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warrants
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warrants
Contents
Knowledge is power
Situation
Knowledge is power
3
Solution
Fill-up on knowledge
4
Over the last few years, there is
hardly a single financial instrument
that has whetted investor appetites
as much as the warrant. Warrants
can be used to make substantial
gains, yet they can also lead to
considerable losses. Anyone
wishing to invest in warrants
needs to know exactly how they
work and what risks they typically
Success factors
The warrant – an everyday product
The basics
Expensive or not?
Dynamic indicators
Types of warrants
Warrant trading and the role of the issuer
Strategies
Finding the right warrant
FAQs
Appendix
Tax treatment of warrants held as private assets
Internet service
Recommended literature
Warrants – glossary*
5
10
15
18
22
25
29
34
36
entail. Losses have all too often
been the result of a lack of
experience in dealing with these
products. Only those who know
what factors can influence the
price of warrants and, above all,
how these factors influence them,
can trade successfully in these
instruments in the long run.
38
40
41
* The warrants glossary contained in the appendix is an integral part
of this brochure.
2 Contents
Situation 3
Fill-up on knowledge
In order to explain the origins,
background and trading of warrants,
we have taken an example from
everyday life. The scenario we
have developed, involving a car
owner needing to fill-up his tank
and a customer-oriented pump
attendant at a petrol station, is
exactly what investors experience
when they trade in warrants on
the stock exchange.
“Fill-up on knowledge” is therefore
the motto of this brochure, which
we hope will leave you tanked up
with information and ready to
venture into the world of warrants.
4 Solution
The glossary enclosed at the end
of the brochure should help you on
your way. This booklet contains a
list of definitions briefly explaining
some of the key terms and
indicators used in warrant trading.
These definitions have been
arranged in alphabetical order to
ease your search and, read in
conjunction with this brochure,
should ultimately help you build
up and increase your knowledge
of this subject.
The X-markets team at Deutsche
Bank hopes you enjoy the ride.
The warrant –
an everyday product
Option contract at a petrol
station
Option contract at a
petrol station
Limited risk – no further
obligations
The best way of explaining the
origins and workings of warrants
is to take an example from
everyday life. Let us assume that
you have just bought your dream
set of wheels – a top-of-the range
sports car with a powerful engine.
Your initial enthusiasm is decidedly
short-lived, however, when you
arrive at the petrol station to fill-up
your new car only to discover that
a litre of premium petrol is going
to set you back a whole euro.
Suddenly remembering what has
been written in the press over the
past few weeks about rising crude
oil prices in Rotterdam as well as
the petrol tax, you are forced to
reckon with the price for a litre of
premium petrol hitting ¤1.50 or
perhaps even ¤2 within the next
two years. Your heart well and
truly sinks as you realise that your
dream car, depending on how fast
it is driven, consumes between 15
and 20 litres per 100 kilometres.
Market value of the options
Maturity of the options
Future expectations
Playing the stock exchange
You then have a flash of inspiration
and enter into the following
agreement with the owner of the
petrol station. You acquire the
right to buy 5,000 litres of premium
petrol at ¤1 per litre over the next
two years. This means you have
purchased 5,000 petrol options,
each entitling you to buy a litre of
petrol under the agreed conditions.
The rest of the deal with the
owner of the petrol station works
as follows. You pay an immediate
¤0.10 per litre for the agreed
volume. The right to buy 5,000
litres of premium petrol at ¤1 per
litre at any time within the next
24 months therefore costs you
¤500. You also agree with the
other party to this agreement that
you may sell your options, in part
or in whole, to another car-owner
at any time. At the end of the day,
the petrol station owner is not
really concerned who he sells the
5,000 litres to.
Success factors 5
Limited risk –
no further obligations
If the price of petrol were to rise
to unexpectedly high levels over
the agreed two years, you would
be in a position to make a huge
profit by buying 5,000 litres of
premium petrol at well below the
market price. If the price rose to
¤2 per litre, you could also consider
selling your options, which, initially
bought for ¤500, would then be
worth ¤5,000. This would be a
great deal all-round, and what is
more, if the price of petrol were
to fall, your risk would be limited
to the sum needed to purchase
the options. If the price per litre
dropped to ¤0.80, for example,
you would not be obliged to buy
the 5,000 litres for ¤1. In this
instance, the options would be
worth nothing and expire worthless
if the price of a litre of petrol
remained below ¤1 for the term
of the option contract.
Let us now assume that during
the agreed period of two years,
the price of premium petrol for
your dream car were to fall
dramatically to rest at ¤0.70. In
this instance, you would not
make use of your right to buy
6 Success factors
5,000 litres of petrol at ¤1 and
would let the options expire. You
would then have to assume the
total loss of the sum paid for the
options, i.e. ¤500. This loss would
have been limited had you sold
the options after a few months.
If the petrol price were to shoot
up to ¤2, you would have the
following choice. Either you could
continue to fill your sports car
with petrol costing a mere ¤1 per
litre or you could sell your options
and make a large profit. Do not
forget that as the buyer, you
simply have rights, whereas the
pump attendant, as the seller, has
rights and obligations.
Market value of the options
Three months later, during a
routine trip to your local petrol
station, you notice that a litre of
petrol now costs ¤1.20. The value
of your options has therefore risen
and, contrary to the other car
drivers you meet at the pumps,
you are happy at how things have
turned out. Of course, all attention
turns to you when they realise
that you only have to pay ¤1 per
litre. You tell them about the deal
with the petrol station and a
number of the higher-price payers
then offer to buy some of your
options. Something along the lines
of a market then materialises. As
most people fear that petrol prices
are going to increase further, you
could sell your options immediately
for ¤0.30 per litre. The prevailing
market value of each option,
which you purchased for ¤0.10,
is therefore ¤0.30.
Maturity of the options
The higher the petrol price per
litre rises above ¤1.10 – i.e. above
your profit threshold – the more
your options are worth and the
more profit you will make. Given
that you may exercise your options
at any time and actually receive
delivery of the petrol, and that
there are parties interested in
buying your options from you,
you are free to choose between
purchasing the 5,000 litres of
petrol over the two years at a
significant discount to the
prevailing market price or selling
your options at the prevailing
market price. The price the other
car drivers are willing to pay will,
of course, be higher the more
expensive a tank of petrol
becomes.
If the price of petrol were to rise
to ¤1.20, you would save ¤0.20 by
exercising your options. However,
the “market value”, i.e. what
others would be prepared to pay
for these options, is ¤0.30. There
is a good reason for this, namely
that three months ago you entered
into an agreement with a two-year
term, i.e. the options are still valid
for another 21 months. During this
period of time, the price of petrol
could rise to unexpectedly high
levels. It therefore follows that the
right to buy petrol at ¤1 per litre
for another 21 months is worth
more than the right to do this only
for another two days, for example.
Another feature of your petrol
options is that you and the pump
attendant have agreed to physical
delivery. This means that upon
exercising the options, you actually
receive physical delivery of the
underlying, in this instance, the
premium petrol.
Success factors 7
Future expectations
Enjoying your role as a warrant
owner, you take your pride and
joy for a spin one morning and
need to refuel again. On the display
board at the petrol station you
notice that the price of premium
petrol has gone up overnight from
¤1.10 to ¤1.30. This price rise is
due to the Organisation of Petrol
Exporting Countries (OPEC) making
a surprise decision to reduce crude
oil production, thereby sending
prices on the crude oil market
in Rotterdam through the roof
and causing oil companies to
react as they always do in these
circumstances, i.e. by hiking
petrol prices. Groups of drivers
can be seen standing around
the pumps embroiled in heated
discussions. An air of panic
abounds as everyone fears that
petrol prices will continue to rise
even higher.
Now well known among local
car drivers, you step onto the
forecourt and become
immediately surrounded by a
8 Success factors
group of them wanting to buy
your options for 60, even 70,
cents per litre. A particularly
worried driver offers to buy 2,000
options for as much as ¤0.80.
A few days later and the situation
is different. Premium petrol has
indeed risen to ¤1.35 a litre, yet
no one expects prices to rise any
further. The government has
announced that, if necessary, it
will lower petrol tax in order to
keep prices stable. When you ask
car drivers what they would be
willing to pay for your options, the
highest bid you receive is ¤0.50.
It therefore goes without saying
that expectations of future price
trends for the underlying affect
the value of an option. Hopefully,
at the height of the panic, you will
have accepted the highest bid and
sold some of your options, leaving
your angst-ridden buyers to curse
the planned petrol tax cuts and
bemoan their unlucky investment
decision.
Playing the stock exchange
Since acquiring your petrol options,
you have developed a keener
interest in petrol price trends and
their influences. One day, you read
an interesting newspaper article
about Deutsche Automobil AG.
