the use of structured products applications, benefits and limitations for the institutional investor

1





The use of structured products:
applications, benefits and limitations
for the institutional investor

Submitted by Anna Georgieva


Supervisors: Marcel Koebeli,
Marc Chesney, Pascal Botteron


December 2005












2

0. Introduction

1. What are structured products?
1.1. A definition
1.2. The generic exposure types

2. Applications

2.1 Payoff diversity

2.2 Isolating risks and exposure
2.2.1 Volatility
2.2.2 Correlation
2.2.3 Inflation
2.2.4 Credit
2.2.5 Hedge Funds

3. The institutional investor
3.1 Business needs and risk preferences
3.2 Institutional investors: readily invested in a structured product on the economy
3.3 Structured products, Indexation and the Core-satellite framework

4. Limitations of structured products as investment vehicles

3

0. Introduction

The institutional investor is in the business of understanding, pricing and managing risks to earn a
return for the benefit of all stakeholders. In this paper I discuss how structured products can be used by
institutional investors.

In a perfect world (Arrow-Debreu state-claim framework) there exist enough securities to recreate any
payoff. Some assumptions of this idealized world are: there exist basic securities, Arrow securities,
that they have a risk-free payoff in any state, no transaction cost, no information asymmetry, all
investors have the same expectations. Then derivatives are redundant instruments, as they can be
replicated. The price of the replicating strategy should be equal to the price of the derivative; otherwise
there is an arbitrage opportunity.

Several research papers discuss the optimal existence of derivatives. [Merton 1971], [Carr Madan

2001], [Carr Madan 1998], [Liu Pan 2003], [Ross 1976]) The research results are usually dependant
on assumptions about the process of the underlying. The case of including derivatives in an investor’s
portfolio is usually solved making the assumption that investor preferences follow a certain
mathematical function. The optimal investment in derivatives is then determined as the solution which
maximizes the investor’s utility function. A closed form solution may or may not be available
depending on the assumptions about the underlying process and the utility function.

I treat the problem in a practical, applied way. Needless to say, financial markets have readily justified
the existence of derivatives and derivatives related products. The focus is on how structured products
can be handy to an institutional investor, as opposed to how do we price, replicate and hedge them.
While in the back of every properly priced derivative there is a lot of mathematics, in this paper I
focus on the investment interpretation and application.

I present structured products as a natural investment choice of an institutional investor who faces the
business constraints of a liability stream and of stakeholder and client expectations. Their main
applications are in creating risk-return flexibility, isolating risks and providing exposure opportunities.
I point at possible specific applications, but there is no almighty product that will magically solve all
investment problems and unless a specific investor is consider it is impossible to make a strong
statement about the best choice.

For a retail institutional investor, structured products present new ways to reach the investment needs
of clients by adding new products to the product basket, preserving the level of distribution fees and
increasing the ability to raise new money.

For the pension or trust fund investor, in particular in a core-satellite framework, structured products
provide payoff flexibility, bundled or unbundled exposure to new and old asset classes, and can be
optimally added as satellites to the investment portfolio.

For the asset manager in an insurance company, structured products stand out with their ability to
implement sophisticated investment views, and to isolate and hedge risks.

Research on the pricing and replication of some of these structures are widely available; others do not
have a closed-form solution. The most flexible approach is using Monte Carlo (MC) pricing tool
Based on the martingale approach of derivatives pricing, this approach can price any possibly payoff
and has gained widespread acceptance among practitioners.



4

1. What are structured products?

1.1 A definition

Structured products are investment instruments that combine at least one derivative with traditional
assets such as equity and fixed-income securities. The value of the derivative may depend on one or
several underlying assets. Furthermore, unlike a portfolio with the same constituents the structured
product is usually wrapped in a legally compliant, ready-to-invest format and in this sense it is a
packaged portfolio.

The usual components of a structured product are a zero-coupon bond component and an option
component. The payout from the option can be in the form of a fixed or variable coupon, or can be
paid out during the lifetime of the product or at maturity. The zero-coupon bond component serves as
buffer for yield-enhancement strategies which profit from actively accepting risk. Therefore the
investor cannot suffer a loss higher than the note, but may lose significant part of it. The zero-coupon
bond component is a floor for the capital protected products. Other products, in particular various
dynamic investment strategies, adjust the proportion of the zero-coupon bond over time depending on
a predetermined rule.

From an economic point of view, the structured product can be broken down in two main components:

Investment view + Payoff structure = Structured product


The investment view is driven by factors such as:
• Investor expectations towards the underlying: bearish, flat, bullish, range bound, ladder etc
• Choice of underlying. The underlying may be available in a readily investable format or has to
be synthetically extracted:
o Single stock
o Basket of stocks
o Index or multiple indices
o Mutual fund, hedge fund, Fund of Hedge Funds, discretionary manager
o Systematically rebalanced strategy
o Volatility, correlation, dispersion
o Hybrid
o Credit
o Inflation
o Commodities etc

The investment view may be based on fundamental or technical research. The choice of the underlying
may depend on the market, on the investor’s expertise, and on fundamental factors.



