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Library of Congress Cataloging-in-Publication Data
Alternative investments and strategies / edited by Rüdiger Kiesel, Matthias Scherer & Rudi Zagst.
p. cm.
ISBN-13: 978-9814280105
ISBN-10: 9814280100
1. Investments Moral and ethical aspects. 2. Portfolio management Moral and ethical aspects.
I. Kiesel, Rüdiger, 1962– II. Scherer, Matthias. III. Zagst, Rudi, 1961–
HG4515.13.A498 2010
332.6 dc22
2010013167
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PREFACE
Asset allocation investigates the optimal division of a portfolio among different asset
classes. Standard theory involves the optimal mix of risky stocks, bonds, and cash
together with various subdivisions of these asset classes. Underlying this is the insight
that diversification allows for achieving a balance between risk and return: by using
different types of investment, losses may be limited and returns are made less volatile
without losing too much potential gain.
These insights are made precise using the benchmark theory of mathematical
finance, the Black-Scholes-Merton theory, based on Brownian motion as the driving
noise process for risky asset prices. Here, the distributions of financial returns of the
risky assets in a portfolio are multivariate normal, thus relating to the standard mean-
variance portfolio theory of Markowitz with its risk-return paradigm as above.
Recent years have seen many empirical studies shedding doubt on the Black-
Scholes-Merton model, and motivating various alternative modeling approaches,
which were able to reproduce the stylized facts of asset returns (such as heavy tails and
volatility clustering) much better.Also, various new asset classes and specific financial
tools for achieving better diversification have been created and entered the investment
universe.
This book combines academic research and practical expertise on these new (often
called alternative) assets and trading strategies in a unique way. We include the prac-
titioners’ viewpoint on new asset classes as well as academic research on modeling
approaches, for new asset classes. In particular, alternative asset classes such as power
forward contracts, forward freight agreements, and investment in photovoltaic facil-
ities are discussed in detail, both on a stand-alone basis and with a view to their
effects on diversification in combination with classical asset. We also analyse credit-
related portfolio instruments and their effect in achieving an optimal asset allocation.

In this context, we highlight aspects of financial structures which may sometimes be
neglected, such as default risk of issuer in case of certificates or the role that model
v
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vi Preface
risk plays within asset allocation problems. This leads naturally to the use of robust
asset allocation strategies.
Extending the classical mean-variance portfolio setting, we include dynamic port-
folio strategies and illustrate different portfolio protection strategies. In particular, we
compare the benefits of such strategies and investigate conditions under which Con-
stant Proportion Portfolio Insurance (CPPI) may be prefered to Option-Based Portfolio
Insurance (OBPI) and vice versa. We also contribute to the understanding of gap risk
by analyzing this risk for CPPI and Constant Proportion Debt Obligations (CPDO) in
a sophisticated modeling framework. Such analyses are supplemented and extended
by an investigation of the optimality of hedging approaches such as variance-optimal
hedging and semistatic variants of classical hedging strategies.
Many of the articles can serve as guides for the implementation of various models.
In addition, we also present state-of-the-art models and explain modern tools from
financial mathematics, such as Markov-Switchingmodels,time-changedLévy models,
variants of lognormal approximations, and copula structures.
This books combines a unique mix of authors.Alsomany of our students improved
the outcome of the project with critical and insightful comments. Particular thanks goes
to Georg Grüll, Peter Hieber, Julia Kraus, Matthias Lutz, Jan-Frederik Mai, Kathrin
Maul, Kevin Metka, Daniela Neykova, Johannes Rauch,Andreas Rupp, Daniela Selch,
and Christofer Vogt.
R. Kiesel, M. Scherer, and R. Zagst
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CONTENTS
Preface v
Part I. Alternative Investments

Chapter 1. Socially Responsible Investments 3
Sven Hroß, Christofer Vogt and Rudi Zagst
1.1 Introduction 4
1.2 Recent Research on SRI 5
1.3 How Sustainable is Sustainability? 6
1.3.1 Description of the Dataset 6
1.3.2 Introduction to Markov Transition Matrices 6
1.3.3 Results of Markov Transition Matrices 7
1.4 SRI in Portfolio Context 8
1.4.1 Description of the Dataset and Statistical Properties 8
1.4.2 Markov-Switching Model 11
1.4.3 Fitting the Model Parameters 11
1.4.4 Simulation of Returns 13
1.4.5 Portfolio Optimization Models 13
1.4.6 Definition of Investor Types 15
1.4.7 Optimal Portfolios 15
1.5 Conclusion 18
Chapter 2. Listed Private Equity in a Portfolio Context 21
Philipp Aigner, Georg Beyschlag, Tim Friederich,
Markus Kalepky and Rudi Zagst
2.1 Introduction 22
2.2 Defining Private Equity Categories 23
2.2.1 Financing Stages 23
2.2.2 Divestment Strategies 24
vii
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2.2.3 Type of Financing 25
2.2.4 Classification of Private Equity Fund Investments 26
2.2.4.1 Venture capital funds 26

