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The Benefits of Hedge Funds in Asset Liability Management


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The Benefits of Hedge Funds in Asset Liability Management

  1. 1. An Edhec Risk and Asset Management Research Centre Publication The Benefits of Hedge Funds in Asset Liability Management September 2005
  2. 2. Abstract: This paper examines the benefits of including hedge funds for investors facing liability constraints. We cast the problem in a stochastic surplus optimisation setup where hedge funds are treated as a complement, and not as an addition, to traditional asset classes, which alleviates the concern over ex- ante modelling of hedge fund returns, a notoriously difficult challenge given the short history and complexity of these alternative investment styles. Our conclusion is that, when added to bonds and stocks, suitably designed portfolios of hedge funds can allow for significant benefits in an ALM context, as can be measured in terms of reduction of the expected mismatch between assets and liabilities. This impact is more pronounced when the relevant objective turns to extreme risks. In fact, we show that the probability of extreme deficits (value of the assets falling below 75% of the value of liabilities) can be reduced by as much as 50% by allocating not more than 20% to hedge funds. Edhec is one of the top five business schools in France and was ranked 12th in the Financial Times Masters in Management Rankings 2005 owing to the high quality of its academic staff (over 100 permanent lecturers from France and abroad) and its privileged relationship with professionals that the school has been developing since it was established in 1906. Edhec Business School has decided to draw on its extensive knowledge of the professional environment and has therefore concentrated its research on themes that satisfy the needs of professionals. Edhec pursues an active research policy in the field of finance. Its “Risk and Asset Management Research Centre” carries out numerous research programmes in the areas of asset allocation and risk management in both the traditional and alternative investment universes. Copyright © 2005 Edhec
  3. 3. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Table of Contents About the Authors 2 Foreword 3 Executive Summary 5 Résumé 9 Zusammenfassung 12 Introduction 16 An Overview of Asset-Liability Management Techniques 18 A Formal Surplus Optimisation Model 20 Allocation to Hedge Funds in the Context of Surplus Optimisation: the Naïve Approach 22 Challenges in Modelling Hedge Fund Returns 22 Challenges in Estimating Parameters for Hedge Fund Return Distributions 24 A Simple Illustration 25 Allocation to Hedge Funds in the Context of Surplus Optimisation: a More Robust Approach 27 Selection Stage 27 Optimisation Stage 28 Numerical Results 31 Conclusion 32 References 33 Appendix: Construction Methodology for the Edhec Alternative Indexes 35 About the Edhec Risk and Asset Management Research Centre 36 About Lyxor AM 39 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 1
  4. 4. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT About the Authors Lionel Martellini is a Professor of Finance at EDHEC Graduate School of Business and the Scientific Director of the Edhec Risk and Asset Management Research Centre. He holds graduate degrees in Economics, Statistics and Mathematics, as well as a PhD in Finance from the University of California at Berkeley. Lionel is a member of the editorial board of The Journal of Portfolio Management and The Journal of Alternative Investments. An expert in quantitative asset management and derivatives valuation, Lionel has published widely in academic and practitioner journals, and has co-authored reference textbooks on Alternative Investment Strategies and Fixed-Income Securities. Volker Ziemann is a Research Engineer at the Edhec Risk and Asset Management Research Centre. He holds a Master’s Degree in Economics from Humboldt-University in Berlin and a Master's Degree in Statistics from ENSAE in Paris, and is currently a PhD student in finance at the University of Aix- en-Provence. 2 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  5. 5. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Foreword Since it was set up, in 2001, the Edhec Risk Like structured products, hedge funds are non- and Asset Management Research Centre has linear payoff products and, probably for the made a point of conducting research that is same reasons, have been very much in the news both independent and pragmatic. in the asset management industry in the last five years. We feel that the present study is coming The concern to render our research work along at a very opportune time. After probably relevant and operational led us, in 2003, to overestimating the long-term performance of publish the first studies on the policies of the hedge funds in the past, investors are beginning European asset management industry. The to doubt their usefulness as a result of the Edhec European Asset Management Practices disappointing performance in recent years. survey allowed a comparison to be established between the academic state-of-the-art in the It seems to us that coming up with an answer area of portfolio management and risks, and of 100% or 0% for hedge funds emanates the practices of European managers. from an identical “in-sample” error. In the absence of modelling of hedge fund This study was completed in the same year by a strategies’ returns, and in view of the low level review of the state-of-the-art and the practices of historical track record, we feel that the use of European alternative multimanagers, the of the technical and conceptual framework of Edhec European Alternative Multimanagement ALM for integrating hedge funds should at Practices survey. least be revisited, if not called into question. In drawing up the latter report, we were able to That is the object of the study that has been observe the gap that exists between the carried out by Professor Lionel Martellini and conclusions of academic research work and the Volker Ziemann. This research is part of a long practices of multimanagers in measuring and line of research into hedge funds and asset reporting on the performance and risks of funds allocation that has recently given rise to output or portfolios of hedge funds. This observation led that is not only academic, with the notable us to carry out research and a survey on this publication of “The Right Place for Alternative fundamental dimension of the relationship Betas in Hedge Fund Performance: an Answer between investors and managers: the Edhec Funds to the Capacity Effect Fantasy” on the reality of of Hedge Funds Reporting Survey. This report was the capacity effect for hedge funds, but also presented in February 2005 to pan-European business-related, with the launch of the Edhec institutional investors and professionals. Hedge Fund Diversifier Benchmarks, which have In 2005, on the occasion of the Edhec Asset been produced in co-operation with Lyxor. Management Days, which brought together To conclude this foreword, I would like to more than 600 professionals in Geneva, we had thank SG CIB and Lyxor, who have supported the honour of presenting our study on the place our research work for many years and have of structured products in asset management, enabled us to publish this research. entitled “Structured Forms of Investment Strategies in Institutional Investors” Portfolios’. This question is a vital one in view of the importance of non-linear payoff products in the Noël Amenc, marketplace, notably following the difficult Professor of Finance, Director of the Edhec Risk and recent years on the stock markets. Asset Management Research Centre THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 3