The carmaker is about to bring
out an attractive, high-performance
car that only consumes 2 litres
per 100 kilometres. The model
looks set to be a roaring success –
especially given the further rise in
petrol prices over the past weeks.
In view of your positive experience
of petrol options, you decide to try
your luck with warrants traded on
the stock exchange.
The problem here is that there are
a whole host of warrants available
on Deutsche Automobil AG shares.
All you have to do now is choose
the right one. With the carmakers’
shares currently trading at ¤43,
you follow a hunch that they will
significantly appreciate in value
and therefore opt for a call warrant.
However, before you part with
your cash, you want to know
which warrants are lucrative.
This involves looking at various
key data on the risk/return profile
of these financial instruments.
These indicators can give you an
idea of not only how much more
expensive a warrant on Deutsche
Automobil AG shares is than
buying the shares directly but also
how much the price of your
warrant can fluctuate over time.
These decisive details are outlined
in the following sections. Departing
from our petrol station scenario,
we would now like to introduce
you to the intriguing world of
warrant trading on the stock
exchange.
Success factors 9
The basics
The right warrant for the right
investor. The choice is wide
and the indicators varied.
The right warrant for the right
investor. The choice is wide
and the indicators varied.
The value of a warrant
It is a well-known fact that
investors can make a lot of
money with warrants, yet can
also suffer considerable losses.
Before you venture into this
market, you should familiarise
yourself with the basics. Warrants
are categorised as derivative
financial instruments. This means
that every warrant is linked to an
underlying financial asset. The
underlying asset performance is
reflected in the price of the warrant
according to a given ratio.
The effects of price
fluctuations
VDAX® – the volatility index
It is generally only worth buying
a warrant if you think the price
of the underlying asset is going
to move considerably. On the
German exchanges, warrants are
issued on a variety of underlying
assets, such as German and
international equities, German
and international equity baskets,
German and international bonds,
bond and share indices, as well
as commodities, such as oil or
precious metals. Index warrants,
followed by equity warrants,
comprise the largest segments
with the highest trading volumes.
Warrants on European and US
10 Success factors
equities, in particular, can be
found in large supply. Those who
want to speculate on the price
movements of blue chips listed
on say the DAX®, the Dow Jones
EuroSTOXX 50SM or the Dow
Jones Industrial AverageSM, will
not be disappointed with a lack of
choice. In fact, the maturities as
well as strike prices of these
instruments are so varied that
investors are likely to find exactly
what they are looking for.
to sell this underlying at a specified
price therefore becomes more
valuable the lower its price.
Those in possession of an option
have the following three choices:
they can either let it expire, sell it
or exercise it. Should you decide in
favour of exercising your option,
you must not forget that there is
an important difference between
American and European options,
namely that you may exercise the
former at any time prior to expiry
and the latter only on the expiry
date. With otherwise identical
indicators, European options often
sell for less than their American
counterparts as the right to
exercise at any time presents an
unquestionable advantage.
The direction in which investors
expect the price to move will
determine whether they buy a
call or a put warrant. This is
because the owner of a warrant
has the right to either buy or sell
the >underlying (also referred to
as the underlying asset) at a certain
price (>strike price) from or to the
>issuer within a specified period
of time (>maturity) according to a
certain ratio (>exercise ratio) on
the capital market, or else receive
an equivalent monetary amount
(further explanations below).
Investors therefore have to decide
whether to purchase >call warrants
(calls) or >put warrants (puts).
Calls are bought when the price of
the underlying is expected to rise,
while puts are opted for when the
price is expected to fall. The right
Success factors 11
Many warrants are settled
nowadays by means of >cash
settlement rather than physical
delivery. Cash settlement was
first introduced because physical
delivery was not possible for certain
warrants, e.g. index warrants –
you cannot physically deliver
the DAX®. Now, however, with
the streamlining of settlement
procedures, even warrants where
physical delivery is possible have
a cash settlement feature.
accelerating rate, ultimately
towards zero. The price of the
warrant upon expiry will be no
more than its intrinsic value. A
warrant always has an intrinsic
value – also known as parity – if
it can be exercised at a profit. This
is determined by whether the spot
price of the underlying is above
or below the strike price. In this
instance, a difference is made
between options that are >in the
money, >at the money or >out of
the money.
The value of a warrant
Warrants can have various features
in order to accommodate investors’
expectations. Below are a number
of terms used for these features.
The price of a warrant is comprised
of the >intrinsic value and the
>time value. The latter is the
difference between the warrant
price and its intrinsic value. The
time value is the consideration
payable for the “lifetime” of the
option. The longer the time to
maturity of the option, the more
valuable it is. This is based on the
belief that a change in price of the
underlying will lead to an increase
in the differential amount achieved
up to the expiry date. As the time
to maturity of an option decreases,
its time value will thus decay at an
12 Success factors
In the case of out-of-the-money
warrants, i.e. with no intrinsic
value, the price simply equals
the time value. If the option
remains out of the money until
maturity, the time value will shrink
to zero and the option will expire
worthless. Out-of-the-money
warrants are ultimately a far riskier
purchase than warrants with
intrinsic value. Warrants that are
extremely out of the money and
soon due to expire are therefore
highly speculative as they carry
the highest risk of total loss. These
warrants will only yield a profit if
the price of the underlying makes
a swift and sharp move in the
desired direction. The probability
of this happening has to be
assessed in each individual case.
The effects of price fluctuations
Price fluctuations are one of the
major factors influencing warrant
pricing and should therefore be
monitored constantly.
One of the key premises of
modern option pricing theory is
that an option will be more
valuable the greater the range of
price fluctuations or >volatility.
The reason for this is that the
probability of the warrant
appreciating in intrinsic value
increases the more intensely the
price of the underlying fluctuates.
As it is possible to make an exact
calculation of >historical volatility,
this is an important indicator for
assessing >expected volatility and
>implied volatility, which are both
priced into options. Past fluctuations
can only ever serve as a guide,
however, as the rate of volatility
can change very rapidly. All traders
have experienced this at some
point or another. For example, a
surprise profit warning that strips
30 percent off an otherwise
conservative or even dull stock
has a major impact on the price
of calls and puts it underlies.
The nature of these events is
that they come as a surprise.
All warrant traders look at the
historical volatility of options
traded at a particular time on
the market and draw their own
conclusions as to their implied
volatility. The latter has a
considerable impact on option
pricing. Conclusions on the
interdependency between the
price of a warrant and that of
its underlying – expressed in
dynamic indicators – can therefore
only be applied as long as the
market view of implied volatility
stays the same.
Buying warrants just before a
sharp rise in volatility can prove
very lucrative. Let us assume, for
example, that you acquire a put
on an automotive stock just
before the company releases a
surprise profit warning. Previously
classed as a relative non-mover,
the stock then sheds 25 percent
overnight. As the owner of that
put, you stand to gain not only
from the expected fall in the price
of the underlying but also from a
sharp rise in volatility.
Success factors 13
Expensive or not?
VDAX® – the volatility index
Following the same reasoning,
you can also suffer significant
losses by buying warrants on
financial assets that are
extraordinarily volatile. Let us
now assume that the price of a
share climbs from ¤100 to ¤200.
You now decide to buy because
you expect this strong rally to
persist. Instead, the share price
remains at the same level for
weeks. Although the underlying
has not fallen in price, calls on
this stock will lose value due to
the return to a lower level of
volatility. In the worst case
scenario, the share price could
rise slightly while the calls continue
to lose value because of the lower
implied volatility. This scenario,
of course, is also affected by the
loss of time value.
14 Success factors
As the level of volatility during
bear markets tends to rise faster
than in bull markets, the above
also applies, and perhaps even
to a greater extent, to markets
following a crash. The reason for
this is that downside trends are
often faster and more furious than
upside trends. The recognised
volatility index VDAX® measures
the implicit volatility of options
trading at the money and due to
expire in 45 days. This index is
predominantly influenced by the
level of volatility expected by
market participants.
The volatility of the underlying
tends to vary greatly. The implied
volatility of the DAX® is therefore
always a lot lower than the
implied volatility of its individual
constituents; one share price goes
up, one goes down, ultimately
having a balancing effect on the
overall volatility of the index.
From the wide range of
warrants on offer, you now
have to select the most
suitable and least expensive
From the wide range of
warrants on offer, you now
have to select the most
suitable and least expensive
Leverage
What happens if …? Indicators
are important, especially given
the fast pace of option trading.
You not only have to know what
they are, you also have to be able
to interpret them.
Static indicators facilitate a
qualitative price assessment of
similar warrants at a given point
in time. These indicators should
only be used to compare warrants
with similar features.
