Four Essays on Investments

Dissertation

zur Erlangung des akademischen Grades

des Doktors der Wirtschaftswissenschaften (Dr. rer. pol.)

an der Universität Konstanz

Fachbereich Wirtschaftswissenschaften

vorgelegt von Olga Kolokolova

Tag der mündlichen Prüfung: 21.07.2009

Referent: Prof. Dr. Jens Carsten Jackwerth

Referent: Prof. Dr. Dr. h.c. Günter Franke

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To My Mother

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Preamble

I would like to extend my heartfelt gratitude to all those who helped me during my four and a

half years of studying and research in the doctoral programme in "Quantitative Economics

and Finance" at the University of Konstanz. Without them, this dissertation could not have

been completed.

I am very grateful to my supervisor Professor Jens Carsten Jackwerth for providing

encouraging working atmosphere at his chair, for his support, guidance, collaboration and

professional advice that helped to develop my research potential.

I wish to thank Professor Günter Franke for his valuable comments on all my research

projects.

I would like to acknowledge Professor Winfried Pohlmeier for his critical discussions of my

empirical investigations and for his helpful methodological suggestions.

I am also very thankful to Professor James E. Hodder for fruitful collaboration.

I wish to thank Monika Fischer for her care and help in solving all problems that could

distract me from research.

I would like to thank my colleagues Radoslav Zahariev, Anna Chizhova, Thomas Weber,

Valeri Voev, Roxana Chiriac, and Ingmar and Sandra Nolte for many inspiring conversations.

And of course I am more than grateful to my family – my parents, my brother, and my

husband – who have always supported me, also during those times when I thought that this

dissertation would be never completed.

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Contents

Introduction ................................................................................................................................ 9

Zusammenfassung .................................................................................................................... 13

Chapter 1 Recovering Delisting Returns of Hedge Funds ....................................................... 18

1.1 Introduction .................................................................................................................... 19

1.2 The Basic Model ............................................................................................................. 21

1.3 Data Characteristics and Implementation ....................................................................... 26

1.4 Results ............................................................................................................................ 31

1.5 Concluding Comments ................................................................................................... 36

Appendix 1.1: Pre-Fee Return Calculation ........................................................................... 37

References ............................................................................................................................ 40

Chapter 2 Birth and Death of Family Hedge Funds: the Determinants ................................... 41

2.1 Introduction .................................................................................................................... 42

2.2 Hypotheses Development ............................................................................................... 44

2.2.1 Company success, experience, and economies of scale and scope .......................... 44

2.2.2 Hedge fund substitution ........................................................................................... 45

2.2.3 Signaling vs. timing ................................................................................................. 46

2.2.4 Flow to new funds .................................................................................................... 47

2.3 Modeling Remarks and Variable Choice ........................................................................ 47

2.3.1 Company success, experience, and economies of scale and scope hypotheses ....... 47

2.3.2 Hedge fund substitution related hypotheses ............................................................ 49

2.3.3 Signaling vs. timing related hypotheses ................................................................... 51

2.3.4 Flow related hypotheses ........................................................................................... 52

2.4 The Data ......................................................................................................................... 54

2.5 Empirical Results ............................................................................................................ 56

2.6 Extensions and Robustness ............................................................................................. 66

2.7 Concluding Remarks ...................................................................................................... 71

Appendix 2.1: Investment Style Classification According to the ALTVEST Database ...... 73

Appendix 2.2: Relative Fund Value Computation ............................................................... 74

Appendix 2.3: Control Variables for Fund Flow .................................................................. 75

References ............................................................................................................................ 77

Chapter 3 Improved Portfolio Choice Using Second Order Stochastic Dominance ................ 81

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3.1 Introduction .................................................................................................................... 82

3.2 Methodology ................................................................................................................... 84

3.2.1 Constructing portfolios using SSD .......................................................................... 85

3.2.2 Competing portfolios ............................................................................................... 89

3.2.3 Testing for significance of an increase of the number of dominating portfolios out-

of-sample ........................................................................................................................... 90

3.3 The Data ......................................................................................................................... 92

3.4 Empirical Results ............................................................................................................ 93

3.4.1 Fixed asset span ....................................................................................................... 94

3.4.2 Enlarged asset span .................................................................................................. 98

3.5 Robustness ...................................................................................................................... 99

3.5.1 Changing lengths of estimation and forecast windows .......................................... 100

3.5.2 Alternative benchmark portfolio composition ....................................................... 100

3.5.3 Market turmoil and structural breaks ..................................................................... 100

3.5.4 Weekly returns ....................................................................................................... 102

3.5.5 Different levels of trimming .................................................................................. 103

3.6 Concluding Comments ................................................................................................. 104

Appendix 3.1: Variance and Covariance of the Dominance Functions in the Davidson

(2007) Test .......................................................................................................................... 106

Appendix 3.2: Bootstrap Procedure of Davidson (2007) ................................................... 107

References .......................................................................................................................... 109

Chapter 4 A Note on the Dynamics of Hedge-Fund-Alpha Determinants ............................ 112

4.1 Introduction .................................................................................................................. 113

4.2 Research Design and Methods ..................................................................................... 116

4.2.1 General model ........................................................................................................ 116

4.2.2 Construction of dummy variables .......................................................................... 119

4.3 The Data ....................................................................................................................... 121

4.4 Empirical Results .......................................................................................................... 126

4.4.1 Base model: baseline alpha and micro-factors ....................................................... 126

4.4.2 Time and style variation of micro-factor effects .................................................... 128

4.5 Conclusion .................................................................................................................... 136

References .......................................................................................................................... 138

Complete Bibliography .......................................................................................................... 141

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List of Tables

Table 1.1. Descriptive Statistics ............................................................................................... 27

Table 1.2: Estimated Probabilities for Mismatches of Different Types ................................... 29

Table 1.3: Simulated Performance Results .............................................................................. 30

Table 1.4: Mean Delisting Returns .......................................................................................... 32

Table 1.5: Mean Delisting Returns for Well-Behaved Residuals ............................................ 33

Table 1.6: Mean Delisting Returns with Investment in the Riskless Asset ............................. 34

Table 1.7: Mean Delisting Returns without Leverage ............................................................. 35

Table 2.1 Investment Companies’ Composition ...................................................................... 55

Table 2.2. Database Sample Statistics ...................................................................................... 56

Table 2.3. Determinants of Hedge Fund Birth ......................................................................... 57

Table 2.4. Determinants of Hedge Fund Death ........................................................................ 59

Table 2.5. Pre- and Post-Launching Portfolio Statistics .......................................................... 60

Table 2.6. Performance of Hypothetical Long-Short Portfolios .............................................. 61

Table 2.7. Sample Statistics of Monthly Percentage Fund Flow ............................................ 62

Table 2.8. Flow to New Hedge Funds within Families ............................................................ 64

Table 2.9. Flow to All New Hedge Funds ................................................................................ 65

Table 2.10. Investment Companies’ Composition by Fund Styles .......................................... 67

Table 2.11. Determinants of Hedge Fund Birth: Style-Wise Regressions ............................... 68

Table 2.12. Determinants of Hedge Fund Death (2) ................................................................ 70

Table 2.13: Hedge Fund Style Classification According to the ALTVEST Database ............ 73

Table 2.14. Control Variables for Fund Flow .......................................................................... 76

Table 3.1. Descriptive Statistics of Daily Returns on the Four Asset Classes ......................... 93

Table 3.2. Out-of-Sample Performance of the Portfolios with the Fixed Asset Span ............. 96

Table 3.3 Descriptive Statistics of Yearly Returns .................................................................. 98

Table 3.4. Out-of-Sample Performance of Portfolios with an Extended Asset Span .............. 99

Table 3.5. Portfolio Performance around Special Events ..................................................... 102

Table 3.6. Out-of-Sample Performance of the Portfolios Based on Weekly Returns ............ 103

Table 3.7. Out-of-Sample Performance with Different Levels of z-Interval Trimming ........ 104

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Table 4.1. Hedge Fund Performance and its Determinants: Evidence from the Literature ... 114

Table 4.2. Time Periods in the Evolution of the Hedge Fund Industry ................................. 119

Table 4.3. Correlation Matrix of the Log AuM and Fund Flows ........................................... 121

Table 4.4. Size Distribution of Hedge Funds as of May 2005 ............................................... 123

Table 4.5. Sample Statistics of Hedge Funds under Study .................................................... 124

Table 4.6. Summary Statistics and Tests of Normality, Heteroscedasticity, and Serial

Correlation on Hedge Fund Residuals ........................................................................... 125

Table 4.7. Panel Regression with Hedge Fund Micro Factors ............................................... 127

Table 4.8. Time Variation of Style Effects ............................................................................ 129

Table 4.9. Time and Style Variation of Age Effects .............................................................. 131

Table 4.10. Time and Style Variation of Size Effects ............................................................ 132

Table 4.11. Time Varying Fee Effects ................................................................................... 135

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List of Figures

Figure 1.1: Pre-Fee vs. Post-fee Net Asset Value .................................................................... 38

Figure 3.1. Example of an SSD Relation between Two Distributions ..................................... 86

Figure 3.2. Histogram of the Bootstrapped Distribution for ΔN under Random Portfolio Choice

.......................................................................................................................................... 95

Figure 3.3. Time Series of Portfolio Weights for the Stock Index .......................................... 97

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Introduction

This dissertation consists of four stand-alone research papers which investigate various

aspects of hedge fund performance and optimal portfolio choice. The hedge fund industry has

been expanding at an exponential rate over the last decade, reaching total assets under

management of over USD 1.5 trillion as estimated at the end of June 2007 (see Reuters’

article, Hedge Fund Assets Rise, August 29, 2007). Hedge funds have become important

players in the global financial market. They attract not only high-net-worth individuals but

also institutional investors like banks, insurance companies, and pension funds. They became

available to individual investors through funds of hedge funds. This success of the hedge fund

industry can be explained by the attractive performance characteristics of hedge funds. Hedge

funds are nearly completely unregulated by authorities, can operate on the derivative market,

use leverage and short sales, and implement all kinds of dynamic non-linear investment

strategies with option-like payoffs (see, for instance, Fung and Hsieh (1997, 2001), Agarwal

and Naik (2004)). On average they deliver high returns with moderate standard deviation that

have low correlation with the market. For this attractive performance, hedge funds charge

large fees. An investor is subject to a management fee, which is normally around 2% of the

assets managed per year, and an incentive (or performance) fee, which is on average 20% of

the end-of-year profits over the highest previously reached fund value (the high-water mark).

Such a nonlinear compensation structure induces additional incentive for hedge fund

managers to dynamically change the riskiness of their portfolios.

Not surprisingly, the academic literature concerning hedge funds has also been rapidly

growing. Empirical hedge fund analysis is challenged by the scarceness of available

information. Hedge funds are not obliged to disclose any details on their strategy and

performance, but may voluntarily report to one or more commercial databases (for example,

TASS, HFR, ALTVEST, BARCLAY, and CISDM). These databases are subject to several

severe biases that complicate inference; and the first is the self-selection bias. The poorly

performing funds (that do not want to have negative advertisement) and extremely profitable

hedge funds (that have already reached the optimal asset level and do not need to attract new

investors) stay uncovered by such databases. Even the direction of this bias cannot, thus, be

clearly determined. Second is the back-filling or instant history bias. Upon entering to a

database, hedge funds can backlist their performance. The backlisting is naturally done only

when the past performance contributes to positive performance track of a fund. This bias

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induces overestimation of general hedge fund profitability. The third one is the survivorship

bias. Modern databases keep reporting the past performance of the defunct funds, partially

ameliorating the bias. However, the problem stays pronounced since hedge funds may stop

reporting at any time. Poorly performing funds can stop reporting before their actual

liquidation. Thus, possibly large and negative last returns stay unobserved for a user of the

database. Well performing funds may decide to close for new investment and stop reporting.

In this case, possibly large positive returns stay unobserved.

The first chapter of this thesis deals with the problem of unobserved hedge fund

returns after delisting. To the best of my knowledge, it is the first paper that explicitly

recovers the unobserved returns of hedge funds after they stop reporting to the database. It is a

joint work with Prof. Jens Carsten Jackwerth and Prof. James E. Hodder. In this paper, a

methodology is proposed for estimating hedge fund delisting returns based on a fund-of-funds

(FoF) being a portfolio of positions in individual hedge funds, some of which may stop

reporting in any given period. The portfolio holdings (positions in hedge funds) are estimated

through a matching algorithm related to principal component analysis. The unobserved

delisting return is modeled as normally distributed with mean and variance to be estimated.

The parameters are estimated using the inferred portfolio holdings for each FoF, where one

realization of the delisting return during the next period is estimated as the difference between

the observed next-period return for each FoF and that period’s return from its estimated

portfolio holdings in live (still reporting) hedge funds. The estimated mean delisting return for

all exiting funds is negative but small, although statistically significantly different from the

average observed returns for all reporting hedge funds. It is nowhere near the values of -50%

of -100% used by some authors (Posthuma and van der Sluis (2004)), which would indicate

complete destruction of the hedge fund’s value. Nevertheless, some funds have large negative

exit returns, which results in substantial variability of our estimated delisting returns.

The second chapter addresses another issue that has not been studied in previous

research. It concentrates not on individual hedge funds, but on hedge funds families. A hedge

fund family is defined as a group of hedge funds controlled by the same investment company.

This chapter investigates the strategic decisions of such families concerning the start and

liquidation of family member funds. These decisions are of crucial importance for investors

since they determine the future opportunity set. However, the existing literature seems to

disregard the family-related dependencies between individual hedge funds. Hedge fund

origination decisions have not been covered in the literature at all, and hedge fund liquidation

research, although very intensive (see, for instance, Liang (2000), Gregoriou (2002), Rouah

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(2005), Chan, Getmansky, Haas, and Lo (2005), and Park (2006)), disregard the fact that

liquidation decisions may be taken strategically by investment companies operating several

funds, and, moreover, can be linked to the origination decision. This chapter fills this gap

providing empirical evidence of the strategic behavior of hedge fund families. It finds that

hedge fund families tend to liquidate funds that have lower potential to earn fee income

compared to other member funds and substitute them by new funds. They choose the

launching time after observing a short period of superior performance of their member funds

in order to achieve spillover effect to new funds. The result is higher flow to their new funds

than to funds launched not within families. The launching decision itself, however, should not

be interpreted as a signal of positive and persistent skill of the managers operating these

funds. New funds are launched after a period of good luck for other member funds, which do

not continue to outperform after the fund start. Additionally, families’ experience in fund

launching and economies of scale and scope positively influence hedge fund origination

decisions similarly to mutual fund families.

The third chapter focuses on the optimal portfolio choice problem. One of the most

widely used criteria for portfolio optimality is a mean-variance criterion. It has, however,

several well-known limitations. It is symmetric, and its theoretical justification requires either

a quadratic utility function or multivariate normality of returns. Furthermore, the

corresponding optimization procedures often result in extreme portfolio weights when using

historical inputs, which implicitly contain estimation errors relative to the true underlying

return distributions. In this chapter, a superior way of ranking candidate portfolio return

distributions is proposed. It is based on second-order stochastic dominance (SSD) as a

comparison criterion. The SSD criterion is compatible with all types of increasing and

concave utility functions. It does not focus on a limited number of moments, but accounts for

the complete return distribution. The developed tests for SSD are nonparametric, thus, no

distributional assumptions are needed. Last but not least, portfolio optimization based on the

SSD criterion results in fairly stable portfolio weights, which overcomes a major problem for

mean-variance optimization procedures. Existing empirical work on portfolio allocation using

the SSD concept has been either restricted to in-sample analysis (see e.g., Post (2003) and

Kuosmanen (2004)) or did not rely on the SSD criterion for estimating the portfolio choice

itself. This chapter has contributed to the literature in a number of ways. It examines whether

a typical pension fund holds an SSD efficient portfolio or if the portfolio it holds can be

improved upon. In doing so, a benchmark portfolio is constructed based on the main asset

classes in which major pension funds invest. Then, a procedure for determining the optimal

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in-sample portfolio is developed, where optimality is defined as the highest degree of

stochastic dominance of the portfolio of interest over a benchmark portfolio. Next, it is tested

whether the dominance of this optimal portfolio is preserved out-of-sample using the

Davidson (2007) test procedure. The performance of the SSD-based portfolio is compared

with other competing portfolio choice approaches such as mean-variance, minimum-variance,

and equally weighted schemes. The chapter also develops a formal bootstrap-based statistical

test that allows for documenting that the SSD-based portfolio choice technique significantly

increases the propensity of stochastically dominating portfolios out-of-sample. Thus, an

approach for improving the existing asset allocation is proposed, which is illustrated on a

particularly interesting application in improving the portfolio holdings of large pension funds.

Such technology can help researchers and fund managers to establish a lower bound on

performance that any risk-averse investor would prefer (or at least be indifferent) to the

proposed portfolio.

The last chapter of the dissertation questions the relations of hedge fund performance

and various micro factors and investigates time variations of these relations. The majority of

studies that have analyzed the determinants of hedge fund performance have come to

contradictory conclusions. Liang (1999), for example, finds a positive relationship between

hedge fund performance and size, as well as between performance and fees. Agarwal, Daniel,

and Naik (2004) document a negative relationship between fund performance and size, and

Kouwenberg and Ziemba (2007) report negative relationship between performance and fees.

The key reason for these inconsistencies is the highly dynamic nature of hedge funds. This

paper specifically focuses on the dynamics of the relations between hedge fund performance

and various micro-factors. It quantifies shifts in the average fund alpha that result from

changes in hedge fund style, age, size, and fee structure and investigates the time variation of

these shifts. The analysis is based on a fixed effect panel regression, which allows

simultaneously controlling for time-series variations and cross-section dependencies in the

hedge fund industry. The empirical results highlight that the hedge fund industry is indeed

very dynamic. It seems to generate a positive and significant alpha on average; however, the

alpha level varies considerably over time. It is hard to predict the exact absolute alpha level

based on the hedge fund micro-factors, but it seems to be possible to rank hedge funds using

the micro information. The results suggest that large funds with high relative inflow charging

higher than median management fees are likely to deliver higher alpha than their peers most

of the time.

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Zusammenfassung

Die vorliegende Dissertation besteht aus vier eigenständigen Forschungsarbeiten, in

denen verschiedene Aspekte der Leistung von Hedgefonds und der optimalen

Portfolioauswahl untersucht werden. Im Laufe der letzten Dekade hat die Hedgefondindustrie

ein außergewöhnliches Wachstum an den Tag gelegt, mit einem Ende Juni 2007 geschätzten

(siehe Reuters Artikel, Hedge Fund Assets Rise, August 29, 2007) Gesamtfondsvolumen von

über 1.5 Milliarden USD. Hedgefonds sind zu einem wichtigen Marktteilnehmer der globalen

Finanzmärkte geworden. Sie ziehen nicht nur sehr wohlhabende Privatinvestoren, sondern

auch institutionelle Investoren wie Banken, Versicherungen und Pensionsfonds an. Dem

Einzelinvestor wurden sie durch Dach-Hedgefonds zugänglich. Dieser Erfolg

der Hedgefondindustrie lässt sich durch die attraktiven Ertragscharakteristiken von

Hedgefonds erklären. Hedgefonds sind durch Behörden nahezu nicht reguliert, können sich

auf dem Derivatenmarkt bewegen, Leerverkäufe durchführen und vielerlei nicht-lineare

Investmentstrategien mit optionsähnlichen Auszahlungsstrukturen implementieren (siehe

etwa, Fund und Hsieh (1997, 2001), Agarwal und Naik (2004)). Im Durchschnitt liefern sie

hohe Renditen mit moderaten Standardabweichungen, welche eine niedrige Korrelation mit

dem Markt aufweisen. Für diese attraktive Leistung berechnen Hedgefonds hohe Gebühren.

Ein Investor unterliegt einer Managementgebühr, welche normalerweise bei ca. 2% des

verwalteten Kapitals pro Jahr liegt, und einer leistungsbezogenen Gebühr, welche im

Durchschnitt bei 20% der Erträge über dem höchsten vergangenen Fondswert (die so

genannte „high-water mark“) liegt. Solch eine nicht-lineare Vergütungsstruktur schafft

zusätzlichen Anreiz für die Hedgefond Manager das Risiko ihrer Portfolios dynamisch zu

variieren.

Nicht überraschenderweise nahm auch der Umfang an akademischer Literatur

bezüglich Hedgefonds rapide zu. Die empirische Forschung wird durch die geringe

Verfügbarkeit von Informationen erschwert. Hedgefonds sind nicht

verpflichtet jegliche Informationen bezügliche ihrer Erträge oder ihrer Strategie preiszugeben.

Sie können jedoch, auf freiwilliger Basis, einem oder mehreren kommerziellen

Datenbankanbietern (z.B. TASS, HFR, ALTVEST, BARCLAY und CISDM) Informationen

zur Verfügung stellen. Diese Datenbaken unterliegen mehreren schwerwiegenden

Verzerrungen, welche die Schlussfolgerungen, die aus ihnen zu ziehen sind, erschweren. Die

erste ist der so genannte „self-selection bias“. Die schlecht abschneidenden (Hedgefonds, die

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kein negatives Aufsehen erregen möchten) und die sehr gut abschneidenden (Hedgefonds, die

schon über die optimale Kapitalausstattung verfügen und deshalb keine neuen Investoren

anziehen müssen) Hedgefonds werden von den Datenbanken nicht erfasst. Deshalb kann nicht

einmal die Richtung dieser Verzerrung zweifelsfrei bestimmt werden. Die zweite Verzerrung

ist der „back-filling“ oder „instant-history bias“. Beim Eintritt in eine Datenbank

können Hedgefonds vergangene Renditen berichten. Gewöhnlicherweise wird dies getan, falls

die vergangenen Renditen zu einer positiven Ertragsentwicklung des Hedgefonds beitrugen.

Diese Verzerrung führt zu einer Überschätzung der generellen Profitabilität von Hedgefonds.

Die dritte Verzerrung ist der „survivorship bias“. Moderne Datenbanken löschen die früheren

Renditen von gelöschten Hedgefonds nicht, was diese Verzerrung teilweise verringert.

Trotzdem bleibt dieses Problem relevant, da Hedgefonds zu jeder Zeit den Informationsfluss

unterbrechen können. Hedgefonds mit schlechten Renditen können vor der eigentlichen

Liquidierung aufhören, Bericht zu erstatten. Aus diesem Grund ist es wahrscheinlich, dass

stark negative letzte Renditen nicht dokumentiert werden. Hedgefonds mit guten Erträgen

verschließen sich eventuell gegen weitere Mittelzuflüsse und hören ebenso auf Bericht zu

erstatten. In diesem Fall werden wahrscheinlich stark positive Erträge von den Datenbanken

nicht erfasst.

Das erste Kapitel dieser Doktorarbeit beschäftigt sich mit dem Problem der nicht

dokumentierten Erträge nach dem „delisting“ des Hedgefonds. Nach meinem bestem Wissen

ist das die erste Abhandlung, welche explizit die nicht dokumentierten Erträge von

Hedgefonds die aufgehört haben Bericht zu erstatten, zurückgewinnt. Es handelt sich um eine

Gemeinschaftsarbeit mit Prof. Jens Carsten Jackwerth und Prof. James E. Hodder. In dieser

Abhandlung wird eine Schätzmethode für delisting-Renditen, basierend auf einem Dach-

Hedgefond (FoF) vorgeschlagen. Hierbei repräsentiert ein Dach-Hedgefonds ein Portfolio

von Hedgefonds, welche zu jedem Zeitpunkt aufhören können Bericht zu erstatten. Die

Bestandteile des Portfolios (Positionen in Hedgefonds) werden durch einen

Abgleichungsalgorithmus, basierend auf einer Hauptkomponentenanalyse, bestimmt. Die

nicht dokumentierte Rendite wird als normalverteilt modelliert, wobei Mittelwert und Varianz

zu schätzen sind. Die Parameter werden mit Hilfe der abgeleiteten Bestandteile jedes FoF

Portfolios geschätzt. Wobei eine Realisation einer delisting-Rendite der nächsten Periode als

Differenz aus der beobachteten Rendite der nächsten Periode jedes FoF und der Rendite

dieser Periode jedes geschätzten Portfoliobestandteiles in noch berichterstattenden

Hedgefonds geschätzt wird. Die geschätzte mittlere nicht dokumentierte Rendite jener

Hedgefonds, die aufhören Bericht zu erstatten, ist negativ, jedoch klein. Aber statistisch

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signifikant unterschiedlich von den durchschnittlich beobachteten Renditen aller

berichterstattenden Hedgefonds. Die delisting-Rendite bewegt sich bei weitem nicht in der

Größenordnung der Werte von -50% bis -100%, welche von einigen Autoren benutzt wurden

(Posthuma und van der Sluis (2004)), was die komplette Vernichtung des Wertes des

Hedgefonds andeuten würde. Dennoch weisen manche Hedgefonds stark negative delisting-

Renditen auf. Dies führt zu einer substanziellen Varianz der geschätzten delisting-Renditen.

Das zweite Kapitel beschäftigt sich mit einem weiteren Problem, welches in

vergangenen Forschungsarbeiten keine Beachtung fand. Hier wird nicht der individuelle

Hedgefond betrachtet, sondern Familien von Hedgefonds. Eine Familie von Hedgefonds ist

definiert als eine Gruppe von Hedgefonds, die jeweils vom gleichen Investmentunternehmen

betrieben werden. Dieses Kapitel beschäftigt sich mit den strategischen Entscheidungen

solcher Familien bezüglich der Gründung und der Liquidation von familienzugehörigen

Hedgefonds. Diese Entscheidungen sind von äußerst wichtiger Bedeutung für Investoren, da

sie die zukünftig verfügbaren Anlagemöglichkeiten festlegen. Trotzdem scheint die

existierende Literatur die familienbezogenen Zusammenhänge zwischen Hedgefonds außer

Acht zu lassen. Entscheidungen hinter der Entstehung von Hedgefonds wurden in der

Literatur bis jetzt nicht behandelt. Forschung bezüglich der Liquidation von Hedgefonds

wurde zwar intensiv betrieben (siehe, zum Beispiel, Liang (2000), Gregoriou (2002), Rouah

(2005), Chan, Getmansky, Haas und Lo (2005), und Park (2006)), jedoch wurde außer Acht

gelassen, dass Entscheidungen zur Liquidation von Hedgefonds eventuell aus strategischen

Gründen von Unternehmen, welche mehrere Hedgefonds betreiben, getroffen werden und

überdies mit Gründungsentscheidungen zusammenhängen können. Dieses Kapitel füllt diese

Lücke indem es empirische Belege für das strategische Verhalten von Familien von

Hedgefonds liefert. Es stellt sich heraus, dass Familien von Hedgefonds dazu tendieren

Hedgefonds mit geringem Potenzial zur Gebührengenerierung, verglichen mit anderen

familienzugehörigen Hedgefonds zu liquidieren und sie mit neuen Hedgefonds zu ersetzen.

Sie suchen den Zeitpunkt der Markteinführung nach einer kurzen Periode

überdurchschnittlicher Erträge der familienzugehörigen Hedgefonds aus, um einen

Überlaufeffekt zu den neuen Hedgefonds zu erzielen. Dies resultiert in einem stärkeren Zulauf

bei ihren neu gegründeten Hedgefonds, als bei Hedgefonds welche keiner Familie von

Hedgefonds angehören. Trotzdem sollte die Gründungsentscheidung an sich nicht als Signal

für gute und nachhaltige Fähigkeiten der Manager, welche diese Hedgefonds leiten,

interpretiert werden. Neue Hedgefonds werden nach einer Glückssträhne anderer

familienzugehöriger Hedgefonds, welche nach der Gründung des Hedgefonds keine weitere

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Outperformance erzielen, gegründet. Des Weiteren begünstigen Skaleneffekte,

Diversifikationseffekte und Erfahrungen der Familien mit der Gründung von Hedgefonds,

ähnlich wie bei Familien von Investmentfonds, die Entscheidung zur Neugründung von

Hedgefonds.

Das dritte Kapitel beschäftigt sich mit dem Problem der optimalen Portfoliowahl.

Eines der am häufigsten genutzten Kriterien für die Portfoliooptimalität ist das Mean-

Variance-Kriterium. Jedoch unterliegt es mehreren wohl bekannten Einschränkungen. Es ist

symmetrisch und seine theoretische Begründung beruht entweder auf der Annahme einer

quadratischen Nutzenfunktion oder auf der Annahme, dass die Renditen einer multivariaten

Normalverteilung folgen. Des Weiteren resultieren die jeweiligen Optimierungsverfahren

häufig in extremen Portfoliogewichten wenn historische Inputs verwendet werden, welche

unweigerlich Schätzfehler bezüglich der echten zu Grunde liegenden Renditeverteilungen

enthalten. In diesem Kapitel wird eine überlegene Methode zur Rangfolgebestimmung der

möglichen Portfoliorendite-Verteilungen vorgeschlagen. Die Methode basiert auf

stochastischer Dominanz zweiter Ordnung (SSD) als Vergleichskriterium. Das SSD Kriterium

ist mit allen Typen von zunehmenden konkaven Nutzenfunktionen kompatibel. Es beschränkt

sich nicht auf eine limitierte Anzahl von Momenten, sondern berücksichtigt die komplette

Renditeverteilung. Die entwickelten Tests für SSD sind nicht-parametrisch, deshalb sind

keine Annahmen bezüglich der Verteilungen nötig. Nicht zuletzt resultiert eine

Portfoliooptimierung basierend auf dem SSD-Kriterium in ziemlich stabilen

Portfoliogewichten, was ein Hauptproblem der Mean-Variance-Optimierungsmethoden

beseitigt. Existierende empirische Arbeit bezüglich der Portfolioallokation mittels des SSD

Konzeptes war entweder auf eine in-sample Analyse (siehe, zum Beispiel, Post (2003) und

Kuosmanen (2004)) beschränkt oder nutzte nicht das SSD-Kriterium zur eigentlichen

Portfolioauswahl. Dieses Kapitel trägt in vielerlei Hinsicht zur Literatur bei. Es untersucht, ob

ein typischer Pensionsfond ein SSD-effizientes Portfolio hält, oder ob das gehaltene Portfolio

Verbesserungspotential aufweist. In diesem Zuge wird ein Vergleichsportfolio, basierend auf

den Hauptanlageklassen in die bedeutende Pensionsfonds investieren, konstruiert. Dann wird

eine Methode zur Bestimmung des optimalen in-sample Portfolios entwickelt. Hierbei ist das

optimale Portfolio definiert als das Portfolio mit der höchsten stochastischen Dominanz über

ein Vergleichsportfolio. Als nächstes wird mittels der Testmethoden von Davidson (2007)

getestet ob die Dominanz dieses Portfolios auch out-of-sample erhalten bleibt. Die Leistung

des SSD-basierten Portfolios wird nun mit anderen Portfolios konkurrierender

Portfolioauswahlmethoden, wie Mean-Variance, Minimum-Variance, oder der

17

Gleichgewichtung, verglichen. In dem Kapitel wird außerdem ein formaler bootstrap-basierter

statistischer Test entwickelt, welcher zu zeigen erlaubt, dass die SSD-basierte

Portfolioauswahlmethode signifikant die out-of-sample Häufigkeit stochastisch

dominierender Portfolios erhöht. Somit wird ein Verfahren zur Verbesserung der

existierenden Portfolio-Strukturierung vorgeschlagen. Das Verfahren wird mit einer

besonders interessanten Anwendung, der Verbesserung von Portfoliobestandteilen großer

Pensionsfonds, illustriert. Solch eine Technik kann Wissenschaftlern sowie Fondsmanagern

helfen eine Untergrenze für die Leistung eines Portfolios, welche jeder risikoaverse Investor

vorzieht (oder zumindest bezüglich derer er indifferent ist), zu ermitteln.

