Private Equity Returns, Cash Flow Timing, and Investor Choices

Private equity returns, cash ﬂow timing, and investor choices

Stephannie Larocque,∗ Sophie Shive† and Jennifer Sustersic Stevens‡§

August 22, 2019

Abstract

In a comprehensive sample, private equity fund lifetimes average 10 years but their cash flow durations average 4 years with substantial variation across funds. This creates cash management challenges for investors and makes the internal rate of return (IRR) an incomplete measure of performance. Do investors consider these facts when choosing between funds? We find that the portion of IRR that stems from cash flow timing - more than half the IRR on average - persists across a private equity firm’s funds and negatively predicts future performance, but facilitates fundraising, especially among insurance companies, endowment plans, and public pension funds, as well as relatively unsuccessful investors.

∗Mendoza College of Business, University of Notre Dame, [email protected]. †Corresponding author. Mendoza College of Business, University of Notre Dame, [email protected]. ‡Ohio University College of Business, [email protected]. §We thank Marc Crummenerl, John Donovan, Steve Foerster, William Goetzmann, Tim Jenkinson, Tim Loughran, Ernst Maug, Ludovic Phalippou, Stefan Ruenzi, Paul Schultz, Yannik Schneider, Sara Ain Tommar, Florin Vasvari, Michael Weisbach, conference participants at the Paris Dauphine 11th Annual Hedge Fund and Private Equity Conference and the Glion Annual Private Capital Conference and seminar participants at the University of Frankfurt, the University of Mannheim, the University of Notre Dame, Ohio University, and York University for helpful comments. We also thank George Jiang and Xue Li for excellent research assistance. We have seen a number of proposals from private equity funds where the returns are really not calculated in a manner that I would regard as honest ... It makes their return look better if you sit there a long time in Treasury bills. - Warren Buﬀett; May 4, 2019

1 Introduction

Private equity is a fast-growing asset class, rivaling hedge funds with over $3.4 trillion under management in 2018, according to Preqin.1 One potential driver of the rapid rise of private equity is the attractive returns that private equity managers (general partners, or GPs) offer investors (limited partners, or LPs). The internal rate of return (IRR) is the headline measure of private equity returns and is used by data providers to rank funds relative to peer funds of the same vintage. Beginning with Kaplan and Schoar (2005), a large and growing literature examines the size and risk profile of private equity returns, typically focusing on IRRs or public market equivalents.2 Whereas prior literature takes the timing of private equity cash flows as given, we estimate the effects of cash-flow timing on reported IRRs and explore whether and to what extent private equity investors consider these effects in their investment decisions. Private equity investments present cash flow profiles that differ from those of other asset classes because fund manager, rather than investor, discretion largely dictates the timing of cash flows into and out of the fund. Since invested capital is often less than committed capital over the life of the fund, investors must be skilled at putting varying amounts of committed capital to good use before and after it is needed by the private equity fund. We assert that the IRR provides an incomplete picture of private equity returns because

1Private equity set to surpass hedge funds in assets, Financial Times, October 24, 2018. 2Public market equivalents, or PMEs, compare the return on an investment in a private equity fund to the return on a contemporaneous investment in a public equity index fund.

1 the return that the investor actually earns on committed capital throughout the life of the fund depends on both the cash flow choices of the general partner and on the investor’s skill and opportunities for reinvesting capital outside the fund. In fact, the more skilled the private equity firm is at market timing, the less plausible the assumption that intermediate cash flows can be reinvested at the IRR.3 As many finance textbooks show, the calculation of IRR assumes that committed capital earns the IRR regardless of whether the capital is invested inside or outside the fund. To see why this results in an incomplete picture of private equity returns, and may mislead investors who focus exclusively on IRR, consider two funds - each of which has $100 of capital committed by its investors that can be “called” by the private equity fund manager, and must then be contributed by the investors, at any time. Fund A calls $100 from investors in year 4 and distributes $120 to those investors in year 5, reporting an IRR of 20%. Fund B calls $100 in year 1 and distributes $500 in year 10, reporting an IRR of 20%. An investment in Fund A earns 20% for one year; an investment in Fund B earns 20% each year for 10 years. Both funds report an IRR of 20%, but fund B is the preferable investment if the investor cannot earn 20% on her capital when it is invested outside of the fund. As this example shows, cash flow timing and the corresponding cash flow duration of the fund can greatly impact the cash actually earned by the investor for a given IRR. We use data on 6,945 private equity funds from Preqin, nearly half of which have cash flow data, in a sample spanning over 40 years. We find that duration averages 4.045 years while mean fund life is 9.9 years. Fund durations also vary widely, with a standard deviation

3Jenkinson and Sousa (2015) show that conditions in the debt and equity markets affect exit choice. Kacperczyk, Nieuwerburgh, and Veldkamp (2014) find that for mutual fund managers, market timing ability and security selection ability are related, but unlike private equity firms, mutual fund managers must manage the entirety of investors’ capital throughout its time in the fund.

2 of almost 2 years.4 Considering that our sample’s mean IRR is 12.5%, a 2-year increase in the amount of time the capital is in the fund would result in an additional 26.6% cash return on capital, with compounding and assuming the same rate of return. We next compare funds’ reported IRRs to the returns implied by their cash-on-cash multiples, or “multiple-implied returns”, which offer a benchmark measure of the return to private equity investors over the entire life of the fund and are largely unaffected by cash flow timing.5 This measure implicitly assumes that committed capital earns zero returns while it is outside the fund, which, while extreme, has the advantage that fund-level cash flow data are not required for its calculation. We study differences between the IRR and the multiple-implied return; we call the difference the “return gap”. While multiple-implied returns are earned by all investors, return gaps are fully earned only by investors who are able to reinvest their capital at the IRR while it is outside the fund. We expect any investment with intermediate cash flows and a multiple greater than one to have a positive gap, as a byproduct of the opportunistic investment process in which private equity firms specialize. To the extent that some GPs aim to time investments to employ capital only when it earns maximum returns, or to the extent that GPs manage cash flows or IRRs, return gaps should be higher and persist across the GP’s funds. A GP policy of trying to employ capital throughout the life of the fund would make the gap persistently lower. In our sample, we confirm that the fund types that tend to have more volatile cash flows and those where the

4Duration is calculated as the duration of distributions less the duration of contributions. The total is divided by four such that duration is in years. In the subset of these funds that are liquidated, duration averages 4.73 years with a standard deviation of 1.86 while fund life averages 12.11 years. For liquidated funds, we calculate fund life as the time it takes for the LP to receive 95% of total cash ﬂows from the fund. 5The cash-on-cash multiple is the ratio of cash distributed to a fund’s investors to cash contributed into the fund by the investors during the fund’s life. See, for example, Lopez-de-Silanes, Phalippou, and Gottschalg (2015) and Phalippou, Rauch, and Umber (2018). Cash-on-cash multiples could be manipulated if the fund allows for recycling of capital returned during the investment period of the fund’s life. Any upward manipulation of this multiple would weaken our results.

3 GP has more discretion in the timing of cash flows tend to have higher return gaps. For robustness, we explore alternate assumptions such as reinvestment of non-committed funds at the market rate of return as in the modified internal rate of return (MIRR), for the subset of funds with cash flow data. Focusing on the return gap, we first examine whether it persists for a given GP and thus reflects investment style. We find some evidence of persistence in the return gap across a GP’s funds, in both quartile transition probabilities and regression analyses where we control for size, vintage, and fund type fixed effects. Next, we find that, while the multiple- implied return of a current fund is positively related to the multiple-implied return of the private equity firm’s subsequent funds, the current fund’s return gap is negatively related to the future fund’s multiple-implied return for many fund types. In the full sample, a one standard deviation increase in the gap is associated with a multiple-implied return of the subsequent fund that is 0.58% lower. The negative relation of the return gap to future performance suggests that it is not a measure of skill and that some resources are wasted on generating high IRRs. Recent research documents that the reported IRRs of past funds affect a private equity firm’s ability to fundraise (Brown, Gredil, and Kaplan (2019)). Sophisticated investors may not be fooled by the effect of cash-flow timing on IRRs, especially if they can observe these effects with access to past funds’ cash-on-cash multiples and cash flow data. Moreover, if LPs were easily able to invest committed capital in similar-yielding investments while it is outside the fund, return gaps would not reduce their returns, and so we would not expect the return gap to be related to a private equity firm’s future fundraising ability. Rather than putting effort into sophisticated cash flow management, investors might prefer to reinvest with private equity firms that have past funds with longer durations and lower historical

4 return gaps. We conduct several analyses of whether return gaps affect investors’ decisions. At the fund level, we find some evidence that the current fund’s return gap is related to the probability of the private equity firm raising a subsequent fund, and consistent evidence that it is positively associated with the size of a private equity firm’s follow-on fund (conditional on its existence). A return gap that is one percent higher in the current fund is associated with a 4% larger size in the subsequent fund. In contrast, the current fund’s multiple-implied return and MIRR are not consistently related to the size of the subsequent fund. At the investor level, when we regress an indicator variable for whether the investor participates in the private equity firm’s next fund (again, conditional on its existence), we find positive and significant coefficients on the current fund’s return gap for some investor categories (insurance companies, endowments, and public pension funds), and no significant negative coefficients. In addition, we build on Cavagnaro, Sensoy, Wang, and Weisbach (2018), who point out that skill can vary greatly within investor classification. We compute versions of their measure of skill to classify investors, and find evidence that the relatively more successful investors weight the return gap less heavily in their decision to reinvest in the GP’s subsequent fund. Overall, our results suggest that return gaps influence investment decisions for a broad cross-section of investors. Last, in additional analysis, we investigate whether return gaps are related to the presence of subscription-line financing loans taken out by the private equity firm and backed by LP commitments to the fund. These subscription lines have come under scrutiny as a way to artificially increase IRR.6,7,8,9

6Why LPs frown on the use of credit lines by GPs, Private Equity International, Oct 6, 2016. 7Private Equity’s Latest Con: Subscription Line Loans Boost Returns and Deceive Investors, CEPR Blog, Nov 17, 2016. 8Buyout Firms Are Magically – and Legally – Pumping Up Returns, Bloomberg, Apr 13, 2017. 9Tempted By A High IRR? Don’t Be, It’s A Misleading Statistic, Forbes, Jun 14, 2018.