One of the most important
indicators when valuing options is
the >premium. The major advantage
of this indicator is that it can be
easily calculated, thus providing a
quick overview of which warrants
are worth investing in. When
buying options, the aim is to invest
a small amount and then make a
proportionally larger gain from any
price movements of the underlying.
The premium shows (in the case
of calls) how much more it would
cost to acquire the underlying by
exercising the option rather than
buying it directly.
Success factors 15
Ultimately, however, an option is
more valuable the longer its time
to maturity and so this indicator,
which fails to take this time
aspect into account, does not
say much at all. A more sensible
way of comparing warrants would
therefore be to calculate the
premium per time unit, usually
per year of time to maturity.
But even this >annual premium
does not quite hit the mark, the
reason being that it is not seen
in relation to the warrant. It is
obvious, for example, that a
premium of ¤1 has to be treated
completely differently according
to whether the warrant costs ¤5,
¤10 or ¤100. The best way to
compare warrants using this
indicator is therefore to calculate
the >percentage premium. This
premium shows how much more
(in percent) it would cost to acquire
the underlying by exercising the
option rather than buying it directly,
thereby serving as a useful criterion
for comparing options.
Asserting that an option is cheaper
the lower the premium would
nevertheless be too simple. A
comparison of warrants is only
16 Success factors
worthwhile if they have similar
maturities and intrinsic values.
Generally speaking, warrants with
a high intrinsic value have low
premiums and warrants with a
low or no intrinsic value will only
have a premium. A comparison
based on the percentage premium
serves two main functions. First,
it provides investors with a quick
and clear overview of which
warrants are suitable. Secondly,
if they have decided on a particular
underlying, it enables them to
compare the premiums of warrants
with similar maturities and strike
prices and then opt for the least
expensive.
Leverage
Arguably the most widely known
options indicator is >leverage,
which shows the extent to which
a warrant moves in line with its
underlying. Current or simple
leverage can be calculated by
dividing the price of the underlying
by the price of the option. If this
ratio deviates from 1.0 or the
underlying assets are denominated
in a foreign currency (foreign
equities), these factors are also
priced into the warrants.
Simple leverage is based on the
assumption that price movements
in the currency units of both the
underlying and the option will be
equivalent. This assumption,
however, does not hold any weight.
Let us take the example of a
warrant granting the right to buy
a share that is trading at ¤100.
The strike price is say ¤200, and
the option is set to expire in two
months. The warrant costs ¤1,
producing a simple leverage ratio
of 100 ÷ 1 = 100. According to
this ratio, a 10 percent rise in the
price of the share to ¤110 would
lead to a 1,000 percent rise in the
price of the warrant to ¤11. In
practice, however, this would
never happen as the share price
would still be a long way off the
strike price of ¤200. If the share
fails to move “into the money”
within the space of two months,
i.e. rises above ¤200, the option
will expire worthless. This ratio is
therefore only ever applicable to
options with a high intrinsic value
and not at all for those without
any. It is for this reason that
elasticity – also referred to as the
omega – is mainly used nowadays
(see next page).
Another key indicator is the
>break-even point, which shows
the price level of the underlying
at which the owner of the warrant
will make a profit. Taking the
example of a warrant costing ¤1,
a strike price of ¤200 and a
exercise ratio of 100:1, the share
price would have to exceed ¤300
in order for the investor to make
a profit.
Success factors 17
Dynamic indicators
Alongside static indicators,
dynamic indicators also
provide key information
on warrants.
Alongside static indicators,
dynamic indicators also
provide key information on
warrants.
Delta
Dynamic indicators reflect changes
in the price of an option relative
to changes in the price, maturity
or volatility of the underlying. As
opposed to their static counterparts,
they allow investors to make a
forecast of the future price
movements of warrants from a
specific point in time and are
generally determined using option
valuation models. They are only
valid for a short period of time and
must be recalculated every time
any key influential factor changes.
Omega
Theta
Gamma
Vega
Rho
Delta
One of these indicators is the
>delta, which belongs to the family
of modern valuation indicators
otherwise known as the “Greeks”
because they are named after
letters of the Greek alphabet. In
modern option pricing theory, this
indicator represents the sensitivity
of the price of a warrant to the
price movements of the underlying.
The delta is calculated exactly
using option valuation models
derived from financial theory. The
delta of a call warrant may lie
between 0 and 1, and for a put
warrant between –1 and 0. A delta
of 0.70 means that, at an exercise
ratio of 1:10, a ¤1 rise/fall in the
18 Success factors
price of the underlying would lead
to a ¤0.07 rise/fall in the price of
the warrant. It can also be used
as a rough guide to whether the
option will have intrinsic value
upon maturity and therefore not
expire worthless. The probability
that the above warrant will not
expire worthless is therefore 70
percent.
In mathematical terms, the delta is
the first derivative of the warrant
price with respect to the price of
the underlying.
particular attention. Using the
Black-Scholes Model, which was
named after its originators and later
further developed, it is possible to
calculate the “fair value” of an
option. This value refers to the
theoretically justified value at
which there is an equal probability
of making a profit or a loss.
Unfortunately, valuation models
such as these are founded upon
basic assumptions that do not
often hold true in real options
markets. These assumptions
include a constant interest rate,
which is the same for credit and
debit interest, and no constraints
on short selling. Despite its flaws,
however, the Black-Scholes Model
has opened up a new perspective
on the valuation of options. As
a detailed discussion of this model
is beyond the scope of this
brochure, we have included a list
of recommended literature in the
appendix that addresses this
subject in great detail.
Omega
Elasticity, which shows the
percentage change in the price
of the warrant relative to the
percentage change in the price
of the underlying, has also been
represented by a Greek letter,
namely >omega. It is obtained
by multiplying the delta by the
leverage ratio. The omega serves
as a useful indicator yet, due to
the fact that the delta changes
with time, can only provide
investors with a snapshot view.
Over the past decades, dynamic
indicators have been used to
develop a series of option price
valuation models. Along with the
binomial model, the fair value
model, devised by the American
mathematicians Fisher Black and
Myron Scholes, has drawn
Success factors 19
Theta
We have already mentioned that
the price of an option is comprised
of its intrinsic and its time value,
and that the closer the expiry
date, the faster the time value
erodes. The >theta measures the
loss of time value per unit of time,
e.g. per day or week, assuming
that the price of the underlying,
along with all other parameters,
remain the same until expiry. This
indicator is usually shown as a
percentage. A weekly theta of 1.5
percent means that, providing the
underlying price moves sideways,
i.e. the intrinsic value remains
constant, the option will lose 1.5
percent of its value every week.
The theta is very much dependent
on whether the option is in the
money, at the money or out of the
money. A warrant with a high
intrinsic value will have the lowest
theta. At-the-money options will
experience the fastest loss of time
value as they move towards their
expiry date. Generally speaking,
the time value of a warrant will
erode the most during the last
three months until maturity.
Investors must be constantly aware
of this loss of value, which is solely
attributable to the decreasing time
to maturity. The closer a warrant
20 Success factors
gets to its expiry date, the greater
the price movement in the direction
predicted by the investor must be
in order both to offset the ever
growing loss of value and ultimately
generate a profit.
In mathematical terms, the theta
is the derivative of the warrant
price with respect to time.
Gamma
Another key indicator is the
>gamma, which defines the
sensitivity of the delta to changes
in the price of the underlying.
The higher the gamma, the greater
the reaction of the delta to such
price movements. A gamma of
0.02 means that if the price of the
underlying rises or falls by ¤1,
the delta will change by 0.02 units.
Options trading at the money have
the highest gammas. Furthermore,
the gamma is higher the shorter
the time to maturity of the option.
Mathematically speaking, the
gamma is the first derivative of
the delta with respect to the price
of the underlying and therefore
the second derivative of the price
trend of the option in relation to
the price movements of the
underlying.
Vega
Rho
The >vega shows the influence
of fluctuations in volatility of the
underlying on the price of the
warrant. You will remember
that volatility is the range of
fluctuations in the price of the
underlying within a given period
of time. Along with the price of
the underlying, the vega is the
most important factor that can
influence the value of an option.
This indicator measures the
degree to which the price of the
warrant moves when the implied
volatility rises or falls by one
percent. A vega of 0.25 means
that if the volatility of the
underlying changes by one
percent, the value of the option
will rise or fall by 0.25 currency
units, adjusted for the exercise
ratio. As is the case with the
gamma, options trading at the
money have the highest vegas.
In contrast to the gamma,
however, the vega is higher the
longer the time to maturity of
the option.