  7. 7. Executive Summary
  8. 8. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Executive Summary Institutional investors in general and pension However, the use of hedge funds funds in particular have been dramatically in asset-liability management affected by negative stock market returns at requires precautions the beginning of the millennium. In the context of a cumulative asset/liability deficit While it is certainly legitimate to seek to that was estimated at more than £55 billion in improve the asset/liability ratio with the help 2003 for the companies in the FTSE 100, of hedge funds, a naïve approach to the institutional investors are seeking new asset question is likely to give extremely unstable classes or forms of investment management results. For example, if we use the historical that would allow them to broaden their data on hedge fund returns without any traditional choice of asset allocation. precautions in a simple relative risk optimisation exercise (optimisation of the information ratio in relation to a stylised Following considerable success benchmark that is perfectly matched with the in private wealth management, investor’s liabilities), the optimal allocation to hedge funds are targeting hedge funds obtained varies from 0% to institutional investment 100% depending on the period used for calibrating the model! Such a lack of An alternative investment offering has been robustness in the analysis suggests that a introduced in the past several years, allowing naïve approach to the place of hedge funds in investors to optimise the risk/return ALM is totally inappropriate. combination of their portfolio. While the original rise of hedge funds was explained by Unlike traditional asset classes (stocks and the success encountered with private clients, bonds), for which we can find both reliable we now expect institutional investors to stochastic models and estimations of long- follow the lead of private banking with term parameters that are indispensable for significant inflows of capital in the next few carrying out a surplus optimisation study, years. Moreover, these inflows have already major obstacles actually prevent institutional begun, with the number of institutional investors today from considering hedge funds investors using alternative investments in to be an ALM class in the same way as constant progression, particularly due to traditional classes. Not only does the absence significant increases in Europe, Australia and of a sufficiently long historical record, Japan. In 2005, hedge fund use by European together with the opaqueness of the data and institutions has doubled to 48% from 24% in the biases that characterise the available 2003. By 2007, European institutions are databases, make any effort at projecting long- expected to dedicate 7.2% of portfolios to term risk and return parameters particularly hedge funds, an increase from the 5.3% illusory, but there is no satisfactory existing estimated for 2005.1 model for hedge fund returns, in spite of 1. Source: Russell Investment Group’s seventh annual report on alternative investment, September 2005. 6 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  9. 9. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Executive Summary recent progress in academic research on the we typically model the return of a global subject. Hedge fund behaviour, which is large-cap equity index, to which we might typically characterised by dynamic possibly add a small-cap stock index, without management strategies that sometimes looking to independently model sector, employ a multitude of complex products, is geographical or style (value versus growth) difficult to capture in the linear models that indices. This approach to alternative are classically used in finance. investment as a complement to traditional investment management is also consistent with the idea that hedge funds are above all A new approach to integrating considered by institutional investors to be hedge funds: as a complement, diversification tools that allow the risks of a not a strategic allocation class stock or bond portfolio to be reduced, rather than a tool for improving long-term returns. In order to cope with these difficulties in This desire to see hedge funds as a modelling hedge funds, and the risk relating diversification tool is reinforced by recent to estimation of the parameters, in particular academic research results which have shown the expected return parameter, which is that the diversification properties (risk highly sensitive to the choice of sample, we reduction benefits) of hedge funds were more propose in this study to adopt a more robust robust from a statistical standpoint than their alternative approach to the place of hedge capacity to provide absolute performance funds in the context of ALM. Rather than (return enhancement benefits). considering hedge funds to be an additional class to the traditional classes in an asset- The study presented here shows that it is liability exercise, we consider hedge funds to possible to construct diversification be complementary management styles for benchmarks that allow the risk related to stocks and bonds. holding stock or bond portfolios to be reduced in a very significant and robust way, by i) This approach, in which hedge funds are not appropriately selecting the alternative regarded as an asset-liability allocation class, strategies and ii) optimising these with proven is in fact consistent with the usual practices techniques (minimising the extreme risks, as of institutional investors with respect to the measured by the Value-at-Risk of the overall traditional management styles. It is indeed portfolio). common to model a very limited number of major asset classes in a stochastic asset- These diversification benchmarks thereby Table 1 Evolution of the long-term volatility liability optimisation exercise, rather than allow the long-term volatility parameters if parameters of stocks and bonds as a seeking to model all the sub-components of the stock and bond classes to be reduced function of the proportions of hedge funds in each class. the class. In the stock universe, for example, significantly. 0% HF 5% HF 15% HF 25% HF 35% HF Stocks 16.50% 15.62% 13.75% 11.99% 10.34% Bonds 8.50% 7.98% 7.21% 6.70% 6.18% THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 7