Das letzte Kapitel dieser Doktorarbeit setzt sich mit dem Zusammenhang zwischen

den Renditen von Hedgefonds und verschiedenen Mikrofaktoren auseinander und untersucht

zeitliche Änderungen dieser Relationen. Die Mehrzahl der Studien bezüglich der Renditen

von Hedgefonds kamen zu widersprüchlichen Ergebnissen. Liang (1999) zum Beispiel

beobachtete einen positiven Zusammenhang zwischen den Renditen von Hedgefonds und

ihrer Größe, wie auch zwischen den Renditen und den Gebühren. Agarwal, Daniel und Naik

(2004) dokumentierten einen negativen Zusammenhang zwischen Rendite und Größe und

Kouwenberg und Ziemba (2007) stellten eine negative Relation zwischen Rendite und

Gebühren fest. Der Hauptgrund für diese Inkonsistenzen liegt in der hochdynamischen Natur

der Hedgefonds begründet. Diese Abhandlung legt besonderen Akzent auf die Dynamik der

Beziehungen zwischen den Renditen von Hedgefonds und diversen Mikrofaktoren. Sie

quantifiziert Verlagerungen im durchschnittlichen Alpha der Hedgefonds, welche aus

Änderungen der Strategie, des Alters, der Größe und der Gebührenstruktur resultieren und

untersucht die zeitlichen Veränderungen dieser Verlagerungen. Die Analyse basiert auf einer

Regression auf Paneldaten mit fixierten Effekten, welche gleichzeitig erlaubt Variationen der

Zeitreihen, sowie Querschnittsabhängigkeiten innerhalb der Hedgefond Industrie zu

berücksichtigen. Die empirischen Ergebnisse streichen heraus, dass die Hedgefond Industrie

in der Tat sehr dynamisch ist. Es scheint als ob durchschnittlich ein positives und

signifikantes Alpha generiert wird; jedoch variiert das generierte Alpha mit der Zeit erheblich.

Es stellt sich als schwierig heraus das exakte absolute Alpha basierend auf Hedgefond

Mikrofaktoren zu schätzen, aber es scheint möglich eine Rangfolge der Hedgefonds,

basierend auf diesen Mikroinformationen, zu erstellen. Die Ergebnisse legen nahe, dass große

Hedgefonds mit hohem relativen Kapitalzufluss, welche Managementgebühren über dem

Median verlangen, wahrscheinlich die meiste Zeit ein größeres Alpha als die restlichen

Hedgefonds generieren.

18

Chapter 1

Recovering Delisting Returns of Hedge

Funds

19

1.1 Introduction

Each year, a substantial percentage of hedge funds stop reporting their results to

publicly available databases. For example, the annual average “delisting” rate was 8.1% in

Morningstar’s ALTVEST database for January 1994 – June 2006 (the data used in this

paper).1 If one is studying hedge-fund performance, this raises the issue of what return should

be attributed to such funds for the period when they stop reporting. Typically, these funds are

described as “dead funds”; but it is clear that not all of them have ceased to exist. The

information in ALTVEST is self-reported by the funds, with only 20% of dead funds

indicating they were being liquidated. Indeed, another 4% indicate that they stopped

providing their returns because they closed to further investments (potentially due to stellar

performance and large previous inflows of investment capital). Moreover, information for the

remaining 76% of delisted funds either does not indicate why they ceased reporting or

provides non-informative statements such as “requested by manager”.

One possibility for addressing this issue is to simply drop the last period from the

analysis, but that ignores the fact that fund investors will actually experience the delisting

return. In contrast, Posthuma and van der Sluis (2004) used 0%, -50%, and -100% to cover

a wide range of possibilities for the unknown delisting return. This drew a strong response

from two practitioners, Van and Song (2005) p. 7, who call the assumption of a delisting

return of -50% “outrageous”. However, if a fund has suffered massive losses and is being

liquidated, a large negative delisting return is definitely possible. This would be the case if

the fund’s mark-to-market valuation prior to delisting underestimated the extent of losses that

would be incurred with liquidation, presumably under adverse circumstances. On the other

hand, a highly successful fund that chooses to restrict further investment and focus on

managing its current funds might well have a substantial positive (but unreported) delisting

return. Moreover, for the vast majority of funds, we do not know why they stop reporting.

There is a literature which explores hedge-fund performance prior to delisting.2

However, the only paper of which we are aware that makes any attempt to examine

performance after delisting is Ackermann, McEnally and Ravenscraft (1999). They used a

combined data set with underlying data from two providers, Managed Account Reports, Inc.

(MAR) and Hedge Fund Research, Inc. (HFR). During 1993-1995, their combined data

1 In what follows, we will use the term “delist” to indicate that the fund has stopped reporting its results to

database providers while other authors have also used the term “exit” instead.

2 See for example, Brown, Goetzmann and Ibbotson (1999), Ter Horst and Verbeek (2007), as well as Liang

(2000).

20

included 37 “terminated” funds (liquidated, restructured, or merged into another fund) plus

an additional 104 funds that stopped reporting without a clear indication as to why they

ceased reporting. That is, a total of 141 delisting funds. Those authors were able to obtain

information on returns for some fraction of the terminated funds (only) via a request to HFR

regarding funds that had been listed in the HFR portion of the joint database. Thus, the

information refers to only a subset of the 37 terminated funds rather than all 141 delisting

funds. The response from HFR indicated an average return for the terminating funds after

delisting of -0.7%, with a surprisingly rapid final redemption that occurred on average only

18 days after delisting. It would appear that some of the terminating funds were in the

process of liquidating while still reporting returns. Unfortunately, that data is rather old

(1993-1995), predating the boom in the hedge-fund industry; and it is based on a relatively

small sample (at most 37 terminating funds). Also, they do not report delisting return

estimates for funds that did not provide a clear reason for delisting or for what would

correspond in the ALTVEST database to being closed to further investment.

In this paper, we propose a methodology for estimating delisting returns based on a

fund-of-funds (FoF) being a portfolio of positions in individual hedge funds, some of which

may stop reporting in any given period. If we had information on the actual FoF portfolio

positions, it would be straightforward to back out returns for delisting funds using that

information plus the FoF returns and the returns of live hedge funds for the delisting month.

Unfortunately, we do not have that information on FoF portfolio positions. Instead, we

estimate those portfolio holdings through a matching algorithm related to principal component

analysis. Once we have inferred the portfolio holdings (positions in hedge funds) for each

FoF in our sample, we can obtain delisting returns during the next period based on the

difference between the observed next-period return for each FoF and that period’s return from

its estimated portfolio holdings in live (still reporting) hedge funds.

Fung and Hsieh (2000) as well as Fung, Hsieh, Naik and Ramadorai (2008) have also

noticed that FoF returns implicitly incorporate the delisting returns of individual hedge funds;

however, they do not use the portfolio connection to actually back out the delisting returns.

Nevertheless, Fung, Hsieh, Naik, and Ramadorai (2008, page 1778) do point out that the

absence of delisting returns leads to a situation where a “fund-of-fund’s return more

accurately reflects the losses experienced by investors in the underlying hedge fund (albeit

indirectly).”

An issue with the matching algorithm is the potential for mismatches where the

estimated FoF portfolio contains a different number of delisted funds than truly occurred for

21

that FoF during the period. We develop an adjustment to correct for this bias and report

below estimates using that methodology. We find different mean delisting returns for hedge

funds that do not provide a clear reason for delisting as opposed to those that liquidate and

those which state they are closed to further investment. However, none of these estimates are

large. Across all delisting hedge funds, the estimated mean delisting return is -1.86%. This

compares with a mean monthly return for all hedge funds in our sample of 1.01%. Thus, we

find that the estimated average delisting return is fairly small and nowhere near values of -

50%. Nevertheless, some funds have large negative exit returns, which results in substantial

variability of our estimated delisting returns.

1.2 The Basic Model

Since we do not have precise information on portfolio holdings for each FoF in our

sample, we need a procedure for estimating those holdings. We use a matching algorithm

based on the concept of principle components. A somewhat similar problem has been

encountered with empirical macroeconomic models in which a short time series needs to be

explained by many potential predictors.3 The macroeconometric approach of aggregating

many predictors (hedge funds in our case) into principle components is not directly applicable

to our setting of FoF returns. After all, each FoF invests into a relatively small number of

individual hedge funds (the reported average for our data is 24) and not into principle

components. However, we use a related idea which keeps the basic approach of principle

components.

As a preliminary step, we need to “gross up” the reported FoF returns to a pre-fee level

– that is, to the return level before management and incentive fees were extracted by the FoF.

That pre-fee FoF return is the return on a portfolio of post-fee hedge fund returns

(management and incentive fees having already been extracted by the respective hedge

funds). As our FoF and hedge-fund return data is all post-fee, we transform the FoF returns to

a pre-fee basis using an algorithm closely related to Brooks, Clare and Motson (2007) that is

described in the Appendix.

In our implementation, we use a 36-month rolling window and consider only FoFs and

hedge funds which report returns for all months in the relevant window. As with many other

implementation choices for our basic methodology, we have examined the robustness of our

3 See e.g. Bai (2003), Bai and Ng (2002), Boivina and Ng (2006), plus Stock and Watson (2002).

22

estimates to variations in the choice of a 36-month window. To avoid cluttering the

exposition, we defer discussion of most such robustness checks until Section 1,4 below. As a

general statement, our qualitative results are quite robust; but there can be some variation in

point estimates and significance tests.

For each FoF, we find the hedge fund whose (post-fee) returns are most highly

correlated with the (pre-fee) returns of that FoF. Then, we regress the FoF returns on the

chosen hedge fund and obtain the residual returns. Next, we find a second hedge fund that is

now the most highly correlated with the residual returns for that FoF. We add that hedge fund

to the portfolio, find new residual returns, and proceed in this fashion until we have 15 hedge

funds in the portfolio. We provide a detailed description of the methodology in the next

section.

Once we work out the set of matched hedge funds for each FoF, we are ready to model

the pre-fee returns of the FoF as a portfolio of the (post-fee) returns on the matched hedge

funds. The (pre-fee) FoF returns are always indicated with an upper-case R, and the live

hedge fund returns (post-fee) are denoted with a lower-case rL. We use T = 36 consecutive

returns to estimate the following regression model for each FoF, with funds indexed by i and

time periods (months) by t:

2

min

[ ] , 1,..., , (0, )

s.t.: 0.25 , 1 1

it Lt i it it i

i i

R r t T N

(1.1)

In order to insure economically sensible portfolio positions, we restrict the loadings i

(portfolio weights for FoFi) on the matched hedge funds to be smaller than 0.25 and larger

than some minimal value min. We further assume that each FoF is fully invested in its set of

matched hedge funds.4

Logically, equation (1.1) should not include a constant term since we do not have an

investable asset with a constant return. One might anticipate that a FoF would have an

approximately constant component in its operation costs; however, we assume operating costs

4 There is an omitted variables problem in that a given FoF may be invested in one or more hedge funds that are

not in our database. ALTVEST is not all-encompassing; and indeed, there are hedge funds that do not report to

any of the publicly available databases. Our procedure assumes that we can implicitly approximate the omitted

funds by a linear combination of hedge funds that are in our database. Simulation studies discussed in Section II

below indicate our methodology works adequately, even with a large number of omitted funds. A similar

argument can be used concerning turnover in the fund of funds. As long as there is a reasonably similar hedge

fund which mimics the time-varying true holdings of the FoF, our method will adequately match the

performance for that FoF.

23

are effectively paid out of the Fund’s management fee and hence do not appear in equation

(1.1). Some 70% of FoF in our data report not using leverage on average. Apparently, most

FoFs also attempt to remain close to fully invested. Hence, we do not include the riskless

asset as one of the investments for our primary implementation of equation (1.1). However,

we do include in our analysis FoFs which indicate average borrowing up to 100% (200%) of

their equity. Those funds represent some 20% and 5%, respectively, of all FoFs in our

data. For such FoFs, we allow investment into the riskless asset with

0 1 (respectively 2)riskless . We use monthly returns based on 3-month T-bills from

the Federal Reserve Statistical Release H.15 as a riskless rate. In those implementations, the

upper limit on i changes then from 0.25 to 0.5 or to 0.75, respectively.

We now turn to the fitted return of the FoF in period T+1. If all the hedge funds in

that particular FoF portfolio are still alive, then the fitted return is simply calculated using the

estimated portfolio weights from equation (1.1) with the observed returns of the matched

hedge funds for period T+1:

, 1 , 1ˆˆ [ ]i T L T iR r (1.2)

Now consider the situation where a hedge fund delists and does not report its return

for that period. We denote that unreported return as rE,T+1

. The econometrics and

computations turn out to be much simpler if we base our estimates on matched portfolios

where there is a single delisting hedge fund. That situation represents approximately 88% of

our matched sample. Note that with one delisting fund in the portfolio, the vector of live

returns rL,T+1

will be one shorter than in the above situation where all hedge funds for a given

FoF portfolio are alive in period T+1. We model the unobserved delisting return rE,T+1

as

being normally distributed with mean E and standard deviation . In period T+1, a FoF

with a (single) delisting hedge fund in its portfolio, will have an actual return that can be

expressed as:

, 1 , 1 , 1 , 1[ , ]i T L T E T i i TR r r (1.3)

where we treat the FoFi replication error i as uncorrelated with estimated delisting returns.5

5 Changing the correlation coefficient to 0.5 or -0.5 does not qualitatively change the results, with only small

changes in the estimated numerical values.

24

We approximate the true betas with the estimated betas and the variances of the

residuals with their estimated values. For support of such assumptions, see the simulations

and robustness checks in Section 1.3 below. The above approach leads to the following

normally distributed quantity:

2 2 2

, 1 , 1 , , ,ˆ ˆ ˆ ˆ( ) ( , )i T L T L i E i E E i E iR r N , (1.4)

where ,

ˆL i and

,ˆ

E i are the estimated betas respectively for the hedge funds staying alive

and those exiting in period T+1 in the matched portfolio of FoFi.

When calculating the log-likelihood, we pay attention to the fact that several FoFs can

invest into the same hedge fund. If that hedge fund delists, then the associated delisting return

rE,T+1

will be the same for all FoFs with that hedge fund in their portfolio. Thus, we add up

the relevant equations (1.3) while keeping the rE,T+1 constant in that case. Not doing so

biased upward in unreported simulations.

The above procedure delivers an unbiased estimate of the mean exit return µE if all

matched portfolios used for the analysis have the number of delisted funds correctly

identified. That is, if a FoF truly invests into k delisted hedge funds, then the corresponding

matching portfolio should also have exactly k delisted funds. Our procedure does not require

precise hedge fund identification, and the returns of the truly delisted funds can be proxied by

returns of different (but correlated) funds in the matching portfolio. The estimate of µE stays

unbiased as long as the number of identified delisted hedge funds coincides with the number

of truly delisted funds. However, one cannot guarantee this correspondence while

constructing the matching portfolios; and the resulting estimate of µE can be biased.

Since we use only matches that have exactly one delisted fund, the following biases

can occur. First, consider a FoF that does not invest into any delisted fund, but the estimated

matching portfolio erroneously has a delisted fund. Using this match, one would estimate not

an unobserved delisting return (on average µE ) but the return of a hedge fund that was still

alive. The higher the share of matches of this type, the more the estimate of µE will be biased

towards the average return of hedge funds that were reporting to the database during that

period, which we denote by µHF. Second, if a FoF truly invests into one delisted hedge fund

and the estimated matching portfolio also has one delisted fund, then the match has perfect

correspondence and does not bias the estimate of µE. Third, consider a FoF that actually has

investments in two or more hedge funds that delist but is matched with a portfolio having only

25

one delisted fund. Trying to compensate for this mismatch would tend to impart an upward

bias in the estimated absolute value of µE. For example, if the number of truly delisted funds

is two, one would obtain an average estimate of µE + (µE - µHF) instead of µE. Our

adjustment procedure does not consider cases with three or more truly delisting hedge funds

since the probability of such a situation is very low for a FoF portfolio invested in 15 hedge

funds. According to our simulations described below, the probability that a FoF has 3 or

more exiting hedge funds while being matched with only one exiting fund is less than one

percent.

The biases due to such mismatches can be corrected, if one knows the share of

matches for each type. Let us denote by pk the probability that a FoF truly invests into k

delisted funds, and the estimated matching portfolio indicates the existence of only one

delisted fund. Then the estimated biased delisting return µEEstimated

is a weighted average of

the unbiased estimate µEUnbiased

and the average return of a hedge funds in the database µHF.6

That is:

0 1 0 11 2Estimated Unbiased Unbiased

E HF E E HFp p p p (1.5)

and we can solve for µEUnbiased

:

0 1 0 1(2 1) 2 2Unbiased Estimated

E E HFp p p p (1.6)

The probabilities pk are not known but can be estimated using a simulation procedure

which is described in the next section.

6 In our adjustment, we use the average monthly return of all hedge funds in the sample. This will include funds

that were alive during a portion of the 1994 – June 2006 period but eventually died and are thus included in the

dead funds portion of the database as of June 2006.

26

1.3 Data Characteristics and Implementation

We begin this section with a description of the data before proceeding to a discussion

of our bootstrap procedure for estimating standard errors. Finally, we describe our adjustment

for the bias induced by potential mismatches regarding the number of delisting funds in a FoF

portfolio.

A. The Data

We use the ALTVEST database which contains 6827 reporting funds during the

January 1994 – June 2006 period. Those funds are classified into dead and live hedge funds

plus dead and live FoFs. We only use funds that report in US dollars and exclude 36 dead

funds that were removed from the live database because of duplicate registration. This leaves

us with 6169 total funds, of which 4873 are hedge funds and 1296 are FoFs. Panel A of

Table 1.1 reports descriptive statistics for those funds. A fund being designated as live or

dead in that table refers to its status as of June 2006. Note that the monthly returns are post-

fee for both hedge funds and FoF in Panel A, just as they are reported in the database.

We eliminate the first 12 returns for each hedge fund in order to mitigate backfill bias.

Our matching procedure requires funds which report returns for at least 36 consecutive

months, and we eliminate all funds which do not satisfy that requirement (after deleting the

first 12 monthly returns for hedge funds). We also exclude FoFs which indicate they are

highly levered, defined as average borrowings exceeding 200% of their equity capital. This

reduces our sample of FoFs by 5.12%. Panel B of Table 1.1 reports descriptive statistics of

the remaining funds. We have 2496 hedge funds, of which 1206 delisted (stopped

reporting) at some time prior to the end of June 2006 and are thus classified as dead funds.

We are not focusing on hedge fund style; however, our data contains a good representation of

several styles with equity long/short (43%), directional (20%), relative value (23%), and

event driven (14%). Among the 759 FoFs, 540 are classified as live funds; however, we

can still use the 219 dead FoFs for windows of time when they were alive. For the FoF

statistics in Panel B, we now report pre-fee returns computed using the algorithm described in

the Appendix. We use the reported fee structure with that algorithm; however, as a point of

information, the typical FoF in our data charges a management fee of 1% and an incentive

fee of 10% per year.

27

Table 1.1. Descriptive Statistics

The table reports descriptive statistics for funds reporting to the ALTVEST database. Panel A is based on all

funds reporting in US dollars during January 1994 - June 2006. Panel B is based on the funds used in our

analysis, after we dropped the first 12 observations for all hedge funds and eliminated any funds that did not

have at least 36 consecutive remaining observations. Return statistics are across funds and based on monthly

returns. Note that all returns in Panel A are post-fee. In Panel B, the FoF returns are grossed up to a pre-fee

basis, while the hedge-fund returns remain post-fee. All values except Number of Funds are averages of the

statistics.

Panel A

Hedge Funds, post-fee Funds of Funds, post-fee

All Live Dead All Live Dead

Number 4873 2130 2743 1296 886 410

Life Time in Years 4.67 5.60 3.94 4.80 5.12 4.10

Mean 1.05 1.13 1.00 0.66 0.68 0.61

Median 0.90 1.01 0.82 0.69 0.74 0.59

STD 4.36 3.58 4.98 2.12 1.75 2.92

Min -9.65 -8.27 -10.72 -4.79 -3.90 -6.72

Max 13.05 11.93 13.92 6.16 5.10 8.45

Skewness 0.09 0.16 0.03 -0.11 -0.15 -0.04

Kurtosis 5.29 5.38 5.22 4.65 4.44 5.12

Sharpe Ratio 0.25 0.32 0.19 0.29 0.33 0.22

Panel B

Hedge Funds, post-fee Funds of Funds, pre-fee

All Live Dead All Live Dead

Number 2496 1290 1206 759 540 219

Life Time in Years 6.40 7.08 5.67 6.79 7.12 5.98

Mean 1.01 1.05 0.97 0.84 0.85 0.80

Median 0.88 0.94 0.81 0.81 0.86 0.71

STD 4.32 3.83 4.85 2.17 1.81 3.06

Min -11.21 -10.06 -12.45 -5.65 -4.70 -8.01

Max 14.65 13.56 15.81 7.56 6.34 10.55

Skewness 0.06 0.12 -0.01 -0.06 -0.13 0.10

Kurtosis 6.18 6.01 6.37 5.64 5.39 6.26

Sharpe Ratio 0.24 0.29 0.19 0.37 0.41 0.26

28

B. Bootstrapped Standard Errors

Theoretical standard errors for our analysis would be problematic due to assumptions

that the true beta is equal to the estimated beta and that the residuals are normally distributed.

These assumptions might well be violated. Moreover, the different FoF matches will

typically have overlapping time series. Because of these issues, we use a bootstrap approach

to estimate standard errors. In particular, we utilize a two-stage procedure that bootstraps

over the matches and also over the returns in each match. For the first stage, we use our

matched portfolios where each match is a sequence of 37 returns for the relevant FoF

complete with the respective matched portfolio of hedge funds. We randomly draw with

replacement the same number of matched portfolios to constitute a bootstrapped set. For the

second stage, we also bootstrap from the monthly return vectors within each match. That is,

we resample by time-slice (keeping the actual returns aligned by month) the 36 months of

FoF and matched hedge fund returns. This, allows re-estimated portfolio weights to differ in

the bootstrap procedure. We obtain parameter estimates for E and via maximum

likelihood. Finally, we use our bias correction to obtain unbiased estimates for µE and .

We repeat this exercise 1,000 times to obtain bootstrapped standard errors which allow for

estimation error in the portfolio weights, non-normal residuals, overlapping time series, and

small sample effects.

C. Adjusting for the Potential Mismatch Bias

Since the probabilities pk are not known, we estimate them using simulation. First, we

construct hypothetical FoFs from existing hedge funds. We randomly draw without

replacement a hedge fund and its vector of consecutive returns from the hedge fund database.

If that hedge fund remains alive, it will have a vector of 37 consecutive returns. If it is a

delisting fund, the vector will have 36 consecutive returns with delisting occurring in month

37. We construct 500 FoFs each consisting of 15 such randomly drawn hedge funds and

flag which funds in a simulated FoF actually delisted. The portfolio weights are uniformly

and randomly selected in the interval 0.02 to 0.07 and normalized to sum to one. We then

move forward six months in time and repeat this exercise, continuing in this manner until we

cover the complete time frame of available data. We next employ our usual matching

procedure. Based on those estimated matches, we compute the frequencies for matches in

which one estimated delisting fund (using our matching procedure) corresponds to 0, 1, 2,

and 3 or more true exits in the simulated FoFs. We repeat the complete simulation 100

29

times, and compute the estimated probabilities pk as averages of the corresponding

frequencies. Table 1.2 below reports the characteristics of the estimated probabilities.

Table 1.2: Estimated Probabilities for Mismatches of Different Types

The table reports the estimated probabilities, via simulation, that the true FoF invests into 0, 1, 2, and 3 or

more delisting hedge funds when the estimated matching portfolio includes exactly one delisting hedge fund.

Number of delisted funds in true FoF (k)

0 1 2 3 or more

Mean Probability (%) 63.48 29.67 5.94 0.91

STD Probability (%) 1.02 1.00 0.45 0.19

The standard deviations of the simulated probabilities are rather small, and we use the mean

probability values for the bias correction.

We investigate the quality of our matching algorithm by constructing hypothetical

FoFs returns from live hedge fund returns. The procedure here is almost identical to that

employed for estimating the probability of a mismatch regarding the number of exiting hedge

funds in a FoF portfolio. The only difference is, that for delisting hedge funds, we introduce a

fictitious delisting return drawn from a Normal distribution with mean -50% or -10% and a

respective standard deviation of 10% or 3%. We again construct 500 FoFs and repeat this

exercise for another eighteen sets of 500 FoFs, each time moving forward by six months and

then drawing hedge fund return vectors. We finally employ our usual estimation procedure to

back out the mean delisting returns.

In implementing this test, we also explore the issue that our database does not contain

all hedge funds. We do this by separating the hedge funds in our database into a “visible” set

and an “invisible” set before generating the hypothetical FoF returns. That is, we split the

database so that only a fraction (100%, 67%, or just 33%) of the total hedge funds will later

be visible to our matching algorithm. For example, suppose we split the total so that 67% of

the hedge funds are in the visible set and another 33% are invisible. We then generate each

hypothetical FoF return by randomly drawing 10 hedge funds from the visible set and 5 funds

from the invisible set. However when we implement the matching algorithm, it is only

allowed to search for matches within the visible set. The estimated mean delisting returns

with this approach are reported in Table 1.3 both with and without the bias correction for

mismatches. The simulations indicate the bias correction is not perfect but has an important

impact, moving the estimated delisting return from -20.30% to -48.13% in the case of a

true -50% delisting return with all hedge funds in the visible set. Similarly in the case of a

30

true mean delisting return of -10%, our bias correction moves the estimated mean from -

4.17% to -10.92%.

Table 1.3: Simulated Performance Results

The table reports the average delisting return and their standard deviations as well as the bootstrapped standard

deviations of the mean delisting return for simulated samples of FoF returns. Each FoF is modeled as a portfolio

of 15 individual hedge funds. For simulated delisting funds, the hypothetical delisting return is drawn from a

normal distribution with given mean (E) and standard deviation (E), expressed in percent per month. The

reported estimates are obtained using our standard procedure with a subset of the hedge funds used to generate

the FoF returns being visible to our matching algorithm. We vary the fraction of visible funds using 100%,

67%, and 33% of the total generating set. We consider two possible delisting return distributions for hedge

funds, characterized by pairs (E, E) of (-50, 10) and (-10, 3). Values are in % per month for the unbiased

results and in parentheses for the biased, estimated results.

Number of Visible Funds

Number of Matches

Mean Delisting Return

Bootstrapped STD of Mean

Delisting Return

STD of Delisting Return

(E, E) = (-50,10)

15 176 -48.13 (-20.30) 4.57 (1.98) 23.70

10 175 -47.20 (-19.87) 4.29 (1.86) 21.70

5 171 -35.74 (-14.93) 3.87 (1.68) 20.10

(E, E) = (-10,3)

15 172 -10.92 (-4.17) 1.60 (0.69) 6.90

10 174 -9.50 (-3.55) 1.38 (0.60) 6.10

5 172 -7.09 (-2.50) 1.71 (0.74) 6.30

In situations where some of the hedge funds held by the simulated FoFs are not in the

visible data, our methodology underestimates the absolute value of the delisting return. This

is due to the algorithm not finding delisting hedge funds that are invisible (hidden) and instead

erroneously including a live fund in the match. This is analogous to the mismatch problem

described above and again biases the estimated mean delisting return toward the average

monthly return for all hedge funds. Since we do not know the extent of delisting funds that

are not in the ALTVEST database but are nonetheless held by our FoFs, we cannot adjust for

that bias. Nevertheless, the results in Table 1.3 indicate that our procedure does recover most

of the simulated mean delisting return (-50% or -10% respectively in the upper and lower

panels) even under the worst case scenario when only 33% of hedge funds in which FoFs

invest are visible. Thus, we are rather confident that our procedure would not miss a large

31

and negative mean delisting return even if the database only contained a modest fraction of

the hedge fund universe.

We recognize the possibility that a FoF alters its portfolio over time rather than

holding it constant for 36 months. Such turnover behavior has implications for our

methodology that are similar to a hedge fund not being included in the database. That is, our

algorithm will tend to include spurious hedge funds in the estimated matches in an attempt to

mimic the true time-varying holdings of the FoF. To examine potential implications of this

problem, we implemented a simulation using a monthly turnover rate for all FoFs of 1.8%

(equivalent to 20% annually, which would correspond to roughly half of each FoF portfolio

over a three-year period). As with invisible funds, this leads to our methodology

underestimating the magnitude of the true simulated delisting return. Nevertheless, we

recovered between 70% and 84% of the correct value. This suggests that our results

reported below may be modest underestimates if FoF turnover is that substantial. If actual

turnover across all FoFs is less than the simulated 20% annual rate, then the effect of this

estimation issue will be lessened. In any case, even if the described problem changed the

magnitude of our estimates by as much as 30%, it would not change the qualitative results.

1.4 Results

In this section, we first describe our main results and then discuss several robustness

tests conducted to validate our results.

A. Main Results

In Table 1.4, we present results based on FoF matches where the adjusted R-squared in

implementing equation (1.1) is at least 50%.7 We also provide the estimated standard

deviation of the delisting returns as well as bootstrapped standard errors for our estimated

mean delisting returns. For the set of all delisting hedge funds, we find an estimated average

monthly delisting return (bias-corrected) of -1.86%. Based on the self-reported reason for

delisting, we find that funds stating they were liquidated had a delisting return of 2.34%.8

Funds that stopped reporting due to being closed for further investment had a delisting return

of 1.99%. Finally, funds that did not clearly state a reason for no longer reporting had a mean

7 Using cut-off values of 25% or 75% does not qualitatively change the results, with only small changes in

the estimated numerical values.

8 This is broadly in line with the findings of Ackermann, McEnally, and Ravenscraft (1999) who report a small,

albeit negative, mean delisting return of -0.7% for terminated funds (which corresponds approximately to our

liquidated funds category).

32

delisting return of -3.27%. Using p-values based on the bootstrapped distribution for delisting

returns indicates that the estimated mean delisting returns for the categories All and No

Reason are significantly different from the average return for all funds of 1.01% (see Panel B

of Table 1.1).9 Both Liquidated and Closed categories have estimated mean delisting returns

that are not significantly different from the 1.01% average return for all funds in the

database.10

This provides rather strong evidence that on average, delisting returns are far from

disaster scenarios with exit returns of -50% or worse. Since the average delisting return is

significantly different from all funds, it would be reasonable to base performance estimates on

a small negative assumed delisting return like -1,86%. Note that simply ignoring the

delisting fund would over-weight the remaining live funds and bias the performance estimate

slightly upward. Nevertheless, that bias is not likely to be serious in most applications.

The maximum likelihood estimate for the standard deviation of all delisting returns,

7.70%, is considerably higher than the average standard deviation of 3.83% for all hedge fund

returns (in Table 1.1, Panel B). This difference is due to the maximum likelihood estimate

also capturing possible portfolio mismatches and estimation errors.

Table 1.4: Mean Delisting Returns

We report the monthly delisting returns (bias-corrected) for FoFs where the adjusted R-squared of the main

regression model is at least 50%. Values are in % per month.

Number of Matches

Mean Delisting Return

Bootstrapped STD of Mean

Delisting Return

Non-parametric p-value for

difference with 1.01

STD of Delisting Return

All 986 -1.86 1.06 0.00 7.70

Liquidated 160 2.34 1.76 0.20 5.20

Closed 36 1.99 4.03 0.29 4.40

No Reason 790 -3.27 1.28 0.00 8.60

B. Robustness Tests

To assess the stability of our results, we implement our procedure using variations on

our basic methodology. Most resulting changes relative to the estimated mean delisting

9 Recall that the categorization of live versus dead in Table 1.1 refers to a fund’s status as of June 2006. Hence

it seems appropriate to make a comparison with the mean return for all funds (1.01%) which refers to monthly

returns when funds were alive. Using the average return on live funds (1.05%) or on dead funds (0.97%) hardly

changes the results, as the average return differences are very minor.

10 We explored whether partitioning the sample based on reported style or fee structure had an economically

important effect on estimated mean delisting returns. However, the reduced sample size in each category led to

inconclusive results.

33

returns in Table 1.4 are within one bootstrapped standard deviation (using the Table 1.4

values) of the original estimate. We interpret such changes as minor and discuss more

substantial changes below.

To begin, we examine accuracy for the matching algorithm and estimated portfolio

weights by comparing the forecast FoF portfolio return in the 37th

month with the actual FoF

return in those matches where we have no delisting funds (consequently, having a full set of

returns for the 37th

month). Our average forecast error is only 0.054%.