5 ,10

In a subset of 994 funds for which we have data, we find that an indicator for the use of subscription lines is not related to the return gap. In further analysis of the funds for which we have cash flows, we find that the earliness of distributions, rather than the lateness of calls, is most related to the return gap. Taken together, our results suggest private equity investors might not fully account for the cash flow timing implications of IRR in their investment decisions. The next section provides background on the private equity industry and the IRR, and describes the computation of the return gap in more detail before moving on to the empirical tests.

2 Private equity and IRR background

2.1 Private equity background

Private equity firms manage one or more funds that hold equity or debt stakes in private companies. During the fundraising stage, the private equity firm obtains capital commitments from investors. As it is uncertain when investment opportunities will arise, committed capital must be available (i.e., contributed) with, typically, 10 days’ notice during the investment period, which is usually the first few years of the fund’s life.11 This forces many investors, especially those who have too little capital to diversify across multiple private equity funds, to hold low-risk, low-yielding assets, or to shoulder investment risk on the committed capital.12 As the fund matures and divests its portfolio companies, it returns 10Private Equity’s Trick to Make Returns Look Bigger, Wall Street Journal, Mar 9, 2018. 11See MJ Hudson’s Alternative Insight (February 2019). Investors who are late in meeting calls may be subject to a lawsuit, punitive interest rates, or loss of stake. Note that this is not simply illiquidity, as the investor is unable to pay a fee or give advanced notice in order to change the timing of cash flows. 12In 2009, however, even the Harvard University endowment was forced into fire sales on the sec- ondary market of $3 billion of its $11 billion worth of commitments to private equity funds, due to

6 (i.e., distributes) capital and profit, less agreed-upon fees, to the fund’s investors. Limited partnership agreements (LPAs) typically stipulate ten-year fund lives, but extensions are possible. Capital, sometimes in the form of locked up IPO shares, is returned to investors throughout the fund’s life at the discretion of the private equity firm. Finally, given that some distributions occur before contributions, funds often never have the entire committed amount invested at any given time during the fund’s life. While exogenous economic forces likely drive most of private equity firms’ decisions about when to call capital and harvest investments, given uncertainty about the economically optimal timing choice, the private equity firm has an incentive to call capital late and harvest investments early or pay large early dividends, in order to maximize the fund’s IRR. A fund could also borrow money in order delay capital calls from investors, as described in Albertus and Denes (2019). This “subscription line” financing shortens the investment period and thus increases the fund’s reported IRR, but decreases the fund’s cash-on-cash multiple due to the interest paid. To illustrate this, we present a typical example of a private equity fund’s cash flows in Appendix A, and the effect on fund-level IRR of a hypothetical subscription line financing arrangement.13 An increasingly sophisticated academic literature examines the size and risk profile of private equity returns, typically focusing on IRRs or PMEs (see Kaplan and Schoar; 2005 and Korteweg and Nagel; 2016). Kaplan and Schoar (2005) and Phalippou and Gottschalg (2009) find that, after fees, private equity funds substantially underperform public markets, but Harris, Jenkinson, and Kaplan (2014) find that private equity funds outperform. the losses in its portfolio and an overcommitment of the capital it had allocated to private equity (https://harvardmagazine.com/2009/09/sharp-endowment-decline-reported). 13Subscription loan interest rates are typically low because the loan is backed by investors’ firm commitments. While subscription line financing’s original purpose was to render capital calls more predictable for investors, today, LPAs allow for subscription lines to be outstanding for 180 or even 360 days (MJ Hudson’s Alternative Insight - February 2019).

7 Sorensen, Wang, and Yang (2014) argue that this outperformance is inadequate to com- pensate investors for the substantially greater risk, leverage, and illiquidity associated with private equity investments. Korteweg and Nagel (2016) generalize the PME using a stochas- tic discount factor methodology and find that venture capital funds underperform after fees, but direct investments in startups outperform public benchmarks.14 Ang, Chen, Goetzmann, and Phalippou (2018) find that private equity investors may at best break even compared to investing in a portfolio of small, illiquid stocks. Private equity fund performance, through the IRR, affects a private equity firm’s ability to fundraise (Brown, Gredil, and Kaplan (2019)). Moreover, the private equity firm’s compensation is tied to the fund’s returns.15 We seek to provide further insight into reported IRRs by decomposing them to estimate the effects of cash-flow timing on reported IRRs, as discussed below.

2.2 Decomposition of IRRs

We seek to compare the reported IRR to the rate of return earned by an investor who leaves capital in the fund from inception to the end of the fund’s life. In the extreme case, if no return is earned on the capital outside of the fund, the cash-on-cash multiple oﬀers a better gauge of the return actually earned by investors over the fund’s life. We can calculate the return implied by the fund multiple for the life of the fund:

14While the PME gives investors a useful comparison to returns that might have been earned in an index fund during the same time period, it does not account for the fact that the GP chooses the timing of the fund’s cash flows and that the investor must find a home for the capital while it is outside the fund. 15Compensation often follows the industry standard of 2/20: 2% management fee on all invested capital and 20% carried interest (i.e., share of profits) on the total return, typically after a hurdle rate of return is achieved. Whether the private equity firm can begin collecting carried interest can be based on the fund’s IRR surpassing a pre-set hurdle rate. Gompers and Lerner (1999); Phalippou (2009); Chung, Sensoy, Stern, and Weisbach (2012); and Hochberg, Ljungqvist, and Vissing-Jørgensen (2014) discuss private equity industry compensation.

8 MultipleReturn = (Multiple)1/T − 1, (1) where T is the life of the fund and Multiple is the fund’s reported cash-on-cash multiple. For instance, a multiple of 2 would signify a 100% return over the life of the fund, which is a 7.2% annual return for a fund with a ten-year life. We then compute the diﬀerence between the reported IRR and this rate of return.

Gap = IRR − MultipleReturn (2)

A gap between reported IRR and the rate of return implied by the fund’s cash-on-cash multiple will naturally arise due to the existence of intermediate cash flows that effectively shorten the investment horizon.16 This will tend to make reported IRRs higher than multiple- implied returns when the multiple is greater than one, and lower when the multiple is less than one. Thus, we expect a negative gap when IRR is negative. While investors are subject to capital calls and returns of capital at unknown dates, they can most likely earn some positive return on the capital while it is outside the fund. Some investors compute a modified IRR, or MIRR, taking into account the returns they think they can earn on the capital while it is not in the fund. The riskier the alternative investment vehicle, however, the more likely it is that investors may not be able to make capital calls from the fund and suffer financial consequences. In some of our analyses, we use the MIRR, which we compute by assuming that cash is invested in the market portfolio

16Kacperczyk, Sialm, and Zheng (2007) compute a return gap for mutual funds by comparing the return reported by the fund to the return earned by the fund’s beginning-of-quarter holdings. Our measures are similar in name only. While their measure, which takes the reported return as the true return to investors, is positively related to a fund manager’s skill in managing intra-quarter trades, our measure uses the multiple- implied return as a lower bound for the true return on investors’ capital during the fund’s lifetime.

9 while it is outside the fund. We then compute the MIRRgap as follows:

MIRRgap = IRR − MIRR (3)

This MIRRgap is the diﬀerence between the IRR and a plausible annualized return that an investor could have earned if she had access to a liquid market index fund for any cash that was not invested in the private equity fund. While this measure is potentially more realistic, it requires cash ﬂow data and thus restricts the sample size.

3 Data

Our data are from Preqin’s Performance, Fund Summary, Cash Flow, and Investor modules, downloaded in July and August of 2019. Preqin obtains data through voluntary input from fund investors and through Freedom of Information Act (FOIA) requests. Preqin data has been used in other academic studies including Ewens, Jones, and Rhodes-Kropf (2013) and Ang, Chen, Goetzmann, and Phalippou (2018). We focus on both the reported IRR and the multiple-implied return for the entire life of the fund; thus our primary analysis retains funds for which Preqin reports both the IRR and cash-on-cash multiple. If a fund is not yet liquidated as of 2019, we require that it is at least 3 years old and we rely on its latest reported interim IRR and multiple. Interim reported IRRs are computed using the assumption that fund-reported net asset values (NAVs) are terminal values that are equal to the market values of these assets. Private equity ﬁrms have historically had some leeway in computing interim asset values for their investors. This has attracted the attention of both researchers and the SEC.17 Conservatively underreporting NAVs, especially early values,

17Cochrane (2005), Korteweg and Sorensen (2010) and Jenkinson, Sousa, and Stucke (2013) ﬁnd that portfolio companies’ net asset values tend to be higher in fundraising periods. Barber and Yasuda (2017)

10 generally boosts the final IRR [see Phalippou (2011)]. However, GPs normally raise their next fund before the first fund is liquidated, and investors use the prior fund’s interim IRR to evaluate participation in a subsequent fund, so it is not clear that interim IRRs should be biased in either direction. Our sample comprises 6,945 private equity funds with vintages between 1971 and 2015 for which we can observe the fund’s IRR and cash-on-cash multiple. Of these funds, 4,377 are not yet fully liquidated as of 2019, and 2,568 are fully liquidated. Also, of the total of 6,945 funds, 3,867 funds have a predecessor fund from the same GP with a vintage that is at least 3 years earlier. For some tests, we require fund cash flow data, and thus use a sub-sample of 3,267 funds, of which 788 are liquidated. Figure1 shows the number of funds in the sample by vintage year. Summary statistics for the full sample of private equity funds appear in columns 1-4 of Panel A in Table2. Closed fund value ( FundValue) averages $667M with a median of $264M. Reported average (median) IRR (IRR) is 12.5% (10.6%), and cash-on-cash multiple (Multiple) is 1.637 (1.471). These compare with the median IRR of 13% described in Harris, Jenkinson, and Kaplan (2014) and with the median cash-on-cash multiple of 1.65 reported by Phalippou, Rauch, and Umber (2018), both for sample periods ending earlier. Summary statistics for the subset of funds with a predecessor fund that is at least 3 years old appear in columns 5-8 of Table2. These funds tend to be slightly larger than the general population of funds, with mean and median initial fund values of $904.6M and $368.0M. Panel B of Table2 presents summary statistics partitioned by the stage of the fund: closed funds that are not yet liquidated, and liquidated funds. This panel shows that further find that funds time their portfolio companies’ strongest exits to coincide with fundraising. Brown, Gredil, and Kaplan (2019) argue that NAV inflation is practiced by unsuccessful GPs, but that LPs see through this behavior. Easton, Larocque, and Stevens (2018) find that private equity NAVs more accurately represent ex post future cash flows following the establishment of ASC 820 (formerly known as SFAS 157), Fair Value Measurement by the Financial Accounting Standards Board (FASB) in 2008.

