Post on 03-Jul-2018
transcript
1
Private equity: strategies for improving performance
Ron Bird*, Harry Liem and Susan Thorp
University of Technology, Sydney
Sydney, Australia
The Paul Woolley Centre for Capital Market Dysfunctionality, UTS
Working Paper Series 12
Previous version: September 2011
This version: April 2012
Abstract
In this paper we investigate whether the average private equity manager creates excess
returns over public markets net of fees. For the purpose of our discussion, private equity
is defined as covering both venture capital and buyout firms. Venture capital firms
provide financing to start up companies. Buyout firms apply leverage to acquire
companies. We investigate excess returns to venture capital and buyouts using a factor
model that allows for liquidity adjustment, volatility clustering and factors specific to
venture capital and buyouts. We find the excess returns for venture capital and buyouts
have been episodic in nature, coinciding with the technology boom of the late 1990s and
the buyout boom of the early 2000s. In addition, the global financial crisis led to
concern on illiquid assets and sales in the secondary markets at deep discounts. We
investigate two methods of improving conventional private equity performance for
institutional investors (Limited Partners). We test the robustness of the methods using
historical and simulated data.
Keywords: buyouts; venture capital; conditional overlay; GARCH.
JEL: G12; G14
* Corresponding author.
E-mail: Ron.Bird@uts.edu.au
Phone: +61 2 9514 7716
Fax: +61 2 9514 7711
Room: CM05D.03.22B
PO Box 123, Broadway NSW 2007, Australia
The authors wish to acknowledge the generous support of the Paul Woolley Centre at the University of
Technology, Sydney. In addition, Thorp acknowledges support under Australian Research Council (ARC)
DP 0877219. The Chair of Finance and Superannuation at UTS receives support from the Sydney
Financial Forum (Global First State Asset Management), the NSW Government, the Association of
Superannuation Funds of Australia (ASFA), the Industry Superannuation Network (ISN), and the Paul
Woolley Centre, UTS.
2
1. INTRODUCTION
The use of private equity by institutional investors was pioneered by U.S. institutional
investors in the mid-1970s, and notably by the Yale Endowment under the leadership of
David Swensen (Swensen 2000). Yale University has continued with this policy,
currently allocating 26 per cent of its assets to private equity.1 Other institutions
followed this successful model to the extent that 5 per cent of institutional assets are
now invested in private equity globally (Baldridge et al., 2010).2 Yet, few investors
have been able to match the returns enjoyed by U.S. endowments. In the private equity
industry, institutional investors such as these endowments are referred to as ‘Limited
Partners’ (LPs), and fund managers as ‘General Partners’ (GPs).3
Lerner et al. (2007) measure the return differential between U.S. endowments and other
Limited Partners at 21 per cent per annum over the period from 1991 to 1998, inferring
that the ability to access superior managers is key to successful investing in the private
equity industry. For endowments, alumni networks lead to access to superior General
Partners and the ability to co-invest (invest alongside the manager, thereby saving on
fees).
Despite the stellar performance enjoyed by some Limited Partners, academic studies
suggest that the median private equity manager has not created excess returns after fees
and various biases are taken into account, see Conroy and Harris (2007), Franzoni et al.
(2009), Kaplan and Schoar (2005), Moskowitz and Vissing Jorgensen (2002), Phalippou
and Zollo (2005) and Swensen (2000). Berk and Green’s (2004) model of rational
1 See http://www.yale.edu/investments/ [Accessed: 23 September 2011]
2 The survey includes 119 institutional firms globally with US$1.3 trillion in assets.
3 Refer to Appendix A for a full description of industry terms.
3
financial intermediation predicts that financial intermediaries will provide zero excess
returns to their investors while capturing a rent that is commensurate with their abilities,
while Biais et al. (2010) suggest that the net returns delivered by financial
intermediaries could even turn negative. The private equity industry may be an example
of rational intermediation: private equity fees are large and complex, with estimates
starting from 7 per cent per annum (Phalippou, 2009) rising to 12 per cent based on the
Yale Endowment’s experience (Swensen, 2000). The 7 per cent fee estimate by
Phalippou (2009) consists of 2 per cent per annum base fee, 2.5 per cent portfolio fees
(transaction, advisory and director fees, taken directly out of the fund holdings) and 2.5
per cent performance fees. Performance fees are 20 per cent above an 8 per cent hurdle
rate. In the case of Yale, the 12 per cent fee estimate reflects the additional performance
fees based on the return differential for U.S. endowments. In addition, Lerner et al.
(2007) estimate 20 per cent of investors use fund of funds, which contributes an
additional 1 per cent base and 10 per cent performance fees.
Given the level of fees, Phalippou et al. (2005, 2007, 2009) suggest an average return to
U.S. private equity of minus 330 basis points below market indices, after all the costs
are taken into account. This can be compared to French (2008), who estimates the cost
of active management at minus 67 basis points for U.S. public equities after all fees are
into account.
Further, the use of stale pricing of private equity assets (i.e., relying on lagged market
valuations of assets for computing returns) can overstate the excess returns created by
managers. Private equity fund managers smooth reported quarterly returns, and during
periods of sharp falls in public markets have the ability to lag valuations of the non-
4
traded assets which make up the majority of their illiquid portfolios. This creates an
artificial stability in unit prices that feeds into returns (Anson, 2006; Gompers and
Lerner, 1997). The reliance on lagged valuations not only creates the illusion of excess
returns during falling markets, but can also potentially overstate realised returns if the
manager relies on lagged valuations to value underperforming investments which in
practice can no longer be exited before the end of the commitment period. Phalippou
and Zollo (2005) refer to this as the ‘living dead’ bias.
We investigate the tension between the evidence for high excess returns of some private
equity managers and the doubts raised once one allows for fees and stale prices. This
paper makes the following contributions to the extant literature. First, we create a factor
model that adjust for liquidity and strategy specific factors, to measure the performance
of private equity investing and improve our understanding of the fundamental drivers of
excess returns.
Second, we investigate two methods designed for Limited Partners for replicating
exposure to private equity. These methods can be applied independently or combined to
increase the reward to risk ratios for investors in the asset class or for performance
evaluation.
The first method demonstrates how a replication approach to private equity can be used
during the commitment period. Limited Partners set aside capital for commitment for
periods of 10 to 14 years and management fees are paid on committed, rather than
invested capital. On average only approximately 50 per cent of committed capital is
invested over the commitment period as the General Partner searches for investment
5
opportunities. Thus, investors tend to over-commit by up to 100 per cent and a 2 per
cent base fee is then effectively increased to three to four per cent (Ljungqvist and
Richardson, 2003; Phalippou and Gottschalg, 2009). Factor replication can offer
benefits in terms of fee reduction, liquidity or performance evaluation. We find that for
our replicator, the increase in liquidity is offset by a reduction in returns.
The second method is designed to overcome some of the illiquidity problems faced by
Limited Partners during the global financial crisis when private equity assets were sold
at deep discounts. An overlay strategy has the ability to reduce risk during periods of
market stress when managers are unable to sell holdings. Because of the illiquid nature
of the underlying holdings, private equity managers are unable to quickly adjust
portfolio positions to changes in market sentiment (unlike, for example, hedge funds).
One option is to trade private equity investments in the secondary market at deep
discounts. However, these actions can lead to large market distortions. The method we
suggest is aimed at the Limited Partner and overcomes illiquidity and is similar to the
method previously proposed to overcome illiquidity in hedge funds by Healy and Lo
(2009).
The remainder of the article is structured as follows. In section 2, we review background
literature on style models used when evaluating private equity performance, while in
section 3 we develop the model used in this study. Our private equity data source is
examined in section 4 and we present our empirical findings in Section 5. Section 6
provides two strategies for improving private equity performance while section 7 offers
conclusions and suggestions for further research.
6
2. BACKGROUND
Table 1 provides a summary of several studies in private equity outlining the style
factor models used. The table also exemplifies the variety of data providers used by
different researchers. Given the limitations and confidentiality of data sources available,
sample selection bias and time period bias contribute to conflicting findings.
<< INSERT TABLE 1 >>
While some authors find evidence of excess returns compared to public equities from
private equity investing, most research concurs these excess returns reduce after various
adjustments. For example, the Dimson (1979) stale pricing adjustment applied by
Anson (2006), Conroy and Harris (2007) and Jones and Rhodes-Kropf (2003) includes
lagged market return data. Other adjustments include adjustment for sample biases, or
where underlying portfolio cash flow data is available, cash flow timing into the S&P
500 to create a Public Market Equivalent (PME) or comparison of Internal Rate of
Returns (IRRs) (Kaplan and Schoar, 2005; Phalippou and Gottschalg, 2009). In
addition, some data may present a time period or sample selection bias. For example,
Peng (2001) and Quigley and Woodward (2003) rely on a venture capital sample ending
just prior to the correction from the technology boom, while Swensen (2000) and
Ljungqvist and Richardson (2003) rely on data from a single Limited Partner. A number
of other biases are discussed in section 5.
Most research applies the equity risk premium (commonly proxied by the S&P 500) as
a key risk factor, although this premium alone may not capture all the risks associated
with private equity investing. The emphasis on the equity risk premium is not
7
surprising: institutional investors continue to use this type of benchmark for their
private equity investments whilst targeting a three to five per cent net of fees out-
performance (Evans, 2008).4 Phalippou (2009) concludes that the literature provides us
with an interesting puzzle: if the average performance of private equity funds is below
the benchmark after fees and biases are taken into account, then why does the marginal
investor allocate to private equity? Phalippou suggests investors underestimate the
impact of fees and rely on biased samples to form their judgement. Swensen (2000,
p.226), perhaps one of the most experienced private equity investors, notes that the
large majority of buyout funds fail to add sufficient value and only the upper quartile of
managers are worth investing in.
3. THE MODEL
Private equity managers provide a package of returns made up of market risk, liquidity
risk, active skill and leverage (Anson 2006). It follows that a comprehensive model of
private equity returns combines all these elements. In this section we create a
multifactor model, in which the equity risk premium is supplemented by additional
associated state variables. In the core intertemporal capital asset pricing model
(ICAPM), Merton (1973) defines state variables as undesirable outcomes against which
investors hedge, thereby creating additional risk premia. For instance, for buyout and
venture capital firms, illiquidity is such a state variable, as investors who commit capital
to private markets are exposed to illiquidity risk. In addition, investors in leveraged
buyouts may be exposed to credit risk as buyout firms take on additional financing,
whereas venture capitalists invest in start up firms and are exposed to small firm and
4 Evans bases his conclusions on a survey of Australian pension funds. This number coincides with the
estimate by Phalippou and Gottschalg (2009) of 4 percent gross of fee alpha per annum, suggesting
excessive fees result in the counterintuitive low net of fee performance.
8
growth risk, as well as exit risk when they decide to enter an Initial Public Offering
(IPO), and are exposed to fluctuations in the stock market.
