Private Equity Portfolio Management and Positive Alphas

INOM EXAMENSARBETE TEKNIK,GRUNDNIVÅ, 15 HP

, STOCKHOLM SVERIGE 2020

Private Equity Portfolio Management and Positive Alphas

RIKARD FRANKSSON

KTHSKOLAN FÖR TEKNIKVETENSKAP

Private Equity Portfolio Management and Positive Alphas Rikard Franksson ROYAL

Degree Projects in Applied Mathematics and Industrial Economics (15 hp) Degree Programme in Industrial Engineering and Management (300 hp) KTH Royal Institute of Technology year 2020 Supervisor at KTH: Ximei Wang Examiner at KTH: Sigrid Källblad Nordin

TRITA-SCI-GRU 2020:107 MAT-K 2020:008

Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

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AbstractThis project aims to analyze Nordic companies active in the sector of Information andCommunications Technology (ICT), and does this in two parts. Part I entails analyzingpublic companies to construct a valuationmodel aimed at predicting the enterprise value ofprivate companies. Part II deals with analyzing private companies to determine if there areopportunities providing excess returns as compared to investments in public companies.In part I, a multiple regression approach is utilized to identify suitable valuation models.In doing so, it is revealed that 1-factor models provide best statistical results in terms ofsignificance and prediction error. In descending order, in terms of prediction accuracy,these are (1) total assets, (2) turnover, (3) EBITDA, and (4) cash flow. Part II uses model(1) and finds that Nordic ICT private equity does provide opportunities for positive alphas,and that it is possible to construct portfolio strategies that increase this alpha. However,with regards to previous research, it seems as though the returns offered by the privateequity market analyzed does not adequately compensate investors for the additional risksrelated to investing in private equity.

Keywords: Nordic private equity performance, private equity valuation, CAPM, port-folio optimization, multivariate linear regression, quadratic optimization

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SammanfattningDet här projektet analyserar nordiska bolag aktiva inom Informations- och Kommunika-tionsteknologi (ICT) i två delar. Del I behandlar analys av publika bolag för att konstrueraen värderingsmodell avsedd att förutsäga privata bolags enterprise value. Del II analyse-rar privata bolag för att undersöka huruvida det finns möjligheter att uppnå överavkastningjämfört med investeringar i publika bolag. I del I utnyttjas multipel regressionsanalys föratt identifiera tillämpliga värderingsmodeller. I den processen påvisas att modeller medenbart en faktor ger bäst statistiska resultat i fråga om signifikans och förutsägelsefel. Ifallande ordning, med avseende på precision i förutsägelser, är dessa modeller (1) totalatillgångar, (2) omsättning, (3) EBITDA, och (4) kassaflöde. Del II använder modell (1) ochfinner att den nordiska marknaden för privata ICT-bolag erbjuder möjligheter för överav-kastning jämfört med motsvarande publika marknad, samt att det är möjligt att konstrueraportföljstrategier som ökar avkastningen ytterligare. Dock, med hänsyn till tidigare forsk-ning, verkar det som att de möjligheter för avkastning som går att finna på marknaden avprivata bolag som undersökts inte kompenserar investerare tillräckligt för de ytterligarerisker som är relaterade till investeringar i privata bolag.

Nyckelord: nordiskt privatkapitals prestation, värdering av privatkapital, CAPM, port-följoptimering, multipel linjär regression, kvadratisk optimering

Contents

1 Introduction 11.1 Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Research Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Background 32.1 Private, Not Public, Equity . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Illiquidity Decreases Investor Autonomy . . . . . . . . . . . . . . 32.1.2 Information Assymetry Increases Uncertainty . . . . . . . . . . . 42.1.3 Lack of Intermediary Decreases Availability . . . . . . . . . . . . 5

2.2 Risk Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 The Value of Equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Cash Flow-Based Approach . . . . . . . . . . . . . . . . . . . . 62.3.2 Comparable Multiples-Based Approach . . . . . . . . . . . . . . 62.3.3 Approach Trade-Off . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 The Nordics and Private Equity Activity . . . . . . . . . . . . . . . . . . 82.5 Project Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

I Building a Valuation Model 10

3 Theoretical Considerations 113.1 Defining Valuation Measures . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Income Statement Measures . . . . . . . . . . . . . . . . . . . . 113.1.2 Statement of Financial Position Measures . . . . . . . . . . . . . 123.1.3 Cash Flow Statement Measures . . . . . . . . . . . . . . . . . . 123.1.4 Other Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.5 Summary of Measures to be Considered . . . . . . . . . . . . . . 13

3.2 Valuation Based on Periodical Measures . . . . . . . . . . . . . . . . . . 143.2.1 Measure Observations Are Not Independent . . . . . . . . . . . . 14

4 Methodology 164.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2 Asset Valuation - Multiples and Regression . . . . . . . . . . . . . . . . 17

4.2.1 Model Specification . . . . . . . . . . . . . . . . . . . . . . . . 174.2.2 Training Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2.3 Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 184.2.4 Fitting Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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4.2.5 Estimating Enterprise Value of Private Companies . . . . . . . . 20

5 Results 215.1 Training Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2 Asset Valuation Regression Model . . . . . . . . . . . . . . . . . . . . . 21

5.2.1 All Possible Regression . . . . . . . . . . . . . . . . . . . . . . 215.2.2 Multi-Factor Candidate Model . . . . . . . . . . . . . . . . . . . 245.2.3 1-Factor Candidate Models . . . . . . . . . . . . . . . . . . . . . 245.2.4 Choice of Final Model - Total Assets . . . . . . . . . . . . . . . 31

5.3 Predictions Using Model . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6 Discussion 346.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346.2 Asset Valuation With Regression . . . . . . . . . . . . . . . . . . . . . . 34

6.2.1 1-Factor Model(s) . . . . . . . . . . . . . . . . . . . . . . . . . 36

II Estimating Risk and Returns of Private Equity 38

7 Methodology 397.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397.2 Asset Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397.3 Asset Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407.4 Portfolio Construction and Strategy . . . . . . . . . . . . . . . . . . . . . 40

8 Results 428.1 Asset Risk and Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . 428.2 Portfolio of Private Equity . . . . . . . . . . . . . . . . . . . . . . . . . 46

9 Discussion 479.1 Private Equity Risk and Returns . . . . . . . . . . . . . . . . . . . . . . 479.2 Nordic Private Equity Portfolio Performance . . . . . . . . . . . . . . . . 48

10 Further Research 50

11 Conclusions 52

References 53

A All Possible Regression 56

B Model Statistics 61

C Non-Existance of Theoretical Return Variance 62

Chapter 1

Introduction

Private equity has been receiving increasing attention over the past few years, reaching anall-time high in investor activity in 2018 [1]. In particular, the Nordic markets for privateequity comprise a large portion of this activity, both in the European region and globally[2]. However, private equity is not as readily, or easily, accesible as publicly traded equity,caused by the lack of an official and regulated trading platform. Furthermore, privateequity exposes investors to risks that are not commonly present at such an extent whenconsidering public equity. Nonetheless, investor activity is booming and the question tobe asked is: does private equity offer positive alphas?

1.1 Project ScopeThe project aims to analyze Nordic medium sized companies active in the sector of ICT,Information and Communications Technology. More specifically, applicable companiesshould be registered with an activity code belonging to sector J - Information and Commu-nication, according to Eurostat’s statistical classification of economic activities [3]. Theterm “medium size” refers to at least one of the following criteria being fulfilled:

• 1m EUR ≤ Operating Revenue < 10m EUR

• 15 ≤ Number of employees < 150

• 2m EUR ≤ Total assets < 20m EUR

By looking at “medium sized” companies, there is some insurance of the companies’ busi-nesses being viable, or at least an indication of proof-of-concept having been established.Thusly, the risks of unexpected short-term default and probabilities of explosive growthshould be smaller. One might rather expect to find opportunities of managerial enhance-ments to boost growth. However, when considering the companies on their own, as op-posed to analyzing funds’ performance, attention is directed towards these companies’abilities to enable growth. In other words, the project is not directed towards analyzing theperformance of funds or the skills of their general partners, the attention, instead, lies uponwhat the market has to offer potential investors. Furthermore, the project does not aim toinclude macro-economical influencial factors but rather intends to investigate companycharacteristics and how to value equity with simple measures.

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2 CHAPTER 1. INTRODUCTION

Lastly, a dataset of deals made in the industry, with companies fulfilling the afore-mentioned critera, was not available at the time of the project writing. Thus, calculationof applicable discounts and premiums is deemed lying outside of the project scope andfigures sampled from relevant research will instead be considered.

1.2 Research QuestionWith booming investor activity and a target market to analyze, the project intends to in-vestigate: Does the Nordic private equity market for medium sized companies active in thesector of Information and Communications Technology offer opportunities for unexpect-edly large returns, as compared to the corresponding public market?

By constructing some optimal portfolio of applicable assets the question can be an-swered depending on the performance of such a portfolio. In turn, the project also aimsto answer: Does the Nordic private equity market for medium sized companies active inthe sector of Information and Communications Technology offer opportunities for returnsexceeding those of comparable public equity, and, if so, does the excess return compensatefor additional risk?

Chapter 2

Background

Private equity fundamentally refers to equity that is not publicly traded and is constitutedby the shares of companies not publicly listed at any exchange. Public exchanges for eq-uity trading impose rules and frameworks that listed companies must comply with. Thisincludes standardized information handling and reporting procedures that specify the ex-tent and details that press-releases, financial statements, and other public announcementsmust adhere to. Simply put, the goal is to ensure information symmetry, i.e., that all in-vestors are equally well-informed. Furthermore, exchanges provide a unified platform fortrading of the listed equity where investors gather to negotiate the prices of shares.

2.1 Private, Not Public, EquityPrivate companies are not required to follow the policies of exchanges and, inherently,often comply with more lax policies regarding information transparancy. Consequently,investments in private equity are riskier than investments in publicly traded equity, stem-ming from the challenges of

• illiquidity,

• information assymetry, and

• lack of intermediary.

2.1.1 Illiquidity Decreases Investor AutonomyWith no official marketplace for trading, there are generally a lot less actors looking to tradeprivate equity. Moreover, private companies are often characterized by few and large own-ers. In effect, finding counterparties for trades is difficult and investors can find themselvesin a position of not being able to enter a position of interest or exit an overdue position.Sorensen, Wang, and Yang [4] find that the cost of illiquidity constitutes 50% of limitedpartners’ total present value costs, in the case of limited partnership funds investing inprivate equity. Furthermore, Franzoni, Nowak, and Phalippou [5] find that the risks ofilliquidity advocates a liquidity risk premium of 3% per annum.

