Private Equity and Liquidity Risk

Private Equity and Liquidity Risk May 2009 Using a comprehensive dataset containing the cash flows of 3,522 liquidated private equity investments that...
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Private Equity and Liquidity Risk May 2009 Using a comprehensive dataset containing the cash flows of 3,522 liquidated private equity investments that spans a time frame ending before the recent financial crisis (1984-2004), we find positive and significant loadings of investment returns on aggregate liquidity innovation measures and liquidity risk factors. The quintile of investments that went through times of largest innovations in liquidity outperform the opposite quintile by a staggering 15% per year. Similarly sizeable, the premium for liquidity risk of private equity ranges from 5% and 12% per year, depending on sub-samples and proxies. Adjusting performance for liquidity risk, the NPV of (gross-of-fees) private equity investments decreases dramatically and gets close to zero. We also find that larger investments have higher exposure to liquidity risk. These results are robust to various changes in the empirical design. Our study has important implications for the performance evaluation of private equity investments. They also indicate that both the increased allocation to private equity and the increased size of private equity investments may lengthen liquidity-based financial crises. They also suggest that capital requirements for banks investing in private equity may be too low.

JEL Classification: G24, G12 Keywords: Private equity, liquidity risk, financial crisis

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1. Introduction From 2003 to mid-2007, two phenomena grew in parallel in financial markets. Liquidity surged to record highs and private equity firms distributed increasingly large amounts of cash to their investors. These investors in turn were re-investing the cash in newly raised private equity funds and much new money was flowing to the private equity industry. Mid-2007, the music stopped. Liquidity suddenly dried up and private equity firms hardly distributed any cash to their investors thereafter. Figure 1 illustrates this phenomenon by plotting the monthly cash distribution of private equity investments in our data set and the Ted spread1, a commonly accepted measure of liquidity. Strikingly, the run-up and subsequent fall in private-equity pay-outs goes hand in hand with the dramatic drying up of liquidity in the financial system at large. This episode suggests that private equity investors may receive higher returns in times of higher liquidity. In light of the recent literature on the pricing of liquidity risk, this fact, if confirmed on a large dataset, would have important consequences for the evaluation of private equity performance and the valuation of private equity investments. In addition, this would suggest that the increased allocation to private equity may lengthen financial crises. As the recent global financial crisis illustrates, liquidity (or lack thereof) is often a major driver of financial crises (see Brunnermeier, 2009, for an overview). If private equity investors have particularly large losses during times of low liquidity, these losses will materialize at a slow pace for a prolonged period of time. This, in turn, can maintain financial markets under stress for longer than they would otherwise. Pastor and Stambaugh (2003), Acharya and Pedersen (2005), and Liu (2006), among others, show that (systematic) liquidity risk is priced for public equity and that investors require a sizeable liquidity risk premium for stocks. In private equity, the effect may be even more dramatic, because divestments appear to cluster at times of high IPO and M&A activities, both of which are related to market liquidity (see Cumming, Fleming and Schwienbacher, 2005). That private equity returns may need a sizeable adjustment because of a large exposure to liquidity risk is also highlighted by Metrick (2007). Using an index of venture 1

The Ted spread is defined as the three-month LIBOR rate minus the Fed Funds rate.

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capital returns and a time-series regression, he estimates a 1% annual premium for liquidity risk. The objective of this paper is to see whether the anecdotal evidence mentioned in the first paragraph above and Metrick’s result hold in a comprehensive dataset of pre-crisis private equity investment returns. In addition, the unique depth of our dataset enables us to document which type of investments are most sensitive to liquidity risk. Finally, our data enable us to further document the issue of private equity performance. Previous research finds that private equity buyout funds underperform public equity after fees (Kaplan and Schoar, 2005; Phalippou and Gottschalg, 2009), but the quality of the data has been sometimes questioned. Here, we report before-fees evidence from a different, audited, and extensive dataset.

Our dataset contains detailed cash-flow information for 3,522 liquidated private equity investments made between 1984 and 2004 in 32 countries.2 Data are anonymous but we have information on investment characteristics (industry, stage, and country), fund characteristics (size and sequence number) and firm characteristics (age and capital under management). We convert all cash flows to US dollars and compute an IRR for each investment. Unlike for traditional asset classes, we do not observe a monthly return. We thus design a new and simple approach. To assess whether high liquidity corresponds to high returns, we regress an investment’s IRR on the average liquidity measure (or risk factor) during the investment’s lifetime. For simplicity, the average is equally-weighted by default. We also show results when the average is value-weighted by an estimate of the investment market value each month. We first show that investment performance is significantly related to the average innovation in aggregate liquidity during the investment’s lifetime. Results are shown for all liquidity measures that are available for our sample period (Pastor and Stambaugh, 2003; Acharya and Pedersen, 2005; and Sadka, 2006). We also show quintile portfolios. 2

We focus on liquidated investments because their performance is not subject to any accounting smoothing. Starting and ending dates are chosen so that all liquidity measures are available for our time period.

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Investments falling in the quintile that went through the largest innovations in liquidity have an average IRR around 40% while the opposite quintile shows an average IRR around 25% (except for Pastor and Stambaugh measure, where it is 6%). The spread varies across liquidity measures (maximum of 34% with Pastor-Stambaugh and minimum of 12% with Acharya-Pedersen) but the spread is statistically significant for each measure. Our second result is a quantification of the liquidity risk premium of private equity investments. To this purpose, we use two asset pricing models with liquidity risk proposed in the literature: the four factor model of Pastor and Stambaugh (2003) and the two-factor model of Liu (2006). The IRR of each investment is regressed on the average risk factors during the investment’s lifetime. The premium varies somewhat as a function of the weighting of the factors and the performance measure that we use. The four-factor model of Pastor and Stambaugh (2003) shows a premium between 5% and 9%, while the twofactor model of Liu (2006) shows a premium between 10% and 12%. Our third result is that investment size is a positive and significant determinant of exposure to liquidity risk. We conjecture that larger investments are more sensitive to exit conditions than smaller investments and thus, via this channel, are more exposed to liquidity risk. Bekaert, Harvey, and Lundblad (2005) argue that liquidity is in large part locally priced. Consistent with this assertion, we find that the effect of US-based liquidity measures are magnified on the sub-set of US investments. Further, we document more generally the performance and risk profile of private equity investments. The average IRR of our liquidated investments is 25%. Using a modified IRR decreases average performance substantially to 11% (if 8% re-investment rate) and 16% (if S&P 500 re-investment rate). These performance figures are gross-offees and the sample is expected to be titled towards winners. Hence, performance appear rather low even without risk correction. In the four-factor model of Pastor-Stambaugh, we find that the market beta is 1.8. There is a positive and significant loading on the value premium, indicating that private equity investments resemble value stocks. There is no loading on the size premium. If we adjust for risk, we find abnormal performance to be close to zero; again, gross-of-fees.

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Our results are robust along a number of dimensions. First, they are robust to the use of different liquidity measures. The different liquidity measures proposed in the literature are weakly correlated because they capture different aspects of liquidity (Korajczyk and Sadka, 2008). Yet, we find that they all lead to significant results. Second, they are robust to adding control variables. Gompers and Lerner (2000) and Ljungqvist, Richardson, and Wolfenzon (2007) show that an important determinant of performance in private equity is the competitive environment at the time investments are started. That is, the level of the supply and demand of private equity capital. We thus add (investment-)year fixed effects and observe that results are similar. Next, we add default spread, as it is a commonly used variable to capture business cycles, which may be in turn related to liquidity. This control does not affect our results. Next, we add overall volatility as proxied by the VIX index.3 This leaves results unaffected for the two liquidity risk models. For the results with innovation in liquidity, results are unaffected for the two Sadka measures. However, neither VIX nor the innovation in liquidity is significant when we use Pastor-Stambaugh and Acharya-Pedersen. Hence, some of our results may be due to volatility risk. As pointed out by Bandi, Moise and Russell (2008), it is difficult to distinguish between aggregate volatility and liquidity, because they are highly correlated. Furthermore, the ultimate drivers of volatility and liquidity may very well coincide. Third, our results are robust to different performance measures and weighting choices for liquidity risk factors. The existence of intermediary cash flows means that performance is sensitive to the opportunity cost of capital for both intermediary distributions and intermediary investments. It also means that the market values of portfolio companies vary over time as a function of the timing and amount of the intermediary cash flows. To gauge the sensitivity of our results along this dimension we carry out two robustness tests: (i) we use different performance measures corresponding to different re-investment assumptions (Modified IRR); and (ii) we value-weight (instead of equally-weight; our default choice) the time series of risk factors and aggregate liquidity innovations. We find that our results are stable across these alternative measures. 3

The VIX Volatility Index (VIX) introduced by the Chicago Board Options Exchange (CBOE) in 1993 is a measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices. For a detailed description see http://www.cboe.com/micro/vix/introduction.aspx.

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Our study has important implications for the performance evaluation of private equity investments. A sizeable liquidity risk premium means that abnormal performance should be adjusted downwards compared to previous research (e.g. Driessen, Lin and Phalippou, 2009). Furthermore, as mentioned above, recent financial crises appear to be accompanied by liquidity problems. Hence, the increased allocation to private equity and, in addition, the increased size of private equity investments, means that in times of liquidity crisis, private equity investments are expected to return lower returns than previously anticipated. That, in turn, may lengthen financial crises. Related to this issue is the question of the regulatory capital requirements for banks. There has been an ongoing debate with Basel II and the European capital requirements directive on how much provision banks should have for private equity investments (see Bongaerts and Charlier, 2008). The exposure of private equity to liquidity risk has been neglected in previous policy pieces. Our results are thus suggestive that capital requirements for banks investing into private equity may be too low.

