Reputation, Volatility and Performance Persistence of Private Equity. Yi Li

Transcription

1 Reputation, Volatility and Performance Persistence of Private Equity Yi Li Federal Reserve Board This version: April 2014 Abstract This paper develops a learning model with managers reputation concerns to shed new light on performance persistence for private equity funds. The model predicts: When the exogenous shock on fund performance is less volatile, performance persistence is more pronounced, the reputation mechanism works better, and fund managers have more incentive to control fund sizes. On the premise that buyout funds are subject to less volatile shocks than venture capital (VC) funds, I hypothesize that the model mechanism is stronger among buyout funds. Using a comprehensive dataset of private equity funds, I document evidence consistent with the model prediction: (i) Buyout funds exhibit strong long-term (over ten years) performance persistence across different funds raised by the same manager, while VC funds show weak short-run persistence. (ii) The size of buyout managers new funds is strongly related to the performance of their previous funds, while the size of VC managers new funds is highly associated with recent VC industry performance rather than individual managers. (iii) Top buyout managers raise smaller funds than they could have, while no such behavior is found for VC managers. This paper is a revised version of a chapter from my doctoral dissertation at Princeton University. I am indebted to my advisors Wei Xiong and David Sraer for their advice and encouragement. For helpful comments and discussions, I would like to thank Valentin Haddad, Zhiguo He, Jakub W. Jurek, Hyun Song Shin, Ming Yang, as well as seminar participants at Chinese University of Hong Kong, City University of Hong Kong, Durham University, Federal Reserve Board, Moody s Analytics, Nanyang Technological University, Princeton University and University of Warwick. All errors are mine. The views expressed in this paper are mine and do not necessarily reflect the views of the Board of Governors or other Federal Reserve staff. Corresponding address: Board of Governors of the Federal Reserve System, 20th Street and Constitution Avenue, Washington, DC, yi.li@frb.gov. 1

2 1 Introduction At the end of March 2012, private equity (PE) funds in total managed over $2 trillion of capital 1, primarily in the form of venture capital (VC) and leveraged buyouts. 2 PE investment is generally made through a limited partnership structure, in which PE firms serve as general partners (GPs), and institutional investors and wealthy individuals serve as limited partners (LPs). LPs provide capital to GPs, and GPs use the capital under management to make investments. Kaplan and Schoar (2005) first document that returns persist strongly across different PE funds raised by the same GP, especially for funds that outperform the industry. Such long-run performance persistence driven by outperformance has not been documented for other investment funds, such as mutual funds 3 and hedge funds. 4 Taking into account the institutional structure of PE funds, I propose a learning model with managers (i.e. GPs ) reputation concerns to explain performance persistence for PE funds, and test the theory with data. In the benchmark model without reputation concerns, fund managers with various ability levels optimally choose fund sizes that increase with their perceived ability levels, and generate the same expected return to investors. This result resembles that of Berk and Green (2004), who show that in the context of mutual funds, with the assumption of decreasing returns to scale, skillful managers do not outperform passive benchmarks because of the infinitely elastic supply of capital. However, the mechanism underlying my model differs from theirs. While fund managers in their model passively experience capital inflows and outflows that respond to recent fund performance (which is true with open-end mutual funds), fund managers in my model choose their fund sizes optimally. This sharp distinction in modeling is driven by the unique institutional structure of PE funds. 5 In the model with reputation concerns, fund managers future payoffs depend on their reputation. In equilibrium, expected fund returns increase with fund managers ability levels, and the 1 Source: Private Equity Report TheCityUK. 2 Other PE strategies include: growth capital, mezzanine capital, distressed, special situations, secondaries, and fund of funds, etc. 3 Long-run persistence in mutual fund performance has been difficult to detect. When detected, it is mostly driven by persistent underperformance. See Carhart et al. (2002), Bollen and Busse (2005), and Sirri and Tufano (1998). 4 Studies on persistence in hedge fund performance have obtained mixed results. Early research provides little evidence of long-run persistence. See, for example, Bares et al. (2003), Edwards and Caglayan (2001), and Brown et al. (2001). Recent research, however, finds some evidence of longer-term (1 to 3 years) performance persistence. See Fung et al. (2008), Jagannathan et al. (2010), and Kosowski et al. (2007). 5 A typical PE fund has a lifespan of years. At the outset, fund managers (i.e. GPs) set a target fund size and start raising capital. Once the fund-raising phase ends, the fund is closed. Investors (i.e. LPs) commit their capital to fund managers for the next years, and fund managers promise not to accept new capital for that fund. 2