We conduct a set of runs which test for potential problems with the residuals of our

main regression model in equation (1.1). First, we use only FoFs where a Jarque-Bera test for

normality of the residuals cannot be rejected. Second, we use only those FoF returns where a

Breusch-Pagan test for no heteroscedasticity cannot be rejected. Third, we use only FoF

returns where a Ljung-Box test for no first order serial correlation cannot be rejected. Fourth,

we use only FoF returns where the average residuals i,t are not significantly different from

zero. In Table 1.5, we report the results for matched portfolios that satisfy the joint restriction

that no rejection at the 10% significance level is allowed for any of the four tests regarding

that particular match. The general picture remains much the same as in our main results from

Table 1.4; however, bootstrapped standard deviations are larger due to reduced sample sizes.

Note that the mean delisting returns for both the Liquidated and the Closed categories

declined by more than one bootstrapped standard deviation. However, these mean estimates

are not significantly different in either table from the average monthly return for all hedge

funds. Moreover, we are following the relatively conservative approach of using the Table

1.4 bootstrapped standard errors which are substantially smaller than those in Table 1.5.

Table 1.5: Mean Delisting Returns for Well-Behaved Residuals

We report the monthly mean delisting returns (bias-corrected) for FoFs where the adjusted R-squared of the

main regression model is at least 50%. We also only use those FoFs where the residuals from regressions on the

model in equation (1.1) do not reject the following four restrictions at the 10% significance level: normally

distributed, homoskedastic, no first-order autocorrelation, and zero average residuals. Values are in % per

month.

Number of

Matches

Mean Delisting Return

Bootstrapped STD of Mean

Delisting Return

Non-parametric p-value for

difference with 1.01

STD of Delisting Return

All 694 -2.98 1.71 0.01 11.10

Liquidated 122 -0.10 2.74 0.44 6.20

Closed 28 -4.58 7.60 0.26 10.70

No Reason 544 -3.56 2.06 0.01 12.50

34

In Table 1.6, we report estimates which allow FoFs that report having no average

leverage to have borrowing or lending positions of up to 10% of their portfolio value.

Several of the estimated mean delisting returns in Panel A of Table 6 are substantially higher

than their counterparts in Table 1.4. The largest move using bootstrapped standard deviations

(from Table 1.4) is the Liquidated category which increased by 2.15 bootstrapped standard

deviations. Note than when we switch to estimates with well-behaved residuals in Panel B,

Table 1.6, the extent of increase for these estimated means is reduced. Table 1.6 illustrates

one of the few robustness checks where we have relatively large changes in estimated mean

delisting returns, on the order of two bootstrapped standard deviations. Nevertheless, the

resulting estimates remain relatively small in the sense of being far from -50% or even -

10%.

Table 1.6: Mean Delisting Returns with Investment in the Riskless Asset

In Panel A, we report the monthly mean delisting returns (bias-corrected) when an investment in the riskless

asset of up to 0.1 in absolute terms is allowed. We only use FoFs where the adjusted R-squared of the main

regression model is at least 50%. Values are in % per month. In Panel B, we only use those FoFs where the

residuals from regressions on the model in equation (1.1) do not reject the following four restrictions at the 10%

significance level: normally distributed, homoskedastic, no first-order autocorrelation, and zero average

residuals.

Number of

Matches

Mean Delisting Return

Bootstrapped STD of Mean

Delisting Return

Non-parametric p-value for

difference with 1.01

STD of Delisting Return

Panel A: All Matches

All 1001 0.20 0.91 0.12 8.10

Liquidated 165 6.12 1.58 0.00 6.10

Closed 35 -1.05 4.25 0.33 10.20

No Reason 801 -1.41 1.09 0.01 8.50

Panel B: Matches with Well-Behaved Residuals

All 726 -0.96 1.29 0.10 9.90

Liquidated 118 4.62 2.07 0.01 6.50

Closed 28 -2.19 6.63 0.40 13.20

No Reason 580 -2.53 1.56 0.04 10.60

35

Table 1.7 provides results obtained when we run our estimation procedure excluding

FOFs that report having non-zero average leverage positions. Again we have several

estimated mean delisting returns in panel A of that table which have increased by somewhat

more than one standard deviation relative to their counterparts in Table 1.4. However, once

again, the situation with well-behaved residuals is much less pronounced. Moreover, the

estimated means remain relatively small. In an additional robustness test, we allowed for a

constant in Equation (1.1) and obtained mean delisting return estimates similar to those in

Table 1.4.

Table 1.7: Mean Delisting Returns without Leverage

In Panel A, we report the monthly mean delisting returns (bias-corrected) for FoFs that report no average

leverage. We only use FoFs where the adjusted R-squared of the main regression model is at least 50%. Values

are in % per month. In Panel B, we only use those FoFs where the residuals from regressions on the model in

equation (1.1) do not reject the following four restrictions at the 10% significance level: normally distributed,

homoskedastic, no first-order autocorrelation, and zero average residuals.

Number of

Matches

Mean Delisting Return

Bootstrapped STD of Mean

Delisting Return

Non-parametric p-value for

difference with 1.01

STD of Delisting Return

Panel A: All Matches

All 900 -0.32 1.22 0.20 9.30

Liquidated 144 5.52 2.45 0.04 6.40

Closed 31 1.03 4.88 0.50 4.90

No Reason 725 -1.65 1.43 0.07 10.10

Panel B: Matches with Well-Behaved Residuals

All 613 -1.93 1.78 0.03 11.70

Liquidated 106 3.32 2.96 0.14 6.80

Closed 21 3.17 6.48 0.50 8.10

No Reason 486 -3.48 2.09 0.01 13.10

We further ran estimates using a rolling window of 24 months, which generated

larger mean delisting returns than in Table 1.4; the largest (Closed category) was 5.73%.

However, estimating 15 portfolio weights using only 24 months of data caused us to have

little confidence in these particular results. There is a potential issue that hedge funds can

revise their reported returns when they later find errors (e.g. due to an audit). We re-ran our

analysis after eliminating the last 6 months of the overall sample and found a mean delisting

return for Closed funds of -4.02%; however, that estimate was based on only 23 matches.

36

When estimating matched portfolios, we allowed the algorithm to stop with fewer than

15 funds as long as any fund would have an estimated weight of less than 0.02. The

resulting estimated mean delisting returns were similar to Table 1.4 except for the Closed

category, which increased by 1.28 bootstrapped standard deviations to 7.16%. Altering the

constraint on the minimum portfolio weight from 0.02 to 0.04 did not change the estimated

means by more than one standard deviation from the means in Table 4. Reducing that

minimum beta constraint to 0.01 had a similar effect, except that the estimated mean

delisting return for the Closed category increased by 1.28 bootstrapped standards deviations

to 6.88%.

To address the concern that small funds might not be realistic targets for FoFs, we

eliminated all funds with assets under management of less than $20 million at the beginning

of relevant 36-month estimation period and obtained similar mean delisting returns to those

in Table 1.4.

1.5 Concluding Comments

Relatively little has been known about returns after hedge funds delist from a database.

Only Ackermann, McEnally, and Ravenscraft (1999) provided an estimate which even

partially addressed this issue. We examine the situation by modeling the econometric

relationship between FoFs and the portfolios of hedge funds into which they invest. This

structure allows us to estimate the average delisting return which turns out to be -1.86% per

month for all delisting hedge funds. That figure is significantly smaller than the average

hedge fund return of 1.01% but much higher than disaster scenarios with large negative

returns such as -50%. When we condition on the self-reported reason for delisting, we find

average delisting returns of 2.34% for liquidated hedge funds, 1.99% for hedge funds that

indicate that they are closed to further investments, and -3.27% for the remaining 76% of

delisting funds that did not provide an informative reason for delisting. Overall, our results

indicate that average delisting returns are economically small. Moreover, this finding is robust

with respect to several tests concerning the methodology and the selection of funds.

37

Appendix 1.1: Pre-Fee Return Calculation

FoFs report their returns net of all fees. In order to reconstruct the pre-fee returns for

FoFs, we use a slightly modified version of the algorithm developed by Brooks, Clare, and

Motson (2007). The incentive fee is normally paid annually, but the reported monthly returns

are adjusted for the accrued incentive fee during the year. In other words, the accrued

incentive fee is deducted when calculating a hedge fund’s reported Net Asset Value (NAV);

but that accrued fee stays invested with the fund until year end. In most cases, the

management fee is paid at the end of each month at 1/12 of the yearly rate. The management

fee calculation uses NAV on the last day of each month before deduction of that month’s

accrued incentive fee. The modification we made relative to Brooks, Clare, and Motson

(2007) involves using the end of month (rather than beginning of month) NAV to calculate

the management fee. That change was based on our review of several hedge-fund

prospectuses that indicated this was the typical procedure.

The figure below illustrates the transition from the pre-fee to post-fee NAV, where

NAV(t) denotes the reported post-fee NAV at the end of period t. NAV(t)* denotes the

associated pre-fee NAV at the end of the period t.

The reported post-fee return captures the change of the reported NAV from NAV(1)

to NAV(2), indicated by the dash-dot line. The pre-fee return changes from the pre-fee

NAV(1)*

less the management fee (that is, equivalent to the reported NAV(1) plus the

incentive fee at time 1) to NAV(2)*. The reconstructed NAV(2)

* is the sum of the reported

NAV(2), the accrued incentive fee at time 2, denoted as IF(2), and the management fee

MF(2). The incentive fee base at each time is the difference between the NAV less the

management fee and the high-water-mark (HWM).

Thus, the total gross return for the period (1 + RGROSSt) can be expressed as follows:

( ) ( ) ( )1

( 1) ( 1)tGROSS

NAV t IF t MF tR

NAV t IF t

(1.7)

( ) ( 1) ( ) ( ) ( 1)

( 1) ( 1)tGROSS

NAV t NAV t MF t IF t IF tR

NAV t IF t

(1.8)

38

Figure 1.1: Pre-Fee vs. Post-fee Net Asset Value

The figure illustrates the transformation of the pre-fee returns to the post-fee returns. The horizontal axis

indicates time periods during which returns are accumulated. At the end of each period, a new net asset value

(NAV) is computed. The NAVs are marked on the vertical axis. NAV(t) stands for the reported post-fee

NAV at the end of period t. NAV(t)* stands for the associated pre-fee NAV at the same time. Solid black

lines indicate the pre-fee NAV change within a given period. The dash-dotted line indicates the change in

reported post-fee NAV within the same period. Reported NAV at the end of a period is obtain by subtracting

from the pre-fee NAV the management fee MF(t) and the incentive fee IF(t). The incentive fee is zero, if the

pre-fee NAV less the management fee is below the high-water mark HWM. Otherwise it is computed as a

share of a difference between the pre-fee NAV less the management fee and the HWM.

If a hedge fund is above HWM at time t based on its post management fee NAV, it

will stay above HWM after paying the percentage incentive fee. Denoting the percentage

incentive fee by IncentiveFee%, we obtain:

max(0, ( ) ) (1 %) max(0, ( ) ) ( )NAV t HWM IncentiveFee NAV t HWM IF t , (1.9)

This leads to the following expression for the accrued incentive fee at time t:

1( ) max(0, ( ) ) 1

1 %IF t NAV t HWM

IncentiveFee

(1.10)

0 1 2

HWM

NAV(1)=NAV(1)*-MF(1)-IF(1)

NAV(1)*-MF(1)

NAV(1)*

NAV(2)=NAV(2)*-MF(2)-IF(2)

NAV(2)*-MF(2)

NAV(2)*

Time

Incentive fee

base

39

Similarly, the reported NAV plus the accrued incentive fee (if any) is a fraction of the

total NAV* equal to the total NAV

* minus the management fee. Thus, if the yearly

management fee expressed in percentage terms is MgmtFee%, we obtain:

%

( ) ( ) ( ) 1 ( ) ( )12

MgmtFeeNAV t MF t IF t NAV t IF t

, (1.11)

The management fee actually paid can be expressed as:

1

( ) ( ) ( ) 1%

112

MF t NAV t IF tMgmtFee

(1.12)

If at year’s end, NAV exceeds HWM, the new HWM for the next year is reset to the level

of the post-fee NAV; and the accrued incentive fee is reset to zero.

Under different assumptions on the exact timing of computing and paying the

management fee, one can obtain a slightly different specification of equation (1.12). For

example, Brooks, Clare, and Motson (2007) seem to assume that the management fee,

although paid at the end of the month, is computed based on the NAV at the beginning of the

month. Thus, they obtain the following expression for the management fee, which introduces

only negligible differences in the resulting pre-fee returns:11

1

( ) ( 1) 1%

112

MF t NAV tMgmtFee

(1.13)

11 Equation (1.13) corresponds to equation (7) in Brooks, Clare, and Motson (2007), where they denote

management fee paid at time t (MF(t) in our version) by MgtFeet.

40

References

Ackermann, C., R. McEnally, and D. Ravenscraft, 1999, The Performance of Hedge Funds:

Risk, Return, and Incentives, Journal of Finance 54 (3), 833-874.

Bai, J., 2003, Inferential Theory for Factor Models of Large Dimensions, Econometrica 71

(1), 135-171.

Bai, J., and S. Ng, 2002, Determining the Number of Factors in Approximate Factor Models,

Econometrica 70 (1), 191-221.

Boivina, J., and S. Ng, 2006, Are More Data Always Better for Factor Analysis?, Journal of

Econometrics 132 (1), 169-194.

Brooks, C., A. Clare, and N. Motson, 2007, The Gross Truth About Hedge Fund Performance

and Risk: The Impact of Incentive Fees, Working paper, University of Reading.

Brown, S. J., W. N. Goetzmann, and R. G. Ibbotson, 1999, Offshore Hedge Funds: Survival

and Performance, 1989-1995, Journal of Business 72 (1), 91-117.

Fung, W., and D. A. Hsieh, 2000, Performance Characteristics of Hedge Funds and

Commodity Funds: Natural Vs. Spurious Biases, Journal of Financial and

Quantitative Analysis 35 (3), 291-307.

Fung, W., D. A. Hsieh, N. Y. Naik, and T. Ramadorai, 2008, Hedge Funds: Performance,

Risk and Capital Formation, Journal of Finance 63 (4), 1777-1803.

Liang, B., 2000, Hedge Funds: The Living and the Dead, Journal of Financial and

Quantitative Analysis 35 (3), 309-326.

Posthuma, N., and P. J. van der Sluis, 2004, A Critical Examination of Historical Hedge Fund

Returns, Chapter 13 in Intelligent Hedge Fund Investing: Successfully Avoiding

Pitfalls through Better Risk Evaluation (Risk Books).

Stock, J. H., and M. W. Watson, 2002, Macroeconomic Forecasting Using Diffusion Indexes,

Journal of Business and Economic Statistics 20 (2), 147-162.

Ter Horst, J. R., and M. Verbeek, 2007, Fund Liquidation, Self-Selection and Look-Ahead

Bias in the Hedge Fund Industry, Review of Finance 11 (4), 605-632.

Van, G. P., and Z. Song, 2005, Hedge Fund Commentary from Van, Working paper, Van

Hedge Fund Advisors International.

41

Chapter 2

Birth and Death of Family Hedge Funds:

the Determinants

42

2.1 Introduction12

The number of hedge funds as well as the assets under their management has been

exponentially growing during the last decade and has accordingly attracted increasing

attention from researchers. Historically, individual hedge funds have been treated as

independent investment vehicles with strategies solely determined by their portfolio

managers. Individual hedge funds, however, are not always independent from each other, but

can be controlled by the same investment company thus taking a form of a family13 of funds.

According to the ALTVEST database used in this study, around 70% of all hedge funds

belong to such families. For these funds, long-term decisions such as fund origination,

liquidation, closure for further investments, fund promotion and fund marketing (through

listing in commercial hedge fund databases) are likely to be to be made strategically by these

over-arching investment companies.

Although strategic behavior of hedge fund families has not been extensively studied in

the literature, there is abundant evidence concerning the strategic behavior of mutual fund

families. See, e.g., Khorana and Servaes (1999) for origination decisions, Zhao (2004) for

decisions to close funds for investments, Nanda, Wang and Zheng (2004) for strategic fund

promotion, and Gaspar, Massa and Matos (2006) for cross-fund subsidization. This paper

concentrates on two major decisions of hedge fund families – fund origination and fund

liquidation – since these primarily effect the opportunity set of investors. Analysis of other

family-related decisions is postponed for future research.

Decisions concerning the founding of new hedge funds have not received much

attention in the existing literature. I am aware of only one paper, Boyson (2008), in which the

performance difference between funds from large and small families is addressed and I which

the author tries to relate the decision to originate a hedge to the increasing market share of the

company. This paper fills this gap by providing some theoretical insights and empirical

evidence on factors driving these decisions.

Hedge fund survival, on the contrary, has been extensively studied in the literature

(see Liang (2000), Gregoriou (2002), Rouah (2005), Chan, Getmansky, Haas and Lo (2005),

and Park (2006)). The authors relate the probability of hedge fund liquidation to its

performance and risk, as well as different organizational factors such as incentive fees and

12 To some extent the results contained in this chapter have circulated under different names: “Hedge Fund

Interlocks and Their Impact on Performance”, “Hedge-Fund-Family Membership and its Impact on

Performance”, “Managerial Beliefs and Family Effect: the Case of Hedge Funds”.

13 The terms “family” and “investment company” will be used interchangeably throughout this paper.

43

lockup periods. Unfortunately, this research seems to disregard the fact that liquidation

decisions may be taken strategically by investment companies operating several funds and,

moreover, that they can be linked to origination decision. The goal of this paper is to inspect

more closely the determinants of birth and death of family held hedge funds while accounting

for possible strategic decisions of investment companies.

The empirical evidence suggests the presence of economies of scale and scope in

hedge fund families similar to mutual fund families14. Larger families and families that have

opened funds in the past are more likely to start new ones. At the same time, hedge fund

families appear to be much more specialized than mutual fund families, and the probability to

start a new fund with a particular style increases in the number of funds with the same style

already launched within the family. Additionally, investment companies tend to liquidate

funds that underperform relative to the company average and are less able to generate fee

income than other family-member funds. The funds having fewer assets under management,

lower fees, and lower value relative to the high-water mark than the family average are more

likely to be liquidated. At the same time, investment companies do not simply liquidate black

sheep in the family; they tend to replace poorly performing funds with new ones.

The fund launching time is chosen by families strategically after a short period of

superior performance of the other member funds. The launching decision itself should thus

not be interpreted as a signal of outstanding family quality that will persist in the future.

Investment companies seem to optimize the launching time in order to encourage money

inflow to the new funds which increases in the past performance of other family member

funds. This past performance effect amplifies the “recognition” effect: in general investors

seem to prefer new funds that are launched within already existing families as opposed to

funds launched by a completely new family.

14

See Khorana and Servaes (1999) for a detailed analysis of mutual fund origination.

44

2.2 Hypotheses Development

2.2.1 Company success, experience, and economies of scale and scope

Investment companies receive profits (fee income) from existing hedge funds. The

total income includes both the management fee income, which is proportional to the assets

under management, and the incentive fee income that depends on the cumulative fund return

and its value relative to the high-water mark. It would be optimal for a hedge fund family to

control large hedge funds delivering high returns.

In maximizing management fee income in the newly originated funds, investment

companies are interested in higher capital inflows to these funds. Intuitively it should be much

easier to attract investors into a new fund if other funds within the family perform well. There

is some evidence for mutual funds that good performance of one fund within a family attracts

higher inflow to other funds within the same family (Nanda, Wang and Zheng (2004)), and

mutual fund families can capitalize on their good reputation by opening new funds (Khorana

and Servaes (1999)). If well performing companies expect high levels of capital inflow into

the new funds, the probability of hedge fund origination should increase with the average

performance of already existing hedge funds within the same company. With respect to this

effect, the following testable hypothesis is considered:

Hypothesis 1. The probability of launching a new hedge fund within a family increases with

increasing average returns in existing family-member funds.

By launching and operating funds, investment companies gain experience and

accumulate procedural information15, including the optimal fund structure and strategy, the

suitable number of analysts, advisors, secretaries, best brokers and banks. They can capitalize

on this information when launching additional funds. In initial stages, moreover, companies

acquire a number of licenses (e.g., Registered Investment Adviser, Commodity Pool

Operator) and physical assets (computer pools, specially developed software); new funds can

at least partially use the assets of existing funds within the family. These kinds of scale and

scope benefits become more pronounced when the number of already launched funds

increases16. Hence, it should be easier for large, experienced companies to launch new funds.

15 Haunschild (1993) investigating the acquisition process finds that this type of information, including which

investment banks should be used, and how the deals should be structured, is very likely to be transmitted through

director interlocks between companies. 16 Similar arguments are used by Khorana and Servaes (1999) for mutual fund origination decisions.

45

Hypothesis 2. The probability of launching a new hedge fund increases with the number of

already existing funds within the family and in their total assets under management.

2.2.2 Hedge fund substitution

Investment companies controlling several funds possess detailed information on

funds’ performance. They can strategically liquidate poorly performing funds and keep only

those with high returns that are able to attract new investors, earn high managerial and

incentive compensation, and to contribute to a good performance record of the family.

According to Massa (2003), mutual fund investors seem to first pick a fund family and then

the individual fund in which to invest. If hedge fund investors have a similar decision making

process, then hedge fund families have additional incentives to improve the average family

quality by liquidating poorly performing funds. Thus, the relative position of a hedge fund

within its family should have a significant influence on the probability of a given hedge

fund’s liquidation.

Hypothesis 3. Relative characteristics of a hedge fund within its family are more valuable

liquidation predictors than their absolute counterparts.

The crucial factors for hedge fund liquidation decision are those that influence

management and incentive fee income of the company. These factors include hedge fund

average return and risk (Liang (2000), Brown, Goetzmann and Park (2001), Park (2006)),

assets under management (Getmansky (2005)), managers’ incentives and their flexibility

(Ackermann, McEnally and Ravenscraft (1999), De Souza and Gokcan (2004), Agarwal,

Daniel and Naik (2009)), and the value relative to the high-water mark (Hodder and

Jackwerth (2007)). Thus, I expect to find that within an investment company hedge funds

having higher than average returns, lower risk, larger assets under management, larger

percentage flows, higher management and incentive fees, longer notice period prior to

redemption, longer lockup periods, and higher value relative to the high-water mark than

other funds within the same investment company are less likely to be liquidated.

Having decided to liquidate a hedge fund, a company commits to redeem the shares of

the investors. Thus, it loses the associated management fee income. Hedge funds, however,

are often liquidated when they are below the high-water mark. Such hedge funds have low

potential to earn incentive fees. Since high-water marks in new funds are reset, investment

46

companies can increase the probability to earn the incentive fees and keep earning

management fees by substituting poorly performing hedge funds with new ones.

Hypothesis 4. The probability of launching a new hedge fund increases given that the

company has recently decided to liquidate another hedge fund.

2.2.3 Signaling vs. timing

If well performing companies are more likely to start new funds, one may be tempted

to interpret a fund’s opening as a signal, indicating outstanding quality of the family that will

persist in the future.17 Performance persistence is indeed not independent from the family

structure. Analyzing mutual fund families, Guedj and Papastaikoudi (2005) document higher

performance persistence of funds belonging to big mutual fund families. They explain this

result by deliberate promotion of well performing funds by their respective families. If the

performance of funds within a family persists, then investing in existing hedge funds from

families that have just launched a new hedge fund should be a beneficial trading strategy for

investors.

This launching signal, however, may turn out to be uninformative with respect to

future family performance. Investment companies may engage in a game of optimal timing.

They will open a new fund to the public after a period of good luck for already existing funds

in order to enjoy spillover effects. A similar strategy in which the spillover effect is combined

with optimal timing is documented by Zhao (2004) for fund closure decisions. The author

shows that mutual fund families close funds for investment after a period of good

performance. The outstanding performance of the closed fund does not persist in the future,

but investors seem to treat the fund closure for further investment as a signal of a good family

quality and increase inflows to other funds within the family. In light of this observation, the

following hypothesis should be tested:

Hypothesis 5. Existing hedge funds within a family outperform prior to the opening of a new

hedge fund, but do not continue to do so afterwards.

17 It is well documented in the literature that traditional investment institutions like mutual funds largely

implement passive investment strategies and their performance does not persist (Droms (2006)). The evidence of

hedge fund performance persistence is rather mixed (see Eling (2007) for a review). For example, persistence at

yearly horizon is documented by Baquero, Ter Horst and Verbeek (2005), and Park and Staum (1998); and no

persistence at yearly horizon is documented by Brown, Goetzmann and Ibbotson (1999), Brown and Goetzmann

(2003), and Chen and Passow (2003).

47

2.2.4 Flow to new funds

Optimizing the timing of a fund opening only makes sense if the spillover effect to

new funds exists and inflows to new funds increase in the past performance of other member

funds. Existing research has proven the significance of spillover effects in mutual fund

families (Khorana and Servaes (1999), Massa (2000), (Ivkovich (2002), Nanda, Wang and

Zheng (2004)). Here I test the existence of a similar effect in hedge fund families:

Hypothesis 6. Capital inflow to newly originated funds within a family increases in the past

performance of other member funds.

If investment companies successfully follow the tactics described above (liquidation of

poorly performing funds in order to improve the average performance record of the family

and timing of fund launching in order to amplify spillover to new funds) they should be able

to attract higher inflows to newly originated funds than companies that start their first fund.

Additionally, they may capitalize on their established reputation, since investors are likely to

associate the expected performance of new funds with the past performance of already

existing funds within the family.

Hypothesis 7. New hedge funds originated within already existing families enjoy higher

inflows than other new funds.

2.3 Modeling Remarks and Variable Choice

2.3.1 Company success, experience, and economies of scale and scope

hypotheses

The origination-related hypotheses are tested in a logistic regression framework. The

dependent variable ,

O

i ty represents a company decision to launch a new fund. It takes a value

of one if company i starts a new fund on date t and zero otherwise.

*

,

,

1, if >0 (company starts a new fund on date ),

0, otherwise.

O

i tO

i t

y i ty

(2.1)

48

*

, ,

, ,

[ , , , ]

_

liqO

i t i t

i t i t

y const CompAvRet NFunds TotalAuM D

Origination controls

(2.2)

*

,

O

i ty is a latent variable that depends on hypotheses-related explanatory factors and a

set of controls (Origination_controls). The error term ηi,t follows logistical distribution.

The hypotheses-related variables include, first, the average return earned on the

existing funds within the family during the last half a year prior to the origination date

(CompAvRet). Positive and significant loading on this factor supports Hypothesis 1.

Hypothesis 2 is related to the number of funds within the company existing on the date of

interest (NFunds) and the natural logarithm of the last half a year average total assets under

management of the existing funds (TotalAuM).

Control variables for origination-related hypotheses

Control variables for the origination related hypotheses include, first, the half-year

average within family cross-fund standard deviation of the returns to proxy for company

diversification. Second, three dummy variables related to fees and restriction periods are

included. The first one takes a value of one if the asset weighted average management fee of

the existing hedge funds of the company is below the industry median, the second one takes a

value of one if the asset weighted average incentive fee of the existing hedge funds is below

the industry median, and the last one takes a value of one if the asset weighted average notice

period prior to the redemption of the existing hedge funds of the company is below the

industry median. These variables should control for company incentives to start new funds in

order to change contractual terms (fees and restriction periods) in a favorable way. The

marginal gains from the change of the contractual terms depend on the currently prevailing

contracts within the company. Those companies that charge on average lower fees and have

shorter restriction periods have the most to gain by launching new funds with higher fees and

longer restriction periods18.

The general market characteristics such as the average return on the S&P 500 index

and the average hedge fund industry return computed during the last half year prior to the

fund’s creation are included in the regression in order to capture the time variation of the

opportunity set of fund families. When the market is booming, more free cash is likely to be

available for further investment. Demand for hedge fund services increases, leading to

18 This reasoning is consistent with Khorana and Servaes (1999), who document that more mutual funds are

opened by families with a greater proportion of funds having lower fees.

49

enlargement of already existing funds, thus making the opening of new hedge funds more

probable. During a recession, there might be a flight to safety. It could lead to lower inflows

of capital to the existing hedge funds, and no need for new hedge funds. Thus, the incentives

of investment companies to start new funds may increase during periods of broad investment

opportunities and decrease during down markets.

2.3.2 Hedge fund substitution related hypotheses

The hedge fund substitution related hypotheses are tested using a logit regression.19

For each company operating several funds, funds having been dropped from the live database

are identified. The dependent variables ,

L

i ty corresponding to these funds take a value of one.

For the other funds that existed on the date of exclusion within that company but were not

removed from the live database, the dependent variable takes a value of zero.

*

,

,

1, if >0 (hedge fund is liquidated on date ),

0, otherwise.

L

i tL

i t

y i ty

(2.3)

*

, ,

,

, ,

_

+ _

_

L

i t i t

i t

i t i t

y const Absolute characteristics

Relative characteristics

Liquidation controls

(2.4)

*

,

L

i ty is a latent variable that depends on a set of explanatory variables. The error term

ηi,t follows logistical distribution.

The set of explanatory variables includes the absolute characteristics of hedge funds

and their performance (Absolute_characteristicsi,t), the values of these characteristics relative

to the company average (Relative_characteristicsi,t), and a set of controls

(Liquidation_controlsi,t). Under the null of strategic fund liquidation by investment companies

(Hypothesis 3), I expect to find significant loadings on the relative factors.

The influence of the liquidation decision on the origination decision (Hypothesis 4) is

tested within regression (2.1)-(2.2). It is captured by a dummy variable Dliq

, which takes a

19 There are three commonly used approaches to survival analysis: the proportional hazard model of Cox (1972)

and its generalization for time-varying covariates (Brown, Goetzmann and Park (2001), Gregoriou (2002),

Rouah (2005) and Park (2006)); a probit model (Liang (2000)); and a logit model (Chan, Getmansky, Haas and

Lo (2005)). Although these methodologies are rather different, Park (2006) notes that they provide similar

results.

50

value of one if during a year prior to or following after hedge fund origination any hedge fund

has been liquidated within the company.

Control variables for liquidation related hypotheses

The commonly used controls for liquidation-related hypotheses include fund

performance, risk, size, and managerial incentives.

In this paper, hedge fund performance is measured as an average return earned by a

hedge fund during the last year prior to its liquidation or the liquidation of another fund within

the same family. Hedge fund risk is proxied by the standard deviation of its return series20.

Hedge fund size is measured by the natural logarithm of the average assets under management

of the fund during the last year. Hedge fund returns and assets under management are

expected to be negatively related to the liquidation probability, whereas return standard

deviation is expected to be positively related to liquidation probability.

Managerial incentives and flexibility are measured by the level of management and

incentive fees, the lengths of the lockup and notice periods prior to redemption, and the fund

value relative to the high-water mark. For each hedge fund a time series of relative values is

constructed, and the values corresponding to the fund liquidation date are included in the

regression. A relative value above one indicates that a hedge fund is above the high-water

mark on the date of interest. The computational details of the high-water mark and the relative

value are provided in Appendix 2.2. I expect to find negative relationships between the

probability of fund liquidation and fees, restriction periods, and the relative fund value.

All of the factors discussed above reflect absolute performance characteristics of the

hedge funds. In order to capture the relative position of a fund within its family, deviations of

hedge fund specific factors from their average values across other funds within the same

company that exist on the date of interest are used.

In addition to the key variables of interest, two control variables are included in the

regression. The first one is the number of funds within a company which is expected to be

negatively related to the liquidation probability.21 The second control variable is the starting

date of a fund, which allows for controlling for the hazard rate variation over time.

20 Hedge fund risk in a survival analysis is often measured by the return standard deviation (e.g., Brown,

Goetzmann and Park (2001) and Rouah (2005)). Park (2006) also uses other risk measures such as semi-

deviation, value-at-risk, expected shortfall, and tail risk. 21 Assume that the company can liquidate only a limited number of hedge funds within each period. If the

number of hedge funds within this company increases, the probability that each particular hedge fund will be

liquidated should decrease.