Payoff structure
The payoff structure is a mathematical formula applied on the underlying. The features of the payoff
structure will include:

• Cash flows timing: periodic coupons from an underlying that pays none; total lump payment

when underlying pays coupon; variable coupon or fixed coupon; fixed coupons during certain
periods of the life of the product etc.
• Risk profile: leverage, conditional capital protection, partial capital protection, full capital
protection
• Maturity: Short-term, medium-term or long-term

The importance of both components is evident when we look at the fundamental exposure types in the
next section. The focus here is that despite the fact that the option types have been known for a long
time, the investment view gives them a different interpretation.

1.2 The fundamental exposure types

The fundamental exposure types are the generic option payoffs. Combining these with a long zero
coupon bond gives the primal structured products, some of which have not failed to go out of fashion.
Figure 1 shows clearly the interaction between investment view and payoff structure. Some authors
seem to refer to prefer bullish payoffs, and consider only the payoffs in upper row of the table,
corresponding to the bullish investment view as structured products.

Fundamental exposure types
+
-
+
-
Premium
+
-
Premium
+
-
+

-
Premium
+
-
Premium
Delta one
(Certificate)
Capital protected
products -
Yield enhancement
products
Bullish
investment view
Bearish
investment view
1) 2)
3) 4)

Figure 1



5

6
The Delta one (certificate) provides full exposure to the underlying. Investor gains wealth as
underlying appreciates and loses wealth as the underlying depreciates. The payoff is the same
independent of the investment view. The other 4 payoffs are:

1) Bullish investment view, yield-enhanced or return-enhanced exposure – capped upside,

unlimited downside. Investor prefers to sell the upside potential and receive a higher return.
Investor is actually bullish on the underlying, but prefers to cash in the expected return, rather
than wait for the uncertain appreciation to realize. Investor practically accepts the downside
risk of the underlying and receives a premium for that, which results in a higher yield
compared to the underlying.

2) Bullish investment view, capital protected exposure – floored downside, unlimited upside. The
investor pays a premium to ensure downside protection, but keep the upside exposure.

3) Bearish investment view, yield-enhanced exposure – capped upside, unlimited downside.
However the structure pays of when the underlying decreases in value.


4) Bearish investment view, capital protected exposure – floored downside, unlimited upside.
Again the structure pays as expected if the underlying decreases in value.


Typically, only payoff type 2), the long call, payoff is considered a capital protected payoff. Yet for an
outright bearish investor, this payoff is detrimental as it leaves him exposed to an appreciation of the
underlying.

The investment view is intrinsically connected to the split between yield-enhancement products, where
the investor chooses the higher risk-return combination, and capital protection, where the investor
prefers a lower risk-return combination.

These generic payoffs have been embraced by the market. I show 3 widely known products that can be
directly matched to 3 of the generic payoffs and also present an investment case for their use. These
are:

1) The Delta One (Certificate) (Figure 2 & Figure 3)

2) The Reverse Convertible – as an example of bullish yield-enhancement payoffs (Figure 5
&Figure 4)
3) The Capital Protected Note – as an example of bullish capital protected payoffs (Figure 6)


Other payoff structures cannot be easily classified as only yield-enhancement or capital protected type.
I discuss some of them Section 2.1











The investor receives the full upside and downside of the underlying.

Certificates are a flexible way to invest in customized baskets and
implement fundamental long-only investment ideas.

Investor goes long a zero strike call.

Short-, mid- to long-term investment horizon.

Investor wants full exposure to the underlying.
Structure
Payout

Investment idea
Delta One (Certificate)
Certificates have the same payoff as the underlying
Underlying price
Performance
100
Initial price
Time
Price
100
 Our investment view is based on an expected increase in peak sales of new products,
industry cost savings as the sales mix shifts towards secondary care, and positive volume
outlook in the US as new prescription drug benefits for seniors start in the end of 2005.
 Structure
– We go long a zero strike call on a basket of the following stocks: AstraZeneca, Novartis,
GlaxoSmithKline, Essilor International, Merck, Pfizer, Cardinal Health Inc.
– The basket can be equally-weighted, performance-weighted or custom-weighted.
– 3 year maturity.
 The certificate pays the performance of the basket.
 Very low structuring fees.
Certificate on a Pharmaceutical Basket
We are bullish on European pharmaceutical companies


Figure 3
Figure 2

7
Reverse Convertibles
Reverse Convertibles are yield-enhancement strategies with short maturity

 A coupon is always paid.
 Depending on the product features the investor is exposed to a different
degree to the downside of the underlying.
 Investor go long a zero-coupon bond and short a put, or a short DIP put
 Short-term investment horizon
 Moderately bullish or range bound view
Structure
Payout
Investment idea
Time
Price
100
100
Initial price
13
Performance
 Given the barrier for the DIN put or the strike for the short put we solve for the coupon.
 The lower the barrier level the lower is the coupon.
 This is a very popular yield-enhancement structure for a bullish investor.
Performance
Barrier
Underlying price
100
Initial price
Priced examples
8.47%
1 year
80%
Porsche
9.8%5.9%Coupon

1 year
70%
Porsche
1 year
No barrier
Porsche
Maturity
Barrier
Underlying
Reverse Convertibles on Porsche
3 examples with different barrier levels
Figure 5
14
Figure 4

8


9
Capital Protected Notes (CPN)
Capital protected notes are downside protected investments

100% of invested capital plus a coupon (or upside participation).