3 strength of this relationship captures the level of performance persistence. 6 Moreover, this model predicts that when the exogenous shock on fund performance is less volatile, performance is more persistent, the reputation mechanism is stronger, and fund managers have more incentive to control fund sizes. 7 By identifying two groups of PE funds exposed to shocks of different volatilities, I test these predictions with data. The main source of data for the empirical study is Preqin, which provides data on fund characteristics such as type, sequence number, size (the amount of committed capital), vintage year (the year in which the fund starts to make its first investment), the identity of the GP behind each fund, and most importantly, fund performance measures, in forms of internal rate of return (IRR) and multiple. Preqin obtains performance data from both public filings by pension funds 8 and voluntary disclosures by GPs and LPs. It has detailed cash flow data for over 1,600 PE funds, and is currently one of the most comprehensive PE datasets, covering 60% of total capital commitment in the 1990s and over 70% in the 2000s, as discussed by Harris et al. (2012). The sample comprises 590 buyout funds and 842 VC funds. The average returns for buyout funds and VC funds are close, while the standard deviation of fund returns is 18.6% for buyouts and 48.9% for VC. This difference between the standard deviation of buyout fund returns and that of VC fund returns motivates the following hypotheses: 9 For buyout funds, performance is more persistent, the reputation mechanism is stronger, and fund managers have more incentive to limit fund sizes. First, I examine the hypothesis on performance persistence for buyout funds and VC funds. I document strong long-term persistence in buyout fund returns across different funds raised by the same GP. Not only the previous fund return and the second previous fund return, but the third previous fund return also has significant explanatory power (at the 1% level significance) for the current fund return. Since a typical buyout GP raises a new fund about every 4 years, the test results indicate that the persistence in buyout fund performance lasts at least 10 years. The 6 Intuitively, the level of performance persistence across different funds raised by the same manager depends on the extent to which the manager s intrinsic ability is reflected by returns of each fund. 7 In the extreme case when the shock is infinitely volatile, all fund managers revert to their benchmark choices, i.e., homogenous fund return among different managers and no performance persistence across funds raised by the same manager. 8 Pension funds are among the major investors (i.e. LPs) of private equity funds. According to FOIA (Freedom of Information Act), pension funds are required to report the performance of their holding assets. 9 The standard deviation of fund returns potentially comes from two sources: the variation in fund managers ability levels, as well as exogenous shocks beyond the control of fund managers, such as macroeconomic factors, equity and debt market conditions, technology revolutions, etc. By assuming that the variation in fund managers ability is almost the same for VC and buyout funds, the standard deviation of fund returns effectively represents the volatility of exogenous shocks. 3

4 case with VC funds is substantially different. Although I find some evidence of persistence in VC fund performance, this persistence is completely between two consecutive funds raised by the same GP. In light of the fact that the average interval between two consecutive VC funds is 3 years, it is possible that this short-term persistence among VC funds is driven by overlapping investment projects (i.e. portfolio companies) rather than the GP s intrinsic ability. In sum, the baseline results on performance persistence for buyout funds and VC funds support the hypothesis that the performance of buyout funds is more persistent, compared to VC funds. To address a potential concern that these results on performance persistence are biased by outliers, 10 I perform a robustness check with data excluding the 1% of funds with the highest IRRs. Test results using these winsorized data show even stronger persistence for buyout funds and even weaker persistence for VC funds, compared to the baseline results. For VC funds in particular, the previous fund return loses its explanatory power for current fund return in some specifications. This robustness check rules out the doubt that the long-term performance persistence of buyout funds is driven by a few funds with extremely good performance. In addition, it reveals that for VC funds, even the short-run performance persistence is vulnerable and likely driven by the top 1% VC funds. I also conduct a series of robustness checks using an alternative performance measure, multiple, and obtain similar results. Second, I study how the reputation mechanism works differently for buyout funds and VC funds. Strength of the reputation mechanism is captured by the extent to which the current fund size depends on performance of past funds raised by the same GP. 11 Test results show that for buyout GPs, the relationship between previous fund performance and the current fund size is strongly positive and significant at the 1% level, while for VC GPs, this relationship is not significant at all, indicating that buyout GPs with better past performance are very likely to be favored when they raise their follow-on funds, and this reputation mechanism does not work for VC GPs. To explore what factors predict VC fund sizes, I include VC industry performance as an additional explanatory variable. 12 While VC fund sizes do not respond to individual GP s past performance, they are positively and significantly associated with the recent performance of the VC industry. These results show that for a buyout GP, its new fund size is strongly related to its 10 While the average annual return on PE investment is about 15%, some star funds yield exceptional annual returns as high as 200%. These outliers can potentially bias regression results in a significant way. 11 Higher payoffs are associated with larger funds, since a great portion of GP s income derives from the sum of annual management fees, approximately 18% of total committed capital (i.e. fund size). See Metrick and Yasuda (2010) and Chung et al. (2012). 12 VC industry performance is defined as the average of IRRs of all VC funds raised 2-4 years earlier, 3-5 years or 4-6 years earlier. 4

5 performance in previous funds. In contrast, for a VC GP, its new fund size depends on recent VC industry performance. Third, I test whether top buyout GPs are more likely to limit their fund sizes than top VC GPs. I capture GP s ability level by calculating the average return across all funds raised by the same GP, 13 and sort GPs into ability terciles: top, medium and bottom. Test results are consistent with my hypotheses. In particular, controlling for characteristics of previous funds, a top buyout GP raises a new fund with size 24% smaller than a medium buyout GP, and a top GP s new fund size is significantly less sensitive to the previous fund return, compared to a medium buyout GP s. These results suggest that top buyout GPs raise smaller funds than they could have and are less likely to exploit on good past performance when raising new capital, compared to medium buyout GPs. For top VC GPs, however, no such behavior is found. Specifically, neither the coefficient on the top dummy nor the coefficient on the interaction term between top dummy and the previous fund return is significant. Last, I test a key assumption of the model, decreasing returns to scale. 14 Existing literature, such as Kaplan and Schoar (2005) and Harris et al. (2012), has not reached a unanimous conclusion on the relationship between PE fund performance and the fund size. 15 In this study, I document a strongly negative relationship between the two after controlling for the number of partners of each GP. 16 This result validates the assumption of decreasing returns to scale and therefore supports the model setup. This paper is closely related to the empirical literature on private equity fund performance. Kaplan and Schoar (2005) are the first to document performance persistence for PE funds. However, they neither provide testable explanations for the persistence nor document the difference between buyouts and VC. 17 Phalippou (2010) finds that VC funds backed by more skilled investors show little performance persistence. Ljungqvist and Richardson (2003), Robinson and Sensoy (2011) and Harris et al. (2012) use cash flow data to study the relative performance of PE funds to the public market, as well as risk characteristics of PE funds. Cochrane (2005), Phalippou and Gottschalg 13 GPs who have raised only one fund are excluded from the sample of this test. 14 By adopting a concave profit-generating function in the model, I implicitly assume decreasing returns to scale, i.e., the larger the fund is, the lower the expected fund return will be. 15 Kaplan and Schoar (2005) document a positive relationship between fund performance and the fund size in the cross-section, however the sign of the coefficient on fund size switches from positive to negative when GP fixed effects are included. Harris et al. (2012) repeat the exercise and find no significant relationship between fund performance and the fund size. 16 The idea of controlling for the number of partners of each GP stems from the fact that these partners skills are highly unscalable. 17 Kaplan and Schoar (2005) do not find differences between buyout funds and VC funds in levels of performance persistence probably because of their much shorter data period ( ) and much lower fund sequence number. 5

