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Governing Multiple Firms
Alex Edmans
Doron Levit
Devin Reilly
LBS, CEPR, and ECGI
Wharton
UPenn
May 2, 2016
Abstract
We study the e¤ect of an investor owning multiple …rms on governance through both
voice and exit, and by both equityholders and debtholders. Under common ownership, an
informed investor has ‡exibility over which assets to retain and which to sell, and sells lowquality assets …rst. This increases adverse selection and thus price informativeness. In an
exit model, the manager’s incentives to work are stronger since the price impact of investor
selling is greater. In a voice model, the investor’s incentives to monitor are stronger since
“cutting-and-running” is less pro…table. Our results contrast with conventional wisdom
that common ownership always weakens governance by spreading an investor too thinly.
Keywords: Corporate governance, banks, blockholders, monitoring, intervention, exit,
trading.
JEL Classification: D72, D82, D83, G34
[email protected], [email protected], [email protected]. For helpful comments, we thank Rui Albuquerque, Alon Brav, Jonathan Cohn, Mara Faccio, Simon Gervais, Moqi
Groen-Xu, Marcin Kacperczyk, Stefan Lewellen, Mary Marchica, Jean-Marie Meier, Giorgia Piacentino, Tarun Ramadorai, David Schoenherr, Rui Silva, Günter Strobl, and seminar participants at
the BI Conference on Corporate Governance, FIRS, HEC Paris, Imperial, LBS, SFS Cavalcade, WFA,
and Wharton. AE gratefully acknowledges …nancial support from the European Research Council.
1
Most theories of corporate governance consider a single …rm. In reality, investors typically hold sizable stakes in several …rms – shareholders own multiple blocks1 and banks lend
large amounts to multiple borrowers. This paper analyzes the e¤ect of common ownership on
governance. Doing so is potentially complex, because governance can be undertaken through
di¤erent channels and by di¤erent types of investors. Starting with the former, investors can
govern through “voice”–direct intervention such as monitoring managers, suggesting a strategic change, or blocking a pet project. Alternatively, they can govern through “exit” – sell
their securities if the manager shirks, reducing the price; ex ante, the threat of exit induces the
manager to work. Moving to the latter, governance can be undertaken by both equityholders
and debtholders, such as banks, mutual funds, pension funds, and hedge funds.
While conventional wisdom is that common ownership weakens governance by spreading
the investor too thinly, we show that it can strengthen governance. Moreover, the channel
through which it does so is common to both voice and exit, and to both equityholders and
debtholders –common ownership increases adverse selection and thus price informativeness.
To demonstrate this channel most clearly, we start with a model in which …rm value is
exogenous and the investor only engages in informed trading. As a benchmark, we analyze the
case of separate ownership. An investor owns n securities of the same class (debt, equity, or any
security monotonic in …rm value) in a single …rm. She subsequently learns private information
on …rm value, which can be high or low. She may also su¤er a privately-observed liquidity
shock that forces her to raise at least a given dollar amount of funds, although she may choose
to sell more (or to sell even absent a shock). Examples include withdrawals from her end
investors, an alternative investment opportunity, or an increase in capital requirements. Based
on her private information and liquidity needs, she retains, partially sells, or fully sells her
stake. The security price is set by a market maker who observes the investor’s trade.
If the …rm turns out to be good (i.e. have high fundamental value) but the investor su¤ers
a liquidity shock, she is forced to partially sell it. Thus, if the …rm turns out to be bad (i.e.
low-value), the investor sells it by the same amount, to disguise the sale as motivated by a
shock. As a result, a bad …rm does not receive too low a price, and a good …rm does not always
enjoy a high price as it is sometimes sold and pooled with bad …rms.
Under common ownership, the investor owns one security in each of n …rms. Each …rm’s
1
See Antón and Polk (2014), Bartram, Gri¢ n, Lim, and Ng (2015), Hau and Lai (2013), and Jotikasthira,
Lundblad, and Ramadorai (2012).
2
securities are traded by a separate market maker, who observes trading in only one …rm. The
key e¤ect of common ownership is that it gives the investor a diversi…ed portfolio of both good
and bad …rms, and thus the choice of which …rms to sell upon a shock. If the shock is small, she
can satisfy it by selling only bad …rms. Then, being sold is not consistent with the …rm being
good and the sale being driven purely by a shock, and so fully reveals the …rm as bad. This
intensi…es adverse selection and leads to a lower price for a sold …rm. For example, Warren
Bu¤ett’s disposal of Exxon Mobil and ConocoPhillips in late 2014 but retention of Suncor
Energy was viewed by the market as a negative signal on the sold companies in particular,
rather than purely due to a liquidity shock (e.g. investment opportunities suddenly appearing
in non-energy sectors). Note that the above result arises even if the market maker does not
observe the investor’s trades in other …rms, nor even which …rms they are. Merely knowing
that she has other …rms in her portfolio, that she could have sold upon a shock, is su¢ cient
for the market maker to give a low price to a fully sold …rm.
In contrast, if the …rm turns out to be good, it can be retained even upon a shock, and thus
receives a high price. This result does not arise simply because common ownership gives the
investor additional securities to sell upon a shock: under both structures, she owns n securities.
Instead it results from her diversi…ed portfolio, which gives her bad …rms that she can sell upon
a shock. If instead all …rms were perfectly correlated, the investor would sometimes have only
good …rms and be forced to sell them upon a shock, and so price informativeness would be the
same as under separate ownership. The key is diversi…cation, not just ‡exibility over which
…rm to sell, and the e¤ect of diversi…cation arises even though the investor is risk neutral.
If the shock is moderate, it cannot be satis…ed by selling only bad …rms, and so the investor
needs to partially sell good …rms as well. However, since the market maker knows that the
investor would have fully sold the …rm upon a shock if it were bad, a good …rm receives a
higher price than under separate ownership. If the shock is large, it forces the investor to sell
good …rms to the same extent as bad …rms – exactly as under separate ownership. Overall,
price informativeness is the same under common ownership and large shocks as under separate
ownership, higher under moderate shocks, and higher still under small shocks. Intuitively, the
smaller the shock, the greater the investor’s ‡exibility over which …rms to sell. Thus, she is
forced to sell fewer good …rms, and so being sold is a greater signal that the …rm is bad.2
2
Note also that adding additional …rms to the investor’s portfolio is critically di¤erent from adding …nancial
slack, such as Treasury bills, where there is no private information. Adding Treasury bills e¤ectively reduces
3
The trading model is ‡exible and tractable, and can be embedded in a model of either voice
or exit. Starting with the former, we endogenize …rm value as depending on an unobservable
and costly intervention action (“monitoring”) by the investor. If she monitors, the …rm is
good, else it is bad. Under separate ownership, monitoring incentives are low. If the investor
monitors, she may su¤er a shock, which forces her to sell and so she does not receive the full
payo¤ from monitoring. Alternatively, she may not monitor and sell (“cut and run”). Selling
leads to a relatively high price under separate ownership, as discussed above. Thus, the payo¤
from monitoring (not monitoring) is relatively low (high), which leads to weak governance.
Under common ownership, the payo¤ to monitoring is higher. With a small shock, the
investor never needs to sell a monitored …rm. With a moderate shock, the investor is forced
to sell a monitored …rm but only partially, and so receives a higher price than under separate
ownership. In addition, the payo¤ to cutting and running is now lower since adverse selection
is intensi…ed. A sale is more indicative that the investor has not monitored, since if she had
monitored and su¤ered a liquidity shock, she would have sold other …rms instead.
In sum, the investor’s per-security monitoring incentives are higher under common ownership than under separate ownership, with the di¤erence decreasing in the size of the shock. On
the other hand, under common ownership the investor only holds one security in each …rm,
rather than n, reducing monitoring incentives –the conventional wisdom that she is spread too
thinly. Overall, we show that governance is stronger under common ownership if the number
of …rms is su¢ ciently small.
We next embed the trading framework into an exit model. Firm value now depends on
an e¤ort decision undertaken by the manager, who is concerned with both fundamental value
and the short-term security price. If the security is equity, his price concerns can stem from
termination threat, reputational considerations, or owning equity that vests in the short-term;
if it is debt, its price may a¤ect his …rm’s reputation in debt markets and thus ability to
raise future …nancing. The second interpretation extends the idea of governance through exit
to debt, an application not been previously studied by the literature. The investor privately
observes managerial actions in her portfolio …rms.
Under separate ownership, e¤ort incentives are low. If the manager works, the investor
may su¤er a shock and sell anyway. If he shirks, his …rm is sold, but does not su¤er too low
shock size within the separate ownership model; adding additional …rms moves us from the separate ownership
to the common ownership model.
4
a price. Under common ownership, the reward for working is higher. With a small shock, a
manager’s …rm is never sold if he works; with a moderate shock, it is only partially sold while
shirking would have led to full sale. The punishment for shirking is also higher, because a sale
is more revealing of shirking and leads to a lower price. Intuitively, common ownership creates
a tournament between the n managers, who know that the investor observes their e¤orts and
will sell the worst performers. Since the market anticipates that the worst performers are
sold, this ampli…es the disciplinary power of exit. In sum, governance is stronger than under
separate ownership, with the di¤erence decreasing in the size of the shock.
We analyze several extensions. First, we consider endogenous information acquisition.3 The
investor now must pay a cost to learn …rm value, otherwise she is uninformed. Conventional
wisdom is that common ownership weakens information acquisition incentives by reducing the
investor’s stake. We show that this need not be the case. Under separate ownership, the
investor obtains no bene…t from information if she ends up su¤ering a shock, since she sells
the …rm to the same extent regardless of whether it is good, bad, or of unknown value. Under
common ownership, if she su¤ers a shock, information is useful as it allows her to satisfy it by
selling bad …rms, rather than …rms of unknown value. As in the core model, common ownership
gives the investor ‡exibility over which …rms to sell upon a shock. The value of this ‡exibility
is higher if the investor knows …rm value, thus providing incentives to gather information.
Second, we allow the market maker to observe the trades in other securities held by the
investor. Prices become even more informative (and thus governance stronger) under common
ownership relative to separate ownership. This is because the market maker can engage in
relative performance evaluation (“RPE”, cf. Holmstrom (1979)) – compare the trade in one
…rm to that in another portfolio company, to better infer whether any sale of the …rst …rm
was due to the manager shirking or the common investor su¤ering a liquidity shock. Note that
the bene…ts of RPE arise even though …rms’fundamental values are uncorrelated. Third, we
study the case in which the investor receives a …xed reservation payo¤ upon exit, independent
of the e¤ect of exit on the …rm’s reputation. The investor is no longer concerned with price
impact, and thus camou‡aging a sale as motivated by a shock. This model applies to the
case of discontinuing a relationship, such as a bank ceasing to lend or a venture capitalist
not investing in a future …nancing round. Fourth, we analyze the case in which information
3
Note that, in the voice model, the investor’s private information is already endogenized through the knowledge of the actions she has taken.