3.1 Market factors
The model that we use to test for excess returns commences with the CAPM (Sharpe,
1964), or the equity market risk premium Rmt - Rft. In the case of venture capital
investments, we also include the returns on the NASDAQ. A NASDAQ listing is one of
the main exit strategies for venture capitalists and also captures the small cap/growth tilt
inherent in venture capital investments. Anson et al. (2011, p.387) suggest ‘Nasdaq
returns dominate venture capital returns’. However, as institutional investors continue
to benchmark themselves against the S&P 500 for their private equity investments, we
capture the NASDAQ factor similar to the small cap premium by Fama French, i.e. an
additional potential return source (‘entrepreneurial premium’) defined as the return on
the NASDAQ in excess of the S&P 500 returns or (RNQ,t – Rmt).
For buyouts, we do not apply the NASDAQ returns. Instead, leverage is important, and
thereby the ability to obtain financing. The global financial crisis emphasised how the
number and size of mega buyout deals collapsed with changes in the credit market. Our
high yield debt measure is a 50/50 mix of the return on the Barclays Capital U.S. high
yield index and the mezzanine debt5 returns provided by Venture Economics, based on
the financing mix suggested by Anson (2006). This factor captures the reliance of
buyouts on the high yield credit markets which are the main source of their leverage
financing. Thus, buyouts are expected to generate a ‘leverage premium’ during good
5 In leveraged buyouts, mezzanine capital is used in conjunction with other securities to fund the purchase
price of the company being acquired. Typically, mezzanine capital will be used to fill a financing gap
between less expensive forms of financing (e.g., senior loans, second lien loan, high yield financing) and
equity. More details on mezzanine capital can be found in appendix A.
9
times in the high yield markets. Refer also Phalippou and Zollo (2005) who find credit
spreads impact buyout performance: they note the two most significant variables to
affect buyouts to be risky corporate bonds and stock market returns. Again, given that
institutional investors continue to benchmark themselves against the S&P 500 we
provide this factor as an additional variable to the equity risk premium.6 In appendix C
we also show how the financing mix can alternatively be used to make an adjustment to
the S&P 500 beta based on general principles provided by Swensen (2000) and Inker
(2008) to compare the excess returns from buyouts to leveraged excess returns in the
S&P 500.7
3.2 Adjustment for liquidity
For private equity, stale pricing adjustment methods based on Dimson (1979) have been
employed by Anson (2006), Conroy and Harris (2007), Gompers and Lerner (1997) and
Jones and Rhodes-Kropf (2003). A discussion of the Dimson method can also be found
in Phalippou (2009). In general these methods rely on including lagged market
variables. The Dimson beta is the sum of regression coefficients on the
contemporaneous and lagged market returns. It estimates the beta of the unobservable
“true” private equity return and captures movements in private equity which may not
show up in reported data for a number of periods. Consistent with Anson (2006) we
6 We test for multicollinearity, and find a correlation of 0.3 between the S&P 500 and the 50/50 financing
mix, which we consider acceptable. This suggests the high yield premium represents a risk premium with
distinct drivers, notably company specific bankruptcy risk. For a discussion of the high yield market and
drivers post the buyout boom
http://www2.goldmansachs.com/gsam/docs/funds_international/education/investment_and_sales_educati
on/case_for_high_yield_sep_10.pdf. [Accessed: 23 September 2011] 7 In addition, we also considered deleveraging buyout returns (the dependent variable in our regression
equations). However, the identified variables on the right hand side of the regression equation would then
also need to be appropriately delevered, which is not straightforward given the market factors identified.
Second, an adjustment would need to be made on the deleveraged performance fees, which in private
equity are complex and involve different types of waterfalls (profit sharing between LPs and GPs) and
clawbacks (which give the LPs rights to reclaim performance profits). Third, we believe investors are in
practice more likely to gear up S&P 500 returns for comparison/benchmarking purposes (as per appendix
C), rather than degear their original investments.
10
include 3 lags of our state variables. As we find the coefficients significant in our
model, this suggests managers use up to 3 lags to arrive at their present appraisal based
value.
3.3 Mean equation
Having identified the relevant risk variables, equations (1a) and (1b) measure whether
significant excess returns are created by private equity managers. Equations (1a) and
(1b) are essentially CAPM (Sharpe, 1964) models extended for the ‘entrepeneurial’ and
‘leverage’ risk premia. For venture capital, the NASDAQ is added as a factor (1a). For
buyouts, a high yield factor is added (1b).
it
l
ltmltNQil
k
ktfktmikiftit RRRRRR
3
0
,,
3
0
,, )()( (1a)
it
l
ltfltHYil
k
ktfktmikiftit RRRRRR
3
0
,,
3
0
,, )()( (1b)
Where Rit is the rate of return of private equity strategy i at time t, Rft is the risk free rate
at time t and αi is the intercept term not explained by the multi-factor model. In terms of
factor exposure, ∑(Rm,t-k – Rf,t-k) represents the equity risk premium in various lags,
where we include up to three lags (k=3). Coefficients βik measure the market sensitivity.
The additional factors are represented by ∑(RNQ,t-l – Rm,t-l) for equation (1a) reflecting
the differential returns on NASDAQ stocks and larger capitalised companies, and
∑(RHY,t-l – Rf,t-l) reflecting the leverage premium obtained by investing in a mix of high
yield and mezzanine debt for equation (1b). Note that the multifactor/multiple lag
methodology has also been employed by Jones and Rhodes-Kropf (2003).
11
Equations (2a) and (2b) extend equations (1a) and (1b) to include the Treynor and
Mazuy (1966) market timing component (Rmt - Rft)2
. Under Treynor and Mazuy a
significant positive coefficient (βtiming) suggests positive market timing ability.
itftmtgti
l
ltmltNQil
k
ktfktmikiftit RRRRRRRR
2
min
3
0
,,
3
0
,, )()()(
(2a)
itftmtgti
l
ltmltHYil
k
ktfktmikiftit RRRRRRRR
2
min
3
0
,,
3
0
,, )()()(
(2b)
While private equity concerns long term commitment, it is of interest to Limited
Partners to understand how private equity performs during equity market downturns.
Consider the experience of the Harvard Endowment and the Wellcome Trust during the
global financial crisis.8 We test the defensive abilities of private equity using equations
(2a) and (2b), but also directly against the S&P 500.
3.4 Variance equation
In the case of private equity, buyout firms apply leverage, and it is important to
understand the leverage implications on volatility of the errors in our model. As a
consequence we use maximum likelihood estimation to apply the GJR-GARCH
(Glosten, Jagannathan and Runkle 1993) which caters for asymmetry in the GARCH
process in up and down markets. Under this model, given the information set Ω at t-1
then εit | Ωt-1 ~ N(0,hit) and the conditional volatility is
hit = γ0 + γ1ε2
i,t-1 + γ2hi,t-1 + γ3ε2
i,t-1It-1 (3)
where It−1 = 0 if εi,t-1 ≥ 0, and It−1 = 1 if εi,t-1 <0.
8 Refer http://www.preqin.com/item/secondaries-deluge-leads-to-asset-pricing-turmoil/101/1098.
[Accessed: 23 September 2011]
12
In this case, γ0 represents a constant intercept impacting the long run unconditional
volatility, γ1 a weighting to the previous period’s squared shock, γ2 a weighting to the
previous period’s predicted volatility and γ3 sensitivity to negative returns shocks. In
addition we estimate t-distributed errors to capture possible fat tails in return
distributions. The expectation is to find evidence of GARCH effects (positive γ1 and γ2)
if the appraisal based process is strongly influenced by market based factors, rather than
on the manager’s discretion (which would result in constant volatility). We also expect
a positive γ3, and fat tailed errors, because of the leverage inherent in buyouts.
4. THE DATA
For our sample, we rely on quarterly data on the return on private equity funds using the
Venture Economics indices, which cover over 2,184 private equity funds. Venture
Economics remains the most frequently used database in terms of academic research,
(see Conroy and Harris, 2007; Kaplan and Schoar, 2005; Phalippou and Gottschalg,
2009). We use the aggregate performance of composites from January 1990 to
December 2009. As a consequence, our findings will reflect an overall average
performance across funds across this time period. Venture Economics gathers its data
from surveys sent to private equity funds and thus relies on self-reporting.
These surveys are voluntarily filled in on a confidential basis and not audited. A pooled
return of all funds is then calculated by Venture Economics by treating all funds as a
single fund by combining their monthly cash flows. This cash flow series is used to
calculate a time-weighted rate of return. For example, the quarterly return Rt of an index
at time t equals (Asset valuationt + Distributionst – Cash inflowst ) / (Asset valuationt-1)
whereby the Asset valuations, Distributions and Cash inflows are the aggregated
numbers reported by industry participants. This method creates an asset weighted return
13
and matches the method many investors use to measure portfolio returns. Similar to a
market-value weighted index in the equity market, this pooled method is considered an
appropriate method for presenting the aggregate performance of private equity funds.9
Chen et al. (2002) and Kaplan and Schoar (2005) claim biases do not occur in the
Venture Economics database despite the voluntary reporting nature. First, Venture
Economics’ dataset is based on anonymous reporting by General and Limited Partners.
Thus there is no incentive to bias performance data upwards as funds cannot be
marketed through the database. Second, private equity funds have a long and fixed
lifespan (10 to 14 years). There is no incentive for a private equity manager to force
early closure and so discontinue reporting returns, as long as fees can be collected. Born
et al. (2005) note successful and unsuccessful projects are intrinsically linked together
within the performance of a fund, thus, unsuccessful investments are always included.
Venture Economics provides by far the most extensive data set available for research.
However, Grabenwarter and Weidig (2005) note Venture Economics actively tries to
complete data retrospectively by asking managers to add data on so far unreported funds
and this possibly biases the sample towards successful funds. Phalippou and Gottschalg
(2009) find evidence industry associations use samples that overrepresent good funds.
9 Unlike Kaplan and Schoar (2005), we were not provided access to the underlying cash flows, but only
the aggregate pooled index data by Venture Economics. Thus, Internal Rate of Return (IRR) or Public
Market Equivalent (PME) based performance methods could not be investigated. A discussion on why
IRR can potentially be used to overstate results can be found in Phalippou (2009). Examples of PME
calculations can be found in Kaplan and Schoar (2005). Jones and Rhodes Kropf (2003) note that using
PME as a performance measure is equivalent to assuming that all private equity investments have a
CAPM beta of one. Phalippou and Zollo (2005) point out this may not hold in practice.
14
On the other hand, Harris et al. (2012) suggest the data in Venture Economics is
downward biased.10
One other and unique bias to private equity is reported by Phalippou and Zollo (2005)
and known as the “living dead” bias, or when investments that can no longer be exited
profitably are maintained at their last appraised value. The extent of this bias depends
on the valuation of non-exited investments at the end of the sample period. Phalippou
and Zollo use a unique and comprehensive data set to calculate this bias by aggressively
writing off residual values (rather than maintaining them at the last reported values) on
funds over 10 years old, over the period from 1980 to 1996. They argue the bias
accounts for up to 2.5 to 3.5 per cent of performance. The evidence on the size of this
bias falls outside the scope of this paper, as we do not have access to the same level of
detail in our data. The biases discussed, as well as the anonymous nature of the
database, are an important limitation of our research.
