free to trade at any price - premium or discount - because there is nothing to keep
it fixed at the theoretical cash surrender value. If there is excess demand or supply in
the open market, then the price of the structured product will fluctuate to reflect that
excess. Eventually, of course, the discount will disappear, but five years prior to
maturity, one will often find that the product differs from its theoretical value by
somewhat significant amounts. If the discount is large enough, it will attract buyers;
alternatively, if there should be a large premium, that should attract sellers.
SIS
One of the first structured products of this type that came to my attention was one
that traded on the AMEX, entitled "Stock Index return Security" or SIS. It also trad
ed under the symbol SIS. The product was issued in 1993 and matured in 2000, so
we have a complete history of its movements. The terms were as follows: The under
lying index was the S&P Midcap 400 index (symbol: $MID). Issued in June 1993, the
original issue price was $10, and $MID was trading at 166.10 on the day of issuance,
so that was the striking price. Moreover, buyers were entitled to 115% of the appre
ciation of $MID above the strike price. Thus, the cash value formula was:
Gopter 32: Structured Products 597
Cash value of SIS $10 + $10 x 1.15 x ($MID - 166.10) / 166.10
where
Guarantee price = $10
Underlying index: S&P Midcap 400 ($MID)
Striking price: 166.10
Participation rate: 115% of the increase of $MID above 166.10
SIS matured seven years later, on June 2, 2000. At the time of issuance, seven-year
interest rates were about 5.5%, so the "money in the bank" formula shows that one
could have made about 4.7 points on a $10 investment, just by utilizing risk-free gov
ernment securities:
Money in the bank= 10 x e0-055 x 7 = 14.70
We can't simply say that the cost of the imbedded call was 4. 7 points, though, because
the participation rate is not 100% - it's greater. So we need to find out the Final Value
of $MID that results in the cash value being equal to the "money in the bank" result.
Using the cash value formula and inserting all the terms except the final value of
$MID, we have the following equation. Note: $MIDMIB stands for the value of $MID
that results in the "money in the bank" cash value, as computed above.
14.70 = 10 + 10 X 1.15 X ($MIDMIB 166.10) I 166.10
Solving for $MIDMIB' we get a value of 233.98. Now, convert this to a percent
gain of the striking price:
Imbedded call price = 233.98 I 166.10 - 1 = 0.4087
Hence, the imbedded call costs 40.87% of the guarantee price. In this example,
where the guarantee price was $10, that means the imbedded call cost $4.087.
Thus, a more generalized formula for the value of the imbedded call can be
construed from this example. This formula only works, though, where the participa
tion rate is a fixed percentage of the strike price.
Imbedded call value= Guarantee price x (Final Index ValueMIB / Striking Price - 1)
Final Index ValueMIB is the final index price that results in the cash value
being equal to the "money in the bank" calculation, where
Money in the bank = Guarantee Price x ert
r = risk-free interest rate
t = time to maturity
Thus, the calculated value of the imbedded call was approximately 4.087 points,
which is an implied volatility of just over 26%. At the time, listed short-term options
598 Part V: Index Options and Futures
on $MID were trading with an implied volatility of about 14%, so this was an expen
sive call in terms of its initial cost.
However, one should remember that owning SIS gave one more than full par
ticipation in the $MID for seven years, with virtually no risk. That has to be worth
something.
As it turned out, $MID was strong during this seven-year period, and SIS
wound up being worth just over $30 per share. So, in the end, the owner of SIS
tripled his money in seven years and had no risk to begin with. Not a bad scenario.
SIS TRACK RECORD
What SIS also imparts to us, though, is a track record of how it traded during its life.
Figure 32-1 shows the discount at which SIS traded during its lifetime. It is the lower
line on the chart. The upper line is the corresponding cash value on the same dates.
Note that the upper line has the exact same shape as the S&P Midcap 400 ($MID)
would, since it is merely $MID multiplied by some arithmetic constant. The graph of
the discount is rather "choppy" because it uses last sales of SIS to compute the dis
count. In reality, since SIS was a somewhat low-volume security, the last sale was not
always representative of the closing bid-asked market in SIS. Nevertheless, the
graph shows that the discount was greater than 2 points at the left side of the graph
(1995) and gradually decreased until it reached zero near maturity (2000).
The graph in Figure 32-1 is useful because it encompasses cases where $MID
traded both above and below the striking price of 166.10. No matter whether SIS was
in-the-money ($MID above 166.1) or out-of-the-money, SIS traded at a discount. As
mentioned previously, this is akin to a closed-end mutual fund trading at a discount
to net asset value.
At a minimum, this discount allows the buyer of SIS to add an additional com
ponent of overall return to his investment. Also, in some cases - when $MID was
trading below the striking price - the buyer of SIS actually has a guaranteed return,
as one might have with a bond paying interest or a stock paying a dividend. The
examples in the next section examine those situations.
SIS TRADING AT A DISCOUNT TO CASH VALUE
When SIS is trading at a discount to cash value, the buyer of SIS actually has some
downside protection.
Example: In late 1996, $MID closed at 238.54 one day, and SIS closed at 13. The
cash value of SIS for that price of $MID is:
Cash Value = 10 + 10 x 1.15 x (238.54/166.10 - 1) = 15.02
Cbapter 32: Strudured Products
FIGURE 32-1.
SIS trading at a discount.
C


NG AT A DISCOUNT TO CASH VALUE
When SIS is trading at a discount to cash value, the buyer of SIS actually has some
downside protection.
Example: In late 1996, $MID closed at 238.54 one day, and SIS closed at 13. The
cash value of SIS for that price of $MID is:
Cash Value = 10 + 10 x 1.15 x (238.54/166.10 - 1) = 15.02
Cbapter 32: Strudured Products
FIGURE 32-1.
SIS trading at a discount.
Cash Value and SIS Discount
30
20
10
0
-1
-2
1997
Date·
599
Therefore, SIS is trading at almost exactly a 2-point discount to cash value. That
is a fairly large discount of 15.4% (2/13 = .154).
One way to look at this would be to say that an investor is making an "extra"
15.4% on his investment. That is, if $MID were at exactly the same price at expira
tion, the cash value would be the settlement price - 15.02. In other words, the "stock
market" as measured by $MID was exactly unchanged. However, the investor would
make a return of 15.4% because he bought SIS at a discount.
In fact, no matter where $MID is at maturity, the investor feels the positive
effect of having bought at a discount.
Thus, the discount can and should be perceived as adding to the overall return of
owning the structured product. These discounts to net asset value are commonplace
with structured products. However, there is another way to view it: as downside pro
tection.
Example: Using the same prices, $MID is at 238.54 and SIS is at 13 - a 15.4% dis
count to the cash value of 15.02. Another way to view what this discount means is to
view it as downside protection. In other words, $MID could decline in price by matu
rity and this investor could still break even. The exact amount of the downside pro
tection can be calculated. Essentially, one wants to know, at what price for $MID
would the cash value be 13?
600 Part V: Index Options and Futures
Solving the following equation for $MID would give the desired answer:
Cash Value = 13 = 10 + 11.5 x ($MID/166.l - 1)
3 = 11.5 x $MID/ 166.1 - 11.5
14.5 x 166.1 / 11.5 = $MID
209.43 = $MID
So, if $MID were at 209.43, the cash value would be 13 - the price the investor
is currently paying for SIS. This is protection of 12.2% down from the current price
of 238.54. That is, $MID could decline 12.2% at maturity, from the current price of
238.54 to a price of 209.43, and the investor who bought SIS would break even
because it would still have a cash value of 13.
Of course, this discount could have been computed using the SIS prices of 13
and 15.02 as well, but many investors prefer to view it in terms of the underlying
index - especially if the underlying is a popular and often-cited index such as the S&P
500 or Dow-Jones Industrials.
From Figure 32-1, it is evident that the discount persisted throughout the
entire life of the product, shrinking more or less linearly until expiration.
SIS TRADING AT A DISCOUNT TO THE GUARANTEE PRICE
In the previous example, the investor could have bought SIS at a discount to its cash
value computation, but if the stock market had declined considerably, he would still
have had exposure from his SIS purchase price of 13 down to the guarantee price of
10. The discount would have mitigated his percentage loss when compared to the
$MID index itself, but it would be a loss nevertheless.
However, there are sometimes occasions when the structured product is trad
ing at a discount not only to cash value, but also to the guarantee price. This situation
occurred frequently in the early trading life of SIS. From Figure 32-1, you can see
that in 1995 the cash value was near 11, but SIS was trading at a discount of more
than 2 points. In other words, SIS was trading below its guarantee price, while the
cash value was actually above the guarantee price. It is a "double bonus" for an
investor when such a situation occurs.
Example: In February 1995, the following prices existed:
$MID: 177.59
SIS: 8.75
For a moment, set aside considerations of the cash value. If one were to buy SIS
at 8. 75 and hold it for the 5.5 years remaining until maturity, he would make 1.25
points on his 8.75 investment- a return of 14.3% for the 5.5-year holding period. As
a compounded rate of interest, this is an annual compound return of 2.43%.
Cl,apter 32: Structured Produds 601
Now, a rate of return of 2.43% is rather paltry considering that the risk-free
T•bill rate was more than twice that amount. However, in this case, you own a call
option on the stock market and get to earn 2.43% per year while you own the call. In
other words, "they" are paying you to own a call option! That's a situation that
doesn't arise too often in the world of listed options.
If we introduce cash value into this computation, the discrepancy is even larg
er. Using the $MID price of 177.59, the cash value can be computed as:
Cash Value = 10 + 11.5 x (177.59/166.10 - 1) = 10.80
Thus, with SIS trading at 8. 75 at that time, it was actually trading at a whopping
19% discount to its cash value of 10.80. Even if the stock market declined, the guar
antee price of 10 was still there to provide a minimal return.
In actual practice, a structured product will not normally trade at a discount to its
guarantee price while the cash value is higher than the guarantee price. There's only
a narrow window in which that occurs.
There have been times when the stock market has declined rather substantial
ly while these products existed. We can observe the discounts at which they then
traded to see just how they might actually behave on the downside if the stock mar
ket declined after the initial offering date. Consider this rather typical example:
Example: In 1997, Merrill Lynch offered a structured product whose underlying
index was Japan's Nikkei index. At the time, the Nikkei was trading at 20,351, so that
was the striking price. The participation rate was 140% of the increase of the Nikkei
above 20,351 - a very favorable participation rate. This structured prod

