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ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 ... ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 ... Document Transcript

  • Management Science What drives private equity fund performance? Journal: Management Science Manuscript ID: draft Manuscript Type: Finance Date Submitted by the n/a Author: Complete List of Authors: Zollo, Maurizio; INSEAD, Strategy Phalippou, Ludo; U. of Amsterdam, Finance Keywords: Finance : Portfolio, Finance : Asset pricing ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Page 1 of 37 Management Science 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Abstract 20 21 Using a unique dataset of private equity funds, this study shows that the performance of 22 private equity funds is highly related to both the state of the business cycle and stock market 23 performance. In addition, we find that private equity funds – like hedge funds - are exposed 24 25 to tail risk. We observe little evidence that idiosyncratic risk is priced. Finally, we document 26 that performance is related to the size and the experience of funds even after controlling for 27 sample selection bias, risk factors and business cycle variables. 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 2
  • Management Science Page 2 of 37 1 2 3 4 5 The growth of private equity funds has outstripped that of almost every class of financial 6 assets over the last twenty five years, growing from $5 billion in 1980 to $300 billion in 2004 7 8 (Lerner et al., 2004, p1). What explains such a spectacular growth? 9 10 11 12 An explanation that is put forward by certain investors is that the risk of investing in 13 14 private equity funds is negligible while performance is above the risk-free rate, which makes 15 it an attractive asset class. As echoed by Lerner et al. (2004, p42) certain investors believe 16 17 that private equity funds, like hedge funds, hold factor-neutral portfolios in that they can 18 19 “generate incremental returns independent of how the broader markets [are] performing.” 20 21 This conjecture is, however, surprising given the high dependence of private equity funds to 22 the state of the public stock-market when exiting investments. In addition, the two major 23 24 asset classes in which private equity funds invest are expected to have high risk: leveraged 25 26 buyouts because of the large amount of debt used to finance these deals and venture capital 27 28 investments because of the staging structure used along with the unique and volatile nature of 29 30 the firms financed (see Cochrane, 2005). 31 32 33 The objective of this paper is to discriminate between these two opposite views on the 34 35 risk of investing in private equity funds thanks to a unique dataset that contains a large cross 36 37 section of funds. With such a dataset, we can measure directly the link between various 38 business cycle variables, sources of risk and fund performance. Specifically, we study how 39 40 the performance of private equity funds relates to a set of variables that are related to business 41 42 cycles (level of interest rates, credit spreads, GDP growth) and the public stock market. In 43 44 addition, the relationship between risk and return may not be linear as it is the case for Hedge 45 Funds (Agarwal and Naik, 2004) and we therefore also include option market factors (call 46 47 and put option written on the stock market). 48 49 50 51 To assess the importance of the relationship between stock market performance and 52 53 private equity fund performance, we also apply the methodology proposed by Ljunqvist and 54 Richardson (2003) that consists in using the information on the industry in which funds invest 55 56 and the type of investment they make (venture capital versus buyout) to compute a beta for 57 58 each investment based on the matching industry betas and making appropriate leverage 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 3
  • Page 3 of 37 Management Science 1 2 3 4 5 assumptions. The investment betas are then aggregated at the fund level to obtain a beta for 6 each fund. 7 8 9 10 Finally, Jones and Rhodes-Kropf (2004) argue that idiosyncratic risk should also be 11 12 priced for private equity funds and we, therefore, also investigate this issue. We also 13 14 investigate whether the characteristics that have been shown to be related to performance in 15 the literature, have marginal explanatory power once we control for business cycle variables, 16 17 systematic risk factors and other control variables. 18 19 20 21 The two methods we use to calculate the average private equity fund beta leads to a 22 similar answer. Namely, we find that the average private equity fund beta is 1.6, which is 23 24 substantially above one, contrary to the widespread belief mentioned above. Furthermore, we 25 26 do not find a statistically significant relation between fund beta and fund performance, but do 27 28 find that private equity fund performance significantly increases with the average return on 29 30 the stock market portfolio during the fund’s life. The decile of funds who invested when the 31 stock-market had the lowest performance (-0.2% per month) has an average profitability 32 33 index of 0.84 (large underperformance compared to the S&P 500) and an IRR of 8.7%. In 34 35 contrast, the decile of funds who invested when the stock-market had the highest performance 36 37 (1.7% per month) has an average profitability index of 1.29 (large overperformance 38 compared to the S&P 500) and an IRR of 21.6%. Similarly, an increase in stock market 39 40 performance of 5% per year over the life of the fund induces an increase in the profitability 41 42 index of private equity funds of 12.5% (2.5% in terms of IRR). 43 44 45 In addition, performance significantly increases with the average return on the call 46 47 options written on the S&P composite index (during the life of the investments.) This shows 48 49 that like hedge funds, private equity funds exhibit tail risk, i.e. non-linear systematic risk (see 50 51 Agarwal and Naik, 2004). The performance of private equity funds is thus unaffected by the 52 53 magnitude of a downturn. A probable explanation is that when the stock market has mild or 54 low returns, the usual exit channels for private equity investments (IPOs, M&As) are closed. 55 56 57 58 The results obtained with business cycle variables indicate uniformly that private 59 60 equity fund performance is significantly pro-cyclical. Performance significantly increases ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 4
  • Management Science Page 4 of 37 1 2 3 4 5 with the average GDP growth rate and decreases with both the average level of corporate 6 bond yields and average credit spreads. Moreover, macroeconomic conditions are found to be 7 8 particularly important at the time investments are made. When either credit spreads or 9 10 corporate bond yields are low at the time investments are made, fund performance is higher. 11 12 For instance, when we sort funds in deciles based on average corporate bond yields, we find 13 14 that the lowest decile (average bond yield is 13.2%) has an average performance of 0.62 and 15 an IRR of 7.9%. In contrast, the decile of funds who invested when the bond yields were 16 17 lowest (average bond yield is 7.8%) has a staggering average profitability index of 1.52 and 18 19 an IRR of 33.9%. This means that between the lowest to the highest decile, the amount 20 21 distributed (in present value terms and per dollar invested) is more than twice as high and the 22 IRR is four times as high. Similarly, a decrease in the yield of BAA bonds of 1% induces an 23 24 increase in the profitability index of 12.5% (5% in terms of IRR). 25 26 27 28 When the effects of the different variables are compared to one another, we find that 29 30 the two dominant factors are the level of corporate bond yields at the time investments are 31 made and the level of the stock-market returns that prevail during the life of investments. 32 33 34 35 Our dataset also enables us to study the other drivers of fund performance. First, we 36 37 further test the hypothesis of Jones and Rhodes-Kropf (2004) according to who idiosyncratic 38 risk should be priced for private equity funds. We do not find strong support for this 39 40 hypothesis. The only exception is when we measure idiosyncratic risk by the Herfindahl 41 42 index for industry concentration (of investments). However, we note that the effect is driven 43 44 by the amount invested in high-tech industries. We attribute most of this empirical 45 discrepancy to the different assumption made regarding the treatment of the residual values 46 47 of the funds. Second, consistent with widespread belief, small and inexperienced funds have 48 49 significantly lower performance even after controlling for risk factors, sample selection bias 50 51 and various control variables. Funds that invest more outside the US and in venture capital 52 53 also witness a lower performance but it is not statistically significant. 54 55 56 This paper is the first to our knowledge to document how business cycle variables and 57 58 systematic risk factors directly influence the performance of private equity funds and to 59 60 document the presence of non-linear risk factors (i.e. right tail risk) for private equity funds. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 5
  • Page 5 of 37 Management Science 1 2 3 4 5 We also show what are the drivers of private equity fund performance that are robust to 6 various control variables, specifications and sample selection bias correction. 7 8 9 10 Our study is closest to the work of Ljungqvist and Richardson (2003), who study the 11 12 determinants of the speed of the capital calls and capital distributions. Ljungqvist and 13 14 Richardson (2003) find that funds return capital more slowly when BAA corporate bond 15 yields are higher, when the return on the Nasdaq is lower, and when there are less M&A 16 17 deals in the same industry. To the extent that performance is correlated with the speed of the 18 19 capital distribution, their results give a sense of how macroeconomic and market conditions 20 21 affect performance. Ljungqvist and Richardson (2003) also estimate fund betas by employing 22 a four-step procedure that we use in this paper. Our study offers the advantage of measuring 23 24 directly the impact of several factors on performance. That is, we can measure by how much 25 26 an increase in either the stock-market return or GDP growth affect the performance of private 27 28 equity funds (instead of the speed at which they return capital as in Ljungqvist and 29 30 Richardson, 2003). In addition, we have about ten times more observations than Ljungqvist 31 and Richardson (2003), we consider novel factors (e.g. option market factors) and we correct 32 33 for sample selection bias. 34 35 36 37 Getting insight into the risk profile of private equity funds as well as the other drivers 38 of their performance is not only interesting per se (e.g. for portfolio allocation or to explain 39 40 growth in this asset class) but also interesting in light of recent research that reports that 41 42 private equity funds have a relatively low performance. For example, Kaplan and Schoar 43 44 (2005) show that, in their sample, private equity funds have a performance that is close to the 45 performance of the S&P 500. This is especially puzzling given our finding of a beta of 1.6. 46 47 48 49 The paper continues as follows: section 1 reviews the literature, section 2 describes 50 51 the data, section 3 is dedicated to the relation between fund performance and both systematic 52 53 risk and business cycle variables, section 4 investigates the pricing of idiosyncratic risk, 54 section 5 reports the relation between fund characteristics and fund performance and section 55 56 6 briefly concludes. 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 6