6 (2009), Jegadeesh et al. (2009) and Korteweg and Sorensen (2010) estimate and analyze risks and returns of PE investments. Gompers and Lerner (1999) and Metrick and Yasuda (2010) study the economics of the PE industry and estimate compensation schemes to GPs. Using Metrick and Yasuda (2010) s framework, Chung et al. (2012) find evidence of additional payoffs for good performance from future fund flows. Lerner et al. (2007) use Preqin as their source of performance measures and document a significant variation in levels of returns that different institutional investors realize from PE. Lopez de Silanes et al. (2009) provide evidence for decreasing returns to scale : investments made at times of a high number of simultaneous investments underperform. Existing literature on modeling performance persistence in PE funds is sparse. One exception is Hochberg et al. (2010), who propose a theory of learning that leads to information hold-up in the VC market. The mechanism of their model is: Investors of a fund learn inside information about the GP of that fund, and use it as hold-up power when the GP raises its next fund. This holdup power diminishes the GP s capability to increase fees in line with performance and therefore generates performance persistence. While their model focuses on the bargaining game between GPs and informed LPs, my model explains how reputation concerns alone lead to performance persistence and how exogenous shocks erode the mechanism. This study also contributes to the more general literature on reputation/career concerns of fund mangers. Demiroglu and James (2010) discuss the role of PE group s reputation in leveraged buyout financing and find that reputable GPs get better loan terms. Guerrieri and Kondor (2012) develop a model to explain how fund mangers career concerns generate a countercyclical reputational premium. Malliaris and Yan (2012) show how fund managers reputation concerns induce a preference over the skewness of strategy returns. The paper proceeds as follows. Section 2 presents the model. Section 3 describes the data. Section 4 conducts empirical analysis. Section 5 concludes. 2 Model Before presenting the model, I briefly discuss the nature of private equity (PE) investments. PE funds are structured as limited partnerships, in which professional managers serve as general partners (GPs), and limited partners (LPs) are largely composed of institutional investors and wealthy individuals, who commit a certain amount of capital (namely, committed capital) to funds. PE funds are categorized into venture capital (VC), buyouts, etc., based on investment types. 6

7 The lifespan of a typical PE fund is years. Fund managers (i.e. GPs) select portfolio companies and invest the majority of the committed capital to them in an agreed time period (usually the first 3-5 years of a fund). When portfolio companies start to make profits, GPs return committed capital and the majority of the excess profits to investors (i.e. LPs). PE fund managers receive both fixed and variable compensation: Management fees are fixed annual payments, typically 1-2% of the committed capital of the fund, 18 and carried interests are performance-based revenue, typically 20% of the excess profits of the fund s investment. 2.1 Model Setup The model features symmetric information among fund managers and investors. Fund managers are heterogenous in their ability levels, denoted as θ i. At t = 0, the prior distribution of θ i is the same across all fund managers, and each fund manager is assigned a fund with the same amount of committed capital to manage. After observing the realized return on the incubation fund, all agents make inferences about the fund manager s ability level, and fund managers are allowed to choose the size of their second funds. The question of interest is whether there is performance persistence across the incubation fund and the second fund raised by the same fund manager. Figure 1 establishes the timing of the model. At t = 0, all fund managers are ex-ante homogeneous, and the prior distribution of their ability level θ i is normal with a mean of µ 0 and a variance of σ 2 0. Each manager is assigned a fund of an identical size S 1. At t = 1, the return on the first fund is realized, denoted as r1 i, which is subject to an i.i.d. exogenous shock. Both fund managers and investors observe the fund return r1 i, and apply Bayes rule to update their beliefs about manager i s ability level. Fund managers are allowed to decide on the size of their second funds, S2 i, and they optimally choose it to maximize their expected future payoffs. 19 At t = 2, the return on the second fund is realized, denoted as r2 i, which is also subject to an i.i.d. exogenous shock. All agents observe the fund return r2 i as well as the fund size Si 2, and apply Bayes rule to update their beliefs about the manager s ability level. Fund managers reputation is defined as their ability levels perceived by investors. Therefore, the reputation of fund manager i 18 Metrick and Yasuda (2010) estimate that the sum of discounted annual management fees is approximately 18% of total committed capital. 19 My model assumes that when GPs raise a new fund, investors do not have negotiation power over the fund size, based on the fact that the target fund size is usually set by GPs and most of the time the target is met. See Hochberg et al. (2010) for an alternative setting in which some informed investors possess a hold-up power and can bargain on the fund size with GPs. My model shows that even without asymmetric information and bargaining power of investors, performance persistence can be generated if fund managers reputation concerns are strong enough. 7

