Francesco Franzoni, Eric Nowak, and Ludovic Phalippou
Private equity performance and liquidity risk
Journal of Finance | Volume 67, Issue 6 (Dec 2012), 2341–2373

Investing in private equity is among the preferred choices for long-term investors, such as endowments and pension funds, who seek to diversify their portfolios. These long term investors are clearly the best suited for holding an illiquid asset like private equity. The diversification benefits of private equity, however, have not been widely documented. In particular, an issue which has not been addressed so far, is whether private equity performance, like that of other asset classes, is affected by liquidity risk.

Liquidity risk has been studied by, among others, Pastor-Stambaugh (JPE 2003), Acharya-Pedersen (JFE 2005), and Sadka (JFE 2006), as an additional source of systematic risk for public equity. In general, liquidity risk refers to the co-movement between unexpected changes in overall market liquidity and asset returns. If an asset tends to have low returns when the overall market exhibits low liquidity, then this asset bears more systematic risk than an asset whose returns increase in low aggregate liquidity states. As a result, this asset's cost of capital should be higher.

A four-factor model for private equity returns

Prior studies have shown that liquidity risk is a relevant component of the cost of capital in different asset classes. Beyond public equity returns (e.g., Pastor-Stambaugh (JPE 2003), Acharya-Pedersen (JFE 2005), Sadka (JFE 2006), evidence of liquidity risk has been found for emerging markets, bond markets, credit derivative markets, and hedge funds. The primary goal of this paper is to quantify liquidity risk in private equity. To carry out this task, we use the four-factor model of Pastor-Stambaugh (JPE 2003). This asset pricing model contains three factors in addition to liquidity risk. The first factor captures market risk, as in the standard CAPM. The other two factors, introduced by Fama-French (JFE 1993), capture two important sources of return variation. The SMB factor is long in small stocks and short in big stocks, while the HML factor is long in high book-to-market (value) stocks and short in low book-to-market (growth) stocks. Empirical evidence shows that these two factors have earned significant returns and so do the securities that load positively on them. The literature is still debating whether these high returns are due to a risk premium or to market anomalies. We do not need to take a stand on the source of these premia as, for our purposes, what matters is to control for known sources of variation in asset returns. The goal is to filter out from a fund's performance the component of returns that originates from these four replicable factors. Using this four-factor model, we can offer one of the first estimates of the cost of capital for private equity, an asset class which, according to some estimates, has reached $3 trillion of assets under management in 2012. Once a cost of capital is estimated, we can assess whether this asset class delivers outperformance (alpha) or not.

1: Cash flows of a typical investment
Date Cash Reinvested Div
(in years) Flows (at 5% / Sem)
0.0 –100 0
0.5 0 0
1.0 0 0
1.5 0 0
2.0 0 0
2.5 50 50
3.0 0 53
3.5 0 55
4.0 150 208
MIRR = (208/100)1/4 – 1 = 20%
IRR = 21%
PV Div at 15% Disc 119
PV Div at 17% Disc 108
The table shows the cash flows of a representative investment. It lasts for four years, pays a final dividend equal to 1.5 times the original investment, and pays an intermediate dividend in year 2.5 which equals half of the initial investment. We show the computation of the modified IRR with a re-investment rate of 5% per semester. At the bottom of the table we report the present value of the dividends using two different discount rates.

We use a unique and comprehensive dataset containing the precise cash flows generated by a large number of liquidated private equity investments. In order to clarify from the start the peculiar structure of our data, Table 1 shows a typical cash flow stream. (In our analysis we use a modified IRR (MIRR). It is like an IRR but instead of making the assumption that intermediate distributions are re-invested into the project at the IRR rate, it makes the assumption that the intermediate distributions are re-invested into the S&P 500. The reader may refer to Phalippou (JEP 2008) for a discussion of the use of IRR versus MIRR in private equity.) There is an initial negative cash flow (the investment) followed by two positive cash flows (an intermediate distribution and the final dividend corresponding to the divestment). Note that we do not have intermediate valuations for the investment. So, there is no time series of returns, which precludes the use of the usual time-series regressions to estimate risk exposures. In such a context, as in Cochrane (JFE 2005), or Korteweg-Sorensen (RFS 2010), we exploit variation in returns across investments to estimate the risk loadings and abnormal performance of the asset class.

Accounting for liquidity risk, private equity has not outperformed

We fit the four-factor model of Pastor-Stambaugh (JPE 2003) to the data and find a significant beta on the liquidity risk factor (0.64), on the market factor (1.3), and on the value premium factor (1.0), but not on the size factor. These four factors together reduce the alpha of this asset class to zero.

1: Liquidity betas for listed stocks
This is the histogram of liquidity betas from the four-factor model devised by Pastor-Stambaugh (JPE 2003) for all listed stocks in the CRSP database with at least two years of monthly returns between January 1966 and December 2008 (20,500 stocks).

This historical 18% risk premium is significantly larger than the 8% hurdle rate commonly set in compensation contracts, suggesting that private equity investors (limited partners) were setting the bar too low for their fund managers (general partners). Expected risk premia may be lower as the equity premium seems to be declining (see, e.g. Graham-Harvey-Kolb (Book 2010)). Imagine a scenario in which the risk-free rate is zero, and each of the four risk premia is 3% p.a. then the benchmark will be: 1.3⋅3% + 1⋅3% + 0.64⋅3% ≈ 9%. Under this scenario the 8% hurdle rate would make more sense. We feel that it is sensible to have time-varying hurdle rates as the risk premia are time-varying as well.

