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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: [email protected]

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.

mailto:[email protected]

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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.

http://www.yale.edu/investments/

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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-

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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

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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.

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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

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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.

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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.

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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.

http://www2.goldmansachs.com/gsam/docs/funds_international/education/investment_and_sales_education/case_for_high_yield_sep_10.pdf

http://www2.goldmansachs.com/gsam/docs/funds_international/education/investment_and_sales_education/case_for_high_yield_sep_10.pdf

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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).

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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]

http://www.preqin.com/item/secondaries-deluge-leads-to-asset-pricing-turmoil/101/1098

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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

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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.


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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.

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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,

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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.

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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]

https://www.cambridgeassociates.com/pdf/Venture%20Capital%20Index.pdf

https://www.cambridgeassociates.com/pdf/Private%20Equity%20Index.pdf

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]

http://us.ishares.com/product_info/fund/overview/HYG.htm

https://www.spdrs.com/product/fund.seam?ticker=JNK

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.


16

Refer http://www.preqin.com/item/secondaries-deluge-leads-to-asset-pricing-turmoil/101/1098.


http://www.preqin.com/item/secondaries-deluge-leads-to-asset-pricing-turmoil/101/1098

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.


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

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http://ideas.repec.org/p/nbr/nberwo/11136.html

http://ideas.repec.org/p/nbr/nberwo/11136.html

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.

http://www.vcexperts.com/vce/library/encyclopedia/glossary.asp

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


n

k

ktktclone FwR1

,

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

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.


Excess return found, but reduced

after Dimson (1979) stale pricing

adjustment.

Phalippou et al.

(2005, 2007,

2009)

1 factor: S&P 500.


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.


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


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




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.


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




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



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



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


50

Table 7 Impact of conditional overlay on VaR (based on 1,000 resampled runs of 12 years)


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.

private equity: strategies for improving performance ron ... · the paul woolley centre for capital...

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