Our study is related to that of Cumming, Fleming and Schwienbacher (2005). They show that venture capitalists invest in different types of companies as a function of market liquidity, which they proxy by the number of IPOs per year. They conclude that their results are “consistent with the view that illiquidity is one reason why venture capitalists require higher returns on their investments.” Sadka (2008) studies the relation between liquidity risk and the return of hedge funds between 1994 and 2007. Consistent with our results, he finds that hedge fund returns are related to aggregate liquidity shocks. Our paper relates to two important strands of literature. First, we connect to the literature on the pricing of liquidity risk.4 A number of papers provide theoretical arguments as to why investors want to be compensated for liquidity risk (e.g. Holmstrom and Tirole, 2001, Acharya and Pedersen, 2005, Lustig, 2009, Chordia, Huh and Subrahmanyam, 2009). The empirical literature was pioneered by Amihud and Mendelson 4

See Amihud, Mendelson, and Pedersen (2005) for a survey.

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(1986) and more recent work emphasizes the importance of systematic liquidity risk in public equity returns (e.g. Amihud, 2002, Pastor and Stambaugh, 2003, Acharya and Pedersen, 2005, Sadka, 2006). Our results extend the evidence of significant liquidity risk to private equity. Along with the contemporaneous work of Sadka (2008), we show that returns to alternative asset classes like private equity or hedge funds are affected by similar factors as stocks. These results indicate that alternative assets may have less diversification benefits than previously assumed. Second, we relate to the literature on risk and return of private equity investments (e.g. Cochrane, 2005, Cumming, Schmidt and Walz, 2009, Kaplan and Schoar, 2005, Phalippou and Gottschalg, 2009, Driessen, Lin and Phalippou, 2008, Lerner, Schoar and Wongsunwai, 2007, Jones and Rhodes Kropf, 2003, Ljungqvist, Richardson and Wolfenzon, 2007, Hochberg, Ljungqvist and Vissing-Jorgensen, 2008). We show that liquidity risk makes up for a sizeable component of private equity returns. Investors should take that into account when computing abnormal performance. This paper is organized as follows. Section 2 describes the private equity data. Section 3 describes the liquidity measures. Section 4 discusses the methodology. Section 5 shows the main empirical results. Section 6 offers robustness tests and section 7 concludes.

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2. Data 2.1. Data source and comparable datasets The dataset is provided by the Center for Private Equity Research (CEPRES), a private consulting firm established in 2001 as a co-operation between the University of Frankfurt and Sal. Oppenheim Banking Group. CEPRES obtains data from private equity firms in exchange for free exclusive access to information services. Participating firms have to disclose the performance of all their investments, including poor ones. We provide further information on the CEPRES database in Appendix 1. The unique aspect of the dataset is that it contains monthly cash flows for each investment. Such a feature is important because it enables us to construct precise duration measures and performance measures (both IRRs and Modified IRRs). It is also allows us to value weight risk factors and liquidity innovations as a function of the timing of the intermediary cash flows, as we explain below. An earlier version of this database covering mainly venture capital is used by Cumming and Walz (2004) and Cumming, Schmidt and Walz (2009). This paper uses the private equity part of the database. The only other database that we know of that contains cash flows at the investment level is the one used by Ljungqvist, Richardson and Wolfenzon (2008). However, these authors aggregate their data at the fund level and analyze the resulting fund cash flow profiles. Hence, their paper studies fund-level cash flows. Another database with fundlevel cash flow is provided by Thomson Venture Economics.5 Having cash flow information at the investment level rather than at the fund level allows us to (i) show novel descriptive statistics, (ii) gives us more power to detect a relation between performance and liquidity, and (iii) to study the interaction between investment characteristics and liquidity exposure.6

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It has been used by Kaplan and Schoar (2005), Phalippou and Gottschalg (2009), Jones and Rhodes-Kropf (2003) and Driessen, Lin and Phalippou (2008). 6 Another dataset with investment-level performance is that of Lopez-de-Silanes, Phalippou and Gottschalg (2009). The dataset comes from hand-collected private placement memoranda; which provide only cash multiples and IRRs but not cash flow details.

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2.2. Sample selection Table 1 shows how we select our sample. We report the number of observations and overall performance after each step. The only variable that we have for all the investments is cash multiple in local currency. Cash multiple is defined as the total amount distributed divided by the total amount invested. We do not have investment size for nonliquidated investment, thus we display only median cash multiples. CEPRES defines private equity investments as including the following categories: Acquisition financing, Leveraged Buy-Outs (LBO), Management Buy-Outs and Buy-Ins (MBO/MBI), Growth, Recapitalisation, Spin off, and Turnaround. We count 6,620 such investments undertaken between 1975 until 2007. Next, we restrict our sample to investments made between 1984 and 2004 because the liquidity variables of Sadka start in mid-1983 and those of Pastor and Stambaugh end in December 2004. We count 5,780 investments between these two dates. Their performance is higher. Median cash multiple increases from 1.56 to 1.66. This occurs mainly because recent investments are held at cost (i.e. the multiple is set to one) and get eliminated at this stage. Next, we select investments that are liquidated. We do this because: (i) these investments’ performance is final (thus not influenced by subjective accounting valuations); (ii) we have cash flow information only for liquidated investments. The sample size decreases to 3,705. The median cash multiple increases from 1.66 to 1.92. This fact occurs because funds liquidate their winners more quickly (see Phalippou, 2009). Finally, we require data on IRR. We count 351 IRR calculations that do not converge. Out of these, 342 have a multiple below 25%; for these, we set their IRR to (199%)^(1/duration). The remaining non-converging have a multiple above 25%; these are reported as missing IRRs. In addition, 167 have no liquidation date. These are mostly bankrupt investments.7 For them, we also set IRR to missing. Our final sample consists of 3,522 observations, with a median cash multiple of 2.05. [Insert Table 1 about here] 7

Ljungqvist, Richardson and Wolfenzon (2008) also report that the date at which investments are officially written off is typically missing in their dataset.

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2.3. Performance Measures Our main performance measure is the Internal Rate of Return (IRR). We compute it on the cash flows (converted into US dollars). The main issue with IRR is that of the re-investment assumption. This means that, if so measured, both the average performance and the dispersion of performance are exaggerated (Phalippou, 2009). Also, the constant in cross sectional regressions of IRR on risk factors cannot be interpreted as an alpha. However, and importantly, our regression analysis aims at estimating the loadings on systematic risk variables. We have no a priori reason to believe these estimates to be biased. Furthermore, the sensitivity of the results to the choice of IRR as dependent variable is gauged using Modified IRR with either a constant 8% re-investment rate or the S&P 500 as the re-investment rate. We label them MIRR (8%) and MIRR (S&P), respectively.8 In Table 2, the mean IRR is around 25% while the mean Modified IRR is at 11% (8% re-investment rate) and 16% (S&P 500 re-investment rate). This shows that only changing the re-investment assumption brings private equity performance close to public equity market returns, gross-of-fees. Phalippou (2009) estimates fees to be in the range of 6-8% for an investment whose performance matches that of the S&P 500 (14% annual over our time period). Net-of-fees, performance thus seems to be rather low. We observe fat tails for all the performance measures. For this reason, from here on, we winsorize all of them at the 5th and 95th percentile. Table 2 shows the correlation between and distribution of the four performance measures. The correlation is very high which indicates that cross-sectional results will not be significantly affected by the re-investment assumption. [Insert Table 2 about here]

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In a similar context, Ljungqvist et al. (2008) use a Modified IRR with 0% re-investment rate. We will use an 8% re-investment rate and the S&P 500 as a re-investment rate in the robustness section.

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2.4.Descriptive statistics Table 3 shows the descriptive statistics of our working sample of private equity investments. Investment size is expressed in year 2000 US dollars and is used to value weight performance (VW). To account for the fact that better performing investment have lower duration, we also construct a duration-times-value-weighted (DVW) mean. Duration is measured from the first to the last cash flow. We show statistics for cash multiple (total amount distributed divided by total amount invested), Internal Rate of Return (IRR) and Modified IRR with either a flat 8% or S&P 500 index as re-investment rate. We break down the statistics by year (Panel A), industry (Panel B), investment stage (Panel C), exit type (Panel D), and country (Panel E). Panel A shows that the number of liquidated investments starts slowly and then takes off rapidly in the second half of the 1980s peaking to 343 investments in 1997. Median size of investment is almost monotonically increasing throughout most of the sample period. The worst year in terms of performance has been 2000. Since then on performance has increased again to levels experienced in the 1990ies. Panel

B

shows

statistics

by

industry.