11 liquidated funds are less than half as large on average as funds that have yet to liquidate, illustrating the tremendous growth in the private equity industry and in fund sizes in the last decade. Computing the multiple-implied return for a fund requires an estimate of the fund’s life. For funds that have not yet liquidated, we use the number of years since the vintage year as the fund’s elapsed life. For liquidated funds with cash flow data, we can observe the realized lifetime fo the fund. Funds often have a negligible amount of capital left undistributed at the tail end of their lives, so we define fund life as the length of time it takes for investors to receive 95% of the fund’s total distributions. This is a conservative choice because using the date of the last distribution as the end of the fund’s life would tend to make the multiple- implied return smaller, and the gap larger. For liquidated funds without cash flow data, we estimate expected fund life by fund type based on liquidated funds for which we have cash flows. Specifically, we take the median fund life by fund type and apply it to these funds.18 Table2 presents summary statistics on the two measures of return gap ( Gap and MIR- Rgap). The gaps, multiple-implied return, and IRR are winsorized at the 1% level to ensure that outliers do not drive our results. The gap for the full sample in Panel A averages 7.76%, more than half of the average IRR, and the median return gap is 5.69%. We also calculate duration for the funds in our sample for which we have cash flow data. As Panel A of Table2 shows, mean (median) duration for the funds in our sample is 4.045 (3.862) years whereas mean fund life is 9.934 years with a median of 10 years. Liquidated funds have mean and median fund lives of 12.11 and 12 years. Figure2 presents a lowess

18For each question that we test, we separately show results for liquidated funds as it is possible that results vary for liquidated funds, where we can observe the fund’s IRR over the full life of the fund, and for non-liquidated funds, where we observe and use the ﬁnal reported IRR for the fund. Examining liquidated funds has the advantage that we know the fund’s realized life, whereas examining non-liquidated funds has the advantage that we do not have to make assumptions about true fund life when there is a negligible amount of capital left in the fund.

12 smooth showing that Gap declines monotonically with duration, as expected. In the extreme, if the duration of the fund’s cash flows equals the life of the fund, the gap is zero. Figure3, panel A presents reported IRRs and return gaps by vintage year. As the preceding paragraphs have described, throughout the paper, we use only the latest reported returns (terminal returns for liquidated funds), due to the mechanically high autocorrelation of interim IRR over the years of a fund’s life. One exception is Figure3, panel B, where we present IRRs and gaps over the years of the fund’s life, for the 4,793 funds for which we have quarterly reports from Preqin in at least 3 separate years. This panel shows that IRR is highest on average in years 5, 6 and 7 of the fund’s life and then the average begins to decrease over later fund years (the most successful funds have perhaps already liquidated). The gap, by contrast, increases throughout the life of the fund, and the average gap is at its highest in years 9 and 10. Throughout the analysis, we will include vintage year fixed effects, which will absorb this variation. Panel B of Figure3 also shows the correlation between the gap in each year and the final reported gap of the fund (excluding the final year, for which the correlation is 1). We can see from this line that the correlation is always above 0.8 after year 3, and converges to 1 ver quickly. This shows that reported IRRs for funds that are not yet liquidated as of August 2019 are likely to be very informative about their final IRRs and return gaps when they do finally liquidate. Figure4 examines IRR and return gap by type of fund and by investor type. Figure4 shows that the fund types that tend to have more volatile cash flows, and also more discretion in the timing of their cash flows, tend to have higher gaps relative to their multiple-implied returns. For example, real estate funds have low gaps on average relative to the multiple- implied return of the funds, as the cash flows to these funds are predictable and are more likely to happen at the beginning and end of the fund. At the other extreme, turnaround

13 funds can be expected to have very volatile cash flows with more discretion given to the GP about when to realize them. These funds have high gaps relative to their multiple-implied returns. To account for this variation, we will include fund type fixed effects in our fund- by-fund analyses. Figure4 Panel B presents gaps by investor type. These gaps may simply reflect the types of funds in which these investors prefer to invest but also may reflect skill in choosing funds that will have higher durations. Before beginning our analysis of the persistence of return gaps and of their economic consequences, we perform a preliminary analysis to compare observed return gaps with simulated return gaps under some simple assumptions. For each fund, we use the fund’s cash-on-cash multiple and simulate cash flows that achieve that multiple. We assume that all of the fund’s cash calls occur in uniformly distributed amounts in the first half of the fund life and add up to the total contribution amount. We further assume that all distributions of cash to investors occur in the last half of fund life, again in random, uniformly distributed dollar amounts that add up to total distributions.19 We do not assume a distribution of cash flows based on the distributions we observe in our dataset as we wish to simulate what a fund’s IRR and return gap would look like without any management of cash flow timing. Results appear in Appendix B. In each of three different fund size categories (small funds with less than $100M, medium funds with $100-499M, and large funds with $500M+), we observe that actual return gaps are significantly larger than simulated return gaps. This suggests that cash calls (distributions) occur later (earlier) on average than in a random uniform distribution during the first (last) halves of the fund’s life.20

19Metrick and Yasuda (2010) describe how GPs typically invest in new companies only in the first five years, with some follow-on investments as well as divestitures made in the final five years of a private equity fund’s life. 20In additional analysis in section 6.4, we investigate the extent to which late cash calls and/or early distributions are associated with return gaps.

14 4 Return gap persistence

If return gaps are the result of private equity firms’ individual cash flow timing policies, we might expect them to persist across funds of a given firm. Alternatively, private equity firms may learn and change their practices over time, or gaps might be randomly distributed across firms and funds. In Table3, we examine whether return gaps from past funds of a private equity firm are related to return gaps for current funds of the same firm. Thus, this analysis is restricted to funds that have a predecessor fund that is at least three years older. In Panel A of Table3, we examine quartiles of the return gap of the current fund and of the return gap from the same private equity fund’s latest fund that is at least 3 years older than the current fund. Quartiles are computed within vintage year and fund type, retaining only those vintage year and type combinations with at least 4 observations. We test whether the observed distribution in each of the 16 cells significantly differs from 1/16 = 6.25%, using two-sided tests. It is apparent that there is more data along the diagonal: lagged gaps in the top (1st) quartile are associated with subsequent gaps in the top quartile in 8.3% of the sample, which is significantly different from 6.25% at the 1% level. The other on- or near-diagonal sample proportions are larger than expected, but the difference from 6.25% is not always statistically different from zero. The far off diagonal elements, by contrast, contain proportions that are sometimes significantly lower than expected. For example, the combination of prior funds that are in the 4th quartile and current funds in the 1st quartile only occurs in 5.2% of the sample, which significantly differs from 6.25% at the 1% level. We note, like Kaplan and Schoar (2005), that these simple tests could be influenced by overlapping lifespans, and thus overlapping economic fundamentals, during a private equity firm’s prior and subsequent funds, even though we require funds to be raised three years apart. We also would like to control for fund type, size, and vintage. We conduct regression

15 analyses in Panels B and C of Table3. We estimate the following equation where the unit of observation is at the fund-level:

Gapi = α0 + α1lag3Gapi + α2lag3MultipleReturni + Controls + i (4)

Lagged values indicate the values from the same private equity firm’s lagged fund that was raised at least three years prior to the current fund i. In this and later tests, we decompose the lagged fund IRR into the gap, lag3Gap, and the multiple-implied return, lag3MultipleReturn. In addition, we control for the log of fund size, logFundValue, and include 42 fund vintage and 24 fund type fixed effects. Standard errors are double-clustered by vintage year and by private equity firm. Panel B of Table3 shows that gaps are persistent, suggesting that the distribution of cash flows along the fund’s life are related to the private equity firm’s management style. In untabulated regressions, results are stronger if we only require one year’s difference between the current and the lagged fund, no doubt because the data set is larger. Column 4 of Panel B shows that results are stronger when both current fund IRR and lagged fund IRR are positive. Recall that a negative IRR results in a negative gap, which is not very meaningful. Panel C of Table3 partitions the sample by size of fund, by fund type, and by the location of the private equity firm. In Panel C, we restrict the sample to positive IRRs and lagged IRRs. Power is lower due to the requirement of a lagged fund and the sample split, but we find that persistence is strongest for small- and medium-sized funds (below $100M and between $100M and $500M) and for buyout funds and for liquidated funds. Since the gap is expected to build over the life of the fund, this latter result is expected. While this observed persistence in gaps across funds of the same private equity firm is not necessarily due to a

16 deliberate attempt to inﬂate IRRs, it may be informative about future funds’ performance. Panels D and E replicate the analysis of panels C and D with modiﬁed IRR instead of IRR. Results are generally similar.

