Are hedge funds of benefit for institutional investors in...

IN DEGREE PROJECT INDUSTRIAL ENGINEERING AND MANAGEMENT,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2017

Are hedge funds of benefit for institutional investors in a low interest-rate environment?

ADNAN AL-KHALAF

STEVE OSKAR GUSTAFSSON

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

INOM EXAMENSARBETE INDUSTRIELL EKONOMI,AVANCERAD NIVÅ, 30 HP

, STOCKHOLM SVERIGE 2017

Är hedgefonder förmånliga för institutionella investerare i en lågräntemiljö?

ADNAN AL-KHALAF

STEVE OSKAR GUSTAFSSON

KTHSKOLAN FÖR INDUSTRIELL TEKNIK OCH MANAGEMENT


by

Adnan Al-Khalaf Oskar Gustafsson

Master of Science Thesis INDEK 2017:162 KTH Industrial Engineering and Management

Industrial Management SE-100 44 STOCKHOLM


av

Adnan Al-Khalaf Oskar Gustafsson

Examensarbete INDEK 2017:162 KTH Industriell teknik och management

Industriell ekonomi och organisation SE-100 44 STOCKHOLM

Abstract

In this study, we have first investigated how Swedish corporate pension funds have responded to the prolonged low-interest rate environment by analyzing the annual reports of the 20 largest Swedish corporate pension funds. Of these 20, only 10 were used in this study. We were able to extract how these pension funds have allocated towards different asset classes since 2006. Our results suggest that Swedish corporate pension fund managers have increased allocation towards alternative investments and reduced allocation towards fixed income assets. Allocation towards equity assets is unchanged throughout the period. These findings suggest that Swedish corporate pension fund managers have managed to incorporate predictive information in their asset allocation based on the US pension fund market.

Secondly, we have constructed a replicating portfolio which represents the average allocation strategy of a Swedish pension fund. We investigated the impact of increasing allocation towards hedge funds. Our findings suggest that an optimal portfolio that maximizes the risk-adjusted return should invest 29% of its wealth towards hedge fund assets while increasing allocation towards fixed income assets and excluding equity assets from the portfolio. Key-words Pension fund, Hedge fund, Optimal portfolio, Strategic asset allocation

Master of Science Thesis INDEK 2017:162


Adnan Al-Khalaf

Oskar Gustafsson

Approved

Examiner

Cali Nuur Supervisor

Tomas Sörensson Commissioner

OE Capital Contact person

Magnus Oscarsson

Examensarbete INDEK 2017:162


Adnan Al-Khalaf

Oskar Gustafsson

Godkänt

Examinator

Cali Nuur

Handledare

Tomas Sörensson

Uppdragsgivare

OE Capital Kontaktperson

Magnus Oscarsson

Sammanfattning

I denna studie har vi först undersökt hur svenska pensionsstiftelser har reagerat på den långvariga lågräntemiljön genom att analysera årsredovisningarna för de 20 största pensionsstiftelserna. Av dessa 20 användes hälften i denna studie. Från årsredovisningar kunde vi avläsa hur pensionsstiftelserna valt att fördela sin allokering i olika tillgångslagar sedan 2006 fram till 2015. Våra resultat tyder på att svenska pensionsstiftelser ökat sin allokering i alternativa investeringar samt minskat sin allokering i räntebärande tillgångslagar. Allokeringen i aktiemarknaden har varit oförändrad under den studerade perioden. Dessa resultat tyder på att svenska förvaltare lyckats inkorporera ”predictive information” i sin allokeringsstrategi som är baserad på den amerikanska pensionsfondsmarknaden.

Vidare har vi byggt en replikerande portfölj som representerar en svensk pensionsstiftelses genomsnittliga allokeringsstrategi. Vi undersökte effekten av att öka allokeringen mot hedgefonder. Våra resultat tyder på att en optimal portfölj som maximerar den riskjusterade avkastningen bör allokera 29% av sin förmögenhet mot hedgefonder och samtidigt öka sin allokering mot räntebärande tillgångsslag och helt utesluta aktierelaterade investeringar.

Nyckelord

Pensionsstiftelse, Hedgfond, Optimal portfölj, Strategisk allokeringspolicy

Acknowledgements

We would give a special thanks to Magnus Oscarsson and Tom Engman at OE Cap-ital who have provided us with insight and inspiration when we most needed.

We would also like to thank Christer Wanngård and Per Olofsson at Sjunde AP-fonden for taking the time to talk to us and providing us with valuable insight.

Moreover, we want to dedicate a special thanks to Sadaf Nykiar at BNP Paribas forproviding us with financial data.

Lastly, we would like to thank Tomas Sörensson who have helped us in our missionto earn a Master of Science degree.

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Contents

List of Tables x

List of Figures xi

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problematization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Expected Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Assumptions and Delimitations . . . . . . . . . . . . . . . . . . . . . . 41.7 Subsequent Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Methodology 62.1 Research Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Sample Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Pension Fund’s Annual Reports . . . . . . . . . . . . . . . . . . 72.3.3 Historical Prices . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Quantitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.1 Statistical tools . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Source Criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.6 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.7 Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Literature & Theoretical Framework 133.1 What is a Hedge Fund . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 What is a Pension Fund . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.1 Allocation towards Hedge Funds . . . . . . . . . . . . . . . . . 173.3.2 Responses to Low Interest-Rate Environment . . . . . . . . . . 18

3.4 Portfolio Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4.1 Strategic Asset Allocation with Mean-Variance Optimization . 193.4.2 The Assumptions of Mean-Variance Optimization . . . . . . . . 23

3.5 Conditional Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . . . 24

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4 Results 264.1 Studied Pension Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2 Pension Fund’s Asset Allocation . . . . . . . . . . . . . . . . . . . . . 274.3 Distribution of Asset Returns . . . . . . . . . . . . . . . . . . . . . . . 294.4 Cumulative Return of Indices . . . . . . . . . . . . . . . . . . . . . . . 314.5 Efficient Frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.6 Cumulative Portfolio Return . . . . . . . . . . . . . . . . . . . . . . . 344.7 Drawdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Discussion 385.1 Pension Funds Asset Allocation During the Period . . . . . . . . . . . 38

5.1.1 Comparison to Previous Research and Theory . . . . . . . . . . 395.1.2 Analysis of Method . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 Optimal Allocation Policy . . . . . . . . . . . . . . . . . . . . . . . . . 415.2.1 Comparison to Previous Research . . . . . . . . . . . . . . . . . 435.2.2 Analysis of Method . . . . . . . . . . . . . . . . . . . . . . . . . 44

6 Conclusion, Implication and Future Research 466.1 Answering the Research Questions . . . . . . . . . . . . . . . . . . . . 466.2 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.3 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

References 49

A Appendices 53

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List of Tables

4.1 20 largest pension funds based on market capitalization . . . . . . . . 264.2 Pension funds included in the analysis . . . . . . . . . . . . . . . . . . 274.3 Portfolio allocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4 Portfolio allocations year-by-year . . . . . . . . . . . . . . . . . . . . . 284.5 Portfolio allocations domestic/foreign . . . . . . . . . . . . . . . . . . . 284.6 Skewness/Kurtosis test . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.7 Indices summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.8 Correlation matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.9 Default portfolio asset constraints. . . . . . . . . . . . . . . . . . . . . 334.10 Return to CVaR ratios for each constraints. . . . . . . . . . . . . . . . 344.11 Portfolio weights for each scenario optimal portfolio. . . . . . . . . . . 354.12 Drawdown for each scenario . . . . . . . . . . . . . . . . . . . . . . . . 37

x

List of Figures

1.1 Historical interest rate levels . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Illustration of the research process. . . . . . . . . . . . . . . . . . . . . . 63.1 Illustration of an efficient frontier . . . . . . . . . . . . . . . . . . . . . 224.1 Histogram of NHX and HOX returns . . . . . . . . . . . . . . . . . . . 294.2 Histogram of MSCI and OMXSPI returns . . . . . . . . . . . . . . . . 294.3 Histogram of WGBI and OMRX all Bond Index returns . . . . . . . . 304.4 Cumulative returns for studied indicies . . . . . . . . . . . . . . . . . . 314.5 Efficient frontiers with different HF constraints. . . . . . . . . . . . . . . . 344.6 Portfolio weights for each scenario optimal portfolio. . . . . . . . . . . 354.7 Cumulative returns for each scenario optimal portfolio . . . . . . . . . 364.8 Drawdown for the different hedge fund allocation policies . . . . . . . 37A.1 SEB-stiftelsen allocations . . . . . . . . . . . . . . . . . . . . . . . . . 53A.2 Svenska Handelsbankens Penssionsstiftelse allocations . . . . . . . . . 53A.3 Ericsson Pensionsstiftelse (A) allocations . . . . . . . . . . . . . . . . . 54A.4 ABB-Koncernens Pensionsstiftelse allocations . . . . . . . . . . . . . . 54A.5 Postens Pensionsstiftelse allocations . . . . . . . . . . . . . . . . . . . 55A.6 Praktikertjänst AB:s Pensionsstiftelse allocations . . . . . . . . . . . . 55A.7 Electrolux-koncernens Pensionsstiftelse allocations . . . . . . . . . . . 56A.8 Danske Bank, Sverige Filias Pensionsstiftelse allocations . . . . . . . . 56A.9 Stora Ensos Svenska Gemensamma Pensionsstiftelse allocations . . . . 57A.10 Byggnads Pensionsstiftelse allocations . . . . . . . . . . . . . . . . . . 57

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1 Introduction

In this chapter we will give a background of the existing problem followed by thepurpose, research question, assumptions and delimitations, and lastly the expectedcontribution of this study.

1.1 Background

The current market condition with its low interest rate environment presents chal-lenges for investors, in particular for institutional investors. Both short-term andlong-term interest rates have been at historic lows for several years in Sweden as wellas for other parts of the globe. In July 1995, the official Swedish bank rate was offeredat 8.91% compared to today’s record low -0.50%. During the same period we also seea similar downward trend in the Swedish 10-year government bond yield, exhibitinga decline from a 10.01% rate to today’s 0.66% (Svenska Riksbanken, 2017).

Figure 1.1: In blue: Swedish 10-year Government Bond Yield. In gray: Swedish officialbank rate. From June 1994 to February 2017 in percent (%).

The prolonged decline in interest rates have led to a substantial and lasting changein investment opportunities in financial markets. This unfamiliar new position forinvestors are acknowledged by Bams et al. (2016), who argues that the new climatepresents new challenges for pension funds and institutional investors. One conse-quence for pension funds have been a considerable increase in the present value ofliabilities for Defined Benefit (DB) plans. At the same time, due to lower expectedreturns, fixed-income as an asset class has become less attractive which has implica-tion for Defined Contribution (DC) as well as for DB funds. According to literatureon return predictability (Fama and French, 1989; Ang and Bekaert, 2007) there are

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expected responses from investors for these types of changes in investment opportu-nities, and also that long-term investors can benefit by incorporating this informationinto their asset allocation (Campbell et al., 2003; Hoevenaars et al., 2008). However,Bams et al. (2016) show that there seems to exist some discrepancy within the pen-sion fund market. They find that pension funds overall have reduced their allocationto equity and increased their allocation to fixed-income and alternative asset classesduring a transition into a low-interest environment, which is inconsistent with thefinancial literature. They come to the conclusion that pension funds are unable toincorporate this predictive information in an optimal way.

Bouvatier and Rigot (2013) investigated how US and Canadian pension funds be-haved during a lasting decline in long-term interest rates and where these pensionsfunds had to look for other sources of higher return. They describe how managementis reorganized in order to improve their strategic asset allocation. An importantaspect in this reorganization are the composition of a “satellite component” in theasset allocation. This satellite component looks for higher performance and betterdiversification (i.e., higher alpha and improved beta) and almost exclusively focus onalternative investments. They argue that the hedge fund industry, with its high andallegedly uncorrelated returns, seems therefore particularly attractive for this com-ponent.

Originally, investing in hedge funds has exclusively been investments for wealthy in-dividuals and families. First in early 2000’s did we begin to see increasing use ofhedge funds from institutional investors as they started to improve their diversifi-cation and start to allocate more wealth to alternative investments (Bouvatier andRigot, 2013; Preqin, 2016). Studies suggest that institutional investors seek to investin hedge funds in order to achieve; reduced volatility, diversification effect, and abso-lute return. In short, hedge funds are attractive to investors because they believe thathedge funds offer the potential to increase expected return at the expense of little orno change in portfolio risk. In 2016, there are over 5000 institutions tracked that areinvested in hedge funds, with this number growing on a daily basis (Preqin, 2016).While many would agree that hedge funds are attractive because of their potential toenhance risk-adjusted performance, they would also agree that allocations to hedgefunds are difficult to analyze. Their light regulation and specific governance raiseissues that exceeds those of traditional investments. Issues that include risks andchallenges in terms of: valuation, liquidity, and operational risk. Mainly it is the lackof transparency and limited information on the valuation of and the assets underlyingthe investments that give rise to the uncertainties for the investors (Bouvatier andRigot, 2013). These are factors that can be viewed as underlying reasons of some

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notable investors - including CalPERS1 and Railpen2 - withdrawing their hedge fundallocation from their portfolio recent years.

1.2 Problematization

The prevailing low-interest environment that we are experiencing are presenting newchallenges for institutional investors that traditionally and primarily are invested infixed income. Decline in interest rates consequently translates into decline in in per-formance and investors have to seek for other sources of return. Hedge funds havelong exhibit features of uncorrelated and absolute returns. These characteristics areattractive for investors and we are learning that the hedge fund industry is at itspeak level. Portfolio managers sees the asset class as an option in their aim to copewith declining performances. However, the hedge fund industry has previously hadnegative connotations in terms of security and transparency and has been criticizedby traditional investors. The discrepancy is becoming increasingly apparent as thegrowing criticism has led to notable institutions withdrawing their hedge fund al-locations. These uncertainties that the hedge fund industry demonstrates makes itdifficult for institutional investors to mandate more allocation towards the asset class.As managers sees the potential benefits of making hedge funds a more significant as-set class in their portfolio, they also recognize that there are uncertain implicationsthat it will bring and this makes it difficult to justify increased allocations.