2.2.4.2 Buyout funds 27
2.2.4.3 Leveraged buyouts (LBO) 27
2.3 Investment Possibilities — One Asset, Many Classes 28
2.3.1 Direct Investments 28
2.3.2 Private Equity Funds 29
2.3.2.1 Key players 29
2.3.3 Cash Flow Structure of a Private Equity Fund 31
2.3.4 Fund-of-Funds 32
2.3.4.1 Structure of a private equity fund-of-funds 32
2.3.4.2 Advantages 32
2.3.4.3 Disadvantages 33
2.3.5 Publicly Traded Private Equity 33
2.3.6 Secondary Transactions 34
2.3.6.1 Types of secondary transactions 34
2.3.6.2 Buyer’s motivation 35
2.4 Private Equity as Alternative Asset Class
in an Investment Portfolio 35
2.4.1 Characteristics of LPE Return Series 36
2.4.2 Modeling Return Series with Markov-Switching Processes 37
2.4.2.1 Markov–Switching models 37
2.4.2.2 Fitting the parameters 39
2.4.2.3 Simulation of return paths 40
2.4.3 Listed Private Equity in Asset Allocation 40
2.4.3.1 Performance measurement 40
2.4.3.2 Portfolio optimization frameworks 42
2.4.3.3 Definition of investor types 43
2.4.3.4 Optimization of portfolios 44
2.5 Conclusion 47
Chapter 3. Alternative Real Assets in a Portfolio Context 51
Wolfgang Mader, SvenTreu and SebastianWillutzky

3.1 Introduction 52
3.2 Overview on Alternative Real Assets 52
3.3 Modeling Photovoltaic Investments 53
3.3.1 General Approach 53
3.3.2 Definition of the Investment Project 54
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Contents ix
3.3.3 Modeling of Risk Factors 56
3.3.3.1 Economic factors 56
3.3.3.2 Non-economic factors 57
3.3.3.3 Historical analysis of monthly global irradiance 58
3.3.3.4 Monte Carlo analysis of yearly global irradiance 61
3.4 Photovoltaic Investments in a Portfolio Context 63
3.4.1 Setting the Portfolio Context 63
3.4.2 Including Photovoltaic Investments in a Portfolio 64
3.4.3 Results 66
3.5 Conclusion 68
Chapter 4. The Freight Market and Its Derivatives 71
Rüdiger Kiesel and Patrick Scherer
4.1 Introduction: the Freight Market 72
4.1.1 Vessels 72
4.1.2 Cargo 72
4.1.3 Routes 73
4.2 Freight Rates: What Drives the Market? 74
4.2.1 Demand for Shipping Capacity 75
4.2.2 Supply of Shipping Capacity 76
4.2.3 Costs 77
4.3 Freight Derivatives: Hedging or Speculating? 77
4.3.1 Forward Freight Agreement 77
4.3.2 Freight Futures 78

4.4 Explanatory Variables 79
4.4.1 Explanatory Power 80
4.4.2 Granger Causality 82
4.4.3 Selection Algorithm “Top Five” 83
4.4.4 Cointegration 84
4.5 Predicting Freight Spot and Futures Rates 86
4.6 The Backtesting Algorithm 88
4.7 Conclusion 90
Chapter 5. On Forward Price Modeling in Power Markets 93
Fred Espen Benth
5.1 Introduction 94
5.2 HJM Approach to Power Forward Pricing 95
5.3 Power Forwards and Approximation by Geometric
Brownian Motion 98
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5.3.1 A Geometric Brownian Motion Dynamics
by Volatility Averaging 101
5.3.2 A Geometric Brownian Motion Dynamics
by Moment Matching 103
5.3.3 The Covariance Structure Between Power Forwards 106
5.3.4 The Distribution of a Power Forward 108
5.3.5 Numerical Analysis of the Power Forward Distribution 110
5.4 Pricing of Options on Power Forwards 114
5.5 Conclusion 119
Chapter 6. Pricing Certificates Under Issuer Risk 123
Barbara Götz, Rudi Zagst and Marcos Escobar
6.1 Introduction 124
6.2 The Model 125
6.3 Pricing of Certificates Under Issuer Risk 126