5 Return gaps and future performance

We next examine whether return gaps are related to future fund performance. High return gaps might simply indicate that private equity firms are skilled, both at managing investor perceptions about their returns, and at generating economic value for investors. Alterna- tively, if a private equity firm expends resources to inflate the fund’s IRR, they may do so at the expense of the fund’s cash-on-cash multiple. Table4 presents regressions of the fund’s multiple-implied return on the earlier fund’s return gap and control variables, as in the following equation:

MultipleReturni = α0 + α1lag3Gapi + α2lag3MultipleReturni + Controls + i

This table shows that, after controlling for lagged multiple-implied return and other controls, for many fund categories there is a negative relation between the return gap of one private equity fund and the multiple-implied return of the subsequent fund of the same private equity firm. This suggests that the gap may be an indicator of value destruction to inflate performance. The results are economically significant. In column 4 of Panel A, the coefficient of -0.0542 on lag3Gap suggests that, for every one standard deviation (0.107 from Table2, column 7) increase in the earlier fund’s return gap, the current fund enjoys a 0.58% lower multiple-implied return. Column 8 shows that results are strongest when the IRR is greater than 8%, the sample in which it is likely that the GP will have met a hurdle rate

17 (Phalippou, Rauch, and Umber (2018)), but also in which it is less likely that the investor will be able to ﬁnd an alternative investment that yields similar performance. In contrast, the multiple-implied return is a strong, positive predictor of the next fund’s multiple-implied return. Panel B shows that this result is fairly consistent across many subsets of the data.

6 Return gaps and fundraising

While some level of return gap is an unavoidable part of investing in any asset class with intermediate cash flows, perhaps investors are able to minimize the effects on their portfolios by directing investments towards private equity firms with historically lower return gaps. Alternatively, they might manage their investments such that the cash returned by the funds that they invest in can be quickly reinvested at a similar rate of return elsewhere. Private equity investors are commonly considered to be sophisticated investors, and they could be expected to clearly understand the pitfalls of IRR. In their recent report to the Norwegian government, Doskeland and Strömberg (2018) point out that though IRR is a flawed measure, they know of no evidence that biases in IRR have an economically measurable impact on LPs’ investment decisions. However, Phalippou and Gottschalg (2009) point out that prospective investors are given very little information when they are deciding between funds. Many investors may only have an IRR or an average IRR of the private equity firm’s past funds.

6.1 Probability of raising a subsequent fund

Do past return gaps affect the probability that the private equity firm will raise a future fund? In this section, the dependent variable is an indicator for whether the private equity firm is able to raise a subsequent fund, and we use a Probit model:

18 Raisei = α0 + α1Gapi + α2MultipleReturni + Controls + i (5)

In columns 1 through 3 of Table5, we find that the probability of a private equity firm raising a subsequent fund is positively associated with each of the IRR, the return gap, and the multiple-implied return of the earlier fund. However, when we include both the return gap and the multiple-implied return, the coefficient on Gap is roughly 1/8th of the size of the coefficient on the multiple-implied return, in the full sample (column 4). Thus, it appears that the probability that the private equity firm raises a subsequent fund is somewhat affected by the return gap on the prior fund.

6.2 Size of subsequent funds

Next, we examine the ability of the private equity ﬁrm to raise larger funds in the future, conditional on raising a subsequent fund. Table6 estimates the following equation:

∆Sizei = α0 + α1lag3Gapi + α2lag3MultipleReturni + Controls + i (6)

The dependent variable is the percentage change in size of the new fund, raised at least 3 years later, compared to the current fund. This variable is winsorized at the 1% level to mitigate the effect of outliers, and funds smaller than $10M are omitted. The regression also includes 42 vintage and 24 fund type fixed effects, and standard errors are clustered by vintage year and by private equity firm. In columns 1 through 3 of Table6, we find that the size of the private equity firm’s follow-on fund, conditional on its existence, is positively associated with each of the IRR, the return gap, and the multiple-implied return of the earlier fund. However, it is important

19 to consider the effect of both components of IRR, and the following columns of Panel A include both multiple-implied return and the return gap. In columns 4, 5, and 6, we do not find evidence of a significant relation between past multiple-implied return and the size of the private equity firm’s follow-on fund, but we do find a positive relation between the return gap of the earlier fund and the increase in size of the subsequent fund. It appears that, in their reinvestment decisions, investors are focusing on the portion of the IRR that is most difficult for them to realize. For example, across the columns of Table6 Panel A, a return gap that is one percentage point (0.01) larger in the earlier fund is associated with a subsequent fund that is 3-5% larger. In subsets of private equity funds, Panel B shows that these results are strongest for large funds and for buyout funds.21 In these tables, the dependent variable is not a measure of return, so we are also able to investigate the effect of an alternative breakdown of the IRR into modified IRR (MIRR) and MIRRgap. The MIRR makes the assumption that any cash flows received by investors are reinvested in the market portfolio until the end of the fund’s life. Computing MIRR requires fund cash flows, however, which shrinks our sample. We estimate the following model:

∆Sizei = α0 + α1lag3MIRRgapi + α2lag3MIRRi + Controls + i (7)

The results of these regressions appear in Table6, panels C and D. These tables show very similar results to those of Panels A and B but with lower power due to the smaller sample size. 21As we have one observation per fund, these results do not directly compare to those of Brown, Gredil, and Kaplan (2019), who find that private equity firms inflate interim NAVs during fundraising periods, especially for liquidated funds. This temporary NAV inflation of active funds may or may not affect the final IRR that is reported for the fund. Moreover, Phalippou (2011) shows that a consistent policy of NAV inflation may decrease IRRs.

20 6.3 Reinvestment decisions at the investor level

We next consider the reinvestment behavior of various types of investors at the investor level. Early literature suggests that some investor types better process information about private equity Lerner, Schoar, and Wongsunwai (2007)). However, more recent evidence suggests that there are not strong diﬀerences across investor types, with respect to their performance (Sensoy, Wang, and Weisbach 2014) and their due diligence and investment activities (Da Rin and Phalippou 2017). Thus, prior literature suggests that all investor types have both strong and weak investors. The Preqin Investors module categorizes private equity LP investors across categories including endowments, public pension plans, and more. We have investor data for 6,205 of the funds in the sample. This data may not include all investors in each fund, and some investor-level commitment amounts are missing. We estimate the following equation across each of the largest investor categories:

Reinvesti,j = α0 + α1Gapi + α2MultipleReturni + Controls + i (8)

In this Probit model, the dependent variable is an indicator variable for whether a given investor j in private equity fund i invests in a subsequent fund with the same private equity firm, and the analysis is at the investor-fund level.22 The median investor reinvests with the same private equity firm 25% of the time during our sample period. We restrict the sample to funds for which the private equity firm goes on to raise a subsequent fund, and we require prior funds to be at least three years younger than current funds in order for LPs to be able to observe performance.

22We obtain similar inferences based using OLS regressions.

21 Results for the six largest categories of investor appear in Panel A of Table7. In this table, we observe that some of the coefficients on the return gap of the fund are significantly positive, and none are significantly negative. In particular, endowments, insurance companies, and public pension funds appear more likely to reinvest if the current fund’s gap is higher, controlling for the multiple-implied return, fund size, and vintage and fund type fixed effects. For example, given a gap that is 1 percentage point higher holding other variables at their means, an insurance company is more than 1% more likely to invest in the private equity firm’s next fund, the unconditional reinvestment rate being 42%. We next conduct an analysis of LP behavior that differentiates LP investors based on past performance, rather than investor type. Cavagnaro, Sensoy, Wang, and Weisbach (2018) create a measure of investor skill that is simply the proportion of the investor’s funds that beat the median IRR for that fund category and vintage. They find that investor type alone is not a good indicator of skill, i.e. that there are skilled investors of all investor types. Using Preqin’s fund categories and vintages (for example, large buyout funds of vintage 1995), we create similar measures of skill which compare the investor’s performance to the median category IRR in our sample and the median category Multiple in our sample. The first skill category, “High IRR,” includes investors who invest in at least four funds in our sample, and whose average indicator variable for beating the median IRR in that category and vintage is greater than 0.5. Similarly, we categorize investors on whether they tend to beat the Preqin IRR benchmark, the median fund multiple, and the median MIRR (for MIRR, we can only examine investor performance in the subset of funds for which we have cash flows). The model we estimate is the same as in Equation8 except that we create an indicator for each type of “high skill,” and we add interaction terms for the indicator variable for whether the investor is “smart” by each of the definitions. Recall that not all investors of a fund appear

22 in Preqin, and so these measures of skill are relative to only the set of investors who do appear in the data. To the extent that the investors that do appear in Preqin perform better or worse than the universe of investors, our results may be biased. Lastly, we require that each fund in this sample is not the last fund of the private equity ﬁrm in our data (through 2019), so that we can observe whether the investor reinvests. In these regressions, we include the return gap and the multiple-implied return for the most recent fund of the private equity ﬁrm that is at least three years older than the fund under consideration, their interactions with the skill indicator, and the skill indicator itself.

Reinvesti,j = α0 + α1HighSkill ∗ Gapi + α2HighSkill ∗ MultipleReturni+

α3Gapi + α4MultipleReturni + α5HighSkill + Controls + i (9)

Results appear in Panel C of Table7. The coefficients on the interaction terms with skill indicators show that, when skill is defined by beating the vintage and fund type IRR benchmark more than 50% of the time, more skilled investors put less weight on the return gap when deciding when to invest, though the coefficient on the interaction term with skill (-0.547) reverses only some of the reliance on the gap (0.830) for the reinvestment choice. For the other variants of the definitions of skill, this relation is weaker. For all types, investors regardless of skill put some weight on the return gap when deciding whether to reinvest. Thus, it does not appear that above-median investors consistently identify and avoid high- gap funds more than below-median investors.

