No. 2004/12. Daniel Schmidt

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1 No. 2004/12 Private equity-, stock- and ixed asset-portfolios: A bootstrap approach to deterine perforance characteristics, diversification benefits and optial portfolio allocations Daniel Schidt

2 Center for Financial Studies The Center for Financial Studies is a nonprofit research organization, supported by an association of ore than 120 banks, insurance copanies, industrial corporations and public institutions. Established in 1968 and closely affiliated with the University of Frankfurt, it provides a strong link between the financial counity and acadeia. The CFS Working Paper Series presents the result of scientific research on selected topics in the field of oney, banking and finance. The authors were either participants in the Center s Research Fellow Progra or ebers of one of the Center s Research Projects. If you would like to know ore about the Center for Financial Studies, please let us know of your interest. Prof. Dr. Jan Pieter Krahnen Prof. Volker Wieland, Ph.D.

3 CFS Working Paper No. 2004/12 Private equity-, stock- and ixed asset-portfolios: A bootstrap approach to deterine perforance characteristics, diversification benefits and optial portfolio allocations Daniel Schidt 1 First draft: March 2003 This version: Deceber 2003 Abstract: In this article, we investigate risk return characteristics and diversification benefits when private equity is used as a portfolio coponent. We use a unique dataset describing 642 US-Aerican portfolio copanies with 3620 private equity investents. Inforation about precisely dated cash flows at the copany level enables for the first tie a cash flow equivalent and siultaneous investent siulation in stocks, as well as the construction of stock portfolios for bencharking purposes. With respect to the ethodology involved, we construct private equity, stock-benchark and ixed-asset portfolios using bootstrap siulations. For the late 1990s we find a draatic increase in the extent to which private equity outperfors stock investent. In earlier years private equity was underperforing its stock bencharks. Within the overall class of private equity, returns on earlier private equity investent categories, like venture capital, show on average higher variations and even higher rates of failure. It is in this category in particular that high average portfolio returns are generated solely by the ability to select a few extreely well perforing copanies, thus copensating for lost investents. There is a high arginal diversifiable risk reduction of about 80% when the portfolio size is increased to include 15 investents. When the portfolio size is increased fro 15 to 200 there are few arginal risk diversification effects on the one hand, but a large increase in anaging expenditure on the other, so that an actual average portfolio size between 20 and 28 investents sees to be well balanced. We provide epirical evidence that the non-diversifiable risk that a constrained investor, who is exclusively investing in private equity, has to hold exceeds that of constrained stock investors and also the arket risk. Fro the viewpoint of unconstrained investors with coplete investent freedo, risk can be optially reduced by constructing ixed asset portfolios. According to the various private equity subcategories analyzed, there are big differences in optial allocations to this asset class for iniizing ixed-asset portfolio variance or axiizing perforance ratios. We observe optial portfolio weightings to be between 3% and 65%. JEL Code: G11 Key Words: Venture Capital, Private Equity, Perforance, Return, Risk, Portfolio, Fund, Diversification, Efficient Frontier, Allocation This article was written in association with Center of Private Equity Research. We are grateful to [in alphabetical order] Matthias Ick, Dr. Thoas Jesch, Dr. Matthias Unser, Prof. Dr. Walz and Prof. Dr. Wahrenburg for helpful coents. The usual disclaier applies. 1 CEPRES Center of Private Equity Research, VCM Venture Capital Manageent GbH, eail-address for correspondence:

4 1. Introduction Modern portfolio theory quantifies the benefits of diversification and deonstrates opportunities for iproving the perforance characteristics of portfolios by cobining assets. Over the last years private equity (PE) has becoe ore reputable within the field of alternative asset classes. By 1996 at the latest, worldwide capital coitents to PE funds were experiencing large increases. Nevertheless, the acceptance of PE as a capital investent alternative has lagged behind that of other asset classes like stocks, bonds or even real estate. Reservations about investing in private equity ay be caused by several factors. Mainly, it has been low arket transparency cobined with the coplexity of understanding both this arket segent and the benefits of portfolio allocations to this asset class that have led to a certain reluctance to treat that eniga, naely private equity as an investent opportunity. Acadeic research that analyzes private equity with respect to portfolio anageent is rare. There are a large nuber of studies devoted to investigating the characteristics of stocks, bonds or real estate as portfolio coponents, but the unsatisfactory data situation does not particularly encourage the analysis of private equity assets in this context. Given a relatively inefficient private equity arket, the logic of portfolio choice is, therefore, based ostly only on the preise that not all eggs should be placed in one basket. Very few approaches exist which try to ake recoendations about optial portfolio copositions which include private equity. Our innovative approach ais to reedy this situation. In this paper we analyze several private equity categories, we derive perforance characteristics using epirical ethods and find evidence on the benefits of adding private equity to a ixed-asset portfolio. This investigation is based on a dataset which is unique with respect to the depth of inforation it contains. The dataset provides to date exact inforation about 3620 investents ade by 123 funds fro 37 investent anagers. Our analysis is based on actual cash flows to and fro portfolio copanies. We begin by siulating investents in individual benchark stocks with the sae tiing. Thus, we observe exact benchark perforances in relation to private equity investents, both of which are easured by the internal rate of return (IRR). Due to the lack of suitable worldwide stock universes that can deliver benchark stocks over the whole period fro 1970 to 2002, we have had to reduce the saple used to 643 US-Aerican portfolio copanies financed between 1980 and Each private equity investent is allocated to one benchark stock fro the Russell 2000 stock universe. Coparable PE and 1