Most

investments

are

in

industrial/manufacturing (635 investments) and consumer/food (359), the traditional private equity industries. A large number of investments are also reported for less traditional industries like healthcare (307) and other services (305). The best-performing investments have been made in the Semiconductor industry (median IRR 63%), followed by Business Services (41%) and Logistics (37%). The worst investments by performance have been made in the internet sector (-65%) and the environmental industry (-71%). Panel C shows that almost three quarter of the number of investment stages are classified as MBOs (2322). Exit channel is provided for about half of the investments. Panel D shows that the majority (1112 exits) are realized through a trade sale. There are only 288 IPO exits. These exits have the highest performance. The second best exit in terms of performance is public merger. [Insert Table 3 about here]

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3. Liquidity 3.1. Liquidity risk and liquidity level Our paper focuses on the compensation for systematic risk originating from timevarying liquidity. A recent literature in asset pricing has argued that investors prefer assets that pay out $1 in times of low liquidity rather than assets that pay out $1 in times of high liquidity. The current crisis illustrates clearly these arguments and emphasizes how private equity was particularly sensitive to liquidity risk. Large private equity investors (endowments such as Harvard, pension funds such as Calpers) would have most probably preferred receiving large dividends from their private equity portfolio in 2008 rather than receiving them in 2006 (ex-post). Harvard endowment has tried to sell a staggering $1.5 billion of private equity stakes in 2008 in an attempt to receive some cash from its private equity division. It failed to sell this stake at a reasonable discount and as of Q1-2009 still has not sold it.9 A related topic is the compensation for the level of liquidity, i.e. the level of transaction costs and the trading restrictions associated with private equity investments. The only study we are aware of in private equity is that of Lerner and Schoar (2004). They

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Private Equity Online – November 7, 2008: “Harvard Management Company is looking to unload roughly $1.5 billion in private equity stakes in the secondary market. A secondary market source described the university endowment, which had $36.9 billion in assets as of 30 June, as a highly sophisticated limited partner making a proactive decision to seek liquidity and rebalance its portfolio based on cash flow models. Although the volume of supply in the secondary market has risen of late, secondary investors expect it to surge further in the first half of 2009 as more LPs make a similar move to access needed liquidity. Harvard is ahead of many limited partners in going to the secondary market and will obtain a more attractive price for its assets than those heading to market six months down the line as the result of supply demand dynamics, the investor said. Harvard’s secondary sale will drive down prices in the secondaries market because it will take $1.5 billion of demand out of the market at a time when supply is not rising, the investor added.” THEN Bloomberg – January 23, 2009: “Harvard University didn’t sell most of the $1.5 billion of stakes in privateequity funds it put on the market last year because offers were too low, said three people familiar with the matter. The university’s $28.8 billion endowment, the richest in higher education, rejected deals as sellers, including schools and pension funds, flooded the market and pushed down prices, said the people, who asked not to be identified because the bidding is private. The Cambridge, Massachusetts university remains interested in unloading the private-equity investments. Harvard, Duke University and Columbia University were among institutions that last year put buyout and venture capital stakes up for sale on the secondary market, where middlemen broker deals. Schools are looking to raise cash as distributions from fund managers dry up and losses on stocks and bonds mount. As much as $40 billion in private-equity interests may go unsold this year as sellers hold out for higher prices, according to Nyppex Holdings LLC, a firm that trades stakes in buyout pools.”

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propose a model and supporting empirical evidence, which show that the liquidity level of private equity funds is a decision variable for the fund managers. Specifically, fund managers make the fund stakes illiquid on purpose to select investors that have deep pockets. Future research may focus on the discount required for the liquidity level of private equity. Having part of a portfolio in an illiquid asset class can be costly if one needs to sell this part of the portfolio for whatever reason (like Harvard endowment in the example above). Studying this problem is interesting, but needs considerable assumptions and does not seem feasible with our data have. For example, one needs to model the probability that an investor receive a liquidity shock and is obliged to sell a given private equity stake. Another related issue is the fact that investors effectively grant a credit line to the private equity fund. The relation between the speed of draw down and the liquidity of the rest of an investor’s portfolio is then crucial to evaluate the cost of this credit line. We do not pursue this direction in the present paper.

3.2 Liquidity measures Non-traded Market-wide Liquidity Measures The literature has proposed several measures of shocks to aggregate (market-wide) liquidity. We use the four measures that are available for our sample period. First, we use the (innovation in the) aggregate liquidity measure of Pastor and Stambaugh (2003), which we denote PS_Liq. It is the aggregate of firm-level (OLS) coefficients of daily returns on signed daily trading volume. Our second measure is the innovation in market illiquidity as computed by Acharya and Pedersen (2005), where the firm-level illiquidity is measured by the ratio of Amihud (2002). We multiply this measure by minus one to obtain a liquidity measure and denote it as AP_Liq. Third and fourth, we adopt the liquidity proxies of Sadka (2006). He proposes a measure of market-wide price impact, which he decomposes in a permanent (variable) and a transitory (fixed) part, which we label Sadka_pv and Sadka_tf, respectively.

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Traded Liquidity Risk Factors We also choose the two traded liquidity factors proposed in the literature. First, Pastor and Stambaugh (2003) have created two time-series of long-short portfolios. One is equally weighted and the other is value-weighted; we denote them IML_ew_PS and IML_vw_PS, respectively. Given that Pastor and Stambaugh (2003) privilege the equallyweighted measure in their study, we use this one. Second, Liu (2006) ranks stocks based on their standardized turnover-adjusted number of zero daily trading volumes over the prior 12 months. Stocks are then assigned to deciles as a function of their liquidity. This author constructs his liquidity factor as the return on the low deciles minus the return on the high deciles portfolio.

3.3. Descriptive statistics Table 4 shows the correlation and distribution of the pricing factors and aggregate liquidity factors plus the default spread and the VIX volatility index. Time period is from January 1984 to December 2004. [Insert Table 4 about here]

The Liu liquidity factor returns a high 0.80% per month. Pastor and Stambaugh liquidity factor returns 0.62% per month. We also note that the liquidity measures and factors are not highly correlated with one another. By construction, they capture different dimensions of liquidity. Consequently, it is important to show results with all the measures. Also of interest, the Liu factor is highly correlated with HML. Hence, as in Liu (2006) we will use this factor only in addition to the market factor (a two-factor model). In contrast, Pastor and Stambaugh (2003) use their factor along with the three Fama-French factors10. The four factors have low correlation with one another. In sub-sequent analysis, we will also use this four factor model.

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We have also tried to include a momentum factor in our analysis. However, private equity returns do not seem to display sensitivity to momentum.

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4. Methodology For the following exposition, let us assume that each investment i consists of only one negative cash flow (I) and one positive cash flow (D) and use the two factor model of Liu (2006). The two factors are the market risk premium (rmt - rft) and the liquidity risk premium (LIQt).Because of the two factor structure, and denoting ut the idiosyncratic shocks, it follows that:  =  ∏ (1 + + , +  , − ,  +   +  ) Dividing by I and taking the natural logarithm on both sides gives 

 ln1 + ,  ≡ ln  = !1 + + , +  , − ,  +   +    



Which we can approximate by the following (we work at a monthly frequency): , = +  " , +   ", − " ,  +  #####   +  ### or , = + " , +   ", − " ,  +  #####  + $, This approximation can be avoided by making a distributional assumption. For example, assuming the ut are normally distributed or lognormally distributed, then maximum likelihood can be used. A key assumption in the above derivation is that of no intermediary cash flows. In our data, we have about 8.9% of the observations without intermediary cash flows. The existence of intermediary cash flows means that performance is sensitive to the opportunity cost of capital for both intermediary distributions and intermediary investments. It also means that the market values of portfolio companies vary over time as a function of the timing and amount of the intermediary cash flows. To gauge the

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sensitivity of our results along this dimension we carry out two robustness tests: (i) we use different performance measures corresponding to different re-investment assumptions (Modified IRR); and (ii) we take market value-weighted average of the factors (in addition to equally-weighting, which is our default choice). The value-weighted approach works as follows. We compute the IRR of an investment and obtain its estimated market value each month as follows

MV0=I0 MVt=MVt-1 * (1+IRR) + It - Dt By definition of IRR, the market value of the investment then moves from the value of the first investment to zero, when the last distribution occurs. These market values are used as weights for the explanatory variables. As an example, if we observe the following cash flow stream: -100, 100, 50; and the liquidity risk factor is 10% in the first period and -10% on the second period. If we just equally weight we have 0%. If we value weight, we use the market values: 100, and 36.6 = 100 × (1 + * − 100 hence we have 100 × 10% + 36.6 × (−10%* = 4.6% 136.6 That is, more weight is put on the first period than the second to reflect the fact that an intermediary dividend is paid.

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5. Empirical Results 5.1. Non-traded Market-wide Innovations in Liquidity Table 5 shows the results of OLS regressions of private equity returns on (nontraded) market-wide innovations in liquidity. Standard errors are based on two dimensional clustering (time and country of the investment), and corresponding t-statistics are reported below in parenthesis. Explanatory variables include the usual three asset pricing factors and four aggregate (market-wide) liquidity measures. Each explanatory variable is the time-series average during the investment’s life of the corresponding variable. The average is equally weighted in Panel A and value weighted in Panel B (as explained above). The results on the non-traded aggregate liquidity factors are all highly statistically significant. In simple regressions the effect is largest. As the other risk factors are correlated with the liquidity variables, the marginal effect of liquidity decreases (but remains significant) when these factors are added to the regressions. In the case of the Sadka_tf factor, the loadings and the statistical significance actually increases in the full four-factor model specification. Hence, the evidence clearly suggests that private equity returns significantly related to innovations in aggregate liquidity.