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d after the initial offering date. Consider this rather typical example:
Example: In 1997, Merrill Lynch offered a structured product whose underlying
index was Japan's Nikkei index. At the time, the Nikkei was trading at 20,351, so that
was the striking price. The participation rate was 140% of the increase of the Nikkei
above 20,351 - a very favorable participation rate. This structured product, trading
under the symbol JEM, was designed to mature in five years, on June 14, 2002.
As it turned out, that was about the peak of the Japanese market. By October of
1998, when markets worldwide were having difficulty dealing with the Russian debt
crisis and the fallout from a major hedge fund in the U.S. going broke, the Nikkei had
plummeted to 13,300. Thus, the Nikkei would have had to increase in price by just
over 50% merely to get back to the striking price. Hence, it would not appear that
JEM was ever going to be worth much more than its guarantee price of 10.
Since we have actual price histories of JEM, we can review how the market
place viewed the situation. In October 1998, JEM was actually trading at 8.75 - only
1.25 points below its guarantee price. That discount equates to an annual com
pounded rate of 3.64%. In other words, if one were to buy JEM at 8.75 and it
matured at 10 about 40 months later, his return would have been 3.64% compound
ed annually. That by itself is a rather paltry rate of return, but one must keep in mind
that he also would own a call option on the Nikkei index, and that option has a 140%
participation rate on the upside.
602 Part V: Index Options and Futures
COMPUTING THE VALUE OF THE IMBEDDED CALL WHEN
THE UNDERLYING IS TRADING AT A DISCOUNT
Can we compute the value of the imbedded call when the structured product itself
is trading at a discount to its guarantee price? Yes, the formulae presented earlier can
always be used to compute the value of the imbedded call.
Example: Again using the example of JEM, the structured product on the Nikkei
index, recall that it was trading at 8. 75 with a guaranteed price of 10, with maturity
40 months hence. Assume that the risk-free interest rate at the time was 5.5%.
Assuming continuous compounding, $8.75 invested today would be worth $10.51 in
40 months.
Money in the bank = 8. 75 x ert
where r = 0.05 and t = 3.33 years (40 months)
Money in the bank= 8.75 x e0-055 x 3-333 = 10.51
Since the structured product will be worth 10 at maturity, the value of the call
is 0.51.
There is another, nearly equivalent way to determine the value of the call. It
involves determining where the structured product would be trading if it were com
pletely a zero-coupon debt of the underwriting brokerage. The difference between
that value and the actual trading price of the structured product is the value of the
imbedded call.
The credit rating of the underwriter of the structured product is an important
factor in how large a discount occurs. Recall that the guarantee price is only as good
as the creditworthiness of the underwriter. The underwriter is the one who will pay
the cash settlement value at maturity - not the exchange where the product is listed
nor any sort of clearinghouse or corporation.
THE ADJUSTMENT FACTOR
In recent years, some of the structured products have been issued with an adjustment
factor. The adjustment factor is generally a negative thing for investors, although the
underwriters try to couch it in language that makes it difficult to discern what is going
on. Simply put, the adjustment factor is a multiplier (less than 100%) applied to the
underlying index value before calculating the Final Cash Value. Adjustment factors
seemed to come into being at about the time that index option implied volatility
began to trade at much higher levels than it ever had (1997 onward).
Cl,opter 32: Structured Products 603
Example: A structured product is issued at an initial price of $10. It ostensibly allows
one to participate in the appreciation of the S&P 500 index over a price of 1,100.00.
However, upon closer inspection, what the product really offers is the opportunity for
one to participate in the appreciation of the S&P 500 index ($SPX) over an adjusted
value, which is a percentage of the $SPX price - not the actual price itself. The cash
value settlement formula is stated as:
Cash settlement value = 10 + 10 x (Adjusted $SPX - 1,100.00) / 1,100.00
The formula looks similar to the "normal" cash settlement value formulae
shown earlier in the chapter, but the term "adjusted $SPX" has yet to be defined. In
fact, it is defined as a percentage of the final $SPX Price - 91.25% in this case. In real
ity, the prospectus says something to the effect that the final price of $SPX will be
adjusted downward by an annual adjustment factor of 1.25%. Thus, at the end of the
seven-year maturity period, the total adjustment factor would be seven times 1.25%,
or 8.75%. The adjusted value is then equal to 100% - 8.75%, or 91.25%.
The adjustment factor is an onerous burden for the investor. It means that the final
value of $SPX will be reduced by the adjustment factor before it is determined how
far, or if at all, $SPX is above the striking price of 1,100.00.
Example: Suppose that $SPX exactly doubles in price during the life of the example
structured product. That is, it finishes at 2,200.00 - exactly twice the amount of the
striking price. Before the cash settlement value can be determined, $SPX must be
adjusted:
$SPX adjusted value = 0.9125 x 2,200.00 = 2,007.50
So the final cash settlement value is based on the adjusted value of $SPX:
Cash settlement value = 10 + 10 x (2,007.50 - l,100.00)/1,100.00 = 18.25
Hence, instead of doubling your money, as you might expect to do since the
$SPX Index doubled in price, you "only" make 82.5%.
Another way to view it: If the index doubles, then the structured product
"should" be worth double the initial price, or 20. But instead, it's


lement value is based on the adjusted value of $SPX:
Cash settlement value = 10 + 10 x (2,007.50 - l,100.00)/1,100.00 = 18.25
Hence, instead of doubling your money, as you might expect to do since the
$SPX Index doubled in price, you "only" make 82.5%.
Another way to view it: If the index doubles, then the structured product
"should" be worth double the initial price, or 20. But instead, it's worth 91.25% of 20,
or 18.25.
Carrying the example a little further, suppose that $SPX had tripled in price by
the maturity date, and was thus at 3,300. In this case, the cash settlement value would
be:
$SPX adjusted value = 0.9125 x 3,300.00 = 3,011.25
Cash settlement value = 10 + 10 x (3,011.25 - l,100.00)/1,100.00 = 27.375
604 Part V: Index Options and Futures
Or, thinking in the alternative, if the index triples, then the structured produc1
(before adjustment factor) would be triple its initial price, or 30. Then 30 x 91.25o/c
== 27.375.
This example begins to demonstrate just how onerous the adjustment factor is.
Notice that if the underlying doubles, you don't make "double" less 8.75% (the
adjustment factor). No, you make "double" times the adjustment factor - 17.5% -
less than double. In the case of tripling, you make 3 x 8.75%, or 26.25%, less than
triple (i.e., the structured product is worth 27.375, not 30, so the percentage increase
was 173. 75%, not 200% - a difference of 26.25%, stated in terms of the initial invest
ment). How can that be? It is a result of the adjustment factor being applied to the
$SPX price before your profit (cash settlement value) is computed.
THE BREAK-EVEN FINAL INDEX VALUE
Before discussing the adjustment factor in more detail, one more point should be
made: The owner of the structured product doesn't get back anything more than the
base value unless the underlying has increased by at least a fixed amount at maturi
ty. In others words, the underlying must appreciate to a price large enough that the
final price times the adjustment factor is greater than the striking price of the struc
tured product. We'll call this price the break-even final index value.
An example will demonstrate this concept.
Example: As in the preceding example, suppose tl1at the striking price of the struc
tured product is 1,100 and the adjustment factor is 8.75%. At what price would the
final cash settlement value be something greater than the base value of 10? That
price can be solved for with the following simple equation:
Break-even final index value== Striking price/ (1- Adjustment factor)
= 1,100 / (0.9125) == 1,205.48.
Generally speaking, the underlying index must increase in value by a specific
amount just to break even. In this case that amount is:
1 / (1 -Adjustment factor) = 1 / 0.9175 = 1.0959
In other words, the underlying index must increase in value by more than 9.5%
by maturity just to overcome the weight of the adjustment factor. If the index increas
es by a lesser amount, then the structured product holder will merely receive back
his base value ( 10) at maturity.
The previous examples all show that the adjustment factor is not a trivial thing.
At first glance, one might not realize just how burdensome it is. After all, one might
605
himself, what does 1.25% per year really matter? However, you can see that it
matter. In fact, our above examples did not even factor in the other cost that any
Investor has when his money is at risk - the cost of carry, or what he could have made
had he just put the money in the bank.
MEASURING THE COST OF THE ADJUSTMENT FACTOR
The magnitude of the adjustment increases as the price of the underlying increases.
lt is an unusual concept. We know that the structured product initially had an
imbedded call option. Earlier in this chapter, we endeavored to price that option.
However, with the introduction of the concept of an adjustment factor, it turns out
that the call option's cost is not a fixed amount. It varies, depending on the final value
of the underlying index. In fact, the cost of the option is a percentage of the final
value of the index. Thus, we can't really price it at the beginning, because we don't
know what the final value of the index will be. In fact, we have to cease thinking of
this option's cost as a fixed number. Rather, it is a geometric cost, if you will, for it
increases as the underlying does.
Perhaps another way to think of this is to visualize what the cost will be in per
centage terms. Figure 32-2 compares how much of the percent increase in the index
is captured by the structured product in the preceding example. The x-axis on the
graph is the percent increase by the index. The y-axis is the percent realized by the
structured product. The terms are the same as used in the previous examples: The
strike price is 1,100, the total adjustment factor is 8. 75%, and the guarantee price of
the structured product is 10.
The dashed line illustrates the first example that was shown, when a doubling
of the index value (an increase of 100%) to 2,200 resulted in a gain of 83.5% in the
price of the structured. Thus, the point (100%, 83.5%) is on the line on the chart
where the dashed lines meet.
Figure 32-2 points out just how little of the percent increase one captures if the
underlying index increases only modestly during the life of the structured product.
We already know that the index has to increase by 9.59% just to get to the break-even
final price. That point is where the curved line meets the x-axis in Figure 32-2.
The curved line in Figure 32-2 increases rapidly above the break-even price,
and then begins to flatten out as the index appreciation reaches 100% or so. This
depicts the fact that, for small percentage increases in the index, the 8.75% adjust
ment factor - which is a flat-out downward adjustment in the index price - robs one
of most of the percentage gain. It is only when the index has doubled in price or so
that the curve stops rising s


