How Much for a Haircut? Illiquidity, Secondary Markets, and the Value of Private Equity
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How Much for a Haircut? Illiquidity, Secondary Markets, and the
Value of Private Equity
Nicolas P. B. Bollen Berk A. Sensoy
Vanderbilt University
Ohio State University
LBS (June 2, 2015) How Much for a Haircut? 1 / 32
Motivation
Alternative asset classes are fraught with illiquidity.
Hedge funds; Subscription periods, lockup restrictions.
Perhaps the most important question facing investors: Do returns and
diversification benefits compensate for the special risks and fees?
In private equity funds, liquidity restrictions are extreme.
LBS (June 2, 2015) How Much for a Haircut? 2 / 32
Motivation
Investors (limited partners, LPs) commit capital for 10-12 years to a partnership.
Generally no option to redeem stakes with the fund, instead must turn to the
secondary market, often at a steep discount.
LPs also face uncertainty in the timing of capital calls for investments in portfolio
companies and payoffs from exited investments.
LBS (June 2, 2015) How Much for a Haircut? 3 / 32
Motivation
For these reasons, often argued PE should command a large liquidity premium.
And often questioned whether observed returns are sufficient.
PME around 1.2-1.3 for buyout, about one for VC since 2000.
• Robinson and Sensoy (2013), Harris, Jenkinson, Kaplan (2014), Phalippou
(2014), Higson and Stucke (2014).
Buyout beats public equities by about 20-30% over the life of the fund, VC just
equals.
LBS (June 2, 2015) How Much for a Haircut? 4 / 32
What do we do?
Build a valuation model for PE commitments.
Take the perspective of a risk-averse LP subject to liquidity shocks.
Explicitly incorporate the secondary market, which the LP accesses when a shock
occurs, and uncertain capital calls and distributions.
Err on the side of taking an upper bound perspective on liquidity costs,
equivalently a lower bound on the attractiveness of PE.
Punchline: Even so, PE should be attractive to many LPs at typical allocations
given observed returns.
Not because of returns, especially in VC, but because of diversification
benefits.
LBS (June 2, 2015) How Much for a Haircut? 5 / 32
Institutional background
PE funds are organized as 10-12 year partnerships.
Fund investors = limited partners, LPs. Typically large institutions such as
university endowments.
Fund investors = general partners, GPs. GPs work at/are PE firms, such as
Kleiner Perkins or Bain Capital.
GP fees typically 2% of committed capital (management fee) plus 20% of profits
(carried interest).
LBS (June 2, 2015) How Much for a Haircut? 6 / 32
Institutional background
LPs commit capital at fund inception and do not have the option to redeem their
stake with the fund.
Commitments are not provided to the GP immediately, but are called when the GP
encounters investment opportunities (portfolio companies).
LPs receive distributions (net of carry) when portfolio companies are exited (IPO,
M&A, liquidation)
Liquidity arrangements are a natural consequence of the illiquidity of portfolio
companies.
From an LP’s perspective, it is not the illiquidity of portfolio companies per se that
matters.
LBS (June 2, 2015) How Much for a Haircut? 7 / 32
The model
LP with CRRA utility of wealth.
3 assets: riskfree security, public equity, private equity.
Evolution of private and public equity asset values follows a trinomial lattice in
discrete time.
In keeping with the real options literature.
Distribution of ending asset values is close to a bivariate normal distribution.
For a set of model inputs, solve the model backward for the LP’s t=0 certainty
equivalent (CE).
LBS (June 2, 2015) How Much for a Haircut? 8 / 32The model
We are mostly interested in solving for the expected return on PE assets that
produces the same CE as a benchmark portfolio containing no PE.
From this we back out the fund’s expected net-of-fee return.
Note this differs from the LP’s expected net-of-fee return, for which we can also
solve.
Calibrate certainty equivalents to a 80/20 portfolio of public equity and the riskfree
security.
20% riskfree allocation is a typical fixed income plus cash endowment allocation
(NACUBO, 2015).
Similar results with a 90/10 benchmark.
LBS (June 2, 2015) How Much for a Haircut? 9 / 32Endowment allocations
2014 NACUBO-Commonfund Study of Endowments
Asset Allocations for U.S. College and University Endowments and Affiliated Foundations,
Fiscal Year 2014
Short-term
Domestic Fixed International Alternative Securities/
Size of Endowment Equities Income Equities Strategies* Cash/
% % % % Other
%
Over $1 Billion 13 8 18 57 4
$501 Million to $1 Billion 20 10 20 44 6
$101 Million to $500 Million 27 14 21 33 5
$51 Million to $100 Million 31 18 21 24 6
$25 Million to $50 Million 38 19 18 18 7
Under $25 Million 43 26 14 10 7
Type of Institution
All Public Institutions 18 11 21 46 4
Public College, University, or System 15 10 22 50 3
Institution-Related Foundations 24 13 22 35 6
Combined Endowment/Foundation 21 11 18 44 6
All Private Colleges and Universities 16 8 18 54 4
LBS (June 2, 2015) How Much for a Haircut? 10 / 32The model - caveats/features
Single private equity fund.
Single capital call and single distribution/payoff.
In a portfolio of portfolio companies, not a single one.
Same as Sorensen, Wang, and Yang (2014).
LP horizon is the horizon of the PE fund.
All of these features suggest an upper bound on liquidity costs.
LBS (June 2, 2015) How Much for a Haircut? 11 / 32Model inputs
Time horizon: 12 years.
Riskfree rate: 4%.
Expected return (10%) and volatility (15%) of public equity.