5. EMPIRICAL RESULTS
5.1 Descriptive statistics
The descriptive statistics for the data are shown in Table 2.
<< INSERT TABLE 2 >>
10
The body of work on private equity research relies on Venture Economics. Harris et al. (2012 p.2) in
their working paper suggest Venture Economics data potentially understates returns based on "evidence
that many funds stopped being updated from around 2001 and yet were retained in the VE database at
latest NAVs.” As NAVs are rolled forward, IRRs decline. However, it should be pointed out that those
funds could have potentially stopped updating because they went out of business after the height of the
NASDAQ boom. Thus, those firm returns could potentially be overstated, rather than understated.
Presumably, there would be little incentive for industry associations such as Venture Economics to bias
returns downward, hence the reluctance to write down NAVs.
Furthermore, Harris et al. rely on data from Burgiss, a provider which uses data from Limited Partners
only, which as Lerner, Schoar and Wong (2007) note, is easily biased by the LP selection. Harris et al.
note “private equity performance in the other commercial sources – other than Venture Economics – is
qualitatively similar to that we find using the Burgiss data.” Thus, we verify our conclusions using data
provided by Cambridge Associates, (not reported here). The results are similar: excess returns in private
equity are episodic, a conclusion also reached by Harris et al.
15
The descriptive statistics for the data are shown in Table 2. Based on the excess return
column in Table 2, the descriptive statistics suggest returns of all strategies exceed the
risk free rate prior to adjustment for market and liquidity factors and various biases. The
standard deviation is found to be higher for venture capital than buyout firms, around
1.7 times based on a comparison of ‘all venture’ versus ‘all buyouts’. In terms of
systematic risk, a beta to the S&P 500 is found for venture capital firms of around 0.6,
compared to 0.3 for buyouts.11
The positive skew in returns for venture capital reflects
the large upside optionality arising in venture capital when portfolio companies go
public at large multiples to their original investment. Buyout returns are more normally
distributed than venture capital with some negative skew coming from the ocurrence of
losses when large buyouts fail. The low liquidity (high serial correlation) in venture
capital reflects strategies of investing in smaller, illiquid companies. Buyouts, investing
in relatively more mature companies exhibit higher liquidity (lower serial correlation).
As can be seen from table 2, both venture capital and buyouts outperform the S&P 500,
prior to adjustments.
5.2 Performance of GARCH models
Results from the estimation of the asset pricing models are shown in Table 3a. For
venture capital, the intercept (α) shows 1.38 percent per quarter, or 5.5 per cent excess
return per annum, and is statistically significant. In terms of the underlying strategies, 4
out of 5 venture capital strategies show evidence of excess returns and dependence on
the (lagged) S&P 500 (βm) and lagged Nasdaq (βNQ). Of interest is that the ‘early seed’
and ‘seed stage’ venture capital show increased dependence on the (lagged) Nasdaq,
11
Various authors suggest this beta may be understated compared to bottom betas estimated from the
underlying investments, refer e.g. Driessen, Lin and Phalippou (2011). The beta figures quoted are the
coefficient on the co-incident market return. Under the Dimson model (1979), lagged betas can be
summed up to provide a more accurate picture. Tables 3 and 5 show the components under a Dimson
regression.
16
whereas ‘balanced’/’latter stage’ venture capital show dependence on the (lagged) S&P
500. Furthermore the summed betas under the Dimson method (∑βm) and (∑βNQ) are all
significant.
We do not find statistically significant excess returns for buyouts in general (‘all
buyouts’), although on an economic basis, 0.57 percent per quarter would translate into
2.3 percent excess return per annum. Buyouts are found to have exposure to the equity
risk premium (βm), but not as much to its lags. This is consistent with the higher
liquidity (lower serial correlation) found in table 2 and the buyout focus on mature
companies. Reliance on financing conditions, or the high yield premium (βHY),
concentrates in ‘mega buyouts’, while some excess returns are found in ‘medium
buyouts’, suggesting this is a possibly profitable niche segment for investors.
Furthermore the summed equity market betas under the Dimson method (∑βm) are
significant for most buyout strategies, whereas credit markets (∑βHY) are significant for
small buyouts.
<< INSERT TABLE 3a >>
We find evidence of ARCH (γ1) and GARCH (γ2) effects, suggesting volatility
persistence and clustering. These effects are concentrated in ‘balanced’/’latter stage’
venture capital and ‘mega buyout firms’, suggesting the appraisal based returns from
these firms are more influenced by prevailing market conditions. Thus, the closer firms
are to their exit stage for venture capital, or the larger the buyout, the more market
related factors impact return volatility.
17
Surprisingly, the volatility leverage coefficient (γ3) is not significant for buyouts. In
addition, most errors estimated by the model turn out to be normally distributed, rather
than having the fat tailed t-distributions expected when leverage amplifies return
volatility. Thus leverage does not impact conditional volatility. We suggest that, unlike
for hedge funds, the appraisal based nature of private equity removes the expected
leverage aspects and results in more normally distributed returns. In essence, managers
manage to smooth downside volatility commonly associated with leverage.
The model explains 51 per cent of the variation in returns for ‘all venture capital’ firms
and 55 per cent of the variation in returns for ‘all buyout’ firms.
Swensen (2000, p.237) argues “over long periods of time, venture investors receive no
more than market like returns with demonstrably higher levels of risk.” To conclude
from the analysis in table 3a that venture capital firms will continue to create excess
returns on a forward looking basis can be misleading. Section 6.3, ‘rolling beta and
excess return analysis’, shows a large portion of the excess returns were created during
the technology boom of the late 1990s. Such a period of exuberance in the NASDAQ is
unlikely to be repeated and influences findings reported by Peng (2001) and Quigley
and Woodward (2003).
Removing the technology boom period, table 3b shows the excess returns disappear for
most of the venture capital strategies. The intercept now indicates venture capital as a
group has not added value over the recent decade, but has in fact detracted value.
18
However, because of the recent buyout boom (2002-2007) the excess returns for many
buyout firms now become statistically significant. Table 3b also shows the buyout boom
did not result in excess returns to mega buyout firms, which were concentrated at the
tail end of this period (2005-2007). In July 2007, turmoil affecting the U.S. mortgage
markets spilled over into the leveraged finance and high-yield debt markets. As 2007
ended and 2008 began, lending standards tightened and the era of "mega-buyouts" came
to an end. Thus, the question arises to what extend the favourable financing conditions
for buyouts during the early 2000s are likely to recur going forward.
Excluding the volatile period surrounding the technology boom increases the adjusted
R2 from the model from 0.51 to 0.67 for venture capital and 0.55 to 0.74 for buyouts.
12
<< INSERT TABLE 3b >>
5.3 Stability of factors
<< INSERT FIGURE 1a>>
<< INSERT FIGURE 1b>>
Figures 1a and 1b show seven year rolling averages for the co-incident betas in our
model, which are calculated by regressing rolling 28 quarterly observations (7 years of 4
quarters) of private equity returns against the identified risk factors. The seven year
period is selected to have sufficient data points to regress against, and also to coincide
12
In addition, a comparative analysis using data from Cambridge Associates and also a Fama French
model was performed as a cross reference for potential biases in the Venture Economics database and to
further test the robustness of our model. Our conclusions remain unchanged: returns to private equity are
episodic in nature. Refer https://www.cambridgeassociates.com/pdf/Venture%20Capital%20Index.pdf
and https://www.cambridgeassociates.com/pdf/Private%20Equity%20Index.pdf [Accessed: 27 February
2012]
19
with the maximum period needed to realise private equity investments (refer Appendix
B).13
Figure 1a shows for venture capital a period of excess returns (alpha) is detected in the
1990s coinciding with the technology boom, during which a high exposure to equity
and NASDAQ markets was undertaken by venture capital managers. A peak in liquidity
was reached around 2000-2001 at the end of the technology boom. Between 2002 and
2007 venture capital turned illiquid, as investors’ interest turned towards Buyouts.
Figure 1b shows buyouts exposure to the high yield markets increased during the
buyout boom in the 2000s, prior to the financial crisis. Buyouts have remained fairly
liquid. In terms of excess returns, these have been episodic in nature, and zero is in the
95 percent confidence bands for most of the time.
The betas to the equity market are surprisingly stable for both venture capital and
buyouts and could be used to replicate private equity returns.
6 Strategies for improving performance
The R2 from our factor model and the stability of the equity market beta have important
implications for investors. Below we outline two strategies to replicate or benchmark
the returns generated by investments in both venture capital and buyouts.
6.1 Strategy 1: Overcoming commitment and illiquidity problems
13
The co-incident betas are reported, rather than the Dimson summed betas, as these will be used for
replication purposes in later sections, i.e. one cannot invest in lagged betas.
20
The first application of the factor model is designed for the institutional investor
(Limited Partner) and is used to test whether exposure to passive factors can be used
replicate or benchmark direct investments in private equity.
We rely on the illiquid asset model of Alexander and Takahashi (2001) to demonstrate
the performance over a typical 12 year commitment period of directly investing in
private equity via active managers versus gaining exposure via a passive factor model.
We assume S&P 500 and NASDAQ exposure can be obtained using liquid futures at
low (negligible) cost, while for exposure to high yield debt we assume a 1 percent
annual management fee.14
Yale has been investing in buyouts since 1973 and venture capital since 1976. Based on
Yale’s experience, Alexander and Takahashi (2001) developed a model for assessing
the impact of changing investment levels during the commitment period (the period for
which an institution commits to a private equity program with a manager, in general
between 10 to 14 years) which has been fitted in terms of parameters based on Yale’s
actual experience. Figure 2 represents the investment pattern of a typical capital
commitment based on Yale’s default settings for contribution rates (contributions refers
to the capital called up each year from the investor whenever the manager finds suitable
investments), fund life, committed capital and capital growth rates.
<< INSERT FIGURE 2>>
14
This reflects fees (but no additional alpha) for an active mandate. Passive high yield exposure can be
obtained at 40-50 basis points per annum, through ETFs such as HYG
http://us.ishares.com/product_info/fund/overview/HYG.htm or JNK
https://www.spdrs.com/product/fund.seam?ticker=JNK [Accessed: 23 September 2011]
21
Figure 2 suggests that once capital is committed for the 12 year period, the majority of
contributions by the investor are called up by the manager over the first five years of the
commitment period. During this period the manager is searching for companies in
which to invest, and starts distributing dividends and capital gains proceeds from year
three onwards. Based on Yale’s experience, 56 per cent of committed capital is invested
over the 12 years and this is represented by the horizontal line in Figure 2. Thus, an over
commitment of capital of about 2 times is suggested by private equity managers.
When we cross-reference Yale’s settings with information provided by DeBrito et al.
(2006) for the Venture Economics database from 1985 to 2004, we find that they
substantiate the patterns provided by Yale.
The fact that fees are typically paid on committed, rather than invested, capital inflates
the cost of investing in private equity, especially during the first 5 years when the over
commitment is greatest.