51

2.3.3 Signaling vs. timing related hypotheses

In order to test whether existing funds in a family outperform an average hedge fund

before the creation of a new fund, but fail to do so afterwards, two sets of equally weighted

portfolios are constructed: “pre-launching” portfolios and “post-launching” portfolios. Each

set consists of two portfolios. The first portfolio in each set, labeled “families-based”,

includes hedge funds that belong to launching families, and the second portfolio, labeled

“random”, consists of randomly chosen funds. In the following, construction of the pre-

launching portfolios is discussed in detail. Post-launching portfolios are constructed

analogously.

Let us denote an investment period by τ. τ will take two values: half a year, for

investigation of short-term portfolio performance, and one year, for investigation of the

longer-term performance. In constructing a families-based portfolio for each family that has

several funds and at least one of them being launched later than the others, funds in existence

τ periods before the new fund launch, are added to the portfolio for these τ periods. If any of

these funds stop reporting within the investment period, I assume that it earns zero returns

until the end of the period. This assumption is consistent with Ackermann, McEnally and

Ravenscraft (1999) and Hodder, Jackwerth and Kolokolova (2008) who document that hedge

fund delisting returns are rather small and that fund value is not completely destroyed upon

ceasing to report. Moreover, since hedge fund share redemption can take up to one year, it

would be unrealistic to assume that an investor can immediately reallocate redeemed shares to

new funds.

In order to assure the same level of diversification in families-based and random

portfolios, both portfolios include equal numbers of funds at each point in time. When adding

hedge funds to the families-based portfolio for the calendar period from t to t+τ, I randomly

pick the same number of funds from the population of all hedge funds existing at time t and

include them for the next τ periods in the random portfolio. As in the families-based portfolio,

if any random fund stops reporting during the investment period, its returns are set to be zero

until the end of the investment period. After the portfolio choice is completed, that is all fund

families are considered, the portfolio returns are computed as a simple average of individual

fund returns.

The post-launching portfolios are constructed analogously with only one difference:

the post-launching families-based portfolio includes hedge funds that existed within a family

before the launching of a new fund, but it will be invested into these funds for τ periods after

52

the start of a new fund. The newly originated funds are not included in the portfolio. The

random portfolio is based on the complete fund population excluding newly originated funds.

In the next step, pure and risk-adjusted performance of the pre- and post-launching

versions of the families-based and random portfolios is compared. I test for the significance of

the mean return difference and of the difference in the Sharpe ratios of the portfolios. For the

Sharpe ratios, the test statistic developed in Jobson and Korkie (1981) with the Memmel

(2003) correction (which controls for different variances of the portfolio returns and their

correlation) is used. In order to account for possible differences in the factor exposures of

these portfolios and nonlinearities in hedge fund investment strategies, I consider a

hypothetical joint portfolio that longs the families-based portfolio and shorts the

corresponding random portfolio. The returns on the resulting long/short portfolio are

regressed on seven factors22, as developed by Fung and Hsieh (2004). The key variable of

interest in this regression is the constant term, which is an estimate of the alpha difference

between the families-based and random portfolios.

If the start of a fund is not an informative signal of outstanding family quality, and

above average performance of member funds prior to new fund origination simply reflects the

timing of the fund start, the families-based portfolio should exhibit higher mean, higher

Sharpe ratio, and a positive and significant alpha during the pre-launching period, but not

during the post-launching one.

2.3.4 Flow related hypotheses

In order to test if flow to new funds is positively related to the past performance of

existing family member funds (Hypothesis 6), I regress the percent flow in the newly

originated funds (NewFundFlowi) on a constant term, average return earned on other family

member funds, a set of family related controls, and a set of general control variables that are

found to be significant predictors of fund flow in the literature. This regression is based only

on funds that are launched within families having at least one fund in operation on the date of

a new fund opening. The error term εi is normally distributed, and can be heteroscedastic.

_i i i i iNewFundFlow Const Family_Return Family Controls Controls (2.5)

22 These factors include the excess return on the S&P 500 index over the risk-free rate as a proxy of the equity

market, the monthly change in the 10-year treasury constant maturity yield as a proxy of the bond market, the

difference in the returns on the Wilshire Small Cap 1750 index and Wilshire Large Cap 750 index, and three

trend-following option-based factors (bond trend-following factor, currency trend-following factor, and

commodity trend-following factor). The trend-following factors were obtained from the web page of David

Hsieh, http://faculty.fuqua.duke.edu/~dah7/HFRFData.htm.

53

In order to test if hedge fund families succeed in generating higher inflows to their

new funds relative to funds launched not within families (Hypothesis 7), a regression similar

to (2.5) is estimated based on flows to all new funds23. In this case family related controls are

substituted by a family dummy (DFamily). It takes a value of one, if a fund of interest is not the

first fund launched within its family, and zero otherwise. The error term is also normally

distributed, and can be heteroscedastic.

,i Family i i iNewFundFlow Const D Controlls (2.6)

For the main run, both regressions are estimated on a quarterly basis. The dependent

variable NewFundFlowi is measured as an average monthly flow into a new fund during the

first quarter after its origination. In order to assess the stability of this effect, the exercise is

repeated based on half-yearly and yearly horizons. In order to diminish the effect of outliers

on the analysis, the highest 1% of new fund flow estimates are trimmed24.

Monthly flow is measured as the ratio of the change in the assets under management

during the month, adjusted for the current month’s return, to the assets under management as

of the end of the previous month:

1

1

(1 )t t tt

t

AuM AuM rFlow

AuM

, (2.7)

where Flowt is the period t flow, AuMt is the assets under management as of the end of period

t, and rt is the post-fee return earned by the fund during period t.

Flow related control variables

If a new fund is expected to perform as well as already existing funds, investors would

prefer families with better a risk/return tradeoff. The higher the share of company assets

invested in the same style as that followed by the newly launched hedge fund, the more

experienced the family is in generating returns by executing this style of investment. This can

result in increasing inflow into the new hedge fund. Old families can have a reputation of

providing stable performance over a long period, and thus the flow to the new funds could

increase in family age. Family heterogeneity can also play role. If a family is very

heterogeneous (there exist funds that perform well and poorly simultaneously) it may indicate

23 Note that here hedge fund performance during the first several months after origination is considered, and we

are likely to encounter backfilled returns and the backfilling bias. These early returns are likely to be higher than

average and fund flow can also consequently be biased upwards. However, I do not investigate the absolute flow

levels, but the difference between flows to family and non-family funds. The backfilling bias cancels out in this

case, and the estimated difference (λ) is a consistent estimate of the true average flow difference. 24 Ding, Getmansky, Liang and Wermers (2008) also excluded 1% of the highest flows from their analysis, in

order to prevent outliers from affecting it.

54

that the next originated fund may also be rather different from the already existing ones.

Investors may be less attracted to these funds, since there is higher uncertainty associated with

their quality. Additionally, investment companies may try to redirect capital from liquidated

funds to new funds. Then, the flow to newly originated fund could increase conditional on the

prior liquidation of another fund within the same family. Following this intuition, I include as

family-related control variables the average return standard deviation of member funds

computed during the same period as the average pre-launching return; cross-fund return

standard deviation, the assets under management of funds within the family that follow the

same style as the newly originated fund, the assets under management of funds following

different styles, company age, and a liquidation dummy. The dummy takes a value of one if

within a year prior to a new fund’s opening any other fund was liquidated within the

company.

In assessing the existence of the spillover effect, one should control for other (family

non-related) factors that potentially influence the fund flow, such as past performance of a

fund, performance of other funds following the same style, fund fees and fund size, as well as

seasonality in the flow pattern.25 The relationship between different hedge fund characteristics

and flow is very complex and differs considerably from that of mutual funds. Detailed

discussion of the general controls used in this paper is provided in Appendix 2.3.

2.4 The Data

The main source of information for the current study is the ALTVEST database26. It

contains monthly returns, assets under management, managerial and incentive fees, notice

periods prior to redemption, lockup periods, and investment company identification for more

than 6800 hedge funds. For the purposes of the paper, only those funds that report their

returns in US dollars between January 1994 and June 2006 are included in the sample. The

database records performance of defunct funds, and the survivorship bias is less pronounced

in the data. There are 36 defunct hedge funds in the ALTVEST database that were removed

from the live database because of duplicate registration. In order to avoid double counting of

the same funds, these funds are deleted from the sample. Since funds of funds can differ

25 See Agarwal, Daniel and Naik (2004), Goetzmann, Ingersoll and Ross (2003), Getmansky (2005), Baquero

and Verbeek (2007), Ding, Getmansky, Liang and Wermers (2008), and Wang and Zheng (2008) for details. 26 The ALTVEST database is provided by Morningstar.

55

substantially from single- and multi-strategy funds27, I exclude funds of funds from the

analysis. While cleaning the data, two hedge funds were found that reported several returns

over 400% per month. These funds are excluded from the sample, since they are likely to

have reported inaccurate performance.

The ALTVEST database contains information on more than 2000 different companies

that operate hedge funds reporting return information in US dollars. On average, each

company controls 2.23 funds. 47% of the companies operate more than one fund, and control

aggregately more than 70% of all hedge funds in the database (Table 2.1). The final sample

includes 4873 individual hedge funds, 3711 of them are controlled by multi-fund companies.

1620 funds are live and 2091 are defunct. The sample statistics of the data are reported in

Table 2.2 and are broadly consistent with common sense intuition. Live funds controlled by

both multi-fund and single-fund companies have higher mean return, lower return standard

deviation, and a higher Sharpe ratio than corresponding dead funds. Hedge funds belonging to

multi-fund families seem to have lower returns and lower return standard deviation than funds

from single-fund families28.

Table 2.1 Investment Companies’ Composition

This table reports the number of companies having different numbers of funds (from 1 to more than 10) as well

as the percentage of such companies. It also reports the total number and the share of hedge funds controlled by

such companies.

Funds per company

Companies Controlled Funds

# % # %

1 1162 53.01 1162 23.85

2 536 24.45 1072 22.00

3 204 9.31 612 12.56

4 95 4.33 380 7.80

5 49 2.24 245 5.03

6 43 1.96 258 5.29

7 25 1.14 175 3.59

8 15 0.68 120 2.46

9 10 0.46 90 1.85

10 or more 53 2.42 759 15.58

More than 1 1030 46.99 3711 76.15

Total 2192 100.00 4873 100.00

27 See Agarwal and Kale (2007) for a performance comparison of multi-strategy funds and funds of hedge funds. 28 Boyson (2008) also documents that hedge funds from larger families tend to have lower mean returns.

56

Since this paper investigates hedge fund birth, it is essential to establish the actual

starting date of hedge funds. Most of databases are subject to the backfilling bias when hedge

funds deliberately report their past returns upon entering to the database. Normally, this is

done only if the past performance is high and can contribute to the good performance track of

hedge funds. However, the ALTVEST database requires hedge funds to report the complete

return history from fund origination, when entering to the database. Comparing the inception

dates of hedge funds and the dates of their first reporting return, I find that indeed a median

hedge fund reports the complete return history; and 90% of hedge funds start reporting their

performance not later than 2 months after inception. Thus, the first date of available return

history is a rather precise indicator of the actual hedge fund date of birth.

Table 2.2. Database Sample Statistics

This table reports the average descriptive statistics of the monthly returns of individual hedge funds reporting to

the ALTVEST database. It is based on individual funds reporting returns in USD between January 1994 and

June 2006. The first two rows report the number of funds and the average life time in years of the funds.

Descriptive statistics of hedge funds belonging to multi-fund families are also reported.

All Funds Multi-Fund Families

All Live Dead All Live Dead

Number 4873 2130 2743 3711 1620 2091

Life time in years 4.670 5.600 3.940 4.905 5.671 4.262

Mean 1.050 1.130 1.000 0.950 1.079 0.841

Median 0.900 1.010 0.820 0.821 0.981 0.686

STD 4.360 3.580 4.980 4.066 3.363 4.656

Min -9.650 -8.270 -10.720 -9.291 -7.853 -10.498

Max 13.050 11.930 13.920 12.461 11.248 13.481

Skewness 0.090 0.160 0.030 0.076 0.142 0.021

Kurtosis 5.290 5.380 5.220 5.409 5.451 5.375

Sharpe Ratio 0.250 0.320 0.190 0.240 0.323 0.170

1st order serial correlation 0.098 0.110 0.090 0.104 0.114 0.096

JB-test (share of funds with p-value below 10%)

0.100 0.111 0.092 0.097 0.107 0.090

2.5 Empirical Results

Table 2.3 reports the estimation results of the logit regression for hedge fund

origination. Consistent with Hypotheses 1 and 2, the probability of a new fund launch

57

increases in the average return of other member funds prior to fund opening, in the number of

funds that have been launched earlier by the family, and in the total assets under management

in the family. The corresponding loadings are highly significant. This result indicates that

family experience and success increase the likelihood of a new fund start in hedge fund

families similar to mutual fund families.

Table 2.3. Determinants of Hedge Fund Birth

This table reports the estimation results of the logit model of hedge fund origination based on all fund families

containing hedge funds launched between June 1994 and June 2006. The dependent variable takes a value of one

if on a given date in a given family a new fund was opened and zero otherwise. Those explanatory variables that

are averages of some characteristics are computed over a six month interval prior to the date of interest. *, **,

and *** indicate significance at the 10, 5, and 1% level respectively.

Variable Coefficient z-statistic

Constant -5.280*** -61.346

# of existing funds in the family 0.140*** 15.590

Average return of existing funds in the family 0.019*** 3.742

Return standard deviation of existing funds in the family 0.051*** 6.073

Logarithm of the total AuM in the existing funds 0.135*** 9.078

Liquidation dummy 0.148** 2.520

Dummy for the average management fee below industry median -0.168*** -3.418

Dummy for the average incentive fee below industry median -0.119* -1.815

Dummy for the average notice period below industry median 0.091* 1.808

Average hedge fund industry return 0.035 0.944

S&P 500 index return 0.037* 1.914

McFadden R-squared 0.043

Estrella R-squared 0.010

Log-Likelihood -8725.8

Surprisingly, if a hedge fund family has on average lower fees than the industry

median, it is less likely to start new funds. This finding contradicts the results obtained for

mutual funds. Mutual fund families with lower fees tend to start new funds in order to reset

fees to the higher level.

As expected, hedge funds are more likely to be launched when the overall market is

performing well. The loading on the S&P 500 index return is positive and significant at the

10% level. The average performance of the hedge fund industry does not seem to have any

impact on the probability of a fund start. This might be due to heterogeneity between hedge

funds following different styles. Average hedge fund industry return may not fully reflect the

58

attractiveness of different hedge fund styles. This question will be further investigated in the

robustness and extensions section.

Table 2.4 reports the estimation results for the logit model of hedge fund liquidation. It

first relates the liquidation probability to the absolute hedge fund characteristics, and second,

adds relative characteristics to the family average. When no family-related factors are

included, the average fund return six months prior to liquidation, the logarithm of its assets

under management, and the percentage flow are negatively related to the liquidation

probability, which is in accordance with the existing literature. After inclusion of the factor

values relative to the company average, the absolute factors lose significance. Only the

loading on the percentage flow remains negative and highly significant. The relative factors

gain significance.

Consistent with Hypothesis 3, hedge funds having higher than company average mean

return and assets under management, higher flows, larger management fees, longer notice

period prior to redemption, and higher value relative to the high-water mark are less likely to

be liquidated. The augmented model also has higher explanatory power. The McFadden R-

squared29 increases from 0.125 to 0.191, and the Estrella R-squared30 increases from 0.136 to

0.210.

The intuition of Hypothesis 4 is also supported by the data. The probability to start a

new fund increases for those families that decide to liquidate any other fund within a year

before or after new fund origination. The corresponding loading of 0.148 is significant at the

5% level (Table 2.3).

Investment companies seem to compare potential to earn profits across all funds under

their control. They tend to liquidate those funds that are poorer than other family members,

and replace them with new funds.

Let us now discuss whether a hedge fund start can be treated as a signal of good

family quality. Table 2.5 reports the descriptive statistics of pre- and post-launching families-

based portfolios and the corresponding random hedge fund portfolios.

29 The McFadden R-squared equals one minus the ratio of the log-likelihood function for the estimated model to

the log-likelihood function for a model with only one intercept. It measures how well the estimated model

performs relative to the only-intercept specification (see Wooldridge (2003), p. 560). 30 The Estrella R-squared is constructed similarly to the McFadden R-squared, but the log-likelihood ratio is

scaled by a factor that depends on the value of the log-likelihood function of the only-intercept model and on the

number of observations. An interpretation of this goodness of fit measure is very similar to that of the R-squared

in a linear regression model (see Estrella (1998)).

59

Table 2.4. Determinants of Hedge Fund Death

This table reports the estimation results of the logit model of hedge fund liquidation. The sample includes those

funds that were removed from the live database within each company and those funds within the company that

were in operation on the date of the removal. The first specification relates the drop probability to the absolute

hedge fund characteristics. Average returns and their standard deviations are computed for half year prior to fund

liquidation. The second specification is augmented by the factors’ values relative to the company average. The

last rows of the table report the McFadden R-squared, the Estrella R-squared, and the value of the log likelihood

function.

1 2

Variable Coefficient z-statistic Coefficient z-statistic

Constant -42.799 -1.341 -84.202** -1.975

Average fund return -0.053** -1.966 -0.006 -0.155

Return standard deviation 0.019 1.411 0.004 0.221

Value relative to the HWM -0.268 -0.761 0.244 0.537

Log AuM -0.197*** -5.686 -0.012 -0.260

Percentage flow -1.945*** -3.328 -1.641*** -2.817

Management fee -0.085 -1.057 -0.043 -0.534

Incentive fee -0.005 -0.542 0.001 0.043

Notice period 0.000 0.012 0.001 0.297

Lockup period 0.009 0.084 -0.033 -0.223

Average leverage -0.003 -0.347 -0.002 -0.177

Fund starting date 0.022 1.368 0.042** 1.972

Number of existing funds -0.240*** -9.307 -0.344*** -11.037

Rela

tive t

o a

n a

ve

rag

e w

ith

in a

co

mp

an

y

Average fund return -0.143** -2.299

Return standard deviation 0.048 1.547

Value relative to the HWM -2.258*** -2.768

Log AuM -0.630*** -7.893

Percentage flow -0.161 -1.431

Management fee -0.263** -2.435

Incentive fee -0.012 -0.565

Notice period -0.014** -2.040

Lockup period 0.143 0.593

Average leverage 0.000 0.022

Fund starting date -0.094*** -2.739

McFadden R-squared 0.125 0.191

Estrella R-squared 0.136 0.210

Log-Likelihood -939.952 -868.878

60

Table 2.5. Pre- and Post-Launching Portfolio Statistics

This table reports sample statistics of the returns of two sets of portfolios: pre-launching and post-launching

portfolios. Each set contains a families-based portfolio (consisting of hedge funds belonging to families

launching new funds), and a random portfolio (consisting of randomly chosen funds during the same period).

The pre-launching families-based portfolios include all funds within fund-families that exist 6/12 months before

additional funds within these families are launched. The post-launching families-based portfolios use funds that

exist in families before the launching of new funds, but these funds are included in the portfolio for 6/12 months

after the new fund is launched.

6 months 12 months

pre-launching post-launching pre-launching post-launching

Families based

(1)

Random

(2)

Families based

(1)

Random

(2)

Families based

(1)

Random

(2)

Families based

(1)

Random

(2)

Mean 1.246 1.087 1.049 1.097 1.160 1.103 0.958 1.035

Median 1.111 1.238 1.058 1.163 1.030 1.260 1.017 1.143

Standard deviation 2.016 2.037 2.185 1.960 1.871 1.908 2.127 1.972

Minimum -4.584 -6.399 -7.222 -6.842 -4.767 -6.834 -7.652 -7.243

Maximum 10.073 7.836 10.160 7.777 8.344 6.992 8.798 7.680

Skewness 0.917 0.051 0.413 -0.140 0.499 -0.201 -0.013 -0.309

Kurtosis 7.055 4.337 6.277 4.739 4.943 4.610 5.762 5.199

Sharpe Ratio 0.460 0.377 0.334 0.397 0.450 0.411 0.300 0.363

p-value mean difference

0.010 0.561 0.227 0.245

p-value SR(1)<SR(2)

0.008 0.966 0.076 0.982

Six months before fund origination, family-member funds seem to outperform their

peers. The families-based portfolio provides an average return of 1.25% per month, which is

significantly higher than that of the random portfolio (1.09%). Moreover, it also delivers a

higher Sharpe ratio, with the difference significantly positive at the 1% level. This effect

becomes less pronounced if one considers a period of one year prior to fund launching. The

average portfolio returns are no longer significantly different, and the Sharpe ratio of the

families-based portfolio is higher than that of the random portfolio only at the 10%

significance level.

After the launch of a hedge fund, families-based portfolios do not outperform the

random portfolios on either horizon. The mean returns of the families-based and random

portfolios are not significantly different from each other. In addition, the random portfolios

seem to have a higher Sharpe ratio, with a difference significant at the 5% level.

A similar pattern is observed if one considers the alpha of a hypothetical portfolio that

longs a families-based portfolio of hedge funds and shorts a random portfolio (Table 2.6). The

61

alpha of this portfolio combination (based on the 6 months investment horizon prior to fund

origination) is approximately 19.9 b.p. per month significant at the 1% level. It decreases by a

factor of two to 9.5 b.p. per month if the portfolio based on the 12 months investment horizon

is considered, and becomes only marginally significant. The alphas of the post-launching

portfolio combinations are not significantly different from zero for both horizons.

Table 2.6. Performance of Hypothetical Long-Short Portfolios

This table reports the estimation results of the regression of portfolios’ returns against the Fung and Hsieh (2004)

seven-factor model. The portfolios are hypothetical. They long funds that belong to families that will launch a

new fund in 6/12 months (pre-launching) or that have launched a new fund 6/12 months earlier (post-launching),

and short the same number of randomly chosen funds. The newly launched funds are not used while constructing

the portfolios. The standard errors are adjusted for heteroscedasticity and serial correlation using the Newey-

West correction with 12 lags. *, **, and *** indicate significance at the 10, 5, and 1% level respectively.

6 months 12 months

pre-launching post-launching pre-launching post-launching

Variable Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat

Alpha 0.199*** 4.442 0.007 0.123 0.095* 1.967 -0.087 -1.408

Return on the S&P 500 index 0.324 1.198 0.282 0.855 0.543** 2.009 -0.268 -0.817

Small Cap - Large Cap -0.214 -1.164 -0.455 -1.285 -0.001 -0.006 0.064 0.268

Change10YTY 0.382 1.085 0.688 1.075 0.057 0.125 0.805 1.443

ChangeSpreadBaa -0.071*** -4.596 -0.023 -0.903 -0.041** -2.169 -0.007 -0.321

PTFS_Bond -0.001 -0.023 0.037 0.688 -0.022 -1.063 0.015 0.311

PTFS_Currency -0.425* -1.805 -0.806 -1.616 0.042 0.230 -0.108 -0.313

PTFS_Commodity -0.729 -1.247 -1.267* -1.703 -0.280 -0.652 -0.695 -1.295

Adjusted R-squared 0.176 0.085 0.126 0.042

Summing up these results, we can conclude that within hedge fund families, member

funds outperform prior to new fund origination. This over performance seems to be a rather

short-lived trend, which is pronounced six months before origination, but in hardly noticeable

on a yearly horizon. Launching time itself is likely to be strategically chosen right after the

positive trend in family performance becomes pronounced enough. The empirical results

indicate that families do not continue to exhibit superior performance either on pure or on

risk-adjusted bases after new fund launching. Thus, launching decision does not indicate

outstanding family quality and should not be interpreted as a positive signal. Nevertheless, by

optimizing the launching time, investment companies may try to “persuade” the market that

they are of good quality and increase flows to new funds.

62

Table 2.7 reports the descriptive statistics of monthly percent flows computed for all

funds (Panel A) and for new funds during the first 6 months after origination (Panel B).

Table 2.7. Sample Statistics of Monthly Percentage Fund Flow

This table reports the sample statistics of the monthly percentage fund flow to all funds, as well as separately to

subgroups of live and dead funds, funds belonging to multi-fund companies and funds belonging to single-fund

companies. Panel A is based on all funds used in the current study, whereas Panel B is based on fund flow

during the first 6 months after fund origination.

All Funds Single-Fund Families Multi-Fund Families

All Live Dead All Live Dead All Live Dead

Panel A: All Funds, All Dates

Mean 0.021 0.028 0.015 0.026 0.027 0.023 0.020 0.028 0.013

Median 0.010 0.013 0.007 0.011 0.009 0.011 0.009 0.014 0.006

STD 0.114 0.114 0.113 0.101 0.093 0.106 0.118 0.120 0.116

Minimum -0.307 -0.320 -0.300 -0.214 -0.201 -0.225 -0.336 -0.350 -0.326

Maximum 0.374 0.409 0.348 0.351 0.377 0.335 0.381 0.417 0.352

Skewness 0.547 0.873 0.283 0.955 1.310 0.729 0.422 0.764 0.130

Kurtosis 11.052 11.991 10.387 10.416 12.353 9.355 11.246 11.900 10.742

Panel B: New Funds, 6 Months after Origination

Mean 0.057 0.069 0.049 0.050 0.054 0.047 0.060 0.072 0.049

Median 0.039 0.047 0.034 0.034 0.037 0.031 0.041 0.049 0.034

STD 0.099 0.103 0.095 0.092 0.093 0.092 0.101 0.106 0.096

Minimum -0.038 -0.028 -0.046 -0.042 -0.036 -0.046 -0.037 -0.026 -0.047

Maximum 0.191 0.210 0.176 0.176 0.181 0.171 0.196 0.217 0.177

Skewness 0.314 0.355 0.278 0.298 0.320 0.278 0.319 0.364 0.279

Kurtosis 2.149 2.146 2.151 2.148 2.160 2.143 2.149 2.142 2.154

On average, percent flow to funds belonging to single-fund families is significantly

higher than that to funds belonging to multi-fund families (2.6% per month vs. 2.0%). This

effect seems to be driven by dead funds. Dead funds have an average flow of 1.3% per month

if they belong to multi-fund families and 2.3% per month if they are the only funds controlled

by an investment company (the difference is highly significant). Mean flows to live funds

from single-fund families and multi-fund families are not significantly different from each

other. At the same time, during the first six months after origination hedge funds belonging to

multi-fund families enjoy higher inflow than that of single-fund families. The difference is

highly significant for live funds and not significant for dead.

63

Table 2.8 reports the estimation results of regression (2.5) which tests the existence of

the spillover effect in hedge fund families.31 Consistent with Hypothesis 6, mean return earned

by other family member funds has a statistically significant and positive effect on the flows to

newly originated funds. It is pronounced at all investigated horizons and is economically

significant. A one percent increase in average family return leads to approximately 1%

increase in average flow to newly originated funds, indicating a positive spillover effect.

Several other family-specific controls are worth mentioning here. First, average

standard deviation of the returns of the member funds (measuring how volatile on average the

returns of each individual family member fund are) and cross-fund return standard deviation

(measuring the degree to which family hedge funds are different from each other) have

negative and in most cases significant impacts on flows to new funds. The more uncertainly

associated with other family members, the more reluctant investors will be to invest into new

funds of this family. Second, investors seem to believe in family experience and

specialization. The higher the assets under management invested within a family into the

same style as that of the new fund (and the lower the assets under management invested into

different styles) are, the higher the inflows to the new fund seem to be. And last but not least,

the decision to liquidate a hedge fund within one year prior to a new fund launch leads to

lower flows to new funds. This effect is highly significant, indicating that families fail to

redirect capital from liquidated funds to new ones under their control and, moreover, investors

treat fund liquidation as a negative signal and decrease flows to new funds in this family.

Altogether, families seem to succeed, however, in generating higher flows to their new

funds. Table 2.9 reports the estimation results of regression (2.6). Supporting the intuition of

Hypothesis 7, hedge funds launched within already existing families have higher flows than

hedge funds originated by a completely new family. This effect is especially pronounced

within the first quarter after origination, in which family membership leads to a 6.1% increase

in average monthly flow. Staying statistically highly significant, its magnitude decreases for

longer horizons. During the first year after origination, family member funds have 2.2%

higher flows than their peers not launched within families. This effect seems to be

economically relevant, given that the average monthly flow to all funds during their life is

2.1% (see Table 2.7, Panel A).

31 In the reported regression only those controls are included that have significant impact on fund flow at least at

one of the investigated horizons. Inclusion of all other controls does not change the main conclusions. The

complete regression with all the controls is available upon request.

64

Table 2.8. Flow to New Hedge Funds within Families

This table reports the estimation results of a regression of average monthly percentage flow to newly originated

funds within already existing families during 3, 6, and 12 months after their launch. The explanatory variables

include a set of controls and family related factors. *, **, and *** indicate significance at the 10, 5, and 1% level

respectively.

3 months 6 months 12 months

Coeff. t-stat Coeff. t-stat Coeff. t-stat

Constant 0.116*** 2.983 0.116*** 4.084 0.068*** 3.149

Mean Family Return 0.007*** 2.856 0.010*** 3.984 0.009*** 3.984

STD Family Return -0.005** -1.983 -0.004** -2.329 -0.001 -0.744

Cross-Fund Return STD in Family -0.007* -1.916 -0.005 -1.616 -0.007*** -2.782

AuM of family funds with the same style 0.053*** 3.309 0.026** 2.359 0.015 1.352

AuM of family funds with different styles -0.015* -1.793 -0.011* -1.936 0.000 0.030

Family Age 0.005 1.425 0.004* 1.724 0.004** 2.207

Liquidation Dummy -0.077*** -3.653 -0.050*** -3.370 -0.032** -2.374

Mean Contemporaneous Return 0.007** 2.206 0.003 1.160 0.001 0.415

STD Contemporaneous Return 0.000 -0.076 0.001 0.307 0.000 0.221

Style Return Contemporaneous -0.023* -1.807 -0.025** -2.442 0.006 0.617

Style Return Past 0.012* 1.702 0.015 1.634 0.001 0.081

Style Return Contemporaneous Squared 0.003* 1.645 0.005** 2.035 -0.001 -0.813

Style Ret Past Squared -0.001 -1.191 -0.003* -1.916 -0.001 -0.390

Ret S&P500 Past -0.005 -1.130 -0.009** -2.112 -0.013*** -3.072

Management Fee -0.005 -1.330 -0.004 -1.329 -0.003* -1.873

Incentive Fee 0.003** 2.107 0.003** 2.371 0.003*** 3.145

Lockup period 0.043*** 2.724 0.019* 1.837 0.011 1.467

Minimum Investment 0.002 0.121 0.027* 1.866 0.000 0.023

Year Beginning -0.012 -0.697 -0.030*** -2.678 -0.024*** -2.860

Adjusted R-squared 0.037 0.039 0.042

65

Table 2.9. Flow to All New Hedge Funds

This table reports the estimation results of a regression of average monthly percentage flow to newly originated

funds 3, 6, and 12 months after their launch. The explanatory variables include a set of controls and a dummy

variable, indicating if the newly originated fund is launched within an already existing family. This dummy is

positive and highly significant for all specifications, indicating higher inflows into new funds within a family. *,

**, and *** indicate significance at the 10, 5, and 1% level respectively.

3 months 6 months 12 months

Coeff. t-stat Coeff. t-stat Coeff. t-stat

Constant 0.084*** 3.266 0.093*** 5.143 0.069*** 4.198

Additional fund in a family 0.061*** 5.581 0.041*** 5.209 0.022*** 3.651

Mean Contemporaneous Return 0.007*** 3.257 0.006*** 3.472 0.006** 2.299

STD Contemporaneous Return -0.001 -0.640 -0.003*** -3.737 -0.001** -2.022

Style Return Contemporaneous -0.015 -1.445 -0.018* -1.909 0.002 0.224

Style Return Past 0.021*** 3.641 0.031*** 4.115 0.012 1.305

Style Return Contemporaneous Squared 0.002* 1.729 0.002 1.598 0.000 -0.329

Style Ret Past Squared -0.001** -2.206 -0.002*** -2.777 -0.001 -0.766

Ret S&P500 Past -0.003 -0.815 -0.006* -1.827 -0.007** -2.133

Ret HF Industry Contemporaneous 0.000 -0.029 0.005 0.514 -0.010 -1.248

Ret HF Industry Past -0.022** -2.487 -0.034*** -3.473 -0.016* -1.947

Management Fee 0.000 0.161 0.000 0.050 -0.001 -0.580

Incentive Fee 0.002** 2.290 0.002*** 2.914 0.002*** 3.423

Lockup Period 0.032*** 3.392 0.016** 2.505 0.009** 1.976

Log AuM -0.134 -0.044 2.6009 1.105 5.777*** 3.016

Year Beginning -0.013 -1.099 -0.023*** -3.082 -0.014** -2.409

Adjusted R-squared 0.024 0.030 0.034

One should note the very low explanatory power of the both regressions (Table 2.8

and Table 2.9). It indicates that even though we can document several significant relations

between flows to newly originated funds and explanatory variables of interest, the complete

variation of the flows cannot be captured. Flows to new funds seem to be driven by different

factors than flows to mature funds, and might be influenced largely by personal managerial

investment and the investment activities of principal shareholders.