5 benchark stock returns are used for bootstrap siulations of several pure and ixed asset portfolios in order to observe changes in risk-return characteristics. Specifically, the analysis is organized in three steps. First, we assess several private equity categories and provide descriptive statistics. Since with respect to the private equity category we observe higher perforance variation of venture capital investents cobined with a higher average but a lower edian return, we recognize the increased need for skilful investent choices when focusing on venture capital. In earlier ties benchark stock investents outperfored PE investents in ters of ean IRRs. It is only since the late 1990s that the overall private equity arket has started perforing uch better. Research has yet to reveal whether this developent is a result of a learning process or of iproved arket echaniss like the establishent of better exit arkets or the eergence of advisors. Will this outperforance continue, or is this erely a teporary bubble? If this is a teporary exogenous shock, then the individual investent ability of the PE anager will be decisive in ensuring that the higher nondiversifiable pe-arket risk is copensated. As a result, in the 'post bubble' arket of the early 21st century we actually observe a run on participating established private equity funds. Investors have becoe cautious; they now search for high quality funds and refuse to invest in newcoers. Is this evidence of the investors' belief that the PE arket is once again, on average, underperforing and of their need to find above average funds that will outperfor the benchark? In a second step we explore differences in the naive risk diversification of portfolios consisting of private equity or stocks. If we increase the portfolio size to nuber 15 investents we observe strong arginal risk diversification. The coplete reduction of diversifiable risk requires an inclusion of at least 200 investents in the portfolio. Whilst there is a sall arginal risk reduction when the portfolio size is increased fro 15 to 200, there is also a large increase in anaging expenditure; so the actual average realworld portfolio size of between 20 and 28 investents sees to be well balanced. Following the new approaches of asset pricing published by Malkiel/Xu (2000) or Jones/Rhodes-Kropf (2002), we assue that a PE anager or a stock portfolio anager is constrained by his statute fro holding all security classes and is, therefore, also precluded fro holding the arket portfolio predicted by the CAPM. We show using epirical ethods that the non-diversifiable risk a constrained PE investor has to hold exceeds that of stock investors and also exceeds the arket risk. It is referred to as the idiosyncratic risk preiu of private equity portfolios. 2

6 Fro the view of non-constrained investors, risk can be optially reduced by constructing ixed asset portfolios. In a third step we, therefore, derive optial allocations to private equity and its benchark stocks in ixed-asset portfolios. Depending on the private equity category involved, we look at changing optial weightings of private equity in order to construct iniu variance or axiu perforance ratio portfolios. Risk is reduced below the risk level that a constrained stock or PE investor has to hold. Results are robust if we use gross and net perforance variables. Finally, a suary and conclusion are given. 2. Related literature Due to the unsatisfactory data situation research deterining optial PE portfolio constellations is rare. Therefore, we focus our literature review on related research, which has been carried out for two other asset classes: stocks and real estate. Given the siilar characteristics of an investent in these asset classes, a coparison of epirical results indicating diversification benefits is worthwhile. a. Optial portfolio size STOCK PORTFOLIOS Starting with Evans and Archner (1968), the financial literature deonstrates on an epirical basis the naive diversification effects of pure stock portfolios when the nuber of assets included is increased. The authors first of all show that the connection between increasing portfolio size and portfolio risk takes the for of a rapidly decreasing asyptotic function. 1 They refute the notion that there is any econoic justification for a portfolio that includes ore than ten securities. 2 Portfolios were built by a rando security selection and a ean portfolio return calculation taken fro a database of 470 stocks. Evidence derived fro siilar epirical ethods is given by Fisher and Lorie (1970) and Elton and Gruber (1977). They show that there is a reduction in diversifiable risk of between 84% and 88% if the stock portfolio size is increased by only 8 stocks. However, both studies find that there are further diversification effects if the portfolio size is increased by ore than 8 stocks. 3 Recent research supports the efficiency of including ore than 10 securities. An analysis of share price data between 1955 and 1984 by Poon, Tayler and Ward (1992) shows a further 23.86% risk reduction when the portfolio size is 1 See figure 3 and 8 for siiliar results 2 See Evans/ Archner (1968), pp See Fischer / Lorie (1970), pp. 116 and Elton / Gruber (1977), pp

