NEWSLETTER zum BAI-WISSENSchAfTSpREIS - Home ... · rungswirtschaft an der Universität Ulm sowie als Visi- ... in der Jury des djp (Deutschen Journalisten Preis). ... Im April 2008

Wissenschaftspreis

2012

N E W S L E T T E R z u m B A I - W I S S E N S c h A f T S p R E I S

S o n d e r a u s g a b e 2 0 1 2

Christoph Frey

StrukturbrücheundGARCH-Modelleinder

VolatilitätsmodellierungvonRohstoffpreisrenditen.

Frederik Bruns

PortfolioDiversification–

Istheanswerblowinginthewind?

dr. heiko JaCoBs

LosingSightoftheTreesfortheForest?

AttentionShiftsandPairsTrading

dr. Janis BaCk

EssaysontheValuationofCommodityDerivatives

Leitartikel __________________________________________________________________ 3-4

ImpressionenderPreisvergabe ________________________________________________ 5-6

DasGremium _______________________________________________________________ 7-9

StrukturbrücheundGARCH-ModelleinderVolatilitätsmodellierungvonRohstoffpreisrenditen.vonChristophFrey_________________________________________________________10-14

PortfolioDiversification–Istheanswerblowinginthewind?vonFrederikBruns_________________________________________________________15-23

LosingSightoftheTreesfortheForest?AttentionShiftsandPairsTradingvonDr.HeikoJacobs _______________________________________________________24-27

EssaysontheValuationofCommodityDerivativesvonDr.JanisBack__________________________________________________________28-33

Impressum__________________________________________________________________ 35

2

I N h A LT S v E R z E I c h N I S

Inhaltsverzeichnis

vorzweiJahrenentschlosssichderBundesverbandAlter-

nativeInvestmentse.V.(BAI),wissenschaftlicheArbeiten

imBereichderAlternativenInvestmentszufördernund

hatdamalszudiesemZweckdenBAI-Wissenschaftspreis

insLebengerufen.

EinerderHauptgründesowiedieIntentionfürdieseFör-

derungwarenundsind,dassdasWissenüberAlternati-

veInvestmentssowohlinderBreitealsauchinderTiefe

leider immer noch sehr rudimentär ist. In weiten Teilen

derÖffentlichkeit,derPolitik,derMedienaberauchauf

Seiten der Investoren herrschen oftmals vielfach Miss-

verständnisse hinsichtlich Nutzen und Risiken von Alter-

nativeInvestments.MitdemWissenschaftspreiswillder

BAI einen Anreiz für Studenten und Wissenschaftler in

Deutschland schaffen, Forschungsarbeit in diesem für

Investoren zukünftig immer wichtigerem Bereich zu lei-

sten. Besonderen Wert wird dabei auch auf einen mög-

lichsthohenPraxisbezugderArbeitengelegt,umeinen

größtmöglichenNutzenfürinstitutionelleInvestorenzu

generieren.

VieledeutscheHochschulenerklärtensichaufAnhiebbe-

reit,denBAIbeiderBekanntmachungdesWissenschafts-

preises zu unterstützen. Daraus resultierend erreichten

denBAIzahlreicheanspruchsvolleBewerbungeninden

vier Kategorien: Dissertationen, Master-/Diplomarbei-

ten, Bachelorarbeiten und Sonstige Wissenschaftliche

Arbeiten. Für diese wurde ein Preisgeld von insgesamt

10.000EuroandieGewinnerausgelobt.

Am 13. Juni 2012 wurde nun der zweite BAI-Wissen-

schaftspreis für exzellente wissenschaftliche Arbeiten

im Bereich Alternative Investments vergeben. Die Prei-

se wurden im MesseTurm in Frankfurt von dem für das

RessortWeiterbildungzuständigeBAI-Vorstandsmitglied

RolfDreiseidlersowievomGremiumsmitgliedHerrnProf.

Dr.DenisSchweizervonderWHUandieGewinnerüber-

reicht.

In der Kategorie Dissertationen überzeugte die Arbeit

vonHerrnDr.JanisBackzumThema„Essaysonthevalu-

ationofcommodityderivatives“.InderArbeitfokussiert

derAutorsichaufdiehöchstanspruchsvolleAufgabeder

PreisfindungvonRohstoffderivaten.DiesistimVergleich

zuDerivatenaufAktiendeutlichkomplexer,dasaisonale

Komponenten, beispielsweise aufgrund der Lagerfähig-

keit von einzelnen Rohstoffen etc. zu berücksichtigen

sind. Dr. Back zeigt eindrucksvoll, wie diese Komponen-

tenindieBewertungintegriertwerdenkönnen.

Bei den Masterarbeiten setzte sich Frederik Bruns mit

dem Thema „Portfolio Diversification – Is the Answer

BlowingintheWind?“durch.Untersuchtwird,oberneu-

erbareEnergieneinengerechtfertigtenPlatzimPortfolio

von institutionellen Investoren haben. Diese Fragestel-

lung isthöchstrelevant fürdiese Industrie,dennsollten

erneuerbareEnergienausRendite-Risiko-Aspektenkeine

BerechtigungininstitutionellenPortfolioshaben,könnte

dieszukünftigeFinanzierungendieserProjekteerschwe-

ren. Herr Bruns kann, unter Verwendung eines einzigar-

tigen Datensatzes, zeigen, dass erneuerbare Energien

attraktiveInvestitionenfürinstitutionelleInvestorendar-

stellen.

SehrgeehrteDamenundHerren,

3

L E I TA R T I k E L

Leitartikel&Vorwort

In der Kategorie Bachelorarbeiten prämierte das bei al-

len Entscheidungen vom Verband unabhängige sechs-

köpfigeGremiumausWissenschaftundPraxisdieArbeit

von Christoph Frey zum Thema „Structural Breaks and

GARCHModelsofCommodityPriceVolatility“.AufBasis

dieserArbeitwerdenstrukturelleVeränderungen inder

Rohstoffrenditemodellierung mittels GARCH untersucht

und wie diese auf Volatilitäten von Rohstoffpreisen wir-

ken. Dieser Arbeit kommt besondere Bedeutung auf-

grundderPreisstellungvonRohstoffderivatensowieim

Risikomanagementzu,woeine„treffsichere“Vorhersage

vonVolatilitätenvonhoherBedeutungist.

In der vierten Kategorie Sonstige Wissenschaftliche Ar-

beitengewanndieArbeit„Loosingsightofthetreesfor

theforest?Pairstradingandattentionshifts“vonHerrn

Dr.HeikoJacobs.IndieserArbeit,dieinKo-Autorenschaft

mit Prof. Weber (Universität Mannheim) geschrieben

wurde, untersuchen die Autoren die Profitabilität einer

beliebten Hedgefondsstrategie, den sogenannten Pair

Trades. Für den zugrundeliegenden Treiber der Profi-

tabilität wird die sog. Attention Shift Hypothese heran-

gezogen. Diese geht davon aus, dass an beispielsweise

„turbulenten“ Börsentagen die Investoren mehr Zeit mit

derErfassungunddemVerstehendes„GroßenGanzen“

verbringen, als Informationen auf Unternehmensebene

zu analysieren. Genau aus dieser Vernachlässigung kön-

nenattraktivePairTradesgehandeltwerden.

Der BAI dankt allen Bewerbern und den Gremiumsmit-

gliedern, ohne deren Mithilfe die Realisierung dieses

Preisesnichtmöglichgewesenwäre,herzlich.

Zusammenfassungen der Gewinnerarbeiten, Informati-

onen zum Gremium und einige Fotos der Preisvergabe

findenSieindieserSonderausgabedesBAINewsletters.

WirmöchtenandieserStellenochdaraufhinweisen,dass

ArbeitenfürdenWissenschaftspreis2013absofortbeim

BAIeingereichtwerdenkönnen.

WirwünschendemLesereinespannendeLektüre!

DerVorstand

Ichbinerfreutzusehen,dassderBAIWissenschaftspreis

auf einem sehr guten Weg ist sich unter den angese-

henen Auszeichnungen für finanzwissenschaftliche For-

schungzuetablieren.SokonnteauchimzweitenJahrder

PreisvergabewiedereinehoheAnzahlaneingereichten

ArbeiteninallenKategorienfestgestelltwerden,dienur

knapphinterderdesletztenJahresliegt.AberdieQuanti-

tätistbekanntlichnureineMessgrößenebenderQualität

derArbeiten–unddiesehatmerklichzugenommen.Alle

prämiertenArbeitenzeichnensichnichtnurdurch inte-

ressantewissenschaftlichundgleichermaßenpraxisrele-

vanteFragestellungenaus,sondernweisenauchmetho-

discheinsehrhohesNiveauauf.

Ihr

Prof.Dr.DenisSchweizer

4

v o R W o R T

Leitartikel&Vorwort

L E I TA R T I k E L

5

I m p R E S S I o N E N d E R p R E I S v E R g A B E

Rolf Dreiseidler, Prof. Dr. Denis Schweizer und der Gewin-ner in der Kategorie Bachelorarbeiten Christoph Frey

BAI Vorstandsmitglied Rolf Dreiseidler

Gremiumsmitglied Prof. Dr. Denis Schweizer

BAI Wissenschaftspreis 2012

Rolf Dreiseidler, Prof. Dr. Denis Schweizer und der Gewin-ner der Kategorie Masterarbeiten Frederik Bruns

Rolf Dreiseidler, Prof. Dr. Denis Schweizer und der Gewin-ner der Kategorie Dissertationen Dr. Janis Back

ImpressionenderPreisvergabe

6

I m p R E S S I o N E N d E R p R E I S v E R g A B E

Rolf Dreiseidler bedankt sich bei Prof. Dr. Denis Schweizer für die Unterstützung bei der Preisvergabe

Von links nach rechts: Roland Brooks (BAI), Prof. Dr. Denis Schweizer, Dr. Janis Back; Frederik Bruns, Dr. Heiko Jacobs, Christoph Frey, Rolf Dreiseidler

Rolf Dreiseidler, Prof. Dr. Denis Schweizer und der Gewin-ner der Kategorie sonst. wissenschaftliche Arbeiten Dr. Heiko Jacobs

ImpressionenderPreisvergabe

Der Wissenschaftspreis wird vom BAI gesponsert und verliehen. Über die Gewinner entscheidet jedoch allein und unabhängig ein Gremium, welches sich aus sechs anerkannten Experten aus Wissenschaft und Praxis zu-sammensetzt.

Die Mitglieder des Gremiums sind:

prof. dr. André Betzer

uni Wuppertal

Herr UNIV.-PROF. DR. An-dréBetzeristInhaberderW3 Professur für Finanz-und Bankwirtschaft ander Bergischen Universi-tät Wuppertal. Er studier-te Volkswirtschaftslehreund promovierte an der

UniversitätBonn.AußerdemabsolvierteerdieLicenceen Economie Internationale et Monnaie et Finance ander Université de Toulouse I (Frankreich). Im Jahr 2010habilitierteersichanderUniversitätMannheim.

dajana Brodmann

head of Alternative Invest-ments & public Equity

Wpv im Lande NRW

Dajana Brodmann arbei-tet seit Januar 2012 alsAbteilungsleiterin Alter-native Investments undAktien beim Versorgungs-

werk der Wirtschaftsprüfer und der vereidigten Buch-prüferimLandeNRW(WPV).ZuihrenAufgabenschwer-punkten zählen neben der Identifikation interessanterInvestmentopportunitäten und externer Manager, dieDueDiligence,dasMonitoringsowiedieIntegrationAl-

ternativer InvestmentsundAktienstrategien indasGe-samtportfolio des WPVs. Zuvor war Dajana Brodmannüber 6 Jahre bei der Bayerischen Versorgungskammer(BVK) maßgeblich am Auf- und Ausbau des internatio-nal ausgerichteten Alternativen-Investment-Portfolios(Hedgefonds, Rohstoffe, Währungen, Private Equity,Infrastruktur,Timber)beteiligtundleitete4Jahrestell-vertretend das Alternative-Investment-Team. DajanaBrodmann ist Diplom Betriebswirtin und Chartered Al-ternativeInvestmentAnalyst(CAIA).

prof. dr. martin Eling

universität St. gallen

Prof. Dr. Martin Eling istDirektor des Instituts fürVersicherungswirtschaftund Professor für Versi-cherungsmanagementander Universität St. Gallen(Schweiz). Zuvor war erDirektor des Instituts für

Versicherungswissenschaft und Professor für Versiche-rungswirtschaft an der Universität Ulm sowie als Visi-ting Professor an der University of Wisconsin-Madison(USA) tätig.ErhatzuFragenderPerformancemessungunddesRisikomanagementinführendenwissenschaft-lichen Zeitschriften (etwa Journal of Banking and Fi-nance,JournalofRiskandInsurance,FinancialAnalystsJournal) publiziert. Seine Promotionsschrift "Hedge-fonds-Strategien und ihre Performance im Asset Ma-nagementvonFinanzdienstleistungsunternehmen"(Dr.rer.pol.,UniversitätMünster)wurdemitdemAcatis-Va-lue-Preis 2006 ausgezeichnet. Er berät zahlreiche Insti-tutionen der Finanzdienstleistungsbranche im In- undAusland.

7

g R E m I u m

Gremium

dr. Lars Jaeger

chief Executive officer

Alternative Beta partners Ag

LarsJaegeristGründerundChief Executive Officer derAlternative Beta PartnersAG in Zug. Davor war erseitJanuar2002PartnerderPartners Group AG, wo er

dasHedgeFonds-undAlternativeBetaGeschäftaufgebauthat. Nach seinem Studium der Physik und Philosophie anderUniversitätBonnundderEcolePolytechniqueinParispromovierte Lars Jaeger 1997 am Max-Planck-Institut fürPhysik komplexer Systeme in Dresden im Bereich Theo-retische Physik (Nichtlineare Dynamik/Chaostheorie), woeranschliessendauchalsPost-DoktorandaufdemGebietnichtlinearer Dynamik tätig war. Seine Berufskarriere be-ganneralsWissen-schaftlerbeiderOlsen&AssociatesAGinZürich,woersichmitderökonometrischenundmathe-matischen Modellierung von Finanzmärkten beschäftigte.Nach zwei Jahren wechselte er zur Credit Suisse AssetManagement als Verantwortlicher für das Risikomanage-ment und die quantitative Hedge-Fonds Analyse in denBereichnichttraditionellerAnlagen.ImJuli2000gründeteer mit Partnern die saisGroup AG, eine auf alternative An-lagestrategien spe-zialisierte Investmentgesellschaft, diesichimDezember2001derPartnersGroupanschloss.LarsJaeger ist „Chartered Financial Analyst“ (CFA) und zertifi-zierter„FinancialRiskManager“(FRM).EristAutordervierBücher„RiskManagementofAlternativeInvestmentStrate-gies”(FinancialTimes/PrenticeHall),„TheNewGenerationof Risk Management for Hedge Funds and Private Equi-ty“(2003),“ThroughtheAlphaSmokescreens–Aguidetohedge fund return sources” (2005), „Alternative Beta Stra-tegiesandHedgeFundReplication”(2008),sowieVerfasserverschiedenerwissenschaftlicherArtikelundregelmässigerSprecheraufdiversenFachtagungen.

dr. katharina Lichtner,

managing director

capital dynamics

Dr. Katharina Lichtner istManaging Director, Co-Head des Investment-Managment-Teams undleitet die Researchabtei-lung bei Capital Dyna-

mics. Frau Dr. Lichtner war verantwortlich für die Ent-wicklung und Einführung der Investitionsprozesse beiCapitalDynamics.SieistMitglieddesVerwaltungsratesunddesExecutiveKomiteesvonCapitalDynamics.FrauDr. Lichtner ist im Vorstand der IPEV (International Pri-vate Equity and Venture Capital Valuation Guidelines),wosienebenanderendieEVCA(EuropeanPrivateEqui-tyandVentureCapitalAssociation)vertritt.Ausserdemist sie Mitglied des Editorial Board von „The Review ofPrivate Equity“, das von PEI Media publiziert wird undin der Jury des djp (Deutschen Journalisten Preis). Vorihrer Tätigkeit bei Capital Dynamics war Frau Dr. Licht-nerBeraterinbeiMcKinsey&Company.FrauDr.Lichtnerpromovierte in ImmunologieundhälteinenMasterofScience in Molekularbiologie und Biochemie vom Bio-centerBasel.

8

g R E m I u m

Gremium

prof. dr. denis Schweizer

Whu otto Beisheim School of management

Prof. Dr. Denis Schweizerstudierte Betriebswirt-schaftslehre an der Jo-hann Wolfgang Goethe-Universität in Frankfurtam Main. Im Anschlusspromovierte er am Stif-

tungslehrstuhl für Asset Management von ProfessorLutzJohanninganderEuropeanBusinessSchool(EBS)inOestrich-WinkelzumThemaAlternativeInvestments.Im April 2008 schloss er seine Promotion mit dem Dis-sertationsthema"SelectedEssaysonAlternativeInvest-ments"ab.

WährenddieserZeitarbeiteteeralswissenschaftlicherAssistentamPFIPrivateFinanceInstitute/EBSFinanza-kademieinOestrich-WinkelundverantwortetedieKon-zeption von Executive Education Programmen. Weiter-hinkonnteer indieserZeitLehrerfahrungensammeln,da er regelmäßig Schulungen in der Executive Educa-tion leitete. Er erhielt die Auszeichnung zum FinancialRisk Manager (FRM) und Certified Financial Planner(CFP).

Im August 2008 wurde Denis Schweizer auf die Juni-orprofessur für Alternative Investments an der WHU –Otto Beisheim School of Management berufen. DenisSchweizer publizierte zahlreiche Artikel zum Themen-gebiet der Alternativen Investments in renommiertenFachzeitschriftenundBüchern.VonSeptember2011bisJanuar2012warDenisSchweizerVisitingScholaranderNewYorkUniversity,USA.

Jurymitglieder, die in ihrer beruflichen Praxis bzw.wissenschaftlichen Tätigkeit in Bezug auf eine ein-gereichte wissenschaftliche Arbeit in Kontakt mitdemAutorstanden,warenvonderBewertungdie-serArbeitausgeschlossen.