ly above the break-even price,
and then begins to flatten out as the index appreciation reaches 100% or so. This
depicts the fact that, for small percentage increases in the index, the 8.75% adjust
ment factor - which is a flat-out downward adjustment in the index price - robs one
of most of the percentage gain. It is only when the index has doubled in price or so
that the curve stops rising so quickly. In other words, the index has increased enough
in value that the structured product, while not capturing all of the percentage gain
by any means, is now capturing a great deal of it.
604 Part V: Index Options and Futures
Or, thinking in the alternative, if the index triples, then the structured product
(before adjustment factor) would be triple its initial price, or 30. Then 30 x 91.25%
= 27.375.
This example begins to demonstrate just how onerous the adjustment factor is.
Notice that if the underlying doubles, you don't make "double" less 8.75% (the
adjustment factor). No, you make "double" times the adjustment factor - 17.5% -
less than double. In the case of tripling, you make 3 x 8.75%, or 26.25%, less than
triple (i.e., the structured product is worth 27.375, not 30, so the percentage increase
was 173. 75%, not 200% - a difference of 26.25%, stated in terms of the initial invest
ment). How can that be? It is a result of the adjustment factor being applied to the
$SPX price before your profit (cash settlement value) is computed.
THE BREAK-EVEN FINAL INDEX VALUE
Before discussing the adjustment factor in more detail, one more point should be
made: The owner of the structured product doesn't get back anything more than the
base value unless the underlying has increased by at least a fixed amount at maturi
ty. In others words, the underlying must appreciate to a price large enough that the
final price times the adjustment factor is greater than the striking price of the struc
tured product. We'll call this price the break-even final index value.
An example will demonstrate this concept.
Example: As in the preceding example, suppose that the striking price of the struc
tured product is 1,100 and the adjustment factor is 8.75%. At what price would the
final cash settlement value be something greater than the base value of 10? That
price can be solved for with the following simple equation:
Break-even final index value = Striking price/ (1- Adjustment factor)
= 1,100 / (0.9125) = 1,205.48.
Generally speaking, the underlying index must increase in value by a specific
amount just to break even. In this case that amount is:
1 / (1 - Adjustment factor) = 1 / 0.9175 = 1.0959
In other words, the underlying index must increase in value by more than 9.5%
by maturity just to overcome the weight of the adjustment factor. If the index increas
es by a lesser amount, then the structured product holder will merely receive back
his base value (10) at maturity.
The previous examples all show that the adjustment factor is not a trivial thing.
At first glance, one might not realize just how burdensome it is. After all, one might
605
himself, what does 1.25% per year really matter? However, you can see that it
matter. In fact, our above examples did not even factor in the other cost that any
htvt?stor has when his money is at risk - the cost of carry, or what he could have made
he just put the money in the bank.
MIASURING THE COST OF THE ADJUSTMENT FACTOR
The magnitude of the adjustment increases as the price of the underlying increases.
It is an unusual concept. We know that the structured product initially had an
hnbedded call option. Earlier in this chapter, we endeavored to price that option.
However, with the introduction of the concept of an adjustment factor, it turns out
that the call option's cost is not a fixed amount. It varies, depending on the final value
of the underlying index. In fact, the cost of the option is a percentage of the final
value of the index. Thus, we can't really price it at the beginning, because we don't
know what the final value of the index will be. In fact, we have to cease thinking of
this option's cost as a fixed number. Rather, it is a geometric cost, if you will, for it
increases as the underlying does.
Perhaps another way to think of this is t.o visualize what the cost will be in per
centage terms. Figure 32-2 compares how much of the percent increase in the index
is captured by the structured product in the preceding example. The x-axis on the
graph is the percent increase by the index. The y-axis is the percent realized by the
structured product. The terms are the same as used in the previous examples: The
strike price is 1,100, the total adjustment factor is 8.75%, and the guarantee price of
the structured product is 10.
The dashed line illustrates the first example that was shown, when a doubling
of the index value (an increase of 100%) to 2,200 resulted in a gain of 83.5% in the
price of the structured. Thus, the point (100%, 83.5%) is on the line on the chart
where the dashed lines meet.
Figure 32-2 points out just how little of the percent increase one captures if the
underlying index increases only modestly during the life of the structured product.
We already know that the index has to increase by 9.59% just to get to the break-even
final price. That point is where the curved line meets the x-axis in Figure 32-2.
The curved line in Figure 32-2 increases rapidly above the break-even price,
and then begins to flatten out as the index appreciation reaches 100% or so. This
depicts the fact that, for small percentage increases in the index, the 8.75% adjust
ment factor -which is a flat-out downward adjustment in the index price - robs one
of most of the percentage gain. It is only when the index has doubled in price or so
that the curve stops rising so quickly. In other words, the index has increased enough
in value that the structured product, while not capturing all of the percentage gain
by


percentage increases in the index, the 8.75% adjust
ment factor -which is a flat-out downward adjustment in the index price - robs one
of most of the percentage gain. It is only when the index has doubled in price or so
that the curve stops rising so quickly. In other words, the index has increased enough
in value that the structured product, while not capturing all of the percentage gain
by any means, is now capturing a great deal of it.
606 Part V: Index Options and Futu
FIGURE 32-2.
Percent of increase captured by structured product.
90
80
70
60
"O
I!: 50 ::,
0..
ttl
(.)
40 :£ 0
30 Break-even: 9.59% Increase
20
10
0 100 200 300 400 500
% Increase by Index
After that, the curve in Figure 32-2 flattens dramatically. It eventually flattens
out completely at 91.25%. That is, if the index increases enough in value (about
3,000% or morel), then the structured product final cash value will reflect the full
91.25% percent of appreciation of the index itself. That kind of increase in seven
years is virtually unattainable. In reality, the index - if it increases at all - will proba
bly be more in line with the values shown on the x-axis in Figure 32-2. In those cases,
especially for increases of 100% or less, the oppressive weight of the adjustment fac
tor significantly harms the return from the structured product.
One could visualize the graph in Figure 32-2 another way, if it would help.
Replace the values on the x-axis with the actual index values: 2,200, 3,300, 4,400,
5,500, and 6,600 would replace the figures shown as 100, 200, 300, 400, and 500.
Thus, the x-axis could then represent the final value of the index (before adjustment).
That might help to relate just how far the index would have to rise in order to over
come the downward adjustment.
Figure 32-3 shows a more conventional look at the comparison between the
index value at maturity and the cash value of the structured product. For example,
the dashed line shows that, with the final value (unadjusted) of the index at 3,300, the
structured product's final cash value would be 27.375, as shown in a prior example.
The line on Figure 32-3 looks like that of owning a call - limited risk, with large
32: Structured Products
PIGURE 32-3.
Cash value of structured product at maturity.
Q)
::,
50
40
~ 30
.c
l{5
(.)
20
10----r
0 1100
Break-even: 1205.48
2200 3300 4400 5500
Index Final Price (Unadjusted)
607
6600
upside profit potential. It is much more difficult to tell that the adjustment factor is
weighing down the value of the structured product so dramatically from this chart.
Both Figures 32-2 and 32-3 are mathematically correct. However, only Figure 32-2
depicts the real cost of owning a structured product with an adjustment factor.
The final graph on this topic, Figure 32-4, shows the cash value of the adjusted
structured product ( the same line as was shown in Figure 32-3), compared with an
unadjusted line. For example, the unadjusted line shows a true doubling of the price
of the structured product if the underlying index has doubled. The difference between
the two lines (the shaded area) can be thought of as the cost of the imbedded call- or
at least as the cost of the adjustment factor. You can see from Figure 32-4 how the
call's "cost" increases as the value of the underlying index increases.
OTHER CONSTRUCTS
The financial engineers who create structured products have come up with a num
ber of different constructs over time. Some resemble spreads, and some have two or
three different products bundled into one. In fact, just about anything is possible. All
that is required is that the underwriter thinks there is enough interest somewhere for
him to be able to create the product, mark it up, and sell it to whomever has inter-
608 Part V: Index Options and Future;
FIGURE 32-4.
Comparison of adiusted and unadiusted cash values at maturity.
50
40
20
0 1100 2200 3300
Cost of the
Call Option
4400 5500
Index Final Price (Unadjusted)
6600
est. In this section, a couple of different constructs, ones that have been brought to
the public marketplace in the past, are discussed.
THE BUI.I. SPREAD
Several structured products have represented a bull spread, in effect. In some cases,
the structured product terms are stated just like those of a call spread in that the final
cash value is defined with both a minimum and a maximum value. For example, it
might be described something like this:
"The final cash value of the (structured) product is equal to a minimum of a base
price of 10, plus any appreciation of the underlying index above the striking price,
subject to a maximum price of 20" (where the striking price is stated elsewhere).
It's fairly simple to see how this resembles a bull spread: The worst you can do
is to get back your $10, which is presumably the initial offering price, just as in any
of the structured products described previously in this chapter. Then, above that,
you'd get some appreciation of the index price above the stated striking price - again
609
the products discussed earlier. However, in this case, there is a maximum that the
c,1.,;h value can be worth: 20. In other words, there is a ceiling on the value of this
1tructured product at maturity. It is exactly like a bull spread with two striking prices,
one at 10 and one at 20. In reality, this structured product would have to be evaluat-
using both striking prices. We'll get to that in a minute.
There is another way that the underwriter sometimes states the terms of the
structured product, but it is also a bull spread in effect. The prospectus might say
something to the effect that the structured product is defined pretty much in the
standard way, but that it is callable at a certain (higher) price on a certain date. In
uther words, someone else can call your structured product away on that date. In
effect, you have sold a call with a higher striking price against you