We go long a zero-coupon bond and long an option with upside
exposure.

Short-, mid- or long-term investment horizon.

Bullish on the underlying, but we want downside protection.

Structure
Payout
Investment idea
Underlying price
Performance
100
Initial price
Lower capital protection with
higher participation rate
Time
Price
100
23

Figure 6


The zero-coupon bond plus option component of the structure has direct implication on the taxation of
structured products. I review these in Appendix 2.





2. Applications of structured products in the portfolio of an institutional investor

In a general framework, the two applications of structured products are payoff flexibility and isolating
or bundling risks.

1. Payoff diversity and flexibility, payoff timing flexibility, leverage

It is almost impossible to define payoff diversity and flexibility that structured products can provide. I
present six structures that exemplify the payoff flexibility and diversity that structure products can
offer. These are:
1) The Autocallable (Figure 7, Figure 8 &Figure 9)
2) The Reverse Convertible Autocallable (Figure 10 & Figure 11)
3) The Springboard (Figure 12)
4) The CertiPlus (Figure 13)
5) The Plain Turbo Certificate (Figure 14)
6) The Leveraged Airbag (Figure 14)

The Autocallable and the Reverse Convertible Autocallable can be easily classified as yield-
enhancement products. The Springboard is a capital protected product. However the Certiplus, the
Plain Turbo Certificate and the Leveraged Airbag cannot be easily classified into one of the
fundamental exposure types, because they are vehicles to express sophisticated investment views.

All examples are applied to a single stock underlying. Considering how central correlation is in the
pricing of baskets, I present examples in section 2.2.


The autocallable acts as a rational investor who has a range bound view on the underlying. If the
underlying appreciates enough, it is autocalled and the structure ceases to exist, that is, the payoff is as
if the investor has taken profit on the underlying. On the other hand of the underlying stays underwater,
the investor receives a coupon. The worst-case scenario occurs when the underlying goes down by
more than the investor expected. Then the investor will receive the bad performing underlying, but this
loss is nevertheless partially offset by the coupons that the investor receives until maturity.
Autocallables
Autocallables are yield-enhancement strategies
 The structure autocalls if the underlying is above the trigger level in the
years before maturity. The investor receives a coupon equal to the number

of years multiplied by the initial coupon level.
 If underlying matures above the initial level and has not been autocalled,
investor receives a coupon equal to the number of years multiplied by the
initial coupon level.
 If underlying matures between barrier and initial price, investor receives
100% back.
 If the underlying matures below the barrier, investor receives only the
performance of the underlying. This is the worst-case scenario.
 We go long a zero-coupon bond, short a down-and-in put (DIP), long a
series of binary calls
 High likelihood of coupon payment and partial protection.
 Short- to mid-term investment horizon.
 Range bound view on the underlying.
Structure
Payout
Investment idea

Figure 7





10


The 4 scenarios show the representative payoffs of the autocallable structure.

In case 1 the structure ceases to exist after period 1, in all other cases it matures after 3
years.

Summary terms
11.5%
100 CHF
3 years
70%
Porsche
Invested
amount
Coupon
Maturity
Barrier
Underlying
Time
Price
100
70
1)
2)
3)
4)
Payoff
65%
100%
100 + 3*11.5% = 134.5%
111.5% (autocalled after 1 year)
Case 4
Case 3
Case 2
Case 1
65

Autocallable of Porsche
Underlying price
100
Initial price
Coupon
Barrier
level
Underlying price
Performance
100
Initial price
Coupon
Barrier
level
123
1)
Autocalled at the end of period 1; Investor
receives 100% of invested capital + coupon.
2)
Product continues until maturity and pays
100% of capital + coupon equal to =
(number of years * coupon).
3)
Product continues until maturity; Investor
receives 100% of invested capital only.
4)
Product continues until maturity; investor
receives the performance of the underlying.
Underlying price
100

Initial price
Barrier
level
Time
Price
100
Barrier
1)
2)
3)
4)
1)
2)
3)
4)
Autocallables
Barrier Autocallable payoff
Figure 8 &Figure 9