The >rho is the indicator used to
measure the influence of interest
rate changes on the value of
options. When pricing options,
the forward rather than the spot
price is used. The forward price
is comprised of the spot price plus
a factor known as the costs of
carry. This factor can be defined
as the total costs of financing the
underlying until the agreed expiry
date of the option. These costs are
affected mainly by the interest rate
level. A rho of 0.50 means that the
option price – adjusted for the
exercise ratio – will change by
¤0.50 if the domestic interest rate
rises or falls by one percentage
point. When trading in currency
options, the foreign interest rate
must also be factored in. Euro/US
dollar warrants, for example, have
two rho indicators – one for the
euro interest rate and one for the
dollar rate. As extreme short-term
interest rate fluctuations are very
rare, however, the rho can often
be disregarded for most other
options.
From a mathematical perspective,
the vega is the first derivative of
the warrant price with respect to
volatility.
In mathematical terms, the rho is
the derivative of the warrant price
with respect to the interest rate.
Success factors 21
Types of warrants
Underlying assets come
in all shapes and sizes
Index warrants
Equity warrants
Basket warrants
Underlying assets come in all
shapes and sizes
Equity warrants
Warrants can be acquired on
various types of underlying and
investors can use these derivatives
to speculate on indices, equities,
baskets, currencies, interest rates
and commodities.
The lion’s share of these warrants
is based on single stocks. Calls
and puts can be acquired on
national and international equities
with various strike prices and
maturities, although liquid stocks
are always a favourite.
Index warrants
Basket warrants
Index warrants are based on the
performance of share or bond
indices. In the case of bond indices,
the German REX® bond index
plays a key role. The most popular
underlying in this market segment,
however, is the DAX®, i.e. the
German share index containing
the top 30 German stocks. Warrants
on the American S&P 500®, the
Nasdaq 100®, the Euro STOXXSM
as well as the Japanese Nikkei 225
indices also attract investor interest,
as do a small number of warrants
based on other major foreign
indices, such as the Austrian ATX®,
the UK’s FTSE 100®, France’s
CAC-40® or the China/Hong Kongbased Hang Seng®.
Warrants on sector indices, such
as the sub-indices of the DAX® or
the Dow Jones Euro STOXXSM, also
have their appeal. These warrants
show parallels to index warrants
in that they offer investors the
opportunity to speculate on the
performance of a sector as a whole.
Currency warrants
Warrants for global markets
22 Success factors
VW and perhaps even Porsche
stocks. Basket warrants therefore
give investors the chance to
speculate on sector trends or the
performance of a particular equity
market rather than on single
stocks. Investors who forecast a
flourishing automotive industry
and yet are unsure which stocks
are going to fare best can buy a
basket warrant and benefit from
upside across the whole sector.
The same applies to the downside,
as basket warrants also come in
the put variety.
Currency warrants
A further market segment consists
of currency warrants. These
derivatives enable investors to
speculate on the performance of
the euro in relation to foreign
currencies. The US dollar is by far
the most important currency in
this segment, although warrants
do exist on the Swiss franc, the
Swedish krona, the British pound,
the Japanese yen and the Canadian
and Australian dollars. In addition,
warrants can be bought for
Their underlying consists of an
equity basket. This basket is, of
course, not put together at random;
the stocks all have a common
denominator in that they may all
belong to the same sector or
originate from the same country,
or both. A suitable example would
be a German automotive basket
containing BMW, DaimlerChrysler,
Success factors 23
Warrant trading
and the role of the issuer
exchange rate changes between
two foreign currencies, such as
the US dollar and the Japanese
yen. It goes without saying that
there are also a large number of
puts on offer that can be used to
speculate on the weakness of a
particular currency or to hedge
against currency losses. This can
prove vital if you own foreign
stocks or are owed a sum of
money in a foreign currency.
Note: you would buy a euro/US
dollar call if you predicted that
the euro was going to strengthen
against the US-dollar and a euro/US
dollar put for the reverse scenario.
Warrants for global markets
The smallest segment of the options
market consists of commodity
warrants. The most popular and
virtually exclusive underlying assets
are gold and silver, measured in
troy ounces (31.1035 grams).
Investors who predict that the
price of gold will shoot up quickly
can achieve a far higher return on
commodity warrants than gold
coins or mine stocks.
24 Success factors
Warrants with bonds as their
underlying are known as bond
warrants. These derivatives can
be used to speculate on the
downside or upside potential of
fixed-income securities and thus
also on a change in the general
level of interest rates on the
capital markets. The German
term Zinsoptionsschein (interest
warrant), however, is a little
misleading as when you buy an
equity call, you predict that the
share prices are going to rise,
whereas when you buy a bond
call, you believe that the price
of bonds is going to rise and are
therefore speculating on a fall
and not a rise in interest rates.
As bonds are more sensitive to
interest rate changes the longer
their time to maturity, bond warrant
buyers must not only consider
the maturity of the warrant but
also that of the underlying. This
problem does not exist for equity
warrants, whose underlying assets
do not have a limited lifespan.
The principal underlying assets
of bond warrants traded in
Germany are Bunds and US
Treasury Bonds.
Key conditions for warrant
trading
Key conditions for
warrant trading
Provision of liquidity
Far from being a recent invention
of the Internet generation, options
date back to the 17th century,
when, during the tulip mania that
swept through Holland, they
granted bearers the right to buy
tulip bulbs. Calls and puts were
also being used as early as the
19th century by farmers on the
Chicago Board of Trade to hedge
against – and, of course, speculate
on – the price fluctuations of
agricultural goods. The enormous
surge in warrant trading, however,
particularly in Germany, came not
so long ago. During the ‘80s, it
was still easy to keep tabs on the
prices of German warrants,
virtually all of them being of the
Sources of information
“traditional” variety, i.e. appearing
as a constituent of a warrantlinked bond issued by companies
as part of a conditional capital
increase.
Soon, however, came the first of
the covered warrants, which are
now the most common type of
warrant issued on the market.
“Covered” means that the issuer
is not the company upon whose
stock the warrant is based. Over
subsequent years, this range of
listed warrants grew to incorporate,
alongside basket warrants and
exotic constructions, calls and
puts on an ever increasing array
of underlying assets. Warrant
trading has continued to gain in
significance ever since and as yet
has shown no signs of ebbing.
Success factors 25
Issuers now compete fiercely with
each other to bring out the best
product. When a series of warrants
expires or there is a large difference
between the price of the underlying
asset and the strike of the listed
warrants, new warrants are issued
at the drop of a hat. For every new
warrant issued, an offering circular
must be published detailing its
terms and conditions. Before the
warrant can be issued, the offering
circular must be checked by the
Zulassungsstelle (Admission Board)
of the German Stock Exchange
or else the Bundesanstalt für
Finanzdienstleistungsaufsicht
(Federal Financial Superisory
Authority) to ensure it meets the
legal requirements. A notice is
also issued in which the issuer
discloses that the offering circular
has been deposited with the
relevant authorities. Once the
warrant has been given a
Wertpapier-Kennnummer or WKN
(German security identification
number) and the issuer has filed
an application with the stock
exchange on which the new
security is to be listed, there is
nothing standing in the way of
the launch.
26 Success factors
The offering circular outlines the
exact terms and conditions of the
warrant, i.e. such features as
maturity, exercise ratio and type
of option (European or American).
Other provisions govern cases in
which the underlying asset may
be subject to changing
circumstances (merger, capital
increase) during the lifetime of
the warrant.
Putting the formalities to one side,
issuers therefore have to fulfil
various criteria in order to remain
competitive. First, they have to
launch products that will attract
investors, demand ultimately
determining supply on the warrant
market. Secondly, they have to
react faster than their peers to new
market conditions. When a share
price collapses, for example, they
should be the first to issue new
warrants with strike prices set at
up-to-date price levels. As is the
case for many other financial
instruments, warrants enjoy an
active market in which, depending
on the price of the underlying, a
price is determined for every
warrant. These derivatives are
mostly launched or listed on a
securities exchange, where brokers
are poised to bring demand and
supply into equilibrium, determining
spot prices for the warrants at the
close of trading or, in the case of
variable-price trading, continually
throughout the session.
Provision of liquidity
In many cases, the liquidity from
orders placed by investors on the
exchange would not be sufficient
for individual warrants. As the
majority of investors is usually
either on the buy-side or the sellside, demand and supply would
therefore not reach equilibrium
without some kind of intervention.
Another reason why in some
segments it would not always
be possible to bring demand and
supply into equilibrium immediately
is that warrants are spread out
over the market. An active marketmaking approach is therefore
always adopted when issuing
warrants on the stock exchange.
The buying and selling of warrants
is, in principle, no more complicated
than trading in other securities,
such as equities or bonds. Banks,
however, are now subject to
legislation requiring them to inform
customers interested in warrants
and other futures and options
transactions of the associated
risks. These risks are now detailed
in a document entitled “Wichtige
Informationen über Verlustrisiken
bei Börsentermingeschäften” (Key
information on the risk exposure
associated with listed options and
futures transactions). Investors
must provide written confirmation
that they have read and understood
the contents of this document on a
regular basis – i.e. every two years.