1.3 Purpose

Firstly, the purpose of this paper is to analyze the pension fund industry and to assesshow it have responded to the prolonged low-interest rate environment. Secondly, theaim is to investigate implications of allocating pension fund assets to the hedge fundindustry. To evaluate the potential benefits of hedge fund investments with respectto risk-adjusted returns.

1.4 Research Questions

Given this purpose we will investigate and answer the following;

Research Question 1 (RQ1)"How has pension funds responded to the recent year’s low-interest levels?"

Research Question 2 (RQ2)1The California Public Employees’ Retirement System decided to divest its entire $4 billion from

hedge funds(Marois, 2014).2Britain’s railway pension scheme decrease their hedge fund allocation significantly (Cohn and

Kumar, 2017).

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"What hedge fund allocation policy contribute to the highest risk-adjusted return forpension funds?"

1.5 Expected Contribution

Due to the discrepancies brought up in Section 1.2 we aim to investigate the pensionand hedge fund industry in order to contribute to a more sound investment climate.Previous research have shown conflicting results regarding the performance of hedgefunds. This knowledge could be important for institutional investors as it could affectfuture investment decisions.

1.6 Assumptions and Delimitations

In this study, we have made a number of assumptions and delimitations which wewill describe below.

• In this paper we have conducted the study in the context of the Swedish market.An assumption made is therefore that behaviour and results that are derivedfrom the Swedish pension fund industry is a reflection of the general industry.

• We have assumed that Swedish corporate pension funds choose to invest inhedge funds in the Swedish and Nordic market with the motivation that home-bias is reasonable to assume. Also, we have delimited the study from the al-ternative to invest in hedge funds with certain strategies for pension funds.Therefore the NHX Composite index is regarded as a acceptable general repre-sentation for hedge funds investments for Swedish corporate pension funds.

• We have assumed that Swedish corporate pension fund’s real-estate investmentsconsist of direct ownership. This assumption motivates the use of ValuegardsNasdaq OMX Valueguard-KTH Housing Index (HOX).

• The cost of investing in different asset classes is something that this study hasnot accounted for and chosen to delimit.

• We have chosen to delimit this study to only regard risk as the movements ofthe prices/returns (variance) of the underlying assets.

1.7 Subsequent Chapters

The remainder of the paper is organized as follows:

• Section 2 clarifies the methodological approach of the paper.

• Section 3 will present background literature, review previous research, andpresent theories connected to the subject.

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• Section 4 presents the results of the empirical study.

• Sections 5 & 6 will assess the results and conclude the paper.

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2 Methodology

In this chapter, we will present the method that will be utilized in order to realize thepurpose of the study and to answer the research questions.

2.1 Research Process

Figure 2.1: Illustration of the research process.

Figure 2.1 demonstrates the research process that has and will be used in this pa-per. Firstly, we identified a problem which led to a problem formulation accordingto Chapter 1.2. This was followed by stating our research questions. Onwards, wewill conduct a literature review and an empirical study including analysis of finan-cial data. Once the results from the empirical study are extracted, the results willbe analyzed. The results and our analysis of the results will form the basis of ourconclusions and recommendations that we will conduct as a last step.

Given the purpose of this paper, we will conduct a literature review including pre-vious research within the field. This will be performed in order to clarify variousphenomenon’s in the right context and give us a deeper understanding of the studiedarea which in turn will help us answer our defined research questions. Once this isdone, we will acquire relevant theory that will help us to perform the research inan academically correct manner. An empirical study will be conducted through thegathering and calculations of financial data that will be described in the followingsections. Lastly, we will perform an analysis and discussion on the obtained resultsfrom the empirical data, based on the empirical study and the literature review –according to the illustrated research process in Figure 2.1.

This study will be performed in a deductive manner and findings from the quantitativestudy will be compared to theory and literature. This approach will help us answerour research question as general results can be found with such a research design. Bybeing aware that a deductive research design might lead us to be less critical, we willwork more critically throughout the study (Collis and Hussey, 2013).

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2.2 Literature Review

The literature that will be used in this study will be collected throughout the researchprocess, however primarily at the beginning. Firstly, a general search on topics regard-ing pension funds, hedge funds and low interest rate environment will be performedand will be narrowed down and become more specific as we identify relevant topics.These searches will be performed in search engines including KTH Primo, GoogleScholar, Diva portal and SSRN. Furthermore, articles and journals will also be partof our literature review. To increase validity of the study we will perform the searchesin both Swedish and English in order to capture what research that have been con-ducted in the Swedish financial market as well as the foreign, in particular Americanmarket. We are aware that there are differences in the Swedish and foreign markets assize and regulations differ and will therefore account for those differences in our study.

The following search words will be used in this study:Pension funds, Hedge fund, Hedge fund allocation, Pension fund allocation in lowinterest rate environment, Hedge funds and low interest rate environment, Hedgefunds and macro-economic variables, Optimal hedge fund allocation, Optimal portfoliotheory, Efficient frontier, Mean-variance framework, Expected Shortfall and Efficientfrontier

2.3 Data Collection

An important part of this study will be based on historical data. The data that willbe required for this study are: information on asset allocation from pension fund’sannual reports for the studied period, historical; hedge fund-, bond-, real estate- andstock- prices.

2.3.1 Sample Time

To increase the validity of the study we will select historical data with a time horizonof 10-years in order to capture different macro-economical states, including periods of:a prolonged decline of interest-rates, generally rising stock-prices, and generally de-clining stock-prices – starting from 2006. This selection is due to the impact all thesestates have on overall performance for investors and their strategic asset allocation.

2.3.2 Pension Fund’s Annual Reports

To get information on pension funds strategic allocation and how these have changedduring the time period, the collection of their annual reports and the interpretationsof these are to be conducted. This will help us answer research question 1. Swedishpension funds are obligated by Swedish regulations to provide an annual report toLänsstyrelsen and these reports are public and can be acquired from Länsstyrelsen.This fact supports the reliability of the study since the data gathering are fully

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replicable. Stockholms Länsstyrelse only store annual reports dated five years backin time and the rest is stored in Stadsarkivet. This means that Stockholm basedpension fund’s annual reports will need to be acquired from Stadsarkivet. SinceLänstyrelsen have a database of all Swedish pension funds, we will request a list of allpension funds with market capitalization information. We will then sort the list andcollect the twenty largest – in terms of market capitalization – pension funds. Oncethe list is obtained we will contact Länsstyrelsen and Stadsarkivet and request theannual reports for each pension fund in our obtained list. From the annual reportswe will be able to extract important information about allocation for each pensionfund. We have chosen a time frame of 10 years, between 2006 and 2015, in order torecognize if the allocation policy have changed over time. The pension funds thatwill be studied can be observed in the table below.

2.3.3 Historical Prices

In order to answer our second research question; “what hedge fund allocation policycontribute to the highest risk-adjusted return for pension funds?", we will need toreplicate a pension fund portfolio which typically consists of the asset classes: fixedincome, real estate, stocks and hedge funds. Through the analysis of the annualreports we will be able to get information on the asset class allocation structure forpension funds. Index data will be used as a proxy for each asset class. This impliesthat our study will be based on secondary data (Collis and Hussey, 2013) meaningthat we will need to use reliable databases. Since we will use index data for our study,we will need to ensure that their way of collecting data can be trusted and we willneed to assure that we use indices that represent Swedish pension fund’s allocationstrategies by using the correct markets. This is an important aspect to consider sincewe want to make a comparable study. Furthermore, monthly data will be used foreach asset class.

Stocks & Equity Funds

When replicating a pension fund’s portfolio we will group stocks and equity fundstogether. We will however differentiate between domestic and foreign stocks and eq-uity funds.

Swedish stocks and equity funds will be represented by OMX Stockholm PI In-dex. This is an all-share index that represents the publicly traded stocks on theStockholm Stock Exchange with the aim to represent the overall development of themarket (NASDAQ, 2017).

Since Swedish pension funds allocate heavily towards Swedish stocks and equity fundswe will choose to separate Swedish and foreign stocks and have two different indices.Foreign stocks and equity funds will be represented by MSCI World Index . This

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index captures large and mid cap companies across 23 developed markets, includingSweden. With that said, we are aware that our replicating portfolio will be somewhatover-weighted towards Swedish stocks investments since MSCI World Index includeSweden, and this is something the reader should be aware of. We will not try to iden-tify the exact weighting towards each instrument that will give the best risk-adjustedreturn, we are rather looking to find the best allocation strategy.

The reason we will pick developed markets is because pension funds are risk averseand emerging markets could be regarded as high risk. Picking emerging marketswould not represent a Swedish pension fund’s asset allocation in a correct manner.

Bonds

Domestic bond investments will be represented by OMRX All Bond Index. TheOMRX index represents the value growth for liquid interest-bearing Swedish bonds.The composite is based on bonds issued by the Swedish National Debt Office andSwedish mortgage institutions (NASDAQ, 2010)

Foreign bond investments will be represented by Citibank’s World GovernmentBond Index (WGBI). This index measures the performance of fixed-rate, local cur-rency, investment grade sovereign bonds. It is a widely used benchmark that currentlycomprises sovereign debt from over 20 countries, denominated in a variety of curren-cies. The WGBI provides a broad benchmark for the global sovereign fixed incomemarket (Citi, 2017).

Real Estate

Real estate investments will be represented by NASDAQ OMX Valueguard-KTHHousing INDEX (HOX). This index is based on hedonistic price model that is updatedmonthly. HOX collects that data from Mäklarstatistik AB and is based on actualtransactions. However, HOX collects data only on residential real estate that are soldas single family homes.

Hedge Funds

Hedge Fund investments will be represented by Nordic Hedge Index Composite (NHX).NHX tracks Nordic hedge fund manager’s performance on a monthly basis. It isimportant to highlight that NHX is representative for the industry and not of aninvestment hedge fund strategy in particular. In this study, we have delimited theuse of particular hedge fund strategies and used NHX as overall representation of theasset class. The index is an equally weighted index towards the following hedge fundstrategies:

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• Equity focused funds - funds trading equity and equity derivatives 3.

• Fixed Income funds - funds trading fixed income and derivatives3.

• Multi-strategy funds - funds are classified as multi-strategy if less than 80%of the fund’s activities comes from one particular classification category3.

• Managed Futures/CTAs - funds trading listed financial and commodityfutures and foreign exchange, usually employing a systematic, model-drivenapproach3.

• Fund of hedge funds - funds investing in other hedge funds, regardless of feestructure3.

2.4 Quantitative analysis

The collected data from the annual reports will give us information about pensionfunds allocation policies, i.e. weightening towards each asset class. In order to get un-derstanding and inference about the risk-return structure for pension funds allocationpolicies, this information will be used together with portfolio theory (as explained inSection 3.4). And together with the collected historical data from the indices we willbe able to calculate efficient frontiers, which are an integral aspect in portfolio theoryfor the risk-return analysis.

By analyzing the efficient frontier we will be able to analyze what type of hedgefund allocation policy that contribute to the highest risk-adjusted return for corpo-rate pension funds. One can state that portfolio A outperforms portfolio B if theexpected return of portfolio A is greater than the expected return of portfolio Bwhile the risk of portfolio A is lower or equal to portfolio B. It is therefore ofinterest to investigate the shape of the efficient frontier for the purpose of this study.By definition, no rational mean-variance investor would choose to hold any portfoliothat is not located on the efficient frontier. The efficient frontier can be defined asthe locus of all non-dominated portfolios in the mean-variance space (Danthine andDonaldson, 2005).

Using historical data to predict future outcomes is a common approach but still anassumption that needs to be highlighted. We will use historical data as a proxy forfuture outcomes, meaning that we will assume that historical information is a goodindication of future outcomes. Furthermore, we wish to highlight that these resultswill be an approximation as there are other risks that needs to be accounted for suchas currency risk, illiquidity risk, and market risk.

3 Hedge fund information gathered from Hedge Nordic’s website: http://nhx.hedgenordic.com/Portfolio.aspx?pxid=156pst=7

10

The calculations for the quantitative analysis are to be conducted in MatLab. Thebuilt in PortfolioCVaR() function are used to create a PortfolioCVaR object for con-ditional value-at-risk portfolio optimization and analysis. The PortfolioCVaR objectworkflow for creating and modeling a CVaR portfolio is:

- first create the object using function PortfolioCVaR(),

- define the asset returns and scenarios using function setScenarios(),

- specify the CVaR portfolio constraints and bounds using functions setDefault-Constraints() and setBounds(),

- specify probability level which the conditional value-at-risk is to be minimizedusing function setProbabilityLevel(),

- and estimating the efficient portfolios and frontiers using function estimateFron-tier().

2.4.1 Statistical tools

In the quantitative study there are certain statistical assumptions that has to beinvestigated. To assure that the inference from the quantitative analysis are validfollowing statistical tools will be used in the calculations.

SkewnessSkewness is a statistical measure used to describe the asymmetry of a distributionaround the mean. A negative skew indicates that the tail on the left side of theprobability density function is longer or fatter than the right side. Conversely, positiveskew indicates that the tail on the right side is longer or fatter than the left side.Skewness measure does not distinguish between the shape of the distribution, i.e.long or fat. As a consequence, skewness does not obey a simple rule. For instance, askewness value of zero means that the tails on both sides even out overall implying asymmetric distribution. However, this could also mean that one tail is long but thinand the other being short but fat.