With less market participants being present, the risk of not being able to exit a positionwhen required is substantial. Being overinvested in private equity thus increases the risk of

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4 CHAPTER 2. BACKGROUND

not being able to meet capital requirements from other undertakings due to cash shortageand might cause involuntary liquidation at discounts [6].

Generally, the transaction costs of trading increases as the liquidity of the underlyingasset decreases and with an assumed relationship between transaction costs and the liq-uidity of an asset it follows that if transaction costs can be quantified then the cost of illiq-uidity should be possible to estimate. Damodaran [7] suggests an estimate of an illiquiditydiscount of asset valuations in the range of 25-35%, where the valuation is performedassuming the asset is liquid. Thus, illiquidity can be conceptualized by considering

• bid-ask spreads,

• price impact of trading, and

• opportunity cost.

Bid-Ask Spreads

The bid-ask spread refers to the difference in price market participants are willing to selland buy assets from the perspective of a prospective investor. With less investors trading anasset there is implicitly less market concensus of what the fair price of the asset should be.With more trading activity more investor assumptions and estimates are aggregated, alongwith other information present, to form market prices. Consequently, less liquid assets,and private companies in particular, have less aggregate information tied to its marketprices. With less information, uncertainty regarding the fair value increases and, in turn,the bid-ask spread widens, increasing the price paid to acquire the asset while decreasingthe price at which the asset can be sold.

Price Impact of Trading

The price impact of trading refers to when an investor either exits a position or enters a newposition in a way that directly affects the available market prices. For example, a buyerenters a position of large volume and acquires all volume present of sellers at certain pricelevels. As a result, offers to sell at such price levels no longer exist and (1) the bid-askspread widens, as well as (2) the total cost of acquisition is greater than if all volume wasacquired at the previously availabile most beneficial price level.

Opportunity Cost

The opportunity cost of trading refers to the timing of investment. An investor might waitto enter or exit a position, hoping for amore profitable opportunity. In doing so, the investormight instead be faced with the opposite situation causing reduced profits. Naturally, thisis difficult to measure and expectations vary. However, the situation is a consequence ofdifferences in public and private information, the time horizon of investments, trading styleof the investor, and so on, and is therefore indeed relevant.

2.1.2 Information Assymetry Increases UncertaintySince private companies do not have to adhere to the rules and directives of regulated eq-uity markets orMTFs the requirements of information transparancy are less extensive – for

CHAPTER 2. BACKGROUND 5

more information see EUs MiFID II. As a result, most private equity investors are signifi-cantly less well-informed when compared to investors targeting public equity. Moreover,large actors in private equity investment make use of personal and professional networksestablished over many years of experience. Thus, information assymetry warrants con-cern since the selling party of any trade of private equity is likely to possess more detailedinformation of the underlying company and its business.

2.1.3 Lack of Intermediary Decreases AvailabilityThe lack of a market place for trading reduces the availability of investment opportunitiesand thus increases the effort required to find suitable investments. This, in turn, decreasesthe potential returns of the investments due to the increased cost of identifying oppor-tunities. Furthermore, often no immediate intermediary is available to increase capitalmobility and encourage investments in private equity. The intermediaries that do exist aremostly constituted by private equity funds and venture capitalists. These intermediariesdo facitilitate access to the private equity markets, but at a cost. Sorensen, Wang, andYang [4], Franzoni, Nowak, and Phalippou [5], and Phalippou and Gottschalg [8] all findthat the performance of these intermediaries, net of fees, is quite poor and that the costof the services is high. So, finding investment opportunities requires effort and thereforeis expensive while intermediaries performing this service demand costly compensation,resulting in decreased availability of investment opportunities at an increased cost.

Note, though, that while private equity fund and venture capital funds act as interme-diaries in gathering capital and deploying it on the market of private equity they provideadditional services. Alongside providing capital to business ventures these actors also pro-vide expertise and experience to aid business development. They provide companies withmanagerial skills and aspects commonly combined with profound industry knowledge. Asa result, investors often invest in the funds general partners’ abilities to leverage privatecompanies’ innovations and solutions in order to enable growth and, in turn, returns.

2.2 Risk CompensationClearly, private equity investments impose risks to an extent that is not commonly presenton the markets for public equity. Corporate finance theory states that the increased riskshould be compensated with a larger risk premium to incentivize investors to carry it.Sorensen, Wang, and Yang [4], Franzoni, Nowak, and Phalippou [5], and Phalippou andGottschalg [8], again, suggest that this, in fact, is not the case for limited partners in a pri-vate equity fund when looking at fund performance net of fees. Lopez-de-Silanes, Phalip-pou, and Gottschalg [9] state that one in 10 investments provides no return at all while onein four investments provides an internal rate of return exceeding 50%.

Thus, there are indications that the market of private equity provides opportunities ofhigh returns, with significant risks, and that providers of capital, or limited partners, toexisting funds are not adequately compensated with larger returns for the risk they carry.


2.3 The Value of EquityPrivate equity is further characterized by a lack of continuous equity valuation. In the caseof publicly listed companies the value of the equity is continuously adjusted by traders sothat expectations and predictions are always included in the valuation of the companies’shares. The liquidity provided by being publicly listed aggregates the public opinion ofcompanies thus yielding valuations of equity that are “agreed upon” by every interestedparty. Private companies, on the other hand, are not subjected to these pricing processesand an intrinsic valuation of the equity must be calculated. Naturally, this is a subjec-tive process. Any intrinsic valuation will include expectations of future performance and,sometimes, expectations of performance increases resulting from the additional knowledgeand expertise provided by the investor.

For funds looking to invest in private equity, Ewens, Jones, and Rhodes-Kropf [10]state that higher discount rates are used to account for risk that includes the funds’ idiosyn-cratic risk. Plenborg and Pimentel [11] state that the risk of illiquidity on its own warrantsa discount between 15-46%, wider than a spread of 25-35% suggested by Damodaran [7].They continue by mentioning the inclusion of a control premium, referring to the differ-ence between status quo value and optimal value stemming from the assumption that moreexperienced management are better equipped to leverage the assets and core business ofthe company to generate value. Furthermore, the control premium reflects the fact thatwhen valuing private equity using multiples the acquired valuation reflect minority shareswhile valuations should include the benefit of controlling shares, as it is more common forinvestors to acquire majority stakes in target companies. This control premium is found tolie between 26-45%. Following findings related to illiquidity discounts, Emory Jr., Den-gel, and Emory Sr. [12] investigate the difference in transaction prices pre- and post-IPOof 543 transactions. They find a mean pre-IPO discount of 30-55%, based on transac-tion timing pre-IPO. Officer [13] finds the discount rate of unlisted targets in the range of15-30%. Further, Silber [14] finds that the illiquidity discount to exceed 30%.

Valuation of equity is usually performed by either, or both, of two methods, namely

• forecasting and discounting cash flows, and

• multiples.

2.3.1 Cash Flow-Based ApproachValuing equity with a cash flow-based approach requires forecasting the future perfor-mance of the target company, in terms of cash flows. This allows for specific and detailedassumptions to be made regarding the components of the cash flow calculations. Thesecash flows are then evaluated in present value terms and specific discount rates can thusbe applied to account for the riskiness of the cash flows.

2.3.2 Comparable Multiples-Based ApproachValuation with multiples is based upon finding a comparable company to the target com-pany. For the comparable company it is assumed that it is similar to the target company interms of risk and business development such that the valuation procedure would highlight


minor differences in assumptions and characteristics. As such, multiples of financial fig-ures of the comparable company is calculated, e.g., Enterprise Value

EBITDA , which allows for simpleestimation of any comparable target company valuation. Reasearch shows that accrual-based multiples outperform cash flow-based multiples, and that multiples excluding biasin accounting information, such as EBITDA in favor of EBIT, provide better estimates ofvalue. Furthermore, combining value estimates has been found to increase the accuracy ofvalue estimates, reasoning that each value estimate provide information, and forward mea-sures provide better accuracy than current measures [11], [15], [16], [17], [18]. Eberhart[19] finds a negative relationship between the information available concerning compa-rable firms and the volatility of the target company’s expected returns close in time tocorporate events, supporting the fact that comparable companies provide analysts withuseful information.

Identifying Comparable Companies

When considering private equity, finding comparable firms can prove difficult and findingrelated financial statements is another challenge in itself. This is why the illiquidity dis-counts and control premiums are useful. The underlying assumptions of applying thesefactors entails valuing companies as if they are liquid and investments represent minorshares. Thus, identifying comparable companies requires less effort since publicly tradedcompanies can be used. On the other hand, the uncertainty of comparable companies in-creases as the dynamics and complexities of public companies differs from that of privatecompanies. Stakeholder pressure and expectations affect managerial decisions, invest-ment horizons, and business practice. Thus, using multiples based on public companiesprovides benefits in terms of effort but introduces a new dimension of uncertainty. Withvaluations being inherently subjective and varying in accuracy, this uncertainty is likelysurpressed by the availability of public companies and the extent of their financial reports.Dittmann and Weiner [20] find that comparable companies in Europe should be identifiedby considering companies with similar return on assets across European countries, as op-posed to regarding industry classification. Herrmann and Richter [21], on the other hand,construct a factor-based approach to finding comparable companies based on measuresof performance. They find that this approach also outperform industry classification infinding comparable companies. Even though research suggests more thorough screeningapproaches for finding comparable companies, industry classification constitutes an ap-proach much more viable in terms of effort, considering that this project aims to value alarge set of companies based on comparables.

2.3.3 Approach Trade-OffWhen determining the valuation of a single company both approaches are practically iden-tical, as no comparable company need be identified. However, usually many target com-panies are to be valued and, consequently, the effort required to utilize a cash flow-basedapproach increases significantly. The multiples-based approach requires dramatically lesseffort to apply but suffers from reduced ability to make qualified assumptions of each targetcompany of interest. Thus, there is a trade-off between the efforts of analyzing each com-pany individually and finding comparable companies to base the valuation upon. Whilethe cash flow-based approach does allow for more control of the valuation it is nonetheless


difficult to accurately forecast performance and it does not guarantee more precise valua-tions when compared to the multiples-based approach. In fact, Plenborg and Pimentel [11]find that more than 90% of professionals utilize the multiples-based approach, indicatingthat many professionals find the practicality of the multiples-based approach is extensiveenough to make it the preferred approach. Using a multiples-based approach introducesanother trade-off regarding which multiples to use. With research favoring forward mea-sures one must determine if the effort required to find the forward measures is worth theincreased accuracy. This trade-off is difficult to quantify or argue due to the subjectivity ofvaluations and measurement of accuracy, since a “true” valuation estimate does not needto exist, and, thus, the choice depends on the opinion of the analyst and the availability ofdata. However, when using the relative valuation approach, i.e., valuation through multi-ples of comparable companies, one should be aware of the fact that any relative valuationwill inherit certain characteristics of the comparable companies. Basing multiples on anindustry that is overvalued will likely cause any consequent valuation to be overvaluedas well [22]. This could be seen as a strength of consistency, and a fallacy of probleminheritance.