Besides conforming to the legal
requirements, anyone interested
in playing the warrants market
should also ensure, on a personal
level, that they have gained some
experience of trading in equities,
bonds, funds or certificates.
Success factors 27
Strategies
As investors are only advised to
invest in warrants using capital
which, in the worst case scenario,
they could afford to lose without
getting into financial difficulty, a
secure financial background is a
prerequisite. Investors have to
keep abreast of the latest market
developments in order to be able
to react appropriately. Moreover,
many empirical studies have shown
that speculating on the stock
exchange is only advisable for
people who have the time and
energy to manage such an
investment. So, if you are currently
snowed under at work or have
personal issues requiring all your
energy, you should perhaps put
any warrant trading aside until
you have less on your agenda.
28 Success factors
Sources of information
90/10 strategy
Warrant owners are more
reliant on up-to-date information
than equity or bond investors,
for example. Electronic media,
especially Teletext or the Internet,
are a good source of free
information. We would recommend
the Internet services offered by
discount brokers and the German
stock exchanges. By entering the
relevant WKN, you can obtain
current prices and sometimes
even the indicators for warrants.
Your first port of call for warrants
of Deutsche Bank AG should, of
course, be our website at:
www.db-xm.com.
Long Call
Long Put
Hedging
Depending particularly on an
investor’s expectations and
objectives, warrants can be used
as part of a wide range of
investment strategies. They can
serve very conservative purposes,
such as the hedging of existing
securities portfolios, or they can
be used aggressively to speculate
on the upside or downside of the
underlying asset. A conservative
securities portfolio could even
be given something of a boost
by investing a percentage of the
capital in warrants.
90/10 strategy
Indeed, anyone interested in
bumping up their portfolio could
adopt the 90/10 strategy, which is
based on a portfolio combining
both fixed-income securities and
warrants. The ratio of fixedincome securities to warrants is
90 percent to 10 percent. The idea
behind this strategy is that the
interest income on bonds held in
the portfolio must be high enough
to offset any total loss made on
the warrants. An investor with
Success factors 29
¤100,000 in disposable capital,
for example, could invest ¤90,000
in Bunds with a two-year maturity
and yielding 5.5 percent. Upon
maturity, when these government
bonds are redeemed, they would
yield a total of 11 percent, or
¤9,900. At the end of the two years,
the investor would therefore have
¤99,900 regardless of whether or
not the warrants were a total flop.
However, if the warrants were also
to generate attractive price gains,
the total performance of the
portfolio would be far greater than
if the investor had simply invested
the whole ¤100,000 in fixedincome securities.
The feasibility of this strategy
does, of course, depend on the
general interest rate level, i.e.
the higher the risk-free return on
investment grade bonds, the
more worthwhile the strategy.
Long Call
The most renowned strategy used
on the warrant markets involves
purchasing call warrants (calls)
and is known in the trade as a
“long call”. As such, the investor
speculates on the price of the
underlying rising until the expiry
date of the warrant. This strategy
only bears fruit if the break-even
point is achieved. The price of the
underlying must rise to more than
30 Success factors
the sum of the strike price plus
the warrant price multiplied by
the exercise ratio at the time of
purchase. Transaction costs are
not included.
Long Put
The opposite strategy, involving
the purchase of put warrants (puts),
is called a “long put”. Here, the
investor believes that the price of
the underlying is going to fall
dramatically. The break-even point
is achieved when the price of the
underlying is less than the strike
price minus the warrant price at
the time of purchase, multiplied
by the exercise ratio. Say, for
example, you buy a put on a share
with a strike price of ¤100 and an
exercise ratio of 1.0. Your warrant
costs you ¤10 and so the breakeven point lies at ¤90. If the share
price falls even further by the time
your option expires, you will make
a profit. Transactions costs are
also not included.
Hedging
Warrants can also serve very
conservative purposes, such as
the hedging of securities portfolios
against any looming downside.
Investors with a large equity
exposure, for example, and who
expect prices to fall, could think
about selling their positions. This,
however, may not be advisable for
tax or other reasons, including the
high transaction costs involved in
the sale and perhaps the repurchase
of the shares at a later date.
Ultimately, however, there is no
need to sell if the investors buy
puts, effectively “insuring”
themselves against any downside.
The theory behind this strategy is
that if share prices fall, the value
of the options will rise, thereby
cancelling out any loss in value.
This hedging strategy, as with any
insurance, nevertheless comes at
a price, namely the purchase price
of the puts, which can be seen as
a kind of insurance premium. If the
downside fails to materialise, the
premium will be lost but investors
can put their minds at rest.
In this instance, a distinction
should be made between a static
and a dynamic hedge. The static
hedge is better suited as a 100%
safeguard on the expiry date of
the warrant, the dynamic variety
for the time period prior to expiry.
For the former, a single calculation
of what type of as well as how
many puts are needed to hedge
the portfolio is made at a specific
point in time. The number remains
the same, hence the term “static”.
For dynamic hedges, on the other
hand, the put position is regularly
adjusted depending on the
performance of the equity portfolio.
The position is therefore considered
“dynamic”.
Whereas professionals in this
field, such as fund and asset
managers, tend to prefer the
dynamic variety, static hedges are
often sufficient to meet the needs
of the private investor, especially
as the constant adjustments would
entail high transaction costs.
A portfolio is the easiest to hedge
if it contains highly capitalised
stocks for which puts are readily
available, or if it almost mirrors a
particular index for which an
equally large amount of puts exist.
In the above cases, investors can
use warrants to hedge either each
individual position or the entire
portfolio. The more valuable the
assets in the portfolio, the higher
the “insurance premium” will be.
Another factor influencing the
premium is the extent of desired
“coverage”, e.g. whether investors
want “all risk” or limited insurance,
whereby they would bear a portion
of any loss incurred.
Investors wanting to hedge
portfolios that more or less mirror
the DAX® can act as follows. Let
us assume that the DAX® is
currently at 3,000 points and that
investors fear it will nose-dive to
Success factors 31
the 2,000 mark. By acquiring a
sufficient number of puts with a
strike price of 3,000 points, they
are fully insured, as it were. This
method of hedging, however,
does not come cheap. Puts with
a strike price of 2,800 points and
identical maturities are significantly
less expensive. Investors buying
the cheaper warrants would
nevertheless have to bear a
portion of the losses were the
index to shed those 1,000 points.
The insurance cover would only
kick in if the DAX® fell below the
2,800 mark. The region between
2,800 and 3,000 points therefore
corresponds to the aforementioned
portion borne by the investors. Of
course, investors may, at a ratio
of 50/50, also acquire warrants
with a strike price of 2,800 and
3,000 points, as well as opt to
bear an even higher portion of
incurred losses or, according to
their requirements, combine any
number of possibilities. The
decision is not an easy one and
must be considered carefully in
each individual case.
When opting for dynamic hedges,
the best way of calculating how
many options are required is via
the delta, i.e. the sensitivity of a
warrant to changes in the price of
the underlying. In the case of puts,
the percentage delta has a minus
sign before it. If the put has a delta
of –50 (–25), two (four) puts are
needed to hedge the underlying
share because the put only
responds at a ratio of 0.5 (0.25)
to changes in share price.
Static hedge
Portfolio value:
DAX®:
Hedge:
Strike price:
Maturity:
Exercise ratio:
Price:
Portfolio value:
DAX®:
Hedge:
Strike price:
Maturity:
Exercise ratio:
Delta:
Price:
¤300,000
3,000 points
put warrant
3,000 points
1 year
1:100
¤3.01
1st step:
Determine the portfolio ratio
Portfolio value / DAX®
300,000 / 3,000 = 100
Scenario:
Changes in the DAX® have the following
impact upon maturity:
Put
position
–100
–30,100
–30,100
–30,100
3,000 points
put warrant
3,000 points
1 year
1:100
–0.49
¤3.01
2nd step:
number of required put warrants
Portfolio ratio x exercise ratio ÷ delta
100 x 100 / delta = 20,408 put warrants
According to this calculation, the hedge
will cost ¤30,100. This represents 10.03
percent of the value of the portfolio.
Equity
portfolio
–10%
–30,000
±0%
±0
+10.03% +30,100
+20%
+60,000
¤300,000
1st step:
Determine portfolio ratio
Portfolio value / DAX®
300,000 / 3,000 = 100
2nd step:
number of required put warrants
Portfolio ratio x exercise ratio
100 x 100 = 10,000 put warrants
DAX®
32 Success factors
Dynamic hedge
Total
portfolio
–30,100
–30,100
±0
+29,900
According to this calculation, the hedge
will cost ¤61,428.57. This represents
20.48 percent of the value of the portfolio.