23 6.4 Subscription-line ﬁnancing and their relation to the gap

In additional analysis that uses a subset of funds, we investigate whether the return gap is related to the use of subscription-line financing, GPs’ increasingly common practice of borrowing backed by LPs’ commitments to the fund. The borrowing is advertised as being for cash management purposes but could be used to shorten the period that LP capital is under management. For a subset of 990 funds, Preqin provides a variable indicating whether the private equity fund uses subscription-line financing (23.6%), is allowed to but has not used it at the time (1.4%), or does not use subscription-line financing (75%). When regressing the gap on these measures in Table8, we find that the use of subscription lines is not related to the gap. In column 1, we include all funds, and have indicators for each of the reporting funds (use, might use, don’t use). In column 2, we only use the funds that report, and have indicators for use and might use. Why are subscription lines not related to the gap? One possibility is that those funds that use them heavily do not report. The other possibility, however, is that use of lines at the beginning of the fund’s life for short periods of time (as was likely done in the historical Preqin data) does not affect IRR very much. To investigate this, we calculate the skewness of distributions and of contributions to the funds for which we have cash flow data. For every year in the life of each fund, we separately calculate the percentage of total cash contributions and percentage of total cash distributions attributable to that fund year. Specifically, we divide the cash contributions (distributions) per fund year by the total cash contributions (distributions) realized from inception to liquidation. These fund-year percent- ages provide a fund-specific distribution of cash contributions and distributions throughout the life of the fund. We then calculate a measure of cash inflow deferral (related to contributions) and a measure of cash outflow acceleration (related to distributions) by applying a

24 weight to each fund-year percentage. For contributions, we weight the fund-year percentage by the fraction of the year in the fund’s life divided by the total fund life, thus weighting later cash inflows more. We sum these over the life of the fund to arrive at ContSkew, the measure of cash inflow deferral. For distributions, we exactly reverse the weights over the life of the fund and multiply each fund-year percentage by the fraction of the fund life minus the fund-year plus one divided by the total fund life, thus weighting earlier cash outflows more. We sum these over the life of the fund to arrive at the measure of cash outflow acceleration, DistSkew. Equations 10 and 11 provide more detail:

T " # X Contt t ContSkew = · (10) PT T t=1 t=1 Contt

T " # X Distt (T − t) + 1 DistSkew = · (11) PT T t=1 t=1 Distt Table9 regresses return gap on these measures of cash flow skew and confirms that both are positively related to the return gap in our full sample, as expected. However, ContSkew, our measure of cash inflow deferral, is not significantly related to the gap in many subsamples, while the coefficient on DistSkew, our measure of cash outflow acceleration at the end of the fund’s life, is highly statistically significant for the full sample, as well as all eight subsamples. Moreover, in most cases, the coefficients on DistSkew are larger than ContSkew. This table shows that ContSkew, the measure of the lateness of contributions, is not consistently related to the gap, while DistSkew, the measure of the earliness of distributions, is more strongly related to the gap. It seems that a policy of large early dividends and early exits is more of a driver of the private equity return gap than is borrowing through subscription lines.

25 7 Conclusion

This study examines private equity funds” internal rates of return (IRRs), the headline measure of performance for private equity funds. Whereas prior literature takes the timing of private equity cash flows as given, we estimate the effects of cash-flow timing on reported IRRs and explore whether and to what extent private equity investors consider these effects in their investment decisions. Focusing on the difference between a fund’s reported IRR and the annual rate of return implied by the fund’s cash-on-cash multiple, we find that this difference or return gap is persistent across successive funds of the same private equity firm, suggesting that it stems, in part, from private equity firms’ choices in the timing of cash flows. We find a negative relation between lagged return gap and the multiple-implied returns of follow-on funds, however, suggesting that IRR inflation, intentional or not, is negatively related to private equity firm skill in producing returns for investors. We further find that return gaps are positively related to the increase in size of the subsequent fund raised by the private equity firm. Moreover, certain investor types (including insurance companies, endowments and public pension funds) and, by some measures, relatively less successful investors appear more likely to reinvest with high return-gap fund managers. By investigating the timing of cash flows throughout a private equity fund’s life and its relation to reported IRR, we document a limitation of the IRR as a measure of private equity fund returns as well as the effects on investor choices.

26 References

Albertus, James F., and Matthew Denes, 2019, Distorting private equity performance: The rise of fund debt, Working Paper.

Ang, Andrew, Bingxu Chen, William N. Goetzmann, and Ludovic Phalippou, 2018, Esti- mating private equity returns from limited partner cash ﬂows, Journal of Finance 73, 1751–1783.

Barber, Brad, and Ayako Yasuda, 2017, Interim fund performance and fundraising in private equity, Journal of Financial Economics 124, 172–194.

Brown, Gregory W., Oleg R. Gredil, and Steven N. Kaplan, 2019, Do private equity funds manipulate reported returns?, Journal of Financial Economics 132, 267–297.

Cavagnaro, Daniel R., Berk A. Sensoy, Yingdi Wang, and Michael S. Weisbach, 2018, Mea- suring institutional investors’ skill at making private equity investments, Forthcoming, Journal of Finance.

Chung, Ji-Woong, Berk A. Sensoy, Lea H. Stern, and Michael S. Weisbach, 2012, Pay for performance from future fund ﬂows: The case of private equity, The Review of Financial Studies 5, 3259–3304.

Cochrane, John, 2005, The risk and return of venture capital, Journal of Financial Eco- nomics 75, 3–52.

Da Rin, Marco, and Ludovic Phalippou, 2017, The importance of size in private equity: Evidence from a survey of limited partners, Journal of Financial Intermediation 31, 64– 767.

Doskeland, Trond, and Per Str¨omberg, 2018, Evaluating investments in unlisted equity for the norwegian government pension fund global ( gpfg ), Discussion paper, NHH and Stockholm School of Economics.

Easton, Peter, Stephannie Larocque, and Jennifer Sustersic Stevens, 2018, Private equity valuation before and after asc 820, Working paper.

27 Ewens, Michael, Charles M. Jones, and Matthew Rhodes-Kropf, 2013, The price of diversiﬁ- able risk in venture capital and private equity, Review of Financial Studies 26, 1853–1889.

Gompers, Paul, and Josh Lerner, 1999, An analysis of compensation in the u.s. venture capital partnership, Journal of Financial Economics 51, 3–44.

Harris, Robert S., Tim Jenkinson, and Steven N. Kaplan, 2014, Private equity performance: What do we know?, Journal of Finance 69, 1851–1882.

Hochberg, Yael V., Alexander Ljungqvist, and Annette Vissing-Jørgensen, 2014, Informa- tional holdup and performance persistence in venture capital, Review of Financial Studies 27, 102–152.

Jenkinson, Tim, and Miguel Sousa, 2015, What determines the exit decision for leveraged buyouts?, Working paper.

, and R¨udigerStucke, 2013, How fair are the valuations of private equity funds?, Working paper.

Kacperczyk, Marcin, Stijn Van Nieuwerburgh, and Laura Veldkamp, 2014, Time-varying fund manager skill, Journal of Finance 69, 1455–1484.

Kacperczyk, Marcin, Clemens Sialm, and Lu Zheng, 2007, Unobserved actions of mutual funds, Review of Financial Studies 21, 2379–2416.

Kaplan, Steven N., and Antoinette Schoar, 2005, Private equity performance: Returns, persistence, and capital ﬂows, Journal of Finance 60, 1791–1823.

Korteweg, Arthur, and Stefan Nagel, 2016, Risk-adjusting the returns to venture capital, Journal of Finance 71, 1437–1470.

Korteweg, Arthur, and Morten Sorensen, 2010, Risk and return characteristics of venture capital-backed entrepreneurial companies, Review of Financial Studies 23, 3738–3772.

Lerner, Josh, Antoinette Schoar, and Wan Wongsunwai, 2007, Smart institutions, foolish choices: The limited partner performance puzzle, Journal of Finance LXII, 731–764.

28 Lopez-de-Silanes, Florencio, Ludovic Phalippou, and Oliver Gottschalg, 2015, Giants at the gate: Investment returns and diseconomies of scale in private equity, Journal of Financial and Quantitative Analysis 50, 377–411.

Metrick, Andrew, and Ayako Yasuda, 2010, The economics of private equity funds, Review of Financial Studies 23, 2303–2341.

Phalippou, Ludovic, 2009, Beware of venturing into private equity, Journal of Economic Perspectives 23, 147–166.

, 2011, Why is the evidence on private equity performance so confusing?, Working paper.

, and Oliver Gottschalg, 2009, The performance of private equity funds, Review of Financial Studies 22, 1747–1776.

Phalippou, Ludovic, Christian Rauch, and Marc Umber, 2018, Private equity portfolio company fees, Journal of Financial Economics 129, 559–585.

Sensoy, Berk, Yingdi Wang, and Michael Weisbach, 2014, Limited partner performance and the maturing ofthe private equity industry, Journal of Financial Economics 112, 320–343.

Sorensen, Morten, Neng Wang, and Jinqiang Yang, 2014, Valuing private equity, Review of Financial Studies 27, 1977–2021.

Tetlock, Paul C., 2007, Giving content to investor sentiment: The role of media in the stock market, The Journal of Finance 62, 1139–1168.