  • Management Science Page 6 of 37 1 2 3 4 5 I. Private Equity Funds 6 I.A. The private equity industry (see Appendix A.I for details) 7 8 Private equity investors are principally institutional investors such as endowments and 9 10 pension funds. These investors, called Limited Partners (LPs), commit a certain amount of 11 12 capital to private equity funds, which are run by General Partners (GPs). GPs search out 13 14 investments and tend to specialize in either venture capital (VC) investments or buyout (BO) 15 investments. In general, when a GP identifies an investment opportunity, it “calls” money 16 17 from its LPs. When the investment is liquidated, the GP distributes the proceeds to its LPs. 18 19 The timing of these cash flows is typically unknown ex ante. 20 21 22 I.B. Literature review: Risk of private equity investments 23 24 We can divide the literature on the risk of investing in private equity into two sets of studies. 25 26 The first, and most extensive set, studies individual venture capital investments of GPs 27 28 (reviewed in sub-section B.1). The second set focuses on the fund level and measure risk 29 30 based on the cash-flow stream from (to) the private equity funds to (from) LPs (reviewed in 31 sub-section B.2). In this sub-section, we also discuss two articles that indicate cyclicality in 32 33 private equity returns (reviewed in sub-section B.3). 34 35 36 37 I.B.1. Venture capital investments of GPs 38 Peng (2001), Quigley and Woodward (2003), and Woodward and Hall (2003) compute a VC 39 40 index and report the correlation between this index and a public stock-market index. The 41 42 index is built from discretely observed valuations (new financing round, IPOs, acquisitions, 43 44 or liquidation). With similar observations, Cochrane (2005) assumes that the change in the 45 log of the company’s valuation follows a log-CAPM and models selection bias explicitly by 46 47 assuming that the probability of observing a new round follows a logistic function of firm 48 49 value. Using a maximum likelihood approach, the alpha and beta of the log-CAPM that are 50 51 most consistent with these observations are then derived. 52 53 The results of these studies vary substantially. Quigley and Woodward (2003) finds a 54 negative alpha and a (CAPM) beta close to 0. Woodward and Hall (2003) estimate that the 55 56 abnormal performance is 8.5% per year and the beta is 0.86. Peng (2001) finds an average 57 58 return of 55% per annum (1987-1999) and the estimated beta ranges from 0.8 to 4.7. Finally, 59 60 Cochrane (2005) reports an alpha of 32% and a beta below 1. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 7
  • Page 7 of 37 Management Science 1 2 3 4 5 There are four major differences between the present paper and the above mentioned 6 studies. First, the above studies focus on (public stock) market risk while we include several 7 8 other risk related variables. Second, the above studies focus on venture capital deals while 9 10 private equity funds – included those that specialize in venture capital – invest in other type 11 12 of deals (mainly leveraged buyouts). The advantage of having data at the fund level is that we 13 14 observe all the cash flows, be them related to venture capital or not. We thus have a more 15 precise picture of what investors actually receive and pay. Third, our cash flows include fees. 16 17 This is also important when studying the risk that investors face because the fee structure is 18 19 highly non-linear. The risk of the cash flows faced by investors is thus likely to be different 20 21 from the risk profile of the individual venture capital deals, even for the private equity funds 22 that specialize in venture capital. Fourth, the sample selection bias is stronger in the dataset 23 24 that is used in the above mentioned studies.1 25 26 27 28 I.B.2. Risk of investing in private equity funds 29 30 Jones and Rhodes-Kropf (2004) offer the only study, to our knowledge, that directly attempt 31 to measure the risk of investing in private equity funds, based on a large cross-section of 32 33 funds.2 They assume that each residual value reported by each fund at quarter-end is a proxy 34 35 for the market value of the fund at that time. Combining these data with cash-flow streams, 36 37 they derive quarterly returns for each portfolio of funds, regress them on the time-series of 38 the three factors of Fama and French (1993), thereby obtaining an alpha and three betas. 39 40 The main difference between the study of Jones and Rhodes-Kropf (2004) and the 41 42 current paper is the assumption regarding residual values. Specifically, we do not rely on the 43 44 45 46 47 48 49 1 If neither an LP nor a GP reports data about a given fund, this fund will not be included in our study but its 50 investments are also unlikely to be included in the deal dataset (used by studies reviewed in sub-section B.1). 51 However, if a fund is included in our dataset, its cash flows will reflect both successful and unsuccessful 52 investments, which is not guaranteed in the deal dataset. For example, let us consider a reporting fund that 53 invests in deal A and deal B. When it calls the cash to finance them, we observe it in the cash-flow dataset. If 54 deal B is unsuccessful, it might not be reported to the deal dataset but it will be too late to erase it from the cash 55 flow dataset. Moreover, fund level studies observe a residual value for unexited investments, which is not 56 observed by the deal-level studies. Finally, if there is a partial exit, it is more likely that we will see the cash but 57 the deal dataset will miss it. 2 58 Note Gompers and Lerner’s (1997) pioneering work on this topic. Their study examines the risk-adjusted 59 performance of a single fund family (Warburg Pincus) by marking-to-market each investment, in order to obtain 60 the fund’s quarterly market values. The resulting time series is regressed on asset pricing factors, giving the alpha and betas of this single fund family. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 8
  • Management Science Page 8 of 37 1 2 3 4 5 time-series of residual values to estimate the risk profile of the funds.3 In addition, we 6 analyze the impact of business cycle variables and correct for sample selection bias. 7 8 9 10 I.B.3. Other related studies 11 12 Two studies point out that the return to private equity is highly time dependent. First, 13 14 Gompers and Lerner (2000) find that the valuation of venture capital investments is higher in 15 years when more new money (over the past year) flew to private equity funds after 16 17 controlling for public market valuation level. If the valuations are higher, it is possible, 18 19 although not certain, that the performance of funds that invest more during those years will be 20 21 lower. From an investor perspective, however, this potential source of variation in 22 performance is likely to be diversifiable (at least partially). What matters most from an 23 24 investor perspective is whether the years of poor performance for private equity funds 25 26 correspond to years of poor performance of the public stock market and years of poor 27 28 economic performance (low cash-flows, high discount rates). This is precisely what we aim 29 30 to measure in this paper and has not been measured before. 31 Second, Kaplan and Schoar (2005) find three patterns that also indicate a strong 32 33 cyclicality: (i) if a fund is raised in a year when the market is high, fund performance is 34 35 lower, (ii) if a fund is raised in a year when the market was high the year before, fund 36 37 performance is lower, (iii) if the public stock market is higher in the three years after a fund is 38 raised, fund performance is higher. Note that Kaplan and Schoar (2005) use what they call a 39 40 “rough proxy for performance (p1817)”, which is a dummy variable that is one if a fund 41 42 “raise a follow on fund.” In contrast, the present study uses a direct measure of performance 43 44 and we are also able to see the co-movements at the time the money is invested (instead of 45 when the money was committed).4 We thus measure the co-movements that matter most to 46 47 investors, as discussed above. 48 49 50 51 52 53 54 55 56 3 This choice is motivated by the finding of Phalippou and Zollo (2004), who show that residual values are 57 systematically biased (e.g. buyout funds have residual values that are systematically more aggressive than those 58 of venture capital funds.) In addition, Gompers and Lerner (1997), Blaydon (2002, and 2003) and Ljungqvist 59 and Richardson (2003) argue that residual values are artificially sticky and unreliable (see also section II.B 60 below). This feature creates a bias in the estimation of betas that cannot easily be corrected. 4 The money is not invested immediately, so it is potentially important and can make a large difference. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 9
