Estimating Private Equity Returns from Limited Partner Cash Flows

• Author: BINGXU CHEN,ANDREW ANG,WILLIAM N. GOETZMANN,LUDOVIC PHALIPPOU
• Date: 01 August 2018
• Published date: 01 August 2018
• DOI: http://doi.org/10.1111/jofi.12688

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 4 •AUGUST 2018

Estimating Private Equity Returns from Limited

Partner Cash Flows

ANDREW ANG, BINGXU CHEN, WILLIAM N. GOETZMANN,

and LUDOVIC PHALIPPOU∗

ABSTRACT

We introduce a methodology to estimate the historical time series of returns to invest-

ment in private equity funds. The approach requires only an unbalanced panel of cash

contributions and distributions accruing to limited partners and is robust to sparse

data. We decompose private equity returns from 1994 to 2015 into a component due

to traded factors and a time-varying private equity premium not spanned by publicly

traded factors. We find cyclicality in private equity returns that differs according to

fund type and is consistent with the conjecture that capital market segmentation

contributes to private equity returns.

PRIVATE EQUITY (PE) IS A MAJOR institutional asset class and represents a sig-

nificant fraction of investments by colleges, foundations, pension funds, and

sovereign wealth funds, among others. A major drawback of PE for purposes of

analysis is the lack of transactions-based performance measures. This greatly

hampers portfolio allocation choice, which typically requires information about

the risk, return, and covariance of asset classes. In liquid markets these es-

timates can be derived from statistical analysis of time series returns. Most

PE time series, however, are based on nonmarket valuations or on multiyear

internal rates of return broken down by fund vintage years.

The primary contribution of this paper is the introduction of a methodol-

ogy based on Bayesian Markov Chain Monte Carlo (MCMC) to estimate a

time series of PE returns using cash flows accruing to limited partners and

factor returns from public capital markets. The identification strategy of this

∗Andrew Ang and Bingxu Chen are at Blackrock Financial Management Inc., William N. Goetz-

mann is at YaleSchool of Management and NBER, and Ludovic Phalippou is at the Said Business

School University of Oxford (corresponding author: ludovic.phalippou@sbs.ox.ac.uk). We have read

the Journal of Finance’s disclosure policy and have no conflicts of interest to disclose. The authors

would like to acknowledge use of the Oxford Supercomputing Centre (OSC) in carrying out this

work. Ang and Chen acknowledge funding from Netspar and Columbia University’s Program for

Financial Studies. We are grateful for helpful comments from two anonymous referees, Jules van

Bisbergen, Elise Gourier,Larry Harris, Charles Jones, Jiro Kondo, Arthur Korteweg, Stefan Nagel,

Christopher Polk, Michael Roberts (the Editor), David Robinson, Morten Sorensen, and partici-

pants at the American Finance Association 2015 meeting, Inquire-UK, Inquire-Europe, London

Business School 2015 private equity conference, NBER 2014 Chicago meeting, McGill University,

Netspar, Society for Financial Studies Finance Cavalcade, World Investment Forum, Princeton

University, and the University of Notre Dame.

DOI: 10.1111/jofi.12688

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1752 The Journal of Finance R

methodology is similar to that of Cochrane (2005), Korteweg and Sorensen

(2010), Driessen, Lin, and Phalippou (2012), Franzoni, Nowak, and Phalippou

(2012), and Korteweg and Nagel (2016). Our contribution with respect to prior

research is that, in addition to estimating factor loadings and αs, we are able

to construct a quarterly time series of returns that is useful for understanding

the intertemporal behavior of the asset class.

Our estimation approach decomposes returns into a component due to expo-

sure to traded factors and a time-varying PE premium not spanned by traded

factors. The factor exposures capture the systematic risks of various classes of

PE and the time-varying PE premium can be interpreted as an αorthogonal to

the traded factors.1

The estimation is based on a model of PE returns that identifies necessary

assumptions and conditions for estimation. Because some of the assumptions

required by the model may be violated in practice, we test its sensitivity with

extensive simulations using both randomly generated data and pseudo-funds

drawing on historical U.S. stock return data. We find that the estimation is

robust to many violations of the assumptions but degrades when underlying

asset returns are not significantly correlated with the traded factors and when

idiosyncratic volatility is extremely high.