66

2.6 Extensions and Robustness

Performance characteristics of hedge funds and factors underlying companies’

decisions to start and to liquidate hedge funds can be rather different for hedge funds

declaring different styles.32 Thus, it is important to check if the main findings of this paper are

also pronounced for funds with different styles. The largest style in the ALTVEST database is

Equity Long/Short that accounts for around 43% of hedge funds. Directional funds excluding

Equity Long/Short represent about 20% of the database. Relative Value and Event Driven

account for 23% and 14% respectively. Details concerning investment style classification in

the ALTVEST database are presented in Appendix 2.1.

Table 10 reports the distribution of companies with respect to styles used by their

underlying funds. Each fund is classified into a particular style if it reports investing more

than 50% of its assets in this style. Funds that do not have any dominating style are classified

as multi-strategy funds. Investment companies represented in the ALTVEST database seem to

be rather specialized. Around 50% of the multi-fund companies specialize in Equity

Long/Short funds. Directional and Relative Value funds each dominate in about 17% of

companies. 13% of companies seem to have an expertise in Event Driven funds, and the rest

specialize in multi-strategy funds. Among those companies that control more than 1 fund, on

average 89.4% of funds belonging to each company follow a common style. The level of

company diversification increases with the number of funds. Among those companies that

control 10 or more funds (53 companies) on average 70.87% of funds in each company follow

one common style. A company operating 10 funds will, thus, have 7 funds with some style in

which the company has the expertise, and the additional 3 funds will follow other styles.

This observation suggests one extension to Hypothesis 3. Company experience may be

style specific, and the probability of a new fund launch with a particular style may increase in

the number of already existing funds with the same style in the company.

32 See Brooks and Kat (2002) for a performance comparison of hedge fund indices representing different styles.

67

Table 2.10. Investment Companies’ Composition by Fund Styles

This table reports the composition of investment companies used in the current study with respect to fund styles.

It reports the number of companies in which the most frequently used fund style is Equity Long/Short,

Directional, Relative Value, Event Driven, or Multi-Strategy. The most frequently used style is defined as a style

which is followed by the majority of funds within the company. The average share of funds with the most

frequent style within a company is also reported.

Funds per company

Companies in which the most frequent style is % of funds with the most

frequent style

ELS Directional Relative Value Event Driven Multi Strategy

# % # % # % # % # %

1 559 48.11 229 19.71 185 15.92 149 12.82 40 3.44 100.00

2 260 48.51 78 14.55 94 17.54 88 16.42 16 2.99 92.02

3 100 49.02 42 20.59 29 14.22 27 13.24 6 2.94 87.68

4 52 54.74 20 21.05 15 15.79 6 6.32 2 2.11 87.41

5 24 48.98 10 20.41 6 12.24 7 14.29 2 4.08 82.24

6 23 53.49 11 25.58 7 16.28 2 4.65 0 0.00 84.65

7 7 28.00 4 16.00 10 40.00 4 16.00 0 0.00 82.57

8 8 53.33 2 13.33 5 33.33 0 0.00 0 0.00 83.09

9 3 30.00 2 20.00 3 30.00 2 20.00 0 0.00 76.03

10 or more 32 60.38 6 11.32 10 18.87 4 7.55 1 1.89 70.87

More than 1 509 49.42 175 16.99 179 17.38 140 13.59 27 2.62 89.44

Total 1068 48.72 404 18.43 364 16.61 289 13.18 67 3.06 94.99

We now estimate the logit model for fund origination for subsamples of funds,

launched with one of the four styles. The total number of funds existing within the company

on the origination date is now split into the number of already existing funds with the same

declared style as the new one and the number of funds declaring any other style. In addition,

the average over the last half year of assets under management invested within the same style

as the one followed by the new fund are used in the regression. Note that style-specific assets

under management are not in logarithms, since companies may have zero investment within

one or more styles. The overall hedge fund market performance is now proxied not by the

average return of all existing hedge funds, but by the average returns on hedge funds

declaring one of the four styles. All averages are computed during the last half year prior to

the fund’s origination. Table 2.11 reports the estimation results of the style-be-style

regressions.

Table 2.11. Determinants of Hedge Fund Birth: Style-Wise Regressions

This table reports the results of the logit models of hedge fund origination. The model is based on all fund families. It is estimated for the launching decisions of hedge funds

following the four main styles separately (Equity Long/Short, Directional, Relative Value, event Driven). The dependent variable takes a value of one if a hedge fund of a given

style is launched within the family on the date of interest. Those explanatory variables that are averages of some characteristics are computed over a six month interval prior to

the date of interest. *, **, and *** indicate significance at the 10, 5, and 1% level respectively.

ELS Directional Relative Value Event Driven

Variable Coefficient z-statistic Coefficient z-statistic Coefficient z-statistic Coefficient z-statistic

Constant -6.482*** -41.760 -6.736*** -30.500 -7.397*** -30.655 -7.662*** -27.451

# of funds in the family following a different style -0.106*** -3.949 -0.001 -0.020 -0.102*** -3.097 -0.089** -1.970

# of funds in the family following the same style as a new fund 0.225*** 16.754 0.556*** 16.102 0.352*** 13.992 0.423*** 12.987

Average return of existing funds in the family 0.026*** 4.852 0.015 1.536 -0.041* -1.933 0.023** 2.038

Average return standard deviation of existing funds in the family 0.053*** 5.246 0.044** 2.407 0.088*** 4.822 0.022 0.938

Logarithm of the total AuM in the existing funds 0.203*** 8.506 0.062* 1.798 0.240*** 6.330 0.220*** 4.948

AuM in the funds of the same style 0.203*** 8.511 0.061* 1.781 0.240*** 6.335 0.219*** 4.943

Liquidation Dummy -0.036 -0.387 0.343*** 2.750 0.451*** 3.621 0.269* 1.728

Dummy for the average management fee below industry median -0.117 -1.566 -0.715*** -6.099 -0.079 -0.706 0.218 1.613

Dummy for the average incentive fee below industry median -0.067 -0.711 -0.067 -0.431 -0.127 -0.803 -0.544*** -2.717

Dummy for the average notice period below industry median 0.104 1.389 0.295** 2.375 0.069 0.612 -0.127 -0.942

Average return of Equity Long/Short funds -0.149*** -2.640 -0.114 -1.353 -0.208** -2.337 -0.253** -2.498

Average return of Directional funds 0.144* 1.741 0.283** 2.296 0.156 1.293 0.241* 1.705

Average return of Relative Value funds 0.246** 2.345 0.142 0.895 0.476*** 3.071 0.482*** 2.644

Average return of Event Driven funds 0.069 0.524 -0.101 -0.522 -0.181 -0.926 -0.103 -0.470

Average return on the S&P 500 index 0.090*** 2.603 0.123** 2.393 0.181*** 3.425 0.138** 2.340

McFadden R-squared 0.066 0.086 0.087 0.086

Estrella R-squared 0.005 0.004 0.004 0.003

Log-Likelihood -4479.046 -2214.154 -2158.549 -1686.830

Company experience indeed seems to be style specific. The number of existing funds

within a family with the same style as the newly originated one exhibits a positive and highly

significant impact on origination probability for all styles. The corresponding loadings vary

from 0.225 for Equity Long/Short funds to 0.556 for Directional funds. The number of funds

following different styles has a negative and significant impact on origination probability for

all styles with the exception of Directional, where the coefficient is not significant.

To investigate whether or not the liquidation probability depends on fund style, I

include additional factors into the corresponding regressions which measure the share of

assets invested into one of three styles (Directional, Relative Value, and Event Driven). The

share of assets invested into the Equity Long/Short style is omitted in order to avoid

multicollinearity of the regressors. None of the style factors turn out to be significant in these

regressions, and the corresponding results are not reported here.

Brown, Goetzmann and Park (2001) show that hedge fund survival depends on the

hedge fund performance relative to other funds within the industry. In order to control for the

relative position of a family fund within the industry while investigating the probability of its

liquidation, the differences between hedge fund specific characteristics and the average values

of these characteristics across all other funds existing on the date of interest are included as

additional control variables. This does not change the results of the analysis. For the sake of

brevity, only the coefficients estimated for the factors relative to the family average are

reported in Panel A of Table 2.12. Hedge fund characteristics relative to the industry average

are not significant in the presence of the factor values relative to the company average.

Investment companies strategically liquidate hedge funds that perform poorer than others.

They seem to compare a fund mainly with its peers within the same company, and not within

the whole industry. Additionally, in order to assess the stability of the results, a model is

estimated in which average returns and their standard deviations are computed based on a

yearly (not half-yearly) horizon prior to hedge fund liquidation. The corresponding loadings

of factors relative to the company average are reported in Panel B of Table 2.12. The obtained

results are rather similar to the main regression. The only difference is that the hedge fund

return standard deviation relative to the company average gains significance in this

regression. Hedge funds having larger return standard deviation within a family are more

likely to be liquidated.

70

Table 2.12. Determinants of Hedge Fund Death (2)

This table reports the estimated loadings of hedge fund characteristics relative to the company average from the

logit model of hedge fund liquidation. The sample includes those funds that were removed from the live database

within each company and those funds within the company that were in operation on the date of the removal. The

drop probability is related to the absolute hedge fund characteristics, their values relative to the company

average, and their values relative to the industry average. Absolute factors (except the percentage flow) and

factors relative to the industry average are not significant and are not reported. In Panel A, average returns and

return standard deviations are computed for half a year prior to hedge fund liquidation. In Panel B, these

characteristics are computed for a year prior to fund liquidation. The last rows of the table report the McFadden

R-squared, the Estrella R-squared, and the log value of the likelihood function.

Panel A Panel B

Variable Coefficient z-statistic Coefficient z-statistic

Constant -105.273* -1.883 -76.857 -1.368

Number of existing funds -0.344*** -10.960 -0.338*** -10.882

Rela

tive t

o a

n a

ve

rag

e w

ith

in a

co

mp

an

y

Average fund return -0.152** -2.378 -0.215*** -2.696

Return standard deviation 0.050 1.595 0.072** 2.158

Value relative to the HWM -2.221*** -2.651 -1.841** -2.183

Log AuM -0.631*** -7.759 -0.642*** -7.929

Percentage flow -0.163 -1.441 0.046 0.749

Management fee -0.260** -2.394 -0.266** -2.457

Incentive fee -0.014 -0.652 -0.014 -0.648

Notice period -0.014** -2.035 -0.015** -2.122

Lockup period 0.151 0.623 0.180 0.740

Average leverage 0.000 0.011 0.000 -0.012

Fund starting date -0.100*** -2.602 -0.101*** -2.634

McFadden R-squared 0.192 0.189

Estrella R-squared 0.209 0.206

Log-Likelihood -867.994 -870.670

The next question is whether higher flows into family-based new hedge funds during

the first year are driven by independent investors’ flows or are completely determined by

initial managerial and company investment. Individual investors that are not the founders of

the hedge funds are not likely to invest in an absolutely new hedge fund. Meanwhile, there

exist funds of hedge funds that primarily focus on emerging hedge funds. Such funds of funds

invest in hedge funds that are at least three months old.33 Thus, hedge fund flows during the

first quarter are likely to reflect purely internal financing. In order to control for this, the flow

regressions (2.5) and (2.6) are re-estimated, excluding the first three months of each hedge

33 This information is obtained from private discussions with funds of funds managers.

71

fund from the analysis. For the sake of brevity, I do not report the complete results and only

discuss the estimates of the coefficients of interest.34

Even after excluding the first three months, the flows to newly originated funds within

families stay positively related to past family returns, again supporting the existence of a

spillover effect. The corresponding coefficient is 0.006, and it is significant at the 5% level for

flows within the following second quarter and at the 1% level for flows during the period

from the 4th

to the 12th

months afterwards.

Comparing the flows to funds launched within the family and outside of families, the

family dummy stays significant after excluding the first quarter flows. Its value is 0.029,

significant at the 1% level for flows from the 4th

to the 6th

months, and 0.010, significant at

the 5% level for flows from the 4th

to the 12th

month. Thus, even though the family dummy

stays statistically significant, the magnitude of the corresponding coefficient decreases by a

factor of two compared with the results of Table 2.9. Hedge funds launched within already

existing families have higher flows than funds not launched within the families. This effect is,

however, not only driven by investor preference for funds from known families, but also by

the internal financing behavior of family hedge funds.

An additional robustness check has been carried out with respect to family-related

factors influencing flows to newly originated funds. If some of the funds within a family are

closed to investment, investors have to allocate their capital among open funds, including a

newly originated one. Thus, the share of funds closed to new investments within a company

can be positively related to flows to new funds. However, this variable turns out to be

insignificant and overall regression results do not change if it is added in eq. (2.5). One of the

reasons for the absence of the effect can be the following: the fund status “closed to new

investment” is reported as of the date of the last database update. Thus, the computed share of

funds closed to new investment is very likely to be different from the actual one for the family

on the date of the new fund launch.

2.7 Concluding Remarks

According to the ALTVEST database, more than 70% of individual hedge funds

belong to fund families that consist of at least two funds. These funds are no longer

independent from each other; strategic decisions determining the future opportunity set of

investors (such as fund creation and fund liquidation decisions) are likely to be interrelated for

34 The complete results are available upon request.

72

these funds. This family related link between individual hedge funds seems to be

underinvestigated in the existing literature.

This paper focuses on the determinants of the birth and death of family hedge funds. It

finds that hedge fund families possess several features similar to those observed in mutual

fund families. Like in mutual fund families, economies of scale and scope are pronounced in

hedge fund families: larger families, experienced in hedge fund launching, are more likely to

start new funds. For hedge funds, however, experience seems to be style specific. Having

started hedge funds with one style, families seem to be reluctant to launch new funds with

other, unfamiliar styles.

In order to improve the average track record of the family and increase profits, hedge

fund families seem to replace poorly performing funds that are not able to generate sufficient

fee income with new ones. Hedge funds having lower than family average assets under

management, lower fees, lower value relative to the high-water mark, and smaller average

return are more likely to be liquidated. Additionally, the exact fund launching time is chosen

by families after a short period of superior performance of other member funds. The

launching decision itself should not be interpreted as I signal of positive and persistent skill of

the managers operating these family member funds. New funds seem to be launched after a

period of good luck for other member funds, which do not continue to outperform after the

fund start. A good performance record is important for fund families since it increases the

spillover to new funds in hedge fund families as in mutual funds families. The money flows to

newly originated funds increase in the past performance of other family member funds.

Hedge fund families fail to redirect capital from liquidated funds to newly originated

ones within the family. They are able, however, to attract higher flows to their new funds

from outside investors (on top of high internal financing) capitalizing on their reputation and

established names.

73

Appendix 2.1: Investment Style Classification According to the ALTVEST

Database

The ALTVEST database divides all funds into three main styles: Directional, Relative

Value, and Event Driven. In addition, it subdivides each style into smaller categories, which

characterize more precisely hedge funds’ investment strategy. In the current work, I consider

Equity Long/Short funds not as a part of the Directional style, but as a separate group, since

these funds represent the largest share of hedge funds reporting to the ALTVEST database.

Below, the fund styles and their sub-categories are reported according to the ALTVEST

classification.

Table 2.13: Hedge Fund Style Classification According to the ALTVEST Database

1. DIRECTIONAL 2. RELATIVE VALUE

Equity Long/Short Capital Structure Arbitrage

Growth Convertible Arbitrage

Value Other

Opportunistic Equities Long/Short Equal Weighted

Short Selling Equities Pairs Trading

PIPES (private investment in public equities) PIPES (private investment in public equities)

Other Fixed Income Arbitrage

Fixed Income High Yield

High Yield Mortgage Backed Securities (agencies)

Mortgage Backed Securities (agencies) Mortgage Backed Securities (commercial)

Mortgage Backed Securities (commercial) Corporate

Corporate Sovereign (non-US)

Sovereign (non-US) Treasuries

Treasuries Other

Other Index or Basis Trade Arbitrage

Global Macro Volatility Arbitrage

Currency Closed End Fund Arbitrage

Futures Other

Mutual Fund Market Timing

Tactical Asset Allocation 3. EVENT DRIVEN

Volatility Trading Merger Arbitrage

Other Corporate Reorganization/Restructure/Spin-Offs

Distressed Securities

Special Situations

Trade Claims

Strategic Block/Activist Trading

Other

74

Appendix 2.2: Relative Fund Value Computation

In order to make the relative value computation as simple as possible, fund inflows are

neglected. New fund shares have their own high-water marks that are different from the initial

one. However, different equalization techniques are used by hedge funds to make sure that all

investors pay incentive fees only on profits earned on their investment. In this paper, the

relative fund value is, thus, computed with respect to the initially issued hedge fund shares.

In the first stage, the cumulative return earned by a hedge fund at each date t is computed.

t

=1= (1 )it iCR r , (2.8)

where riτ denotes the return earned by the fund i during period τ, and itCR is the cumulative

return earned by the fund i from its origination up to the period t.

The high-water mark (HWM) of each hedge fund is initially set to one. It is recomputed every

January and does not change through the following year. If the cumulative return earned by

December (CRiD) is higher than the current high-water mark, the new high-water mark is set

to the level of the cumulative return; otherwise it stays unchanged.

, if =

, if

Current

iD iD iNew

i Current Current

i iD i

CR CR HWMHWM

HWM CR HWM

(2.9)

The relative value of fund i for period t (Valueit) is computed as a ratio of the cumulative

return earned by the fund up to this period over the corresponding high-water mark.

itit

it

CRValue

HWM

(2.10)

75

Appendix 2.3: Control Variables for Fund Flow

This section gives an overview of hedge fund flow related explanatory variables. The

results reported in Table 2.8 and 2.9 include only those control variables that turn out to be

significant in at least one of the considered regressions. To check the robustness of the results,

all other control variables discussed in this section were included in the regressions. The

results do not change, and none of the additional controls are significant. For the sake of

brevity, the results containing all the controls are not reported. The first column of Table 2.14

lists the control variables used in the paper, and the second column of the table gives some

comments and reviews the related literature. All average values and standard deviations are

computed for the corresponding investigation period after hedge fund origination. The

investigation periods are 3, 6, and 12 months.

There are two commonly used controls that are omitted in the current analysis: fund

closure to new investment and investment illiquidity35. The first one is irrelevant for

analyzing flows into new funds, since after origination all funds are open to the public. In

order to measure investment illiquidity one would need a sufficiently long time series to be

able to compute any measure of illiquidity36. Thus, these factors are omitted from the current

analysis.

35 See Ding, Getmansky, Liang, and Wermers (2008). 36 The simplest measure is the first order serial correlation of the returns; more sophisticated illiquidity measures

are discussed in Getmansky, Lo, and Makarov (2004).

76

Table 2.14. Control Variables for Fund Flow

Control Variables for New Fund Flows Comments

Average monthly return Past performance is one of the key variables driving hedge fund flow.

Since newly originated hedge funds do not have any track record, I

use contemporaneous performance instead.

Squared average monthly return The performance is positively but nonlinearly related to current

flows37. Agarwal, Daniel and Naik (2004) find a convex flow-

performance relation; Getmansky (2005) finds a concave flow-

performance relation; Baquero and Verbeek (2007) document a linear

relation. Ding, Getmansky, Liang and Wermers (2008) argue that in

the absence of share restrictions the flow-performance relation is

convex, but it becomes concave in the presence of the restrictions.

Since the past performance of newly originated funds is not available,

the squared contemporaneous performance is used instead.

Standard deviation of the monthly returns Ding, Getmansky, Liang and Wermers (2008) also control in their

regression for the standard deviation of the past returns.

Average past and contemporaneous

returns of all funds, following the same

style as the newly originated fund, and

their squared values

Getmansky (2005) shows that investors follow outperforming styles.

The squared values allow for controlling for nonlinearities.

Average past and contemporaneous

returns of all existing hedge funds and

their squares

Wang and Zheng (2008) document that on the aggregate level fund

flow is positively related to the past and contemporaneous

performance of the hedge fund industry as a whole.

Average contemporaneous and past

returns of the S&P500 index.

These factors proxy for general market conditions

Internet bubble dummy This dummy controls for possible regime shifts in the fund flow

pattern during the Internet bubble (Fung and Hsieh (2004), Fung,

Hsieh, Naik and Ramadorai (2008)).

Seasonal dummies for a year beginning (a

year end), taking a value of one if the fund

origination month lies during the first

(last) quarter of a year.

Hedge fund flows are seasonal. Cumming and Dai (2008) shows that

because of the tax effects, investors are reluctant to invest in hedge

funds during the later months in a year, resulting in higher flows

during earlier months and lower flows during later months.

Managerial and incentive fees; lockup and

notice periods; fund average leverage

Hedge funds with higher managerial incentives seem to enjoy higher

flows (Agarwal, Daniel and Naik (2004), Aragon and Qian (2007)),

whereas hedge funds with higher impediments to capital withdrawal

(lockup and notice periods) seem to have lower flows (Agarwal,

Daniel and Naik (2004)).

Assets under management at fund

origination date

Ding, Getmansky, Liang and Wermers (2008) show that hedge funds

that have larger assets on average experience higher flows.

The share of the AuM invested within

Directional, Relative Value, and Event

Driven styles38

Ding, Getmansky, Liang and Wermers (2008) argue that funds

following different investment styles exhibit different average flow

and flow volatility.

Minimum investment in fund Fund flow can depend on the minimum investment level (Cumming

and Dai (2008)).

37 For mutual funds, the relation between past performance and current flow is positive and convex. See

Chevalier and Ellison (1997), Sirri and Tufano (1998), and Del Guercio and Tkac (2002). 38 I do not use the Equity Long/Short variable in order to avoid multicollinearity of the regressors.

77

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81

Chapter 3

Improved Portfolio Choice Using Second

Order Stochastic Dominance

82

3.1 Introduction

In this paper, we examine the use of second-order stochastic dominance as both a way

to measure performance and also as a technique for constructing portfolios. Large money

managers such as pension funds currently use a variety of methods to estimate portfolio risk

and performance. Typical risk measures include return standard deviation, return semi-

variance, value at risk, and expected shortfall. Pure performance is often proxied by expected

return.39 Risk-adjusted performance measures express a function of both risk and return using

a single number. Widely-used measures include the Sharpe ratio, the Treynor ratio, and

Jensen’s alpha. Even with estimates of such measures in hand, there is the complex issue of

ranking different return distributions. Fundamentally, that ranking should depend on investor

preferences; and various assumptions have been used. Several popular approaches employ

some variation of portfolio optimization within the Markowitz (1952) mean-variance

framework.40 However, the basic mean-variance criterion has several well-known limitations.

It is symmetric, and its theoretical justification requires either a quadratic utility function or

multivariate normality of returns. It thus considers only the first two moments of the return

distribution. Furthermore, the corresponding optimization procedures often result in extreme

portfolio weights when using historical inputs, which implicitly contain estimation errors

relative to the true underlying return distributions.

A particularly interesting application of this problem in ranking return distributions

concerns large pension funds such as California Public Employees’ Retirement Systems

(CALPERS), New York State Common Retirement Fund, and State of Wisconsin Investment

Board (SWIB). Such funds have under management massive amounts of money that is

intended to support the retirement benefits for very large numbers of individuals. Hence,

these are major institutional investors representing the interests of numerous individuals with

presumably differing preferences. Frequently, a pension fund has fixed target portfolio

holdings which are periodically reviewed and approved by its supervisory board. These target

portfolio allocations are typically rather stable over time with occasional minor adjustments.41

39 See Levy (2006), Ch. 1 for a detailed discussion of different risk and performance measures.

40 Cumby and Glen (1990), for example, investigate whether US-only investors could benefit from international

diversification. De Roon, Nijman and Werker (2001) among others question whether including emerging-market

securities can improve performance of portfolios otherwise invested in only developed markets. Glen and Jorion

(1993) analyze whether the investors with a well-diversified international portfolio of stocks and bonds will

benefit by adding currency futures to their portfolio. Bajeux-Besnainou and Roland (1998) investigate dynamic

asset allocation in a mean-variance framework. 41 However, there may be more frequent portfolio rebalancing to keep the portfolio weights reasonably close to

the target as security prices move.

83

Typically, pension funds invest primarily in two asset classes: stocks and bonds.

Some funds also diversify into real estate and other alternative investments. For example,

CALPERS reported a target allocation as of December 31, 2008 that was composed of 19% in

global fixed income, 66% in global equity, 10% in real estate, and 5% in inflation linked

securities.42 In 2007, SWIB had a target of 58% in stocks, 30% in fixed income, 5% in real

estate, and 5% in private equity and debt, with the remaining 2% in a category labeled as a

multi-asset portfolio.43

We propose to rank portfolio return distributions based on second-order stochastic

dominance (SSD) as a comparison criterion. The SSD criterion is compatible with all

increasing and concave utility functions. If a return distribution “A” second order

stochastically dominates another distribution “B”, then all investors with increasing and

concave utility function will prefer A to B. The SSD criterion does not focus on a limited

number of moments but accounts for the complete return distribution, considering both gains

and losses. The developed tests for SSD are nonparametric; and thus, no distributional

assumptions are needed for their implementation. Last but not least, we find that portfolio

optimization based on the SSD criterion results in fairly stabile portfolio weights, which

overcomes a major problem for mean-variance optimization procedures.

SSD is a powerful tool for ranking distributions. It has been used, for example, to

evaluate post merger stock performance (Abhyankar, Ho and Zhao (2005)) and to analyze

aggregated investors’ preferences and beliefs (Post and Levy (2005)). Russell and Seo (1980)

apply this concept to a theoretical portfolio choice problem and discuss the properties of the

SSD criterion compared to the mean-variance approach. They show, that the sets of mean-

variance efficient portfolios and SSD efficient portfolios overlap but do not coincide. The

concept of stochastic dominance was empirically applied to the portfolio choice problem by

Post (2003) and Kuosmanen (2004). These authors test for stochastic dominance of a

specified portfolio (the market portfolio) with respect to all other portfolios that can be

constructed in a given asset span. Going one step further, Scaillet and Topaloglou (2005)

augment their testing procedures to allow for time varying return distributions and test for the

SSD efficiency of the market portfolio. The main limitation of all these works is that they

only analyze in-sample performance. For practical portfolio allocation problems, it is essential

to establish the out-of-sample properties of SSD efficient portfolios.

42 See http://www.calpers.ca.gov/index.jsp?bc=/investments/assets/assetallocation.xml

43 See http://www.swib.state.wi.us/asset_allocations.asp. According to SWIB, the multi-asset portfolio “invests

primarily in equity and debt opportunities in developed and emerging markets, and also includes investments in

real estate, natural resources, private equity, and money market instruments”.

84

Out-of-sample stochastic dominance analysis was conducted by Meyer, Li and Rose

(2005). These authors consider benefits of international portfolio diversification compared

with a New Zealand-only portfolio. They use the concept of third-order stochastic

dominance, arguing that second-order stochastic dominance tests lack power. Their in-

sample portfolio choice, however, is still conducted using the mean-variance approach with a

fixed target return.

Thus, existing empirical work on portfolio allocation using the SSD concept has been

either restricted to in-sample analysis or did not rely on the SSD criterion for estimating the

portfolio choice itself. In this paper, we extend the above work in several ways. We examine

whether a typical pension-fund portfolio is SSD efficient or if that portfolio can be improved.

In doing so, we consider the main asset classes in which major pension funds invest and form

a corresponding benchmark portfolio. We then develop a procedure to determine the optimal

in-sample portfolio. Here, we define optimality as the highest degree of second-order

stochastic dominance for a candidate portfolio over the benchmark portfolio. Second, we test

whether the dominance of this SSD-based optimal portfolio is preserved out-of-sample. We

also compare the performance of our SSD-based portfolio with other competing portfolio

choice approaches such as mean-variance, minimum-variance, and equally weighted schemes.

The analysis is conducted using non-overlapping moving windows in order to investigate time

stability of the results. We also develop a formal statistical test that allows us to document

that our SSD-based portfolio choice technique significantly increases the propensity for

selecting portfolios that also dominate out-of-sample. Thus, we propose an approach to

improve the asset allocation of pension funds and other money managers. Such technology

can help to establish a lower bound on performance that any risk-averse investor would prefer

(at least be indifferent) compared with a typical benchmark portfolio.

3.2 Methodology

We first provide an overview of our methodological approach and then discuss the

steps in more detail. Consider a fixed benchmark-portfolio (BENCH) of s assets that

represents a typical portfolio allocation for a pension fund which is held for a time period

from t0 - Δt to t0. For the same time period, the SSD-based portfolio (SSDBASED) which

dominates BENCH the most is constructed. The level of dominance is measured as a value of

the test statistic of Davidson (2007). We also examine the performance of a group of other

competing portfolios, including the mean-variance portfolio with the highest Sharpe ratio

85

(MEANVAR). A practical problem with MEANVAR is that it tends to have very unstable

and sometimes extreme weights on individual securities.44 As we shall see, this results in

poor out-of-sample performance for MEANVAR. We include two other portfolio strategies

in our comparison group which are less susceptible to this instability issue. Those two

portfolios are the minimum-variance portfolio (MINVAR), estimated over the same time

period, and the equally weighted portfolio (EQUAL).45 The performance of SSDBASED is

compared with the benchmark out-of-sample during the period t0 to t0+Δt to see which

dominates in the SSD sense. This is also done for each of the three competing portfolios

(MEANVAR, MINVAR, and EQUAL). The analysis is repeated using T non-overlapping

moving windows. Finally, we test if our choice mechanism based on in-sample SSD

optimization significantly increases the propensity of dominating portfolios (relative to the

benchmark) with out-of-sample data as compared to the other portfolio choice mechanisms

considered.

To make sure that all our constructed portfolios would be feasible choices for pension

funds which could be precluded from shorting, we impose short sale constraints in the

portfolio selection process. Thus, portfolio weights are restricted to be positive and sum up to

one for each of the considered portfolios.

The following sub-sections address the above steps in more detail.

3.2.1 Constructing portfolios using SSD

This section briefly introduces the concept of second-order stochastic dominance, then

proceeds by summarizing the existing tests for a SSD relationship between two distributions.

Finally, it describes the test procedure of Davidson (2007) and the corresponding test statistic,

which is used as a criterion function for the SSD-based portfolio choice procedure.

Definition of the second order stochastic dominance

Graphically, second-order stochastic dominance (SSD) implies that two cumulative

distribution functions cross but the area under the dominating distribution is always smaller or

equal to that of the dominated distribution for each threshold level z. If those distributions do

not cross, first order stochastic dominance is observed. Figure 3.1 illustrates the SSD relation

between two distributions.

44 This is a well-known problem when inputs to mean-variance optimization procedures are estimated from

realized returns and hence contain estimation error relative to a true underlying distribution (see, e.g., Michaud

(1989) and Jorion (1992)).

45 One could come up with alternative portfolio choice procedures that might outperform MINVAR and

EQUAL, but it is important to avoid data mining and/or building informed priors into the analysis.

86

Figure 3.1. Example of an SSD Relation between Two Distributions

This figure plots two intersecting empirical cumulative distribution functions characterized by the SSD relation.

The area under the dominating distribution is always smaller than that of dominated distribution. On the

horizontal axis, possible values y of the random variables are shown, with the vertical axis indicating values F(y)

of the corresponding cumulative distribution functions.

