Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of Renewable Energy Investments [1 ed.] 9783842837997, 9783842887992

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Reihe Alternative Investments Bd. 1

Frederik Bruns

Windfall Profit in Portfolio Diversification?

Copyright © 2013. Diplomica Verlag. All rights reserved.

An Empirical Analysis of the Potential Benefits of Renewable Energy Investments

Diplomica Verlag

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Bruns, Frederik: Windfall Profit in Portfolio Diversification? An Empirical Analysis of the Potential Benefits of Renewable Energy Investments, Hamburg, Diplomica Verlag GmbH Umschlaggestaltung: Diplomica Verlag GmbH, Hamburg Covermotiv: © buchachon - Fotolia.com ISBN: 978-3-8428-3799-7 © Diplomica Verlag GmbH, Hamburg 2013 Bibliografische Information der Deutschen Nationalbibliothek:

Copyright © 2013. Diplomica Verlag. All rights reserved.

Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar.

Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes der Bundesrepublik Deutschland in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechtes. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Die Informationen in diesem Werk wurden mit Sorgfalt erarbeitet. Dennoch können Fehler nicht vollständig ausgeschlossen werden und die Diplomica GmbH, die Autoren oder Übersetzer übernehmen keine juristische Verantwortung oder irgendeine Haftung für evtl. verbliebene fehlerhafte Angaben und deren Folgen.

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Vorwort Sehr geehrter Leser, im Jahre 2010 entschloss sich der Bundesverband Alternative Investments e. V. (BAI), wissenschaftliche Arbeiten im Bereich der sog. Alternativen Investments zu fördern. Zu diesem Zweck wurde damals der BAI-Wissenschaftspreis ins Leben gerufen. Einer der Hauptgründe sowie die Intention für diese Förderung waren und sind, dass das Wissen über Alternative Investments sowohl in der Breite als auch in der Tiefe leider immer noch sehr rudimentär ist. In weiten Teilen der Öffentlichkeit, der Politik, der Medien, aber auch auf Seiten der Investoren herrschen oftmals vielfache Missverständnisse hinsichtlich Nutzen und Risiken von Alternative Investments. Mit dem Wissenschaftspreis will der BAI einen Anreiz für Studenten und Wissenschaftler in Deutschland schaffen, Forschungsarbeit in diesem für institutionelle Investoren zukünftig immer wichtiger werdenden Bereich zu leisten. Viele deutsche Hochschulen erklärten sich auf Anhieb bereit, den BAI bei der Bekanntmachung des Wissenschaftspreises zu unterstützen. Daraus resultierend erreichten den BAI zahlreiche anspruchsvolle Bewerbungen in den vier Kategorien „Dissertationen“, „Master-/Diplomarbeiten“, „Bachelorarbeiten“ und „Sonstige Wissenschaftliche Arbeiten“. Für diese wurde jährlich neben einem Award ein Preisgeld von 10.000 Euro an die Gewinner ausgelobt. Wir freuen uns sehr, dass der Diplomica Verlag die Reihe „Alternative Investments“ ins Leben gerufen hat. Diese Publikation wird sicherlich auch dazu beitragen, das Thema Alternative Investments einer Vielzahl von Personen näherzubringen. Wir wünschen dem Leser nun eine spannende Lektüre!

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Ihr Bundesverband Alternative Investments e. V.

5

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Copyright © 2013. Diplomica Verlag. All rights reserved. Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Preface and Acknowledgments My aim in writing this book is to combine the interest of both academics and practitioners in the Alternative Asset class of Renewable Energies. The idea for the topic actually dates back to 2010 when I was completing my first internship at Allianz. I became curious to find out more about the possibilities of an investor to diversify his portfolio by using “new” asset classes such as Renewables. Modern Portfolio Theory thereby occurred to me as the perfect tool in exploring this route. This book would not have been possible without a number of people. First and foremost, I would like to thank David Jones and the rest of the Renewable Energies team at Allianz for providing me with the opportunity to work on such a unique project. I am sincerely grateful for their continued support and interest during completion of this book. My debt also goes to Hans Finsterer and Rainer Husmann for establishing the contact to the Renewable Energies team and for providing me with a first insight into the world of Alternative Assets. Second, I owe debt to anyone contributing from the academic side. I am grateful to all students and professors at the universities of Bonn, Heidelberg and New York who have shared their knowledge and insights during my studies and who provided me with the required background for this work. My special thanks go to Prof. Dr. An Chen for her interest in the topic and her supervision. I am also thankful to Jan Weltzien for his review, comments and feedback. In addition, I would like to thank the people at Bundesverband Alternative Investments e.V. and the Diplomica Verlag for enabling me to publish this book and making the topic available to a wider audience.

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Finally, I want to give special thanks to my father not only for his continuous support during this work but also for his guidance, feedback and review for any of my previous academic works. It goes without saying that I am also grateful to my sister and my friends who supported and encouraged me during the work on this book, and especially to my girlfriend for her love and support even across borders.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Copyright © 2013. Diplomica Verlag. All rights reserved. Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Table of contents Preface and Acknowledgments ................................................................................................ 7 List of abbreviations ............................................................................................................... 11 List of figures .......................................................................................................................... 13 List of tables ............................................................................................................................ 14 1 Introduction and literature overview................................................................................. 15 2 Renewable Energy as an Alternative Asset class .............................................................. 19 2.1 Classification .................................................................................................................. 19 2.1 Main characteristics ........................................................................................................ 21 2.3 Investors.......................................................................................................................... 24 3 Modern Portfolio Theory .................................................................................................... 27 3.1 Mean-variance framework .............................................................................................. 27 3.2 Estimating correlation structures .................................................................................... 29 3.3 Optimal portfolios with investor liabilities ..................................................................... 32 4 Application to Renewable Energy investments ................................................................ 35 4.1 Return distributions ........................................................................................................ 35 4.2 Diversification possibilities ............................................................................................ 38 4.3 Discussion of the asset-only perspective ........................................................................ 40 4.4 Liability hedging credit .................................................................................................. 42 5 Empirical analysis ............................................................................................................... 47 Copyright © 2013. Diplomica Verlag. All rights reserved.

5.1 Data ................................................................................................................................. 47 5.2 Statistical analysis........................................................................................................... 51 5.3 Empirical results ............................................................................................................. 55 5.3.1 Diversification possibilities in a multi-asset portfolio............................................. 55 5.3.2 Diversification possibilities within a wind portfolio ............................................... 60 5.3.3 Hedging benefits of solar......................................................................................... 66

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

6 Conclusion and outlook ...................................................................................................... 69 Appendix ................................................................................................................................. 71 Appendix A: Renewable Energy instruments and remuneration ......................................... 71 Appendix B: Discussion of the holding period return measure ........................................... 72 Appendix C: Structure of the income statement for a wind farm ........................................ 79 Appendix D: Empirical distributions of the wind farms ...................................................... 82 Appendix E: Proxy indices and discussion of the asset classes ........................................... 84 Appendix F: Empirical distributions and autocorrelation of the asset classes ..................... 87 Appendix G: Value at Risk and Conditional Value at Risk .................................................. 89 Appendix H: Calculation of the optimal portfolios in the multi-asset framework .............. 91 Appendix I: Regressions for the wind portfolio................................................................... 95 Appendix J: Security Market Line of the single-index model for wind .............................. 99

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References ............................................................................................................................. 101

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Copyright © 2013. Diplomica Verlag. All rights reserved.

List of abbreviations ALM

Asset Liability Management

APT

Arbitrage Pricing Theory

ARIMA

Autoregressive Integrated Moving Average

CAGR

Constant Annual Growth Rate

CAPEX

Capital Expenditures

CAPM

Capital Asset Pricing Model

CML

Capital Market Line

CVaR

Conditional Value at Risk

DCF

Discounted Cash Flow

DEWI

Deutsches Windenergie-Institut (German Wind Energy Institute)

EBIT

Earnings before Interest and Taxes

EBITDA

Earnings before Interest, Taxes, Depreciation and Amortization

EPIA

European Photovoltaic Industry Association

EURIBOR

Euro Interbank Offered Rate

EWEA

European Wind Energy Association

FCF

Free Cash Flow

FRA

French wind farm in the data set

GER

German wind farm in the data set

GWEC

Global Wind Energy Council

IRR

Internal Rate of Return

ITA

Italian wind farm in the data set

MPT

Modern Portfolio Theory

MVP

Minimum Variance Portfolio

MW

Megawatt

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Net Present Value

PPA

Power Purchase Agreement

ROI

Return on Investment

SAAR

Seasonally Adjusted Annual Rate

SML

Security Market Line

SOL

Solar park in the data set

SR

Sharpe Ratio

SRI

Socially Responsible Investment

TP

Tangency Portfolio

TR

Total Return

VaR

Value at Risk

WACC

Weighted Average Cost of Capital

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NPV

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

List of figures Figure 1: Market development of wind energy ........................................................................ 15 Figure 2: Market development of solar energy ........................................................................ 16 Figure 3: Classification of Renewable Energy investments ..................................................... 20 Figure 4: Example for the long-term volatility of wind ........................................................... 23 Figure 5: Example for the long-term volatility of irradiation................................................... 23 Figure 6: Seasonality of a representative wind farm ................................................................ 37 Figure 7: Seasonality of a representative solar park ................................................................. 37 Figure 8: Example for a cash flow profile of an endowment assurance .................................. 43 Figure 9: Example for a cash flow profile of an annuity .......................................................... 44 Figure 10: Example for a cash flow profile of stocks, bonds and Renewables ........................ 45 Figure 11: Geographical dispersion of the wind and solar parks in the empirical analysis ..... 48 Figure 12: Autocorrelation of the unadjusted returns (ROI) for a representative wind farm ... 50 Figure 13: Autocorrelation of the adjusted returns (SAAR) for a representative wind farm ... 51 Figure 14: The “Wind Farm Market Line” ............................................................................... 54 Figure 15: Historical performance of the asset classes............................................................. 56 Figure 16: Historical performance of the optimal portfolio ..................................................... 60 Figure 17: Scatterplot of the Italian wind farm with the market .............................................. 62 Figure 18: Diversifiable and non-diversifiable risk of each wind farm ................................... 65 Figure 19: The effect of diversification .................................................................................... 66 Figure 20: Hedging wind and solar with budget values ........................................................... 67

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Figure 21: Hedging wind and solar with actuals ...................................................................... 68

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

List of tables Table 1: Seasonality ratios of the wind farms .......................................................................... 50 Table 2: Descriptive statistics of the unadjusted monthly returns (ROI) of the wind farms.... 52 Table 3: Descriptive statistics of the adjusted annualized returns (SAAR) of the wind farms 52 Table 4: Correlation between the wind farms .......................................................................... 54 Table 5: Investment universe for the asset allocation problem ................................................ 56 Table 6: Statistical analysis of the asset classes ....................................................................... 57 Table 7: Correlation matrix of the asset classes ....................................................................... 58 Table 8: Weights for the optimal portfolios ............................................................................. 59 Table 9: Weights for the wind market portfolio ....................................................................... 61 Table 10: Summary of the single-index model for wind ......................................................... 63

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Table 11: Multi-index model for the Italian wind farm ........................................................... 64

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

1

Introdu uction an nd literaature oveerview

Overr the last ten n years, Reenewable Ennergy has been b the fasstest growinng industry segment inn the energy e secto or, reaching a global innvestment voolume of $2211 billion in 2010.1 T The majorityy of thhe vast expaansion stemss from the w wind and soolar industryy. As exempplified in F Figure 1 andd 2, tootal installed d capacity in Megawaatt (MW) skkyrocketed for both teechnologies during thee last decade. d Win nd power tooday is amoong the leadding energy sources agaainst climatte change inn the U.S. U and Eu urope as well as in China. It will play p a key rrole in reachhing the am mbitious EU U Reneewable Enerrgy target of o at least 220% of final energy coonsumption by 2020. Inn Germany,, 17% of electriciity has already been generated byy Renewablle Energies in 2010, w with wind ass the laargest contrributor. F Figure 1: Maarket development of wind d energy

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Sourcce: GWEC Gloobal Wind 20110 Report (ww ww.gwec.net).

1 Accoording to Bloom mberg New Eneergy Finance (22011), p.12.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 2: Market deevelopment of o solar energgy

Source: EP PIA Global Ma arket Outlookk for Photovolttaics until 20115 (www.epia.org).

Beemer (22009) explaains the growth of the Renewablee Energy inndustry as a combinatiion of several driiving forcess. Due to a rise in eneergy demand and an inncreased “ggreen awareeness” following from the debate d on cllimate channge, Renew wables gaineed more annd more political attention. The T addition nal motivattion for beinng less depeendent on eenergy resouurces, such as oil or gas, resulted in thee creation of o stable reggulatory fraameworks. F Furthermoree, strong technological im mprovementss for wind and especiially solar made thesee energy soources a seerious competitorr to conven ntional pow wer supplierrs. These factors f led to a favorrable investtment environmeent compareed to many other o infrasttructure facilities.

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Conventionnal wisdom m would sugggest that thhe main inveestors in Reenewable Ennergies beloong to the utility sector. How wever, morre than halff of the wiind farms inn Europe, for instancee, are currently owned o by financial f invvestors.2 A large groupp of these iinvestors arre either peension funds or innsurance co ompanies.3 They T investt into this new n asset class due to several s attraactive characterisstics such ass stable cashh flows andd independennce from caapital markeets. As institutiional investtors get morre and moree attracted to t Renewabble Energiess, they also try to find out hoow these in nvestments generally g fiit into the rest r of theirr portfolio. The objectiive of this book is i to apply the main cooncepts from m Modern Portfolio Theory (MPT T) to Renew wable Energy invvestments and a therebyy discuss ttheir potenttial role inn an instituutional inveestor’s 2 See EWEA (2009), ( p. 285. 3 Indeed, two pension funds (PensionDanmaark and PKA) just recently beccame co-ownerrs of Denmark’ss largest offshoore p “Anholt” (see DONG press p release off 28 March 20111, www.dongennergy.com). wind farm project

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

portfolio. As of Markowitz (1952), an investor can mitigate an individual asset’s risk by building a portfolio with low (or in the best case negatively) correlated assets.4 This is due to the fact that in a reasonably sized portfolio, the risk from volatile returns does not exclusively depend on the risk of the individual assets but is dominated by covariance risk, the so-called diversification effect. The present work is a first attempt to explore the diversification potential of Renewables from the perspective of a financial investor. There are mainly two areas of interest. The first area concerns the benefits from diversification when wind and solar parks are added to an existing portfolio of an institutional investor.5 Secondly, the question of how this investor can diversify away risk within the asset class Renewables itself will be addressed. There are only few published articles on this specific topic. Many studies apply Modern Portfolio Theory to the energy mix of a country and thereby assess the potential future role of Renewables.6 Other studies already approached the role of Renewable Energies from a financial perspective. Mader et al. (2010), for instance, include solar investments (photovoltaics) into a portfolio of stocks and bonds and thereby find positive effects of diversification. Beemer (2009) explores diversification benefits of the Renewable Energy and Cleantech sector by creating a respective index that consists of listed companies.

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Dunlop (2004a) was the first to apply the MPT framework to a specific part of Renewable Energy investments, namely wind farms. His book deals with the question of how much production risk can be diversified away by investing into a portfolio of wind farms rather than a single wind park. He thereby uses a CAPM-style model to test various portfolios consisting of 10 wind farms against a self-created market index. The results are striking. In the case of a combination of the Southern European and U.S. portfolio, up to 30% of the production risk of a single wind farm can be diversified away. The other research papers on this topic have either not been published yet or are supplied by wind energy consultants that presented them during conferences. Hulsch and Strack (2006) combine five wind farms from Germany and France into a portfolio and find a risk reduction for the annual energy yield of up to 42%. This can be achieved because correlations between the monthly energy yields among the countries are as low as -1%. The authors also translate the results into a cash flow model and find that the debt capacity of the portfolio is 17% higher than the sum of the individual wind farms’ capacities. By subsequently applying a higher leverage, it is shown that an investor can boost the Net Present Value (NPV) of the projects by 19%. Marco et al. (2009) test the diversification effect for 75 sites in Europe and find a benefit as large as 25% for the annual volatility. Their paper thereby uses monthly wind speeds as a proxy for the energy production. Chaves-Schwinteck (2011), who provides the most recent study, finds a reduction in the uncertainty of the annual energy production of 35% due to low correlations. 4 Whenever the term “low” correlation is being used in this book, it will refer to a low positive correlation. Likewise, a “high” correlation will refer to a high positive correlation. Negative correlations will be stated separately. 5 The terms wind “park” and wind “farm” are being used as synonyms in this book. 6 For instance, see Awerbuch and Berger (2003), Albrecht (2007) or Madlener et al. (2009).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Most of the previous studies were limited to study the effect of diversification on reducing production risk. This was due to the fact that actual financial data for privately owned wind and solar parks is usually hard to acquire. The present study, however, had the unique opportunity to work with exclusive financial data from one of the largest institutional investors into Renewable Energies. This data set both enabled a comparison of Renewable Energy investments to other assets and helped in exploring the risk-return characteristics of the asset class itself.

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The rest of the book is structured as follows. Section 2 gives an overview on Renewable Energy investments and introduces their main characteristics. In section 3, the theoretical framework of Modern Portfolio Theory will be briefly reviewed. This theory will then be applied to the asset class of Renewables in section 4. In the second part of the book, the main concepts from the theoretical framework will be employed for an empirical analysis (section 5). This analysis will cover both the diversification benefits of Renewables in a multi-asset portfolio and within the asset class itself. Section 6 will finally review the main findings and provide a perspective for future research directions.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

2

Renewable Energy as an Alternative Asset class

2.1 Classification Renewable Energy is electricity and thermal energy which is created from natural resources such as wind or sunlight.7 This energy is said to be sustainable, which means that resources are not being used before they can recreate. The most common Renewable Energies are wind, solar and geothermal heat. In recent years, there has been a trend of privately investing into Renewable Energy projects (wind or solar parks), which led to the creation of an own asset class.8 This is mainly due to several attractive characteristics for financial investors. Before starting to analyze the characteristics of Renewable Energy investments, it is worthwhile to examine what is commonly referred to as an “asset class” in the first place. Greer (1997) defines an asset class as a “set of assets that bear some fundamental economic similarities to each other, and that have characteristics that make them distinct from other assets that are not part of that class.”9 Mader et al. (2010) enhance the definition by a similar “sensitivity towards major market factors”.10 Both in the academic literature and amongst practitioners, there currently exists no universally accepted definition of Alternative and Traditional Assets.11 The most common and probably least arguable description is to label Alternative Assets as anything other than stocks and bonds and the latter two in turn as Traditional Assets.12 Asset classes within the Alternatives spectrum that can be frequently found in empirical studies are real estate, private equity, hedge funds and commodities.13 A further Alternative Asset class that is currently on the rise are so-called infrastructure investments. Inderst (2010), who provides an overview on the literature about this asset class, further subdivides infrastructure investments into economic and social infrastructure. Following this classification, the author sees Renewable Energy investments as one sub-category of the economic infrastructure bucket.14

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Another classification by Mader et al. (2010) groups Renewable Energy investments into the class of so-called Alternative Real Assets.15 This classification stresses the direct exposure to real facilities and specific projects. Further Real Assets such as commodities, inflation-linked bonds and real estate are labeled as Traditional Real Assets. On the other hand of the overlying Alternative Assets class are private equity and hedge fund investments. 7 According to Böttcher (2009), p. 9. 8 According to Deloitte (2011), p. 3. 9 Greer (1997), p. 86. 10 Mader et al. (2010), p. 2. 11 According to Fraser-Sampson (2011), p. 2. 12 See e.g. Inderst (2010), p. 71., Fraser-Sampson (2011), p.3. 13 For instance, see Schneeweis et al. (2002), Schweizer (2008) or Fischer and Lind-Braucher (2010). 14 The other sub-categories of economic infrastructure are transport, utilities and communication. 15 Other Alternative Real Assets are shipping, aviation and infrastructure according to the authors.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 3 shows a combination of the two classifications of Inderst (2010) and Mader et al. (2010). It should be mentioned that Renewable Energy investments are not limited to wind and solar, as the figure might suggest. Most of the other Renewables (e.g. hydro, geothermal heat or biomass), however, are not yet in a state to be interesting for financial investors.16 Therefore, this book restricts the attention to the most common Renewable Energy investments, namely wind and solar parks. Figure 3: Classification of Renewable Energy investments

Traditional Assets

Stocks

Bonds

Alternative Assets

Private Equity

Real Assets

Hedge Funds

Government Corporate

Traditional

Alternative

Commodities

Infrastructure

Real Estate

Economic

Social

…

…

Renewables Solar

Wind

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Source: compiled by the author following Inderst (2010) and Mader et al. (2010).

