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, larocque.1@nd.edu.†Corresponding author. Mendoza College of Business, University of Notre Dame, sshive1@nd.edu.‡Ohio University College of Business, stevenj1@ohio.edu.§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 AinTommar, Florin Vasvari, Michael Weisbach, conference participants at the Paris Dauphine 11th AnnualHedge Fund and Private Equity Conference and the Glion Annual Private Capital Conference and seminarparticipants at the University of Frankfurt, the University of Mannheim, the University of Notre Dame, OhioUniversity, and York University for helpful comments. We also thank George Jiang and Xue Li for excellentresearch 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.

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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 abilityand security selection ability are related, but unlike private equity firms, mutual fund managers must managethe entirety of investors’ capital throughout its time in the fund.

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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 isdivided by four such that duration is in years. In the subset of these funds that are liquidated, durationaverages 4.73 years with a standard deviation of 1.86 while fund life averages 12.11 years. For liquidatedfunds, 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 contributedinto the fund by the investors during the fund’s life. See, for example, Lopez-de-Silanes, Phalippou, andGottschalg (2015) and Phalippou, Rauch, and Umber (2018). Cash-on-cash multiples could be manipulatedif the fund allows for recycling of capital returned during the investment period of the fund’s life. Anyupward manipulation of this multiple would weaken our results.

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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

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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.

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,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 commit-

ments 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 in-

vestment 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 theinvestor 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

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(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 mar-

kets, 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 commit-ments. While subscription line financing’s original purpose was to render capital calls more predictable forinvestors, today, LPAs allow for subscription lines to be outstanding for 180 or even 360 days (MJ Hudson’sAlternative Insight - February 2019).

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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 com-

pensation 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 indexfund during the same time period, it does not account for the fact that the GP chooses the timing of thefund’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 capitaland 20% carried interest (i.e., share of profits) on the total return, typically after a hurdle rate of returnis achieved. Whether the private equity firm can begin collecting carried interest can be based on thefund’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 equityindustry compensation.

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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 returnreported by the fund to the return earned by the fund’s beginning-of-quarter holdings. Our measures aresimilar in name only. While their measure, which takes the reported return as the true return to investors, ispositively 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.

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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 thatportfolio companies’ net asset values tend to be higher in fundraising periods. Barber and Yasuda (2017)

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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. Figure 1 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 Table 2. 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 Table 2. 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 Table 2 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 seethrough this behavior. Easton, Larocque, and Stevens (2018) find that private equity NAVs more accuratelyrepresent 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.

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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

Table 2 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 Table 2 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. Figure 2 presents a lowess

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

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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.

Figure 3, 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 Figure 3, 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 Figure 3 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.

Figure 4 examines IRR and return gap by type of fund and by investor type. Figure 4

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

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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. Figure 4 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 fiveyears, with some follow-on investments as well as divestitures made in the final five years of a private equityfund’s life.

20In additional analysis in section 6.4, we investigate the extent to which late cash calls and/or earlydistributions are associated with return gaps.

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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 Table 3, 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 Table 3, 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 Table 3. We estimate the following equation where the unit

of observation is at the fund-level:

Gapi = α0 + α1lag3Gapi + α2lag3MultipleReturni + Controls+ εi (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 Table 3 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 Table 3 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.

Table 4 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+ εi

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

Table 2, 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 Stromberg (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+ εi (5)

In columns 1 through 3 of Table 5, 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. Table 6 estimates the following equation:

∆Sizei = α0 + α1lag3Gapi + α2lag3MultipleReturni + Controls+ εi (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 Table 6, 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 Table 6 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+ εi (7)

The results of these regressions appear in Table 6, 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 thefinal IRR that is reported for the fund. Moreover, Phalippou (2011) shows that a consistent policy of NAVinflation 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+ εi (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 Table 7. 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 Equation 8 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+ εi (9)

Results appear in Panel C of Table 7. 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 Table 8, 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 contri-

butions) 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:

ContSkew =T∑t=1

[Contt∑Tt=1Contt

· tT

](10)

DistSkew =T∑t=1

[Distt∑Tt=1 Distt

· (T − t) + 1

T

](11)