Formally, distribution A with a cumulative distribution function FA(y) is said to

second-order stochastically dominate another distribution B with a cumulative distribution

function FB(y) if for all possible threshold levels z, the expected losses with respect to this

threshold in distribution A are not larger than that in distribution B with at least one strict

inequality for some level of z.

( ) ( ) ( ) ( ), z

z z

A Bz y dF y z y dF y

(3.1)

Statistical tests for second order stochastic dominance

Testing for stochastic dominance is not trivial; however, statistical tests for SSD have

been developed and their properties demonstrated (see for example, Anderson (1996), Kaur,

Prakasa Rao and Singh (1994), Davidson and Duclos (2000), Barrett and Donald (2003),

Linton, Maasoumi and Whang (2003), Davidson (2007)). The main differences among these

87

tests are the way the null hypothesis is formulated, the type of test statistic employed, the

ability of the test to handle correlated samples, and the approach to computing p-values.

For the purpose of this paper, the most appealing test specification is the one of

Davidson (2007). We rely on this test in establishing the SSD relation between different

portfolio return distributions in our out-of sample tests. We also use the test statistic of

Davidson (2007) to measure the degree of dominance of one portfolio over another in

constructing our SSDBASED portfolio using in-sample data.

The Davidson (2007) test possesses a number of characteristics that make it superior

to other SSD-test specifications. First of all, this test allows for correlated samples. This is an

important limitation for most existing tests of stochastic dominance, which can deal only with

uncorrelated samples. When comparing portfolios that consist of the same assets (but in

different proportions), we have to consider correlated samples. Apart from Davidson (2007),

the only test procedure of which we are aware that can explicitly handle correlated samples is

that of Davidson and Duclos (2000).

The Davidson and Duclos (2000) test specification, however, compares distributions

only at a fixed number of arbitrarily chosen points. This limitation can potentially lead to

inconsistent results (see Davidson and Duclos (2000), p. 1446, as well as Barrett and Donald

(2003), p.72). Consistency is assured only in those tests that use all available sample points,

such as Kaur, Prakasa Rao and Singh (1994) and Davidson (2007).

Additionally, the Davidson (2007) test starts with the null hypothesis of non-

dominance of one distribution over another, whereas the majority of other SSD tests have as

their null hypothesis dominance – see, e.g., Anderson (1996), Davidson and Duclos (2000),

plus Barrett and Donald (2003). Rejecting the null of dominance does not imply dominance

of the second distribution, since it can also happen that the test fails to rank these

distributions. On the other hand, rejecting the null of non-dominance delivers an unambiguous

result of dominance.46

The distribution of the Davidson (2007) test statistic under the null of non-dominance

is asymptotically normal, but the p-values should be bootstrapped to assure better finite

sample properties and higher power of the test. Although the bootstrap procedure is not

standard in this case, it is worked out in detail by Davidson (2007).

Applying SSD tests to time series data, one needs to be concerned about the

performance of the tests if there is time dependence in the data, such as autocorrelation in

46 This formulation of the null hypothesis is also used by Kaur, Prakasa Rao and Singh (1994); however, their

approach can not cope with correlated samples.

88

returns or GARCH effects in volatility. Unfortunately, no test so far explicitly accounts for

such time-series effects. Nolte (2008) shows that the Davidson (2007) test loses power if the

data are strongly serially correlated. As we will document below, serial correlation is not

pronounced in the data used for the current study. Furthermore, he shows that the Davidson

(2007) test performs well in the presence of GARCH effects. Thus, we feel comfortable using

the Davidson (2007) approach.

Test statistic of Davidson (2007) and portfolio choice based on it

As the true return generating process is not known, one cannot directly compute and

compare the integrals from eq. (3.1). Rather, one has to use their sample counterparts.

Following the notation of Davidson (2007), we label the sample counterparts of the integrals

from eq. (3.1) as 2 ( )KD z , where K denotes the two sample distributions (A or B) that are

being compared. We will refer to 2 ( )KD z as a dominance function:

2

,

1

1max( ,0)

KN

K i K

iK

D z yN

, (3.2)

where NK is a number of observations in sample K, yi,K is the i-th observation in this sample,

and z is the threshold of interest.

In order to obtain meaningful test statistics, the set of thresholds {z} includes all

unique observation from both samples {yi,A} and {yi,B} lying in the joint support of those

samples such that there is at least one observation in each sample above max(z) and at least

one below min(z).47

In the next step, for each level of z the standardized difference between the two

dominance functions is computed:

2 2

1/ 22 2 2 2

( ) ( )( )

ˆ ˆ ˆ( ( )) ( ( )) 2 ( ( ), ( ))

B A

A B A B

D z D zt z

Var D z Var D z Cov D z D z

, (3.3)

where ˆ ( )Var and ˆ ( )Cov are the estimated variance and covariance of the dominance

functions respectively. The precise form of these estimates is stated in the appendix A3.1.

47 For more powerful tests one needs to trim the set of thresholds, a discussion which we defer until later.

89

Second-order stochastic dominance of distribution B by distribution A implies that the

quantity in eq. (3.3) is always non-negative, including the smallest t(z) value. Thus, in order

to test the null hypothesis that A does not SSD B, we need to focus only on one number – the

smallest value of t(z). This is exactly the test statistic used by Davidson (2007):

* min ( )z

t t z . (3.4)

The test statistic t* is asymptotically normally distributed. To test for the SSD relation

between two distributions, one computes the corresponding statistic t* and determines the

associated p-values either using bootstrapping or the standard normal distribution, if the

sample size is large. Davidson (2007) describes an appropriate bootstrap procedure for the

distribution of the statistic under H0, which we summarize in appendix A3.2.

The larger the value of t*, the higher the likelihood of rejecting the null; and

thus, the higher is the likelihood of distribution A dominating distribution B. When

constructing in-sample portfolios based on the SSD, we use the test statistic t* as our criterion

function. Under the null hypothesis, the alternative portfolio to be constructed does not

dominate the benchmark portfolio. We search for a set of portfolio weights W that maximizes

the test statistic. Thus, the optimal portfolio we construct has the highest probability to reject

H0 among all possible portfolios constructed in a given asset span.

3.2.2 Competing portfolios

In constructing the competing portfolios, we start with the mean-variance portfolio

optimization (Markowitz (1952)) including the additional short-sale constraints

(MEANVAR). These constraints are imposed to ensure that the portfolio is allowable for a

pension fund with potential restrictions on short selling. Moreover, the short-sale constraints

reduce the sensitivity of the mean-variance optimization to estimation errors, outliers, and

mistakes in the data -- see, for example, Jagannathan and Ma (2003) who use short sale

constraints in combination with a minimum-variance portfolio.

Nevertheless, even with short sales constraints, the mean-variance optimization often

exhibits unstable and extreme portfolio weights. In order to stabilize the estimates, different

approaches have been used by various authors. Some try to augment the optimization

procedure, while others directly combine different portfolio choice approaches. Within the

first group, Barry (1974) and Brown (1979) introduce a correction of the variance-covariance

90

matrix for returns based on a Bayesian diffuse prior. Stein (1955) plus James and Stein

(1961) correct the estimated mean returns by “shrinking” them toward the mean of the global

minimum-variance portfolio (Bayes-Stein shrinkage). Pastor (2000) combines the data driven

optimization with beliefs in an asset pricing model. Within the second group, several

portfolio choice techniques are used simultaneously; and the optimal portfolio is constructed

via combining the portfolio weights delivered by these approaches. Following this path, Kan

and Zhou (2007) use a mixture of mean-variance and minimum-variance portfolios. Most of

these approaches go at least somewhat in the direction of the minimum-variance portfolio.

That portfolio disregards differences in asset mean returns and is based solely on the variance-

covariance structure of returns. Consequently, it exhibits more stability than the maximum

Sharpe ratio (MEANVAR) approach; and we have opted to use the minimum-variance

approach (MINVAR) with the additional short-sale constraints as our second competing

portfolio allocation procedure.

There are other advanced techniques to improve mean-variance portfolio optimization.

MacKinlay and Pastor (2000) develop a missing-factor model, in which they adjusted the

variance-covariance matrix for non-observed factors in an asset pricing framework. Garlappi,

Uppal and Wang (2007) use a multi-prior model. These models, however, do not necessarily

perform well out-of-sample. DeMiguel, Garlappi and Uppal (2009) compare the performance

of 14 different models with the naive equally weighted scheme and find that none of the

advanced models consistently outperform this simplest strategy out-of-sample. They use

three comparison criteria for each strategy: the out-of-sample Sharpe ratio, the certainty-

equivalent return for a mean-variance investor, and turnover measured as trading volume.

The authors argue that the simple equally-weighted portfolio allocation strategy should be a

natural benchmark in portfolio analysis. It is preference free and does not rely on any

estimation. Thus, it does not incorporate estimation errors; and it delivers a reasonable level

of diversification. Following their arguments, we include the equally weighted portfolio

(EQUAL) as a third competing portfolio in our analysis.

3.2.3 Testing for significance of an increase of the number of dominating

portfolios out-of-sample

We conduct the complete analysis for all estimation and forecast windows. That is, T

periods of in-sample fitting for all portfolios of interest and the corresponding out-of-sample

performance comparison based on the SSD criterion. This yields three relevant summary

statistics regarding out-of-sample performance: (1) the number of cases in which a given

91

portfolio choice approach provides portfolios that dominate the benchmark out-of-sample

(N+), (2) the number of cases in which those portfolios belong to the same dominance class as

the benchmark (N0), and (3) the number of cases in which those portfolios are dominated by

the benchmark (N–).

The crucial question now is whether a proposed portfolio choice mechanism

significantly increases the propensity of dominating portfolios out-of-sample. In order to test

this, we focus on the null hypothesis of no relationship between the choice mechanism and

out-of-sample dominance. We define a corresponding test statistic (ΔN) as a difference

between the number of cases in which the chosen portfolio dominates the benchmark out-of-

sample and the number of cases in which the chosen portfolio is dominated by the

benchmark:

ΔN = N+ –

N

– (3.5)

We will reject the null of no relationship if the probability of observing (under the

null) a statistic larger or equal to a given ΔN is sufficiently small. The distribution of the ΔN

under the null is not standard and is generated using a bootstrap procedure. Having no

relationship between a portfolio choice technique and future portfolio performance is

equivalent to randomly picking the portfolio weights. Observed out-of-sample dominance in

this case is driven purely by random noise. In order to generate such a distribution of the ΔN,

we randomly choose the portfolio weights on the interval from 0 to 1 and scale them by their

sum. We undertake this procedure separately for each of the forecast windows. Note that in

rescaling the weights, we impose the same short-sale constraints for the bootstrapped

portfolios as in our original optimization. Using the relevant weights for each forecast

window, hypothetical alternative (random noise) portfolios are constructed. We test for the

SSD relationship between the true benchmark return distribution and the corresponding

random-noise portfolio distribution in each of the forecast windows and compute the first

realization of ΔN – that is, the difference between the number of cases where the random

portfolio dominates the benchmark and the number of cases where the benchmark dominates

the random portfolio. We repeat the procedure 1,000 times, generating a distribution of the

test statistic, which is then used for the dominance test described above. The corresponding

p-value for a given level of the statistic ΔN is computed as the share of observations in the

bootstrapped distribution which are equal or larger than that level of the statistic ΔN.

The proposed bootstrap procedure requires re-sampling of portfolio weights and not of

the individual return observations. Thus, any time or cross-sectional dependence existing in

92

the original return time series will be preserved in the bootstrapped portfolios. The SSD test

of Davidson (2007) will have the same power when testing the SSD relationship between the

bootstrapped portfolios as when the original portfolios are used.

3.3 The Data

The majority of pension funds diversify their investment across stocks and bonds.

Quite a few pension funds also invest a modest proportion of their assets into real estate.

Recently, some pension funds started adding to their portfolios other, less standard, asset

classes. To proxy for the last category, we use commodity investing as an additional

alternative strategy. We approximate the performance of these four asset classes by daily

returns on corresponding indices. The source of the data is Thomson Datastream.

Performance of the stock market is proxied by the total (i.e. cum dividend) return on

the S&P 500 index. The performance of the bond market is modeled through the returns on

Barclays US aggregate bond index, which mimics the Lehman Brothers aggregate bond

index. The real estate investment is proxied by the total return on the Datastream US real

estate index, and commodity market performance is measured by returns on Moody's

commodities index. The time series of daily returns covers 20 years from January 12, 1989 to

December 31, 2008 and includes 4,997 observations. The S&P 500 index as well as the

Lehman Brothers aggregate bond index is investable through exchange traded funds.48 The

Datastream US real estate index and the Moody's commodities index are indicative.49

Descriptive statistics of the data are reported in Table 3.1. Panel A of Table 3.1 reports the

annual returns’ statistics, and Panel B reports the statistics based on daily returns.

48 See, for example, iShares (http://de.ishares.com/fund/overview.do).

49 Currently, there exist similar investable exchange traded funds; however, their shorter history makes them

unsuitable for the current analysis.

93

Table 3.1. Descriptive Statistics of Daily Returns on the Four Asset Classes

This table reports descriptive statistics of the percentage returns on four indices from January 12, 1989 to

December 31, 2008. Panel A is based on the annual returns. Panel B is based on the daily returns. We use the

S&P 500 index cum dividends to proxy for the stock market, Barclays US aggregate bond index for the bond

market, the Datastream US real estate index for the real estate investment, and Moody's commodities index for

investing in commodities.

Mean Median STD Min Max Skewness Kurtosis

Panel A: Annual Returns

Stock 9.73 10.73 20.56 -38.68 37.65 -0.56 2.73

Bond 0.46 0.46 4.71 -9.16 10.15 -0.21 2.89

Real Estate 11.35 18.01 26.41 -46.80 68.97 -0.29 3.34

Commodities 4.86 1.74 14.85 -27.17 32.07 -0.01 2.52

Panel B: Daily Returns

Stock 0.04 0.06 1.11 -9.03 10.80 -0.28 11.74

Bond 0.00 0.00 0.26 -1.75 1.28 -0.23 5.58

Real Estate 0.04 0.03 1.37 -18.64 18.75 0.26 43.87

Commodities 0.02 0.00 0.69 -7.14 8.49 -0.15 18.42

The daily returns on all the indices exhibit excess kurtosis and are thus not normally

distributed. This fact, however, does not matter for the SSD-based portfolio choice which

does not require normality. The stock, real estate, and commodity indices exhibit small

negative first-order autocorrelation, while the bond index exhibits small positive

autocorrelation. This should not introduce any problems in our optimization procedure since

the levels of the serial correlation in daily returns are small (the largest in absolute value is

7.9% for the real estate index). The bootstrap test used to establish significance for an

increased number of out-of-sample dominating portfolios does not require time-independent

data and is thus also unaffected.

The MEANVAR portfolio is the portfolio with the highest Sharpe ratio. For

computing the Sharpe ratios, we use returns on the 90-day Treasury bill as the risk-free rate.

The returns are obtained from the Federal Reserve statistical release H.15.

3.4 Empirical Results

In constructing a benchmark portfolio to represent a typical pension fund, we use

portfolio weights of 65% in stocks, 25% in bonds, and 10% in real estate. The resulting

portfolio has a 0.028% mean daily return and a 0.698% daily standard deviation over the

entire 20-year period.

94

In our tests, we use one-year estimation windows and one-year forecast windows.

With 20 years of data and the first year used for the initial estimation, we obtain 19 non-

overlapping estimates for out-of-sample portfolio performance.50

We first start by investigating whether performance of the benchmark portfolio can be

improved in the SSD sense by varying portfolio weights on the three typical asset classes.

We are not yet considering adding a position in commodities – i.e., the asset span stays

constant. This exercise is rather relevant, since some pension funds may be restricted from

diversifying to other asset classes. In a second step, we repeat the analysis allowing

diversification into the commodities market.

Implementing the SSD tests, we need to choose an interior interval in the joint support

of the benchmark and the alternative portfolios (the levels of z) on which the test statistic t* is

computed. In choosing that interval, there is a tradeoff between power of the test and stability

of the results with respect to rare events. The more that distribution tails are trimmed, the

higher is the test’s ability to rank distributions but the less informative this ranking will be

regarding distribution tails. For the basic set of tests, we use a 10% tail cutoff of both the

largest and smallest returns of the distribution; however, we investigate the results’ sensitivity

to the choice of lower cutoff level in our robustness section.

3.4.1 Fixed asset span

If only in-sample analysis is used, it is possible to find portfolios that second-order

stochastically dominate the benchmark in nearly 95% of periods. This high number is not

surprising, since one is ex-post very likely to find some asset combinations that are better than

a specified benchmark in-sample.

In a related vein, the simulated distribution of ΔN under random portfolio choice is

rather interesting. Its histogram, constructed using 1,000 replications, is plotted in Figure 3.2.

The random portfolio itself performs rather well compared to the static benchmark portfolio,

resulting in many more out-of-sample dominating portfolios than dominated ones. This

phenomenon is consistent with the observation that the randomly chosen portfolio on average

mimics the weights of an equally-weighted portfolio, which we will see performs reasonably

well compared to the benchmark (see the subsequent discussion and results in Table 3.2).

50 There is an implicit assumption here that funds only alter their target portfolio weights annually. This is

probably realistic, where changes likely require approval of a supervisory board. However, these funds may well

rebalance much more frequently in response to security price changes. Since our estimation keeps all weights

fixed during the year, we effectively assume that the pension funds rebalance their portfolios on a daily

frequency back to the fixed weights (or weekly frequency in our extensions section).

95

Figure 3.2. Histogram of the Bootstrapped Distribution for ΔN under Random Portfolio

Choice

This figure plots the bootstrapped distribution of the ΔN –that is, the difference between the number of

dominating (winner) and dominated (loser) portfolios with respect to the benchmark, measured out-of-sample.

Possible values of ΔN are on the x-axis, with frequencies on the y-axis. The total number of periods and, thus, the

maximum possible value of ΔN is 19. The sample is based on 1,000 replications.

Results for the out-of-sample portfolio analysis are summarized in Table 3.2. We use

“Win” to indicate that a given portfolio dominates the benchmark out-of-sample. “Loss”

indicates that a portfolio is dominated by the benchmark, and “Tie” indicates that both

portfolios lie in the same dominance class. The SSD-based portfolio performs very well. It

wins against the benchmark in 84% of the periods. The minimum-variance portfolio wins

over the benchmark in 63% of cases, and the equally weighted portfolio wins over the

benchmark 47% of the time. Note that portfolios constructed using one of these three methods

are not dominated out-of-sample by the benchmark in any of these tests. There are ties (the

alternative portfolio lies in the same dominance class as the benchmark) but no losses.

In contrast, the mean-variance portfolio performs rather poorly. It generates out-of-

sample dominance during only 16% of periods and loses against the benchmark in 26% of

periods. This appears due to the instability and extreme weighting issues of the mean-variance

approach that were discussed earlier. Moreover, such results indicate the mean-variance

approach is a poor choice for any investor with an increasing and concave utility function.

-20 -15 -10 -5 0 5 10 15 200

0.05

0.1

0.15

0.2

Number of Winners - Number of Losers

Fre

qu

en

cy

96

Table 3.2. Out-of-Sample Performance of the Portfolios with the Fixed Asset Span

This table reports the number and percentage of forecast windows, where the considered portfolios dominate the

benchmark (Win), are dominated by the benchmark (Loss), and lie in the same dominance class (Tie). The

alternative portfolios are based on three asset classes: stock, bond, and real estate. The last column reports the p-

values for the difference between the number of the out-of-sample dominating and dominated portfolios.

Out-of-Sample Win Tie Loss p-Values

# % # % # %

SSDBASED 16 84 3 16 0 0 0.000

MEANVAR 3 16 11 58 5 26 1.000

MINVAR 12 63 7 37 0 0 0.011

EQUAL 9 47 10 53 0 0 0.227

The last column of Table 3.2 reports p-values from the bootstrapped distribution of the

difference between the number of the out-of-sample dominating and dominated portfolios

(ΔN). The in-sample SSD-based selection procedure significantly increases the propensity of

dominating portfolios out-of-sample compared to an uninformative choice mechanism with a

zero bootstrapped p-value, followed by a minimum-variance portfolio choice approach with a

p-value of 0.011. Interestingly, the mean-variance portfolio significantly loses against the

random choice mechanism.51 That is, the p-value for random choice outperforming mean-

variance is zero (1 – 1.000).

From the perspective of second-order stochastic dominance, the benchmark portfolio

does not seem to be appropriately structured. Indeed, choosing equal weights always does at

least as well and sometimes better than the benchmark. The above results suggest the in-

sample SSD-based portfolio choice mechanism is superior to the other techniques tested in

delivering out-of-sample dominating portfolios.

Regarding time-stability of portfolio weights, the mean-variance weights are the most

volatile and the minimum-variance portfolio choice weights are the least volatile (if the

constant holdings are disregarded). As an illustration, Figure 3.3 plots the time series of stock

proportions in all the tested portfolios.

51 Another potential specification of the mean-variance efficient portfolio is a portfolio that in-sample has the

same mean as BENCH, but with minimized variance. It this case one obtains an intermediate result, much as

expected: the portfolio performs better than MEANVAR but not quite as well as MINVAR. The corresponding

p-value of this portfolio choice mechanism of not being better than random choice is 0.11.

97

Figure 3.3. Time Series of Portfolio Weights for the Stock Index

This figure plots the time series of stock proportion determined by the three methods: SSD-based portfolio

choice (SSDBASED), mean-variance portfolio choice (MEANVAR), and minimum-variance portfolio choice

(MINVAR). Other assets in the portfolios are bonds and real estate.

Correlation between the stock proportions recommended by the SSD-based and

minimum-variance schemes is very high (85%), whereas the correlation between the optimal

stock proportion of the SSD-based approach and mean-variance is very small and negative

(-0.3%). These observations extend to the correlations for the bond and real-estate

proportions.

Table 3.3 reports the descriptive statistics of the returns delivered by the considered

portfolios. Panel A is based on the annual returns, and Panel B is based on daily returns.

Comparing to BENCH, the SSD-based approach seems to preserve the mean annual return

while shrinking the variance in particular by avoiding large losses. This results in

SSDBASED having positive skewness on a yearly horizon. MINVAR also decreases the

portfolio variance considerably at a cost of dramatic decline in the mean return (2.19% vs.

6.94% for BENCH). It avoids large losses but also limits large gains. EQUAL performs rather

similar to BENCH, only slightly decreasing the return variance, whereas the contribution of

MEANVAR differs from all the other portfolios. MEANVAR has a higher mean return then

BENCH but it is also more volatile, with the largest losses and gains of all portfolios.

1990 1995 2000 20050

0.2

0.4

0.6

0.8

1

Date of Forecast Start

Op

tim

al W

eig

ht

SSDBASED MEANVAR MINVAR

98

Table 3.3 Descriptive Statistics of Yearly Returns

This table reports the descriptive statistics of the returns in percent delivered by different portfolio choice

strategies, including the pension fund benchmark (BENCH), the SSD-based portfolio (SSDBASED), the

maximum Sharpe ratio portfolio (MEANVAR) and the equally weighted portfolio (EQUAL). Panel A is based

on the annual returns. The statistics are computed using 19 yearly returns from 1990 to 2008. Panel B uses daily

returns for the same time period.

Mean Median STD Min Max Skewness Kurtosis

Panel A: Annual Returns

BENCH 6.94 7.03 14.58 -31.37 29.07 -0.70 3.72

SSDBASED 6.43 5.15 9.89 -8.74 28.19 0.80 2.86

MEANVAR 9.04 11.44 15.68 -39.61 31.73 -1.53 5.95

MINVAR 2.19 1.66 5.72 -7.66 15.97 0.39 3.16

EQUAL 6.82 7.69 13.17 -28.69 28.92 -0.89 4.12

Panel B: Daily Returns

BENCH 0.03 0.05 0.74 -6.57 6.94 -0.24 11.89

SSDBASED 0.02 0.03 0.39 -4.24 2.77 -0.31 8.34

MEANVAR 0.03 0.04 0.89 -8.54 10.24 -0.46 18.85

MINVAR 0.01 0.01 0.25 -1.53 1.57 -0.21 5.41

EQUAL 0.03 0.04 0.60 -5.65 7.02 -0.23 23.43

3.4.2 Enlarged asset span

By enlarging the asset span, one can only improve the optimal portfolio allocation.

We expect that by allowing diversification into commodities, the share of dominating

portfolio out-of-sample should increase. The results reported in Table 3.4 are in line with this

intuition. For each alternative portfolio choice technique, the number of dominating portfolios

increases compared to the results reported in Table 3.2. The number of the out-of-sample

dominated portfolios stays at a zero level for the SSD-based, minimum-variance, and equally

weighted portfolios, while decreasing to 4 for the mean-variance portfolio.

The p-values reported in the last column of Table 3.4 indicate that the SSD-based

portfolio significantly increases the propensity for dominating portfolios out-of-sample, with

a zero p-value. Additionally, the minimum-variance contribution becomes highly significant

with a p-value is 0.001. The mean-variance portfolio retains its losing position. Again, it

performs significantly worse than the random portfolio.

99

Table 3.4. Out-of-Sample Performance of Portfolios with an Extended Asset Span

This table reports the number and percentage of forecast windows, where the considered portfolios dominate the

benchmark (Win), are dominated by the benchmark (Loss), and lie in the same dominance class (Tie). The

alternative portfolios are based on four asset classes: stock, bond, real estate, and commodities. The last column

reports p-values for the difference between the number of the out-of-sample dominating and dominated

portfolios.

Out-of-Sample Win Tie Loss p-Values

# % # % # %

SSDBASED 17 89 2 11 0 0 0.000

MEANVAR 6 32 9 47 4 21 1.000

MINVAR 15 79 4 21 0 0 0.001

EQUAL 10 53 9 47 0 0 0.544

Generally, the pattern discussed in sub-section 3.3.1 for the fixed asset span is

preserved for the enlarged asset span. We see here that equal weighting dominates the

benchmark portfolio in about 50% of instances, with the other roughly 50% of the time being

in the same dominance class. The minimum-variance approach also does a reasonable job in

delivering out-of-sample dominating portfolios. The SSD-based approach delivers the best

performance. If the proposed SSD-based choice mechanism is used in-sample, the propensity

of the dominating portfolios out-of-sample significantly increases.

The optimal portfolio weights’ behavior for the enlarged asset span is in line with the

one depicted in Figure 3.3. The descriptive statistics of the resulting portfolios are also

broadly similar to the ones reported in Table 3.3 for the fixed asset span. Both the portfolio

weights and descriptive statistics are omitted here for sake of briefness.

3.5 Robustness

In this section, we assess the stability of our results. First, we investigate the

sensitivity of the result to changing the length of the estimation and forecast windows.

Second, we test if the main patterns in our results are preserved if the benchmark portfolio

composition is changed. Third, we investigate whether the proposed procedure of the optimal

portfolio choice performs well during structural breaks, in which the estimation and forecast

windows may be characterized by different return dynamics. Next, we implement our

procedure using weekly instead of daily returns. Fifth, we repeat the base analysis using

different levels of trimming for the set of thresholds (z) used in the statistical test of Davidson

(2007). All our results survive on robustness tests.

100

3.5.1 Changing lengths of estimation and forecast windows

Instead of using one year estimation and forecast windows, we implement the analysis

based on quarterly and two-year windows. The results only change minimally on the quarterly

horizon. Based on two-year windows, the SSD-based approach is the only one that

significantly increases the number of dominating portfolios out-of-sample. For sake of

briefness, we do not report the numerical values of the estimates.

3.5.2 Alternative benchmark portfolio composition

The current benchmark composition is 25% in bonds, 65% in stock, and 10% in real

estate. We use alternative benchmark portfolios that invest (1) 20% in bonds, 75% in stock,

and 5% in real estate, (2) 35% in bonds, 60% in stock, and 5% in real estate, and (3) 20% in

bonds, 60% in stock, and 20% in real estate. The general ranking of portfolio choice

approaches does not change. SSDBASED always significantly increases the number of

dominating portfolios out-of-sample, followed by MINVAR. MINVAR has slightly worse

statistical support exhibiting larger p-values than SSDBASED, with only one exception: if the

benchmark portfolio is rather aggressive with 75% of stock investment, SSDBASED and

MINVAR have equal p-values of 0.002.

3.5.3 Market turmoil and structural breaks

We are interested in the stability of results concerning performance of the SSD-based

portfolios during market turmoil and related structural breaks. To this end, we investigate if

the SSD-efficient portfolios constructed during calm periods or during periods when the

market is rising preserve their efficiency during subsequent periods with adverse market

dynamics. As in the standard runs, we use three asset classes with a one-year estimation

window, which is now just prior to the event of interest. The one-year forecast window then

starts just prior to the event and always includes the event. We focus on four distinct events

listed below.

1. The Russian default: The official day of the Russian default is the August 17, 1998,

when the Russian government and the Central Bank of Russia announced the

restructuring of ruble-denominated debt and a three month moratorium on the

payment of some bank obligations. Prior to this date, however, investors' fears of

possible default led to the collapse of the Russian stock, bond, and currency markets

as early as August 13, 1998. Thus, we choose the corresponding estimation and

forecast windows in such a way that the complete month August 1998 is included into

101

the latter. The estimation window is from August 1, 1997 to July 31, 1998, and the

forecast window is August 1, 1998 to July 31, 1999.

2. The end of the Internet Bubble: The NASDAQ Composite index heavily loads on

(internet) technology stock. It nearly doubled its value over the years 1999 and early

2000. It first dropped in value on March 13, 2000 after having reached its historical

peak on March 10, 2000. We use a period of the bull market from March 1, 1999 to

February 29, 2000 for the estimation of the portfolio weights, and assess the portfolio

performance during the bear market from March 1, 2000 to February 28, 2001.

3. The terrorist attack of September 11, 2001: The estimation window is from September

1, 2000 to August 31, 2001, and the forecast window is September 1, 2001 to August

31, 2002.

4. The financial crisis 2008: The financial crisis of 2008 hit in September 2008 when

several large US banks and financial firms including Lehman Brothers collapsed,

leading to bankruptcies of other companies and worldwide recession. The first signs of

the coming turmoil appeared, however, much earlier. In July 2007 the spread between

the three-month LIBOR and three-month T-bill interest rate (TED spread) that proxies

for the overall credit riskiness in the economy spiked up; and on August 9, 2007 the

US Federal Reserve and the European Central Bank injected $90bn into financial

markets. As in the current analysis we try to completely exclude information about the

upcoming events from the estimation windows. Thus, we choose the estimation

window from July 1, 2006 to June 30, 2007, and the forecast window from July 1,

2007 to December 2008. Note, that in this case the forecast window is longer than one

year. It includes not only the first signs of the crises but also the turbulent period of

Fall 2008.

Table 3.5 reports the estimation results based on the fixed asset span of three asset classes

(stocks, bonds, and real estate). Results based on the enlarged asset span are similar and are

not reported here. Since we only have one event in each case, we cannot compute our usual

test statistic ΔN of wins minus losses. Instead, the table reports the test statistics t* of

Davidson (2007) and the corresponding p-values for the null hypothesis that an alternative

portfolio does not dominate the benchmark out-of-sample. The hypothesis is rejected if the p-

values are small.

102

Table 3.5. Portfolio Performance around Special Events

This table reports out-of-sample performance tests statistics and the corresponding p-values for four different

portfolio choice mechanisms, including the SSD-based portfolio (SSDBASED), the mean-variance portfolio

(MEANVAR), the minimum-variance portfolio (MINVAR), and the equally weighted portfolio (EQUAL). The

portfolios are based on three asset classes: stocks, bonds, and real estate. The forecast windows are placed after

the special events: (1) Russian default, (2) End of the internet bubble, (3) Terrorist attack of September 11,

2001, and (4) Subprime crisis 2007-2008.