7 raised fro 10 to 25 stocks. 4 Hellevik and Herann (1996) investigate naive risk diversification of securities traded on the Geran stock exchange between 1974 and They find in nearly all cases a risk diversification of 80% if the portfolio reaches a size between 9 and 19 securities. 5 Other studies by Tole (1982), Newbold and Poon (1993), and De Vassal (2001) contradict the usual assuption that a portfolio of ax. 25 stocks in size would be sufficiently diversified. 6 Using stocks fro the Russel 1000 index to siulate portfolios De Vassal akes no certain recoendations about the optial portfolio size, but he deterines a portfolio size of up to 100 securities to be useful. REAL ESTATE PORFOLIOS There are various characteristics of private equity which correspond to those of real estate. Both assets are not traded in a peranent arketplace with quoted arket prices, and both incorporate low liquidity and indivisibility. Furtherore, an investent in these asset classes is characterized by high transaction costs and inforation that is both liited in its public availability and has a highly asyetric distribution. 7 In view of these siilarities we give a review of real estate literature dealing with risk/return topics. Both Miles and McCue (1984) and Grisso, Kuhle and Walther (1987) find nonsysteatic risk diversification effects of between 83% and 90%, respectively, when the portfolio size is increased to include 10 real estate objects. 8 The arginal risk diversification decreases rapidly if the portfolio size is raised beyond 10 properties. More recent studies recoend a larger portfolio size in order to achieve optial risk diversification. Brown (1997) finds risk diversification to be at the sae level as systeatic risk for a portfolio size which ranges fro 30 up to several hundred properties. He takes into consideration the high dispersion of individual real estate perforances. 9 Byrne and Lee (1999), using siilar ethodology, support these findings. They recoend a portfolio size of at least 200 properties. 10 Byrne and Lee (2000) even find epirical evidence to suggest that properties are needed to reduce the risk of a property portfolio down to the arket level. 11 Miles and McCue (1984), Hartzell, 4 See Poon / Taylor / Ward (1992), pp See Hellevik / Heran (1993), pp See Tole (1982), pp. 9; Newbould / Poon (1993), pp. 86; De Vasal (2001), pp See Kallberg, Lui and Greig (1996), pp. 359 ff. 8 See Miles / McCue (1984), pp. 63; Grisso, Kuhle and Walther (1987), pp See Brown (1997), pp. 136 ff. 10 See Byrne/Lee (1999), pp See Byrne/Lee (2000), pp. 12; In their recent study Byrne and Lee (2001) deterine different risk attitudes connected with the anageent of large or sall portfolios. They show next to decreasing non-systeatic risk 4

8 Heckan and Miles (1987), and Brown (1997) copare the relative levels of nonsysteatic risk of real estate and stock portfolios. They indicate a non-systeatic risk level between 90% and 94% for real estate and between 62% and 70% for stocks. 12 According to the authors, these differences show a greater need for holding real estate portfolios which are larger than stock portfolios in order to reach individual arket risk levels. PRIVATE EQUITY PORTFOLIOS Due to the lag in suitable PE data there is only liited epirical research available which reveals the diversification effects of PE portfolios with increasing size. The anageent coplexity of PE portfolios is entioned by Statan (1987), Kanniainen and Keyschnigg (2000), and Cuing (2001). They suppose that the threshold of optial portfolio size is reached when a further increase would lead to a rise in arginal costs which is higher than that in arginal benefits. They deterine factors influencing the portfolio size, but do not offer any recoendations with respect to optial PE portfolio sizes. 13 Nor do any other studies provide epirically-based recoendations as are ade for other asset classes. Instead they are liited to investigations concerning the actual portfolio size of PE portfolios without answering the question about whether these are the optial portfolio constellations. The 178 funds of CEPRES data saple (saple status, May 2003) have included an average of about 25 and a edian of about 20.5 portfolio copanies. 14 b. Optial asset allocations to ixed portfolios STOCKS, BONDS AND REAL ESTATE A nuber of studies have presented evidence which argues that real estate is offering investors diversification benefits. Kuhle (1987) investigates the risk/return characteristics of ixed stock and real estate portfolios. He uses data fro 26 Real Estate Investent Trusts (REIT) and 42 coon stocks to build ixed portfolios with changing asset allocations. He calculates perforance ratios as the ratio between return and risk to exaine the return/risk characteristics of ixed portfolios. His results show that the an increasing systeatic risk with increasing portfolio size. They attribute this effect to a larger nuber of riskier investents held in large portfolios. 12 See Miles / McCue (1984), pp. 66; Hartzell / Heckan / Miles (1987), pp. 248; Brown (1997), pp See Statan (1987), pp. 354; Kanniainen / Keuschnigg (2000), pp. 5; Cuing (2001), pp This is siilar to the nuber of one specific fund's portfolio copanies observed by other authors. Recent studies ade by Ljungqvist / Richardson (2003) observed an average nuber of 22 portfolio copanies in one fund, Reid / Terry / Sith (1997) indicate an average nuber of 28 (according to a survey of 20 funds). 5