29 Number of funds 0 100 200 300 400 500 1970 1975 iue1 ubro ud yvnaeyear vintage by funds of Number 1: Figure 1980 1985 1990 30 vintage 1995 2000 2005 2010 2015 Fund Gap −.2 0 .2 .4 .6 0 iue2 udgpadfn duration fund and gap Fund 2: Figure 5 Fund Duration 31 10 15 lorprstecreaino h a nec o-nlya ihtefia eotdgpin gap final reported about B final informative Panel the highly are with reports. life year funds. interim fund’s non-final liquidated the historical each for during using in gaps reported life, gap gaps fund’s that the (IRR) illustrating presents of of return B 2019, correlation year Panel of the by values. rate final reports gap internal are also the fund these funds, of and liquidated values IRR For reported year. reported vintage latest by the gap presents return and A Panel 3: Figure

IRR/Gap IRR/Gap 0 .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 0 .1 .2 .3 .4 .5 1970 3 1975 4 a aetvle yvnaeyear vintage by values Latest (a) 5 b yya ftefn’ life fund’s the of year By (b) 1980 enIRMeanGap Corr(gap, finalgap) Mean IRR 6 1985 7 enIRMeanGap Mean IRR Year offundlife 8 32 1990 9 vintage 10 1995 11 2000 12 13 2005 14 2010 15

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 2015 Correlation between gap and final gap .14 Turnaround .12

Balanced Secondaries Buyout .1 Mean Gap

Venture/Early Stage Expansion / Late Stage

.08 Growth Co−investment Natural Resources Special Situations Debt Mezzanine Real Estate .06 Infrastructure Fund of Funds .03 .04 .05 .06 .07 Mean multiple−implied return

(a) By fund type

.09 Family Office

Other Investment Company .08 Superannuation Scheme Private Equity Firm Corporate Investor Bank

Fund of Funds Manager Wealth Manager .07 Insurance Company Mean Gap

Private Pension Fund Foundation Sovereign Wealth Fund

.06 Endowment Plan

Government Agency Public Pension Fund .05 .035 .04 .045 .05 .055 Mean multiple−implied return

(b) By investor type

Figure 4: Mean return gap and multiple-implied return by fund type and by investor type

33 Table 1: Variable deﬁnitions

Variable Description Source Duration Duration of distributions less duration of contributions. Duration of dis- Preqin cash flow mod- tributions (contributions) calculated as the percentage of distributions ule (contributions) occurring in any given quarter, multiplied by the quarter in the fund’s life, then summed over the fund’s life. The total is divided by four such that duration is in years. FundLife The time elapsed from vintage year to 2017 for closed funds that are Preqin cash flow mod- not yet liquidated, and the time from vintage year to when 95% of cash ule flows are distributed for liquidated funds. LogFundValue log of the fund closed value in millions. Preqin Gap The difference between a fund’s reported IRR and the rate of return im- Preqin plied by the fund’s multiple as in equation3. This variable is winsorized at the 1% level. ContSkew Using LP fund contribution amounts and dates, we weight the fund-year Preqin cash flow data percentage of contributions by the fraction of the year in the fund’s life divided by the fund life, thus weighting later cash inflows more. We sum these over the life of the fund. See equation 10. DistSkew Using LP fund distribution amounts and dates, we multiply each fund- Preqin cash flow data year percentage of distributions by the fraction of fund life minus the fund-year plus one divided by the fund life, thus weighting earlier cash flows more. We sum these over the life of the fund to arrive at this measure of cash outflow acceleration. See equation 11. IRR The fund’s reported internal rate of return, winsorized at the 1% level. Preqin lag3- A lagged measure for a fund with a vintage at least 3 years older than Preqin the current fund. MIRR The fund’s modified internal rate of return, calculated using funds that Preqin have cash flow data and assuming that money not invested in the fund is invested in the CRSP total market portfolio. The measure is winsorized at the 1% level. MIRRGap The difference between the MIRR and the multiple-implied return. Preqin Multiple The fund’s reported multiple. Preqin MultipleReturn The rate of return implied by the fund’s multiple. This variable is Preqin return data winsorized at the 1% level. RaiseNextFund Indicator variable for whether the private equity firm raises a future Preqin fund. Repeat Investment Indicator variable for whether the fund investment by the investor is a Preqin repeat with the same GP.

34 Table 2: Fund-level summary statistics This table presents summary statistics for the funds in the sample. Panel A summarizes the full sample and the subsample of funds that have at least one prior fund from the same private equity firm that is at least 3 years older (This is the sample used in Tables3,4 and 6). Panel B breaks the sample into closed funds that are not yet liquidated, and funds that are liquidated. Variable definitions appear in Table1. Some variables require cash flow data to compute, and thus the sample sizes are smaller.

Panel A

(1) (2) (3) (4) (5) (6) (7) (8) Full sample Has lagged fund VARIABLES mean p50 sd N mean p50 sd N

IRR 0.125 0.106 0.154 6,945 0.125 0.108 0.144 3,867 Multiple 1.637 1.471 0.829 6,945 1.615 1.466 0.760 3,867 MultipleReturn 0.0468 0.0446 0.0555 6,945 0.0480 0.0451 0.0519 3,867 Gap 0.0776 0.0569 0.113 6,945 0.0774 0.0591 0.107 3,867 MIRR 0.0792 0.0812 0.0453 3,317 0.0834 0.0842 0.0424 2,238 MIRRgap 0.0233 0.0149 0.102 3,317 0.0280 0.0191 0.101 2,238 FundLife 9.934 10 4.153 3,267 9.590 9 4.109 2,210 Duration 4.045 3.862 1.963 3,267 3.897 3.729 1.900 2,210 FundValue 667.0 264 1,357 6,945 904.6 368 1,685 3,867 RaiseFutureFund 0.788 1 0.409 6,945 0.819 1 0.385 3,867 ContSkew 0.237 0.226 0.0934 788 0.232 0.227 0.0844 419 DistSkew 0.507 0.518 0.147 788 0.513 0.520 0.147 419

35 Panel B

(1) (2) (3) (4) (5) (6) (7) (8) Closed but not liquidated Liquidated VARIABLES mean p50 sd N mean p50 sd N

IRR 0.106 0.0980 0.117 4,377 0.157 0.127 0.197 2,568 Multiple 1.514 1.416 0.615 4,377 1.845 1.617 1.070 2,568 MultipleReturn 0.0436 0.0407 0.0473 4,377 0.0522 0.0531 0.0667 2,568 Gap 0.0619 0.0541 0.0835 4,377 0.104 0.0672 0.147 2,568 MIRR 0.0838 0.0839 0.0417 2,515 0.0646 0.0709 0.0526 802 MIRRgap 0.0167 0.0135 0.0869 2,515 0.0440 0.0219 0.137 802 FundLife 9.285 9 4.141 2,515 12.11 12 3.387 752 Duration 3.839 3.600 1.947 2,515 4.733 4.568 1.860 752 FundValue 854.0 355.9 1,619 4,377 348.3 152.8 594.9 2,568 RaiseFutureFund 0.767 1 0.423 4,377 0.824 1 0.381 2,568 ContSkew 0.237 0.226 0.0934 788 DistSkew 0.507 0.518 0.147 788

36 Table 3: Are return gaps persistent across a private equity firms’ funds? Panel A presents quartiles of the current and lagged return gap of private equity firms. Lagged return gap is the return gap for the latest fund that was raised at least three years prior to the current fund by the same general partner. Quartiles are computed by vintage and fund type for every vintage and type combination with at least 4 funds. Significance of the two-sided test of the difference of each proportion from 0.0625 (1/16th), appear as ***, ** and * for 1%, 5% and 10% significance levels. Panels B and C present the result of regressions for various subsamples of a fund’s return gap (Gap) on the lagged gap (lag3Gap) and multiple-implied return (lag3MultipleReturn), and fund size (logFundValue). Panels D and E replicate the analysis of panels B and C with the lagged IRR split into lag3MIRR and lag3MIRRgap rather than lag3MultipleReturn and lag3Gap. Variable definitions appear in Table1. Standard errors are double-clustered by vintage year and by private equity firm. There are 24 fund type and 42 vintage year fixed effects. Panel A

Current fund gap quartile 1 2 3 4 Prior 1 0.083*** 0.082*** 0.067 0.054** fund 2 0.064 0.069 0.056* 0.048*** gap 3 0.061 0.064 0.075 0.059* quartile 4 0.052*** 0.048*** 0.056* 0.061

37 Panel B

(1) (2) (3) (4) Full Full Full IRR & VARIABLES Sample Sample Sample Lag3IRR>0

lag3Gap 0.0908*** 0.0512 0.0572* 0.114*** (0.00) (0.13) (0.09) (0.00) lag3MultipleReturn 0.157** 0.146** 0.0401 (0.01) (0.02) (0.56) logFundValue -0.00360** -0.00668*** (0.05) (0.00)

Observations 3,867 3,867 3,867 3,177 R-squared 0.145 0.148 0.150 0.185 Vintage FE YES YES YES YES Fund Type FE YES YES YES YES

38 Panel C

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Small Medium Large VARIABLES Funds Funds Funds Venture Buyout Other U.S. Europe Other Closed Liquidated

lag3Gap 0.212** 0.125** 0.0492 0.170** 0.119*** 0.0956** 0.135*** 0.0298 0.125** 0.0694** 0.147*** (0.01) (0.03) (0.14) (0.02) (0.01) (0.03) (0.00) (0.63) (0.05) (0.04) (0.01) lag3MultipleReturn -0.217 0.198* 0.0248 -0.0968 -0.119 0.112* 0.0348 0.173 -0.182 0.00972 0.213 (0.11) (0.09) (0.74) (0.64) (0.33) (0.09) (0.69) (0.31) (0.34) (0.89) (0.20) logFundValue 0.0206 -0.000471 -0.00223 0.00133 -0.0118*** -0.00385* -0.00542** -0.00968** -0.00864 -0.00461** -0.00541 (0.16) (0.94) (0.47) (0.87) (0.00) (0.08) (0.02) (0.02) (0.29) (0.03) (0.14)

Observations 459 1,374 1,344 405 836 1,936 2,355 580 242 2,339 838 R-squared 0.318 0.235 0.143 0.466 0.215 0.133 0.194 0.264 0.389 0.071 0.253 Vintage FE YES YES YES YES YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES YES YES YES YES 39 Panel D

(1) (2) (3) (4) (5) Full Full Full Full MIRR & VARIABLES Sample Sample Sample Sample Lag3MIRR>0

lag3MIRRgap 0.131*** 0.110** 0.110** 0.116** (0.00) (0.01) (0.01) (0.01) lag3MIRR 0.294*** 0.113 0.113 0.0923 (0.00) (0.11) (0.12) (0.40) logFundValue 0.000199 -0.000281 (0.94) (0.91)

Observations 1,575 1,575 1,575 1,575 1,495 R-squared 0.116 0.125 0.126 0.126 0.126 Vintage FE YES YES YES YES YES Fund Type FE YES YES YES YES YES