KurtosisKurtosis is another statistical measure used to describe the shape of a given distri-bution. This measure is related to the tails of a distribution and a higher kurtosisnumber is the result of infrequent extreme deviations (or outliers), as opposed tofrequent modestly sized deviations.

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DrawdownDrawdown is a common risk measure that measures any time the cumulative returnsdips below the maximum cumulative return. Drawdowns are measured as a percent-age of the maximum cumulative return, in effect, measured from peak (top) to thesubsequent trough (bottom).

2.5 Source Criticism

One way to ensure the use of high quality sources is by finding three separate sourcesof information that leads to the same conclusion. This method will be used to thehighest degree possible throughout this study. In the case where three sources aredifficult to find, we will at least use two different sources that leads to the sameconclusion. A single source that cannot be confirmed by another will thus not beused. We will use published books and articles as our primarily sources.

2.6 Reliability

According to Collis and Hussey (2013) results are considered to be reliable if a re-peat study obtains the same results as the original study. For an empirical study ofquantitative nature it is therefore important to clearly describe the research design.The first part of this study is based on annual reports that can be obtained fromLänsstyrelsen and Stadsarkivet as they are open to the public. This means that any-one would be able to obtain the same results given that the same pension funds areanalyzed. However, some minor deviations might happen since interpretations andassumptions on what investment category an investment should represent will needto be made when none or limited information is available about a specific investment.

The second part of the study would also fulfill the reliability requirement as we havespecified each index that will be used to represent each investment category. Wehave also specified the studied period and the research design, i.e. maximizing therisk adjusted return based on an appropriate risk measure. Although some deviationsregarding the exact weighting towards each asset class might take place, the sameconclusions will be obtained. This means that this study is reliable and repeatabilitycan be achieved.

2.7 Validity

Validity refers to the quality of a test and if it measures what is purported to measure(Collis and Hussey, 2013). In a quantitative study an important part is the use ofa suitable method. In this study, we will investigate the assumptions of the mean-variance framework and based on the results choose appropriate risk-measure thataccount for the nature of the distributions of the returns for the studied asset classes.

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3 Literature & Theoretical Framework

In this section we will present background information about Hedge funds and Pensionfunds, review previous research on low-interest environments and on asset allocationto hedge funds during such conditions, and lastly present relevant theory connected tothe subject to be studied.

3.1 What is a Hedge Fund

Hedge funds are a part of the investment category that are seen as ‘alternative’ whencompared to traditional asset class investments, e.g. mutual funds, equity and fixedincome. Generally, alternative investments has more unregulated investment policies(AIFM - Directive 2011/61/EU). Hedge funds began as investment partnerships thatcould take long and short positions. Since then they have evolved into multifacetedorganizational structures that are difficult to put into simple definitions. However, anumber of features that characterizes hedge funds includes flexible investment strate-gies, relatively sophisticated investors, substantial managerial investments, and strongmanagerial incentives (Ackermann et al., 1999).

Ackermann et al. (1999) continues explaining that, due to a limited number of in-vestors, hedge funds typically are largely unregulated. This allows them to be ex-tremely flexible in their investment options allowing them to use short selling, lever-age, derivatives, and highly concentrated investment positions, in order to enhancereturns or reduce systematic risk. They also have the option to move quickly acrossdiverse asset classes in an attempt to time the market.

These structural aspects of hedge funds are in sharp contrast to the organizationalstructure of the more common investment option in mutual funds. Mutual fundsare often regulated by the the financial supervisory authority4 and have prospectusdisclosure requirements, in order to keep their investors informed about their invest-ments and also limit potentially risky activities. These regulations and disclosurerequirements generally limits mutual funds of using derivatives, short selling, andconcentrate investments.

A downside for this flexibility that hedge funds are favoured by, can be that they arefaced with advertising restrictions together with general capital inflow difficulties.Mutual funds and other traditional investment institutions can gather a lot of fundinvestors by promoting simple understandable strategies. Mass selling of hedge fundstrategies tend to be more difficult to promote since these strategies usually are toocomplex for the typical investor to comprehend (Stulz, 2007). Hedge funds there-

4Finansinspektionen (FI) is the Swedish counterpart.

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fore typically attract mainly institutions and wealthy individual investors. These areinvestors who agrees to conditions which include higher minimum investment limitsand liquidity lock-up periods.

Hedge funds are also characterized by strong performance incentives. Lan et al.(2013) studies the economics of hedge funds and in particular the management com-pensation. In their paper they explain that the typical management compensationfor hedge funds features both management fee and performance-based incentive fees.The management fee is charged as a fraction of the Asset Under Management (AUM),e.g., 2%. However, what often differentiates hedge funds from mutual funds is theincentive fee. This fee is calculated as a fraction of the fund profit, e.g., 20%. The“two-twenty” compensation is often viewed as a industry norm.

Fung and Hsieh (1997) investigates the characteristics of the dynamic trading strate-gies of hedge funds, where they also discuss compensation structures as an underlyingfactor of the fund performance. For mutual funds, most managers have investmentmandates with relative return targets. As they are typically limited to low or noleverage and also constrained to hold assets in a well-defined number of asset classes,their mandates are to meet or exceed the returns on these asset classes, e.g., a stockmarket benchmark index (Fung and Hsieh, 1997; Al-Sharkas, 2005). Knowing thatthe fund inflows have been going to the top-rated funds, rated according to their re-spective benchmark, and that mutual fund managers are compensated based on theamount of AUM. Thus, managers have an incentive to outperform their benchmarkin order to increase their AUM and ultimately their compensation. This implies thatthey are likely to generate returns that tend to be highly correlated to the return ofthese benchmarks.

Hedge fund managers on the other hand derive a great deal of their compensationfrom incentive fees, paid only when the manager makes positive return. Also, a com-mon addition in their incentive contracts is the “high-water-mark” (HWM) feature,which keeps track of the maximum value of the invested capital and requires themto make up all previous losses before an incentive fee is paid (Fung and Hsieh, 1997).These conditions typically gives hedge fund managers investment mandates with ab-solute return targets, regardless of the market environment. To achieve absolutereturn they utilize their more flexible investment options that allows them to chooseamong more asset classes and to employ dynamic trading strategies that frequentlyinvolve leverage, short sales, and derivatives. This implies that these managers aremore likely to generate absolute returns, contrary to mutual funds more relative re-turn.

Since hedge funds have a greater flexibility in their investment options it allows man-agers to employ various investment strategies. In order to compare performance,

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risk and other characteristics, it is helpful to categorize hedge funds by investmentstrategies. A common way to classify hedge funds was described by Fung and Hsieh(1997) as a distinction of the “style” and “location” of the fund. Here, “style” refersto the type of position the fund manager is taking, such as taking long and/or shortsecurity positions e.g., betting on particular type of corporate events, or maintainingmarket neutrality. The concept of style is not relevant with mutual funds since im-plicitly this categorization has buy-and-hold, long-only style. A standard style herewould then be something like; small cap value stock or large cap growth stocks. Thestylistic differences for mutual funds involve only the location variable. With “loca-tion” it is referred to which assets and asset classes the strategy is applied to, suchas equity, fixed income, currencies, commodity, as well as the geographical location.Another related approach is to separate hedge funds according to whether they aredirectional or market neutral (Connor and Woo, 2004). Directional funds take betson market movements and consequently have a return strongly correlated with themarket. Market neutral funds on the contrary keep a low correlation with the overallmarket return by applying derivatives and short positions. Hedge fund strategies arecontinually changing, limiting the attempts of establishing any formal classificationfor hedge funds. Hedge Fund Research (HFR), one of the main hedge fund databases,has however constructed a ‘Strategy Classification System’ for all investment man-agers present in their HFR Database, grouping them under five broad themes: equityhedge, event driven, relative driven, macro, and fund of hedge funds.

3.2 What is a Pension Fund

Institutional investors are defined as the professional management of assets on behalfof the majority of individuals. Under this definition pension funds are categorized asinstitutional investors (Basile, 2016). The characteristics of a pension fund can bedescribed as a pool of assets that is formed with contributions to a pension plan forthe purpose of financing pension plan benefits. The fund members have some claimagainst the assets of the pension fund. A pension fund can take on two differentforms, either a special purpose entity with legal personality or a legally separatedfund without legal personality managed by a financial institution on behalf of the fundmembers (Basile, 2016). Pension funds are subject to different regulatory frameworkcompared to other institutional investors.

Swedish Regulations & Policies

A pension fund is an independent legal entity with its own board according to Swedishlaw. Being a legal entity, a Swedish pension fund must comply with the rules set byAct (1967:531) also called "Tryggandelagen" (Länsstyrelsen, 2017), which in the re-mainder of the paper will be referred to as the "assurance act". The assurance actconsists of regulations regarding general provisions, accounting and supervision to

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mention a few (Sveriges Riksdag). The purpose of a Swedish pension fund can onlybe to secure the promise of the employer’s pension obligations (Finansinspektionen,2017). For pension funds allocating pension to at least 100 employees additional spe-cial provisions apply, e.g. regarding allocation. These provisions are supervised bythe Swedish Financial Supervisor Agency (FSA), also known as Finansinspektionen(FI) (Länsstyrelsen, 2017).

A corporation that form a ’pension fund’ manages the occupational pension in the’pension fund’ and it is seen as an alternative to hiring an insurance company (Palm,2014). In March 2017 there are in Sweden 1657 registered and active pension funds,the pension fund with the greatest asset value being "Konsumentkooperationens pen-sionsstiftelse" with 22’938’769’000 SEK to manage5.

The assurance act has been in order since 1968 and in the act it is stated that theemployer is indefinitely responsible for its pension commitments and that a pensionfund cannot promise the pension. In other words, a pension fund is not entitled to payout pension. Instead, the assets in the pension fund functions as security and the em-ployer is entitled to claim compensation for the pension costs that arise (Palm, 2014).

Each and every business is entitled to form a pension fund with the purpose of secur-ing their employees occupational pension. Once the employer sets up a pension fund,it is up to the employer to make the necessary depositions. There are no restrictionsor provisions regarding the magnitude of the first deposition (Palm, 2014). The em-ployer is also to provide an objective description where it should be stated whomare covered by the pension fund’s insurance. The provided objective description areinstalled as the pension fund’s statues/bylaws where it should also be stated thenumber of members the pension fund’s board is to have. According to the assuranceact the employer and the beneficiaries must nominate as many members of the boardeach, with the aim that no single party solely determine the future of the pensionfund (Palm, 2014). The board of the pension fund are entirely responsible for themanagement of the funds so as to best serve the pension fund’s defined objectives.The board are entitled to employ external managers, however the board can neverneglect the responsibility for the management of the funds (Palm, 2014)

In the assurance act it is stated that the allocation of capital should be satisfactorywithout any further description regarding what satisfactory allocation implies. How-ever, according to Domstolsverket (1979) satisfactory allocation should be interpretedsuch that risk outweighs potential returns. Further guidelines are presented by theSwedish government proposition 2004/05:165 where it is stated that the prudent per-son rule should be the fundamental principle when allocating capital in a pension

5Data obtained from Länsstyrelsens foundation register 22nd March 2017.

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fund (2004/05:165, 2005). The prudent person rule is aimed towards the decisionprocess rather than the result of the allocated capital. This implies that a risky allo-cation could be regarded to follow the prudent person rule if the allocation decisionis based on a well defined strategy. Conversely, a low risk allocation could breach theprudent rule principle (2004/05:165, 2005). Moreover, the members of the board areresponsible for establishing an allocation policy and an impact analysis. The alloca-tion policy is the board’s main regulatory document and should be the basis of allallocations. The impact analysis is a report aimed to account for the financial con-sequences of the pension fund’s allocation policy/strategy (Finansinspektionen, 2005).

Another restriction a Swedish pension fund must comply with regarding allocation isthe fact that they are not allowed to hold any stocks in the pension fund’s companywithout the consent of the supervisory authority, i.e. Finansinspektionen (Palm,2014). However, a pension fund is allowed to give a loan to the company which issomething that favours both parties. The pension fund earns interest returns andthe company is allowed to reduce its pension costs by the fact that the interest coststhat normally would be payed to a bank is now in fact payed to the pension fund.Such loan can only take place if there exists a reassuring security. Furthermore, thepension fund is allowed to give compensations to the company that is equivalent tothe company’s pension costs. This is possible if the net worth is higher than the valueof the pension commitments. The pension fund is also allowed to give compensationsfrom the year’s returns even though the net worth is lower than the value of the pen-sion commitments as the pension funds assets are not depleted if the compensationis from the year’s returns (Palm, 2014).

Moreover, pension funds should draw up annual reports independent of the com-pany according to the assurance act. The annual report should include an incomestatement, a balance sheet, notes and a management report. It is also mandatoryfor a pension fund to present the capital value of the pension commitments in themanagement report. A pension fund is obligated to have an accountant (Palm, 2014).

3.3 Previous Research

3.3.1 Allocation towards Hedge Funds

Hoevenaars et al. (2008) considers strategic asset allocation of long-term investorswho face risky liabilities in the US in their paper and asks the question; is there morein the investment universe than stocks and bonds? In order to do this and studythe risk characteristics of assets – other than just stocks and bonds – they extendthe term structure of the risk-return trade-off6 for assets like commodities, credits,real estates and hedge funds. To answer the question they derive the optimal asset

6Explained by Campbell and Viceria (2005).

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allocation and compare it with a suboptimal portfolio that is restricted to stocks, T-bills and bonds only. They show that the costs from investment constraints excludinghedge funds and credits are high for the long-term investor. The high sharpe ratiothey derive implies that hedge funds are very attractive from a return enhancementperspective as well as liability hedge perspective.