  10. 10. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Executive Summary As a result, introducing these diversification Conclusion benchmarks as complements to the traditional classes (stocks and bonds) enables ALM While most institutional investors are looking performance to be improved significantly, even into hedge funds as a possible solution to the for reasonable quantities of investment in challenges posed by asset-liability management hedge funds. In particular, we find that the in the presence of serious concerns over the size introduction of only slightly more than 11% of of the equity and bond premium and the hedge funds into the overall allocation can lead associated risks, very little is known about how to a reduction of more than 27% in the to include these alternative investment styles in probability of the value of the assets falling an ALM context. below 75% of that of the liabilities (asset-liability Figure 1 deficit greater than 25%). Moreover, it should This study provides evidence of the Improvement of expected relative be noted that an allocation to hedge funds of shortfall and probability of a contribution of hedge funds in a surplus shortfall greater than 25% as a approximately 20% allows the probability of optimisation context. To this end, we have function of the effective proportion allocated to hedge funds. extreme risk to be reduced by more than 50%. proposed a pragmatic approach that does not treat hedge funds as an addition but rather as Relative Diversification Benefits 40% a complement to traditional asset classes Improvement in relative expected shortfall (stocks and bonds), which alleviates the 30% Improvement in probability of extreme loss concern over the modelling of hedge fund return distributions and parameter Improvement 20% estimation. Our conclusion is that suitably designed hedge fund portfolios can be 10% particularly attractive when the objective of optimising expected returns is constrained to 0% 2% 7% 12% 17% meeting liabilities. This is due to hedge funds’ Effective Allocation to Hedge Funds benefits in terms of diversification properties, which in turn is related to their appealing behaviours in terms of the impact on tail- distribution and extreme risks of stock and bond portfolios. 8 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  11. 11. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Résumé Les investisseurs institutionnels en général et Cependant leur utilisation dans les fonds de pension en particulier ont été la gestion actif-passif suppose fortement affectés par les replis des marchés des précautions actions au début du millénaire. Dans un contexte de déficit cumulé actif/passif estimé S’il paraît a priori légitime de chercher à en 2003 à plus de 55 milliards de livres pour améliorer le ratio actif/passif à l’aide de fonds les sociétés du FTSE 100 les investisseurs alternatifs, la recherche académique a institutionnels sont à la recherche de cependant montré qu’une approche naïve de la nouvelles classes d’actifs ou formes de gestion question donnait des résultats extrêmement qui leur permettraient d’élargir leur choix instables. Par exemple, si l’on utilise sans traditionnel d’allocation d’actifs. précaution les données historiques sur la rentabilité des hedge funds dans un simple exercice d’optimisation en risque relatif Après un succès considérable (optimisation du ratio d’information par rapport dans la gestion privée les à un benchmark stylisé parfaitement adossé au hedge funds ciblent la gestion passif de l’investisseur), l’allocation optimale en institutionnelle fonds alternatifs obtenue varie de 0% à 100% en fonction de la période utilisée pour la calibration Une offre de gestion alternative se met en du modèle ! Un tel manque de robustesse dans place depuis plusieurs années, permettant l’analyse suggère qu’une approche naïve de la aux investisseurs d’optimiser le couple place des hedge funds dans la gestion actif- rendement/risque de leur portefeuille. Tandis passif est ainsi totalement inadaptée. que le succès originel des fonds alternatifs a longtemps été expliqué par le succès rencontré A la différence des classes d’actifs auprès de la clientèle privée, on s’attend traditionnelles (actions et obligations), pour désormais à ce que les investisseurs lesquels sont disponibles à la fois des modèles institutionnels imitent l’exemple des banques stochastiques fiables et des estimations de privées avec d’importants afflux de capitaux au paramètres long terme indispensables à la cours des prochaines années. Le mouvement conduite d’une étude d’optimisation de surplus, a d’ailleurs déjà commencé, avec une des obstacles majeurs empêchent en fait augmentation importante des investissements aujourd’hui les investisseurs institutionnels de dans la gestion alternative par les investisseurs considérer les fonds alternatifs comme une institutionnels, notamment en Europe, en classe de gestion actif-passif au même titre Australie et au Japon. En 2005, l’utilisation des que les classes traditionnelles. Non seulement hedge funds par les institutions européennes a l’absence de profondeur historique, ainsi que doublé, pour atteindre 48% par rapport à 24% l’opacité des données et les biais qui en 2003. A l’horizon 2007, on s’attend à ce que caractérisent les bases disponibles, rendent les investisseurs institutionnels européens tout effort de projection long terme des intègrent les hedge funds dans leurs paramètres de risque, et surtout de rendement, portefeuilles à hauteur de 7,2%, comparé à un particulièrement illusoire, mais il n’existe par chiffre estimé à 5,3% pour 2005.1 ailleurs pas aujourd’hui, malgré de récents 1. Source : Russell Investment Group, septième rapport annuel sur la gestion alternative, Septembre 2005. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 9