[Insert Table 5 Liquidity factors in private equity returns about here]

In order to provide some economic magnitudes, we also show quintile portfolios based on the average liquidity innovations that an investment faced over its life. Results are shown in Table 6. Investments falling in the quintile that went through the largest innovations in liquidity have an average IRR around 40% while the opposite quintile shows an average IRR around 25% (except for the Pastor and Stambaugh measure, for which it is 6%). The spread varies across liquidity measures (from a maximum of 34% with Pastor- Stambaugh to aminimum of 12% with Acharya-Pedersen) but the spread is statistically significant for each measure. The spread is also similar when using MIRR. A 15% annual spread in performance certainly means that the relation between liquidity

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innovations and performance in private equity is not merely statistically but also economically significant.

[Insert Table 6 Performance by quintiles of liquidity innovations about here]

5.2. Traded Liquidity Risk Factors Table 7 shows the results for the estimation of the two asset pricing models with liquidity risk: the four-factor model of Pastor and Stambaugh (2003) and the two-factor model of Liu (2006). The IRR of each investment is regressed on the average risk factors during the investment’s lifetime. Standard errors are based on two dimensional clustering (time and investment country), and corresponding t-statistics are reported below, between parenthesis. Panel A contains results when we use equally weighted average factors. Panel B and C show how results change with value-weighted instead of equally-weighted factors and with MIRR instead of IRR, respectively. The loadings on liquidity premium vary somewhat, but are always statistically significant. The liquidity risk premium varies as a function of the weighting of the factors and the performance measure that we use. The four-factor model of Pastor and Stambaugh (2003) implies a liquidity premium between 5% (0.63*0.62% per month, Panel C) and 9% (1.12*0.62% per month, Panel B). The two-factor model of Liu (2006) implies a liquidity premium between 10% (0.95*0.80% per month, Panel B) and 12% (1.23*0.80% per month, Panel A). In the four-factor of Pastor-Stambaugh, we find that the market beta varies between 1.35 and 1.85. There is a positive and significant loading on the value premium, indicating that private equity investments resemble value stocks. There is, however, no loading on the size premium.

[Insert Table 7 PE returns and liquidity risk models about here]

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5.3. Abnormal Performance We now go back to the evidence on private equity performance that we discussed above. We have shown raw performance numbers. Now that we have measures of risk, it is interesting to measure the decrease in NPV due to risk adjustment and, in particular to liquidity risk. Results are shown in Table 8. We display the NPV and PI on the aggregated cash flows (all vintage years pooled together). We begin by discounting with a beta of one on the market factor. We find a large PI and positive NPV. Next, we show the result for the two factor model of Liu, if we set the market beta to one and if we set it to 2.35 (as estimated in Table 6). We observe that both the NPV and PI decrease significantly. After market risk and liquidity risk correction, PI on the aggregate cash flow is only 1.07. This means that gross of fees, the value created is 6% of the value invested (for the whole investment’s life). Metrick and Yasuda (2008) estimate fees to be about 20% in present value terms. This estimate would imply that, net of fees and after risk adjustment, the NPV for private equity investors is likely to be negative. We repeat the same exercise with the Pastor and Stambaugh measure. Consistent with a lower liquidity premium for this measure, we find a higher PI and NPV. But the results are qualitatively the same as those above. [Insert Table 8 about here]

5.4. Investment size and exposure to liquidity risk Investments in private equity have become larger over time. This is mainly due to larger fund size, which in turn enables larger stakes in any given portfolio companies. To make some predictions about the performance of the recent private equity investment wave, it is thus important to verify whether larger investments command a different liquidity premium. For valuation purposes, it is also crucial to know whether the liquidity premium should be further adjusted as a function of size. As size increases over time, we de-trend it by subtracting every year the average size for all investments made in that year. We then include size and the interaction between

20

size and liquidity in the regressions executed above. Results in Table 9 suggest that investment size is a positive and significant determinant of exposure to liquidity risk. The interaction between size and liquidity is statistically significant at the 1% level in the four-factor model of Pastor-Stambaugh. It is also strongly significant when interacted with both the Acharya-Pedersen and Sadka_pv innovations in liquidity. However, it is not significant in the two factor model of Liu and with Sadka_tf. Finally, it is only marginally significant with the innovation in PastorStambaugh liquidity. Larger investments are thus more sensitive to liquidity risk. This is consistent with the idea that a liquidity exit market (in particular an IPO market) is more important for these investments. [Insert Table 9 Risk exposure as a function of size about here]

6. Robustness 6.1. US versus non-US Above, we have used only US liquidity factors. As pointed out by Bekaert, Harvey, and Lundblad (2007) liquidity risk is mainly local. Although their results are on emerging markets, we expect a similar situation for non-US countries (about two third of our sample) and maybe for the US as well. We do not have yet global and local liquidity risk measures. Hence, for now, we simply show results separately for the sub-sample of US and non-US investments. In Table 10, Panel A shows results for the sub-sample of US investments and Panel B for other countries. On the US subsample, the loading on Pastor-Stambaugh liquidity risk factor doubles, bringing the PS liquidity premium to 10.5% per year. The loading on Liu liquidity risk factors remains about the same, but loses statistical significance. For liquidity innovation, the Pastor-Stambaugh measure also gets stronger on the US subsample. It is similar to what happens with Sadka_tf. Sadka_pv and Acharya-Pedersen seem stronger on non-US investments. [Insert Table 10 US vs non-US investments about here]

21

6.2. Control variables Gompers and Lerner (2000) and Ljungqvist, Richardson and Wolfenzon (2007) show that an important determinant of performance in private equity is the competitive environment at the time investments are started. That is, the level of the supply and demand of private equity capital. We thus add (investment-)year fixed effects to all our specifications. Results are shown in Table 11. Results are a bit stronger for the two liquidity risk models. For liquidity innovations, only the PS specification loses significance. [Insert Table 11 Controlling for year effects about here]

Next, we add default spread and aggregate volatility (VIX index) to our specifications (Table 12). The default spread is commonly used variable as a conditioning variable in asset pricing to capture business cycles. As such, it may be related to liquidity. Table 12 shows that results are unaffected when controlling for default spread. For volatility, the conclusions are more articulated. Controlling for volatility leaves results unaffected for the two liquidity risk models. For the results with innovation in liquidity, results are unaffected for the two Sadka measures, but not for the other two measures. In fact, neither VIX nor the innovation in liquidity is significant, when we use Pastor-Stambaugh and Acharya-Pedersen. Hence, it is possible that liquidity and volatility drive private equity returns in a similar way . As pointed out by Bandi, Moise and Russell (2008), it is difficult to distinguish between aggregate volatility and liquidity because they are highly correlated. Liquidity and volatility are likely to share similar macroeconomic determinants [Insert Table 12 Further controls: Default spreads and VIX about here]

7. Conclusion Using a comprehensive dataset containing the cash flows of 3,522 liquidated private equity investments made before the recent financial crisis (1984-2004), we find positive and significant loadings of investment returns on aggregate liquidity innovation measures and liquidity risk factors. The quintile of investments that went through times of

22

largest innovations in liquidity outperform the opposite quintile by a staggering 15% per year. Similarly sizeable, the premium for liquidity risk of private equity ranges from 5% and 12% per year, depending on sub-samples and proxies. Adjusting performance for liquidity risk, the NPV of (gross-of-fees) private equity investments decreases dramatically and gets close to zero. We also find that larger investments have higher exposure to liquidity risk. These results are robust to various changes in the empirical design. Our study has important implications for the performance evaluation of private equity investments. They also suggest that both the increased allocation to private equity and the increase size of private equity investments may exacerbate liquidity-based financial crises.

23

References Acharya, Viral V., and Lasse Heje Pedersen, 2005, Asset Pricing with Liquidity Risk. Journal of Financial Economics, 77: 375-410. Amihud, Yakov, 2002, Illiquidity and Stock Returns: Cross-Section and Time-Series Effects. Journal of Financial Markets, 5(1): 31-56. Amihud, Yakov, and Haim Mendelson, 1986, Asset Pricing and the Bid-Ask Spread. Journal of Financial Economics, 17: 223-249. Amihud, Yakov, Haim Mendelson, and Lasse Heje Pedersen, 2005, Foundations and Trends in Finance, 1(4): 269-364. Bandi, Federico M., Claudia E. Moise, and Jeffrey R. Russell, 2008, The Joint Pricing of Volatility and Liquidity. Working Paper, Chicago Booth and Case Western. Bekaert, Geert, Campbell Harvey, and Christian Lundblad, 2007, Liquidity and Expected Returns: Lessons from Emerging Markets. Review of Financial Studies, 20(6): 17831831. Bongaerts, Dion and Erwin Charlier, 2009, Private equity and regulatory capital. Journal of Banking and Finance, 33: 1211–1220. Brunnermeier, Markus, 2009, Deciphering the Liquidity and Credit Crunch 2007-08. Journal of Economic Perspectives, 23(1): 77-100 Chordia, Tarun, Avanidhar Subrahmanyam, and V. Ravi Anshuman, 2001, Trading Activity and Expected Stock Returns. Journal of Financial Economics, 59: 3-32. Cochrane, John, 2005, The Risk and Return of Venture Capital. Journal of Financial Economics, 75: 3-52. Cumming, Douglas J., 2008. Contracts and Exits in Venture Capital Finance. Review of Financial Studies, 21(5): 1947-1982. Cumming, Douglas J., Grant Fleming and Armin Schwienbacher, 2005, Liquidity Risk and Venture Capital Finance. Financial Management, 34: 77-105. Cumming, Douglas J., Daniel Schmidt, and Uwe Walz, 2009, Legality and Venture Capital Governance around the World. Journal of Business Venturing, forthcoming. Cumming, Douglas, and Uwe Walz, 2004, Private Equity Returns and Disclosure around the World. Working Paper, EFA 2004 Maastricht.