2.4 The Nordics and Private Equity ActivityCreandum [2] states that the Nordics account for approximately 50% of European privateequity exits and approximately 7% globally, in monetary figures. In 2016 the averageannual sum of exit values exceeded 4b USD and Information technology is highlighted asthe most valuable sector. Høegh-Krohn [1] supports these figures and continues to statethat in 2018 approximately 24b EUR was raised by buyout- and venture capital funds, andthat more than 13b EUR was invested. The amount of invested capital in Nordic privateequity has more than doubled, on average, between 2016 and 2018, denoting an all-timehigh. Moreover, 59% of all venture investments in 2018 were attracted by the tech sectorand mainly in ICT, Information and Communications Technology [1].

2.5 Project GoalThis project aims to analyze private companies in the Nordics acting in the sector of ICTin an attempt to provide insights regarding the state of the market and the presence of fi-nancially beneficial investment opportunities. In particular, this project aims to investigatewhether or not these companies provide investment opportunities with positive alphas. Inthe process of finding such opportunities, the project further aims to develop a simple val-uation procedure based on a combination of “common” multiples for valuation. As such,the project will cover an investigation of what multiples are most significant in valuingNordic private equity within ICT and the magnitude of these multiples.

Hopefully, this project will provide insights that can be used to gain an increased un-derstanding of the Nordic private equity market, the risks investors are exposed to, and thebasic differences to public equity investments. Lastly, this project will make an attempt todescribe the performance of Nordic private equity and explain any unexpected differencesin returns.

In effect, this report hopefully aids in strengthening the trend of previous years with


increasing investor activity in private equity, which is a key component to continue nur-ture the entrepreneurially spirited founders and employees that shape the landscape ofeconomic growth and technical innovation, and that characterizes private equity.

The report is divided in two parts where Part I regards the construction of the valu-ation model required to estimate the value of private companies. Part II is based on theestimated values of private companies resulting from Part I and contains the market andportfolio analysis answering the questions of whether or not private equity offers invest-ment opportunities with positive alphas.

In effect, to answer the research questions listed in the introduction the following mustfirst be considered:

• How can the value of private companies be estimated, and what are the parametersneeded to do so?

• How is the alpha of private equity calculated?

• What is an appropriate portfolio strategy and how does it perform?

Part I

Building a Valuation Model

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Chapter 3

Theoretical Considerations

3.1 Defining Valuation MeasuresThe project will utilize regression analysis to calculate measure loadings to be used forcombining multiple measures of companies’ performance and state to estimate their value.But, before defining the model of regression such measures must be considered and de-fined.

Available research considered unanimously find that forward measures improve theaccuracy of valuation [11], [15], [16], [17], [18]. However, finding or calculating forwardmeasures for the 7,834 companies to be analyzed is simply not feasible given the scopeof the study. Regarding other types of measures there is less consensus of their rank-ing in valuation accuracy. Nonetheless, different measures provide proxies for underlyinginformation regarding a company’s state and performance. As long as this underlying in-formation is not identical for two measures, using more measures increases the extent ofthe information basis provided by the measures at hand. Measures to be considered canbe categorized according to measures based on figures found in:

• income statements,

• statements of financial position,

• cash flow statements,

• other types of statements.

3.1.1 Income Statement MeasuresConsider the measures from the income statement, turnover and EBITDA. A company’sturnover indicates the amount of business being generated and maintained. Per annumit measures outcomes of activities – such as product launches, market expansion, directsales, etc. – often performed prior to the year investigated. As such, it can include infor-mation of long-term strategy performance, short-term sales initiatives, and more. Thus,evaluated independently on a per annum basis reveals little more than the size of currentlyconducted business. The yearly growth of turnover, on the other hand, provides a measure

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12 CHAPTER 3. THEORETICAL CONSIDERATIONS

of how well implemented strategies and initiatives perform in terms of growing the busi-ness. Furthermore, EBITDA then provides a measure of the company’s ability to generateprofits, excluding accounting policies, from the business activities.

In conclusion, measures as provided by the income statement that should be consid-ered in a model of company value entail (1) turnover, (2) yearly turnover growth, and (3)EBITDA.

3.1.2 Statement of Financial Position MeasuresIn the case of the statement of financial position, companies disclose information regard-ing their asset portfolio and capital structure, among other figures. Measures of leverageand asset distribution provides useful information in terms of a company’s structure. Dueto system imperfections caused by e.g., taxes, companies are incentivized to maintain acapital structure where debt is prevalent. Seemingly high proportions of debt in a firm’scapital structure implies a managerial belief of steady rates of income streams and a ro-bustness of business that can support debt in a sustainable manner, as well as incentivizesmanagers to actively supervise the financial health of the firm. This means that measuringrelative debt in a company can potentially provide information concerning the stability of acompany’s revenues, managerial belief and confidence, and manager’s financial attention.

Moreover, the distribution of investments in different asset types can reveal the direc-tion of interest and intent of a company. Especially in the industry of ICT, where tangibleassets, apart from investments in offices and similar, is generally dominated by invest-ments in computers and other technical assets. Acquiring large amounts of hardware willnot necessarily boost long-term competitiveness as a large portion of the investments willbe obsolete in just a few years. Investments in intangible assets such as software systemsand solutions, research projects, etc., on the other hand, provide opportunities for nurtur-ing the long-term growth of the company and, in effect, its value. While intangible assets,just like tangible assets, are exposed to the risk of becoming obsolete, it represents an assetclass that often can be more easily updated and extended to increase its usability and lifespan.

Apart from intangible assets, the total book-value of assets provides an accountingvaluation of the basis of the business. As such, it provides a measure of company sizeuseful to relate the performance of companies of similar, and differing, size.

So, measures that can be extracted from the statement of financial position and thatshould be included in a valuation model include (4) relative level of debt (leverage), (5)relative level of intangible assets and (6) total assets.

3.1.3 Cash Flow Statement MeasuresThe statement of cash flows is generally highly regarded by valuation analysts. Currentvaluation practice and research regards a company’s cash flows as the basis of valuation.Shortly put, the sum of a company’s future cash flows, in present value terms, equals thevalue of the company. However, as previously stated it is not feasible to estimate these cashflows for all the companies considered. Instead, consider the fundamental informationmediated by the bottom line of the cash flow statement: does the company generate asurplus of cash flow and, if so, how much?

CHAPTER 3. THEORETICAL CONSIDERATIONS 13

Thus, the single measure based on the cash flow statement that should be included ina valuation model is (7) cash flow.

3.1.4 Other MeasuresOther measures to be considered, that are not included in the statements mentioned, in-clude number of employees. The number of employees provides a measure of companysize as well as some indication of limitation in the amount of business that can be con-ducted.

Whether or not the company is publicly listed could be applicable in a valuation regres-sion model to incorporate information of related deals and acquisitions which would allowfor direct incorporation of illiquidity discounts and control premiums. Though, since thecalculation of such factors is not included in the scope of the project, such factors are dis-carded from the regression model and instead applied using figures from research at a laterstage.

Consequently, other measures to be included in a valuation model is simply constitutedby (8) number of employees.

3.1.5 Summary of Measures to be ConsideredSummarizing considerations and conclusions regarding measures and information resultsin the following list of measures that should be included in a regression model aimed atestimating the value of companies:

1. turnover,

2. yearly turnover growth,

3. EBITDA,

4. relative level of debt,

5. relative level of intangible assets,

6. total assets,

7. cash flow, and

8. number of employees.

These 8 measures can be categorized according to the type of information they provideconcerning the companies analyzed, namely:

• Company size

◦ turnover

◦ total assets

◦ number of employees

• Financial efficiency

14 CHAPTER 3. THEORETICAL CONSIDERATIONS

◦ yearly turnover growth

◦ EBITDA

◦ cash flow

• Financial structure

◦ relative level of debt

◦ relative level of intangible assets

Consequently, it can be argued that the measures this project aims to analyze are not onlyselected based on rational arguments, but also constitute measures widely used by industryprofessionals [20], [16], [15], [11].

3.2 Valuation Based on Periodical MeasuresIndustry professionals usually utilize either, or both, of the multiples-based approach anddiscounting cash flows when estimating the value of a company. The multiples-basedapproach is fundamentally dependent on an assumption of a linear dependence betweencompany valuation and some particular multiple. Discounting cash flows, on the otherhand, can be represented as follows

V0 =∞∑t=1

CFtRDt

. (3.1)

Where V0 is the estimated value of the company, CFt is the cash flow generated in the t:thperiod of time, andRD

t the discount rate used for t units of time. Clearly, such an approachrequires explicit assumptions of future cash flows, appropriate discount rates, and treatingcash flows in perpetuity. Forecasting cash flows entails estimating future revenues, costs,and asset allocations. As such, the methodology of the discounted cash flows approachentails invastigating (1) company size, (2) financial efficiency, and (3) financial structureas core parts of the valuation procedure.

3.2.1 Measure Observations Are Not IndependentNote that equation 3.1, like the multiples-based approach, in fact is of linear nature if CFttreated as given. However, in forecasting cash flows of firms a common approach basesthe forecast on assuming some exponential growth in revenue – growth of relevant marketconstitutes a popular baseline of growth – and determining other variables as fixed portionsof the revenue. Assumptions can be made complex and extensive – this constitutes anargument of magnitude used both in favor and opposition of the valuation approach – withmany variables being included. The key issue, though, results from the fact that practicallyevery financial measure is heavily dependent on past performance of said measure. Inthe discounted cash flow approach this is illustrated by forecasting e.g., revenue based onexponential growth – any type of relative growth, or recession, inherits this problematique– making the time-dimensionality dependency explicit.

CHAPTER 3. THEORETICAL CONSIDERATIONS 15

To explicitly define this dependence between yearly observations, let I(St) define thesum of revenues in period t generated by a set of revenue streams, i.e.,

I(St) = I(ω1) + I(ω2) + ...+ I(ωk), (3.2)St = {ω1, ω2, ..., ωk}. (3.3)

Let the individual revenue stream ωi correspond to revenue generated by some businessactivity. Next, consider the revenue streams of period t+ 1, St+1, and define it as

St+1 = (St\LSt) ∪NSt+1, (3.4)

whereLSt refers to the revenue streams lost in period t andNSt+1 refers to the new revenuestreams of period t + 1. Thus, we can formulate the revenue generated in period t + 1 asa function of the revenue generated in period t,

I(St+1) = I(St, LSt, NSt+1) = I(St)− I(LSt) + I(NSt+1). (3.5)

We can further extend the formula for any number of years, such that

I(St+2) =I(St)− I(LSt) + I(NSt+1)− I(LSt+1) + I(NSt+2), (3.6)I(ST ) =I(St)− I(LSt) + I(NSt+1)− I(LSt+1) + I(NSt+2) (3.7)

+ ...− I(LST−1) + I(NST ).