Appendices D and E describe the steps used in a simulation through a direct investment
(based on simulated Yale model allocations) and a replicating portfolio based upon the
factors in our model. 1,000 runs are created of possible 12 year commitment periods,
whereby we preserve the serial correlation and economic relationships in our data series
and allow for time-varying beta.
For venture capital, we find a replicating asset converges to an 80 percent weight to the
S&P 500 and 10 percent to the NASDAQ with the remainder in cash. For buyouts we
find the replicating weights converge to 40 percent S&P 500, 15 percent high yield and
22
the remainder in cash. Venture capital and buyouts represent illiquid investments as
managers require investors to lock in their money over a 10 to 14 year commitment
period. In equations (1a) and (1b) we measured the illiquidity adjustment by using
lagged market returns. In practice, we cannot replicate lagged returns. Thus, to replicate
contributions from the illiquidity premium using market based instruments we use a
concept proposed by Golts and Kritzman (2010): a long position in an illiquid asset
equals a long position in a liquid asset and a short position in the liquidity premium. The
short liquidity option proxy consists of a quarterly, at the money put option sale on the
S&P 500. It is assumed that liquidity risk is asymmetric, and changes in liquidity
coincide with declines in the S&P 500. Additional details on the liquidity option model
and other possible liquidity proxies considered can be found in Appendix E. Table 4
represents the out of sample performance over 1,000 simulation runs.
<<INSERT TABLE 4>>
As can be seen from Table 4, the factor model underperforms direct investments by 1.4
to 1.5 per cent per annum, which suggests some give up in return for the increased
liquidity. At the same time, we do not find this difference to be significant at the 90 or
95 percent confidence levels from our simulation. In slightly less than half the
simulations, the replicator outperforms the direct investment. This is shown in figure 3.
<< INSERT FIGURE 3>>
23
In addition, the size of various biases suggested in literature which may exist in the
Venture Economics database can still account for the difference.15
The low returns for
the direct investment reflect a combination of only half the committed capital being
invested on average, and the lower private equity returns over the 1997-2009 period
which we use as the out of sample dataset for our simulation. For the replicating
product, the low returns reflect the deteriorating capital markets conditions over the
same period.
A high tracking error is observed between the factor based approach and the direct
investment approach over the 12 year period, reflecting a comparison of smoothed
returns of active managers and market based factors. The factor models’ worst possible
12 year run suggests a loss higher than that of the direct investment, but it can also be
argued that the smoothed returns obtained from the managers are subject to stale
pricing. In any case, table 4 suggests replicators can potentially be used for performance
benchmarking at the end of the commitment period. While there is a give up in returns,
there is an increase in liquidity. If investors cannot access superior private equity
managers, they can in the interim invest using a factor based approach, and maintain
liquidity while waiting for capacity to be released. However, investors need to be aware
they are then exposed to market based factors, rather than smoothed manager returns.
As per table 4, replicators have higher volatility and downside risk.
6.2 Strategy 2: Implementing a conditional hedge
Investors’ experience during the global financial crisis acknowledged that alternative
assets have embedded equity and illiquidity risk, and that focusing hedging solely on
the public equities portion of a traditional balanced fund may result in overoptimistic
15
For example the upwards bias in reported database returns from investment managers noted by
Phalippou and Zollo (2005) and Phalippou and Gottschalg (2009).
24
diversification expectations. Whereas many traditional asset classes remained liquid, a
number of alternative investments turned extremely illiquid. We suggested earlier that
investors consider the experience of the Harvard Endowment and the Wellcome Trust
who were forced to sell private equity holdings at large discounts in the secondary
market.16
In this section we extend a method first proposed by Healy and Lo (2009) for hedge
funds to create liquidity when investors are unable to redeem from illiquid asset classes
as market conditions deteriorate. Implementation ultimately depends on the Limited
Partner’s overall portfolio risk budget in terms of ability to take on basis risk (the
tracking risk between the underlying asset and the overlay we propose), liquidity risk
from an overall portfolio perspective, as well as the Limited Partner’s ability to
negotiate suitable cost effective instruments.
6.2.1 Usefulness of a hedging overlay
Our analysis starts with the question of whether it is actually worthwhile to hedge
downside risk in private equity, given that managers tend to smooth returns (and thus
have the ability to offer stale pricing) during periods of market downturns and thereby
understate the downside risk associated with investment via active private equity
managers. Table 5 presents the result from estimating equations (2a) and (2b), whereby
we use the Treynor Mazuy coefficients to measure defensive abilities.
<< INSERT TABLE 5 >>
16
Refer http://www.preqin.com/item/secondaries-deluge-leads-to-asset-pricing-turmoil/101/1098.
[Accessed: 23 September 2011]
25
Table 5 shows the Treynor Mazuy coefficients (βtiming) suggest that the performance of
venture capital and buyout strategies deteriorates during equity down markets. The
small firms and levered buyouts that play an important role in private equity strategies
tend to rely on sub-investment grade debt, and financing becomes more difficult to
obtain for these firms during periods of market stress than is the case for large
investment grade firms with more established credit facilities. Table 5 thus suggests
potential performance improvement if risk factor exposure can be hedged out during
periods of market stress.
6.2.2 Developing a hedging program
A successful hedging program requires that the risk factors in a linear risk model
account for a significant fraction of the variability in the manager’s returns, as we have
found to be the case in our model. Hedging these factors only during periods when the
portfolio is deemed to be at higher risk and forgoing the overlay during other periods
may seem like market-timing, but in fact is closer to volatility-timing, a considerably
less daunting challenge (Healy and Lo, 2009). In fact, there is evidence that volatility is
both time-varying and persistent, as we detect GARCH effects. Investors do respond
dynamically to sharp changes in risk, which is consistent with a conditional
implementation of beta overlay strategies. Based on Healy and Lo, a hedge Rht for
strategy i can be constructed as follows:
n
k
ktikht FR1
(4)
Rht+Rit = αi+εit (5)
26
such that the sum of the Rht and Rit contains no factor exposures.
Following equation (6), the investor is expected to hold a combination of the direct
investment and the conditional hedging portfolio (the overlay). We apply an overlay
method based on a number of assumptions regarding investor behaviour. First, we use
the volatility index (VIX) as an important indicator of deteriorating market conditions.
Various indicators exist to detect the presence of a ‘risky’ environment. Healy and Lo
(2009) suggest a moving average system or an absolute VIX number. In our model, we
test various hedge levels whenever the quarterly VIX in the preceding period exceeds
long term historical stock volatility of 15 per cent to 20 per cent. We test the use of 20
per cent, 30 per cent and 40 per cent as trigger levels, with 30 proving to be the base
case.
Second, to set up the hedge ratios we use the dynamic process introduced earlier. The
period from 1990-1996 provides the initial beta (hedging weights) estimates. We then
apply the quarterly update and regress over the lengthened lookback period to determine
the weights of specific risk factors to hedge for the subsequent period. We measure the
impact based on the out of sample returns realised under the market conditions existing
from 1997 to 2009.
Our multifactor hedges require investors to be able to short the S&P 500 and NASDAQ
futures for venture capital using stock index futures. In addition, for buyouts, the
availability of high yield credit default swaps (CDS) can be used to obtain the desired
27
short high yield credit exposure. Based on discussions with market participants, we
conservatively assume an annual hedging cost of 1 percent for the CDS exposure17
.
Experience during the global financial crisis suggests that where possible, the hedging
process be separately managed at the investor level, rather than within an investment
product, especially where such a product contains mainly exposure to illiquid assets.
For large investors, the hedge overlay program can then access the liquid assets in the
Limited Partner’s overall portfolio for meeting marked to market calls. Table 6 shows
the out of sample performance under a single (historical) path.
<< INSERT TABLE 6 >>
As can be seen from table 6, adopting the conditional hedge under most cases increases
returns for both venture capital and buyout firms under various VIX thresholds. At the
same time risk, as defined by standard deviation, is reduced and the distributions
become more normal as the hedge removes outliers during the process.
As a final robustness test, we compare the impact of the hedge under simulated market
conditions. We simulate returns provided by the managers and the associated capital
market factors required to set up the hedge (the S&P 500, the NASDAQ, the high yield
premium and the VIX) for 1,000 runs of 12 years. By simultaneously resampling the
data across four rolling quarters (rows) as well as across economic variables (columns)
we preserve the serial dependence within variables and also the relationships across
17
The cost of rolling is estimated at 70 bp by various market participants based on the HY17 Markit CDX
North America high yield index. This is considered the most liquid index which rolls every 6 months, and
contains exposure to 100 non-investment grade entities. Bloomberg code CXPHY017 [index].
Alternatively, there are the HYG and JNK ETFs which can be shorted, which we discussed earlier.
28
variables and the VIX. If the VIX is found to be above the hedge threshold during the
current quarter, the hedging overlay is applied for the next quarter. A distribution of
1,000 runs is obtained as shown in Table 7.
<<INSERT TABLE 7>>
Table 7 suggests that when the hedge is applied across a large range of possible
simulated capital market conditions, in half the cases the hedge results in improved
returns or risk reduction. However, the table also indicates that the potential benefits are
of a larger magnitude than potential losses.
7. CONCLUSIONS
We suggest the excess returns in venture capital and buyouts have been episodic in
nature, coinciding with the technology boom of the late 1990s, and the buyout boom of
the early 2000s. Ang et al. (2009, p.136) conclude that “there is little convincing
evidence of superior risk adjusted returns to private equity and venture capital.
Arguably some recent alternative vehicles simply repackage certain systematic factors
in much more expensive forms.” Confirming this argument, we find that 50 to 70 per
cent of the variation in private equity returns is explained by the style tilts introduced in
our model.
We investigate two strategies that can be used to benchmark or improve performance of
this asset class for investors. The strategies can be used independently or combined. Our
first proposed strategy serves to replicate or benchmark private equity performance
during the commitment period against a factor model. We find this strategy
29
underperforms direct investments, but provides better liquidity. Our second proposed
strategy suggests excess returns and liquidity can be improved by applying a conditional
overlay to improve protection during periods of market stress. We test both strategies
for robustness using historical data and simulation models.
A number of areas are of interest for further research. First, while some literature
suggests that the average private equity manager underperforms public markets, there is
also acknowledgement that U.S. Endowments have been very successful private equity
investors. A wide dispersion of manager returns and the persistence of top quartile
performance by managers has been documented (Aigner et al., 2008). Research into the
characteristics of these successful managers has the potential to improve excess returns
accruing to investors. Caution is advised however: Phalippou (2010) suggests the entry
of skilled investors eliminates excess performance persistence for venture capital firms,
confirming the Berk and Green argument.
Second, investors who, unlike the U.S. endowments, find they cannot access top
quartile managers until new funds are raised, can consider gaining synthetic exposure in
the interim, along the lines that we have described in this paper. We note however, that
this exposes investors to traditional market factors, and notably the equity risk premium.
Thus, there is a cost in diversification benefits, and the reliance on market based (non-
smoothed) factor risk increases experienced volatility compared to a direct investment.
In addition, although our dynamic beta analysis suggests that some of the factor betas
have been fairly stable, this may not be the case going forward as the private equity
industry continues to evolve. For example, in the 1990s private equity focused on
venture capital and the technology boom whereas in recent times it has become
30
synonymous with large scale buyouts. As more data points become available, greater
insight can be gained into the stability of the factor betas.