16 According to Dunlop (2004b), p. 87.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

2.1 Main characteristics When assessing the main characteristics of Renewable Energy investments, a good starting point is to have a look at the broader asset class of infrastructure investments. Inderst (2010) groups the main characteristics for infrastructure investments into economic and financial characteristics. Economically, due to natural monopolies, government regulations and concessions, infrastructure assets generally operate under limited competition. Financially, low correlations with other asset classes, predictable cash flows and inflation-hedge benefits make this asset class resilient against financial crises.17 In case of a direct investment into actual projects (toll roads, gas pipelines etc.), Inderst (2010) determines the main risks to be regulatory risks, financial risks (from leverage or refinancing) and, depending on the level of development, construction and operational risks. Many of the characteristics of infrastructure investments can be applied to Renewable Energies almost one to one. Both solar and wind power receive substantial political support in terms of subsidies and the legal framework. Therefore, they also operate in a limited competition environment. The main risks in Renewable Energy projects according to Böttcher (2009) are: ƒ

Production risk (from the input resource that generates electricity)

ƒ

Technology risk

ƒ

Completion risk (for construction projects)

ƒ

Operational risk

ƒ

Regulatory risk (changes to the regulatory framework)

ƒ

Financial risk (from debt financing)

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While production risk contains a general uncertainty of the input resource (e.g. wind), many of the other risks can be mitigated through appropriate contractual structuring.18 Probably the most important characteristic of Renewable Energy investments lies in its cash flow profile. Wind and solar investments tend to have a high cash generation with operating margins of around 80%.19 A major component for the revenues of these investments is the long-term power purchase agreement (PPA). The PPA sets the price, or the so-called “tariff”, for any electricity produced from the wind or solar park. Some countries, such as Germany or France, guarantee a fixed feed-in tariff for almost the whole lifetime of the projects. In France, the tariff is even partly escalated with inflation. This provides the investors with high comfort from secured cash flows.

17 Inflation hedging benefits, for instance, are examined in Martin (2010). 18 According to Raftery et al. (1999), p. 496. 19 See Dunlop (2004b), p. 85 for wind and Awerbuch (2000), p.1030 for solar.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Other countries, such as Italy, China or the U.S., do not provide the comfort of a long-term fixed price. In these countries, the government determines the amount of “green energy” in the overall energy supply but not the price for any electricity sold. This is also generally referred to as a quota-based system.20 The market price solution comes with an additional risk for potential investors, since electricity prices can fluctuate during the holding period of the asset. Nevertheless, a certain amount of inflation-protection can still be expected as electricity prices often tend to rise with inflation. A map in Appendix A shows the two different tariff solutions for several EU countries as well as the current remuneration for Renewables in the largest markets. In case of a fixed feed-in tariff regime, production risk seems to be the major leftover risk for this asset class.21 This also stems from the fact that the tariff is often guaranteed by A-rated counterparties which significantly mitigates credit risk.22 For wind farms, however, production risk should not be underestimated as annual wind-speeds tend to be volatile. The risk from the input resource for solar parks appears to be lower. This is due to the fact that irradiation, which is the main input for energy creation from solar parks, tends to be more stable.23 Figure 4 and 5 exemplify the long-term volatility of both wind speeds and irradiation for a representative region.

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For both solar and wind parks, the expected production can be described by a function of the annual wind speed or solar irradiation at the respective location. In most cases, a specialized consultancy is being hired to provide an estimate of this production, which is also called the annual energy yield.24 Depending on the availability of the data (wind or irradiation measurements), uncertainties of these estimates can range between 10-30% for onshore wind and slightly lower for solar parks.25 Thus, in addition to the volatile input resource (wind and irradiation) there exists the risk of an overestimate of the energy yield by consultants.

20 See e.g. Böttcher (2009), p. 99. 21 For solar parks there might be an additional risk that single modules are stolen. However, this risk can be mitigated relatively easily by setting up electric fences or comparable security equipment. 22 It thereby has to be differentiated between a state budget financing and a pass-through solution to the end consumer. Whether the sovereign crisis in the Eurozone will have an impact remains to be seen. 23 According to Awerbuch (2000), p. 1031. 24 See Böttcher (2009), p. 159 and p. 246. 25 See Strack and Winkler (2003), p. 54. Böttcher (2009) states that even if data about irradiation for more than 15 years is available, the uncertainty can still be around 4%.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figu ure 4: Examp ple for the lon ng-term volatiility of wind

Source:: compiled by the author onn the basis of Winkler (20100).

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Figure 5: Example ffor the long-term volatilityy of irradiatioon

Source: compiled by the author onn the basis of B Böttcher (2009 9).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

The last favorable characteristic of Renewable Energy investments, which also corresponds to many other infrastructure investments, relates to correlations. There is no logical reason for any correlation with stock or bond markets.26 Both annual wind speeds and irradiation are assumed to be randomly distributed. If a bad wind year coincides with a financial crisis, this can be seen as a random event. Therefore, investors can expect fairly high diversification potential when investing into Renewable Energies alongside other asset classes. Due to a direct exposure to real facilities, Renewable Energy investments are generally suitable for project finance.27 The value of a wind or solar park can be determined bottom-up by a discounted cash flow model (DCF) leading to a specific Net Present Value (NPV) or Internal Rate of Return (IRR). Sensitivities can then be assessed by e.g. a Monte-Carlo simulation.28 A top-down market-based valuation via multiples or betas cannot easily be applied to this asset class, since available data on actual transactions is limited.29 In the case of wind investments, a typical project has around EUR 1-1.4m / MW of investment cost and a capacity between 10-20 MW.30 Thus, a reasonably sized portfolio can be created with a rather small amount of funds for a large investor. For solar, the investment costs per MW are usually higher and vary according to the tariff regime in the respective country.31 Both solar and wind parks have an operational life of 20-25 years and little to no residual value.32 Thus, the investments are generally suitable for long-term investors who are planning to hold these illiquid assets until they have reached the end of their lifetime. Structurally, these investments are often organized in limited partnership fund structures, which also stems from the investor groups that are interested in this specific asset class.

2.3 Investors There are mainly two financial investor groups that invest into wind and solar parks according to the literature: 1. Investors with long-term liabilities33 and 2. Socially Responsible Investment (SRI) funds.34

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Examples for investors with long-term liabilities are endowments, pension funds and insurance companies. The latter two appear to be the main institutional investors into Renewable Energies.

26 See Awerbuch (2000), p.1030. 27 See e.g. Munoz et al. (2011). 28 See Pforte et al. (2008) or Madlener et al. (2010). 29 According to Mader et al. (2010), p. 54. A recent market study by Deloitte (2011) however tries to create an Enterprise Value per MW multiple for both solar and wind farms based on a private data set. 30 See EWEA (2009), p. 200 and Dunlop (2004a), p. 84. 31 A recent study by Deloitte (2011) finds solar Enterprise Value / MW multiples to be in the EUR 3.5-4.9m range. 32 See Dunlop (2006), p. 82 and Böttcher (2009), p. 162. 33 See Dunlop (2006), p. 81. 34 See Pforte et al. (2010), p. 66.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

After two big crises on the stock market, namely the Dotcom Crisis in the early 2000s and the Subprime Crisis in 2008, many long-term investors were seeking for new opportunities in order to diversify their dominant equity and bond portfolios.35 Pension funds, for instance, were still heavily invested in stocks due to a favorable performance in the 1990s. However, the turbulences on the stock market revealed the shortcomings of this strategy and yet resulted in another major shift in asset allocation.36 This time, the investors required high-yield assets that lay in between bonds and equities. The risk-return characteristics of real assets such as infrastructure or Renewables thereby seemed to be the perfect match. Especially the 20 year secured cash flow profile of a wind or solar park appeared to be highly attractive for longterm investors such as pension funds and insurance companies. Although the main motivation for investing into these assets might have evolved from financial objectives, it could well be that also non-financial objectives played an important role. Davis (2000), for instance, reports that more and more pension funds try to invest in a socially responsible way, which is certainly granted in a Renewable Energies investment. The second group of Renewable Energy investors that is frequently quoted are Socially Responsible Investment funds. According to Hroß et al. (2010), SRI is defined as “the integration of environmental, social, and corporate governance considerations into investment management processes and ownership practices hoping that these factors can have an impact on financial performance.”37 The Socially Responsible Investment technique has emerged out of several empirical papers about the performance of SRI vis-à-vis non-SRI funds, combined with the public and political attention on climate change as a whole.38 Out of this interest, a number of financial services providers have created SRI funds that e.g. directly invest into wind and solar projects and hence let the investors participate in the “environmentally friendly returns”.

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Summing up, Renewable Energy investments appear to offer several attractive characteristics to long-term investors. However, since the asset class is relatively new, it is not yet clear how these investments generally fit in to the rest of an investor’s portfolio. The next chapter will therefore briefly review the main concepts from a theory that can assist in finding the optimal portfolio composition.

35 An overview on these historic developments can be found in Inderst (2010). 36 The term “asset allocation” in this book refers to the long-term strategic asset allocation as opposed to the rather short term tactical asset allocation. This is being used since the main investor groups considered in this study are long-term investors. 37 Hroß et al. (2010), p. 4. 38 Hroß et al. (2010) provide a survey article on SRI. The pioneering study stems from Hamilton et al. (1993).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

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3

Modern Portfolio Theory

3.1 Mean-variance framework The seminal paper by Markowitz (1952) laid the groundwork for what is now known as Modern Portfolio Theory.39 When facing an investment decision under uncertainty, the payoff of the respective asset is described by a return distribution. If this distribution follows a normal distribution, the investor can restrict his attention to the mean and standard deviation of the asset’s returns. The contribution of Markowitz is that when an asset is considered in isolation, the investor has to assess its total risk, i.e. standard deviation of the returns. When holding a diversified portfolio of several assets, however, the non-diversifiable risk of an asset is relevant for the investor. This idea can be shown mathematically by the following. The expected return of a portfolio of N assets, generally measured by the holdings period return, is equal to the weighted average of the individual returns, or mathematically: ே

‫ ܧ‬ሺܴ௉ ሻ ൌ ෍ ܺ௜ ‫ܧ‬ሺܴ௜ ሻ ௜ୀଵ

where ‫ܧ‬ሺܴ௜ ሻ denotes the expected return of the i’th asset and ܺ௜ the respective weight in the portfolio. In matrix notation, this can be expressed as: ܺଵ ‫ ܧ‬ሺܴ௉ ሻ ൌ ሾ‫ܧ‬ሺܴଵ ሻ ǥ ‫ܧ‬ሺܴே ሻሿ ൥ ‫ ڭ‬൩ ܺே The risk of a portfolio however, if measured by the standard deviation of returns, does not exclusively depend on the variances of the individual assets. This can be seen by grouping together variance and covariance terms of the assets, which are denoted by ߪ௜ଶ and ߪ௜௝ . The variance of a portfolio of N assets can then be expressed as: ே ଶ

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ߪ௉ ൌ

෍ ܺ௜ଶ ߪ௜ଶ ௜ୀଵ

ே

ே

൅ ෍  ෍ ܺ௜ ܺ௝ ߪ௜௝ ௜ୀଵ ௝ୀଵ ௝ஷ௜

39 Most of the notation in this book will be adapted from the standard text book on Modern Portfolio Theory which is Elton et al. (2010). For an overview on Modern Portfolio Theory, see Elton and Gruber (1997).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

In matrix notation, this can be written as: ଶ

ߪ௉ ൌ ሾܺଵ

‫ڮ‬

ߪଵଶ ܺே ሿ ቎ ‫ڭ‬ ߪேଵ

‫ڮ‬ ‫ڰ‬ ‫ڮ‬

ߪଵே ܺଵ ‫ ڭ‬቏൥ ‫ ڭ‬൩ ߪேଶ ܺே

where the matrix in the formula corresponds to the variance-covariance matrix. The standard deviation ߪ௉ is simply the square root of the portfolio variance. Now, as the number of assets in the portfolio becomes large, the risk becomes more and more dominated by the covariance between these assets. This can easily be seen by assuming equal weights (1/N) for the fractions of the risky assets and letting N become large.40 Fama (1976) was the first to illustrate this result empirically by randomly selecting stocks and combining them to form an equally weighted portfolio. With fewer than 15 stocks the portfolio standard deviation already approached the average covariance between the securities.41 Thus, if an investor plans to build a portfolio, the objective should be to select assets that have low or, in the best case, negative correlation ߩ௜௝ , as the covariance is defined as ߪ௜௝ ൌ ߩ௜௝ ߪ௜ ߪ௝ . Since the number of possible combinations of different assets is infinite, the academic literature has proposed two portfolios that could be of interest for an investor. One of these optimal portfolios is the so-called Minimum Variance Portfolio (MVP). It corresponds to the combination of assets that delivers the lowest risk for any feasible portfolio. If short sales are not allowed, this can be attained by solving the following optimization problem: ‹ ߪ௉ ଶ s.t. (1) σே ௜ୀଵ ܺ௜ ൌ ͳ (2) ܺ௜ ൒ Ͳ‫݅׊‬

[1]

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The second optimal portfolio that could be of interest for an investor is the so-called Tangency Portfolio (TP).42 This combination of assets has maximum excess return over the risk-free rate measured in terms of portfolio risk. The academic literature refers to this ratio as the Sharpe Ratio (SR), which can also be calculated for each single asset i. 43 Assuming no shortsales again and riskless lending and borrowing, the optimization problem for this portfolio looks as follows:44

40 See e.g. Elton et al. (2010), p. 58-61. 41 The results can be found in Fama (1976), p. 253-254. 42 The name „Tangency Portfolio“ stems from the fact that graphically this portfolio plots the tangency between the riskless rate and the efficient frontier in return standard deviation space. 43 See Sharpe (1994). 44 This is a quadratic programming problem, which can be solved by standard computer packages, e.g. Microsoft Excel’s Solver tool.

28

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

ƒš

‫ ܧ‬ሺܴ௉ ሻ െ ܴி ߪ௉

s.t. (1) σே ௜ୀଵ ܺ௜ ൌ ͳ (2) ܺ௜ ൒ Ͳ‫݅׊‬

[2]

where ܴி is the return of the risk-free rate.45 If a risk-free rate does not exist, the term simplifies to the so-called risk-adjusted performance. Equation [2] can generally be enhanced by further constraints (e.g. upper limits for the weights of the assets). However, in the present work these alterations are not relevant for the future analysis and will hence not be discussed any further. In order to obtain the optimal portfolios in the mean-variance framework, there have to be reliable estimates for all the inputs. The most common starting point is to use historical data of return, risk and correlations as an estimate for future ones.46 However, in the case of correlations, there have to be a lot of estimates if the number of considerable assets is relatively large. For instance, if there are 100 assets to be considered in a portfolio, there are also 100 estimates for the return and variance of these assets. For the correlations between these assets, however, there have to be N*(N-1)/2 = (100*99)/2 = 4,950 estimates, which can be a challenging exercise for financial analysts.47

3.2 Estimating correlation structures Since the main inputs for portfolio analysis, i.e. covariances, are generally hard to estimate, there have been a number of models established in the literature that try to help estimating correlation structures. The most widely used model is the so-called single-index or market model by Sharpe (1967).48 This model assumes that the co-movement of stocks is due to a single common influence, namely the movement of the market. The return of a stock i, the dependent variable, can thus be written as: ܴ௜ ൌ ߙ௜ ൅ ߚ௜ ܴ௠ ൅ ߳௜ In the equation:

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ƒ

ߙ௜ describes stock i's return component in percentage terms that is independent of the market performance – the expected value of a random variable ܽ௜ ൌ ߙ௜ ൅ ߳௜ with ‫ ܧ‬ሺ߳௜ ሻ ൌ Ͳ and ‫ݎܽݒ‬ሺ߳௜ ሻ ൌ ߪఢ௜ଶ

45 The idea of introducing a risk-free rate to the mean-variance framework stems from Tobin (1958). 46 See Elton et al. (2010), p. 88. 47 See Elton et al. (2010), p. 132. 48 According to Elton et al. (2010), p.132.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

ƒ

ܴ௠ is the rate of return of the market, also in percent – a random variable with ଶ ‫ݎܽݒ‬ሺܴ௠ ሻ ൌ ߪ௠

ƒ

ߚ௜ is a constant that measures the expected change in ܴ௜ given ܴ௠ , or to put it in other words, it measures the sensitivity of a stock to market movements.

The equation is expected to hold each moment in time, in particular ߙ௜ , ߚ௜ and ߪఢ௜ଶ have to be constant over time. In this model, the only reason why security returns are correlated is because of a common movement with the market, or ‫ܧ‬൫߳௜ ߳௝ ൯ ൌ Ͳ. All other movements are completely random. In addition, it is common to assume that ‫ ܧ‬ሺ߳௜ ܴ௠ ሻ ൌ Ͳ.49 If the single-index model holds, it can easily be shown that the expected return of a portfolio of stocks with weights ܺ௜ is given by: ே

ே

ܴത௉ ൌ ෍ ܺ௜ ߙ௜ ൅ ෍ ܺ௜ ߚ௜ ܴത௠ ௜ୀଵ

௜ୀଵ

where ܴത௠ is the expected return of the market. ே Defining ߙ௉ ൌ σே ௜ୀଵ ܺ௜ ߙ௜ and ߚ௉ ൌ σ௜ୀଵ ܺ௜ ߚ௜ , this simplifies to

ܴത௉ ൌ ߙ௉ ൅ ߚ௉ ܴത௠ The risk of a portfolio, if measured by the standard deviation of returns, is defined as: ே

ே

ே

ଶ ൅ ෍ ܺଶߪଶ ߪ௉ ൌ ඩ෍  ෍ ܺ௜ ܺ௝ ߚ௜ ߚ௝ ߪ௠ ௜ ఌ௜ ௜ୀଵ ௝ୀଵ

௜ୀଵ

Following the same simplification, this can also be written as: ே

ߪ௉ ൌ

ଶ ඩߚ௉ଶ ߪ௠

൅ ෍ ܺ௜ଶ ߪఌ௜ଶ

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௜ୀଵ

Again, by assuming equal weights, it can be seen that the importance of the residual risk ߪఌ௜ଶ diminishes as N becomes large.50 This term is therefore generally referred to as the diversifiaଶ ble risk.51 Since ߪ௠ on the other hand is constant and hence cannot be diversified away, one can use ߚ௜ as measure for security i's risk. The term ߚ௉ ߪ௠ , which is a linear combination of the single securities’ betas ߚ௜ , is then labeled as the non-diversifiable risk. By adding several stocks into a portfolio with a low beta, an averaging down effect and a reduction of risk can

49 See Elton et al. (2010), p. 133. 50 See Elton et al. (2010), p. 137-139. 51 See e.g. Elton et al. (2010), p.139.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

be expected. In case beta was negative, the respective stock would serve as a hedge against the market. The beauty of the single-index model lies in the use of beta as a risk measure. The number of estimates required to forecasting the expected return and standard deviation of the portfolio reduces substantially. By a simple time series regression one can obtain estimates for ߙ௜ , ߚ௜ and ߪఢ௜ଶ for each stock.52 Further, one needs an estimate for the expected return ܴ௠ and the ଶ of the market. In total, these are 3N+2, or in the 100 stocks case 302 estimates. variance ߪ௠ Compared to the 4,950 estimates for the correlation structure from before, this can simplify the portfolio selection problem tremendously. Another nice feature of the single-index model is that it corresponds to the most prominent equilibrium model of capital markets, namely the Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964). The CAPM states that the expected return on a single asset i denoted by ‫ܧ‬ሺܴ௜ ሻ, only depends on three factors: the risk-free rate ܴி , the expected return on the market portfolio ‫ ܧ‬ሺܴெ ሻ and the sensitivity towards the market ߚ௜ . Mathematically, the linear relationship can be expressed with the following equation: 53 ‫ ܧ‬ሺܴ௜ ሻ ൌ ܴி ൅ ߚ௜ ሾ‫ܧ‬ሺܴெ ሻ െ ܴி ሿ with ߚ௜ ൌ

ఙ೔೘ మ ఙ೘

[3]

The idea behind this equation is that an investor is only willing to invest in an asset if he is compensated for both the time value of money (represented by the risk-free rate) and the additional risk he is taking (sensitivity towards the market). The term ‫ ܧ‬ሺܴெ ሻ െ ܴி is generally referred to as the risk premium of the market.54 A straightforward extension of the single-index model, which can also be used for estimating correlation structures, is the so-called multi-index model. This model states that stocks might move together not only because of the movement with the market but also because of other influences such as economic factors or industry indices. These additional sources of covariance are captured by simply adding the relevant influences to the return equation. In a typical multi-index model, the return of a stock i can be explained by the following equation ௃

ܴ௜ ൌ ߙ௜ ൅ ෍ ߚ௜௝ ܴ௝ ൅ ߳௜ Copyright © 2013. Diplomica Verlag. All rights reserved.