5
asymmetry (parametrized by the di¤erence in valuation between good and bad …rms), and
thus the price impact of selling, di¤ers across …rms. In both cases, the results remain robust.
The model has a number of implications. Starting with the trade-only model, adverse
selection – and thus price decline upon a sale – is stronger when an informed seller owns
multiple securities. If all trades are observable, the price of a sold security is increasing in the
amount sold in other securities due to RPE. The “price”can refer either to the literal trading
price, or market perceptions of quality. For example, if a bank stops lending to a borrower,
that borrower’s perceived creditworthiness falls less if the bank stops lending to other borrowers
also. Indeed, Darmouni (2016) …nds that a borrower whose loan is terminated is more likely
to …nd a new lender if the original lender terminated other loans. Beyond security trading,
a director’s decision to quit a …rm is a more negative signal if he serves on other boards; a
conglomerate’s decision to exit a business line is a more negative signal of industry prospects
than if a focused …rm scaled back its operations; a worker’s labor market reputation and ability
to …nd a new job are higher if made redundant as part of a mass layo¤ rather than in isolation.
Indeed, Gibbons and Katz (1991) …nd that workers laid o¤ due to plant closures …nd a new
job faster and at higher wages than those laid o¤ individually.4
Applied to governance, the model shows that common ownership can strengthen governance, particularly if liquidity shocks and the number of …rms are small. This result applies
to governance by both equityholders and debtholders, and through both voice and exit. A
bank’s incentive to monitor a borrower, or a hedge fund’s incentive to intervene, can rise if the
investor owns multiple …rms. A manager’s incentive to work is stronger if his lender or main
shareholder owns large positions in multiple …rms. Overall, our model potentially justi…es why
shareholders own blocks in multiple …rms and banks lend large amounts to multiple borrowers,
despite the free-rider problem. Existing justi…cations are typically based on diversi…cation of
risk. While conventional wisdom might suggest that the common ownership induced by diversi…cation concerns weakens governance, our model suggests that the opposite may be the
case. An important exception is Diamond (1984), who shows in a costly state veri…cation
framework that diversi…cation incentivizes a bank to repay its end investors. We focus on
a di¤erent channel: diversi…cation increases adverse selection in …nancial markets and thus
4
Gibbons and Katz (1991) also contain a model in which the market infers worker quality from …rm …ring
decisions; Darmouni (2016) contains a similar model applied to banking. Unlike us, both models contain a
single worker (…rm). In addition, worker (…rm) quality is exogenous; here it depends on an action.
6
governance through both voice and exit. In addition, in Diamond (1984), monitoring does not
create value after a project is …nanced. Our results also potentially provide a novel bene…t of
spin-o¤s, which shift an investor from owning a stake in one company to two, and a cost of
stock-…nanced mergers which have the opposite e¤ect.
Relatedly, while existing studies typically use the size of the largest blockholder or the
number of blockholders as a measure of governance, our paper theoretically motivates a new
measure –the number of other large stakes owned by its main shareholder or creditor. Faccio,
Marchica, and Mura (2011) empirically study a related measure, the concentration of a security
in an investor’s portfolio. They argue that diversi…cation is desirable because a concentrated
investor will turn down risky, positive-NPV projects, unlike our channel. Separately, our
results suggest that greater ex-post transparency of trades (e.g. due to blockchains as studied
by Yermack (2016)), may improve governance.5
This paper builds on a long-standing literature of governance through voice (e.g. Shleifer
and Vishny (1986), Burkart, Gromb, and Panunzi (1997), Bolton and von Thadden (1998),
Maug (1998), Kahn and Winton (1998), Pagano and Roell (1998), and Faure-Grimaud and
Gromb (2004)) and a newer one on governance through exit (e.g. Admati and P‡eiderer (2009)
and Edmans (2009)) –see Edmans (2014) for a survey of both literatures. While McCahery,
Sautner, and Starks (2016) …nd that institutional investors use both governance mechanisms
frequently, most theories analyze only one. Edmans and Manso (2011), Levit (2013) and Fos
and Kahn (2015) feature both, but model each using quite di¤erent frameworks. Conventional
wisdom is that voice and exit are separate governance mechanisms, and their e¤ectiveness is
driven by very di¤erent determinants – voice depends on managerial entrenchment and the
value created by blockholder actions, and exit depends on stock liquidity, the manager’s shortterm concerns, and the value created by managerial actions. We construct a unifying framework
that can be adapted to either voice or exit, and show that common ownership enhances both
through the same channel. More broadly, all of the above models study a single …rm. The
only theory of multi-…rm governance of which we are aware is the voice model of Admati,
P‡eiderer, and Zechner (1994), which features no information asymmetry and instead focuses
on the trade-o¤ between risk-sharing and the free-rider problem.
5
Away from governance, Matvos and Ostrovsky (2008) and Harford, Jenter, and Li (2011) study how
common ownership of two …rms a¤ects the likelihood of them merging, and Azar, Schmalz, and Tecu (2015)
analyze how it a¤ects their competitive behavior in the product market.
7
1
Trade-Only Model
This section considers a pure trading model in which …rm values are exogenous, to highlight
the e¤ect of common ownership on how an informed investor trades on private information,
and in turn security prices and price informativeness. In Section 2, we endogenize …rm value
by allowing it to depend on intervention by the investor in a model of governance through
voice, and in Section 3 it depends on e¤ort by a manager in a model of governance through
exit. These models will demonstrate how the increased price informativeness, resulting from
common ownership, improves both governance mechanisms.
1.1
Setup
We consider two versions of the model. The …rst is a preliminary benchmark of separate
ownership, with a single …rm and a single investor. Speci…cally, the investor (“she”) owns n
divisible securities out of a total of m
1. The security can be debt, equity, or any
n
security monotonic in …rm value. The investor is an institution who has private information on
…rm value, such as a hedge fund, mutual fund, or bank. The second version is the main model
of common ownership, where the investor owns one security in each of a continuum of …rms
of mass n. Note that, in both models, the investor owns n securities. Let z denote the number
of securities held by the investor in a single …rm, i.e. z = n (1) under separate (common)
ownership. The remaining m
z securities out of this class, and any other classes of securities,
are owned by dispersed investors (households) who play no role.6
The model consists of three periods. At t = 1, Nature chooses the fundamental value
of each …rm i, Ri 2
R; R , where R > R > 0 and Ri are independently and identically
distributed (“i.i.d.”) across …rms. If Ri = R (R), the value of each security is vi = v (v),
where
Pr Ri = R 2 (0; 1) is common knowledge. We invoke the law of large numbers so
that the actual proportion of …rms for which Ri = R is .7 In the separate ownership model,
the investor privately observes vi , and in the common ownership model, she privately observes
6
We assume that, when moving from separate to common ownership, the n 1 securities no longer held by
the investor are now held by households. If, instead, they are held by other large investors, the net bene…ts of
common ownership are generally stronger than in the current setup: see Edmans and Manso (2011).
7
Invoking the law of large numbers leads to signi…cant tractability. In a previous version of the paper, the
investor held two …rms rather than a continuum under common ownership. The analysis with a …nite number
of …rms is more complicated but leads to similar results and does not provide additional insights.
8
[vi ]ni=0 . De…ne
v
v
v > 0, where m
R
R: the aggregate gain across the m
securities from Ri = R cannot exceed the overall gain in …rm value.8 We use “good” (“bad”)
…rm to refer to a …rm with vi = v (v).
At t = 2, the investor is subject to a portfolio-wide liquidity shock
and Pr [ = L] =
2 (0; 1]. The variable
2 f0; Lg, where L > 0
is privately observed by the investor and represents
the dollar amount of funds that she must raise. If she cannot raise , she raises as much as
possible. Formally, failing to raise
imposes a cost K > 0 multiplied by the shortfall in funds,
which is su¢ ciently large to induce her to meet the liquidity need to the extent possible. The
investor may choose to raise more than
the model allows for
dollars, i.e. we allow for voluntary sales. Note that
= 1, i.e. common knowledge that the investor has su¤ered a shock,
such as a …nancial crisis.
After observing the shock, the investor sells xi 2 [0; z] securities in …rm i. We use “fully
sold” to refer to …rm i if xi = z, and “partially sold” if xi 2 (0; z). In the common ownership
model, if xi = xj 8 i 6= j, we say that the investor engages in “balanced exit.”Otherwise, she
engages in “imbalanced exit.” The sold securities xi are purchased by the market maker for
…rm i (“it”), which can more generally refer to a competitive pool of investors. Each …rm has
a separate market maker who is competitive and risk-neutral, and observes only xi and not
xj , j 6= i, , nor vi . Each market maker sets the security price pi (xi ) at t = 2 to equal the
security’s expected value. We denote p
[pi (xi )]ni=0 and x
[xi ]ni=0 . We allow the market
maker to observe trades in other …rms with a lag in Section 3.4.1 and in real time in Appendix
D.2.
At t = 3, …rm value, security values, and payo¤s are realized. The investor’s utility in the
separate and common ownership models are respectively given by
uI (x; v; p; ) = xp (x) + (n x) v K max f0;
xp (x)g :
Z
Z
uI (x; v; p; ) =
[xi pi (xi ) + (1 xi ) vi ] di K max 0;
xi pi (xi ) di :
(1)
(2)
The equilibrium concept we use is Perfect Sequential Equilibrium. Here, it is de…ned as
follows: (i) A trading strategy by the investor that maximizes her expected utility uI given each
market maker’s price-setting rule and her private information on v (vi ) and (ii) a price-setting
8
If this were true, the value of the other classes would be decreasing in R and so their owners would have
incentives to reduce …rm value (cf. Innes (1990)).
9
rule by each market maker that allows it to break even in expectation, given the investor’s
strategy. Moreover, (iii) each market maker uses Bayes’ rule to update its beliefs from the
investor’s trades, (iv) all agents have rational expectations in that each player’s belief about
the other players’ strategies is correct in equilibrium, (v) the pricing function is monotonic,
i.e. pi (xi ) is weakly decreasing, holding constant xj , j 6= i,9 and (vi) o¤-equilibrium beliefs are
credible as de…ned by Grossman and Perry (1986).10 Since …rms are ex-ante identical, we focus
on symmetric equilibria, in which each market maker uses a symmetric pricing function. We
also assume that the investor does not sell a good …rm if she does not su¤er a liquidity shock.