9 overall perforance of ixed asset portfolios is not significantly different fro that of portfolios consisting only of coon stocks. 15 The exceptions are those ixed asset portfolios that contain at least a 2/3 share of REITs. However, these results are distorted because Kuhle constructs portfolios fro data that cobines single stocks and already diversified real estate portfolios (REITs). 16 Other studies published at this tie, like Webb and Rubens (1987) or Webb, Curico and Rubens (1988), present siilar results. They consider a 43% or respectively 66% investent in real estate to be the optial allocation. 17 Brown and Schuck (1996) estiate via bootstrap siulations ex ante standard deviations, returns and correlations between stocks and real estate. They find an optial allocation to real estate to be around 40% (portfolio size: 1000 assets). The ipact of a changing overall portfolio size is also exained. The ean weighting of real estate which is required to achieve a iniu variance portfolio decreases to 14.2% with decreasing portfolio size (1 asset). 18 Liang, Meyer and Webb (1996) also used bootstrap siulations to build ixed portfolios. They cannot provide any reliable recoendation concerning the optiu coposition of ixed-asset portfolios. 19 Making adjustents to their ethodology, Ziobrowski, Cheng and Ziobrowski (1997) produce different conclusions. They show that investors with a low risk preference should not invest ore than 10% of their portfolio's capital in real estate. This corresponds to the average investent size in real estate by institutional investors. 20 Data of superior quality are used by Kallberg, Lui and Greig (1996). They use exact cash flow data of real estate investents to calculate the odified internal rate of return (MIRR). In conclusion, they find a real estate allocation up to 9 per cent to be optial, when they odel the efficient frontier indicating the best risk/return characteristics of ixed stock, bond and real estate portfolios. 21 Ziobrowski and Ziobrowski (1997) also generate portfolios of financial and real estate assets and deterine the efficient frontier. They recoend a higher allocation of about 20-30% to real estate. These findings correspond to those of Brinson, Diereier and Schlarbau (1986), whose results recoend a 20% investent share in real estate. 22 Using expected returns derived fro an equilibriu odel, Ennis and Burik (1991) find that the ost 15 See Kuhle (1987), pp See Georgiev (2002), pp. 3 and 5. They show that the arket prices used here for the REITs do not necessarily represent the underlying arket value of the underlying assets and have a higher correlation to stock than to real estate perforances. 17 See Webb / Rubens (1997),pp 13 and Webb / Curico / Rubens (1988), pp See Brown/ Schuck (1996),pp See Liang/ Meyer/ Webb (1996), pp See Ziobrowski/ Cheng/ Ziobrowski (1997), pp See Kallberg/ Lui/ Greig (1996), pp See Brinson, Diereier and Schlarbau (1986), pp. 22 6

10 efficiently diversified portfolios include real estate investents in the range of 10% to 15% of total assets. 23 PRIVATE EQUITY The low transparency of private equity arkets and, the resulting unsatisfactory data situation ake an exact coparison of the returns on PE and other asset classes difficult. In general, we have no annual returns for PE investents that are coparable to those of other assets with continually quoted arket prices. There is only a series of cash flows with no interediate values, which given a full distribution allows the annualized internal rate of return (IRR) to be calculated over the entire life of the investent. There are no studies based on real cash flows that calculate PE IRRs and at the sae tie the cash inflow equivalent IRRs of investents in other asset classes. Most studies use proxies to siulate characteristics of PE investents. The following studies have attepted to quantify the return/risk characteristics of PE, and soe authors try to give a recoendation about the optial allocation to PE. Probably the ost faous investigation is that by Cochrane (2003), who analyzes a dataset fro 1987 to He atches under certain assuptions inforation fro two separate databases to calculate venture capital backed copany returns. Cochrane only observes returns of portfolio copanies which go public or out of business, but not of those that reain private. 24 He corrects for this saple bias by using axiu likelihood estiates to identify and easure the increasing probability of going public or being acquired. Without a selection bias correction he finds arithetic average returns of 69.8%, and with bias correction average returns that decrease to 59%. Ljungquist and Richardson (2003) try to quantify PE fund perforance using a superior data basis, but offer no evidence with respect to the optial allocation to PE in ixed-asset portfolios. They use data collected fro the portfolio of only one single investor. This dataset is in danger of including a selection bias. They explore IRRs easured on the basis of actual funds cash flow data. They do not have data at the copany level and only ake an approxiation about whether the analyzed funds are copletely realized. 25 Results indicate a siple weighted ean IRR for ature funds of around 20%. Using a repeated valuation odel to correct for selection bias in the reporting of values, Quigley and Woodward (2002) try to 23 See Ennis/Burik (1991), pp See Cochrane (2003), table 1, next to the issing data of copanies which reain private (45.5%), Corranes saple just includes 9% lost investents. This is less than the nuber of lost investents in our saple and does not correspond to the usual default rates in venture capital. 25 Ljungquist and Richardson (2003), pp. 6 ff. 7

11 build a VC index for the period between 1987 and the first quarter of They focus on individual portfolio copanies and find for ixed-asset portfolios (PE, stocks and bonds) an optial allocation to PE to be between 10% and 15%. 26 McFall La and Ghaleb- Harter show that an investor should invest between 19% and 51% in PE. 27 Bader (1996) recoends under varying assuptions a PE allocation between 10% and 39%. 28 Pradhuan, Kan and Chbani (2001) and Merrill Lynch (1995) all use sall caps to proxy PE investents. These studies indicate benefits by investing 15% or 10% of total capital, respectively, in PE. 29 Superior data are used by Chen, Baierl and Kaplan (2002) to construct an efficient frontier. They use real IRR data fro 148 PE funds that have been liquidated as of June 30, 1999.The earliest date of investent is January 1, No exact cash flow data were available to calculate coparable perforances for other asset classes taking into consideration the exact investent tiing. Their results produce an efficient frontier consisting of VC and the S&P 500 index that justifies allocations between 2% and 9% to VC for constructing the iniu variance portfolio or axiu Sharpe ratio portfolio Data and ethodology Bencharking PE investent perforances against those of other asset classes is difficult. In contrast to quoted assets with daily arket prices there are only two occasions, the date of investent and the date of divestent, when a arket-deterined value is known for PE investents. If the historical series of cash flows over the entire life of investent after liquidation is known, then the annualized internal rate of return (IRR) can be calculated. Using an interi IRR based on net asset values to get annual rate of returns is just an estiation of reality. Thus, up until today with recent datasets, an exact coparison of PE (easured by the IRR as the annualized internal rate of return over the entire life of investent) and stock investent perforance (easured by a volatile annual rate of return) was not possible. The dataset we use contains exact and coplete inforation about 3619 PE investents ade between 1970 and the end of We have access to precisely dated cash flows down to the copany level, the exact assignent of every copany to its fund and its investent anager and, furtherore, a large aount of investent anager, 26 Quigley/ Woodward (2002), pp McFall, La and Ghaleb-Harter (2001), pp Bader (1996), pp Pradhuan, Kan and Chbani (2001), pp Chen, Baierl and Kaplan (2002), pp