௝ୀଵ

where ߚ௜௝ is the sensitivity of security i to index j, and ܴ௝ is the respective index return.

52 See Elton et al. (2010), p. 139. 53 This equation only holds under relatively strict assumptions (see Elton et al. (2010), p. 281). These are: no transaction costs, infinite divisibility of assets, absence of personal income tax, individual trades have no effect on prices, investors only care about mean and variances, unlimited short sales, unlimited riskless lending and borrowing, homogeneous expectations and all assets are marketable. 54 See e.g. Copeland et al. (2005), p. 171.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

The theoretical background to multi-index models stems from the Arbitrage Pricing Theory (APT) formulated by Ross (1976). The APT is a straightforward extension of the CAPM and has the advantage that it holds under more general assumptions.55 In a nutshell, it states that the return of an asset is linearly related not only to one but to many factors (e.g. inflation, interest rates or GDP).56 Using approximate arbitrage arguments (basically the law of one price), the model comes to the conclusion that, in equilibrium, each factor has a certain risk premium. The asset returns are then determined by the sensitivities towards these factors. The parameters for a multi-index model, again, can be estimated by simple regression analyses. Multivariate regressions have the nice feature that they result in uncorrelated indices and uncorrelated residuals to the indices, which is needed for multi-index models. However, the more indices are incorporated into the analysis, the more estimates are required. This results in a trade-off between number of estimates and accuracy of the model. Fortunately, several empirical studies have found that correlation structures can already be accurately predicted by using only three to four indices.57 For stocks, the most prominent version of the multi-index model stems from Fama and French (1993). This model pre-specifies the indices returns ܴ௝ by replacing them with certain firm characteristics. In addition to the sensitivity towards the market, stock returns as of the FamaFrench model can solely be explained by the respective company size (small or large market capitalization) and its book to market value ratio.

3.3 Optimal portfolios with investor liabilities An important extension of the mean-variance framework discussed so far is the inclusion of liabilities into the asset allocation decision. This is due to the fact that almost all investors have to meet some future obligations.58 Typically, long-term investors such as insurance companies, pension funds or endowments will face a certain set of liabilities in the future. An insurance company, for instance, should build its portfolio of assets recognizing that future claims have to be met.

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In the academic literature, liabilities have been extensively treated in the immunization literature.59 Immunization proposes that the set of liabilities should be matched by holding a set of assets with the same duration (usually bonds). This idea basically assumes that the investor is interested in a minimum variance solution.

55 The assumptions of the APT are comparable to the ones of the CAPM (i.e. perfectly competitive and frictionless markets and homogeneous beliefs). However, for the APT there are no assumptions needed on investors’ preferences and no identification of a market portfolio. (see Copeland et al. (2005), p.177.) 56 It is beyond the scope of this book to explain the APT in more detail. For an overview, please refer to Elton et al. (2010), p. 355 or Copeland et al. (2005), p. 176. 57 The most prominent ones are Roll and Ross (1980) and Fama and French (1993). For an overview, see Elton et al. (2010), p. 163-173. 58 According to Elton et al. (2010), p. 262. 59 For an overview, see Elton and Gruber (1997), p. 1751.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Another part of the literature initiated by the work of Sharpe and Tint (1990), as well as Elton and Gruber (1992), treats liabilities as assets with negative cash flows. This simplification enables an investor to include a potentially complex set of liabilities into the two-dimensional framework of portfolio optimization. The riskless asset then corresponds to a portfolio of bonds with cash flows matching the future stream of liabilities. Once these liabilities have been “defeased”, the investor can optimize over the remaining assets. The idea of net worth optimization can be expressed mathematically by the following. The return on net worth (or surplus) S is defined as assets A minus (the market value of) liabilities L at each point in time, or: ܴௌ ൌ

ܵ௧ାଵ െ ܵ௧ ሺ‫ܣ‬௧ାଵ െ ‫ܮ‬௧ାଵ ሻ െ ሺ‫ܣ‬௧ െ ‫ܮ‬௧ ሻ ൌ ሺ‫ܣ‬௧ െ ‫ܮ‬௧ ሻ ܵ௧

This can be simplified to: ሺͳ ൅ ܴௌ ሻ ൌ

‫ܣ‬௧ାଵ ‫ܮ‬௧ାଵ െ ܵ௧ ܵ௧

Rearranging terms, by multiplying the first term on the right hand side by ௅

஺೟ ஺೟

and the second

one by ೟, this results in: ௅೟

ሺͳ ൅ ܴௌ ሻ ൌ ሺͳ ൅ ܴ஺ ሻ

‫ܣ‬௧ ‫ܮ‬௧ െ ሺͳ ൅ ܴ௅ ሻ ܵ௧ ܵ௧

By using the fact that ܵ௧ ൌ ‫ܣ‬௧ െ ‫ܮ‬௧ again, this in turn simplifies to ܴௌ ൌ ܴ஺

‫ܣ‬௧ ‫ܮ‬௧ െ ܴ௅ ܵ௧ ܵ௧

The mean and variance of net worth can then be expressed as ஺ ௅ ܴതௌ ൌ ܴത஺ ೟ െ ܴത௅ ೟ and ௌ೟

஺

ଶ

ௌ೟

௅

ଶ

஺

௅

ௌ೟

ௌ೟

ߪௌଶ ൌ ߪ஺ଶ ቀ ೟ቁ ൅ ߪ௅ଶ ቀ ೟ቁ െ ʹ ቀ ೟ቁ ቀ ೟ቁ ߪ஺௅

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ௌ೟

ௌ೟

It follows from the latter equation that, in addition to the asset allocation decision, an investor also has to consider the correlation between assets and liabilities. Those assets which serve as ఙ a hedge, in this case a high correlation coefficient ߩ஺௅ ൌ ಲಽ , are desirable for a portfolio. ఙಲ ఙಽ

Sharpe and Tint (1990) refer to this as the liability hedging credit of an asset. Note that the term hedging might be confusing since returns are required to move in the same direction. This appears to stand against the asset-only framework, where negative correlations were preferred. However, keeping in mind that liabilities are negative while assets are positive per se, a favored common development of the two indeed seems to be plausible.

33

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

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Comparable to the mean-variance framework, a portfolio manager can either choose to maximize over return of the assets ܴത஺ , minimize their risk ߪ஺ଶ or maximize the correlation between assets and liabilities ߩ஺௅ . The other factors, namely ܴത௅ and ߪ௅ଶ , cannot be influenced by the investment manager and hence have to be taken as given.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

4

Application to Renewable Energy investments

4.1 Return distributions After having reviewed the main concepts of Modern Portfolio Theory, the next step in the analysis is to apply them to the new asset class of Renewables. In their pioneering article on wind farm financing, Raftery et al. (1999) found that annual mean wind speeds over the longterm follow a normal distribution with a standard deviation of 6%.60 According to Böttcher (2009), the same is generally true for solar irradiation. Depending on geographical factors, irradiation is normally distributed with standard deviations between 4-5%. Since the underlying assumptions of Markowitz (1952) therefore seem to be fulfilled, bundling several parks into a portfolio should substantially reduce risk, if represented by the standard deviation. However, it remains to be assessed whether also the returns of wind and solar parks follow a normal distribution. The energy production of a wind park, for instance, is not necessarily normally distributed, because the turbines have to be switched off at high wind speeds.61 In addition, it could be that variable electricity prices in a country with a quota-based system will introduce additional distortions to the return distribution. The empirical analysis in this study will try to shed some light on these objections. The first input factor that has to be determined when applying MPT to Renewable Energy investments is a measure for the expected return ‫ ܧ‬ሺܴ௜ ሻ. Wind and solar parks are usually evaluated via DCF models. Hence the right measure for the expected return should be the project IRR.62 The IRR measure appears to be appropriate since these projects have little to no residual value and e.g. a 9.5% dividend yield can result in only a 7% IRR. The shortcoming of using a DCF model, however, relates to the fact that there have to be a number of assumptions (e.g. appropriate discount rate). Actual performance data cannot easily be included, unless there is available data for the whole lifetime of the project. This is why a proxy has to be found, which approximates the expected return of wind and solar parks with only few observations. The proxy thereby has to come sufficiently close to a DCF valuation and should capture the effect that the park has no residual value in the end.

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A common method that works for many asset classes is to use the historical holding period return over T periods as a proxy for the expected return. The holding period return is defined as:63 ‫ ݊ݎݑݐܴ݁݀݋݅ݎ݈݁ܲ݃݊݅݀݋ܪ‬ൌ 

σ்௧ୀ଴ ΨǦ݄ܿܽ݊݃݁݅݊݉ܽ‫ ݁ܿ݅ݎ݌ݐ݁݇ݎ‬൅ ݅݊ܿ‫݁݉݋‬ ܽ‫݁ܿ݅ݎ݌ݐ݁ݏݏ‬௧ୀ଴

60 Actually, wind speeds do not really follow a normal distribution because they are naturally capped at 0 m/s. Therefore, a Weibull distribution is commonly used in practice (see EWEA (2009), p.42). However, the shape around the mean is comparable to a normal distribution. 61 According to Pforte et al. (2008), p. 68. 62 According to Dunlop (2006), p. 82. 63 According to Elton et al. (2010), p. 36.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Most empirical studies approximate this figure by using a Total Return (TR) index for the respective asset class for a certain period and interval.64 The resulting average return is then annualized accordingly, e.g. by multiplying the average monthly returns by 12. Appendix B provides a thorough explanation of the use of the holding period return measure and compares it between the asset classes stocks, bonds and Renewables. Since there are no observable market prices for Renewables, the use of the holding period is not straightforward.65 The approach in this book is to approximate returns with a common performance measurement figure, the Return on Investment (ROI) in percentage, which is defined as:66 ܴܱ‫ ܫ‬ൌ

‫ܶܫܤܧ‬ ‫݈ܽݐ݅݌ܽܥ݀݁ݐݏ݁ݒ݊ܫ‬

The ROI appeared to be the most reasonable estimator for the holding period return of the wind and solar parks since it can incorporate actual performance data. Furthermore, the numerator (EBIT) includes both depreciation, which approximates the loss in value of the investment, and the income generated by the park during the respective period.

Copyright © 2013. Diplomica Verlag. All rights reserved.

An additional benefit of the ROI measure is that it implicitly scales wind and solar parks of different sizes to a comparable measure. Other empirical studies scaled their parks by capacity (MW) in order to compare the respective performances.67 While this technique does allow for a comparison of production levels across countries, it might be inappropriate for returns. First, it could well be that an investor is willing to pay more for a wind or solar park in a country with a fixed feed-in tariff since the risk is expected to be lower. Second and foremost, an EBIT per MW measure cannot incorporate the fact that production in different countries is remunerated at different tariffs. The respective tariff, however, will influence the initial value of a park and hence the price that an investor has to pay. Using a MW-scaling would in both cases overstate the performance of projects in countries with high tariffs, since it would neglect higher initial investments that were required. The second input factor that has to be determined for the mean-variance framework is an appropriate estimator for risk ߪ௜ଶ . Again, when estimating risk for stocks, a common method is to use historical returns from a Total Return index and then calculate the annual risk by multiplying e.g. the monthly standard deviation by ξͳʹ. This method however assumes that returns are independently identically distributed which might be appropriate for some asset classes, but certainly not for Renewable Energy investments. Both wind and irradiation are highly seasonal inputs. Hence, annualizing monthly data using this assumption would neglect potential autocorrelations arising from the inter-annual variability. In Northern and Middle

64 See e.g. Schweizer (2008) or Fischer and Lind-Braucher (2010). 65 It is highly recommended that the reader refers to Appendix B in order to gain more information about the use of the holding period return for a wind or solar park. 66 See e.g. Copeland et al. (2005), p. 473. 67 See e.g. Dunlop (2004a) or Deloitte (2011).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Euroope, for instance, windd speeds arre usually hhigh duringg the winteer and low during thee summ mer monthss. The exactt opposite iss true for soolar, where iirradiation iis relativelyy high in thee summ mer. In ord der to exem mplify seasonnality of thhe input ressources, Figgure 6 and 7 show thee expeected inter-aannual produuction distriibution for a representaative wind and a solar paark. Figgure 6: Season nality of a rep presentative wind farm

Wind d park GER 1 fro om the empiricaal analysis in thiss book

Sourcce: compiled bby the author.

Copyright © 2013. Diplomica Verlag. All rights reserved.

Figgure 7: Seasonality of a representative solar park

Solarr park SOL 1 from the empirical analysis in thiss book

Sourcce: compiled bby the author.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Since the inherent seasonality is known in advance, it cannot be regarded as a real “risk”. An investor should therefore restrict his attention to that part of volatility of the returns that does not account for seasonality. This can be achieved by eliminating the seasonality of wind or solar park returns by using appropriate adjustment techniques, as it will be shown in the empirical analysis of this book.

4.2 Diversification possibilities When applying the concepts of Modern Portfolio Theory to Renewable Energy investments, there are at least three possible areas of diversification that an investor might benefit from: 1. Diversification potential of Renewable Energies in a multi-asset portfolio 2. Diversification possibilities within either a wind or solar portfolio 3. Hedging benefits when combining wind and solar parks in a portfolio

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The first area addresses the question of what happens when either wind or solar parks (or both) are added to a portfolio already consisting of stocks, bonds and Alternative Assets. Mader et al. (2010) were the first to apply this idea to solar investments. A critical assumption in their study is the comparison of returns of the different assets. Long-term illiquid Renewables projects have to be compared to listed assets that can be traded at each point in time. In addition, transaction costs and the fact that solar projects are a run-off business have to be considered in the return calculations. Since a mark-to-market modeling would require strong and consistent assumptions (e.g. the appropriate level of the discount factor), the authors choose to follow a slightly different approach. They start off with a predefined initial portfolio of stocks, bonds and the solar park. In the following, any incoming cash flows from the photovoltaic project are reinvested into the Traditional Assets. This technique results in a decrease of the absolute allocation of the solar project over time and hence appropriately models the run-off character. The results show that if photovoltaic investments are added to a portfolio of stocks and bonds, the expected return can be enhanced by 70bp or portfolio risk can be reduced by 31%. It should be emphasized again that these results stem from initially fixed proportions in the three asset classes. The respective Minimum Variance or Tangency Portfolio of the asset classes has not been assessed in this study. The second area of diversification, the one within a Renewable Energies portfolio, has already been assessed in many empirical studies.68 While these studies restrict the attention to wind investments, the general idea also applies to the solar part of the asset class. Hulsch and Strack (2006), for instance, define three main areas of diversification possibilities that might arise when bundling several wind farms into a portfolio: 2.1 Geographical diversification 2.2 Technical diversification 68 See Dunlop (2004a), Hulsch and Strack (2006), Marco et al. (2009) or Chaves-Schwinteck (2011).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

2.3 Energy yield calculation diversification Geographical diversification relates to both the input resource (wind and solar irradiation) and different regulatory regimes in different countries. The former idea recognizes the fact that e.g. the strong wind available at a certain site might complement poor wind speeds at another, so that the overall production for the portfolio is smoothened.69 The latter argues that the risk of regulatory changes (e.g. a retrospective change to the tariff system) can be mitigated when placing the wind or solar parks in several countries, instead of focusing on one specific regulatory regime.70 The second area of diversification within wind or solar considers the technical equipment. Most wind turbine manufacturers guarantee high availability ratios of 95%-98% (meaning that the turbine does not work only 7-18 days in a year). However, there remains some diversification potential when investing into different turbine types.71 This is mainly to reduce the risk of simultaneous design faults.72 For solar, the benefits from technical diversification might be even greater. This is due to the fact that solar panels are prone to so-called degradation, the characteristic that the performance of the panels decreases over their lifetime. Since the amount of degradation can vary significantly amongst producers, investing into different panels should reduce the risk from technical flaws. Awerbuch (2000) even claims that technology risk for photovoltaics should be fully diversifiable. The third area of diversification concerns the energy yield calculations. As indicated earlier, the annual energy yields of both wind and solar parks are usually estimated by consultants. Since they all have different estimation techniques, the final outcome of the predicted energy yield can differ quite substantially.73 Hence it could be a wise idea to diversify amongst consultants when investing into several wind or solar parks. Alternatively, one could also use several consultants for a single project and e.g. take the average of their results.

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Coming back to an overall Renewable Energies portfolio, the last area of diversification considers the hedging benefits of wind and solar.74 When investing into comparable solar and wind parks at once the resulting portfolio should be naturally hedged.75 A perfect hedge corresponds to a negative correlation of exactly -1, i.e. the returns of these two investments should at any point in time move in opposite directions, or “counter-seasonal”.76 In this case, including both solar and wind parks in a portfolio should enable an investor to almost completely diversify away any seasonal fluctuations within the year. Although a perfect hedge is

69 See Dunlop (2004a), p. 84. 70 According to EWEA (2009), p. 224. 71 According to Chaves-Schwinteck (2011), p. 6. 72 See EWEA (2009), p. 224. 73 According to Hulsch and Strack (2006). 74 According to the author’s knowledge and research, this idea has not been assessed in any study yet. 75 This should not be mixed up with a financial hedge, which would refer to a position in a derivative contract (for Renewables in a weather derivative). 76 One could also reason that counter-seasonality might be achieved when investing e.g. in wind in both the Northern and Southern hemisphere. Since this analysis however restricts the attention to investments in Europe, it will not be assessed further on.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

probably quite difficult to attain in practice, the inherent seasonality pattern of wind and solar investments should nevertheless lead to substantially more stable portfolio returns.

4.3 Discussion of the asset-only perspective The pioneering work by Dunlop (2004a) revealed that when holding a portfolio of wind parks, they more and more resemble bond rather than equity investments. This is mainly due to smoother returns that can be expected. Therefore, a straightforward approach would be to find the optimal weights according to the MVP and TP by solving the optimization problem in equation [1] and [2]. Unfortunately, there are some areas of conflict that have to be considered when applying the mean-variance framework to Renewables. While the following part of the present work will focus the attention on wind investments, the ideas can be applied to solar parks accordingly.77 The first area of conflict relates to the fact that within stocks, one can see the entire investment universe at once whereas with wind parks one cannot.78 This means that one can e.g. use all stocks from an index and find the respective weights for the optimal portfolios. Similarly, one could choose a representative index for several asset classes (e.g. bonds, stocks and Alternatives) and optimize accordingly.79 For wind farms, however, this approach might not be appropriate since each wind farm is unique in the sense that it can be put into the portfolio only once. Let alone short-selling is not possible with a wind farm. Therefore, finding the optimal weight for a respective wind farm does certainly not guarantee that the investor can also implement this recommendation, as he might not be able to perfectly replicate the farm.