Table 9 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

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29

01

00

20

03

00

40

05

00

Nu

mb

er

of

fun

ds

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015vintage

Figure 1: Number of funds by vintage year

30

−.2

0.2

.4.6

Fu

nd

Ga

p

0 5 10 15Fund Duration

Figure 2: Fund gap and fund duration

31

0.1

.2.3

.4.5

IRR

/Ga

p

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015vintage

Mean IRR Mean Gap

(a) Latest values by vintage year

0.1

.2.3

.4.5

.6.7

.8.9

1C

orr

ela

tio

n b

etw

ee

n g

ap

an

d f

ina

l g

ap

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.1

.11

IRR

/Ga

p

3 4 5 6 7 8 9 10 11 12 13 14 15Year of fund life

Mean IRR Mean Gap

Corr(gap, final gap)

(b) By year of the fund’s life

Figure 3: Panel A presents the latest reported values of fund internal rate of return (IRR)and return gap by vintage year. For liquidated funds, these are final values. Panel B presentsreported IRR and the gap by year of fund’s life, using historical interim reports. Panel Balso reports the correlation of the gap in each non-final year with the final reported gap in2019, illustrating that gaps reported during the fund’s life are highly informative about finalgaps for liquidated funds.

32

BalancedBuyout

Co−investment

Debt

Expansion / Late Stage

Fund of Funds

Growth

Infrastructure

Mezzanine

Natural Resources

Real Estate

Secondaries

Special Situations

Turnaround

Venture/Early Stage

.06

.08

.1.1

2.1

4M

ea

n G

ap

.03 .04 .05 .06 .07Mean multiple−implied return

(a) By fund type

BankCorporate Investor

Endowment Plan

Family Office

Foundation

Fund of Funds Manager

Government Agency

Insurance Company

Investment CompanyOther

Private Equity Firm

Private Pension Fund

Public Pension Fund

Sovereign Wealth Fund

Superannuation Scheme

Wealth Manager

.05

.06

.07

.08

.09

Me

an

Ga

p

.035 .04 .045 .05 .055Mean 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-

tributions (contributions) calculated as the percentage of distributions

(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.

Preqin cash flow mod-

ule

FundLife The time elapsed from vintage year to 2017 for closed funds that are

not yet liquidated, and the time from vintage year to when 95% of cash

flows are distributed for liquidated funds.

Preqin cash flow mod-

ule

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-

plied by the fund’s multiple as in equation 3. This variable is winsorized

at the 1% level.

Preqin

ContSkew Using LP fund contribution amounts and dates, we weight the fund-year

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.

Preqin cash flow data

DistSkew Using LP fund distribution amounts and dates, we multiply each fund-

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.

Preqin cash flow data

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

the current fund.

Preqin

MIRR The fund’s modified internal rate of return, calculated using funds that

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.

Preqin

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

winsorized at the 1% level.

Preqin return data

RaiseNextFund Indicator variable for whether the private equity firm raises a future

fund.

Preqin

Repeat Investment Indicator variable for whether the fund investment by the investor is a

repeat with the same GP.

Preqin

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 Tables 3, 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 Table 1. 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 Table 1. 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

Pan

elC

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

Sm

all

Med

ium

Larg

e

VA

RIA

BL

ES

Fu

nd

sF

un

ds

Fu

nd

sV

entu

reB

uyou

tO

ther

U.S

.E

uro

pe

Oth

erC

lose

dL

iqu

idate

d

lag3G

ap

0.2

12**

0.1

25**

0.0

492

0.1

70**

0.1

19***

0.0

956**

0.1

35***

0.0

298

0.1

25**

0.0

694**

0.1

47***

(0.0

1)

(0.0

3)

(0.1

4)

(0.0

2)

(0.0

1)

(0.0

3)

(0.0

0)

(0.6

3)

(0.0

5)

(0.0

4)

(0.0

1)

lag3M

ult

iple

Ret

urn

-0.2

17

0.1

98*

0.0

248

-0.0

968

-0.1

19

0.1

12*

0.0

348

0.1

73

-0.1

82

0.0

0972

0.2

13

(0.1

1)

(0.0

9)

(0.7

4)

(0.6

4)

(0.3

3)

(0.0

9)

(0.6

9)