8 at t = 2 is µ i 2 = E 2[θ i r1 i, ri 2 ], on which fund managers expected future payoffs after t = 2 depend. Figure 1: Model Timeline 1 st Fund 2 nd Fund Future Funds t = 0 t = 1 t = 2 t = 3 θ i ~ N (µ 0, σ 02 ), S 1 assigned r i 1 realized Update belief θ i ~ N (µ i 1, (σ i 1) 2 ) Choose S i 2 r i 2 realized Update belief θ i ~ N (µ i 2, (σ i 2) 2 ) Future payoffs depend on µ i 2 Fund managers vary in their skills in generating net profits. Let Π i t denote net profits of fund-t run by fund manager i: Π i t = θ i (St) i 1 γ + ɛ i tst, i (2.1) where 0 < γ < 1, ɛ i t N(0, σɛ 2 t ), and S1 i = S 1. The concavity of this function implies that for a given fund manager, the more assets under management, the lower the fund return will be. 20 ɛ i t captures the exogenous shock, which is i.i.d. across fund managers, and σ 2 ɛ t is the volatility of the exogenous shock. Fund manager i s net income from fund t is a combination of management fees and performancebased bonus (namely, carried interests), net of management costs of the fund: I i t = αs i t + βπ i t λs i t, (2.2) 20 In the empirical part of this paper, I formally test whether PE funds show decreasing returns to scale. 8

9 where α stands for management fees per dollar of committed capital, β is the carry level, and λ represents costs per dollar of committed capital. 21 I assume that λ > α, so that management fees alone are not sufficient to cover management costs. By definition, the net-of-fee return of fund t run by manager i can be written as rt i = (1 β)π i t/st, i i.e. rt i = (1 β)(θ i (St) i γ + ɛ i t). (2.3) This function shows that the fund return is a combination of the fund manager s ability level (scaled down by the fund size) and an i.i.d. exogenous noise. Less information on the fund manager s ability level is inferred when the fund size is larger and the exogenous shock is noisier. 2.2 Benchmark Model without Reputation Concerns Before delving into the model with fund managers reputation concerns, I first solve the simple model without reputation concerns and use it as a benchmark. If fund managers have no reputation concerns, i.e., if their future payoffs after t = 2 do not depend on how they perform in their first two funds, they simply choose S i 2 to maximize their expected payoffs from the second fund: where I i 2 is defined in (2.2). max E 1 [I2] i S2 i The first-order condition generates the benchmark fund-2 size for manager i: Ŝ i 2 = [ β(1 γ)µ i 1 λ α ] 1 γ, (2.4) where µ i 1 = E 1[θ i r1 i ]. Plugging (2.4) into (2.3), I obtain the benchmark fund-2 return for manager i: Taking expectations on (2.5), I have r 2 [θ i = (1 β) i λ α ] β(1 γ)µ i + ɛ i 2. (2.5) 1 ˆr E 1 [ r i 2 (1 β)(λ α) ] =. (2.6) β(1 γ) When fund managers are not concerned about their reputation, (2.4) shows that the optimal 21 Since GP skills are highly unscalable in PE investments, larger funds demand proportionally more efforts from GPs, including attracting capital, evaluating investment projects, cultivating and restructuring portfolio companies, and exiting. These additional efforts can be taken either by fund managers themselves, which incurs proportionally more opportunity costs of entrepreneurship, or by hiring more employees, which incurs proportionally more costs of labor. Either way it implies that costs of managing a PE fund is approximately proportional to its size. 9

10 size that they choose for their second fund is an increasing function of their perceived ability levels, specifically, proportional to (µ i 1 ) 1 γ. While fund managers with higher perceived ability levels raise larger funds, they do not generate higher expected returns for their investors. As is shown in (2.6), fund managers with different ability levels are expected to yield the same level of return on their second fund, and the expected return on the second fund is independent of the realized return on the first fund. In sum, without fund managers reputation concerns, there is no performance persistence across different funds raised by the same fund manager. 2.3 Model with Reputation Concerns In the model with reputation concerns, fund managers future payoffs after t = 2 depend on their reputation at t = 2, which is defined as their perceived ability level µ i 2. In the setting of symmetric information, both managers and investors follow Bayes rule to update their beliefs on managers ability. update their beliefs on θ i to be θ i N(µ i 1, (σi 1 )2 ), where µ i 1 = µ 0 + (σ i 1) 2 = At t = 1, after observing the realized r1 i, all agents σ 2 0 σ S2γ 1 σ2 ɛ 1 ( S γ 1 1 β ri 1 µ 0 ) (2.7) σ 2 0 σ2 ɛ 1 S 2γ 1 σ σ2 ɛ 1. (2.8) Since (σ i 1 )2 is the same across all fund managers, I denote (σ i 1 )2 σ At t = 2, after observing S i 2 and the realized ri 2, all agents update their beliefs of θi to be θ i N(µ i 2, (σi 2 )2 ): µ i 2 = µ i 1 + σ1 2 ( (S i 2 ) γ ) σ1 2 + (Si 2 )2γ σɛ β ri 2 µ i 1 (2.9) (σ i 2) 2 = σ 2 1 σ2 ɛ 2 (S i 2 ) 2γ σ σ2 ɛ 2, (2.10) Plugging (2.3) into the equations above, µ i 2 can be written as µ i 2 = µ i 1 + σ1 2 [ (θ i σ1 2 + (Si 2 )2γ σɛ 2 µ i 1) + (S2) i γ ɛ i ] 2 2 (2.11) Fund managers future payoffs after t = 2 depend on their perceived ability levels at t = 2 and take a cubic form: Calculation of µ i t and (σ i t) 2 is provided in appendix. 23 This future payoff function features a convex reward (punishment) to good (bad) reputation, which can be justified by the following reasons. Reputation not only affects future fund sizes, but also determines whether fund managers 10