  • Page 9 of 37 Management Science 1 2 3 4 5 II. Data 6 In this section, we detail our data sources, our sample selection scheme, and our performance 7 8 estimate. We also offer descriptive statistics about the characteristics of private equity funds 9 10 and their investments. 11 12 13 14 II.A. Data sources 15 In this study, we use several sources of data. Data on both Treasury bill rates and stock 16 17 performance are from CRSP (via WRDS). Data on corporate bond yields are from the 18 19 Federal Reserve Bank of Saint Louis. Data on private equity funds have been obtained from 20 21 two datasets maintained by Thomson Venture Economics. These datasets cover funds raised 22 from 1980 to 2003. Venture Economics records the amount and date of all cash flows as well 23 24 as the aggregate quarterly book value of all unrealized investments for each fund until 25 26 December 2003 (residual values). Cash flows are net of fees as they include all fee payments 27 28 to the General Partners (GPs, or fund managers), and distributions are reduced by the carried 29 30 interest and other charges. Venture Economics also collects information on fund investments 31 through its Vxpert database. The unique feature of our dataset is that Venture Economics 32 33 have provided us with identifiers that link the two datasets. This way, we know both the 34 35 investments and the cash flows for a large cross section of funds.5 36 37 38 II.B. Sample selection and treatment of residual values 39 40 Until a fund is entirely liquidated, the existence of non-exited investments prevents a precise 41 42 estimation of fund performance as neither the fund nor its underlying investments are 43 44 publicly traded. The unique assessment of the value of non-exited investments is the 45 accounting value that is reported quarterly by funds. However, these accounting valuations 46 47 are unreliable.6 A solution proposed by Kaplan and Schoar (2005) is to focus on a sample of 48 49 quasi-liquidated funds. In such a sample, the treatment of accounting values has a reduced 50 51 impact but the sample might not be representative. As our dataset allows us to correct 52 53 54 5 Details about these databases as well as certain corrections that we undertake are provided in the appendix A. 55 6 The US National Venture Capital Association proposed certain mark-to-market guidelines for the valuation of 56 PE fund investment in 1989 which have become a quasi-standard for the industry since then. Nevertheless, the 57 discussion in the PE industry about appropriate rules for the valuation of unrealized investments is ongoing and 58 accounting practices vary to the point that LPs sometimes receive significantly different valuations from 59 different GPs who jointly invest in the same company. In general, however, the accounting value of a deal stays 60 equal to the amount invested in that deal. Interested readers may refer to Blaydon and Horvath (2002, 2003) for a detailed discussion of accounting practices. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 10
  • Management Science Page 10 of 37 1 2 3 4 5 partially for sample selection biases (see below), we follow Kaplan and Schoar (2005) in that 6 we select a sample of quasi-liquidated funds (i.e. raised between 1980 and 1996 and is either 7 8 officially liquidated or have not reported any cash-flow over the last two years.) 9 10 In addition, certain funds in this sample have implausibly high residual values (so- 11 12 called ‘living-deads’). Hence, we write-off the residual values of officially liquidated funds 13 14 and funds that do not have any cash flow reported over the last four years (and are raised 15 before 1993). There are 212 such funds in our sample. They have invested $17 billion and 16 17 report $9 billion of residual values. The total residual value is thus more than 50% of the total 18 19 amount invested by these funds, which we think is implausible give the age of these funds 20 21 and their prolonged inactivity. For the other funds, we assume that their residual values 22 (reported at the end of December 2003) equal the present value of their future cash-flow 23 24 streams, as do Kaplan and Schoar (2005). 25 26 Finally, we use the profitability index (PI) as a performance measure. PI equals the 27 28 present value of cash inflows divided by the present value of cash outflows, using the return 29 30 of the S&P 500 to discount both cash-flows. 31 Table 1 32 33 An additional selection requirement for funds to be included in our study is that they 34 35 have information about at least four investments. We count 705 funds that satisfy these 36 37 criteria out of the 2844 funds raised between 1980 and 1996. Table 1 reports our sample 38 characteristics. Generally, the descriptive statistics are similar to those reported in the 39 40 literature (see Kaplan and Schoar, 2005). Venture funds are significantly smaller than buyout 41 42 funds, with an average invested capital of $48 million for venture funds compared to $225 43 44 million for buyout funds. Moreover, reflecting the fact that the private equity industry is 45 young and rather inexperienced, over one third of the funds in our database are first-time 46 47 funds (i.e. they are the first fund raised by the parent firm). 48 49 Performance data are also similar to what is reported in the literature. If we do not 50 51 correct for sample selection bias, value-weight by deflated capital committed and eliminate 52 53 ‘living-deads’, private equity funds in our sample have an average PI of 1.02 for buyout 54 funds and 1.07 for venture capital funds, indicating a slight outperformance with respect to 55 56 the S&P 500. 57 58 Table 2 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 11
  • Page 11 of 37 Management Science 1 2 3 4 5 From Table 1, we see that our sample tend to over-represent both large funds and 6 venture capital funds and tend to under-represent first-time funds. The fact that our sample is 7 8 not representative of the universe of funds is confirmed by a Probit regression (Table 2). The 9 10 dependant variable is a dummy variable that takes the value one if the fund is included in the 11 12 sample and zero otherwise. From this regression, we deduce the lambda of each fund, which 13 14 reflects the likelihood of a fund to be selected in the sample. This vector of lambda is added 15 to all the regressions in this paper to control for the fact that our sample is not representative 16 17 of the universe but rather is biased toward a certain type of funds (see Greene, 2003, for 18 19 details on Heckit regression and Cumming and Walz, 2004, for an application in the context 20 21 of private equity funds). 22 23 24 II.C. Descriptive statistics 25 26 We now turn to the description of investments, which is reported in Table 3. We find that 27 28 venture funds have almost twice as many investments as buyout funds. Venture funds invest 29 30 in 28 (22) companies on average (median) and buyout funds in 17 (11) companies for an 31 average period of almost five years for venture capital deals and four years for buyout deals. 32 33 These figures are consistent with the findings of Gompers and Lerner (1999) for a different 34 35 sample: they note that venture funds typically invest in two dozen firms over about three 36 37 years. 38 Table 3 39 40 Several important elements are worth mentioning. First, we find that venture funds 41 42 have 9% of their investments on average in buyouts and that as much as 18% of the 43 44 investments of buyout funds are on average in venture deals. This indicates that a few funds 45 in each category (and more so among buyout funds) are diversified across deal types. 46 47 Consequently, care should be taken when interpreting differences in the behavior of funds 48 49 according to their objectives (buyout versus venture capital). Second, the industry focus is 50 51 very similar for both venture funds and buyout funds as they both concentrate 40% of their 52 53 portfolio in one industry (out of 48 industry categories). Funds thus appear to be fairly 54 specialized. Third, and finally, more than half of the deals undertaken by venture funds are in 55 56 high-technology industries (in terms of value). 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 12
  • Management Science Page 12 of 37 1 2 3 4 5 III. Systematic risk, business cycle, and private equity fund performance 6 In sub-section A, we propose a first methodology to assess the (CAPM) beta for private 7 8 equity funds. In sub-section B, we study how business cycle variables, stock market 9 10 performance, and option market performance relate to the performance of private equity 11 12 funds. Finally, in sub-section C, we compare the magnitude of the beta obtained from our two 13 14 methodologies (the one in sub-section A and the one in sub-section B). 15 16 17 III.A. CAPM Beta 18 19 In this sub-section, we propose a methodology to assess the CAPM-beta of private equity 20 21 funds along the lines of Kaplan and Ruback (1995) and Ljungqvist and Richardson (2003); 22 construction details are presented in the appendix B. 23 24 As in Ljungqvist and Richardson (2003), we first identify each portfolio company 25 26 held by a fund. Second, given this identification, we assign portfolio companies to one 27 28 industry group. Third, we assume that the betas on asset are the same inside a given industry 29 30 and obtain a beta for each investment made by GPs by making further assumptions regarding 31 the leverage of each investment.7 The fundamental idea is to compute the beta on asset that 32 33 prevails in each industry, assign it to each private equity investment made in this industry, 34 35 and lever it up as a function of the deal type (venture capital or buyout). Fourth, we compute 36 37 the average equity beta of the fund using the capital disbursements as weights. 38 Given our assumptions, note that variations in betas reflect a combination of the 39 40 riskyness of the industry in which funds invest, the type of investments made and the time 41 42 duration of each investment. 43 44 To compute betas, we assume that the leverage of buyouts decreases linearly over 45 time from a debt-to-equity ratio of 3 (at entry) down to the leverage that prevails in the 46 47 industry (at exit). The beta on debt is assumed to be 0.25 and the beta for venture deals is 48 49 assumed to be the same as the beta of the 20%-smallest stocks in the corresponding industry. 50 51 Importantly, stock betas are computed using Dimson’s correction. The choice of the beta on 52 53 debt is based on Cornell and Green (1991), who evaluate the beta for high-grade debt (from 54 1977 to 1989). The choice of debt-to-equity ratio is based on Cotter and Peck (2001) and on 55 56 57 7 58 Note that here, and throughout this paper, we do not separate US and EU funds. We use only US data. Such a 59 convention does not affect significantly our results given that non-US investments represent only 12% of our 60 observations (in unreported results we re-run the main regressions with US funds only and have found virtually identical results). Note also that US and EU data have a relatively high positive correlation. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 13