Third, biases have not been central to our discussion. Some biases are unique to private
equity. The ‘living dead’ bias reported by Phalippou and Zollo (2005) suggests
managers rely on lagged valuations to value underperforming investments which in
practice can no longer be exited. This reduces reported excess returns and investors may
in reality experience an underperformance versus public markets or even against our
proposed replicating solutions. Apart from the lack of available data, some biases such
as ‘self selection’ bias (whether or not funds decide to include themselves within a
particular database) are notoriously hard to measure. Thus, this paper serves only as a
starting point for further research on the fees, transparency and valuation methods
currently offered by the industry.
31
REFERENCES
Aigner, P., Albrecht, S., Beyschlag, G., Friederich, T., Kalepky, M., and R. Zagst, 2008. What
Drives PE? Analyses of Success Factors for Private Equity Funds, Journal of Private Equity
11(4), 63-85.
Alexander, S., and D. Takahashi, 2001. Illiquid Alternative Asset Modeling, Yale International
Center for Finance working paper.
Anson, M.J.P., 2006. Handbook of Alternative Assets, Wiley.
Baldridge, J., Cormier, J., and V. Leverett, 2010. 2010 Global Survey on Alternative Investing,
Russell Investments.
Berk, J.B., and R.C. Green, 2004. Mutual fund flows and performance in rational markets,
Journal of Political Economy 112(6), 1269–95.
Biais, B., Rochet, J.C., and P. Woolley, 2009. Rents, learning and risk in the financial sector and
other innovative industries, Paul Woolley Centre working paper, Toulouse School of
Economics.
Black, Fischer, and M. Scholes, 1973. The Pricing of Options and Corporate Liabilities, Journal
of Political Economy 81(3), 637–654.
Conroy, R.M. and R.S. Harris, 2007. How Good are Private Equity Returns?, Journal of
Applied Corporate Finance 19(3), 96-108.
Cornell, B., and K. Green, 1991. The investment performance of low-grade bond funds, Journal
of Finance 46(1), 29-48.
Corrado, C.J., and T.W. Miller, 2005. The forecast quality of CBOE Implied volatility indices,
Journal of Futures Markets 25(4), 339-373.
De Brito, N., De Figueiredo, R., and R. Meredith, 2006. Portfolio Management with Illiquid
Investments, Citi Alternative Investments.
Dimson, E., 1979. Risk measurement when shares are subject to infrequent trading, Journal of
Financial Economics 7(2), 197-226.
Driessen, J., Lin, T.C., and L. Phalippou. 2011. A new method to estimate risk and return of
non-traded assets from cash flows: the case of private equity funds, Journal of Financial and
Quantitative Analysis, Forthcoming.
Evans, J., 2008. Study of Australian Superannuation fund attitudes to private equity investing,
Australian School of Business Research Paper.
Fama, E.F., and K.R. French, 1993. Common Risk Factors in the Returns on Stocks and Bonds,
Journal of Financial Economics 33(1), 3–56.
Ferson, W.E., 2009. The problem of alpha and performance measurement, University of
Southern California working paper.
Ferson, W.E., and R.W. Schadt, 1996. Measuring Fund Strategy and Performance in Changing
Economic Conditions, Journal of Finance 51(2), 425-462.
Franzoni, F., Nowak, E., and L. Phalippou, 2009. Private Equity and Liquidity Risk, University
of Lugano and Swiss Finance institute working paper.
French, K. R., 2008. Presidential address: the cost of active investing, Journal of Finance 63(4),
1537-1573.
Glosten, L.R., Jagannathan, R. and D.E. Runkle, 1993. On the Relation between the Expected
Value and the Volatility of the Nominal Excess Returns on Stocks, Journal of Finance 48(5),
1779-1801.
Golts, M., and M. Kritzman, 2010. Liquidity Options, Revere Street, working paper.
Gompers, P.A, and J. Lerner, 1997. Risk and Reward in Private Equity Investments: the
Challenge of Performance Assessment, Journal of Private Equity 1(2), 5-12.
Gottschalg, O., and A.P. Groh, 2007. The Risk-Adjusted Performance of US Buyouts, HEC
School of Management, working paper.
Grabenwarter, U., and T. Weidig, 2005. Exposed to the J-Curve: Understanding and Managing
Private Equity Fund Investments, Euromoney Investors.
Griffin, T.M., 2010. Effect of the recession on private equity and leveraged buyouts: burned, but
the phoenix is rising from the ashes, Gibbons.
32
Harris, R.S., Jenkinson, T., and S. Kaplan, 2012, Private Equity Performance: What Do We
Know?, Fama-Miller Working Paper; Chicago Booth Research Paper No. 11-44; Darden
Business School Working Paper No. 1932316
Healy, A. and A. Lo., 2009. Jumping the Gates: Using Beta-Overlay Strategies to
Hedge liquidity constraints, Journal of Investment Management 7(3), 11-30.
Jones, C., and M. Rhodes-Kropf, 2003. The price of diversifiable risk in venture capital and
private equity, Columbia University working paper.
Ick, M. M., 2005. Private Equity Returns: Is There Really a Benefit of Low Co-movement with
Public Equity Markets?, University of Lugano working paper.
Kaplan, S., and A. Schoar, 2005. Private Equity Performance: Returns, Persistence and Capital,
Journal of Finance 60(4), 1791-1823.
Korteweg, A. and M. Sorensen, 2008. Estimating Risk and Return of infrequently traded Assets:
A Bayesian Selection model of Venture Capital, Columbia University working paper.
Lerner, J., Schoar, A. and W. Wong, 2007. Smart Institutions, Foolish Choices: the limited
partner performance puzzle, Journal of Finance 52(2), 731-764.
Ljungqvist, A., and M.P., Richardson, 2003. The Cash Flow, Return and Risk Characteristics of
Private Equity, NYU Finance Working Paper No. 03-001.
Merton, R.C., 1981. On market timing and investment performance I: An equilibrium theory of
value for market forecasts, Journal of Business, 54(3), 363-406.
Miller, M., and F. Modigliani, 1963. Corporate income taxes and the cost of capital: a
correction, American Economic Review 53 (3), 433–443.
Moskowitz, T.J., and A. Vissing-Jorgensen, 2002. The Returns to Entrepreneurial Investment:
A Private Equity Premium Puzzle?, American Economic Review 92(4), 745-778.
Pastor, L. and R.F. Stambaugh, 2003. Liquidity Risk and Expected Stock Returns, Journal of
Political Economy 111(3), 642-685.
Peng, L., 2001. Building a Venture Capital Index, Yale Working Paper.
Phalippou, L., 2007. Investing in private equity funds: a survey, CFA Institute Research
Foundation/University of Amsterdam.
Phalippou, L. and Gottschalg, 2009. The Performance of Private Equity Funds, Review of
Financial Studies 22(4), 1747-1776.
Phalippou, L., and M. Zollo, 2005. The performance of private equity funds,
INSEAD/University of Amsterdam, EFA Moscow meetings.
Phalippou, L., 2009. Beware of Venturing into Private Equity, Journal of Economic
Perspectives 23(1), 147–166.
Phalippou, L., 2010. Venture capital funds: flow-performance relationship and performance
persistence, Journal of Banking and Finance 34(3), 568-577.
Phalippou, L., and O. Gottschalg, 2009. The performance of private equity funds, Review of
Financial Studies 22(4), 1747-1776.
Phalippou, L., and M. Zollo, 2005. The performance of private equity funds,
INSEAD/University of Amsterdam, EFA Moscow meetings.
Quigley, J.M., and S.E. Woodward, 2003. An Index for Venture Capital, University of
California, Berkeley, Working Paper.
Shparber, M. and S. Resheff, 2004. Valuation of cliquet options, Tel Aviv university working
paper.
Sharpe, W.F., 1964. Capital asset prices: A theory of market equilibrium under conditions of
risk, Journal of Finance 19(3), 425-442.
Swensen, D.F., 2000. Pioneering Portfolio Management, Free Press.
Swensen, D.F., 2005. Unconventional Success: a Fundamental Approach to Personal
Investment, Free Press.
Treynor, J.L., and K. Mazuy, 1966. Can Mutual Funds Outguess the Market?, Harvard Business
Review 44(4), 131-136.
33
Appendix A Private equity industry terms
The following definitions are sourced from the Thomson Reuters & The Australian Private Equity &
Venture Capital Association Limited Yearbook 2009 and VC Experts’ The Glossary of Private Equity and
Venture Capital (www.vcexperts.com/vce/library/encyclopedia/glossary.asp).
Capital Call
When a venture capital firm has decided where it would like to invest, it approaches its investors in order
to draw down the money. The money will already have been committed to the fund but this is the actual
act of transferring the money.
Committed Capital
Capital committed by investors. Cash to the maximum of these commitments may be requested or drawn
down by the private equity managers usually on a deal-by-deal basis. To the extent that capital invested
does not equal capital committed, limited partners will have their private equity returns diluted by the
much lower cash returns earned on the uninvested portion.
Early Stage Venture Capital
This is a fund investment strategy involving investment in companies for product development and initial
marketing, manufacturing and sales activities. Revenues exist, but since this is a capital-intensive stage,
profits are minimal if they exist at all.
General Partner (GP)
The partner in a limited partnership responsible for all management decisions of the partnership. The GP
has a fiduciary responsibility to act for the benefit of the limited partners (LPs), and is fully liable for its
actions.
Latter Stage Venture Capital
A fund investment strategy which provides financing for the growth of a company that has moved beyond
the expansion stage to increase its sales volume and generate consistent growth. It is
considered the last venture capital stage of financing prior to a liquidity event (i.e. an IPO or acquisition
of the company).
Leveraged Buyout (LBO)
A takeover of a company, using a combination of equity and borrowed funds. Generally, the target
company's assets act as the collateral for the loans taken out by the acquiring group. The acquiring group
then repays the loan from the cash flow of the acquired company. For example, a group of investors may
borrow funds, using the assets of the company as collateral, in order to take over a company. Or the
management of the company may use this vehicle as a means to regain control of the company by
converting a company from public to private. In most LBOs public shareholders receive a premium to the
market price of the shares.
Limited Partner (LP)
An investor in a limited partnership who has no voice in the management of the partnership. LPs have
limited liability and usually have priority over GPs upon liquidation of the partnership.
Mezzanine Debt
A hybrid of debt and equity financing that is typically used to finance the expansion of existing
companies. Mezzanine financing is basically debt capital that gives the lender the rights to convert to an
ownership or equity interest in the company if the loan is not paid back in time and in full. It is generally
subordinated to debt provided by senior lenders such as banks and venture capital companies.
Seed Stage Venture Capital
An investment strategy involving portfolio companies at its earliest phase of development to
promote a business concept before a company is started. Capital invested in companies at this point
have not yet fully established commercial operations, and may also involve continued research and
product development. Because it is the earliest stage of development, it is considered as the riskiest of
the various financing stages.