d product, but it is also a bull spread in effect. The prospectus might say
something to the effect that the structured product is defined pretty much in the
standard way, but that it is callable at a certain (higher) price on a certain date. In
uther words, someone else can call your structured product away on that date. In
effect, you have sold a call with a higher striking price against your structured prod
Ut1:. Thus, you own an imbedded call via the usual purchase of the structured prod
uct and you have written a call with a higher strike. That, again, is the definition of a
bull spread.
When analyzing a product such as this, one must be mindful that there are two
calls to price, not only in determining the final value, but more importantly in deter
mining where you might expect the structured product to trade during its life, prior
to maturity. An option strategist knows that a bull spread doesn't widen out to its max
imum profit potential when there is still a lot of time remaining before expiration,
unless the underlying rises by a substantial amount in excess of the higher striking
price of the spread. Thus, one would expect this type of structured product to behave
in a similar manner.
The example that will be used in the rest of this section is based on actual "bull
spread" structured products of this type that trade in the open marketplace.
Example: Suppose that a structured product is linked to the Internet index. The
strike price, based on index values, is 150. If the Internet index is below 150 at matu
rity, seven years hence, then the structured product will be worth a base value of 10.
There is no adjustment factor, nor is there a participation rate factor. So far, this is
just the same sort of definition that we've seen in the simpler examples presented
previously. The final cash value formula would be simply stated as:
Final cash value = 10 x (Final Internet index value/150)
However, the prospectus also states that this structured product is callable at a
price of 25 during the last month of its life.
This call feature means that there is, in effect, a cap on the price of the under
lying. In actual practice, the call feature may be for a longer or shorter period of time,
and may be callable well in advance of maturity. Those factors merely determine the
expiration date of the imbedded call that has been "written."
610 Part V: Index Options and Futures
The first thing one should do is to convert the striking price into an equivalent
price for the underlying index, so that he can see where the higher striking price is
in relation to the index price. In this example, the higher striking price when stated
in terms of the structured product is 2.5 times the base price. So the higher striking
price, in index terms, would be 2.5 times the striking price, or 375:
Index call price = ( Call price / Base price) x Striking price
= (25 I 10) X 150
= 375
Hence, if the Internet index rose above 375, the call feature would be "in effect"
(i.e., the written call would be in-the-money). The value at which we can expect the
structured product to trade, at maturity, would be equal to the base price plus the
value of the bull spread with strikes of 10 and 25.
Valuing the Bull Spread. Just as the single-strike structured products have
an imbedded call option in them, whose cost can be inferred, so do double-strike
structured products. The same line of analysis leads to the following:
"Theoretical" cash value = 10 + Value of bull spread - Cost of carry
Cost of carry refers to the cost of carry of the base price (10 in this example).
By using an option model and employing knowledge of bull spreads, one can
calculate a theoretical value for the structured product at any time during its life.
Moreover, one can decide whether it is cheap or expensive - factors that would lead
to a decision as to whether or not to buy.
Example: Suppose that the Internet index is trading at a price of 210. What price can
we expect the structured product to be trading at? The answer depends on how
much time has passed. Let's assume that two years have passed since the inception
of the structured product (so there are still five years of life remaining in the option).
With the Internet index at 210, it is 40% above the structured product's lower
striking price of 150. Thus, the equivalent price for the structured product would be
14. Another way to compute this would be to use the cash value formula:
Cash value= 10 x (210 / 150) = 14
Now, we could use the Black-Scholes (or some other) model to evaluate the two
calls - one with a striking price of 10 and the other with a striking price of 25. Using
a volatility estimate of 50%, and assuming the underlying is at 14, the two calls are
roughly valued as follows:
Underlying price: 14
Cl,opter 32: Structured Products
Option
5-year call, strike = 10
5-year call, strike = 25
Theoretical Price
7.30
3.70
611
Thus, the value of the bull spread would be approximately 3.60 (7.30 minus
3.70). The structured product would then be worth 13.60- the base price of 10, plus
the value of the spread:
"Theoretical" cash value= 10 + 3.60 - Cost of carry= 13.60 - Cost of carry
It may seem strange to say that the value of the structured product is actually
less than the cash value, but that is what the call feature does: It reduces the worth
of the structured product to values below what the cash value formula would indi
cate.
Given this information, we can predict where the structured product would trade at
any price or at any time prior to maturity. Let's look at a more extreme example, then,
one in which the Internet index has a tremendously big run to the upside.
Example: Suppose that the Internet index has risen to 525 with four years of life
remaining until maturity of the structured product. This is well above the index
equivalent call price of 375. Again, it is first necessary to translate the index price


any time prior to maturity. Let's look at a more extreme example, then,
one in which the Internet index has a tremendously big run to the upside.
Example: Suppose that the Internet index has risen to 525 with four years of life
remaining until maturity of the structured product. This is well above the index
equivalent call price of 375. Again, it is first necessary to translate the index price
back to an equivalent price of the structured product, using either percentage gains
or the cash value formula:
Cash value = 10 x (525/ 150) = 35
Again, using the Black-Scholes model, we can determine the following theo
retical values:
Underlying price: 35
Option
3-year c~strike = 10
3-year call, strike = 25
Theoretical Price
25.50
14.70
Now, the value of the bull spread is 10.80 (25.50 minus 14.70). The deepest in
the-money option is trading near parity, but the (written) option is only 10 points in
the-money and thus has quite a bit of time value premium remaining, since there are
three years of life left:
"Theoretical" cash value = 10 + 10.80 = 20.80 - Cost of carry
612 Part V: Index Options and Futures
Hence, even though the Internet index is at 525 - far above the equivalent cal
price of 375 - the structured product is expected to be trading at a price well belo\\
its maximum price of 25.
Figure 32-5 shows the values over a broad spectrum of prices and for various
expiration dates. One can clearly see that the structured product will not trade"near
its maximum price of 25 until time shrinks to nearly the maturity date, or until the
underlying index rises to very high prices. In particular, note where the theoretical
values for the bull spread product lie when the index is at the higher striking price of
375 (there is a vertical line on the chart to aid in identifying those values). The struc
tured product is not worth 20 in any of the cases, and for longer times to maturity, it
isn't even worth 15. Thus, the call feature tends to dampen the upside profit poten
tial of this product in a dramatic manner.
The curves in Figure 32-5 were drawn with the assumption that volatility is
50%. Should volatility change materially during the life of the structured product,
then the values would change as well. A lower volatility would push the curves up
toward the "at maturity" line, while an increase in volatility would push the curves
down even further.
FIGURE 32-5.
Value of bull spread structured product.
At Maturity
25
1 Year Left
20 3Years Left
15
5
100 150 200 250 300 350 400 450 500 550 600
Price of Index
Gtpter 32: Structured Products
MULTIPLE EXPIRATION DATES
613
In some cases, more than one expiration date is involved when the structured prod
uct is issued. These products are very similar to the simple ones first discussed in this
chapter. However, rather than maturing on a specific date, the final index value -
which is used to determine the final cash value of the structured product - is the
average of the underlying index price on two or three different dates.
For example, one such listed product was issued in 1996 and used the S&P 500
index ($SPX) as the underlying index. The strike price was the price of $SPX on the
day of issuance, as usual. However, there were three maturity dates: one each in April
2001, August 2002, and December 2003. The final index value used to determine the
cash settlement value was specified as the average of the $SPX closings on the three
maturity dates.
In effect, this structured product was really the sum of three separate struc
tured products, each maturing on a different date. Hence, the values of the imbed
ded calls could each be calculated separately, using the methods presented earlier.
Then those three values could be averaged to determine the overall value of the
imbedded call in this structured product.
OPTION STRATEGIES INVOLVING STRUCTURED PRODUCTS
Since the structured products described previously are similar to well-known option
strategies (long call, bull spread, etc.), it is possible to use listed options in conjunc
tion with the structured products to produce other strategies. These strategies are
actually quite simple and would follow the same lines as adjustment strategies dis
cussed in the earlier chapters of this book.
Example: Assume that an investor purchased 15,000 shares of a structured product
some time ago. It is essentially a call option on the S&P 500 index ($SPX). The prod
uct was issued at a price of 10, and that is the guarantee price as well. The striking
price is 700, which is where $SPX was trading at the time. However, now $SPX is
trading at 1,200, well above the striking price. The cash value of the product is:
)ox (1,2001100) = 11.14
Furthermore, assume that there are still two years remaining until maturity of
the structured product, and the investor is getting a little nervous about the market.
He is thinking of selling or hedging his holding in the structured product. However,
the structured product itself is trading at 16.50, a discount of 64 cents from its theo-
614 Part V: Index Options and Futurei
retical cash value. He is not too eager to sell at such a discount, but he realizes tha
he has a lot of exposure between the current price and the guarantee price of 10.
He might consider writing a listed call against his position. That would conver
it into the equivalent of a bull spread, since he already holds the equivalent of a lonf
call via ownership of the structured product. Suppose that he quotes the $SP)
options that trade on the CBOE and finds the following prices for 6-month options
expiring in December:
$SPX: 1,200
Option
December 1,200 call
December 1,250 call
December 1,300 call
Price
85
62
43
Suppose that he likes the sale of the December 1,250 call for 62 points. How
many should he sell against his position in order to have a proper hedge?
First, one must compute a multiplier that indicates how many shares of the
structured