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A second shortcoming concerns the illiquidity of the asset class. According to Pforte et al. (2008), the wind farm market is a private market without a public trading place and in general low transparency. Wind farms come to the market once and are usually not traded within their operational lifetime. When the farms are traded, transaction costs are usually a lot higher than for stocks and bonds, since during the acquisition phase intensive technical and legal due diligence have to be undertaken. Due to these circumstances, there might be an additional risk for this asset class, which cannot easily be incorporated into the mean-variance framework. Since the investor is committed to a long-term asset, which he cannot easily sell off, the resulting weights in the optimal portfolio for these investments might be overstated. A final shortcoming relates to the usual trade-off between risk and return. If investors are riskaverse, then they are generally willing to invest in a riskier asset only when it also delivers a higher expected return.80 In a capital market equilibrium model such as the CAPM, this positive linear relationship is reflected in the Security Market Line (SML). The SML is simply

77 The choice of wind farms simply stems from the available literature. 78 According to Dunlop (2004a), p. 87. 79 This approach can be found in many empirical studies on optimal asset allocation (See Schweizer (2008), Schneeweis et al. (2002) and Fischer and Lind-Braucher (2010)). 80 This argument can be found in any standard text book on financial theory, e.g. Copeland et al. (2005).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

the graphical representation of equation [3] in the beta-return space.81 In equilibrium, each asset must be priced so that it exactly falls on the SML. In his work on wind farms, Dunlop (2004a) states that the trade-off between risk and return might not exist for this asset class. This is due to natural competitive advantages of certain countries with strong and steady wind resources vis-à-vis others. Dunlop therefore suspects that wind parks would not neatly line up on a SML. This, however, is only approximately shown in his study, with capacity utilization as a proxy for returns and production volatility as the measure for risk. While the argument by Dunlop that wind farms would not line up on the SML appears intuitive, it totally abstracts from the underlying regulatory structures. It could be that the market indeed “prices” the additional benefit from having e.g. a stable fixed feed-in tariff. Subsequently, the required returns for a variable price regime would have to be higher due to higher risk. However, in this case Dunlop expects the private equity market for wind to be highly inefficient across borders. Although several shortcomings have already been discussed, there is particularly one area where MPT might be even more appropriate compared to other asset classes: the single-index model. In his seminal article, Dunlop (2004a) uses a CAPM-style single-index model in order to assess diversification benefits within a portfolio of wind investments.82 A critical variable thereby is the right choice of the market portfolio. Since there currently does not exist a public benchmark index for wind investments, Dunlop simply creates one from all the wind parks in his data set.83 Subsequently, he regresses each single wind farm against the index in order to receive the respective betas for the individual wind parks. The empirical findings of Dunlop suggest that a CAPM-style single-index model has several advantages over the mean-variance framework. First, the betas from the single-index model can give a rough guide to what wind regions might be profitable instead of focusing on one specific wind farm that had to be replicated for the optimal portfolios.

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Second and foremost, unlike stocks, betas for wind and solar parks should be stable over time. This stems from the fact that both wind and irradiation vary around a certain long-term mean as previously shown in Figures 4 and 5. Both the variation and the mean, however, are known in advance, which implies that past betas can accurately predict future ones. For stocks, on the contrary, high betas in the past do not necessarily turn into high betas in the future.84 Third and last, the advantage of predictability should also apply to the correlation structures of wind and solar investments. There is no logical reason why the correlation matrix should 81 Note that beta is being used as the appropriate measure of risk since the rest of an asset’s risk can be diversified away in a large portfolio. 82 Dunlop (2004a) uses the name CAPM model although he basically creates a market model à la Sharpe (1967). 83 There actually do exist several indices that measure wind or production in respective regions compared to their long-term average (e.g. Anemos, BDB Keiler-Häuser, IWET for Germany). However, there is no such index yet that allows a comparison between several regions in Europe, let alone including return data. 84 For an empirical investigation, see e.g. Sharpe and Cooper (1972).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

substantially change over time. For most other asset classes, however, correlations do vary significantly in the course of time. For instance, correlations between stocks are substantially higher during bear markets.85 Since the notion of a global crisis does not apply to Renewables (at least regarding the main input resource), a CAPM-style model might lead to an accurate estimate of the “unchanging” correlation structure.

4.4 Liability hedging credit The reader might have noticed that the previous investigations of applying MPT to Renewable Energy investments have been undertaken from an asset-only perspective. This was simply due to the available literature which has, so far, abstracted from liabilities.86 Section 3.3 of this book however already indicated that many long-term investors, such as insurance companies or pension funds, should incorporate their liability structure when deciding on the optimal asset allocation. Therefore, the next step when applying MPT to Renewable Energy investments is to assess the liability hedging credit of this asset class.87 In other words, it has to be analyzed whether the (negative) returns of the liabilities of e.g. pension funds or insurance companies generally show a high correlation with the returns from wind and solar parks.88

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The liability structure of both pension funds and life insurance companies heavily depend on the “products” they offer. Therefore, an obvious starting point when assessing the liability hedging credit is to have a closer look at the cash profile of specific products. The main product that might come to one’s mind when thinking about life insurance is endowment assurance.89 This insurance product provides the policyholder with a fixed cash payout if death occurs in a predefined period, in exchange for his regular premium payments.90 If he survives the period, he receives a cash payout that is either fixed (non-profit) or dependent on the performance of the assets that were purchased with the premiums (unit-linked). In case of premature termination of the policy, the insurant receives a surrender value. All of these payouts assume that the insurance company has sufficient funds at any point in time (no default). Figure 8 shows an example of a simplified cash flow profile of an endowment assurance from the perspective of the insurance provider.

85 See e.g. Campbell et al. (2002). 86 According to the author’s knowledge and research. 87 Further benefits according to tax, accounting or the regulatory framework (e.g. Solvency II treatment for insurance companies) go beyond the scope of this book. 88 A liability in this sense is a cash outlay at a specific date in order to meet a contractual obligation (as defined in Davis (2000), p. 5.). 89 For an overview on insurance products from an academic perspective see Blake (1999). 90 See Blake (1999), p. 329.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 8: Exxample for a cash flow proofile of an end dowment asssurance

Sourcce: compiled bby the author.

Copyright © 2013. Diplomica Verlag. All rights reserved.

A common prod duct that botth life insurrance companies and pension fundds offer is ann annuity.911 A liffe annuity, for instancce, makes a series off payments until deathh of the annnuitant, inn 9 Pension annuities ha exchhange for an n immediatee lump-sum m payment.92 ave a simillar paymentt struccture during g the retirem ment of thee annuitant. However,, payments are commoonly drawnn from m a pension fund that thhe scheme m member conntributed to during his work life. T The amountt of the regular peension paym ments eitherr solely depends on thee performannce of the fuund (definedd contrribution), orr is also linkked to certaain characteeristics of thhe beneficiaary such as ffinal salary,, age or o length of o service (defined bennefit). Furthhermore, deefined beneefit pensionns are oftenn linkeed to inflation, a featurre that also exists in m many life annnuity produucts. This iis why bothh pension funds and a life insuurance com mpanies are generally iinterested inn assets thaat comprisee 93 F certaain inflation n hedging benefits. b Figure 9 shhows a sim mplified cassh flow proofile for ann annuuity providerr in a graphhical represeentation.

91 Diffferences in the payoff structurre of these two providers are analyzed a in Broeeders et al. (20111) and go beyoond the scope of this t book. 92 Seee Broeders et all. (2011), p. 3. 93 Acccording to Davis (2000), p. 8.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 9: Example for a cash flow prrofile of an an nnuity

Source: com mpiled by the aauthor.

Copyright © 2013. Diplomica Verlag. All rights reserved.

The questiion that folllows is how w the resultiing liabilityy structure ffrom the deescribed prooducts can be maatched with h assets. Sinnce the foccus of this study is onn Renewables, it has to be assessed inn particular, which prodducts are a ggood matchh for this assset class. Figure 10 proovides an example for a simp plified cashh flow struccture of threee different asset classees: stocks, bbonds and Renew wables. All figures werre calibrateed accordingg to the asssumptions from f the hoolding period retuurn investigations in Apppendix B. Comparingg Figure 10 to the previious two figgures, it can be seen s that en ndowment assurance a seems to bee a good maatch to bonnds (althouggh the initial inveestment slightly distorts the picture). The early surreender part of this prooduct, however, has h to be matched m withh short-term m liquid asssets.94 Stockks are generrally suitable for unit-linkedd policies and a productts of pensioon funds, w where the cash payoutt depends oon the performancce of the in nvestments. Finally, a w wind or solaar park withh an upfronnt investmennt and predictablee and relativ vely stable cash c flows tthereafter apppears to prrovide a good hedge aggainst annuities. In I addition,, this asset class c shouldd also offer certain inflation hedging benefits. This is due to thhe fact that electricity e p prices can be expected to rise withh inflation.955

94 According to Blake (19999), p. 330. 95 It has been argued before that in many coountries such ass Germany, Rennewables are remunerated at a fixed feed-in taariff. However, once o this tariff falls f below the electricity pricee in the market,, an owner wouuld certainly sw witch to sell the electricity at a the open marrket and hence benefit b from thee rise in inflatioon.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Fig gure 10: Example for a caash flow profiile of stocks, b bonds and Renewables

Sourcce: compiled by b the author

Copyright © 2013. Diplomica Verlag. All rights reserved.

Afterr having an nalyzed the cash flows matching ppossibilitiess of Renew wables, the nnext step inn Asset Liability Managemen M nt (ALM) iss to minimizze the risk thhat contracttual obligattions cannott be met. m This caan be achieeved by alsso matching the matuurity of the assets andd liabilities.. Histoorically, inssurance com mpanies werre more foccused on ann exact matcch and hencce preferredd fixedd-income asssets with reelatively ceertain cash flows f such as bonds.96 Pension fuunds, on thee otherr hand, tend ded to run a larger mism match and invested i moore heavily in equities,, since theirr liabillities are alsso more unccertain. Duraation matchiing for a wind or solarr park mighht not be as straightforw ward as e.g. for bonds.. This is due to th he fact that these t investtments do not really haave a “maturrity” in the sense that a largee inflow off money cann be expectted at the end e of the investment period. Hoowever, thee durattion of stab ble cash floows over 200-25 years might be m matched wiith a slighttly differentt approoach. An ex xample for a rather unnconventionnal maturityy match woould be to uuse the cashh flows from Ren newables to cover adm ministrative expenses e off a life insuurance comppany. It cann be exxpected thaat these exppenses geneerally last for f a compaarable periood, and shoould remainn relatiively stablee once a poliicy has beenn sold.

96 Acccording to Broeeders et al. (20111), p. 4.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Apparently, there are two shortcomings of Renewable Energy investments concerning the liability hedging credit. First, as mentioned before, these investments are less liquid than Traditional Assets which trade on the markets. Therefore, Renewables do not seem to be a good match for products with early surrender guarantees. The second shortcoming refers to the inherent seasonality of wind and solar. There might be a mismatch between steady outflows from the annuity (or administrative expenses) and seasonally variable inflows from the wind or solar park. Furthermore, there is the risk of below-average wind years which might not make up for the payments of the liabilities.

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As indicated earlier, both of these shortcomings might be overcome relatively easily. First, there is substantial potential in offsetting the inherent seasonality by investing into solar and wind at once. Secondly, spreading the projects around several countries in Europe with low correlated wind speeds might mitigate below-average wind years in a specific region. It is now time for an empirical investigation of the proposed mechanisms.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

5

Empirical analysis

5.1 Data The empirical analysis in this section of the book uses exclusive data from one of the largest institutional investors in Renewable Energies in Europe. The full data set initially consisted of monthly production and financial data from August 2006 – October 2011 for 28 operating wind and 3 solar parks. In order to increase the number of observations, the budget values for November and December 2011 were added to the initial data.97 The parks were spread around different areas in Germany, France and Italy. Figure 11 shows the geographical positions of all wind and solar parks that were employed for the empirical analysis. Since the parks started operating at different points in time, the subsequent analyses will consider different time periods and portfolios. The longest period with consistent data and a reasonably sized portfolio was for a 3-year horizon from January 2009 - December 2011. This part of the data set comprised nine German wind farms, one Italian farm and one from France. Unfortunately, the first operating solar park started commissioning not until March 2010 and hence limited the possible analyses for this part of the asset class. Returns were defined according to the performance measure ROI that has already been described in Section 4.1 of the book, as well as in more detail in Appendix B. For each wind farm i, the ROI in each month t was calculated as: ܴܱ‫ܫ‬௜௧ ൌ

‫ܶܫܤܧ‬௜௧ ܱ‫ݐ݂݅݋ݎܲ݃݊݅ݐܽݎ݁݌‬௜௧ െ ‫݊݋݅ݐܽ݅ܿ݁ݎ݌݁ܦ‬௜ ൌ ‫݈ܽݐ݅݌ܽܥ݀݁ݐݏ݁ݒ݊ܫ‬௜଴ ‫݈ܽݐ݅݌ܽܥ݀݁ݐݏ݁ݒ݊ܫ‬௜଴

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Starting with the Invested Capital, this figure included all transaction costs e.g. arising from due diligence. This way, the resulting returns for the wind and solar parks appeared to be in a close comparison to other asset classes. In addition, the previously described potential distortions to the weights for the optimal portfolios, arising from the illiquidity of this asset class, could have been mitigated.

97 This was due to the fact that the actuals were not available for these months before completion of this book.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 11: Geographical dispersion of the wind and solar parks in the empirical analysis

GER 6

GER 1,2,4,8

GER 5 GER 3,9,7 GER 14 FRA

SOL 2

SOL 1

ITA

Source: compiled by the author using Google Maps.

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GER 1 will be used as a representative wind park in the multi-asset framework in section 5.3.1; GER 1-9, FRA and ITA will be part of the statistical analysis in section 5.2 and the CAPM-style model in section 5.3.2; SOL 1 & 2 and GER 3 & 14 will be used for the hedging analysis in section 5.3.3.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

The Operating Profit figures were available from the income statements of the wind farms. As thoroughly explained in Appendix C, the Operating Profit in these statements represented an EBITDA figure.98 In order to receive the EBIT, a lump sum depreciation was deducted from the Operating Profit in each month. The lump sum value was calculated by dividing the respective Invested Capital by 300, which simply scales the 25 years lifetime to a linear monthly depreciation.99 This economic depreciation served as a proxy for the periodic loss in market value over the project life.100 The simplification was chosen to ensure comparability among the projects since the measured depreciation from the income statements varied according to different accounting and tax regimes.101 A more detailed explanation of the used figures from the income statements can be found in Appendix C. The lump sum approach overstates the measured depreciation, since the book values of the assets (turbines, foundations etc.) were below the Invested Capital. In addition, the simplified approach also overstates the economic depreciation of the market value from a DCF valuation in the first years. This is due to the fact that the decay of the market value in a DCF model does not have a linear shape, as it is explained in more detail in Appendix B. In total, the approach in this study might have led to lower returns than the ones that an investor might expect. However, it appeared to be a reasonable simplification when comparing a set of different wind farms.

Copyright © 2013. Diplomica Verlag. All rights reserved.

The calculated ROIs of several wind farms initially showed a 12th-order autocorrelation and were not normally distributed. Figure 12 exemplifies this autocorrelation for a representative wind farm. In order to remove seasonality of the input resource wind, the monthly returns were transformed into so-called Seasonally Adjusted Annual Rates (SAAR). This adjustment technique is frequently used in practice when the contribution of each month to the annual outcome is known in advance.102 For the wind farms in the data set, the seasonality ratios were available since they had been estimated by wind consultants for each park (as explained in section 4.1). Table 1 shows the seasonality ratios for the used wind farms.

98 Usually, the Operating Profit is being used as a synonym for the EBIT (see e.g. Copeland et al. (2005), p. 508). 99 The idea is further explained in Appendix B. 100 In Financial Theory, economic depreciation is generally defined as the rate of change in the market value of the firm (see e.g. Jones (2008), p. 59). Measured depreciation, on the other hand, is the decay of the book value of the assets in the firms over time. The terms appeared to apply to wind and solar projects alike. 101 Some projects were e.g. allowed for an accelerated depreciation in the first years. Hence using the actual depreciation would have led to significantly lower returns in the first periods. Since the data in this study did not comprise the whole lifetime of a project this would have distorted the estimated expected returns substantially. 102 See e.g. Evans (2002), p. 205-208.

49

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figu ure 12: Autoccorrelation off the unadjustted returns (R ROI) for a reepresentative wind farm

Autocorrelatio on Table* N° obss. Standard Error E Lag #1 1 Lag #2 2 Lag #3 3 Lag #4 4 Lag #5 5 Lag #6 6 Lag #7 7 Lag #8 8 Lag #9 9 Lag #10 Lag #11 Lag #12

G 1 GER 65 0.124 0.322 0.339 0.025 -0.077 -0.115 -0.222 -0.166 -0.020 -0.043 0.158 0.219 0.367

* Autocorrela ations larger than two standard errors arre consideredd significant annd shown in bbold.

Table 1: Seasonalitty ratios of th he wind farmss

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Sum

GER 1 11.70% 12.00% 11.10% 7.90% 6.00% 5.90% 5.30% 5.40% 6.50% 9.00% 8.50% 10.60% 100%

GER 2 11.68% 12.01% 11.09% 7.92% 6.01% 5.92% 5.34% 5.42% 6.51% 9.01% 8.51% 10.59% 100%

GER 3 11.68% 12.01% 11.09% 7.92% 6.01% 5.92% 5.34% 5.42% 6.51% 9.01% 8.51% 10.59% 100%

ITA 16.00% 13.30% 9.00% 8.20% 6.30% 3.40% 5.60% 6.00% 6.20% 7.20% 8.40% 10.40% 100%

GERR 4 1 11.48% 1 11.37% 1 10.92% 7.78% 6.20% 5.67% 5.69% 5.80% 6.33% 8.97% 8.85% 1 10.93% 100%

GER 5 11.00% % 11.00% % 11.00% % 8.67% % 6.00% % 6.00% % 6.00% % 6.00% % 6.00% % 8.67% % 8.67% % 11.00% % 100% %

GER 6 11.68% 12.01% 11.09% 7.92% 6.01% 5.92% 5.34% 5.42% 6.51% 9.01% 8.51% 10.59% 100%

GEER 7 11.68% 12.01% 11.09% 7.92% 6.01% 5.92% 5.34% 5.42% 6.51% 9.01% 8.51% 10.59% 100%

GER 8 11.68% % 12.01% % 11.09% % 7.92% % 6.01% % 5.92% % 5.34% % 5.42% % 6.51% % 9.01% % 8.51% % 10.59% % 100% %

GER 9 11.68% 12.01% 11.09% 7.92% 6.01% 5.92% 5.34% 5.42% 6.51% 9.01% 8.51% 10.59% 100%

FRA 12.49% 8.99% 8.39% 8.39% 6.89% 5.59% 6.09% 7.29% 6.19% 10.69% 7.89% 11.09% 100%

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The respecctive valuess for the SA AARs for each wind farm fa i in eaach month t were calcuulated according to t the follow wing formuula: ܵ‫ܣ‬ ‫ܴܣܣ‬௜௧ ൌ

ܴܱ‫ܫ‬௜௧௧ ܵ݁݁ܽ‫݋݅ݐܴܽ ݕݐ݈݅ܽ݊݋ݏ‬௜௧

Using this simplificattion, the “truue” volatiliity of the reeturns couldd have beenn estimated. As it becomes evident e from Figure 13, also thhe problem m of autocoorrelation ccould have been removed.

50

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

A diffferent apprroach in ordder to remove seasonallity would hhave been to t use an X12-ARIMA A 103 proceess. This would havve been an ooption if thhe seasonaliity of the reespective paark was nott know wn in advan nce and had to be estim mated. Figure 13: Autocorrela ation of the adjusted returrns (SAAR) ffor a represen ntative wind ffarm

Autoccorrelation Tablee* N° obs. S Standard Error Lag #1 Lag #2 Lag #3 Lag #4 Lag #5 Lag #6 Lag #7 Lag #8 Lag #9 Lag #10 Lag #11 Lag #12

GER 1 5 65 0.124 4 0.112 2 0.270 0 0.085 5 0.018 8 0.080 0 -0.085 5 -0.014 4 0.022 2 -0.030 0 0.076 6 0.175 5 0.162 2

* Auto ocorrelations larger than tw wo standard eerrors are conssidered signifi ficant and show wn in bold.

5.2 Statisticcal analysiis

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The descriptivee statistics for f both thhe unadjusteed monthlyy returns (R ROI) and thhe adjustedd annuualized returrns (SAAR)) of the winnd farms caan be foundd in Table 2 and 3 resppectively. Inn orderr to gain information about the distributioon of the reeturns, the Jarque-Berra test wass perfoormed.104 Th he results frrom the Jarqque-Bera teest for the unnadjusted ddata in Tablee 2 show, ass indiccated beforee, the non-nnormality off returns forr several winnd farms. For F the adjussted returnss in Taable 3 it beccomes eviddent that forr all wind pparks the hyypothesis off a normal distributionn fails to be rejectted at a signnificance levvel of 5%. Therefore, T aassuming a normal n disttribution forr thesee returns ap ppears to bee a relativeely sensiblee assumption. This is even e true ffor the onlyy windd farm with no fixed feeed-in tarifff (ITA), which surprisiingly has thhe highest p-value. Thee empiirical distrib butions (histogram) andd their norm mal density approximattions for thee used windd farm ms are shown n in Appenddix D.

