZ is above 60 at expiration. Now assume that XYZ is
Chapter 27: Arbitrage 441
between 50 and 60 at expiration. In that case, the out-of-the-money, written options
would expire worthless-the January 60 call and the January 50 put. This would leave
a long, in-the-money combination consisting of a January 50 call and a January 60
put. These two options must have a total value of 10 points at expiration with XYZ
between 50 and 60. (For example, the arbitrageur could exercise his call to buy stock
at 50 and exercise his put to sell stock at 60.) Finally, assume that XYZ is below 50 at
expiration. The calls would expire worthless if that were true, but the remaining put
spread- actually a bear spread in the puts -would be at its maximum potential of 10
points. Again, the box spread could be liquidated for 10 points.
The arbitrageur must pay a cost to carry the position, however. In the prior
example, if interest rates were 6% and he had to hold the box for 3 months, it would
cost him an additional 14 cents (.06 x 9½ x 3112). This still leaves room for a profit.
In essence, a bull spread ( using calls) was purchased while a bear spread ( using
puts) was bought. The box spread was described in these terms only to illustrate the
fact that the arbitrageur is buying and selling equivalent positions. The arbitrageur
who is utilizing the box spread should not think in terms of bull or bear spread, how
ever. Rather, he should be concerned with "buying" the entire box spread at a cost of
less than the differential between the two striking prices. By "buying" the box spread,
it is meant that both the call spread portion and the put spread portion are debit
spreads. Whenever the arbitrageur observes that a call spread and a put spread using
the same strikes and that are both debit spreads can be bought for less than the dif
ference in the strikes plus carrying costs, he should execute the arbitrage.
Obviously, there is a companion strategy to the one just described. It might
sometimes be possible for the arbitrageur to "sell" both spreads. That is, he would
establish a credit call spread and a credit put spread, using the same strikes. If this
credit were greater than the difference in the striking prices, a risk-free profit would
be locked in.
Example: Assume that a different set of prices exists:
XYZ common, 75
XYZ April 70 call, 8½
XYZ April 70 put, 1
XYZ April 80 call, 3
XYZ April 80 put, 6
By executing the following transactions, the box spread could be "sold":
442
Sell a call (bear) spread:
Buy April 80 call
Sell April 70 call
Net credit on calls
Sell a put (bull) spread:
Buy April 70 put
Sell April 80 put
Net credit on puts
Total credit of position
3 debit
81/2 credit
1 debit
6 credit
Part IV: Additional Considerations
5 credit
10 1/2 credit
In this case, no matter where XYZ is at expiration, the position can be bought back
for 10 points. This means that the arbitrageur has locked in risk-free profit of¼
point. To verify this statement, first assume that XYZ is above 80 at April expiration.
The puts will expire worthless, and the call spread will have widened to 10 points -
the cost to buy it back. Alternatively, if XYZ were between 70 and 80 at April expira
tion, the long, out-of-the-money options would expire worthless and the in-the
money combination would cost 10 points to buy back. (For example, the arbitrageur
could let himself be put at 80, buying stock there, and called at 70, selling the stock
there - a net "cost" to liquidate of 10 points.) Finally, if XYZ were below 70 at expi
ration, the calls would expire worthless and the put spread would have widened to 10
points. It could then be closed out at a cost of 10 points. In each case, the arbitrageur
is able to liquidate the box spread by buying it back at 10.
In this sale of a box spread, he would earn interest on the credit received while
he holds the position.
There is an additiona


ly, if XYZ were below 70 at expi
ration, the calls would expire worthless and the put spread would have widened to 10
points. It could then be closed out at a cost of 10 points. In each case, the arbitrageur
is able to liquidate the box spread by buying it back at 10.
In this sale of a box spread, he would earn interest on the credit received while
he holds the position.