lowing prices for 6-month options
expiring in December:
$SPX: 1,200
Option
December 1,200 call
December 1,250 call
December 1,300 call
Price
85
62
43
Suppose that he likes the sale of the December 1,250 call for 62 points. How
many should he sell against his position in order to have a proper hedge?
First, one must compute a multiplier that indicates how many shares of the
structured product are equivalent to one "share" of the $SPX. That is done in the
simple case by dividing the striking price by the guarantee price:
Multiplier = Striking price/ Base price
= 700 / 10 = 70
This means that buying 70 shares of the structured product is equivalent to
being long one share of $SPX. To verify this, suppose that one had bought 70 shares
of the structured product initially at a price of 10, when $SPX was at 700. Later,
assume that $SPX doubles to 1,400. With the simple structure of this product, which
has a 100% participation rate and no adjustment factor, it should also double to 20.
So 70 shares bought at 10 and sold at 20 would produce a profit of $700. As for $SPX,
one "share" bought at 700 and later sold at 1,400 would also yield a profit of $700.
This verifies that the 70-to-l ratio is the correct multiplier.
This multiplier can then be used to figure out the current equivalent structured
product position in terms of $SPX. Recall that the investor had bought 15,000 shares
initially. Since the multiplier is 70-to-l, these 15,000 shares are equivalent to:
$SPX equivalent shares = Shares of structured product held/ Multiplier
= 15,000 / 70 = 214.29
That is, owning this structured product is the equivalent of owning 214+ shares
of $SPX at current prices. Since an $SPX call option is an option on 100 "shares" of
$SPX, one would write 2 calls (rounding off) against his structured profit position.
Since the SPX December 1,250 calls are selling for 62, that would bring in $12,400
less commissions.
615
Note that the sale of these calls effectively puts a cap on the profit potential of
investor's overall position until the December expiration of the listed calls. If $SPX
were to rise substantially above 1,250, his profits would be "capped" because the two
were sold. Thus, he has effectively taken his synthetic long call position and con
verted it into a bull spread (or a collared index fund, if you prefer that description).
In reality, any calls written against the structured product would have to be
margined as naked calls. In a virtual sense, the 15,000 shares of the structured prod
Ut't "cover" the sale of 2 $SPX calls, but margin rules don't allow for that distinction.
In essence, the sale of two calls would create a bull spread. Alternatively, if one thinks
uf the structured product as a long index fully protected by a put (which is another
way to consider it), then the sale of the $SPX listed call produces a "collar."
Of course, one could write more than two $SPX calls, if he had the required
margin in his account. This would create the equivalent of a call ratio spread, and
would have the properties of that strategy: greatest profit potential at the striking
price of the written calls, limited downside profit potential, and theoretically unlim
ited upside risk if $SPX should rise quickly and by a large amount.
In any of these option writing strategies, one might want to write out-of-the
money, short-term calls against his structured product periodically or continuously.
Such a strategy would produce good results if the underlying index does not advance
quickly while the written calls are in place. However, if the index should rise through
the striking price of the written calls, such a strategy would detract from the overall
return of the structured product.
Changing the Striking Price. Another strategy that the investor could use
if he so desired is to establish a vertical call spread in order to effectively change
the striking price of the (imbedded) call. For example, if the market had advanced
by a great deal since the product was bought, the imbedded call would theoreti
cally have a nice profit. If one could sell it and buy another, similar call at a high
er strike, he would effectively ~olling his call up. This would raise the striking
price and would reduce downside risk greatly (at the cost of slightly reducing
upside profit potential).
Example: Using the same product as in the previous example, suppose that the
investor who owns the structured product considers another alternative. In the pre
vious example, he evaluated the possibility of selling a slightly out-of-the-money list
ed call to effectively produce a collared position, or a bull spread. The problem with
that is that it limits upside profit potential. If the market were to continue to rise, he
would only participate up to the higher strike (plus the premium received).
616 Part V: Index Options and Futu,
A better alternative might be to roll his imbedded call up, thereby taking s01
money out of the position but still retaining upside profit potential. Recall that t
structured product had these terms:
Guarantee price: 10
Underlying index: S&P 500 index ($SPX)
Striking price: 700
As in the earlier example, the investor owns 15,000 shares of the structun
product. Furthermore, assume that there are about two years remaining until mat
rity of the structured product, and that the current prices are the same as in the pr
vious example:
Current price of structured product: 16.50
Current price of $SPX: 1,200
For purposes of simplicity, let's assume that there are listed two-year LEAP
options available for the S&P index, whose prices are:
S&P 2-year LEAPS, striking price 700: 550
S&P 2-year LEAPS, striking price 1,200: 210
In reality, S&P LEAPS options are normally reduced-value options, meanin.
that they are for one-tenth the value of the index and thus sell for one-tenth the pricE
However, for the purposes of this theoretical example, we will assume


listed two-year LEAP
options available for the S&P index, whose prices are:
S&P 2-year LEAPS, striking price 700: 550
S&P 2-year LEAPS, striking price 1,200: 210
In reality, S&P LEAPS options are normally reduced-value options, meanin.
that they are for one-tenth the value of the index and thus sell for one-tenth the pricE
However, for the purposes of this theoretical example, we will assume that the full
value LEAPS shown here exist.
It was shown in the previous example that the investor would trade two of thest
calls as an equivalent amount to the quantity of calls imbedded in his structurec
product. So, this investor could buy two of the 1,200 calls and sell two of the 700 calli
and thereby roll his striking price up from 700 to 1,200. This roll would bring in 34(
points, two times; or $68,000 less commissions.
Since the difference in the striking prices is 500 points, you can see that he is
leaving something "on the table" by receiving only 340 points for the roll-up. This is
common when rolling up: One loses the time value premium of the vertical spread.
However, when viewed from the perspective of what has been accomplished, the
investor might still find this roll worthwhile. He has now raised the striking price of
his call to 1,200, based on the S&P index, and has taken in $68,000 in doing so. Since
he owns 15,000 shares of the structured product, that means he has taken in 4.53 p~r
share (68,000 / 15,000). Now, for example, if the S&P crashes during the next two
years and plummets below 700 at the maturity date, he will receive $10 as the guar
antee price plus the $4.53 he got from the roll - a total "guarantee" of $14.53. Thus,
he has protected his downside.
Otpt,r 32: Structured Products 617
Note that his downside risk is not completely eliminated, though. The current
prke of the structured product is 16.50 and the cash value at the current S&P price
11117.14 (see the previous example for this calculation), so he has risk from these lev
down to a price of $14.53.
His upside is still unlimited, because he is net long two calls - the S&P 2-year
1,,EAPS calls, struck at 1,200. The two LEAPS calls that he sold, struck at 700, effec
tively offsets the call imbedded in the structured product, which is also struck at 700.
This example showed how one could effectively roll the striking price of his
structured product up to a higher price after the underlying had advanced. The indi
vidual investor would have to decide if the extra downside protection acquired is
worth the profit potential sacrificed. That depends heavily, of course, on the prices of
the listed S&P options, which in turn depend on things such as volatility and time
remaining until expiration.
Of course, one other alternative exists for a holder of a structured product who
has built up a good profit, as in the previous two examples: He could sell the prod
uct he owns and buy another one with a striking price closer to the current market
value of the underlying index. This is not always possible, of course, but as long as
these products continue to be brought to market every few months or so by the
underwriters, there will be a wide variety of striking prices to choose from. A possi
ble drawback to rolling to another structured product is that one might have to
extend his holding's maturity date, but that is not necessarily a bad thing.
A different scenario exists when the underlying index drops after the structured
product is bought. In that case, one would own a synthetic call option that might be
quite far out-of the-rrwney. A listed call spread could be used to theoretically lower
the call's striking price, so that upside movement might more readily produce prof
its. In such a case, one would sell a listed call option with a striking price equal to the
striking price of the structured product and would buy a listed call option with a
lower striking price - one more in line with current market values. In other words,
he would buy a listed call bull spread to go along with his structured product.
Whatever debit he pays for this call bull spread will increase his downside risk, of
course. However, in return he ~s the ability to make profits more quickly if the
underlying index rises above the new, lower striking price.
Many other strategies involving listed options and the structured product could
be constructed, of course. However, the ones presented here are the primary strate
gies that an investor should consider. All that is required to analyze any strategy is to
remember that this type of structured product is merely a synthetic long call. Once
that concept is in mind, then any ensuing strategies involving listed options can easily
be analyzed. For example, the purchase of a listed put with a striking price essential-
618 Part V: Index Options and Future
ly equal to that of the structured product would produce a position similar to a 101
straddle. The reader is left to interpret and analyze other such strategies on his OWI
LISTS OF STRUCTURED PRODUCTS
The descriptions provided so far encompass the great majority of listed structure
products. There are many similar ones involving individual stocks instead ofJndice
(often called equity-linked notes). The concepts are the same; merely substitute
stock price for an index price in the previous discussions in this chapter.
Some large insurance companies offer similar products in the form of annuities
They behave in exactly the same way as the products described above, except tha
there is no continuous market for them. However, they still afford one the opportu
nity to own an index fund with no risk Many of the insurance company products, in
fact, pay interest to the annuity holder - something that most of the products listed
on the stock exchanges do not.
Both the CBOE and American Exchange Web sites (www.cboe.com and
www.amex.com) contain details of the structured products listed on their respective
exch