Importantly, the liquidity risk premium is about 3% annually, which implies a roughly 10% discount in the valuation of the typical investment (see Table 1). We also note that a liquidity risk beta of 0.64 exceeds the corresponding estimate for the large majority (86%) of traded stocks. These results thus suggest that private equity is significantly exposed to the same liquidity risk factor as public equity and other asset classes. The diversification gains that can originate from private equity may thus be lower than previously thought given this additional risk exposure

2: Explaining private equity returns (Log(1+MIRR))
Model Market FF PS
IML 0.638***
Rm – Rf 0.948*** 1.395*** 1.294***
(0.14) (0.26) (0.25)
HML 0.719*** 1.020***
(0.39) (0.29)
SMB –0.124 –0.040
(0.25) (0.24)
Constant 0.006*** 0.000 –0.002
(0.001) (0.000) (–0.003)
Sigma 0.049 0.048 0.046
Adj. R2 0.849 0.853 0.865
N, 1975–2007 139 139 139
Standard errors are in parentheses. One, two, and three stars mark statistical significance at the 10%, 5%, and 1% level, respectively.
Portfolios are formed by the starting date of the investment and must contain at least twenty investments. Each explanatory variable is computed by taking its average value during the portfolio life.Each observation is weighted by the square root of the investment duration to correct for unequal variance. The factor models are standard. IML is the Pastor-Stambaugh (JPE 2003) illiquid minus liquid portfolio.

Capital constraints and funding liquidity

Prompted by the finding of a significant loading on liquidity risk, we study the economic channel that relates private equity returns to market liquidity. We conjecture that due to their high leverage, private equity investments are sensitive to the capital constraints faced by the providers of debt to private equity, who are primarily banks and hedge funds. Adapting the Brunnermeier-Pedersen (RFS 2009) “funding liquidity” theory to private equity, the story is that times of low market liquidity are likely to coincide with times when private equity managers may find it difficult to refinance their investments. In these periods, they may be forced to liquidate the investments or to accept higher borrowing costs, which in turn translate into lower returns for this asset class. Then, we conjecture that the link between private equity returns and market liquidity occurs via a so-called funding liquidity channel.

Empirically, we proxy for the evolution in funding liquidity with changes in the credit standards as reported in the Federal Reserve's Senior Loan Officer Survey. This survey asks loan officers at main banks whether they tightened or loosened their lending standards relative to the previous quarter. Axelson-Jenkinson-Stromberg-Weisbach (JF 2013) argue that, in the private equity context, “this measure captures non-price aspects of credit market conditions, such as debt covenants and quantity constraints.” They find this measure to be strongly related to the amount of leverage used to finance private equity investments.

Turning to the empirical evidence on this channel, we first document a strong relation between private equity investment returns and the average innovation in market liquidity (as measured by Pastor-Stambaugh (JPE 2003)) during the investment's life. The average difference in performance for investments at the extreme deciles of market liquidity innovations is a striking 46% per year. This means that the 10% of the investments that had the best average liquidity conditions (compared to what was expected) during their life outperforms the 10% of the investments with the worst average liquidity conditions (compared to what was expected) during their life by 46% p.a. As there are other important determinants of private equity returns which may also be correlated with liquidity conditions, we verify and do confirm this simple result in a multiple regression setting, in which we control for investment characteristics and macroeconomic variables.

2: Annual performance by deciles of liquidity conditions
This is the average investment MIRR in each decile of the Pastor-Stambaugh (JPE 2003) liquidity condition variable.

Next, we test our conjecture that funding liquidity is the link between these two variables. We first show that returns are significantly related to the tightening in credit standards. A one-standard deviation increase in this measure of the deterioration in funding liquidity decreases the annual return by 16%. Second, when including both the measure of funding liquidity and that of market liquidity, we observe that funding liquidity absorbs half of the market liquidity effect. In addition, we conduct a time-series test using the aggregate cash flows of all the private equity investments each month. Consistent with the cross-sectional evidence, we find that net cash flows (dividends minus investments) are lower at times of tightening in credit standards and at times of worsening liquidity conditions.

Our results are important for two related reasons. First, they improve our understanding of the economic channel underlying the relationship between private equity returns and market liquidity. Market liquidity is found to be closely related to a measure of funding liquidity, which in turn is a determinant of the ease of refinancing for leveraged deals as shown by Axelson-Jenkinson-Stromberg-Weisbach (JF 2013). Second, these results provide empirical support for the theory of Brunnermeier-Pedersen (RFS 2009) relating funding liquidity to market liquidity. Our empirical evidence shows that there is indeed a negative relationship between a dry-up in funding liquidity (the tightening in credit standards) and innovations in market liquidity (the Pastor and Stambaugh measure).






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3: Explaining investment-annualized private equity MIRRs with liquidity conditions
P&S liquidity conditions 0.114*** 0.051** 0.051
(0.028) (0.023) (0.029)
Tightening of credit standards –0.195*** –0.164*** –0.172***
(0.031) (0.026) (0.035)
Industrial production growth –0.003
Delta credit spread 0.006
Relative number of M&A deals 0.011
Delta realized long term volatility –0.022
Rm–Rf 0.068** –0.013 –0.015 –0.019
(0.032) (0.031) (0.029) (0.048)
Growth investment –0.036** –0.042** –0.041** –0.040**
(0.018) (0.017) (0.017) (0.017)
Investment size 0.005 –0.001 0.000 0.001
(0.014) (0.009) (0.000) (0.010)
Fund size –0.001 –0.003 –0.003 –0.002
(0.004) (0.004) (0.005) (0.004)
Country and industry fixed effects yes yes yes yes
Adj. R2 0.093 0.118 0.123 0.124
N (1990–2007) 3,763 3,763 3,763 3,763
Standard errors are in parentheses. One, two, and three stars mark statistical significance at the 10%, 5%, and 1% level, respectively.
Details on the variables can be found in our original paper.

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