  • Page 13 of 37 Management Science 1 2 3 4 5 Lerner et al. (2004), who argue that a 3:1 debt-to-equity ratio for buyouts is rather typical 6 (though slightly conservative).8 7 8 Table 4 9 10 The average estimated betas are reported in Table 4. We document how betas differ 11 12 between venture funds and buyout funds and between large funds and small funds. The 13 14 average beta of buyout funds is 1.7 and is similar to the average beta of venture funds, which 15 is 1.6. Similarly, small funds have an average beta of 1.65 and large funds have an average 16 17 beta of 1.56. We also report how these estimates change as we modify our assumptions about 18 19 buyout leverage. We observe little overall effect. The beta of buyout funds, however, doubles 20 21 when we use (for the entire length of the investment) a debt-to-equity ratio of 3 instead of the 22 industry average, which are the two most extreme assumptions one can make about leverage. 23 24 When we relate beta to performance, we find a positive but not statistically significant 25 26 relation [unreported results]. This result holds irrespective of both the control variables that 27 28 we use and our leverage assumptions. This result might not appear very surprising given that 29 30 the relation between stock-beta and stock performance has also been found to be weak. 31 To summarize, the beta of private equity funds is expected to be substantially higher 32 33 than 1 and (CAPM) beta does not appear to be a driver of fund performance. 34 35 36 37 III.B. Fund exposure to risk factors and business cycle variables 38 In this section, we investigate how business cycles, option market performance and stock 39 40 market performance influence private equity fund performance. 41 42 Using available data about the underlying investments of funds, we can compute the 43 44 exposure of each fund to several factors. Construction details are given in the appendix B, but 45 the idea is straightforward. 46 47 Assume that we want to know the influence on performance of the level of credit 48 49 spreads that prevails during the life of the investments. Given that we know when a given 50 51 investment starts and finishes, we can compute the time-series average (TSA) level of credit 52 53 spreads that prevails during the life of this investment. Let us denote it TSAcs(i) for each 54 investment i. Then, we compute the (cross-sectional) average of TSAcs(i) across all the 55 56 investments i of a given fund f, resulting in Acs(f). Acs(f) is labeled ‘fund loading on credit 57 58 spreads’. Indeed, if a fund invests mainly during times when credit spreads are high then its 59 60 8 Debt/equity ratio in buyouts has decreased over time, from 95%/5% in the 80s to 70%/30% in the late 90s. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 14
  • Management Science Page 14 of 37 1 2 3 4 5 ‘loading on credit spreads’ will be high. Finally, by running a cross-sectional regression of 6 fund performance on the vector of Acs(f), we assess the exposure/sensitivity of fund 7 8 performance to the level of credit spreads. 9 10 We compute the exposure to variables which are related to the state of the aggregate 11 12 economy (level of cash flows and level of discount rates), the stock option market and public 13 14 stock market. Namely, we consider (i) real GDP growth rate, (ii) BAA-bond yields, (iii) 15 credit spreads, (iv) stock market portfolio performance, and (v) the performance of options 16 17 written on the S&P. All these variables are taken at a quarterly frequency. 18 19 Credit spread is the difference between the yield on the corporate-BAA bond and the 20 21 10-year treasury bonds. This variable captures both the probability of default and the 22 expected recovery rate in case of default in the economy. The credit spread can thus be seen 23 24 as a business cycle variable.9 When credit spreads are relatively large, investors expect the 25 26 probability of corporate default to be relatively high. It thus corresponds to periods of poor 27 28 economic prospects (low cash flows, i.e. bad economic times). The same holds true for 29 30 corporate bond yields. Credit spread being simply a relative bond yield. In addition, corporate 31 bond yields measure the level of discount rates. When corporate bond yields are high, 32 33 discount rates tend to be high and the value of the firm tends to be low (bad economic times). 34 35 The stock market portfolio (proxied by the CRSP value weighted index) loading aims 36 37 at assessing the impact of investing in periods of high stock market performance. The option- 38 based risk factors consist of out-of-the-money European call and put options on the S&P 500 39 40 composite index traded on the Chicago Mercantile Exchange. These option-based factors are 41 42 proposed by Agarwal and Naik (2004), who argue that it is important to take into account 43 44 option-like features to evaluate the risk of hedge funds. In the context of private equity, both 45 venture and buyout investments are likely to have an option-like payoff: buyout investments 46 47 as they are highly levered and venture investments as they are carried up by stages with, each 48 49 time, a target market value beyond which there is a new round of financing. This point is 50 51 emphasized by Cochrane (2005) who states that “venture capital investments are like 52 53 options.” 54 Finally, we compute both the average earnings-to-price ratio (price multiples) and the 55 56 state of the IPO market that prevails (amount of equity issued) in the year when investments 57 58 9 59 Note that Gertler and Lown (2000) find that credit spread “has had significant explanatory power for the 60 business cycle (...) it outperforms other leading financial indicators, including the term spread, the paper bill spread and the federal funds rate.”. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 15
  • Page 15 of 37 Management Science 1 2 3 4 5 are exited. Similarly, we compute both the average yields of Corporate-BAA bonds and the 6 average credit spread that prevail when investments are made (i.e. at entry). These indicators 7 8 being related to the valuation of firms at entry and exit, they may play an important role for 9 10 performance. 11 12 Table 5 13 14 In Table 5, we report how these loadings relate to performance. In order to compare 15 the economic importance of each loading, variables are standardized by subtracting their 16 17 sample mean and dividing by their sample standard deviation (i.e. each variable is expressed 18 19 in terms of z-score). Importantly, note that this standardization does not affect the t-statistics 20 21 at all. Finally, each regression includes a correction variable (vector of lambdas, see Greene 22 2003 for details about Heckit regressions) to account for a potential sample selection bias.10 23 24 As these loadings have a high correlation among one another (especially the business 25 26 cycle variables), we first report their statistical and economic significance one at a time. The 27 28 signs of each proxy always indicate that private equity funds offer pro-cyclical performance. 29 30 Private equity funds that entered investments at time when interest rates and credit spreads 31 were high underperform. Performance increases substantially when investments take place 32 33 during times of high GDP growth, high public stock market performance, high returns for call 34 35 options, and low returns on put options. The exit variables are not statistically significant 36 37 unlike entry variables. Among entry variables, the yield on risky corporate bonds (rated 38 BAA) is the most important variable. In Panel C, we show that this variable remains 39 40 significant irrespective of the other variables we add in the regression. It appears that the two 41 42 most significant variables are the yield on risky corporate bonds at the time of investment and 43 44 the average stock market return during the life of the investment. Hence, private equity funds 45 perform worse at times when the economic prospects are poor in general (high corporate 46 47 bond yields) and when the stock market performance is low. 48 49 The significance of the public stock market return is slightly superior to the 50 51 significance of the call option return. The two variables are however highly positively 52 53 correlated and both are significant when we control for corporate bond yields at entry. The 54 result of the call option return is particularly interesting because this factor has also been 55 56 found significantly related to hedge fund performance by Agarwal and Naik (2004). It shows 57 58 that, like hedge funds, private equity funds bear significant right-tail risk. That is, the 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 16
  • Management Science Page 16 of 37 1 2 3 4 5 performance is mainly realized when the public stock-market has high returns. If the public 6 stock-market return is below a certain threshold then private equity performance is very low 7 8 irrespective of how low public stock market returns are. 9 10 The advantage of standardizing explanatory variables is that we can readily compare 11 12 their economic significance across specifications and detect which variable is most important. 13 14 A drawback is that we do not see directly the economic impact of the explanatory variable on 15 the dependant variable. When we do not standardize [unreported results], we observe that an 16 17 increase in stock market performance of 5% per year over the life of the fund induces an 18 19 increase in the performance of private equity funds by 12.5% (i.e. the present value of the 20 21 distribution increases by 12.5%). The same impact is obtained if the yield on BAA bond 22 would be 1% lower on average at the time the investments were made. It is, therefore, clear 23 24 that our macroeconomic variables have a tremendous impact on fund performance. 25 26 Another way to see the impact of both stock-market performance and bond yield is to 27 28 simply form fund deciles based either on the average stock-market performance during the 29 30 life of a fund or on the average bond yield at the time the investment is made by a fund. 31 Results are reported on graph 1. 32 33 Graph 1 34 35 We find that the decile of funds who invested when the stock-market had the lowest 36 37 performance (-0.2% per month) has an average profitability index of 0.84 (large 38 underperformance compared to the S&P 500). In contrast, the decile of funds who invested 39 40 when the stock-market had the highest performance (1.7% per month) has an average 41 42 profitability index of 1.29 (large overperformance compared to the S&P 500). In terms of 43 44 IRR, the performance is on average 8.7% for the lowest decile and 21.6% for the highest 45 decile. 46 47 Consistent with our regression results, the performance spreads are even more 48 49 dramatic when we sort on average bond yields. We find that the decile of funds who invested 50 51 when bond yields were highest (13.2%) has an average performance of 0.62. In contrast, the 52 53 decile of funds who invested when the bond yields were lowest (7.8%) has an average 54 performance of 1.52. In terms of IRR, the performance is on average 7.9% for the lowest 55 56 decile and a staggering 33.9% for the highest decile. This performance differential is 57 58 extremely large by any standards. 59 60 10 We have run all the regressions without such a correction and have found very similar results. Typically, the ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 17