9

g R E m I u m

Gremium

Einführung

Rohstoffe unterliegen zwei entscheidenden Preisbil-dungsprozessen. Zum einen bestimmen Angebot undNachfrage auf internationalen Handelsmärkten denWert der Rohstoffe. Jüngste Beispiele hierfür sind fal-lende Preise für Mais und Weizen in den VereinigtenStaaten oder steigende Kosten für Metalle verursachtdurcheinehöhereNachfrageinderchinesischenWirt-schaft.AufderanderenSeitehabenRohstoffindizeseinrasantes Wachstum erlebt, das vor allem durch Inve-stitionen von institutionellen Anlegern seit dem EndedesBörsencrashsumdasJahr2000verursachtwordenist.1InvestorensuchenhiereinenDiversifikationseffekt,daRohstoffegewöhnlicheinegeringeodersogareinenegativeKorrelationmitAktienaufweisen.

In der Bachelorarbeit wird die Volatilität bzw. Varianzvon Rohstoffpreisrenditen untersucht. Dabei wird derFrage nachgegangen, inwiefern dynamische AspektewiestrukturelleVeränderungenundBrücheinderRen-ditenmodellierungberücksichtigtwerdenkönnen.

Rohstoffpreise besitzen einen hohen realwirtschaft-lichen Wert. Plötzliche Preisfluktuationen könnenschwere Krisen auf internationalen Handelsmärktenverursachen und haben großen Einfluss auf das Ein-kommen der Produzenten.2 Die Bedeutung der Unter-suchung liegt deshalb in der robusten Modellierungund Vorhersage der zeitveränderlichen Volatilität vonRohstoffpreisen mithilfe der Generalized Autoregres-sive Conditional Heteroskedastic (GARCH) Modelle imHinblickaufstrukturelleBrüche.DesWeiterenistdiesekonsistenteSchätzungderVolatilitätvorallembeiderWertbestimmung von Derivaten und Portfolios sowieimRisikomanagementvonInteresse.

1 Vgl.TangundXiong(2010)

2 Vgl.KorenundTenreyro(2007)

TypischeRenditezeitreihenvonFinanzmärktenweisenoftEigenschaftenauf,diebeiderMethodederkleinstenQuadrate eine sinnvolle Parameterschätzung nichtmöglichmachenunddiederAnnahmederNormalver-teilung widersprechen. Dies gilt ebenso für Renditenvon Rohstoffpreisen. GARCH-Modelle haben den Vor-teil,dietypischenEigenschaftenfinanziellerZeitreihenabbildenzukönnen,diesichvorallemdurcheinezeit-veränderlicheVolatilität (Volatilitätsclustern) und eineleptokurtische Verteilung der Renditen auszeichnen.Neben dem berühmten Leverageeffekt, der empirischnachgewiesen werden kann, existiert bei Rohstoffendarüber hinaus ein Inventory-Effekt, der besagt, dassdieVolatilität mit dem Preis steigt. Dieser kann durchdie Anwendung asymmetrischer GARCH-Modelle wiedem exponentiellen GARCH-Modell (EGARCH) berück-sichtigtwerden.

DieArbeitnutzttäglicheZeitreihendatenvonThomsonReuters® Data Stream. Der Schwerpunkt liegt auf dentäglichen Log-Renditen zehn verschiedener Rohstoffeaus unterschiedlichen Bereichen: Weizen, Mais undKaffee(Landwirtschaft);Baumwolle(Fasern);Rohöl(En-ergie) sowie Gold, Silber, Zink, Kupfer und Aluminium(Metalle).FürjedenRohstoffwerdendreiverschiedeneSerieninBetrachtgezogen:dieSpot-PreiseinUS-Dollar,derS&P500GoldmanSachsCommoditySpot-IndexundderMerrillLynchCommodityeXtra(MLCX)Spot-Index.

10

von Christoph Frey

Christoph Frey

STRuk TuRBRüchE uNd gARch-modELLE IN dER voL ATILITäTSmodELLIERuNg voN RohSToffpREISRENdITEN.

k ATEgoRIE: BAchELoR ARBEITEN

StrukturbrücheundGARCH-ModelleinderVolatilitätsmodellierungvonRohstoffpreisrenditen

DerZeitraumderUntersuchungerstrecktsichvom1. Ja-nuar1991biszum1. Januar2011.Diesergibtmehrals5200täglicheBeobachtungenfürjedeZeitreihe.

Die Idee der GARCH-Modelle ist es, die aktuelle Vari-anzeinerZeitreihezumZeitpunkttbedingtaufvorhe-rigen Beobachtungen der Varianz und unabhängigenquadriertenSchockszumodellieren.DabeiwirdinderRegel davon ausgegangen, dass die Daten von einemstabilen Prozess generiert wurden und somit Parame-terschätzungen für ein Modell im gesamten Beobach-tungszeitraum stabil sind. Dies ist eine sehr kritischeAnnahme,daFinanzmärktehäufigeralsstatistischbe-gründbar von Krisen und Schocks getroffen werden.WieinHillebrand(2005)gezeigtwird,führtdasIgnorie-renvonstrukturellenVeränderungenbeiderSchätzungvonGARCH-ModellenzuhoherunechterPersistenzunddieSummeallerautoregressivenParameter imModellkonvergiert zu eins. Dies entspricht allerdings geradeeiner konstanten Varianz im Prozess. Das einfachsteundstärksteModellistdasGARCH(1,1)-Modellmitfol-gendermathematischerDefinition:

Hier ist σt|t-12 die konditionale Varianz (=Volatilität)zumZeitpunkttbedingtaufderInformationzumZeit-punkt t-1 und εt-12 ist ein unabhängiger Schock, derhier durch rt-12, der logarithmierten Tagesrendite,substituiertwird.DiesesStandard-GARCH-Modellwirddadurch eingeschränkt, dass positive und negativeSchocks den gleichen Einfluss haben (durch das Qua-drieren)undweitereParametereinschränkungennötigsind,damitdiePositivitätderkonditionalenVarianzge-währleistetwerdenkann.

Dies Nachteile werden zum Beispiel vom ExponentialGeneralized AutoRegressiv Heteroskedastic (EGARCH)Modell von Nelson (1991) vermieden. In seiner ein-fachstenFormalsEGARCH(1,1)istesgegebendurch

HierwirdalsodielogarithmierteVarianzmodelliertundgleichzeitigwerdendieSchocksεt-1nichtquadriert.So

könnenauchasymmetrischeEffektewiederLeverage-effektnachgeprüftwerden.

Um eine sinnvolle Schätzung der Volatilität durchzu-führen, ist es notwenig, strukturelle Brüche zu iden-tifizieren und diese zu berücksichtigen. Da weder dieGröße noch das Datum zukünftiger Brüche heute be-kannt sind, ist es darüber hinaus von Bedeutung, Vo-latilitätsmodellezuverwenden,die Informationenausverschiedenen Perioden verarbeiten und die Möglich-keit eines strukturellen Wandels berücksichtigen. EsgehthierdeshalbumdreiwesentlicheFragen.Erstens,welcheTestssindinderLage,StrukturbrüchebeiRoh-stoffpreisenzuerkennen?Zweitens,wieverändernsichdie Parameterschätzungen der GARCH-Modelle zwi-schen einzelnen Strukturbrüchen? Und drittens, wel-cheGARCH-ModelleproduzierendiekleinstenVorher-sagefehlerfürdieVolatilität?

Schätzen von GARCH-Modellen

Zunächst wird eine Definition des Begriffs strukturellerBruch im Kontext der Zeitreihenanalyse benötigt. In derökonomischenTheorieisteinStrukturbrucheinbesondersschnellerWandel inderWirtschaftsstruktureinesLandesodereinerRegion.EinBeispielhierfüristderZusammen-bruchderSowjetunionunddieplötzlicheEinführungderfreien Marktwirtschaft in Osteuropa. Der Strukturwandelselbsterfolgt inderRegelübereinen längerenZeitraumund beschreibt unter anderem die Veränderung des Ar-beitsmarktesundderindustriellenZusammensetzungei-nerVolkswirtschaft.HierwirdjedocheineehertechnischeDefinitiondesBegriffsbenötigt:

Ein Strukturbruch ist eine permanente Verschiebung derRegressionsparameter eines Zeitreihenmodells zum Zeit-punkt t. Der Zeitpunkt t wird auch als Änderungspunktbezeichnet und ist im Allgemeinen für eine bestimmteZeitreihevonDatennichtbekannt.

DerersteTeilderArbeituntersuchtdieAuswirkungenstruk-turellerBrücheaufdieunbedingteVarianzunddamitindirektauf die Parameterschätzungen von GARCH-Modellen. Diesfolgtintuitiv,daeinStrukturbruchinderunbedingtenVari-anzeinesProzesseseinenBruchimautoregressivenProzessder konditionalen Varianz verursacht.3 Dafür wird zunächstnach strukturellen Brüchen gesucht. Es zeigt sich, dass die

3 Vgl.RapachandStrauss(2008)

Untersuchung erstreckt sich vom 1. Januar 1991 bis zum 1. Januar 2011. Dies ergibt mehr als 5200 tägliche Beobachtungen für jede Zeitreihe.

Die Idee der GARCH-Modelle ist es, die aktuelle Varianz einer Zeitreihe zum Zeitpunkt t bedingt auf vorherigen Beobachtungen der Varianz und unabhängigen quadrierten Schocks zu modellieren. Dabei wird in der Regel davon ausgegangen, dass die Daten von einem stabilen Prozess generiert wurden und somit Parameterschätzungen für ein Modell im gesamten Beobachtungszeitraum stabil sind. Dies ist eine sehr kritische Annahme, da Finanzmärkte häufiger als statistisch begründbar von Krisen und Schocks getroffen werden. Wie in Hillebrand (2005) gezeigt wird, führt das Ignorieren von strukturellen Veränderungen bei der Schätzung von GARCH-Modellen zu hoher unechter Persistenz und die Summe aller autoregressiven Parameter im Modell konvergiert zu eins. Dies entspricht allerdings gerade einer konstanten Varianz im Prozess. Das einfachste und stärkste Modell ist das GARCH (1,1)-Modell mit folgender mathematischer Definition:

𝜎𝜎𝑡𝑡|𝑡𝑡−12 = 𝛼𝛼0 + 𝛼𝛼1𝜀𝜀𝑡𝑡−12 + 𝛽𝛽1𝜎𝜎𝑡𝑡−1|𝑡𝑡−2

2

Hier ist 𝜎𝜎𝑡𝑡|𝑡𝑡−12 die konditionale Varianz (=Volatilität) zum Zeitpunkt t bedingt auf der Information zum

Zeitpunkt t-1 und 𝜀𝜀𝑡𝑡−12 ist ein unabhängiger Schock, der hier durch 𝑟𝑟𝑡𝑡−12 , der logarithmierten Tagesrendite, substituiert wird. Dieses Standard-GARCH-Modell wird dadurch eingeschränkt, dasspositive und negative Schocks den gleichen Einfluss haben (durch das Quadrieren) und weitere Parametereinschränkungen nötig sind, damit die Positivität der konditionalen Varianz gewährleistet werden kann.

Dies Nachteile werden zum Beispiel vom Exponential Generalized AutoRegressiv Heteroskedastic (EGARCH) Modell von Nelson (1991) vermieden. In seiner einfachsten Form als EGARCH (1,1) ist es gegeben durch

ln�𝜎𝜎𝑡𝑡|𝑡𝑡−12 � = 𝛼𝛼0 + 𝛼𝛼1

𝜀𝜀𝑡𝑡−1

�𝜎𝜎𝑡𝑡−1|𝑡𝑡−22

+ 𝛾𝛾1 ��𝜀𝜀𝑡𝑡−1


� + 𝐸𝐸 � 𝜀𝜀𝑡𝑡−1


�� + 𝛽𝛽1ln (𝜎𝜎𝑡𝑡−1|𝑡𝑡−22 ).

Hier wird also die logarithmierte Varianz modelliert und gleichzeitig werden die Schocks εt−1 nicht quadriert. So können auch asymmetrische Effekte wie der Leverageeffekt nachgeprüft werden.

Um eine sinnvolle Schätzung der Volatilität durchzuführen, ist es notwenig, strukturelle Brüche zu identifizieren und diese zu berücksichtigen. Da weder die Größe noch das Datum zukünftiger Brüche heute bekannt sind, ist es darüber hinaus von Bedeutung, Volatilitätsmodelle zu verwenden, dieInformationen aus verschiedenen Perioden verarbeiten und die Möglichkeit eines strukturellen Wandels berücksichtigen. Es geht hier deshalb um drei wesentliche Fragen. Erstens, welche Tests sind in der Lage, Strukturbrüche bei Rohstoffpreisen zu erkennen? Zweitens, wie verändern sich die Parameterschätzungen der GARCH-Modelle zwischen einzelnen Strukturbrüchen? Und drittens, welche GARCH-Modelle produzieren die kleinsten Vorhersagefehler für die Volatilität?

Untersuchung erstreckt sich vom 1. Januar 1991 bis zum 1. Januar 2011. Dies ergibt mehr als 5200 tägliche Beobachtungen für jede Zeitreihe.

Die Idee der GARCH-Modelle ist es, die aktuelle Varianz einer Zeitreihe zum Zeitpunkt t bedingt auf vorherigen Beobachtungen der Varianz und unabhängigen quadrierten Schocks zu modellieren. Dabei wird in der Regel davon ausgegangen, dass die Daten von einem stabilen Prozess generiert wurden und somit Parameterschätzungen für ein Modell im gesamten Beobachtungszeitraum stabil sind. Dies ist eine sehr kritische Annahme, da Finanzmärkte häufiger als statistisch begründbar von Krisen und Schocks getroffen werden. Wie in Hillebrand (2005) gezeigt wird, führt das Ignorieren von strukturellen Veränderungen bei der Schätzung von GARCH-Modellen zu hoher unechter Persistenz und die Summe aller autoregressiven Parameter im Modell konvergiert zu eins. Dies entspricht allerdings gerade einer konstanten Varianz im Prozess. Das einfachste und stärkste Modell ist das GARCH (1,1)-Modell mit folgender mathematischer Definition:

𝜎𝜎𝑡𝑡|𝑡𝑡−12 = 𝛼𝛼0 + 𝛼𝛼1𝜀𝜀𝑡𝑡−12 + 𝛽𝛽1𝜎𝜎𝑡𝑡−1|𝑡𝑡−2

2

Hier ist 𝜎𝜎𝑡𝑡|𝑡𝑡−12 die konditionale Varianz (=Volatilität) zum Zeitpunkt t bedingt auf der Information zum

Zeitpunkt t-1 und 𝜀𝜀𝑡𝑡−12 ist ein unabhängiger Schock, der hier durch 𝑟𝑟𝑡𝑡−12 , der logarithmierten Tagesrendite, substituiert wird. Dieses Standard-GARCH-Modell wird dadurch eingeschränkt, dasspositive und negative Schocks den gleichen Einfluss haben (durch das Quadrieren) und weitere Parametereinschränkungen nötig sind, damit die Positivität der konditionalen Varianz gewährleistet werden kann.

Dies Nachteile werden zum Beispiel vom Exponential Generalized AutoRegressiv Heteroskedastic (EGARCH) Modell von Nelson (1991) vermieden. In seiner einfachsten Form als EGARCH (1,1) ist es gegeben durch

ln�𝜎𝜎𝑡𝑡|𝑡𝑡−12 � = 𝛼𝛼0 + 𝛼𝛼1

𝜀𝜀𝑡𝑡−1


+ 𝛾𝛾1 ��𝜀𝜀𝑡𝑡−1


� + 𝐸𝐸 � 𝜀𝜀𝑡𝑡−1


�� + 𝛽𝛽1ln (𝜎𝜎𝑡𝑡−1|𝑡𝑡−22 ).

Hier wird also die logarithmierte Varianz modelliert und gleichzeitig werden die Schocks εt−1 nicht quadriert. So können auch asymmetrische Effekte wie der Leverageeffekt nachgeprüft werden.

Um eine sinnvolle Schätzung der Volatilität durchzuführen, ist es notwenig, strukturelle Brüche zu identifizieren und diese zu berücksichtigen. Da weder die Größe noch das Datum zukünftiger Brüche heute bekannt sind, ist es darüber hinaus von Bedeutung, Volatilitätsmodelle zu verwenden, dieInformationen aus verschiedenen Perioden verarbeiten und die Möglichkeit eines strukturellen Wandels berücksichtigen. Es geht hier deshalb um drei wesentliche Fragen. Erstens, welche Tests sind in der Lage, Strukturbrüche bei Rohstoffpreisen zu erkennen? Zweitens, wie verändern sich die Parameterschätzungen der GARCH-Modelle zwischen einzelnen Strukturbrüchen? Und drittens, welche GARCH-Modelle produzieren die kleinsten Vorhersagefehler für die Volatilität?