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Driessen, Joost, T. Chun Lin, and Ludovic Phalippou, 2008, A New Method to Estimate Risk and Return of Non-Traded Assets from Cash Flows: The Case of Private Equity Funds. NBER Working Paper 14144. Fontaine, Jean-Sebastien and Garcia, Rene, 2008, Bond Liquidity Premia. SSRN Working Paper 966227. Gompers, Paul A. and Josh Lerner, 2000, Money Chasing Deals: The impact of fund inflows on private equity valuations. Journal of Financial Economics, 55: 281–325. Hasbrouck, Joel, 2009, Trading Costs and Returns for US Equities: Estimating Effective Costs from Daily Data, Journal of Finance, forthcoming. Hochberg, Yael V., Alexander Ljungqvist, and Annette Vissing-Jorgensen, 2008, Informational Hold-up and Performance Persistence in Venture Capital. Working Paper. Hochberg, Yael V., Alexander Ljungqvist, and Lu Yang, 2007, Whom You Know Matters: Venture Capital Networks and Investment Performance. Journal of Finance, 62 (1), 251-301. Holmström, Bengt, and Jean Tirole, 2001, LAPM: A Liquidity-Based Asset Pricing Model. Journal of Finance, 56 (5): 1837-1867. Jones, Charles, and Matthew Rhodes-Kropf, 2004, The Price of Diversifiable Risk in Venture Capital and Private Equity. Working Paper, Columbia University. Kaplan, Steve and Antoinette Schoar, 2005, Private Equity Performance: Returns, Persistence and Capital Flows. Journal of Finance, 60: 1791-1823. Kaplan, Steve N., Berk A. Sensoy and Per Strömberg, 2002, How well do venture capital databases reflect actual investments? Working Paper, University of Chicago. Korajczyk, Robert and Ronnie Sadka, 2008, Pricing the Commonality Across Alternative Measures of Liquidity. Journal of Financial Economics. 87(1): 45-72. Lerner, Josh, Antoinette Schoar, and Wan Wongsunwai, 2007, Smart Institutions, Foolish Choices? The Limited Partner Performance Puzzle. Journal of Finance, 62 (2): 731764. Lopez De Silanes, Florencio, Ludovic Phalippou, and Oliver Gottschalg, 2009, Private Equity Investments: Performance and Diseconomies of Scale. Working Paper.

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Liu, Weimin, 2006, A Liquidity-Augmented Capital Asset Pricing Model. Journal of Financial Economics, 82: 631–671. Ljungqvist, Alexander and Matthew Richardson, 2003, The Cash Flow, Return and Risk Characteristics of Private Equity. Working Paper, NYU Stern School of Business. Ljungqvist, Alexander, Matthew Richardson, and Daniel Wolfenzon, 2008, The Investment Behavior of Buyout Funds, NBER Working Paper W14180. Lustig, H., 2009. The Market Price of Aggregate Risk and the Wealth Distribution. NBER Working Paper W11132. Martínez, Miguel A., Belén Nieto, Gonzalo Rubio, and Mikel Tapia, 2005, Asset Pricing and Systematic Liquidity Risk: An Empirical Investigation of the Spanish Stock Market. International Review of Economics and Finance, 14: 81-103. Metrick, Andrew, 2007, Venture Capital and the Finance of Innovation, Wiley & Sons. Metrick, Andrew and Yasuda, Ayako, 2008, The Economics of Private Equity Funds, Swedish Institute for Financial Research Conference on The Economics of the Private Equity Market. Available at SSRN: http://ssrn.com/abstract=996334. Pástor, Lubos and Robert F. Stambaugh, 2003, Liquidity Risk and Expected Stock Returns. Journal of Political Economy, 111(3): 642-685. Petersen, Mitchell A., 2009, Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches. Review of Financial Studies, 22(1): 435-480. Phalippou, Ludovic, 2009, Beware of Venturing into Private Equity, Journal of Economic Perspectives, 23(1): 147–66. Phalippou, Ludovic and Oliver Gottschalg, 2009, The Performance of Private Equity Funds. Review of Financial Studies, 22(4): 1747-1776. Sadka, Ronnie, 2006, Momentum and Post-Earnings-Announcement Drift Anomalies: The Role of Liquidity Risk. Journal of Financial Economics, 80: 309-349. Watanabe, Akiko and Masahiro Watanabe, 2008, Time-Varying Liquidity Risk and the Cross Section of Stock Returns. Review of Financial Studies, 21 (6): 2449-2486.

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Appendix 1: Detailed information on the CEPRES database CEPRES receive their data directly from GPs, which are participating in the data exchange community. After signing the contracts, they send via email (i) standardized data request sheets; and/or (ii) quarterly reports of their funds and/or usual Due Diligence Packages (containing PPM, quarterly reports, further track record information); in the latter case GPs, do not prepare the standard sheets themselves, but CEPRES does the work of data preparation. The data CEPRES receive are gross (before fees) cash-flows at the portfolio company level and net (of fees) cash-flows on the fund level. They also gather further information about the companies (country, sector, stage etc.) and funds (focus, size, etc.) GPs get valuable information in exchange, exclusively, and for free. CEPRES services exclusively provided to participating GPs include: (i) Mezzanine Market Report (20 pages loaded with information on the mezzanine market, risk, return, pricing etc., published quarterly); (ii) access to the Private Equity Analyzer Premium, an online database application, which allows members to benchmark their own investments to “the market”. CEPRES requests to have all the investments of a given fund, but PE firms are not obliged to deliver all their funds. Most of the customers of other CEPRES services (benchmarking reports and risk management) are LPs. They have to disclose information about their investments to them for these services. Therefore, CEPRES have these sources to cross-check the completeness and correctness of the data. GPs know that and have a further incentive to provide accurate data. Furthermore, all data are made anonymous and sufficiently aggregated to impede deciphering. Therefore, GPs have no incentive to do window dressing or cherry picking. An online description of the database is available at: http://privateequityinsight.com/analyser_faq.jsp

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Table 1: Sample selection and performance. The table shows the median multiple at each step of our sample selection process. Multiple is the total amount distributed divided by total amount invested. All cash flows are in local currency. Liquidated investments are those officially liquidated as of December 2004. Multiple (local currency) Median N obs Buyout, 1975-2007

1.557

6620

Buyout, 1984-2004

1.660

5780

Buyout, 1984-2004, liquidated

1.922

3705

Working sample: Buyout, 1984-2004, liquidated, with duration information

2.049

3522

Table 2: Correlation and distribution of performance measures. The table shows the correlation matrix for the natural logarithm of duration plus four performance measures. Performance measures are winsorized at the 5th and 95th percentile. Duration is the time elapsed between the first to last cash flow. Mean is value-weighted (VW) by deflated investment size. The distribution of each variable is displayed underneath the correlation matrix. Duration Duration IRR (dollar) MIRR S&P (dollar) MIRR 8% (local) Multiple (local) Mean (VW) Median St. Deviation 5th percentile 95th percentile N

IRR (dollar)

MIRR S&P (dollar)

MIRR 8% (local)

Multiple (local)

1.00 -0.12 -0.08 -0.08 0.09

1.00 0.93 0.94 0.73

1.00 0.98 0.70

1.00 0.71

1.00

51.35 49.00 28.73 13.00 115.00 3522

0.24 0.26 0.78 -1.00 2.05 3522

0.16 0.21 0.52 -0.89 1.29 3522

0.11 0.18 0.54 -0.97 1.22 3522

2.42 2.05 2.70 0.00 10.17 3522

Table 3: Descriptive statistics. This table shows the descriptive statistics for our working sample. Investment size is expressed in 2000 US dollars. VW is value-weighted using investment size and DVW is duration-times-value-weighted. Duration is the time elapsed between the first to last cash flow. Performance measures are multiple (total distributed divided by total invested), Internal Rate of Return and Modified IRR with either a flat 8% or S&P 500 index as re-investment rate. Performance and sample distribution are displayed by year (Panel A), by industry (Panel B), by investment stage (Panel C), by exit type (Panel D). Panel A: Performance by year Size Mutiple Year N obs Median Median Mean VW 1984 17 2.223 4.439 5.736 1985 48 2.813 2.575 3.756 1986 69 2.130 2.795 3.649 1987 98 1.971 1.540 2.296 1988 155 1.480 1.771 2.519 1989 139 2.523 1.538 3.528 1990 186 3.283 1.920 2.830 1991 234 3.738 2.877 2.963 1992 247 4.503 2.294 2.693 1993 237 4.269 2.636 2.918 1994 368 4.570 2.384 2.873 1995 285 6.886 2.206 2.610 1996 341 6.889 2.035 2.621 1997 343 8.765 2.120 2.622 1998 237 11.928 1.862 1.939 1999 207 10.603 1.343 1.719 2000 183 6.152 0.798 1.189 2001 71 11.936 1.667 2.300 2002 33 7.304 1.405 1.943 2003 20 9.983 1.423 2.413 2004 4 22.802 1.28 1.119