11

Autocallable Reverse Convertible
1
0
t
f
UNDERLYING
UNDERLYING


An autocall occurs in year i if the following occurs

Example for Swiss underlyings, 3 years, 60% Barrier, CHF
Underlying
Coupon
UBS
Novartis
Roche
Swiss Re
Ciba
Credit Suisse
4.00%
3.50%
5.20%
5.00%
3.95%
4.90%
Underlying price
100
Initial price
Coupon
Barrier
level
Underlying price
Performance
100
Initial price
Coupon
Barrier
level

123
1) Autocalled at the end of period 1; Investor
receives 100% of invested capital + coupon.
2) Product continues until maturity and pays a
coupon every year. 100% of capital is
repaid at maturity.
3) Every year a coupon is paid. At maturity the
investor receives 100% back
4) Every year a coupon is paid. Since the
barrier is triggered the investor receives the
performance of the stock at maturity.
Underlying price
100
Initial price
Time
Price
100
Barrier
1)
2)
3)
4)
1)
2)
3)
4)
Underlying
Coupon
Autocallable Reverse Convertible
Autocallable on the Spread

Figure 10 & Figure 11

12
Underlying price
Performance
100
Initial price
Springboard
The Springboard profits from a sophisticated upside exposure view

The springboard provides leveraged exposure up to the level of the
short deleveraged call

Long leveraged zero-strike call, short deleveraged call

Short- to mid-term investment horizon.

Bullish range bound view
Structure
Payout
Investment idea
Time
Price
100
Figure 12
Underlying price
Performance
100
Initial price
Barrier

Strike
CertiPlus
The CertiPlus products combine downside protection up to a certain level and upside
potential
 We cash in a high coupon as long as the underlying stays between the
barrier level and the strike level, but we are exposed to the downside
below the barrier
 We go long a zero strike call and long a down-and-out put (DOP)
 Short- to mid-term investment horizon
 Range bound bullish/bearish on underlying
Structure
Payout
Investment idea
Time
Price
100
Figure 13

13

Plain Turbo Certificate
– Outperformance between the 2 strikes.
– Full downside exposure.
– Long ATM call, long zero strike call,
short 2 OTM calls.
– Short-term investment horizon.
Variations
Turbos generate an Outperformance compared to the Underlying
Underlying price
100

Initial price
Cap Level

Leveraged Airbag
– Outperformance on the upside and partial
downside protection.
– Long zero strike call, long ATM put,
short a leveraged OTM put, long a fraction
of an ATM call.
– Mid-term investment horizon.
Underlying price
100
Initial price
Strike
Level
Performance
Performance

Figure 14

14


15

2. Isolating risk and gaining exposure: volatility, correlation, inflation, credit, hedge funds

Structured products provide the capacity to isolate and trade asset classes that are mixed-in in
traditional assets or may not be directly investable due to constraints on the asset side or the investor
side. I look at 5 specific investment classes: volatility, correlation, inflation, credit and hedge funds.
Not all of them are recognized as asset classes; however the existence of structured products shows
investor interest.

An asset class is a set of investments that exhibit similar and distinctive investment characteristics

(return, volatility and relationship to the returns of other investment assets). The asset class represents
a distinctive type of risk. For accepting this risk any rational investor expects to earn an appropriate
return. The rational investor judiciously accepts risk and expects an appropriate return.

2.1 Volatility

Derivatives are both directional and volatility instruments (Neftci provides an excellent exposition).
That is, the investor makes a bet both on the direction which the underlying will take and on implied
vs. actual volatility. If the actual volatility exceeds implied volatility the long side of the transaction
will realize a profit, assuming all other factors the same. Vice versa, if the actual volatility is lower that
implied volatility the short side of the transaction will realize a profit at the maturity of the option.
Volatility is an exogenous input in the Black-Scholes (or another pricing formula or Monte carlo
simulation) and it shows the volatility view of the investor.

The specific dynamics of volatility can be summarized in the following 4 points
• It jumps when the market crashes
• It reverts back towards its long-term mean
• It experience high and low regimes
• It is usually negatively correlated with the underlying asset return

[GM 1998], [Qu 2000] discuss volatility as an asset class. [Carr and Madan 1998] provide the
replication and pricing formula for volatility and variance swaps.

Volatility structured products can be used to make sophisticated bets on volatility. An excellent
exposition on the pricing of volatility products are the classic [Derman ??], [Hosker ??] and [Mougeot
2005]. The following table summarizes some of the applications.