  12. 12. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Résumé progrès de la recherche académique sur le composantes de la classe. Dans l’univers des sujet, de modèles satisfaisants des rentabilités actions par exemple, on modélise typiquement la des fonds alternatifs, dont le comportement, rentabilité d’un indice global de valeurs de large typiquement caractérisé par des stratégies de capitalisation, auquel on ajoute éventuellement gestion dynamique faisant parfois appel à une un indice de valeurs de petite taille, sans multitude de produits complexes, est difficile chercher à modéliser de façon indépendante des à capturer par les modèles linéaires indices sectoriels, géographiques, ou encore par classiquement utilisés en finance. styles de gestion (valeur contre croissance). Cette approche de la gestion alternative en tant que complément de la gestion traditionnelle est par Une nouvelle approche de ailleurs cohérente avec l’idée que les fonds l’intégration des hedge funds : alternatifs sont avant tout considérés par les un complément et non une investisseurs institutionnels comme des outils de classe d’allocation stratégique diversification, permettant de réduire les risques d’un portefeuille action ou obligation, plutôt Pour faire face à ces difficultés de modélisation qu’un outil d’amélioration de la rentabilité à long des fonds alternatifs, et au risque lié à terme. Cette volonté de voir en la gestion l’estimation de paramètres, en particulier du alternative un outil de diversification est paramètre de rentabilité, si fortement sensible confortée par des résultats récents de la au choix de l’échantillon, nous proposons dans recherche académique qui ont montré que les cette étude une approche alternative, plus propriétés de diversification (risk reduction robuste, de la place des hedge funds dans le benefits) des fonds alternatifs étaient nettement contexte de la gestion actif-passif. Plutôt que de plus robustes que leur faculté à offrir de la considérer les hedge funds comme une classe performance absolue (return enhancement additionnelle aux classes traditionnelles dans benefits). un exercice actif-passif, nous considérons les hedge funds comme des styles de gestion L’étude présentée ici montre qu’il est possible de complémentaires aux actions et aux obligations. construire des benchmarks de diversification permettant de réduire de façon très significative Cette approche consistant à ne pas regarder la et robuste le risque lié à la détention de gestion alternative comme une classe portefeuilles actions ou obligations, sur la base d’allocation actif-passif est en fait cohérente i) d’une sélection adaptée de stratégies avec la pratique courante des investisseurs alternatives et ii) d’une optimisation de celles-ci institutionnels dans leur approche des styles de selon des techniques éprouvées (minimisation gestion traditionnels : il est en effet d’usage de des risques extrêmes mesurés par la Value-at- Tableau 1 modéliser dans un exercice d’optimisation Risk du portefeuille global). Evolution des paramètres de long terme de volatilité des classes « obligations » stochastique actif-passif un nombre très limité et « actions » en fonction de grandes classes d’actifs, plutôt que de Ces benchmarks de diversification permettent des proportions de hedge funds incorporées dans chaque classe. chercher à modéliser l’ensemble des sous- ainsi de réduire significativement les paramètres long terme de volatilité des classes actions et 0% HF 5% HF 15% HF 25% HF 35% HF Stocks 16.50% 15.62% 13.75% 11.99% 10.34% obligations. Bonds 8.50% 7.98% 7.21% 6.70% 6.18% 10 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  13. 13. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Résumé De ce fait, l’introduction de ces benchmarks de Conclusion diversification en tant que compléments des classes traditionnelles (actions et obligations) Alors que la plupart des investisseurs permet d’améliorer significativement la institutionnels considèrent les hedge funds performance d’une gestion actif-passif, et comme une solution possible aux défis posés ce même pour des quantités raisonnables par la gestion actif-passif, lorsqu’ils sont d’investissement en fonds alternatifs. Nous confrontés à de sérieuses préoccupations au obtenons ainsi que l’introduction d’à peine un sujet de la taille de la prime de risque des peu plus de 11% de fonds alternatifs dans placements en actions et obligations et des l’allocation globale peut permettre une risques qui leurs sont associés, on en sait très réduction de plus de 27% de la probabilité que peu sur la manière d’inclure ces styles la valeur de l’actif descende à moins de 75% d’investissements alternatifs dans un contexte de celle du passif (déficit actif-passif supérieur de gestion actif-passif. Figure 1 à 25%). Il est par ailleurs à noter qu’une Amélioration de l’espérance du déficit relatif et de la probabilité allocation en hedge funds d’environ 20% Cette étude fournit la preuve de l’intérêt des d’obtenir un déficit supérieur à 25% permet de diminuer cette probabilité de risque en fonction de la proportion effective hedge funds dans un contexte d’optimisation allouée aux hedge funds. extrême de plus de 50%. de surplus. A cette fin, nous avons proposé une approche pragmatique qui ne traite pas Avantages relatifs de diversification 40% les hedge funds comme un ajout mais plutôt Amélioration de l’espérance de déficit relatif comme un complément des classes d’actifs Amélioration de la probabilité de perte extrême 30% traditionnelles (actions et obligations). Ceci permet de réduire les difficultés de Amélioration 20% modélisation des distributions des rentabilités des hedge funds et d’estimation des 10% paramètres. Notre conclusion est que des portefeuilles de hedge funds conçus de façon 0% 2% 7% 12% 17% appropriée peuvent être particulièrement Allocation effective aux hedge funds attrayants lorsqu’il existe une contrainte sur l’objectif d’optimisation des rentabilités espérées de façon à ce que cet objectif soit en adéquation avec le passif. Cet attrait est dû aux avantages procurés par les hedge funds en termes de propriétés de diversification. Ces propriétés sont liées aux comportements intéressants des hedge funds en termes d’impact sur la queue de distribution et sur les risques extrêmes des portefeuilles d’actions et d’obligations. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 11