This is intuitive since the price can never exceed the value of a good …rm v, but simpli…es
the analysis as we need not consider equilibria under which a good …rm is partially sold, but
still fully revealed as good as bad …rms are sold in greater volume. Prices and governance are
exactly the same without this restriction.
Note that, under both ownership structures, we hold constant the investor’s information
advantage: she always has a perfect signal on …rm value. Conventional wisdom suggests that, if
information acquisition is endogenous, the investor will acquire less information under common
ownership as her stake falls from n to 1. In Section 4 we analyze this extension and show that
information acquisition may in fact be stronger under common ownership.
1.2
Trade Under Separate Ownership
Proposition 1 characterizes all equilibria under separate ownership.
Proposition 1 (Separate ownership, trade only): An equilibrium under separate ownership
9
Focusing on weakly decreasing price functions imposes some restrictions on o¤-equilibrium prices, and thus
the amounts sold in equilibrium. However, since these restrictions do not a¤ect on-equilibrium prices, they
generally do not a¤ect the investor’s strategy in Section 2 or the manager’s strategy in Section 3 (when we
introduce real actions). In addition, weakly decreasing pricing functions are consistent with other microstructure
theories (e.g. Kyle (1985)) and empirical evidence (e.g. Gorton and Pennacchi (1995), Ivashina (2009)).
10
Loosely speaking, an equilibrium fails the Grossman and Perry (1986) re…nement (i.e., is not a Perfect
Sequential Equilibrium) if there exists a subset of sender types (the investor, in our setting) that will deviate to
b (b
b (b
a strategy x
xi ) if, conditional upon observing x
xi ), the receiver (the market maker, in our setting) believes
that this subset of types deviated and the complement of this subset did not deviate. The main implication is
that, if there is an equilibrium in which the investor raises at least L dollars, then there cannot be an equilibrium
in which the investor is unable to raise at least L dollars, and if the investor cannot raise at least L dollars in
any equilibrium, then in any equilibrium the investor sells her entire portfolio upon a shock.
10
always exists. In any equilibrium, the investor’s trading strategy in …rm i is:
xso (vi ; ) =
and prices of …rm i are:11
8
<0
:x ( ) = n
so
if vi = v and
o
min pL=n
;1
otherwise
( )
n
8
>
v
>
>
<
pi (xi ) = pso ( ) = v +
>
>
>
:v
=0
(3)
;
so
if xi = 0
+1
(4)
if xi 2 (0; xso ( )];
if xi > xso ( ) :
We will refer to the investor’s type as (vi ; ), i.e. a pair that indicates her information on
the value of …rm i and whether she has su¤ered a liquidity shock. (Sometimes we will de…ne
the type as referring only to vi , in which case it refers to both (vi ; 0) and (vi ; L)).
Equation (3) shows that, if the …rm is bad, the investor sells the same amount (xso ( )) as
if it were good and she had su¤ered a shock, to disguise the motive for her sale. The price of a
sold security, pso ( ), is relatively high as the market maker attaches a probability
+1
that
the sale was of a good …rm and due to a shock. Thus, the adverse selection problem is not so
severe under separate ownership. The amount xso ( ) is the minimum required to satisfy the
shock: if it were greater, type-(v; L) would deviate and sell less, retaining more of a good …rm
and receiving no lower a price (since prices are non-increasing).
Since the market maker breaks even in expectation, the investor’s trading gains when selling
xso ( ) of a bad …rm equal her trading losses when forced to sell xso ( ) of a good …rm due
to a shock. Thus, the possibility of trade has no e¤ect on the ex ante value of the investor’s
portfolio, which is n (v +
). In Sections 2 and 3, when we endogenize vi , we will show that
the possibility of trade changes portfolio value by a¤ecting governance.
1.3
Trade Under Common Ownership
Under common ownership, the investor decides not only how much of her portfolio to sell, but
also which …rms. Proposition 2 characterizes all equilibria.
11
While the prices on the equilibrium path are unique, the prices o¤-equilibrium are not. The pricing function
in equation (4) ensures monotonicity. A similar comment applies to subsequent pricing functions.
11
Proposition 2 (Common ownership, trade only): An equilibrium under common ownership
always exists.
(i) If L=n
v (1
) then in any equilibrium
xco (vi ; ) =
and prices of …rm i are:
where
= Pr [e
x = 0].
(ii) If v (1
8
<0
if vi = v
i
:x
e s.t. E [e
x] 2 v(1=n ) ; 1 if vi = v,
h
8
<v +
pi (xi ) =
:v
+ (1
)
(5)
if xi = 0
(6)
if xi > 0:
) < L=n < v then there exists an equilibrium in which
xco (vi ; ) =
8
>
0
>
>
<
xco ( ) =
>
>
>
:1
if vi = v and
=0
L=n v
v+
pco ( )
< 1 if vi = v and
if vi = v and
= 0, or vi = v and
=L
(7)
= L;
and prices of …rm i are:
(iii) If v
1
+1
8
>
v
>
>
<
pi (xi ) = pco ( ) = v +
>
>
>
:v
if xi = 0
+(1
)(1
)
if xi 2 (0; xco ( )];
(8)
if xi > xco ( ) :
< L=n then there exists an equilibrium as described by Proposition 1, except
xso is replaced by xso =n.
(iv) No other equilibrium exists.
The intuition is as follows. If L=n
), the liquidity shock is su¢ ciently small that
v (1
it can be satis…ed by selling only bad …rms. She thus retains all good …rms, regardless of
12
whether she su¤ers a shock. Since the shock requires her to sell
L
v(1 )
only in aggregate across
the bad …rms, she may retain some bad …rms and does so with probability (“w.p.”) . ( > 0
a¤ects the analysis of exit, but has no e¤ect on the analysis of voice.) As a result, a retained
…rm is not fully revealed and only priced at v +
+ (1
)
rather than v. Any …rm that is at
least partially sold is fully revealed as being bad and priced at v.
For v (1
) < L=n < v, the shock is su¢ ciently large that the investor must sell some
good …rms to satisfy it. Thus, a partial sale does not fully reveal a …rm as bad, and so the
investor never retains bad …rms. As a result, retained …rms are fully revealed as good and
priced at v. However, the shock remains su¢ ciently small that the investor can sell good …rms
less than bad …rms (engage in imbalanced exit). Upon a shock, she sells bad …rms fully and
xco ( ) from each good …rm. As a result, if there is no shock, she also sells xco ( ) from each
bad …rm, to pool with a good …rm and disguise her sale as being motivated by a shock. Thus,
(v; L) is pooled with (v; 0).12
Finally, for v
1
+1
L=n, the shock is su¢ ciently large that it forces the investor to sell
good …rms as much as bad …rms (engage in balanced exit). Thus, (v; L) is pooled with not only
(v; 0) (as in the moderate-shock case) but also (v; L), reducing the expected price of a good
…rm further, and increasing the price of (v; L) above v. Since the investor’s trading strategy
is the same as under separate ownership ((v; L), (v; 0), and (v; L) are all pooled), prices are
exactly the same. Note that, for v
1
+1
L=n < v, both the imbalanced exit equilibrium of
part (ii) and the balanced exit equilibrium of part (iii) can be sustained. In this range, while
the investor has the ability to satisfy a shock by selling bad …rms more, she also has the option
to do so by selling good …rms to the same degree as bad …rms. While doing so increases her
trading losses on good …rms, it reduces them on bad …rms, since bad …rms are now pooled with
good …rms upon a shock. For simplicity, we will refer to an equilibrium with the properties of
parts (i), (ii), and (iii) of Proposition 2 as type-(i), (ii), and (iii) equilibria.13
We denote the investor’s equilibrium payo¤ from owning security i (including the possibility of trade), given , by Vco (vi ; ) under common ownership and Vso (vi ; ) under separate
12
We continue to use “type” to refer to (vi ; ); this is a slight abuse of terminology since, under common
ownership, the investor’s type consists of the entire vector of …rm values.
13
The investor has no incentive to buy additional securities, because such purchases would be fully revealed
as stemming from information. This would be true even if the investor had the possibility of receiving positive
liquidity shocks, as long as she has the option to hold the in‡ow as cash rather than being forced to buy more
of her existing holdings. This treatment is consistent with the investor’s option to raise more than L and hold
the excess as cash.
13
ownership. Similarly, we denote the expected equilibrium price of …rm i’s, given value vi under
common and separate ownership by Pco (vi ; ) and Pso (vi ; ), respectively.
Proposition 3 (Price informativeness and payo¤ precision): Suppose
(i) If v (1
) < L=n or
+(1
Pco (v; )
with strict inequalities if L=n
)(1
)
, then
Pso (v; ) and Pco (v; )
v
2 (0; 1), then:
1
+1
. If L=n
(9)
Pso (v; ) ;
) and
v (1
>
+(1
)(1
)
, then
Pco (v; ) < Pso (v; ) and Pco (v; ) > Pso (v; ) :
(10)
Vso (v; ) and Vco (v; )
(11)
(ii)
Vco (v; )
with strict inequalities if L=n
v
1
+1
Vso (v; ) ;
. Both Vso (v; )
Vso (v; ) and Vco (v; )
Vco (v; ) decrease in L=n:14
Expression (9) gives conditions under which the expected price of a good (bad) …rm is
higher (lower) under common ownership than separate ownership, i.e. closer to fundamental
value so that price informativeness is higher. Under common ownership, the investor has a
diversi…ed portfolio of good and bad …rms. This allows her to choose which …rms to sell upon a
shock –in particular, she sells bad …rms …rst. In the moderate-shock equilibrium of part (ii) of
Proposition 2, a shock causes her to fully sell bad …rms and partially retain good …rms. Thus,
a fully sold …rm is priced at v, and so bad …rms receive a lower expected price under common
ownership. Scholes (1972), Mikkelson and Partch (1985), Holthausen, Leftwich, and Mayers
(1990), and Sias, Starks, and Titman (2006) show that sales by large shareholders reduce the
stock price due to conveying negative information; Dahiya, Puri, and Saunders (2003) …nd
similar results for loan sales. Our model predicts that the price declines upon a sale are greater
under common ownership.15
If v 1+1
< L=n < v , more than one equilibrium exists. The comparative statics with respect to L=n
implicitly assume that, in this range, once the type of the equilibrium is chosen (i.e., type-(ii) or (iii)), it does
not change as we increase L=n, as long as it exists.
15
In He (2009), the price impact of a sale is stronger if the asset is more correlated with other assets in the
investor’s portfolio. Retaining an asset is even more costly when it is positively correlated with the rest of the
14
14
A similar intuition applies to the small-shock equilibrium of part (i), whether the investor
fully retains good …rms. As a result, the sale of …rm i cannot be attributed to a shock because, if
…rm i were good and the investor had needed liquidity, she would have sold other …rms instead.
