FOM Fachhochschule für Oekonomie & Management Essen

&

Avans + Breda

Study program in

Business Economics

Diploma Thesis/Bachelor Thesis

in partial submission of the Degree in

Diplom-Kaufmann (FH)/

Bachelor of Business Administration

Analysis and Valuation of Bonus Certificates

Author: Jess

Puthenpurackal

Essen, 25 September 2008

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I

Table of Contents

Table of Contents I

Tables and Figures III

List of Abbreviations IV

1 Introduction 1

1.1 Problem Definition 1

1.2 Procedure 2

2 Basics 3

2.1 Definition of Certificates 3

2.2 Components of Certificates 4

2.2.1 Fixed Income Securities 4

2.2.2 Stocks 5

2.2.3 Standard Derivatives 7

2.2.3.1 Options 7

2.2.3.2 Futures 10

2.2.4 Exotic Options 11

3 Benefits of Bonus Certificates 13

3.1 Investors 13

3.2 Issuers 18

3.3 The German Bonus Certificates Market 19

4 Characteristics of Bonus Certificates 24

4.1 Description of Bonus Certificates 24

4.1.1 Underlying 24

4.1.2 Conversion Ratio 25

4.1.3 Barrier 25

4.1.4 Bonus Level 26

4.1.5 Maturity 27

4.1.6 Default Risk 28

4.1.7 Costs 29

4.2 Design of Bonus Certificates 31

4.2.1 Zero-Strike-Call 32

4.2.2 Down-and-Out Put 33

4.2.3 Payoff-Profiles 34

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II

4.3 Pricing of Bonus Certificates 36

4.3.1 Black-Scholes-Model 36

4.3.2 Underlying 40

4.3.3 Volatility 43

4.3.4 Dividends 44

4.3.5 Interest Rate 46

4.3.6 Maturity 47

4.3.7 Divergence of Pricing: Fair Value ­ Secondary Market 49

4.4 Taxation 50

4.5 Special Forms of Bonus Certificates 52

4.5.1 Capped Bonus Certificates 52

4.5.2 Quanto Bonus Certificates 54

4.5.3 Reverse Bonus Certificates 56

4.5.4 Multi Bonus Certificates 58

5 Empirical Analysis 60

5.1 Dresdner Bonus-Barrier-Certificate I 60

5.1.1 Description 60

5.1.2 Design 60

5.1.3 Pricing 61

5.1.4 Taxation 62

5.2 AGI Bonus Barrier Fund 63

5.2.1 Description 63

5.2.2 Design 64

5.2.3 Pricing 65

5.2.4 Taxation 66

5.3 Comparison: Dresdner Bonus-Barrier Certificate ­ AGI Bonus Barrier 67

5.4 Impact of current Stock Exchange Collapse on Bonus Certificates 68

6 Conclusion 71

Bibliography 75

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III

Tables and Figures

Figure 1: Dax Performance Index vs. DivDAX Performance Index 6

Figure 2: Long Call 8

Figure 3: Short Call 8

Figure 4: Long Put 9

Figure 5: Short Put 9

Figure 6: Efficient Frontier 16

Figure 7: Open Interest - Volume of retail certificates 20

Figure 8: Payoff profile Down-and-Out Put 34

Figure 9: Asymetrical Payoff Profile of a DaOP 42

Figure 10: Impact of Volatility on DaOP 43

Figure 11: Payoff Profile Zero-Strike-Call 45

Figure 12: TUI 46

Figure 13: Impact of Maturity on DaOP 48

Figure 14: Payoff Profile Capped Bonus Certificate 54

Figure 15: Interest rate level 56

Figure 16: Payoff Profile Reverse Bonus Certificate 57

Figure 17: Dresdner Bonus Barrier Certificate 62

Figure 18: First Payoff Profile AGI Bonus Barrier 65

Figure 19:Second Payoff Profile AGI Bonus Barrier 65

Figure 20: Third Payoff Profile AGI Bonus Barrier 66

Figure 21: VDAX Volatility Index 69

Table 1: Payoff-matrix of a Bonus Certificate 17

Table 2: Market shares for investment certificates (Market Volume) 21

Table 3: Open Interest Volume December 2007 and May 2008 22

Table 4: Market share Bonus Certificates 23

Table 5: Rating of Issuers 29

Table 6: Value Drivers for Hedge/ Quanto Costs 55

Table 7: Bonus Certificates with Barrier Violations 69

Table 8: Pricing Bonus Certificate 72

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IV

List of Abbreviations

§

Paragraph

>

Greater-than

<

Less

-than

Greater-than

or

equal

to

Less-than

or

equal

to

For all

=

Equals;

is

equal

to

Delta

Rho

Theta

Lambda

Vega

Standard

deviation

Expected return

Sum of

AGI

Allianz

Global

Investors

B

Barrier

BC

Bonus

Certificate

BL

Bonus

Level

bn

billion

C

Call

CAPM

Capital

Asset

Pricing

Model

cov

covariance

D

dividend

DDV

Deutscher

Derivate

Verband

DaOP

Down-and-Out

Put

e exponential

function

EstG

Einkommenssteuer Gesetz

F

Riskless

asset

FX

Foreign

exchange

G

Gain

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V

HVB

Hypo Vereinsbank

I

Performance factor

ISIN

International

Securities

Identification

Number

K

Strike price

k

correlation

coefficient

L

loss

ln

natural

logarithm

function

MIFID

Markets

in

Financial

Instruments

Directive

N(d)

cumulative

normal

distribution

function

OTC

Over

the-counter

P

Premium

PV

Present value

r

risk-free

interest

rate

RCB

Reverse

Convertible

Bonds

S

Underlying price

S & P

Standard and Poor′s

T

Expiration

date

t time

to

maturity

x

stock

ZC

Zero-strike call

ZEW

Zentrum

für

Europäische

Wirtschaftsforschung

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1

1 Introduction

1.1 Problem Definition

Since 1989, retail certificates have become core in the field of retail banking (Pilz

2006). Particularly, the stock crash between 2000 and 2003 has fostered the success

story of these investment products because many private investors have sustained

enormous losses with their stock exposures. Therefore, they have been looking for

alternatives to traditional investment forms which are lower in risk but gaining

satisfactory returns (Schiereck 2004).