(0.3

1)

(0.3

4)

(0.8

9)

(0.2

0)

logF

un

dV

alu

e0.0

206

-0.0

00471

-0.0

0223

0.0

0133

-0.0

118***

-0.0

0385*

-0.0

0542**

-0.0

0968**

-0.0

0864

-0.0

0461**

-0.0

0541

(0.1

6)

(0.9

4)

(0.4

7)

(0.8

7)

(0.0

0)

(0.0

8)

(0.0

2)

(0.0

2)

(0.2

9)

(0.0

3)

(0.1

4)

Ob

serv

ati

on

s459

1,3

74

1,3

44

405

836

1,9

36

2,3

55

580

242

2,3

39

838

R-s

qu

are

d0.3

18

0.2

35

0.1

43

0.4

66

0.2

15

0.1

33

0.1

94

0.2

64

0.3

89

0.0

71

0.2

53

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

S

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

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

Pan

elE

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

Sm

all

Med

ium

Larg

e

VA

RIA

BL

ES

Fu

nd

sF

un

ds

Fu

nd

sV

entu

reB

uyou

tO

ther

US

Eu

rop

eO

ther

Clo

sed

Liq

uid

ate

d

lag3M

IRR

gap

0.4

10**

0.2

14***

0.0

575

0.1

31**

0.2

02***

0.1

37***

0.1

37***

0.1

76

-0.1

68

0.1

01**

0.2

49***

(0.0

4)

(0.0

0)

(0.1

6)

(0.0

1)

(0.0

0)

(0.0

0)

(0.0

0)

(0.1

3)

(0.2

6)

(0.0

1)

(0.0

1)

logF

un

dV

alu

e0.0

352

0.0

145*

0.0

00356

0.0

139*

-0.0

00493

-0.0

0157

-0.0

00561

0.0

0147

0.0

171

-0.0

0169

0.0

154

(0.1

7)

(0.1

0)

(0.9

5)

(0.1

0)

(0.9

1)

(0.5

9)

(0.8

2)

(0.7

5)

(0.3

0)

(0.5

9)

(0.1

2)

Ob

serv

ati

on

s70

581

924

266

466

843

1,3

35

174

66

1,3

27

248

R-s

qu

are

d0.5

69

0.2

18

0.1

06

0.3

21

0.2

42

0.1

37

0.1

29

0.3

51

0.3

37

0.0

73

0.2

88

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

S

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

41

Tab

le4:

Isa

fund’s

gap

rela

ted

toth

eG

P’s

futu

rep

erfo

rman

ce?

This

table

pre

sents

the

resu

lts

ofre

gres

sion

sof

Multiple

return

onth

ere

turn

gap

and

the

mult

iple

-im

plied

retu

rn

for

the

late

stfu

nd

that

was

rais

edat

leas

tth

ree

year

spri

orto

the

curr

ent

fund

by

the

sam

ege

ner

alpar

tner

(lag3G

apan

dlag3MultipleReturn

),an

dfu

nd

size

(logFundV

alue).

Reg

ress

ions

incl

ude

vin

tage

year

and

fund

typ

e

fixed

effec

ts.

Var

iable

defi

nit

ions

app

ear

inT

able

1.Sta

ndar

der

rors

are

dou

ble

-clu

ster

edby

vin

tage

year

and

by

pri

vate

equit

yfirm

.T

her

ear

e24

fund

typ

ean

d42

vin

tage

year

fixed

effec

ts.

Pan

elA

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Fu

llF

ull

Fu

llF

ull

Fu

llL

ag3

IRR

0>

Lag3

IRR

Lag3

IRR

VA

RIA

BL

ES

Sam

ple

Sam

ple

Sam

ple

Sam

ple

Sam

ple

>0

<0.0

8>

0.0

8

lag3IR

R0.0

253***

(0.0

1)

lag3G

ap

0.0

126

-0.0

542***

-0.0

503***

-0.0

550***

7.9

3e-

05

-0.0

556***

(0.2

6)

(0.0

0)

(0.0

0)

(0.0

0)

(1.0

0)

(0.0

0)

lag3M

ult

iple

Ret

urn

0.1

82***

0.2

65***

0.2

58***

0.2

40***

0.3

43***

0.2

08***

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

1)