Thus, a sold …rm is fully revealed as being bad and priced at v. The one complication is that,
since sold …rms are fully revealed as bad, the investor no longer has strict incentives to sell bad
…rms. Thus, she retains bad …rms w.p.
. If
>
+(1
)(1
)
, then price informativeness is
lower under common ownership (Pco (v; ) > Pso (v; ) in expression (10)). When we endogenize
…rm value in Sections 2 and 3, equilibria will di¤er according to e¢ ciency, i.e. expected …rm
value. In the most e¢ cient equilibria,
+(1
)(1
)
and so (9) holds; intuitively the most
e¢ cient equilibrium will involve the highest possible price informativeness.
In addition to reducing the expected price of bad …rms, common ownership also increases
the expected price of good …rms. Under separate ownership, a good …rm is automatically sold
under a shock; under common ownership and a small shock, it is retained. This result does
not simply arise because common ownership gives the investor more securities to sell to satisfy
a shock: she owns n in both models. Again, the intuition is that common ownership gives her
a diversi…ed portfolio of both good and bad …rms. Where the shock is small, she can always
satisfy it by selling only bad …rms. On the other hand, being retained no longer reveals a …rm
as being good. If
is su¢ ciently small, the latter e¤ect is weaker, and so Pco (v; ) > Pso (v; )
overall. With a moderate shock, a good …rm is sold, but only partially. The market maker
knows that, if the …rm were bad and the investor had su¤ered a shock, it would have been
sold fully. Thus, it is priced at v +
v+
+1
+(1
)(1
)
(i.e. pooled with only (v; 0)) rather than
(i.e. pooled with (v; 0) and (v; L)) under separate ownership. With a large shock,
the investor’s trading behavior is exactly the same as under separate ownership, and so price
informativeness is no higher.
While part (i) concerns the closeness of prices to fundamental value (price informativeness),
part (ii) concerns the closeness of the investor’s payo¤ to fundamental value, which we call
“payo¤ precision.”The investor’s payo¤ from …rm i is given by (1
xi ) vi +xi pi . Since her payo¤
depends on the price, just as common ownership generally improves price informativeness, it
always improves payo¤ precision. Note that payo¤ precision always improves, even if price
informativeness does not (i.e. (10) holds). This is because the value of a bad …rm is v, and the
portfolio, and particularly so when the asset is low-quality. Thus, retention is a stronger signal of asset quality,
leading to a steeper pricing function. His model features risk aversion rather than liquidity shocks.
15
price received for selling a bad …rm is also v (under the small-shock equilibrium). Thus, the
investor’s payo¤ is v regardless of the frequency with which she retains bad …rms. Similarly,
good …rms are fully retained and worth v to the investor, regardless of
and thus the price the
market maker attaches to a retained …rm.
Note that the e¤ect of common ownership on price informativeness stems from diversi…cation, rather than simply owning multiple …rms. If the …rms were perfectly correlated, prices
would be as in the separate ownership benchmark as the investor would not be able to sell bad
…rms more and good …rms less upon a shock –either all …rms are good, or all …rms are bad.
This result implies that price informativeness (and, as we will show, governance) is increasing
in the diversi…cation of an investor’s portfolio.
In addition, the results show that diversifying by adding additional …rms to the investor’s
portfolio is di¤erent from adding …nancial slack, i.e. liquid securities (such as Treasury bills)
on which the investor has no private information. We start with the separate ownership model
and study the e¤ect of adding A dollars of liquid securities to the investor’s portfolio. If A
L,
then the addition e¤ectively insulates the investor from a liquidity shock, leading to maximum
price informativeness. Indeed, the net liquidity shock, L A, is now negative. If instead A < L,
the addition e¤ectively reduces the liquidity shock to L
A; since price informativeness in the
separate ownership model is independent of the liquidity shock (as long as it is positive), it
is una¤ected by the new securities. Intuitively, since liquid securities are always fairly priced,
selling them to satisfy a shock involves no loss. Upon a shock, if the …rm turns out to be good,
the investor will sell liquid securities …rst and only raise L
A from the …rm. If the …rm is
bad, the investor will again sell liquid securities …rst and raise only L
A from the …rm, since
raising more would fully reveal the …rm as bad.
Now instead consider the e¤ect of adding A < L dollars of securities in a new …rm j. Upon
a shock, if the initial …rm i is good (and new …rm j is bad), the investor will sell …rm j …rst
and thus only partially sell …rm i – the same as if the investor instead had liquid securities.
The critical di¤erence is if …rm i is bad (and new …rm j is good). Now, the investor will not
sell …rm j …rst. Unlike liquid securities, securities in …rm j su¤er an adverse selection discount
and so she su¤ers a loss by selling them if they are good. She instead fully sells …rm i. Even
though doing so fully reveals …rm i as bad, it is better than fully selling the higher-quality j. In
sum, adding liquid securities reduces the net liquidity shock but keeps us within the separate
ownership model where, upon a shock, the sale volume is independent of …rm quality. Adding
16
a …rm moves us to the moderate-shock common ownership model where, upon a shock, the
investor partially (fully) sells a good (bad) …rm.
2
Governance Through Voice
We now endogenize …rm value as depending on an action by the investor. Speci…cally, at
t = 1, the investor takes a hidden action ai 2 f0; 1g, where ai = 1 leads to Ri = R and
thus vi = v, and ai = 0 leads to Ri = R and thus vi = v. Action ai = 1 imposes a cost
e
ci 2 [0; 1) on the investor, which she privately observes prior to deciding her action16 ; Section
2.4.3 shows that the results remain robust to a publicly-known monitoring cost. The action
ai is broadly de…ned to encompass any action that improves …rm value but is costly to the
investor. Examples include advising the …rm on strategy, using her business connections to
bene…t the …rm, preventing the …rm’s manager from extracting perks or empire-building, or
choosing not to take private bene…ts for herself.
The probability density function of e
ci is given by f and its cumulative distribution function
is given by F . Both are continuous and have full support. We assume e
ci are i.i.d. across …rms,
and that E[e
ci ]
R
R, so that ai = 1 is ex-ante e¢ cient. We refer to ai = 1 as “monitoring”
and ai = 0 as “not monitoring”. A good (bad) …rm is now a …rm that has been monitored (not
monitored). We assume that, if the investor is indi¤erent between monitoring and not, she
monitors; this indi¤erence only arises for a measure zero of e
ci . Through her private knowledge
of a, the investor continues to have private information on v.
The investor’s utility conditional on x and e
c
[e
ci ]ni=0 is now given by:
uI;V oice = uI (x; a; p; )
Z
ci ai di:
(12)
under common ownership, and analogously under separate ownership. The equilibrium de…nition is similar to Section 1, with the following additions: (vii) the investor’s monitoring rule
in each …rm i maximizes her expected utility given e
c, her expected trading strategy, and each
market maker’s price-setting rule, and (viii) each market maker forms expectations about
16
The cost of monitoring will depend on …rm-speci…c factors that are, in part, privately known to the investor
(as in Landier, Sraer, and Thesmar (2009)). For example, she may have private information on the business
ties that she may lose if she engages in perk prevention, on how easily she can use her business connections to
bene…t the …rm, or on the extent to which she can extract private bene…ts.
17
that are consistent with (vii), instead of taking it as given.
2.1
Preliminaries
We …rst derive results that hold under both separate and common ownership. When deciding
her action, the investor trades o¤ the cost of monitoring with the increase in security value.
Lemma 1 states that this trade-o¤ gives rise to a threshold strategy: she monitors …rm i if and
only if her cost is su¢ ciently low.17
Lemma 1 In any equilibrium and under any ownership structure there is a c such that (“s.t.”)
the investor chooses ai = 1 if and only if e
ci
c.
Ex-ante total surplus (…rm value minus the cost of monitoring) in equilibrium is R +
F (c ) R
R
E [cjc < c ] , which is increasing in c if and only if c
vestor’s threshold satis…es c
z . Since z
m
R. The in-
R
R, a higher c always increases
R
total surplus. We thus de…ne e¢ ciency as the maximization of c . From part (viii) of the equilibrium de…nition,
implementation of
= F (c ). Given the market maker’s expectations of
and the investor’s
through her actions, prices and trading strategies are determined as in
Section 1. Therefore, our equilibrium characterizations below only specify the thresholds
2.2
.
Voice Under Separate Ownership
Proposition 4 characterizes all the thresholds that emerge in any equilibrium under separate
ownership.
Proposition 4 (Separate ownership, voice): In any equilibrium under separate ownership with
voice, the monitoring threshold, cso;voice , is given by the solution of c =n =
voice
( )
1
min
v+(
L=n
v (1
))
;
1
+1
Prices and trading strategies are characterized by Proposition 1, where
voice
(F (c )), where
:
is given by
(13)
so;voice
F cso;voice .
17
Note that di¤erent equilibria under di¤erent ownership structures can have di¤erent thresholds; the threshold c in Lemma 1 refers to a generic threshold.
18
Intuitively, cso;voice solves
Vso (v; F (c ))
c =n = Vso (v; F (c )) :
(14)
The right-hand side (“RHS”) of (14) is the investor’s payo¤ from holding a bad …rm, given
that the market maker expects the probability of monitoring to be F (c ). The left-hand side
(“LHS”) is her payo¤ from holding a good …rm, net of monitoring costs.
Even ignoring the free-rider problem (i.e. that the investor owns n < m securities), governance is imperfect (cso;voice < n ) for two reasons. First, the payo¤ to monitoring is relatively
low. While monitoring increases security value to v, w.p.
shock and has to sell xso;voice
xso
so;voice
the investor su¤ers a liquidity
units for less than their fair value of v. Second,
the payo¤ from not monitoring and selling is relatively high. Regardless of whether she suffers a shock, a non-monitoring investor sells xso;voice and pools with (v; L), receiving a price
pso;voice
pso
so;voice
that exceeds the fair value of v.18
Turning to comparative statics, the investor’s threshold is decreasing in the shock L. A
larger shock means that she must sell more securities xso;voice to satisfy it. This reduces her
payo¤ from monitoring, and also allows her to sell more, and thus pro…t more, if she cuts
and runs (since she pools with (v; L)). The threshold is increasing in
for two reasons.