Favre and Galeano (2002) recognizes the problems of non-normal distributed returnsfrom hedge funds in their empirical study of a Swiss pension fund investing part of itswealth in hedge funds. They show that the traditional mean-variance framework as aperformance measure is not optimal for hedge funds due to survivorship bias, liquidityrisk, limited information on the valuation of the assets underlying the investments,etc. (Bouvatier and Rigot, 2013; Ackermann et al., 1999). Favre and Galeano (2002)develops a method based on a modified Value-at-Risk model to take into account thenon-normality of asset returns. They show that even if you apply a Value-at-Riskmodification and correcting for the non-normality, it is still beneficial – albeit not ashigh as predicted taking biases and liquidity risk into account – to invest in a welldiversified hedge fund portfolio for an institutional investor.

3.3.2 Responses to Low Interest-Rate Environment

How should pension funds and institutional investors respond to a prolonged lowinterest rate environment according to the models of strategic asset allocation? Re-sults from the literature implies that they should increase allocations to equity andreduce allocations to bonds. Past empirical research has identified various economicvariables as predictors for expected returns. Some of these variables are: short-terminterest rate (Campbell, 1987; Ang and Bekaert, 2007); the yield spread betweenlong-term and short-term interest rates (Shiller et al., 1983; Fama and French, 1989;Cochrane and Piazzesi, 2005); the dividend-price ratio (Campbell and Shiller, 1988;Fama and French, 1988). Bams et al. (2016) show how these predictive macroeco-nomic variables can be used when deriving optimal portfolios for long-term investorslike pension funds. Using an approximate solution method for the optimal portfolio7

they show that for investors who faces time-varying investment opportunity (i.e. alasting change in investment opportunities), portfolio allocation to stocks is; neg-atively related to short-term interest rates, negatively related to yield spread andpositively related to dividend-price ratio8. This indicates that when the short-terminterest rates decline, the allocations to stocks should increase in a portfolio. More-over, Ang and Bekaert (2007) shows that when short-term rates are low, the returnson equity tend to be high. In conjunction with these findings, Bams et al. (2016)exploits the observation using the time switching market-timing model for asset al-location9. The results again show that allocation to equity should be high when the

7Developed by Campbell et al. (2003).8Opposite sign for excess bond returns.9Developed in Ang and Bekaert (2002)

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interest rates are low.

These findings imply that in low interest rate environments pension funds and insti-tutional investors should increase allocations to equity class and decrease allocationto fixed income if they were to follow the finance literature. However, Bams et al.(2016) have analyzed the fundamental changes in portfolios of pension funds in NorthAmerica and identifies some discrepancy given these expected responses. Overall theyfind that pension funds have reduced their allocation to the equity asset class andincreased their allocation to fixed income and alternative assets. This is inconsistentwith the literature on return predictability from a market timing perspective. Theysuggest that pension funds are unable to incorporate these predictive information(e.g. that low-interest rates levels signals increase to equity and decrease to fixedincome) in their strategic asset allocation.

When there is a decline in long-term interest rates, institutional investors and pensionfunds will have to look for other sources to achieve higher and sometimes requiredreturns. Consequently, they tend to steadily reorganize their management in order toimprove their strategic asset allocation. They employ a ‘core-satellite’ organizationstructure (Bouvatier and Rigot, 2013). It consists of defining a strategic asset alloca-tion where the assets are divided into two components: core and satellite. The corecomponent’s (75%-90%) objective is to avoid risks related to the variability of theassets and aims to match liabilities of the pension funds. The assets can be mangedeither in an active or passive way, as well as internally or externally. Generally, theseassets are invested in traditional asset classes in liquid markets, e.g., bonds and largecap equity. The satellite component (10%-25%) aims to achieve higher performance(by generating positive alpha returns) and for a better diversification (by improvingbeta). The satellite is exclusively managed externally since these investments requiresspecific expertise that pension funds usually do not have in-house. Consequently, thehedge fund industry seems particularly attractive for the satellite component, giventheir objective of high and allegedly uncorrelated returns.

3.4 Portfolio Theory

3.4.1 Strategic Asset Allocation with Mean-Variance Optimization

A key step towards a quantitative and disciplined approach to strategic asset al-location was taken by Harry Markowitz, in his seminal article “Portfolio Selection”(Markowitz, 1952). The ideas expressed in that work constitutes the basis of what hasto come to be known as Modern Portfolio Theory, Mean-Variance Optimization andMean-Variance analysis. Further achievements acknowledged to Markowitz; the def-inition in technical and formal terms of the concept of diversification, and the notion

19

of the investor as a decision-maker in a two dimensional space, are worth mentioningand are integral to the theory (Basile, 2016).

Markowitz’s Mean-Variance Framework

The concept of diversification is quantified with reference to the statistical notionof covariance/correlation between asset classes. The portfolio variance are therebydefined not only in terms of the stand-alone risk of the asset classes, but also in termsof how one asset class interacts with another.

Regarding the investor as a decision-maker Markowitz (1952) rejected, unlike mostprevious authors, an investor profile aimed exclusively on maximizing expected re-turns. Instead he preferred an investor profile that considers expected return as‘something desirable’ and variance in returns as ‘something undesirable’. The de-cision criterion known as the mean-variance principle derives from this notion ofinvestor preference (Basile, 2016). The decision-criterion stipulates that for two port-folios, A and B, with expected return µA and µB and expected risk, σA and σB , Acan be said to dominate (be certainly preferable to) B if:

µA > µB and σA ≤ σB

with at least one verified strong inequality. Standard deviation of the return is thetraditional statistical measure of the risk and corresponds to the dispersion of thereturns around the mean.

Before introducing the portfolio optimization model, we first introduce some of theterminology that will be used10. The composition of a portfolio ofN risky asset classes(with N ≥ 3) is given by the vector w of size N × 1, where wi is the percentage ofasset class i in the portfolio:

w =

w1

w2

...

wi

...

wN

where

∑Ni=1 wi = 1 or, equivalently, w’e = 1 with e’ = [1,1,...,1].

10Most of the theory and concepts regarding portfolio theory as reported in this section are takenfrom Basile (2016) textbook ’Asset Management and Institutional Investors’.

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The properties of expected return and risk of the single asset classes can be repre-sented in the vectors µ and σ, respectively, both of dimension N × 1:

µ =

µ1

µ2

...

µi

...

µN

,σ =

σ1

σ2...

σi...

σN

.

The correlation matrix, C, and the covariance matric, Σ, both of dimension N ×N ,show information on the interaction (i.e. the relationship) between possible pairs ofasset classes. This can be represented with the symbol ρij for correlation and thesymbol σij for covariance.

C =

ρ11 ρ12 . . . ρ1i . . . ρ1N

ρ21 ρ22 . . . ρ2i . . . ρ2N...

.... . .

......

...

ρi1 ρi2 . . . ρii . . . ρiN...

......

.... . .

...

ρN1 ρN2 . . . ρNi . . . ρNN

, Σ =

σ11 σ12 . . . σ1i . . . σ1N

σ21 σ22 . . . σ2i . . . σ2N...

.... . .

......

...

σi1 σi2 . . . σii . . . σiN...

......

.... . .

...

σN1 σN2 . . . σNi . . . σNN

The terms ρii and σii on the main diagonal of the matrices C and Σ respectivelydenote correlation and covariance of an asset class with itself, correpsonding to thevalues 1 and σ2

i . The terms σij (i.e. not on the main diagonal of the matrix Σ) isequivalent to the expression ρijσiσj .

Using the stated parameters and notations, the expected portfolio return µP can becalculated by either (3.1a) or (3.1b):

µP =

N∑i=1

wiµi (3.1a)

µP = w’µ. (3.1b)

Conversely, portfolio risk is expressed as the variance σ2P and can be obtained using

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either (3.2a) or (3.2b):

σ2P =

N∑i=1

N∑j=1

wiwjσij orN∑i=1

N∑j=1

wiwjσiσjρij

orN∑i=1

w2i σ

2i +

N∑i=1

N∑j=1j 6=i

wiwjσij (3.2a)

σ2P = w’Σw. (3.2b)

Efficient Frontier

As of the approach to the strategic asset allocation, consider a rational investorwho acts in a single period investment horizon with the aim of maximizing expectedutility, i.e. behaving myopic. For each level of expected return an investor wouldchoose – in the feasible set – the portfolio with the minimum variance. The portfolioscorresponding to this description can be called mean-variance efficient portfolios.Within the risk-return space, the set of mean-variance efficient portfolios are identifiedas the efficient frontier. Essentially, the efficient frontier provides the portfolios withthe best trade-off between expected return and risk, for each level of expected returnor for each level of risk. The portfolios below the efficient frontier are called eitherdominated or inefficient portfolios – those above the frontier are not among the feasibleportfolios. The portfolio with the smallest possible variance, on the efficient frontier,is often referred as the global minimum-variance portfolio (GMVP).

Figure 3.1: Feasible set of portfolios and the efficient frontier. Graph from (Basile, 2016).

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The mean-variance efficient frontier are derived by the application of an algorithmformulated by Markowitz to address the so-called Mean-Variance Optimization prob-lem.In general terms, an optimization problem/algorithm has three basic components:

• An objective function, that is, a mathematical expression of what we want tooptimize (i.e. minimize or maximize)

• A set of decision variables (initially unknown, by definition) on which the valueof the mathematical expression to be optimized depends on

• A set of restriction, by the form of equality and/or inequality constraints, thatare to be applied to some or all of the set of decision variables.

The Mean-Variance Optimization (MVO) seeks to establish what weight to assignthe asset classes in order minimize portfolio risk (standard deviation or variance) fora targeted expected portfolio return (µ∗P ), while ensuring the sum of the weights isequal to 1 (i.e. 100% investment) and that each weight is non-negative.In algebraic terms, the Mean-Variance Optimization can be expressed as:

minw

N∑i=1

N∑j=1

wiwjσij

subject toN∑i=1

wiµi = µ∗P

N∑i=1

wi = 1

wi ≥ 0

or

minw

w’Σw

subject to

w’µ = µ∗P

w’e = 1

[w] ≥ 0.

(3.3)

This formulation of the Mean-Variance Optimization has: the equality constraintcorresponding to the total portfolio weights must equal 1 (the budget constraint),the inequality constraint corresponding to that short selling of any asset class is notpermitted (the long only or non-negativity constraint).

3.4.2 The Assumptions of Mean-Variance Optimization

To build strategic (policy) portfolios with the Mean-Variance Optimization as a tech-nique and criterion implies that you are aware of the underlying assumptions which itis based upon. The assumptions concerns the investors’ preferences (i.e. the decision-making process) and the behaviour of the series of asset class returns. More specifi-cally, the Mean-Variance Optimization assumes that:

• Investors have a single-period investment horizon

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• The returns of the asset classes are normally distributed (Gaussian distribution),i.e., that they conform to the classic "bell-curve". More specifically, that theyfollow a multivariate normal distribution

• Investors present a quadratic utility function.

The first hypothesis concerns the myopic, single-period nature of the model. To il-lustrate the importance of this element the words of Mossin (1968) gives a accurateinterpretation: "By a single-period model is meant a theory of the following structure:the investor makes his portfolio decision at the beginning of a period and then waitsuntil the end of the period when the rate of return on his portfolio materializes. Hecannot make any intermediate changes in the composition of his portfolio. The in-vestor makes his decision with the objective of maximizing expected utility of wealthat the end of the period (final wealth).” By having this framework you characterizethe return environment as a stationary asset class return distribution. This impliesconstant relative risk aversion, no intermediate flows on the part of the investor (i.e.portfolio return can be considered path-independent), and the absence of transactionscost and serial auto-correlation.

The assumption of normal distribution of asset class returns makes it possible for theextensive description of the return behaviour to be digested into the estimated firsttwo statistical moments, i.e., expected return and variance. It allows for the easyaggregation of risks across assets and over time.

The third hypothesis of the model considers the "rule" that investors assign a value totheir level of satisfaction that depends on the possible choices that different portfoliosoffers. The rule corresponds to quadratic utility function, as it allows individualinvestors’ expected utility to depend exclusively on mean and variance.

3.5 Conditional Value-at-Risk

When making investment decision, an investor has to balance between risk and re-turns. Markowitz (1952) established a framework for investment decision where theinvestor maximizes the expected return of the portfolio and minimizes the risk, mea-sured by the variance of the portfolio. To use portfolio variance as the risk measurehas its limitations. Variance is a measure of the volatility of returns and is a sym-metrical measure that does not take into consideration the direction of the movementof the volatility. An asset experiencing better than expected return are consideredas risky as an asset suffering from lower than expected return. Other approachesare available to measure the portfolio risk, the most traditional being Value-at-Risk(VaR). Some of the most agreed on advantages for the use of VaR as a risk measureis:

• It measures risk with a simple and understandable number,

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• It is recognized by practitioners,

• Many academic studies have been done on the subject,

• It measures the downside risk (contrary to a symmetrical measure),

• It is easy to understand and implement.

In short, VaR answers the question: what is the maximum loss with a specifiedconfidence level? In this study, however, we will be using Conditional Value-at-Risk(CVaR) as risk measure. CVaR is also known as mean shortfall, mean excess loss, ortail VaR. Although VaR is a very popular measure of risk, it has some undesirablemathematical characteristics, and it assumes joint normal (or log-normal) distributionof the underlying market parameters (Uryasev, 2000). CVaR on the other hand is amore consistent measure mainly since it has sub-additive and convex properties. Also,since CVaR always is greater or equal to VaR, the minimization of CVaR also leadsto near optimal solutions in VaR terms. Moreover, these two measures are equivalentwhen the return-loss distribution is normal (Rockafellar and Uryasev, 2000). Anotheradvantage for the use of CVaR is that it can be optimized using linear programming(LP) and nonsmooth optimization algorithms, which allow handling portfolios withvery large numbers of instruments and scenarios. A description of the implementationand in-depth approach for minimization of CVaR and optimization problems withCVaR constraints can be found in Uryasev (2000) review paper.