(1) Russian default 1998

(2) End of the internet bubble 2000

(3) Terrorist attack of Sep. 11, 2001

(4) Subprime crisis 2007-2008

t-stat p-value t-stat p-value t-stat p-value t-stat p-value

SSDBASED 3.501 0.000 5.620 0.000 6.203 0.000 5.949 0.000

MEANVAR -8.534 1.000 -10.888 1.000 1.771 0.038 -7.517 1.000

MINVAR 3.463 0.000 5.704 0.000 5.805 0.000 6.064 0.000

EQUAL 2.038 0.021 4.905 0.000 4.394 0.000 -0.150 0.599

In all cases, the SSD-based portfolio as well as the minimum-variance portfolio have

significantly better performance than the benchmark during the out-of-sample period. The

equally-weighted portfolio also out-performs the benchmark except for the subprime crises

2008. During that period, the equally weighted portfolio lies in the same dominance class as

the benchmark. The mean-variance portfolio, as in previous tests, performs poorly around the

special events. In three of four instances MEANVAR is dominated by the benchmark out-of-

sample.

3.5.4 Weekly returns

In this sub-section, we check whether our results are an artifact of using daily returns

or whether they can also be documented with weekly returns. Using weekly returns implies

that the portfolios are rebalanced to the target levels each week, whereas within a week

pension funds follow a buy-and-hold strategy. It also decreases the number of observations

considerably. Thus, we cannot rely on the asymptotic properties of the Davidson (2007) test

in determining winning and losing distributions and have to use the bootstrapped p-values.

Table 3.6 reports out-of-sample performance of the alternative portfolios relative to the

benchmark based on weekly returns.

103

Table 3.6. Out-of-Sample Performance of the Portfolios Based on Weekly Returns

This table reports the number and percentage of forecast windows, where the considered portfolios dominate the

benchmark (Win), are dominated by the benchmark (Loss), and lie in the same dominance class (Tie). The

alternative portfolios are based on weekly returns on three asset classes: stock, bond, and real estate. The last

column reports p-values for the difference between the number of the out-of-sample dominating and dominated

portfolios.

Out-of-Sample Win Tie Loss p-Values

# % # % # %

SSDBASED 7 37 12 63 0 0 0.003

MEANVAR 0 0 15 79 4 21 0.996

MINVAR 6 32 13 68 0 0 0.026

EQUAL 3 16 16 84 0 0 0.215

With weekly returns, we sharply decrease the number of observations; and the power

of the test decreases. Consequently, it becomes more difficult to rank the portfolio return

distributions according to their dominance relation. For example, the SSD-based portfolio

dominates the benchmark in 37% of forecast windows based on weekly returns, compared to

84% of forecast windows with daily returns. Nevertheless the results of Table 3.6 are

consistent with the results for daily returns. The SSD-based portfolio choice mechanism

significantly increases the propensity of dominating portfolios out-of-sample with the

corresponding p-value of 0.003, followed by the minimum-variance approach with a p-value

of 0.026.

3.5.5 Different levels of trimming

As described previously, the Davidson (2007) test statistic is computed using sets of z-

values that lie in the joint support of the two distributions being compared. So far, we

trimmed the 10% largest and 10% smallest observations from the joint support to assure

higher test power. To check whether tail behavior adversely influences our previous results,

we now perform the analysis using smaller levels of tail trimming, namely, 5% and 1%. We

use the fixed asset span and daily returns for the stock, bond, and real estate indices. Table 3.7

summarizes the new estimation results.

As expected, increasing the z-interval towards the tails makes it more difficult to rank

the distributions based on the dominance criteria. For example, the percentage of forecast

windows where the dominance of the SSD-based portfolio is documented deceases from 84%

with 10% tail trimming (Table 3.2), to 63% for 5% trimming, and 32% for 1% trimming.

104

Table 3.7. Out-of-Sample Performance with Different Levels of z-Interval Trimming

This table reports the number and percentage of forecast windows, where the considered portfolios dominate the

benchmark (Win), are dominated by the benchmark (Loss), and lie in the same dominance class (Tie). The

alternative portfolios are based on daily returns on three asset classes: stock, bond, and real estate. The last

column reports p-values for the difference between the number of the out-of-sample dominating and dominated

portfolios. Panel A reports the results for 5% trimming of the z-interval. Panel B reports the results for 1%

trimming of the z-interval. The z-interval is an interval lying in the joint support of the distributions to be

compared, on which the Davidson (2007) test statistic is computed.

Out-of-Sample Win Tie Loss p-Values

# % # % # %

Panel A: 5% trimming

SSDBASED 12 63 7 37 0 0 0.000

MEANVAR 3 16 12 63 4 21 1.000

MINVAR 10 53 9 47 0 0 0.000

EQUAL 6 32 13 68 0 0 0.227

Panel B: 1% trimming

SSDBASED 6 32 13 68 0 0 0.003

MEANVAR 1 5 17 89 1 5 0.996

MINVAR 5 26 14 74 0 0 0.061

EQUAL 4 21 15 79 0 0 0.240

Nevertheless, even with 1% trimming, the SSD-based portfolios as well as the

minimum-variance and equally weighted portfolios are never dominated by the benchmark.

Moreover, the SSD-based portfolio choice approach still significantly increases the propensity

of dominating the benchmark out-of-sample, even with 1% trimming. In this case, the p-

value is 0.003. The estimates in Table 3.7 support our previous qualitative results. The SSD-

based portfolio choice technique stays superior when compared to all other considered

approaches, with the minimum-variance approach being second best even when the z-interval

includes nearly the complete tails. Moreover, the mean-variance approach continues to

perform poorly.

3.6 Concluding Comments

Most criteria for portfolio selection (e.g., the mean-variance approach), require an

assumption on investor preferences or on the form of the return distribution. We propose

using second-order stochastic dominance to rank portfolios, since this criterion is rather

general and it can be applied to all increasing and concave utility functions. Indeed, all risk-

averse investors will prefer a second-order dominating distribution to a dominated one.

105

With in-sample analysis, it is typically possible to exploit knowledge of the data to

find portfolio weights such that the resulting portfolio dominates a specified benchmark. A

more interesting empirical question is whether one could find a way to determine portfolio

weights with in-sample data such that the resulting portfolio dominates the benchmark out-of-

sample.

Investigating that question, we propose an SSD-based portfolio choice approach. The

portfolio weights are chosen such that the SSD test statistic of Davidson (2007) is maximized

in sample. We then test the performance of that approach out-of-sample. Using 20 years of

daily returns on four asset classes (stocks, bonds, real estate, and commodities), we show that

this approach significantly increases the number of out-of-sample dominating portfolios

relative to a benchmark that is intended to proxy for a typical pension fund portfolio.

Moreover, this SSD-based approach is also superior to other portfolio choice techniques, such

as the mean-variance (with maximum Sharpe ratio) and equally-weighted portfolios. The

minimum variance portfolio choice approach delivers comparable results, although it still

performs slightly worse than the SSD-based approach out-of-sample and it considerably

lowers the mean return on the portfolio.

Using the SSD-based approach, we do not find a single case in our tests where the

SSD-based portfolio is dominated by the benchmark out-of-sample. There are cases where

the SSD-based approach and the benchmark lie in the same dominance class, meaning that

there are some investors that would prefer one to another and other investors with the reverse

choice. This represents the worst case performance for the SSD-based portfolio in our tests.

In contrast, the mean-variance portfolio generally performs poorly out-of-sample and

is often dominated by the benchmark. We also report results for minimum-variance and

equally weighted portfolios. In our tests, these portfolio choice alternatives are inferior to the

SSD-based portfolio choice technique in term of the propensity of out-of-sample dominance;

however, they do improve upon the benchmark in the number of cases.

One of the possible extensions of this analysis would be using the third order

stochastic dominance (TSD) criterion to possibly discriminate between portfolio return

distributions that lie in the same dominance class according to the SSD criterion.

106

Appendix 3.1: Variance and Covariance of the Dominance Functions in the

Davidson (2007) Test

The values of the Davidson (2007) test statistic are computed for each of the chosen

levels of a threshold z as shown in eq. (3.3). Implementing this equation requires estimation

of the variances and covariance of the corresponding dominance functions. The estimates can

be obtained using the original dada sample as follows:

2 2 2 2

,

1

1 1ˆ ( ( )) max( ,0) ( ) , ,

N

K i K K

i

Var D z z y D z K A BN N

, (3.6)

2 2 2 2

, ,

1

1 1ˆ ( ( ), ( )) max( ,0) max( ,0) ( ) ( )

N

A A i A i B A B

i

Cov D z D z z y z y D z D zN N

, (3.7)

where samples A and B are required to have the same number of observations N, and yi,K is

the i-th observation in sample K.

107

Appendix 3.2: Bootstrap Procedure of Davidson (2007)

In this appendix we briefly summarize the main steps of the bootstrap procedure

developed in Davidson (2007). The summary is based on section 7 of Davidson (2007). The

null hypothesis of the underlying test is that distribution A does not dominate distribution B.

The distributions A and B are correlated and the corresponding samples have equal number of

observations N. The observations from A and B are, thus, paired in couples (yi,A, yi,B).

1. The z-interval from the interior of the joint support of the distributions A and B is

chosen, such that there is at least one point in each sample above the maximum z

and below the minimum z.

2. The dominance functions 2 ( )AD z and

2 ( )BD z are computed for all values of z as in

eq. (3.2). If for some z 2 2( ) ( )A BD z D z , the algorithm stops and the non-dominance

of A cannot be rejected.

3. The minimum test statistic t* is computed as in eq. (3.4) based on t(z) from eq.

(3.3). The corresponding level on z, on which the minimum is attained, is z*.

4. A set of probabilities pi of drawing each pair of observations (yi,A, yi,B) under the

null of non-dominance of A is determined. The probabilities are the solution of the

following Lagrange-multiplier problem:

, ,log 1 ( * ) ( * )i i i i i B i A

i i i

n p p p z y z y

, (3.8)

where ni is a number of pairs equal to (yi,A, yi,B) in the original samples A and B,

ni=1 for all i if all pairs are unique, λ is a Lagrange multiplier corresponding to a

constraint that the probabilities sum up to unity, µ is a Lagrange multiplier

corresponding to a constraint that the dominance functions of A and B computed at

z* are equal, and , ,( * ) max( * ,0)i K i Kz y z y , K = A, B.

5. The weighted dominance functions 2 ( )KD z , K=A,B for all levels of z are

constructed.

2

,

1

( ) ( )N

K i i K

i

D z p z y

(3.9)

108

If 2 2( ) ( )A BD z D z for all z except of z*, step 6 is omitted.

6. The value z* is replaced by *z , at which the difference 2 2( ) ( )B AD z D z is minimized.

The steps 4 through 6 are repeated until the condition at step 5 is satisfied.

7. The M bootstrapped samples of A and B are constructed, by randomly drawing

with replacement the paired observation (yi,A, yi,B) with unequal probabilities pi.

8. For each of M bootstrapped samples, the corresponding minimum test statistic *

jt

is computed (j =1,..,M) as in eq. (3.4).

9. The bootstrapped p-value is a proportion of the *

jt , which are larger than the initial

value t*. The null hypothesis of non-dominance is rejected if the bootstrapped p-

value is sufficiently small.

109

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112

Chapter 4

A Note on the Dynamics of Hedge-Fund-

Alpha Determinants

113

4.1 Introduction

As the hedge fund industry is expanding, it is attracting more and more attention from

investors and academics. The increasing quantity of research papers and reported empirical

findings, although providing additional insights into the different aspects of hedge fund

performance, does not yet seem to have converged to a well established and overall accepted

set of results. The majority of studies that have analyzed the determinants of hedge fund

performance have come to contradictory conclusions, even with respect to the direction of

influence of the considered factors.

The current literature typically models hedge fund return time series using a set of

common macro factors. For example, Favre and Ranaldo (2005) use the higher-moment

adjusted CAPM, where the authors introduce as additional factors squared and cubic

deviation of the return on the S&P 500 index from its average. The seven-factor model of

Fung and Hsieh (2004) uses the S&P 500 as a proxy for the equity market, adds bonds, size,

and credit spread factors, as well as three option-based trend-following factors based on

bonds, currency, and commodities. Agarwal and Naik (2000) propose an eight-factor model

based on eight tradable indices, including emerging markets and gold. Alas, these approaches

ignore the panel (cross-sectional) dimension of the data which contains micro-level

information pertaining to individual funds. Such information includes variables that can help

to explain the cross-section of hedge fund performance, such as the style of the fund (Brown

and Goetzmann (2003)) or the level of its fees (Brown, Goetzmann and Liang (2004)).

The impact of the micro-factors has been investigated in cross-sectional settings by

several authors. However, since the dynamic (time-varying) nature of the considered

relationships was largely ignored, these studies came to contradictory conclusions. For

instance, Liang (1999) finds a positive relationship between hedge fund performance and size,

as well as between performance and fees. Agarwal, Daniel and Naik (2004) document a

negative relationship between fund performance and size, and Kouwenberg and Ziemba

(2007) report negative relationship between performance and fees. The results of the major

studies on the relationship between hedge fund performance and different micro-factors are

summarized in Table 4.1.

114

Table 4.1. Hedge Fund Performance and its Determinants: Evidence from the

Literature

This table lists the central questions related to hedge fund performance and groups the research according to their

findings. In brackets the reference databases and the analyzed time period are specified.

Positive relationship Negative Relationship No Relationship

Rel

ati

on

ship

bet

wee

n P

erfo

rma

nce

an

d: F

un

d s

ize

Amenc, Curtis and Martellini

(2003) [CISDM, 1996-2002]

De Souza and Gokcan (2003)

[TASS]

Getmansky (2005), [TASS, 1994-

April 2003]

Liang (1999) [HFR, 1994-June

1997]

Brorsen and Harri (2004) [LaPorte

Asset Allocation, up to 1998]

Gregoriou and Rouah (2003)

[ZCM and LaPorte, 1994-1999]

Goetzmann, Ingersoll and Ross

(2003) [US. Offshore Funds

Directory, 1990-1996]

Koh, Koh and Teo (2003)

[AsiaHedge, EurekaHedge, 1999-

March 2003]

Agarwal, Daniel and Naik (2004),

[HFR, TASS, MAR, 1994-2000]

Naik, Ramadorai and Strömqvist

(2007) [HFR, TASS, CISDM,

1994 – 2002]

Fung, Hsieh, Naik and Ramadorai

(2008) [HFR, TASS, CISDM,

1994-2002]

Fee

s

Ackermann, McEnally and

Ravenscraft (1999) [TASS,1988-

1995]

Kazemi, Schneeweis and Martin

(2002) [TASS, HFR, 1994 -2000]

Koh, Koh and Teo (2003)

[AsiaHedge, EurekaHedge, 1999-

March 2003]

Kouwenberg and Ziemba (2007)

[MAR, 1995 - November 2000]

Agarwal, Daniel and Naik (2009),

[CISDM, HFR, MSCI, TASS,

1994-2002]

Liang (1999) [HFR, 1994-June

1997]

De Souza and Gokcan (2003)

[TASS]

Amenc, Curtis and Martellini

(2003) [CISDM, 1996 – 2002]

Ag

e

Howell (2001) [TASS, 1994-

2000]

Liang (1999) [HFR, 1994-June

1997]

Amenc, Curtis and Martellini

(2003) [CISDM, 1996 – 2002]

Agarwal, Daniel and Naik (2004)

[HFR, TASS, MAR, 1994-2000]

Koh, Koh and Teo (2003)

[AsiaHedge, EurekaHedge, 1999-

March 2003]

The evidence of the impact of fund size and fund fees on performance is completely

mixed; the evidence of the impact of fund age on performance is more coherent, suggesting

that younger funds do not underperform relative to older funds.

Another strand of the literature analyzes hedge fund abnormal return (alpha), and has

also produced a variety of observations and conclusions. Ackermann, McEnally and

Ravenscraft (1999) find that from 1988 to 1995 hedge funds outperformed mutual funds, but

not standard market indices. Liang (1999) also claims that hedge funds offer better risk-return

trade-offs compared to mutual funds. Agarwal and Naik (2000) show that hedge funds

115

outperform the market benchmark by 6% - 15% per year. Ibbotson and Chen (2005) find an

average alpha of 3.7 percent per year from 1999 till 2004, which is positive and significant.

Kosowski, Naik and Teo (2007) find that on average hedge fund alpha is positive, but

insignificant. At the same time, however, the performance of top funds cannot be explained

by pure luck. These funds exhibit positive and significant alphas. Naik, Ramadorai and

Strömqvist (2007) report that during the period from 1995 to 2004 hedge funds generated

significant alphas, but that the level of alpha declined substantially over this period. Fung,

Hsieh, Naik and Ramadorai (2008) document that funds of funds showed positive and

significant alpha only during one period between October 1998 and March 2000. Also of note

is that funds following different styles seem to have, on average, different alphas. For

example, Ibbotson and Chen (2006) obtain the largest alpha estimate for Equity Long Short

hedge funds based on an index regression from 1995 to April 2006.

Different results obtained in the literature are due to differences in performance

measures, statistical methodology, databases, time periods, and, last but not least, the highly

dynamic nature of hedge funds. Exposure to various macro-factors as well as the influence of

micro-level characteristics varies over time and with respect to different strategies. Both time

and cross-sectional variation of hedge fund returns (and alphas) cannot be captured by

separate time-series or cross-sectional analyses. This paper addresses these problems by using

a fixed effect panel regression approach that controls jointly for temporally varying and cross-

sectional dependencies of hedge funds. Although the proposed approach does not allow us to

find precise estimates of individual fund alphas, it does allow us to rank different groups of

hedge funds according to their average alphas and to document the dynamics of the

relationship between hedge fund alpha and fund specific micro-factors such as fund style,

size, flows, and fees; this setup also allows us to identify factors with time-stable effects that

can be used to better predict the future alpha.

The results indicate that hedge funds declaring different styles may deliver rather

different alphas; there is, however, no constantly winning style. The best style during one

period does not necessarily stay the best during the subsequent period. At the same time, if the

time variation of the average hedge funds profitability is taken into consideration, very little

incremental difference in the alphas of hedge funds of different styles can be documented.

Additionally I document several stable relations between hedge fund alpha and certain micro-

factors. Large hedge funds with high relative fund inflow, charging higher than median

management fees seem to deliver higher alphas. The fund ranking based on these

relationships is rather stable over time and for different styles, but the magnitude of actual

116

alpha shifts varies considerably over time. The relationship between incentive fee and alpha,

on the contrary, is rather volatile, and cannot be used for stable hedge fund ranking.

4.2 Research Design and Methods

This section first presents the general structure of the models and estimation

methodology, and then proceeds with detailed description of the variables in use.

4.2.1 General model

The paper uses a panel regression approach with fixed effects that allows to jointly

control for time dynamics as well as for cross-sectional dependencies between hedge funds.

Within the class of panel models, one can consider either fixed effect or random effect

models. Random effect models require fund specific effects to be uncorrelated with the

factors. We cannot make such an assumption here, since managerial skill is likely to be

correlated with flows, assets under management (AuM), and fees. Moreover, if the true model

is a random effect model and it is estimated as if it were a fixed effect model, the estimates

are still consistent, although they are not efficient. The reverse in not true: estimating the true

fixed effect model as a random effect model leads to inconsistent estimates. A fixed effect

panel model is therefore chosen for the current study.

Hedge funds often use option-like, non-linear investment strategies (see Fung and

Hsieh (1997), Fung and Hsieh (2001), and Agarwal and Naik (2000)). In order to control for

this aspect of the returns, the Fung and Hsieh (2004) seven-factor approach is chosen as the

base time-series model. The market factors (Xit) contain the excess return on the S&P 500

index over the risk-free rate as a proxy for the equity market, the monthly change in the 10-

year treasury constant maturity yield as a proxy for the bond market, the difference in the

returns on the Wilshire Small Cap 1750 index and Wilshire Large Cap 750 index, and three

trend-following option-based factors (bond trend-following factor, currency trend-following

factor, and commodity trend-following factor). The trend-following factors were obtained

from the web page of David Hsieh52. Since each hedge fund can follow a unique investment

strategy, it is allowed for fund-specific factor loadings.

In the time series framework, structural breaks and possible regime shift also need to

be taken into account. In addition to the commonly used two break points framing the internet

52 http://faculty.fuqua.duke.edu/~dah7/HFRFData.htm

117

bubble, I identify two new break points in the data and introduce corresponding time

dummies in the regression (TimeD ). The time dummies adjust for the general profitability of

the hedge fund industry within each period. The use of time period dummies allows us to

identify the periods, which were profitable for the hedge fund industry as a whole.

In the cross-sectional dimension, fund specific information is used. First, hedge fund

styles are included. iStyle denotes a vector of four components, each indicating a percentage

of assets under management invested by fund i within one of four main styles (Equity

Long/Short, Directional, Relative Value, and Event Driven). Group-dummies for other micro-

factors such as fund age (Age

itD ), fund assets under management (AuM

itD ), absolute and

relative fund flow (FlowAbs

itD and FlowRel

itD ), and management and incentive fees (MFee

itD and

IFee

itD ) are also used. Factor

itD denotes a vector of three dummies [,1 ,2 ,3, ,Factor Factor Factor

it it itD D D ] that

indicate if a fund is characterized by a low level of a given factor at a given time, a medium

level, or a high one respectively. The loadings corresponding to styles and the group-dummies

for each micro-factor are restricted to sum up to zero. These restrictions allow quantification

of the expected changes in the fund alpha conditional on changes in hedge fund age, assets

under management, fees, and style. In terms of interpretation, the constant term in the

regression characterizes an average baseline alpha of hedge funds. The style, time, age, AuM,

flow and fees dummies reflect the deviation from the average alpha of funds belonging to a

particular category.

The base model can be then specified as:

5

Re

1

,

, , , , , ,

it it it i it

Time Age AuM FlowAbs Flow l MFee IFee

it t i it it it it ti ti

r X

D Style D D D D D D

(4.1)

where

rit is the excess return over the risk-free rate on fund i for period t.

α is a baseline hedge fund alpha.

it is time varying difference of the alpha of fund i and the baseline alpha level α; this

difference is a function of fund specific micro-factors.

Xit is a set of macro-factors.

i is a vector of macro-factor loadings specific for each fund.

118

Time

tD is a set of time-dummies, taking a value of one if the current time t belongs to one of

the five pre-specified periods τ.

are the loadings on the time-dummies, which are constant for all funds.

Factor

itD are the vectors of micro-factor dummies.

iStyle is a vector representing the percentage of AuM invested in each of four styles.

γ is a vector of micro-factor loadings, which is constant for all funds.

it is an error term.

Getmansky, Lo and Makarov (2004) show that hedge fund returns often are serially

correlated up to an order of two which can be attributed to apparent illiquidity and smoothing

of reported returns. In order to control for serial correlation, for each hedge fund i the error

term it is modeled as an MA(2) process. Equation (4.1) is estimated using generalized least

squares. In the first stage, the OLS regression is estimated and the residuals are obtained.

Then the residuals’ variance-covariance matrix is estimated under the assumption that the

residuals corresponding to each particular hedge fund are serially correlated up to an order

two. In the second stage, the factor loadings are re-estimated using the estimated variance-

covariance matrix of the residuals. Since the MA(2) residual structure may not completely

capture residual heteroscedasticity, Newey-West corrected standard errors with 12 lags are

computed.

Style profitability is likely to vary over time and the relationship between other micro-

factors and fund alpha is likely to change both with time and style. These changes are

analyzed by augmenting eq. (4.1) by time-style factors, time-group-dummies, and style-

group-dummies for each of the factors in turn. Identifying the time varying contribution of

different micro-factors to a particular hedge fund’s performance is important for analyzing

stability of commonly discussed effects such as decreasing return to scale or decline in hedge

fund alpha over time, as well as for further investigation of business-cycle effects and

predictability of fund alpha.

In carrying out this analysis, a regression similar to eq. (4.1) is estimated, in which a

product of the time dummies and the dummies corresponding to the micro-factors of interest

is included. This is then repeated for each combination of interest. For example, in order to

estimate the time-variation of style effects, the following regression is estimated.

5 4 5

Re

1 1 1

,

, , , , ,

it it it i it

Time Time Age AuM FlowAbs Flow l MFee IFee

it t s t si it it it it ti ti

s

r X

D D Style D D D D D D

(4.2)

119

where s is a loading on the cross-product of the time-dummy for period τ and the style factor

for style s. It can be interpreted as the incremental alpha of a hedge fund following style s

during period τ.

4.2.2 Construction of dummy variables

Time Dummies

In the existing literature, three major periods of evolution in the hedge fund industry

are commonly recognized: before the internet bubble, the internet bubble, and after the

internet bubble53. In this paper, five distinct time periods are identified based on a cross-

section of hedge fund volatility and growth of the total AuM. The pre-bubble and post-bubble

periods are divided additionally into two sub-periods each54. Such division allows for better

capturing of the time variation in hedge fund alphas. In order to find the exact breakpoints, I

conduct a Chow test based on the regression of the time series of average hedge fund returns

using the Fung and Hsieh (2004) seven factor model. For all the chosen break points the null

hypothesis of no structural break is rejected at the 1% significance level. This particular

choice of the break points assures that the effects of the corresponding time dummies are the

most pronounced. At the same time, the results are robust to shifting the break points one

month backward or forward. The resulting 5 time periods are listed in Table 4.2.

Table 4.2. Time Periods in the Evolution of the Hedge Fund Industry

This table discusses the time periods that correspond to different stages of the evolution of the hedge fund

industry. The first column gives the breakpoints, the second column characterizes the cross-section of hedge

fund returns and the AuM, and the third column lists corresponding market events.

Period Characteristics Market Events

1 Until Sep.

1997

Moderate cross-section hedge fund return

volatility; slow increase in the total AuM.

2 Oct. 1997 to

Sep. 1998

Increasing cross-section return volatility East Asian currency crisis, Russian Default, LTCM

debacle;

3 Oct. 1998 to

Mar. 2000

Very high cross-section returns’ volatility. The Internet bubble.

4

Apr. 2000 to

Feb. 2005

Decreasing cross-section return volatility,

rapid increase in the total AuM.

Economic recession in Europe (2000-2001), in the

US (2001-2003); September 11/2001; accounting

scandal and bankruptcy of WorldCom (July 2002).

5 March. 2005

to Jun. 2006

Low cross-section return volatility, stable

total AuM.

53 Fung and Hsieh (2004), Fung, Hsieh, Naik and Ramadorai (2008). 54 The data ends in the middle of 2006, thus the financial crises of 2008 is not covered.

120

Age Dummies

The age dummies indicate different sub-periods of the life of each hedge fund:

1. “Young funds” not older than 4 years (28% of funds stop reporting before this age).

2. “Middle-age funds” with age between 5 and 9 years (52% of funds stop reporting

within this age interval).

3. “Old funds” with age over 10 years (20% of funds stop reporting within this age

interval).

If, for example, during a given month t, a hedge fund’s age is between 5 and 9 years, the

corresponding age dummy Age

itD 2, takes a value of 1, and other two age dummies (Age

itD 1, and

Age

itD 3, ) take a value of zero.

Asset under Management, Relative and Absolute Flow Dummies

In order to construct the assets under management (AuM) dummies, at each point in

time hedge funds are divided into 3 sub-groups according to their AuM:

1. Low AuM group: includes the 30% of all funds having the lowest AuM existing on the

date of interest.

2. Middle AuM group: includes the 40% of funds with AuM lying between the 30th

and

70th

quantiles existing on the date of interest.

3. High AuM group: includes the 30% of funds with the highest AuM of all funds

existing on the date of interest.

Note that the critical levels of the AuM, which separate the fund groups, depend on the

calendar time. For example, a fund with 100 million in AuM belongs to the high AuM group

in 1995, but a fund with the same AuM in 2003 is considered to have only middle AuM.

For the Absolute and Relative Flow dummies, the sub-division into three categories is

performed analogously.

In the fund by fund regressions, one cannot use simultaneously variables, related to the

AuM, and Relative and Absolute Flows since they will be collinear. However, in the panel

setting they are not. $10 million in absolute flow can be just 1% relative flow for a large fund

(the dummy of low relative flows takes a value of 1), and 50% relative flow for a small fund

(the dummy for high relative flow takes a value of 1). The empirical correlation coefficients

for log(AuM) and absolute and relative flows are, thus, rather small (see Table 4.3).

121

Table 4.3. Correlation Matrix of the Log AuM and Fund Flows

This table reports the empirical correlation coefficient of the logarithm of the asset under management, absolute

flow, and relative flow computed for pooled individual hedge funds that reports their returns and the AuM

during any consecutive 24 months between January 1994 and July 2006.

log(AuM) FlowAbs FlowRel

log(AuM) 1 FlowAbs 0.105 1 FlowRel 0.001 0.035 1

Management and Incentive Fee Dummies

While constructing the management/incentive fee dummies, hedge funds are divided

into 3 sub-groups according to the relative level of their management/incentive fee:

1. Low fee group: includes funds with management/incentive fees below the median.

2. Middle fee group: includes funds with management/incentive fees equal to the

median.

3. High fee group: includes funds with management/incentive fees above the median.

The median fee is computed relative to all funds existing on the date of interest. The

median incentive fee stays constant over time at the level of 20%. The median management

fee increases from 1% in 1994 to 1.5% in 2004 and stays at this level until the end of the

investigation period. As a robustness check, the actual fund fees are compared not with the

median, but with the average fees of all funds existing on the date of interest. There seems to

be a slight upward trend in the average fees of hedge funds, but the results remain

qualitatively the same.

4.3 The Data

For the current research, the ALTVEST database55 is used, containing monthly

returns, the assets under management, fees and other information for more than 6,800 live and

dead hedge funds. Two funds that reported several times monthly returns over 400% are

deleted, since these funds do not seem to have reported accurate performance records. I also

excluded from the sample 36 defunct funds that report “Duplicate Registration” as a reason

for being excluded from the live database. The sample is restricted to those hedge funds that

report their returns in US dollars (91% of funds), and only those that have 24 consequent

55 The ALTVEST database is provided by Morningstar.

122

return observations after 1994 are considered. The analysis starts from January 1994, since

before this date the majority of databases do not contain any information on defunct funds.

Thus, prior to 1994, the database may not be survivorship bias free. Hedge funds are required

to have minimum of 24 consecutive observations in order to assure stability of the results in

the time-series dimension. This filtering results in a dataset consisting of 4,767 hedge funds.

Additionally, the sample is restricted to those hedge funds continuously reporting their assets

under management (AuM), which further restricts the sample to 3,034 funds.

Not all the funds, however, seem to be relevant for investors. Funds of funds, pension

funds, insurance companies, and banks are more likely to be interested in hedge funds of

relatively large size that are able to absorb large investments. Following Kosowski, Naik and

Teo (2007) only those hedge funds with the assets under management over $20 million are

considered. As soon as a fund reaches AuM of $20 million, it is included in the sample and

stays in the sample until its liquidation or the end of the investigation period (June, 2006). By

excluding the smallest funds, 38% of funds are lost. In terms of the AuM belonging to these

funds, however, just around 1% of the total assets under management in the industry is lost,

and the current analysis covers by far most of the assets under management of funds reporting

to the ALTVEST database. Table 4.4 illustrates the distribution of hedge funds across

different size categories as of May 2005. Around 67% of all funds exceed $20 million in

AuM as of May 2005. 98% of the total AuM is controlled by funds managing more than $ 20

million. Thus, excluding funds holding less than $20 million does not lead to any bias.

123

Table 4.4. Size Distribution of Hedge Funds as of May 2005

This table reports the distribution of hedge funds across different size categories as of May 2005. From the total

of 3034 hedge funds that report the AuM, 2146 existed in May 2005. As a measure of size, for each hedge fund

the AuM reported on that date is used.