103 Thhe X-12-ARIM MA is a seasonall adjustment proogram developeed by the U.S. C Census Bureau (see w www.census.gov v/srd/www/x12a). 104 Seee Bera and Jarrque (1987). Thhe test can be peerformed by e.gg. using STATA A’s “sktest” com mmand.

511

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Table 2: Descriptive statistics of the unadjusted monthly returns (ROI) of the wind farms

Mean Std. Dev.

GER 1 0.50% 0.50%

GER 2 0.42% 0.37%

GER 3 0.35% 0.29%

ITA 0.56% 0.62%

GER 4 0.45% 0.41%

GER 5 0.32% 0.38%

GER 6 0.41% 0.32%

GER 7 0.28% 0.28%

GER 8 0.39% 0.25%

GER 9 0.31% 0.24%

FRA 0.27% 0.25%

Min Max Skewness Kurtosis Sum

-0.22% 2.56% 1.356 6.234 33%

-0.14% 1.76% 1.168 5.055 25%

-0.17% 1.05% 0.616 2.936 21%

-0.41% 3.38% 1.861 9.400 32%

-0.74% 1.77% 0.539 5.272 24%

-0.28% 1.59% 0.931 4.480 17%

-0.29% 1.06% 0.102 2.895 20%

-0.35% 1.05% 0.498 3.539 14%

-0.19% 1.03% 0.279 3.331 19%

-0.10% 1.05% 0.615 3.452 15%

-0.13% 0.85% 0.635 2.628 10%

65

60

60

57

53

53

49

49

48

47

36

18.64 0.0001 No

13.45 0.0012 No

4.07 0.1304 Yes

26.53 < 0.0001 No

7.53 0.0232 No

9.07 0.0107 No

0.1 0.9509 Yes

3.31 0.1915 Yes

1.25 0.5350 Yes

4.04 0.1327 Yes

3.02 0.2209 Yes

N° obs. Jarque Bera p-value Normally distributed

The descriptive statistics from Table 3 reveal that annual return and risk (measured by the mean and standard deviation of the SAARs) differ significantly amongst projects. The reader should bear in mind that this could stem not only from the operating results of the wind parks, but also from the initial price (Invested Capital) that the investor has paid. As expected, the highest risk (6.06%) lies within the wind farm which is exposed to variable electricity prices (ITA). Table 3: Descriptive statistics of the adjusted annualized returns (SAAR) of the wind farms Avg. wind year return Mean Std. Dev. Min Max Skewness Kurtosis N° obs. Jarque Bera p-value Normally distributed

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Risk-adjusted performance

GER 1 7.57% 5.65% 5.18%

GER 2 6.76% 4.75% 3.66%

GER 3 5.48% 3.91% 2.97%

ITA 9.49% 6.28% 6.06%

GER 4 5.25% 4.24%

GER 5 3.66% 4.30%

GER 6 5.01% 4.18%

GER 7 3.07% 3.17%

GER 8 4.59% 2.76%

GER 9 3.62% 2.77%

FRA 3.18% 3.02%

-4.20% 21.84% 0.641 3.425

-2.26% 15.07% 0.470 3.017

-3.18% 9.81% 0.077 2.446

-6.79% 21.11% 0.166 2.875

-6.77% 15.44% 0.063 3.346

-3.97% 14.44% 0.454 3.111

-4.84% 16.65% 0.516 4.151

-5.36% 11.32% 0.038 3.653

-2.96% 10.35% -0.337 3.415

-1.93% 11.10% 0.565 3.382

-2.25% 10.75% 0.711 3.124

65

60

60

57

53

53

49

49

48

47

36

5.14 0.0766 Yes

2.54 0.2808 Yes

1.16 0.5599 Yes

0.3 0.8610 Yes

0.59 0.7438 Yes

2.26 0.3238 Yes

4.79 0.0912 Yes

1.24 0.5380 Yes

1.76 0.4151 Yes

3.47 0.1760 Yes

3.71 0.1568 Yes

1.09

1.30

1.32

1.04

1.24

0.85

1.20

0.97

1.66

1.31

1.05

For the absolute level of the returns, it deserves mentioning, that the historical estimates of the wind parks are somewhat understating the long-term average returns that an investor can expect for this asset class. First, the small sample overweighs the rather low returns arising from technical difficulties in the early months of a project (the “ramp-up phase”). Over the lifetime, these difficulties should be leveled out by subsequently higher performance, and thus result in higher average returns. Secondly, the sample includes a long range of below average wind years. Referring back to the long-term volatility of wind in Figure 4, wind speeds in

52

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Germany have been below the long-term average for three years in a row (2008-2010). Indeed, 2010 was actually one of the lowest reported wind years in history.105 Returns for an average wind year can be expected to be higher. For instance, the annual return for GER 1 in 2007, which was an average wind year, was 7.57% (see Table 3). Unfortunately, the representative average return was not available for several wind farms in the data set, which were operating only in below average wind years. Therefore, the analysis continues using the historical returns since the date of inception of the respective wind farm as an estimator for the expected return.

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The next step in the statistical analysis was to find out whether the returns of the wind farms in the data set are somehow related. Figure 14 plots the projects in the usual risk-return space. Note that this illustration uses the standard deviation (instead of the beta) as the relevant measure of risk and therefore does not correspond to the SML. It becomes evident that, apart from two outliers, GER 5 & 8, the projects line up quite nicely on what has been labeled by the author as the “Wind Farm Market Line”.106 The line has been found by a simple linear regression, indicating that an increase in 1% in risk would require an increase of 1.133% in return. The intercept has been set to zero since a wind farm with zero risk should also produce no returns, simply because it does not exist. From the first impression of the graph, one might reason that the market indeed seems to price the trade-off between risk and return, contrary to the conjecture by Dunlop (2004a). It could also be that only the investor prices the risk-return trade-off. However, given that the investor has been out in the market acquiring these projects, the concept can be applied to the market accordingly. The exemplified trade-off between risk and return appears to be even valid for the market across borders, since the wind farms stem from three different countries. However, care has to be taken with the interpretation of the Wind Farm Market Line. The standard deviation might not be the right measure for risk as it does not include covariances.

105 See Winkler (2010), p. 4. 106 This term does not refer to the Capital Market Line (CML). The CML describes the linear relationship between risk and return of efficient portfolios when investors have homogeneous beliefs (see e.g. Copeland et al. (2005)).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figurre 14: The “W Wind Farm Market M Line”

The last sttep in the sttatistical annalysis was to find outt how the reeturns of thhe different wind farms in thhe data set move togeether. Tablee 4 thereforre reports thhe correlatiion matrix. As it becomes evident from m the table, correlationss between thhe differentt wind farm ms mainly deepend on their geeographical dispersion.. Not surprisingly, the correlationss between thhe German wind farms are all very hig gh. There iss one excepption, GER R 6, which ssits right att the edge oof the German North N Sea an nd thereforee has slightlly lower corrrelations w with the otheer Germanss. The results for the other tw wo countriees are astonnishing. Bothh the Italiann and the French windd farm have extreemely low (sometimees even neggative) corrrelations w with the Geerman oness and therefore offer o a fairrly high divversificationn potential. Before asssessing the diversificcation potential of o several wind w farms in a portfollio, howeveer, the subseequent anallysis will reestrict the attentioon to a singlle wind farm m, which shhall be incluuded in a muulti-asset poortfolio.

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Table 4: 4 Correlatioon between th he wind farmss

GER 1 GER 2 GER 3 ITA GER 4 GER 5 GER 6 GER 7 GER 8 GER 9 FRA

GERR 1 1.000 0.931 0.855 0.041 0.743 0.694 0.407 0.801 0.781 0.822 0.080

GER 2 0.9311 1.0000 0.8255 -0.0211 0.7500 0.7022 0.4111 0.7588 0.7899 0.8388 -0.0022

GER 3 0.855 0.825 1.000 0.005 0.744 0.652 0.378 0.879 0.757 0.916 0.182

ITA 0.041 -0.021 0.005 1.000 0.018 -0.025 -0.175 0.082 -0.152 0.042 0.110

GER 4 0.743 0.750 0.744 0.018 1.000 0.707 0.526 0.753 0.708 0.811 0.103

GER 5 0.694 0.702 0.652 -0.025 0.707 1.000 0.346 0.619 0.589 0.637 -0.139

GER 6 0.407 0.411 0.378 -0.175 0.526 0.346 1.000 0.447 0.569 0.492 0.123

GER 7 0.801 0.758 0.879 0.082 0.753 0.619 0.447 1.000 0.730 0.861 0.153

GER 8 0.7881 0.7889 0.7557 -0.1552 0.7008 0.5889 0.5669 0.7330 1.0000 0.6992 0.1332

GER 9 0.822 0.838 0.916 0.042 0.811 0.637 0.492 0.861 0.692 1.000 0.152

54

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

FRA 0.080 -0.002 0.182 0.110 0.103 -0.139 0.123 0.153 0.132 0.152 1.000

5.3 Empirical results 5.3.1 Diversification possibilities in a multi-asset portfolio The first part of the empirical analysis tries to evaluate the benefits of Renewable Energy investments in a multi-asset portfolio. A similar analysis has already been undertaken by Mader et al. (2010), who include photovoltaic investments into a portfolio consisting of fixed proportions of stocks and bonds. For wind investments, however, no such study exists in the literature so far.107 Since consistent data for the portfolio of wind investments was only available for a 3 year period, the analysis in this section of the book slightly departs from the previous investigations. For the asset allocation problem, the analysis uses monthly returns in % from August 2006 until August 2011 for one representative wind farm, GER 1, and several other asset classes. The use of only one wind farm is due to the fact that for a five year time frame, only data for GER 1 have been available. A five year horizon seems to be relatively short compared to other studies on asset allocation, which usually use an 8-10 year horizon.108 In addition, the time frame is also heavily distorted by the recent financial crises leading to very low returns for several asset classes. Nevertheless, this might actually be viewed as a strength of this study. Long-term investors invest into Renewable Energies because they seek for investments that are uncorrelated to financial markets. Therefore, it seems plausible to choose a historical period of turbulence if one wanted to exemplify the benefits of this asset class.

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The investment universe considered in this section of the book consists of two Traditional Asset classes (stocks and bonds) as well as six Alternative Assets (hedge funds, commodities, private equity, infrastructure, real estate and wind farms). The underlying risk-free rate has been determined to be 2.34%. This value is equal to the average of the 1-month EURIBOR during the five year horizon. All data (apart from the wind farm) have been taken from the Bloomberg database. Stocks were further divided into European and emerging markets in order to account for international diversification. The former are referred to as "European stocks" in the following. Table 5 summarizes the used asset classes and their respective proxy indices. A detailed description of the indices and a short discussion can be found in Appendix E. The choice of the asset classes and their representative index was based on several empirical studies on asset allocation including Alternatives.109 Other than previous studies, however, this analysis also incorporates the asset class infrastructure. This was mainly because infrastructure investments were proposed to be the closest comparable to Renewable Energy, as already described in section 2.2 of the book.

107 According to the author’s research and knowledge. 108 See e.g. Fischer and Lind-Braucher (2010) or Schweizer (2008). 109 Primarily the studies by Fischer and Lind-Braucher (2010) and Schweizer (2008).

55

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Ta able 5: Investtment universe for the assset allocation problem

Investm ment Universse Traditional Assets Asset class Stocks - European Sto ocks - Emerging Maarkets Bonds

Proxyy index MSCI Europe Total Reeturn (TR) MSCI Emerging Markeets TR Barclaays Capital Euro o Aggregate TR

Altern native Assets Asset class Hedge Funds Commodities Private Equityy Infrastructuree Real Estate Wind farms

Proxy ind dex Dow Jonees Credit Suisse Hedge Fund Ind dex Dow Jonees UBS Commod dity Index TR LPX Europe TR NMX Infrrastructure Euro ope TR FTSE EPR RA / NAREIT Euro ope TR GER 1

The empirrical analyssis is underrtaken from m the view of an investor basedd in a Euroopean country. All indices arre thus denoominated inn EUR. Thee investor iss assumed tto be subjecct to a home biass, which means m that he h prefers to invest iin Europeann countriess.110 In adddition, whenever possible, p hee prefers to have h a relattively low ccurrency expposure in hiis portfolio.111 Figure 15 shows the historical performance p e of all asseet classes fo for the wholle time fram me. It becomes evident that apart from emerging m markets, thee wind farm m has outperrformed all other asset classes in the an nalyzed tim me frame. Thhis is mainlly due to thhe sharp decline of all asset classes exccept for bon nds during thhe Subprim me Crisis starrting in Sepptember 20007.

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Figure 15: Historical peerformance of o the asset classes

110 This idea stems from Freench and Poterbba (1991), who state that both individuals i andd institutions in most countries hold only moddest amounts off foreign equity in their portfoliio. 111 This is whhy the indices for fo stocks, bondds, private equitty, infrastructurre and real estatte are all Europeean indices. Forr commodiities and hedge funds there are no such indicees available. Hence a significannt USD-exposuure exists for theese two indices. The T same appliees to emerging markets m which are also subjectt to currency rissk.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Using this graph as a first impression, the next step is to have a closer look on the return distributions. Table 6 reports the results from the statistical analysis of the asset classes. The outcome is generally in line with what one might have expected. Bonds are at the lower while private equity is at the higher risk end (standard deviation of 3.31% vs. 30.42%). Evidently, bonds also offer fairly high mean returns (4.10%) compared to the other asset classes, which were all hit by the Subprime Crisis. The annualized mean and standard deviation in Table 6 were found by multiplying the monthly values by 12 and ξͳʹ respectively. The Jarque-Bera statistics refer to the monthly distributions of the asset classes. It deserves mentioning that the return and risk of the wind farm (bold figures), however, correspond to the seasonally adjusted values, derived with the techniques from section 5.2. These values differ from Table 3 due to the different time frame that has been analyzed. Since the focus of this study lies on wind farms, no further adjustments to the other asset classes have been made. For all asset classes, the empirical distributions (histogram) and their normal density approximations, as well as the autocorrelation tables, are also shown in Appendix F. In addition to the descriptive statistics and the Jarque-Bera test, three additional concepts have been added to Table 6. The first one, the Sharpe Ratio, has already been explained in section 3.1. This ratio evaluates the risk-return attractiveness of a certain asset class. Evidently, the wind farm offered the best risk-return profile (SR of 0.60) during the crisis period while many other asset classes even had negative Sharpe Ratios. Table 6: Statistical analysis of the asset classes

Mean Std. Dev.

Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind Farm 0.34% 0.33% -0.07% -0.27% 0.02% -0.36% 0.45% 0.96% 2.11% 4.76% 8.78% 4.56% 6.42% 1.49%

Annualized Mean Annualized Std. Dev.

-1.28% 17.79%

8.89% 22.34%

4.10% 3.31%

3.95% 7.31%

-0.90% 16.49%

-3.24% 30.42%

0.23% 15.78%

-4.30% 22.23%

5.44% 5.16%

Min Max Skewness Kurtosis

-12.75% 14.41% -0.304 3.845

-19.53% 16.88% -0.625 4.320

-1.98% 3.08% 0.327 3.388

-6.91% 3.81% -1.396 5.767

-12.81% 9.51% -0.714 3.782

-26.12% 33.11% -0.027 6.646

-11.13% 10.49% -0.172 2.513

-20.39% 20.16% -0.485 5.493

-0.22% 2.56% 1.503 6.977

61

61

61

61

61

61

61

61

61

Jarque Bera p-value Normally distributed

3.04 0.2183 Yes

6.72 0.0347 No

1.95 0.3780 Yes

17.38 0.0002 No

6.32 0.0425 No

8.71 0.0128 No

1.10 0.5771 Yes

8.24 0.0162 No

20.65 < 0.0001 No

Sharpe Ratio Value at Risk * Cond. Value at Risk*

-0.20 -30.55% -35.42%

0.29 -27.85% -54.97%

0.53 -1.34% -10.92%

0.22 -8.08% -19.04%

-0.20 -28.02% -33.12%

-0.18 -53.28% -59.51%

-0.13 -25.73% -32.79%

-0.30 -40.88% -41.56%

0.60 -3.04% -16.09%

Prob. of return  0%

47%

65%

89%

71%

48%

46%

51%

42%

85%

N° obs.

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Eur. Stocks Em. Markets -0.11% 0.74% 5.14% 6.45%

* confidence level of 95%

The other two concepts, Value at Risk (VaR) and Conditional Value at Risk (CVaR), are a measure of the downside potential of a respective asset class. In a nutshell, Value at Risk describes the maximum loss that is not exceeded with a given probability (e.g. 95%) within a

57

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

specified period.112 Conditional Value at Risk then measures the conditional expected return in this case expected loss – given this loss is beyond the VaR level. The concepts are further explained in Appendix G. It becomes evident that the wind farm has the lowest downside risk after bonds according to both the VaR and the CVaR measure. This is not surprising since returns should stem from relatively stable cash flows (or in this analysis Operating Profits). Indeed, if the assumption of normally distributed returns for a wind farm is approximately correct, the probability that returns are non-negative would lie at an astonishing 85%. We have learned from Markowitz (1952) that the risk of a portfolio of assets with normally distributed returns is dominated by the covariance risk, when the number of assets in the portfolio becomes large. Table 7 therefore reports the correlation matrix of the asset classes, which is the basis for the diversification potential. It can be seen that only bonds (and to some degree the wind farm) offer the desired negative correlation with other asset classes. As expected, correlations between the wind farm and the other assets are close to zero. Apart from commodities, all other asset classes have fairly high correlations, which confirm the findings on increased correlations in bear markets in many empirical studies.113 Surprisingly, this is also true for infrastructure investments, which were supposed to be the closest comparable to Renewables. Correlations to the European and emerging stock markets lie at a high 0.847 and 0.651 respectively. This result, however, might have been due to the use of a listed infrastructure index as a proxy for the asset class. Having examined the descriptive statistics and correlations of the return series, the asset classes can now be undertaken a portfolio optimization as described in section 3.1. Estimators for expected return and risk are the historical mean and standard deviation of the asset classes’ proxy. There have been no adjustments to the data, apart from the wind farm, which has been adjusted for its seasonality. The correlation matrix from Table 7 is the basis for the variancecovariance-matrix that is required in order to calculate ߪ௉ଶ . Using all these inputs, equation [1] and [2] were optimized accordingly. In order to keep the analysis general, there have been no additional restrictions introduced (e.g. limit holdings arising from regulatory constraints). Table 8 summarizes the results from the portfolio optimization problem. An explanation of the detailed calculations can be found in Appendix H. Table 7: Correlation matrix of the asset classes

Copyright © 2013. Diplomica Verlag. All rights reserved.

Eur. Stocks

Eur. Stocks Em. Markets 1.000 0.843

Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate -0.126 0.732 0.321 0.903 0.847 0.848

Wind Farm -0.129

Em. Markets

0.843

1.000

-0.138

0.761

0.472

0.776

0.651

0.736

-0.207

Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind Farm

-0.126 0.732 0.321 0.903 0.847 0.848 -0.129

-0.138 0.761 0.472 0.776 0.651 0.736 -0.207

1.000 -0.238 -0.266 -0.113 -0.064 -0.009 -0.015

-0.238 1.000 0.578 0.680 0.607 0.552 0.014

-0.266 0.578 1.000 0.326 0.261 0.312 0.040

-0.113 0.680 0.326 1.000 0.755 0.876 -0.092

-0.064 0.607 0.261 0.755 1.000 0.724 -0.080

-0.009 0.552 0.312 0.876 0.724 1.000 -0.133

-0.015 0.014 0.040 -0.092 -0.080 -0.133 1.000

112 See Elton et al. (2010), p. 259. 113 See for instance Campbell et al. (2002), Jones and Wilson (2004) or Bernhart et al. (2009).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Table 8: Weights for the optimal portfolios

Eur. Stocks Em. Markets Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind Farm Return Risk (Std. Dev.) Sharpe Ratio

1. Traditional Portfolio MVP 1 TP 2 4.12% 0.00% 1.17% 8.67% 94.71% 91.33% 3.93% 4.51% 3.15% 3.36% 0.50 0.65

2. Alternative Portfolio MVP 2 TP 2 0.00% 0.00% 0.00% 4.81% 78.61% 83.63% 19.56% 11.56% 1.82% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 3.98% 4.31% 2.69% 2.99% 0.61 0.66

3. Portfolio with Wind MVP 3 TP 3 0.00% 0.00% 0.00% 6.76% 61.90% 53.28% 15.58% 0.00% 1.11% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 21.41% 39.96% 4.31% 4.96% 2.38% 2.74% 0.83 0.96

The optimal portfolios were found for three different subsets of the investment universe. First, the MVP and TP were calculated for stocks and bonds only, which corresponds to a portfolio optimization for Traditional Assets. In this case, due to the poor performance of stocks during the crisis, the optimal portfolios are almost completely dominated by bonds (>90%).