In order to fall in line with this growing specific demand of investors, major German

banks have invented the new asset class of retail certificates. These products can offer

depositors characteristics for every market scenario as its explicit strength (Löhr and

Cremers 2007).

This booming development reached its peak in December 2007, as German private

investors hold 135 bn EUR of retail certificates in their deposits (Barthel 2008).

Because of their attractive risk-return profile, Bonus Certificates, which were issued for

the first time by the German bank Sal. Oppenheim in 2003, have gained a key position

in this sector with a market share of 21.9% (Fischer 2008). The barrage of newly issued

products has led to the circumstance that many private investors are facing the problem

of lack in transparency concerning the structure of Bonus Certificates.

The present diploma thesis intends to provide the reader an extensive overview on the

investment segment of Bonus Certificates. Thereby the author focuses on the

conception and pricing of this financial structured product in order to develop an

investment guideline for investors, how to deal with this complex derivative. In

particular, the author analyses the influence of the input factors, both on each embedded

option component and on the Bonus Certificate as a whole. Hence, investors may get a

better insight of the disproportionate valuation of Bonus Certificates over maturity.

Due to current negative market situation, the author has also a look into the impact of

issuer′s default risk and barrier violation on Bonus Certificates.

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2

1.2 Procedure

The present diploma thesis consists of 6 chapters. Chapter 1 covers the problem

definition and the author′s procedure with this thesis.

Chapter 2 deals with the fundamental basics of this topic which comprises the definition

and the components of certificates in general. Thus, the reader is able to classify Bonus

Certificates in the complex of structured products.

Now that the fundamentals of certificates have been clarified, the benefits for investors

and issuers are discussed in chapter 3. So, the reader may understand why the examined

German Bonus Certificate market has experienced a tremendous boom over the last five

years.

With the so forth given background on the fundamentals and benefits of Bonus

Certificates, the reader is taken to chapter 4 introducing to the main part of the present

diploma thesis. Thereby the author describes the main features of Bonus Certificates

and explains how investors can exclude information from special ratios for their

investment decision. The chapter then reveals both integrated option components of

Bonus Certificate and the possible payoff profiles of the structured product at maturity.

Thereafter, the reader dives into the world of option pricing by getting to know the

theoretical background of the Black-Scholes-Model. In this context, the author depicts

the impact, of the value drivers of a Bonus Certificate, on the pricing of its option

components and the structured product as a whole. Moreover, with respect to the

valuation of Bonus Certificates, the author works out whether there exist any

divergences in pricing between the theoretical fair value and the price quoted at the

secondary market. In the last two subchapters, the author completes the main part by

illustrating the taxation and special forms of Bonus Certificates.

In Chapter 5, the author finally conducts an empirical analysis of a single Bonus

Certificate and a Bonus Certificate Fund. Both examined investment products are

presented in a certain pattern allowing the reader to capture their description, design,

pricing and taxation. The author concludes the empirical analysis of these investment

instruments with an individual comparison taking their parameters as a whole into

account. Thereafter the author focuses on the impact of the current stock market crash

on Bonus Certificates in order to give the reader a differentiated overview of

disadvantages and opportunities in such a specific market situation.

Chapter 6 covers the author′s final conclusion.

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3

2 Basics

2.1 Definition of Certificates

Certificates are structured financial products that combine fixed income securities,

stocks and derivatives in the form of a single security (Spremann and Gantenbein 2005).

These products can diverge much in the features they offer - from capital-guaranteed to

speculative products - from unlimited to limited maturity (Preissner 2007). Today

issuers are able to engineer certificates in large numbers of variations.

From its legal definition, a certificate is a debenture of issuer that may be lenders or

other financial institutions. Once investors purchase this securitized derivative, they turn

into creditors of the issuing bank. If the issuer were to have difficulty, meeting its

payments or become insolvent, the invested capital is not protected. Hence the holder of

a certificate also bears a creditworthiness risk (Haarengel and Scheuble 2006).

Certificates have similarities to conventional asset classes, like bonds or stocks. But in

contrast to these investments, certificates do not incorporate any steady interest or

dividend payments, because the redemption of a certificate is derived from the

performance of an underlying asset in a stipulated way (Pilz 2006).

Furthermore these derivatives differ from classic asset classes by improving investors′

risk-return profile (Löhr and Cremers 2007).

In some cases issuers manifest in their offering terms, a special right to call for

repayment. Hence they can convert structured products, with unlimited maturity into

investment with limited maturity (Schmidt 2008).

In contrast to certificates as a whole, Bonus Certificates are one of the equity-linked

structured products that built-in exotic options in its design. Bonus Certificates can be

considered as second generation of retail certificates which incorporates partial capital

protection dependent, on the price of the underlying asset, over the term to maturity of

the certificate. The yield of the investment in Bonus Certificates is also linked with the

performance of a predetermined underlying asset over a set period (Götte 2007).

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