AuM in $ million

Total existing in May 2005 <1 1-10 10-20 20-50 50-100

100-1000 >1000

All hedge funds

Number 2146 52 376 250 410 318 638 76

In % of all funds in this category 100% 2.42% 17.52% 11.65% 19.11% 14.82% 29.73% 3.54%

In % of all AuM in this category 100% 0.01% 0.50% 0.97% 3.55% 5.94% 51.71% 37.32%

Single strategy funds

Number 1149 37 238 142 227 152 322 16

In % of all funds in this category 100% 3.22% 20.71% 12.36% 19.76% 13.23% 28.02% 1.39%

In % of all AuM in this category 100% 0.02% 0.82% 1.43% 5.07% 7.33% 67.29% 18.06%

Multi strategy funds

Number 433 6 84 51 75 60 125 30

In % of all funds in this category 100% 1.39% 19.40% 11.78% 17.32% 13.86% 28.87% 6.93%

In % of all AuM in this category 100% 0.00% 0.43% 0.76% 2.51% 4.27% 38.30% 53.74%

Funds of funds

Number 564 9 54 57 108 106 191 30

In % of all funds in this category 100% 1.60% 9.57% 10.11% 19.15% 18.79% 33.87% 5.32%

In % of all AuM in this category 100% 0.00% 0.23% 0.64% 2.70% 5.67% 44.84% 45.92%

After excluding the smallest funds and ensuring that the funds being investigated have

at least 24 consecutive observations, the sample consists of 1,873 funds. 988 of them are

single strategy funds, 428 are multi strategy funds, and 457 are funds of hedge funds. Since

ordinary hedge funds and funds of funds may be subject to different risks, funds of funds are

excluded from the analysis. At the same time, both single- and multi-strategy funds are

investment vehicles of the same type. Most of them implement various strategies during their

life. The multi-strategy funds are to some extent more honest, reporting more information

about their actual style than single-strategy funds. Both single- and multi-strategy funds are

considered in this analysis. Table 4.5 summarizes the descriptive statistics of the hedge funds

under study.

124

Table 4.5. Sample Statistics of Hedge Funds under Study

This table reports the sample statistics of the hedge funds used in the current study. The first row reports the

number of funds belonging to single strategy and multi strategy groups. The mean and median returns, return

standard deviation, skewness, kurtosis, and the first order autocorrelation of returns are reported for live and

dead funds separately as well as for the joint sample. Monthly returns are net of all fees, incentive fees prorated

during the year. The last row reports the average life time in months after reaching an AuM of $20 million.

Characteristic

Distribution across funds

Single strategy Multi strategy

All Live Dead All Live Dead

Number of funds 988 602 386 428 253 175

Mean return Average 0.892 1.036 0.668 0.786 0.924 0.587

STD 0.937 0.845 1.027 0.752 0.521 0.962

Median Average 0.821 0.954 0.614 0.663 0.853 0.388

STD 0.902 0.796 1.012 0.978 0.529 1.348

Standard deviation

Average 3.690 3.422 4.108 3.607 2.858 4.689

STD 3.203 2.781 3.733 4.602 2.331 6.488

Skewness Average 0.069 0.109 0.005 0.003 -0.117 0.176

STD 1.107 1.026 1.221 1.399 1.443 1.318

Kurtosis Average 5.310 5.121 5.604 6.408 6.704 5.980

STD 5.387 5.243 5.598 9.381 10.845 6.730

1st order autocorrelation

Average 0.143 0.140 0.147 0.139 0.156 0.114

STD 0.192 0.185 0.202 0.178 0.162 0.197

Average life time in months after reaching AuM of $20 mio

58.172 61.502 52.979 64.11 71.704 53.131

Consistent with common intuition and the descriptive statistics of other widely used

databases56, the live funds tend to have higher mean returns and smaller return standard

deviations than dead funds. The difference in mean returns between live and dead funds is

significant at the 1% level for single-strategy funds and at the 5% level for multi-strategy

funds. The difference in return standard deviation is significant at the 5% level for single-

strategy funds and at the 1% level for multi-strategy funds.

Single and multi-strategy funds report their styles by indicating the percentage of

AuM invested within the particular style. The following four self-reported styles seem to be

the largest in the ALTVEST database57: Equity Long/Short (ELS) accounts for 45% of hedge

56 Other widely used databases are: TASS (e.g., used by Getmansky, Lo and Makarov (2004), Fung, Hsieh,

Naik and Ramadorai (2008)); HFR (Ackermann, McEnally and Ravenscraft (1999), Liang (2000), and Fung,

Hsieh, Naik and Ramadorai (2008)); MAR (Ackermann, McEnally and Ravenscraft (1999), and Fung, Hsieh,

Naik and Ramadorai (2008)). 57 Here, a hedge fund is classified as following a particular style if it invests more than 50% of its assets within

this style.

125

funds under study, Directional excluding ELS accounts for 15%, Relative Value accounts for

27%, and Event Driven accounts for 13%.

In order to have a closer look at the return distribution of hedge funds under

consideration, for each hedge fund the Fung and Hsieh (2004) seven-factor model is

estimated. The average adjusted R-squared of these models is just 25%. Table 4.6 reports the

average estimated hedge fund alphas, the associated t-statistics, as well as the test results for

normality, heteroscedasticity, and first order serial correlation of the residuals.

Table 4.6. Summary Statistics and Tests of Normality, Heteroscedasticity, and Serial

Correlation on Hedge Fund Residuals

This table reports the alpha characteristics and the results of the normality, heteroscedasticity, and the first order

serial correlation tests of residuals from the Fung and Hsieh (2004) 7-factor model estimated for each hedge fund

separately.

Mean Test of

normality Test of

heteroscedasticity Test of first order serial correlation

Number of

funds

Alpha % per

month

Alpha t-stat

Residuals’ Skewness

Residuals’ Kurtosis

Share of funds with Jarque-Bera p<0.1

Share of funds with Breusch-Pagan p<0.1

Share of funds with Ljung-Box

p<0.1

Single strategy 988 0.479 1.485 0.129 4.547 0.401 0.329 0.260

Multi Strategy 428 0.413 1.808 0.036 5.194 0.453 0.402 0.248

Among single- and multi-strategy funds, approximately 40% of the associated

estimations do not result in normally distributed residuals. The residuals are heteroscedastic

for more than 30% of the estimations and serially correlated for approximately 25% of the

estimations. Thus, the proposed MA(2) specification for the error term is justified, and the

heteroscedasticity and serial correlation correction of the standard errors is essential.

All existing hedge fund databases are subject to several biases. One of the most severe

is the self-selection bias. Hedge funds voluntarily decide to report to the database. Poorly

performing funds do not report their returns since their managers would prefer to avoid

publicity. At the same time, extremely well performing funds also are reluctant to report their

performance, since they are likely to be held privately by a group of investors, or simply do

not need to attract additional investment. Thus, the self-selection bias has both negative and

positive impact on the sample (Ackermann, McEnally and Ravenscraft (1999), Liang (2000),

and Brown, Goetzmann and Park (2001)). The resulting impact of this bias cannot easily be

estimated and to the best of my knowledge there is no research that addresses this issue.

The backfilling bias can also be pronounced in the data. Ackermann, McEnally and

Ravenscraft (1999), Fung and Hsieh (2000), and Ibbotson and Chen (2005) propose to delete

126

first 12 return observations to control for this bias. Since this paper considers hedge fund’s

returns only after its assets under management reach the $20 million threshold, for the

majority of funds under study, first year returns are automatically excluded from the analysis.

For those funds that turn out to be large from their origination, the first year returns are

additionally excluded to control for the backfilling bias.

The ALTVEST database contains information on defunct funds and, thus, the

survivorship bias is at least partly ameliorated with the dead fund base.

4.4 Empirical Results

The following section first discusses the results from the base model (4.1), and then

presents the finer scale analysis of the relation between the various micro-factors and the

hedge fund alpha by estimating equations of the form (4.2) for each considered micro-factor.

4.4.1 Base model: baseline alpha and micro-factors

Table 4.7 reports the baseline alpha and the loadings on the micro-factors’ group-

dummies estimated using eq. (4.1). The adjusted R-squared of the regression is 34%.

The results indicate that the baseline alpha is 45 b.p. per month and is highly

significant. This alpha level is a grand average across all hedge funds with different styles,

ages, sizes, and fees computed over twelve and a half years. This average alpha, however, is

not stable over time. There are periods during which hedge funds perform poorly, delivering

on average an alpha significantly lower than the baseline level. This happens, for example,

both before and after the Internet bubble. During the Internet bubble, hedge funds performed

much better, delivering on average an alpha that is 38 b. p. per month higher than the baseline

level58. Among different styles, the ELS funds seem deliver an alpha that is on average 4 b.p.

higher than that of other funds. This effect is significant at the 10% level and is consistent

with Ibbotson and Chen (2006), who report the highest alpha estimate for Equity Long Short

hedge funds based on the index regression from 1995 to April 2006.

58 The finding is consistent with Fung, Hsieh, Naik and Ramadorai (2008) who find that funds of hedge funds

have positive and significant alpha only during the Internet bubble.

127

Table 4.7. Panel Regression with Hedge Fund Micro Factors

This table reports the estimated baseline alpha and the loadings on the micro-factors from the base panel model.

The estimation is conducted using hedge funds with AuM larger than $20 million. The first 12 observations for

each hedge fund are excluded. The error term for each hedge fund follows an MA(2) process.

Variable Coefficient t-statistic

Baseline Alpha 0.449*** 9.054

Time

Jan1994-Sep1997 0.068 1.241

Oct1997-Sep1998 -0.266*** -2.594

Oct1998-Mar2000 0.384*** 4.975

Apr2000 - Feb2005 -0.162*** -4.244

Mar2005-Jun2006 -0.025 -0.643

Style

ELS 0.044* 1.716

Directional -0.023 -0.687

Relative Value 0.009 0.331

Event Driven -0.030 -0.976

Young 0.018 0.816

Age Middle Age -0.005 -0.203

Old -0.014 -0.452

Low -0.053** -1.970

AuM Middle 0.007 0.364

High 0.046* 1.901

FlowAbs

Low -0.051 -1.118

Middle 0.028 0.923

High 0.023 0.591

FlowRel

Low 0.007 0.143

Middle -0.098*** -3.528

High 0.091** 2.095

MgmtFee

Below median -0.083*** -3.825

Median -0.023 -0.957

Above median 0.106*** 4.303

IncFee

Below median -0.026 -0.551

Median -0.043 -0.996

Above median 0.069 0.886

Adjusted R-squared 0.338

No significant relationship between hedge fund age and alpha can be found within the

base model. At the same time the results provide some evidence of a positive relationship

between hedge fund alpha and fund size. Smaller funds seem to have lower alphas than

medium size funds, and the largest thirty percent of funds have on average the highest alphas.

This effect is also pronounced for relative fund flow. Funds with high relative inflow enjoy

significantly higher alpha than funds with moderate or low inflow. At the same time,

differences in the absolute flows do not seem to induce any significant deviations from the

baseline alpha.

128

The relationship between management fee and alpha seems to be positive and close to

linear. Funds with management fee below the median significantly underperform relative to

the funds having the median management fee. And funds with a management fee above the

median have alphas which are significantly higher than the baseline level. The incentive fee

does not have any explanatory power in terms of hedge fund alpha. The majority of hedge

funds in the ALTVEST database require a 20% incentive fee. Thus, the incentive fee level

seems to be common across the industry, and it does not seem to have any link to hedge fund

quality.

4.4.2 Time and style variation of micro-factor effects

This section considers time variation in the micro-factors’ effects. It seeks to

document whether or not the general ranking of different groups of hedge funds changes

across time periods. Equations of type (4.2) are estimated, in which the products of the time

dummies and micro-factor group-dummies are added to the regression.

Time Variation of Style Profitability

Table 4.8 reports the estimated loadings on the time-style factors. Panel A reports the

loadings on the time-style variables, if one does not control for the general variability of

hedge fund performance and excludes time-dummies from the analysis. The results indicate

that the average alphas delivered by hedge funds of different styles vary considerably over

time. It is not only the absolute values of the style-specific alphas that change over time, but

style ranking also changes. During the first period (January 1994 to September 1997)

Directional funds clearly underperform, delivering an incremental alpha of -30 b.p. which is

significant at the 1% level. Event Driven funds seem to provide the highest alpha during the

first and the last of the considered time periods, which is significant at the 10% level. The

ELS funds clearly outperform during the internet bubble.59

At the same time, when controlling for the overall time-variation of hedge fund

profitability using the time dummies (Panel B of Table 4.8) one finds less variation in the

incremental style-specific alphas. The ELS funds continue to exhibit the highest alpha during

the internet bubble, earning in addition to the baseline level an extra 79 b.p. per month.

However, during the other four periods, all styles seem to perform similarly in terms of their

59 Superior performance of the ELS funds during the bubble is not surprising. Most of them have long bias and

are positively correlated with the market. Through increasing leverage, hedge funds amplify profits on up

markets.

129

incremental alphas. Although for some periods hedge funds of different styles may

underperform relative to the baseline level (for example, the Relative Value funds seem to

have the lowest alpha during 2 out of 5 periods), these effects are only marginally significant.

The only exception is Directional funds that underperformed during the internet bubble

relative to the baseline level considerably, which is compensated by the performance of the

ELS funds.

Table 4.8. Time Variation of Style Effects

This table reports the time-varying style components of the total alpha, estimated based on a panel regression of

type (4.2). Panel A presents the results for the specification without pure time-dummies. Panel B reports the

results for the specification in which the time-dummies are also included. For each of the five time periods, the

loadings on the styles are required to sum up to zero.

Panel A Panel B

Variable Coefficient t-stat Coefficient t-stat

Jan1994-Sep1997

ELS 0.077 0.908 0.039 0.353

Directional -0.298*** -2.560 -0.096 -0.814

Relative Value 0.063 0.668 0.007 0.081

Event Driven 0.158* 1.782 0.050 0.566

Oct1997-Sep1998

ELS -0.202 -0.954 0.041 0.148

Directional 0.290 1.007 0.080 0.251

Relative Value -0.200 -1.107 -0.317* -1.793

Event Driven 0.113 0.522 0.196 0.878

Oct1998-Mar2000

ELS 0.646*** 4.116 0.788*** 5.059

Directional -0.829*** -4.913 -0.702*** -4.378

Relative Value -0.048 -0.341 0.031 0.228

Event Driven 0.230* 1.658 -0.117 -0.872

Apr2000 - Feb2005

ELS -0.035 -1.026 -0.007 -0.176

Directional 0.044 1.052 0.027 0.630

Relative Value 0.050 1.585 0.042 1.291

Event Driven -0.059 -1.554 -0.061 -1.558

Mar2005-Jun2006

ELS -0.042 -1.108 0.040 1.066

Directional 0.077 1.403 -0.004 -0.065

Relative Value -0.114** -2.164 -0.086* -1.675

Event Driven 0.080* 1.701 0.049 1.137

Adjusted R-squared

0.539

There are two main conclusions to be drawn here. First, superior performance in hedge

funds of a particular style in one year does not imply that the funds of this style will also be

the best in the future. Second, there are common trends in the hedge fund industry that

determine average hedge fund profitability and alpha. If one controls for these common trends

130

and waves, differences in the incremental style alphas become just marginally significant, if at

all.60

Time and Style Variation of Age Effects

Using the base model and controlling for the backfilling bias, no significant difference

in the performance of funds of different ages is documented (Table 4.7). The results are rather

stable over time (Panel A of Table 4.9). There could be however some variation of age

influence on the fund alpha across different styles (Panel B of Table 4.9). Within the ELS and

Relative Value styles, young funds seem to outperform, adding 6 b.p. to the baseline alpha.

Within the Event Driven style, on the contrary, old funds outperform, delivering an additional

9 b.p. per month. All these effects, however, are significant only at the 10% level. There does

not seem to be any pronounced relationship between a fund’s age and its alpha.

Time and Style Variation of Size Effects

In order to capture the time variation of size effects, a regression of type (4.2) is

estimated including, first, time-asset under management dummies, and then time-absolute

flow dummies and time-relative flow dummies. For all the model specifications, the sum of

the time-factor dummies for each of the five time periods is equal to zero. Panel A of Table

4.10 summarizes the results reporting the values of the loadings for each time-factor dummy

variable.

The direction of the AuM effect is fairly stable over time. Hedge funds with large

AuM normally outperform funds with low AuM. This is true for all time periods except the

Internet Bubble, during which no significant difference in the performance of funds of

different sizes can be seen. Moreover, starting from April 2000, the relationship between the

AuM and the alpha seems to completely stabilize, for which we see that the smallest funds

have the lowest alpha, followed by the middle-sized funds, and the large funds, delivering the

highest alpha.

In terms of fund flow influence on hedge fund alpha, after April 2000 no significant

relationship between the absolute fund flow and the alpha can be observed, which is

consistent with the joint results. Before this period, funds with low absolute flow

60 Consistent with this finding, during the current financial crises we observe that hedge funds following all

styles simultaneously performed poorly. According to the Credit Suisse/Tremont Hedge Fund Database report,

in October 2008 the ELS index dropped by 7.24%, Global Macro by 4.61%, Fixed Income Arbitrage by 17.75%,

Emerging Markets by 15.36%, Convertible Arbitrage by 10.70%, and the Multi-Strategy hedge fund index

dropped by 8.09%.

131

underperformed, which is consistent with our general finding of an increasing return to scale

effect.

Table 4.9. Time and Style Variation of Age Effects

Panel A of this table reports the estimated time varying loadings on the age dummies, and Panel B reports the

estimated style varying loadings on the age dummies from a panel regression of type (4.2). For each of the time

periods and fund styles, the loadings are restricted to sum up to zero.

Age Coefficient t-stat

Panel A

Jan1994-Sep1997

Young 0.098 1.335

Middle Age -0.117 -1.483

Old 0.019 0.203

Oct1997-Sep1998

Young 0.055 0.354

Middle Age -0.309** -1.995

Old 0.253 1.528

Oct1998-Mar2000

Young 0.159 1.237

Middle Age -0.136 -0.959

Old -0.023 -0.127

Apr2000 - Feb2005

Young -0.016 -0.538

Middle Age -0.005 -0.150

Old 0.021 0.486

Mar2005-Jun2006

Young 0.040 1.213

Middle Age -0.004 -0.118

Old -0.036 -0.899

Adjusted R-squared 0.349

Panel B

ELS

Young 0.068* 1.653

Middle Age 0.002 0.044

Old -0.070 -1.414

Directional

Young -0.014 -0.226

Middle Age 0.004 0.059

Old 0.010 0.119

Relative Value

Young 0.062* 1.717

Middle Age 0.007 0.196

Old -0.069 -1.426

Event Driven

Young -0.051 -1.105

Middle Age -0.041 -0.977

Old 0.092* 1.907

Adjusted R-squared 0.343

132

Table 4.10. Time and Style Variation of Size Effects

Panel A of this table reports the estimated time varying loadings on the AuM dummies, the absolute flow

dummies, and the relative flow dummies from a panel regression of type (4.2). Panel B reports the estimated

style varying loadings on these factors. For each of the time periods and styles, the loadings are restricted to sum

up to zero.

AuM Flow Absolute Flow Relative

Coefficient t-stat Coefficient t-stat Coefficient t-stat

Panel A

Jan1994-Sep1997

Low -0.042 -0.480 -0.127 -1.271 -0.119 -1.179

Middle -0.196** -2.283 0.125* 1.791 -0.228*** -3.418

High 0.238** 2.413 0.002 0.025 0.347*** 3.672

Oct1997-Sep1998

Low -0.407** -2.247 -0.360** -2.356 -0.159 -1.035

Middle 0.591*** 3.866 0.455*** 3.088 -0.239* -1.784

High -0.184 -1.061 -0.095 -0.578 0.397** 2.410

Oct1998-Mar2000

Low 0.157 1.258 -0.314** -2.470 -0.359*** -2.610

Middle 0.015 0.152 0.127 1.131 -0.719*** -7.003

High -0.172 -1.433 0.187 1.332 1.078*** 6.709

Apr2000 - Feb2005

Low -0.150*** -4.317 -0.007 -0.136 -0.018 -0.338

Middle -0.029 -1.098 -0.016 -0.477 -0.170*** -5.332

High 0.179*** 6.123 0.022 0.537 0.188*** 4.215

Mar2005-Jun2006

Low -0.081** -2.120 0.013 0.247 0.124** 2.305

Middle -0.076** -2.405 0.015 0.371 -0.228*** -6.414

High 0.157*** 4.436 -0.028 -0.523 0.104** 2.004

Adjusted R-squared

0.408 0.338 0.381

Panel B

ELS

Low -0.146*** -3.463 -0.199*** -3.490 -0.126** -1.998

Middle 0.060* 1.703 0.060 1.461 -0.107** -1.981

High 0.086** 2.001 0.138** 2.521 0.233*** 3.813

Directional

Low 0.071 1.079 -0.063 -0.801 0.194** 2.438

Middle 0.102* 1.907 0.111** 1.959 -0.160*** -3.084

High -0.173*** -3.150 -0.047 -0.651 -0.034 -0.453

Relative Value

Low -0.057 -1.068 -0.045 -0.810 0.151*** 2.584

Middle -0.028 -0.770 0.094** 2.269 -0.129*** -3.454

High 0.085** 2.323 -0.050 -0.900 -0.022 -0.418

Event Driven

Low -0.139** -2.460 -0.164*** -2.739 0.022 0.327

Middle -0.007 -0.162 -0.001 -0.020 -0.155*** -3.678

High 0.146*** 3.453 0.165*** 3.220 0.133** 2.076

Adjusted R-squared

0.371 0.369 0.533

The joint results for the baseline model suggest that there is a convex relationship

between the relative flow and fund alpha. This pattern is stable for all time periods. Hedge

funds with medium relative flows have the lowest alpha, whereas the highest alpha is in most

133

cases delivered by hedge funds enjoying the largest relative flow. Nevertheless, the magnitude

of these differences varies widely. If during the Internet Bubble, hedge funds with the largest

flow had an alpha 1.08% per month higher than the baseline level (significant at the 1%

level), in 2005-2006 they deliver only 10 b.p. in addition to the baseline level (significant at

the 5% level).

Considering the style variation of size effect, the direction of size effects is relatively

stable across all styles (Panel B of Table 4.10). Larger funds seem to deliver the highest alpha

within all styles, except for Directional funds. In terms of the absolute flow influence, hedge

funds with low flow have a smaller alpha than hedge funds with medium flow. The winning

funds are however different across styles. The highest alpha for the ELS and Event Driven

funds is delivered by funds with the largest absolute flow, whereas for Directional and

Relative Value styles, the largest alpha belonged to funds with medium absolute flow.

Directional and Relative Value funds are rather similar in terms of the relative flow impact on

their alpha. The relationship seems to be convex; funds with the lowest relative flow deliver

the highest alpha, funds with medium flow deliver the lowest alpha, and the alpha of funds

with the highest flow is not significantly different from the baseline alpha level.

Time and Style Variation of Fee Effects

In the joint specification, no significant effect of the incentive fee level on the hedge

fund alpha can be documented. The reason seems to be not the absence of the effect, but its

high time variation. Panel A of Table 4.11 reports the time varying fee effects. During the

first of the considered time periods (from January 1994 to August 1997), hedge funds with

incentive fees below the median underperformed relative to other funds. Low fee funds

delivered an alpha that was 24 b.p. per month lower than the baseline level, whereas funds

with the median incentive fee delivered an alpha 16 b.p. per month higher than the baseline

level. Both effects are significant at the 5% level. The situation reverted after April 2000.

During the last two periods, hedge funds with the median incentive fee underperformed

relative to other funds. Moreover, from February 2005 to June 2006 the highest alpha was

earned by hedge funds with incentive fee below the median. These funds generated additional

24 b.p. per month, significant at the 1% level. The funds with the median incentive fee, on the

contrary, significantly underperformed and had an alpha 37 b.p. lower than the baseline level.

In terms of the variation of the incentive fee effect with respect to the reported fund style,

little variation can be documented (Panel B of Table 4.11). For all styles, there is no

134

significant difference in the alphas of funds having different incentive fee levels, with the one

exception of the Relative Value funds. For these funds the alpha seems to be positively related

to the incentive fee level, and hedge funds charging higher fees than the median incentive fee

deliver 14 b.p. on top of the baseline alpha significant at the 5% level. Hence, the effect of the

incentive fee can change dramatically over time. Not only the magnitude of the effect is

variable, but also its direction. With respect to fund style, however, very little variation can be

observed.

The management fee effect seems to be more stable both over time and fund style.

Starting from the Internet Bubble, hedge funds with management fee below the median

delivered lower alpha than funds having the median- or higher than the median fees. Hedge

funds with their fees above the median fee outperform other funds from April 2000 to January

2005, delivering an additional 11 b.p. of monthly alpha, significant at the 1% level. In terms

of the style variation, nearly no relationship between management fee and hedge fund alpha

can be seen for ELS and other Directional funds. For the Relative Value and Event Driven

funds, hedge funds having higher than the median management fee deliver an alpha 10-12

b.p. per month higher than the baseline level.

Summarizing these results, ranking hedge funds based on their charged incentive fee

does not seem to be very informative. On average, no significant relationship between hedge

fund incentive fee and alpha can be found. For different sub-periods, however, both positive

and negative significant relationships are observed. The incentive fee cannot be treated as a

stable predictor of hedge fund alpha. The management fee effect, on the contrary, seems to be

more stable. Hedge funds charging higher management fees seem to deliver alphas at least not

lower than that delivered by funds charging smaller management fees. This effect is stable

across time and fund styles.

135

Table 4.11. Time Varying Fee Effects

Panel A of this table reports the estimated time varying loadings on the management and incentive fee dummies

from a panel regression of type (4.2). Panel B reports the estimated style varying loadings on these factors. For

each of the time periods and hedge fund styles, the loadings are restricted to sum up to zero.

Management Fee Incentive Fee

Coefficient t-stat Coefficient t-stat

Panel A

Jan1994-Aug1997

Below median -0.192 -1.470 -0.244** -2.453

Median 0.059 0.696 0.161** 2.100

Above median 0.133 1.501 0.083 0.743

Sep1997-Sep1998

Below median 0.033 0.121 -0.213 -0.673

Median 0.049 0.286 -0.026 -0.090

Above median -0.082 -0.402 0.240 0.449

Oct1998-Mar2000

Below median -0.482*** -2.959 -0.153 -0.647

Median 0.290** 2.148 0.241 1.168

Above median 0.193 1.546 -0.088 -0.236

Apr2000 - Jan2005

Below median -0.084** -2.314 -0.024 -0.407

Median -0.024 -0.607 -0.089* -1.701

Above median 0.108*** 3.370 0.113 1.241

Feb2005-Jun2006

Below median -0.028 -0.624 0.235*** 2.969

Median 0.095** 2.411 -0.369*** -4.857

Above median -0.067 -1.121 0.133 1.039

Adjusted R-squared

0.359

0.489

Panel B

ELS

Below median 0.076* 1.816 -0.172 -0.877

Median -0.078 -1.547 -0.066 -0.349

Above median 0.002 0.037 0.238 0.636

Directional

Below median -0.112 -1.512 0.020 0.259

Median 0.006 0.080 -0.054 -0.749

Above median 0.107 1.597 0.034 0.268

Relative Value

Below median -0.026 -0.577 -0.110* -1.900

Median -0.077* -1.777 -0.028 -0.628

Above median 0.103*** 2.664 0.138** 2.049

Event Driven

Below median -0.095** -2.170 0.187 1.182

Median -0.024 -0.489 0.006 0.045

Above median 0.119** 2.124 -0.193 -0.803

Adjusted R-squared

0.409

0.338

136

4.5 Conclusion

The hedge fund industry has been attracting increasing interest of researchers over the

last decade. Much effort has been spent on analyzing the determinants of hedge fund alpha.

Most studies, however, come to contradictory conclusions with respect to the direction of

influence of different micro-factors on hedge fund performance. The inconsistency of these

results is driven not only by differences in the used databases and methodologies, but also by

the highly dynamic nature of hedge funds themselves. The impact of micro-factors on hedge

fund alpha varies over time and with respect to different hedge fund styles. This paper

addresses this variation by estimating a fixed effect panel regression, in which micro-factor

dummies are included. The loadings on these micro-factors are first kept constant for all

funds, then, time variation of these loadings is investigated, and finally their variation across

styles is considered. The micro-factor loadings quantify the deviation of the alpha of a hedge

fund belonging to a particular group, say, a group of hedge funds with high inflows, from the

average baseline alpha of the whole industry.

The empirical results indicate that the baseline alpha is 45 b.p. per month and is highly

significant. On average during the last twelve years hedge funds have been performing rather

well overall. Equity Long/Short funds seem to perform better than other styles, delivering on

average an alpha that is 4 b.p. higher than the baseline level. At the same time, style

profitability changes noticeably over time, and during different time periods there are

different winning styles. It is difficult, however, to use this information on the currently

winning style to predict the future development. Superior performance of hedge funds of a

particular style within one period does not imply that the funds of this style will also be the

best in the future.

Moreover, this paper documents high variation of the average alpha over time. I do not

find a negative trend in the average alpha, but rather the succession of periods of high

profitability by periods of low profitability and vice versa. The Internet Bubble seems to be a

period of high alphas, framed by two periods of alphas lower than the baseline level. Starting

from March 2005, the average alpha does not seem to deviate significantly from the baseline

level. These common trends in the hedge fund industry determine the average hedge fund

alpha. If one controls for these fluctuations, the differences in the incremental alphas of funds

of different styles become only marginally significant. Hedge funds of different styles do not

seem to be that different in terms of their alphas, if the average profitability level of the

industry is taken into consideration.

137

In terms of the micro-factors’ influence on the hedge funds alpha, I do not find any

significant relationship between hedge fund age and alpha in the current sample of hedge

funds. This absence of relationship is stable across time and fund styles.

The relationship between hedge fund alpha and fund size is found to be positive. This

effect is pronounced for the assets under management and seems to be stable over time and

across fund styles. The relationship between contemporaneous relative fund flow and fund

alpha is convex. Funds with the highest flow tend to have the highest alpha, whereas funds

with medium flow tend to have the lowest alpha. Although the fund ranking based on the

assets under management or relative fund flow is stable over time, the magnitude of alpha

differences between funds of different size/flow groups varies widely. If during the Internet

Bubble hedge funds with high flow delivered an alpha of more than 1% per month higher than

the baseline level, in 2005-2006 they add only 10 b.p. per month on top of the baseline alpha.

I document a positive relationship between a hedge fund management fees and the

corresponding alpha. Hedge funds charging lower than the median management fee tend to

deliver the lowest alpha. This effect is stable and pronounced after October 1998. The

incentive fee does not seem to have any explanatory power in terms of hedge fund alpha on

average, since the effect of the incentive fee is very volatile.

The hedge fund industry is highly dynamic. It seems to generate a positive and

significant alpha on average; however, the level of this alpha varies considerably over time. It

is difficult to predict the exact absolute alpha level based on hedge fund micro-factors, but it

seems to be possible to rank hedge funds using this micro information. The empirical results

suggest that large funds with high relative inflow charging higher than median management

fees are likely to deliver higher alpha than their peers most of time.

138

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Erklärung

Ich versichere hiermit, dass ich die vorliegende Arbeit mit dem Thema

Four Essays on Investments

ohne unzulässige Hilfe Dritter und ohne Benutzung anderer als der angegebenen Hilfsmittel

angefertigt habe. Die aus anderen Quellen direkt oder indirekt übernommenen Daten und

Konzepte sind unter Angabe der Quelle gekennzeichnet. Weitere Personen, insbesondere

Promotionsberater, waren an der inhaltlich materiellen Erstellung dieser Arbeit nicht

beteiligt.61 Die Arbeit wurde bisher weder im In- noch im Ausland in gleicher oder ähnlicher

Form einer anderen Prüfungsbehörde vorgelegt.

Konstanz, den 9. Mai 2009 _________________________

(Olga Kolokolova)

61 Siehe hierzu die Abgrenzung zu Kapiteln 1 und 3 auf der folgenden Seite.

151

Abgrenzung

Ich versichere hiermit, dass ich Kapitel 2 und 4 der vorliegenden Arbeit ohne Hilfe Dritter

und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe. Kapitel 1 und

3 entstammen einer gemeinsamen Arbeit mit Herrn Prof. Jens Carsten Jackwerth (Universität

Konstanz) und Herrn Prof. James E. Hodder (University of Wisconsin-Madison). Meine

individuelle Leistung bei der Erstellung des Kapitels 1 ist 65%. Bei der Entwicklung des

theoretischen Konzept (25% der gesamten Arbeit) ist meine individuelle Leistung 30%, der

empirische Teil (50% der gesamten Arbeit) wurde vollständig von mir hergestellt, und beim

Zusammenschreiben des Kapitels (25% der gesamten Arbeit) ist meine individuelle Leistung

30%. Meine individuelle Leistung bei der Erstellung des Kapitels 3 ist 65% mit dem

prozentualen Verhältnis wie im Kapitel 1.