For the revenue streams of period k ∈ {t + 1, t + 2, ..., T} to be independent of thoseof period t it must be that St ∩ Sk = ∅ or, equivalently, LSt = St. In practice, thisinfers that a company must lose all of its business every period of time and generate newbusiness for the following period, independent of the business previously terminated, forthe revenues of multiple periods in sequence to be independent in this regard. Such ascenario is highly unlikely, particularly when considering companies of the size presentin this project’s analysis. Of course, the same line of arguing is applicable for most otherfinancial measures. In conclusion, multiple observations regarding a single company mustbe treated as dependent.

Returning to the discussion regarding forecasting cash flows, it should be noted thatwhen estimating future revenues a common approach is to assume current business ac-tivities will grow or be complemented. In the notations of this section we denote this:St+1 = St ∪NSt+1. Again, the inter-period dependency becomes transparent.

Chapter 4

Methodology

4.1 Data CollectionThe dataset used in this project can be acquired through Orbis [23] and entails 7,822 com-panies, of which 102 are public, that fulfill the following criteria:

• Size classification: At least one of...

◦ 1m EUR ≤ Operating Revenue (turnover) < 10m EUR

◦ 15 ≤ Number of employees < 150

◦ 2m EUR ≤ Total assets < 20m EUR

• Geographical region: the Nordics

• Activity code (NACE Rev.2): Section J (58-63)

• Other: Operating revenue available for last year of time period investigated

Bureau van Dijk [23] states that the data provided by Orbis is standardized to account fordiffering legal filing obligations and accounting differences across countries. Furthermore,figures are presented in EUR thousands using exchange rates as of each period’s closingdate. Thus, no further treatment or standardization of the figures acquired is made, exceptfor basic formatting.

The dataset covers the time period 2011-2018 and contains the following variables:

• Income statement

◦ Turnover

◦ EBITDA

• Statement of financial position

◦ Intangible fixed assets

◦ Cash & cash equivalents

◦ Total assets

16

CHAPTER 4. METHODOLOGY 17

◦ Long-term debt

◦ Loans

◦ Total shareholder funds and liabilities

• Cash flow statement

◦ Cash flow

• Other

◦ Number of employees

◦ Public (last observed year)

In other words, the dataset contains 62,576 observations of annual financial data, in groupsof 8 observations related to a specific company.

4.2 Asset Valuation - Multiples and RegressionThis project aims to construct a regression model for estimating the Enterprise Value ofcompanies – see Investopedia [24]. In short, the enterprise value of a company is a proxyof the cost of acquiring the company in its entirety – although, a controlling premium isusually present in an actual takeover – and can be denoted

Enterprise value =Market capitalization+ Long-term debt+ Loans− Cash & cash equivalents.

4.2.1 Model SpecificationThe regression model will, initially, contain the following variables:

• Dependent variable: enterprise value

• Independent variables:

◦ turnover

◦ total assets

◦ number of employees

◦ yearly turnover growth

◦ EBITDA

◦ cash flow

◦ leverage

◦ technical leverage

18 CHAPTER 4. METHODOLOGY

Where the two measures of leverage are defined as

Leverage =Long-term debt+ Loans

Total shareholder funds & liabilities,

Technical leverage =Intangible fixed assets

Total assets.

4.2.2 Training DataThe regression model will be trained on a subset of the dataset described in section 4.1.This subset contains the companies that are, or have previously been, publicly listed.1This subset is, in turn, split in 8 sets by each observation’s respective reporting year toavoid observation co-dependence as described in section 3.2.1. These sets will furtheron be referred to as FY1 through FY8, where FY1 refers to observations of 2011, FY2observations of 2012, and so on.

Note that FY1 cannot provide data of yearly turnover growth, as this measure is calcu-lated and not provided. Thus, FY1 will not be present in the model selection process andthe model evaluation process. However, if the model selected based on these processesdoes not contain yearly turnover growth as an independent variable the model will be usedto predict valuations of observations from 2011 – that would otherwise correspond to FY1.

4.2.3 Model AssumptionsTraining the regression model with data on publicly traded companies will cause assump-tions and properties of publicly traded companies to be implicitly included in the model.This includes assumptions of liquidity, accessability, absence of control premium, andmore.

Furthermore, the model is based on assumptions following standard multi-variate re-gression, i.e.,

y = Xβ + ε, (4.1)ε ∼ N(0, σ2In),

where y denotes the observations of the dependent variable, X observations of the inde-pendent variables – including ones for the intercept. β denotes loading for the independentvariables, ε the error terms, and In the n-dimensional identity matrix. X and β are treatedas given variables, such that

E[y] = Xβ,

Var(y) = σ2In.

1The analysis includes previously listed companies to avoid survivorship bias resulting from companiesbeing unlisted.


4.2.4 Fitting ModelIn the process of fitting the regressionmodel every possible submodel of the full model willalso be considered to investigate if they offer improved prediction performance. Thusly,the approach that will be followed can be outlined as:

1. evaluating the full model and every submodel,

2. choosing one candidate model, and

3. evaluating the candidate model.

Evaluating Every Model

To evaluate every possible model based on the choice of independent variables an all pos-sible regression approach will be utilized. Let k be the number of independent variablespresent in a model. Then, for every k = 1, 2, ..., 8 there are

(8k

)models to be analyzed.

Montgomery, Peck, and Vining [25, pp. 334–337] state that when a regression equa-tion is used for prediction purposes we, generally, want to minimize the mean squaredprediction error (MSPE). Hence, for every such model, the models’ respective MSPE willbe cross-validated to form a measure of prediction performance. That is, for every modelthe measure

MSPE = E[ 8∑i=2

8∑j=2

1{j 6=i} · (yFYj − yFYj ,FYi)2]

(4.2)

is calculated, where 1 denotes the indicator function, yFYi denotes observations of the de-pendent variable from set FYi, and yFYj ,FYi denotes the predicted values of the dependentvariable in set FYj of a model trained on set FYi.

That is, for every model, the model is trained on set FYi and its mean prediction errorcalculated on sets FYj , where j = 2, 3, ..., 8 and j 6= i. Then, the model’s performance iscross-validated for every possible training set, so that i = 2, 3, ..., 8.

Recall that FY1 is omitted due to lack of yearly turnover growth.

Choosing and Evaluating the Candidate Model

The candidate model will be chosen based on minimizing the MSPE. Then, it will beevaulated by considering the statistical significance of the model and its parameters, aswell as considering three types of residuals as defined by Montgomery, Peck, and Vining[25, pp. 130–135], namely:

• unscaled residuals - denoted ei,

• standardized residuals - denoted di, and

• studentized residuals - denoted ri.


Here,

ei = yi − yi, (4.3)

di =ei√

MSRes, (4.4)

ri =ei√

MSRes(1− hii), (4.5)

MSRes =

∑ni=1 e

2i

n− p, (4.6)

hii = (X(X>X)−1X>)ii, (4.7)

and p is the number of independent variables present in the model.

4.2.5 Estimating Enterprise Value of Private CompaniesThe approved valuation model will be trained on FY8 and used to estimate the enterprisevalue of every private company present in the dataset. The results of the estimation mustbe analyzed to ensure a reasonably stable valuation model has been constructed such thatfurther analysis of the private company valuations yield acceptable results in terms ofreliability, as will be presented in Part II.

Chapter 5

Results

5.1 Training DataFigure 5.1 shows a correlation plot of the independent variables and the dependent vari-able, based on observations in FY8. Clearly, the observation for which enterprise valueexceeds 3b EUR – figures are presented in EUR thousands – is far from the main cloud ofdatapoints. This observation represents a company of vastly different size than any otherobservation in the training set. In fact, this observed company is more than 10 times aslarge, in terms of enterprise value, as any other observed company of the training set. Con-sequently, it seems as though there are too few observations in the range spanned by thisobservation and the main cloud of datapoints to properly analyze the data. The influenceand leverage of this observation is of unreasonable magnitude to allow for any conclusionsto be made regarding the other observations of the training set. As such, this observationwill be removed with figure 5.2 showing the results of elimination. Observations of vari-ables total assets, cash flow, turnover, EBITDA, and number of employees does indicatethat there is a linear relationship with enterprise value.

As regards yearly turnover growth, there are observations of companies that have ex-perienced a dramatical increase in turnover which inherently yields observations of highinfluence – in a linear model setting. Apart from the unusually large deviations in yearlyturnover growth, these observations do not significantly differ from any other observationsand will not be eliminated.

5.2 Asset Valuation Regression ModelIn the following results and analysis, results of model comparisons use statistics basedon cross-validation using FY2-FY8. However, when analyzing a single model the resultsare based on training the model on FY8 as this is the procedure that will be utilized whenapplying the model for Part II. Hence, the reader is advised to consider that model statisticsmight differ depending on context.

5.2.1 All Possible RegressionTable 5.1 lists the top three performing submodels, based on minimizing the MSPE, com-pared to the full model. AppendixA presents amore extensive table ofmodel performance.

21

22 CHAPTER 5. RESULTS

Figure 5.1: Correlation plot of FY8

CHAPTER 5. RESULTS 23

Figure 5.2: Correlation plot of FY8 with eliminated influencial observation


Table 5.1: Top 3 performing (sub)models and full model comparison, with index based onthe minimum of MSPE

p Independent variables Index MSPE8 TA TECH.LEV LEV CF TURNOVER YTG EBITDA NOE 3.947 3.68e+094 TA TECH.LEV LEV CF 1.007 9.389e+083 TA TECH.LEV LEV 1 9.324e+082 TA LEV 1.005 9.374e+08

The 3-factor model with independent variables total assets, leverage, and technical lever-age represents the model with minimum MSPE.

5.2.2 Multi-Factor Candidate ModelThe results of fitting the 3-factor candidate model are presented in table 5.2. At a 95% levelof confidence, only total assets and the intercept are statistically significant. Furthermore,the parameter sum of squares of leverage and technical leverage are significantly smallerthan those of the intercept and total assets, indicating that their inclusion in the modelmight provide little aid in explaining the variation in the dependent variable.

The 2-factor model with independent variables total assets and leverage performs lessthan a percent worse than the 3-factor model, as seen in table 5.1. Thus, following theinsignificance of terms in the 3-factor model, technical leverage is eliminated, yieldingthe 2-factor model with statistics presented in table 5.3.