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The second subset of the portfolio optimization considered all assets but the wind farm. This idea was motivated by previous empirical findings that one can improve the portfolio return or decrease portfolio risk by also investing into Alternative Assets.114 Indeed, portfolio risk could have been decreased from 3.15% to 2.69% (or in relative terms by 15%) for the MVP compared to the Traditional Portfolio. However, the Sharpe Ratio of the TP could have been increased only marginally (0.65 to 0.66). It deserves mentioning that only hedge funds (and to a degree commodities for the MVP) contribute to these results. All other Alternative Assets are irrelevant for the portfolio optimization for this set of the investment universe. The third and last subset considered all asset classes in the data set. It becomes evident that both the wind farm’s weights (>20%) and its incremental contribution to the MVP and TP are remarkable. In case of the MVP, portfolio risk could have been further reduced by 12% compared to the Alternative Portfolio. For the TP, the return was enhanced from 4.31% to 4.96%, a difference of 65 basis points, while simultaneously reducing the risk from 2.99% to 2.74%. The results, again, suggest that many asset classes (European stocks, private equity, infrastructure and real estate) should not be represented in any of the optimal portfolios. While this recommendation clearly stands against the asset allocation of many institutional investors, the result appears to be plausible for the chosen downturn period and set of assumptions. The high weights for the wind farm might decrease when analyzing a longer time frame, and once the additional illiquidity risk of this asset class is being recognized.

114 See Schneeweis et al. (2002), Schweizer (2008), Fischer and Lind-Braucher (2010).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 16 finally sho ows the histtorical perfo formance off the optimaal portfolioos from the three different suubsets of th he data. It becomes evident that a high proportion in bonnds and the wind farm durinng the crisess (TP 3) wouuld have ressulted in a ssteady perfoormance andd an appreciation of almost 30%, 3 which h is unconneected to the turbulencess on the stocck market. F Figure 16: Hiistorical perfformance of tthe optimal portfolio

Summing up, the ressults from the t empiriccal analysis so far sugggest that thhe benefits from adding a wind Portfolio aand a portfo w farm to both a Traditional T folio of Alteernatives caan be substantiall during perriods of finaancial crisess. In a way, wind farmss seem to offfer a fairly good alternative to bonds. They enablle investorss to protect themselvess from the sharp decliine of several othher asset claasses, whichh are prone tto market tuurbulences.

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5.3.2 Divversificatiion possib bilities wiithin a win nd portfoolio After the diversificattion potentiial of wind investmennts in a muulti-asset poortfolio has been explored, the next sttep in the empirical e aanalysis is to discuss diversificattion possibilities within a wind w portfoliio. The anallysis generaally follows the design of Dunlop (2004a) ( by using a single-index model in i order to assess a the ddiversificatioon effect. The modell that was teested empiriically for eaach wind farrm i had thee following form: ܵ‫ܴܣܣ‬௜ ൌ ߙ௜ ൅ ߚெ௜ ݉ ݉ܽ‫ ݐ݁݇ݎ‬൅ ߜ௜ ߚ௉௜ ‫ ݁ܿ݅ݎ݌‬൅ ߳௜ with ߜூ்஺ ൌ ͳ and ߜீாாோ௜ ൌ ߜிோ஺ ൌ Ͳ.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

For this part of the analysis, the data set again corresponds to the consistent portfolio of 11 wind farms from section 5.1. The first challenge was to find an appropriate benchmark for the first independent variable, which tries to reflect the return of a market index and is hence labeled market. For stocks, a common choice would have been one of the MSCI indices, but since there does not exist a Total Return index for wind energy, something similar had to be created. The analysis followed the idea of Dunlop (2004a) and developed a market portfolio for the wind farm market that consisted of all the 11 wind farms in the data set, weighted by their total installed capacity in the respective country and year. The corresponding weights can be found in Table 9. This method was considered to be appropriate since it accurately reflects market size and investability in the respective country. Table 9: Weights for the wind market portfolio 2009

Installed capacity (in MW)

GER ITA FRA Sum

25,777 4,849 4,574 35,200

2011

2010 73% 14% 13% 100%

27,214 5,797 5,660 38,671

70% 15% 15% 100%

29,393 6,767 7,394 43,554

67% 16% 17% 100%

Source: numbers for 2009 and 2010 from GWEC (2011), estimates for 2011 based on baseline scenarios from EWEA (2011a).

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The binary variable ߜ in front of the second independent variable, the price, takes a value of one when the wind farm is in Italy (a country with no fixed feed-in tariff), and zero when the wind farm is either in Germany or in France (countries with a fixed feed-in tariff).115 Since there was only one Italian wind farm in the data set, this already reflected the price risk in the overall market. The reason for extending the single-index model in this case is that the return pattern of a wind farm in a country with no fixed feed-in tariff might not be entirely explained by a model which only includes the movement of the market. A scatter plot of the Italian wind farm with the market in Figure 17 indeed confirms the need for an additional variable. As no data about observable market prices in Italy were available, the price variable was measured by a proxy: the monthly revenue from the sale of Green Certificates of the Italian wind farm in EUR million.

115 The binary variable does not refer to a dummy variable. It simply means that different regressions have been run.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Fig gure 17: Scattterplot of thee Italian wind d farm with th he market

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p an n overview of applyingg the singlee-index model to the wind w farmss. The Table 10 provides results from m applying the multi-iindex versioon (market and price aas independdent variables) to the Italian wind farm m can be fouund in Tablle 11. It beccomes eviddent that inccluding the price variable foor the Italian n wind farm m improves the fit of thhe regressionn significanntly (Adjustted R2 increases from f 0.171 to 0.516). However, tthe market vvariable ceaases to be ssignificant iin the multi-indexx model (p p-value of 0.0630). A summaryy of all undderlying reegressions aand a of the methhod are provvided in Apppendix I. thorough explanation e

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Total Risk (Std. Dev. SAAR) -Non-diversifiable -Diversifiable

Correlation to Market

Turbine manufacturer Wind consultant

Implied Expected Return Hist. Return (Mean SAAR)

N° obs.

 p-value M p-value Adjusted R2

4.65% 4.21%

36

GER 2 -0.004 0.5280 1.072 < 0.0001 0.609

4.54% 3.43%

36

GER 3 -0.011 0.0710 1.046 < 0.0001 0.669

4.03% 3.37% 0.66%

2.85% 2.25% 0.60%

2.66% 2.19% 0.47%

5.74% 2.53% 3.21%

3.05% 2.34% 0.71%

A d

4.85% 4.98%

36

GER 4 0.001 0.8620 1.118 < 0.0001 0.578

3.78% 1.80% 1.98%

A d

3.72% 3.42%

36

GER 5 -0.003 0.8200 0.858 0.0030 0.204

4.48% 5.14%

36

GER 6 0.007 0.5860 1.033 < 0.0001 0.317

4.54% 3.19%

36

GER 7 -0.014 0.0530 1.046 < 0.0001 0.609

3.55% 4.78%

36

GER 8 0.012 0.0840 0.817 < 0.0001 0.470

4.62% 3.43%

36

GER 9 -0.012 0.0270 1.064 < 0.0001 0.736

2.16% 3.18%

36

FRA 0.010 0.3640 0.497 0.0390 0.093

4.34% 4.34%

36

1.000 1.000

Market

3.73% 2.16% 1.56%

2.78% 2.19% 0.59%

2.46% 1.71% 0.74%

2.59% 2.23% 0.36%

3.02% 1.04% 1.98%

2.09% 2.09% 0.00%

A B B C D b, c, d a, e, f, g d d d Anemos Anemos Anemos, GHWind Consu Anemos Windtest, A DEWI, Natural Power 0.44 0.77 0.48 0.58 0.79 0.70 0.86 0.35 1.00

A c

5.24% 6.60%

36

ITA 0.014 0.5070 1.207 0.0070 0.171

Table 10: Summary of the single-index model for wind

A A A a, b a, b a, b WindConsultWindConsultWindConsul GH 0.84 0.79 0.82

6.99% 4.72%

36

GER 1 -0.023 0.0130 1.611 < 0.0001 0.693

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Table 11: Multi-index model for the Italian wind farm

ITA

 -0.0041842

p-value 0.7940

M 0.6552777

p-value 0.0630

P 0.0622778

p-value < 0.0001

Adjusted R2 0.516

The betas from the regressions, ߚெ , can now be used as a best guess measure for risk. A value of ߚெ ൐ ͳ (൏ ͳ) means that the particular wind farm is riskier (less risky) than the market. The corresponding p-values in Table 10 reveal that all betas are statistically significant at a 5% level of significance. Table 10 also shows that most intercept coefficients, ߙ, are not statistically different from zero. In the CAPM model, the alphas would refer to the risk-free rate ܴி .116 Since this study, however, is interested in the betas as a risk measure, a further interpretation of ߙ can be omitted. The Adjusted R2 column in Table 10 shows that the fit of each regression is relatively high (൐ ͲǤͷ), with the exception of the Italian and the French wind farm and GER 5, 6 and 8. For the former two, this result could have been expected since the market portfolio is a weighted average of mainly German wind farms. A well-diversified market portfolio might have resulted in higher and therefore somewhat more realistic R2s. Appendix J finally provides a discussion of the corresponding Security Market Line for the derived CAPM-style model.

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After having applied the single-index model (and the multi-index version for ITA) to the wind farms, the next step was to explore the effects of diversification. In order to receive consistent results, the single-index model has also been used for the Italian wind farm. The nondiversifiable risk was then calculated as ߚ௜ெ ߪ௠ while the diversifiable risk is simply the rest of a wind farm’s annualized standard deviation. The results for each wind farm can be found in Table 10. It should be emphasized that the total risk, measured by the annualized standard deviations, differs from Table 3 in section 5.2 since only the 3 years period had been assessed (apart from FRA where the two periods coincide). A graphical representation of nondiversifiable and diversifiable risk is provided in Figure 18. The biggest potential for diversifying away risk evidently lies within the Italian and the French wind farm. This result, again, is not really surprising since the market portfolio mainly consists of German wind farms. However, also two German wind farms, GER 5 and 6, appear to have fairly high diversification potential.

116 Many studies on fund performance instead regress the excess return over the risk-free rate on the market, in order to find the “real” alpha (Jensen’s alpha). (see Elton et al. (2010), p. 655)

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Figure 18: Diversifiable D and non-diveersifiable risk k of each wind farm

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The next step in i the analyysis was too find out hhow much risk can be diversifieed away byy holdiing a portfo olio of onlyy five windd farms insttead of a siingle one. A As in the aapproach off Dunllop (2004a)), the small portfolio hhas been buuilt up step--by-step by adding winnd farms too the riskiest r one (ITA). Sinnce the anaalysis was using u the C CAPM-stylee model forr estimatingg covaariance strucctures, addiing wind faarms with loow betas shhould lead to an averaaging downn effecct of risk. The T results from f this prrocedure caan be foundd in Figure 19. The corrrespondingg regreessions are also a explainned in Appeendix I.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Fig gure 19: The eeffect of diverrsification

The impacct of diversiification cann be seen fr from the redduction of ߚெ௉ when m more wind farms 2 are added to t the smalll portfolio. Besides, thee Adjusted R increasees as well siince the porrtfolio is getting closer c to thee market portfolio. Initiially, the Itaalian wind ffarm had ann annual stanndard deviation of o 5.74%. By B adding the t French wind farm and anotheer three Gerrman ones tto the portfolio, the t actual risk r could hhave been rreduced to 2.00%. 2 Thiss equals a risk r reductiion of 65% in reelative term ms. The divversificationn thereby incorporatees geographhical dispersion, different tuurbines and different wind w consulttants, as shoown in Table 10. How wever, it migght be that the maajor effect stems s from geographiccal diversifiication. In aaddition, coomparing the risk of 2.00% to the implied risk frrom the sinngle-index m model (ߚெ௉௉ ߪ௠ ሻ of thee final porttfolio, which is 1..84%, the beta seems too be a relatiively good m measure of risk.

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It also becomes evideent from Figgure 19 thatt the portfolio risk alw ways falls beelow the avverage risk of the combined wind w farms. Furthermoore, the riskk of the fivee wind farm m portfolio is also lower thann any indiv vidual wind farm’s riisk. The reesults thereefore provide an emppirical verificationn of the pro opositions by b Markowitz (1952), and apply tthe idea of Fama (19776) on stocks to thhe asset classs of Renew wables.

5.3.3 Heedging ben nefits of solar s As indicated earlier, there t has not n been enoough data to t perform an in-depthh analysis oof the hedging beenefits of so olar. Howevver, the mainn idea can aalready be eexplored wiith only few w data points. Duee to counterr-seasonalityy, solar shoould work ass a natural hhedge againnst wind. An obviouus starting point p is to have a lookk at budgett values forr a represenntative solaar and wind park and see iff hedging would w be poossible “in theory”. Fiigure 20 ploots the buddgeted inter-annuaal distributtion of Prooduction annd Operatinng Profit oof represenntative parkks. It

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

becomes eviden nt for both performanc p ce indicators that hedging wind annd solar, eqquivalent too the average a of th he two (greeen line), alm most entirelyy offsets thee inherent seasonality. s

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Figu ure 20: Hedging wind and solar with bu udget values

As the t reader might m havee noticed, the t figures however uuse differennt parks as a hedgingg partnner. For Pro oduction, hedging seem ms to be generally possiible with tw wo parks of ccomparablee capacity (in MW W). For thhe Operatingg Profit, thhis does noot necessarily work sinnce feed-inn tarifffs for solar are substanntially highher than for wind (see Appendix A A). As exem mplified onn the right r hand side s in Figuure 20, a 6 MW solar park might offer the same s annuaal Operatingg Profiit as its 32.5 MW win nd counterppart. Now, if a financcial investorr tries to benefit from m

677

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

counter-seaasonality, he h has to coonsider its hhedging poosition on thhe profit raather than oon the productionn side. Extending the framew work from budget valuues to actuals, the heddged line foor the Operrating Profit doess not look as a smooth anymore, an as exemplifieed in Figuree 21.117 How wever, this ffigure had to connsider diffeerent years for the intter-annual distribution. d . The actuaal values foor the Operating Profit for November N and Decem mber of thee year 20111 were not available bbefore completionn of this book. Therefoore, the twoo winter moonths from tthe previouss year weree used in order too be able to simulate a whole yearr. These twoo months, hhowever, haave been paarticularly bad wind w months, since the whole winnter of 20100/11 had beeen cold and hence not rreally windy. Figure 21: 2 Hedging w wind and sola ar with actuaals

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What can be b seen from m Figure 211 is that thee general heedging idea indeed seem ms to work. This is even truue for bad wind month ths (e.g. Deecember 2010), which could havee been offsset by better thann expected solar s profits. Whether this short time t frame,, however, is represenntative for the whhole 25 yeaar lifetime of a wind or solar park remains to be asssessed in fuurther ns. empirical investigatio i

117 Unfortunaately, the analyssis could not coonsider the actuual inter-annual distribution of Production (coounterpart to thee left hand sidee of Figure 20) since s SOL 2 staarted operating not until January 2011 and hennce the Novem mber and Decem mber months inn 2010 were missing.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

6

Conclusion and outlook

This book attempted to explore diversification benefits of Renewable Energy investments by using the theoretical background from Modern Portfolio Theory. It has been shown that many concepts such as the mean-variance framework and the famous CAPM model can be applied almost one-to-one to these investments. Furthermore, the analysis revealed that investing into wind and solar parks might be especially beneficial for long-term investors such as insurance companies or pension funds, who want to protect their portfolios against capital market turbulences. The empirical results suggest that substantial diversification benefits can be attained when adding Renewable Energy investments, represented by a single wind park, into a portfolio of Traditional and Alternative Assets. Indeed, Renewables were one of the few asset classes that offered steady returns during the Subprime Crisis and hence justified their role as a protection against financial turbulence. The second part of the empirical analysis explored diversification possibilities within a portfolio of several wind farms by using a single-index CAPM-style model. It was shown that the risk of a single wind farm could have been reduced by 65% when investing into a portfolio of only five wind farms instead. This could have been attained by diversifying around several countries, technologies and energy yield consultants. The last part of the empirical analysis tried to shed some light on the benefits from hedging wind with solar investments. Although the data has been limited for this analysis, preliminary results suggest that the benefits might be substantial. An investor can almost completely offset the seasonal variability of the input resources (wind and solar irradiation) and thereby create a portfolio with stable returns all over the year.

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The results from the empirical analysis should be interpreted with care for a number of reasons. First and foremost, the sample only consisted of a small number of observations. This is especially true for the CAPM-style model that has been used in order to assess the interasset class diversification possibilities (section 5.3.1). The small amount of data might have influenced the values of the betas derived from this model. Also the multi-index model that has been used for the Italian wind farm might be improved with more data. Secondly, the market portfolio in this part of the analysis only consisted of wind farms from three different countries. The use of a well-diversified (wind) market portfolio instead, as originally intended in the CAPM model, might have an influence on the resulting betas from the regressions.118 When having access to more data, the analysis could be extended into several directions . Two extensions were already mentioned several times in the book. First, the optimal asset allocation could allow for the inclusion of liabilities of long-term investors. Unfortunately, there has not been any available data from the financial investor on the liability structure of the involved entities, let alone the offered products. Therefore, the empirical analysis in this book 118 This has been theoretically pointed out in an earlier work by Roll (1977).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

was restricted to an asset-only perspective. The second extension concerns the hedging benefits of solar which could have been assessed only qualitatively in this study, also due to limited data. There are several other potential research directions that have been indicated in this book. As the reader might have noticed, the analysis in this study was focusing on onshore wind farms. The current trend in the industry, however, goes to large scale offshore projects with investment volumes of up to EUR 1.5 bn and capacities around 200 MW.119 Since the wind resource tends to be more stable offshore, there might be a role for long-term financial investors that want to place a large amount of funds into these projects. There is also further hedging potential within the asset class of Renewables. First, an investor is not limited to hedge wind with solar in order to remove seasonality. Instead, if one invested into a portfolio of only wind parks, but in both the Northern and Southern hemisphere, benefits from counter-seasonality should be accordingly.120 The second hedging potential relates to the use of weather derivatives.121 As the market for these financial instruments becomes more and more developed, they might become of use alongside Renewable Energy investments, e.g. to hedge against poor wind or solar irradiation years. Indeed, hedging against poor wind years might become an important tool in the future since the impact of global warming on long-term wind speed trends is far from clear.122

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The amount of available data had an influence not only on the possible analyses in this study, but probably also on the results. However, this could serve as a motivation for future research activities on this asset class. If one had access to long-term data, possibly for the lifetime of actual solar and wind parks, the results from the present work could be back-tested and further tools from MPT and financial theory could be applied accordingly. Since the future of Renewable Energies looks promising from an industry perspective, it should not be any different for future research.

119 Indeed, EWEA (2011b) expects annual investment for European offshore to reach 10 billion Euros by 2020. 120 From a financial perspective, however, this would neglect currency effects. 121 Weather derivatives are futures and options on e.g. heating and cooling degree days in a specific region (for an overview of the products please visit http://www.cmegroup.com/trading/weather/). Since the underlying does not have a value for the investor, pricing of these derivatives differs from standard option pricing (see for instance Golden et al. (2007) for an overview). 122 Although most authors claim that a trend cannot be identified yet, declining wind speeds in the last few years led to a general nervousness around investors (see e.g. Thomas et al. (2009) or Winkler (2010)).

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Appendix Appendix A: Renewable Energy instruments and remuneration Tariff solutions in EU countries

Fixed feed-in tariff

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Quota-based system

Source: compiled by the author on the basis of Böttcher (2009). .