Median 0.658 0.463 0.282 0.151 0.127 0.138 0.155 0.357 0.287 0.424 0.335 0.250 0.253 0.313 0.236 0.123 -0.147 0.462 0.435 0.855 1.159

IRR Mean VW 0.643 0.735 0.350 0.322 0.358 0.175 0.340 0.381 0.307 0.438 0.469 0.265 0.300 0.266 0.031 -0.038 -0.198 0.591 0.657 1.016 0.223

Mean DVW 0.252 0.256 0.308 0.125 0.107 0.132 0.140 0.320 0.294 0.462 0.298 0.232 0.243 0.296 0.180 0.065 -0.053 0.324 0.303 0.847 0.889

MIRR 8% Median Mean VW 0.314 0.311 0.267 0.447 0.193 0.174 0.101 0.204 0.091 0.260 0.095 0.116 0.115 0.228 0.223 0.251 0.198 0.196 0.273 0.265 0.224 0.184 0.174 0.169 0.175 0.168 0.215 0.095 0.204 -0.031 0.115 -0.093 -0.111 -0.224 0.284 0.325 0.288 0.360 0.597 0.621 0.695 0.065

Mean DVW 0.162 0.152 0.161 0.049 0.045 0.055 0.063 0.195 0.172 0.264 0.161 0.141 0.139 0.141 0.061 -0.005 -0.112 0.094 0.180 0.502 0.484

MIRR S&P Median Mean Mean VW DVW 0.321 0.391 0.298 0.315 0.522 0.260 0.271 0.239 0.246 0.146 0.243 0.100 0.131 0.316 0.124 0.141 0.186 0.130 0.167 0.298 0.143 0.275 0.303 0.252 0.238 0.261 0.232 0.353 0.333 0.328 0.273 0.277 0.231 0.190 0.233 0.196 0.184 0.249 0.178 0.190 0.128 0.168 0.168 0.017 0.090 0.089 -0.109 -0.010 -0.118 -0.229 -0.117 0.332 0.401 0.142 0.494 0.509 0.295 0.762 0.714 0.599 0.791 0.148 0.564

Table 3: continued Panel B: Performance by industry Industry Industrial/Manuf. Consumer/Food Healthcare/LS other Services Software Retail Media IT Others Telecom Financial Services Unspecified Semiconductor Leisure Internet Materials Business Services Textiles Construction Nat. Resour./Energy Logistics HighTech Transportation Traditional products Hotel Waste/Recycling Environment

N obs

Size Median

635 359 307 305 266 202 184 166 134 129 124 111 65 64 63 60 50 50 49 41 37 34 30 21 18 11 4

5.271 6.719 4.002 5.582 1.559 7.874 12.687 3.505 5.985 4.653 6.404 7.185 4.620 8.369 4.527 5.398 6.060 8.512 8.384 8.527 7.923 4.551 5.902 4.717 6.766 2.981 1.935

Mutiple Median Mean VW 1.873 2.512 2.048 2.591 1.725 2.459 2.072 2.033 2.376 3.142 2.214 3.068 2.377 2.641 2.133 2.205 1.928 2.123 2.315 2.110 2.407 2.023 1.412 1.793 3.008 2.788 1.239 1.883 0.161 1.672 2.033 2.642 2.690 2.964 1.310 1.595 2.118 2.409 2.051 1.709 2.649 2.522 1.081 2.271 2.505 2.608 1.767 1.859 1.776 2.081 1.573 1.951 0.137 0.288

Median 0.240 0.263 0.203 0.263 0.319 0.279 0.350 0.267 0.241 0.309 0.405 0.201 0.631 0.072 -0.647 0.243 0.405 0.097 0.382 0.275 0.366 0.073 0.382 0.157 0.217 0.228 -0.711

IRR Mean VW 0.275 0.282 0.220 0.142 0.432 0.330 0.363 0.040 0.227 -0.057 0.049 0.348 0.409 0.132 0.010 0.124 0.814 0.074 0.372 0.012 0.261 0.407 0.322 0.066 0.194 0.578 -0.784

Mean DVW 0.246 0.252 0.208 0.092 0.310 0.321 0.319 0.323 0.169 0.089 0.225 0.172 0.479 0.135 0.081 0.122 0.691 0.125 0.292 0.009 0.204 0.398 0.308 0.070 0.169 0.438 -0.809

MIRR 8% Median Mean VW 0.169 0.112 0.183 0.162 0.127 0.130 0.195 0.061 0.232 0.215 0.184 0.168 0.234 0.220 0.148 -0.121 0.166 0.099 0.219 -0.127 0.219 -0.045 0.142 0.186 0.297 0.180 0.048 0.063 -0.567 -0.095 0.159 0.092 0.302 0.323 0.084 -0.032 0.220 0.231 0.229 -0.005 0.291 0.138 0.061 0.095 0.192 0.192 0.130 0.074 0.157 0.177 0.089 0.255 -0.619 -0.663

Mean DVW 0.091 0.146 0.120 0.033 0.117 0.169 0.189 0.117 0.076 0.022 0.117 0.067 0.207 0.058 -0.021 0.138 0.248 -0.012 0.149 0.006 0.147 0.076 0.174 0.067 0.153 0.135 -0.665

MIRR S&P Median Mean Mean VW DVW 0.185 0.172 0.154 0.210 0.221 0.197 0.158 0.162 0.160 0.219 0.139 0.119 0.262 0.255 0.162 0.224 0.216 0.209 0.257 0.273 0.239 0.211 -0.105 0.142 0.211 0.120 0.084 0.246 -0.091 0.073 0.267 -0.019 0.159 0.170 0.219 0.133 0.422 0.263 0.293 0.097 0.134 0.124 -0.436 -0.051 0.021 0.221 0.140 0.196 0.306 0.427 0.341 0.106 0.054 0.083 0.238 0.302 0.215 0.214 0.024 0.039 0.308 0.164 0.178 0.051 0.163 0.130 0.270 0.223 0.230 0.139 0.111 0.105 0.209 0.184 0.152 0.210 0.272 0.188 -0.284 -0.346 -0.274

Table 3: continued Panel C: Performance by investment stage Size Stage N obs Median MBO/MBI Growth LBO Aquisition Financing Recapitalisation Turnaround Spin Off

2288 761 193 111 105 59 5

6.793 1.510 7.849 15.008 4.704 6.540 2.930

Panel D: Performance by exit channel Size Median Exit N obs Sale Write-off IPO Public Merger

1157 309 292 75

6.537 5.006 8.315 8.158

Mutiple Median Mean VW 2.078 2.319 1.497 2.200 2.618 2.838 2.160 2.612 2.384 2.946 1.461 1.318 0.000 0.794

Mutiple Median Mean VW 2.048 2.443 0.000 0.035 3.488 3.595 3.264 2.532

Median 0.278 0.139 0.319 0.330 0.356 0.425 -0.983

Median 0.295 -1.000 0.599 0.434

IRR Mean VW 0.226 0.080 0.238 0.483 0.323 0.303 -0.742

Mean DVW 0.220 0.123 0.244 0.378 0.281 0.070 -0.833

MIRR 8% Median Mean VW 0.197 0.089 0.093 -0.015 0.218 0.158 0.224 0.330 0.198 0.176 0.207 0.130 -0.733 -0.649

Mean DVW 0.094 0.034 0.164 0.246 0.168 -0.021 -0.665

MIRR S&P Median Mean Mean VW DVW 0.221 0.141 0.151 0.133 0.051 0.101 0.266 0.185 0.191 0.242 0.384 0.290 0.247 0.237 0.225 0.224 0.156 0.006 -0.719 -0.536 -0.503

IRR Mean VW 0.348 -0.977 0.556 0.443

Mean DVW 0.264 -0.967 0.429 0.402

MIRR 8% Median Mean VW 0.216 0.216 -0.968 -0.886 0.401 0.341 0.261 0.212

Mean DVW 0.155 -0.809 0.246 0.187

MIRR S&P Median Mean Mean VW DVW 0.235 0.254 0.194 -0.801 -0.719 -0.571 0.435 0.386 0.302 0.291 0.274 0.234

Table 4: Correlations and distributions of the factors. This table shows the correlation matrix for the (time-series of the) five traded risk factors (market premium, value premium, size premium and two illiquid minus liquid factors) plus the four measures of innovation in aggregate liquidity. The time period is from January 1984 to December 2004. The frequency is monthly. The Sadka factors have been multiplied by 100.