Again, the statistics of the 2-factor model highlight issues with statistical insignificanceof model parameters. Leverage is not statistically significant at a confidence level of 95%.Looking back at figure 5.2, it is not to surprising given the sporadic nature of the relationbetween leverage and enterprise value. As as result of this, we turn to the 1-factor models.

5.2.3 1-Factor Candidate ModelsTable 5.4 present the performance of the 1-factor models, with an index comparison versusthe best performing model – that is, the 3-factor model previously mentioned. Further-more, table 5.5 presents a comparison between these models based on R2. These tablesagree on the following points:

• number of employees and yearly turnover growth perform the worst,

• total assets outperform turnover, which outperformsEBITDA, that outperforms cashflow, and

• technical leverage performs poorly.

The 1-factor model with leverage as independent variable does perform best in terms ofminimizing MSPE, but has an R2 value of less than 3%. With such a low value of R2 themodel is ruled out for further analysis. Hence, models to be analyzed entail the 1-factormodels with independent variables total assets, turnover, EBITDA, and cash flow.


Table 5.2: 3-factor model statistics

Multiple R2 0.535Adjusted R2 0.514

ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 1.19e+04 3.58e+03 3.33 0.0014TA 8.75e-01 1.10e-01 7.96 2.9e-11LEV -1.23e+04 1.48e+04 -0.83 0.4085TECH.LEV -9.70e+03 7.51e+03 -1.29 0.2009

Analysis of VarianceTerm Df Sum Sq Mean Sq F-value Pr(> F )

TA 1 1.44e+10 1.44e+10 74.24 1.9e-12LEV 1 2.00e+08 2.00e+08 1.04 0.31TECH.LEV 1 3.23e+08 3.23e+08 1.67 0.20Residuals 67 1.30e+10 1.93e+08

Table 5.3: 2-factor model statistics


ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 8.48e+03 2.42e+03 3.51 0.0008TA 8.97e-01 1.09e-01 8.22 8.9e-12LEV -1.50e+04 1.48e+04 -1.01 0.3146


TA 1 1.44e+10 1.44e+10 73.52 2e-12LEV 1 2.00e+08 2.00e+08 1.03 0.31Residuals 68 1.33e+10 1.95e+08


Table 5.4: 1-factor modelsp Independent variables Index MSPE1 LEV 1.344 1.254e+091 TA 1.706 1.59e+091 TURNOVER 1.713 1.597e+091 EBITDA 1.874 1.747e+091 CF 1.896 1.768e+091 TECH.LEV 2.109 1.966e+091 NOE 2.134 1.99e+091 YTG 4.593 4.282e+09

Table 5.5: 1-factor models with R2 comparisonp Independent variables Index R2

1 TA 1 0.36491 TURNOVER 0.8522 0.3111 EBITDA 0.5603 0.20451 CF 0.3821 0.13941 TECH.LEV 0.1207 0.044041 LEV 0.0585 0.021351 NOE 0.04451 0.016251 YTG 0.01392 0.005081

Total Assets

In the 1-factor model with independent variable total assets, the variable is statisticallysignificant.


ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 7.07e+03 1.98e+03 3.58 6.4e-04TA 9.18e-01 1.07e-01 8.57 1.8e-12


TA 1 1.44e+10 1.44e+10 73.5 1.8e-12Residuals 69 1.35e+10 1.95e+08

Furthermore, figure 5.3 presents the residuals of this model. The figure indicates thatthe residuals do not show any apparent systematic behaviour and that residuals are of


Figure 5.3: Residuals of 1-factor model with total assets

reasonable scale. Hence, there is no indication of severe issues with the model and data.

Turnover

The second 1-factor model to consider is based on turnover as its independent variable.The table below shows that the variable is statistically significant.



ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 8.17e+03 1.79e+03 4.56 2.2e-05TURNOVER 8.39e-01 8.89e-02 9.44 4.8e-14


TURNOVER 1 1.57e+10 1.57e+10 89.1 4.8e-14Residuals 69 1.22e+10 1.76e+08

Figure 5.4 presents the residuals of this model. Again, the figure indicates that the residualsdo not show any apparent systematic behaviour and that residuals are of reasonable scale.Hence, there is no indication of severe issues with the model and data.

EBITDA

The third 1-factor model to consider uses EBITDA as its independent variable. Like theprevious two 1-factor models, the independent variable is statistically significant.


ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 1.78e+04 1.94e+03 9.15 1.6e-13EBITDA 4.59e+00 7.57e-01 6.07 6.2e-08


EBITDA 1 9.69e+09 9.69e+09 36.8 6.2e-08Residuals 69 1.82e+10 2.63e+08

Figure 5.5 presents the residuals of this model. The figure indicates a presence of modelinsufficiency. The residuals are showing signs of systematic behaviour with a clustering


Figure 5.4: Residuals of 1-factor model with turnover


Figure 5.5: Residuals of 1-factor model with EBITDA

of observations with negative residuals. Furthermore, the residuals show some non-lineartendencies with an upwards sloping curve with minimum at the most dense cluster ofpoints. Consequently, the model is deemed unreliable and is eliminated from the set ofcandidate 1-factor models.

Cash Flow

The last 1-factor model to consider is based on cash flow as its independent variable. Thetable below shows that the variable is statistically significant.



ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 1.81e+04 1.97e+03 9.21 1.2e-13CF 4.68e+00 7.93e-01 5.90 1.2e-07


CF 1 9.34e+09 9.34e+09 34.9 1.2e-07Residuals 69 1.85e+10 2.68e+08

Figure 5.6 presents the residuals of this model. The figure reveals the same kind of patternsas for the model with EBITDA as independent variable. There are indications of systematicbehaviour and non-linearity. Again, the model is deemed unreliable and it is eliminatedfrom further analysis.

5.2.4 Choice of Final Model - Total AssetsOf the two remaining candidate models, namely the ones with independent variables totalassets and turnover, their rankings based on performance, in terms of R2 and MSPE, isnot unanimous. Total assets performs best in terms of MSPE and turnover in terms ofR2. However, the models’ purpose is prediction and, hence, the model with independentvariable total assets is more suitable in this regard, as the results indicate that it providessuperior prediction performance.

5.3 Predictions Using ModelUsing the 1-factor model with total assets as independent variable to estimate the enter-prise value of the private companies present in the dataset yields the plot for FY1-FY8presented in figure 5.7.


Figure 5.6: Residuals of 1-factor model with cash flow


Figure 5.7: Plot of model predictions with training set observations in black, modelledrelationship in red, and 95% prediction interval in blue

Chapter 6

Discussion

6.1 DatasetThe dataset acquired contained many observations with missing values. As a result, therewere less observations that could be used for model training. As stated in section 5.1, thedata showed promise for identification of linear relationships, but some observations weretoo extreme to be considered suitable for the analysis. The extent of the problem withmissing data is made clear when considering the fact that out of 1,088 observations ofpublic, or previously public, companies only 328 observations are extensive enough to beusable in the project. Then, considering the fact that approximately one in 8 observationscan be used for training purposes, due to observation dependency issues, this figure isfurther reduced to less than 90 observations for the largest subset.

Regarding the reliability of the data, Bureau van Dijk [23] states that it is standardizedto eliminate accounting differences. Nonetheless, accounting principles and regulation al-low for two companies with identical financial situations to report slightly different figuresin their financial statements. As such, standardizing the data in terms of currency, reportdates, calculation formulas, etc., does increase the reliability of the data in a setting suchas the one of this project, but it can not account for every practice maintained at companiesand, thus, can not be completely standardized. Consequently, when dealing with financialfigures of companies one must be aware of the inherent presence of noise in the data.

This project relies on Bureau Van Dijk to provide accurate data of companies’ finan-cials. As an internationally large actor it seems reasonable that Bureau Van Dijk wouldwork hard to ensure the quality of their data. But, to quickly validate the correctness of thedata 20-30 observations of the 1,088 observations of public, or previously public, com-panies was sampled. With these samples, the figures were cross-referenced with thosereported by the companies in annual reports as well as with historical exchange rates toarrive at the conclusion that the data seemed to be precise and correct.

6.2 Asset Valuation With RegressionModelling company valuationwith amultiple regressionmodel does not seem to be straight-forward. The results do indicate that multiple regressionmodels offers potential for smallerprediction errors. That is, however, at the expense of statistical significance and explain-ability. Since the best 1-factor model is, in fact, approximately 1.7 times worse at predic-

34

CHAPTER 6. DISCUSSION 35

tion than the best 3-factor model it is tempting to overlook the insignificance problems.The 3-factor model includes technical leverage and leverage, two measures that are notpresent in the 1-factor candidate models. The question is then: What kind of informationthese measures provide that relates to the valuation of companies, that is not present in theother independent variables? The coefficient estimate of both of these parameters is neg-ative which indicates that debt financing and investments in intangible assets reduces theenterprise value. In general, debt financing should increase the enterprise value of the firmdue to the effect of leverage and increased managerial confidence. The fact that it seemsto do the exact opposite might be a consequence of the low interest rates of recent years.Lower interest reduces the tax advantage caused by incurring debt and the managerial at-tention required to maintain levels of returns. It may be that investors react to decreasingadvantages of leverage, or that investors are risk averse responding to increased uncertaintyregarding interest rates, resulting from less than usual characteristics of the debt market.On the other hand, that increased technical leverage would decrease the perceived value ofa company in the ICT industry is surprising. However, the fact that the 2-factor model withtechnical leverage eliminated performs only 0.5% worse could explain it as a coincidenceand since this is not part of the project scope it will not be analyzed further.

The prediction interval generated by the final model is wide. Recall figure 5.7 showingthe predicted enterprise values with 95% confidence intervals, clearly the model can notassure that a company with a predicted valuation of 60m EUR is actually worth anything,based on total assets, with confidence level at 95%. The lack of linearity in the data usedto train the model affects the precision of the model to a point that renders it impracti-cal. This might be an issue of model misspecification, or a choice of target companiesthat do not exhibit similar enough behaviour. Targeting a more narrow range of targetcompanies – e.g., required a certain level of technical leverage to target companies moreinvested in building technologically competitive businesses – might reveal more apparentrelationships between financials and perceived value. Such relationships could also beinvestigated by doing the opposite and actually widening the range of target companiesand collecting more variables to, in turn, utilize generalized regression models to analyzecompanies based on certain characteristics. By investigating more companies in a widerrange of characteristics it is possible to investigate if companies share characteristics basedon groupings such as profitability, capital structure, ownership structure, and more, that isexcluded in this analysis. Assuming to be able to identify explicit relationships in a groupof companies selected by the values of a few financial figures might be oversimplified andtoo limiting. Although, these limitations do aid in highlighting the fact that the basic fi-nancial figures analyzed do not provide enough information to confidently explain whyinvestors value companies of said characteristics the way they do within the ICT-sector.