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4 Results

In this section we will presents the results from the empirical study and the quantita-tive approach, which will later be used to answer our research questions.

4.1 Studied Pension Funds

From the list obtained from Länsstyrelsen, the following pension funds were chosen tobe analyzed further. These were chosen by market capitalization (20 largest pensionfunds).

Corporation’s Pension funds Org. nr. Market Cap (SEK)

Konsumentkooperationens 802001-8423 22 938 769 000Ericsson (A) 802424-5899 19 399 323 000Posten 802404-2635 18 775 205 000Skandinaviska Enskilda Bankens (SEB) 802000-7871 17 028 615 000Nordea Bank Sverige 802000-2765 13 997 543 000Svenska Handelsbanken 802001-3564 13 254 383 000Praktikertjänst AB 802008-4094 11 190 505 000AstraZeneca AB 802410-5465 7 524 303 600Volvo Personvagnar 802424-0122 7 297 605 050Saab Pensionsstiftelse 802425-1020 5 392 749 796ABB-koncernens 878002-3829 5 340 139 000Skanska Trean Allmän 802409-1319 3 762 012 955Stora Ensos Svenska Gemensamma 802424-8620 3 042 562 000Sandviks Pensionsstiftelse i Sverige 885501-4356 2 339 425 000

Danske Bank, Sverige Filials 822000-6251 2 290 856 000Gemensamma Pensionsstiftelse

Electrolux-koncernen 802405-5082 2 007 339 313Lantmännens Gemensamma Pensionsstiftelse 802477-3700 1 679 787 000GroddenPensionsstiftelsen för tjänstemän och arbetsledare 802407-3960 1 659 996 000vid Svenska Cellulosa Aktiebolaget SCA (nr 2)Svenska Byggnadsarbetarförbundet 802007-6280 1 440 216 000Atlas Copco-gruppens gemensamma 802408-7952 1 236 729 138pensionsstiftelse

Table 4.1: 20 largest pension funds based on market capitalization

After analyzing the annual reports of the pension funds in Table 4.1, only half of the

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sample were included in this study and the other half were excluded due to limitedinformation in the annual reports. The pension funds included in the analysis of thisstudy can be studied in the table below.

Corporation’s Pension funds Org. nr.

Skandinaviska Enskilda Bankens (SEB) 802000-7871

Svenska Handelsbankens 802001-3564

Ericsson (A) 802424-5899

ABB-Koncernen 878002-3829

Postens 802404-2635

Praktikertjänst AB 802008-4094

Electrolux-koncernen 802405-5082

Danske Bank, Sverige Filias 822000-6251

Stora Ensos Svenska Gemensamma 802424-8620

Byggnads 802007-6280

Table 4.2: Pension funds included in the analysis

4.2 Pension Fund’s Asset Allocation

In this section, we present general descriptive statistics concerning pension funds’allocations from the data. In Table 4.3 the average weighting for each asset classis presented. Fixed income and equity are the primary assets, accounting a total of89.32% of the total portfolio. Both asset classes constitutes approximately the sameproportion of the portfolio and account for 46.65% and 42.67% respectively. Theremainder of the portfolio is allocated towards alternative investments (approximately11%) and comprises mainly of hedge funds (5.87%) and real estate (3.28%).

Fixed Alternative Hedge Real(% of total assets) Equity Income Investments funds Estate Other

Mean 42.67 46.65 10.97 5.87 3.28 1.13St. Deviation 2.94 3.62 5.00 1.61 1.99 0.84Min / Max 36.79/48.0 41.88/54.0 3.28/19.0 2.91/8.00 0.00/6.00 0.13/2.00

Table 4.3: Average portfolio allocation (2005-2015).

Table 4.4 gives a breakdown of pension funds’ average allocation year by year. Equityallocation does not exhibit a clear trend over the years and stays overall close toits mean at 42.24% throughout the period. From 2005 to 2008 allocation to fixed

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income has a steady rise from 43.27% to 54.37%. After this period the allocationexhibits a decline and decreases 2008-2015 to 43.80%. Allocation towards alternativeinvestments exhibit a clear increase from 3.28% to 18.57% throughout the period. Inconjunction with this increase, also hedge funds’ and real estate assets exhibits anoverall increase in allocation. From 2005 to 2015, allocation to hedge funds exhibitsan increased from 2.91% to 7.68% and real estate an increase from 0% to 5.40%.

(average % Fixed Alternative Hedge Realof total assets) Equity Income Investments funds Estate Other

Full sample2005 47.45 48.07 3.28 2.91 0.00 1.922006 47.70 46.74 4.12 3.27 0.55 2.262007 44.12 49.73 5.33 4.18 1.48 1.882008 37.63 54.37 9.04 6.17 2.50 0.772009 42.75 48.19 8.37 5.92 1.94 2.362010 43.67 46.28 12.23 6.32 3.69 0.272011 36.79 42.55 14.73 6.41 5.16 0.392012 40.56 48.42 13.32 6.59 4.19 0.362013 43.96 43.17 15.50 7.23 5.53 0.472014 43.53 41.88 16.14 7.85 5.67 1.682015 41.22 43.80 18.57 7.68 5.40 0.13

Table 4.4: Breakdown of pension funds allocation by year.

If we break down pension funds’ average allocation further by looking at domesticand foreign distribution we can see in Table 4.5, that in terms of equity, pensionfunds allocate about equal proportions in domestic as in foreign. Both accounting forapproximately 22%. In fixed income however, we observe that allocations are clearlyskewed towards domestic fixed income securities, with an average of 43.5% of totalassets as opposed to foreign with an average 8.57%.

average % Standardof total assets) Mean Deviation Min Max

Domestic Equity 21.76 2.75 17.91 28.0Foreign Equity 22.19 2.08 18.17 26.0Domestic Fixed Income 43.5 5.29 35.77 54.0Foreign Fixed Income 8.57 2.02 4.90 12.0Hedge Funds 5.87 1.61 2.91 8.00Real Estate 3.28 1.99 0.00 6.00Other 1.13 0.84 0.13 2.00

Table 4.5: Domestic/foreign breakdown of pension fund asset allocation (2006-2015).

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4.3 Distribution of Asset Returns

In the mean-variance framework described by Markowitz (1952) one of the assump-tions were that the asset returns are to be normally distributed. It is therefore ofinterest to analyze the return distribution for each asset class.

0

10

20

30

40

-0.04 -0.02 0.00 0.02NHX Composite

Frequency

Histogram for NHX Composite

0

10

20

30

-0.06 -0.03 0.00 0.03 0.06HOXSWE Index

Frequency

Histogram for HOXSWE Index

Figure 4.1: Histogram of the returns for NHX Composite and OMX Valuegard-KTHHousing Index (HOX). In red: the fitted distribution of the log-returns. In blue: thenormal distribution with empirical mean and standard-deviation.

0

5

10

15

-0.2 -0.1 0.0 0.1MSCI World Index

Frequency

Histogram for MSCI World

0

4

8

12

-0.2 -0.1 0.0 0.1OMXSPI Index

Frequency

Histogram for OMXSPI Index

Figure 4.2: Histogram of the returns for MSCI World Index and OMXSPI Index. Inred: the fitted distribution of the log-returns. In blue: the normal distribution withempirical mean and standard-deviation.

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0

30

60

90

-0.005 0.000 0.005 0.010 0.015WGBI Index

Frequency

Histogram for WGBI Index

0

20

40

60

-0.01 0.00 0.01 0.02 0.03OMRX All Bond

Frequency

Histogram for OMRX All Bond Index

Figure 4.3: Histogram of the returns for World Government Bond Index (WGBI) andOMRX All Bond Index. In red: the fitted distribution of the log returns. In blue:the normal distribution with empirical mean and standard-deviation.

In Figure 4.1 we can see that the fitted distribution and the log-normal distributiondo not match. We also can observe a second smaller "hump" in the fitted distribu-tion. The HOX index indicates no clear skewness, however the fitted histogram is notsmooth and a smaller "hump" are observed. With this graphical evidence we cannotconclude that the returns are normally distributed.

In Figure 4.2 we observe that both distributions are left skewed and have thicker lefttails compared to the log-normal distribution. Furthermore, the distribution of MSCIWorld Index have a clear "hump" left of the mean. This indicates that the returnsare not normally distributed for the equity indicies.

In Figure 4.3 both WGBI and OMRX All Bond indicies seem to be normally dis-tributed. However the left tails seem to be somewhat thicker. Before we can drawany conclusion we choose to do a skewness and kurtosis analysis shown in Table 4.6below.

Index Skewness Kurtosis

NHX Composite -0.8249 5.7354HOXSWE 0.0644 4.4756MSCI World -1.1124 6.3162OMXSPI -1.4959 8.4077WGBI 0.1956 2.7251OMRX All Bond 0.5679 3.7358

Table 4.6: Skewness and Kurtosis analysis of indices

It is suggested by Gravetter and Wallnau (2014) and Shanmugam (2015) that skew-ness and kurtosis values between ±2 would be acceptable for a sample to be con-sidered normally distributed. It seems that all indicies fulfills this requirement from

30

a skewness perspective, however none do from a kurtosis perspective. This can beexplained by the fact that the studied indicies have thicker tails. It seems reasonableto use another risk-measure other than the standard deviation that is suggested inthe mean-variance framework, as we cannot conclude that our samples are normallydistributed. Therefore, CVaR will be used as the risk measure in the remainder ofthe analysis.

4.4 Cumulative Return of Indices

Jan 06 Jul 07 Jul 08 Jul 09 Jul 10 Jul 11 Jul 12 Jul 13 Jul 14 Jul 15 Jul 16

-0.5

0.0

0.5

1.0

HOXSWENHX CompositeMSCI WorldOMRX All BondOMXSPISBWGU

Return

Cumulative returns

Figure 4.4: Cumulative returns for studied indicies

Figure 4.4 illustrates the cumulative returns of the studied indicies. We can ob-serve that HOXSWE index have had the highest growth by a considerable margin,35 percentage points more than OMXSPI and 36 percentage points more than NHXComposite. OMXSPI and NHX Composite differ with only 1%. However, from thebeginning of 2009 OMXSPI outperformed NHX Composite. NHX Composite is lessvolatile and did not experience the same drop observed between August 2007 to Jan2009. The index showing smallest volatility seem to be Citi Bank’s WGBI, which isillustrated by the smooth curve. As for equity, domestic equity have outperformedforeign equity.

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In Table 4.7 below, we can observe that HOXSWE have had the highest mean returnat 0.51%, shortly followed by OMXSPI at 0.46%. OMXSPI is more volatile (i.e.higher standard deviation), meaning that HOXSWE also have a higher risk-adjustedreturn. WGBI is the index with the highest risk-adjusted return although its meanis the lowest observed, explained by its low volatility.

HOXSWE NHX Comp. MSCI World OMRX All OMXSPI WGBICumulative Ret. 101% 65% 34% 53% 66% 47%

Median 0.0042 0.0040 0.0106 0.0032 0.0114 0.0028Mean 0.0051 0.0036 0.0031 0.0030 0.0046 0.0027

Std.Dev 0.02 0.01 0.05 0.01 0.05 0.00Std.Dev. Sharpe: 0.31 0.33 0.07 0.40 0.10 0.63

VaR Sharpe (Rf = 0%, p=99%): 0.13 0.11 0.02 0.26 0.03 0.43CVaR Sharpe (Rf = 0%, p=99%): 0.09 0.11 0.02 0.26 0.03 0.35

Table 4.7: Indices summary including cumulative returns.

Correlation analysis

In Table 4.8 below the correlations between the indices are presented. What can beobserved is that NHX Composite is highly correlated with both domestic and foreignequity. MSCI World and OMXSPI also show overall high correlation. Moreover,OMRX All Bonds do not seem to be positively correlated to any of the other indices.The same is true for WGBI. HOXSWE is somewhat positively correlated towardsNHX Composite and OMXSPI.

HOXSWE NHX Comp. MSCI World OMRX All B. OMXSPI WGBIHOXSWE 1.00 0.25 0.07 -0.17 0.28 -0.01

NHX Comp. 0.25 1.00 0.75 -0.36 0.75 -0.13MSCI World 0.07 0.75 1.00 -0.45 0.69 -0.12

OMRX All B. -0.17 -0.36 -0.45 1.00 -0.36 0.06OMXSPI 0.28 0.75 0.69 -0.36 1.00 -0.12

WGBI -0.01 -0.13 -0.12 0.06 -0.12 1.00

Table 4.8: Correlation matrix for entire period (Jan 2006 - Oct 2007)

4.5 Efficient Frontier

We have seen that the asset class indices have indicated returns with non-normaldistribution. Therefore, we have proceeded to look at the portfolio optimization usinganother framework, that is, using a mean-CVaR setting. In this section, we show theresults of optimizing portfolios by minimizing CVaR for target expected returns. Theset of these optimal portfolios gives us an efficient frontier. For the default allocationpolicy, the constraints used were set from the results obtained in Section 4.2. Herethe constraints was set as the maximum allocation that each asset class showed in

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the data in Table 4.3. These constraints are used as our representation for how thegeneral pension fund sets their allocation constraints. We then compare differentscenarios assuming that, firstly, no hedge funds are available for investment purposesand then that a maximum of 8% (what our result showed), 20%, and 100%, maybe invested in hedge funds. Table 4.9 presents the limits for the different scenarios.Furthermore, the default policy is subject to full investment constraint (all weightssum up to 1) as well as no short selling (all weights are non-negative).