Straddle Delta-
hedged
option

Variance
swap
Gamma
swap
Conditional
variance
swap
Corridor
variance
swap
Correlat
ion
swap
Volatility bet + + ++ ++ ++ ++ –
Volatility
hedging
– – ++ + + ++ –
Dispersion
trading
+ – ++ ++ – – –
Correlation
trading
– – + ++ – – ++
Asymmetric
vol bets
– – - + ++ ++ –
Smile
trading
– – ++ ++ + + –

16
While volatility swaps on currencies exist, the main application seems to be in equity index and swap
rate volatility. For an indexed investor, the volatility swap is of direct interest as it can help be used to
manage the tracking error. Apart from the swaps presented above, other volatility products are:

• Volatility options – An example is a call option on volatility. The option gains rapidly in value
when volatility increases sharply.
• Volatility swaps combined with equity futures – volatility swaps entail an implicit directional
view on market price movements. There is evidence of negative correlation between the equity
market performance and the level of volatility. Volatility tends to be high during market
crashes. Thus, the seller of volatility swaps has an implicit expectation that the equity market
will increase in values and the buyer has an implicit expectation that the equity market will
decrease in value. To hedge the directional effect of the volatility swap the investor can trade
equity futures.
• Volatility bonds – the coupon is proportional to the difference in the swap rates of a certain
maturity, for example the 20 year swap rate, between the start and the end date of each year.
The investor is buying a series of 20 year swaption straddles.


Here I show an example where variance swaps can be directly used to hedge secondary guarantees
offered by insurance companies. Secondary guarantees exist in two forms: death benefits and living
benefits. Among living benefits the most popular product are the guaranteed minimum withdrawal
benefits (GMWBs), which guarantee the principal, may allow step-ups and allows set percentages of
withdrawal each year, even if account values is zero. The key attraction to customer of this product is
the protection against another bear market and they give life insurers a competitive advantage over
mutual fund providers.

The main risk for the insurer offering such a guarantee is a prolonged equity downturn which poses a
“catastrophe” type risk. The GMWBs will go deep in the money potentially creating large losses for

the insurance company if they are not properly hedged.

Because secondary guarantees are long-term illiquid benefits with liabilities that are expected to
extend over a 20-30 year time period and contain the uncertainty of policyholder utilisation rates, there
are essentially no financial derivatives that can be found to form a perfect hedge. Even if derivatives
were available for 20-30 year periods, the counterparty risk over such long durations would be
unacceptably high.

The long-term illiquid nature of the benefits means that they are suited to dynamic hedging strategies.
The insurer will establish a portfolio of fairly short-dated futures and put and call options which can be
rolled over providing a rolling hedge to offset the guarantee risks based on assumptions about future
market behaviour and policyholder utilisation. The dynamic element of the strategy lies in using
futures and options that are typically fairly short dated at around 3-9 months as these are normally the
most liquid. By rolling the positions over and adjusting those to reflect changes in the book, often on a
daily basis, a fairly effective continuous hedge against most market risks can be achieved.
The three Greeks of concern are:


Hedging Greek Risk Typically used instruments
Delta Change in the market value of the
fund
Equity Futures
Vega Change in the market volatility Put and call options (straddles)
Rho Change in interest rates US Treasury futures


The straddles are the easiest way to partially hedge volatility, however they do not provide pure
exposure to volatility. The problem with the straddle is that once the stock price has moved away from
the initial level, the straddle delta is not zero anymore. Also, since both options are initially in the
money, straddles are usually expensive.

For the insurance company, the variance swap is the best hedging solution. The variance swap is a
forward contract that pays at maturity the difference between the realized variance of an underlying
and the initially defined variance strike price K.


Carr and Madan show that the variance swap can be replicated by a continuum of puts and
calls inversely wghted by the sware of their strike price. The solution is model-free.

The perfect hedge involve buying a continuum of put with strike from 0 to Fo, the current
level, and buys a continuum of call options with strikes from Fo to infinity:
The Variance Swap
Buyer and seller exchange payments based on the level of variance
Variance buyer Variance seller
NKVariance *
N*
2
σ
⎥
⎦
⎤
⎢
⎣
⎡
+=
∫∫
∞
0
0
)(

1
)(
12
][
0
2
0
0
2
,0
2
F
F
rT
T
f
dKKC
K
dKKP
KT
e
V
σ

Figure 15


2.2 Correlation

Correlation is a key input into the pricing formula of baskets of securities. Therefore, in a manner
similar to betting on volatility, the investor can bet on correlation. If realized correlation is lower or
higher than the implied correlation the investor may realize a gain or loss depending on whether the
investor is long or short correlation.

While in linear payoffs correlation and volatility are positively correlated, there are payoffs where the
investor can profit from high volatility and low correlation of the stocks in the basket. These are the
so-called dispersion payoffs. I give an example to show why such a product can be interesting for an
investor.



17


Correlation is usually measured as


BA
BA
BACov
σσ
ρ
,
),(
,
= and
∑
−−=
n

ii
BBAA
n
BACov
1
))((
1
),(
and
)ln(
1
A
i
A
i
i
S
S
A
−
= ,
∑
=
n
i
A
n
A
1
1

This formula clearly makes the assumption that the log returns of the two assets are normally
distributed, and may underestimate or overestimate true correlation if this is not the case.

Correlation is a measure of the diversification and is closely linked to the volatility of the basket.