First, it (trivially) increases the value created by monitoring. Second, it increases the price
pso;voice received from sold …rms, since pso;voice incorporates the possibility that the …rm is
(v; L). Due to this higher price, she has to sell fewer units if she monitors and su¤ers a shock,
thus increasing the payo¤ to monitoring. The threshold is increasing in v due to the second
channel: it raises pso;voice and thus reduces xso;voice . It is increasing in n because the monitoring
gains are applied to more units, and also because the per-security shock L=n falls with n. The
threshold is decreasing in . The more likely the shock, the higher the price pso;voice received
for selling xso;voice , because the sale may be of a good …rm in response to a shock. This higher
price increases the payo¤ to not monitoring and selling. In addition, higher
18
means that a
Note that multiple thresholds are possible, since if the market maker believes that the investor monitors
intensively (cso;voice is high), prices upon sale are high and so the investor can satisfy her liquidity needs
by selling only a small amount xso;voice . This in turn increases the payo¤ to monitoring and sustains the
equilibrium. Similarly, if the market maker believes that the investor monitors little, prices upon sale are low
and so the investor must sell a large amount to satisfy her liquidity leads, reducing the payo¤ to monitoring
and sustaining the equilibrium. As a result, governance is self-ful…lling. The comparative statics described in
the text deal with stable equilibria, i.e. those in which voice (F (c)) intersects the line h(c) c=n from above.
19
monitoring investor has to sell more frequently. The e¤ect of F ( ) is ambiguous.
2.3
Voice Under Common Ownership
Proposition 5 below gives the most e¢ cient equilibrium under common ownership. A single asterisk
refers to an equilibrium, and a double asterisk
refers to the most e¢ cient
equilibrium.
Proposition 5 (Common ownership, voice): There are v (1
F ( )) < y
y
v such that
the monitoring threshold under the most e¢ cient equilibrium is given by
cco;voice
where
8
>
>
>
>
>
>
>
<c
the largest solution of c =
ii
=
>maxfc ; c g
>
>
ii
iii
>
>
>
>
:c
the largest solution of c =
iii
voice
( )
"
1
L=n
1
v(
(1
if L=n
voice
voice
v (1
(F (c )) if v (1
(F (c ))
F ( ))
F ( )) < L=n < y
if y
L=n < y
if y
L=n;
(15)
v (1
)
)+ )+
1
+
#
:
(16)
Prices and trading strategies are characterized by Proposition 2.
There are two e¤ects of common ownership on governance. First, the investor now owns
1 rather than n securities in each …rm, which reduces her monitoring incentives. This is the
standard cost of diversi…cation: it spreads an investor more thinly. The second is that it
increases the investor’s incentives to monitor for a given number of securities held. We use the
term “per-security monitoring incentives”to refer to the second e¤ect.
These incentives are stronger under common ownership because it increases the payo¤ to
monitoring and reduces the payo¤ to cutting and running. Under a small shock (L=n
v (1
F ( ))), we have a type-(i) equilibrium. In the most e¢ cient type-(i) equilibrium, mon-
itored …rms are always retained and yield the investor v, and unmonitored …rms are fully
revealed by being sold and yield her v. As a result, the per-security incentives to monitor are at the highest possible level of
(v (1
, and so
= F ( ). Under a moderate shock
F ( )) < L=n < v), we have a type-(ii) equilibrium where (v; L) is now pooled with
20
(v; 0), which reduces (increases) the payo¤ to monitoring (not monitoring). Price informativeness (and thus governance) is lower than under small shocks, but remains higher than
under separate ownership, since (v; L) is not pooled with (v; L). The most e¢ cient type-(ii)
equilibrium involves
= F (cii ). Brav et al. (2006) …nd that stock prices fall by 4% if an
activist hedge fund subsequently exits; our model predicts that this decline, and thus monitoring incentives, will be stronger under common ownership. Separately, when F ( ) is low (i.e.
monitoring costs are high), we are more likely to be in the small-shock case where governance is
strongest under common ownership. Intuitively, the implicit commitment to monitor provided
by common ownership is particularly important when the investor’s appetite for monitoring is
low in the …rst place.
Under a large shock (v
1
+1
< L=n), we have a type-(iii) equilibrium where (v; L) is pooled
with both (v; 0) and (v; L). Upon a shock, the investor sells all …rms to the same degree, and
so receives the same price regardless of whether she has monitored. Price informativeness is
the same as under separate ownership, and so per-security monitoring incentives are also the
same: equation c =
voice
(F (c )), which de…nes ciii , is the same as (13), which de…nes cso;voice ,
except without the coe¢ cient n. The most e¢ cient type-(iii) equilibrium involves
For v
1
+1
= F (ciii ).
< L=n < v, both type-(ii) and (iii) equilibria are sustainable and so either
equilibrium may be the most e¢ cient. Proposition 5 states that there exists y such that, if
L=n < y, the type-(ii) equilibrium is most e¢ cient. There also exists y
L=n
y, the type-(iii) equilibrium is most e¢ cient; for y
e¢ cient.19 The proof in Proposition 5 shows that, if
v
v+
y such that, if
L=n < y, either may be most
, then y = y = v, and so where
the type-(ii) equilibrium exists, it is always the most e¢ cient equilibrium.
Corollary 1 (Common ownership, voice, threshold comparison): The monitoring threshold in
the most e¢ cient equilibrium, cco;voice , is decreasing in L=n. The investor’s per-security monitoring incentives are strictly higher under common ownership than under separate ownership
if L=n < y, weakly higher if y
L=n < y, and the same if L=n
19
y.
The e¢ ciency trade-o¤ between type-(ii) and type-(iii) equilibria is as follows. The price at which an
investor can sell a good …rm is lower in a type-(iii) equilibrium (pso ( ) < pco ( )), which increases the investor’s
incentives to monitor. However, lower prices also imply that the investor must sell more of a good …rm upon
a shock, which also allows her to sell more of a bad …rm without being revealed; both forces decrease her
incentives to monitor. The proof of Proposition 5 shows that, when is small and L=n is large, the di¤erence
in prices is more important than the di¤erence in quantities, and so the type-(iii) equilibrium is more e¢ cient.
21
The intuition for the e¤ect of L=n is that the strength of governance depends on price informativeness. Common ownership improves price informativeness because it gives the investor a
choice of which …rms to sell upon a shock; thus, her trade is more driven by fundamental value
and less driven by the shock. This choice is greatest when the shock is small, as she then only
needs to sell bad …rms. The larger the shock, the greater the extent to which she has to sell
good …rms, which leads to less informative prices.
The above discussion has concerned per-security monitoring incentives, the bene…t of common ownership. However, the investor’s threshold, and thus governance, is also a¤ected by the
cost of common ownership described previously. Proposition 6 shows that, despite this cost,
common ownership is still superior if the number of …rms is su¢ ciently low, so that the decline
in the number of securities from n to 1 and thus the e¤ect of being spread too thinly is small.
Proposition 6 (Comparison of equilibria, voice): There exist 1 < n and L
v (1
F ( ))
such that:
(i) If n > n and L > 0 then any equilibrium under separate ownership is strictly more
e¢ cient than any equilibrium under common ownership.
(ii) For any 0 < L
L there is 1 < n (L) such that if 1 < n < n (L) then any equilibrium
under common ownership is strictly more e¢ cient than any equilibrium under separate
ownership.
While Proposition 5 characterizes the most e¢ cient equilibrium, alternative equilibria also
exist. For example, if v
1
+1
L=n < v, we could have a balanced exit equilibrium which
leads to weaker governance than imbalanced exit. Even so, part (ii) of Proposition 6 shows that
our main result continues to hold even when the least e¢ cient equilibrium is considered. The
reason is that, if L
v (1
F ( )), all equilibria involve fully retaining good …rms and so the
price of any …rm that is at least partially sold is v. Since the investor’s payo¤ from a bad …rm is
v regardless of whether it is retained or sold, she receives v if she does not monitor, irrespective
of the equilibrium frequency
with which a bad …rm is retained. Thus, the threshold is
any equilibrium for which L
v (1
in
F ( )).
Proposition 6 solves for the ownership structure that maximizes …rm value. However, if
the investor could choose ownership structure, she would select the one that maximizes her
expected portfolio value minus monitoring costs (expected trading pro…ts are zero under both
22
structures): she only internalizes the e¤ect of her monitoring on her z securities rather than
the entire …rm. This result is given in Proposition 7:
Proposition 7 (Investor’s choice of equilibrium, voice): For any 0 < L
1 < n (L)
L , there exists
n (L) such that, if 1 < n < n (L), the investor’s expected payo¤ net of monitoring
costs under any equilibrium of common ownership is strictly higher than under any equilibrium
under separate ownership.
2.4
2.4.1
Extensions of the Voice Model
Observable Monitoring
Common ownership improves governance since it increases adverse selection and thus serves as
a commitment for the investor not to cut and run. To highlight how greater commitment is the
channel through which common ownership improves governance, we analyze a model variant
in which the monitoring decision and thus …rm value is observable, and so commitment is a
non-issue. The investor’s payo¤ is z (v +
)
c if she monitors and zv if she does not, which
yields c = z . Thus, per-security monitoring incentives are the same under both ownership
structures, and so governance is always inferior under common ownership, due to the investor
being spread more thinly (z = 1 rather than n).20
Intuitively, if the monitoring decision is observable, the bene…ts of common ownership
disappear. The intuition can be seen in two ways. First, price informativeness and thus payo¤
precision are perfect, and cannot be improved upon by common ownership. Second, under
unobservable monitoring, the investor can make trading pro…ts by deviating from the market
maker’s equilibrium expected threshold. Greater price informativeness reduces the investor’s
trading losses from being forced to sell a good …rm upon a shock, and reduces her trading
pro…ts from cutting and running. Both forces increase the level of monitoring to which she can
e¤ectively commit. Under observable monitoring, any deviations are observed and so prices
are fully revealing under both ownership structures. Thus, our model predicts that common
20
If L=n is large, the investor faces a cost K from not meeting her liquidity needs. In the core model, she
cannot avoid this cost by monitoring more intensively, since the monitoring threshold is unobservable and so
does not a¤ect the market maker’s pricing function (see the proof of Lemma 4 in the Appendix). Where the
monitoring threshold is observable, the investor may increase her monitoring intensity to be able to satisfy the
shock. This consideration does not change our result that the bene…t of common ownership disappears when
the investor can commit to her monitoring intensity.
23
ownership is bene…cial for unobservable interventions, but not observable ones. Carleton,
Nelson, and Weisbach (1998), Becht, Franks, Mayer, and Rossi (2009), and McCahery, Sautner,
and Starks (2016) provide evidence that a signi…cant amount of shareholder intervention occurs
behind the scenes and is unobservable to outsiders; the literature on governance through voice
typically assumes monitoring to be unobservable (e.g. Maug (1998), Kahn and Winton (1998)).