6.3.1 Building Blocks 126
6.3.2 Index Certificates 130
6.3.3 Participation Guarantee Certificates 132
6.3.4 Bonus Guarantee Certificates 134
6.3.5 Discount Certificates 135
6.3.6 Bonus Certificates 136
6.4 Conclusion 139
Chapter 7. Asset Allocation with Credit Instruments 147
Barbara Menzinger, Anna Schlösser and Rudi Zagst
7.1 Introduction 148
7.2 Simulation Framework 150
7.3 Framework for Total Return Calculation 153
7.4 Optimization Framework 156
7.4.1 Mean-Variance Optimization 156
7.4.2 CVaR Optimization 157
7.5 Model Calibration and Simulation Results 157
7.5.1 Mean-Variance Approach 162
7.5.2 Conditional Value at Risk 164
7.5.3 Comparison of Selected Optimal Portfolios 167
7.6 Summary and Conclusion 170
Chapter 8. Cross Asset Portfolio Derivatives 175
Stephan Höcht, Matthias Scherer and Philip Seegerer
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Contents xi
8.1 Introduction to Cross Asset Portfolio Derivatives 175
8.1.1 Definitions and Examples 176
8.2 Collateralized Obligations 179
8.3 A Comparison of CFO with CTSO 179
8.3.1 Structural Features of CFO 179
8.3.2 Structural Features of CTSO 181

8.3.3 The Different Risks 181
8.3.4 Correlation of Tail Events in CTSO 181
8.4 Pricing Cross Asset Portfolio Derivatives 182
8.4.1 Pricing Trigger Swaps 182
8.4.2 Pricing nth-to-Trigger Baskets 183
8.4.3 Pricing CTSO 184
8.4.4 Modeling Approaches 185
8.4.4.1 The structural approach 185
8.4.4.2 The copula approach 186
8.4.5 An Example for an nth-to Trigger Basket 188
8.4.5.1 A pricing exercise of Example 3
(structural approach) 188
8.4.5.2 A pricing exercise of Example 3
(copula approach) 189
8.4.5.3 Resulting model spreads 190
8.5 Outlook 194
8.6 Conclusion 195
Part II. Alternative Strategies
Chapter 9. Dynamic Portfolio Insurance Without Options 201
Dominik Dersch
9.1 Introduction 202
9.2 Simple Strategies 203
9.2.1 Buy-and-Hold 203
9.2.2 Stop-Loss 203
9.2.3 The Bond Floor Strategy 204
9.2.4 Plain Vanilla CPPI 205
9.3 Historical Simulation I 206
9.4 Advanced Features 209
9.4.1 Transaction Costs 210
9.4.2 Transaction Filter 210

9.4.3 Lock-in Levels 211
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9.4.4 Leverage and Constrain of Exposure 212
9.4.5 Rebalancing Strategies for the Risky Portfolio 213
9.4.6 CPPI and Beyond 213
9.5 Historical Simulation II 214
9.5.1 Transaction Costs and Transaction Filter 214
9.5.2 Lock-in Levels 216
9.5.3 The Use of Leverage 220
9.5.4 CPPI on a Multi-Asset Risky Portfolio 222
9.6 Implement a Dynamic Protection Strategy with ETF 223
9.7 Closing Remarks 224
Chapter 10.How Good are Portfolio Insurance Strategies? 227
Sven Balder and Antje Mahayni
10.1 Introduction 228
10.2 Optimal Portfolio Selection with Finite Horizons 230
10.2.1 Problem (A) 233
10.2.2 Problem (B) 234
10.2.3 Problem (C) 235
10.2.4 Comparison of Optimal Solutions 238
10.3 Utility Loss Caused by Guarantees 242
10.3.1 Justification of Guarantees and Empirical Observations 242
10.3.2 Utility Loss 242
10.4 Utility Loss Caused by Trading Restrictions
and Transaction Costs 246
10.4.1 Discrete-Time CPPI 246
10.4.2 Discrete-Time Option-Based Strategy 249
10.4.3 Comments on Utility Loss and Shortfall Probability 250
10.5 Utility Loss Caused by Guarantees