11 V i 3 = V (µ i 2 ˆµ) 3, (2.12) where V and ˆµ are constants. ˆµ is the reputation threshold under which managers future payoffs turn negative. Therefore, at t = 1 fund managers solve the following problem: where I i 2 and V i 3 max E 1 [I i S2 i 2 + V3 i ], (2.13) are defined by (2.2) and (2.12), respectively. The first-order condition yields β(1 γ)µ i 1(S i 2) γ = (λ α) + (µ i 1 ˆµ) 6γσ2 1 κv (Si 2 )2γ 1 [1 + κ(s i 2 )2γ ] 2, (2.14) where κ σɛ 2 2 /σ1 2, representing the relative volatility of exogenous shocks. Comparing (2.14) to the first-order condition in the benchmark model: β(1 γ)µ i 1(S i 2) γ = λ α, (2.15) I derive the following lemma: Lemma 1. In the model with fund managers reputation concerns, at t = 1, (i) For managers with perceived ability level µ i 1 > ˆµ, Si 2 (µi 1 ) < Ŝi 2 (µi 1 ), and E 1[r2 i (µi 1 )] > ˆr. (ii) For managers with perceived ability level µ i 1 < ˆµ, Si 2 (µi 1 ) > Ŝi 2 (µi 1 ), and E 1[r2 i (µi 1 )] < ˆr. Lemma 1 shows that fund managers with perceived ability levels higher than the threshold choose to raise smaller-than-benchmark funds and consequently generate expected returns higher than the benchmark level, while fund managers with perceived ability levels lower than the threshold choose to raise larger-than-benchmark funds and hence generate expected returns lower than the benchmark level. Proposition 1 summarizes main results of the model with managers reputation concerns. It presents the existence of performance persistence across the incubation fund and the follow-on fund, and shows how performance persistence and the reputation mechanism evaporate as the volatility of exogenous shocks increases. are able to raise future funds. Reputation also influences costs of raising capital from investors (fund managers with good reputation can raise capital for a new fund very quickly and capture transient investment opportunities, while it may take several years and a lot more effort for low-reputation fund managers to close a new fund), the bargaining power in purchasing portfolio companies, and costs of getting loans from banks (especially for buyouts, as documented by Demiroglu and James (2010)). Furthermore, reputation plays a role in fund managers future employment opportunities, even after they leave the PE industry. 11

12 Proposition 1. With Assumption 1 and 2 provided in appendix, at t = 1, for fund manager i with perceived ability level µ i 1 [µ, µ]:24 (i) The expected return of the second fund increases with the realized return of the first (i.e. incubation) fund, i.e. de 1[r i 2 ] dr i 1 > 0. (ii) The more volatile the exogenous shock is, the closer the expected fund-2 return is to the benchmark level, i.e., d E 1[r i 2 ] ˆr dκ < 0. As κ, E 1 [r2 i (µi 1 )] ˆr. The first part of Proposition 1 shows a positive relationship between the expected return on the second fund and the realized return on the incubation fund, which proves performance persistence across different funds raised by the same fund manager. The second part of Proposition 1 addresses how exogenous shocks influence the effectiveness of the reputation mechanism and levels of performance persistence. It shows that the expected return on the second fund gradually approaches the benchmark level as the volatility of exogenous shocks increases. Intuitively, as exogenous shocks become more volatile, fund returns become weaker signals of managers ability levels. Hence, future payoffs depend less on perceived ability levels, and fund managers incentive to deviate from their benchmark choice diminishes. When the volatility of exogenous shocks becomes extremely high relative to the variation in fund managers ability levels (i.e. as κ ), even with reputation concerns, all fund managers choices revert to benchmark, and performance persistence disappears. Figure 2 illustrates how the relationship between expected fund-2 return and the fund manager s perceived ability level (µ i 1 ) wears off as κ, the ratio of σ2 ɛ 2 to σ1 2, gradually rises from 0.2 to 100. Since µ i 1 is a linear function of the realized fund-1 return ri 1, Figure 2 also shows how the relationship between expected fund-2 return and realized fund-1 return gets weaker as κ increases. Specifically, when κ rises, expected returns on the second funds of higher-ability managers (those with µ i 1 > ˆµ) shift down towards the benchmark, while expected returns on the second funds of of lower-ability managers (those with µ i 1 < ˆµ) shifts up towards the benchmark. When κ approaches 100 (i.e., when exogenous shocks become extremely volatile), fund managers with various ability levels generate almost the same level of expected return. Proposition 1 also implies that reputation concerns incentivize higher-ability fund managers to limit their fund sizes and lower-ability fund managers to increase their fund sizes, and these incentives decrease with the volatility of exogenous shocks. An intuitive explanation is that the 24 Expressions of µ and µ are given in (D.1). 12