  • Page 17 of 37 Management Science 1 2 3 4 5 We also note that the relation between private equity fund performance and stock- 6 market performance is non-linear. This is due to the fact that the relation between stock- 7 8 market performance and private equity fund performance is weaker when we do not control 9 10 for bond yields (see Table 5) and as noted below, private equity fund performance resembles 11 12 to a call option written on the stock market. 13 14 15 III.C. Comparing CAPM Betas 16 17 In the section A above, we have estimated the (CAPM) beta of a fund by looking at the type 18 19 of investments made by the fund, when each investment was made, and in which industry 20 21 they were made. In the section B above, we have estimated an implicit beta by regressing the 22 cross section of fund performance on the average stock market return during the life of their 23 24 respective investments. In this section, we compare these two estimates of beta. 25 26 Let us assume that there is no intermediate cash-flows during the life of a fund (i.e. 27 28 there is only one cash flow at the end of fund’s life and one take down at the beginning). In 29 30 this case, the natural logarithm of the profitability index can be approximated as follows: 31 Log (PI) = T * Log [(1 + Ri)/(1 + Rm)] ~= T * (Ri - Rm) 32 33 Where Ri is the average performance of a private equity investment at a quarterly frequency, 34 35 Rm is the average market performance at a quarterly frequency during the life of an 36 37 investment, and T is the number of quarters during which a fund invests in a given project. 38 From the regressions in panel A of table 5, we see that ‘a one standard deviation 39 40 increase in average market return corresponds to a 0.08 standard deviation increase in total 41 42 private equity performance (PI).’ If we do not standardize, this coefficient is close to 10. 43 44 From Table 3, we see that the average length of a project is T = 56/3 = 18 quarters. Hence, 45 we estimate that T * (Ri - Rm) = 10 * Rm, that is Ri = (28/18) * Rm = 1.56 * Rm. 46 47 The implied beta from Table 5 is therefore 1.56, which is very close to the 1.6 48 49 estimated in sub-section A using the industry matching methodology. This shows that our 50 51 results are very consistent across methodologies in addition of being intuitively reasonable. 52 53 54 55 56 57 58 59 60 statistical significance of the coefficients is higher when we do not correct for sample selection bias. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 18
  • Management Science Page 18 of 37 1 2 3 4 5 IV. The pricing of Idiosyncratic risk 6 Jones and Rhodes-Kropf (2004) point out that GPs are forced to hold considerable 7 8 idiosyncratic risk and that idiosyncratic risk should be an important determinant of 9 10 performance. In this section, we investigate whether idiosyncratic risk is indeed a driver of 11 12 fund performance after controlling for various factors. 13 14 Jones and Rhodes-Kropf (JR, 2004) propose a model whereby more idiosyncratic risk 15 should be associated with higher returns, in equilibrium. The idea is that investors want GPs 16 17 to specialize so that they have higher performance.11 In equilibrium, GPs obtain a 18 19 compensation that increases with the amount of idiosyncratic risk and “all else equal, the 20 21 return received by the investors is increasing in the amount of realized idiosyncratic risk, 22 even though they face competitive market conditions” (their theorem 4). To test this 23 24 implication they argue that a reasonable proxy for idiosyncratic risk is the number of 25 26 investments that a fund makes. In the absence of this information, they use the number of 27 28 take-downs. Our dataset, in contrast, offers the unique opportunity to measure directly the 29 30 number of investments made by each fund, and thereby, testing the above claim. In addition, 31 our dataset offer the possibility to construct several proxies that capture closely the spirit of 32 33 JR’s model. Namely, we compute the proportion invested in the dominant industry, and 34 35 Herfindahl indices for both type and industry concentration based on the number of 36 37 investments across deal type (venture deals vs buyout deals) and across 48 industries.12 38 Table 6 39 40 Jones and Rhodes-Kropf (JR, 2004) find that the number of take-downs is negatively 41 42 related to the performance for 379 buyout funds. As they see the number of take-downs as a 43 44 proxy for the number of investments and, in turn, as a proxy for idiosyncratic risk, they 45 conclude that this empirical result supports their claim. Note that JR find the opposite for 46 47 venture capital funds and argue that the number of take-downs is not a good proxy for the 48 49 number of investments of Venture Capital funds. We, however, can observe the number of 50 51 52 11 Being focused enables GPs to work with smaller and more specialized teams that may learn faster via a high 53 number of similar deals. An additional benefit is that GPs build tight links with the industry which may improve 54 performance. It may also happen that unskilled managers diversify because they have failed in a certain type of 55 deal and thus try something different or are forced to change (e.g. a manager that ends up with a couple of BO in 56 bankruptcy may not have access to the debt market anymore). Finally, there is casual evidence (Lerner et al., 57 2004) that several funds have invested in a country, industry, or private equity type that is different to their 58 stated objective in order to have a track record in that investment category and then raise a new fund in that 59 category. In other words, GPs have an incentive to build their reputations at the expense of LPs. Interestingly, 60 we note that, nowadays, most contracts explicitly limit this type of behavior. 12 The 48 industries are as defined in Fama and French (1997). ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 19
  • Page 19 of 37 Management Science 1 2 3 4 5 investments of Venture Capital funds and still find a positive relation (see Table 6). We thus 6 conclude that the fact that their theoretical prediction is contradicted for venture capital funds 7 8 can not be attributed to the number of take-downs being a bad proxy for venture capital 9 10 funds. 11 12 Nonetheless, the industry Herfindahl is significantly positively related to performance. 13 14 The Herfindahl based on the type of deals is also positively related to performance but not 15 significantly so.13 However, we note that when we control for the fraction invested in high- 16 17 tech industries, this effect vanishes.14 This result holds irrespective of the control variables 18 19 we use (including systematic risk factors) and whether we control for sample selection bias or 20 21 not. We also find the same result if we use portfolios of funds (as do JR) and if we do not 22 write-off any residual values (as do JR). 23 24 JR offer a second set of results consistent with their hypothesis. For these results, they 25 26 compute idiosyncratic risk directly by assuming that quarterly observed residual values are 27 28 unbiased proxies for the market value of a private equity fund. This assumption is 29 30 controversial, however, as documented by Gompers and Lerner (1997), Blaydon (2002, 31 2003), Ljunqvist and Richardson (2003), and Phalippou and Zollo (2005). We then conclude 32 33 that there is little evidence that idiosyncratic risk is priced, but this issue warrants further 34 35 research. 36 37 38 V. Fund characteristics and fund performance 39 40 In this section, we focus on the characteristics that are related to performance. The main goal 41 42 here is to verify that characteristics that have been shown to impact performance (e.g. fund 43 44 size, Kaplan and Schoar, 2005) still do so after controlling for systematic risk factors, 45 business cycle variables and sample selection bias. 46 47 The first characteristic under investigation is fund size and fund size squared. Size is 48 49 an important characteristic that captures several performance-related dimensions such as 50 51 reputation, economies of scale, and learning. Indeed, a larger fund may learn faster as it 52 53 makes more deals than a smaller fund. An often-invoked downside of running a large fund is, 54 however, that it increases the difficulty of finding enough good deals. 55 56 57 13 Note that a similar result is reported by Gompers and Lerner (2002, chap. 5). They find that companies that 58 are funded by corporate investors that have a well-defined strategic focus enjoy greater success. 14 59 Industry groups are defined as follows. Health comprises three Fama French (1997) industries: healthcare, 60 medical equipment, and pharmaceutical products. High-tech comprises four Fama French (1997) industries: electrical equipment, telecommunications, computers, and electronic equipment. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 20
  • Management Science Page 20 of 37 1 2 3 4 5 The second characteristic is the proportion invested outside the US. Kaplan et al. 6 (2003) and Hege et al. (2003) document that certain European private equity investments 7 8 have lead to very poor performance. They advance various reasons for this, such as a wrong 9 10 type of contract used and institutional differences. In addition, the private equity industry 11 12 outside the US is younger and thus at a lower point in the learning curve. 13 14 Third, Gompers and Lerner (1999) and Kaplan and Schoar (2005) find that 15 performance depends on the fund sequence number.15 The fourth characteristic is the 16 17 proportion invested in venture capital and the average length of the investments as longer 18 19 time duration for investments might signal living-deads and thus lower performance. Finally, 20 21 we include the amount of capital committed in a given year as Gompers and Lerner (2000) 22 propose this as a proxy for the amount of “money chasing deals.” 23 24 Table 7 25 26 Results are reported in Table 7. We do not find evidence of a concave relationship 27 28 between performance and fund size but do find a positive relation between size and 29 30 performance as in Kaplan and Schoar (2005). Neither do we find evidence of a “money 31 chasing deals” effect.16 This finding is driven by both the inclusion of our control variables 32 33 and by our performance measure. 34 35 We confirm the importance of family experience for fund performance as measured 36 37 by fund sequence. This effect is of considerable magnitude and in line with what Gompers 38 and Lerner (1999) and Kaplan and Schoar (2005) report for different samples. Fund sequence 39 40 appears as the best determinant of fund performance. The next best explanatory variable is 41 42 the fraction invested in high-technology industries. Likely, funds raised before 1996 (our 43 44 sample) that have invested in high-tech industries have benefited from the buoyant IPO 45 market of the late 90s. Finally, we note that funds that keep their investments longer tend to 46 47 have lower performance. However, caution is required in interpreting this correlation as the 48 49 time duration of investments is an endogenous variable for which we do not have good 50 51 instruments. 52 53 54 55 56 15 Fund families raise one fund at a time. The first fund ever raised by a given fund family is assigned a 57 sequence number of 1, the second fund is assigned a sequence number of 2 etc. 16 58 We note, however, that capital committed in a given year is not a precise measure of the money chasing deals 59 as the capital committed in the previous years that is not invested yet is also chasing deals. In addition, Kaplan 60 and Schoar (2005) also find that there is no relation between number of funds raised in the same year and performance. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 21