Asset Class Scenario 1 Scenario 2 Scenario 3 Scenario 4

OMXSPI ≤ 30% ≤ 30% ≤ 30% ≤ 30%MSCI World ≤ 30% ≤ 30% ≤ 30% ≤ 30%OMRXBOND ≤ 55% ≤ 55% ≤ 55% ≤ 55%WGBI ≤ 15% ≤ 15% ≤ 15% ≤ 15%HOXSWE ≤ 6% ≤ 6% ≤ 6% ≤ 6%NHX ≤ 0% ≤ 8% ≤ 20% ≤ 100%

Table 4.9: Default portfolio asset constraints.

In Figure 4.5, we have computed and plotted the efficient frontiers for the differentscenarios (i.e., with increasing hedge fund constraints), with minimized CVaR at a99% confidence level. We can observe a shift in the efficient frontier for differentinvestment policies. The graph suggests that policies with higher allowed allocationtowards hedge fund investments, renders in the efficient frontier shifting to the left.This is interpreted as: for a given target return, a policy allowing a higher allocationto hedge funds reduces the portfolio risk. It is important to highlight that the hedgefund index is representative of the industry but not of an investment strategy inparticular.

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Figure 4.5: Efficient frontiers with different HF constraints.

4.6 Cumulative Portfolio Return

For each scenario we were able to obtain four different efficient frontiers as illustratedin Figure 4.5. Each of these efficient frontiers consists of various efficient portfolioswith specific weighting and target returns. For each scenario, we chose the optimalportfolio to be the one with the highest risk-adjusted return represented by the as-terisks (*) on the frontiers in Figure 4.5. This was done by taking Pr

CV aRp=0.99, where

Pr stands for portfolio return and CV aRp=0.99 for the conditional Value-at-Risk at a99% confidence level. In Table 4.10 below, the risk-adjusted return for these scenariooptimal portfolios are presented.

HF = 0% HF ≤ 8% HF ≤ 20% HF ≤ 100%

Pr

CV aRp=0.9915.75% 21.96% 39.29% 42.31%

Table 4.10: Return to CVaR ratios for each constraints.

From the results in Table 4.10 we can see a clear trend: the more we are allowed toallocate in hedge funds, the better risk-adjusted return we are able to obtain. Lookingback at Table 4.7 we can observe that only domestic and foreign (OMRX All Bond

34

& WGBI) fixed income has better risk-adjusted returns.

Since pension funds has obligation to secure their employer’s pension obligation, theinvestors has a risk aversion mind-set and would therefore not be willing to take onmore risk without being compensated with premium return. By this reasoning wechoose these portfolios (i.e. the portfolios with the highest risk-adjusted returns) tobe the optimal portfolios and to make a comparable analysis of the different scenarios.Table 4.6 presents an illustration of the weighting of the scenario optimal portfolios.

0.0

0.2

0.4

0.6

0.8

1.0

Weigh

ts

HF0 HF8 HF20 HF100

HOXSWENHX Composite

MSCI WorldOMRX All Bond

OMXSPIWGBI

Figure 4.6: Portfolio weights for each scenario optimal portfolio.

We can observe that when allowed, more is allocated towards hedge funds and less isto equity (both domestic and foreign). This is further supported by Table 4.11 wherethe exact weighting to each asset class for the different scenarios are presented.

HF = 0% HF ≤ 8% HF ≤ 20 HF ≤ 100%HOXSWE 0.06 0.06 0.06 0.06

NHX Composite 0.00 0.08 0.20 0.29MSCI World 0.11 0.08 0.04 0.00

OMRX All Bond 0.55 0.55 0.55 0.50OMXSPI 0.13 0.08 0.00 0.00

WGBI 0.15 0.15 0.15 0.15

Table 4.11: Portfolio weights for each scenario optimal portfolio.

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Using the weights from Table 4.11 we plotted the performance for each scenariooptimal portfolio (HF0, HF8, HF20, HF100) by computing the cumulative returnsduring the period Jan 2006 - Oct 2017.


0.0

0.1

0.2

0.3

0.4

0.5

0.6

HF0HF8HF20HF100

Return

Cumulative returns

Figure 4.7: Cumulative returns for portfolios with four different allocation strategiestowards hedge funds; 0% in HF, ≤ 8% in HF, ≤ 20% in HF and ≤ 100% in HF.

From Figure 4.7 we can see that scenarios that allows for higher hedge fund allocationare outperforming those with less. Initially, a higher performance from the portfolioswith less hedge fund allocation (i.e., HF0 and HF8 in Table 4.4) is shown, but whenlooking throughout the entire period these tends to fall more drastically for eachdecline. This is particularly apparent during the period July 2007-January 2009.

4.7 Drawdown

Figure 4.8 below illustrates the drawdowns of the optimal portfolios from the fourdifferent scenarios during the studied period.

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-0.08

-0.06

-0.04

-0.02

0.00

HF0HF8HF20HF100

Value

Drawdown

Figure 4.8: Drawdown for the different hedge fund allocation policies

We can observe that the largest drawdown for all portfolios – except HF100 – is be-tween October 2007 and September 2009. HF100 experiences it’s worst drawdown inApril 2015. It is also apparent that the portfolios that are restricted to invest less inhedge funds, are the ones that experience the largest drawdowns.

Length To Trough RecoveryFrom Trough To Depth (months) (months) (months)

HF0 2007-10 2008-09 2009-09 -9.07% 24 12 12HF8 2007-10 2008-09 2009-06 -5.58% 21 12 9HF20 2008-04 2008-08 2008-11 -1.21% 8 5 3HF100 2015-04 2015-05 2015-06 -0.93% 3 2 1

Table 4.12: Biggest drawdowns for portfolios HF0, HF8, HF20 and HF100

Table 4.12 presents the largest drawdown for each portfolio. We can observe a draw-down up to -9.07% for the portfolio that is not allowed to invest in hedge funds. Ittakes 12 months to through and another 12 months before the losses experiencedto through are regained. It can be observed that the more a portfolio is allowed toallocate to hedge funds, the smaller are the losses.

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5 Discussion

In this section we will discuss the results obtained from the empirical study based onannual reports, quantitative approach, as well as the literature review. The advantagesand disadvantages of the method will also be discussed.

5.1 Pension Funds Asset Allocation During the Period

When we compare the allocations for pension funds at the start of the period againstthose in end, seen in Table 4.4, the biggest difference we can observe is that alterna-tive investments have had a remarkable increase. The asset class shows a steady riseof approximately 15 percentage points throughout the period. In conjunction withthis rise we also observe that there are increases in allocation to hedge funds as wellas real estate investments. These increases are mostly due to reallocations in equitiesand fixed income.

Equity and fixed income does not exhibit any substantial change in their relativeproportion when comparing 2005 to 2015, and has approximately equal proportion.Their added total stays fairly consistent throughout the period which is not remark-able since both these are the traditional primary asset classes in a portfolio andshould not fluctuate much. The two asset classes isolated however develops with neg-ative correlation during the period. The first years when allocation to fixed incomeincreases, we see that allocation to equity decreases. Similar negative correlationmovements are observed throughout the period. This behaviour is supported whenwe examine the correlation matrix in Table 4.8 where we see that the fixed incomeindices have negative correlations to the other indices.

When we look at pension funds average allocation year-by-year from Table 4.4 we seethat there are no apparent upward of downward trend for equity allocation during theperiod. What we can see is that the years before 2008 equity allocation decreased andthen increased the years after. This period is of interest since the subprime mortgagecrisis was at its pinnacle 2008. According to our results, pension funds managed theirasset allocation favourable during this financial crisis in terms of; reduction in equitybefore the crash (before the value plummets) and increases the allocation after (whenthe value recovers).

The year 2008 also exhibit a clear shift when we look at how pension funds allocatetheir funds to fixed income. For the years 2006-2008 there is a clear rise to fixedincome and allocation increased by just over 8 percentage points to the high-pointof 54%. The years following 2008 however the overall trend is downward and theallocation level drops back to approximately 44% towards the end of the period. Anapparent explanation to this decline could be the fact that the long- and short-term

38

interest rates have had a prolonged decline and that investors have responded tothis. The trend of declining fixed income allocations together with the exhibitedrise in alternative investments is a behaviour that is consistent with what previousstudies suggests long-term investors should employ as a measure when faced with thelow-interests levels, which will be addressed in following section.

5.1.1 Comparison to Previous Research and Theory

Since the beginning of the 2000’ institutional investor have had an increasing interestto alternative investment, particularly the promise of decorrelated and high returnsthat hedge funds have shown. They have seen this to be a way to further diversifytheir portfolio (Bouvatier and Rigot, 2013; Preqin, 2014). This trend can also berecognized from our results where we find that pension funds have found a growinginterest in overall allocation to alternative investment through the years, with an in-crease from 3.28% to 18.57%. Also hedge fund allocation have increased during thisperiod. In terms of hedge funds, investors have generally had issues understandingtheir complex strategies and limited information on the assets underlying the invest-ments. Recent notable examples of institutional investors being skeptical towardsthe hedge fund industry is CalPERS and Railpens withdrawal of their funding fromthe industry (Marois, 2014; Cohn and Kumar, 2017) – their motivation branded astoo complex and costly. The issue of hedge funds being an asset class with highcosts is an important aspect. In this paper however, we have delimited the studyfrom costs overall due limited access to information regarding pension funds, hedgefunds and their cost structure. These difficulties to understand hedge fund strate-gies, their valuation, their return drivers, together with the skepticism shown fromthese major institutions, explains the low allocation to alternative investments andhedge funds in in the beginning of the period. But as seen from previous research(e.g. the contribution of high Sharpe ratio) (Hoevenaars et al., 2008; Favre andGaleano, 2002) hedge funds are favourable and attractive for an investor portfolio ina risk-adjusted return perspective. Similar findings are also obtained in our study,discussed in Section 5.2. These results suggests that there could be of interest forinstitutional investors to direct some of their attention to the hedge fund industry,which is also supported in the allocation increase shown from our results in Table 4.4.

Given the economic landscape with interest rates remaining at record low-levels, Bamset al. (2016) studied how institutional investors in North America are responding toa prolonged low-interest period. In their study they incorporate certain economicvariables as predictive indicators in order to derive returns, given mentioned invest-ment opportunities. They suggest that there are – theoretically – responses investorsought to consider when faced with certain investment opportunities, such as a last-ing low-interest period. Their findings implies that pension funds should direct theirallocations more to equity and reduce allocation to fixed income in order to attain op-

39

timal returns. In their study they do however conclude that pension funds are unableto incorporate this information. In this study we do not get the same result as Bamset al. (2016) in terms of response to a low-interest environment from pension funds.Our results shows that pension funds reduced their fixed income most recent years,which is consistent with the theory. We can not however see an increase in equityallocation as recommended. The fact that previous research and this paper studiesdifferent time periods is one explanation as to why there are signs to differing results.Investor might have reacted to previous performances and studies, and adjusted theirstrategies to further optimize their allocation.

The increase towards alternative investment also suggests that there may exist anemployment of a "core-satellite" organization structure as described by Bouvatierand Rigot (2013). In their paper they explain that since institutional investors tra-ditionally are heavily invested in fixed income they have to seek for other sources ofreturn in a low-interest rate environment. The core component objective is to avoidrisks and the satellite components objective is to achieve better risk-adjusted returns.The observed increase in alternative investment suggests that there might been a re-organization and that a satellite component could have been employed amongst thepension funds during the period.

5.1.2 Analysis of Method

Institutional investors are defined as the professional management of assets on behalfof the majority of individuals Basile (2016). This implies that the management hasto have a risk-averse focus for the good of the majority. We chose to use a corpo-rate pension fund as a proxy for an institutional investor. A pension fund has tocomply with the rules of the assurance act. Essentially, this means that the pensionfund has to secure the promise of the employer’s pension obligations. It implies thatthe pension fund management has to have risk-averse objectives in order to securethis obligations. This motivated the use of pension fund as our representation ofan institutional investor. In order to get a proxy of how a typical corporate pen-sion fund allocate their funds, the average of the 10 largest (i.e. large in terms ofmarket capitalization) pension funds were computed. Aware that an average is notrepresentative of individual investors and their objectives, the use of this average asa proxy is an assumption made in the study. The limited access to information onpension fund reduced the final data-set down to the 10 largest pension funds. Toadd on the quantitative analysis, interviews with actors within the industry wouldfurther build on the understanding of the motives and incentives on portfolio policiesset by the managers. For further research, to get a more accurate result a use of alarger data-set and interviews with industry actors is suggested. Also to consider isthe "disturbance noise" of human error in interpretation of financial documents andconversion into statistical inference.

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5.2 Optimal Allocation Policy

We will first present an overview of our results and comment on the links to theoryand previous research. This will then be followed by an in depth analysis.

• Efficient frontierWe found that the efficient frontier shifted to the left when more was allocatedtowards hedge funds. This result implies that a more optimal portfolio for longterm investors consists of a higher proportion of hedge funds, as the portfoliobecomes more efficient given that hedge funds have a higher risk-adjusted returncompared to equity funds – which is consistent with the theory.

• Low interest rate environmentOur results suggest that in a low interest rate environment pension funds shoulddecrease their allocation towards equity and increase their allocation towardsfixed income and alternative investments. These results are inconsistent withprevious research. Bams et al. (2016) suggest that pension fund should decreasetheir allocation towards fixed income and increase their allocation towards eq-uity and hedge fund assets.