To show the link between correlation and volatility, let us consider a basket of two stocks, A and B,
and assume that both have a constant volatility of 25%. As the correlation increases from -100% to
100% the volatility of the basket will increase at a decreasing rate and will finally be equal to the
arithmetic average of the volatilities of the two stocks (Figure 16). The non-linear rate of decrease is
due to the fact that volatility is a power function in correlation.


Correlation in %
-100% -50% 0% 50% 100%
0%
5%
10%
15%
20%
30%
25%
Volatility of the basket in %
Correlation in %
-100% -50% 0% 50% 100%
0%
5%
10%
15%

20%
30%
25%
-100% -50% 0% 50% 100%-100% -50% 0% 50% 100%
0%
5%
10%
15%
20%
30%
25%
0%
5%
10%
15%
20%
30%
25%
Volatility of the basket in %

Figure 16


Correlation is not considered a separate asset class, possibly due to its direct linked to volatility.
Correlation in credit derivatives markets has become a key input commensurate to volatility in equity
derivatives markets. I discuss it briefly in section 2.4. Correlation between asset classes is also still a
research topic.

Correlation is also the measure of diversification. Correlation is low when the stocks in the basket
move apart, and is high when the stocks in the basket move concordantly. When the market is bullish
and correlation is high, the investor wants to be long correlation, so that he can profit from the
leverage effect. Yet, when market is bearish and correlation is high the investors wants to be short
correlation, so that he can benefit from the diversification effect.

Dispersion bets are bets that stocks in the basket will move in different directions. The best payoff is
achieved when we take the difference between the best performing stock and the worst performing
stock. This can be achieved through a combination of a long lookback call plus a long lookback put.

18
This is obviously the primal volatility trade, and due to the lookback feature it can be prohibitively
expensive.

With the proper payoff structure, the dispersion of the stocks in the basket can generate higher IRR or
consistent and uncorrelated performance.

First, I compare the price and the IRR of a structured product that pays off the average of call spreads
on a basket of stocks and a structured product that pays the call spread on the average of basket of
stocks. I introduce the floor and the cap in order to obtain financially sensible prices and results.

Basket of Call Spreads
The coupon is the average of the call spreads on the underlyings
 100% of invested at maturity.
 The coupon depends on the return of the stocks in the basket and is
capped.
 The annual coupon is paid accordingly to the following formula:
 We go long a zero-coupon bond and 3 long call spreads on the indecis.
 Mid- to long-term investment horizon.
 Moderately bullish on a basket of 3 indices (NKY, SPX, FTSE)
 But we want downside protection.
Structure
Payout
Investment idea
∑
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜

⎝
⎛
3
1
i,0
ti,
,Min ,
3
1
i
CapLevel
Index
Index
FloorLevelMax

Figure 17

19
Call Spread on a Basket
The coupon of the Call Spread on a Basket depends on the average performance of a
basket

100% of invested at maturity.

The coupon depends on the average return of the stocks in the basket
and is capped.

The annual coupon is paid accordingly to the following formula:

We go long a zero-coupon bond and a long call spread on the indices in

the basket.

Mid- to long-term investment horizon.

Moderately bullish on a basket of 3 indices (NKY, SPX, FTSE)

But we want downside protection.
Structure
Payout
Investment idea
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∑
=
3
1i

i,0
ti,
,
Index
Index
Min x
3
1
, CapLevelFloorLevelMax

Figure 18
I choose 2 indices that are correlated (the S&P 500 and the FTSE 100) and one (the Nikkei) that is not
correlated.

Historical Performance
0
50
100
150
200
250
300
350
400
450
500
Dec-90 Oct-91 Aug-92 Jun-93 Apr-94 Feb-95 Dec-95 Sep-96 Jul-97 May-98 Mar-99 Jan-00 Nov-00 Sep-01 Jul-02 Apr-03 Feb-04 Dec-04
Index
NKY
FTS E

S&P 500
Performance of the 3 indices during the backtest period 20-Dec-1990 until 20-Dec-2005

Figure 19

20

The correlation matrix fed into the MC prices is the same. (3 year period 20-Dec-2002 until 20-Dec-
2005, daily observations)

Correls (avg) 57.00%
20-Dec-02
UKX NKY SPX
UKX
100.00% 51.59% 67.84%
NKY
51.59% 100.00% 51.56%
SPX
67.84% 51.56% 100.00%

Figure 20

The call spread on the basket clearly dominates the average of the call spreads, because of the bubble
period. The call spread on the basket is a dispersion trade compared to the basket of call spreads as the
average of the basket out or underperforms the individual call spreads as the indices disperse up or
down, while the call spread on the individual indices does not allow them to disperse outside of the
cap and the floor. Despite the fact that there is no leverage applied, we observe a leverage effect that
will clearly be stronger if correlation would increases and vice versa.