  14. 14. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Zusammenfassung Institutionelle Anleger im Allgemeinen und Dennoch, der Gebrauch von Pensionsfonds im Besonderen litten erheblich Hedge Funds im Rahmen des unter den negativen Aktienrenditen zu Beginn Aktiv-Passiv Managements des Jahrtausends. Im Kontext von sich (ALM) gebietet Vorsicht kumulierenden Aktiv-Passiv-Defiziten, welche für die am FTSE 100 gelisteten Unternehmen im Obwohl es legitim ist, eine Verbesserung der Jahre 2003 auf etwa £55 Mio. geschätzt wurden, Aktiv-Passiv-Struktur mit Hilfe von Hedge suchen institutionelle Anleger nun nach neuen Funds zu erzielen, sollte man Vorsicht walten Anlageformen, die ihnen ermöglichen, den lassen, da ein unüberlegter Einsatz zu extrem Horizont in der Asset Allokation zu erweitern. instabilen Ergebnissen führen kann. Wenn man beispielsweise historische Daten in einem Optimierungskontext verwendet (z.B. Nach ihrem bemerkenswerten maximale Information Ratio (IR)), so variiert Erfolg im Privatkundengeschäft, der optimal in Hedge Funds zu investierende drängen Hedge Funds nun auch Anteil zwischen 0% und 100%, je nachdem ins Blickfeld institutioneller welchen Zeitraum man für die Analyse Anleger verwendet. Ein solcher Mangel an Robustheit zeigt, dass ein unüberlegtes Investment in Im Laufe der vergangenen Jahre wurden Hedge Funds in einem ALM-Kontext nicht alternative Investment-Angebote am Markt ratsam ist. eingeführt, die es dem Investor ermöglichen die Risiko-Rendite-Struktur seines Portfolios zu Im Gegensatz zu traditionellen Anlageklassen optimieren. Während der Aufschwung der (Aktien und Obligationen), für die wir sowohl Hedge Funds vor allem durch den Erfolg im bewährte stochastische Modelle, als auch Privatkundengeschäft erklärt wurde, wird nun verlässliche langfristige Parameterschätzungen erwartet, dass institutionelle Investoren ihrem zur Verfügung haben (diese sind unerlässlich, Beispiel folgen und in den nächsten Jahren um einen Mehrwert aus komplexen Modellen nennenswerte Summen in den Markt fließen zu erhalten), verhindern zahlreiche werden. Diese Kapitalzuflüsse haben im Schwierigkeiten Hedge Funds in der selben Art Übrigen schon begonnen und die Zahl der und Weise wie traditionelle Anlageklassen als institutionellen Anleger, die alternative ALM-Anlageklasse zu verstehen. Nicht nur das Investments benutzen, steigt, vor allem in Fehlen von ausreichend langen Datenreihen Europa, Australien und Japan, stetig an. Im Jahre lässt eine Projektion von Risiko- und Rendite- 2005 hat sich der Anteil der europäischen Struktur illusorisch erscheinen, sondern auch Institutionen, die in Hedge Funds investieren, auf die Abwesenheit zufrieden stellender Modelle 48% verdoppelt (2003: 24%). Für das Jahr 2007 für Hedge Fund Renditen (trotz gegenwärtiger wird angenommen, dass diese Institutionen Fortschritte in der akademischen Forschung). 7.2% in Hedge Funds investieren, während sich diese Ziffer auf 5.3% für 2005 beläuft.1 1. Quelle: 7 Jahresbericht über alternative Investments der Russell Investment Group, September 2005. 12 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  15. 15. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Zusammenfassung Das Verhalten von Hedge Funds, welches Anlageklassen zu betrachten, ist auch insofern durch dynamisches Anlageverhalten und die nachzuvollziehen, als dass institutionelle Implementierung von teilweise komplexen Investoren Hedge Funds vor allem als Produkten gekennzeichnet ist, lässt sich nur Diversifizierungsvehikel benutzen und sehr schwierig mit Hilfe der klassischerweise nicht als Instrument um hohe Renditen zu verwendeten, linearen Modellen beschreiben. erzielen. Dies wird durch aktuelle akademische Forschung belegt, die zeigt, dass vom statistischen Standpunkt aus gesehen, die Ein neuer Ansatz Hedge Funds Diversifizierungseigenschaften von Hedge Funds zu integrieren: Komplementäre robuster sind, als die Fähigkeit absolute Renditen statt strategische Anlageklasse zu generieren. Um diese Schwierigkeiten zu bewältigen und Die hier vorliegende Arbeit zeigt, dass es das Risiko beim Schätzen der Parameter möglich ist, Diversifizierungs-Benchmarks zu einzudämmen, welches vor allem durch die konstruieren, die es erlauben, das mit den Wahl des Analysezeitraums erschwert wird, Aktien und Obligationen verbundene Risiko schlagen wir in unserer Studie einen robusteren nennenswert und robust zu reduzieren. Dies Ansatz zum Einsatz von Hedge Funds in einem wird erreicht, indem i) alternative Strategien ALM-Kontext vor: anstatt Hedge Funds als eine sachgemäß ausgewählt werden und ii) ihre eigenständige Anlageklasse zu verstehen, Gewichte gemäß bewährter Techniken führen wir Hedge Funds als Komplement zu optimiert werden (Minimierung extremer Aktien und Obligationen ein. Risiken, gemessen mit Hilfe des Value-at-Risk des Gesamtportfolios). Dieser Ansatz ist konform mit der gängigen Praxis unter institutionellen Anlegern, Hedge Diese Diversifizierungs-Benchmarks erlauben Funds nicht als eine eigene Aktiv-Passiv-Klasse es den langfristigen Volatilitätsparameter der zu betrachten. In der Tat ist es eher gebräuchlich, Aktien- und Obligationsklassen nennenswert nur die Hauptanlageklassen stochastisch zu zu verringern. modellieren, anstatt alle Unterkomponenten in den Modellierungsprozess einzubeziehen. Wenn Als Ergebnis stellen wir fest, dass die Zugabe man beispielsweise das Zusammenspiel von der Diversifizierungs-Benchmarks zu den Large-Cap- und Small-Cap-Indizes untersucht, traditionellen Klassen (Aktien und Obligationen) so modelliert man diese ohne dabei die es ermöglicht, die ALM-Performance signifikant Tabelle 1 Entwicklung der langfristigen geographischen, sektoriellen oder andere zu erhöhen, selbst wenn nur geringe Hedge- Volatilitätsparameter von Aktien und Obligationen in Abhängigkeit des Hedge- Gegebenheiten zu berücksichtigen. Der Ansatz, Fund-Anteile zugelassen werden. Als ein Fund-Zusatzes zu der jeweiligen Klasse Hedge Funds als Komplement zu traditionellen nennenswertes Resultat finden wir zum 0% HF 5% HF 15% HF 25% HF 35% HF Aktien 16.50% 15.62% 13.75% 11.99% 10.34% Obligationen 8.50% 7.98% 7.21% 6.70% 6.18% THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 13
  16. 16. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Zusammenfassung Beispiel, dass mit der Zugabe von etwa 11% Schlussfolgerung Hedge Funds zum Gesamtportfolio die Wahrscheinlichkeit, dass der Wert der Aktiva Während die meisten institutionellen Anleger unter 75% des Wertes der Passiva fällt (Aktiv- Hedge Funds als eine mögliche Lösung für Grafik 1 Passiv-Defizit größer als 25%), um 27% gesenkt die Herausforderungen im Aktiv-Passiv- Verringerung des Aktiv-Passiv- Defizits und der Wahrscheinlichkeit, werden kann. Diese Wahrscheinlichkeit sinkt Management (Unsicherheit über Höhe der dass dieses größer als 25% ist gar um mehr als 50% wenn man etwa 20% der (in Abhängigkeit des Hedge-Fund- Risikoprämien und der damit verbundenen Anteils im Gesamtportfolio) Aktiva in Hedge Funds investiert. Risiken im traditionellen Sektor) ins Auge fassen, ist sehr wenig über Methoden Relative Diversifizierungs-Benefize 40% bekannt, wie alternative Investment-Vehikel Relative Verringerung des Aktiv-Passiv-Defizits im ALM-Kontext einzusetzen sind. Relative Verringerung der Wahrscheinlichkeit großer Defizite (>25%) 30% Diese Studie liefert den Beweis, dass Hedge Verbesserung 20% Funds einen positiven Beitrag in der Überschuss-Optimierung leisten. Zu diesem 10% Zweck haben wir einen pragmatischen Ansatz vorgeschlagen, der Hedge Funds nicht als 0% 2% 7% 12% 17% eigenständige Anlageklasse versteht, sondern Effektive Allokation in Hedge Funds eher als komplementär zu traditionellen Klassen (Aktien und Obligationen). Damit umgehen wir die Schwierigkeit, Hedge-Fund-Renditen und ihre Verteilung zu modellieren. Wir schlussfolgern, dass geeignete Hedge Fund Portfolios besonders attraktiv sind, wenn es darum geht, optimale Lösungen für die Asset- Allokationen unter Berücksichtigung der Verbindlichkeiten (Passiva) zu finden. Dies ist mit den besonderen Diversifizierungseigenschaften der Hedge Funds zu erklären, die sich vor allem aus ihrem positiven Einfluss auf die Extremrisiken und deren Verteilung der Aktien- und Obligations-Portfolios ableiten lassen. 14 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  17. 17. The Benefits of Hedge Funds in Asset Liability Management