11StrukturbrücheundGARCH-ModelleinderVolatilitätsmodellierungvonRohstoffpreisrenditen

verwendeten Cumulative Sum (CUSUM) Tests mehrdeutigeErgebnisseimBezugaufdieAnzahlunddieZeitpunktederStrukturbrüche liefern. Diese Tests berechnen eine kumu-lierteSummeüberdieQuadratederRenditenundstandardi-sierendannüberdenrelativenBezugspunktinderBeobach-tungsperiode.DasMaximumderTeststatistik,diezujedemZeitpunkt der Daten berechnet wird, wird dann als Punktinterpretiert,andemeinestrukturelleVeränderungstattge-fundenhat.DieCUSUM-Testssindsokonstruiert,einenein-zigenStrukturbruchineinerDatenreihezufinden.Ummeh-rereBrüchezufinden,schlagen InclánundTiao (1994)denIterativeCumulativeSumofSquare (ICSS)vor,beidem ite-rativnachmehrerenBrüchengesuchtwird.DieseMethodefindethierAnwendung.EswerdenvierverschiedeneArtendieserTestsuntersuchtundeszeigtsich,dasseinzigdiean-gepassteInclán-Tiao-StatistikdasIdentifizierenzuvielerBrü-che inkurzenZeitabständennacheinandervermeidet.DieswirdbesondersinderfolgendenGrafikderBaumwollzeitrei-hedeutlich,diestellvertretendfürdieandernZeitreihenundRohstoffeangesehenwerdenkann.HierbeiwurdendievierCUSUM-Tests durchgeführt und die identifizierten Struk-turbrüche durch die Standardabweichungen im jeweiligenRegimezwischenzweiBrüchengekennzeichnet.Mansieht,dassderTestvonInclan-Tiao(1994)(1.Zeitreihevonoben)zuvieleBrüche inkurzenZeitintervallen identifiziertunddassdie angepasste Inclán-Tiao-Statistik von Sansó et al. (2004)(2. Zeitreihe von oben) deutlich weniger Brüche ausweist.DiedritteZeitreihezeigtdieErgebnissedesKokoszka-LeipusTests (1999), der ebenfalls konsistente Ergebenisse für alleRohstoffe liefert. Inder letzenundviertenAbbildungsiehtman,dassderTestvonLeeetal.(2003),deraufdenFehlernderGARCH-Modellebasiert,keinenStrukturbruchfeststellt.DieshängtmitderPowerdesTestszusammen,dahierdieNullhypotheseeinesStrukturbruchszuoftverworfenwird.

EinHauptergebnisderUntersuchungfürRohstoffrenditenbestehtdarin,dassdieverschiedenenCUSUM-Testskaumdie gleichen Zeitpunkte eines Strukturbruchs erkennen.Esleitetsichdanachab,dassdieex-postaleInterpretationsehrschwierigist.InderUntersuchungwerdenmöglicheökonomische Gründe wie besondere Handelsereignisseetc. für Brüche in einer bestimmten Zeitreihe genannt.Darüber hinaus ist das Timing der Brüche bei allen un-tersuchten Rohstoffen unterschiedlich. Es könnten alsoberechtigte Zweifel an einem Diversifikationseffekt fürInvestorenbestehen,dersichineinemallgemeinenRoh-stoff-Portfolioergebenwürde.

ImnächstenSchrittwirdgezeigt,dassdasstatischeSchät-zenderGARCH-ModelleaufdergesamtenBeobachtungs-periodedurchdas IgnorierenvonStrukturbrüchenzuei-ner hohen Persistenz im Modell führt. Diese kann durchdieEinführungvonDummy-Variablen,diebeimAuftreteneines Bruchs den Wert eins haben, und durch die Schät-zung der GARCH-Modelle auf den einzelnen Teilinterval-lenzwischenzweiBrüchensowiedurchdieAnwendungvon EGARCH-Modellen reduziert werden. Die stark un-terschiedlichen Parameterschätzungen zwischen zweiBrüchen für ein Modell bewiesen, dass hier unterschied-liche Eigenschaften der Zeitreihen vorherrschen. Es zei-gensichaußerdemasymmetrischeEffekteabhängigvomVorzeichenfrühererSchocksinderbedingtenVarianzderGARCH-Modelle.DieParameterschätzungenfürdieunter-schiedlichen EGARCH Modelle sind ebenfalls signifikant,allerdingssindsieimAllgemeinenkleineralsfürdiesym-metrischen GARCH-Modelle. Während die Existenz desInventory-Effekts indes nicht für alle Rohstoffe bestätigtwerden kann, wird ein Leverageeffekt für alle Zeitreihennachgewiesen.

Volatilitätsvorhersage unter strukturellen Brüchen

ImzweitenTeilderArbeitstehtdieVorhersagequalitätver-schiedenerGARCH-ModelleimFokus.HierbeiwerdendreiBenchmark-Modelle, die die Möglichkeit struktureller Brü-che ignorieren, und sechs konkurrierende GARCH-Spezifi-kationen,dieBrücheaufunterschiedlicheArtenberücksich-tigen, definiert. Dabei wird der Beobachtungszeitraum inzweiPeriodenunterteilt,ineineSchätz-undeineVorhersa-geperiode.DiePrognosehorizontewerdenauf1,20,60und120Tagefestgesetzt.DieFrageisthier,obdieModelle,diedieMöglichkeitvonstrukturellenBrüchenberücksichtigen,niedrigere Prognosefehler erzeugen als die Benchmark-Modelle. Dies sind das GARCH(1,1) und das EGARCH(1,1)-Abbildung 1 - Baumwolle Series - Log-Returns mit 3 Standardabwei-

chungen,1991-2011


ModellmiteinemexpandierendenSchätzfenster,beidemjede im h-ten Schritt gemachte Volatilitätsvorhersage fürdiePrognoseim(h+1)-stenSchrittverwendetwird.Dasletz-te Benchmark-Modell ist der von J. P. Morgan entwickelteRiskMetrics™-Ansatz. Die sechs konkurrierenden Modellesind zum einen ein Moving-Average-Modell, bei dem dieaktuelleVarianzdurchdenarithmetischenDurchschnittderletzten 250 Handelstage geschätzt wird, sowie verschie-deneGARCH(1,1)undEGARCH(1,1)Konfigurationen,diemiteinem gleitenden Schätzfenster definiert werden. DabeiwirddieHälftebzw.einViertelderLängederSchätzperio-degewähltunditerativnachjederVolatilitätsschätzungderersteWertdesFenstersdurchdenletzengeschätztenWertersetzt.DieseModelleberücksichtigenBrücheindirektda-durch, dass die Schätzfenster mitgenommen werden undsonurdieaktuellstenObservationengenutztwerden.Dasletzte Modell ist wiederum ein GARCH(1,1), dass diesmalabernurmitdenBeobachtungenseitdemletztenStruktur-

bruchgeschätztwird.EinProblemergibtsichhier,wennderletzteBruchsehrspätinderSchätzperiodeaufgetretenistunddementsprechendnurwenigeBeobachtungenfürdieParameterschätzungen vorhanden sind. Die Auswertungder Vorhersagequalität wird mithilfe sogenannter Loss-Functions (Fehlerfunktionen) durchgeführt. Je geringerderVorhersagefehlerist,dasheißtjegeringerdieDifferenzzwischenwahremundgeschätztemWertist,destobesserist das Modell. Da die Volatilität eine latente Variable undfürdenAnlegernichtzubeobachtenist,wirdhierdiequa-drierteRenditealsProxybenutzt.Eswirdgezeigt,dassmit-hilfe der konkurrierenden Modelle geringere Vorhersage-fehler gemacht werden als mit den Benchmark-Modellen.Allerdings variiert die bevorzugte Modellspezifikation jenachbetrachtetemRohstoff,Prognosehorizontundspezi-fizierter Verlustfunktion. Die EGARCH-Modelle bilden hierkeineAusnahme.DiefolgendeTabellefasstdieErgebnissezusammen:

Tabelle1-ZusammenfassungFehlerfunktionimVerhältniszumGARCH(1,1)-ModellModel #best Mittelwert Median SA Max Min

A.MSFEFehlerfunktion

GARCH(1,1)exp.Fenster 4

EGARCH(1,1)exp.Fenster 5 1.000 1.044 0.399 1.971 0.098

RiskMetrics 4 0.942 0.999 0.305 1.545 0.129

GARCH(1,1)0.5gl.Fenster 7 0.956 1.005 0.144 1.367 0.695

EGARCH(1,1)0.5gl.Fenster 11 0.926 0.968 0.322 1.525 0.125

GARCH(1,1)0.25gl.Fenster 2 0.941 1.011 0.113 1.353 0.818


GARCH(1,1)m.Brüchen 3 0.991 1.043 0.274 1.902 0.796

MovingAverage 1 1.017 1.023 0.337 1.733 0.143

Model #best Mittelwert Median SA Max Min#

B.QLIKEFehlerfunktion



RiskMetrics 6 1.089 1.017 0.258 1.735 0.610

GARCH(1,1)0.5gl.Fenster 3 0.999 1.010 0.088 c 0.705


GARCH(1,1)0.25gl.Fenster 5 0.975 1.050 0.078 1.176 0.830


GARCH(1,1)m.Brüchen 3 1.060 1.078 0.118 1.282 0.832

MovingAverage 0 1.222 1.152 0.306 1.935 0.613

Model #best Mittelwert Median SA Max Min

C.MVaRFehlerfunktion



RiskMetrics 1 1.071 1.05 0.095 1.323 0.88

GARCH(1,1)0.5gl.Fenster 3 0.979 1.002 0.011 1.026 0.98


GARCH(1,1)0.25gl.Fenster 6 0.956 1.004 0.02 1.048 0.976


GARCH(1,1)m.Brüchen 5 0.989 0.995 0.043 1.141 0.926

MovingAverage 12 0.994 0.997 0.081 1.201 0.827


Referenzen:

Bollerslev,T.(1986):“GeneralizedAutoregressiveConditionalHete-roskedasticity,”JournalofEconometrics,31,307–327.

Engle, R. (1982): “Autoregressive Conditional HeteroskedasticitywithEstimatesoftheVarianceofUnitedKingdomInflation,”Eco-nometrica:JournaloftheEconometricSociety,50,987–1007.

Hansen,P.(2005):“ATestforSuperiorPredictiveAbility,”JournalofBusinessandEconomicStatistics,23,365–380.

Hillebrand, E. (2005): “Neglecting Parameter Changes in GARCHModels,”JournalofEconometrics,129,121–138.

Inclan,C.andG.Tiao(1994):“UseofCumulativeSumsofSquaresforRetrospectiveDetectionofChangesofVariance,”JournaloftheAmericanStatisticalAssociation,913–923.

Kokoszka,P.andR.Leipus(1999):“TestingforParameterChangesinARCHModels,”LithuanianMathematicalJournal,39,182–195.

Lee,S.,Y.Tokutsu,andK.Maekawa(2003): “TheResidualCusumTestfortheConstancyofParametersinGARCH(1,1)Models,”Sub-mittedforpublication.

Nelson,D.(1991):“ConditionalHeteroskedasticityinAssetReturns:ANewApproach,”Econometrica:JournaloftheEconometricSoci-ety,59,347–370.

Rapach,D.andJ.Strauss(2008):“StructuralBreaksandGARCHMo-delsofExchangeRateVolatility,”JournalofAppliedEconometrics,23,65–90.

Sansó, A., V. Aragó, and J. Carrion-i Silvestre (2004): “Testing forChanges intheUnconditionalVarianceofFinancialTimeSeries,”RevistadeEconomíaFinanciera,32–53.

Anmerkung:Die Einträge hier sind berechnet für alle vier Prognoseho-rizonte, also für s=1, s=20, s=60 und s=120. "#best" zeigt an, wie oft das Modell den geringsten Prognosefehler er-zeugt hat. SA steht für Standardabweichung.

InTabelle1 istzusehen,dassdasModellmitdemge-ringstenmittlerenPrognosefehlerfürdiedreiverschie-denen Fehlerfunktionen jeweils unterschiedlich ist.Hierbei ist zu beachten, dass in der Tabelle alle Wer-te als Quotient zum GARCH(1,1) mit expandierendenSchätzfenster eingetragen sind. Ein Wert größer alseins bedeutet damit, dass das jeweilige Modell einengrößeren Schätzfehler produziert hat. Es ist deutlichzuerkennen,dassdiekonkurrierendenModelleoftei-nen geringen Schätzfehler produzieren. Dies gilt vorallemauchfürdieEGARCHSpezifikationen,dieoftdasbeste Modell darstellen. In zahlreichen Fällen ist derdurchschnittliche Prognosefehler sowie dessen Medi-an für die konkurrierenden Modelle kleiner als für dieBenchmarks. Allerdings sind diese Ergebnisse nichtso klar wie erwartet. Die Unterschiede zwischen denverschiedenen Fehlerfunktionen zeigen eindrucksvoll,dassdieseebenfallsnurZufallsvariablenundabhängigvonderDatenlagesind.Esbleibtfestzustellen,dassdaspräferierte GARCH-Prognosemodell für die Volatilitätvom Rohstoff, dem Zeithorizont und der Fehlerfunkti-on für die Auswertung abhängt. Die Anwendung vonklassischenundgetrimmtenMittelwertkombinationen

über die konkurrierenden Modelle konnte hingegenden Vorhersagefehler signifikant reduzieren. Schließ-lich konnte mit Hilfe des Superior Predictive Ability(SPA) Tests von Hansen (2005) nachgewiesen werden,dassdiekonkurrierendenModellezumindestimmittle-renPrognosefehlernichtschlechteralsdieBenchmark-Modellesind.

Esbleibtoffen,obkompliziertereGARCH-Modelle,beidenen die ökonomische Interpretation der Parameterschwieriger ist,genauereVolatilitätsprognosenprodu-zierenoderwiedieoptimaleFenstergrößebeiderPro-gnosemitGARCH-Modellenzuwählenist.

Kontakt

ChristophFreyTelefon:017696125399E-Mail:[email protected]


mailto:christoph.frey%40gmail.com?subject=

Introduction

Overthelasttenyears,RenewableEnergyhasbeenthefa-stestgrowing industrysegment in theenergysector, rea-chingaglobal investmentvolumeof$211billion in2010.1Conventional wisdom would suggest that the main inve-stors in Renewable Energies belong to the utility sector.However, more than half of the wind farms in Europe, forinstance,arecurrentlyownedbyfinancialinvestors.2Alargegroupof these investorsareeitherpensionfundsor insu-rancecompanies.Theyinvestintothisnewassetclassduetoseveralattractivecharacteristicssuchasstablecashflowsandindependencefromcapitalmarkets.

As institutional investors get more and more attracted toRenewableEnergies,theyalsotrytofindouthowthesein-vestmentsgenerallyfit intotherestoftheirportfolio.TheobjectiveofthisthesisistoapplythemainconceptsfromModern Portfolio Theory (MPT) as of Markowitz (1952) toRenewable Energy investments and thereby discuss theirpotential role inan institutional investor’sportfolio.Therearemainlytwoareasofinterest.Thefirstareaexploresdi-versificationpossibilitieswithintheassetclassRenewablesitself.Secondly,thequestionofhowaninvestorcandiver-sifyawayriskwhenaddingwindandsolarparkstoanexi-stingportfoliowillbeaddressed.

Mostofthepreviousstudieswere limitedtostudytheef-fectofdiversificationonreducingproductionriskforwindparks.3Thiswasduetothefactthatactualfinancialdataforprivatelyownedwindandsolarparksisusuallyhardtoac-quire.Thepresentstudy,however,hadtheuniqueoppor-tunitytoworkwithexclusivefinancialdatafromoneofthelargestinstitutionalinvestorsintoRenewableEnergies.ThisdatasetbothenabledacomparisonofRenewableEnergyinvestments to other assets and helped in exploring therisk-returncharacteristicsoftheassetclassitself.

1 BloombergNewEnergyFinance(2011).

2 SeeEWEA(2009),p.285.

3 Seee.g.Dunlop(2004)orHulschandStrack(2006).

Renewable Energy as an Alternative Asset class

ThemaincharacteristicsofRenewableEnergyinvestmentsare generally in line with the broader asset class of infra-structure investments.4 Economically, due to natural mo-nopolies, government regulations and concessions, theseinvestments tend to operate under limited competition.Bothsolarandwindpower,forinstance,receivesubstantialpoliticalsupportintermsofsubsidiesandthelegalframe-work.Financially, lowcorrelationswithotherassetclasses,predictablecash flowsand inflation-hedgebenefitsmaketheseinvestmentsresilientagainstfinancialcrises.

ProbablythemostimportantcharacteristicofRenewableEnergyinvestmentsliesinitscashflowprofile.Windandsolarinvestmentstendtohaveahighcashgenerationwithoperatingmarginsofaround80%.Amajorcomponentfortherevenuesoftheseinvestmentsistheprice,ortheso-called“tariff”, foranyelectricityproducedfromthewindorsolarpark.Somecountries,suchasGermanyorFrance,guaranteeafixedfeed-intariff foralmostthewhole life-timeoftheprojects.Othercountries,suchasItaly,ChinaortheU.S.,implementedamarketsolution,wherepricescanfluctuateduringtheholdingperiodoftheasset.

In case of a fixed feed-in tariff regime, production riskseemstobethemajor leftoverrisk for theassetclass.For

4 Foranoverview,seeInderst(2010).

15

von Frederik Bruns

Frederik Bruns

poRTfoLIo dIvER SIfIc ATIoN – IS ThE ANSWER BLoWINg IN ThE WINd?

k ATEgoRIE: dIpLom-/mA STER ARBEITEN

PortfolioDiversification–Istheanswerblowinginthewind?

wind farms, this risk should not be underestimated sinceaverage annual wind-speeds can fluctuate substantially.For solar parks, the risk appears to be lower since irradia-tion,whichisthemaininputforenergycreationfromsolarparks, tendstobemorestable.Theexpectedannualpro-ductionforbothtechnologiesisusuallybeingestimatedbyaspecializedconsultancy.5Thus,inadditiontothevolatileinputresource(windandirradiation)thereexiststheriskofanoverestimatebytheseconsultants.

The last favorable characteristic of Renewable Energy in-vestmentsrelatestocorrelations.Thereisnologicalreasonforanycorrelationwithstockorbondmarkets.Bothannualwind speeds and irradiation are assumed to be randomlydistributed. Therefore, investors should expect fairly highdiversification potential when investing into Renewablesalongsideotherassetclasses.

Diversification possibilities within a Renewables portfolio

The empirical analysis in this study uses exclusive datafromoneofthelargestinstitutionalinvestorsinRenewableEnergies inEurope.The fulldataset initiallyconsistedofmonthlyproductionandfinancialdatafromAugust2006–December2011for28operatingwindand3solarparks.Sincethewindandsolarparksstartedoperatingatdiffe-rentpointsintime,thesubsequentanalyseswillconsiderdifferenttimeperiodsandportfolios.Thelongestperiodwithconsistentdataandareasonablysizedportfoliowasfora3-yearhorizonfromJanuary2009-December2011.ThispartofthedatasetcomprisednineGermanwindfar-ms,oneItalianfarmandonefromFrance.Unfortunately,the first operating solar park started commissioning notuntilMarch2010andhencelimitedthepossibleanalysesforthispartoftheassetclass.