There is an additional factor in the profitability of the box spread. Since the sale
of a box generates a credit, the arbitrageur who sells a box will earn a small amount
of money from that sale. Conversely, the purchaser of a box spread will have a charge
for carrying cost. Since profit margins may be small in a box arbitrage, these carrying
costs can have a definite effect. As a result, boxes may actually be sold for 5 points,
even though the striking prices are 5 points apart, and the arbitrageur can still make
money because of the interest earned.
These box spreads are not easy to find. If one does appear, the act of doing the
arbitrage will soon make the arbitrage impossible. In fact, this is true of any type of
arbitrage; it cannot be executed indefinitely because the mere act of arbitraging will
force the prices back into line. Occasionally, the arbitrageur will be able to find the
option quotes to his liking, especially in volatile markets, and can establish a risk-free
Chapter 27: Arbitrage 443
arbitrage with the box spread. It can be evaluated at a glance. Only two questions
need to be answered:
1. If one were to establish a debit call spread and a debit put spread, using the same
strikes, would the total cost be less than the difference in the striking prices plus
carrying costs? If the answer is yes, an arbitrage exists.
2. Alternatively, if one were to sell both spreads - establishing a credit call spread
and a credit put spread - would the total credit received plus interest earned be
greater than the difference in the striking prices? If the answer is yes, an arbi
trage exists.
There are some risks to box arbitrage. Many of them are the same as those risks
faced by the arbitrageur doing conversions or reversals. First, there is risk that the
stock might close at either of the two strikes. This presents the arbitrageur with the
same dilemma regarding whether or not to exercise his long options, since he is not
sure whether he will be assigned. Additionally, early assignment may change the prof
itability: Assignment of a short put will incur large carrying costs on the resulting long
stock; assignment of a short call will inevitably come just before an ex-dividend date,
costing the arbitrageur the amount of the dividend.
There are not many opportunities to actually transact box arbitrage, but the fact
that such arbitrage exists can help to keep markets in line. For example, if an under
lying stock begins to move quickly and order flow increases dramatically, the special
ist or market-markers in that stock's options may be so inundated with orders that
they cannot be sure that their markets are correct. They can use the principles of box
arbitrage to keep prices in line. The most active options would be the ones at strikes
nearest to the current stock price. The specialist can quickly add up the markets of
the call and put at the nearest strike above the stock price and add to that the mar
kets of the options at the strike just below. The sum of the four should add up to a
price that surrounds the difference in the strikes. If the strikes are 5 points apart,
then the sum of the four markets should be something like 4½ bid, 5½ asked. If,
instead, the four markets add up to a price that allows box arbitrage to be established,
then the specialist will adjust his markets.
VARIATIONS ON EQUIVALENCE ARBITRAGE
Other variations of arbitrage on equivalent positions are possible, although they are
relatively complicated and probably not worth the arbitrageur's time to analyze. For
example, one could buy a butterfly spread with calls and simultaneously sell a but
terfly spread using puts. A listed straddle could be sold and a synthetic straddle
444 Part IV: Additional Considerations
could be bought - short stock and long 2 calls. Inversely, a listed straddle could be
bought against a ratio write - long stock and short 2 calls. The only time the arbi
trageur should even consider anything like this is when there are more sizable mar
kets in certain of the puts and calls than there are in others. If this were the case, he
might be able to take an ordinary box spread, conversion, or reversal and add to it,
keeping the arbitrage intact by ensuring that he is, in fact, buying and selling equiv
alent positions.
THE EFFECTS OF ARBITRAGE
The arbitrage process serves a useful purpose in the listed options market, because it
may provide a secondary market where one might not otherwise exist. Normally,
public interest in an in-the-money option dwindles as the option becomes deeply in
the-money or when the time remaining until expiration is very short. There would be
few public buyers of these options. In fact, public selling pressure might increase,
because the public would rather liquidate in-the-money options held long than exer
cise them. The few public buyers of such options might be writers who are closing
out. However, if the writer is covered, especially where call options are concerned,
he might decide to be assigned rather than close out his option. This means that the
public seller is creating a rather larger supply that is not offset by a public demand.