Price and IRR Comparison
 Underlying Indices: SPX, NKY, FTSE
 Maturity of 5 years with annual coupons
 Floor 95%, cap 120%
 Charts on the left show IRR distribution
(top) and historical IRR
0%
10%
20%
30%
40%
50%
-
4
.
9
%

t
o

-
0
.
7
%
-
0
.
7

%

t
o

3
.
5
%
3
.
5
%

t
o

7
.
7
%
7
.
7
%

t
o

1

1
.
9
%
1
1
.
9
%

t
o

1
6
.
1
%
1
6
.
1
%

t
o

2
0
%

Call spread on basket Basket of call spreads
C
a
ll
sprea
d
on
basket
B
as
k
et o
f
ca
ll

spreads
Average
9.93% 7.76%
Min
-5.00% -5.00%
Max
20.00% 18.82%
Price
21.99% 22.18%
Range
Call spread on
basket
Basket of call
spreads

-4.9% to -0.7%
18% 18%
-0.7% to 3.5% 6% 5%
3.5% to 7.7%
10% 8%
7.7% to 11.9% 12% 44%
11.9% to 16.1%
23% 20%
16.1% to 20% 30% 5%
-10%
-5%
0%
5%
10%
15%
20%
25%
Dec-95
Dec-96
Dec-97
Dec-98
Dec-99
Dec-00
Dec-01
Dec-02
Dec-03
Dec-04
Dec-05
Basket of call spreads
Call spread on basket

16-Apr1996
11-Jul-2001

Figure 21


21
Two Examples from the Backtest
FTSE NKY S&P 500
FTSE
return
NKY
return
S&P 500
return Average
Call spread
on FTSE
Call spread on
NKY
Call Spread on
S&P 500
Basket of call
spreads
Call spread on
basket
16-Apr-91 2,519.50 26,813.30 387.62
16-Apr-92 2,638.60 17,959.76 416.04 5% -33% 7% -7%
4.7% 0.0% 7.3% 4.0% 0.0%
16-Apr-93 2,824.40 20,297.86 448.94 12% -24% 16% 1%
12.1% 0.0% 15.8% 9.3% 1.2%

18-Apr-94 3,138.20 20,277.36 442.46 25% -24% 14% 5%
20.0% 0.0% 14.1% 11.4% 4.8%
17-Apr-95 3,208.80 16,304.15 506.13 27% -39% 31% 6%
20.0% 0.0% 20.0% 13.3% 6.2%
16-Apr-96 3,825.30 21,868.17 645.00 52% -18% 66% 33%
20.0% 0.0% 20.0% 13.3% 20.0%
IRR 9.8% 5.9%
FTSE NKY S&P 500
FTSE
return
NKY
return
S&P 500
return Average
Call spread
on FTSE
Call spread on
NKY
Call Spread on
S&P 500
Basket of call
spreads
Call spread on
basket
11-Jul-96 3,749.00 21,892.58 645.67
11-Jul-97 4,799.50 19,875.49 916.68 28% -9% 42% 20%
20.0% 0.0% 20.0% 13.3% 20.0%
13-Jul-98 5,958.20 16,360.39 1,165.19 136% -25% 80% 64%
20.0% 0.0% 20.0% 13.3% 20.0%
12-Jul-99 6,545.50 18,274.18 1,399.10 160% -17% 117% 87%

20.0% 0.0% 20.0% 13.3% 20.0%
11-Jul-00 6,475.80 17,504.36 1,480.88 157% -20% 129% 89%
20.0% 0.0% 20.0% 13.3% 20.0%
11-Jul-01 5,391.90 12,005.11 1,180.18 114% -45% 83% 51%
20.0% 0.0% 20.0% 13.3% 20.0%
IRR
13.3% 20.0%

Figure 22
I show two particular examples in Figure 22. In the last two columns “Basket of call spreads” and
“Call spread on basket” I show the calculation of the IRR.

The second dispersion payoff structure shows how dispersion can be used to create decorrelated
returns.(Figure 23 & 24)
Dispersion
The coupon is the average of calls on the absolute value difference between the
performance of each index and the average of the basket

100% of invested at maturity.

The coupon is calculated as follows:

We go long a zero-coupon bond and 3 long call spreads on the indecis.

Mid- to long-term investment horizon.

Indices within the basket will disperse

We want downside protection and decorrelated returns
Structure

Payout
Investment idea
)
3
1
3
1
,(
3
1
3
1
1,
,
1,
,
∑∑
==
−−
−
ii
ti
ti
ti
ti
Index
Index
Index
Index
CapLevelMin