34
Appendix B Characteristics of venture capital and buyout firms
Private equity investments are defined as either venture capital (VC) or buyout (BO) funds. The following
table from Anson (2006) summarises the key differences.
Venture Capital (VC) Buyout (BO)
Company Start up Mature
Competitive advantage New technology Distribution, marketing,
production
Financing Equity Debt
Target IRR 1)
40-50% 20-30%
Shareholder position Minority Control of company
Board Seats 1 or 2 All
Valuation Compare to other companies Discounted cash flow
Investment Strategy Finance, innovation Improve operating efficiency
Time to exit 2-5 years 4-7 years
Exit option IPO, acquisition IPO, acquisition or
recapitalisation IRR refers to the Internal Rate of Return, or the solution to the following equation:
T
-I0 + ∑ CFt / (1+IRR)t + NAVT / (!+IRR)T = 0 t=1
Where I0 is the initial investment, CFt is the net distribution at time t, and NAVT is the estimated net asset value of yet to be
liquidated holdings.
35
Appendix C Bottom up beta models
While our GARCH model results suggest venture capital and buyouts have created episodic excess returns, one additional approach can be used to verify the existence of
excess returns to buyouts. Because of the smoothing employed by the managers, the estimated beta and leverage effects can be understated when deriving a factor model. This
motivates various authors to rely on bottom up derived betas. Phalippou (2009) suggests matching private equity to the publicly traded stock of a company in the same
industry and similar size. For buyouts, an additional adjustment is made due to leverage. Various authors (Gottschalg and Groh, 2007; Inker, 2008; Phalippou and Zollo,
2005; Swensen, 2000) explicitly adjust the beta to the S&P 500 returns to reflect the leverage in buyouts.
18 Comparable leverage to buyouts is then created based on the
formula by Modigliani and Miller (1963).
βL= βU + (βU – βD) [1+(1- T) φ] βU = [βL + βD (1- T) φ] / [1+ (1- T) φ]
whereby the levered beta (βL) is a function of the unlevered beta (βU), the cost of debt (βD), a corporate tax shield (T) and the ratio of debt to equity (φ). Under this model, the
high yield factor is incorporated through the cost of financing (βD). We assume a debt beta (βD) of 0.25, based on the beta estimate of our 50/50 financing mix to the S&P 500,
which coincides with the debt beta applied by Phalippou and Zollo (2005) and Cornell and Green (1991). From table below, we find that buyouts, net of fees, over the
specified period performed in line with the S&P 500 on a levered basis. However, because of the return smoothing, the managers report lower volatility.
Total Return
(% pa)
Excess Return
versus geared
S&P 500 (% pa)
Standard
deviation
(% pa)
Best quarter
(%)
Worst quarter
(%) Beta Skew Kurtosis Liquidity
Small buyouts 12.04 -0.08 10.3 13.8 -12.0 0.27 0.00 0.09 0.37
Medium buyouts 15.73 3.61 17.7 55.7 -14.5 0.32 2.51 13.63 0.13
Large buyouts 11.30 -0.82 12.6 18.9 -18.8 0.30 -0.39 1.44 0.25
Mega buyouts 11.09 -1.03 12.3 18.8 -15.7 0.33 -0.32 1.13 0.13
All buyouts 12.17 0.05 11.3 15.5 -15.1 0.32 -0.56 0.87 0.28
Geared S&P 500 12.12 -- 22.4 25.9 -41.0 1.37 -0.91 2.43 -0.01
In this table, the descriptive statistics match table 2. The ‘excess returns’ column now measures the excess returns versus the leveraged S&P 500. We estimate time-varying
leverage for the buyout industry using data provided by Anson (2006) and Griffin (2010). The S&P 500 is delevered based on time-varying data provided by an anonymous
U.S. credit manager cross referenced with Swensen (2000, 2005).
18
Some of these authors assign leverage based on unique datasets of the underlying investments, thereby further refining for size and industry. We do not have access to such
level of data.
36
Appendix D Private equity simulation model based on direct investment
D1. Yale allocation model (standard settings)
The following allocation model to private equity is based on the Yale Endowment’s experience.
The model is able to incorporate and respond to actual experience. A more detailed description
may be found in Alexander and Takahashi (2001).
Parameters Description Initial Settings (Yale)
RC Rate of contribution 25% in year one, 33.3% in year
2, 50% in subsequent years
CC Capital commitment ($) $100
L Life of fund (years) 12
B Factor describing changes in the rate of
distribution over time
2.5
G Annual Growth rate 13%
Y Yield (%) 0%
Variables Formula
PIC Paid in capital
1
0
t
tC
RD Rate of distribution Max[Y,(t/L)^B]
Outputs Formula
C Capital contributions ($) Ct=RCt(CC-PICt)
D Distributions ($) Dt=RD*[NAVt-1*(1+G)]
NAV Net Asset Value NAVt=[NAVt-1 *(1+G)] + Ct-Dt
The model is initially applied to a single path. C2 creates a simulation model (multiple paths).
D2. Combination with bootstrap (1000 runs)
G uses resampled output.
Venture Economics provides 20 years of quarterly observations (1990-2009), thereby offering 80
historical data points. An additional 1000 runs of industry growth during the 12 years of
commitment are created by using resampling with replacement.
To arrive at the returns to investors, for each path the percentage invested capital is calculated
based on the Yale model. The uninvested capital is assumed to be invested at the risk free rate.
Thus, a weighted average return is calculated over the life of the partnership.
37
Appendix E Private equity simulation model based on replication
The full replication model is:
Rilliquid asset,t = Rlong position in liquid asset,t (E1, E2) + Rshort position in liquidity option,t (E3)
1. Long position in liquid asset
Risk factors are combined to form passive factor model returns at time t.
Rventure capital,t= β1,t-1RS&P500,t + β2,t-1 RNASDAQ,t
(E1)
Rbuyout,t= β1,t-1RS&P500,t + β2,t-1Rhigh yield,t (E2)
The risk factors used to build up the clone returns are the same as in equations (1a) and (1b) but
there is no α in the equations above. In addition, there are no lagged components. Similar to alpha,
the lagged components cannot be purchased in practice. Thus, the beta is measured as the co-
incident beta, as experienced by investors, rather than the summed Dimson beta.
The beta weights β1,t-1 and β2,t-1 are determined by regressing quarterly data up to time t-1 and the
regression is updated using a lengthened lookback period as each new data point comes in. Thus an
investor will know the weights to apply at the start of each quarter to obtain the clone returns for
time period t.
New data points are created using a block bootstrap method. The ‘block’ refers to the resampling
of continuous blocks of time (4 quarter periods) to capture the 3 period lagged dependencies
detected in our factor model. In this manner, we resample with replacement from the out of sample
period from 1997-2009. We create 1,000 runs of alternative 12 year paths of industry returns. In
effect, we create 1,000 runs x 12 years x 4 quarters = 48,000 data points to overcome the limited
historical data set.
2. Short position in liquidity option
Quarterly European options are easy to implement in the marketplace for investors, as they are
exchange traded and liquid. Under normal times, a premium is received by investors as a proxy for
exposure to illiquid investments. Under stressed environments, the put option is considered
exercised, as investors become forced sellers in secondary markets at deep discounts.
Rshort position in liquidity option,t = R3m at the money put option (E3)
We also considered other proxies for liquidity. Commonly used proxies such as bid-ask spread or
trading volume are not available for private equity. We considered Listed Private Equity (based on
the LPX 50 index returns) but we find Listed Private Equity does not generate a premium, but
instead underperforms public equity over the period investigated. We also examined the returns of
the smallest decile stocks in terms of market capitalisation minus the returns on the largest decile
stocks. Again we find the results unsatisfactory.19
19
Data available from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
[Accessed: 23 September 2011]
n
k
ktktclone FwR1
,
38
Figure 1: Seven year rolling beta and alpha estimates
The solid lines in figure 1 represent the seven year rolling betas in our model, which are calculated by regressing rolling 28 data periods (7 years x 4 quarters) of private
equity returns against the identified risk factors. The dotted lines represent the 95 per cent confidence bands.
1A. Venture Capital
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Mar
-97
Mar
-98
Mar
-99
Mar
-00
Mar
-01
Mar
-02
Mar
-03
Mar
-04
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Eq
uit
y b
eta
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Mar
-97
Mar
-98
Mar
-99
Mar
-00
Mar
-01
Mar
-02
Mar
-03
Mar
-04
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Nasd
aq
beta
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Mar
-97
Mar
-98
Mar
-99
Mar
-00
Mar
-01
Mar
-02
Mar
-03
Mar
-04
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Illi
qid
uit
y b
eta
-20.0%
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
20.0%
Mar-
97
Mar-
98
Mar-
99
Mar-
00
Mar-
01
Mar-
02
Mar-
03
Mar-
04
Mar-
05
Mar-
06
Mar-
07
Mar-
08
Mar-
09
Alp
ha
39
1B. Buyouts
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Mar
-97
Mar
-98
Mar
-99
Mar
-00
Mar
-01
Mar
-02
Mar
-03
Mar
-04
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Eq
uit
y b
eta
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Mar
-97
Mar
-98
Mar
-99
Mar
-00
Mar
-01
Mar
-02
Mar
-03
Mar
-04
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Hig
h y
ield
beta
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Mar
-97
Mar
-98
Mar
-99
Mar
-00
Mar
-01
Mar
-02
Mar
-03
Mar
-04
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Illi
qid
uit
y b
eta
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
Mar-
97
Mar-
98
Mar-
99
Mar-
00
Mar-
01
Mar-
02
Mar-
03
Mar-
04
Mar-
05
Mar-
06
Mar-
07
Mar-
08
Mar-
09
Alp
ha
40
Figure 2 Base case for private equity allocation simulation model
Figure 2 suggests capital investment patterns based on Yale’s default settings for contribution rates, fund life, committed capital and capital growth rates. On average, 56 per
cent of committed capital is invested over the 12 year period. A peak in invested capital is reached in year 5.
0
20
40
60
80
100
120
0 1 2 3 4 5 6 7 8 9 10 11 12
year
% o
f c
om
mit
ted
ca
pit
al
Contributions
Distributions
Invested Assets
Average investment level
41
Figure 3 Simulation outcome for allocation model
Figure 3 shows the outcome of 1,000 simulation runs comparing the returns of the direct investment to
the replicator. Excess returns are defined as the returns of the direct investment minus the returns on the
replicator at the end of the 12 year commitment period for venture capital and buyout investments. The
shaded bars represent the runs where the replicator outperforms the direct investment.
Venture Capital Buyouts
0
10
20
30
40
50
60
70
80
90
100
-38% -28% -18% -8% 2% 12% 22% 32% 42%
Simulated excess returns Normal distribution
Mean = 1.39% p.a.
Stddev = 10.24%
Min = -29.43%
Max = 64.32%
0
20
40
60
80
100
120
-38% -28% -18% -8% 2% 12% 22% 32% 42%
Simulated excess returns Normal distribution
Mean = 1.47% p.a.
Stddev = 8.95%
Min = -25.72%
Max = 56.72%
42
Table 1 An overview of literature on private equity excess returns
Paper Factors (style benchmarks) and data
provider
Results
Gompers and
Lerner (1997)
1 factor: S&P 500.