12 fund, and copany-specific inforation. We are not confronted by selection bias like Cochrane owing to issing copany data. Our saple includes all investent inforation ade by the funds investigated, including those which reain private, are written off or are lost. This data is derived fro the records of CEPRES Private Equity Analyzer which collects detailed PE data on a copletely anonyous basis. Therefore, we do not know anything about the identity of the copany, fund or investent anager. Nevertheless, the saple is well balanced. Table 1 presents the origin of the saples investent anager and portfolio copanies. There is possibly a certain survivorship bias because data are derived ainly fro those PE anagers who have reported over the last years. Fro these general partners we also obtain inforation which describes their forer ature funds. Unfortunately, we have no inforation about fund anagers who were not in business until the id 1990s. To avoid estiation biases due to the subjective valuation treatent we concentrate our study on copletely liquidated investents with real cash flow history. This follows the approach used by Cochrane (2003). 31 Therefore, the overall dataset is reduced to 1539 copletely realized, lost or written off investents. Inforation about the aount and date of all cash flows to and fro the PE investents enables a cash flow equivalent and siultaneous investent siulation in stocks. For every single PE investent we choose another benchark stock to siulate coparable perforance (both easured in IRR). 32 In order to choose the right benchark it is essential to find stocks fro one hoogeneous universe. There is no unifor sall cap stock universe in Europe, South Aerica and Asia that covers at least the last twenty years. All ajor stock indices covering sall caps eerged in the last ten years. We, therefore, confine our research to US-Aerican PE portfolio copanies between 1980 and 2002 and draw bencharks to US-Aerican sall cap stocks quoted within this period. The dataset is reduced to 642 US-Aerican PE investents. The coparison between the coplete and the reduced saple shows no significant differences in perforance. The hypothesis of no difference in ean IRRs is not rejected. Table 2 presents a very low t-value. The saple includes PE investents fro all financing stages: early-, expansion-, later stage, bo/lbo, turnaround and ezzanine. Table 3 presents the saple's exact coposition. The saple's portfolio copanies are operating in a well-balanced industry range. The reduced saple's coposition does not 31 See Chorane (2003), pp.3 32 As it is recoended in Ehrhardt/ Koerstein (2001), pp. 455 or Barber/ Lyon (1997). 9

13 deviate far fro that of the coplete saple. Thus, when we use the reduced saple we expect to find siilar results to those obtained fro analyzing the whole saple. Following the ethodology of De Vassal (2001), we atch a saple of firs which had been original constituents of the sall-cap universe, Russell The Russell 2000 easures the perforance of the 2000 sallest copanies of the Russell 3000 index and represents approxiately 8% of its arket capitalization. The Russell 3000 represents approxiately 98% of the U.S. equity arket available for investent. We divided the PE saple into two investent periods of 10 and 12 years between 1980 and 1990 and 1990 and 2002, respectively. To benchark PE investents which were ade in the 80s we use original constituents of the Russell 2000 in its coposition of the year 1980 and their total return perforance through to the end of PE investents ade between 1990 and 2002 are allocated to original constituents of the Russell 2000 in its coposition of the year For stocks of copanies that did not survive the entire holding period of the allocated PE investent, we recognize the total return until the last reported stock price and siulate, in addition, a reinvestent in another size and industry-atched stock fro the sae index coposition. Each PE portfolio copany is acting in the sae industry as its benchark stock. To avoid size effects we ranked all PE investents according to their investent size and all stocks according to their arket capitalization. By eans of this ranking we allocated each PE investent to a coparable benchark stock. Owing to large deviations in the stocks arket capitalization and the PE investent costs, an exact size atch was not possible. 33 In accordance with the described ethodology, every PE investent is allocated to one stock in the sae industry. A siulated investent of each PE cash flow in the allocated benchark stock at sae cash flow date and with a siultaneous divestent delivers exact benchark IRRs. In particular, we created an investent in the benchark stock with the sae tiing and aount, whenever a draw down or distribution on private equity copany level occurred. The aount was translated in to a nuber of shares of the benchark copany by dividing the investent cash flow by the stock's current arket price, i.e. buying shares for the equivalent aount at the current quote. 33 The average arket capitalisation of one stock was around 29 illion US-Dollar, the average financing costs of one private equity investent were around 9 illion US-dollar. 10