  • Page 21 of 37 Management Science 1 2 3 4 5 The lower performance of small and inexperienced funds shown by Kaplan and 6 Schoar (2005) is, therefore, an empirical fact that is robust to control for sample selection 7 8 bias and for other important variables (in particular risk factors and business cycle variables). 9 10 We find this result intriguing and worthwhile of further research. 11 12 Overall, we find five key determinants of fund performance: the level of corporate 13 14 bond yield at the time of investments, the return of the public stock-market during the life of 15 investments, the fraction invested in high-tech industries, the size of the fund and the 16 17 experience of the fund family. These five variables explain 10% of the cross-sectional 18 19 variation in fund performance (Table 7, specification 5). 20 21 22 VI. Conclusion 23 24 Private equity funds’ growth has outstripped that of almost every class of financial assets 25 26 over the last twenty five years. In 2005, Blackstone Capital raised the largest private equity 27 28 fund ever, with $11 billion committed. The total amount in the hand of private equity funds 29 30 waiting to be deployed is in the range of half a trillion of US dollars and this money is 31 expected to be deployed worldwide. For example, in 2005 alone, $360B of private equity 32 33 capital has flown to emerging market economies. Given the high amount of leverage used by 34 35 such fund, these figures should be multiplied about threefold to compute the asset value of 36 37 these large and global flows. 38 These large amounts of money come mainly from institutional investors. Some of 39 40 these investors increase their allocation to private equity funds based on the belief that returns 41 42 are largely uncorrelated with market returns. For example, Lerner et al. (2004) report that 43 44 Yale endowment fund, one of the largest investor in private equity funds, believes that private 45 equity funds can “generate incremental returns independent of how the broader markets were 46 47 performing.” This paper shows that, in reality, the performance of private equity funds is 48 49 highly pro-cyclical as it positively co-varies with the business cycles and the stock market. 50 51 This widespread belief is therefore erroneous. 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 22
  • Management Science Page 22 of 37 1 2 3 4 5 References 6 Agarwal, V., and N.Y. Naik, 2004, Risks and portfolio decisions involving hedge funds, 7 8 Review of Financial Studies 17, 63-98. 9 10 Blaydon, C. and M. Horvath, 2002, What’s a company worth? It depends on which GP you 11 12 ask, Venture Capital Journal, May. 13 14 Blaydon, C. and M. Horvath, 2003, LPs need to trust General Partners in setting valuations, 15 Venture Capital Journal, March. 16 17 Cochrane, J., 2005, The risk and return of venture capital, Journal of Financial Economics 18 19 forthcoming. 20 21 Cornell, B. and K. Green, 1991, The investment performance of low-grade bond funds, 22 Journal of Finance 46, 29-48. 23 24 Cotter, J. and S. Peck, 2001, The structure of debt and active equity investors: The case of the 25 26 buyout specialist, Journal of Financial Economics 59, 101-147. 27 28 Cumming, D. and U. Walz, 2004, Private equity returns and disclosure around the world, 29 30 mimeo. 31 Fama, E. and K. French, 1997, Industry cost of equity, Journal of Financial Economics 43, 32 33 153-193. 34 35 Fernandez, P., 2004, The value of tax shields is not equal to the present value of tax shields, 36 37 Journal of Financial Economics, forthcoming. 38 Fung, W., and D. Hsieh, 2004, Hedge Fund Benchmarks: A Risk Based Approach, Financial 39 40 Analyst Journal 60, 65-80. 41 42 Gertler, M., and C.S. Lown, The information in the high yield bond spread for the business 43 44 cycle: evidence and some implications, NBER working paper 7549. 45 Gompers, P., and J. Lerner, 1999, An analysis of compensation in the U.S. venture capital 46 47 partnership, Journal of Financial Economics 51, 3-44. 48 49 Gompers, P., and J. Lerner, 2000, Money chasing deals? The impact of fund inflows on 50 51 private equity valuations, Journal of Financial Economics 55, 281-325. 52 53 Greene, W.H., 2003, Econometric analysis, 5th edition, Prentice Hall. 54 Hege, U., F. Palomino and A. Schwienbacher, 2003, Determinants of venture capital 55 56 performance: Europe and the United States, Mimeo. 57 58 Jones, C. and M. Rhodes-Kropf, 2004, The price of diversifiable risk in venture capital and 59 60 private equity, Working paper, Columbia University. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 23
  • Page 23 of 37 Management Science 1 2 3 4 5 Kaplan, S.N., 1995, The valuation of cash flow forecasts: An empirical analysis, Journal of 6 Finance 50, 1059-1093. 7 8 Kaplan, S.N. and R. Ruback, 1995, The valuation of cash flow forecasts: An empirical 9 10 analysis, Journal of Finance 50, 1059-1093. 11 12 Kaplan, S.N. and A. Schoar, 2005, Private equity performance: Returns, persistence, and 13 14 capital flows, Journal of Finance, forthcoming. 15 Lerner, J., F. Hardymon, and A. Leamon, 2004, Venture capital and private equity: A 16 17 casebook, 3rd edition, John Wiley & Sons. 18 19 Ljungqvist, A., and M. Richardson, 2003, The investment behavior of private equity fund 20 21 managers, working paper NYU. 22 Phalippou, L., and M. Zollo, 2005, Performance of private equity funds: another puzzle?, 23 24 INSEAD working paper. 25 26 27 28 Appendix A: Industry description and datasets 29 30 A.I. Industry description 31 A brief description of the industry is offered in this appendix. For a more detailed description, 32 we advise interested readers to refer to Lerner et al. (2004) and Gompers and Lerner (2002). 33 34 Private Equity funds are typically structured as limited liability partnerships in which 35 a specialized Private Equity firm serves as the general partner (GP) and institutional investors 36 or high-net-worth individuals provide the majority of capital as limited partners (LP). Most 37 Private Equity funds are closed-end funds with a finite life of 10 or 12 years, which may be 38 extended with the consent of the majority of the shareholders (Gompers and Lerner, 1999). 39 40 During this period, the GP undertakes investments of various types (e.g. venture capital, 41 bridge financing, expansion capital, leveraged buyouts), with the obligation to liquidate all 42 investments and return the proceeds to the investors by the end of the fund's life. A minority 43 of funds, so-called "evergreen" funds have an infinite life and no obligation to liquidate their 44 positions. 45 At the time of the fund's inception, LPs commit to a percentage of total fund size. In 46 47 the first years of the fund life (typically the six first years), the GP makes capital calls (or 48 take-downs) to LPs whenever it finds an investment opportunity. Typically, within two 49 weeks, LPs have to provide the corresponding cash. The total amount of such "capital calls" 50 can exceed the capital committed at the fund's birth, but this is relatively rare. In fact, it is 51 more common for a fund to liquidate without having invested all the capital committed. 52 53 Whenever a fund receives returns on its investments, proceeds are proportionally 54 distributed to LPs, net of fees and so-called "carried interest". These distributions can be in 55 form of cash or shares (common, preferred, or convertibles). GP receives compensation in 56 varying forms. A fixed component, a yearly management fee (between 1% and 3%) of the 57 total committed capital is charged to LPs. In addition, GPs can receive fees for each 58 transaction performed (fixed or as a percentage of deal value) and participates in the fund 59 60 returns through "carried interest" which often specifies that 20% of all net gains (or gains beyond a certain "hurdle rate") accrue to the GP whilst the rest is distributed among LPs. ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 24
  • Management Science Page 24 of 37 1 2 3 4 5 PE firms often manage several funds, raising a new fund three to five years after the 6 closing of the fundraising process for the previous fund. Note also that some PE funds are 7 structured as non-partnership captive or semi-captive vehicles with one dominant (or 8 exclusive) LP. This is mainly the case with funds that are managed by subsidiaries of large 9 insurance companies or banks that invest the parent company's money. 10 11 12 A.II. VentureXpert content and corrections 13 Venture Economics’ Private Equity Performance Database (also called cash-flow dataset in 14 the text) is the most comprehensive source of financial performance of both US and European 15 Private Equity funds and has been used in previous studies (e.g., Kaplan and Schoar, 2005). It 16 covers about 88% of venture funds and 50% of buyout funds in terms of capital committed. 17 18 In terms of number of funds, it offers cash-flow series for about 40% of both Europe funds 19 and US funds. Venture Economics builds and maintains this dataset based on voluntarily 20 reported information about cash flows between GPs and LPs in Private Equity funds. Venture 21 Economics obtains and crosschecks information from both GPs and LPs, which increases the 22 reliability of this dataset. Finally, the aggregate residual values of unrealized investments 23 24 (i.e., non-exited investments) are obtained from audited financial reports of the partnership. 25 Venture Economics makes certain simplifying assumptions about cash flows. First, 26 cash flows are assumed to take place at the end of the month. Second, stock distributions are 27 valued based on the closing market price the day of distribution to LPs. In the case of an IPO, 28 GPs have to hold on to the stock until the end of the lockup period. After this date, however, 29 30 they have some flexibility regarding when to distribute the stock to the LPs. In addition, the 31 valuation at the time of stock distribution to LPs differ from the value of actual realizations 32 by LPs, as LPs may hold the shares for a while and may face substantial transaction costs 33 (mainly via the price impact of their trade). 34 For each fund, Venture Economics collects information on underlying investments 35 through its VentureXpert database, starting from 1980 (Vxpert in the text). This database 36 37 contains information on Private Equity investments in 29 739 companies. Several of these 38 investments have received funding at different points in time (e.g. subsequent rounds in VC 39 investments) and by different private equity funds, so that the total number of investments 40 amounts to 134 641. Data on investments include information about the target company 41 (location, industry description, age), the investment (time of investment, stage, group of co- 42 43 investors, equity amount provided by each fund, exit date and exit mode for liquidated 44 investments), and the fund (investment focus, vintage year). Note that the industry 45 description of the target company is codified by Vxpert. We have converted each of these 46 industry codes into one of the 48 industries as defined by Fama and French (1997) ourselves. 47 Due to the confidential character of Private Equity investments, the composition of 48 this dataset is based on information Venture Economics obtained through its relationships 49 50 with the GP and LP community over the past decades. However, despite all these efforts, a 51 complete coverage of all investments by all funds remains difficult to achieve. Consequently, 52 missing information about certain investments is accommodated in the following way. 53 Vxpert includes a number of investments with a 0 value. These correspond to 54 confidential investments with an undisclosed equity amount. We assign an equity value to 55 56 these deals according to the following logic. If we have information about at least three other 57 investments of the same fund at the same stage (four stages are defined: early, intermediate, 58 late VC, and buyout), we assigned the average amount of these investments to the focal 59 investment (71% of the missing cases). Whenever there are too few investments of the same 60 category by the same fund, we turned to the firm level (i.e., consider all investments made by ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 25