Data provided by Warburg Pincus.
Excess return found, but reduced
after marked to market adjustment.
Risk free rate not deducted.
Swensen (2000) 1 factor: S&P 500.
Data provided by Yale portfolio
542 buyout deals.
Buyouts underperform compared to
an equally leveraged version of the
S&P 500.
Peng (2001) 1 factor: S&P 500 or NASDAQ.
Data provided by OffRoad Capital.
Excess return found for venture
capital, but sample ends at
technology boom.
Moskowitz and
Vissing-Jorgensen
(2002)
1 factor: CRSP index.
Private household data on own businesses
provided by SCF/FFA data
No excess return found for private
entrepreneurial investments (family
businesses).
Quigley and
Woodward (2003)
1 factor: S&P 500 or NASDAQ.
Data provided by Sand Hill Econometrics
Excess return found for venture
capital, based on self-built index,
and performance to 1999.
Kaplan and
Schoar (2005)
1 factor: S&P 500.
Data provided by Venture Economics.
No excess returns found.
Jones and Rhodes-
Kropf (2003)
1 factor: NYSE, AMEX and NASDAQ
Fama French factors
Data provided by Venture Economics
No excess return found. Dimson
(1979) adjustment.
Ljungqvist and
Richardson (2003)
1 factor: S&P 500.
Data provided by a single undisclosed LP,
with 73 investments
Excess return found, but limited
sample.
Ick (2005) 1 factor: S&P 500, NASDAQ, Russell
2000, Dow Jones Industrial Average,
MSCI World. Data from CEPRES
Marginal excess return found,
underperformance on risk to reward
basis.
Anson (2006) 1 factor, S&P 500, lagged up to 4 periods.
Data provided by Venture Economics
Excess return found, but reduced
after Dimson (1979) stale pricing
adjustment.
Phalippou et al.
(2005, 2007,
2009)
1 factor: S&P 500.
Data provided by Venture Economics
Phalippou and Zollo (2005) also examine
Negative 3 per cent excess return
after assuming biases.
y = -0.6365x2 + 0.6306x + 0.0281
R2 = 0.3131
-30.0%
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0%
S&P 500
Ve
ntu
re C
ap
ita
l
43
bond yields, and options on the S&P 500.
Conroy and Harris
(2007)
1 factor: S&P 500.
Data provided by Venture Economics
No excess return found, after
Dimson (1979) adjustment.
Korteweg and
Sorensen (2008)
3 factors: equity premium, Fama and
French small cap and value premium, and
Monte Carlo correction.
Data provided by Sand Hill Econometrics
No excess return found.
Franzoni, Nowak
and Phalippou
(2009)
S&P 500, Fama and French small cap and
value premium, liquidity factor
corresponding to a long position in high
liquidity stocks and a short position in
low liquidity stocks (Pástor and
Stambaugh, 2003).
Data provided by CEPRES
No excess return found.
Driessen, Lin and
Phalippou (2011)
S&P 500
Data provided by Venture Economics
No excess returns found.
44
Table 2 Returns to private equity: Descriptive Statistics
Descriptive statistics are calculated using quarterly data from March 1990 to December 2009. The data are net of fees log returns in USD from the Venture Economics (VE)
database. The total number of observations is 80 quarters. The total return is annualised by multiplying log quarterly results by four. Excess returns are the return less the 3
month T-bill rate. The annualised standard deviation is the standard deviation of the log quarterly return scaled by the square root of four. Beta is the estimated slope
coefficient from the regression of strategy returns on the S&P 500 index. Liquidity is the estimated first order serial correlation coefficient for returns.
Total Return
(% pa)
Excess Return
versus risk
free rate (%
pa)
Standard
deviation
(% pa)
Best
quarter
(%)
Worst
quarter
(%)
Beta to
S&P 500 Skew Kurtosis Liquidity
Early/Seed VC 13.82 10.0 23.4 58.8 -22.8 0.63 1.57 6.51 0.67
Seed Stage VC 6.70 2.8 17.3 29.8 -22.1 0.36 0.69 1.81 0.25
Early Stage VC 14.06 10.2 23.7 59.2 -23.1 0.64 1.56 6.40 0.67
Balanced VC 14.74 10.9 18.3 53.9 -17.1 0.65 1.96 10.57 0.44
Latter Stage VC 14.76 10.9 14.9 37.0 -18.3 0.57 0.50 4.80 0.42
All venture 14.41 10.5 19.0 52.8 -18.4 0.63 1.60 8.45 0.57
Small buyouts 12.04 8.2 10.3 13.8 -12.0 0.27 0.00 0.09 0.37
Medium buyouts 15.73 11.9 17.7 55.7 -14.5 0.32 2.51 13.63 0.13
Large buyouts 11.30 7.4 12.6 18.9 -18.8 0.30 -0.39 1.44 0.25
Mega buyouts 11.09 7.2 12.3 18.8 -15.7 0.33 -0.32 1.13 0.13
All buyouts 12.17 8.3 11.3 15.5 -15.1 0.32 -0.56 0.87 0.28
S&P 500 7.89 4.1 16.3 19.3 -24.8 1.0 -0.78 1.10 0.12
45
it
l
ltmltNQil
k
ktfktmikitit RRRRRfRa
3
0
,,
3
0
,, )()()1(
hit = γ0 + γ1ε2
i,t-1 + γ2hi,t-1 + γ3ε2i,t-1It-1
it
l
ltfltHYil
k
ktfktmikitit RRRRRfRb
3
0
,,
3
0
,, )()()1(
hit = γ0 + γ1ε2i,t-1 + γ2hi,t-1 + γ3ε
2i,t-1It-1
Early/Seed
Venture Capital
Seed
Venture Capital
Early Stage
Venture Capital
Balanced Venture Capital
Latter Stage
Venture Capital
All Venture
Capital
Small Buyout
Medium Buyout
Large Buyout
Mega Buyouts
All Buyouts
α βm
βm,t-1
βm,t-2
βm,t-3
∑ βm βNQ / βHY βNQm t-1 / βHY, t-1 βNQm t-2 / βHY, t-2 βNQm t-3 / βHY, t-3
∑ βNQ / βHY γ0 γ1 (ARCH)
γ2 (GARCH)
γ3
γ1 + γ2 + 0.5 γ3
t-dist errors Adj R
2
Log Likelihood
0.0295***
0.1318
-0.0251
0.5908***
0.1596
0.8571***
0.6893***
0.5494***
0.1015
0.1963**
1.5365***
0.0022
0.2341
0.3989
-0.2104
0.2231
N/A^^
0.52 92.39
0.0002
0.5171
0.0492
0.0026
0.1534
0.7223***
0.5318***
0.2218**
0.2646***
0.0976
1.1158***
0.0012***
1.0459**
-0.030
-0.1761
0.9278
N/A^^
0.31
113.64
0.0298***
0.1437
-0.0221
0.5989***
0.1644
0.8849***
0.6726***
0.5539***
0.1048
0.1937
1.5250***
0.0024
0.2276
0.4113
-0.2251
0.5263
N/A^^
0.51 90.86
0.0140***
0.3023***
0.1630***
0.0866*
0.0937**
0.6465***
0.4194***
0.0438
0.0334
0.0106
0.5072
0.00005
0.1684
0.8620***
-0.5662
0.7473
2.60***
0.50
135.97
0.0233***
0.2398***
0.1110
0.1542*
0.1607*
0.6657***
0.4195***
0.1143
0.0855
0.0766
0.6959***
0.0000
0.1308
0.7823***
0.1055
0.9657
N/A^^
0.71
153.24
0.0138***
0.3234***
0.0965**
0.2023***
0.1476**
0.7698***
0.2708***
0.0842
0.0437
0.0358
0.4345**
0.0000^
0.3100***
0.6568***
0.0000
0.9668
N/A^^
0.51
134.62
0.0038
0.1459
-0.0624
0.0956
0.0571
0.2362
0.3972
0.2677
0.1010
0.4922*
1.2581***
0.0005
0.0605
0.7152
0.0279
0.7891
NA^^
0.43
144.61
0.0186**
0.2625**
0.1142
0.1318
0.1539
0.6624***
0.1409
-0.0759
0.0795
0.0056
0.1501
0.0014
0.3611
0.1589
0.1783
0.6091
5.36
0.23
120.12
0.0109
0.3691***
0.1893
0.1895*
0.1463
0.8942***
-0.0640
-0.0179
-0.1483
-0.1782
-0.4084
0.0018
-0.1137
0.4501
0.0487
0.3607
11.47
0.27
126.51
0.0035
0.4038***
0.0394
0.0467
0.095
0.5849***
0.2794*
-0.0450
0.3564**
-0.1574
0.4334
0.0002
0.0369
0.6787**
-0.0198
0.7057
N/A^^
0.49
126.64
0.0057
0.3823***
0.0523
0.0579
0.0681
0.5606**
0.2463
0.0901
0.2104
0.0374
0.5842
0.0003
-0.0170
0.7642
0.0270
0.7605
N/A^^
0.55
152.61
* significant at the 10 per cent level ** significant at the 5 per cent level *** significant at the 1 per cent level ^ Variance targetting used to impose a long-run variance estimate for cases where numerical
convergence was not reached under the standard GJR model ^^ t-distributed errors converged to normally distributed errors
Table 3a Full period (1990-2009) results of GARCH model for quarterly private equity fund returns (Augmented CAPM)
46
it
l
ltmltNQil
k
ktfktmikitit RRRRRfRa
3
0
,,
3
0
,, )()()1(
hit = γ0 + γ1ε2
i,t-1 + γ2hi,t-1 + γ3ε2i,t-1It-1
it
l
ltfltHYil
k
ktfktmikitit RRRRRfRb
3
0
,,
3
0
,, )()()1(
hit = γ0 + γ1ε2i,t-1 + γ2hi,t-1 + γ3ε
2i,t-1It-1
Early/Seed Venture Capital
Seed Venture Capital
Early Stage Venture Capital
Balanced Venture Capital
Latter Stage Venture Capital
All Venture
Capital
Small Buyout
Medium Buyout
Large Buyout
Mega Buyouts
All Buyouts
α βm
βm,t-1
βm,t-2
βm,t-3
∑ βm βNQ / βHY βNQm t-1 / βHY, t-1 βNQm t-2 / βHY, t-2 βNQm t-3 / βHY, t-3 ∑ βNQ / βHY γ0 γ1 (ARCH)
γ2 (GARCH)
γ3
γ1 + γ2 + 0.5 γ3
t-dist errors Adj R
2
Log Likelihood
-0.0051
0.2915***
0.0082
0.1125
0.1802**
0.5924**
0.1456
0.1532
0.1965
0.1287
0.6240***
0.0000
-0.1509
0.9445***
0.2865
0.8368
N/A^^
0.51 74.02
-0.024**
-0.0107
0.0324
-0.0773
0.1491
0.0935
0.5481
-0.0333
0.1727
0.0230
0.7105***
0.0017
0.3827
0.0490
-0.3674
0.2480
N/A^^
0.17 59.19
-0.0057
0.2974**
0.0254
0.1185
0.1817*
0.6230***
0.1567
0.1609
0.1777
0.1352
0.6305***
0.0000
-0.1511
0.8137***
0.2975
0.8113
N/A^^
0.52 72.25
0.0063
0.4322***
0.0738
0.1127
0.1868
0.7966***
0.0535
0.1184
0.0975
0.0491
0.3185*
0.0003
0.0479
0.7161
0.0390
0.7825
N/A^^
0.66 71.30
0.0160***
0.2839***
0.1183
0.1834**
0.1029
0.6885***
0.2294
0.0472
0.0897
0.0853
0.4516***
0.0002
0.0885
0.5754
-0.0590
0.3172
N/A^^
0.68 75.33
-0.0039
0.3472***
0.0884
0.1117
0.1720
0.7193***
0.1529
0.0860
0.1314
0.1157
0.4860**
0.0002
-0.1143*
0.7096*
0.1345
0.6631
N/A^^
0.67 71.71
0.0245***
0.3527
0.0110
0.1491
0.3149***
0.8277***
0.0526
-0.0539
0.0399
-0.1124
0.1510
0.0001
0.0085
0.9042
-0.0556
0.8849
N/A^^
0.48 71.07
0.0502***
0.4055**
0.1880
0.2912
0.5195**
1.4042***
-0.0760
-0.5222
0.1827
-1.0424**
-1.4579
0.0000
-0.2073
1.1063***
0.0679
0.9329
N/A^^
0.48 75.98
0.02444***
0.3125***
0.1342
0.2051***
0.1056
0.7574***
0.1363
-0.0558
-0.1542
-0.0497
-0.1234
0.0000
0.0192
0.7658***
0.0000
0.7838
N/A^^
0.67
99.12
0.0222
0.3491**
0.0807
0.2320
0.1654
0.8272***
0.3286
0.0992
-0.1320
-0.1356
0.1602
0.0003
0.0605
0.524
-0.0146
0.5776
N/A^^
0.72 77.07
0.0247
0.3468
0.1194*
0.2315
0.2249
0.9226***
0.3075
-0.0106
-0.1175
-0.2772**
-0.0978
0.0000
-0.0024
0.8175
0.0832
0.8567
N/A^^
0.74 82.30
* significant at the 10 per cent level ** significant at the 5 per cent level *** significant at the 1 per cent level
^^ t-distributed errors converged to normally distributed errors
Table 3b Post technology boom (2000-2009) Results of GARCH model for quarterly private equity fund returns (Augmented CAPM)
The variables are as per table 3a, but the results are reported over the 2000-2009 time period.