Lastly, there is the question regarding whether or not it is reasonable to expect anytypes of linear relationships when considering company valuation and financial figures.As discussed in section 2.3, the main methods of valuation are based on either multi-ples of financial figures, or discounting future cash flows. Assuming that every investorconsiders the valuation multiples approach, the linear relationship between valuation andfinancial figures should be more explicit, or at least a more systematic behaviour. Thecash flow-based approach, on the other hand, induces more uncertainty in that regard. Itincludes assumptions regarding business development, market conditions, investors’ per-sonal opionions, and more. As such, it is unlikely that strictly linear relationships would

36 CHAPTER 6. DISCUSSION

be present. Perhaps the aggregate of a collection of such analyses offers a possibility ofsystematically similar assumptions. However, it is unlikely that every investor applies anyof these methods to justify their decisions. Valuations of public companies encompass thebehaviour of investors that do not always act rationally and objectively. While some relyon conclusions that can be drawn from valuation procedures, others rely on advice, publicopinion, or gut feeling. In other words, public company valuations depend onmany factorsand it is likely that the implications of such factors on valuations are difficult to capture infinancial statements and they require a wider scope to be investigated.

6.2.1 1-Factor Model(s)The 1-factor models considered in this project can be compared to the valuation multiplesdiscussed by existing research, but it is relevant to keep in mind that the 1-factor modelsinclude an intercept term otherwise commonly omitted. This project has shown that forNordic public companies of medium size, active in the ICT sector, the performance of aselection of multiples can be ranked as follows:

1. total assets,

2. turnover,

3. EBITDA, and

4. cash flow.

This is in line with the findings of e.g., Lie and Lie [16], as well as Plenborg and Pimentel[11]. However, Yee [17], Plenborg and Pimentel [11], as well as Cheng and McNamara[26], among many others, advocate the use of more than one multiple to calculate an av-erage valuation of a target company. Finding the best averaging method can be definedas a multiple regression setting just like the one this project has targetted. Table A.4 ofthe appendix actually highlights that averaging multiples can, in fact, produce valuationsof less precision in terms of prediction error. Some multi-factor models outperform the1-factor model using total assets, and some do not. However, in averaging multiples thevariance of the predictions inherently increases as a result of multicollinearity, since all ofthe multiples mentioned above exhibit similar behaviour linked to enterprise value. Aver-aging these multiples will cause the variance of the enterprise value estimate to increaseand the confidence interval of the estimation to be wider. Hence, while combinations ofmultiples does provide potential to include more information in the valuation procedure,it also introduces issues that may counteract the value of including them. Consequently,while it may be true that averaging value estimates can provide benefits and that it is acommon procedure in professional practice, averages should be looked upon with cautionand objectivity to avoid conclusions with lacking statistical support.

Whether or not it is reasonable to assume that a model dependent on a single parametercould provide valuation estimates of use is subject to every analyst’s decision. This projecthas shown that such models provide little explanation of the valuations of companies, withregards to the companies covered by the project scope. That being said, these results donot necessarily apply to situations where multiples based on a few comparable companiesare used to value a few others, as the relationships between multiples and valuation might


be stronger or weaker. Identifying a few companies with strong similarities in underlyingbusinesses, financial structures, and ownership structures should offer opportunities formore significant valuations, but would also seriously limit the generality of the model.It is possible that this is one of the key issues of the model developed in this project,that companies of fundamental similarity are spread thin in an extensive dataset, or thatfundamental similarities do not exist at all.

Part II

Estimating Risk and Returns of PrivateEquity

38

Chapter 7

Methodology

7.1 Data CollectionThe dataset used in estimating the risk and returns of private equity is constituted by thesubset of private companies of the dataset used in Part I. These observations are extendedwith an estimated enterprise value, using the 1-factor model with total assets developed inPart I.

7.2 Asset ReturnsFollowing the results of the previous part, it is assumed that the value-process of privateequity follows the regression model developed, i.e., that it follows total assets linearly.Furthermore, we assume that the returns of the assets follows the capital asset pricingmodel (CAPM) [27], so that

Ri −Rf = αi + β>i (f −Rf ), (7.1)

whereα is the excessive return, β therisk factor loadings, f the risk factors, andRf the risk-free interest rate. The expected value of an asset’s return is easily derived from equation7.1, i.e.,

E[Ri] = αi +Rf + β>(f −Rf ). (7.2)

So, using the CAPM, the returns of private equity is modelled using a simple regressionmodel, where Ri − Rf is the dependent variable, f − Rf the independent variable, Rf aconstant, and α the intercept.

The observed returns of assets are given by the value-process derived from the enter-prise values of the model of Part I. The risk-free interest rates based are proxied usingSwedish 7-year Government Bonds, downloaded from Sveriges Riksbank [28]. The aver-age rate per year covering FY1-FY8 are:

39


Period SE GVB 7Y Avg.FY1 2.4164%FY2 1.3197%FY3 1.8054%FY4 1.2385%FY5 0.3887%FY6 0.0029%FY7 0.2417%FY8 0.2816%

One risk factor will be used, namely the Nasdaq OMX Nordic 120 [29]. The developmentof the risk factor is defined as its relative price development from the opening price ofJanuary to the closing price of December, for each year, corresponding to how the returnsof private equity has been calculated. This data is readily available from Nasdaq GlobalIndexes [30].

Period NOMXN120FY1 -17.80%FY2 16.99%FY3 17.80%FY4 6.98%FY5 12.20%FY6 -1.37%FY7 7.49%FY8 -10.15%

7.3 Asset RiskAs regards the risk of the private companies considered, it will be quantified using thesquare root of the variance of estimated returns. However, this procedure is limited to esti-mating the variance by considering the estimated returns as samples of the distribution ofthe returns, as the theoretical variance does not exist. Appendix C provides an explanationwhy this is the case.

7.4 Portfolio Construction and StrategyThe extent of the data available is restrictive in terms of evaluating portfolio strategies.Preferably, there would be at least twice as many years of observations to allow for the


construction of a forward-looking asset allocation strategy that is evaluated based on out-comes. However, with only 7 years of price developments available the portfolio strategywill entail basing investment decisions on the previous years’ price development and noconsiderations of forecasting.

The portfolio strategy is based on an assumption of

E[Ru|R1, R2, ..., Rt] = Rt, (7.3)t, u ∈ N, t < u, (7.4)

i.e., next investment period’s decisions are based on an assumption of returns being iden-tical to the previous year. Then, the strategy is based on identifying a portfolio of assetsthat minimizes the volatility of the portfolio, while maximizing the expected returns. Fur-thermore, short-selling is not allowed and at least 75% of the available capital must beinvested. The strategy is denoted as the optimization problem

minx

x>t Cxt,

S.t. µ>t xt ≥ r,

0.75 ≤n∑j=1

xjt ≤ 1,

xjt ≥ 0, ∀j, (7.5)

Bt = 1{Bt≤Bt−1}0.99Bt− + 1{Bt>Bt−1}(0.99Bt− − 0.2(Bt− −Bt−1)),

B1 = 100.

Where C is the covariance matrix of assets, x the portfolio – i.e., a vector of asset weights– of investment allocations, µ the expected returns of assets, r a return constraint, B thefund size, and t the relevant time period.

The strategy is structured so as to behave similarly to an investment fund investing inprivate equity. The strategy demands that 1% of the outgoing fund balances are paid inmanagement fees, that 20% of profits are paid in incentive fees, and that investors’ capitalare bound until the fund’s maturity date – 6 years in this case. It would be reasonableto limit investments to acquiring at least 25% of equity per investment. However, thiswould cause the quadratic optimization problem to no longer be convex and increase itscomplexity. Hence, such a constraint will not be enforced.

The portfolio with minimum variance, of those resulting from the optimization prob-lem 7.5, is chosen to minimize the overall riskiness of the portfolio.

A fund size of 100m EUR is assumed and the portfolio strategy is implemented in FY2with discrete adjusting every two years, in the sense that every position in the portfolio isevaluated and divestiture to release capital for other investment opportunities is allowed.

Chapter 8

Results

8.1 Asset Risk and ReturnsTable 8.1 presents the yearly alphas, betas, and returns of Nordic ICT private equity. Thevolatility figure presented is calculated as the historical volatility over FY1-FY8. Thetable shows that the ICT private equity market y outperform the Nordic public marketfor 7 consecutive years, with an increasing outperformance. From an outperformance ofapproximately half of a percent the market grows to achieve an outperformance of nearlythree percent. Furthermore, the volatility of returns is 1.15%, less than 10% of that ofthe comparable index. Considering the full span of FY1-FY8, the private equity marketsubject for the analysis has an alpha of 0.5658% and a beta of −0.039596. Moreover,covering FY1-FY8 as well as during individual years, the private equity market has a smallbeta and, surprisingly, a negative beta.

Figure 8.1 displays a random sample of 5 companies’ returns as compared to the returnsof NOMXN120. The estimated values of the companies are presented as circles with theirrespective CAPM-fit represented in dotted lines. As one might expect, the linear relation-ship between company returns and the returns of NOMXN120 is not always explicit andthe residuals are relatively large for some companies. The returns of the private companiesis more generally visualized in figure 8.2. The figure shows that every year a majority ofcompanies yield positive returns, and that most companies offer profits and losses less than25%. Figure 8.3 shows the corresponding histograms from which it becomes clear that amajority of all companies offer positive returns, for every year analyzed. Furthermore, thehistogram implies a distribution with thin tails centered slightly above zero, supportingthe low volatility of aggregate returns.

42


Table 8.1: Private Equity Market CharacteristicsYear Alpha∗ Beta∗ Return NOMXN120FY1 0.5238% -0.04021 3.0925% -17.80%FY2 1.2818% -0.10921 -0.5754% 16.99%FY3 1.5519% -0.10107 0.9095% 17.80%FY4 1.8940% -0.07454 1.5956% 6.98%FY5 1.9396% -0.05804 2.2678% 12.20%FY6 2.1509% -0.04965 1.1181 % -1.37%FY7 2.7856% -0.07165 1.6267 % 7.49%

Volatility 1.15% 12.4%∗ Calculated as the value-weighted average of the underlying assets.

Figure 8.1: Plot of Randomly Sampled Private Company Returns


Figure 8.2: Ordered returns of private companies with positive returns in blue, negativereturns in red, and returns exceeding 25% in both directions in orange

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Table 8.2: Portfolio PerformanceYear Returns Returns Net of Fees Excess Returns∗ % of Funds InvestedFY2 4.9050% 2.8749% 3.4503% 87.417%FY3 4.5913% 2.6271% 1.7176% 87.417%FY4 4.9210% 2.8876% 1.2920% 85.454%FY5 5.5001% 3.3451% 1.0783% 85.454%FY6 4.9327% 2.8968% 1.7787% 97.293%FY7 5.1599% 3.0763% 1.4496% 97.293%

Tot. Growth 15.71%∗ Net of fees, as compared to private equity market returns.