However, they still afford one the opportu
nity to own an index fund with no risk Many of the insurance company products, in
fact, pay interest to the annuity holder - something that most of the products listed
on the stock exchanges do not.
Both the CBOE and American Exchange Web sites (www.cboe.com and
www.amex.com) contain details of the structured products listed on their respective
exchanges. A sampling at the time of this writing showed the following breakdowns
of listed structured products:
Underlying Index Percent of Listed Products
Broad-based index (S&P 500, e.g.) 23%
Sector index
Stocks
43%
34%
If you browse those lists, an investor may find indices or stocks that are of particular
interest to him. In addition, it may be possible to find ones trading at a substantial
discount to cash settlement value, something a strategist might find attractive.
PERCS
Part II: Products Designed
to Provide /,/Income"
At the beginning of this chapter, it was stated that most listed structured products~
fall into one of two categories. The first category was the type of structured prod
uct that resembled the ownership of a call option. The second portion, to be dis-
0.,t,r 32: Structured Products 619
t'Ussed in the remainder of this chapter, resembles the covered write of a call
option. These often have names involving the term preferreds. Some are called
Trust Preferreds; another popular term for them is Preferred Equity Redemption
Cumulative Stock (PERCS). We will use the term PERCS in the following exam
ples, but the reader should understand that it is being used in a generic sense - that
any of the similar types of products could be substituted wherever the term PERCS
is used.
A PERCS is a structured product, issued with a maturity date and tied to an
individual stock. At the time of issuance, the PERCS and the common stock are usu
ally about the same price. The PERCS pays a higher dividend than the common
stock, which may pay no dividend at all. If the underlying common should decline in
price, the PERCS should decline by a lesser amount because the higher dividend
payout will provide a yield floor, as any preferred stock does.
There is a limited life span with PERCS that is spelled out in the prospectus at
the time it is issued. Typically, that life span is about three years. At the end of that
time, the PERCS becomes ordinary common stock.
A PERC S may be called at any time by the issuing corporation if the company's
common stock exceeds a predetermined call price. In other words, this PERCS stock
is callable. The call price is normally higher than the price at which the common is
trading when the PERCS is issued.
What one has then, if he owns a PERCS, is a position that will eventually
become common stock unless it is called away. In order to compensate him for the
fact that it might he called away, the owner receives a higher dividend. What if one
substitutes the word "premium" for "higher dividend"? Then the last statement
reads: In order to compensate him for the fact that it might be called away, the owner
receives a premium. This is exactly the definition of a covered call option write.
Moreover, it is an out-of-the-money covered write of a long-term call option, since
the call price of the PERCS is akin to a striking price and is higher than the initial
stock price.
Example: XYZ is selling at $35 per share. XYZ common stock pays $1 a year in div
idends. The company decides to issue a PERCS.
The PERCS will have a three~ life and will be callable at $39. Moreover, the
PERCS will pay an annual dividend of $2.50.
The PERCS annual dividend rate is 7% as compared to 2.8% for the common
stock.
If XYZ were to rise to 39 in exactly three years, the PERCS would be called.
The total return that the PERCS holder would have made over that time would be:
620
Stock price appreciation 139 - 35):
Dividends over 3 years:
Total gain
Total return:
Annualized return:
Part V: Index Options and Future.
4
7.50
11.50
11.50/35 = 32.9%
32.9%/3 = 11%
If the PERCS were called at an earlier time, the annualized return might be ever
higher. ·
CALL FEATURE
The company will most likely call the PER CS if the common is above the call price
for even a short period of time. The prospectus for the PERCS will describe any
requirements regarding the call. A typical one might be that the common must close
above the call price for five consecutive trading days. If it does, then the company
may call the PERCS, although it does not have to. The decision to call or not is strict
ly the company's. The PERCS holder has no choice in the matter of when or if his
shares are called. This is the same situation in which the writer of a covered call finds
himself: He cannot control when the exercise will occur, although there are often
clues, including the disappearance of time value premium in the written listed call
option. The PERCS holder is more in the dark, because he cannot actually see the
separate price of the imbedded call within the PERCS. Still, as will be shown later,
he may be able to use several clues to determine whether a call is imminent.
Most PERCS may be called for either cash or common stock. This does not
change the profitability from the strategist's standpoint. He either receives cash in
the amount of the call price, or the same dollar amount of common stock. The only
difference between the two is that, in order to completely close his position, he would
have to sell out any common stock received via the call feature. If he had received
cash instead, he wouldn't have to bother with this final stock transaction.
In the case of most PERCS, the call feature is more complicated than that pre
sented in the preceding example. Recall that the company that issued the PERCS
can call it at any time during the three years, as long as the common is above the call
price. The holder of the XYZ PERCS in the example would not be pleased


ved
cash instead, he wouldn't have to bother with this final stock transaction.
In the case of most PERCS, the call feature is more complicated than that pre
sented in the preceding example. Recall that the company that issued the PERCS
can call it at any time during the three years, as long as the common is above the call
price. The holder of the XYZ PERCS in the example would not be pleased to find
that the PER CS was called before he had received any of the higher dividends that
the PERCS pays. Therefore, in order to give a PERCS holder essentially the same
return no matter when the PERCS is called, there is a "sliding scale" of call prices. -
At issuance, the call price will be the highest. Then it will drop to a slightly
lower level after some of the dividends have been paid (perhaps after the first year).
621
This lowering of the call price continues as more dividends are paid, until it finally
reaches the final call price at maturity. The PERCS holder should not be confused
this sliding scale of call prices. The sliding call feature is designed to ensure that
PERC S holder is compensated for not receiving all his "promised" dividends if the
PERCS should be called prior to maturity.
Example: As before, XYZ issues a PERCS when the common is at 35. The PERCS
pays an annual dividend of $2.50 per share as compared to $1 per share on the com
mon stock. The PERCS has a final call price of 39 dollars per share in three years.
If XYZ stock should undergo a sudden price advance and rise dramatically in a
very short period of time, it is possible that the PERCS could be called before any
dividends are paid at all. In order to compensate the PERCS holder for such an
c>ecurrence, the initial call price would be set at 43.50 per share. That is, the PERCS
can't be called unless XYZ trades to a price over 43.50 dollars per share. Notice that
the difference between the eventual call price of 39 and the initial call price of 43.50
is 4.50 points, which is also the amount of additional dividends that the PERCS
would pay over the three-year period. The PER CS pays $2.50 per year and the com
mon $1 per year, so the difference is $1.50 per year, or $4.50 over three years.
Once the PERCS dividends begin to be paid, the call price will be reduced to
reflect that fact. For example, after one year, the call price would be 42, reflecting
the fact that if the PERCS were not called until a year had passed, the PERCS hold
er would be losing $3 of additional dividends as compared to the common stock
($1.50 per year for the remaining two years). Thus, the call price after one year is set
at the eventual call price, 39, plus the $3 of potential dividend loss, for a total call
price of 42.
This example shows how the company uses the sliding call price to compensate
the PERCS holder for potential dividend loss if the PERCS is called before the
three-year time to maturity has elapsed. Thus, the PER CS holder will make the same
dollars of profit - dividends and price appreciation combined - no matter when the
PERCS is called. In the case of the XYZ PERCS in the example, that total dollar
profit is $11.50 (see the prior example). Notice that the investor's annualized rate of
return would be much higher if he were called prior to the eventual maturity date.
One final point: The call price §lides on a scale as set forth in the prospectus for
the PERCS. It may be every time a dividend is paid, but more likely it will be daily!
That is, the present worth of the remaining dividends is added to the final call price
to calculate the sliding call price daily. Do not be overwhelmed by this feature.
Remember that it is just a means of giving the PERCS holder his entire "dividend
premium" if the PERCS is called before maturity.
622 Part V: Index Options and Futures
For the remainder of this chapter, the call price of the PERCS will be referrea
to as the redemption price. Since much of the rest of this chapter will be concemec
with discussing the fact that a PERCS is related to a call option, there could be somE
confusion when the word call is used. In some cases, call could refer to the price at
which the PER CS can be called; in other cases, it could refer to a call option - either
a listed one or one that is imbedded within the PERCS. Hence, the word redemp
tion will be used to refer to the action and price at which the issuing compa:J)ly may
call the PERCS.
A PERCS IS A COVERED CALL WRITE
It was stated earlier that a PER CS is like a covered write. However, that has not yet
been proven. It is known that any two strategies are equivalent if they have the same
profit potential. Thus, if one can show that the profitability of owning a PER CS is the
same as that of having established a covered call write, then one can conclude that
they are equivalent.
Example: For the purposes of this example, suppose that there is a three-year listed
call option with striking price 39 available to be sold on XYZ common stock. Also,
assume that there is a PERCS on XYZ that has a redemption price of 39 in three
years. The following prices exist:
XYZ common: 35
XYZ PERCS: 35
3-year call on XYZ common with striking price of 39: 4.50
First, examine the XYZ covered call write's profitability from buying 100 XY2 and
selling one call. It was initially established at a debit of 30.50 (35 less the 4.50
received from the call sale). The common pays $1 per year in dividends, for a total of
$3 over the life of the position.
XYZ Price Price of a Profit/loss on Total Profit/loss
in 3 Years 3-Year Call Securities Incl. Dividend
25 0 -$550 -$250
30 0 -50 +250
35 0 +450 +750
39 0 +850 + 1,150
45 6 +850 + 1,150
50 11 +850 + 1,150
O.,,ter 32: Structured Products 623
TI1is is the typical picture of the total return from a covered write - potential losses on
the downside with profit potential limited above the striking price of the written call.
Now look at the profitability of buying th