and Borrowing Constraints 252
10.6 Conclusion 254
Chapter 11.Portfolio Insurances, CPPI and CPDO, Truth or Illusion? 259
Elisabeth Joossens and Wim Schoutens
11.1 Introduction 260
11.2 Credit Risk and Credit Default Swaps 261
11.2.1 Credit Risk 261
11.2.2 Credit Default Swaps (CDS) 265
11.3 Portfolio Insurances 267
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Contents xiii
11.4 Modeling of CPPI Dynamics Using Multivariate
Jump-Driven Processes 270
11.4.1 Multivariate Variance Gamma Modeling 270
11.4.2 Swaptions on Credit Indices 273
11.4.2.1 Black’s model 273
11.4.2.2 The variance gamma model 274
11.4.3 Spread Modeling by Correlated VG Processes 275
11.4.3.1 The pricing of CPPIs 275
11.4.3.2 Gap risk 279
11.5 Recent Developments for CPPI 281
11.5.1 Portfolio Insurance: The Extreme Value Approach
to the CPPI Method 282
11.5.2 VaR Approach for Credit CPPI 283
11.5.3 CPPI with Cushion Insurance 284
11.6 A New Financial Instrument: Constant Proportion Debt Obligations . . . 285
11.6.1 The Structure 285
11.6.2 CPDOs in the Spotlight 289
11.6.3 Rating CPDOs Under VG Dynamics 289
11.7 Comparison Between CPPI and CPDO 291

11.8 Conclusions 292
Chapter 12.On the Benefits of Robust Asset Allocation for CPPI Strategies 295
Katrin Schöttle and Ralf Werner
12.1 Motivation 296
12.2 The Financial Market 296
12.2.1 The Basic Financial Market 297
12.2.2 The Riskless Asset 298
12.2.3 The Risky Asset 298
12.2.4 Classical Mean–Variance Analysis 300
12.2.5 The Trading Strategy 302
12.3 The Standard CPPI Strategy 302
12.3.1 The Simple Case 303
12.3.2 The General Case 305
12.3.3 Shortfall Probability of CPPI Strategies 308
12.3.4 Improving CPPI Strategies 310
12.3.5 CPPI Strategies Under Estimation Risk 313
12.4 Robust Mean–Variance Optimization and Improved CPPI Strategies . . . 316
12.4.1 Robust Mean–Variance Analysis 317
12.4.2 Uncertainty Sets Via Expert Opinions or Related Estimators . . . 317
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12.4.3 Uncertainty Sets Via Confidence Sets 319
12.4.4 Usage and Implications for CPPI Strategies 321
12.4.5 CPPIs with Robust Asset Allocations 323
12.5 Conclusion 324
Chapter 13.Robust Asset Allocation Under Model Risk 327
Pauline Barrieu and Sandrine Tobelem
13.1 Background 328
13.2 A Robust Approach to Model Risk 329
13.2.1 The Absolute Ambiguity Robust Adjustment 330

13.2.2 Relative Ambiguity Robust Adjustment 333
13.2.3 ARA Parametrization 334
13.3 Some Definitions Relative to the Ambiguity-Adjusted
Asset Allocation 335
13.4 Empirical Tests 336
13.4.1 Portfolios Tested 337
13.4.2 Performance Measures 339
13.4.3 Results 340
13.4.3.1 Performances of the different models 341
13.4.3.2 SEU portfolio 342
13.4.3.3 Ambiguity robust portfolios 342
13.5 Conclusion 343
Chapter 14.Semi-Static Hedging Strategies for Exotic Options 345
Hansjörg Albrecher and Philipp Mayer
14.1 Introduction 346
14.2 Hedging Path-Independent Options 347
14.2.1 Plain Vanilla Options with Arbitrary Strikes are Liquid 348
14.2.2 Finitely Many Liquid Strikes 349
14.3 Hedging Barrier and Other Weakly Path Dependent Options 350
14.3.1 Model-Dependent Strategies: Perfect Replication 351
14.3.2 Model-Dependent Strategies: Approximations 357
14.3.3 Model-Independent Strategies: Robust Strategies 359
14.4 Hedging Strongly Path-Dependent Options 361
14.4.1 Lookback Options 362
14.4.2 Asian Options 364
14.5 Case Study: Model-Dependent Hedging of Discretely
Sampled Options 367
14.6 Conclusion and Future Research 370
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Contents xv