Thefirstinputfactorthathastobedeterminedwhenapp-lyingMPTtoRenewableEnergyinvestmentsisameasurefortheexpectedreturn.WindandsolarparksareusuallyevaluatedviaDCFmodels,sincetheparksareassumedtohavenoresidualvalueintheend.HencetherightmeasurefortheexpectedreturnshouldbetheprojectIRR.Howe-ver,actualperformancedatacannoteasilybeincludedinthesemodels,unlessthereisavailabledataforthewholelifetimeoftheproject.Thisiswhyaproxyhastobefound,which approximates the expected return with only few

5 SeeBöttcher(2009),p.159andp.246.

observations.TheproxyhastocomesufficientlyclosetotheDCFvaluation.

Returns in this study were therefore defined according totheReturnonInvestment(ROI)figure.Foreachwindfarmi,theROIineachmonthtwascalculatedas:

TheROIappearedtobethemostreasonableestimatorfortheexpectedreturnsinceitcanincorporateactualperfor-mance data. Furthermore, the numerator (EBIT) includesbothdepreciation,whichapproximatesthelossinvalueoftheinvestment,andtheincomegeneratedbytheparkdu-ringtherespectiveperiod.

TheOperatingProfitfigureswereavailablefromtheincomestatementsofthewindfarmsandrepresentedanEBITDAfi-gure.InordertoreceivetheEBIT,alumpsumdepreciationwasdeductedineachmonth.Thelumpsumvaluewascal-culatedbydividingtherespectiveInvestedCapitalby300,whichsimplyscalesthe25yearslifetimetoalinearmonthlydepreciation.Thiseconomicdepreciationservedasapro-xy for the periodic loss in market value over the projectlife.Thesimplificationwaschosentoensurecomparabilityamongtheprojectssincethemeasureddepreciationvariedaccordingtodifferentaccountingandtaxregimes.

ThesecondinputfactorthathastobedeterminedfortheMarkowitz framework is an appropriate estimator for risk.Bothwindandirradiationarehighlyseasonalinputs.Hence,annualizingmonthlyreturnsbymultiplyinge.g.themonth-lystandarddeviationby√12wouldneglectpotentialauto-correlations arising from the inter-annual variability. Sincethe inherent seasonality however is known in advance, itcannotberegardedasareal“risk”.Aninvestorshouldthe-refore restricthisattention to thatpartofvolatilityof thereturnsthatdoesnotaccountforseasonality.Inordertore-moveseasonalityoftheinputresourcewind,themonthlyreturnsinthisstudyweretransformedintoSeasonallyAd-justed Annual Rates (SAAR). The respective values for theSAARsforeachwindfarmiineachmonthtwerecalculatedaccordingtothefollowingformula:

investors in Renewable Energies in Europe. The full data set initially consisted of monthly

production and financial data from August 2006 – December 2011 for 28 operating wind and 3

solar parks. Since the wind and solar 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.

The first input factor that has to be determined when applying MPT to Renewable Energy

investments is a measure for the expected return. Wind and solar parks are usually evaluated via

DCF models, since the parks are assumed to have no residual value in the end. Hence the right

measure for the expected return should be the project IRR. However, actual performance data

cannot easily be included in these models, 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 with

only few observations. The proxy has to come sufficiently close to the DCF valuation.

Returns in this study were therefore defined according to the Return on Investment (ROI) figure.

For each wind farm i, the ROI in each month t was calculated as:

𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖 =𝐸𝐸𝐸𝐸𝑆𝑆𝐸𝐸𝑖𝑖𝑖𝑖

𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐼𝐼𝐶𝐶𝐶𝐶𝑖𝑖0=𝑆𝑆𝐶𝐶𝐼𝐼𝑂𝑂𝐶𝐶𝐼𝐼𝐶𝐶𝐼𝐼𝑂𝑂 𝑃𝑃𝑂𝑂𝑃𝑃𝑃𝑃𝐶𝐶𝐼𝐼𝑖𝑖𝑖𝑖 − 𝐷𝐷𝐼𝐼𝐶𝐶𝑂𝑂𝐼𝐼𝐷𝐷𝐶𝐶𝐶𝐶𝐼𝐼𝐶𝐶𝑃𝑃𝐼𝐼𝑖𝑖

𝑆𝑆𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐼𝐼𝐶𝐶𝐶𝐶𝑖𝑖0

The ROI appeared to be the most reasonable estimator for the expected return 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.

The Operating Profit figures were available from the income statements of the wind farms and

represented an EBITDA figure. In order to receive the EBIT, a lump sum depreciation was

deducted 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. This

economic depreciation served as a proxy for the periodic loss in market value over the project

life. The simplification was chosen to ensure comparability among the projects since the

measured depreciation varied according to different accounting and tax regimes.

The second input factor that has to be determined for the Markowitz framework is an appropriate

estimator for risk. Both wind and irradiation are highly seasonal inputs. Hence, annualizing

monthly returns by multiplying e.g. the monthly standard deviation by √12 would neglect

potential autocorrelations arising from the inter-annual variability. Since the inherent seasonality

however 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. In

order to remove seasonality of the input resource wind, the monthly returns in this study were

transformed into Seasonally Adjusted Annual Rates (SAAR). The respective values for the

SAARs for each wind farm i in each month t were calculated according to the following formula:

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖 =𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖

For the wind farms in the data set, the seasonality ratios were available since they had been

estimated by wind consultants for each park. Using this simplification, the “true” volatility of the

returns could have been estimated.

The descriptive statistics for the adjusted annualized returns (SAAR) of the wind farms can be

found in Table 1. It becomes evident that the hypothesis of a normal distribution fails to be

rejected at a significance level of 5%, even for the only wind farm with variable prices (ITA).

Therefore, assuming a normal distribution for the adjusted returns appears to be a relatively

sensible assumption and MPT can be applied accordingly.

Table 1: Descriptive statistics of the wind farms

GER 1 GER 2 GER 3 ITA GER 4 GER 5 GER 6 GER 7 GER 8 GER 9 FRAAvg. wind year return 7.57% 6.76% 5.48% 9.49% - - - - - - -Mean 5.65% 4.75% 3.91% 6.28% 5.25% 3.66% 5.01% 3.07% 4.59% 3.62% 3.18%Std. Dev. 5.18% 3.66% 2.97% 6.06% 4.24% 4.30% 4.18% 3.17% 2.76% 2.77% 3.02%

Min -4.20% -2.26% -3.18% -6.79% -6.77% -3.97% -4.84% -5.36% -2.96% -1.93% -2.25%Max 21.84% 15.07% 9.81% 21.11% 15.44% 14.44% 16.65% 11.32% 10.35% 11.10% 10.75%Skewness 0.641 0.470 0.077 0.166 0.063 0.454 0.516 0.038 -0.337 0.565 0.711Kurtosis 3.425 3.017 2.446 2.875 3.346 3.111 4.151 3.653 3.415 3.382 3.124

N° obs. 65 60 60 57 53 53 49 49 48 47 36

Jarque Bera 5.14 2.54 1.16 0.3 0.59 2.26 4.79 1.24 1.76 3.47 3.71p-value 0.0766 0.2808 0.5599 0.8610 0.7438 0.3238 0.0912 0.5380 0.4151 0.1760 0.1568Normally distributed Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Risk-adjusted performance 1.09 1.30 1.32 1.04 1.24 0.85 1.20 0.97 1.66 1.31 1.05

16PortfolioDiversification–Istheanswerblowinginthewind?

For the wind farms in the data set, the seasonality ratioswereavailablesincetheyhadbeenestimatedbywindcon-sultants foreachpark.Using this simplification, the “true”volatilityofthereturnscouldhavebeenestimated.

The descriptive statistics for the adjusted annualized re-turns (SAAR)of thewindfarmscanbefound inTable1. Itbecomesevidentthatthehypothesisofanormaldistribu-tionfails toberejectedatasignificance levelof5%,evenfortheonlywindfarmwithvariableprices(ITA).Therefore,assuminganormaldistributionfortheadjustedreturnsap-pearstobearelativelysensibleassumptionandMPTcanbeappliedaccordingly.

For theabsolute levelof thereturns, itdeservesmentio-ning,thatthehistoricalestimatesofthewindparksareso-mewhatunderstatingthelong-termaveragereturnsthataninvestorcanexpect.First,thesmallsampleoverweighstheratherlowreturnsarisingfromtechnicaldifficultiesintheearlymonthsofaproject (the“ramp-upphase”).Se-condly,thesampleincludesalongrangeofbelowaveragewind years. Wind speeds in Germany, for instance, havebeenbelowthelong-termaverageforthreeyearsinarow(2008-2010).

The second input factor that has to be determined for the Markowitz framework is an appropriate

estimator for risk. Both wind and irradiation are highly seasonal inputs. Hence, annualizing

monthly returns by multiplying e.g. the monthly standard deviation by √12 would neglect

potential autocorrelations arising from the inter-annual variability. Since the inherent seasonality

however 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. In

order to remove seasonality of the input resource wind, the monthly returns in this study were

transformed into Seasonally Adjusted Annual Rates (SAAR). The respective values for the

SAARs for each wind farm i in each month t were calculated according to the following formula:

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖 =𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖𝑖𝑖

For the wind farms in the data set, the seasonality ratios were available since they had been

estimated by wind consultants for each park. Using this simplification, the “true” volatility of the

returns could have been estimated.

The descriptive statistics for the adjusted annualized returns (SAAR) of the wind farms can be

found in Table 1. It becomes evident that the hypothesis of a normal distribution fails to be

rejected at a significance level of 5%, even for the only wind farm with variable prices (ITA).

Therefore, assuming a normal distribution for the adjusted returns appears to be a relatively

sensible assumption and MPT can be applied accordingly.

Table 1: Descriptive statistics of the wind farms

GER 1 GER 2 GER 3 ITA GER 4 GER 5 GER 6 GER 7 GER 8 GER 9 FRAAvg. wind year return 7.57% 6.76% 5.48% 9.49% - - - - - - -Mean 5.65% 4.75% 3.91% 6.28% 5.25% 3.66% 5.01% 3.07% 4.59% 3.62% 3.18%Std. Dev. 5.18% 3.66% 2.97% 6.06% 4.24% 4.30% 4.18% 3.17% 2.76% 2.77% 3.02%

Min -4.20% -2.26% -3.18% -6.79% -6.77% -3.97% -4.84% -5.36% -2.96% -1.93% -2.25%Max 21.84% 15.07% 9.81% 21.11% 15.44% 14.44% 16.65% 11.32% 10.35% 11.10% 10.75%Skewness 0.641 0.470 0.077 0.166 0.063 0.454 0.516 0.038 -0.337 0.565 0.711Kurtosis 3.425 3.017 2.446 2.875 3.346 3.111 4.151 3.653 3.415 3.382 3.124

N° obs. 65 60 60 57 53 53 49 49 48 47 36

Jarque Bera 5.14 2.54 1.16 0.3 0.59 2.26 4.79 1.24 1.76 3.47 3.71p-value 0.0766 0.2808 0.5599 0.8610 0.7438 0.3238 0.0912 0.5380 0.4151 0.1760 0.1568Normally distributed Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Risk-adjusted performance 1.09 1.30 1.32 1.04 1.24 0.85 1.20 0.97 1.66 1.31 1.05

Table1:Descriptivestatisticsofthewindfarms

Figure1:The“WindFarmMarketLine”

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.

First, the small sample overweighs the rather low returns arising from technical difficulties in the

early months of a project (the “ramp-up phase”). Secondly, the sample includes a long range of

below average wind years. Wind speeds in Germany, for instance, have been below the long-term

average for three years in a row (2008-2010).

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 1 plots the projects in the usual risk-return space. 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”. 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. 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.

Figure 1: The “Wind Farm Market Line”

The last step in the statistical analysis was to find out how the returns of the different wind farms


Thenextstepinthestatisticalanalysiswastofindoutwhether the returnsof thewind farms in thedatasetaresomehowrelated.Figure1plotstheprojectsintheusual risk-returnspace. Itbecomesevident that,apartfromtwooutliers,GER5&8,theprojectslineupquitenicely on what has been labeled by the author as the“WindFarmMarketLine”.Thelinehasbeenfoundbyasimple linearregression, indicatingthatan increase in1%inriskwouldrequireanincreaseof1.133%inreturn.The intercept has been set to zero since a wind farmwith zero risk should also produce no returns, simplybecause it does not exist. The exemplified trade-offbetween risk and return appears to be even valid forthe market across borders, since the wind farms stemfromthreedifferentcountries.

The last step in the statistical analysis was to find outhowthereturnsofthedifferentwindfarmsinthedataset move together. The correlation matrix in Table 2shows that correlations between the different windfarmsmainlydependontheirgeographicaldispersion.Notsurprisingly,thecorrelationsbetweentheGermanwind farms are all very high. The results for the othertwo countries, however, are astonishing. Both the Ita-lian and the French wind farm have extremely low(sometimes even negative) correlations with the Ger-manonesandshouldthereforeofferafairlyhighdiver-sificationpotential.

Afterhavinganalyzedthemainstatisticalpropertiesofthewindfarms,thenextstepintheanalysiswastofindouthowmuchriskcanbediversifiedawaybyholdingaportfolioofonlyfivewindfarmsinsteadofasingleone.This could have been achieved by applying a“CAPM-style” single-index model to the data set. The modelthatwastestedempiricallyforeachwindfarmihadthefollowingform:

The first challenge was to find an appropriate bench-markforthemarketportfolio.SincetheredoesnotexistaTotalReturn index forwindenergy, somethingsimi-larhadtobecreated.TheanalysisfollowedtheideaofDunlop(2004)anddevelopedamarketportfolioforthewindfarmmarketthatconsistedofallthe11windfarmsinthedataset,weightedbytheirtotalinstalledcapaci-tyintherespectivecountryandyear.Thismethodwasconsideredtobeappropriatesinceitaccuratelyreflectsmarketsizeandinvestabilityintherespectivecountry.

Following the CAPM approach, a small portfolio hasthenbeenbuiltupstep-by-stepbyaddingwindfarmswithlowbetastotheriskiestone(ITA).Thebetasfromtheregressions,βMi,servedasabestguessmeasureforrisk.Theimpactofdiversificationcanbeseenfromthereduction ofβMP in Figure 2. Besides, the Adjusted R2increasesaswellsincetheportfolioisgettingclosertothemarketportfolio.Initially,theItalianwindfarmhadanannualstandarddeviationof5.74%.ByaddingtheFrench wind farm and another three German ones tothesmallportfolio,theactualriskcouldhavebeenre-ducedto2.00%.Thisequalsariskreductionof65%inrelativeterms.Thediversificationtherebyincorporatedgeographical dispersion, different turbines and diffe-rentwindconsultants.

in the data set move together. The correlation matrix in Table 2 shows that correlations between

the different wind farms mainly depend on their geographical dispersion. Not surprisingly, the

correlations between the German wind farms are all very high. The results for the other two

countries, however, are astonishing. Both the Italian and the French wind farm have extremely

low (sometimes even negative) correlations with the German ones and should therefore offer a

fairly high diversification potential.

Table 2: Correlation between the wind farms

After having analyzed the main statistical properties of the wind farms, the next step in the

analysis was to find out how much risk can be diversified away by holding a portfolio of only

five wind farms instead of a single one. This could have been achieved by applying a “CAPM-

style” single-index model to the data set. The model that was tested empirically for each wind

farm i had the following form:

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖 = 𝛼𝛼𝑖𝑖 + 𝛽𝛽𝑀𝑀𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝜖𝜖𝑖𝑖

The first challenge was to find an appropriate benchmark for the market portfolio. 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 (2004) 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. This method was considered to be appropriate since it

accurately reflects market size and investability in the respective country.

Following the CAPM approach, a small portfolio has then been built up step-by-step by adding

wind farms with low betas to the riskiest one (ITA). The betas from the regressions, 𝛽𝛽𝑀𝑀𝑖𝑖, served

GER 1 GER 2 GER 3 ITA GER 4 GER 5 GER 6 GER 7 GER 8 GER 9 FRAGER 1 1.000 0.931 0.855 0.041 0.743 0.694 0.407 0.801 0.781 0.822 0.080GER 2 0.931 1.000 0.825 -0.021 0.750 0.702 0.411 0.758 0.789 0.838 -0.002GER 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 0.110GER 4 0.743 0.750 0.744 0.018 1.000 0.707 0.526 0.753 0.708 0.811 0.103GER 5 0.694 0.702 0.652 -0.025 0.707 1.000 0.346 0.619 0.589 0.637 -0.139GER 6 0.407 0.411 0.378 -0.175 0.526 0.346 1.000 0.447 0.569 0.492 0.123GER 7 0.801 0.758 0.879 0.082 0.753 0.619 0.447 1.000 0.730 0.861 0.153GER 8 0.781 0.789 0.757 -0.152 0.708 0.589 0.569 0.730 1.000 0.692 0.132GER 9 0.822 0.838 0.916 0.042 0.811 0.637 0.492 0.861 0.692 1.000 0.152FRA 0.080 -0.002 0.182 0.110 0.103 -0.139 0.123 0.153 0.132 0.152 1.000

Table2:Correlationbetweenthewindfarms

in the data set move together. The correlation matrix in Table 2 shows that correlations between

the different wind farms mainly depend on their geographical dispersion. Not surprisingly, the

correlations between the German wind farms are all very high. The results for the other two

countries, however, are astonishing. Both the Italian and the French wind farm have extremely

low (sometimes even negative) correlations with the German ones and should therefore offer a

fairly high diversification potential.

Table 2: Correlation between the wind farms

After having analyzed the main statistical properties of the wind farms, the next step in the

analysis was to find out how much risk can be diversified away by holding a portfolio of only

five wind farms instead of a single one. This could have been achieved by applying a “CAPM-

style” single-index model to the data set. The model that was tested empirically for each wind

farm i had the following form:

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖 = 𝛼𝛼𝑖𝑖 + 𝛽𝛽𝑀𝑀𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝜖𝜖𝑖𝑖

The first challenge was to find an appropriate benchmark for the market portfolio. 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 (2004) 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. This method was considered to be appropriate since it

accurately reflects market size and investability in the respective country.