  • Page 25 of 37 Management Science 1 2 3 4 5 the same GP) and apply the same procedure. Whenever there are too few investments made 6 even by the firm, we rely on the average per stage across the entire sample. Similarly, Vxpert 7 provides information on many investments but relatively few divestments. This can be 8 explained by the confidential character of many divestitures. We then have to correct for 9 certain missing holding periods. First, certain investments are still in the database as "active 10 11 investments" with a holding period of more than seven years (i.e., that started before 1996). 12 Second, some investments are reported as terminated but lack an exit date. The same logic as 13 above is then applied. We estimate the average length for each type of deal and deduce the 14 exit date. For 82% of the cases there were enough investments in the same stage operated by 15 the same fund to use the stage-fund average length. It is important to note that these simple 16 interpolations aim at neutralizing these anonymous deals in our weighting exit success 17 18 scheme. 19 Recently, Kaplan, Sensoy and Stromberg (2002) studied the accuracy of Vxpert and 20 point out that discrepancies arise from the treatment of milestone rounds; many are missing in 21 the dataset. However, we do not use this information in our analysis. Note that Gompers and 22 Lerner (2002, chap. 16) also describe and discuss the quality of the databases collected by 23 24 Venture Economics. They report a coverage of deals of about 90% in terms of value and note 25 that the number of rounds is overstated. Their analysis shows that VE data do not suffer from 26 any significant biases that would impair our analysis. Regarding buyout investments, we do 27 not know any study that discusses the accuracy of Vxpert. It is nonetheless known that 28 buyouts have not been the focus of Venture Economics until recently and thus several deals 29 30 are missing. Casual checking of Vxpert reveals that at least the largest deals are present (e.g. 31 Nabisco). 32 33 34 35 36 37 Appendix B: Systematic risk of private equity fund portfolios 38 39 We evaluate the systematic risk of private equity fund portfolios in three steps. We first 40 estimate industry-wide unlevered beta. Second, we assign each company (deal) to an industry 41 and assume that the unlevered beta of the company is the same as the corresponding industry- 42 43 aggregate. We lever it up for BOs and VCs in a different fashion. Finally, we aggregate each 44 deal beta at the fund level. 45 46 1. Estimation of industry-wide unlevered betas 47 48 First, we assume that the CAPM holds, hence the risk-return trade-off for the equity of firm h 49 50 is: Rh = R f + β he ( Rm - R f ) e 51 (1) 52 Rf β he 53 Where is the risk-free rate (proxied by T-bill 30 days), is the stock's systematic risk, 54 Rm 55 and is the market portfolio (proxied by the CRSP value-weighted index). Estimating (1) 56 57 β ethe at a monthly frequency, using h, t Dimson's correction and rolling over the past 60 months, 58 we obtain a time series of for each stock. These betas are then unlevered using the 59 60 following relationship: ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 26
  • Management Science Page 26 of 37 1 2 β h, t E h ,t + β h, t (1 − τ ) Dh ,t e d 3 β h, t = u 4 E h ,t + (1 − τ ) Dh ,t 5 6 (2) 7 8 Where Eh,t is the capitalization of firm h at the beginning of the month, Dh,t is the book value 9 (from Compustat) of the long-term debt, updated yearly. We further assume that the 10 corporate utax rate τ is constant across both firms and time, and equals 35%. Finally, we 11 β h, t βd h, t 12 denote the systematic risk of the unlevered firm and we denote the systematic risk 13 14 β h, t of debt. Following Cornell and Green (1991), who estimate the systematic risk of high-grade d 15 debt, we assume that equals 0.25. 16 17 Relation (2) makes some simplifying assumptions. In particular, it values interest tax 18 shields at the full corporate tax rate and assumes that the value of tax shields has the same 19 systematic risk as the unlevered firm. More details and comments on these issues can be found in Kaplan and Ruback(1995)E h ,t Fernandez (2004). 20 21 wh ,t = N i and Next, each stock is assigned to one of the 48 industries defined in Fama and French 22 23 ∑ E h ,t (1997). Then, individual betas are1 aggregated in each industry to obtain a time-series of Ni 24 β i, t ∑ wh ,t β h, t industry=(unlevered) betas: u u h= 25 h =1 26 (3) , with , i = 1,…,48 27 28 29 30 β i,se Finally, we construct the (equally-weighted) average equity betas for the 20%-smallest stocks t 31 in each industry and denote it as . 32 33 34 2. Estimation of equity betas for venture capital and buyout deals 35 36 37 Each investment j, carried out by a given fund, has a VEIC number assigned by 38 VentureXpert. Using their industry description, we assign each VEIC number to one of the 48 39 industries (manually, by eye match). 40 β i,se Each venture capital investment is assigned an equity beta for each month between t 41 42 the date of entry (dentry) and the date of exit (dexit) of the deal. The equity beta is 43 44 β venture β i,se described above. That is, each i,se dentry capital investment operating in industry i is assigned a dexit 45 time-series of equity betas: ( ,..., ). 46 47 For buyout investments, we need to lever-up the unlevered beta. To begin with, we 48 need to make an assumption about debt levels. We investigate three scenarios: 49 50 S1: A buyout starts with a debt-to-equity ratio of 3, i.e. a debt-to-asset ratio of 75%. This 51 ratio then linearly decreases down to the industry average debt-to-equity ratio. 52 S2: A buyout has a debt-to-equity ratio of 3 throughout investment’s life. 53 54 S3: A buyout has a debt-to-equity ratio equals to the industry average debt-to-equity ratio. 55 56 S1 is the most realistic scenario while S2 and S3 serve as a sensitivity check of our 57 assumption about the decrease in leverage. A debt-to-asset ratio of 75% is common in 58 practice, as document by Cotter and Peck (2002). 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 27
  • Page 27 of 37 Management Science 1 2 3 4 5 Using equation (2)βand assuming that the systematic risk of the unlevered investment u i, t 6 (in industry i at time t) is , we deduce the systematic risk of the given buyout investment 7 8 for each month of its life. 9 10 3. Aggregation at the fund level 11 12 13 If funds invested all capital committed at inception and exited all the investments at 14 liquidation, then the aggregation would be trivial. We would simply value-weight each 15 investment characteristic and compute the average at the fund level. Since it is not the case, 16 we process with a close analog that is adopted for all the characteristics of the deals (e.g. the 17 above estimate of systematic risk, loadings on credit spread, GDP, etc.). The characteristic X 18 of each deal, each month, is multiplied by the amount invested in this deal (Ij). These 19 20 amounts are then summed over investments and time, and then divided by the sum of the 21 length of each investment times their amount. In other words, we value-weight the 1 Nf 22 X f = Nf ∑ investment characteristics of each L j I j , f X j , f at the fund level, where the weights are both investment 23 length and ∑ L j I j , fdependent. amount j =1 24 Thej =characteristic Xj,f of each investment j of fund f is then summarized by Xf at the 1 25 26 fund level as follows: 27 28 (4) , where Ij,t=Ij if the deal j is active at time t, and Ij,t=0 29 30 31 32 otherwise. 33 34 Example 1: Assume credit spreads are 2% from 1980 to 1990 and 4% from 1991 to 2003. A 35 fund invests in two deals: 1000 in deal 1 that starts in Jan 1988 and ends in Dec 1992, and 36 37 100 in deal 2 that starts in Jan 1991 and ends in Dec 2000. The loading of this fund to credit 38 spreads is 3000*2%+3000*4%=3% 39 40 Example 2: Assume that earning-to-price ratios are 10 from 1980 to 1994 and 20 from 1995 41 to 2003. Consider the fund in example 1. The loading of this fund to the ratio at exit is 42 65000/6000=10.8 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901 28