Interventions by banks (outside of bankruptcy) are even more likely to be unobserved.
2.4.2
Index Funds
To highlight the role of price informativeness in improving governance, we now consider the
case of passive index funds, which Appel, Gormley, and Keim (2016) …nd engage in monitoring.
The bene…t of common ownership does not apply to such funds, because they always engage in
balanced exit, and only if there are out‡ows (i.e. a liquidity shock): an index fund must raise
exactly
in revenue. As a result, she is unable to strategically sell bad …rms more than good
…rms, and so her trades (and thus prices) are uninformative. Indeed, Corollary 2 shows that
the per-security monitoring incentives of an index fund are independent of ownership structure.
Corollary 2 The per-security monitoring incentives of the index fund are the same under any
ownership structure. The monitoring threshold under common ownership, cco;voice;index , is given
by the solution of c = (F (c )), where
( )
1
min 1;
L=n
v+
:
(17)
Some commentators (e.g. Bhide (1993)) argue that the ability to cut and run reduces
monitoring incentives. One may think that index funds may therefore have greater monitoring
incentives than the active funds considered in the core model – since index funds cannot
disproportionately sell bad …rms, they are locked in to monitor. Our model shows that this
need not be the case: if L=n < v (1
) then cco;voice =
> cco;voice;index , and so active funds
monitor more than index funds. The intuition is twofold. First, the ‡ipside of index funds’
inability to cut-and-run –to disproportionately sell bad …rms –is that they are also unable to
disproportionately retain good …rms if they su¤er a shock. A shock forces them to sell good
…rms to the same extent as bad …rms, reducing their payo¤ to monitoring. Second, the active
fund’s ability to cut and run means that, when L=n is small, she is unable to commit not to
24
sell the worst assets in her portfolio, leading to a severe adverse selection problem upon selling
and thus a powerful commitment to monitor.
2.4.3
Common Monitoring Cost
In our voice model, the investor trades on her private information on …rm value. This stems
from her private information on whether she has monitored, which in turn arises from her
private information on her …rm-speci…c monitoring cost. Appendix C considers the case in
which the monitoring cost is common knowledge, and monitoring instead increases …rm value
with a given probability, rather than with certainty. The investor’s private information now
stems from her knowledge of whether monitoring is successful and her monitoring intensity.
The results continue to hold, and the models are very similar. Intuitively, common ownership
improves governance by giving the investor greater ‡exibility over how she can trade on her
private information. It does not matter whether this information is on the monitoring cost or
the success and intensity of monitoring.
3
Governance Through Exit
This section now endogenizes …rm value as depending on an action taken by a manager rather
than the investor. Each …rm is now run by a separate manager (“he”), who takes action
ai 2 f0; 1g at t = 1. Examples of ai = 0 include shirking, cash ‡ow diversion, perk consumption,
and empire building. We now refer to ai = 0 as “shirking” and ai = 1 as “working.” A good
(bad) …rm is one in which the manager has worked (shirked). Action ai = 1 imposes a cost
e
ci 2 [0; 1) on manager i, which is i.i.d. and privately observed by the manager prior to deciding
his action. The e¤ort cost e
ci can also be interpreted as a private bene…t from shirking.
Manager i’s objective function is given by:
uM;i = R (ai ) + !pi
e
c i ai :
(18)
The manager cares about …rm value and also the t = 2 security price; these price concerns are
captured by !.21 If the security is equity, ! refers to stock price concerns, which are standard
21
An alternative objective function would be uM;i = R (ai ) + !pi e
ci ai , where < 1 captures the fact that
the manager does not own the entire …rm. This is equivalent to the objective function uM;i = R (ai )+ ! pi eci ai .
25
in theories of governance through exit and can stem from a number of sources introduced in
prior work. Examples include takeover threat (Stein (1988)), concern for managerial reputation
(Narayanan (1985), Scharfstein and Stein (1990)), or the manager expecting to sell his own
securities at t = 2 (Stein (1989)). To our knowledge, exit theories have not previously considered
the potential application to debt securities. The manager may care about the short-term debt
price, or the …rm’s reputation in debt markets, as it will a¤ect the ease at which he can raise
additional debt (e.g. Diamond (1989)).
The investor only trades, but unlike the trade-only model of Section 1, her trades improve
governance by changing the manager’s e¤ort incentives. As in the trade-only model, she
privately observes vi under separate ownership and v
[vi ]ni=0 under common ownership, but
[e
ci ]ni=0 . As before, her utility is given by (1)
neither she nor the market makers observe e
c
under separate ownership and (2) under common ownership. We will abuse language slightly
by using the phrase “the manager will be sold” to refer to the securities of the …rm run by
the manager being sold. We continue to focus on symmetric equilibria, in which the managers
follow the same strategy and each market maker uses a symmetric pricing function. The
equilibrium concept is as in Section 1 with the following additions: (vii) a decision rule by each
manager i that maximizes his expected utility uM;i given his information on e
ci , other managers’
strategies, the market maker’s price-setting rule, and the investor’s trading strategy, and (viii)
each market maker forms expectations about
3.1
that are consistent with (vii).
Preliminaries
Similar to the voice model, we …rst derive the following threshold rule that holds under both
separate and common ownership:
Lemma 2 In any equilibrium and under any ownership structure, there is a c such that
manager i chooses ai = 1 if and only if e
ci
Manager i works only if the value gain R
his cost. The maximum price rise is
any equilibrium, c
R
c.
R plus ! times the expected price rise exceeds
, which arises if the price is fully informative. Thus, in
R + ! . We refer to c = R
R+!
as “maximum governance.”
Thus, (18) is equivalent to a utility function in which the manager’s weight on …rm value is , with his weight
on the security price and cost of e¤ort being normalized by to economize on notation.
26
3.2
Exit Under Separate Ownership
Proposition 8 characterizes all the thresholds that emerge in any equilibrium under separate
ownership.
Proposition 8 (Separate ownership, exit): In any equilibrium under separate ownership with
exit, the unique threshold for each manager, cso;exit , is given by the solution of c =
where
exit
( )=R
R+!
!
1
+1
1
exit
(F (c ))
(19)
:
Prices and trading strategies are characterized by Proposition 1, where
is given by
so;exit
F cso;exit .
Intuitively, cso;exit solves
R + !Pso (v; F (c ))
(20)
c = R + !Pso (v; F (c )) ;
where Pso (vi ; ) is de…ned in Proposition 3. The RHS of (20) is manager i’s payo¤ from
shirking and the LHS is his payo¤ from working.
The manager’s threshold cso;exit increases with his price concerns !. If he shirks, the investor
sells xso;exit
xso
so;exit
and reduces the price to pso;exit
pso
so;exit
. A higher ! makes
this price reduction more costly to the manager, and so he is more likely to work. Unlike in the
voice model, the threshold is independent of L and v. In the voice model, these parameters
a¤ect the number of securities the investor is forced to sell upon a shock. Here, it is the manager
who takes the action and his incentives depend only on (fundamental value plus) the expected
security price from the two actions, not the magnitude of the trade xso;exit .22 Since the expected
price reduction from shirking,
so;exit
so;exit +1
so;exit
, is independent of L and v, these parameters
do not a¤ect the threshold. The threshold is independent of n because it is the manager who
takes the action, unlike in the voice model where the investor’s incentives to monitor depend
on her stake n. For similar reasons to the voice model, the threshold is increasing in
decreasing in . Finally, if FG (c) > FB (c) 8 c, then
22
G
>
B
and
(governance is stronger) but
Note that, unlike in the voice model (see footnote 18), there is no multiplicity of equilibria since the amount
the investor sells to satisfy her liquidity shock does not a¤ect the manager’s e¤ort incentives. He is concerned
only with the price impact of trade, not the actual trading volumes.
27
cG < cB . When the distribution of e¤ort costs is lower, in the sense of …rst-order stochastic
dominance, e¤ort is more likely, and so the market maker attaches a higher probability that a
sale is of a good …rm due to a shock. Thus, the price of a sold …rm is higher, reducing e¤ort
incentives.
3.3
Exit Under Common Ownership
Proposition 9 below characterizes the most e¢ cient equilibrium under common ownership.
Proposition 9 (Common ownership, exit): The working threshold under the most e¢ cient
equilibrium is given by
cco;exit
8
>
)g
minfR R + !; F 1 (1 L=n
>
>
v
<
= cii;exit the largest solution of c =
>
>
>
:c
if L=n
exit
(F (c )) if v 1
if v
so;exit
where
ii;exit
v 1
ii;exit
ii;exit
< L=n < v
L=n;
(21)
F cii;exit and
exit
( )=R
R+
! 1
1
1
+
!
1
(22)
:
Prices and trading strategies are characterized by Proposition 2.
The intuition behind Proposition 9 is the same as in Proposition 5 under voice, except for
the small-shock equilibrium of v 1
ii;exit
. This equilibrium involves su¢ cient bad …rms
that, if the shock is su¤ered, it can be satis…ed without selling any good …rm. If there are
insu¢ cient bad …rms under the highest possible threshold of R
“create” additional bad …rms by lowering the threshold to F
1
R + !, the equilibrium can
(1
L=n
),
v
so the shock can be
satis…ed by selling only bad …rms. These lower incentives to work are achieved by the investor
retaining bad …rms w.p.
voice model, even if
> 0 under no shock, which increases the payo¤ to shirking. In the
> 0, the investor’s incentives to monitor are unchanged as her payo¤
from not monitoring is v regardless of whether the …rm is retained or sold.
Governance through exit is stronger under common ownership for two reasons. First,
common ownership increases the punishment for shirking. Under separate ownership, exit is
28
consistent with the investor su¤ering a liquidity shock and so a sold …rm receives a relatively
high price. Here, under a small shock, exit is fully revealing of shirking and leads to the
lowest possible price of v. The greater punishment for shirking (lower price for the manager)
is analogous to the lower price received by the investor from cutting and running under voice.
Under a moderate shock, a bad …rm is fully sold upon a shock and thus fully revealed. Second,
common ownership increases the reward for working. Under separate ownership, a good …rm is
automatically sold under a shock. Under common ownership, it is retained upon a small shock
and only partially sold upon a moderate shock. The greater reward for working is analogous
to the higher payo¤ to monitoring under voice.
For a small or moderate shock (L=n < v), governance is strictly superior under common
ownership; for a large shock it is the same because prices and trading strategies are the same.
This result is stated in Proposition 10.
Proposition 10 (Comparison of most e¢ cient equilibrium, exit): The working threshold under the most e¢ cient equilibrium, cco;exit , is decreasing in L=n, strictly higher than under
separate ownership if L=n < v, and the same if L=n
v.