13 information content of fund returns decreases with the fund size. While higher-ability managers have incentives to manifest their ability levels (hence rasing smaller-than-benchmark funds), lowerability managers have incentives to prevent investors from learning (hence raising larger-thanbenchmark funds). Figure 3 depicts how fund sizes gradually approach benchmark levels as the volatility of exogenous shocks increases (i.e., as κ increases from 0.2 to 100). With reputation concerns, fund managers with higher-than-threshold ability levels (i.e. those with µ i 1 > ˆµ) raise smaller-thanbenchmark funds, and the more volatile exogenous shocks are, the less likely are these top managers to limit their fund sizes. On the other hand, fund managers with lower-than-threshold ability levels (i.e. those with µ i 1 < ˆµ) raise larger-than-benchmark funds, and the more volatile exogenous shocks are, the less incentive these bottom managers have to expand their funds. In sum, the model with fund managers reputation concerns predicts that when the exogenous shock on fund performance is less volatile, performance persistence is stronger, the reputation mechanism works better, and top fund managers have more incentive to limit their fund sizes. 3 The Data 3.1 Data Sources The main data source for the empirical study is Preqin. It provides PE fund characteristics, such as vintage year (the year in which the fund made its first investment), size (the amount of committed capital), type (venture capital, buyout, mezzanine, growth, distressed and special situation, secondaries, fund of funds, etc.), sequence number, and most importantly, performance measures. It also provides GP profiles, such as firm location and number of partners/employees. 25 As described by Harris et al. (2012) and Lerner et al. (2007), Preqin collects data primarily from public filings by pension funds, from FOIA requests to public pension funds, and from voluntary disclosures by both GPs and LPs. With access to full cash flow data for over 1,600 PE funds, Preqin makes its own assessment of the reliability of the different sources of performance data available, and provides the number considered most reliable. The performance measure I use in this study is the internal rate of return (IRR), which is the discount rate at which the net present value of all the cash inflows equals the net present value of 25 The data on the number of partners, however, are only partially available from Preqin. For missing values, I hand collect them from PE firms websites. 13

14 all cash outflows of the investment. IRRs are directly provided by Preqin, net of management fees and carried interests. 26 Preqin also reports an alternative measure of fund performance, Multiple, which is the ratio between the total value that investors have derived from their investments - i.e. distributed cash and securities plus the value of the remaining capital in the fund and their total cash investment. 27 The correlation between IRR and Multiple is 81%. In some tests, I employ Multiple to check the robustness of the baseline results. For most tests involving fund returns, I only include funds raised before 2005, considering the fact that younger funds are associated with more unrealized valuations and therefore more inaccurate IRRs. For funds with the vintage year 2004 or earlier, at least 8-9 years of cash flows have been realized, and I consider IRRs of these funds are accurate enough in measuring the final performance, even though some of the funds have not fully exited yet. 28 As reviewed by Harris et al. (2012), in addition to Preqin, three other commercial datasets also provide PE performance data: Venture Economics (VE), Cambridge Associates (CA), and Burgiss. In terms of data quality, Harris et al. (2012) suggest that it is highly likely that VE returns understate fund performance, while CA and Burgiss, as well as Preqin, provide consistent fund returns despite different sample selection criteria. In terms of data coverage, Preqin catches up substantially over time. While in the 1980s, funds documented by Preqin only covers about 40% of total capital commitments in PE industry, it covers about 60% in the 1990s and over 70% in the 2000s, which makes itself currently one of the most comprehensive datasets. Therefore, even though data obtained from Preqin may suffer from the possibility of selection bias, like any other dataset, the selection bias is likely to be minimal Ideally, I would like to calculate IRRs myself using fund-level cash flow data, but unfortunately these data are not available to me. However, the quality of the Preqin data has been cross-checked by Harris et al. (2012) and Lerner et al. (2007). 27 The shortcoming of Multiple is that it does not reflect the time value of money, and therefore will not show whether one partnership has returned value to investors more quickly or more slowly than another. 28 Lerner et al. (2007) use funds with at least 5 years of realized cash flows for their performance analysis. Kaplan and Schoar (2005) justify this criteria by arguing that the estimated IRR at the end of 5 years after the fund is established is highly correlated with realized IRR when the fund exits, with an correlation coefficient of Preqin collects most of the fund performance data through third-party disclosure, i.e. disclosure by public pension funds. If public pension funds had superior abilities in choosing which PE funds to invest in, fund performance recorded by Preqin would have an upward bias. According to Lerner et al. (2007), public pension funds do not outperform other institutional investors in terms of PE investment (while university endowments do), which suggests that Preqin does not have a significant selection bias. 14