Following the CAPM approach, a small portfolio has then been built up step-by-step by adding

wind farms with low betas to the riskiest one (ITA). The betas from the regressions, 𝛽𝛽𝑀𝑀𝑖𝑖, served

GER 1 GER 2 GER 3 ITA GER 4 GER 5 GER 6 GER 7 GER 8 GER 9 FRAGER 1 1.000 0.931 0.855 0.041 0.743 0.694 0.407 0.801 0.781 0.822 0.080GER 2 0.931 1.000 0.825 -0.021 0.750 0.702 0.411 0.758 0.789 0.838 -0.002GER 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 0.110GER 4 0.743 0.750 0.744 0.018 1.000 0.707 0.526 0.753 0.708 0.811 0.103GER 5 0.694 0.702 0.652 -0.025 0.707 1.000 0.346 0.619 0.589 0.637 -0.139GER 6 0.407 0.411 0.378 -0.175 0.526 0.346 1.000 0.447 0.569 0.492 0.123GER 7 0.801 0.758 0.879 0.082 0.753 0.619 0.447 1.000 0.730 0.861 0.153GER 8 0.781 0.789 0.757 -0.152 0.708 0.589 0.569 0.730 1.000 0.692 0.132GER 9 0.822 0.838 0.916 0.042 0.811 0.637 0.492 0.861 0.692 1.000 0.152FRA 0.080 -0.002 0.182 0.110 0.103 -0.139 0.123 0.153 0.132 0.152 1.000


Figure2:Theeffectofdiversification

as a best guess measure for risk. The impact of diversification can be seen from the reduction of

𝛽𝛽𝑀𝑀𝑀𝑀 in Figure 2. Besides, the Adjusted R2 increases as well since the portfolio is getting closer to

the market portfolio. Initially, the Italian wind farm had an annual standard deviation of 5.74%.

By adding the French wind farm and another three German ones to the small portfolio, the actual

risk could have been reduced to 2.00%. This equals a risk reduction of 65% in relative terms. The

diversification thereby incorporated geographical dispersion, different turbines and different wind

consultants.

Figure 2: The effect of diversification

Diversification potential in a multi-asset portfolioAfter having assessed diversification possibilities within a Renewables portfolio, the next step in

the analysis was to evaluate the benefits of Renewable Energy investments in a multi-asset

portfolio. The analysis in this section of the paper uses monthly returns in % from August 2006

until August 2011 for one representative wind farm, GER 1, and several other asset classes. A

five year horizon appears to be relatively short and the time frame is heavily distorted by the

Diversification potential in a multi-asset portfolio

After having assessed diversification possibilities withina Renewables portfolio, the next step in the analysiswas to evaluate the benefits of Renewable Energy in-vestments inamulti-assetportfolio.Theanalysis in thissection of the paper uses monthly returns in % fromAugust 2006 until August 2011 for one representativewind farm, GER 1, and several other asset classes. Afive year horizon appears to be relatively short and thetime frame is heavily distorted by the recent financialcrises. However, it seems plausible to choose a histo-rical period of turbulence if one wanted to exemplifythe benefits of“uncorrelated” Renewables investments.

Theinvestmentuniverseconsideredinthissectionofthepaper can be found inTable 3.The underlying risk-freeratehasbeendeterminedtobe2.34%,whichisequaltotheaverageofthe1-monthEURIBORduringthefiveyearhorizon. All data (apart from the wind farm) have beentakenfromtheBloombergdatabase.StockswerefurtherdividedintoEuropeanandemergingmarketsinordertoaccountforinternationaldiversification.

Table3:Investmentuniversefortheassetallocationproblem

recent financial crises. However, it seems plausible to choose a historical period of turbulence if

one wanted to exemplify the benefits of “uncorrelated” Renewables investments.

The investment universe considered in this section of the paper can be found in Table 3. The

underlying risk-free rate has been determined to be 2.34%, which 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.

Table 3: Investment universe for the asset allocation problem

Figure 3 shows the historical performance of all asset classes for the whole time frame. It

becomes evident that apart from emerging markets, the wind farm has outperformed all other

asset classes in the analyzed time frame. This is mainly due to the sharp decline of all asset

classes except for bonds during the Subprime Crisis starting in September 2007.

Asset class Proxy index Asset class Proxy indexStocks Hedge Funds Dow Jones Credit Suisse Hedge Fund Index- European Stocks MSCI Europe Total Return (TR) Commodities Dow Jones UBS Commodity Index TR- Emerging Markets MSCI Emerging Markets TR Private Equity LPX Europe TRBonds Barclays Capital Euro Aggregate TR Infrastructure NMX Infrastructure Europe TR

Real Estate FTSE EPRA / NAREIT Europe TRWind farms GER 1

Investment UniverseTraditional Assets Alternative Assets


Figure 3 shows the historical performance of all assetclassesforthewholetimeframe.Itbecomesevidentthatapartfromemergingmarkets,thewindfarmhasoutper-formedallotherassetclassesintheanalyzedtimeframe.Thisismainlyduetothesharpdeclineofallassetclassesexcept for bonds during the Subprime Crisis starting inSeptember2007.

Usingthisgraphasafirstimpression,thenextstepistohaveacloserlookonthereturndistributions.Table4re-portstheresultsfromthestatisticalanalysisoftheassetclasses.Annualizedmeanandstandarddeviationinthistablewere foundbymultiplying themonthlyvaluesby12 and √12 respectively. The Jarque-Bera statistics refertothemonthlydistributionsoftheassetclasses.Itdeser-vesmentioningthatthereturnandriskofthewindfarm(boldfigures),however,correspondtotheseasonallyad-

justedvalues.InadditiontothedescriptivestatisticsandtheJarque-Beratest,thetablealsoevaluatestheSharpeRatio, Value at Risk (VaR) and Conditional Value at Risk(CVaR)oftheassetclasses.Evidently,thewindfarmoffersthebestrisk-returnprofilewiththehighestSharpeRatioandrelativelylowdownsidepotential.

Figure3:Historicalperformanceoftheassetclasses

Figure 3: Historical performance of the asset classes

Using this graph as a first impression, the next step is to have a closer look on the return

distributions. Table 4 reports the results from the statistical analysis of the asset classes.

Annualized mean and standard deviation in this table were found by multiplying the monthly

values by 12 and √12 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. In addition to the descriptive statistics and

the Jarque-Bera test, the table also evaluates the Sharpe Ratio, Value at Risk (VaR) and

Conditional Value at Risk (CVaR) of the asset classes. Evidently, the wind farm offers the best

risk-return profile with the highest Sharpe Ratio and relatively low downside potential.20PortfolioDiversification–Istheanswerblowinginthewind?

Table4:StatisticalanalysisoftheassetclassesTable 4: Statistical analysis of the asset classes

The diversification potential of the respective asset classes can again be assessed by having a

look at the correlation matrix, shown in Table 5. 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.

Table 5: Correlation matrix of the asset classes

Having examined the descriptive statistics and correlations of the return series, the asset classes

Eur. Stocks Em. Markets Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind FarmMean -0.11% 0.74% 0.34% 0.33% -0.07% -0.27% 0.02% -0.36% 0.45%Std. Dev. 5.14% 6.45% 0.96% 2.11% 4.76% 8.78% 4.56% 6.42% 1.49%

Annualized Mean -1.28% 8.89% 4.10% 3.95% -0.90% -3.24% 0.23% -4.30% 5.44%Annualized Std. Dev. 17.79% 22.34% 3.31% 7.31% 16.49% 30.42% 15.78% 22.23% 5.16%

Min -12.75% -19.53% -1.98% -6.91% -12.81% -26.12% -11.13% -20.39% -0.22%Max 14.41% 16.88% 3.08% 3.81% 9.51% 33.11% 10.49% 20.16% 2.56%Skewness -0.304 -0.625 0.327 -1.396 -0.714 -0.027 -0.172 -0.485 1.503Kurtosis 3.845 4.320 3.388 5.767 3.782 6.646 2.513 5.493 6.977

N° obs. 61 61 61 61 61 61 61 61 61

Jarque Bera 3.04 6.72 1.95 17.38 6.32 8.71 1.10 8.24 20.65p-value 0.2183 0.0347 0.3780 0.0002 0.0425 0.0128 0.5771 0.0162 < 0.0001Normally distributed Yes No Yes No No No Yes No No

Sharpe Ratio -0.20 0.29 0.53 0.22 -0.20 -0.18 -0.13 -0.30 0.60Value at Risk * -30.55% -27.85% -1.34% -8.08% -28.02% -53.28% -25.73% -40.88% -3.04%Cond. Value at Risk* -35.42% -54.97% -10.92% -19.04% -33.12% -59.51% -32.79% -41.56% -16.09%

Prob. of return ≥ 0% 47% 65% 89% 71% 48% 46% 51% 42% 85%

* confidence level of 95%

Eur. Stocks Em. Markets Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind FarmEur. Stocks 1.000 0.843 -0.126 0.732 0.321 0.903 0.847 0.848 -0.129

Em. Markets 0.843 1.000 -0.138 0.761 0.472 0.776 0.651 0.736 -0.207Bonds -0.126 -0.138 1.000 -0.238 -0.266 -0.113 -0.064 -0.009 -0.015

Hedge Funds 0.732 0.761 -0.238 1.000 0.578 0.680 0.607 0.552 0.014Commodities 0.321 0.472 -0.266 0.578 1.000 0.326 0.261 0.312 0.040Private Equity 0.903 0.776 -0.113 0.680 0.326 1.000 0.755 0.876 -0.092Infrastructure 0.847 0.651 -0.064 0.607 0.261 0.755 1.000 0.724 -0.080

Real Estate 0.848 0.736 -0.009 0.552 0.312 0.876 0.724 1.000 -0.133Wind Farm -0.129 -0.207 -0.015 0.014 0.040 -0.092 -0.080 -0.133 1.000The diversification potential of the respective asset

classes can again be assessed by having a look at thecorrelationmatrix,showninTable5. Itcanbeseenthatonlybonds(andtosomedegreethewindfarm)offerthedesirednegativecorrelationwithotherassetclasses.Asexpected, correlations between the wind farm and theotherassetsareclose tozero.Apart fromcommodities,allotherassetclasseshavefairlyhighcorrelations.

Having examined the descriptive statistics and correla-tions of the return series, the asset classes can now beundertakenaportfoliooptimizationinthestyleofMar-kowitz.Inordertokeeptheanalysisgeneral,therehavebeennoadditionalrestrictionsintroduced(e.g.limithol-dings arising from regulatory constraints). Table 6 sum-marizestheresultsfromtheportfoliooptimizationpro-blem.

Table 4: Statistical analysis of the asset classes

The diversification potential of the respective asset classes can again be assessed by having a

look at the correlation matrix, shown in Table 5. 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.

Table 5: Correlation matrix of the asset classes

Having examined the descriptive statistics and correlations of the return series, the asset classes

Eur. Stocks Em. Markets Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind FarmMean -0.11% 0.74% 0.34% 0.33% -0.07% -0.27% 0.02% -0.36% 0.45%Std. Dev. 5.14% 6.45% 0.96% 2.11% 4.76% 8.78% 4.56% 6.42% 1.49%

Annualized Mean -1.28% 8.89% 4.10% 3.95% -0.90% -3.24% 0.23% -4.30% 5.44%Annualized Std. Dev. 17.79% 22.34% 3.31% 7.31% 16.49% 30.42% 15.78% 22.23% 5.16%

Min -12.75% -19.53% -1.98% -6.91% -12.81% -26.12% -11.13% -20.39% -0.22%Max 14.41% 16.88% 3.08% 3.81% 9.51% 33.11% 10.49% 20.16% 2.56%Skewness -0.304 -0.625 0.327 -1.396 -0.714 -0.027 -0.172 -0.485 1.503Kurtosis 3.845 4.320 3.388 5.767 3.782 6.646 2.513 5.493 6.977

N° obs. 61 61 61 61 61 61 61 61 61

Jarque Bera 3.04 6.72 1.95 17.38 6.32 8.71 1.10 8.24 20.65p-value 0.2183 0.0347 0.3780 0.0002 0.0425 0.0128 0.5771 0.0162 < 0.0001Normally distributed Yes No Yes No No No Yes No No

Sharpe Ratio -0.20 0.29 0.53 0.22 -0.20 -0.18 -0.13 -0.30 0.60Value at Risk * -30.55% -27.85% -1.34% -8.08% -28.02% -53.28% -25.73% -40.88% -3.04%Cond. Value at Risk* -35.42% -54.97% -10.92% -19.04% -33.12% -59.51% -32.79% -41.56% -16.09%

Prob. of return ≥ 0% 47% 65% 89% 71% 48% 46% 51% 42% 85%

* confidence level of 95%

Eur. Stocks Em. Markets Bonds Hedge Funds Commodities Private Equity Infrastructure Real Estate Wind FarmEur. Stocks 1.000 0.843 -0.126 0.732 0.321 0.903 0.847 0.848 -0.129

Em. Markets 0.843 1.000 -0.138 0.761 0.472 0.776 0.651 0.736 -0.207Bonds -0.126 -0.138 1.000 -0.238 -0.266 -0.113 -0.064 -0.009 -0.015

Hedge Funds 0.732 0.761 -0.238 1.000 0.578 0.680 0.607 0.552 0.014Commodities 0.321 0.472 -0.266 0.578 1.000 0.326 0.261 0.312 0.040Private Equity 0.903 0.776 -0.113 0.680 0.326 1.000 0.755 0.876 -0.092Infrastructure 0.847 0.651 -0.064 0.607 0.261 0.755 1.000 0.724 -0.080

Real Estate 0.848 0.736 -0.009 0.552 0.312 0.876 0.724 1.000 -0.133Wind Farm -0.129 -0.207 -0.015 0.014 0.040 -0.092 -0.080 -0.133 1.000

Table5:Correlationmatrixoftheassetclasses


can now be undertaken a portfolio optimization in the style of Markowitz. In order to keep the

analysis general, there have been no additional restrictions introduced (e.g. limit holdings arising

from regulatory constraints). Table 6 summarizes the results from the portfolio optimization

problem.

Table 6: Weights for the optimal portfolios

The optimal portfolios were found for three different subsets of the investment universe. First, the

Mean Variance Portfolio (MVP) and Tangency Portfolio (TP) were calculated for stocks and

bonds only, which corresponds to a portfolio optimization for a “Traditional Portfolio”. In this

case, due to the poor performance of stocks during the crisis, the optimal portfolios are almost

completely dominated by bonds (>90%).

The second subset of the portfolio optimization, the “Alternative Portfolio”, considered all assets

but the wind farm. For this particular portfolio, the risk could have been decreased by 15% in

relative terms for the MVP. However, the Sharpe Ratio of the TP could have been increased only

marginally. 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.

The third and last subset considered all asset classes in the data set. It becomes evident that both

the wind farm’s weights 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%, while

simultaneously reducing the risk from 2.99% to 2.74%. Although the “Portfolio with Wind”

MVP 1 TP 2 MVP 2 TP 2 MVP 3 TP 3Eur. Stocks 4.12% 0.00% 0.00% 0.00% 0.00% 0.00%

Em. Markets 1.17% 8.67% 0.00% 4.81% 0.00% 6.76%Bonds 94.71% 91.33% 78.61% 83.63% 61.90% 53.28%

Hedge Funds - - 19.56% 11.56% 15.58% 0.00%Commodities - - 1.82% 0.00% 1.11% 0.00%Private Equity - - 0.00% 0.00% 0.00% 0.00%Infrastructure - - 0.00% 0.00% 0.00% 0.00%

Real Estate - - 0.00% 0.00% 0.00% 0.00%Wind Farm - - - - 21.41% 39.96%

Return 3.93% 4.51% 3.98% 4.31% 4.31% 4.96%Risk (Std. Dev.) 3.15% 3.36% 2.69% 2.99% 2.38% 2.74%Sharpe Ratio 0.50 0.65 0.61 0.66 0.83 0.96

1. Traditional Portfolio 2. Alternative Portfolio 3. Portfolio with Wind

The optimal portfolios were found for three differentsubsets of the investment universe. First, the Mean Va-riancePortfolio(MVP)andTangencyPortfolio(TP)werecalculatedforstocksandbondsonly,whichcorrespondstoaportfoliooptimizationfora“TraditionalPortfolio”.Inthiscase,duetothepoorperformanceofstocksduringthe crisis, the optimal portfolios are almost completelydominatedbybonds(>90%).

Thesecondsubsetoftheportfoliooptimization,the“Al-ternative Portfolio”, considered all assets but the windfarm. For this particular portfolio, the risk could havebeen decreased by 15% in relative terms for the MVP.However,theSharpeRatiooftheTPcouldhavebeenin-creasedonlymarginally.Itdeservesmentioningthatonlyhedgefunds(andtoadegreecommoditiesfortheMVP)contribute to these results. All other Alternative Assetsareirrelevant.

The third and last subset considered all asset classes inthedataset.Itbecomesevidentthatboththewindfarm’sweightsanditsincrementalcontributiontotheMVPandTPareremarkable.IncaseoftheMVP,portfolioriskcouldhavebeenfurtherreducedby12%comparedtotheAl-ternativePortfolio.FortheTP, thereturnwasenhancedfrom4.31%to4.96%,whilesimultaneouslyreducingtherisk from 2.99% to 2.74%. Although the “Portfolio withWind”clearlystandsagainsttheassetallocationofmanyinstitutionalinvestors,theresultappearstobeplausibleforthechosendownturnperiodandsetofassumptions.

Outlook

Whenhavingaccesstomoredata,theanalysisfromthisstudycouldbeextendedintoseveraldirections.First,theoptimalassetallocationcouldallowfor the inclusionofliabilities of long-term institutional investors. A wind orsolar park with an upfront investment and predictableandrelativelystablecashflowsthereafterappearstobeagoodmatchfore.g.annuityproductsofinsurancecom-paniesorpensionfunds.