8.2 Portfolio of Private EquityThe fund-imitating portfolio strategy’s back-testing results are presented in table 8.2, wherethe expected volatility of the returns do not exceed a limit of 5%. The portfolio providespositive returns net of fees for every active year and yields positive returns when the pri-vate equity market does not, in FY2. It does so with a relatively low level of risk, less than5% volatility, and ultimately yields more than 15% in growth over the span of 6 years, netof fees. Excluding fees yields more than 34% growth over 6 years, at a risk level less thanhalf of that of the comparable public equity index/portfolio (NOMXN120). During thesame period, NOMXN120 grew by more than 50%. Note that the portion of the fund thatremained uninvested is not modelled to be invested in any interest carrying assets, or anyother asset class for that matter.

The particular portfolio presented here is one out of many possible configurations pro-viding risk exposure and returns of neglible differens, given the vast amount of candidatecompanies that could be included in the portfolio. This portfolio simulates positions in 27companies with ownership stakes exceeding 4% for the smallest investments. The aver-age investment amounts to approximately 4 mEUR. This kind of investment pattern is notnecessarily impractical nor is it unreasonable.

Chapter 9

Discussion

9.1 Private Equity Risk and ReturnsIt was argued that the variance of asset returns is not defined, see appendix C, whichraises some questions regarding the validity of model assumptions. However, consider thesampled distribution of the volatility of assets, as presented in figure 9.1. Given the shapeof the distribution, it is not unlikely that the variance follows some distribution belongingto the exponential family. Consequently, finding that the variance is “well-behaved” mightimply that both it and the mean is not undefined, as more sporadic behavior would beexpected. Hence, valuing companies independently per annum and assuming the estimatedvalues are independent is likely less than ideal. A common approach to modelling thereturns of assets assumes that the returns are log-normally distributed and linear in factors,an assumption that does not produce undefined variance but rather behaviour similar to thatobserved in this project.

However, the assumptions of Part II are derived based on the assumptions of Part I and,thus, in order to improve themodelling it could be of interest to reverse the procedure. Thatis, deriving model assumptions of company valuation based on the assumptions of e.g.,log-normal returns.

With regards to the practical implications of the volatility, the market analysis coversa set of more than 4,500 companies in comparison to the 120 companies present in thecomparable index. The observed difference in volaility when comparing private and publicequity returns might thus be a result of different sample sizes. With almost 40 times asmany companies being present in the private equity market analysis, it is not surprisingthat the aggregate behaviour is less volatile than that of a smaller index.

The aggregate market characteristics indicate that the Nordic market for private com-panies active in the sector of ICT is growing steadily. Furthermore, the results indicatethat the private equity market does provide opportunities for positive alpha investmentsfor every year analyzed. Though, this is the case when only considering NOMXN120 as arisk factor. Identifying more risk factors – e.g., global indices, loan term structures, etc. –might have an impact on the alpha of the market analyzed and could offer an opportunityto further investigate the risk exposure of private equity.

It is surprising to find that the private equitymarket has a negative beta on theNOMXN120risk factor, and that it is almost zero. Inherently, this unintuitively suggests that it shouldbe possible to hedge a position in public ICT equity with a position in corresponding

47

48 CHAPTER 9. DISCUSSION

Figure 9.1: Volatility of private equity assets

private equity. This characteristic could be explained by the fact that aggregating the per-formance of every company subject to this analysis has a diversifying effect that eliminatesthe volatile price developments of public equity and that the characteristics of the privateequity market is significantly different from those of public equity. The exclusion of thelarger trading volumes of public equity likely decreases the volatility of the private equityprices, a fact indicating that these results should be looked upon with caution. In line withthe discussions regarding risk in sections 2.1 and 2.2, there are risks that might be difficultto capture with risk factors in a CAPM-setting and that should be analyzed before the re-sults presented could be generalized. Furthermore, with private companies not having tocomply with rules and guidelines to the same extent as public companies, the beta mightbe affected by different information policies and financial reporting requirements – suchas depreciation policies since total assets has been used as the main parameter to estimateenterprise value. On the other hand, with a large number of companies being present inthe analysis such factors should have a mitigated effect.

9.2 Nordic Private Equity Portfolio PerformanceFirst and foremost, the portfolio strategy outlined in section 7.4 is a basic one. It lacksa forward-looking perspective that is difficult to apply to the dataset. A profound issuestems from the fact that the prediction intervals of valuations are wide and, in turn, thedevelopment of the value processes of companies imprecise. As such, the uncertaintyregarding estimations being similar to real outcomes is large and implementing forecastingin the portfolio strategy would likely increase this uncertainty. Hence, with observations


covering a longer historical period it might be practical to extend the strategy with a future-facing module.

Furthermore, the initial investments of any portfolio strategy should include appro-priate discounts for transaction costs – or, equivalently, illiquidity – but what about exitevents? Most research available on the subject list numerous reasons as to why discountsare justified when acquiring equity, but does not mention whether this is the case whenexiting the same position. It could be argued that large investors are more likely to haveaccess to networks of other investors that inherently reduces the transaction costs associ-ated with trading private equity and, in turn, reduces the discounts when exiting a position.Assuming that exit discounts are zero is not deemed reasonable due to a lack of marketinsights and discounting both the entry- and exit prices with the same factor would yieldno difference in returns, thus, discounts have been omitted from the calculations. Witha dataset of deals and transactions in Nordic ICT private equity, it would be possible toestimate the necessary parameters and the results easy to implement. Without such data,any assumptions regarding discounts would lack credibility and are consequently left forfurther research.

In section 2.1.1 it is noted that Franzoni, Nowak, and Phalippou [5] argues that therisks of illiquidity, when considering private equity, advocates a liquidity risk premiumof 3% per annum. Assuming that this is appropriate and applicable for the market underconsideration, the returns of the private equity market does not adequately compensateinvestors for the risk exposure. The portfolio strategy does provide enough returns tocompensate for the risk premium, but the theoretical fees diminishes the compensation toa degree such that the returns only exceed the risk compensation for two years, of the 6during which it is active. These results support the findings of Sorensen, Wang, and Yang[4], Franzoni, Nowak, and Phalippou [5], and Phalippou and Gottschalg [8].

With regards to the portfolio strategy, It seems as though the portfolio strategy providesexcess returns as compared to the market it is active in. In effect, it outperforms the publicequity of Nordic companies to an even larger extent. A value-weighted portfolio of allthe private companies also provides opportunities for excess returns, but holding such aportfolio is infeasible, if not practically impossible. Acquiring a value-weighted position in4,500 private companies would likely be too demanding to provide any net excess returnsgiven the resources required to accomplish the task. However, the returns of both of theseportfolios does not seem to adequately compensate investors for the risk exposure resultingfrom holding positions in private equity. Furthermore, these results should be looked uponwith caution due to the issues related to the valuation model. I believe the approach used inthis project is useful for insights in the characteristics of Nordic ICT private equity, and thatadjustments to the model assumptions made offer opportunities for further improvements.

Chapter 10

Further Research

The extent of research carried out on Nordic private equity is limited. Research regardingdeals and acquisitions made in relevant and related markets offers an opportunity to ex-tend knowledge about the financial dynamics of Nordic private equity. Furthermore, thisproject has revealed results that are in line with existing research regarding company val-uation and rankings of valuation multiples, but has also found that common practices ofcombining multiples can decrease, rather than improve, the precision of valuation. Theseresults warrant further investigation for validation and to see to what an extent they apply.

With regards to valuation procedures, it became apparent that the financial figuresused in this project to analyze the valuation of companies do not explain the observedbehaviour to a satisfactory degree. This adds to the already extensive search of precisevaluation models, and what kind of information they should include. The results did indi-cate that leverage and what was defined as technical leverage did reduce the MSPE of thevaluation model when included, but were statistically insignificant regression parameters.The fact that the 1-factor model with total assets as single factor performed approximately1.7 times worse than the model including both of the leverage measure indicates that thereseems to be some kind of information present in the measures that could improve valua-tion precision. Why that is and how these parameters can be utilized in a prediction modelto yield statistically significant results presents an opportunity for further insights in theinformation contents of financial measures.

The valuation procedure also indicated that there are reasons to investigate more gen-eralized regression models for analyzing Nordic private equity. Linear behaviour of com-panys of larger size was observed. This could present an opportunity to develop modelswith groupings of observations to analyze whether there exists populations with specificcharacteristics and to find what kind of characteristics that define the boundaries of groupsof companies with similar valuation behaviour.

The portfolio strategy was said to lack a forward-looking perspective. The reason ofthis was because of a short period of time of company valuations and financial perfor-mance was analyzed, yielding little room for resonable forecasts. Performing a similaranalysis using a dataset covering a longer period of time would increase the feasibility ofperforming forecasts in a portfolio strategy and providing more information to the invest-ment decisions being made. This could provide an opportunity to develop a more robustportfolio strategy that is less naive. While it certainly is not guaranteed that historical per-formance could predict future performance, this still is a fundamental assumption in the

50

CHAPTER 10. FURTHER RESEARCH 51

development of the valuation model as well as the portfolio strategy. In other words, aforecasting module is a reasonable extension of the portfolio strategy.

Chapter 11

Conclusions

To conclude, finding reliable data to a meaningful extent has proven challenging. Find-ing, among few observations, linear relationships between financial figures and enterprisevalues of companies resulted in simple regression models with a single multiple and in-tercept proving most useful. This due to a lack of statistical significance of multi-factormodel parameters. In effect, identifying an appropriate valuation model to utilize resultedin comparing 1-factor models – including intercepts – of total assets, turnover, EBITDA,and cash flow. The results indicate that the 1-factor models with best valuation accuracyis, in descending order,

1. total assets,

2. turnover,

3. EBITDA, and

4. cash flow.

However, of these models, ebitda and cash flow showed indications of severe model issueswith systematic behaviour prevalent in residuals and were not further explored.

With regards to the characteristics of Nordic ICT private equity, the analysis is affectedby the valuation model yielding wide prediction intervals. The Nordic ICT private equitymarket does not offer unexpectedly large returns, as compared to the public market. Theoverall market returns are small and less volatile in comparison. It does however offeropportunities for returns exceeding those of the public market, in terms of positive al-phas for every year analyzed. Furthermore, this return can be further increased with theportfolio strategy applied in this project. In effect, both a value-weighted portfolio and amin-variance portfolio offers returns that exceeds expectations in relation to the compa-rable public market. The private equity market subject to this analysis has a negative andsmall beta on the NOMXN120 risk factor and, thus, generally carries less of the risk ex-posure of the risk factor as well as it offers opportunities for hedging. Subsequently, theseresults indicate that the private equity offers unexpectedly large returns at lower risks inrelation to the NOMXN120 risk factor. However, the returns of the private equity arelikely subjected to risk factors that are not covered by public equity and further analysis isrequired to make more general conclusions.