Rm-Rf HML SMB IML Liu IML PS PS LIQ AP Liq Sadka tf Sadka pv Def. spread VIX Mean Median St. Deviation 5th percentile 95th percentile

Rm-Rf 1.00 -0.49 0.18 -0.75 -0.08 0.34 0.10 -0.03 0.11 -0.03 -0.37

HML

SMB

IML Liu

IML PS

PS LIQ

AP Liq

Sadka tf

Sadka pv

Def. spread

VIX

1.00 -0.44 0.70 -0.29 -0.06 0.02 0.15 0.03 -0.04 0.05

1.00 -0.31 0.17 0.04 0.12 0.08 0.16 0.06 -0.11

1.00 0.04 -0.17 0.02 0.23 0.08 -0.03 0.09

1.00 -0.01 -0.02 0.00 0.10 0.03 0.05

1.00 0.06 0.09 0.28 -0.10 -0.42

1.00 0.22 0.25 0.08 -0.18

1.00 0.20 -0.03 -0.17

1.00 -0.06 -0.31

1.00 0.32

1.00

0.66 1.10 4.49 -7.15 7.10

0.38 0.34 3.25 -4.37 5.47

0.04 -0.17 3.44 -4.92 5.08

0.80 1.16 4.21 -6.35 7.63

0.62 0.90 4.75 -7.92 6.28

0.00 0.01 0.05 -0.07 0.06

-0.02 -0.02 0.17 -0.28 0.26

0.00 0.01 0.24 -0.34 0.27

-0.02 0.05 0.55 -1.01 0.65

0.95 0.89 0.29 0.60 1.45

20.52 19.53 6.87 11.85 31.93

Table 5: Innovation in Aggregate Liquidity and Private Equity Returns. This table shows the result of OLS regression (pooled panel). Explanatory variables include the usual three asset pricing factors (market premium, value premium, size premium) and four measures of innovation in aggregate liquidity. Each explanatory variable is computed by taking its average value during investment’s; the average is equally weighted in Panels A and C and value weighted in Panel B. Weights are based on estimated markets values (see text). Panels A and B have IRR as dependent variable while Panel C has MIRR (with S&P 500 as re-investment rate). A constant is always included but not displayed. Standard errors are based on a two dimensional clustering (month/year of the investment and investment country); corresponding t-statistics are reported below each coefficient in parentheses. Panel A: IRR and equally-weighted average factors PS Liq Liq. Innov. 1.392 0.974 0.967 0.300 (4.400) (2.710) (2.680) (3.210) Rm-Rf 0.838 1.104 (2.040) (1.900) HML 0.385 (0.710) SMB 0.091 (0.190) N Adj. R2

3522 0.037

3522 0.042

3522 0.042

3522 0.013

AP Liq 0.221 (2.480) 1.419 (3.740)

3522 0.038

0.213 (2.170) 1.532 (2.810) 0.246 (0.410) -0.150 (0.290)

15.187 (1.670)

3522 0.038

3522 0.004

Sadka tf 15.066 18.174 (1.800) (2.040) 1.564 1.363 (3.870) (3.040) -0.140 (0.240) -0.412 (0.800) 3522 0.035

3522 0.036

14.048 (3.020)

3522 0.015

Sadka pv 8.763 8.902 (1.940) (1.770) 1.366 1.385 (3.500) (2.440) 0.172 (0.300) -0.297 (0.510) 3522 0.036

3522 0.036

Table 5: continued Panel B: IRR and value-weighted average factors PS Liq Liq. Innov. 1.318 1.143 1.146 0.220 (5.407) (4.494) (4.566) (2.335) Rm-Rf 0.392 0.493 (1.255) (1.275) HML 0.124 (0.282) SMB 0.183 (0.477)

AP Liq 0.167 (1.967) 1.057 (3.425)

0.166 (1.733) 1.068 (2.794) 0.015 (0.028) 0.014 (0.033)

10.980 (1.362)

3522 0.027

3522 0.026

3522 0.003

Panel C: Modified IRR and equally-weighted average factors PS Liq AP Liq Liq. Innov. 1.292 0.803 0.789 0.289 0.209 (5.050) (2.810) (2.742) (3.747) (2.806) Rm-Rf 0.980 1.277 1.441 (3.031) (2.761) (4.719) HML 0.449 (0.981) SMB 0.045 (0.113)

0.199 (2.425) 1.593 (3.586) 0.312 (0.624) -0.160 (0.378)

13.051 (1.680)

3522 0.059

3522 0.005

N Adj. R2

N Adj. R2

3522 0.042

3522 0.049

3522 0.044

3522 0.060

3522 0.044

3522 0.062

3522 0.01

3522 0.019

3522 0.058

Sadka tf 7.946 9.918 (1.004) (0.990) 1.126 1.023 (3.370) (3.052) -0.135 (0.244) -0.092 (0.193) 3522 0.023

3522 0.023

Sadka tf 12.929 14.129 (1.864) (1.936) 1.578 1.505 (4.851) (4.222) 0.043 (0.086) -0.353 (0.825) 3522 0.054

3522 0.054

14.793 (3.685)

3522 0.022

13.631 (3.579)

3522 0.021

Sadka pv 10.916 11.776 (2.640) (2.529) 0.851 0.692 (2.530) (1.622) -0.199 (0.404) -0.109 (0.239) 3522 0.032

3522 0.032

Sadka pv 8.248 8.199 (2.209) (1.989) 1.392 1.460 (4.392) (3.153) 0.246 (0.503) -0.294 (0.618) 3522 0.056

3522 0.057

Table 6: Performance by quintiles of liquidity innovations. The table shows the performance of portfolio of investments. Each portfolio is a quintile based on the average liquidity innovations an investment faced. Results are shown for all four measures of liquidity innovations. Performance measures are (winsorized) IRR and MIRR expressed annually and equally weighted. T-statistics for the difference in mean test are in parentheses. Quintile:

Low

2

IRR

0.060

0.164

MIRR

-0.005

IRR

3

High

High - Low

PS Liq 0.429 0.305

0.400

0.103

0.289

0.275

0.306

0.340 (8.152) 0.311 (11.501)

0.266

0.199

AP Liq 0.238 0.437

0.384

MIRR

0.156

0.119

0.196

0.326

0.298

IRR

0.262

0.341

Sadka tf 0.248 0.262

0.438

MIRR

0.186

0.235

0.186

0.192

0.313

IRR

0.236

0.278

Sadka pv 0.250 0.306

0.500

MIRR

0.134

0.195

0.187

4

0.242

0.369

0.118 (3.425) 0.142 (6.138)

0.176 (1.926) 0.127 (1.238)

0.264 (5.848) 0.235 (7.775)

Table 7: Private equity returns and liquidity risk models. This table shows the result of OLS regression (pooled panel). Explanatory variables include the usual three asset pricing factors (market premium, value premium, size premium) and two illiquid minus liquid portfolios (i.e. traded liquidity risk factors). Each explanatory variable is computed by taking its average value during investment’s; the average is equally weighted in Panels A and C and value weighted in Panel B. Weights are based on estimated markets values (see text). Panels A and B have IRR as dependent variable while Panel C has MIRR (with S&P 500 as re-investment rate). A constant is always included but not displayed. Standard errors are based on a two dimensional clustering (month/year of the investment and investment country); corresponding t-statistics are reported below each coefficient in parentheses.

IML Liu IML PS Rm-Rf HML SMB

N Adj. R2

Panel A: IRR, eq.-w. avg. fac. 1.226 (2.997) 0.776 (2.102) 1.566 1.816 2.227 1.801 (4.103) (3.645) (4.609) (3.554) 0.444 1.228 (0.788) (2.210) -0.077 0.002 (0.144) (0.004) 3522 0.031

3522 0.032

3522 0.043

3522 0.038

Panel B: IRR, value-w. avg. fac. 0.951 (2.142) 1.116 (4.244) 1.162 1.296 1.661 1.348 (3.561) (3.509) (3.836) (3.526) 0.201 1.313 (0.411) (2.433) 0.099 0.279 (0.227) (0.694) 3522 0.022

3522 0.022

3522 0.032

3522 0.044

Panel C: MIRR, eq.-w. avg. fac. 1.143 (3.428) 0.625 (1.984) 1.580 1.857 2.196 1.846 (5.172) (4.656) (5.679) (4.527) 0.496 1.128 (1.052) (2.436) -0.092 -0.028 (0.208) (0.065) 3522 0.049

3522 0.051

3522 0.065

3522 0.057

Table 8: Abnormal performance of private equity investments. The table reports Net Present Value (NPV) and Profitability Index (PI) with different discount rates. The sample is all liquidated investments made between 1984 and 2004. All cash flows are aggregated, then their NPV is computed; it is expressed in million of US dollars. The discount rate is based on realized returns and the loadings shown on the Left Hand Side of the table; i.e. discount rate in month t is the sum of one, the risk free rate in month t, and the sum of risk loading times realization of risk factor in month t. The profitability index is the ratio of the discounted value of the aggregate dividends over the discounted value of the aggregate investments. Risk exposures β smb β hml 0.00 0.00

Abnormal PE performance Agg. NPV Agg. PI 7.62E+09 1.79

β capm 1.00

β Liu 0.00

1.00 2.23

1.23 1.23

0.00 0.00

0.00 0.00

0.00 0.00

1.21E+09 1.65E+08

1.31 1.07

1.00 1.00 1.80

0.00 0.00 0.00

0.00 0.01 0.01

0.00 1.23 1.23

0.78 0.78 0.78

2.68E+09 1.11E+09 2.57E+08

1.76 1.51 1.21

β IM L P S 0.00

Table 9: Liquidity Risk and Investment Size This table shows the result of OLS regression (pooled panel). Explanatory variables include either of the six liquidity variables (two liquidity risk measures and four innovation in aggregate liquidity measures), investment size, the product of the liquidity variable with size, and the usual three asset pricing factors (market premium, value premium, size premium). Each explanatory variable (except size) is computed by taking its average value during investment’s; the average is equally weighted. A constant is always included but not displayed. Standard errors are based on a two dimensional clustering (month/year of the investment and investment country); corresponding t-statistics are reported below each coefficient in parentheses.