• Hedge fundsOur results suggest that hedge funds do not follow a normal distribution. Theuse of CVaR as a risk measure is therefore motivated. Moreover, we find thathedge funds are highly correlated to equity. This is inconsistent with the theory,which suggest that hedge funds are to achieve absolute return regardless of themarket environment. Lastly, we find that hedge funds is an attractive assetclass for long term investors as return-to-risk ratio is maximized for portfoliosallowing more allocation to hedge funds (up to 29%) compared with portfolioswith less allocation towards hedge funds. These findings are consistent with thefindings of Hoevenaars et al. (2008) and Favre and Galeano (2002).

The results based on our data, suggests that the current allocation policies pensionfunds employ are not optimal. The results show that as we allocate more towardshedge funds (up to 29%), the more the efficient frontier shifts to the left – which isinterpreted as: feasible target returns can be achieved with less risk. This could bedue to the fact that, for the studied period, hedge funds have experienced better risk-adjusted return compared to equity assets. Traditionally, pension funds are primarilyinvested to equity (in our results this asset class make up 43% of their portfolios). Byassessing the results obtained in Table 4.10 we could see a clear trend: the more weare allowed to allocate towards hedge funds, the better risk-adjusted return we areable to obtain. Looking at Table 4.7, we could also observe that only domestic andforeign fixed income (OMRX All Bond & WGBI) had better risk-adjusted returns.

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This implies that the more we are allowed to allocate towards hedge funds, the less weshould allocate towards asset classes with less risk-adjusted return. In our case, weshould observe less allocation towards equity, both domestic and foreign. We couldalso observe a higher return-to-risk ratio in Table 4.10 as more is invested towardshedge funds. This observed result is down to the fact that we allow more investmentsin an asset class that have had better risk-adjusted return. Although equities haveexperienced high returns after the financial crisis experienced in 2008, they have stillbeen volatile and does not make up for the losses experienced during the financialcrisis.

Although we experience a low interest rate environment (i.e. Swedish 10-year govern-ment bond rate have decreased from 3,325 % in January 2006 to 0.8271% in October2017 11) our results suggest that given the possibility to allocate more wealth to-wards hedge fund assets, more should be allocated towards hedge funds while lessshould be allocated towards equity assets. These results are somewhat unexpectedand conflicts return predictability theory. These results could however be explainedby analyzing Tables 4.8 and 4.7. In Table 4.8 we can observe that hedge funds arehighly correlated with equity assets (both domestic and foreign). At the same time,in Figure 4.7 we can observe that hedge funds have higher monthly mean return thanMSCI World and approximately 28% less mean return than OMXSPI. However, sinceboth MSCI World and OMXSPI are significantly more volatile than NHX Composite,NHX Composite has the best return to risk ratio. These observations in combinationimplies that since hedge funds are highly correlated with domestic and foreign equityassets and at the same time deliver less risk to the portfolio, hedge funds are a bettersubstitute to equity assets. The fact that our results suggests that more should beallocated towards fixed income can be explained by observing Table 4.7. In Table 4.7we can see that domestic and foreign fixed income assets have the highest return torisk ratio. In parallel, both OMRX All Bond and WGBI are negatively or lowly cor-related to the other asset classes, as can be observed in Table 4.8. Thus, offering highdiversification effect. These results partly explains the reasons behind the reductionor omission of equity funds in portfolios HF0, HF8, HF20 and HF100.

Another feasible explanation could be the construction of the optimization problem.We opted to optimize the portfolio by minimizing the risk without adding any tar-get return constraint. Since equity assets are the most risky, they are not preferredin an optimal portfolio with a target to minimize risk. However, adding a feasiblemonthly target return above the mean return of NHX Composite (0.36%) with thesame weight constraints would mostly likely have resulted in more allocation towardsdomestic equity funds. This is due to the fact that the mean return of domesticequity funds are higher than 0.36%, as can be observed in Table 4.7.

11http://www.riksbank.se/sv/Rantor-och-valutakurser/Sok-rantor-och-valutakurser/?g7-SEGVB10YC=onfrom=2006-01-01to=2017-12-09f=MonthcAverage=Averages=Commasearch

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When applying the obtained optimal weights for the four portfolios with differenthedge fund allocation policy (HF0, HF8, HF20 & HF100) we plotted the cumulativeportfolio returns and observed in Figure 4.4 that portfolios HF0 and HF8 outper-formed portfolios HF20 and HF100 before the financial crisis. However, during thefinancial crisis both HF20 and HF100 avoided large losses. Although equity assetshave had good mean returns after the financial crisis, HF0 and HF8 do not manageto outperform HF20 and HF100 over the studied period. In Figure 4.8 and Table 4.12we can observe that HF0 and HF8 experience a loss of 9.07% and 5.58% respectivelywhile portfolio HF100 did not experience it’s worst trough until May 2015 whichlanded at a modest 0.93%. This can be explained by the fact that HF0 and HF8both consist of equity assets while HF100 does not and it was the equity class assetsthat were most affected by the financial crisis. However, it is worth mentioning thatan important delimitation of this paper is the cost structure of investing in differentasset classes which could have an impact on the results. A further discussion touchingon this topic can be read later in Section 5.2.2.

5.2.1 Comparison to Previous Research

Previous literature conducted by Campbell (1987); Ang and Bekaert (2007); Shilleret al. (1983); Fama and French (1989); Cochrane and Piazzesi (2005) have identifiedvarious macro-economic variables as predictors for expected return. Such predictorsare short-term interest rate, the yield spread between long-term and short-term inter-est rates and dividend-price ratio. Their findings suggest that when interest rates arelow, more should be allocated towards equity assets. Bams et al. (2016) shows thatthese predictive macro-economic variables can be used to derive an optimal portfolioand shows that portfolio allocation to stocks is negatively correlated to short-terminterest rates – implying that when short-term interest rates are low, more should beallocated towards equity. Ang and Bekaert (2007) also show that when short-terminterest are low, equity returns tend to be high. Our findings suggest that returnon equity are higher than all equity assets except return on real-estate, these find-ings are aligned with the findings of Ang and Bekaert (2007). Although returns arehigher, so is the risk and from a portfolio perspective with the aim to minimize risk,equity assets are not regarded as optimal. Our results suggests that more should beallocated towards interest rates and hedge funds and less towards equity assets evenin a low interest rate environment. These findings are inconsistent and contradictsliterature on return predictability. However, these findings are consistent with thefindings of Bams et al. (2016) who studied how pension funds in North America havereacted to prolonged low interest rate environment and finds that they have increasedtheir allocation towards fixed income and alternative investments and decreased theirallocation towards equity assets.

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Hoevenaars et al. (2008) study the effect of investing in other instruments than stocksand bonds for long-term investors. They extend the term structure of risk-returntrade-off explained by Campbell and Viceria (2005) for assets like real-estate andhedge funds. They show that the costs from investment constraints excluding hedgefunds are high for long-term investments. Their results are consistent with our find-ings that suggest a higher return to risk ratio is obtained for portfolios allocatingtowards hedge fund assets. Favre and Galeano (2002) recognizes that hedge fundsreturns are not normally distributed and incorporate a modified Value-at-Risk riskmeasure in order to account for the non-normally distribution of hedge fund returns.They still find that investing in hedge-fund assets is highly beneficial and find that themodified Sharpe ratio is increased when more is allocated towards hedge funds. Thisis consistent with our findings. Our results suggest that an optimal portfolio shouldallocate approximately 29% towards hedge funds. Favre and Galeano (2002) findsthat the 89% should be allocated towards hedge funds in a mean-variance frameworkwhen there are no constraints.

5.2.2 Analysis of Method

After analyzing the distribution of the six asset classes that makes up a typicalSwedish pension fund we found that none of the asset classes could be regarded asnormally distributed after analyzing the Kurtosis results of our returns. Therefore,we chose to modify the mean-variance framework and opted to use CVaR as a risk-measure. CVaR is a risk-measure that account for non-normally distributed returns.By using CVaR as a risk measure, we manage to account for the greater probabilityof extreme negative returns in the empirical distribution which accounts for greaterdownside risk than is captured by the measurement of the standard deviation alone.

Two important delimitation’s in the study are the cost of investing in different assetclasses and currency risk. Generally hedge funds are considered as a costly invest-ment asset class as described in section 3.1. One can argue that since this study doesnot account for costs, it is not a reflection of the real world investment environment.However, we argue that the aim of this study is to find an optimal allocation strategybased on the overall development of the different asset classes a Swedish corporatepension fund usually invest in. Furthermore, the results from Section 4.2 on pensionfunds average allocation shown in Table 4.3, are used as constraints when generatingefficient frontiers. These numbers are to correspond to the policy constraints for atypical Sedish pension fund. This does not necessarily have to be true in reality, butis an assumption in this study.

Regarding currency risk, one should bear in mind that Swedish krona variance of aforeign investment adds up to the variance in the local currency, the variance of theexchange rate and twice the covariance of the investment return and the exchange

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rate. Currency risk could potentially increases the volatility of the foreign invest-ments and could have an impact on hedge fund investments. However, we argue thata systematic policy of complete currency hedging would eliminate the contribution ofcurrency risk, thus the total volatility of a portfolio would be unaffected. However,hedging also have a cost and could potentially contribute to lower portfolio returns.We argue that we aim to focus solely on hedge fund characteristics and their implica-tions on portfolio assets allocation and have therefore chosen to assume that Swedishcorporate pension funds are able to full hedge against currency risk without affectingoverall portfolio return.

The choice of indices for hedge funds and real-estate is also a subject worth discussing.We chose to use Hedge Nordic’s NHX Composite index which could potentially con-tain a survivorship bias. This index is frequently updated and does not includehedge funds that have went bankrupt and are therefore upwardly biased. Moreover,NHX Composite index could also have self-selection bias as managers apply to beincluded in the index. This could mean that only managers with good hedge fundperformance choose to be included in this index. We have made the assumption thatSwedish corporate pension funds have a direct ownership in real estates and thereforehave used Nasdaq OMX Valueguard-KTH Housing Index (HOX) which measures ac-tual transactions on sold properties in Sweden. This assumption might not representthe real world as many pension funds invest indirectly in real-estate assets through,for instance, mutual funds.

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6 Conclusion, Implication and Future Research

In this section we will presents the conclusion from the results and analysis. Theresearch questions will also be answered. This section will also present suggestions onfuture research regarding possible extensions of our study.

6.1 Answering the Research Questions

The purpose of the study was firstly, to analyze the pension fund industry and assesshow it has responded to the prolonged low-interest rate environment. And then in ex-tension, to investigate implication of allocating pension fund assets to the hedge fundindustry, particularly to evaluate the potential benefits of hedge fund investments.Answering the first question was done by conducting an empirical study where annualreports were analyzed from 10 major corporate pension funds. The results from thisstudy laid the foundation for further research and we could proceed with the study.By acquiring historical financial data, further empirical research was conducted toanswer the second research question.

The first research question (RQ1) to be answered:

"How has Swedish corporate pension funds responded to the recent years low-interest levels?"

When evaluating how a response to the prevailing low-interest environment shouldbe considered in terms of strategic asset allocation we have used previous studiesand financial literature regarding the subject of economic predictive indicators. It iswith respect to these indicators and in relation to these examples we can compareand assess how the Swedish corporate pension fund industry has reacted. From ourresults we can see that pension funds have during the studied period increased theirallocation to hedge funds. There have also been an overall reduction in fixed incomeallocation recent years. Both these behaviours is consistent to what the literaturesuggest to be the optimal measures in terms of return predictability. According toprevious studies and literature, the optimal responses institutional investors couldemploy to their strategic asset allocation in order to capture predicted returns is: re-duction of fixed income allocations, increases to hedge funds, and increase to equity.Our results cannot support that pension funds have increased their equity allocation.With this said, we can from our results conclude that the pension fund industry havemanaged to respond to the current prolonged low-interest environment in a mannerthat is consistent with the financial literature and theory.

The second research question (RQ2) to be answered was:

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"What hedge fund allocation policy contribute to the highest risk-adjusted re-turn for Swedish corporate pension funds?"

After identifying the allocation policy of a typical corporate pension fund and thegathering of financial data for each asset class that pension funds usually allocatein, we applied portfolio theory in order to solve for the optimal portfolio given thedifferent hedge fund constraints. We found that an optimal Swedish corporate pensionfund portfolio should allocate 29% of its assets in hedge funds when usingHOXSWEas an index for real-estate assets, NHX Composite for hedge fund assets, MSCIWorld for foreign equity assets, OMXSPI for domestic equity assets, WGBI forforeign fixed income assets and OMRX All Bond for domestic fixed income assets.Our results were obtained by modifying the mean-variance framework where we usedCVaR as a risk measure in order to account for non-normality of returns. Our resultsalso suggest that Swedish corporate pension funds should allocate more than theyhave historically towards fixed income assets and none in equity assets in order toobtain the highest risk-adjusted return.

6.2 Implications

Our findings that pension funds are able to respond as expected to market changes inthe economy and that they are able to reorganize their strategic allocation through-out a prolonged low interest rate environment have implications. So does our resultson how an optimal pension fund allocation strategy should allocate its assets.

Our study suggests that pension fund managers have been able to respond to changesin investment opportunity changes that are consistent with financial literature. Sinceinstitutional investors’ manages assets concerning a large amount of individuals andthat these assets certainly affect a major part of associated individuals, it is there-fore of interest that these managers are examined and accountefdd for. Pension fundmanagers are responsible to make sound investment decisions with the purpose offinancing pension plan benefits. In order to fulfill this purpose, these mangers needto account for the market conditions in which they invest in. Our results implies thatthis decision making is at a level that provides a sense of security and trust and thatinstitutional investors are working in the right direction to fulfill their commitments.