Expected return on PE assets.
Volatility of PE assets: 30% for buyout (BO), 45% for VC.
Correlation between public and private equity: 0.3 for BO, 0.6 for VC.
Implies unlevered BO beta = 0.6, VC beta = 1.8.
LBS (June 2, 2015) How Much for a Haircut? 12 / 32Model inputs
LP risk aversion.
Capital call probability.
GP’s distribution probability. Increasing function of ratio of GP payoff to maximum
possible.
Probability of liquidity shock. Base rate of 1% per quarter, matching disaster
frequency documented in the macro literature.
This increases by 1%age point for each net decrease in public equity value.
If a shock hits, PE must be sold at a haircut that can be large with countercyclical
probability.
Show results for different haircut parameters.
LBS (June 2, 2015) How Much for a Haircut? 13 / 32Why sell?
Have to.
Worried about meeting capital calls on unfunded commitments.
Need to reduce PE exposure to meet allocation targets.
Need to change strategy.
We think of the liquidity shock as a reduced form way of capturing all of these
(countercyclical) effects.
Another possibility: voluntary precautionary sales in anticipation of a future
liquidity shock.
Turns out not to happen unless parameters are extreme.
LPs want to hold to maturity, suggesting that the investment horizon per se is
not a problem given the alternative.
LBS (June 2, 2015) How Much for a Haircut? 14 / 32Capital call probability
LBS (June 2, 2015) How Much for a Haircut? 15 / 32Probability of large haircut
LBS (June 2, 2015) How Much for a Haircut? 16 / 32Risk aversion
LBS (June 2, 2015) How Much for a Haircut? 17 / 32Impact of call/distribution uncertainty
LBS (June 2, 2015) How Much for a Haircut? 18 / 32Impact of call/distribution uncertainty
Uncertain, random calls lower CEs.
Randomness of distributions is outweighed by GP’s strategic distribution timing.
LBS (June 2, 2015) How Much for a Haircut? 19 / 32Breakevens: three assets, VC
LBS (June 2, 2015) How Much for a Haircut? 20 / 32Breakevens: three assets, BO 1X leverage
LBS (June 2, 2015) How Much for a Haircut? 21 / 32Breakevens: three assets, BO 3X leverage
LBS (June 2, 2015) How Much for a Haircut? 22 / 32Required returns
Required returns:
Decrease in the efficiency of the secondary market.
(Generally) increase in LP risk aversion.
(Generally) increase in the allocation to private equity.
Effects mutually reinforcing:
Impact of inefficient secondary markets greater when risk aversion is high
and even more so when the PE allocation is high.
LBS (June 2, 2015) How Much for a Haircut? 23 / 32Required returns
Comparisons to empirical fund returns. PME about 1 for VC, 1.2 for buyout.
Historical performance of PE is sufficient to justify its risks and fees:
At least for relatively risk tolerant LPs at 20%-40% allocations .
Even though assumptions err on the side of an upper bound on liquidity costs.
For instance, allowing for partial liquidations will make PE more attractive.
LBS (June 2, 2015) How Much for a Haircut? 24 / 32Hold-to-maturity fund returns vs. LP realized returns
Returns reported in private equity databases and used in all empirical research
are hold-to-maturity fund returns.
They are an upper bound on the expected investment experience of an LP subject
to liquidity shocks that trigger secondary sales.
This wedge is about 1.5-3 percentage points of IRR with efficient secondary
markets.
3-5 percentage points when less efficient.
PME differences are less than the cumulated IRR differences because liquidity
shocks are more likely when public equity values are low.
LBS (June 2, 2015) How Much for a Haircut? 25 / 32Hold-to-maturity fund reported vs. LP realized returns, VC
LBS (June 2, 2015) How Much for a Haircut? 26 / 32Hold-to-maturity fund reported vs. LP realized returns, BO 1X
leverage
LBS (June 2, 2015) How Much for a Haircut? 27 / 32Hold-to-maturity fund reported vs. LP realized returns, BO 3X
leverage
LBS (June 2, 2015) How Much for a Haircut? 28 / 32The Impact of Fees
A perennial debate in private equity is whether observed fees are excessive.
One way to shed light on this is to ask what fraction of the gross value generated
by the fund accrues to the GP through fees.
Relative to a hypothetical zero-fee fund, the standard 2-20 fee structure increases
the breakeven private equity asset return by about 5-6 percentage points, or about
50%.
GP fees capture about one-third of the gross returns generated by the fund.
LBS (June 2, 2015) How Much for a Haircut? 29 / 32The impact of fees
LBS (June 2, 2015) How Much for a Haircut? 30 / 32Optimal allocations
The model can also be used to generate optimal allocation to assets given an
expected return on PE assets.
Here, we find that expected asset returns in the 15-20% range generate
allocations in the 30%-40% range for the most risk-tolerant LPs, and 10%-20% for
more risk averse ones.
Close to the empirical distribution of endowment allocations.
This is true even though the allocation consists of a single PE fund.
LBS (June 2, 2015) How Much for a Haircut? 31 / 32Summary
We present a model of commitments to private equity funds explicitly incorporating
two major sources of illiquidity from an LPs perspective.
Stochastic cash flows and the prospect of secondary sales at a haircut.
The model also naturally embeds the payoff volatility associated with holding a
fund to maturity.
Although our estimates if anything overstate liquidity costs, PE is still attractive to a
reasonable range of LPs at observed returns and allocations.
Casts doubt on claims that PE should command a large liquidity premium.
LBS (June 2, 2015) How Much for a Haircut? 32 / 32You can also read