The market created by the arbitrageur, especially in the basic put or call arbitrage,
essentially creates the demand. Without these arbitrageurs, there could conceivably
be no buyers at all for those options that are short-lived and in-the-money, after pub
lic writers have finished closing out their positions.
Equivalence arbitrage - conversion, reversals, and box spreads - helps to keep
the relative prices


ted by the arbitrageur, especially in the basic put or call arbitrage,
essentially creates the demand. Without these arbitrageurs, there could conceivably
be no buyers at all for those options that are short-lived and in-the-money, after pub
lic writers have finished closing out their positions.
Equivalence arbitrage - conversion, reversals, and box spreads - helps to keep
the relative prices of puts and calls in line with each other and with the underlying
stock price. This creates a more efficient and rational market for the public to oper
ate in. The arbitrageur would help eliminate, for example, the case in which a public
customer buys a call, sees the stock go up, but cannot find anyone to sell his call to
at higher prices. If the call were too cheap, arbitrageurs would do reversals, which
involve call purchases, and would therefore provide a market to sell into.
Questions have been raised as to whether option trading affects stock prices,
especially at or just before an expiration. If the amount of arbitrage in a certain issue
becomes very large, it could appear to temporarily affect the price of the stock itself.
For example, take the call arbitrage. This involves the sale of stock in the market. The
corresponding stock purchase, via the call exercise, is not executed on the exchange.
Thus, as far as the stock market is concerned, there may appear to be an inordinate
amount of selling in the stock. If large numbers of basic call arbitrages are taking
place, they might thus hold the price of the stock down until the calls expire.
Chapter 27: Arbitrage 445
The put arbitrage has an opposite effect. This arbitrage involves buying stock in
the market. The offsetting stock sale via the put exercise takes place off the exchange.
If a large amount of put arbitrage is being done, there may appear to be an inordi
nate amount of buying in the stock. Such action might temporarily hold the stock
price up.
In a vast majority of cases, however, the arbitrage has no visible effect on the
underlying stock price, because the amount of arbitrage being done is very small in
comparison to the total number of trades in a given stock. Even if the open interest
in a particular option is large, allowing for plenty of option volume by the arbi
trageurs, the actual act of doing the arbitrage will force the prices of the stock and
option back into line, thus destroying the arbitrage.
Rather elaborate studies, including doctoral theses, have been written that try
to prove or disprove the theory that option trading affects stock prices. Nothing has
been proven conclusively, and it may never be, because of the complexity of the task.
Logic would seem to dictate that arbitrage could temporarily affect a stock's move
ment if it has discount, in-the-money options shortly before expiration. However, one
would have to reasonably conclude that the size of these arbitrages could almost
never be large enough to overcome a directional trend in the underlying stock itself.
Thus, in the absence of a definite direction in the stock, arbitrage might help to per
petuate the inertia; but if there were truly a preponderance of investors wanting to
buy or sell the stock, these investors would totally dominate any arbitrage that might
be in progress.
RISK ARBITRAGE USING OPTIONS
Risk arbitrage is a strategy that is well described by its name. It is basically an arbi
trage - the same or equivalent securities are bought and sold. However, there is gen
erally risk because the arbitrage usually depends on a future event occurring in
order for the arbitrage to be successful. One form of risk arbitrage was described
earlier concerning the speculation on the size of a special dividend that an underly
ing stock might pay. That arbitrage consisted of buying the stock and buying the put,
when the put' s time value premium is less than the amount of the projected special
dividend. The risk lies in the arbitrageur's speculation on the size of the anticipated
special dividend.
MERGERS
Risk arbitrage is an age-old type of arbitrage in the stock market. Generally, it con
cerns speculation on whether a proposed merger or acquisition will actually go
through as proposed.