Chapter 15.Discrete-Time Variance-Optimal Hedging in Affine
Stochastic Volatility Models 375
Jan Kallsen, Richard Vierthauer, Johannes Muhle-Karbe
and Natalia Shenkman
15.1 Introduction 376
15.2 Discrete-Time Variance-Optimal Hedging 377
15.3 The Laplace Transform Approach 378
15.4 Application to Affine Stochastic
Volatility Models 380
15.5 Numerical Illustration 388
Index 395
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Part I
Alternative Investments
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1
SOCIALLY RESPONSIBLE
INVESTMENTS
SVEN HROß
∗
, CHRISTOFER VOGT
†
and RUDI ZAGST
‡
HVB-Stiftungsinstitut für Finanzmathematik,
Technische Universität München, Boltzmannstr. 3,
85747 München, Germany

∗

†

‡

Within thelasttwo decades, the market of sociallyresponsibleinvesting (SRI) hasseen
unprecedented growth and has become more and more important, not only because of
the current financial crisis. This chapter gives a survey of the asset class SRI in general,
i.e., market development and investment possibilities. Moreover, the question “How
sustainable is sustainability?” is addressed by analyzing SAM Group sustainability
rankings of the years 2001–2007. Furthermore, the ability of SRI to contribute to
diversification within a portfolio is scrutinized. The analysis is based on simulated
returns generated by an autoregressive Markov-Switching model and accounts for
different levels of investors’ risk aversion. Optimal portfolios consisting of stocks,
bonds, and the respective SRI index show that risk–averse investors mix SRI to an
established portfolio consisting of bonds and stocks to reduce the risk and increase
the performance. Additionally, the asset class SRI is found to be a substitute for the
asset class stocks.
3
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4 Hroß et al.
1.1. INTRODUCTION
There are different ways to describe socially responsible investing (SRI). Reference 1
defines SRI as the integration of environmental, social, and corporate governance
(ESG) considerations into investment management processes and ownership practices
hoping that these factors can have an impact on financial performance. Responsible
investment can be practiced across all asset classes.
Several reasons can be stated, why the field of SRI has gained great public interest
as well as rising economic importance in recent years. Simultaneously to the on-going

climate change debate, public scrutiny and political attention have put pressure on
businesses to consider both social and environmental issues in their activities.
Accompanied by these developments, the SRI market grew strongly during the last
decade. SRI does no longer represent a negligible economical niche, but as stated in [2]
it might play a crucial financial role in the future. The current size of the worldwide
SRI market is according to [3] approximately
5 trillion. With 53% market share, the
greatest part of the SRI market is based in Europe followed by the United States with
39%. The rest of the world represents only 8% of the SRI market.
According to [4], the size of the SRI market in the United States was $639 bil-
lion in 1995 and then grew up to $2159 billion in 1999, which means an average
annual growth rate of 36%. From 1999 to 2005, SRI investment volumes only slightly
grew up to $2290 billion, but then growth accelerated again resulting in $2711 billion
in 2007.
The European SRI market experienced an average growth rate of 51% since 2002
from an absolute investment volume of
336 billion in 2002 up to 2665 billion in
2007. Reference 3 estimates that the share of SRI in the total European fund market is
about 17.6% in 2008 and largely driven by institutional investors.
There are several possibilities to invest into SRI. For example, the SAM Group
(www.sam-group.com) offers a wide range of funds covering the total SRI market and
also special funds, e.g., on Islamic sustainability. There are also sustainably managed
fixed-income funds available. Another possibility is the direct investment into non-
listed companies or projects. In this context, projects like wind farms or solar parks can
be mentioned as suitable investment possibilities. Moreover, certificates are available
on the market which allow the investor to participate in the SRI market, e.g., index
certificates on the European Renewable Energy Index (ERIX Index Certificate, Societe
Generale, ISIN: DE000SG1ERX7).
The structure of this chapter is as follows. Section 1.2 gives an overview on recent
research on SRI. Section 1.3 answers the question “How sustainable is sustainability?”