Thesecondextensionconcernsthehedgingbenefitsofsolar. Due to counter-seasonality of the input resource,includingbothsolarandwindparksinaportfoliocouldenable an investor to almost completely diversify awaythe inherent risk of the asset class. Although a perfecthedgemightbedifficulttoattaininpractice,theseaso-nalitypatternofwindandsolar investmentsshouldne-verthelessleadtosubstantiallymorestableportfoliore-turns.

Table6:Weightsfortheoptimalportfolios


Contact FrederikBrunsAnalystAllianzSpecialisedInvestmentsLimited27Knightsbridge,[email protected].:+442070713435

ReferencesBloombergNewEnergyFinance(2011):GlobalTrendsinRenewableEnergyInvestment2011–AnalysisofTrendsandIssuesintheFinancingofRenewableEnergy,Bloom-bergNewEnergyFinanceWhitePapers,26September2011,www.bnef.com.

Böttcher,J.(2009):FinanzierungvonErneuerbare-Ener-gien-Vorhaben,Oldenbourg,München.

Dunlop,J.(2004):ModernPortfolioTheoryMeetsWindFarms,JournalofPrivateEquity7(2),83-95.

EWEA(2009):WindEnergy–TheFacts:Aguidetothetechnology,economicsandfutureofwindpower,Earth-scan,London.

Hulsch,F.andStrack,M.(2006):ExploitingPortfolioEf-fectsinDiversifiedProjectBundles–Aquantitativeanaly-sisofpotentialsandimplicationsforfinancialenginee-ring,presentedattheGermanWindEnergyConferencein2006.

Inderst,G.(2010):Infrastructureasanassetclass,EIBPaperSeries15(1),70-105.

Markowitz,H.(1952):PortfolioSelection,JournalofFinance7(1),77-91.


mailto:frederik.bruns%40allianzcapitalpartners.com?subject=

www.bnef.com

Abstract:

Thispaperaimsatenhancingtheunderstandingoftheprofitabilityofpairstrading,apopularandcomputati-onally intense relative-value arbitrage approach. Pairstradingexploitsstatisticalmethodstoidentifyeconomi-cally linked firms.Comprehensiveempirical studiesonpairstradingare(still)veryrare.ThisissurprisinggivenitslargeseeminglyabnormalreturnsreportedinGatevet al. (2006) as well as its apparent popularity amongsophisticated practitioners such as hedge funds. As aconsequence, it is stillanopenquestionwhen,where,andwhypairstradingisparticularlyprofitable.Weherefocusontheroleofonespecificpotentialdriverofpairstrading profits in depth: Time-varying limited investorattention,forwhichwedesignanovelproxy.Byunco-veringarichsetofempiricalregularitiesrelatedtotheapparently time-varying risk-return trade-off of pairstrading, thisstudymightbeofhighrelevancetoprac-titioners. From a broader perspective, our results lendsupporttothenotionthattherelativeefficiencyoffun-damentallyrelatedassetsmightnotbestableovertime,butbeaffectedbyinvestorattentionshifts.

Summary:

We test asset pricing implications of the investor at-tentionshifthypothesisproposedinrecenttheoreticalwork (e.g. Peng and Xiong (2006)). Our objective is todirectly assess how the dynamics of investor inatten-tion affect the relative pricing efficiency of linked as-sets. We thereby study a promising and so far widelyneglectedsetting,whichdiffersconceptually fromtheones the literature on limited attention has addressedsofar:Stockpairstrading(Gatevetal. (2006)),apopu-lar proprietary relative arbitrage approach, which betson the future performance of stocks with very similarpastperformance.Morespecifically,themajorresearchquestionsdealtwitharethefollowing:Howtoproxyforunobservableinvestorattentionallocation?Isthepriceformationoflinkedstocksaffectedbytime-varyingin-vestorattention?Morespecifically,doshocksinlimitedattentiontowardsfirm-levelinformationhindermarketparticipants fromkeepingrelativepricesofstockpairsinline,therebygivingrisetocross-returnpredictability?

Toanswerthesequestions,wedesignanovelproxyforlimited investor attention in the time series, which re-liesontheintuitionbehindrecentmodelsonthedyna-

k ATEgoRIE: SoNSTIgE WISSENSchAf TLIchE ARBEITEN

24

Dr. Heiko Jacobs

von Dr. Heiko Jacobs and Prof. Dr. Dr. h.c. Martin Weber,

University of Mannheim

LoSINg SIghT of ThE TREES foR ThE foREST? ATTENTIoN ShIfTS ANd pAIRS TRAdINg

Prof. Dr. Dr. h.c. Martin Weber

LosingSightoftheTreesfortheForest?AttentionShiftsandPairsTrading

micsofattentionallocation. Itaimsat identifyingdaysonwhichmarketparticipantsare likelytobeforcedtospend more (or less) resources than usual on under-standing“thebigpicture”.Thegoalistoseparate“highdistractiondays”,duringwhichturbulentmarketcondi-tions are assumed to demand investors’ full attention,from “low distraction days”, during which we expectsufficient resources toprocesscomplex interactionsatthe firm-level. Inotherwords, theproxyaimsatquan-tifying the unexpected daily information load marketparticipants need to process in order to timely assessthe overall market situation. Building on the premisethat information shocks partly manifest themselves inabnormalreturns,wedosobycondensingthemagni-tude and dissemination of unanticipated daily returnshocksinabroadrangeofmarketsegmentsintoasin-gleratio.Wefirstverifytheusefulnessofourproxybye.g. showing that is has predictive power for the ma-gnitudeofthepost-earningsannouncementdrift.Thisis suggested by previous work as e.g. Hirshleifer et al.(2009).Wethentestwhethertheproxyisabletoexplainvariations in the magnitude of profits to pairs trading,buildingontheideathatinvestorsmight“losesightofthe trees (stock-level information) for the forest (moreaggregateinformation)”.

Thenatureofpairstradingisverysimple,thoughcom-putationally costly. It consists of a for-mation periodfollowed immediately by a trading period. First, oneidentifiesthosestockpairswhosehistoricalpriceshave“movedtogether themost”.Weherebyconsider in to-talcloseto500millioneligiblestockpairs.Themonthlytop 100 pairs are then selected for trading in the fol-lowing six months trading period. Importantly, thesefirms are not only statistically, but also fundamentallylinked:Theirfutureearningssurprisesshowasignificantcomovement. During the trading period, one shorts(buys) the relatively overpriced winner (underpricedloser),wheneverthecumulativereturnshavedivergedbymorethantwohistoricalstandarddeviations. If thefuture resembles the past, prices are likely to finallyconvergenceagain,therebygeneratingpositivereturnsonzero-costportfolios.Morespecifically,aftertheope-ning,thepairisholdforuptoonemonth.Ifpricescon-verge before this cut-off date, the trade is closed witha gain. Otherwise, positions are offset, which, if pricesdivergeevenfurther,resultsinaloss.Figure1illustratesthetradingprocesswithanexample.

Figure1:IllustrationofPairsTradingProcess

information shocks partly manifest themselves in abnormal returns, we do so by condensing the magnitude and dissemination of unanticipated daily return shocks in a broad range of market segments into a single ratio. We first verify the usefulness of our proxy by e.g.showing that is has predictive power for the magnitude of the post-earnings announcement drift. This is suggested by previous work as e.g. Hirshleifer et al. (2009). We then test whether the proxy is able to explain variations in the magnitude of profits to pairs trading, building on the idea that investors might “lose sight of the trees (stock-level information) for the forest (more aggregate information)”.

The nature of pairs trading is very simple, though computationally costly. It consists of a for-mation period followed immediately by a trading period. First, one identifies those stock pairs whose historical prices have “moved together the most”. We hereby consider in total close to 500 million eligible stock pairs. The monthly top 100 pairs are then selected for trading in thefollowing six months trading period. Importantly, these firms are not only statistically, but also fundamentally linked: Their future earnings surprises show a significant comovement. During the trading period, one shorts (buys) the relatively overpriced winner (underpricedloser), whenever the cumulative returns have diverged by more than two historical standard deviations. If the future resembles the past, prices are likely to finally convergence again, thereby generating positive returns on zero-cost portfolios. More specifically, after the opening, the pair is hold for up to one month. If prices converge before this cut-off date, the trade is closed with a gain. Otherwise, positions are offset, which, if prices diverge even further, results in a loss. Figure 1 illustrates the trading process with an example.

Figure 1: Illustration of Pairs Trading Process

0,5

0,6

0,7

0,8

0,9

1

1,1

Sep-07 Oct-07 Nov-07 Dec-07 Jan-08 Feb-08 Mar-08

Nor

mal

ized

pric

es

Valspar Corp Speedway Motorsports

Pair opened (prices diverge)

Pair closed (prices converge again within a month)

25LosingSightoftheTreesfortheForest?AttentionShiftsandPairsTrading

Here, pairs trading works perfectly. Clearly, this is notalways the case. Is pairs trading in some situations sy-stematically more profitable than in other scenarios? Inouranalysis,weareparticularly interestedinwhether itmakesanydifferencewhetherstocksdivergeonhighorlowdistractiondays.Ourbaselinefindingiscapturedinfigure2.

Itdisplays,inevent-time,theaverageone-monthreturnonlong-shortUSstockpairsbydistractionproxydecileranks.Findingsarebasedonmorethan100,000round-triptradesbetweenJanuary1962andDecember2008.Thelower(up-per)linecanbeinterpretedaslower(upper)boundforthereturnachievedbythestrategy.Thereappearstobeaclo-setomonotonic increase intheprofitabilitybydistractiondeciles.Forinstance,theaverageone-monthreturnontho-selong-shortUSstockpairsin1962to2008whichhappentoopenonhighdistractiondays isabouttwiceashighasthereturnonpairswhichopenon lowdistractiondays. Inline with the implications of limited investor attention, wealsofindthatpairsdivergingonhighdistractiondaysarefarmorelikelytoconvergeagainwithininthenextfewdays.

These return differences appear robust. For instance, theyarequitepersistentovertimeandnotsensitivetothespe-cificdesignofthedistractionproxy.Theyexhibitlittleexpo-

suretowell-knownriskpremiasuchassize,value,momen-tum or short-term reversal. They survive comprehensivemultivariateregressiontests,includingforinstancecontrolsfor calendar effects or market-level conditions on the dayofdivergence(e.g.squaredmarketreturn,volatility, turno-ver).Moreover, thereturndifferencescannotbeexplainedsatisfactorily by proxies for time-varying arbitrage risk.Tradedstockstendtobelargeandliquid,andstandardpaircharacteristicsareverysimilaracrossdistractiondeciles.Tomitigate concerns that unobserved variables might driveourresults,wealsoexamine,withsimilarresults,returnstoasubsetofpairsthathappentodivergeonbothhighandlowdistractiondays.

Our findings are not limited to the US market. The returndifferencebetweenhighandlowdistractiondays isaper-sistent phenomenon which,withvaryingdegree, isobser-vable ineachof theeightmajornon-USstockmarketsweadditionallystudy.

Alternative proxies for limited attention, which we derivefrom the previous literature, often have some incrementaleffect.Theseproxiesinclude,forinstance,downmarketpe-riods,thenumberofcompetingevents,ortherelativede-mand for market-level information measured by shocks inGooglesearchqueries.Moreover,USpairsopening imme-

Figure2:OneMonthReturnonUSStockPairsbyDistractionProxyDecileRanks

Here, pairs trading works perfectly. Clearly, this is not always the case. Is pairs trading in some situations systematically more profitable than in other scenarios? In our analysis, we are particularly interested in whether it makes any difference whether stocks diverge on high or low distraction days. Our baseline finding is captured in figure 2.

Figure 2: One Month Return on US Stock Pairs by Distraction Proxy Decile Ranks

It displays, in event-time, the average one-month return on long-short US stock pairs by distraction proxy decile ranks. Findings are based on more than 100,000 round-trip trades between January 1962 and December 2008. The lower (upper) line can be interpreted as lower (upper) bound for the return achieved by the strategy. There appears to be a close to monotonic increase in the profitability by distraction deciles. For instance, the average one-month return on those long-short US stock pairs in 1962 to 2008 which happen to open on high distraction days is about twice as high as the return on pairs which open on low distraction days. In line with the implications of limited investor attention, we also find that pairs diverging on high distraction days are far more likely to converge again within in the next few days.

These return differences appear robust. For instance, they are quite persistent over time and not sensitive to the specific design of the distraction proxy. They exhibit little exposure to well-known risk premia such as size, value, momentum or short-term reversal. They survive comprehensive multivariate regression tests, including for instance controls for calendar effects or market-level conditions on the day of divergence (e.g. squared market return, volatility, turnover). Moreover, the return differences cannot be explained satisfactorily by proxies for time-varying arbitrage risk. Traded stocks tend to be large and liquid, and standard pair characteristics are very similar across distraction deciles. To mitigate concerns that

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

1.80%

2.00%

1 2 3 4 5 6 7 8 9 10

Aver

age

One

Mon

th E

vent

-Tim

e R

etur

n

Distraction Deciles (1=low distraction day, 10=high distraction day)

Upper bound (less conservative return computation)

Lower bound (conservative return computation)


diatelybeforeholidays,wheninvestordistractionislikelytobeparticularlyhigh,tendtobemoreprofitableandtocon-vergemoreoftenthanpairsonaverage.Inlinewithourhy-potheses, the impactof investordistractionappears lowerfor pairs consisting of firms from the same industry or forpairsconsistingofwholevalue-weightedindustries.Finally,pairsparticularlyneglected(covered)bythemediaappearmore(less)profitable,andexhibitahigher(lower)sensitivitytochangesinthelevelofinvestordistraction.

Collectively,ourresultslendbroadsupporttotheideathatthe relativeefficiency of linked assetsmight not be stableovertime,butbeaffectedbyshort-termattentionshifts.

Inourview,ourempiricalapproachprovidesapromisingse-tuptogaininsightsabouttheimpactoftime-varyinginve-storinattentiononassetpricingforseveralreasons:

1. Itsquantitativenatureallowsusto identifysetsof fun-damentally linked firms, for which cross-stock informa-tiontransferislikelytobeinhibitedinmomentsofhighdistraction. We rely on an intuitive, parsimonious wayof identifying firms which are somehow economicallyrelateddespitemainlyoperatingindifferentmarketseg-ments. In sum, the economic link between two typicalfirmsinouranalysismightbethoughtofaspotentiallybeingstrong,butsimultaneouslyoftenalsolessexplicit,obvious,andtransparent,andthuspronetobeingneg-lectedparticularlyeasily.

2. Thetypeofreturnpredictability inpairstradingisdiffe-rentfromthetypeofreturnpredictabilitythathasbeenlinkedtolimitedattentionintheliteraturesofar.Previousstudiesassetshaveanalyzedthelaggedpriceresponseofstockstotheirownpastreturns,lead-lageffectsbetweenportfoliosofstocks,orreturnpredictabilityalongthesup-plychain.Pairstrading,however,isaboutpredictingtherelative performance of two individual, typically ratherlargestockswithanoftennon-obviousrelationship,outofwhichneitheristhesystematicleader.Linkingthistypeofcross-predictabilityof returns tovariations in investordistraction,is,toourknowledge,new.

3. Thenatureofpairstradingprofitsfitswellwiththeideaof attention constraints impeding timely informationspill-over.Itsprofitabilitytendstoalmostmonotonicallydeclineinevent-time.Importantly,thedayofdivergenceappearstobeacriticaldate.Infact,alargefractionofthecumulativereturndifferenceupondivergenceisattribu-

tabletothedayofdivergenceitself.Thus,identifyingcir-cumstancesinwhichthisbehaviorisexantemorelikelytobecausedbytemporarymarketfrictionsisakeytothestrategy'ssuccess.

4. Ingeneral,comprehensiveempiricalstudiesonpairstra-ding are still rare. This is surprising given its large see-minglyabnormalreturnsreportedinGatevetal.(2006)as well as its apparent popularity among practitioners.Moreover,verylittleisknownaboutpairstradinginin-ternationalmarkets,eventhoughonlyveryfewtradingstrategies have survived the test of time and indepen-dentscrutiny.Asaconsequence, it isstillanopenque-stionwhen,where,andwhypairstradingisparticularlyprofitable. We address this gap in the literature with adatasetcomprisingabout14,000stockswith25millionfirmdaysfromeightmajornon-USstockmarkets.

5. Fromabroaderperspective,ourfindingsmighthelptoshed light on other pervasive puzzles. In a number ofrelated scenarios such as closed-end funds, dual classshares,ortwinstocks,therearealsopricediscrepanciesbetween similar assets, which are difficult to reconcilewithstandardtheory.

Contact

Dr.HeikoJacobsUniversityofMannheimChairofBusinessAdministrationandFinance,esp.BankingD-68131Mannheim,GermanyPhone:+49-(0)621-181-3453E-Mail:[email protected]

ReferencesGatev, E. G., W. N. Goetzmann, and K. G. Rouwenhorst,2006,“Pairstrading:Performanceofarelative-valuearbi-tragerule,”ReviewofFinancialStudies,19,797-827.

Hirshleifer,D.,S.S.Lim,andS.H.Teoh,2009,“Driventodis-traction:Extraneouseventsandunderreactiontoearningsnews,”JournalofFinance,64,2289-2325.

Peng,L.,andW.Xiong,2006,“Investorattention,overcon-fidenceandcategorylearning,”JournalofFinancialEcono-mics,80,563-602.


mailto:jacobs%40bank.bwl.uni-mannheim.de?subject=

28

Executive Summary1

Commoditypricedynamicsareofvital importance forhedgersandinvestorsalike.Duetofundamentalsupplyanddemandcharacteristics,manycommoditymarketsexhibitaseasonalbehavior.Theseseasonalfluctuationsoncommoditymarketsarepresentnotonlyinthepricelevelbutalsointhevolatility.Thisthesisacknowledgestheseseasonalfluctuationsandcontributestothelite-raturebyproposingdifferentmodels for thevaluationof commodity derivatives which are able to capturethis seasonal behavior. In a first step, standard spotprice models are extended for seasonal volatility. In asecondstep,anewseasonalstochasticvolatilitymodelispresented.Thepresentedmodelsaretestedinempi-rical studies by utilizing extensive data on commodityfuturesoptions.Aneconomicallyandstatisticallysigni-ficant improvement of pricing accuracy is gained byincluding the proposed seasonal volatility adjustmentandtherebyconfirmingthe importanceofthepresen-tedmodelextensions.