446 Part IV: Additional Considerations
Example: XYZ, which is selling for $50 per share, offers to buy out LMN and is offer
ing to swap one share of its (XYZ's) stock for every two shares of LMN. This would
mean that LMN should be worth $25 per share if the acquisition goes through as pro
posed. On the day the takeover is proposed, LMN stock would probably rise to about
$22 per share. It would not trade all the way up to 25 until the takeover was approved
by the shareholders of LMN stock. The arbitrageur who feels that this takeover will
be approved can take action. He would sell short XYZ and, for every share that he is
short, he would buy 2 shares of LMN stock. If the merger goes through, he will prof
it. The reason that he shorts XYZ as well as buying LMN is to protect himself in case
the market price of XYZ drops before the acquisition is approved. In essence, he has
sold XYZ and also bought the equivalent of XYZ (two shares of LMN will be equal to
one share of XYZ if the takeover goes through). This, then, is clearly an arbitrage.
However, it is a risk arbitrage because, if the stockholders of LMN reject the offer,
he will surely lose money. His profit potential is equal to the remaining differential
between the current market price of LMN (22) and the takeover price (25). If the
proposed acquisition goes through, the differential disappears, and the arbitrageur
has his profit.
The greatest risk in a merger is that it is canceled. If that happens, stock being
acquired (LMN) will fall in price, returning to its pre-takeover levels. In addition, the
acquiring stock (XYZ) will probably rise. Thus, the risk arbitrageur can lose money
on both sides of his trade. If either or both of the stocks involved in the propos


rential disappears, and the arbitrageur
has his profit.
The greatest risk in a merger is that it is canceled. If that happens, stock being
acquired (LMN) will fall in price, returning to its pre-takeover levels. In addition, the
acquiring stock (XYZ) will probably rise. Thus, the risk arbitrageur can lose money
on both sides of his trade. If either or both of the stocks involved in the proposed
takeover have options, the arbitrageur may be able to work options into his strategy.
In merger situations, since large moves can occur in both stocks ( they move in
concert), option purchases are the preferable option strategy. If the acquiring com
pany (XYZ) has in-the-money puts, then the purchase of those puts may be used
instead of selling XYZ short. The advantage is that if XYZ rallies dramatically during
the time it takes for the merger to take effect, then the arbitrageur's profits will be
increased.
Example: As above, assume that XYZ is at 50 and is acquiring LMN in a 2-for-l stock
deal. LMN is at 22. Suppose that XYZ rallies to 60 by the time the deal closes. This
would pull LMN up to a price of 30. If one had been short 100 XYZ at 50 and long
200 LMN at 22, then his profit would be $600 - a $1,600 gain on the 200 long LMN
minus a $1,000 loss on the XYZ short sale.
Compare that result to a similar strategy substituting a long put for the short
XYZ stock. Assume that he buys 200 LMN as before, but now buys an XYZ put. If
one could buy an XYZ July 55 put with little time premium, say at 5½ points, then
he would have nearly the same dollars of profit if the merger should go through with
XYZ below 55.
Chapter 27: Arbitrage 447
However, when XYZ rallies to 60, his profit increases. He would still make the
$1,600 on LMN as it rose from 22 to 30, but now would only lose $550 on the XYZ
put - a total profit of $1,050 as compared to $600 with an all-stock position.
The disadvantage to substituting long puts for short stock is that the arbitrageur
does not receive credit for the short sale and, therefore, does not earn money at the
carrying rate. This might not be as large a disadvantage as it initially seems, however,
since it is often the case that it is very expensive - even impossible - to borrow the
acquiring stock in order to short it. If the stock borrow costs are very large or if no
stock can be located for borrowing, the purchase of an in-the-money put is a viable
alternative. The purchase of an in-the-money put is preferable to an at- or out-of-the
money put, because the amount of time value premium paid for the latter would take
too much of the profitability away from the arbitrage if XYZ stayed unchanged or
declined. This strategy may also save money if the merger falls apart and XYZ rises.