This same method can be applied to
hedging based on equity warrants. In
order to determine the required number
of puts, the value of the equity position
to be hedged is divided by the share
price, thereby taking the delta of warrants
into account.
While the number of warrants for static
hedges remains the same until the expiry
date, the number of puts is constantly
changed in the case of dynamic hedges.
The static hedge is therefore used to
safeguard a portfolio at a specific point
in time, whereas the dynamic variety is
used for a specific period of time. If the
delta remains the same, warrants will be
bought or sold to consistently maintain
a delta-neutral position.
Success factors 33
Finding the right warrant
Toss-up between risk appetite
and indicator analyses
Toss-up between risk appetite
and indicator analyses
Market-smoothing service
All investment decisions are centred
around certain principles, such as
investment type and the investor’s
risk appetite, i.e. conservative/riskaverse or more aggressive/risktolerant. The investment objective
is also important: is the investment
for speculative purposes, for
reducing risk exposure or hedging,
or does the investor want to make
specific adjustments to risk/return
profiles with a combination of
financial instruments?
Long trading hours:
an important criterion
Market-smoothing service
Compared to direct investments,
warrants vary on a qualitative
as well as quantitative level. In
order to make a well-balanced
investment decision, investors
must have access to reliable and
up-to-date information as well as
be fully aware of the risk/return
profile of these investments.
Knowledge and understanding
of all parameters affecting the
performance of warrants is
therefore essential.
The selection process can be
broken down into three phases:
the information phase, the decision
phase and finally the control phase.
At first, detailed information on
34 Success factors
the market environment as well
as the product features and
respective underlying assets must
be obtained. A basic prerequisite
for investing in warrants is a very
clear idea on how the price of
the underlying is going to develop
as well as the period of time in
which this price movement is
going to occur.
In the second phase, a decision
should then be made on the
maximum risk tolerance of the
investor, the amount of capital to
be invested and which warrant
features would best suit the
investor’s investment objectives.
Other factors include the quality
of the information provided by
the issuer as well as marketsmoothing and other services.
The third phase ultimately begins
when the warrants are acquired
and includes all measures
undertaken up to the exercise or
sale of the position. During this
phase, the investor mainly
measures the performance of the
warrants, monitors their prices
and controls the investment.
The aforementioned key features
of a warrant – call or put, maturity
and strike price – are selected
according to investor expectations,
such as the direction and extent of
price movements in the underlying
as well as the investment horizon
and the choice of strike price in
relation to the prevailing market
price.
Speculative investors would choose
a short maturity as well as a strike
price that is either “at the money”
or slightly “out of the money”. The
more conservative investor would
opt for longer maturities and a
strike price “in the money”.
When investing in warrants,
there is little point in focusing on
individual indicators. A combination
of indicators will provide a more
overall picture, which is vital.
Investors who predict a sudden
and sharp change in prices are
going to opt for different warrants
than investors who wish to
speculate on slow but steady
price movements. Something to
watch out for, in any case, is that
warrants have sufficient time to
maturity, i.e. warrants with a delta
of less than 0.15 for calls and
–0.15 for puts should be avoided.
The smaller the delta, the greater
the influence of implied volatility.
If investors have a choice of two
otherwise identical warrants, they
should opt for the one with the
lowest implied volatility due to its
price advantage.
They should also watch out for
the spread. Due to the bid-offer
spread between the purchase and
sale of warrants, the price of the
warrant must rise by at least the
spread amount in order to ensure
a loss-free investment. Investors,
however, should not be fooled
by what look like narrow spreads.
A one-cent spread for a warrant
with an exercise ratio of 100:1
means a one-euro spread for
the underlying. By contrast, a
two-cent spread for a warrant
with an exercise ratio of 10:1
means an underlying spread of a
mere 20 cents. Investors should
therefore look at the homogenised
spread.
Long trading hours:
an important criterion
Finally, various services provided
by the issuer as well as the
marketability of warrants are
also significant factors. When
considering warrants on underlying
assets issued in the USA, investors
should remember these derivatives
can be traded until 22:00.
Success factors 35
FAQs
What is the difference between
a warrant and an option?
What is the difference between
a warrant and an option?
Why are there so many
different warrants on certain
financial assets, such as the
DAX®, the US dollar or a
number of single stocks?
Warrants, as opposed to options,
represent certificated option rights.
Both grant the right, but not the
obligation, to buy or sell a financial
asset at specific conditions. All
warrants have a WKN and when
issued, are accompanied by an
offering circular that specifies their
terms and conditions (maturity,
exercise ratio etc.). Warrants are
normally issued by banks, whereas
options are usually made available
by and only traded on futures and
options exchanges.
Why are there so many
warrants available on certain
stocks and not one single
warrant on others?
Does the large number of
warrants available not dampen
their individual liquidity?
Why are there so many
different warrants on certain
financial assets, such as the
DAX®, the US dollar or a
number of single stocks?
Fierce competition exists between
the 30 or so warrant issuers in
Germany, which explains the
large number of these derivatives
available on the favourite underlying
assets of investors. Pronounced
equity market trends can lead to
large gaps between the prices of
these underlying assets and the
strike prices of the existing listed
warrants. Issuers respond by
creating new warrants with more
up-to-date strikes. The increasing
36 Success factors
number of “exotic” warrants has
also meant that at the beginning
of 2003, a total of 30,000 warrants
were traded on the German stock
exchanges.
Why are there so many
warrants available on certain
stocks and not one single
warrant on others?
This is an example of where
demand determines supply. Issuers
mainly launch warrants for which
they can be sure of a high level
of investor demand. Furthermore,
warrants are generally not issued
on the shares of companies that
have not officially given their
authorisation.
Does the large number of
warrants available not dampen
their individual liquidity?
No, because issuers always
guarantee a liquid market for
the warrants they launch. They
constantly quote bid and ask
prices at which their warrants
can be bought or sold (OTC or
“off-exchange” trading). Therefore,
as opposed to low-trading shares,
you do not have to worry that
your warrant orders will not be
settled due to a lack of liquidity.
What is the difference
between OTC (off-exchange)
and “normal” (on-exchange)
warrant trading?
What is the difference
between OTC (off-exchange)
and “normal” (on-exchange)
warrant trading?
Does the warrant issuer lose
out if the investor makes a
profit on the warrant?
A trade is effected on the stock
exchange when an investor finds
another investor who is willing to
act as counterparty, i.e. willing to
accept the former investor’s bid
or offer at a specific price. If this
does not occur, the broker will
approach the issuer. OTC or
off-exchange trading involves
investors dealing directly with a
warrant issuer via their bank. The
issuer acts as a market-maker,
from or to whom investors can
buy or sell warrants at any time.
There is also a difference in
trading hours: on-exchange
trading takes place between 9:00
and 20:00, off-exchange trading
for longer. Deutsche Bank AG
quotes prices for its products
between 8:00 and 22:00.
Companies sometimes
undertake capital increases,
mergers or change the
nominal value of their shares.
What happens to the warrants
issued on such underlying
assets?
Companies sometimes
undertake capital increases,
mergers or change the nominal
value of their shares. What
happens to the warrants
issued on such underlying
assets?
In the above cases, the terms
and conditions of the warrants
are adjusted accordingly. These
adjustments are specified in the
offering circular accompanying
each warrant and ensure that the
mentioned measures do not place
the investor at any disadvantage.
The investor is placed in the same
economic position as before the
measures.
Does the warrant issuer lose
out if the investor makes a
profit on the warrant?
No, because issuers hedge their
positions and therefore do not
speculate contrary to the investor.
This is also the reason why there
are hardly any warrants issued on
illiquid stocks, which cannot be
sufficiently hedged.
Success factors 37
Tax treatment of warrants
held as private assets
Sale of warrants
Sale of warrants
Settlement at maturity
As is the case with other securities,
the profits or losses arising from
the sale of warrants are taxable,
under certain circumstances, as
income from the disposal of
private assets (Einkünfte aus
privaten Veräußerungsgeschäften)
(formerly known as speculative
gains), but only if the period
between purchase and sale is
less than one year. By the same
token, the proceeds from the sale
of warrants held for longer than
one year are tax free.
If the entire proceeds from the
disposal of private assets during
a single calendar year are less
than ¤512, these are also tax free
(exemption limit). If this limit is
exceeded, the entire proceeds
are subject to tax.