Note that the cost of common ownership (the investor owning 1 rather than n securities
in each …rm) is absent here, because the manager’s incentives depend only on expected prices,
rather than the number of securities traded per se. However, the reduction in the number of
securities may weaken exit in reality: for example, it may lower her incentives or ability to
gather information in each …rm by spreading her too thinly. We model endogenous information
acquisition in Appendix D.1 and show that it may in fact rise under common ownership. If it
falls, this is a cost of common ownership against which the bene…t we identify in this paper
should be traded o¤.
While Proposition 9 focuses on the most e¢ cient equilibrium, in Appendix A.3 we consider
all equilibria and show that, if
is su¢ ciently high, any equilibrium under common ownership
is weakly more e¢ cient than the separate ownership benchmark. If
and L are su¢ ciently
low, there exist equilibria that are less e¢ cient than the benchmark. This can occur under
the small-shock equilibria (low L), where the investor never sells good …rms. Therefore, the
price upon selling is v, and so there are equilibria in which she does not sell bad …rms. This
reduces the punishment for shirking, and also the reward for working by lowering the price of
29
a retained …rm below v. Under the e¢ ciency criterion, the most e¢ cient equilibrium will be
chosen and governance is always weakly stronger under common ownership.
3.4
Extensions of the Exit Model
3.4.1
All Trades Observed With a Lag
One variant of the exit model is for the market maker in …rm i to observe only the trades in
…rm i in real-time (at t = 2), and the trades in …rm j with a lag via 13F, 13D, or 13G …lings23
at a new date t = 2:5. Under this variant, prices at t = 2 will be as in the the core model, but
they may be di¤erent at t = 2:5. This is because the market can now observe the trades in
all …rms, and thus engage in “relative performance evaluation”to infer more precisely whether
the trade in …rm i was motivated by low …rm value or a liquidity shock.
This post-trade price movement will a¤ect the manager’s incentives, if his concerns ! relate
to the price at t = 2:5. (While the trade revelation date will typically be a few weeks or months
after the trade date, it may be several years before …rm value is realized). Thus, prices and
trading strategies conditional upon
do not change, but the manager’s threshold does. (Note
that post-trade observability does not a¤ect the voice model, since it is the investor who takes
the action and she is not concerned with post-trade prices.)
Proposition 11 characterizes the threshold that arises. Thus far, under separate ownership,
we have considered a single …rm. When trades are observed with a lag under common ownership, the market maker can use trades in other …rms to infer the likelihood of a liquidity shock.
Thus, we will also consider a separate ownership benchmark in there are n investor-…rm pairs,
and shocks are perfectly correlated across the investors so that the market maker can engage
in similar inference. However, we will show that common ownership is weakly superior even
when compared to this higher benchmark.
Proposition 11 (Exit, all trades observed with a lag). Consider the exit model where all
trades are observed at t = 2:5, and the concerns ! relate to the price at this date. In any
equilibrium, the unique working threshold under separate ownership is cso;exit if there is a single
23
If the investor has total investments exceeding $100 million, she has to report her holdings across all stocks
every quarter via 13F …lings. Moreover, if her stake in stock j previously exceeded 5% and she is a 13D …ler
(i.e. previously stated an activist intent), she has to report sales of 1% or more within 10 days; if she is a 13G
…ler (i.e. previously stated a passive intent), she has to report sales of 5% or more within 45 days of year end.
30
investor-…rm pair, and
cso;exit;obs = R
R+!
(1
)
if there are n investor-…rm pairs and the investors su¤er perfectly correlated shocks. Under
common ownership, the working threshold under the most e¢ cient equilibrium is
cco;exit;obs
8
<R
=
:R
if L=n < v;
R+!
R+!
(1
) if L=n
(23)
v:
The intuition is as follows. Under common ownership, if L=n < v, i.e. the liquidity shock is
not so large that it forces the investor to fully sell good …rms, maximum governance is achieved.
In particular, it is achieved even upon a moderate shock, even though such a shock forces her
to partially sell good …rms. In the core model, governance is imperfect under a moderate shock
because (v; L) is pooled with (v; L): the market maker cannot discern whether a partially-sold
…rm was a good …rm sold due to a shock, or a bad …rm voluntarily sold. This reduces the
reward for working and punishment for shirking. Here, prices at t = 2:5 depend not on the
absolute trade in a given …rm, but the trade relative to that in other …rms. If other …rms are
sold more, the market maker infers a shock and thus that the partially-sold …rm is good; if
other …rms are sold less, it infers no shock and thus that the partially-sold …rm is bad. Thus,
regardless of whether there is a shock, good …rms are sold less and bad …rms are sold more,
and so both are fully revealed.24
If L=n
v, the shock is so large that it forces the investor to fully sell all …rms, and so
there are no security price incentives to work. However, if there is no shock (w.p. 1
),
price incentives are at the maximum possible (! ). Bad …rms are fully sold and fully revealed,
because the market maker observes at t = 2:5 that other …rms are retained, and so the sale
cannot have been driven by a shock.
Moving to separate ownership, if shocks are uncorrelated, the market maker learns nothing
24
Gervais, Lynch, and Musto (2005) show that mutual fund families can add value by monitoring multiple
managers, since …ring one manager increases investors’perceived skill of retained managers. Inderst, Mueller,
and Münnich (2007) show that when an investor …nances several entrepreneurs, an individual entrepreneur
may exert greater e¤ort. To obtain re…nancing, he needs to deliver not only good absolute performance, but
also good performance relative to his peers. In Fulghieri and Sevilir (2009), multiple entrepreneurs compete
for the limited human capital of a single venture capitalist. These e¤ects are similar to the RPE channel in our
exit model. However, these papers do not consider the case of our core model where trades in other …rms are
unobservable, nor is there an analog of the liquidity shock (or the voice model).
31
about vi by observing xj , and so the threshold is the same as in the core model. If shocks are
correlated, governance is superior to the core model. In particular, if there is no shock and
…rm i is partially sold, the market maker can observe at t = 2:5 that other …rms are unsold.
Thus, there cannot have been a (systemic) shock, fully revealing …rm i as bad and leading
to maximum governance. However, if there is a shock, there are no price incentives to work.
Since all investors su¤er the shock, all sell to the same degree, regardless of whether their …rm
is good or bad, and so the market maker cannot distinguish between good and bad …rms. This
is di¤erent from common ownership, where a single investor coordinates the trades across the
di¤erent …rms and thus satis…es her liquidity needs by selling bad …rms more and good …rms
less. As a result, governance under separate ownership and correlated shocks is strictly weaker
than under common ownership, except if there is a large shock in which case it is the same,
since the single investor must sell all …rms and is unable to coordinate.
Note that the bene…ts of RPE arise even though …rm values are not correlated. Typically,
RPE allows common shocks to be …ltered out: observing xj provides information on the value
of …rm j and thus the value of …rm i. Instead, observing xj is valuable because it provides
information about the investor, in particular whether she has su¤ered a shock. Since the shock
is at the portfolio level, the investor makes her trading decisions in response to a shock at the
portfolio level, and so observing other trades in her portfolio is valuable.
These results have implications for the optimal organization of market making: measures
that lead to market makers observing trades in more securities, e.g. mergers of market makers
or greater transparency of trades, may improve governance. They also provide the testable
implication that a security price should react to disclosures of trades in other securities by its
major investors.
4
Further Extensions
While Sections 2.4 and 3.4 consider extensions of the voice and exit models, respectively, this
section considers extensions common to both models. The full analyses are in the Appendix;
we discuss the intuition here.
Endogenous Information Acquisition. Under both ownership structures, the core model
holds constant the investor’s information advantage: she always has a perfect signal on v.
32
Conventional wisdom suggests that, if information acquisition is endogenous, the investor will
acquire less information as her stake falls from n to 1 –she is spread too thinly.25 Appendix
D.1 shows that information acquisition may actually rise under common ownership.
In this extension of the trade-only model, the investor pays a cost e
ci 2 [0; 1) with CDF
F ( ) to learn the value of …rm i, otherwise she is uninformed. e
ci are i.i.d. and privately
observed by the investor, as is her decision to acquire information. Similar to the voice model,
she acquires information if and only if e
ci is below this threshold. Under separate ownership,
the investor obtains no bene…t from information if she ends up su¤ering a liquidity shock, since
she sells the …rm to the same extent regardless of whether it is good, bad, or of unknown value.
Thus, her monitoring incentives are particularly weak when the frequency of a liquidity shock
is high. Under common ownership and small shock sizes, the investor obtains no bene…t
from information if she does not su¤er a shock. She retains both good …rms and …rms with
unknown value, and so learning that a …rm is good does not change her trading strategy. She
sells bad …rms, but since she only receives v from doing so, she makes no pro…t from knowing
that the …rm is bad. Instead, the bene…ts from information under common ownership arise
if the investor su¤ers a shock. If uninformed, she has to satisfy the shock by selling …rms of
unknown quality, which will include some good …rms. Information allows her to identify bad
…rms, and satisfy the shock by selling them. The value of this ‡exibility is higher if the investor
knows …rm value, and so common ownership provides incentives to acquire information. Since
the bene…ts to information under separate (common) ownership only arise if there is no shock
(a shock), information acquisition incentives are higher under common ownership if liquidity
shock is su¢ ciently probable.
Even when information acquisition is lower under common ownership, this must be traded
o¤ against the bene…ts of common ownership identi…ed by our core model. In particular,
common ownership can be more e¢ cient even if information acquisition is less: low information
of which a high proportion is incorporated in prices may dominate high information of which
a low proportion is incorporated in prices.
Single Market Maker. Appendix D.2 considers the case of a single market maker, who
25
The investor may be endowed with more information if her stake gives her improved access to management.
Even though Regulation FD prohibits managers from selectively disclosing material information, investors still
talk to managers to learn their views on market conditions, strategic choice, etc. In the voice model of Section
2, the investor’s information private information is fully endogenized through the knowledge of whether she has
monitored. That model explicitly features the impact of being spread too thinly on monitoring incentives.
33
can observe the trades in all …rms in real time. For small liquidity shocks, governance under
common ownership is at the maximum possible level for both voice and exit, and thus stronger
than under separate ownership. This result is similar to Proposition 11, the exit model where
all trades are observed with a lag, and the intuition is the same. By comparing the trade in
…rm i to that in …rm j, the market maker can better discern whether a sale was due to a
liquidity shock or low …rm value, thus increasing price informativeness and payo¤ precision.