  18. 18. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Introduction Recent difficulties have drawn attention to the strategies can only generate a simple linear risk management practices of institutional exposure to the return on underlying asset investors in general and defined benefit pension classes (go up and down with the indices), the plans in particular. A perfect storm of adverse main benefit of hedge fund strategies is market conditions over the past three years has actually that they allow for a non-linear devastated many corporate defined benefit exposure with respect to stock and bond pension plans. Negative equity market returns returns in such a way that the downside risk have eroded plan assets at the same time as is typically limited.2 This is because hedge fund declining interest rates have increased market- managers, who operate in the absence of to-market value of benefit obligations and regulatory constraints, can incorporate a contributions. In extreme cases, this has left variety of dynamic investment strategies corporate pension plans with funding gaps as and/or investments in derivatives likely to large as or larger than the market capitalisation generate non-linear payoffs (Fung and Hsieh of the plan sponsor. For example, in 2003, the (1997)). While the assessment of the benefits companies included in the S&P 500 and FTSE 100 hedge funds offer when included in an indices faced a cumulative deficit of $225 billion investor’s portfolio has given rise to a and £55 billion respectively (Credit Suisse First burgeoning literature (e.g., Agarwal and Naik Boston (2003) and Standard Life Investments (2004)), this question has not been examined (2003)), while the worldwide deficit reached an in an ALM framework. This paper can be seen estimated 1,500 to 2,000 billion USD (Watson as an attempt to fill this void. Wyatt (2003)). From a conceptual standpoint, there are two The fact that institutional investors have been possible approaches that lead to the inclusion so dramatically affected by market downturns of hedge funds in an ALM context. A first had led to major changes in institutional money approach to a formal model of introduction of management, including notably the need for an hedge funds in an ALM context consists of increased focus on asset-liability management treating hedge funds as a supplement to (ALM). In this context, institutional investors in traditional asset classes, i.e., considering general, and under-funded pension funds in hedge funds as an additional asset class that particular, are desperately seeking new asset can be added to stocks and bonds in a classes or investment styles that could be cast traditional ALM surplus optimisation exercise. in a surplus optimisation context and that In what follows, we will argue that this would offer access to equity-like premium approach, while seemingly straightforward, is without all the associated downside risks. too simplistic and involves a level of sample- dependence that is too high to be of any Because of their focus on absolute practical relevance, as is perhaps best performance and risk control, hedge funds are evidenced by the fact that it often leads to typically suggested as a natural alternative to very unreasonably high (close to 100%) levels stocks and bonds. While long-only investment of optimal allocation to hedge funds. 2. It has recently been shown that financial products which offer non-linear return profiles are particularly useful in an ALM context (see for example Draper and Shimko (1993)). 16 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  19. 19. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Introduction In this paper, we introduce a competing, more The rest of this paper is organised as follows. cautious, approach, which consists of treating The next section presents an overview of hedge funds as a complement, as opposed to asset-liability management techniques. We an addition, to traditional asset classes. then present a formal surplus optimisation Overall, the results obtained with this more model and discuss some conceptual and robust approach strongly suggest that, when technical challenges related to the added to bonds and stocks, suitably designed introduction of hedge funds in the context of portfolios of hedge funds can allow for surplus optimisation. In the following section, significant, yet reasonable, benefits in an ALM we propose a novel approach that treats context, as can be measured in terms of alternative investment strategies as a reduction of the expected mismatch between complement, as opposed to an addition, to assets and liabilities. This impact is more traditional asset classes. After that, we pronounced when the relevant optimisation present a formal numerical experiment and objective includes a focus on extreme risks. In test for the impact of introducing hedge fact, we show that the probability of extreme funds in terms of surplus optimisation deficits (value of the assets falling below 75% benefits based on reasonable parameter of the value of liabilities) can be reduced by values. A conclusion and list of references 50% by allocating 20% to hedge funds. These follow, while some information on hedge fund results should be taken into account by indices is relegated to a dedicated appendix. investors who are constrained to meeting liabilities. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 17