52

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https://www.riksbank.se/en-gb/statistics/search-interest--exchange-rates/



https://indexes.nasdaqomx.com/docs/Methodology_NOMXN.pdf

https://indexes.nasdaqomx.com/docs/Methodology_NOMXN.pdf

REFERENCES 55

[30] Nasdaq Global Indexes. NASDAQ OMX Nordic 120 (NOMXN120). url: https://indexes.nasdaqomx.com/Index/History/NOMXN120 (visited on04/19/2020).

https://indexes.nasdaqomx.com/Index/History/NOMXN120

https://indexes.nasdaqomx.com/Index/History/NOMXN120

Appendix A

All Possible Regression

The following 3 pages present tables with suggested regression (sub)models for every pnumber of independent variables. Intra-index is an indexation based on every respectivegroup’s smallest MSPE, grouped by p. Index is an indexation based on the overall smallestMSPE. See section 4.2.4 for further details on how MSPE is calculated.

56

APPENDIX A. ALL POSSIBLE REGRESSION 57

Table A.1: Best performing submodels in terms of MSPE.

pIn

depe

nden

tvar

iabl

esIn

tra-

Inde

xIn

dex

MSP

E8

TATE

CH.LEV

LEV

CF

TURNOV

ERYTG

EBITDA

NOE

13.94

73.68

e+09

7TA

TECH.LEV

LEV

CF

TURNOV

EREB

ITDA

NOE

11.69

41.57

9e+0

96

TATE

CH.LEV

LEV

CF

TURNOV

ERNOE

11.11

51.04

e+09

5TA

TECH.LEV

LEV

CF

TURNOV

ER1

1.01

99.49

9e+0

84

TATE

CH.LEV

LEV

CF

11.00

79.38

9e+0

83

TATE

CH.LEV

LEV

11

9.32

4e+0

82

TALE

V1

1.00

59.37

4e+0

81

LEV

11.34

41.25

4e+0

9

58 APPENDIX A. ALL POSSIBLE REGRESSION

Table A.2: Top 3 performing submodels in terms of MSPE.

pIn

depe

nden

tvar

iabl

esIn

tra-

Inde

xIn

dex

MSP

E1

8TA

TECH.LEV

LEV

CF

TURNOV

ERYTG

EBITDA

NOE

13.94

73.68

e+09

27

TATE

CH.LEV

LEV

CF

TURNOV

EREB

ITDA

NOE

11.69

41.57

9e+0

93

7TA

TECH.LEV

LEV

CF

YTG

EBITDA

NOE

1.97

63.34

73.12

1e+0

94

7TA

LEV

CF

TURNOV

ERYTG

EBITDA

NOE

2.17

23.67

83.43

e+09

56

TATE

CH.LEV

LEV

CF

TURNOV

ERNOE

11.11

51.04

e+09

66

TATE

CH.LEV

LEV

TURNOV

EREB

ITDA

NOE

1.11

61.24

41.16

e+09

76

TATE

CH.LEV

LEV

CF

EBITDA

NOE

1.48

81.65

91.54

7e+0

98

5TA

TECH.LEV

LEV

CF

TURNOV

ER1

1.01

99.49

9e+0

89

5TA

TECH.LEV

LEV

CF

NOE

1.01

41.03

49.63

7e+0

810

5TE

CH.LEV

LEV

CF

TURNOV

ERNOE

1.05

91.07

91.00

6e+0

911

4TA

TECH.LEV

LEV

CF

11.00

79.38

9e+0

812

4TA

LEV

CF

TURNOV

ER1.01

71.02

49.55

1e+0

813

4TA

TECH.LEV

LEV

TURNOV

ER1.01

81.02

59.55

8e+0

814

3TA

TECH.LEV

LEV

11

9.32

4e+0

815

3TA

LEV

CF

1.01

11.01

19.43

e+08

163

TALE

VTU

RNOV

ER1.03

21.03

29.62

2e+0

817

2TA

LEV

11.00

59.37

4e+0

818

2LE

VTU

RNOV

ER1.02

21.02

79.57

9e+0

819

2LE

VCF

1.23

81.24

51.16

e+09

201

LEV

11.34

41.25

4e+0

921

1TA

1.26

91.70

61.59

e+09

221

TURNOV

ER1.27

41.71

31.59

7e+0

9

APPENDIX A. ALL POSSIBLE REGRESSION 59

Table A.3: One-factor models comparison

pIn

depe

nden

tvar

iabl

esIn

tra-

Inde

xIn

dex

MSP

E1

8TA

TECH.LEV

LEV

CF

TURNOV

ERYTG

EBITDA

NOE

118

.12

5.00

4e+1

02

7TA

TECH.LEV

LEV

CF

YTG

EBITDA

NOE

12.62

7.23

3e+0

93

6TA

TECH.LEV

LEV

CF

EBITDA

NOE

11.81

75.01

6e+0

94

5TA

TECH.LEV

LEV

EBITDA

NOE

11.13

33.12

9e+0

95

4TA

TECH.LEV

LEV

NOE

11.00

32.76

8e+0

96

3TA

LEV

NOE

11

2.76

1e+0

97

2TA

LEV

11.04

32.88

e+09

81

TA1

1.89

75.23

8e+0

99

1EB

ITDA

1.00

31.90

35.25

6e+0

910

1CF

8.33

15.8

4.36

3e+1

011

1TU

RNOV

ER10

.23

19.41

5.35

9e+1

012

1TE

CH.LEV

17.14

32.52

8.97

9e+1

013

1NOE

17.91

33.97

9.37

9e+1

014

1LE

V20

.92

39.68

1.09

6e+1

115

1YTG

23.96

45.45

1.25

5e+1

1

60 APPENDIX A. ALL POSSIBLE REGRESSION

Table A.4: Factor models of popular multiplesp

Inde

pend

entv

aria

bles

Intr

a-In

dex

Inde

xM

SPE

14

TACF

TURNOV

EREB

ITDA

12.07

21.93

2e+0

92

3TA

LEV

TECH.LEV

11

9.32

4e+0

83

3TA

CF

TURNOV

ER1.66

11.66

11.54

9e+0

94

3TA

TURNOV

EREB

ITDA

1.74

1.74

1.62

2e+0

95

3TA

CF

EBITDA

1.97

91.97

91.84

5e+0

96

3CF

TURNOV

EREB

ITDA

2.26

82.26

82.11

4e+0

97

2TA

CF

11.63

91.52

8e+0

98

2CF

TURNOV

ER1.01

1.65

61.54

4e+0

99

2TA

EBITDA

1.04

81.71

81.60

2e+0

910

2TA

TURNOV

ER1.06

1.73

71.62

e+09

112

TURNOV

EREB

ITDA

1.07

41.76

11.64

2e+0

912

2CF

EBITDA

1.49

2.44

22.27

7e+0

913

1TA

11.70

61.59

e+09

Appendix B

Model Statistics

[H] Multiple R2 0.587Adjusted R2 0.533

ParametersTerm Estimate Std. Error t-value Pr(> |t|)(Intercept) 1.10e+04 4.05e+03 2.73 0.0083TA 3.16e-01 3.72e-01 0.85 0.3994TECH.LEV -6.27e+03 7.81e+03 -0.80 0.4250LEV -1.04e+04 1.49e+04 -0.70 0.4895CF -1.72e-01 4.73e+00 -0.04 0.9711TURNOVER 4.60e-01 4.09e-01 1.12 0.2651YTG 7.41e+01 7.33e+01 1.01 0.3165EBITDA 8.27e-01 4.84e+00 0.17 0.8649NOE 8.45e+00 2.10e+01 0.40 0.6891


TA 1 1.44e+10 1.44e+10 77.35 1.7e-12TECH.LEV 1 3.89e+08 3.89e+08 2.10 0.153LEV 1 1.34e+08 1.34e+08 0.72 0.399CF 1 5.90e+08 5.90e+08 3.18 0.079TURNOVER 1 6.24e+08 6.24e+08 3.36 0.072YTG 1 2.01e+08 2.01e+08 1.08 0.302EBITDA 1 4.19e+06 4.19e+06 0.02 0.881NOE 1 3.00e+07 3.00e+07 0.16 0.689Residuals 62 1.15e+10 1.86e+08

61

Appendix C

Non-Existance of Theoretical ReturnVariance

The return of an asset at time t is defined as

Rt =Vt+1

Vt, (C.1)

where V is the predicted value of the valuation model developed in Part I, i.e.,

V = y = Xβ + ε, (C.2)

β = argminβ

(y −Xβ)>(y −Xβ) = (X>X)−1X>y, (C.3)

E(V ) = E(Xβ) = Xβ, (C.4)

V ar(V ) = V ar(Xβ) = σ2X(X>X)−1X> = σ2H. (C.5)

With the assumption that observations are independent and ε ∼ N(0, σ2) we have that forpredictions V0 and V1

Vi ∼ N(xiβ, σ2x>i (X

>X)−1xi), (C.6)

R0 =V1V0. (C.7)

(C.8)

Now, introduce an auxiliary variable, T , and let R = R0 such that

62

APPENDIX C. NON-EXISTANCE OF THEORETICAL RETURN VARIANCE 63

R =V1V0, (C.9)

T = V0, (C.10)(C.11)

V1 = RV0 = RT, (C.12)V0 = T, (C.13)

(C.14)

J =

∣∣∣∣∣v u

0 1

∣∣∣∣∣ = v. (C.15)

Then, the joint distribution of R and T , and the distribution of R = V1V0

is given by

fR,T (r, t) = fV1(rt)fV0(t)|v|, (C.16)

fR(r) =

∫ ∞−∞

fR,T (r, t)dt (C.17)

=

∫ ∞0

fV1(rt)fV0(t)tdt−∫ 0

−∞fV1(rt)fV0(t)tdt. (C.18)

It can be shown that the integral of rfR(r) over R does not exist, but an easier approachis available. Since V0 and V1 are assumed independent,

E[R] = E[V1V0

] = E[V1]E[1

V0], (C.19)

but for E[V −10 ] to exist the following expression must be finite

∫R

1

|v|e−

12σ2

(v−x0β)2dv, (C.20)

which it, clearly, is not. Hence, the theoretical mean of R does not exist and, in turn,neither does the variance of R.

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