all Securities Incl. Dividend
25 0 -$550 -$250
30 0 -50 +250
35 0 +450 +750
39 0 +850 + 1,150
45 6 +850 + 1,150
50 11 +850 + 1,150
O.,,ter 32: Structured Products 623
TI1is is the typical picture of the total return from a covered write - potential losses on
the downside with profit potential limited above the striking price of the written call.
Now look at the profitability of buying the PER CS at 35 and holding it for three
(Assume that it is not called prior to maturity.) The PER CS holder will earn a
total of $750 in dividends over that time period.
XYZ Price Profit/Loss on Total Profit/Loss
in 3 Years PERCS Incl. Dividend
25 -$1,000 -$250
30 -500 +250
35 0 +750
>=39 +400 + 1, 150
This is exactly the same profitability as the covered call write. Therefore, it can be
concluded with certainty that a PERCS is equivalent to a covered call write. Note
that the PER CS potential early redemption feature does not change the truth of this
statement. The early redemption possibility merely allows the PERCS holder to
receive the same total dollars at an earlier point in time if the PERCS is demanded
prior to maturity. The covered call writer could theoretically be facing a similar situ
ation if the written call option were assigned before expiration: He would make the
same total profit, but he would realize it in a shorter period of time.
The PERCS is like a covered write of a call option with striking price equal to
the redemption price of the PERCS, except that the holder does not receive a call
option premium, but rather receives additional dividends. In essence, the PERCS
has a call option imbedded within it. The value of the imbedded call is really the
value of the additional dividends to be paid between the current date and maturity.
The buyer of a PERCS is, in effect, selling a call option and buying common
stock. He should have some idea of whether or not he is selling the option at a rea
sonably fair price. The next section of this chapter addresses the problem of valuing
the call option that is imbedded in the PERCS.
PRICE BEHAVIOR
The way that a PERCS price is often discussed is in relationship to the common
stock. One may hear that the PERCS is trading at the same price as the common or
at a premium or discount to the common. As an option strategist who understands
covered call writing, it should be a simple matter to picture how the PERCS price
will relate to the common price.
624 Part V: Index Options and Futures
FIGURE 32-6.
PERCS price estimate versus common stock.
44
(I)
iii 39 6 Months
E
~ w
(I)
u
ct 34
Cf)
(.)
a: w a.
29
0 1-.J. ____ ,__ ___ ...._ ___ _._ ___ __._ ___ _.__
25 30 35 40
Stock Price
45 50
First, consider the out-of-the-money situation. If the underlying common
declines in price, the PERCS will not decline as fast because the additional dividends
will provide yield support. The PER CS will therefore trade at a higher price than the
common. Howeve1~ as the maturity date nears and the remaining number of addi
tional dividends dwindles to a small amount, then the PER CS price and the common
price will converge.
The opposite effect occurs if the underlying common moves higher. The
PERCS will trade at a lower price than the common when the common trades above
the issue price. In fact, since there is a redemption price on the PERCS, it will not
trade higher than the redemption price. The common, however, has no such restric
tion, so it could continue to trade at prices significantly higher than the PERCS does.
These points are illustrated in Figure 32-6, which contains the price curves of two
PER CS: one at issuance, thus having three years remaining, and the other with just six
months remaining until the maturity of the PERCS. For purposes of comparison, it
was assumed that there is no sliding redemption feature involved. Several significant
points can be made from the figure. First, notice that the PERCS and the common._
tend to sell at approximately the same price at the point labeled "I." This would be the
price at which the PER CS are issued. This issue price must be below the redemption
price of the PERCS. More will be said later about how this price is determined.
Oapter 32: Structured Products 625
Another observation that can be made from the figure is that the PERCS pric
ing curves level off at the redemption price. They cannot sell for more than that
price.
Now look on the left-hand side of the figure. Notice that the more time remain
Ing until maturity, the higher the PERCS will trade above the common stock. This is
because of the extra dividends that the PER CS pay. Obviously, the PERCS with three
years until maturity has the potential to pay more dividends than the one with three
months remaining, so the three-year PERCS will sell for more than the six-month
PERCS when the common is below the issue price. Since either PERCS pays more
dividends than the common, they both trade for higher prices than the common.
When the common trades above the issue price (point 'T'), the opposite is true.
The six-month PERCS trades for a slightly higher price than the three-year PERCS,
but both sell for significantly less than the common, which has no limit on its poten
tial price.
One other observation can be made regarding the situation in which the com
mon trades well below the issue price: After the last additional dividend has been
paid by the PERCS, it will trade for approximately the same price as the common in
that situation. ·
Viewed strictly as a security, a PERCS may not appear all that attractive to some
investors. It has much, but not all, of the downside risk of the common stock, and not
nearly the upside potential. It does provide a better dividend, however, so if the com
mon is relatively unchanged from the issue price when the PERCS matures, the
PERCS holder will have come out ahead. If this description of the PER CS does not
appeal to you, then neither should co


l that attractive to some
investors. It has much, but not all, of the downside risk of the common stock, and not
nearly the upside potential. It does provide a better dividend, however, so if the com
mon is relatively unchanged from the issue price when the PERCS matures, the
PERCS holder will have come out ahead. If this description of the PER CS does not
appeal to you, then neither should covered call writing, for it is the same strategy; a
call option premium is merely substituted for the higher dividend payout.
PERCS STRATEGIES
Since the PERCS is equivalent to a covered write, strategies that have covered writes
as part of their makeup are amenable to having PERCS as part of their makeup as
well. Covered writing is part of ratio writing. Other modifications to the covered writ
ing strategy itself, such as the protected covered write, can also be applied to the
PERCS.
PROTECTING THE PERCS WITH LISTED OPTIONS
~
The safest way to protect the PERC S holding with listed options is to buy an out-of
the-nwney put. The resultant position - long PERCS and long put - is a protected
covered write, or a "collar." The long put prevents large losses on the downside, but
it costs the PERCS holder something. He won't make as much from his extra divi
dend payout, because he is spending money for the listed put. Still, he may want the
downside comfort.
626 Part V: Index Options and Futures
Once one realizes that a PERCS is equivalent to a covered write, he can easily
extend that equivalence to other positions as well. For example, it is known that a
covered call write is equivalent to the sale of a naked put. Thus, owning a PERCS is
equivalent to the sale of a naked put. Obviously, the easiest way to hedge a naked put
is to buy another put, preferably out-of-the-money, as protection.
Do not be deluded into thinking that selling a listed call against the PERCS is
a safe way of hedging. Such a call option sale does add a modicum of downside pro
tection, but it exposes the upside to large losses and therefore introduces a potential
risk into the position. It is really a ratio write. The subject is covered later in this
chapter.
REMOVING THE REDEMPTION FEATURE
At issuance, the imbedded call is a three-year call, so it is not possible to exactly
duplicate the PERCS strategy in the listed market. However, as the PERCS nears
maturity, there will be listed calls that closely approximate the call that is imbedded
in the PERCS. Consequently, one may be able to use the listed call or the underly
ing stock to his advantage.
If one were to buy a listed call with features similar to the imbedded call in a
PERCS that he owned, he would essentially be creating long common stock. Not that
one would necessarily need to go to all that trouble to create long common stock, but
it might provide opportunities for arbitrageurs.
In addition, it might appeal to the PERCS holder if the common stock has
declined and the imbedded call is now inexpensive. If one covers the equivalent of
the imbedded call in the listed market, he would be able to more fully participate in
upside participation if the common were to rally later. This is not always a profitable
strategy, however. It may be better to just sell out the PERCS and buy the common
if one expects a large rally.
Example: XYZ issued a PERCS some time ago. It has a redemption price of 39; the
common pays a dividend of $1 per year, while the PER CS pays $2.50 per year.
XYZ has fallen to a price of 30 and the PERCS holder thinks a rally may be
imminent. He knows that the imbedded call in the PERCS must be relatively inex
pensive, since it is 9 points out-of-the-money (the PERCS is redeemable at 39, while
the common is currently 30). Ifhe could buy back this call, he could participate more
fully in the upward potential of the stock.
Suppose that there is a one-year LEAPS call on XYZ with a striking price of 40.
If one were to buy that call, he would essentially be removing the redemption fea-
ture from his PERCS.
Assume the following prices exist:
Gapter 32: Structured Products
XYZ Common: 30
XYZ PERCS: 31
XYZ January 40 LEAPS call: 2
627
If one buys this LEAPS call and holds it until maturity of the PERCS one year
from now, the profit picture of the long PERCS plus long call position will be the fol
lowing:
Total Value
XYZ Price in PERCS January 40 of long PERCS
January Next Year Price LEAPS + long LEAPS
25 25 0 25
30 30 0 30
35 35 0 35
40 39 0 39
45 39 5 44
50 39 10 49
Thus, the PE RCS + long call position is worth almost exactly what the common
stock is after one year. The PERCS holder has regained his upside profit potential.
What did it cost the investor to reacquire his upside? He paid out 2 points for
the call, thereby more than negating his $1.50 dividend advantage over the course of
the year (the common pays a $1 dividend;'the PERCS $2.50). Thus, it may not actu
ally be worth the bother. In fact, notice that if the PERCS holder really wanted to
reacquire his upside profit potential, he would have been better off selling his
PERCS at 31 and buying the common at 30. If he had done this, he would have taken
in 1 point from the sale and purchase, which is slightly smaller than the $1.50 divi
dend he is forsaking. In either case, he must relinquish his dividend advantage and
then some in order to reacquire his upside profit potential. This seems fair, however,
for there must be some cost involved with reacquiring the upside.
Remember that an arbitrageur might be able to find a trade involving these sit
uations. He could buy a PERCS, sell the common short, and buy a listed call. If there
were price discrepancies, he could profit. It is actions such as these that are required
to keep prices in their proper relationship.
1
CHANGING THE REDEMPTION PRICE OF THE PERCS
When covered writing was discussed as a strategy, it was shown that the writer may
want to buy back the call that was written and sell


