Estimating Private Equity Returns from Limited Partner Cash Flows

Andrew Ang, Bingxu Chen, Will Goetzmann, Ludovic Phalippou

Q-Group, Apr 2014

Liquidating Harvard: A Cautionary Example

“Liquidating Harvard” Columbia Case available from http://www8.gsb.columbia.edu/caseworks/node/236/Liquidating%2BHarvard

Endowment Performance (post Jack Meyer)

Harvard Endowment

Harvard Endowment

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Harvard Endowment Asset Allocation June 30, 2008

Liquid 27% Dev Mkt Equity, Liquid Commodities, Govt BondsSemi-Liquid 35% Emg Mkt Equity, High-Yield Bonds, Hedge FundsIlliquid 39% Private Equity, Timber/Land, Real Estate

Total 100%

● Harvard was an early adopter of the “endowment” model based on diversification concepts extended to illiquid assets (thanks to Swensen, Leibowitz, and others)

“Returns” on Illiquid Assets

● Illiquid asset “returns” are not returns

● Harvard University President Faust, on the 22% loss between July 1 and October 31, 2008:

“Yet even the sobering figures is unlikely to capture the full extent of actual

losses for this period, because it does not reflect fully updated valuations in

certain managed asset classes, mostly notably private equity and real

estate.”

● Returns of illiquid alternatives are biased upwards, and their risk estimates are biased downwards

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Infrequent Trading

● Infrequent trading biases volatility and beta estimates downwards.

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0

0.5

1

1.5

2

2.5

3

3.5Quarterly Sampling

Infrequent Trading

● Infrequent trading biases volatility and beta estimates downwards.

8

0

0.5

1

1.5

2

2.5

3

3.5Daily Sampling

Infrequent Trading

● Infrequent trading biases volatility and beta estimates downwards.

9

0

0.5

1

1.5

2

2.5

3

3.5Daily vs Quarterly Sampling

Quarterly Sampling vol = 0.23

Daily Sampling vol = 0.28

Sample Selection Bias

● Selection biases the average return upwards, systematic risk downwards, and idiosyncratic volatility downwards.

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Excess Market

Excess Return True

Sample Selection Bias

● Selection biases the average return upwards, systematic risk downwards, and idiosyncratic volatility downwards.

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Excess Market

Excess Return True

Fitted

Building a Private EquityReturn Index

“Estimating Private Equity Returns from Limited Partner Cash Flows” http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2356553

Current Approaches

Based on

● NAVs

● Deal-level

● IRRs

● Multiples

Do not represent returns, and not based on the actual cash flows received by LPs

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Private Equity Returns

● Based on cashflows to LPs

– What you actually “eat”

– Data from Prequin and proprietary datasets

● Decompose into market and other factors, and the private equity-specific return (PE “alpha” or “premium”)

● Can be updated in “real time” to create a private equity return index

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How Does It Work?

● Suppose the private equity total return, g, follows

– rmt is the market return

– f is the return specific to PE

– Risk-free return is zero

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5% 1.5t mt tg r f

How Does It Work?

● Consider the cashflows of four funds, living between times t=0 to t=4

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Market

Return rmt

PE

factor ft

PE

return gt Fund 1 Fund 2 Fund 3 Fund 4

0 -100 -1001 5.6% -7.5% 5.9% 105.9 0 -100 -1002 10.0% -2.5% 17.5% -100 124.4 117.5 03 -8.2% 2.5% -4.8% 95.2 -100 111.94 12.8% 7.5% 31.7% 131.7

IRR 1% 12% 23% 6%

How Does It Work?

● According to a NPV condition, PV(Investments) = PV(Distributions)

● With four funds, there are four unknowns—can solve using a non-linear root solver

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1 2 1 1 2 3

1 2

2 3 2 2 3 4

2 3

100 105.9 95.2Fund 1: 100 ,

(1 )(1 ) (1 ) (1 )(1 )(1 )

124.4Fund 2: 100 ,

(1 )(1 )

100 117.5 131.7Fund 3: 100 ,

(1 )(1 ) (1 ) (1 )(1 )(1 )

111.9Fund 4: 100 .

(1 )(1 )

g g g g g g

g g

g g g g g g

g g

How Does It Work?