We apply the estimation procedure to quarterly cash flow data from insti-

tutional limited partnership investments obtained from Preqin covering the

period 1996 to 2015. We construct return indices for PE as a whole as well as

for subclasses (venture capital, buyout). We find that the estimated time series

of PE returns is more volatile than those measured using standard industry

indices. Moreover, it exhibits negligible serial dependence, in contrast to indus-

try indices. This result is consistent with smoothing induced by a conservative

appraisal process or by a delayed and partial adjustment to market prices,

which often arises in illiquid asset markets (see, e.g., Geltner (1991), Ross and

Zisler (1991)). We further find that the time series variation in returns differs

widely across subclasses and is highly cyclical. The cycles correspond well with

the time series variation in funding cycles and with anecdotal evidence about

peaks and troughs in the performance of each of the subclasses. This result

suggests that considerable diversification can be obtained within just the PE

domain.

The second contribution of the paper is to test whether PE returns are

spanned by portfolios constructed from publicly traded securities. This has

an important bearing on whether low-cost PE replication strategies are fea-

sible. We find that the PE specific factor is significant, which shows that the

PE premium is not perfectly replicable by simple passive PE strategies. Our

analysis of this factor suggests that part, but not all, of it is related to a proxy

for illiquidity.

1We use the term “alpha” loosely here to denote a premium not captured by exposures to

included factors. It may reflect actions under the control of the fund managers as well as other

factors.

Private Equity Returns 1753

The third contribution of this paper is to test an economic theory about the

source of PE returns. We use the estimated total return series for buyout funds

to test the market segmentation theory that buyout funds add value when

spreads between equity and fixed income yields are large (see, e.g., Kaplan and

Str¨

omberg (2009)). We find support for this hypothesis: buy-out fund returns

are higher when the cross-market spread is larger.

Finally, although PE is unique in its cash flow structure and fee structure,

our methodology may be useful in other market settings in which asset mar-

ket values are infrequently observed and cash flow streams in between these

market valuations are significant.

The paper is organized as follows. In Section I, we derive the model from first

principles and use simulations to shed light on robustness, with a particular

focus on when the methodology works well or poorly. In Section II,wediscuss

the data. Section III presents estimation results on the risk, return, and time

series characteristics of PE, and tests the market segmentation hypothesis.

Finally, in Section IV we conclude.

I. Methodology: Derivations and Tests

The intuition behind the methodology is that the present value of capi-

tal distributions is equal to the present value of capital investments when

the discount rate is the time series of the average realized returns across the

set of underlying illiquid investments, that is, the index of returns. Since the

minimal aggregation level that we can work on empirically is a fund, we have

one moment condition per fund. Further, since the number of funds is higher

than the number of time periods, the system is overidentified and we can use

maximum likelihood estimation to estimate which path the latent return in-

dex is more likely to have followed given the observed cash flow amounts and

timing.2

In this section, we derive an approach to estimating a PE return index based

on historical fund cash flows. As with all models developed for empirical appli-

cation, it relies on assumptions that may be satisfied or violated depending on

the underlying data-generating process. We list these assumptions and discuss

how violations of them may affect estimation outcomes. This exercise offers a

guideline for testing the robustness of the approach in later sections. In ad-

dition, an important benefit of the derivations below is that we derive from

first principles the public market equivalent (PME) introduced by Kaplan and

Schoar (2005).

A. Derivation

Consider a PE fund that makes Ninvestments at times ti,i∈{1,..., N},

of amount Ii. Each investment pays a single terminal dividend DTjat times

2One basic requirement is that at least one capital distribution occurs in each quarter, but we

find that the number of capital distributions is high enough, even during the financial crisis.