The loss on the long put may well be less than the loss would be on short XYZ stock.
Note also that one could sell the XYZ July 55 call short as well as buy the put.
This would, of course, be synthetic short stock and is a pure substitute for shorting
the stock. The use of this synthetic short is recommended only when the arbitrageur
cannot borrow the acquiring stock. If this is his purpose, he should use the in-the
money put and out-of-the-money call, since if he were assigned on the call, he could
not borrow the stock to deliver it as a short sale. The use of an out-of-the-money call
lessens the chance of eventual assignment.
The companion strategy is to buy an in-the-money call instead of buying the
company being acquired (LMN). This has advantages if the stock falls too far, either
because the merger falls apart or because the stocks in the merger decline too far.
Additionally, the cost of carrying the long LMN stock is eliminated, although that is
generally built into the cost of the long calls. The larger amount of time value pre
mium in calls as compared to puts makes this strategy often less attractive than that
of buying the puts as a substitute for the short sale.
One might also consider selling options instead of buying them. Generally this
is an inferior strategy, but in certain instances it makes sense. The reason that option
sales are inferior is that they do not limit one's risk in the risk arbitrage, but they cut
off the profit. For example, if one sells puts on the company being acquired (LMN),
he has a bullish situation. However, if the company being acquired (XYZ) rallies too
far, there will be a loss, because the short puts will stop making money as soon as
LMN rises through the strike. This is especially disconcerting if a takeover bidding
war should develop for LMN. The arbitrageur who is long LMN will participate nice
ly as LMN rises heavily in price during the bidding war. However, the put seller will
not participate to nearly the same extent.
448 Part IV: Additional Considerations
The sale of in-the-money calls as a substitute for shorting the acquiring compa
ny (XYZ) can be beneficial at certain times. It is necessary to have a plus tick in order
to sell stock short. When many arbitrageurs are trying to sell a stock short at the same
time, it may be difficult to sell such stock short. Morever, natural owners of XYZ may
see the arbitrageurs holding the price down and decide to sell their long stock rather
than suffer through a possible decline in the stock's price while the merger is in
progress. Additionally, buyers of XYZ will become very timid, lowering their bids for
the same reasons. All of this may add up to a situation in which it is very difficult to
sell the stock short, even if it can be borrowed. The sale of an in-the-money call can
overcome this difficulty. The call should be deeply in-the-money and not be too long
term, for the arbitrageur does not want to see XYZ decline below the strike of the
call. If that happened, he would no longer be hedged; the other side of the arbitrage
- the long LMN stock - would continue to decline, but he would not have any
remaining short against the long LMN.
L


an in-the-money call can
overcome this difficulty. The call should be deeply in-the-money and not be too long
term, for the arbitrageur does not want to see XYZ decline below the strike of the
call. If that happened, he would no longer be hedged; the other side of the arbitrage
- the long LMN stock - would continue to decline, but he would not have any
remaining short against the long LMN.
LIMITS ON THE MERGER
There is another type of merger for stock that is more difficult to arbitrage, but
options may prove useful. In some merger situations, the acquiring company (XYZ)
promises to give the shareholders of the company being acquired (LMN) an amount
of stock equal to a set dollar price. This amount of stock would be paid even if the
acquiring company rose or fell moderately in price. If XYZ falls too far, however, it
cannot pay out an extraordinarily increased number of shares to LMN shareholders,
so XYZ puts a limit on the maximum number of shares that it will pay for each share
of LMN stock. Thus, the shareholders ofXYZ are guaranteed that there will be some
downside buffer in terms of dilution of their company in case XYZ declines, as is
often the case for an acquiring company. However, ifXYZ declines too far, then LMN
shareholders will receive less. In return for getting this downside guarantee, XYZ will
usually also stipulate that there is a minimum amount of shares that they will pay to
LMN shareholders, even if XYZ stock rises tremendously. Thus, if XYZ should rise
tremendously in price, then LMN shareholders will do even better than they had
anticipated. An example will demonstrate this type of merger accord.