14 Shares Index yt negative cash flow = yt t = 1,2,..., T Stock _ arket _ price t Here t denotes the current onth and y refers to a particular copany. Whenever a cash outflow, i.e. a disburseent to the fund s investors occurred, we divided the positive copany cash flow by the su of all positive copany cash flows to weigh the particular cash flow. We ultiplied this fraction with the su of all shares of the index and the current index level. As a result, a positive cash flow was created for the IRR calculation of the benchark stock. PE _ copany cash flow benchark _ stock yt T positive cash flow t = * copany _ shares* arket _ price T PE _ positive copany cash flow 1 yt 1 Here t denotes the current onth and y refers to a particular copany. This approach creates a cash flow pattern for benchark stocks that iics the pattern of the underlying private equity copany investent. Using this cash flow pattern, we can easily copute the IRR for the respective benchark stock and thus obtain the perforance the investor would have achieved if he had invested in the bencharked copany. Each PE IRR (PE n ) has its counterpart benchark IRR (S n ). There is no dilution of benchark perforances due to different investent periods or different perforance easures. We overcoe the usual probles of non-perforance coparability between these two asset classes. We siulate portfolios built fro a changing nuber of PE or stock investents by using the bootstrap ethodology. We construct portfolios fro equally weighted real PE investents and easure their cross-section ean return, volatility and other descriptive statistics. This approach does not take into account the different single starting points and the different capital weightings of investents carried out by real-life private equity funds. In this paper, however, we ai to siulate portfolios in order to exaine the overall properties and dynaics of private equity investent perforance patterns and not in order to evaluate the investent anagers ability with respect to tiing and capital weighting. 34 The bootstrap ethodology used is described in the appendix. 4. Assessing private equity and its stock benchark risk/return characteristics 34 Further discussion about the suitability of different ethodologies, see Burgel (1998), pp

15 SAMPLE PERIOD Investents between 1980 and 2002 We begin by exaining the coplete saple coprising US PE portfolio copanies financed between 1980 and the end of The first panel of table 4 shows the descriptive statistics of PE investents and of benchark investents in stocks. Each set represents one portfolio consisting of 642 investents that are copletely coparable in ters of tiing and cash inflow. On the one hand these are investents in PE portfolio copanies and on the other hand in stocks. The ean return of PE investents shows an IRR of 36,49%. This in line with expectations, is ore than three ties higher than that of equal investents in stocks (11,59%). Besides higher ean returns, PE investents are characterized by higher cross section volatility. However, PE s standard deviation of 242% is only about twice as high as that of stocks [103%]. The high returns of PE portfolios are generated on the whole by only a few high perforing copanies. In the case of PE, the saple therefore shows higher axiu returns and a wider range of investent perforances (PE: 3026%/ stocks: 1943%). Figure 1 shows the typical IRR distribution of PE investents. In contrast to the benchark, PE perforance distribution is characterized by two peaks. This is the result of a high nuber of lost investents, a relatively low nuber of odestly perforing investents, but a large nuber of well and soe extreely well perforing investents. 35 SAMPLE PERIOD Investents between 1980 and 1990 Reducing the saple to investents ade between 1980 and 1990 we see deterioration in the perforance of both PE and stocks. The ean return of PE is nearly zero and underperfors benchark stocks. Analytically, this is the consequence of fewer extreely high perforing PE investents. The axiu perforance of PE investents ade in the 1980s does not exceed an IRR of 642%. A edian return of 8.77%, however, exceeds the edian benchark return. This reflects, despite a large nuber of totally lost investents, the overall high figure for odestly perforing PE investents. However, extreely well perforing investents, which are able to copensate in ters of ean IRR for the huge aount of failures, on average does not reain. Within this period PE arkets had not really been established. It was not until the 1990s that an efficient and professional PE arket was developed by consultants with knowledge of M&A, by the establishent of new, well functioning and ore liquid exit- 35 This corresponds partly to the findings of Cochrane (2001),pp. 10. Analyzing only the returns to ipo or trade sale, he deterines a few outstanding returns of thousands of percent and any relatively ore odest returns. 12

16 channels, and last but not least by the acadeic investigation of these topics, e.g. entrepreneurship. In the period between 1980 and 1990 the correlation between PE and the benchark stocks perforance is lower than that easured over the full saple period [-0,044]. SAMPLE PERIOD Investents between 1990 and 2002 Investents which were ade in the last decade (vintage year 1990 to 2002) exhibit different characteristics. Our saple data reflects the well perforing capital arket oveents of the 1990s. High perforing PE investents, especially those realized during the bubble between 1996 and 2001, ade it possible to reach a ean IRR of 56.8%. The variation in PE investent perforances (standard deviation 295%) increases as well. Even if the benchark investents also show a relatively high perforance of 16.39%, PE outperfors the stock investents. In this period, the correlation between PE and stock investents also increases fro to This atches the result of Longin and Solnik (1995), which deonstrate epirically the rise of a correlation between national stock arkets in periods of high volatility. 36 Especially in the last years of the 20th century the return volatility of all asset arkets was increasing. SAMPLE PERIOD Realization date before and after January 1997 We observe extraordinary returns in the last decade. One reason ay be the booing years between the end of 1996 and In all probability there will be no siilar recovery in the near future that will raise perforances to reach forer absolute heights. Nevertheless, we have to ask whether PE in the future will still outperfor stocks as a result of ore developed PE arkets, or whether the forer outperforance of PE relative stocks was only the result of a larger bubble of PE arkets copared to the stock arkets. PE perforance is largely deterined by the condition of the exit arkets. To test robustness we exclude fro the overall saple all investents realized in the boo years after Table 4.1 panel 4 presents a drop in average PE return to 7.9%, but also shows a relatively high edian return of 17.6%. The edian return is higher than that of the benchark investents. However, there is a greater degree of skewness to the left and axiu perforances do not reach the sae heights as the benchark investents. Before 1997, PE seeed to be characterized by a constantly high nuber of odestly 36 See Longin / Solnik (1995), pp