  20. 20. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT An Overview of Asset-Liability Management Techniques Asset-Liability Management (ALM) denotes the number of limitations. First of all, it will adaptation of the portfolio management generally be impossible to find inflation- process in order to handle the presence of linked securities whose maturity corresponds various constraints relating to the commitments exactly to the liability commitments. that figure in the liabilities of an institutional Moreover, most of those securities pay out investor’s balance sheet (commitments to coupons, which leads to the problem of paying pensions, insurance premiums, etc.). reinvesting the coupons. To the extent that There are therefore as many types of liability perfect matching is not possible, there is a constraints as there are types of institutional technique called immunisation, which allows investors, and thus as many types of approaches the residual interest rate risk created by the to asset-liability management. imperfect match between the assets and liabilities to be managed in an optimal way. ALM-type management techniques can be This interest rate risk management technique classified into several categories. A first can be extended beyond a simple duration- approach called cash-flow matching involves based approach to fairly general contexts, ensuring a perfect match between the cash including for example hedging non-parallel flows from the portfolio of assets and the shifts in the yield curve (see for example commitments in the liabilities. Let’s assume Priaulet, Martellini and Martellini (2003)), or for example that a pension fund has a to simultaneous management of interest rate commitment to pay out a monthly pension to risk and inflation risk (Siegel and Waring a retired person. Leaving aside the complexity (2004)). It should be noted, however, that this relating to the uncertain life expectancy of technique is difficult to adapt to hedging the retiree, the structure of the liabilities is non-linear risks related to the presence of defined simply as a series of cash outflows to options hidden in the liability structures (see be paid, the real value of which is known Le Vallois et al. (2003)), and/or to hedging today, but for which the nominal value is non-interest rate related risks in liability typically matched with an inflation index. It is structures. possible in theory to construct a portfolio of assets whose future cash flows will be Another, probably more important, identical to this structure of commitments. To disadvantage of the cash-flow matching do so, assuming that securities of that kind technique (or of the approximate matching exist on the market, would involve purchasing version represented by the immunisation inflation-linked zero-coupon bonds with a approach) is that it represents a positioning maturity corresponding to the dates on which that is extreme and not necessarily optimal the monthly pension instalments are paid out, for the investor in the risk/return space. In with amounts that are proportional to the fact we can say that the cash-flow matching amount of real commitments. approach in asset-liability management is the equivalent of investing in the risk-free asset in This technique, which provides the advantage an asset management context. It allows for of simplicity and allows, in theory, for perfect perfect management of the risks, namely a risk management, nevertheless presents a capital guarantee in the passive management 18 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  21. 21. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT An Overview of Asset-Liability Management Techniques framework, and a guarantee that the liability representation of the uncertainty relating to a constraints are respected in the ALM set of risk factors that impact the liabilities. framework. However, the lack of return, These can be financial risks (inflation, interest related to the absence of risk premia, makes rate, stocks) or non-financial risks this approach very costly, which leads to an (demographic ones in particular). When unattractive level of contribution to the necessary, agent behaviour models are then assets. developed, which allows the impact of decisions linked to the exercising of certain In a concern to improve the profitability of the implicit options to be represented. For assets, and therefore to reduce the level of example, an insured person can (typically in contributions, it is necessary to introduce exchange for penalties) cancel his/her life asset classes (stocks, government bonds and assurance contract if the guaranteed corporate bonds) which are not perfectly contractual rate drops significantly below the correlated with the liabilities into the strategic interest rate level prevailing at a date allocation. It will then involve finding the best following the signature of the contract, which possible compromise between the risk makes the amount of liability cash flows, and (relative to the liability constraints) thereby not just their current value, dependent on taken on, and the excess return that the interest rate risk. investor can hope to obtain through the exposure to rewarded risk factors. Different Different optimisation models are used by techniques are then used to optimise the institutional investors within the framework surplus, i.e., the excess value of the assets of ALM (see for example Mulvey et al. (2005) compared to the liabilities, in a risk/return for an example), and it is impossible to provide space. In particular, it is useful to turn to an exhaustive list here.3 We now describe the stochastic models that allow for a specific model we use in this study. 3. Finally, and for the sake of completeness, it is appropriate to mention non-linear risk-profiling management techniques, the goal of which is to provide a compromise between a risk-free and return-free approach on the one hand, and a risky approach that does not allow the liability constraints to be guaranteed on the other (see in particular Leibowitz and Weinberger (1982) for the contingent optimisation technique or Amenc, Malaise and Martellini (2004) for a generalisation in terms of a dynamic core-satellite approach). THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 19
  22. 22. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT A Formal Surplus Optimisation Model A surplus optimisation model is basically liability sides from an ex-ante basis. On the founded on optimising the match between asset side, Monte-Carlo analysis is used to the asset and liability sides of financial generate 10,000 random paths for each asset structures in companies. class using geometric Brownian motions and we generate scenarios. Instead of making assumptions on the detailed allocation to single assets or funds in S(t) = S(0) exp (( µ− 1 2 ) σ t + σB(t) ) investors’ portfolios, one uses proxies for the different asset classes. In the context of this where B(t) is a Brownian motion with B(t) exercise, we consider three basic underlying (0, t) so that: asset classes (in addition to hedge funds, which will be introduced later): stocks, S(t + s) = S(t) exp (( µ− 1 2 ) r σ t + :sN ) nominal bonds and inflation-indexed bonds with N N(0, ). (TIPS). The portfolio return RPF is then given as: n In order to take the correlation of the RPF, t = i Ri, t t = 1...T i=1 underlying asset classes into account we will introduce the 3-dimensional geometric where i represents the proxy for the asset Brownian motion: class i and i its weight in the portfolio. Sa(t + s) = Sa(t) exp µa − (( 1 )r σ t + :sNa 2 a ) The purpose of surplus optimisation is to find the allocation that minimises at horizon T (here Sb(t + s) = Sb(t) exp µb − (( 1 2 b )r σ t + :sNb ) taken to be equal to 10 years) the relative expected shortfall SF beyond a certain target , Sc(t + s) = Sc(t) exp (( µc − 1 )r σ t + :sNc 2 c ) which is defined as follows: with the 3-dimensional Gaussian: ( RPF,T − L T RPF,T − L T ) 2 ( ) ( )( SF( ) = − E < Na 0 σa σa σb σa σc LT LT ) ab ac 2 Nb ~N 0 σa σb ab σb σb σc bc where L denotes the company’s liabilities. 