by using Markov transition matrices. Section 1.4 then analyzes SRI in a portfolio con-
text by generating optimal portfolios for different investors using a Markov-Switching
model and different optimization frameworks. Finally, Sec. 1.5 concludes.
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Socially Responsible Investments 5
1.2. RECENT RESEARCH ON SRI
During the last years, several empirical studies analyzed whether SRI produces or
destroys shareholder wealth. Many early studies on the performance of SRI use regres-
sion models with one or two factors and try to measure Jensen’s alpha. Reference 5
compares 32 SRI funds to 320 non-SRI funds in the United States between 1981 and
1990 and finds no significant average alphas with respect to a value-weighted NYSE
index. More advanced studies apply a matching approach to compare SRI and non-SRI
funds with similar characteristics, e.g., fund universe and size. Within this approach,
management and transaction costs can be included into the analysis, see, e.g., [6]
or [7]. As a result, no significant performance differences between SRI and non-SRI
could be observed. One problem is that important characteristics might not be taken
into consideration. Reference 8 applies a four factor model according to [9] using as
regression factors the excess market return, SMB (“Small-minus-Big”: The difference
between the return of a small- and of a large-cap portfolio), HML (“High-minus-Low”:
The return difference between a value- and a growth-portfolio, i.e., a portfolio con-
taining firms that dispose of a high book-to-market ratio versus firms with a low value
relating to this ratio), and MOM (“Momentum”: The return difference betweeen two
portfolios, one consisting of last year’s best performers and the other of the worst
performers) in order to analyze the performance of United States, German, and British
SRI funds. The authors build two portfolios for each country, one containing all SRI
funds, the other the conventional funds, and find under — as well as outperformance of
SRI, but none of the differences are significant. Furthermore, SRI funds seem to have
an investment bias toward growth stocks (low book-to-market value) and small caps
(lower market-capitalization). Reference 10 uses eco-efficiency rankings of Innovest
to evaluate two equity portfolios that differ in eco-efficiency. The high-ranked portfo-

lio shows significantly higher returns than its low-ranked counterpart over the period
1995–2003. In contrast, [11] finds that SRI investors have to pay for their constrained
investment style.Another approach is to look at SRI equity indices to avoid usual prob-
lems of mutual funds during a performance analysis, e.g., transaction costs of funds
or effects of management skills. Reference 12 analyzes 29 SRI indices and applies
different settings to test for differences in risk-adjusted performance compared to a
suitable benchmark. The study concludes that SRI screens do not lead to significant
performance difference of SRI indices. Yet, no final answer to the question whether
SRI produces or destroys shareholder wealth can be given. Independent of these find-
ings, SRI market growth might simply come from the non-financial utility gained by
SRI investors. To the authors’ best knowledge, there is yet no such study scrutinizing
this effect. Therefore, the focus of Sec. 1.4 lies on the benefits of SRI in a portfolio
context. For this, optimal portfolios of bonds, stocks, and SRI will be constructed for
different investor types and in different optimization frameworks.
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6 Hroß et al.
1.3. HOW SUSTAINABLE IS SUSTAINABILITY?
In this section, the endurance of sustainability is analyzed. This is especially important
for an SRI investor, who does not want to have too many reallocations in his portfolio.
Moreover, sustainability scores should be enduring by the pure definition of the word
“sustainability”. For thisaim,sustainability scores fromSAMGroup,one of theworld’s
most respected companies in the field of SRI assessment, are scrutinized. This study
is implemented using Markov transition matrices.
1.3.1. Description of the Dataset
The dataset used for the analysis contains the sustainability scores (hereinafter called
total score) of 822 companies. The methodology for calculating the total score of a
firm is given as follows. A company’s economic, ecologic, and social performance is
analyzed, where each of the three dimensions is divided into several criteria. These cri-
teria are weighted with an individual percentage of contribution to derive the final total
score. There are general criteria for all industries and specific criteria for companies