  • Management Science Page 28 of 37 1 2 3 Table 1: Descriptive statistics – Sample characteristics 4 5 This table displays descriptive statistics of two samples as of December 2003. The “universe” 6 7 consists of all funds raised between 1980 and 1996 that are mentioned in either the cash-flow 8 9 database of Venture Economics or in Vxpert. “Our sample” consists of quasi-liquidated funds 10 11 raised between 1980 and 1996 for which more than four investments are reported in Vxpert. A 12 quasi-liquidated fund is a fund that is either officially liquidated or has not shown any sign of 13 14 activities over the last two years (2002 and 2003). Statistics for venture and buyout funds within 15 16 each sample are reported separately. We report, respectively and for each sample, (i) the average 17 18 (equal weights) of the capital invested by funds in $million (Size), the proportion of (ii) first-time 19 funds, (iii) second-time and third-time funds, (iv) experienced funds (the GP group has already 20 21 raised more than 3 funds at fund inception) and (v) the average (value-weighted by deflated size) of 22 23 the profitability index of each fund (present value of money distributed divided by present value of 24 25 money taken). Finally, we report the number of observations for each sub-sample. 26 27 28 Universe Our sample 29 30 VC BO VC BO 31 32 33 34 Size (million) 16.4 91.4 48.6 225 35 36 37 First time (%) 0.38 0.52 0.31 0.34 38 39 Second&Third time (%) 0.33 0.28 0.40 0.45 40 41 Experienced (%) 0.29 0.20 0.29 0.21 42 43 44 Average Performance (PI) 45 46 (value weighted by deflated size, 47 48 Uncorrected) n.a. n.a. 1.07 1.02 49 50 Standard deviation of PI n.a. n.a. 1.17 1.25 51 t-stat (H0: PI=1) n.a. n.a. 1.39 0.21 52 53 54 55 Nber of obs. 2034 810 539 166 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Page 29 of 37 Management Science 1 2 3 4 5 6 7 8 9 10 Table 2: Estimation of selection bias 11 12 This table reports the results of a Probit regression to model the fund selection process. The 13 14 dependant variable is a dummy variable that takes the value 1 if the fund is in our sample and zero 15 otherwise. The independent variables are fund characteristics: the natural logarithm of the total 16 17 amount invested, and the natural logarithm of the sequence number of the fund in its private equity 18 19 firm family (sequence), fraction of non-US investments, fraction of venture-capital investments. A 20 21 constant is included but not reported. 22 23 24 25 Dependent variable: 1(if in sample) 26 27 28 Size (ln) 0.11 (13.74) 29 30 Sequence number (ln) -0.05 (1.44) 31 32 % non-US -0.82 (-8.14) 33 34 % Venture capital 0.68 (8.33) 35 36 37 Nber obs. 2844 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Management Science Page 30 of 37 1 2 3 Table 3: Descriptive statistics – Investment behavior 4 5 This table displays descriptive statistics about the investment characteristics of the 705 funds in our 6 7 sample. We report, for all funds as well as for venture funds and buyout funds separately, the 8 9 average (equal weights) and median (in italics) of (i) the number of investments, (ii) the length (in 10 11 months) of investments, (iii) the Herfindahl index based on the number of industries in which the 12 fund invested, the proportion (in terms of amount invested) invested in (iv) venture capital deals, 13 14 (v) the health industry (healthcare, medical equipment, and pharmaceutical products), (vi) the high- 15 16 technology industry (electrical equipment, tele-communications, and computers), (vii) Europe and 17 18 (viii) the dominant industry (i.e. the industry in which the fund has invested the most). 19 20 21 All Venture Buyout 22 23 24 25 Nber investments 26.02 27.53 16.66 26 27 21.00 22.00 11.00 28 Deal length (months) 56.16 57.27 49.27 29 30 54.61 56.47 45.86 31 32 Herfindahl industry 0.26 0.27 0.20 33 34 0.22 0.23 0.19 35 % Venture capital 0.81 0.91 0.18 36 37 0.95 0.97 0.14 38 39 % Health 0.20 0.23 0.07 40 41 0.15 0.18 0.00 42 43 % Hi-tech 0.47 0.51 0.17 44 0.47 0.53 0.12 45 46 % European 0.12 0.07 0.38 47 48 0.00 0.00 0.02 49 50 % Dominant industry 0.42 0.42 0.41 51 0.38 0.39 0.35 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Page 31 of 37 Management Science 1 2 3 4 5 6 7 8 9 10 11 12 Table 4: Systematic risk 13 14 This table displays the estimated fund CAPM-Beta. The methodology is detailed in the text and in 15 16 the appendix. We display results obtained under three different assumptions. For Beta1, we assume, 17 18 for buyout deals, a beta on debt of 0.25 and a debt-to-equity ratio that decreases linearly from 3 (at 19 entry) to the industry average (at exit); and, for venture deals, we assume that Beta equals the 20 21 average of the betas of the smallest (25%) public firms in the same industry. Beta3 (Beta2) is like 22 23 Beta1 but assumes that the debt-to-equity ratio for buyout deals is always 3 (the industry average). 24 25 26 27 Beta1 Beta2 Beta3 28 (D/E from 3 to average) (D/E = ind. average) (D/E = 3) 29 30 All 1.60 1.48 1.73 31 32 VCs 1.58 1.53 1.63 33 34 BOs 1.73 1.14 2.32 35 36 37 Largest 25% 1.56 1.52 1.60 38 39 Smallest 25% 1.65 1.39 1.91 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Management Science Page 32 of 37 1 2 3 Table 5: Performance and business cycles 4 5 This table presents the results of multiple regressions, in which the dependent variable is ln(PI); 6 7 where PI is the profitability index (see text for definition). Explanatory variables include: 1) 8 9 average corporate bond yield (BAA) and credit spread (BAA bond yield minus 10 years Treasury- 10 11 Bill); during the quarter when the investment was made, 2) average real GDP growth, corporate 12 bond yield, public stock-market portfolio return (CRSP-VW), return of the out-of-the-money call 13 14 option on the S&P composite index and return of the out-of-the-money put option on the S&P 15 16 composite index; during the life of the investments, 3) average earning-to-price ratio (for all stocks 17 18 listed on the NYSE/AMEX/NASDAQ) and the amount of money raised through an IPO during the 19 year when investment was exited. There are 705 observations. The t-statistics are reported between 20 21 parentheses. All the variables are expressed as a z-score. A vector of lambdas (which controls for 22 23 the fact that the fund was selected in our sample; Heckit methodology, see Greene, 2003) is 24 25 included in all regressions but is not reported. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Page 33 of 37 Management Science 1 2 3 Panel A: Regression of performance on macroeconomic variables during investments 4 5 1 2 3 4 5 6 7 Market 0.08 (1.89) 8 9 GDP 0.18 (4.42) 10 11 BAA-yield -0.16 (-3.90) 12 OTM Call Option 0.06 (1.24) 13 14 OTM Put Option -0.06 (-1.32) 15 16 17 18 Panel B: Regression of performance on macroeconomic variables at entry and exit of investments 19 20 1 2 3 4 5 21 At entry: 22 23 Credit spread -0.12 (-2.93) -0.06 (-1.20) 24 25 BAA-yield -0.16 (-3.98) -0.13 (-2.83) 26 27 At exit: 28 29 IPO 0.06 (1.55) 30 E/P 0.05 (1.20) 31 32 33 34 Panel C: Regression of performance on macroeconomic variables 35 36 1 2 3 4 37 38 39 BAA-yield entry -0.19 (-4.56) -0.08 (-1.76) -0.20 (-4.64) -0.17 (-4.18) 40 41 Market during 0.13 (3.01) 42 43 GDP during 0.13 (2.72) 44 45 OTM Call Option during 0.12 (2.78) 46 OTM Put Option during -0.08 (-1.98) 47 48 49 50 R-square 4.1% 3.8% 3.9% 3.2% 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Management Science Page 34 of 37 1 2 3 4 5 6 7 8 9 Table 6: Pricing of idiosyncratic risk 10 11 This table is like Table 5 except for the set of explanatory variables that is used, which include here 12 i) the average corporate bond yield (BAA) during the quarter when the investment was made, ii) the 13 14 average public stock-market portfolio return, iii) the natural logarithm of the number of capital calls 15 16 (i.e. take-downs), iv) the natural logarithm of the number of investments, v) the Herfindahl index 17 18 for industry concentration of investments, v) the Herfindahl index for the concentration of 19 investment types (venture capital versus buyout), and the proportion (in terms of amount invested) 20 21 invested in vi) the dominant industry (i.e. the industry in which the fund has invested the most), 22 23 (vii) the health industry (healthcare, medical equipment, and pharmaceutical products), (vii) the 24 25 high-technology industry (electrical equipment, tele-communications, and computers). A vector of 26 27 lambdas (which controls for the fact that the fund was selected in our sample; Heckit methodology, 28 see Greene, 2003) is included in all regressions but is not reported. There are 705 observations. 29 30 31 32 1 2 3 4 5 6 33 34 35 36 BAA-yield entry -0.13 (-2.91) -0.22 (-5.01) -0.19 (-4.49) -0.20 (-4.75) -0.19 (-4.50) -0.24 (-5.46) 37 Market during 0.11 (2.48) 0.13 (2.88) 0.13 (2.90) 0.13 (3.02) 0.13 (3.07) 0.13 (3.12) 38 39 Nber takes 0.13 (3.00) 40 41 Nber investment 0.09 (2.07) 42 43 Herfindahl indus 0.07 (1.85) 0.03 (0.70) 44 Herfindahl type 0.06 (1.51) 45 46 %dominant indus 0.06 (1.57) 47 48 % in Health -0.08 (-1.86) 49 50 % in High-tech 0.13 (2.72) 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Page 35 of 37 Management Science 1 2 3 4 5 6 7 8 9 Table 7: Drivers of fund performance 10 11 This table is like Table 5 except for the set of explanatory variables that is used, which include here 12 i) the average corporate bond yield (BAA) during the quarter when the investment was made, ii) the 13 14 average public stock-market portfolio return, the proportion invested in iii) the high-technology 15 16 industry (electrical equipment, tele-communications, and computers), iv) the average length of the 17 18 investments, v) the natural logarithm of the amount invested by the fund, the proportion invested in 19 vi) venture capital and vii) non-US companies, vii) size squared, viii) the amount committed to all 20 21 private equity funds during the year of fund creation and the natural logarithm of the sequence 22 23 number of the fund in its private equity firm family (sequence). A vector of lambdas (which 24 25 controls for the fact that the fund was selected in our sample; Heckit methodology, see Greene, 26 27 2003) is included in all regressions but is not reported. There are 705 observations. R-square ranges 28 from 9% to 10% (specification 5). 29 30 31 32 1 2 3 4 5 33 34 35 36 BAA-yield entry -0.17 (-2.70) -0.17 (-2.68) -0.13 (-1.87) -0.16 (-2.51) -0.14 (-2.38) 37 Market during 0.10 (2.14) 0.10 (2.17) 0.10 (2.14) 0.10 (2.14) 0.11 (2.72) 38 39 % in High-tech 0.20 (4.31) 0.04 (0.25) 0.20 (4.39) 0.19 (4.12) 0.17 (3.99) 40 41 Length investment -0.10 (-1.74) -0.10 (-1.74) -0.09 (-1.58) -0.10 (-1.81) 42 43 Size (log) 0.08 (1.93) 0.08 (1.95) 0.09 (1.98) 0.08 (1.77) 0.09 (2.21) 44 % venture capital -0.07 (-1.37) -0.06 (-1.37) -0.07 (-1.38) -0.07 (-1.49) 45 46 % non-US -0.08 (-1.69) -0.08 (-1.17) -0.08 (-1.59) -0.06 (-1.35) 47 48 Size (log) - squared 0.16 (1.16) 49 50 Total committed 0.06 (1.13) 51 Sequence nber 0.17 (4.24) 0.17 (4.01) 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Management Science Page 36 of 37 1 2 3 4 5 6 Graph 1 7 Each fund is assigned to a decile based on either the average bond yield at the time of investment 8 (graph 1.a) or the average stock market performance during investment (graph 1.b). The average 9 profitability index across funds in each decile is then computed and plotted. 10 11 12 Graph 1.a. 13 14 1.4 15 16 1.3 17 1.2 Profitability index 18 19 1.1 20 21 1 22 23 0.9 24 0.8 25 26 0.7 27 28 0.6 29 0.5 30 31 -0.17 0.78 1.07 1.14 1.18 1.22 1.26 1.32 1.42 1.69 32 33 Average stock-market performance 34 35 36 37 38 Graph 1.b. 39 40 41 1.7 42 43 1.5 44 Profitability index 45 46 1.3 47 48 1.1 49 50 51 0.9 52 53 0.7 54 55 56 0.5 57 7.81 8.09 8.40 9.02 9.66 10.11 10.50 10.98 11.68 13.23 58 59 Average bond yield 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901
  • Page 37 of 37 Management Science 1 2 3 This paper aims to contribute to our understanding of the drivers of performance in 4 5 private equity funds. As such, it should help managers responsible for the allocation of 6 assets for institutional investors, and in particular for limited partnership structures, make 7 better investment decisions. 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ScholarOne, 375 Greenbrier Drive, Charlottesville, VA, 22901