This twelve-month cut-off point
can be particularly disadvantageous
for warrant bearers. Investors
who are interested in tax-free
profits, for example, may only
opt for warrants with more than
a one-year maturity at the time
of purchase, which limits their
choice considerably. It is also very
difficult to predict trends that will
last for a whole year. The investor
is therefore often faced with a
dilemma: either to realise gains
and then pay tax on them or hold
38 Appendix
the warrants beyond the one-year
cut-off – ultimately running the
risk of those gains disappearing.
A stock exchange lore says that a
taxable profit is better than a taxfree loss.
The tax treatment of realised
losses arising from the sale of
warrants is as follows.
Losses are tax deductible if they
are incurred during the one-year
cut-off period, yet they may only
be offset against taxable income
from the sale of other private
assets (e.g. shares). These losses
are primarily offset against income
realised during the same year. If
this is not possible, the losses can
also be carried back to the previous
year and then carried forward to
future calendar years for an
indefinite period. This guarantees
that losses realised during the
one-year cut-off period can be used
to lower an investor’s tax liability
instead of just being written off –
as was previously the case.
Investors who notice their
warrants are in negative territory
just before the end of this twelvemonth period could consider
selling them and – provided they
are unable to offset them against
income from the sale of private
assets from the same calendar
year – either carrying the incurred
loss back to the previous year or,
upon request to the tax authorities,
forward to the following year(s).
Investors who realise this kind of
income in 2001 and then suffer
corresponding losses in 2002 may
carry back those losses in their
2003 income tax assessment. The
income from the disposal of private
assets that was taxed in 2001 would
then be reduced by the amount of
the loss carryback and the remitted
tax paid back to the investors.
If investors decide in favour of a
loss carryforward, proceeds from
the sale of private assets during the
following year(s) are only taxable if
they exceed the loss carryforward.
The half-income procedure
(Halbeinkünfteverfahren), whereby
private investors are only liable to
tax on 50% of capital gains and
dividends from shares, does not
apply to warrants, even if they
grant subscription rights. Warrants
cannot be placed on a par with
shares as they do not represent
any shareholder rights.
Settlement at maturity
Cash settlement
Nowadays, most warrants are
no longer settled by means of
physical delivery of the underlying;
instead, their terms and conditions
provide for cash settlement. If the
cash settlement takes place within
one year of purchasing the warrant,
a disposal of private assets exists
pursuant to § 23 Sub-section 1
No. 4 EStG (German Income Tax
Act). The gain or loss on disposal
then equals the difference between
the cash amount and the acquisition
costs (plus ancillary costs such as
transaction costs) of the warrant.
Subscription to shares
The exercise of a warrant and the
ensuing subscription to shares
initially have no tax implications.
As of the exercise date, however,
the acquired shares are subject to
a new cut-off period. This means
that investors have to hold the
securities in their portfolios for
more than twelve months in order
to realise any capital gains tax free.
The acquisition costs of the shares
consist of the strike price as well
as the acquisition and ancillary
costs of the warrant.
According to the tax authorities,
losses arising when warrants
expire worthless (cash settlement
or subscription to shares) are not
tax deductible. Instead, investors
are advised to sell these warrants
within the one-year cut-off period
and thereby make use of the
tax loss in their income tax
assessment.
Appendix 39
Internet service
We have set up a user-friendly
service centre for you at the
following Internet address:
www.db-xm.com. This website
Recommended
literature
contains a clear and comprehensive
list of available warrants, providing
you with information at the touch
of a button.
Fugger, H., und Koch, J.:
Mehr Geld verdienen mit
Optionsscheinen.
München 1999;
ISBN: 3-932114-08-6
Hull, J.:
Options, Futures and Other
Derivatives.
Upper Saddle River 2000;
ISBN: 0130224448
Klotz, A., und Philipp, J.:
Die Welt der Optionsscheine.
München 2000;
ISBN: 3-932114-33-7
Finding the right warrant for you:
Function 1: If you already know
the WKN of a specific warrant,
enter this in the “Schnellsuche
(Quick search)” box and you will
be able to view the features of
the warrants.
Function 2: If you are looking for
a warrant on a particular stock,
simply select “Produktsuche
(Product search)” before entering
the type of stock in “Produktart
(Type of product)” and the name
of the stock in “Name des
Basiswerts (Name of underlying)”.
Function 3: If you would like to
get an overview of the warrants
offered by Deutsche Bank, simply
40 Appendix
select “Produktsuche (Product
search)”, enter the desired type of
warrant and a list of all our
available warrants will appear.
Should you have any further
questions, you may, of course,
also contact us directly. Contact
addresses can be found on the
back page of this brochure.
For more information on warrants,
please consult the brochure
entitled “Basisinformationen
über Vermögensanlagen in
Wertpapieren” (Basic information
on securities investments) as
well as the various term sheets
available on the website given
above.
Natenberg, S.:
Option Volatility & Pricing:
Advanced Trading Strategies
and Techniques.
NYC 1994;
ISBN: 155738486X
Schaeffer, B.:
Millionen mit Optionen.
München 1999;
ISBN: 3-932114-15-9
Schwanfelder, W.:
Optionsscheine für Einsteiger.
Franfurt 1998;
ISBN: 3-593-36060-8
Uszczapowski, I.:
Optionen und Futures verstehen.
München 1999;
ISBN: 3-423-05808-0
Appendix 41
42 Appendix
Warrants glossary
Product information
Telephone info line
E-mail
Internet
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+49 (69) 9 10-3 88 07
[email protected]
www.db-xm.com
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Address
Deutsche Bank AG
X-markets-Team
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60272 Frankfurt am Main
Deutsche Bank AG
D-60262 Frankfurt am Main
Key data for sample
calculations
A
American option – At the money
The sample calculations used in the following definitions are
based on the following key data for shares of the fictitious
Deutsche Automobil AG.
Key data used for the sample calculations
Strike price:
Price of the underlying:
Time to maturity:
Warrant price:
¤0.50
30.5%
Delta:
0.546
Vega:
0.2
Gamma:
Ask price
The price demanded for a financial instrument. Issuers or
brokers sell at this price.
At the money
When the price of the underlying is equivalent or very close to
the strike price. See also >out of the money, >in the money
¤43
exactly one year
1 to 10
Theta (weekly):
Warrants that may be exercised at any time prior to expiry;
also known as American-style options.
¤45
Exercise ratio:
Implied volatility:
American option
–1.12%
Potential price floors
Type of warrant
in the money
at the money
0.3
out of the money
2
Intrinsic
value
Call
Put
strike price
<
underlying
strike price
>
underlying
>0
strike price
=
underlying
strike price
=
underlying
=0
strike price
>
underlying
strike price
<
underlying
=0
3
B–C
C–E
Basket – Cash settlement
Current leverage – Expected volatility
Basket
An “equity basket” comprising of several single stocks and used
as the underlying of basket warrants.
Bid price
The price offered for a financial instrument. On the warrants
market, this is the price at which issuers or brokers offer to buy
a warrant and at which investors can sell it.
Break-even point
Current leverage
Leverage shows the percentage increase or decrease in the price
of the warrant if the share price rises or falls by 1 percent. This,
however, assumes a constant premium. See also >omega.
Delta
An indicator that shows absolute changes in the price of the
warrant if the price of the underlying changes.
If the price of a Deutsche Automobil AG share rises from ¤43 to
¤44, the price of the warrant will increase from ¤0.50 to ¤0.56.
Calculation: delta (0.546) x exercise ratio (0.1) x movement in
the share price. If the share price were to fall by ¤1 euro, the
warrant would lose ¤0.055 in value. In the case of put warrants,
the delta is negative as the price of a put rises if the price of the
underlying falls. With call warrants, the delta is therefore between
0 and 1; with put warrants, it is between 0 and –1.
Indicates the price level above (below) which the investor will
make a profit in the case of a call (put). Transaction costs are
not taken into account.
Call:
warrant price
exercise ratio
+ strike price
Example:
¤0.50
+ ¤45 = ¤50
0.1
Put:
strike price –
Example:
¤0.50
¤45 –
0.1
= ¤40
Call
See >call warrant.
Call warrant (call)
Warrant granting the right to buy the underlying at the strike
price according to a certain exercise ratio prior to or on the
agreed expiry date, or to receive payment of a differential
amount. A call warrant is often simply referred to as a call.
Cash settlement
Instead of delivery of the underlying, a cash settlement may
also be agreed in the terms and conditions of the warrant. If
this is the case, the difference between the current price of the
underlying and the strike price (adjusted for the exercise ratio)
is paid out. This is standard practice.
4
European option
Warrants that may only be exercised on the expiry date; also
known as European-style options.
Exercise
Use of the right granted by the option. This requires written
notice of intent.
Exercise ratio
Indicates the number of options per warrant and specifies the
amount of the underlying that the owner of a single warrant is
entitled to buy or sell.