22
Figure 23
Dispersion – Price and IRR
 Underlying Indices: SPX, NKY,
FTSE
 Maturity of 5 years with annual
coupons
 Cap level 5.5%
 Charts on the left show IRR
distribution (top) and historical IRR
0%
10%
20%
30%
40%
50%
60%
2
.
8
%

t
o

3
.
2

%
3
.
2
%

t
o

3
.
6
%
3
.
6
%

t
o

4
%
4
%

t
o

4

.
4
%
4
.
4
%

t
o

4
.
8
%
4
.
8
%

t
o

6
%
0%
1%
2%
3%
4%

5%
6%
7%
Dec-95
Jun-96
Dec-96
Jun-97
Dec-97
Jun-98
Dec-98
Jun-99
Dec-99
Jun-00
Dec-00
Jun-01
Dec-01
Jun-02
Dec-02
Jun-03
Dec-03
Jun-04
Dec-04
Jun-05
Dec-05
Average
4.73%
Min 2.81%
Max 5.50%
Price
20.80%

Range
Frequenc
y
2.8% to 3.2%
0.4%
3.2% to 3.6%
4.6%
3.6% to 4%
7.9%
4% to 4.4%
15.8%
4.4% to 4.8%
20.7%
4.8% to 6%
50.6%

Figure 24


2.3 Inflation


Inflation presents a major risk to institutional investors concerned with capital preservation. The
purpose of inflation derivatives and inflation structured products is the transfer of inflation risk.
Although cash instruments already exist (inflation-linked bonds) inflation derivatives allow for tailor-
made solutions. I discuss some of these after a brief review of the market.

Inflation products are attractive to banks, pension funds, mutual funds and insurance companies.

Institutions that are natural inflation payers can benefit from issuing inflation-linked debt in the market

or from selling inflation. Inflation derivatives are attractive to debt investors who prefer real returns
rather than nominal returns or to investors who are looking to hedge their inflation exposure.
Furthermore, inflation linked securities will have a lower nominal cost to the issuer reflecting the
lower risk premium as the real rate is guaranteed.


23
Investment managers face implicit inflation risks. Inflation receivers are typically institutional
investors who need to pay inflation-linked cash flows. For example, the liabilities of pension and
superannuation funds, workers compensation insurers and disability insurers are linked directly to
inflation or indirectly linked to inflation through salary or other income levels. Furthermore, fixed-
income specialist mutual funds/unit trusts have been established to invest in inflation indexed
securities. If the current trend of a changeover from defined-benefit to defined contribution pension
schemes continues, retail investors and mutual funds can become key players in the market of private
pension schemes, long-term savings solutions and retirement income products and they will look to
provide inflation hedge for their clients.

The Market for Inflation Products
Overview of the participants in the gloabal inflation market
Inflation Payers
Sovereigns
Utilities
Agencies
Project Finance
Real Estate
Retailers
Other
Payers/receivers
Investment banks
Hedge funds

Relative value funds
Other
Inflation receivers
Pension funds
Insurance companies
Inflation mututal funds
Retail banks
Corporates (ALM)
Others
Global
Inflation
Market


Figure 25
The case of inflation as a separate asset class is discussed in [Borutta 1997] and [Lamm 1998]. The
key arguments for considering inflation as an asset class considering its risk-return characteristics are:

•
Inflation linked securities will underperform conventional investments in times of low inflation,
but will outperform at times of high inflation. This is a distinguishing return feature.
•
Inflation linked securities have lower volatility than conventional securities
•
The correlation of inflation linked securities with other asset classes is similar to conventional
fixed-income securities. At time of high inflation however, it will be negative as inflation
linked securities will not experience loss of value.


The whole variety of fixed-income payoffs such as forwards, various option on inflation, swaptions on

inflation etc, can be applied to inflation. Unlike inflation-linked bonds, inflation derivatives can be
applied as an overlay on the existing asset allocation, or included as partial hedges.

The inflation swap is a flexible solution to hedge inflation risk. It is a bet on the breakeven inflation
level and is similar to an unfunded interest rate swap, except for the fact that the underlying payments
depend on the level of an inflation index.




24
Breakeven Inflation
– If we think of nominal yields as being (~ Fisher equation):
– Rearranging the equation:
Breakeven inflation is the spread between nominal yield and real yield
Inflationyield Realyield Nominal
+
=
yield Realyield Nominalinflation Breakeven
−
=
(Ex-ante) (Ex- post) Investor Preference
Breakeven
inflation
=
Actual/realized
inflation
Investor is
indifferent
between an

IL bond and a nominal bond
Breakeven
inflation
>
Actual/realized
inflation
Investors
make money by holding nominal bonds
as
infl
ation component of payout is less than expected
Breakeven
inflation
<
Actual/realized
inflation
Investors
make money by holding IL bonds
as they
receive protection from higher than expected inflation

Figure 26

 For institution with an inflation exposure
– Hedge concentrations of inflation risk
– Hedge inflation exposures that are not traded in the cash market
– Easily match the maturity of the inflation exposed liability.
– The swap is off-balance sheet and there is no regulatory charge
 For investors and arbitrageurs
– Take a view on inflation, go long or short inflation which may not be possible with

inflation linked bonds
Inflation buyer
Inflation
Seller
The Inflation Swap
Applications
Net Index Increase
LIBOR - spread
Fixed rate
Or

Figure 27

25