1. Introduction

Whilecommoditymarketshavealonghistory,morere-centfinancialinnovationseasetheaccesstocommodi-tyinvestmentsforabroadrangeofinvestors.Commo-ditiesareconsumablephysicalassetsthatplayacentralroleineconomicgrowthandwelfare.Tradinginphysi-calassetsofteninvolveshightransactioncosts.Forthisreason,tradingincommoditiestakesplaceprimarilyinfuturesmarkets.Futurescontractsreflectexpectationsofmarketparticipantsregardingfuturespotpricesandaresubjecttotheinteractionofdemandandsupplyfor

1ThisworkwascompletedduringmytimeasPhDstudentatWHU–Otto Beisheim School of Management and during my time as visitingscholaratSternSchoolofBusiness(NewYorkUniversity)andPrincetonUniversity.

differentdeliverydates.Commodityderivatives,likefu-turescontracts,havethefunctionofmakingcommodi-ty risks tradable and allowing for a more efficient riskallocation.Thereby,specificfundamentaleconomicfac-torshavetobetaken intoaccountwhenassessingthecharacteristicsofcommodityinvestments.

From a portfolio management perspective, commodi-tiesarefrequentlyconsideredtohaveanattractiverisk-returnprofile.Analyzingthepropertiesofcommoditiesasanassetclass,itisusuallyfoundthataddingcommo-dityinvestmentstoaportfolioleadstoamoreefficientassetallocation.Often,asignificantdiversificationpo-tentialofcommoditiesisnotedduetoalowornegati-ve correlation with other traditional asset classes. Fur-thermore,commoditiesarefoundtohavethepropertyofbeingagoodinflationhedge.Studiesregardingthebenefits from commodity investments comprise thework of, e.g., Bodie and Rosansky (1980), Jensen et al.(2002), Mulvey et al. (2004), Gorton and Rouwenhorst(2006), Erb and Harvey (2006), Miffre and Rallis (2007),and Geman and Kharoubi (2008). In the light of incre-asedpricevolatilityduetoderegulationandtheenor-mousdemandfornaturalresourcesofrisingeconomieslikeChinaorIndia,commoditymarketsareinthefocusnotonlyfromanacademicperspectivebutalsofromaneconomicperspective.

When assessing the risk and return characteristics ofcommodity investments, studies often fail to acknow-ledge the seasonal characteristics of commodity mar-

von Dr. Janis Back

Dr. Janis Back

E SSAyS oN ThE vALuATIoN of commodIT y dERIvATIvE S

k ATEgoRIE: dISSERTATIoNEN

EssaysontheValuationofCommodityDerivatives

kets. Naturally, this seasonal behavior should be con-sidered in the context of portfolio management andhasdramatic implicationsforthepricingofderivativescontractswrittenonthesecommodities.Theaspectofseasonal volatility in the valuation of commodity deri-vativesisinthefocusofthisthesis.

Thefirstmainpartofthethesis”EssaysontheValuati-onofCommodityDerivatives”containsadiscussionofthetheoreticalbackgroundandempiricalobservationswith regard to the relationship between commodityspotandfuturescontractsandtheirpricedynamics.Acomprehensiveoverviewofvaluationmodels forcom-modityderivativesispresented.Theuniquecharacteri-stics of commodities and their implications for the va-luation of commodity contingent claims are describedwherebythefocusissetonseasonality.Theimportanceof seasonal variations in volatility for the valuation ofcommodity options is then analyzed in two empiricalstudies, which represent the main contribution of thisthesis.

2. Commodity Price Dynamics and Derivatives Valu-ation

In comparison to other financial markets, commoditymarkets exhibit several peculiarities. From a financi-al perspective, e.g., storage and transportation costsand the perishability of goods hinder the applicationofstandardarbitragerelationships for thevaluationofcommodity contingent claims. In contrast to other fi-nancialmarkets,thefuturescurvecaneitherbeupwardsloping (contango) or downward sloping (backwarda-tion) leading either to losses or gains when rolling in-vestments to the next contract month. Furthermore,commodity price dynamics are regularly characterizedbymean-reversionandcandisplay jumpsandhigh le-velsofvolatility–duetoscarcityforacommoditywhiledemand is relatively inelastic, forexample.Thespecialnature of commodities implies that their price dyna-mics exhibit some unique characteristics which needto be considered when deciding about investment orhedging strategies or when valuing commodity con-tingent claims. Thereby, a thorough understanding ofcommodity price dynamics is important for hedgersandinvestorsalike.

One further stylized fact of commodities is that pricemovements in many commodity markets show signifi-cantseasonalpatterns.Theseasonalbehaviorofcom-modity price dynamics can be induced either by thedemandorbythesupplyside.Prominentexamplesareweather-relateddemandpatternsforenergycommodi-tiesandthevaryingsupplyofagriculturalcommoditiesaccording to harvesting cycles. As such, seasonality ispresentatthepriceleveland,furthermore,manycom-modity markets contain a strong seasonal componentinvolatility.Whileseasonalityat theprice leveland itsimplications for the valuation of commodity futures iswidely recognizedandrelativelywellunderstood, lite-rature considering seasonality in volatility is very limi-ted.Thisthesisaimstoshedlightontheseasonalvaria-tionsinvolatilityandtheir implicationsforcommodityderivativesprices.

Thevolatilityofcommodity futurespriceswillbehighduring periods when new information enters the mar-ketandsignificantamountsofsupplyordemanduncer-taintyareresolved.For,e.g.,heatingoil,thisisthecaseduring the winter when heating is needed. In agricul-turalmarkets,thisistrueshortlybeforeandduringtheharvesting period. Information regarding the subse-quentharvestbecomesavailableduringthistimecau-singahigher fluctuation inprices,whileaminimumistypically reachedduringthewintermonths. InFigures1and2,onecanobservethatforsoybeansandheatingoiltherealizedvolatilityvariesconsiderablythroughout

contingent claims are described whereby the focus is set on seasonality. The importance of seasonal variations in volatility for the valuation of commodity options is then analyzed in two empirical studies, which represent the main contribution of this thesis.

2. Commodity Price Dynamics and Derivatives ValuationIn comparison to other financial markets, commodity markets exhibit several peculiarities. From a financial perspective, e.g., storage and transportation costs and the perishability of goods hinder the application of standard arbitrage relationships for the valuation of commodity contingent claims. In contrast to other financial markets, the futures curve can either be upward sloping (contango) or downward sloping (backwardation) leading either to losses or gains when rolling investments to the next contract month. Furthermore, commodity price dynamics are regularly characterized by mean-reversion and can display jumps and high levels of volatility – due to scarcity for a commodity while demand is relatively inelastic, for example. The special nature of commodities implies that their price dynamics exhibit some unique characteristics which need to be considered when deciding about investment or hedging strategies or when valuing commodity contingent claims. Thereby, a thorough understanding of commodity price dynamics is important for hedgers and investors alike.

One further stylized fact of commodities is that price movements in many commodity markets show significant seasonal patterns. The seasonal behavior of commodity price dynamics can be induced either by the demand or by the supply side. Prominent examples are weather-related demand patterns for energy commodities and the varying supply of agricultural commodities according to harvesting cycles. As such, seasonality is present at the price level and, furthermore, many commodity markets contain a strong seasonal component in volatility. While seasonality at the price level and its implications for the valuation of commodity futures is widely recognized and relatively well understood, literature considering seasonality in volatility is very limited. This thesis aims to shed light on the seasonal variations in volatility and their implications for commodity derivatives prices.

Figure 1: Seasonal pattern of soybean front-month futures volatilities from January 1990 to 2009. Furthermore, the seasonal volatility pattern was approximated by a trigonometric function.

The volatility of commodity futures prices will be high during periods when new information enters the market and significant amounts of supply ordemand uncertainty are resolved. For, e.g.,heating oil, this is the case during the winter when heating is needed. In agricultural markets, this is true shortly before and during the harvesting period. Information regarding the subsequent harvest becomes available during this time causing a higher fluctuation in prices, while a minimum is typically reached during the winter months. In Figures 1 and 2, one can observe that for soybeans and heating oil the realized volatility varies considerably throughout the year, ranging from 17% to 30% in the case of soybeans, and 27% to 48% in the case of heating oil.

Figure 2: Seasonal pattern of heating oil front-month futures volatilities from January 1990 to 2009. Furthermore, the seasonal volatility pattern was approximated by a trigonometric function.

It is of vital importance that these pronounced seasonal variations in volatility are taken into account, for both risk management and the pricing of commodity derivatives. This thesis

29EssaysontheValuationofCommodityDerivatives

Figure 1: Seasonal pattern of soybean front-month futures volatili-ties from January 1990 to 2009. Furthermore, the seasonal volatility pattern was approximated by a trigonometric function.

theyear,rangingfrom17%to30%inthecaseofsoybe-ans,and27%to48%inthecaseofheatingoil.

Itisofvitalimportancethatthesepronouncedseasonalvariations in volatility are taken into account, for bothriskmanagementandthepricingofcommodityderiva-tives.This thesisconcentratesonthe latteraspectandcontributes to the literature concerning the valuationof commodity contingent claims. Since assumptionsregardingvolatilityareespeciallyimportantforoptionsprices,thefocusisontheroleofseasonalvolatilityforthepricingofcommodityoptions.

3. Seasonality and the Valuation of Commodity Op-tions

Motivated by the observation of these pronouncedseasonal patterns in volatility, the first empirical studyispresentedwheretheroleofseasonalvolatilityinthecontext of pricing models for commodity derivativesis investigated. Following the ideas of Richter and Sø-rensen(2002)andGemanandNguyen(2005),one-andtwo-factor continuous-time spot price models are ex-tended by including deterministic time-dependentcomponents in order to take the seasonal behavior ofcommoditiesintoaccount.

3.1ModelDynamics

Intheone-factormodel,thelogarithmofthespotprice,ln St,ofacommodityisassumedtofollowanOrnstein-

Uhlenbeckprocesswithseasonalityinlevelandvolati-lity.Let

wheres(t) isadeterministicfunctionoftimecapturingthe seasonality of a commodity’s price level. It can beshownthatithasnoimpactonoptionpricesand,hence,we refrain from specifying the function s(t) explicitly.LetZtXbeastandardBrownianmotion.ThestochasticcomponentXtisassumedtofollowthedynamics

withκ > 0denotingthedegreeofmean-reversionto-wards the long-run meanμ of the process. The volati-lityoftheprocess ischaracterizedbyσXandthefunc-tionφ(t),whichdescribestheseasonalbehaviorof theasset’svolatility.Whileadeterministicseasonalcompo-nentatthepricelevel,s(t),canbeneglectedintermsofoptionspricing,thisisnottruefortheseasonalpatternobservedinthevolatility.

ConsideringtheempiricalvolatilitypatternsinFigures1and2,wefollowGemanandNguyen(2005)andspecifythefunctionφ(t)describingtheseasonalfigureas

whereθgovernstheamplitudeofthesine-functionandζtheshiftalongthetime-dimension.

In a similar fashion, the two-factor model of Schwartzand Smith (2000) is extended by a seasonal volatili-ty component. Hence, a one- and a two-factor modelwith seasonal volatility and the respective benchmarkmodels without seasonal volatility are considered inthisstudy.Giventhemodeldynamics,valuationformu-las for futures contracts and options written on thesefutures can be derived and implemented for both theone-andthetwo-factormodels.

3.2EmpiricalStudy

Theempiricalstudyconsidersthesoybeanandheatingoil markets where a seasonal volatility pattern is indu-ced from harvesting cycles and temperature-relateddemand variations, respectively. The extensive data

Figure 2 : Seasonal pattern of heating oil front-month futures vo-latilities from January 1990 to 2009. Furthermore, the seasonal volatility pattern was approximated by a trigonometric function.

contingent claims are described whereby the focus is set on seasonality. The importance of seasonal variations in volatility for the valuation of commodity options is then analyzed in two empirical studies, which represent the main contribution of this thesis.

2. Commodity Price Dynamics and Derivatives ValuationIn comparison to other financial markets, commodity markets exhibit several peculiarities. From a financial perspective, e.g., storage and transportation costs and the perishability of goods hinder the application of standard arbitrage relationships for the valuation of commodity contingent claims. In contrast to other financial markets, the futures curve can either be upward sloping (contango) or downward sloping (backwardation) leading either to losses or gains when rolling investments to the next contract month. Furthermore, commodity price dynamics are regularly characterized by mean-reversion and can display jumps and high levels of volatility – due to scarcity for a commodity while demand is relatively inelastic, for example. The special nature of commodities implies that their price dynamics exhibit some unique characteristics which need to be considered when deciding about investment or hedging strategies or when valuing commodity contingent claims. Thereby, a thorough understanding of commodity price dynamics is important for hedgers and investors alike.

One further stylized fact of commodities is that price movements in many commodity markets show significant seasonal patterns. The seasonal behavior of commodity price dynamics can be induced either by the demand or by the supply side. Prominent examples are weather-related demand patterns for energy commodities and the varying supply of agricultural commodities according to harvesting cycles. As such, seasonality is present at the price level and, furthermore, many commodity markets contain a strong seasonal component in volatility. While seasonality at the price level and its implications for the valuation of commodity futures is widely recognized and relatively well understood, literature considering seasonality in volatility is very limited. This thesis aims to shed light on the seasonal variations in volatility and their implications for commodity derivatives prices.

Figure 1: Seasonal pattern of soybean front-month futures volatilities from January 1990 to 2009. Furthermore, the seasonal volatility pattern was approximated by a trigonometric function.

The volatility of commodity futures prices will be high during periods when new information enters the market and significant amounts of supply ordemand uncertainty are resolved. For, e.g.,heating oil, this is the case during the winter when heating is needed. In agricultural markets, this is true shortly before and during the harvesting period. Information regarding the subsequent harvest becomes available during this time causing a higher fluctuation in prices, while a minimum is typically reached during the winter months. In Figures 1 and 2, one can observe that for soybeans and heating oil the realized volatility varies considerably throughout the year, ranging from 17% to 30% in the case of soybeans, and 27% to 48% in the case of heating oil.

Figure 2: Seasonal pattern of heating oil front-month futures volatilities from January 1990 to 2009. Furthermore, the seasonal volatility pattern was approximated by a trigonometric function.

It is of vital importance that these pronounced seasonal variations in volatility are taken into account, for both risk management and the pricing of commodity derivatives. This thesis

concentrates on the latter aspect and contributesto the literature concerning the valuation of commodity contingent claims. Since assumptions regarding volatility are especially important for options prices, the focus is on the role of seasonal volatility for the pricing of commodity options.

3. Seasonality and the Valuation of Commodity OptionsMotivated by the observation of these pronounced seasonal patterns in volatility, the first empirical study is presented where the role of seasonal volatility in the context of pricing models for commodity derivatives is investigated.Following the ideas of Richter and Sørensen (2002) and Geman and Nguyen (2005), one- andtwo-factor continuous-time spot price models are extended by including deterministic time-dependent components in order to take the seasonal behavior of commodities into account.

3.1 Model DynamicsIn the one-factor model, the logarithm of the spot price, ln 𝑆𝑆𝑡𝑡, of a commodity is assumed to follow an Ornstein-Uhlenbeck process with seasonality in level and volatility. Let

ln 𝑆𝑆𝑡𝑡 =𝑋𝑋𝑡𝑡 + 𝑠𝑠(𝑡𝑡)

where 𝑠𝑠(𝑡𝑡) is a deterministic function of time capturing the seasonality of a commodity’s price level. It can be shown that it has no impact on option prices and, hence, we refrain from specifying the function 𝑠𝑠(𝑡𝑡) explicitly. Let 𝑍𝑍𝑡𝑡𝑋𝑋 be a standard Brownian motion. The stochastic component 𝑋𝑋𝑡𝑡 is assumed to follow the dynamics

d𝑋𝑋𝑡𝑡 = κ(𝜇𝜇 − 𝑋𝑋𝑡𝑡)d𝑡𝑡 + 𝜎𝜎𝑋𝑋𝑒𝑒𝜑𝜑(𝑡𝑡)d𝑍𝑍𝑡𝑡𝑋𝑋

with κ > 0 denoting the degree of mean-reversion towards the long-run mean 𝜇𝜇 of the process. The volatility of the process is characterized by 𝜎𝜎𝑋𝑋 and the function 𝜑𝜑(𝑡𝑡), which describes the seasonal behavior of the asset’s volatility. While a deterministic seasonal component at the price level, 𝑠𝑠(𝑡𝑡), can be neglected in terms of options pricing, this is not true for the seasonal pattern observed in the volatility.

Considering the empirical volatility patterns inFigures 1 and 2, we follow Geman and Nguyen (2005) and specify the function 𝜑𝜑(𝑡𝑡) describing the seasonal figure as

𝜑𝜑(𝑡𝑡) = 𝜃𝜃 sin(2𝜋𝜋(𝑡𝑡 + ζ))

where 𝜃𝜃 governs the amplitude of the sine-function and ζ the shift along the time-dimension.

In a similar fashion, the two-factor model of Schwartz and Smith (2000) is extended by a seasonal volatility component. Hence, a one- and a two-factor model with seasonal volatility and the respective benchmark models without seasonal volatility are considered in this study. Given the model dynamics, valuation formulas for futures contracts and options written on these futures can be derived and implemented for both the one-and the two-factor models.

3.2 Empirical StudyThe empirical study considers the soybean and heating oil markets where a seasonal volatility pattern is induced from harvesting cycles and temperature-related demand variations, respectively. The extensive data set consists of 156,129 soybean and 475,472 heating oil option prices. In a first step, the model parameters are estimated for every day in our observation period covering approximately five years for both markets. Model parameters are obtained byminimizing root mean squared errors (RMSE) between observed market prices and theoretical model prices. Given the estimated model parameters, time series of pricing errors for the one- and two-factor seasonal volatility models and the respective benchmark models can be obtained – for both the soybean and the heating oil data set and in- and out-of-sample.