(0.0

0)

logF

un

dV

alu

e-0

.00236***

-0.0

0290***

-0.0

0173

-0.0

0349***

(0.0

0)

(0.0

0)

(0.2

1)

(0.0

0)

Ob

serv

ati

on

s3,8

67

3,8

67

3,8

67

3,8

67

3,8

67

3,5

28

792

2,7

36

R-s

qu

are

d0.1

48

0.1

43

0.1

70

0.1

79

0.1

81

0.1

77

0.1

71

0.1

88

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

S

42

Pan

elB

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

Sm

all

Med

ium

Larg

e

VA

RIA

BL

ES

Fu

nd

sF

un

ds

Fu

nd

sV

entu

reB

uyou

tO

ther

US

Eu

rop

eO

ther

Clo

sed

Liq

uid

ate

d

lag3G

ap

-0.0

423

-0.0

507**

-0.0

380***

-0.0

474***

-0.0

106

-0.0

409***

-0.0

536***

-0.0

623***

0.0

0215

-0.0

319***

-0.0

483**

(0.2

2)

(0.0

2)

(0.0

0)

(0.0

1)

(0.5

4)

(0.0

0)

(0.0

0)

(0.0

0)

(0.9

6)

(0.0

1)

(0.0

1)

lag3M

ult

iple

Ret

urn

0.3

60***

0.2

40***

0.1

61***

0.2

87***

0.1

47***

0.2

28***

0.2

67***

0.2

43***

0.1

24

0.1

85***

0.3

22***

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

1)

(0.0

0)

(0.0

0)

(0.0

0)

(0.3

2)

(0.0

0)

(0.0

0)

logF

un

dV

alu

e0.0

0824**

-0.0

00858

0.0

00600

0.0

0780***

-0.0

0216

-0.0

0383***

-0.0

0155*

-0.0

0361**

-0.0

0605***

-0.0

0108

-0.0

0443**

(0.0

4)

(0.7

3)

(0.6

4)

(0.0

0)

(0.1

4)

(0.0

0)

(0.0

6)

(0.0

2)

(0.0

1)

(0.1

7)

(0.0

3)

Ob

serv

ati

on

s564

1,7

11

1,5

92

616

959

2,2

92

2,9

03

667

297

2,8

19

1,0

48

R-s

qu

are

d0.2

64

0.1

96

0.1

97

0.3

77

0.1

66

0.1

76

0.1

96

0.2

48

0.1

85

0.1

83

0.2

55

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

S

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

43

Tab

le5:

Do

hig

her

retu

rnga

ps

hel

pth

epri

vate

equit

yfirm

rais

ea

subse

quen

tfu

nd?

This

table

pre

sents

Pro

bit

regr

essi

ons

ofan

indic

ator

for

rais

ing

asu

bse

quen

tfu

nd

onth

ere

turn

gap

and

the

mult

iple

-im

plied

retu

rnan

dfu

nd

size

.V

aria

ble

defi

nit

ions

app

ear

inT

able

1.Sta

ndar

der

rors

are

clust

ered

by

vin

tage

year

.T

her

ear

e24

fund

typ

ean

d42

vin

tage

year

fixed

effec

ts.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Fu

llF

ull

Fu

llF

ull

Fu

llIR

R0<

IRR

IRR

VA

RIA

BL

ES

Sam

ple

Sam

ple

Sam

ple

Sam

ple

Sam

ple

>0

<0.

08>

0.0

8

IRR

1.71

5***

(0.0

0)

Gap

1.86

1***

0.48

1*0.

582*

*0.

495*

1.02

2-0

.216

(0.0

0)(0

.06)

(0.0

2)(0

.07)

(0.3

9)(0

.41)

Mu

ltip

leR

etu

rn4.

982*

**4.

444*

**4.

819*

**3.

498*

**2.

747

2.079***

(0.0

0)(0

.00)

(0.0

0)(0

.00)

(0.2

2)(0

.01)

logF

un

dV

alu

e0.

178*

**0.

174*

**0.

169*

**0.

174***

(0.0

0)(0

.00)

(0.0

0)(0

.00)

Ob

serv

atio

ns

6,94

56,

945

6,94

56,

945

6,94

56,

013

1,69

34,3

20

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

S

Pse

ud

oR

-squ

ared

0.09

190.