17 perforing investents, together with fewer extreely well perforing investents with 4 digit IRRs. Even if there was a constant frequency of lost investents over tie, in the early years the nuber of extreely well perforing investents was too low - and the relative nuber of lost investents too high - to outperfor the stock benchark in ters of ean IRR. The high nuber of odestly perforing investents could not copensate for the high nuber of lost investents. Investents which had been realized in the boo years after 1997 outperfored the benchark in ters of ean and edian IRR. The return outperforance was priced by a strong increase in return volatility. Further analysis will show to what extent this risk was diversifiable. To avoid selection bias we take note of all realized investents including those which were written off or lost. Nevertheless, there could be a potential for bias. Badly perforing investents fro previous years with no chance to exit ay still be held by the fund and will dilute the overall fund's perforance. Such copany data are only partly considered by using coplete investent inforation of all ature funds. To test for robustness we reduce the saple to those investents which are taken exclusively fro realized, and in a second step fro alost realized (at least 70% of funds investents are copletely realized), funds (see table 4.1 panel 6, 7). Thus we integrate all investents ade by the funds into the analysis and avoid potential selection bias. Results confir the findings of the analyses which are ade for investents realized before Most funds which started to invest in the late 1990s have not yet been copletely realized and, therefore, their investents are not taken into account in this saple subset. The extreely high returns of the last few years are not recognized if we analyze this subset. Table 4.1 panel 7 describes investents taken fro copletely realized funds. Most funds which were raised in the late 1990s contain at least one noncopletely realized investent. Consequently, all investents done by those funds are excluded fro the analysis. Consequently, the saple Investents taken fro fully realized funds includes investents conducted ainly in the 1980s and very early 1990s. Funds which had been raised in this period are usually realized by today. As a result, the perforance data are siilar to those of the saple that describes investents fro the 1980s. We cannot, however, evaluate the exact perforance of funds which have been raised in the late 90tis and are still not copletely realized but have profited fro the exit environent of the last years. SAMPLE PERIOD - Suary 14

18 To suarize: it is only in the late 1990s that we observe private equity investents outperforing their public arket investent equivalent. We do not know yet if this developent is a result of a learning process or of iproved arket echaniss, such as the establishent of better exit arkets or the eergence of advisors, or whether it is erely due toly a teporary bubble. This will be an iportant factor which helps to decide the future developent of the whole PE industry. If the overall industry does not function well, the individual skills of PE investent anagers will be increasingly decisive as a factor for success. A arket clearance of low quality PE anagers will help to save the industry's reputation! Due to the large capital aounts in the arket, which have to be allocated to private equity, it is however uncertain, whether a arket clearance will be possible. The real world shows, that the institutional investent pressure forces non privileged arket participants without invitation to A-funds to invest in B-funds. As a result, the overall perforance will be still odest and could underperfor the traditional arkets. Today, private equity funds are again beginning to raise an expected overall aount of 60 billion US-dollars (expectations 2004) in venture capital that was sidelined after the Nasdaq plunged in Market experts argue, that again we are seeing soe effects of the overhang at play. 37 Due to the high copetition for the best deals, copanies that definitely will not contribute to an extraordinary pe arket outperforance are again financed as the way out of the capital overhang. INVESTMENT STAGES Venture Capital vs. Buy Outs Table 4.2 shows descriptive statistics of saple subsets which represent investents in different financing stages. We observe strongly increased average returns for pure venture capital investents copared to all other private equity investents without VC, such as MBO/LBO and turnaround investents (all PE without venture capital = PE w/t VC). The PE w/t VC ean IRR does not exceed its benchark by uch. The higher ean return of venture capital is connected to a higher variation (313% versus 51%) of returns within a wider range of possible outcoes (ax. perforance of VC: 2962% versus PE w/t VC: 148%). Our results do not copletely correspond to those of Ljungquist and Richardson (2003). They analyze perforance at the fund level and derive an outperforance for funds with investent focus on buyouts (against venture capital). 38 Although average returns in our saple are lower, the edian return of PE w/t VC is 37 See Francisco Baby, Navigating a bounce in venture capital, CBS.MarketWatch.co, March , pp.1 38 See Ljungquist and Richardson (2003), pp.21; they observe an average return of % for buyout funds versus for venture funds. 15

19 uch higher than that of pure venture capital investents and of its benchark. Venture capital receives high average returns owing only to soe extreely well perforing outliers (Figure 2). Due to the high nuber of lost investents (25.48%), the right copany selection and the capital weightings are decisive for the overall outperforance of VC funds. Given equal weightings, we observe for venture capital investents an average return of 47.81%. The subsaple PE w/t VC has a lot of odestly perforing investents and an average IRR of 7.62%. The right portfolio coposition is not as dependent on the anager's ability to choose highflyers. Furtherore, there is a big difference between the correlations of both PE categories copared to their benchark stocks. In contrast to PE w/t VC, which has a high correlation of 0.25 to stock investents, VC is practically uncorrelated to the stock benchark. Copared to the overall venture capital saple, purely early stage investents are characterized by a decreasing average outperforance (21.39% versus 37.12%) against the benchark. The edian return is even negative. This is the result of a very high frequency of lost investents (38%). Only a few extreely well-perforing investents contribute to a high average return. Nevertheless, the overall saple's best perforing investents are early stage investents. This leads to a wide range and high variation of investent returns. The portfolio anager's ability to select well-perforing investents deterines the overall early stage-fund perforance. The chance of selecting badly perforing portfolio copanies is high during early stage investing. INVESTMENT STAGES Mezzanine vs. Non-Mezzanine Our final analysis is presented in panels 4 and 5 of table 4.2. We explore perforance differences dividing the full saple into ezzanine-financed and nonezzanine-financed investents. We observe siilar results as before. Mezzanine investents are characterized by a lower ean return outperforance (14.37% versus 27.54%) against its benchark, but a higher outperforance of edian returns (22.43% versus 5.88%). The reason is siilar to that of preceding explanations. Mezzanine investents are exposed to lower risk than the saple's other investents. Thus, we observe lower variation in returns within a saller range of outcoes and a lower frequency of total lost investents (only 4%). 5. Effects of naive diversification when portfolio size is increased 16