15 3.2 Descriptive Statistics Table 1 reports descriptive statistics of the 1432 PE funds raised by 502 GPs between 1980 and Among these 1432 funds, 590 are buyout funds, and 842 are VC funds. Other types of PE funds, such as mezzanine, growth, distressed and special situation, secondaries, fund of funds, are excluded from the sample. Also, this study centers on U.S. funds with an investment focus inside America. 30 Panel A of Table 1 summarizes fund-level characteristics. The typical fund in my sample is a third fund 31 with a size of $362.7 million and an IRR of 15.5%, and there is substantial variation across funds. Buyout funds are much larger than VC funds, with an average size of $639.4 million compared to $168.9 million. The average performance of buyout funds and VC funds, in terms of IRR or Multiple, is close, 32 although VC fund performance is much more volatile. The standard deviation of IRR is 18.6% for buyout funds and 48.9% for VC funds. Moreover, for VC funds the mean of any performance measure is much higher than the median, suggesting that the sample includes some VC funds that perform exceptionally well. Figure 4 illustrates a comparison in IRR distribution between buyout funds and VC funds. The average sequence number is 3.1 for buyout funds and 3.6 for VC funds. Although the sample includes funds raised as late as 2008, on average more than 90% of the committed capital have already been drawn by GPs to make investments. Panel B of Table 1 presents firm-level (i.e. GP-level) characteristics. In general, buyout firms have slightly larger management teams than VC firms. A typical buyout firm has 8 partners, and a typical VC firm has 6 partners. On average, each firm raises 3 funds during the sample period, regardless of the GP type. Also, a typical buyout firm raises a new fund every 4 years, while a typical VC firm raises a new fund every 3 years. Table 2 reports average fund sizes and returns, broken down into vintage years. For both buyouts and VC, the number of funds in the sample increases over the 1980s and the 1990s, peaks in 2000, declines afterwards, and picks up since Figure 5 illustrates the evolution of PE fund sizes, broken down into buyout funds and VC funds. The average buyout fund size gains steadily before 2005, and shoots up afterwards because 30 Preqin provides locations of PE firms (i.e. GPs ) headquarters. However, it does not provide locations of portfolio companies of each fund. I require that all funds in the sample have their GPs headquarters inside America. Among these U.S.-based funds, I exclude funds with their committed capital shown in currencies other than U.S. dollars, as well as funds with their names indicating an investment focus outside America, such as European Fund I, or Asian Fund IV. 31 The average sequence number is The equal-weighted average IRR is 15.2% for buyout funds and 15.8% for VC funds. The equal-weighted average multiple is 1.8 for buyout funds and 1.9 for VC funds. 15

16 of the boom of mega-buyouts, exceeding $1 billion. 33 The average VC fund size peaks at $285 million in 2001, retreats to its 1990s level afterwards, and starts to edge up since 2005, reaching $278 million in Figure 6 depicts how PE fund performance changes over time, broken down into buyout funds and VC funds. 34 Buyout funds raised in 1980s and early 2000s on average perform better than funds raised in 1990s and late 2000s. VC funds raised in 1980s on average deliver steady performance, and those raised in 1990s (except 1999) achieve spectacular average returns because of the internet bubble, whose burst leaves VC funds raised in 2000s struggling. Most of my analysis on fund performance is restricted to funds with vintage years 2004 and earlier. Table 3 presents the fraction of first-, second-, third-, fourth-, and fifth-time funds in this subsample. Among the 1026 funds in the subsample, 26.7% are first-time funds, 22.0% are secondtime funds, 16.4% are third-time funds, 12.8% are fourth-time funds, 7.9% are fifth-time funds, and the remaining 14.2% are funds with sequence numbers higher than 5. The highest sequence number for buyout funds is 10, and the highest sequence number for VC funds is 12. Compared to the sample used by Kaplan and Schoar (2005), my sample has much longer time horizon and higher average sequence number. While in their sample, only 22% are funds with sequence numbers higher than 3, in my subsample this proportion is 35%. The longer sample period and the higher sequence number facilitate the test of long-term performance persistence for PE funds. 4 Empirical Results The model predicts that when exogenous shocks are less volatile, fund performance is more persistent, the reputation mechanism works better, and top fund managers have more incentive to limit fund sizes. On the premise that buyout funds are subject to less volatile shocks than VC funds, I establish the conjecture that the model mechanism is stronger among buyout funds. In particular, I test the following hypotheses: Hypothesis 1. While buyout funds exhibit strong long-term performance persistence across different funds raised by the same GP, VC funds show weak short-run persistence. Hypothesis 2. The size of a buyout GP s new fund is strongly related to the performance of its 33 Fund sizes have been adjusted by annual CPIs, with CPI in 1983 equal to 100. Because CPI after 2005 is higher than 200, the average buyout fund size after 2005, in nominal term, is over $2 billions. 34 Note that performance measures of funds raised in the late 2000s are less accurate than those of funds raised earlier. 16

17 previous funds, whereas the size of a VC GP s new fund is highly associated with the recent VC industry performance rather than the individual GP s. Hypothesis 3. Top buyout GPs raise smaller funds than they could have, while top VC GPs do not limit their fund sizes. 4.1 Performance Persistence To test for the effect of performance persistence, as described in Hypothesis 1, I use performance measure (IRR) as dependent variable and lagged performance measures as explanatory variables, while controlling for a host of other fund characteristics including the fund size, the sequence number, and the year fixed effect: F undirr i t = β β τ F undirrt τ i + η log(f undsize i t) + γsequence i t + F E year, (4.1) τ=1 where F undirr i t is the IRR of the t-th fund raised by PE firm i. 35 Table 4 reports test results for buyout funds. In sum, I find strong persistence in buyout fund returns across different funds raised by the same firm. Column (1) tests the simplest permutation of (4.1), a regression of current fund IRR on lagged fund IRR, controlling for year fixed effect. The coefficient on lagged IRR is positive and strongly significant (at 1% level), and the point estimate is 0.27 with a standard error of This coefficient implies that a 1% increase of return in the previous fund is associated with a 27 basis point better performance in current fund. Because two consecutive funds raised by the same GP are likely to share investment in some portfolio companies, a potential concern arises that the performance persistence shown in column (1) is driven by overlapping investment projects rather than GPs ability. To address this concern, column (2) reports a regression of the current fund return on the second previous fund return. The coefficient remains positive and significant, with the point estimate of 0.10 and a standard error of Column (3) runs the regression on the third previous fund return. The coefficient on F undirrt 3 i is positive and significant at the 1% level; The point estimate is 0.13 with a standard 35 Testing performance persistence for PE funds is distinct from testing performance persistence for mutual funds or hedge funds. PE funds invest in long-term projects that usually start generating profits several years after, their returns exhibit a pronounced life-cycle pattern, which makes examining returns across years within a single fund pointless in determining whether there is performance persistence for the underlying PE firm (i.e. GP). Therefore, we employ the (final) returns of several funds raised by the same GP to test performance persistence for PE funds. 36 Standard errors are calculated by clustering at the firm (i.e. GP) level to adjust for serial correlation and heteroskedasticity. I also run unreported regressions with standard errors clustered by vintage year and obtain similar results. 17