0824

0.09

770.

0983

0.11

80.

101

0.11

00.1

08

44

Tab

le6:

Are

retu

rnga

ps

rela

ted

toth

esi

zeof

the

pri

vate

equit

yfirm

’ssu

bse

quen

tfu

nd?

This

table

pre

sents

regr

essi

ons

ofth

ep

erce

nta

gech

ange

insi

zeof

the

curr

ent

fund

from

the

mos

tre

cent

earl

ier

fund

by

the

sam

ege

ner

alpar

tner

(chsize)

onth

ere

turn

gap

and

the

mult

iple

-im

plied

retu

rnfo

rth

ela

test

fund

that

was

rais

edat

leas

tth

ree

year

spri

orto

the

curr

ent

fund

by

the

sam

ege

ner

alpar

tner

(lag3G

apan

d

lag3MultipleReturn

)an

dfu

nd

size

(logFundV

alue).

The

dep

enden

tva

riab

leis

win

sori

zed

atth

e1%

leve

l.V

aria

ble

defi

nit

ions

app

ear

inT

able

1.Sta

ndar

der

rors

are

dou

ble

-clu

ster

edby

vin

tage

year

and

by

pri

vate

equit

yfirm

.

Ther

ear

e24

fund

typ

ean

d42

vin

tage

year

fixed

effec

ts.

Pan

elA

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Fu

llF

ull

Fu

llF

ull

Fu

llL

ag3

IRR

0>

Lag

3IR

RL

ag3

IRR

VA

RIA

BL

ES

Sam

ple

Sam

ple

Sam

ple

Sam

ple

Sam

ple

>0

<0.

08>

0.0

8

lag3

IRR

3.14

4***

(0.0

0)

lag3

Gap

4.01

1***

3.57

8***

4.06

9***

4.33

2***

1.28

94.5

96***

(0.0

0)(0

.00)

(0.0

0)(0

.00)

(0.7

6)(0

.00)

lag3

Mu

ltip

leR

etu

rn7.

170*

**1.

715

-2.0

93-1

.636

2.00

9-2

.450

(0.0

0)(0

.27)

(0.1

3)(0

.33)

(0.7

8)(0

.26)

lag3

logF

un

dV

alu

e-0

.890

***

-0.8

81**

*-0

.924

***

-0.8

79***

(0.0

0)(0

.00)

(0.0

0)(0

.00)

Ob

serv

atio

ns

3,86

73,

867

3,86

73,

867

3,86

73,

528

792

2,7

36

R-s

qu

ared

0.09

60.

096

0.08

50.

096

0.21

10.

212

0.22

20.2

11

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

S

45

Pan

elB

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

Sm

all

Med

ium

Larg

e

VA

RIA

BL

ES

Fu

nd

sF

un

ds

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nd

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entu

reB

uyou

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ther

US

Eu

rop

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ther

Clo

sed

Liq

uid

ate

d

lag3G

ap

0.5

57

1.2

37**

4.0

40***

1.0

08

4.3

11***

5.3

70***

3.6

59***

5.3

58**

4.5

20*

4.0

24***

3.6

69***

(0.1

9)

(0.0

4)

(0.0

0)

(0.2

3)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

1)

(0.0

8)

(0.0

0)

(0.0

0)

lag3M

ult

iple

Ret

urn

0.0

877

0.2

09

-4.5

88*

1.4

17

-3.1

40

-3.0

13*

-1.5

36

-3.7

42

-2.1

91

-2.5

10

-1.1

18

(0.9

1)

(0.8

8)

(0.0

6)

(0.4

7)

(0.3

4)

(0.0

9)

(0.3

3)

(0.1

7)

(0.6

7)

(0.1

8)

(0.6

9)

lag3lo

gF

un

dV

alu

e-0

.767***

-1.6

28***

-2.2

15***

-0.9

17***

-0.7

51***

-0.9

55***

-0.9

19***

-0.7

24***

-0.9

31***

-0.9

00***

-0.9

92***

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

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0)