40 Panel E

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Small Medium Large VARIABLES Funds Funds Funds Venture Buyout Other US Europe Other Closed Liquidated

lag3MIRRgap 0.410** 0.214*** 0.0575 0.131** 0.202*** 0.137*** 0.137*** 0.176 -0.168 0.101** 0.249*** (0.04) (0.00) (0.16) (0.01) (0.00) (0.00) (0.00) (0.13) (0.26) (0.01) (0.01) logFundValue 0.0352 0.0145* 0.000356 0.0139* -0.000493 -0.00157 -0.000561 0.00147 0.0171 -0.00169 0.0154 (0.17) (0.10) (0.95) (0.10) (0.91) (0.59) (0.82) (0.75) (0.30) (0.59) (0.12)

Observations 70 581 924 266 466 843 1,335 174 66 1,327 248 R-squared 0.569 0.218 0.106 0.321 0.242 0.137 0.129 0.351 0.337 0.073 0.288 Vintage FE YES YES YES YES YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES YES YES YES YES 41 Table 4: Is a fund’s gap related to the GP’s future performance? This table presents the results of regressions of Multiple return on the return gap and the multiple-implied return for the latest fund that was raised at least three years prior to the current fund by the same general partner (lag3Gap and lag3MultipleReturn), and fund size (logFundValue). Regressions include vintage year and fund type fixed effects. Variable definitions appear in Table1. Standard errors are double-clustered by vintage year and by private equity firm. There are 24 fund type and 42 vintage year fixed effects. Panel A

(1) (2) (3) (4) (5) (6) (7) (8) Full Full Full Full Full Lag3 IRR 0 > Lag3 IRR Lag3 IRR VARIABLES Sample Sample Sample Sample Sample >0 <0.08 >0.08

lag3IRR 0.0253*** 42 (0.01) lag3Gap 0.0126 -0.0542*** -0.0503*** -0.0550*** 7.93e-05 -0.0556*** (0.26) (0.00) (0.00) (0.00) (1.00) (0.00) lag3MultipleReturn 0.182*** 0.265*** 0.258*** 0.240*** 0.343*** 0.208*** (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) logFundValue -0.00236*** -0.00290*** -0.00173 -0.00349*** (0.00) (0.00) (0.21) (0.00)

Observations 3,867 3,867 3,867 3,867 3,867 3,528 792 2,736 R-squared 0.148 0.143 0.170 0.179 0.181 0.177 0.171 0.188 Vintage FE YES YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES YES Panel B

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Small Medium Large VARIABLES Funds Funds Funds Venture Buyout Other US Europe Other Closed Liquidated

lag3Gap -0.0423 -0.0507** -0.0380*** -0.0474*** -0.0106 -0.0409*** -0.0536*** -0.0623*** 0.00215 -0.0319*** -0.0483** (0.22) (0.02) (0.00) (0.01) (0.54) (0.00) (0.00) (0.00) (0.96) (0.01) (0.01) lag3MultipleReturn 0.360*** 0.240*** 0.161*** 0.287*** 0.147*** 0.228*** 0.267*** 0.243*** 0.124 0.185*** 0.322*** (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) (0.32) (0.00) (0.00) logFundValue 0.00824** -0.000858 0.000600 0.00780*** -0.00216 -0.00383*** -0.00155* -0.00361** -0.00605*** -0.00108 -0.00443** (0.04) (0.73) (0.64) (0.00) (0.14) (0.00) (0.06) (0.02) (0.01) (0.17) (0.03)

Observations 564 1,711 1,592 616 959 2,292 2,903 667 297 2,819 1,048 R-squared 0.264 0.196 0.197 0.377 0.166 0.176 0.196 0.248 0.185 0.183 0.255 Vintage FE YES YES YES YES YES YES YES YES YES YES YES

43 Fund Type FE YES YES YES YES YES YES YES YES YES YES YES Table 5: Do higher return gaps help the private equity firm raise a subsequent fund? This table presents Probit regressions of an indicator for raising a subsequent fund on the return gap and the multiple-implied return and fund size. Variable definitions appear in Table1. Standard errors are clustered by vintage year. There are 24 fund type and 42 vintage year fixed effects.

(1) (2) (3) (4) (5) (6) (7) (8) Full Full Full Full Full IRR 0 < IRR IRR VARIABLES Sample Sample Sample Sample Sample >0 <0.08 >0.08

IRR 1.715*** (0.00) Gap 1.861*** 0.481* 0.582** 0.495* 1.022 -0.216

44 (0.00) (0.06) (0.02) (0.07) (0.39) (0.41) MultipleReturn 4.982*** 4.444*** 4.819*** 3.498*** 2.747 2.079*** (0.00) (0.00) (0.00) (0.00) (0.22) (0.01) logFundValue 0.178*** 0.174*** 0.169*** 0.174*** (0.00) (0.00) (0.00) (0.00)

Observations 6,945 6,945 6,945 6,945 6,945 6,013 1,693 4,320 Vintage FE YES YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES YES Pseudo R-squared 0.0919 0.0824 0.0977 0.0983 0.118 0.101 0.110 0.108 Table 6: Are return gaps related to the size of the private equity firm’s subsequent fund? This table presents regressions of the percentage change in size of the current fund from the most recent earlier fund by the same general partner (chsize) on the return gap and the multiple-implied return for the latest fund that was raised at least three years prior to the current fund by the same general partner (lag3Gap and lag3MultipleReturn) and fund size (logFundValue).The dependent variable is winsorized at the 1% level. Variable definitions appear in Table1. Standard errors are double-clustered by vintage year and by private equity firm. There are 24 fund type and 42 vintage year fixed effects. Panel A

(1) (2) (3) (4) (5) (6) (7) (8) Full Full Full Full Full Lag3 IRR 0 > Lag3 IRR Lag3 IRR

45 VARIABLES Sample Sample Sample Sample Sample > 0 < 0.08 >0.08

lag3IRR 3.144*** (0.00) lag3Gap 4.011*** 3.578*** 4.069*** 4.332*** 1.289 4.596*** (0.00) (0.00) (0.00) (0.00) (0.76) (0.00) lag3MultipleReturn 7.170*** 1.715 -2.093 -1.636 2.009 -2.450 (0.00) (0.27) (0.13) (0.33) (0.78) (0.26) lag3logFundValue -0.890*** -0.881*** -0.924*** -0.879*** (0.00) (0.00) (0.00) (0.00)

Observations 3,867 3,867 3,867 3,867 3,867 3,528 792 2,736 R-squared 0.096 0.096 0.085 0.096 0.211 0.212 0.222 0.211 Vintage FE YES YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES YES Panel B

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Small Medium Large VARIABLES Funds Funds Funds Venture Buyout Other US Europe Other Closed Liquidated

lag3Gap 0.557 1.237** 4.040*** 1.008 4.311*** 5.370*** 3.659*** 5.358** 4.520* 4.024*** 3.669*** (0.19) (0.04) (0.00) (0.23) (0.00) (0.00) (0.00) (0.01) (0.08) (0.00) (0.00) lag3MultipleReturn 0.0877 0.209 -4.588* 1.417 -3.140 -3.013* -1.536 -3.742 -2.191 -2.510 -1.118 (0.91) (0.88) (0.06) (0.47) (0.34) (0.09) (0.33) (0.17) (0.67) (0.18) (0.69) lag3logFundValue -0.767*** -1.628*** -2.215*** -0.917*** -0.751*** -0.955*** -0.919*** -0.724*** -0.931*** -0.900*** -0.992*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Observations 564 1,711 1,592 616 959 2,292 2,903 667 297 2,819 1,048 R-squared 0.574 0.538 0.417 0.359 0.174 0.229 0.221 0.229 0.340 0.231 0.240 Vintage FE YES YES YES YES YES YES YES YES YES YES YES

46 Fund Type FE YES YES YES YES YES YES YES YES YES YES YES Panel C

(1) (2) (3) (4) (5) (6) (7) (8) Full Full Full Full Full Lag3 IRR 0 > Lag3 IRR Lag3 IRR VARIABLES Sample Sample Sample Sample Sample >0 <0.08 >0.08

lag3MIRRgap 1.904*** 1.527** 1.623** 1.850** 0.545 1.985* (0.00) (0.04) (0.01) (0.03) (0.84) (0.08) lag3MIRR 4.443*** 4.443*** 1.962 2.533 1.328 4.887 -1.537 (0.01) (0.01) (0.34) (0.13) (0.56) (0.30) (0.61) lag3logFundValue -0.976*** -0.930*** -0.986*** -0.931*** (0.00) (0.00) (0.00) (0.00)

Observations 2,045 2,045 2,045 2,045 2,045 1,842 464 1,378 R-squared 0.083 0.085 0.083 0.086 0.214 0.205 0.231 0.208 Vintage FE YES YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES YES 47 Panel D

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Small Medium Large VARIABLES Funds Funds Funds Venture Buyout Other U.S. Europe Other Closed Liquidated

lag3MIRRgap 1.815** -1.114* 2.827*** -0.0749 6.301*** -0.132 1.594** 3.494 1.727 1.365* 1.618 (0.03) (0.08) (0.00) (0.96) (0.00) (0.90) (0.03) (0.11) (0.71) (0.10) (0.13) lag3MIRR -2.304 1.042 -2.284 1.575 -2.062 4.814* 2.464 -2.864 8.209 2.926 -1.086 (0.26) (0.41) (0.31) (0.61) (0.62) (0.07) (0.12) (0.41) (0.25) (0.16) (0.80) lag3logFundValue -0.612*** -1.364*** -1.783*** -1.283*** -0.920*** -0.972*** -1.006*** -0.734*** -1.304*** -0.959*** -1.281*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Observations 133 829 1,083 325 563 1,157 1,720 236 89 1,676 369 R-squared 0.590 0.487 0.358 0.351 0.178 0.241 0.220 0.375 0.421 0.219 0.330 Vintage FE YES YES YES YES YES YES YES YES YES YES YES