2 Nc 0 , σa σc ac σb σc bc σc In the remaining sections, the optimal allocation will be obtained as a solution to the The calibration of the model is performed following optimisation: using long-term estimates (see exhibit 1). For mean return and volatility on stocks, bonds * = arg min SF(0) and TIPS, we have used Dimson, Marsh and Staunton’s (2002) 1900-2000 estimates; for volatility on TIPS, and for the correlation In order to optimise expected values of the matrix, we have used Kothari and Shanken’s portfolio distribution, we need to generate (2004) 1953-2000 estimates.4 stochastic scenarios for both the asset and 4. For stocks we have used data on world markets (see table 34-1 page 311). For bonds, because of the impact of a high inflation period in some European countries in the vicinity of World War II, we have focused on the US estimate (see table 6-1 page 79), and we have added a 0.4% credit spread to the 2.1% real rate plus a 3.3% inflation estimate. For the return on TIPS, we have used the US inflation rate (3.3%) plus the real short - term rate (1%), in the absence of a reliable estimate of the long-term risk premium for that asset class. 20 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT
  23. 23. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT A Formal Surplus Optimisation Model Exhibit 1 On the liability side, in an attempt to focus on Long-term parameter estimates. a stylised institutional investor, we take the Correlation Stocks Bonds TIPS return on liabilities to be equal to the return Stocks 1 on inflation-indexed bonds to which we add Bonds 0.24 1 TIPS -0.05 0.52 1 300 basis points. This is because most Mean 10.4% 5.8% 4.3% institutional investors’ liabilities are impacted Volatility 16.5% 8.5% 6.58% by two main risk factors, inflation and interest As explained below, we do not attempt to rates. As a result liabilities are perfectly estimate long-term parameter values for correlated with the return on TIPS in our hedge funds, as we believe that doing so model. In practice, TIPS is certainly the asset would be of little relevance, nor do we attempt class that exhibits the highest correlation with to model hedge funds returns, a notoriously liabilities, even though the correlation is not challenging task. We will instead model the perfect due to the presence of a number of introduction of hedge funds through their extraneous sources of risk beyond inflation impact on these long-term parameter values and interest rates. for stocks and bonds; in particular we will estimate the decrease in stock and bond The relative expected shortfall is then given as: s s ( ) 10000 R PF,T − L T volatility that can be achieved by the introduction of suitably selected hedge fund SF(0) = − 1 n ∑ s LT ⋅ 1{ s s R PF,T − L T < 0 } s=1 strategies to be included in the stock, or bond, where the exponent s denotes the scenario allocation of an institutional investor. and n is the number of scenarios yielding deficits after 10 years: ( ) 10000 n= ∑ 1{ s=1 s s R PF,T − L T < 0 } THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT 21
  24. 24. THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT Allocation to Hedge Funds in the Context of Surplus Optimisation: the Naïve Approach There are two possible approaches that lead to Challenges in Modelling the inclusion of hedge funds in an ALM Hedge Fund Returns context, one that consists of treating hedge funds as a supplement to traditional asset The fact that hedge funds have started to gain classes, and one that consists of treating widespread acceptance while remaining hedge funds as a complement to traditional somewhat mysterious investment vehicles has asset classes. enhanced the need for better measurement and benchmarking of their performance. In this section, we will argue that while the While understanding the risk exposures of first approach, which consists of considering hedge funds has actually become a rather hedge funds as an additional asset class that important and fertile area of academic can be added to stocks and bonds in an ALM research, and even though it has long been surplus optimisation exercise, is a recognised that a better understanding of straightforward attempt at formalising the hedge fund risks is needed for individuals and benefits of hedge funds in an ALM context, it institutions who wish to make investment nonetheless faces a number of conceptual decisions involving hedge funds, a and technical difficulties. satisfactory description of the dynamics of hedge fund returns has yet to be developed. First, and most importantly perhaps, this approach to hedge fund investing in an ALM The issues regarding the nature of risks context is implicitly based upon the associated with different hedge fund assumption that hedge funds can be treated strategies are actually challenging because of as a coherent asset class in an ALM stochastic the complex nature of the strategies and simulation exercise. This is certainly not limited disclosure requirements faced by satisfying from a conceptual standpoint, and hedge funds. In particular, since hedge fund a strong case can be made that hedge funds returns exhibit non-linear option-like do not constitute a homogenous new asset exposures to traditional asset classes (Fung class, but rather a set of very diverse and Hsieh (1997, 2000)), standard asset investment strategies. pricing models offer limited help in evaluating the performance of hedge funds. The Secondly, from a technical standpoint, it must importance of taking into account such be recognised that i) there are not yet any option-like features has been underlined by truly satisfying models for representing the recent research. In particular, Fung and Hsieh dynamics of hedge fund returns that can be (2002) and Mitchell and Pulvino (2001) stress used in an ex-ante Monte Carlo simulation the importance of taking into account option- approach, and ii) even if such models existed like features while analysing the performance the lack of a long history of hedge fund of “trend-following” and “risk-arbitrage” returns and various concerns over the quality strategies, respectively. More recently, of hedge fund return data would make the Agarwal and Naik (2003) build on these estimation of reliable parameter values a very insights and extend our understanding of challenging task. hedge fund risks to a wide range of equity- 22 THE BENEFITS OF HEDGE FUNDS IN ASSET LIABILITY MANAGEMENT