Ob

serv

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on

s564

1,7

11

1,5

92

616

959

2,2

92

2,9

03

667

297

2,8

19

1,0

48

R-s

qu

are

d0.5

74

0.5

38

0.4

17

0.3

59

0.1

74

0.2

29

0.2

21

0.2

29

0.3

40

0.2

31

0.2

40

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

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ES

YE

SY

ES

YE

SY

ES

YE

S

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

YE

SY

ES

46

Pan

elC

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Fu

llF

ull

Fu

llF

ull

Fu

llL

ag3

IRR

0>

Lag3

IRR

Lag3

IRR

VA

RIA

BL

ES

Sam

ple

Sam

ple

Sam

ple

Sam

ple

Sam

ple

>0

<0.0

8>

0.0

8

lag3M

IRR

gap

1.9

04***

1.5

27**

1.6

23**

1.8

50**

0.5

45

1.9

85*

(0.0

0)

(0.0

4)

(0.0

1)

(0.0

3)

(0.8

4)

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8)

lag3M

IRR

4.4

43***

4.4

43***

1.9

62

2.5

33

1.3

28

4.8

87

-1.5

37

(0.0

1)

(0.0

1)

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4)

(0.1

3)

(0.5

6)

(0.3

0)

(0.6

1)

lag3lo

gF

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alu

e-0

.976***

-0.9

30***

-0.9

86***

-0.9

31***

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

Ob

serv

ati

on

s2,0

45

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45

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45

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45

2,0

45

1,8

42

464

1,3

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d0.0

83

0.0

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0.0

86

0.2

14

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05

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31

0.2

08

Vin

tage

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Fu

nd

Typ

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ES

YE

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47

Pan

elD

(1)

(2)

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(5)

(6)

(7)

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(9)

(10)

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all

Med

ium

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e

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nd

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idate

d

lag3M

IRR

gap

1.8

15**

-1.1

14*

2.8

27***

-0.0

749

6.3

01***

-0.1

32

1.5

94**

3.4

94

1.7

27

1.3

65*

1.6

18

(0.0

3)

(0.0

8)

(0.0

0)

(0.9

6)

(0.0

0)

(0.9

0)

(0.0

3)

(0.1

1)

(0.7

1)

(0.1

0)

(0.1

3)

lag3M

IRR

-2.3

04

1.0

42

-2.2

84

1.5

75

-2.0

62

4.8

14*

2.4

64

-2.8

64

8.2

09

2.9

26

-1.0

86

(0.2

6)

(0.4

1)

(0.3

1)

(0.6

1)

(0.6

2)

(0.0

7)

(0.1

2)

(0.4

1)

(0.2

5)

(0.1

6)

(0.8

0)

lag3lo

gF

un

dV

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e-0

.612***

-1.3

64***

-1.7

83***

-1.2

83***

-0.9

20***

-0.9

72***

-1.0

06***

-0.7

34***

-1.3

04***

-0.9

59***

-1.2

81***

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

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0)

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0)

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serv

ati

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83

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236

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qu

are

d0.5

90

0.4

87

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58

0.3

51

0.1

78

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20

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75

0.4

21

0.2

19

0.3

30

Vin

tage

FE

YE

SY

ES

YE

SY

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YE

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ES

YE

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Fu

nd

Typ

eF

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YE

SY

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SY

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YE

SY

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YE

SY

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48

Tab

le7:

Det

erm

inan

tsof

inve

stor

s’re

pea

tin

vest

men

tsw

ith

the

sam

epri

vate

equit

yfirm

This

table

pre

sents

the

resu

lts

ofP

robit

regr

essi

ons

ofth

elike

lihood

that

apri

vate

equit

yin

vest

orw

ill

inve

st

wit

hth

eP

Efirm

agai

nin

the

futu

re.

The

dep

enden

tva

riab

le,Reinvest

,is

anin

dic

ator

vari

able

for

whet

her

a

give

nin

vest

orj

inpri

vate

equit

yfu

ndi

inve

sts

ina

subse

quen

tfu

nd

wit

hth

esa

me

GP

atle

ast

3ye

ars

afte

rth

e

vin

tage

ofth

ecu

rren

tfu

nd.

