Optimal ownership structure in private equity

AuthorJinqiang Yang,Yang Liu,Bo Liu
Date01 January 2018
Publication Date01 January 2018
DOI: 10.1111/eufm.12130
Optimal ownership structure in private equity
Bo Liu
Yang Liu
Jinqiang Yang
School of Management and Economics,
University of Electronic Science and
Technology of China, No.2006, Xiyuan
Ave, West Hi-Tech Zone, Chengdu,
611731, China
Email: Liub@uestc.edu.cn
School of Finance, Shanghai University
of Finance and Economics, No.777
Guoding Road, Yangpu District,
Shanghai, China 200433
Emails: liuyangbread@yeah.net;
We develop a tractable model to analyse the valuation of a
general partner (GP) and the ownership allocation in a
private equity (PE) fund. Our results indicate that holding
ownership will increase GPs value. We further explore the
influential factors that affect GPs optimal ownership
decision. Our model predicts that GPs managerial skill has
positive effects on GPs shareholding choice. Factors such
as leverage, unspanned risks, GPs compensation have
negative impacts on GP ownership decision. The funds
maturity has a non-monotonic and concave influence.
Moreover, the widely used performance measures implied
by our model are consistent with empirical findings.
illiquidity, incomplete market, managerial compensation, ownership
structure, private equity
The authors are especially grateful to John Doukas (the Editor) and two anonymous referees for very helpful suggestions.
Bo Liu acknowledges support from the National Natural Science Foundation of China (#71373036 and #71573033) and the
Science and Technology Support Program of Sichuan Province (#2013GZ0116). Yang Liu acknowledges support from the
Natural Science Foundation of China (# 71472117) and Shanghai University of Finance and Economics Postgraduate
Innovation Funds (CXJJ-2014-315). Jinqiang Yang acknowledges support from the National Natural Science Foundation of
China (#71202007 and #71522008), Innovation Program of Shanghai Municipal Education Commission (#13ZS050) and
Chen GuangProject of Shanghai Municipal Education Commission and Shanghai Education Development Foundation
Eur Financ Manag. 2018;24:113135. wileyonlinelibrary.com/journal/eufm © 2017 John Wiley & Sons, Ltd.
A private equity (PE) fund is a closed-ended, finite partnership whereby the limited partner (LP) and
general partner (GP) share the residual profits after paying debt holders. To establish the ownership
allocation, PE contracts usually involve items about the GPs shareholding. Robinson and Sensoy
(2013) examine 837 PE funds and find that 79% have GP ownership above 0.99%. Given the huge
amount of global PE investment, the issue of ownership allocation is significant and requires
theoretical explanation and support. Incentive-based compensation is a common explanation for GPs
owning a significant share of PE funds, as the LP attempts to align the GPs interests with the
underlying project. The traditional view is that ownership holding, as well as carried interest, are used
to reduce the principal-agent problems. However, there exist two potential limitations. First, under the
traditional view, ownership holding and carried interest have the same effect. Therefore, it is unclear
why the GP should be awarded with ownership if carried interest has already been adopted. Second, it is
difficult to quantify the effects of the GPs ownership holding on the principal-agent problem, and
hence, one cannot accurately analyse the issues surrounding the GPs compensation structure.
PE fund assets are illiquid, and their risk exposure is difficult to hedge with publicly traded
securities due to PE fundsunique characteristics. PE fund shares are not as easily tradable as public
securities since the secondary market is inactive and there are tremendous discounts when selling PE
fund shares. Kleymenova, Talmor, and Vasvari (2012) report an average bid discount of 25.2% on PE
secondary transactions over the 20032010 period. Nadauld, Sensoy, Vorkink, and Weisbach (2016)
report discounts of slightly more than 50% in the 2009 crisis period. The discounts are significant and
large, even as an alternative investment. Sorensen, Wang, and Yang (2014) (SWY hereafter) calculate
the illiquidity cost due to the unspanned risks of the underlying assets and lock-up period resulting from
PE being a closed-end fund, with the main result being that the GP must generate sufficient risk-
adjusted excess return to compensate the LP for bearing the idiosyncratic risks. SWY mainly define
and solve LPs valuation problem with non-GPs ownership holding.
To overcome the limitations of traditional explanations for a GPs ownership levels, we develop a
tractable model to theoretically analyse the GPs valuation with ownership holdings based on the SWY
model. We improve on their model by allowing the GP to hold positive shares and solve GPs
optimality problem. In our model, the GP can take on firm-level idiosyncratic risks except those that
must be borne by the LP. The GPs will be increased relative to the case in which the GP has no
ownership. For a risk-averse GP in our model, the improvement in marginal valuation from risk-benefit
sharing outweighs the cost when the GPs shareholding ratio is relatively low. When the GP holds more
shares, the illiquidity discount from bearing idiosyncratic risks becomes noticeable, and the trade-off
between the utility increase and illiquidity discount determines the GPs optimal ownership preference.
Our numerical results indicate that risk-benefit sharing means that GPs will benefit from holding some
shares. Compared with the traditional view of incentive compensation, which treats shareholding by
GPs as an effective way to reduce the principal-agent problem, our model shows that increase in value
for the GP offers another reasonable explanation for why a GP would like to hold an ownership stake in
a PE firm.
In addition to the utility improvement resulting from risk-benefit sharing, the ownership allocation
arrangement will also increase the GPs value via an earlier earnings realisation. Following the
waterfall compensation structure, the carried interest would be realised only if the liquidation value of
PE assets exceeds the sum of debt repayment and investorspreferred return. The distribution
clustering around the carried interest threshold is a result of this mechanism. There exists an incentive
for the GP to time distributions such that they cluster at and just after a fundamental assets value
exceeds the catch-up region in which carried interest takes effect. By doing so, the GP immediately

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