ns. He could buy a PERCS, sell the common short, and buy a listed call. If there
were price discrepancies, he could profit. It is actions such as these that are required
to keep prices in their proper relationship.
1
CHANGING THE REDEMPTION PRICE OF THE PERCS
When covered writing was discussed as a strategy, it was shown that the writer may
want to buy back the call that was written and sell another one at a different strike.
628 Part V: Index Options and Futu,
If the action results in a lower strike, it is known as rolling down; if it results in a hi§
er strike, it is rolling up.
This rolling action changes the profit potential of the position. If one rolls dov;
he gets more downside protection, but his upside is even more limited than it prei
ously was. Still, if he is worried about the stock falling lower, this may be a prop
action to take. Conversely, if the common is rallying, and the covered writer is mo
bullish on the stock, he can roll up in order to increase his upside profit potenti~(
course, by rolling up, he creates more downside risk if the common stock should sue
denly reverse direction and fall.
The PERCS holder can achieve the same results as the covered writer. He ca
effectively roll his redemption price down or up if he so chooses. His reasons fc
doing so would be substantially the same as the covered writer's. For example, if th
common were dropping in price, the PERCS holder might become worried that hi
extra dividend income would not be enough to protect him in the case of furthe
decline. Therefore, he would want to take in even more premium in exchange fo
allowing himself to be called away at a lower price.
Example: XYZ issued PERCS when both were trading at 35. Now, XYZ has fallen t<
30 with only a year remaining until maturity, and the PERCS holder is nervous abou
further declines. He could, of course, merely sell his stock; but suppose that ht:
prefers to keep it and attempt to modify his position to more accurately reflect hb
attitude about future price movements.
Assume the following prices exist:
XYZ Common: 30
XYZ PERCS: 31
XYZ January 40 call: 2
XYZ January 35 call: 4
Ifhe buys the January 40 call and sells the January 35 call, he will have accomplished
his purpose. This is the same as selling a call bear spread. As shown in the previous
example, buying the January 40 call is essentially the same as removing the redemp
tion feature from the PERCS. Then, selling the January 35 call will reinstate a
redemption feature at 35. Thus, the PERCS holder has taken in a premium of 2
points and has lowered the redemption price.
If XYZ is below 35 when the options expire, he will have an extra $200 profit
from the option trades. If XYZ rallies and is above 35 at expiration, he will be effec
tively called away at 37 (the striking price of 35 plus the two points from the rollr,
instead of at the original demand price of 39. In actual practice, if the January 35 call
629
were assigned, the trader could then be simultaneously long the PERCS and short
common stock, with a long January 40 call in addition. He would have to unwind
pieces separately, an action that might include exercising the January 40 call (if
It were in-the-money at expiration) to cover the short common stock.
The conclusion that can be drawn is that in order to roll down the redemption
fiature of a PERCS, one must sell a vertical call spread. In a similar manner, if he
wanted to roll the strike up, he would buy a vertical call spread. Using the same
example, one would still buy the January 40 call ( this effectively removes the redemp
tion feature of the PERCS) and would then sell a January 45 call in order to raise the
redemption price. Thus, buying a vertical call spread raises the effective redemption
price of a PERCS.
There is nothing magic about this strategy. Covered writers use it all the time.
It merely evolves from thinking of a PERCS as a covered write.
SELLING A CALL AGAINST A LONG PERCS IS A RATIO WRITE
It is obvious to the strategist that if one owns a PERCS and also sells a call against it,
he does not have a covered write. The PERCS is already a covered write. What he
has when he sells another call is a ratio write. His equivalent position is long the com
mon and short two calls.
There is nothing inherently wrong with this, as long as the PERCS holder
understands that he has exposed himself to potentially large upside losses by selling
the extra call. If the common stock were to rally heavily, the PERCS would stop ris
ing when it reached its redemption price. However, the additional call that was sold
would continue to rise in price, possibly inflicting large losses if no defensive action
were taken.
The same strategies that apply to ratio writing or straddle writing would have to
be used by someone who owns a PERCS and sells a call against it. He could buy com
mon stock if the position were in danger on the upside, or he could roll the call(s) up.
A difference between ordinary ratio writing and selling a listed call option
against a PERCS is that the imbedded call in the PERCS may be a very long-term
call (up to three years). The listed call probably wouldn't be of that duration. So the
ratio writer in this case has two different expiration dates for his options. This does
not change the overall strategy, but it does mean that the imbedded long-term call
will not diminish much in price due to thepssage of time, until the PERCS is near
er maturity.
Neutrality is normally an important consideration for a ratio writer. If one is
long a PERCS and short a listed call, he is by definition a ratio writer, so he should
630 Part V: Index Options and Futures
be interested in neutrality. The key to determining one's neutrality, of course, is tc
use the delta of the option. In the case of the PERCS stock, one would have to usE
the delta of the imbedded call.
Example: An investor is long 1,000 shares ofXYZ PERCS maturing in tw


long a PERCS and short a listed call, he is by definition a ratio writer, so he should
630 Part V: Index Options and Futures
be interested in neutrality. The key to determining one's neutrality, of course, is tc
use the delta of the option. In the case of the PERCS stock, one would have to usE
the delta of the imbedded call.
Example: An investor is long 1,000 shares ofXYZ PERCS maturing in two years. He
thinks XYZ is stuck in a trading range and does not expect much volatility in the near
future. Thus, a ratio write appeals to him. How many calls should he sell in order to
create a neutral position against his 1,000 shares?
First, he needs to compute the delta of the imbedded option in the PER CS, and
therefore the delta of the PERCS itself. The delta of a PERCS is not 1.00, as is the
delta of common stock.
Assume the XYZ PERCS matures in two years. It is redeemable at 39 at that
time. XYZ common is currently trading at 33. The delta of a two-year call with strik
ing price 39 and common stock at 33 can be calculated (the dividends, short-term
interest rate, and volatility all play a part). Suppose that the delta of such an option is
0.30. Then the delta of the PER CS can be computed:
PERCS delta= 1.00- Delta of imbedded call
= 1.00 - 0.30 = 0.70 in this example
Assume the following data is known:
Security
XYZ Common
XYZ PERCS
XYZ October 40 call
Price
33
34
2
Delta
1.00
0.70(!)
0.35
Being long 1,000 PER CS shares is the equivalent of being long 700 shares of
common (ESP= 1,000 x 0.70 = 700). In order to properly hedge that ESP with the
October 40 call, one would need to sell 20 October 40 calls.
Quantity to sell = ESP of PER CS/ESP of October 40 call
= 700/(100 shares per option x 0.35)
= 700/35 = 20
Thus, the position - long 1,000 PER CS, short 20 October 40 calls - is a neutral one
and it is a ratio write.
One may not want to have such a steep ratio, since the result of this example is
the equivalent of being long 1,000 common and short 30 calls in total (10 are imbed
ded in the long PERCS). Consequently, he could look at other options - perhaps
writing in-the-money October calls - that have higher deltas and won't require so
many to be sold in order to produce a neutral position.
Cl,apter 32: Structured Produds 631
To remain neutral, one would have to keep computing the deltas of the options,
both listed and imbedded, as time passes, because stock movements or the passage
of time could change the deltas and therefore affect the neutrality of the position.
HEDGING PERCS WITH COMMON STOCK
Some traders may want to use the common stock to hedge the purchase of PERCS.
These would normally be market-makers or block traders who acquire the PERCS in
order to provide liquid markets or because they think they are slightly mispriced. The
simplest way for these traders to hedge their long PERCS would be with common
stock.
This strategy might also apply to an individual who holds PERCS, if he wants to
hedge them from a potential price decline but does not actually want to sell them (for
tax reasons, perhaps).
In either case, it is not correct to sell 100 shares of common against each 100
shares of PERCS owned. That is not a true hedge. In fact, what one accomplishes by
doing that is to create a naked call option. A PERCS is a covered write; if one sells
100 shares of common stock from a covered write, he is left with a naked call. This
could cause large losses if the common rallies.
Rather, the proper way to hedge the PERCS with common stock is to calculate
the equivalent stock position of the PERC S and hedge with the calculated amount of
common stock. The example showed how to calculate the ESP of the PERCS: One
must calculate the delta of the imbedded call option, which may be a long-term one.
Then the delta of the PERCS can be computed, and the equivalent stock position can
be determined.
Example: V sing the same prices from the previous example, one can see how much
stock he would have to sell in order to properly hedge his PERCS holding of 1,000
shares.
Assume XYZ is trading at 33, and the PE RCS has two years until maturity. If the
PERCS is redeemable at 39 at maturity, one can determine that the delta of the
imbedded option is 0.30 (see previous example). Then:
Delta of PE RCS = 1 - Delta of imbedded call
= 1- 0.30
= 0.70
Hence, the equivalent stock position of 1,000 PERCS is 700 shares (1,000 x
0.10). 1 Consequently, one would sell short 700 shares of XYZ common in order to
hedge this long holding of 1,000 PERCS.
632 Part V: Index Options and Futures
This is not a static situation. If XYZ changes in price, the delta of the imbedded
option will change as well, so that the proper amount of stock to sell as a hedge will
change. The deltas will change with the passage of time as well. A change in volatili
ty of the common stock can affect the deltas, too. Consequently, one must constant
ly recalculate the amount of stock needed to hedge the PERCS.
What one has actually created by selling some common stock against his long
PERCS holding is another ratio write. Consider the fact that being long 1,000
PE RCS shares is the equivalent of being long 1,000 common and short 10 imbedded,
long-term calls. If one sells 700 common, he will be left with an equivalent position
of long 300 common and short 10 imbedded calls - a ratio write.
The person who chooses to hedge his PER CS holding with a partial sale of com
mon stock, as in the example, would do well to visualize the resulting hedged posi
tion as a neutral ratio write. Doing so will help him to realize that there is both upside
and downside risk if the underlying common stock should become very volatile (ratio
writes have risk on both the upside and the downside). If the common remains fair
ly stable, the value of the imbedded call will decrease and he will profit. However, if
it is a long-term imbedded call (that is, if there is a long time until maturity o