Liquidity Liquidity * Size Size Rm-Rf HML SMB

N Adj. R2

IML PS 0.743 (2.150) 0.006 (2.770) 0.000 (0.800) 1.802 (3.570) 1.209 (2.180) -0.032 (0.070)

IML Liu 1.223 (3.030) 0.000 (0.000) 0.000 (0.210) 2.226 (4.640)

PS 1.389 (4.560) 0.007 (1.560) 0.000 (1.550)

Liq 0.962 (2.730) 0.007 (1.580) 0.000 (1.500) 1.102 (1.900) 0.393 (0.740) 0.064 (0.140)

AP 0.309 (3.370) 0.006 (2.780) 0.000 (2.930)

Liq 0.223 (2.310) 0.006 (2.950) 0.000 (3.120) 1.520 (2.800) 0.258 (0.450) -0.187 (0.370)

3522 0.040

3522 0.043

3522 0.038

3522 0.043

3522 0.018

3522 0.042

Sadka tf 15.473 18.399 (1.720) (2.060) 0.183 0.137 (0.490) (0.440) 0.000 0.000 (0.060) (0.110) 1.357 (3.030) -0.137 (0.240) -0.425 (0.830) 3522 0.004

3522 0.036

Sadka pv 14.411 9.241 (3.090) (1.820) 0.214 0.216 (3.410) (3.680) 0.000 0.000 (0.120) (0.270) 1.395 (2.430) 0.207 (0.360) -0.325 (0.570) 3522 0.017

3522 0.039

Table 10: US versus non-US investments. This table shows the result of OLS regression (pooled panel). Explanatory variables include either of the six liquidity variables (two liquidity risk measures and four innovation in aggregate liquidity measures) and the usual three asset pricing factors (market premium, value premium, size premium). Each explanatory variable is computed by taking its average value during investment’s; the average is equally weighted. Panel A shows results for the sub-sample of US investments while Panel B shows results for the other countries. A constant is always included but not displayed. Standard errors are based on a two dimensional clustering (month/year of the investment and investment country); corresponding t-statistics are reported below each coefficient in parentheses. Panel A: US investments, performance IML PS IML Liu Liquidity 1.351 1.343 (2.460) (1.610) Rm-Rf 2.974 3.427 (3.020) (3.740) HML 1.709 (1.600) SMB 0.342 (0.320) N Adj. R2

1327 0.095

1327 0.087

IRR in US PS Liq 1.502 (3.080) 1.858 (1.960) 0.357 (0.410) 0.467 (0.530) 1327 0.102

dollars AP Liq 0.205 (1.240) 2.772 (2.790) 0.318 (0.310) 0.181 (0.160)

Sadka tf 30.357 (2.460) 2.338 (2.890) -0.553 (0.570) -0.223 (0.200)

Sadka pv 4.946 (0.540) 2.772 (2.790) 0.234 (0.240) 0.169 (0.130)

1327 0.079

1327 0.089

1327 0.076

Sadka tf 7.370 (0.520) 1.022 (1.730) 0.220 (0.300) -0.394 (0.700)

Sadka pv 12.130 (2.160) 0.636 (0.950) 0.094 (0.140) -0.540 (0.930)

2195 0.015

2195 0.023

Panel B: Non-US investments, performance IRR in US dollars IML PS IML Liu PS Liq AP Liq Liquidity 0.382 1.177 0.498 0.203 (1.080) (2.700) (1.120) (1.630) Rm-Rf 1.212 1.633 0.858 0.932 (2.080) (3.330) (1.120) (1.430) HML 0.855 0.422 0.211 (1.290) (0.670) (0.310) SMB -0.200 -0.152 -0.305 (0.380) (0.290) (0.550) N Adj. R2

2195 0.016

2195 0.026

2195 0.017

2195 0.021

Table 11: Robustness - Time Fixed Effects. This table shows the result of OLS regression (pooled panel). Explanatory variables include either of the six liquidity variables (two liquidity risk measures and four innovation in aggregate liquidity measures) and the usual three asset pricing factors (market premium, value premium, size premium). Each explanatory variable is computed by taking its average value during investment’s; the average is equally weighted. Year fixed effects based on the year of investment is included in each regression. A constant is always included but not displayed. Standard errors are based on a two dimensional clustering (month/year of the investment and investment country); corresponding t-statistics are reported below each coefficient in parentheses.

0.220 (0.530)

0.577 (0.970) 0.511 (0.920) 0.801 (1.440)

IML PS 0.741 (2.030) 0.605 (1.000) 1.298 (2.040) 0.852 (1.580)

3522 0.067

3522 0.069

3522 0.073

Liquidity Rm-Rf HML SMB

N Adj. R2

IML Liu 1.290 (2.560) 1.068 (1.770)

PS Liq 0.620 (1.520) 0.296 (0.480) 0.546 (0.990) 0.753 (1.400)

AP Liq 0.296 (2.190) 0.336 (0.540) 0.299 (0.510) 0.471 (0.820)

Sadka tf 20.367 (2.050) 0.128 (0.230) -0.097 (0.180) 0.387 (0.760)

Sadka pv 14.558 (2.400) 0.005 (0.010) 0.203 (0.360) 0.587 (1.050)

3522 0.074

3522 0.072

3522 0.074

3522 0.073

3522 0.076

Table 12: Robustness - Default spread and Volatility. This table shows the result of OLS regression (pooled panel). Explanatory variables include either of the six liquidity variables (two liquidity risk measures and four innovation in aggregate liquidity measures), default spread (deference between yield on BAA corporate bonds and 3 month T-bill yield), the VIX volatility index (volatility of S&P 500 stock index options), and the usual three asset pricing factors (market premium, value premium, size premium). Each explanatory variable is computed by taking its average value during investment’s; the average is equally weighted. A constant is always included but not displayed. Standard errors are based on a two dimensional clustering (month/year of the investment and investment country); corresponding t-statistics are reported below each coefficient in parentheses. Traded factors Liquidity Def. Spread VIX Rm-Rf HML SMB

N Adj. R2

IML PS 0.772 0.825 (2.146) (2.106) -0.798 (0.353) -0.190 -0.184 (2.676) (2.522) 1.616 1.182 1.128 (3.147) (2.007) (1.979) 1.301 0.816 0.855 (2.341) (1.350) (1.372) 0.125 -0.043 0.006 (0.224) (0.085) (0.011) 0.914 (2.276) -2.052 (0.891)

3522 0.039

3520 0.046

IML Liu 0.934 0.961 (1.997) (2.051) 1.492 (0.777) -0.118 -0.129 (1.633) (1.777) 2.331 1.845 1.965 (4.275) (3.316) (3.283)

1.262 (3.107) 1.002 (0.507)

3520 0.046

3522 0.043

0.250 (2.435) -1.981 (0.879)

1.173 (2.023) 0.414 (0.774) 0.047 (0.090)

-0.079 (0.771) 1.025 (1.734) 0.223 (0.390) 0.027 (0.055)

0.698 (1.319) 1.129 (0.536) -0.090 (0.879) 1.102 (1.882) 0.238 (0.418) -0.038 (0.071)

3522 0.042

3520 0.043

3520 0.043

3520 0.046

3520 0.046

Liquidity innovations Liquidity Def. Spread

0.981 (2.685) 0.893 (0.428)

VIX Rm-Rf HML SMB

N Adj. R2

PS Liq 0.713 (1.337)

AP Liq 0.099 (0.807)

Sadka tf 16.871 26.256 (1.851) (2.521) 4.112 (1.782) -0.178 -0.205 (2.524) (2.803) 1.447 0.808 0.856 (3.098) (1.576) (1.602) -0.262 -0.486 -0.707 (0.443) (0.799) (1.128) -0.685 -0.431 -0.828 (1.153) (0.875) (1.451)

24.842 (2.428) 2.819 (1.159)

1.307 (2.275) 0.147 (0.249) -0.058 (0.106)

-0.142 (1.607) 1.216 (2.113) 0.042 (0.070) -0.145 (0.279)

0.091 (0.630) 0.216 (0.088) -0.147 (1.468) 1.229 (2.120) 0.046 (0.076) -0.155 (0.280)

3522 0.039

3520 0.040

3520 0.040

3522 0.037

3520 0.043

3520 0.046

9.138 (1.807) 0.807 (0.362)

1.445 (2.509) 0.191 (0.331) -0.345 (0.558) 3522 0.036

Sadka pv 8.571 8.956 (1.751) (1.839) 1.763 (0.809) -0.174 -0.187 (2.535) (2.630) 0.824 0.922 (1.304) (1.466) -0.200 -0.181 (0.327) (0.296) -0.331 -0.437 (0.589) (0.715) 3520 0.044

3520 0.044

1.5

200

PE payout Ted spread (bp)

.5

100

Ted spread (bp)

PE payout

1

150

50

08 20

07 20

06 20

05 20

04 20

03 20

02 20

20

01

0

0

Figure 1: Private equity payout and liquidity The figure plots the monthly dividend payout of private equity deals in the CEPRES dataset (PE payout) and the monthly Ted spread (defined as the three-month LIBOR rate minus the Fed Funds rate in basis points). Dividend payout is constructed as the six-month moving average of the total dividends paid divided by the six-month moving average of the total investments in those deals.