.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

ƒ 20 years duration

ƒ 211-287 EUR/MWh depending on the installation style (rooftop or ground)

ƒ 48.7 EUR/MWh base tariff for the remaining lifetime

ƒ 83.6 EUR/MWh for a period of 15 years

ƒ 89.3 EUR/MWh for the first five years – extended based on a reference yield (usually 10-15 years)

ƒ Partly escalated with inflation

ƒ 20 years duration

ƒ Auction system for ground mounted photovoltaics: start tariff is 120 EUR/MWh

ƒ Annually escalated (depending on inflation and development of real wages)

France

Germany

Remuneration for wind and solar parks as of 2011

ƒ 20 years duration

ƒ 264 EUR/MWh – “staircase” system: start tariff for new projects is being reduced in every half-year

ƒ Remuneration depending on market conditions

ƒ Green certificates scheme

Italy

Source: electricity laws in the respective countries: Erneuerbare Energien Gesetz 2011, Tariff Arrêté 2008, Conto Energia 4. Remuneration is only shown for the three countries that are also part of the empirical analysis in this pape

Solar

Onshore Wind

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

σ்௧ୀ଴ ΨǦ݄ܿܽ݊݃݁݅݊݉ܽ‫ ݁ܿ݅ݎ݌ݐ݁݇ݎ‬൅ ݅݊ܿ‫݁݉݋‬ ܽ‫݁ܿ݅ݎ݌ݐ݁ݏݏ‬௧ୀ଴

0 0 +1.2

Jan 0 0 +1.2

Feb 0 0 +1.2

Mar 0 0 +0.9

Apr 0 0 +0.9

May 0 0 +0.6

Jun 0 0 +0.6

Jul 0 0 +0.9

Aug

0 0 +0.9

Sep

0 0 +1.2

Oct

t=1 Dec 0 +5 0 +8 +1.2 +1.2 Nov

… … … … …

t=2 Dec +5 +8 +1.2

… … … … …

t=25 Dec +175 +108 +1.2

Payback period (in years) 14.25 13 8.33

The table above uses several simplifying assumptions in order to express the general idea. It has been assumed that the investment horizon is the same for all asset classes and equal to 25 years. In addition, also the initial investment (asset price at t=0) is the same amongst asset

Stock Bond Wind farm

t=0 Dec -100 -100 -100

For wind and solar parks, the holding period return has to be derived using a slightly different approach. The asset price at t=0 coincides with the price at which the park is purchased (initial investment). Thereafter, the investors receive periodic (usually monthly) cash flows that depend on revenues and costs. Thus, from a pure cash perspective, an example for the cash flows from the three assets might look as follows:

For stocks and bonds, determination of this return measure is straightforward. The change in market price for both asset classes can be observed at the stock and bond market every (trading) day. The same is true for the historical asset price at the point of investment. For the income that is received during the holding period, the two assets differ slightly since stocks receive dividends and bonds receive coupons. While both are supposed to be annual payments, the former are a lot less certain while the latter are usually fixed (unless a default occurs). At maturity, bond holders receive their principal back, which usually coincides with the initial investment at t=0. The stock holder on the other hand will receive the stock price in t=T, which equals the sum of %-changes of this price over the investment horizon.

‫ ݊ݎݑݐܴ݁݀݋݅ݎ݈݁ܲ݃݊݅݀݋ܪ‬ൌ 

As described in section 4.1 of the book, the holding period return is defined as:

Appendix B: Discussion of the holding period return measure

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Feb Mar 10.0% 10.0%

Apr 7.5%

May 7.5%

Jun 5.0%

Jul 5.0%

Aug 7.5%

Sep Oct Nov Dec 7.5% 10.0% 10.0% 10.0%

123 Usually, dividends are paid out after the day of the annual shareholder meeting, which differs among companies. For simplification, the payment in this analysis was assumed to coincide with the coupon payment from the bond. 124 For the sake of simplicity, the analysis restricts the attention to wind farms. The same could be derived for solar parks which would have a reverse seasonality.

It becomes evident from the cash flow table above that the wind farm has by far the shortest payback period, i.e. years until the investor gets the initial investment back. This stems from the high periodic cash flows during the year. The payback method, however, does not consider any cash flows after the payback period and also fails to discount them. Therefore, the next step in the analysis is to change the cash perspective back to the holding period return perspective again. Using the assumptions from before, the table for the holding period return looks as follows:

Seasonality of wind

Jan 10.0%

classes and equal to 100 units. Stocks are assumed to pay out a fixed annual dividend of 5 units every December in each year.123 The stock price at the end of the investment horizon is equal to 175 units. This corresponds to a Constant Annual Growth Rate (CAGR) of around 6%. Bonds have a fixed annual coupon of 8 units paid out in December of each year. The principal is paid back at maturity (no default). Wind farms are assumed to deliver an annual yield of 12 units until the end of their lifetime.124 This has been scaled according to Dunlop (2006) who states a benchmark return of 12% for wind power project equity. The yield goes according to the following simplified seasonality pattern:

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

100 100 0 0

100 100 0

Bond - present value (r=8%) -  coupons - face value

Wind farm - market value -  yields

Stock - price (6% CAGR) -  dividends

t=0 Dec 100 100 0

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101 99.7 1.2

100 100 0 0

Jan 101 100.5 0

102 99.3 2.4

100 100 0 0

Feb 101 101.0 0

103 99.0 3.6

100 100 0 0

Mar 102 101.5 0

103 98.7 4.5

100 100 0 0 104 98.3 5.4

100 100 0 0

Apr May 102 103 102.1 102.6 0 0

104 98.0 6.0

100 100 0 0

Jun 103 103.1 0

104 97.7 6.6

100 100 0 0

Jul 104 103.6 0

105 97.3 7.5

100 100 0 0

Aug 104 104.2 0

105 97.0 8.4

100 100 0 0

Sep 105 104.7 0

106 96.7 9.6

100 100 0 0

Oct 105 105.2 0

107 96.3 10.8

100 100 0 0 108 96.0 12.0

108 100 8 0

t=1 Nov Dec 106 106 105.8 101.3 0 5

… … …

… … …

… … … … …

300 0 300

300 0 200 100

t=25 Dec 300 175 125

Holding Period Return 200%

Holding Period Return 200%

Holding Period Return 200%

The exemplified holding period return for stocks (bold figures) at each point in time consists of the appreciation in value of the stock price (from the annual CAGR of around 6%) plus the sum of the received dividends until that date. Note that the stock price is assumed to always drop according to the same value after a dividend is paid out.125 For the bond holding period return, the analysis uses very strong assumptions for simplicity reasons. The price of a bond at t=0 is defined as ்

ܲ‫ ݁ܿ݅ݎ‬ൌ ෍ ௧ୀ଴

‫ܥ‬ ܲ ൅ ௧ ሺͳ ൅ ‫ݎ‬ሻ ሺͳ ൅ ‫ݎ‬ሻ்

where C is the annual coupon, P the principal payment at maturity and r the appropriate discount factor (t period spot rate).126 If the discount factor coincides with the coupon payment in % of the principal and does not change over time (flat yield curve), the bond’s present value at each point in time is equal to the principal payment at maturity. While this is a rather radical simplification of reality, it has been used to keep the analysis simple. It follows from the assumptions, that the holding period return for the bond is equal to the sum of the coupons plus the expected principal payment at maturity. In order to derive a comparable holding period return for the wind farm, the measure has to include both the loss in market value over the lifetime and the cumulated yields from generated income. While the latter can be observed, simulating the loss in market value can be a rather challenging exercise.

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The market value of a wind farm is usually determined via a DCF model. This is due to the fact that this model can accurately reflect the run-off character of this business, i.e. the fact that the wind farm will be worth nothing at the end of the lifetime. The present value of the wind farm at any point in time is simply the discounted sum of its future cash flows for the rest of the life of the asset. Since the cash flows are discounted at a certain rate, the development of the market value from the initial value to zero receives a concave shape. This stems from the fact that the future cash flows become more and more valuable as time passes (since they are discounted at higher factors). Hence, the loss in value (economic depreciation) from the DCF model increases as the project goes along. If one wanted to properly simulate the development of the market value, appropriate assumptions on the discount rate and the remaining cash flows have to be made. The decay of the book value of a wind farm (measured depreciation) follows a completely different pattern. Usually, the initial book value of the depreciable assets is below the investment, since the developer (seller of the wind farm) receives a premium for taking the risk of developing the wind farm. The fixed assets are then written-down over a certain period according to the accounting treatment in the respective country. As of the German Accounting 125 This is a standard assumption which can be found in any book on Option Pricing (e.g. Sundaram, R. and Das, S. (2011): Derivatives – Priniciples and Practice, McGraw-Hill Irwin, New York, p. 272) 126 See e.g. Elton et al. (2010), p. 529.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Standdards (HGB B), for insttance, the aassets can be linearlyy depreciateed over 16 years. Thee Interrnational Acccounting Standards S (IIFRS), on thhe other haand, allow ffor a deprecciation overr the liifetime of th he project (25 ( years). T The followiing graph exxemplifies tthe development of thee bookk vs. the maarket value,, as well ass the market value appproximationn that has beeen used inn this book b (explaained in morre detail bellow):

The market valu ue from thee DCF valuuation (bluee line) uses several sim mplifying asssumptions.. As before, the wind w farm was w assumedd to deliverr an annual cash flow of o 12 units. These cashh flows were disccounted at a fixed ratee of around 11%. This rate has beeen scaled, so that thee initiaal market vaalue exactlyy equaled 100 units (inn order to bbe comparabble to the aassumptionss from m before). Th he initial boook value (rred line) of tthe wind farrm was assuumed to be 20% below w the innitial markeet value andd has been liinearly deprreciated oveer 16 years (as in Germ many).

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The market m valu ue approxim mation (greeen line) thatt has been uused in the present p studdy follows a ratheer simple ap pproach. It has h been assumed that the initial iinvestment of 100 unitss is linearlyy depreeciated oveer the lifetim me of the pproject (25 years). Thiis certainly overstates the loss inn markket value in the first years and thus probably underestima u ates expecteed returns ffor the windd farm ms. Howeverr, simulatingg the remaiining cash fflows and a common discount d ratee for all thee windd farms in th he empiricaal analysis w would havee been a whhole book onn its own. O Overall, thee approoach appeaared to be a reasonablee simplificaation, sincee the loss inn market value lies inn betw ween the meaasured and the econom mic depreciaation, as eviddent from thhe above figgure. Com ming back to o the holdinng period reeturn table from f beforee, it can be seen that tthe terminall valuees of all assets are equual to 300 uunits and hhence all terrminal holdding period returns aree 200% %. These vaalues have been b scaledd in order to guaranteee a close coomparison oof the threee assett classes. Summ ming up, th he analysis reveals thaat the returnn profile off the assets can be fairrly differentt withiin the perio ods, althouggh the averaage annual return overr the 25 yeaar investmennt period iss ͲΨൗ ൌ ͺΨ the same s Ψቁ. While the holdinng period rreturn for stocks s and bonds hass ቀʹͲͲ ʹͷ

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

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already been theoretically assessed in the literature, the measure for Renewables derived in this book is novel.127

127 According to the author’s research and knowledge. For stocks and bonds, see e.g. Elton et al. (2010), p. 36-40.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Appendix C: Structure of the income statement for a wind farm The income statement that was available for each single wind farm had the following layout: in EUR k

Total Production (in MWh)

x

Energy Sales Revenue Green Certificate Revenues (ITA only)

x x

Insurance Income Other Income Badwill Total Other Income Total Revenue Technical & Commercial Management Service Agreement Land Lease Agreement Substation Agreement Electricity Consumption Grid Agreement Meter Operator Agreement Operating Costs & Infrastrucure Legal, Tax & Audit Insurance Repair & Maintenance Other Costs Other Operating Cost Total OPEX Operating Profit Decomissioning Guarentee Interest Income / Expense Other Tax Other Income & Expenses Depreciation Copyright © 2013. Diplomica Verlag. All rights reserved.

MONTH

Profit Before Tax Tax Profit After Tax Dividend Net Profit

x x x ________ x ________ x (x) (x) (x) (x) (x) (x) (x) ________ (x) (x) (x) (x) (x) ________ (x) ________ (x) ________ x (x) x (x) ________ x (x) ________ x (x) ________ x (x) ________ x ________ ________

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

The usual spreadsheet approach for a DCF valuation (entity approach) would value the free cash flows (FCF) from operations by discounting them by the weighted average cost of capital (WACC). The resulting value then has to be added to the present value of the nonoperating cash flow and subtracted by the market value of debt. As none of the wind farms in the data set was leveraged and none had any marketable securities, the initial entity value would simply consist of the discounted (operating) cash flows. Furthermore, the WACC would coincide with the cost of equity. Using actual data, the optimal approach in order to assess the holding period return of a wind farm would be to sum up the operating cash flows over the lifetime of the project and compare it to the initial investment. The 25 year return could then be divided by 25 in order to receive an average annual return that can be expected for a project. Since there was no available data for the whole lifetime of the projects, however, the average annual return had to be estimated from performance figures. As described in section 4.1 and 5.1 of the book, the appropriate measure has been determined to be the Return on Investment, defined as: ܴܱ‫ ܫ‬ൌ

‫ܶܫܤܧ‬ ܱ‫ ݐ݂݅݋ݎܲ݃݊݅ݐܽݎ݁݌‬െ ‫݊݋݅ݐܽ݅ܿ݁ݎ݌݁ܦ‬ ൌ ‫݈ܽݐ݅݌ܽܥ݀݁ݐݏ݁ݒ݊ܫ‬ ‫݈ܽݐ݅݌ܽܥ݀݁ݐݏ݁ݒ݊ܫ‬

Since there was no leverage in the projects, the Return on Investment equaled the Return on Equity, which is usually of interest for an investor. The reason for choosing the Operating Profit over the Operating FCF was that cash flows were often influenced by periodic events (e.g. annual payment of Service Agreement vs. semi-annual payment of Land Lease). The return figure however was required to reflect an average value. Since the Operating Profit spreads all cost items evenly over the year, it appeared to be a more sensible figure for this purpose. There are further problems with the use of the Operating FCF as the basis for returns. The Operating FCF is defined as:128

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ܱ‫ ܨܥܨ݃݊݅ݐܽݎ݁݌‬ൌ ‫ ܶܫܤܧ‬െ ܶܽ‫ ݏ݁ݔ‬൅ ‫ ݊݋݅ݐܽ݅ܿ݁ݎ݌݁ܦ‬൅ ܹ‫ ݈ܽݐ݅݌ܽܥ݃݊݅݇ݎ݋‬െ ‫ݐ݊݁݉ݐݏ݁ݒ݊ܫ‬ It can be seen from the formula that the Operating FCF subtracts taxes, which should not be included in the return figure since the returns for the other asset classes are also without tax. The Operating FCF also adds back the depreciation, which, however, should be included in the return figure (discussed in more detail below). The Working Capital part of the formula is not especially relevant for wind farms since neither CAPEX nor trade receivables / payables are substantial during the lifetime of the project. Lastly, the Investment part in the Operating FCF measure usually equals the initial investment for a Renewables project, which has already been included in the ROI measure. Therefore, the remaining figure that had to be assessed for the relevant return calculation is the EBIT.

128 See e.g. Copeland et al. (2005), p. 508.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Other than in many standard income statements, the Operating Profit in the one above essentially describes the EBITDA figure, which is usually defined as:129 ‫ ܣܦܶܫܤܧ‬ൌ ܴ݁‫ ݁ݑ݊݁ݒ‬െ ‫ ݈݀݋ݏݏ݀݋݋݂݃݋ݏݐݏ݋ܥ‬െ ‫ݏ݁ݏ݊݁݌ݔܧ‬ where Expenses include everything but interest, amortization, depreciation and taxes. It can be seen from the income statement above that the Operating Profit indeed coincides with the definition of the EBITDA figure. It should be emphasized again that the used definition for the Operating Profit might depart from conventional terminology by many authors, who use the Operating Profit as a synonym for the EBIT. The next step in the analysis was to derive an EBIT measure from the income statement above. The EBIT is generally defined as:130 ‫ ܶܫܤܧ‬ൌ ܱ‫ ݁݉݋ܿ݊ܫ݃݊݅ݐܽݎ݁݌‬െ ‫݊݋݅ݐܽ݅ܿ݁ݎ݌݁ܦ‬ One could have simply deducted the actual depreciation of the wind farm in the respective month from the Operating Profit in the above income statement. However, depreciations in the income statements have been substantially different among the projects. This was due to the fact that the projects were in different countries with different accounting treatment (e.g. some projects had an accelerated depreciation while others did not). As a result, the returns of the wind farms would have been less comparable. In addition, the respective returns would have been substantially lower in the first months of the project where the accounted depreciation was higher. If one wanted to come up with a comparable return measure for all projects, a different approach had to be used from here.

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A straightforward approach was to linearly depreciate the assets over their whole lifetime (see Appendix B). This technique appropriately captured the fact that the park loses value over time and has a value of zero at the end of the lifetime. The value and the definition of the depreciable assets of the wind farms (usually turbines, substations and access roads), however, again differed between the projects. Therefore, the analysis had to make use of a rather strict assumption. The economic depreciation used in this analysis simply consists of a monthly linear depreciation of the initial investment of the respective wind farm over the whole lifetime of the project (25 years). This might slightly overstates the measured depreciation of the fixed assets, whose book values were below the initial investment. Thus, the average returns in this study are somewhat too low. However, the approach appeared to be reasonable for the sake of comparison between the projects.

129 This can be found in any standard text book on key performance figures, e.g. Temple, P. (2007): Unternehmenskennzahlen, Wiley VCH, p. 49-55. 130 See e.g. Copeland et al. (2005), p. 508.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Appendix D: Empirical distributions of the wind farms

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The following figures show the empirical distributions (histogram) of the adjusted annualized returns (SAAR) for the wind farms in the data set, as well as the respective normal density approximation.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Appendix E: Proxy indices and discussion of the asset classes The MSCI Europe Index is a free float-adjusted market capitalization weighted index that is designed to measure the equity market performance of the developed markets in Europe. The MSCI Europe Index consists of the following 16 developed market country indices: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and the United Kingdom. (for more information please visit www.msci.com)

The MSCI Emerging Markets Index is a free float-adjusted market capitalization index that is designed to measure equity market performance of emerging markets. The MSCI Emerging Markets Index consists of the following 21 emerging market country indices: Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India, Indonesia, Korea, Malaysia, Mexico, Morocco, Peru, Philippines, Poland, Russia, South Africa, Taiwan, Thailand, and Turkey. (for more information please visit www.msci.com)

The Barclays Capital Euro-Aggregate Index tracks fixed-rate, investment-grade Euro-denominated securities. Inclusion is based on the currency of the issue, and not the domicile of the issuer. The principal sectors in the index are Treasury, Corporate, Government-Related and Securitised. Securities in the index are part of the PanEuropean Aggregate and the Global Aggregate Indices. The Euro-Aggregate Index was launched on July 1, 1998. (for more information please visit www.barcap.com/indices)

The Dow Jones Credit Suisse Core Hedge Fund Index is designed to represent the liquid, investable hedge fund universe. It is the first index to reflect the performance of managed accounts and other regulated fund structures sourced from across a range of platforms. The index utilizes a UCITS III compliant methodology and is valued daily. The index includes 40 fund components. (for more information please visit www.hedgeindex.com/)

The Dow Jones UBS Commodity Index aims to provide broadly diversified representation of commodity markets as an asset class. The index is made up of exchange-traded futures on physical commodities. The index represents 19 commodities, which are weighted to account for economic significance and market liquidity. Weighting restrictions on individual commodities and commodity groups promote diversification. (for more information please visit www.djindexes.com/)

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The LPX Europe covers all private equity companies listed in Europe which fulfill certain liquidity criteria. The index is characterized by a high degree of diversification across investment styles such as buyout and venture. The index construction methodology is manifested and published in the guide to the LPX equity index series. (for more information please visit www.lpx-group.com/)

The NMX Europe provides liquid and tradable exposure to companies around the European region which provide basic infrastructure facilities. Basic infrastructure companies have a protected market position due to their cost structure (high sunk cost and decreasing average cost). The low technology risk and inelastic demand of the goods and services provided translate in a comparatively low correlation to other asset classes and a linkage to long term GDP growth. The NMX Europe is well diversified across infrastructure sectors. The universe of the NMX index family is based on the following infrastructure subsectors: toll roads/bridges, airports, ports, pipeline networks (water, gas, and oil), communication networks. (for more information please visit www.lpx-group.com/)

The FTSE EPRA/NAREIT Index Series are designed to represent general trends in eligible real estate equities worldwide. Relevant real estate activities are defined as the ownership, disposure and development of incomeproducing real estate. The FTSE EPRA/NAREIT Europe measures the performance of European-listed real estate. It offers the purest and most diverse representation of this market by both geography and property type. The index currently has 82 constituents. (for more information please visit www.epra.com/ or www.ftse.com/)