48 Fund Type FE YES YES YES YES YES YES YES YES YES YES YES Table 7: Determinants of investors’ repeat investments with the same private equity firm This table presents the results of Probit regressions of the likelihood that a private equity investor will invest with the PE firm again in the future. The dependent variable, Reinvest, is an indicator variable for whether a given investor j in private equity fund i invests in a subsequent fund with the same GP at least 3 years after the vintage of the current fund. Thus, the unit of observation is at the LP-fund level. In Panels A and B, investors are divided by category. In Panel C, skilled investors are those which, throughout our sample have fund investments that have beat the median IRR, Preqin IRR benchmark, median Multiple, or median MIRR for that category and vintage more than half of the time. There are 24 fund type and 42 vintage year fixed effects.Variable definitions appear in Table1. Standard errors are double-clustered by vintage year and by private equity firm. Panel A

(1) (2) (3) (4) (5) (6) 49 VARIABLES Endowment Plan Foundation Fund of Funds Manager Insurance Company Private Pension Fund Public Pension Fund

Gap 0.846** 0.359 0.559 1.136*** 0.463 0.488* (0.03) (0.24) (0.18) (0.00) (0.19) (0.06) MultipleReturn 2.199*** 3.271*** 4.438*** 3.976*** 4.078*** 4.997*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) logFundValue 0.0324 0.00764 0.0521 0.0610** 0.0783*** 0.183*** (0.32) (0.76) (0.21) (0.03) (0.00) (0.00)

Observations 5,687 8,689 7,907 6,065 13,256 20,113 Vintage FE YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES Pseudo R-squared 0.106 0.0951 0.140 0.0839 0.105 0.0836 Panel B

(1) (2) (3) (4) (5) (6) VARIABLES Endowment Plan Foundation Fund of Funds Manager Insurance Company Private Pension Fund Public Pension Fund

MIRRgap 0.967** 0.500 0.538 1.146*** 0.884*** 0.711*** (0.02) (0.18) (0.27) (0.00) (0.00) (0.01) MIRR 2.927** 3.400*** 4.955*** 5.820*** 4.543*** 6.424*** (0.02) (0.00) (0.00) (0.00) (0.00) (0.00) logFundValue -0.0257 0.00237 0.0659 0.0791*** 0.0803*** 0.175*** (0.50) (0.94) (0.15) (0.00) (0.00) (0.00)

Observations 4,189 6,198 6,059 4,309 10,018 16,082 Vintage FE YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES Pseudo R-squared 0.0937 0.0957 0.143 0.0860 0.111 0.0862 50 Panel C

(1) (2) (3) (4) VARIABLES IRR Benchmark Multiple MIRR

HighSkillXGap -0.547*** -0.286 -0.216 (0.00) (0.14) (0.19) HighSkillXMultipleReturn 0.106 0.114 0.430 (0.79) (0.80) (0.21) Gap 0.830*** 0.754*** 0.689** (0.00) (0.01) (0.01) MultipleReturn 3.888*** 3.919*** 3.620*** (0.00) (0.00) (0.00) HighSkill 0.0165 0.0214 0.0801*** 0.280*** (0.45) (0.31) (0.00) (0.00) logFundValue 0.106*** 0.107*** 0.105*** 0.106*** (0.00) (0.00) (0.00) (0.00) HighSkillXMIRRgap -0.0194 (0.95) HighSkillXMIRR -0.263 (0.66) MIRRgap 0.903*** (0.00) MIRR 4.942*** (0.00)

Observations 58,633 57,990 58,610 49,579 Vintage FE YES YES YES YES Fund Type FE YES YES YES YES Pseudo R-squared 0.0776 0.0785 0.0783 0.0816

51 Table 8: Subscription-line financing and fees The dependent variable is the return gap and the independent variables of interest are indicators for whether the fund uses subscription-line financing. Variable definitions appear in Table1. Standard errors are double-clustered by vintage year and by private equity firm.

(1) (2) VARIABLES Gap Gap

UseSLC -0.00267 0.00131 (0.56) (0.86) MightUseSLC -0.0214 -0.0210 (0.17) (0.18) NoSLC -0.00171 (0.79) MultipleReturn 1.191*** 0.953*** (0.00) (0.00)

Observations 6,945 994 R-squared 0.397 0.338 Vintage FE YES YES Fund Type FE YES YES

52 Table 9: Return gaps and the skewness of contributions and distributions The dependent variable is the return gap and the independent variables are measures of the lateness of cash calls and the earliness of exits of the fund. Variable deﬁnitions appear in Table1. Standard errors are double-clustered by vintage year and by private equity ﬁrm.

(1) (2) (3) (4) (5) (6) (7) Full Small Medium Large VARIABLES Sample Funds Funds Funds Venture Buyout Other

ContSkew 0.241*** 0.354 0.238 0.187 0.0377 0.264*** 0.197 (0.01) (0.37) (0.13) (0.17) (0.89) (0.00) (0.14) DistSkew 0.421*** 0.435* 0.446*** 0.307** 0.488*** 0.341*** 0.231** (0.00) (0.09) (0.00) (0.01) (0.00) (0.00) (0.01)

Observations 788 105 413 270 201 282 305 R-squared 0.267 0.347 0.365 0.300 0.423 0.290 0.288 Vintage FE YES YES YES YES YES YES YES Fund Type FE YES YES YES YES YES YES YES

53 Appendix A. This Appendix shows a base case set of cash flows typical to a private equity fund that spans 10 years. There are capital calls in years 0-2, no cash flows in intermediate years and cash distributions in the later years. The lower half of the table shows a hypothetical case of subscription line financing for the same fund, where the first two capital calls are borrowed until year 2 at an interest rate of 1% per year. The private equity fund has closed size 100, ignoring annual management fees. Baseline cash flows for years 0 through 9 are given in the first line. In the second case with subscription line financing, the cash flows from years 1 and 2 are borrowed until year 3 at the simple interest rate of 1% per year, costing $3 in year 3. Thus, the LP multiple is lower under subscription-line financing, but the reported IRR is higher and the carry earned by the GP is 14.45 compared to 0.

0 1 2 3 4 5 6 7 8 9 Fund cash ﬂows -50 -50 0 0 0 0 0 0 75 110 LP cash ﬂows -50 -50 0 0 0. 0 0 0 75 110 Fund IRR 7.90% Fund Multiple 1.85 Carry to GP 0.00 LP IRR 7.90% LP Multiple 1.85

0 1 2 3 4 5 6 7 8 9 Fund cash ﬂows 0 0 -103 0 0 0 0 0 75 110 LP cash ﬂows 0 0 -103 0 0 0 0 0 75 95.6 Fund IRR 9.30% Fund Multiple 1.80 Carry to GP 14.45 LP IRR 8.00% LP Multiple 1.66

54 Appendix B. How do empirical gaps compare to a simulated setting? A natural gap between reported IRR and the rate of return implied by the fund’s cash-on- cash multiple arises due to the existence of intermediate cash flows that effectively shorten the investment horizon. This gap could be due to exogenous cash flow shocks or to investment decisions by GPs. To the extent that we would expect different optimal investment and liquidation times for each holding of each fund, we would expect cash flows to be fairly random across investment and liquidation periods of the fund. In turn, we would expect the average return gap to be close to an average return gap computed using these random cash flows. To investigate this possibility, we simulate cash flows for each fund by using the fund’s cash-on-cash multiple and simulating cash flows that achieve that multiple. For each fund type (e.g., buyout or turnaround, and etc.), we estimate the median life over all funds of that type using the cash flow data. We estimate fund life as the time it takes in years for LPs to receive 95% of the cash flows from the fund. For the simulation, we assume that all LP investments occur in uniformly distributed amounts in the first half of the fund life and add up to the total contribution amount. We further assume that all distributions to LPs occur in the last half of fund life, again in random dollar amounts that add up to total distributions. For odd fund lives, we assume a zero payout in the middle year. To be clear, in the simulation we do not assume a distribution of cash flows based on the distributions we observe in our dataset as we wish to simulate what a fund’s IRR and return gap would look like without any management of cash flow timing. Figure A.1 presents a lowess plot of these results, broken down among small funds (less than $100M) in Figure A.1a, medium funds ($100-499M) in Figure A.1b, and large funds ($500M+) in Figure A.1c.23 Note that expected gaps are negative for negative IRRs because shortening the horizon over which negative returns are realized makes the IRR more negative. Figure A.1 shows that for all fund sizes, reported IRRs are close to simulated IRRs for low multiple-implied returns, and that the two quantities begin to diverge for positive multiple- implied returns. For all three fund size categories, the divergence seems largest for multiple- implied returns of roughly 20% per year. For each category, a t-test of the difference between simulated and true return gaps finds that actual return gaps are significantly larger than simulated return gaps. This suggests that cash calls occur later on average than in an assumed, random uniform distribution during the first half of the fund’s life, and/or that

23See Tetlock (2007) for details of lowess estimation.

55 itiuin cu ale hni nasmd admuiomdsrbto ntels half last the in distribution uniform life. random fund’s assumed, the an of in than earlier occur distributions for multiples data. Results cash-on-cash funds the life. because large in fund’s A.1c and smaller the Figure ($100-499M), are of in funds funds half shorter investments medium large last is $100M), the these LP axis in than horizontal all occur (less The LPs where funds ($500M+). to small multiple, payouts for all that appear and achieve fund’s half are the that ﬁrst using the by ﬂows in obtained cash are occur gaps simulating Simulated and gaps. IRR multiple actual and Simulated A.1: Figure

−.2 0 .2 .4 .6 .8 −.1 culIRrwa SimulatedIRRrawgap Actual IRRrawgap 0 a ml Funds Small (a) raw_Multiple_Return .1

−.1 0 .1 .2 .3 .4 −.1 .2 culIRrwa SimulatedIRRrawgap Actual IRRrawgap c ag Funds Large (c) 0 .3 raw_Multiple_Return 56

0 .5 1 1.5 −.1 .1 culIRrwa SimulatedIRRrawgap Actual IRRrawgap 0 b eimFunds Medium (b) .2 raw_Multiple_Return .1 .2 .3