Expected volatility
The expected price fluctuation range of a warrant’s underlying
within a specified future time period, which usually corresponds
to the option's time to maturity.
warrant price
exercise ratio
5
Gamma
G–I
I–L
Gamma – Implied volatility
In the money – Leverage
Indicator that shows changes in the delta following price
movements of the underlying.
If the Deutsche Automobil AG share price moves by a currency
unit, the delta also moves. A Gamma of 0.03 (Gamma x exercise
ratio) means the delta of the call will increase from 0.546 to
0.576 if the share price rises to ¤44. If the share price falls to
¤42, the delta will fall to 0.516. It is important to note that, in
the case of put warrants, the delta increases if the price of the
underlying decreases and the delta falls if the price of the
underlying rises.
Hedging
Historical volatility
Implied volatility
Describes the situation when a warrant has an intrinsic value i.e.
in the case of calls, the current price of the underlying is above,
and in the case of puts, below the strike price. See also >at the
money, >out of the money
Intrinsic value
The actual value of an option when exercised at a particular
point in time – also known as parity. This equals the (positive)
difference between the strike price and the current price of the
underlying, taking into account the exercise ratio.
Intrinsic value of call =
(price of the underlying – strike price) x exercise ratio
Limits the risk involved in a securities transaction by means of
a second countertransaction. For example, in the case of put
warrants, hedges may be used to insure against price losses in
a securities portfolio.
Example:
Example:
Volatility as determined on the basis of prices of options and
warrants traded at a particular time on the market.
Volatility =
volatility per trading day
x
(in index points)
公僒僒僒僒
number of
trading days
Example:
僒
僒 = 800 points
50 x 公256
In the light of these expectations, future volatility is calculated
to be 800 points on an annual basis or, assuming the basic
value (3,000 points), 26.6 percent. This calculation is based on
the assumption of 256 trading days per year.
(¤43 – ¤45) x 0.1 = ¤0*
Intrinsic value of put =
(strike price – price of the underlying) x exercise ratio
Price fluctuation range of a warrant's underlying during a
specified period in the past.
Example of volatility:
Let us assume that the DAX is at 3,000 points, and you
anticipate a daily fluctuation range of 50 points i.e. 1.6 percent.
You can now calculate the expected volatility of your options for
any time period using the following formula:
6
In the money
(¤45 – ¤43) x 0.1 = ¤0.2
*Note: the intrinsic value of an option can never be negative.
Issuer
Institution that issues the warrant and serves as debtor for the
option it represents – e.g. Deutsche Bank AG.
Leverage
Leverage shows the extent to which a warrant moves in line with
its underlying. The current leverage of a warrant is calculated by
dividing the price of the underlying by the price of the warrant
(adjusted for the exercise ratio). >current leverage, >omega.
Leverage:
price of the underlying
x exercise ratio
warrant price
Example:
¤43
x 0.1 = 8.60
¤0.50
7
L–P
P
Long call – Physical delivery
Premium – Premium (annual)
Long call
The purchase of a call warrant in order to speculate on a rise in
the price of the underlying.
Long put
The purchase of a put warrant in order to speculate on a fall in
the price of the underlying.
Maturity
Omega
Premium
Call:
The “lifetime” of a warrant as determined in the terms and
conditions. The option expires upon maturity.
Omega – also referred to as elasticity – is regarded as “refined”
leverage as it takes into account the delta. The result is often
described as elasticity or gearing. The omega indicates the
percentage change in the price of the warrant relative to a one
percent change in the share price.
Example:
8.6 x (0.546 x 0.1) = 0.47%
If, therefore, the share price rises by 1 percent from ¤43 to
¤43.43, the warrant price will increase by 0.47% to ¤0.502.
Describes the situation when a warrant has no intrinsic value i.e.
in the case of calls, the current price of the underlying is below,
and in the case of puts, above the strike price. See also >at the
money, >in the money
Parity
Synonym for the >intrinsic value of a warrant.
Parity-related indicators
Generic term for warrant indicators that are based on the
intrinsic value (e.g. break-even point, premium).
Physical delivery
If stipulated in the option's terms and conditions, the call owner's
portfolio is credited with the underlying at the agreed strike price
upon exercising the option. The owner of a put is entitled to sell
the underlying in line with the agreed terms and conditions. A
cash settlement may be agreed instead of physical delivery.
8
warrant price
exercise ratio
+ strike price – price of the underlying
Example:
¤0.50
+ ¤45 – ¤43 = ¤7
0.1
Put:
warrant price
exercise ratio
+ price of the underlying – strike price
Example:
¤0.50
+ ¤43 – ¤45 = ¤3
0.1
Omega = leverage x (delta x exercise ratio)
Out of the money
The amount by which the cost of acquiring the underlying by
exercising the warrant exceeds the cost of buying the underlying
directly.
Premium (annual)
The time to maturity of the warrant also affects the premium
level. Premiums are therefore compared on an annual basis.
The formula for this is quite simple:
premium (percentage)
= annual premium
time to maturity in years
Example for a call warrant:
16.28%
= 16.28% p.a.
1 year
Example for a put warrant:
6.98%
= 6.98% p.a.
1 year
9
Premium (percentage)
P
R–T
Premium (percentage) – Put warrant (put)
Rho – Theta
In the case of warrants, the calculation formula for the
percentage premium is as follows:
Call:
(
warrant price
+ strike price – price of the underlying
exercise ratio
x 100
price of the underlying
)
Example:
¤0.50
+ ¤45 – ¤43
0.1
x 100 = 16.28%
¤43
(
Put:
(
)
warrant price
+ price of the underlying – strike price
exercise ratio
x 100
price of the underlying
)
Example:
¤0.50
+ ¤43 – ¤45
0.1
x 100 = 6.98%
¤43
(
)
Put
See >put warrant
Put warrant (put)
Warrant granting the right to sell the underlying at the strike
price according to a certain exercise ratio prior to or on the
agreed expiry date. It may also entitle the owner to receive
payment of an appropriate differential amount. A put warrant
is often simply referred to as a put.
10
Rho
Indicator which shows the influence of changes in general
interest-rate levels on the price of warrants.
Spread
The difference between the bid and ask prices. The spread can
be specified as a percentage or in currency units. Note: in order
to compare the spreads of warrants, they must be homogenised
i.e. they must be based on the same exercise ratio.
Straddle
Simultaneous purchase of calls and puts on the same underlying
as well as identical strike prices and maturities. The aim is to
benefit from sudden price changes and/or an increase in volatility.
Strike price
The price at which the financial instrument underlying the option
may be bought (calls) or sold (puts) as well as the price which is
used to calculate the cash settlement, where applicable.
Theta
Indicator which shows the influence of time on the price of
warrants. It indicates the extent to which the warrant price
changes on a daily basis as the time to maturity decreases.
If, in the space of a week (i.e. 7 days, not 5 working days), the
warrant loses 1.12 percent or ¤0.006 in value, its price will fall
from ¤0.50 to ¤0.49.
11
Time value
T
U–W
Time value
Underlying (underlying asset) – Warrant
The time value is the difference between the current warrant
price and its intrinsic value. The time value is to be interpreted as
the consideration paid for the advantages (leverage effect) that
the warrant buyer has over the direct investor. It is based on the
liquidity advantage as the warrant buyer has to pay less than the
buyer of the underlying.
Underlying
(underlying asset)
The financial instrument underlying the warrant e.g. a share or
share index. Often also referred to as the underlying asset.
Vega
Indicator which shows how sensitive warrant prices are to
changes in volatility. The price of the warrant includes an implied
volatility of 30.5 percent. If the implied volatility increases by
1 percent to 31.5 percent, the warrant will gain ¤0.02 in value
(Vega x exercise ratio) and will increase to ¤0.52. Similarly, the
warrant will lose ¤0.02 if the implied volatility falls by one
percentage point.
Volatility
Volatility measures the fluctuation range of the underlying's
price within a specified time period e.g. a year. See also
>historical volatility, >implied volatility.
Warrant
International common naming for securitised options.
Time value = price of the warrant – the warrant's intrinsic value
Example for a call warrant:
¤0.50 – ¤0 = ¤0.50*
* The price of the call in the example comprises only
time value.
Example for a put warrant:
¤0.50 – ¤0.20 = ¤0.30
Value of the time premium
Erosion of time value as the warrant approaches maturity
5
4
3
2
1
0
90 days
60 days
30 days
Time to maturity
0
The chart shows the erosion of time value as we approach
maturity in case the warrant has no intrinsic value.
12
13
The sponsors of the indices mentioned in this brochure have no
relationship to the products on offer other than the licensing of
the indices. They do not endorse, recommend or promote them.
All trademarks for the aforementioned indices are owned by the
respective index sponsor.
14