18 error of The fact that an average buyout GP raises a new fund every 4 years implies that a third previous fund is usually raised more than 10 years ago. Nevertheless, a 1% increase of return in that fund is associated with a 13 basis point higher return in current fund. Column (5) shows that the coefficient on the third previous fund return remains its significance even after I control for the previous fund return. Columns (6)-(9) of Table 4 further control for fund sizes and fund sequence numbers. Coefficients on the fund size and the sequence number are both insignificant, while coefficients on all previous fund returns remain the same. Results in column (9) show that a 1% increase in previous fund returns is associated with a combined 64 basis point increase in current fund return, which is obtained by summing all the significant coefficients on previous fund returns. Table 5 presents test results for VC funds. In sum, I find short-run performance persistence in VC fund returns across different funds raised by the same GP. Column (1) in Table 5 contains the regression of current fund return on the lagged fund return. The coefficient on the lagged IRR is positive and significant, with the point estimate of 0.23 and a standard error of However, in Columns (2) and (3), when current fund IRR is regressed on IRRs of the second and the third previous fund, respectively, coefficients on lagged fund returns do not significantly differ from zero. The point estimates of these two coefficients are 0.02 and -0.01, respectively. Adding the previous fund return to explanatory variables does not improve the significance of the coefficient on the second or third previous fund return, but drives the coefficient negative, as shown in Columns (4) and (5). These results show that performance persistence in VC funds lasts only for two consecutive funds, the interval of which is on average 3 years. Therefore, it is possible that the short-run performance persistence in VC funds is driven by overlapping portfolio companies in the two consecutive funds rather than GPs ability. Columns (6)-(9) of Table 5 further control for fund sizes and sequence numbers. Coefficients on all previous fund returns are basically unchanged compared to Columns (2)-(5). My results on performance persistence for VC funds differs from Kaplan and Schoar (2005), who document strong performance persistence for VC funds. While their sample comprises funds raised before 1996, my sample consists of funds raised before Given that VC fund performance is in general much more steady before 1996 than after that, it is not surprising to find much less performance persistence for VC funds with data of longer period and higher average sequence number. The persistence of buyout fund performance, on the other hand, improves compared to the findings of Kaplan and Schoar (2005). 18

19 4.2 Robustness of Performance Persistence Some PE funds have exceptionally high returns. 37 To address the concern that a few outlying funds with abnormally high returns bias the results, I repeat all the exercises in Table 4 and Table 5 with data excluding the 1% of funds with the highest IRRs. Table 6 reports test results for buyout funds with the winsorized data. Compared to the baseline results in Table 4, in general the explanatory power of previous fund returns for current fund performance improves. Specifically, the point estimate of the coefficient on the second previous fund return increases from 0.10 to 0.24, and the point estimate of the coefficient on the third previous fund return increases from 0.13 to 0.26, without losing their significance. These results show that the long-term performance persistence of buyout funds is not driven by a few outliers. Table 7 presents test results for VC funds with the winsorized data. Compared to the baseline results in Table 5, the explanatory power of previous fund returns for current fund performance significantly weakens. In particular, the point estimate of the coefficient on the first previous fund return decreases from 0.23 to 0.17, and loses its significance when other fund characteristics are controlled for, as shown in Columns (7)-(9) of Table 7. Meanwhile, the coefficients on the second and third previous fund returns remain insignificant. These results suggest that the top 1% of VC funds significantly contribute to the existence of short-run performance persistence documented in Table 5. In addition to using the winsorized data to check the robustness, I also extend the sample to include all funds raised before 2008 and repeat the exercise. The results are basically unchanged. So far, IRR is the only performance measure I use in the analysis. To test whether the results on performance persistence survive an alternative performance measure, I repeat all the tests in Table 6 and Table 7, replacing IRR with Multiple : 38 F undmultiple i t = β β τ F undmultiple i t τ + η log(f undsize i t) + γsequence i t + F E year, (4.2) τ=1 where F undmultiple i t is the Multiple of the t-th fund raised by PE firm i. Table 8 presents test results for buyout funds when Multiple is used as the performance measure. Columns (1)-(3) show that coefficients on all three previous fund multiple s are positive 37 For instance, a few VC funds yield annual returns as high as over 200%. 38 Another performance measure of interest is PME (public market equivalent), which is the fund performance relative to public markets. Calculation of PME requires detailed cash flow data, which I do not have. However, as pointed out by Harris et al. (2012), this relative performance measure can be well predicted by absolute performance measures like IRR and Multiple. 19