Example: Assume that XYZ is at 50 and it intends to acquire LMN for a stated price
of $25 per share, as in the previous example. However, instead of merely saying that
it will exchange two shares of LMN for one share of XYZ, the company says that it
wants the offer to be worth $25 per share to LMN shareholders as long as XYZ is
between 45 and 55. Given this information, we can determine the maximum and
minimum number of shares that LMN shareholders will receive: The maximum is
Chapter 27: Arbitrage 449
the stated price, 25, divided by the lower limit, 45, or 0.556 shares; the minimum is
25 divided by the higher limit, 55, or 0.455.
This type of merger is usually stated in terms of how many shares of XYZ will
be issued, rather than in terms of the price range that XYZ will be able to move in.
In either case, one can be derived from the other, so that the manner in which the
merger deal is stated is merely a convention. In this case, for example, the merger
might be stated as being worth $25 per share, with each share of LMN being worth
at least 0.455 shares of XYZ and at most 0.556 shares of XYZ. Note that these ratios
make the deal worth 25 as long as XYZ is between 45 and 55: 45 times 0.556 equals
25, as does 0.455 times 55.
If the acquiring stock, XYZ, is between 45 and 55 at the time the merger is com
pleted, then the number of shares of XYZ that each LMN shareholder will receive is
determined in a preset manner. Usually, at the time the merger is announced, XYZ
will say that its price on the closing date of the merger will be used to establish the
proper ratio. As a slight alternative, sometimes the acquiring company will state that
the price to be used in determining the final ratio is to be an average of the closing
prices of the stock over a stated period of time. This stated period of time might be
something like the 10 days prior to the closing of the merger.
Example: Suppose that the closing price of XYZ on the day that the merger closes is
to be the price used in the ratio. Furthermore, suppose that XYZ closes at 51 on that
day. It is within the prestated range, so a calculation must be done in order to deter
mine how many shares of XYZ each LMN shareholder will get. This ratio is deter
mined by dividing the stated price, 25, by the price in question, 51. This would give
a final ratio of 0.490196. The final ratio is usually computed to a rather large number
of decimal points in order to assure that LMN shareholders get as close to $25 per
share as possible.
The above two examples explain how this type of merger works. A merger of
this type is said to have "hooks" - the prices at which the ratio steadies. This makes
it difficult to arbitrage. As long as XYZ roams around in the 45 to 55 range, the arbi
trageur does not want to short XYZ as part of his arbitrage, because the price of XYZ
does not affect the price he will eventually receive for LMN 25. Rather, he would
buy LMN and wait until the deal is near closing before actually shorting XYZ. By
waiting, he will know approximately how many shares of XYZ to short for each share
of LMN that he owns. The reason that he must short XYZ at the end of the merger
is that there is usually a period of time before the physical stock is reorganized from
LMN into XYZ. During that time, if he were long LMN, he would be at risk if he did
not short XYZ against it.
450 Part IV: Additional Considerations
Problems arise if XYZ begins to fall below 45 well before the closing of the
merger, the lower "hook" in the merger. If it should remain below 45, then one
should set up the arbitrage as being short 0.556 shares ofXYZ for each share of LMN
that is held long. As long as XYZ remains below 45 until the merger closes, this is the
proper ratio. However, if, after establishing that ratio, XYZ rallies back above 45, the
arbitrageur can suffer damaging losses. XYZ may continue to rise in price, creating a
loss on the short side. However, LMN will not follow it, because the merger is struc
tured so that LMN is worth 25 unless XYZ rises too far. Thus, the long side stops fol
lowing as the short side moves higher.
On the other hand, no such problem exists if XYZ rises too far from its original
price of 50, going above the upper "hook" of 55. In that case, the arbitrageur wo