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Discussion of the indices

The used proxy indices for Traditional Assets are standard indices in the academic literature. Elton et al. (2010), for instance, claim that a common choice for empirical analyses for stocks are the international stock market indices by Morgan Stanley International (MSCI) since they include dividends and thus appropriately measure the holding period return (or Total Return). The same is true for the used bond index in this study. The Barclays Euro Aggregate Index, which is the successor of the commonly used Lehman Brothers Aggregate Bond Index, is computed on a monthly basis and assumes that any interest paid during the month is reinvested at the end of this month. The price of this index consists of the quoted price (which should be the present market value of the bond) plus the accrued interest, and thus resembles a Total Return index again. For Alternative Assets, the choice of a representative proxy index to capture their performance is not straightforward. This stems from the fact that most Alternatives are not quoted. Therefore, proxy indices have to be found, which capture their main risk-return characteristics. Schweizer (2008) and Fraser-Sampson (2011) provide an overview on proxies for Alternative Assets (except for infrastructure investments). The findings can be summarized as follows: •

Hedge Funds:

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There are mainly two reasons for investing in hedge funds. First, using less regulated investment vehicles, managers of these funds can more easily generate positive alphas (i.e. excess returns for the risk borne). Secondly, due to low correlations with the stock market, hedge funds serve as a good diversifier in portfolios. Although there are a lot of different hedge fund strategies, empirical studies mainly use broad hedge fund indices, such as the Dow Jones Credit Suisse Core Hedge Fund Index, to represent the performance characteristics of this asset class. A common characteristic of these indices is the often cited non-normality of returns. This means that the return patterns of hedge funds in general do not follow a normal distribution (instead they usually exhibit fat tails and a high excess kurtosis, as it can be seen in Appendix F). Using the mean-variance framework can therefore be misleading when finding the optimal weight for this asset class. In addition, hedge fund indices are often prone to the socalled survivorship bias. This bias relates to the fact that the index does not include funds that failed or were merged within the respective time frame. As a result, annual returns are found to be overstated by 2-3%. A final characteristic of hedge fund indices is positive autocorrelation, e.g. arising from illiquid portfolio positions (this can also be seen in Appendix F). •

Commodities: There are several ways to invest in commodities. Investors can either directly invest in the physical good or participate in stocks of natural resource companies, commodity funds or commodity futures indices (indirect investing). Most studies use the latter practice, and therefore indices such as the Dow Jones-UBS Commodity Index, as a proxy representing the asset class.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

•

Private Equity (Leveraged Buyouts and Venture Capital): Due to a lack of data and low transparency of the market itself, risk-return characteristics of private equity are probably the most difficult to capture by a proxy. Many empirical studies use reported cash flows or the appraised value of unrealized investments for returns. However, most of this data is self-reported and therefore subject to selection biases. Another approach is thus to use listed private equity companies as a proxy for the asset class (e.g. the LPX50 Index). This method however is heavily criticized by the industry since measured returns can stem from the cash positions of the companies and thus might differ from the performance of the underlying participations. Listed private equity companies typically hold large cash positions (uninvested capital), which can result in higher returns during periods of high interest rates. Although the shortcomings of the LPX index as a proxy for private equity are recognized, it has been used in the empirical analysis of the present work as well. This is simply because there does not exist a publicly available database for private equity that could have been employed.

•

Real Estate:

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When measuring the performance of the asset class real estate, most empirical studies use Real Estate Investment Trusts (REITs) and their respective indices, such as the FTSE EPRA / NAREIT Index, as a proxy. This is due to strong evidence of comovement with the direct real estate market, as well as relative independence to movements in stock markets. However, this proxy is far from being generally accepted since these quoted vehicles indeed seem to move with stocks and thus might not be entirely appropriate for simulating real estate exposure.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Appendix F: Empirical distributions and autocorrelation of the asset classes Empirical distributions and normal density approximation

The following figures show the empirical distributions (histogram) of the monthly returns (TR) of the asset classes in the data set, as well as the respective normal density approximation. Used abbreviations:

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stocks = European stocks, em = Emerging markets stocks, bond = Bonds, hf = Hedge funds, commodity = Commodities, pe = Private equity, infra = Infrastructure, reit = Real estate.

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Autocorrelation of the asset classes Autocorrelation Table* Eur. Stocks N° obs. 57 Standard Error 0.132 Lag #1 0.286 Lag #2 0.029 Lag #3 0.220 Lag #4 0.311 Lag #5 0.009 Lag #6 -0.186 Lag #7 -0.028 Lag #8 0.101 Lag #9 -0.099 Lag #10 -0.196 Lag #11 0.123 Lag #12 0.098

Em. Markets 57 0.132 0.233 0.230 0.146 0.162 -0.047 -0.196 -0.022 0.004 -0.010 -0.087 0.110 -0.050

Bonds 57 0.132 0.141 -0.106 0.060 0.045 -0.075 0.030 -0.031 -0.096 0.012 -0.011 0.179 0.070

Hedge Funds Commodities Private Equity Infrastructure Real Estate 57 57 57 57 57 0.132 0.132 0.132 0.132 0.132 0.468 0.053 0.522 0.202 0.349 0.280 0.315 0.126 -0.022 -0.096 0.139 0.001 0.202 0.263 0.203 0.131 0.255 0.213 0.219 0.388 0.005 -0.067 -0.055 -0.075 -0.010 -0.035 -0.187 -0.295 0.021 -0.334 -0.032 0.008 -0.184 0.158 0.033 -0.074 -0.106 0.060 0.043 0.254 -0.144 0.025 0.026 -0.114 -0.038 -0.119 -0.303 -0.113 -0.206 -0.209 -0.090 0.181 0.062 0.021 0.197 -0.205 -0.161 0.105 -0.020 0.219

* Autocorrelations larger than two standard errors are considered significant and shown in bold.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

App pendix G:: Value at Risk and d Conditioonal Valu ue at Risk Valuee at Risk deescribes thee maximum m loss that iss not exceedded with a given probability (e.g.. 95%)) within a specified s peeriod. Whenn assuming normally ddistributed returns r thiss formalizess to: ܸܴܽ ሺܴ௜ ሻ ൌ ‫ ܧ‬ሺܴ௜ ሻ ൅ ‫ݖ‬ఈ ߪሺܴ௜ ሻ wherre ‫ݖ‬ఈ is thee quantile of o the standdard normall distributioon at a conffidence levvel of (1-).. Althoough VaR has h becomee a standardd risk meassure in finaancial theorry, it has ann importantt shorttcoming: lo osses that fall f beyondd the threshhold level are negleccted. Therefore, manyy authoors include a further esstimator forr risk in their analysis, namely thee Expected Shortfall orr Condditional Vallue at Risk. This estim mator measuures the connditional exxpected retuurn - in thiss case expected lo oss – givenn this loss iss beyond thhe VaR leveel. In case of o normallyy distributedd returrns this form malizes to ‫ ܴܸܽܥ‬ሺܴ௜ ሻ ൌ െ ൤‫ ܧ‬ሺܴ௜ ሻ ൅

߮ሺ‫ݖ‬ఈ ሻ ߪ ߪሺܴ௜ ሻ൨ ܰሺ‫ݖ‬ఈ ሻ

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wherre ߮ሺήሻ is th he density function f annd ܰሺήሻ the distributionn function of o the standdard normall distriibution.

The graphical g reepresentatioon above is for the casee of a standaard normal distributionn with meann zero and standarrd deviationn of one.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

The Value at Risk in this case describes the maximum loss that is not exceeded with a confidence level of 1-. If the confidence level is set to 95%, the VaR for a standard normal distribution is about 1.65 standard deviations away from the mean. The Conditional Value at Risk measures the expected value given the VaR threshold. Thus, the CVaR measures the expected value of the interval from െλ to -1.65, in this case equal to 2.06 standard deviations away from the mean. Sources: Favre, L. and Galeano, J. (2002): “Mean-Modified Value-at-Risk Optimization with Hedge Funds”, Journal of Alternative Investments 5 (2), 21-25. Fischer, E. and Lind-Braucher, S. (2010): “Optimal Portfolios with Traditional and Alternative Investments: An Empirical Investigation”, Journal of Alternative Investments 13(2), 58-77.

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Yamai, Y. and Yoshiba, T. (2005): “Value-at-risk versus expected shortfall: A practical perspective”, Journal of Banking and Finance 29 (4), 997-1015.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Appendix H: Calculation of the optimal portfolios in the multi-asset framework The results from the portfolio optimization problem in this section refer to the Portfolio with Wind, i.e. all asset classes in the data set have been considered. The calculations for the other two optimal portfolios (labeled as “Traditional” and “Alternative Portfolio” in section 5.3.1) are straightforward modifications and therefore left to the reader. The first portfolio that had to be calculated was the Minimum Variance Portfolio, which refers to the combination of assets with the lowest risk (i.e. standard deviation of annual returns). As outlined before, this corresponds to the following optimization problem: ‹ ߪ௉ ଶ s.t. (1) σே ௜ୀଵ ܺ௜ ൌ ͳ (2) ܺ௜ ൒ Ͳ‫݅׊‬ The first step was to find ߪ௉ ଶ . Using matrix notation from section 3.1, this corresponds to: ଶ

ߪ௉ ൌ ሾܺଵ

‫ڮ‬

ߪଵଶ ܺே ሿ ቎ ‫ڭ‬ ߪேଵ

‫ߪ ڮ‬ଵே ܺଵ ‫ڰ‬ ‫ ڭ‬቏ ൥ ‫ ڭ‬൩ ൌ ࢄԢπࢄ ‫ߪ ڮ‬ேଶ ܺே

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where  denotes the variance-covariance matrix of the asset classes.  can be found by using the correlation matrix in Table 7 (since ߪ௜௝ ൌ ߩ௜௝ ߪ௜ ߪ௝ ) as well as the monthly standard deviations for the respective asset classes from Table 6. The resulting values for  are as follows:

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Eur. Stocks Em. Markets Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind Farm

Eur. Stocks Em. Markets 0.0026381 0.0027928 0.0027928 0.0041586 -0.0000617 -0.0000853 0.0007943 0.0010359 0.0007842 0.0014491 0.0040726 0.0043933 0.0019824 0.0019121 0.0027965 0.0030472 -0.0000988 -0.0001986

Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate -0.0000617 0.0007943 0.0007842 0.0040726 0.0019824 0.0027965 -0.0000853 0.0010359 0.0014491 0.0043933 0.0019121 0.0030472 0.0000912 -0.0000480 -0.0001208 -0.0000950 -0.0000277 -0.0000055 -0.0000480 0.0004458 0.0005814 0.0012611 0.0005840 0.0007480 -0.0001208 0.0005814 0.0022664 0.0013650 0.0005670 0.0009522 -0.0000950 0.0012611 0.0013650 0.0077130 0.0030192 0.0049374 -0.0000277 0.0005840 0.0005670 0.0030192 0.0020760 0.0021181 -0.0000055 0.0007480 0.0009522 0.0049374 0.0021181 0.0041195 -0.0000021 0.0000044 0.0000286 -0.0001205 -0.0000545 -0.0001275

0.000127021

6.8424E-05

9.6402E-05

Wind Farm 21.41%

4.71817E-05

Wind Farm -0.0000988 -0.0001986 -0.0000021 0.0000044 0.0000286 -0.0001205 -0.0000545 -0.0001275 0.0002218

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4.71817E-05

4.71817E-05 4.71817E-05

Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate 61.90% 15.58% 1.11% 0.00% 0.00% 0.00%

The next step in the analysis was to minimize portfolio risk by finding the optimal combination of the weights ࢄ. This was achieved using Excel’s Solver tool by recognizing constraints (1) and (2). The results for the optimal weights are: Eur. Stocks Em. Markets 0.00% 0.00%

8.21853E-05

and the corresponding values for ࢄԢπ: 7.30864E-05

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

Finally, ࢄԢπࢄ can be found by simple matrix multiplication again. The result for the portfolio variance is 0.00472% (Note: this corresponds to the cell in Excel that has been minimized by Solver). The monthly standard deviation is simply the square root of this term, equal to 0.69%. The final step was to annualize this standard deviation by multiplying it by ξͳʹ, which in turn gives the final result of 2.38%. This assumes that returns are independent and identically distributed (i.i.d.), which might be a reasonable assumption for a portfolio of assets. The expected return of the resulting MVP can be found by using matrix notation from section 3.1 again: ܺଵ ‫ ܧ‬ሺܴ௉ ሻ ൌ ሾ‫ܧ‬ሺܴଵ ሻ ǥ ‫ܧ‬ሺܴே ሻሿ ൥ ‫ ڭ‬൩ ൌ ࡾԢࢄ ܺே The values for ‫ ܧ‬ሺܴ௜ ሻ for the individual asset classes are estimated by the respective monthly returns from Table 6. Using simple matrix multiplication, the expected return for the MVP results in a value of 0.36%. Again, annualizing this value by multiplying by 12 gives the final result of 4.31%. The second portfolio that had to be calculated was the Tangency Portfolio, or equivalently the combination of assets that results in the highest Sharpe Ratio. As explained in section 3.1, this can be found by solving: ƒš

‫ ܧ‬ሺܴ௉ ሻ െ ܴி ߪ௉

s.t. (1) σே ௜ୀଵ ܺ௜ ൌ ͳ (2) ܺ௜ ൒ Ͳ‫݅׊‬

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The ratio in the first line corresponded to the cell that had to be maximized using Excel’s Solver. For the annual risk-free rate, a value of 2.34% has been assumed, as discussed in section 5.3.1. The calculation of the other two inputs, ‫ ܧ‬ሺܴ௉ ሻ and ߪ௉ , generally follows the same design as for the MVP.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

4.62646E-05 4.50713E-05

0.000198279

9.2706E-05

0.00015213

Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate 53.28% 0.00% 0.00% 0.00% 0.00% 0.00%

4.19696E-05

Wind Farm 39.96%

7.40794E-05

Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

The resulting optimal weights for the MVP are as follows: Eur. Stocks Em. Markets 0.00% 6.76%

0.000156365

The corresponding values for ࢄԢπ are: 0.000116456

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and finally the portfolio variance ࢄԢπࢄ is equal to 0.00625%. As before, this value has been transformed to an annualized standard deviation of 2.74%. The expected return of this combination of assets equals 4.96% and the corresponding Sharpe Ratio is 0.96 .

94

Appendix I: Regressions for the wind portfolio The regressions generally used the Ordinary Least Squares (OLS) estimator because the null hypothesis of homoscedasticity failed to be rejected (see p-values from Breusch-Pagan test, labeled as “Het.test”). In the two cases marked in bold in the table below, however, the hypothesis of homoscedasticity has been rejected. In these cases, the OLS estimator with White’s robust standard errors has been used since the exact structure of the heteroscedasticity was not known. The resulting robust standard errors are also marked in bold. The generalized linear regression model is based on the following assumptions: ƒ

‫ ܧ‬ሾߝȁܺሿ ൌ Ͳ

ƒ

‫ ܧ‬ሾߝߝԢȁܺሿ ൌ ߪ ଶ π

The table below reports the results from the regressions of the adjusted annualized returns (SAAR) of each wind farm on a constant (ߙ) and the ݉ܽ‫ݐ݁݇ݎ‬, or: ܵ‫ܴܣܣ‬௜ ൌ ߙ௜ ൅ ߚெ௜ ݉ܽ‫ ݐ݁݇ݎ‬൅ ߳௜  (st.err)

GER 1 GER 2 GER 3 ITA GER 4 GER 5 GER 6 GER 7 GER 8 GER 9

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FRA

-0.0227439 (0.0086657) -0.0044013 (0.0068997) -0.0110656 (0.0059325) 0.0135823 (0.0202646) 0.0013475 (0.0054271) -0.002994 (0.0130701) 0.0065638 (0.0119394) -0.0135187 (0.1529504) 0.0123483 (0.0069326) -0.0119282 (0.0051567) 0.0102418 (0.0107965)

p-value 0.0130 0.5280 0.0710 0.5070 0.8620 0.8200 0.5860 0.0530 0.0840 0.0270 0.364

M (st.err)

1.611157 (0.1803529) 1.071916 (0.1435988) 1.045802 (0.1234685) 1.207445 (0.4217552) 1.117889 (0.1519192) 0.8577773 (0.2720197) 1.03275 (0.2484873) 1.046108 (0.0058866) 0.817137 (0.1442847) 1.064492 (0.1073241) 0.497267 (0.2675309)

p-value

p-value Het. Test

Adj. R2

F-Stat p-value

N° obs.

< 0.0001

0.0540

0.693

< 0.0001

36

< 0.0001

0.2214

0.609

< 0.0001

36

< 0.0001

0.5188

0.669

< 0.0001

36

0.0070

0.9834

0.171

0.0071

36

< 0.0001

0.0212

0.578

< 0.0001

36

0.0030

0.6730

0.204

0.0034

36

< 0.0001

0.4665

0.317

0.0002

36

< 0.0001

0.0327

0.609

< 0.0001

36

< 0.0001

0.2657

0.470

< 0.0001

36

< 0.0001

0.0711

0.736

< 0.0001

36

0.039

0.0260

0.093

0.0392

36

It becomes evident from the table that a possible shortcoming of the performed regressions might be the small number of observations. These could heavily influence the estimates of the coefficients. The underlying assumption of the presence of large sample properties (e.g. normally distributed disturbances) might not be the best description of this relatively small sample.

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

p-value 0.6552777 (0.3404833)

M (st.err)

0.0630

p-value 0.0622778 (0.0123969)

P (st.err)

< 0.0001

p-value

0.0615

p-value Het. Test

0.516

Adj. R2

< 0.0001

F-Stat p-value

36

N° obs.

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 (st.err)

-0.0041842 (0.0158825) 0.7940

For the Italian wind farm, as outlined in section 5.3.2 of the book, another important explanatory variable might be the price of any sold energy. This price is not fixed in the Italian framework, which differs from Germany. Therefore, the Italian wind farm SAAR has also been regressed on both the market and the price variable. The latter was measured by a proxy due to limited data, i.e. revenues from Green Certificates sales in EUR million. The results from this regression can be found in the table below.

ITA

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Windfall Profit in Portfolio Diversification?: An Empirical Analysis of the Potential Benefits of Renewable Energy Investments : An Empirical Analysis of the Potential Benefits of

It follows from the regression that the price indeed has an influence on the return of the Italian wind farm. However, the market variable ceases to be significant once the two variables are incorporated into the regression. It remains to be shown that the fit of this regression will improve compared to the previous regression without the price variable. In other words the following test has to be undertaken: ‫ܪ‬଴ ǣߚ௉ ൌ Ͳ‫ݏݒ‬Ǥ‫ܪ‬ଵ ǣߚ௉ ് Ͳ In order to show the improvement of the fit, an F-test will be used in the following.131 The corresponding F-statistic with J and n-K degrees of freedom is equal to: ሺܴଶ െ ܴோଶ ሻȀ‫ܬ‬ ̱‫ ܨ‬ሾ‫ܬ‬ǡ ݊ െ ‫ܭ‬ሿ ሺͳ െ ܴ ଶ ሻȀሺ݊ െ ‫ ܭ‬ሻ Where: •

ܴ ଶ is the unrestricted model (including price),

•

ܴோଶ is the restricted model (without the price) and

•

J is the number of variables to be excluded in the restricted regression, n is the number of observations and K is the number of estimated parameters in the unrestricted regression (including the constant).

The unrestricted regression is the following: ܵ‫ܴܣܣ‬ூ்஺ ൌ ߙூ்஺ ൅ ߚெூ்஺ ݉ܽ‫ ݐ݁݇ݎ‬൅ ߚ௉ூ்஺ ‫ ݁ܿ݅ݎ݌‬൅ ߳ூ்஺ which returns an ܴଶ ൌ ͲǤͷͶ͵Ͷ. The restricted regression is: ܵ‫ܴܣܣ‬ூ்஺ ൌ ߙூ்஺ ൅ ߚெூ்஺ ݉ܽ‫ ݐ݁݇ݎ‬൅ ߳ூ்஺ and gives an ܴோଶ ൌ ͲǤͳͻͶʹ. The resulting F-statistic is

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ሺͲǤͷͶ͵Ͷ െ ͲǤͳͻͶʹሻȀͳ ൌ ʹͷǤʹͶ̱‫ ܨ‬ሾͳǡ͵͵ሿ ሺͳ െ ͲǤͷͶ͵ͶሻȀሺ͵͸ െ ͵ሻ with a p-value of