This study finds that the inclusion of a deterministic seasonal function in volatility significantly reduces options pricing errors. Specifically, one can observe that incorporating seasonal volatility reduces the RMSE of theoretical model implied prices and observed market prices in every instance, i.e. for both markets, for the one- and the two-factor models,in-sample and out-of-sample, and for every maturity bracket and moneyness category in which we have divided our data set.

Table 1: Pricing error reductions due to seasonality extension. Pricing errors are calculated as root meansquared errors for the one- and two-factor models with and without seasonal volatility.

Model In-Sample Out-of-Sample

Soybeans1-Factor 15.10% 11.04%2-Factor 17.85% 12.61%

Heating Oil1-Factor 20.49% 15.33%2-Factor 14.18% 9.42%

Results significant at the 1% level (Wilcoxon Sign test)

The out-of-sample pricing errors for the one- andtwo-factor models are reduced by 11.04% and 12.61% for the soybean options, and by 15.33% and 9.42% for the heating oil options,








































setconsistsof156,129soybeanand475,472heatingoiloptionprices. Inafirststep,themodelparametersareestimated for every day in our observation period co-vering approximately five years for both markets. Mo-delparametersareobtainedbyminimizing rootmeansquared errors (RMSE) between observed market pri-ces and theoretical model prices. Given the estimatedmodelparameters, timeseriesofpricingerrors for theone-andtwo-factorseasonalvolatilitymodelsandtherespective benchmark models can be obtained – forboth the soybean and the heating oil data set and in-andout-of-sample.

This study finds that the inclusion of a deterministicseasonal function involatilitysignificantlyreducesop-tions pricing errors. Specifically, one can observe thatincorporating seasonal volatility reduces the RMSE oftheoreticalmodel impliedpricesandobservedmarketprices in every instance, i.e. for both markets, for theone-andthetwo-factormodels,in-sampleandout-of-sample,andforeverymaturitybracketandmoneynesscategoryinwhichwehavedividedourdataset.


Soybeans 1-Factor 15.10% 11.04%

2-Factor 17.85% 12.61%

HeatingOil 1-Factor 20.49% 15.33%

2-Factor 14.18% 9.42%

Resultssignificantatthe1%level(WilcoxonSigntest)

Theout-of-samplepricingerrorsfortheone-andtwo-factormodelsarereducedby11.04%and12.61%forthesoybeanoptions,andby15.33%and9.42%forthehe-atingoiloptions,respectively.Theresultsarehighlysi-gnificant–notonlyeconomicallybutalsostatisticallyata1%significancelevel.Inarobustnesscheck,thesameresultswereobtained.Furthermore,inaregressionana-lysisofpricingerrors, it isdocumentedthatsystematicmispricingofsoybeanandheatingoilfuturesoptionsisreducedduetotheseasonalityadjustment.

3.3Summary

The highlighted seasonal effects are well-known inthe literature, but their impact on commodity optionspricing has never been thoroughly investigated. Twostandardcontinuoustimecommodityderivativesvalu-ation models are extended to incorporate seasonalityinvolatility.Usinganextensivedatasetofsoybeanandheatingoiloptions,theempiricaloptionspricingaccu-racy of these models is compared with their constantvolatilitycounterparts.Theresultsshowthatincorpora-tingthestylizedfactofseasonallyfluctuatingvolatilitysignificantly improves options valuation performance.Thisleadstotheconclusionthatseasonalityinvolatilityshouldbeaccountedforwhendealingwithoptionsonseasonalcommodities.

4. Seasonal Stochastic Volatility: Implications for the Pricing of Commodity Options

Whenanalyzingthepricingerrorsintheoptionpricingstudy presented above, evidence for a volatility smi-leeffectwas found.For this reason,anovelmodel forthe pricing of commodity futures options is proposedwhere volatility is stochastic, not deterministic. Thisnewmodelallowsforstochasticvolatilitywhilethevo-latilityprocesstakesintoaccounttheobservedseasonalpattern.

4.1CommodityFuturesPriceDynamics

Inthisnewmodel,wespecifythepricedynamicsofthefuturescontractdirectlyinsteadofderivingfuturespri-ces fromthespotpricedynamics.Particularly,wepre-sentanovelstochasticvolatilitymodelwherethelong-termmeanofthevarianceprocessisdescribedthroughaseasonalfunction.Thecommodityfuturespricedyna-micsunderthephysicalmeasureareassumedtofollow

whereFt(T)isthefuturespriceattwithmaturityTandμisthedriftofthefuturespriceprocessunderthephy-sical measure. Vt is the instantaneous variance of the

Table 1: Pricing error reductions due to seasonality extension. Pricing er-rors are calculated as root mean squared errors for the one- and two-factor models with and without seasonal volatility.

respectively. The results are highly significant –not only economically but also statistically at a 1% significance level. In a robustness check, the same results were obtained. Furthermore, in a regression analysis of pricing errors, it isdocumented that systematic mispricing of soybean and heating oil futures options isreduced due to the seasonality adjustment.

3.3 SummaryThe highlighted seasonal effects are well-known in the literature, but their impact on commodity options pricing has never been thoroughly investigated. Two standard continuous time commodity derivatives valuation models are extended to incorporate seasonality in volatility. Using an extensive data set of soybean and heating oil options, the empirical options pricing accuracy of these models is compared with their constant volatility counterparts. The results show that incorporating the stylized fact of seasonally fluctuating volatility significantly improves options valuation performance. This leads to the conclusion that seasonality in volatility should be accounted for when dealing with options on seasonal commodities.

4. Seasonal Stochastic Volatility: Implications for the Pricing of Commodity OptionsWhen analyzing the pricing errors in the option pricing study presented above, evidence for a volatility smile effect was found. For this reason, a novel model for the pricing of commodity futures options is proposed where volatility is stochastic, not deterministic. This new model allows for stochastic volatility while the volatility process takes into account the observed seasonal pattern.

4.1 Commodity Futures Price DynamicsIn this new model, we specify the price dynamics of the futures contract directly instead of deriving futures prices from the spot price dynamics. Particularly, we present a novel stochastic volatility model where the long-term mean of the variance process is described through a seasonal function. The commodity futures price dynamics under the physical measure are assumed to follow

d𝐹𝐹𝑡𝑡(𝑇𝑇) =𝜇𝜇𝐹𝐹𝑡𝑡(𝑇𝑇)d𝑡𝑡 + 𝐹𝐹𝑡𝑡(𝑇𝑇)�𝑉𝑉𝑡𝑡d𝑍𝑍𝑡𝑡𝐹𝐹

d𝑉𝑉𝑡𝑡 = κ(𝜃𝜃(𝑡𝑡) − 𝑉𝑉𝑡𝑡)d𝑡𝑡 + 𝜎𝜎�𝑉𝑉𝑡𝑡d𝑍𝑍𝑡𝑡𝑉𝑉

𝜃𝜃(𝑡𝑡) = �̅�𝜃𝑒𝑒ηsin(2𝜋𝜋(𝑡𝑡+ζ))

where 𝐹𝐹𝑡𝑡(𝑇𝑇) is the futures price at t with maturity T and 𝜇𝜇 is the drift of the futures price process under the physical measure. 𝑉𝑉𝑡𝑡 is the instantaneous variance of the futures returns, κ is

the mean-reversion speed of the variance process, 𝜃𝜃(𝑡𝑡) is the long-term variance level to which the process reverts, and σ is the volatility-of-volatility parameter. 𝑍𝑍𝑡𝑡𝐹𝐹 and 𝑍𝑍𝑡𝑡𝑉𝑉 are two standard Brownian motions with instantaneous correlation ρ. The long-term variance parameter 𝜃𝜃(𝑡𝑡) is generalized to be a deterministic function of time. The long-term mean variance level is assumed to be �̅�𝜃, which is superimposed by a seasonal component. Again, the shape of the seasonal adjustment is specified by two parameters: the size of the seasonal effect is governed by η (amplitude) and ζ (shift along the time-dimension)

The model framework allows for the derivation of semi closed-form options pricing formulas in the spirit of Heston (1993). In contrast to relatedmodels proposed by Geman and Nguyen (2005) and Richter and Sørensen (2002), our model hasthe crucial advantage of enabling us to compute option values in an efficient way which is of significant importance if one wants to apply the model in practice. In an appendix, detailed comments are given on how an efficient implementation of our seasonal stochastic volatility model can be obtained.

4.2 Empirical StudyThis computational tractability allows us to empirically study the pricing performance of our model using an extensive data set of natural gas futures options. The natural gas market is characterized by high volatility, which evolves stochastically while following a pronounced seasonal pattern. Due to inelastic demand and supply, demand variations during the heating period can cause large price changes and lead to a higher volatility during the cold season.

Analogeous to Broadie et al. (2007), a two-step procedure for the model estimation is employed,where the Markov chain Monte Carlo (MCMC) technique is utilized. In contrast to other studies, not only the cross-section of options prices but also the time series of futures contracts is utilized in the model estimation.

Analyzing an extensive data set with 367,469 prices of natural gas futures options, the results of this empirical study show that our model is superior for the pricing of commodity options with seasonalities. Compared to the standard stochastic volatility model of Heston (1993), our model yields substantial improvements in pricing accuracy. In particular, root mean squared errors of implied volatilities are reduced by 5.48% and 6.38% for two different objective functions which were employed in the estimation procedure. The obtained results are both statistically and


futures returns, κ is the mean-reversion speed of thevariance process, θ(t) is the long-term variance leveltowhich theprocess reverts,andσ is thevolatility-of-volatilityparameter.ZtFandZtVaretwostandardBrow-nian motions with instantaneous correlation ρ. Thelong-term variance parameterθ(t) is generalized to bea deterministic function of time. The long-term meanvariance level isassumedtobeθ,which issuperimpo-sedbyaseasonalcomponent.Again, theshapeof theseasonaladjustmentisspecifiedbytwoparameters:thesizeoftheseasonaleffectisgovernedbyη(amplitude)andζ(shiftalongthetime-dimension)

Themodelframeworkallowsforthederivationofsemiclosed-formoptionspricingformulasinthespiritofHe-ston (1993). Incontrast to relatedmodelsproposedbyGeman and Nguyen (2005) and Richter and Sørensen(2002),ourmodelhasthecrucialadvantageofenablingustocomputeoptionvaluesinanefficientwaywhichisofsignificantimportanceifonewantstoapplythemo-del inpractice. Inanappendix,detailedcommentsaregivenonhowanefficientimplementationofourseaso-nalstochasticvolatilitymodelcanbeobtained.

4.2EmpiricalStudy

Thiscomputationaltractabilityallowsustoempiricallystudy the pricing performance of our model using anextensive data set of natural gas futures options. Thenatural gas market is characterized by high volatili-ty, which evolves stochastically while following a pro-nouncedseasonalpattern.Duetoinelasticdemandandsupply, demand variations during the heating periodcancauselargepricechangesandleadtoahighervola-tilityduringthecoldseason.

Analogeous to Broadie et al. (2007), a two-step proce-dure for themodelestimation isemployed,where theMarkovchainMonteCarlo(MCMC)techniqueisutilized.Incontrast toother studies,notonly thecross-sectionofoptionspricesbutalsothetimeseriesoffuturescon-tractsisutilizedinthemodelestimation.

Analyzing an extensive data set with 367,469 prices ofnaturalgasfuturesoptions,theresultsofthisempiricalstudy show that our model is superior for the pricingof commodity options with seasonalities. Comparedto the standard stochastic volatility model of Heston(1993), our model yields substantial improvements in

pricingaccuracy.Inparticular,rootmeansquarederrorsof impliedvolatilitiesarereducedby5.48%and6.38%fortwodifferentobjectivefunctionswhichwereemplo-yed in the estimation procedure. The obtained resultsare both statistically and economically significant andconsistentfordifferentrobustnesschecks.

4.3Summary

In this study, the stochastic volatility model of Heston(1993) is extended to allow volatility to vary with theseasonalcycle.Theproposedmodelframeworkenablesthederivationofsemiclosed-formsolutionsforpricingfuturesoptions.Then,theempiricalperformanceinpri-cingnaturalgasoptionsisstudied.Theempiricalresultsshow that the suggested model indeed increases theaccuracy of pricing natural gas contracts, in terms ofbothstatisticalandeconomicsignificance.

5. Conclusion

Overall, itcanbeconcludedthatseasonalvariationsinvolatility need to be considered when valuing optionswrittenonfuturesforcommoditiesexhibitingseasona-lity.Thisistrueforbothaspotpricemodelsettingwithdeterministic volatility and the presented stochasticvolatilityframework.Thepresentedmodelsareapplica-ble to every commodity market exhibiting seasonalityin volatility. This thesis contributes to the literature bydocumentingtheimportanceofseasonalvolatilityand,mostimportantly,bypresentinghowthiscanbeconsi-deredincommodityoptionspricingmodels.

Naturally,consideringseasonality involatility isofcru-cialimportancenotonlyforthevaluationofcommoditycontingentclaimsbutalsoforinvestmentandhedgingstrategies as well as risk management in general. De-pending on the time of the year, commodity marketscan exhibit very distinct behavior. In the context ofportfoliomanagement,failingtotakethisintoaccount,can lead to a wrong assessment of the risk and returncharacteristicsand,therefore,toaninefficientassetal-location.

Contact

[email protected]


mailto:janis.back%40whu.edu?subject=

References

Z.BodieandV.I.Rosansky.Riskandreturnincommodityfutures.FinancialAnalystsJournal,36:27–39,1980.

M.Broadie,M.Chernov,andM.Johannes.Modelspecifica-tionandriskpremia:Evidencefromfuturesoptions.Jour-nalofFinance,62:1453–1490,2007.

C.B.ErbandC.R.Harvey.Thestrategicandtacticalvalueofcommodity futures. Financial Analysts Journal, 62:69–97,2006.

H.GemanandC.Kharoubi.WTIcrudeoil futures inport-foliodiversification:Thetime-to-maturityeffect.JournalofBanking&Finance,32:2553–2559,2008.

H. Geman andV.-N. Nguyen. Soybean inventory and for-ward curve dynamics. Management Science, 51:1076–1091,2005.

G.GortonandK.G.Rouwenhorst.Factsandfantasiesaboutcommodity futures. Financial Analysts Journal, 62:47–68,2006.

S.L.Heston.Aclosed-formsolutionforoptionswithsto-chastic volatility with applications to bond and currencyoptions.ReviewofFinancialStudies,6:327–343,1993.

G.R.Jensen,R.R.Johnson,andJ.M.Mercer.Tacticalassetallocationandcommodityfutures.JournalofPortfolioMa-nagement,28:100–111,2002.

J.MiffreandG.Rallis.Momentumstrategiesincommodityfutures markets. Journal of Banking & Finance, 31:1863–1886,2007.

J.M.Mulvey,S.S.N.Kaul,andK.D.Simsek.Evaluatingatrend-following commodity index for multi-period assetallocation. Journal of Alternative Investments, 7:54–69,2004.

M.RichterandC.Sørensen.Stochasticvolatilityandseaso-nalityincommodityfuturesandoptions:Thecaseofsoy-beans.WorkingPaper,2002.


Prämiert werden Arbeiten im Bereich alternativer Investments mit

Schwerpunkt Hedgefonds, Private Equity sowie Rohstoffeinsbesondere aus den Disziplinen:

Betriebswirtschaftslehre | Volkswirtschaftslehre Rechtswissenschaften | (Wirtschafts-) Mathematik | Physik

Bundesverband Alternative Investments e. V.

BAI Wissenschaftspreis

DasPreisgeld von insgesamt € 10.000,- wird an die Gewinner folgender Kategorien ausgelobt:

Teilnehmen können Studierende, Doktoranden sowie wissenschaftliche Mitarbeiter

deutscher Hochschulen und Forschungseinrichtungen.

DieJury besteht aus hochrangigen Wissenschaftlern und Experten aus der Praxis.

Abgabetermin 31.Dezember2012

Informationen Detaillierte Informationen und Teilnahmebedingungen finden Sie unter:

w w w . b v a i . d e Rubrik Wissenschaf tsförderung

Dissertationen/Habilitationen

Sonstige wissenschaftliche Arbeiten

Bachelorarbeiten

Diplom-/Masterarbeiten

Wissenschaftspreis

2013

haftungsausschluss

Die Informationen des BAI-Newsletters stellen keine Auf-forderung zum Kauf oderVerkauf vonWertpapieren,Ter-minkontraktenodersonstigenFinanzinstrumentendar.

Eine InvestitionsentscheidungsollteaufGrundlageeinesBeratungsgespräches mit einem qualifizierten Anlagebe-ratererfolgenundaufkeinenFallaufderGrundlagedieserDokumente/Informationen. Alle Angaben und Quellenwerden sorgfältig recherchiert. Für Vollständigkeit undRichtigkeit der dargestellten Informationen kann keineGewährübernommenwerden.

Impressum

Sonderausgabe1/2012

VerantwortlicheRedakteure:RolandBrooksFrankDornseiferChristinaGaul

Erscheinungsweise:jährlich

BAIe.V.PoppelsdorferAllee106D-53115Bonn

Tel.+49-(0)228-969870Fax+49-(0)228-9698790

[email protected]

Satz & Layout

VANAMELANDUG(haftungsbeschränkt)

Markgrafenstraße1a51063Köln

Tel.+49-(0)221-222547-0Fax+49-(0)221-222547-47

[email protected]

35Impressum

I m p R E S S u m

http://www.bvai.de

mailto:info%40bvai.de?subject=

http://www.vanameland.de

mailto:info%40VANAMELAND.de?subject=

Documents

NEWSLETTER zum BAI-WISSENSchAfTSpREIS - Home ... · rungswirtschaft an der Universität Ulm sowie als Visi- ... in der Jury des djp (Deutschen Journalisten Preis). ... Im April 2008