47
Table 4 Performance of direct investment versus factor model during commitment period
Table 4 presents a comparison of direct investment versus the factor based approach to private equity. 1000 runs of 12 year commitment periods are simulated. For the direct
investment, results are based on cash flow patterns from the Yale allocation model.
Venture Capital Buyouts
Direct investment Factor model Direct investment Factor model
Return (%pa) 5.0 3.6 4.9 3.4
Risk (%) 6.5 7.8 6.6 5.9
Reward to risk 0.8 0.5 0.7 0.6
Best period (%pa) 66.8 29.0 62.6 23.8
Worst period (%pa) -16.5 -24.4 -15.6 -18.5
Tracking error (%) 10.3 9.0
Returns are presented net of fees in USD and reflect the average of possible return outcomes at the end of the 12 year commitment period. E.g. if the average return per
annum Rcommitment period = (R1+R2 + .. + R12)/12, then Return (%pa) in Table 4 shows an average of all Rcommitment period obtained over 1000 possible runs. Risk reflects the
standard deviation of average return outcomes at the end of the 12 year period, or σ(Rcommitment period). Reward to risk equals return divided by risk. Best period reflects the
average annual return under the best possible 12 year outcome or max(Rcommitment period). Worst period reflects the average annual return under the worst possible 12 year
period or min(Rcommitment period). Tracking error is calculated as the standard deviation of the difference in outcome between the direct investment and the factor model over
1000 runs of 12 year periods, i.e. σ(Rdirect investment,commitment period – Rfactor model, commitment period).
48
itftmtgti
l
ltmltNQil
k
ktfktmikiftit RRRRRRRRa
2
min
3
0
,,
3
0
,, )()()()2(
hit = γ0 + γ1ε2
i,t-1 + γ2hi,t-1 + γ3ε2i,t-1It-1
itftmtgti
l
ltmltHYil
k
ktfktmikiftit RRRRRRRRb
2
min
3
0
,,
3
0
,, )()()()2(
hit = γ0 + γ1ε2i,t-1 + γ2hi,t-1 + γ3ε
2i,t-1It-1
Early/Seed Venture Capital
Seed Venture Capital
Early Stage Venture Capital
Balanced Venture Capital
Latter Stage Venture Capital
All Venture Capital
Small Buyout
Medium Buyout
Large Buyout
Mega Buyouts
All Buyouts
α βm
βm,t-1
βm,t-2
βm,t-3
∑ βm βNQ / βHY βNQm t-1 / βHY, t-1 βNQm t-2 / βHY, t-2 βNQm t-3 / βHY, t-3
βNQ / βHY βtiming
γ0 γ1 (ARCH)
γ2 (GARCH)
γ3
γ1 + γ2 + 0.5 γ3
t-dist errors Adj R
2
Log Likelihood
0.0261*
0.1470
0.0000
0.6059***
0.1811
0.9340***
0.6881***
0.5456***
0.0942
0.1864
1.5143***
0.4036
0.0025
0.2482
0.3523
-01687
0.5161
N/A^^
0.51 93.55
0.0040
0.0398
0.0414
0.0026
0.1479
0.2317
0.5278***
0.2168**
0.2614**
0.0953
1.1013***
-0.4396
0.0012***
1.0501**
-0.0312
-0.1775
0.8570
N/A^^
0.31
114.02
0.0260
0.1605
0.0060
0.6164***
0.1884
0.9713***
0.6713***
0.5497***
0.0970
0.1821
1.5001***
0.4518
0.0027
0.2439
0.3610
-0.1781
0.5158
N/A^^
0.51 92.30
0.0171***
0.2996***
0.1649***
0.1220**
0.0421
0.6286***
0.3987***
0.0144
0.0013
0.0512
0.4656*
-0.5744***
0.0005
0.2481***
0.9101***
-1.0243
0.6461
2.45***
0.48
138.30
0.0167***
0.3097**
0.0880
0.2252***
0.1329**
0.7558***
0.5295***
0.1631***
0.0740
0.1211**
0.8877***
0.8502**
0.0000
0.0555
0.8946***
0.0126
0.9564
N/A^^
0.73
147.87
0.0143***
0.2863***
0.1378***
0.0923*
0.1185**
0.6349***
0.4649***
-0.0327
-0.0593
-0.0711
0.3018**
-0.3645***
0.0000
0.2316***
0.8871***
-0.4743***
0.8815
3.55***
0.41
149.72
0.0118***
0.1365
-0.0849
0.0920
0.0471
0.1907
0.3676
0.2327*
0.0897
0.4444
1.1344**
-0.7967
0.0002
0.0182
0.8906*
0.0280
0.8126
N/A^^
0.44
172.43
0.0311***
0.2741***
0.1041
0.1009
0.1379
0.6170***
0.0542
-0.2291
0.1454
-0.1344
-0.1639
-0.9508
0.006
0.6785
0.4063
-0.2150
0.9770
3.76*
0.19
121.43
0.0117
0.3513***
0.1952*
0.1965*
0.1181
0.8611***
-0.1279
-0.0439
-0.1552
-0.2379
-0.5649
0.1338
0.0018
-0.1203*
0.3745
0.0555
0.2818
12.41
0.25
126.03
0.0059
0.4006***
0.0356
0.0485
0.0970
0.5817***
0.2733
-0.0533
0.3394*
-0.1790
0.3805
-0.2373
0.0002
0.0360
0.6749**
-0.0199
0.7000
N/A^^^
0.49
137.74
0.0086
0.3716***
0.0506
0.0675
0.0578
0.5475**
0.2421
0.0679
0.2026
0.0276
0.5402
-0.3544
0.0003
-0.0109
0.7037
0.0212
0.7034
N/A^^
0.55
152.89
* significant at the 10 per cent level ** significant at the 5 per cent level *** significant at the 1 per cent level ^^ t-distributed errors converged to normally distributed errors Table 5 Results of GARCH model for quarterly deleveraged private equity fund returns (Augmented Treynor and Mazuy model) 1990-2009
49
Table 6 Impact of conditional overlay 1990-2009
Table 6 represents the out of sample performance for Venture Capital (VC) and Buyouts (BO) of
applying the conditional overlay. Returns are presented net of fees in USD based on annualised quarterly
data. Risk is calculated by multiplying quarterly standard deviation by the square root of 4. Skew
represents the skew of the quarterly returns. Kurtosis refers to the excess kurtosis versus a normal
distribution. Reward to risk is defined as the return divided by the risk.
VIX = 25 without overlay with overlay
VC BO VC BO
Return (%pa) 10.8 10.4 12.2 9.3
Risk (%pa) 22.4 12.0 20.9 11.0
Skew 1.7 -0.8 1.0 -0.5
Kurtosis 8.5 0.9 2.8 -0.2
Reward to risk 0.5 0.9 0.6 0.9
VIX = 30 without overlay with overlay
VC BO VC BO
Return (%pa) 10.8 10.4 11.6 10.5
Risk (%pa) 22.4 12.0 22.5 11.2
Skew 1.7 -0.8 1.7 -0.6
Kurtosis 8.5 0.9 6.6 -0.2
Reward to risk 0.5 0.9 0.5 1.0
VIX = 35 without overlay with overlay
VC BO VC BO
Return (%pa) 10.8 10.4 11.6 10.9
Risk (%pa) 22.4 12.0 22.4 10.9
Skew 1.7 -0.8 1.7 -0.6
Kurtosis 8.5 0.9 6.6 -0.1
Reward to risk 0.5 0.9 0.5 1.0
50
Table 7 Impact of conditional overlay on VaR (based on 1,000 resampled runs of 12 years)
Venture Capital Buyouts
Percentile
Excess
return
Risk
reduction
Excess
return
Risk
reduction
0.05 -2.5 -2.4 -2.2 -3.9
0.10 -2.0 -1.8 -1.8 -2.3
0.25 -1.2 -0.8 -1.1 0.2
0.50 0.0 0.4 -0.3 5.5
0.75 1.5 2.1 0.8 10.7
0.90 2.7 4.6 1.8 15.2
0.95 3.6 6.7 2.6 17.3
Table 7 represents the impact on excess return and risk reduction for Venture Capital and Buyouts of
applying the conditional overlay on simulated data. 1,000 runs of 12 year returns are created for both the
direct investment and the hedged asset by using resampling with replacement. The hedge becomes active
whenever the VIX in the previous period exceeds the predefined threshold. Excess return represents the
additional return per annum from applying the hedge. Risk reduction represents the percentage reduction
in standard deviation.