20 In this section we explore the diversification benefits of PE portfolios with increasing size and copare the to those of benchark portfolios that are coposed of public arket return equivalents. Owing to our available data with inforation down to the copany level, for the first tie it has becoe possible to construct own portfolios with varying size. We perfor a bootstrap siulation of portfolios each including a certain nuber of investents. After deriving 5,000 bootstrap saples for each portfolio size, we then calculate cross-section variation over the saples outcoes. THE RISK Frequency distribution of portfolio returns Figure 3 shows changes in standard deviation over the bootstrap portfolios when the portfolio size is increased. Figures 4 to 6 represent the frequency distributions of returns on funds consisting of different nubers of investents. As described in the preceding section, all PE investents exhibit higher perforance dispersion and therefore higher absolute risk than their stock benchark investents. Although there is a stronger diversification of absolute risk for PE portfolios copared to the stock portfolios, in this section, we observe siilar relative naive diversification effects. The distribution of portfolio returns approaches noral distribution with increasing size. Since there is a relativly high rate of total lost investents within the private equity asset class, building portfolios decreases the risk of failure. It is already the case with a portfolio consisting of only 5 PE investents that there is a alost zero per cent probability of total loss. The probability of negative absolute returns, however, is not decreasing but increasing - before ore than 5 investents are included in the portfolio (see table 5). This is not caused by the relatively high nuber of lost or negatively perforing, but rather by the sall nuber of extreely well perforing investents. Portfolios have to reach a iniu size to increase the probability that at least one high perforing investent is included. This is in accordance with the coon assuptions ade in the context of PE investent. Though we find siilar decreases in the standard deviation of PE and stock portfolios with increasing size, table 5 shows soe differences when the quartile distribution is analyzed for returns on both asset classes. Whilst we find a siilar probability of negative returns (35.22% versus 30.35%), PE is characterized by a high nuber of investents that perfor worse than inus fifty per cent. This is the result of any failing investents with an IRR of inus one hundred per cent. If we increase portfolio size, the nuber of PE portfolios perforing worse than inus 50 per cent does not decrease as fast as the nuber of stock portfolios exposed to that worse perforance. 17

21 However, in all cases there is a higher nuber of negative perforing stocks (<0%) than of PE portfolios. THE (NON-)DIVERSIFIABLE RISK Standard deviation of portfolio returns In recent ties new approaches to asset pricing, which deviate slightly fro the traditional assuptions ade by the CAPM, have been published. Malkiel/Xu (2000) or Jones/Rhodes-Kropf (2002) argue that in practice the assuption that investors can hold any cobination of the arket portfolio and risk free assets is often violated. They indicate that these so called constrained investors are unable to hold the arket portfolio for reasons such as transaction costs, liquidity constraints or other exogenous factors. 39 With respect to portfolio construction within the PE sector, a significant length of tie is required to assess the deal flow and ake investent decisions. The PE anager identifies only a sall nuber of investents, which will be included in his certain portfolio. Furtherore, the investents are highly illiquid and transaction costs are excessively high. Jones/Rhodes-Kropf (2002) show that, dependent on the nuber of portfolio constituents, PE anagers are exposed to changing, but real, levels of idiosyncratic risk. Because of their PE investent statute PE anagers are constrained and unable to hold the arket portfolio. 40 Frequently they are subject to investent restrictions which even relate to private investent. Therefore, even if the PE anager increases the portfolio size to an infinite nuber of private equity portfolio constituents, he still faces liited arket non-diversifiable risk, the so-called PE arket risk. With respect to the cobination of asset classes, the PE arket portfolio that is available to a constrained PE anager is less diversified than the arket portfolio. In keeping with this assuption, the constrained stock anager holds the stock-arket portfolio in case of full diversification (with respect to the nuber of stocks and their industries) occurring within his asset class. 41 Increasing the overall nuber of portfolio constituents, we give epirical evidence of naive risk diversification down to the level of stock- or PE arket risk. 42 Table 6 shows that the PE arket risk exceeds the stock-arket risk. This is in line with the hypothesis of Jones /Rhodes-Kropf (2002). We show epirically that the non- 39 Malkiel, G.M./Xu,Y. (2000) 40 For a discussion of investent statutes and restrictions see Feinendegen, S. / Schidt, D.M. / Wahrenburg, M. (2002) and Schidt, D.M. / Wahrenburg, M. (2003). 41 See Malkiel/ Xu (2000), pp.2 ff. for general discussion 42 See Jones /Rhodes-Kropf (2002), pp. 4 18

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