Thus,

the

unit

ofob

serv

atio

nis

atth

eL

P-f

und

leve

l.In

Pan

els

Aan

dB

,in

vest

ors

are

div

ided

by

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gory

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elC

,sk

ille

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vest

ors

are

thos

ew

hic

h,

thro

ugh

out

our

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ple

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efu

nd

inve

stm

ents

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ian

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ben

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ark,

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ian

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iple

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eth

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tim

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fund

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effec

ts.V

aria

ble

defi

nit

ions

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ear

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able

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rors

are

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ble

-clu

ster

edby

vin

tage

year

and

by

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vate

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yfirm

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ES

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dow

men

tP

lan

Fou

nd

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on

Fu

nd

of

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nd

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ran

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om

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vate

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sion

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nd

Pu

bli

cP

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on

Fu

nd

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59

0.5

59

1.1

36***

0.4

63

0.4

88*

(0.0

3)

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4)

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8)

(0.0

0)

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9)

(0.0

6)

Mu

ltip

leR

etu

rn2.1

99***

3.2

71***

4.4

38***

3.9

76***

4.0

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97***

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

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0)

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0)

logF

un

dV

alu

e0.0

324

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0764

0.0

521

0.0

610**

0.0

783***

0.1

83***

(0.3

2)

(0.7

6)

(0.2

1)

(0.0

3)

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0)

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0)

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serv

ati

on

s5,6

87

8,6

89

7,9

07

6,0

65

13,2

56

20,1

13

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

S

Pse

ud

oR

-squ

are

d0.1

06

0.0

951

0.1

40

0.0

839

0.1

05

0.0

836

49

Pan

elB

(1)

(2)

(3)

(4)

(5)

(6)

VA

RIA

BL

ES

En

dow

men

tP

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nd

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on

Fu

nd

of

Fu

nd

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ceC

om

pany

Pri

vate

Pen

sion

Fu

nd

Pu

bli

cP

ensi

on

Fu

nd

MIR

Rgap

0.9

67**

0.5

00

0.5

38

1.1

46***

0.8

84***

0.7

11***

(0.0

2)

(0.1

8)

(0.2

7)

(0.0

0)

(0.0

0)

(0.0

1)

MIR

R2.9

27**

3.4

00***

4.9

55***

5.8

20***

4.5

43***

6.4

24***

(0.0

2)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

(0.0

0)

logF

un

dV

alu

e-0

.0257

0.0

0237

0.0

659

0.0

791***

0.0

803***

0.1

75***

(0.5

0)

(0.9

4)

(0.1

5)

(0.0

0)

(0.0

0)

(0.0

0)

Ob

serv

ati

on

s4,1

89

6,1

98

6,0

59

4,3

09

10,0

18

16,0

82

Vin

tage

FE

YE

SY

ES

YE

SY

ES

YE

SY

ES

Fu

nd

Typ

eF

EY

ES

YE

SY

ES

YE

SY

ES

YE

S

Pse

ud

oR

-squ

are

d0.0

937

0.0

957

0.1

43

0.0

860

0.1

11

0.0

862

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 Table 1. 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 thelateness of cash calls and the earliness of exits of the fund. Variable definitions appear inTable 1. 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

−.2

0.2

.4.6

.8

−.1 0 .1 .2 .3raw_Multiple_Return

Actual IRR rawgap Simulated IRR rawgap

(a) Small Funds

0.5

11.5

−.1 0 .1 .2 .3raw_Multiple_Return

Actual IRR rawgap Simulated IRR rawgap

(b) Medium Funds

−.1

0.1

.2.3

.4

−.1 0 .1 .2raw_Multiple_Return

Actual IRR rawgap Simulated IRR rawgap

(c) Large Funds

Figure A.1: Simulated and actual IRR gaps. Simulated gaps are obtained by using the fund’smultiple and simulating cash flows that achieve that multiple, where all LP investmentsoccur in the first half and all payouts to LPs occur in the last half of the fund’s life. Resultsare appear for small funds (less than $100M), medium funds ($100-499M), and large funds($500M+). The horizontal axis is shorter in Figure A.1c because cash-on-cash multiples forthese large funds are smaller in the data.

distributions occur earlier than in an assumed, random uniform distribution in the last half

of the fund’s life.

56