in a certain sector.
The complete dataset consists of 4432 total scores for the different firms and years
between 2001 and 2007. However, not every company receives a sustainability score
by SAM every year, simply due to the fact that there are firms that are not willing to
participate in the assessment process every year. To be more precise, only 185 com-
panies were evaluated by SAM Group in every single of the seven assessment years.
The companies in the dataset are a mixture of worldwide well-known multinational
companies, such as Adidas AG, Allianz SE, the Coca-Cola Company, and Sony Cor-
poration, as well as rather regional established firms such as Eniro AB from Sweden
or the Italian Beni Stabili SpA. It can be seen from Table 1.1 that the total scores
over the whole time period range between a rather low rating of 4.97 and a very high
score of 92.37, i.e., that the predefined range between 0 and 100 is actually utilized.
Interestingly, the median and mean of the overall total scores are slightly above 50,
and barely half of the companies received a sustainability score between 43 and 65.
1.3.2. Introduction to Markov Transition Matrices
In this section, Markov transition matrices are used to analyze the evolution of the
sustainability scores. A high degree of variation within the total scores would be
Table 1.1 Statistics on Total Score.
Minimum 1st quartile Median Mean 3rd quartile Maximum
4.97 43.60 55.48 53.67 65.19 92.37
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Socially Responsible Investments 7
counter-intuitive, due to the fact that sustainability is a long-term affair and thus should
not be subject to large-sized jumps, unless extraordinary events occur, e.g., an envi-
ronmental disaster on an oil producer’s platform. For the following analysis, data of
those companies are used for which the sustainability scores are available for two
consecutive years. For the entire six-year time period, this leads to a total dataset of
2125 observations. The calculation of the transition matrices is performed as follows:
For every single year, companies are ranked by their sustainability score, whereby for
every year the 25% best rated companies are assigned to the 1st quartile, the next 25%

to the 2nd quartile, and so on. Based on this allocation, empirical transition probabil-
ities from one of the four quartiles to any of the four quartiles after one year can be
calculated.
1.3.3. Results of Markov Transition Matrices
From the average one-year transition probabilities in Table 1.2, it can be seen that the
probability of staying in the current quartile is the highest and ranges from 47.53% for
the 2ndquartileto 72.21% for thelastquartile.Additionally, the probabilitydecreasesin
the distance between two quartiles. Furthermore, the probability that a top-ranked firm
will end up in the 4th quartile in the following year is only 0.37% and the probability
of a “bad” company to be part of the first quartile in the following period is 1.23%.
Moreover, Markov transition matrices for every single year 2001–2007 were scru-
tinized. The results for the single years are quite similar to the average observation in
Table 1.2. Finally, a six-year Markov transition matrix was computed. The results are
shown in Table 1.3.
Nearly half of the companies that were ranked in the first quartile in 2001 were
still in the first quartile in 2007. The probability that a highly sustainable company will
be part of the worst quartile at the end of the six years is 5.36% and the probability
of the opposite case, i.e., a “bad” company ending as a sustainability leader after six
years, is 7.02%.
Table 1.2 Average One-Year Markov Transition Proba-
bilities (Year 2001–2007).
Next year quartile
1 (%) 2 (%) 3 (%) 4 (%)
Last year quartile
1 69.74 25.00 4.90 0.37
2 23.83 47.53 24.35 4.29
3 5.15 21.74 49.94 23.17
4 1.23 5.96 20.60 72.21
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8 Hroß et al.

Table 1.3 Markov Six-Year Transition Probabilities
(Year 2001–2007).
Next year quartile
1 (%) 2 (%) 3 (%) 4 (%)
Last year quartile
1 46.43 26.79 21.43 5.36
2 25.00 39.29 32.14 3.57
3 21.43 14.29 32.14 32.14
4 7.02 19.30 14.04 59.65
Altogether, the results provide evidence to the assumption that sustainability rank-
ings do not have a high degree of short-term variation.
1.4. SRI IN PORTFOLIO CONTEXT
After having analyzed the sustainability of sustainability in the preceding section, this
section will scrutinize how SRI can be evaluated with regard to the portfolio context.
The main questions to be answered are whether investors shall add SRI investments
to their portfolio, and if so, with which weighting.
In the conducted portfolio case study, the SRI market is represented by the
Advanced Sustainable Performance Index (ASPI). The ASPI is a European index con-
sisting of 120 companies and is published by Vigeo Group, an extra-financial supplier
and rating agency in the field of sustainable development and social responsibility
(for further information see [13]). In order to include dividend payments to the anal-
ysis, total return indices are used, i.e., dividends are reinvested. This approach has
two main advantages. First, the index already represents a selected basket of the asset
category SRI and the time series are readily available. Second, the predefined index is
widespread and thus has the advantage that the companies’ specific risks are already
eliminated by diversification. As a result, only the diversification effect of the asset
class SRI itself is observed.
1.4.1. Description of the Dataset and Statistical Properties
The portfolio analysis is based on daily log-returns of the asset classes bonds (repre-
sented by the JP Morgan Global Government Bond Index), stocks (represented by the

Dow Jones Total Markets World Index), and SRI (represented, as described above, by
the ASPI index) between 1 January 1992 and 30 September 2008. The main empirical
statistics are shown in Table 1.4.