● If the private equity return, g, were constant then there would be four funds/equations with one unknown resulting in an over-identified system

● Similarly, if g is persistent (not iid), then we also require fewer funds/equations

● Identification is achieved by having funds with different cashflows at different start dates, and different end dates

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Model

● Total private equity return:

● Private equity-specific component is allowed to be persistent:

● NPV condition for distributions, D, and invested capital, I:

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't t tg F f

1t t f tf f

2 212

( )log( ) log ( , )

( )i

i

PV DPME N

PV I

2020

Time

Index ValuesPrivate Equity Total Return Index vs. US Index Funds

0.9

20

1

2

3

4

5

6

7

8

9

10

Mar1993

Sep2010

Dec1993

Dec1994

Dec1995

Dec1996

Dec1997

Dec1998

Dec1999

Dec2000

Dec2001

Dec2002

Dec2003

Dec2004

Dec2005

Dec2006

Dec2007

Dec2008

Dec2009

Vanguard Small Cap Index Inv Vanguard 500 Index Inv PE total return

Comparison with Industry Indexes

● Our cash flow-implied returns are more volatile, with lower autocorrelations than industry indexes

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2222

Time

Index ValuesDecomposition of Private Equity Return Index into Passive and Premium Components

0.9

20

1

2

3

4

5

6

7

8

9

10

Mar1993

Sep2010

Dec1993

Dec1994

Dec1995

Dec1996

Dec1997

Dec1998

Dec1999

Dec2000

Dec2001

Dec2002

Dec2003

Dec2004

Dec2005

Dec2006

Dec2007

Dec2008

Dec2009

PE total return PE Premium PE Passive

2323

Time

Return ValuesPrivate Equity Premium

-3.0%

3.0%

-2.8%-2.6%-2.4%-2.2%-2.0%-1.8%-1.6%-1.4%-1.2%-1.0%-0.8%-0.6%-0.4%-0.2%0.0%0.2%0.4%0.6%0.8%1.0%1.2%1.4%1.6%1.8%2.0%2.2%2.4%2.6%2.8%

Jun1993

Sep2010

Dec1994

Dec1995

Dec1996

Dec1997

Dec1998

Dec1999

Dec2000

Dec2001

Dec2002

Dec2003

Dec2004

Dec2005

Dec2006

Dec2007

Dec2008

Dec2009

PE Premium

2424

Alphas

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Model

βmarket βsize βvalue βilliquidity In-sample

Alpha Persistence of Alpha

CAPM 1.41a 0.05a 0.40 0.24 0.01 0.19 3 factors (FF) 1.49a 0.41 0.09 0.04a 0.43 0.23 0.31 0.27 0.01 0.19 4 factors (PS) 1.41a 0.41 0.03 0.36 0.00 0.48 0.21 0.26 0.23 0.27 0.02 0.19 EW CAPM 1.42a -0.04a 0.45 0.18 0.01 0.19 EW FF 1.47a 0.40 -0.11 -0.04a 0.47 0.20 0.25 0.21 0.01 0.19 EW PS 1.40a 0.33 -0.19 0.26 -0.05a 0.47 0.22 0.30 0.25 0.27 0.02 0.19

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-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1993 1995 1997 1999 2001 2003 2005 2007

IRRs

PE R

etur

ns

PE Returns vs IRRs (Corr = -0.03)

PE Returns (LH) IRRs (RH)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1993 1995 1997 1999 2001 2003 2005 2007 Mul

tiple

s

PE R

etur

ns

PE Returns vs Multiples (Corr = 0.04)

PE Returns (LH) Multiples (RH)

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1993 1995 1997 1999 2001 2003 2005 2007 PMEs

PE R

etur

ns

PE Returns vs PMEs (Corr = 0.14)

PE Returns (LH) PMEs (RH)

Pro-Cyclical Investing in Private Equity

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Private Equity Returns Over the Business Cycle

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Private Equity Returns

● Reported returns on PE are not returns!

● IRRs and multiples are not returns!

● Develop a time series of private equity values representing the returns to an investor (LP), not a fund, and not a manager (GP)

● Decompose private equity returns into passively replicable returns, and the unique return to private equity (“alpha” or “premium”)

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