Hedge funds have long been seen as an asset class with attractive characteristics(e.g. high and uncorrelated returns) for long-term institutional investors. But theasset class have also been linked with unclear and uncertain performance drivers.There have been criticism and ambiguous views in how hedge fund is of benefit fora institutional investors. With this study we aim to build on the understanding onhow this asset class can contribute in a strategic asset allocation. Our results are inline with previous studies but it does also exhibit conflicting results. This highlights

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that changes in the financial market and that geographical premise implies that newmeasures ought to be considered and that the literature are constantly evolving. Withthis study we have contributed with an addition to the literature and to the decisionbasis for future decision making for institutional investors and for future conditions.

6.3 Future Research

For future research, the generalization can be increased by including more pensionfunds in the study. However, corporate pension funds do not always disclose theirallocation strategy in their annual reports. In order to successfully include more pen-sion funds we recommend to perform interviews with each pension fund. This willalso ensure a deeper understanding of their allocation strategy.

In order to get even more reliable results, we recommend to construct a hedge fundindex in order to avoid survivorship bias and self-selection bias by picking hedgefunds based on market capitalization. We would also suggest to account for costs ofinvesting in different asset classes. We would also suggest to perform the optimizationproblem by choosing more than one risk-measure and compare the results in order tofurther strengthen the reliability of the results.

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A Appendices

Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 81,95% 83,50% 84,37% 86,05% 87,82% 85,87% 84,64% 84,88% 87,77% 89,34% Swedish 45,92% 41,41% 38,03% 44,29% 45,14% 41,57% 44,38% 48,55% 51,97% 53,99% Foreign 1,79% 4,34% 2,69% 2,37% 3,25% 4,96% 4,55% 3,73% 3,31% 3,32% Swedish equity funds 3,23% 3,45% 3,26% 3,99% 3,64% 4,25% 3,88% 3,82% 3,49% 4,08% Foreign equity funds 31,01% 34,30% 40,39% 35,41% 35,79% 35,09% 31,82% 28,78% 29,01% 27,95% Fixed Income 18,05% 16,50% 15,63% 13,95% 11,95% 13,82% 14,70% 14,60% 12,13% 10,58% Swedish 5,26% 3,67% 2,45% 1,52% 4,78% 4,91% 4,50% 3,78% 4,86% Foreign 0,93% 0,31% 2,86% 3,82% 4,71% 4,09% 5,98% 5,30% 5,47% 4,82% Swedish fixed income funds 0,62% 10,70% 2,87% 0,26% 0,24% Foreign fixed income funds 11,25% 5,48% 6,24% 7,68% 5,73% 4,95% 3,80% 4,80% 2,62% 0,66% Cash Alternative investments Hedge funds Private Equity Real estate CommoditiesOther 0,00% 0,00% 0,00% 0,00% 0,22% 0,31% 0,66% 0,53% 0,10% 0,08%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.1: SEB-stiftelsen allocations

Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 94,41% 95,53% 94,21% 93,65% 95,73% 94,02% 94,24% 94,64% 91,80% 92,98% Swedish 84,63% 84,89% 83,66% 81,57% 82,50% 79,71% 78,71% 78,10% 79,72% 80,25%

Foreign 5,88% 5,95% 5,64% 6,53% 7,74% 7,94% 8,24% 7,67%

Swedish equity funds 0,21% 0,86% 0,52% 2,31% 2,64%

Foreign equity funds 3,70% 3,83% 4,92% 5,04% 5,49% 6,37% 7,29% 8,87% 9,77% 10,09%

Fixed Income 3,96% 2,67% 2,60% 4,22% 3,06% 4,06% 4,13% 3,79% 7,33% 5,83% Swedish Foreign Swedish fixed income funds Foreign fixed income funds Cash Alternative investments 0,00% 0,00% 0,00% 0,57% 0,76% 0,69% 0,65% 0,97% Hedge funds 0,57% 0,76% 0,69% 0,65% 0,97% Private Equity Real estate CommoditiesOther 1,63% 1,79% 3,19% 2,12% 1,21% 1,35% 0,87% 0,88% 0,22% 0,22%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.2: Svenska Handelsbankens Penssionsstiftelse allocations

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Foreign 13,01% 13,01% 12,43% 12,87% 17,34% 15,15% 15,19% 15,24% 10,61% 6,75%

Swedish equity funds Foreign equity funds Fixed Income 74,06% 68,01% 73,21% 64,48% 61,77% 62,16% 60,23% 46,25% 45,04% 60,54% Swedish 36,96% 43,30% 55,17% 44,94% 37,81% 46,13% 43,64% 29,62%

Foreign 37,10% 24,71% 18,04% 19,54% 23,96% 16,03% 16,59% 16,63%

Swedish fixed income funds Foreign fixed income funds Cash Alternative investments 0,00% 9,39% 8,54% 10,74% 12,26% 15,45% 19,64% 26,22% 27,22% 30,89% Hedge funds 5,39% 6,76% 10,66% 13,81% 14,72% 15,66% Private Equity 0,94% 1,51% 1,95% 2,57% 4,06% 5,53% Real estate 2,17% 3,64% 4,84% 9,84% 8,44% 9,70% Commodities 3,76% 3,54% 2,19%Other 0,00% 0,00% 0,00% 7,14% 0,00% 0,00% 0,00% 1,37% 15,82% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.3: Ericsson Pensionsstiftelse (A) allocations

Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 36,60% 29,23% 24,66% 31,57% 33,60% #N/A 17,99% 31,58% 29,65% 27,49% Swedish Foreign Swedish equity funds 26,85% 9,54% 7,56% 11,02% 13,45% #N/A 4,68% 5,59% 5,72% 5,87%

Foreign equity funds 9,75% 19,69% 17,10% 20,55% 20,15% #N/A 13,32% 25,99% 23,94% 21,62%

Fixed Income 57,40% 64,98% 69,74% 65,04% 63,52% #N/A 81,89% 68,37% 69,78% 62,51% Swedish 19,21% 23,90% 23,41% 22,35% 21,78% #N/A

Foreign Swedish fixed income funds 38,19% 41,08% 46,34% 22,56% 21,64% #N/A 45,12% 30,15% 36,74% 33,43%

Foreign fixed income funds 20,12% 20,09% #N/A 36,77% 38,22% 33,03% 29,08%

Cash Alternative investments 6,00% 5,79% 5,60% 3,39% 2,88% #N/A 0,12% 0,05% 0,57% 10,00% Hedge funds 5,13% 5,33% 5,39% 3,15% 2,71% #N/A 0,02% 0,01% 0,02% 0,02% Private Equity 0,87% 0,46% 0,21% 0,24% 0,18% #N/A 0,10% 0,04% 0,02% Real estate 0,53% 9,99% CommoditiesOther 0,00% 0,00% 0,00% 0,00% 0,00% #N/A 0,00% 0,00% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% #N/A 100,00% 100,00% 100,00% 100,00%

Figure A.4: ABB-Koncernens Pensionsstiftelse allocations

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Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 25,04% 23,71% 15,44% 25,98% 22,77% 12,61% 21,38% 31,75% 33,79% 23,57% Swedish 5,01% 5,93% 4,63% 7,33% 6,61% 1,99% 6,54% 7,77% 4,90%

Foreign 20,03% 17,78% 10,81% 18,65% 16,15% 10,62% 14,84% 23,98% 28,89%

Swedish equity funds Foreign equity funds Fixed Income 53,00% 47,55% 44,43% 37,42% 32,72% 38,28% 33,80% 26,26% 20,14% 24,71% Swedish 53,00% 47,55% 44,43% 37,42% 32,72% 38,28% 33,80% 26,26% 20,14% 24,71%

Foreign Swedish fixed income funds Foreign fixed income funds Cash Alternative investments 21,96% 28,73% 40,13% 36,60% 44,51% 49,12% 44,82% 41,99% 46,07% 51,72% Hedge funds 15,96% 18,39% 20,61% 18,24% 20,20% 22,50% 21,32% 21,45% 24,53% 28,50% Private Equity 1,59% 1,59% 2,85% 2,40% 3,22% 3,35% 4,69% 4,75% 5,87% 6,14% Real estate 4,41% 8,76% 16,67% 12,59% 12,84% 15,65% 16,32% 15,80% 15,66% 16,60% Commodities 3,38% 8,25% 7,61% 2,49% 0,00% 0,00% 0,49%Other 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.5: Postens Pensionsstiftelse allocations


Foreign 16,99% 20,67% 18,62% 23,43% 20,14% 20,34% 33,66% 35,83% 36,74% 24,71%

Swedish equity funds Foreign equity funds Fixed Income 46,34% 60,39% 62,47% 50,11% 53,11% 58,94% 54,55% 53,18% 52,67% 65,44% Swedish 41,46% 56,92% 57,64% 45,62% 47,70% 52,70% 47,16% 47,27% 46,00% 60,17%

Foreign 4,88% 3,47% 4,83% 4,48% 5,41% 6,24% 7,39% 5,91% 6,67% 5,27%

Swedish fixed income funds Foreign fixed income funds Cash Alternative investments 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% Hedge funds Private Equity Real estate CommoditiesOther 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.6: Praktikertjänst AB:s Pensionsstiftelse allocations

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Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 53,79% 42,90% 34,01% 43,65% 46,02% 44,53% 47,79% 46,50% 49,55% 51,79% Swedish 2,72% 2,12% 1,41% 4,07% 4,18% 2,45% 3,55%

Foreign 0,02%

Swedish equity funds 5,61% 7,77% 8,36% 5,50% 1,27% 3,69% 3,99% 4,20%


Fixed Income 29,96% 52,98% 54,82% 43,09% 38,29% 40,42% 35,95% 28,81% 29,12% 26,61% Swedish 24,21% 49,13% 51,97% 30,33% 23,37% 23,49% 17,72% 15,28% 15,81% 15,81%

Foreign 0,00% 2,85% 3,02% 4,48% 1,41% 1,28% 1,21% 1,29%

Swedish fixed income funds 3,09% 3,85% 3,75% 3,57% 2,49%

Foreign fixed income funds 2,67% 9,74% 10,44% 15,52% 16,95% 8,57% 8,44% 8,31%

Cash Alternative investments 0,00% 0,00% 11,17% 13,25% 15,70% 15,04% 16,26% 24,68% 21,33% 21,59% Hedge funds 11,17% 13,25% 9,40% 8,46% Private Equity 3,26% 5,53% Real estate 3,04% 2,27% CommoditiesOther 16,24% 4,11% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.7: Electrolux-koncernens Pensionsstiftelse allocations

Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 12,45% 12,62% 9,06% 11,58% 11,62% 9,42% 10,10% 11,31% 12,10% 10,57% Swedish Foreign Swedish equity funds Foreign equity funds 12,45% 12,62% 9,06% 11,58% 11,62% 9,42% 10,10% 11,31% 12,10% 10,57%


Foreign 7,54% 7,65% 6,72% 6,24% 5,72% 5,94% 4,73% 4,96%

Swedish fixed income funds 13,73% 15,05% 13,82% 14,36% 15,18% 14,47% 14,93% 14,86% 13,33% 83,95%

Foreign fixed income funds Cash Alternative investments 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% Hedge funds Private Equity Real estate CommoditiesOther 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.8: Danske Bank, Sverige Filias Pensionsstiftelse allocations

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Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 32,96% 36,59% 20,22% 26,34% 22,62% 20,44% 22,66% 25,01% 27,11% 30,50% Swedish 4,03% 4,10% 3,51% 5,90% 5,66% 4,67% 5,18%

Foreign Swedish equity funds 7,06% 6,67% 3,38% 4,71% 4,03% 3,59% 3,80%

Foreign equity funds 21,87% 25,81% 13,34% 15,74% 12,93% 12,19% 13,67%

Fixed Income 62,00% 56,26% 72,92% 62,61% 61,58% 62,66% 60,44% 54,74% 47,81% 42,67% Swedish 62,00% 53,65% 64,49% 55,21% 51,82% 54,62% 50,54%

Foreign 2,61% 8,43% 7,40% 9,76% 8,04% 9,90%

Swedish fixed income funds Foreign fixed income funds Cash Alternative investments 5,04% 7,15% 6,86% 11,05% 15,80% 16,90% 16,90% 20,25% 25,08% 26,84% Hedge funds 5,04% 5,54% 6,01% 10,05% 8,02% 10,40% 10,98% 12,69% 15,67% 16,44% Private Equity Real estate 1,62% 0,85% 1,01% 7,78% 6,50% 5,93% 7,56% 9,40% 10,39% CommoditiesOther 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00% 100,00%

Figure A.9: Stora Ensos Svenska Gemensamma Pensionsstiftelse allocations

Allocations 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Equity 60,22% 54,89% 38,58% 41,17% 43,66% 37,50% 41,23% 40,98% 44,23% 42,86% Swedish Foreign Swedish equity funds 31,13% 28,17% 18,85% 18,65% 17,37% 9,83% 10,40% 12,93% 14,93% 10,34%



Foreign 2,80% 2,64% 1,84% 1,67% 1,62% 1,58%

Swedish fixed income funds 34,44% 39,96% 56,22% 44,63% 42,77% 49,48% 46,27% 44,71% 44,64% 48,91%

Foreign fixed income funds Cash Alternative investments 0,00% 0,00% 0,00% 2,66% 6,69% 6,62% 8,85% 10,82% 8,90% 7,49% Hedge funds 2,66% 4,87% 4,64% 7,12% 9,14% 7,21% 7,49% Private Equity Real estate Commodities 1,82% 1,97% 1,73% 1,68% 1,69%Other 4,71% 4,50% 4,49% 3,65% 1,27% 1,33% 1,29% 1,19% 0,00% 0,00%Sum 100,00% 100,00% 100,00% 100,00% 100,00% 100,01% 100,00% 100,00% 100,00% 100,00%

Figure A.10: Byggnads Pensionsstiftelse allocations

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ISSN 2017:162

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