Fixed Payo¤ Upon Sale. Appendix D.3 considers the case in which the investor receives
a …xed reservation payo¤ upon sale, independent of the e¤ect that sale has on the …rm’s
reputation. This model applies to the case of discontinuing a relationship, such as a bank
terminating a lending relationship with a borrower, or a venture capital investor choosing
not to invest in a future …nancing round.26 Here, the investor receives her outside option
regardless of how much she sells, and is thus unconcerned with her price impact. Nevertheless,
the core results generally hold. In the voice model, it is no longer the case that the incentives
to cut-and-run are lower under common ownership – doing so yields the …xed reservation
payo¤, regardless of ownership structure. However, the second channel through which common
ownership improves monitoring incentives continues to hold: if the investor su¤ers a shock, and
the shock is su¢ ciently small, she has a choice of which …rms to sell under common ownership.
She can thus retain monitored …rms, and enjoy the full payo¤ to monitoring.
Under exit, we distinguish between two cases. First, if the …xed reservation payo¤ exceeds
v, the investor always fully sells a bad …rm, regardless of ownership structure, and so a shirking
manager is fully punished even under separate ownership (as long as the shock is not large
enough to force the investor to sell her entire stake). Since e¤ort incentives are already at
the highest possible level, they are not improved by common ownership. However, if the …xed
payo¤ is less than v, the investor only sells the minimum amount to satisfy her liquidity need,
regardless of …rm value. Thus, under separate ownership, the manager has no price incentives
to work. Under common ownership, the investor sells working …rms less and shirking …rms
more, giving price incentives to work and improving governance.
Heterogeneous Valuation Distributions. Appendix D.4 considers the case in which …rms
have di¤erent valuation distributions, and so information asymmetry
26
and thus the price
The latter application assumes that non-participation does not a¤ect the value of the venture capital
investor’s original investment, for example because there is a large supply of available capital in the future
…nancing round.
34
impact of selling di¤ers across …rms. It remains the case that governance through both voice
and exit are stronger under common ownership with small shocks. Regardless of
and thus
price impact, the investor always receive (weakly) more than v by selling a bad …rm and less
than v by selling a good …rm, and thus is always better o¤ by selling securities that she knows
to be bad and retaining securities she knows to be good. Thus, regardless of whether
is
constant or di¤ers across …rms, it remains the case that, if the shock is su¢ ciently small,
common ownership allows the investor to fully retain good …rms upon a small shock, and so a
sale fully reveals that a …rm is bad.
Spin-o¤s and Mergers. Appendix D.5 applies our model to study the governance e¤ects of
spin-o¤s and mergers. After a spin-o¤, the investor holds stakes in two …rms which she can trade
independently; prior to the spin-o¤, she is e¤ectively forced to trade both to the same degree.27
The spin-o¤ allows her to sell bad …rms more and good …rms less, strengthening governance
both through voice and exit; stock-…nanced mergers have the opposite e¤ect. The theories of
Aron (1991) and Habib, Johnsen, and Naik (1997) also point to separate security prices for
each division as a channel via which spin-o¤s create value, but the bene…ts of separate security
prices are not due to stronger governance. In addition, here it is separate trading, rather than
only separate security prices, that is key –if the investor is an index fund, or if the divisions
are perfectly correlated, the bene…ts do not arise.
5
Conclusion
This paper has shown that common ownership can improve governance through both voice
and exit, and by both equityholders and debtholders. The common channel is that common
ownership gives the investor a diversi…ed portfolio of good and bad …rms. As a result, she
has greater ‡exibility over which …rms to sell, and will sell bad …rms …rst. This intensi…es the
adverse selection problem –the sale of a …rm is a stronger signal that it is bad, since if it were
good and the investor had su¤ered a liquidity shock, she would have sold bad …rms …rst. In
addition to reducing the expected price for a bad …rm, common ownership also increases the
expected price for a good …rm, since the investor may not have to sell it, or may only have to
sell it partially, if she su¤ers a shock.
27
This is similar to Corollary 2, which analyzed index funds, but here the investor can choose to raise more
than in revenue.
35
In a voice model, this greater price informativeness enhances the investor’s incentives to
monitor. If she cuts and runs, she receives a low payo¤ due to severe adverse selection. If
instead monitors, she is more likely to be able to retain the …rm and thus enjoy the full value
created by monitoring. In an exit model, greater price informativeness enhances the manager’s
incentives to work. If he shirks, the investor sells, which has a particularly negative price
impact. If he works, he is more likely to be retained as the investor can sell other …rms upon
a shock. Both models suggest that centralization of investment among a small number of
investors may improve governance. In both models, a smaller shock increases the investor’s
‡exibility over which …rms to sell, thus increasing price informativeness and the strength of
governance under common ownership. The above channels operate even if the market maker
is unable to observe the investor’s trading in other securities. If it can, governance is even
stronger due to the market maker’s ability to engage in relative performance evaluation. This
result suggest that greater ex-post transparency of trades may improve governance.
On the other hand, consistent with conventional wisdom, common ownership is costly as
it spreads the investor more thinly. In a voice model, this directly reduces her incentives to
intervene; however, common ownership remains superior if the shock and number of …rms are
su¢ ciently small. In the exit model, the investor may in fact acquire more information under
common ownership. If she acquires less, this cost must be traded o¤ with the bene…ts of
common ownership identi…ed by this paper.
Note that our results do not require the investor to choose ownership structure to deliberately maximize price informativeness (and thus governance) or even be cognizant of this e¤ect
of her ownership structure choice. Even if she chooses common ownership to reduce risk, our
result suggest that diversi…cation for private risk reduction reasons has a social bene…t by
improving governance. This result parallels the governance through exit literature, where the
investor trades purely to maximize pro…ts, but such trading has the side bene…t of improving
price informativeness and thus governance.
The core result of our trade-only model, that having private information over multiple
assets worsens adverse selection, can be applied outside a trading context. Examples include a
director’s decision to quit a board, a …rm’s decision to exit or scale back a line of business, or
an employer’s decision to …re a worker. In all of these cases, the negative inference resulting
from termination is attenuated is stronger if the decision-maker had many other relationships
that she could have terminated instead.
36
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40
A
Proofs of Main Results
This section contains proofs of our main results. Proofs of auxiliary results are in Appendix B.
A.1
Proofs of Section 1
Proof of Proposition 1.
Let x (v; ) be an equilibrium strategy for type-(v; ). If the
equilibrium involves mixed strategies, then x (v; ) is a set. We start by proving that there is
a unique x > 0 such that xi (v; L) = xi (v; 0) = xi (v; L) = x. We argue six points:
1. If x0i 2 xi (v; L) [ xi (v; 0) then x0i > 0. By choosing xi = 0, type-v receives a payo¤ of v.
However, note that there is x00i > 0 s.t. x00i 2 xi (v; L). Therefore, pi (x00i ) > v with positive
probability. By choosing x00i ; type-v increases her revenue and obtains an expected payo¤
strictly greater than v. Therefore, 0 62 xi (v; L) [ xi (v; 0).
2. If x0i 2 xi (v; 0) then x0i 62 xi (v; L) [ xi (v; 0). Suppose not. Since x0i 2 xi (v; L) [ xi (v; 0),
with positive probability pi (xi ) < v. Based on point 1, it must be x0i > 0. Since x0i > 0,
type-(v; 0) will deviate to xi = 0, which generates a strictly higher payo¤ of v.
3. If x0i 2 xi (v; 0) then x0i 62 xi (v; L). Suppose not. Based on point 2, x0i 2 xi (v; 0)
implies x0i 62 xi (v; L) [ xi (v; 0). Therefore, pi (x0i ) = v w.p. 1, and type-(v; L) can satisfy
her liquidity need by choosing x0i . She chooses x00i 6= x0i only if pi (x00i ) = v w.p. 1.
Thus, there is no x00i 2 xi (v; L) s.t. x00i 2 xi (v; L) [ xi (v; 0). Therefore, pi (x000
i ) = v 8
x000
i 2 xi (v; L) [ xi (v; 0) w.p. 1, and so type-(v; ) receives a payo¤ of v. However, type(v; 0) can always choose x0i and secure a payo¤ strictly larger than v, since pi (x0i ) = v
w.p. 1. We conclude, if x0i 2 xi (v; 0), then x0i 62 xi (v; L) [ xi (v; L) [ xi (v; 0).
4. xi (v; L) = xi (v; L) [ xi (v; 0). Suppose on the contrary there is x0i 2 xi (v; L) s.t. x0i 62
xi (v; L) [ xi (v; 0). The contradiction follows from the same arguments as in point 3.
Suppose on the contrary there is x0i 2 xi (v; L) [ xi (v; 0) s.t. x0i 62 xi (v; L). Based on
point 2, it must be x0i 62 xi (v; 0), and so pi (x0i ) = v w.p. 1. Moreover, note that if
x00i 2 xi (v; L) then x00i > 0 and pi (x00i ) > v w.p. 1. However, type-(v; 0) can always choose
x00i and secure a payo¤ strictly larger than v, a contradiction.
5. If x0 2 xi (v; 0) then x0 < x00 8 x00 2 xi (v; L) [ xi (v; L) [ xi (v; 0). Suppose on the contrary
there are x0 2 xi (v; 0) and x00 2 xi (v; L) [ xi (v; L) [ xi (v; 0) s.t. x0
x00 . Based on
the previous points, x0 62 xi (v; L) [ xi (v; L) [ xi (v; 0), and so x0 > x00 . Moreover, since
41
x0 62 xi (v; L) [ xi (v; 0), w.p. 1 pi (x0 ) = v. However, type-(v; L) has a pro…table deviation
to x0 : she receives a payo¤ of v and also satis…es her liquidity need. Indeed, since x0 > x00
and x00 2 xi (v; L), then if the investor can satisfy her liquidity need by choosing x00 , she
can do so by choosing x0 .
6. xi (v; L) is a singleton (types-(v; L), (v; L), and (v; 0)). Suppose on the contrary there
are x0 < x00 where x0 ; x00 2 x (v; L). Since
= L it must be 0 < x0 . Based on point 3,
x0 ; x00 2 xi (v; L) [ xi (v; 0), and so pi (x0 ) 2 (v; v) and pi (x00 ) 2 (v; v). Since type-(v; L)
must be indi¤erent between x0 and x00 , then
x00 pi (x00 ) + (1
(x00
x0 ) (pi (x00 )
x00 )v = x0 pi (x0 ) + (1
v) = x0 (pi (x0 )
x0 )v ,
pi (x00 )) :
This implies pi (x0 ) < pi (x00 ). Since x0 < x00 , type-v strictly prefers x00 over x0 . This implies
that x0 2 xi (v; L)nxi (v; L), a contradiction.
Given the claims above, Bayes’rule implies pi (x) = pso ( ). We prove that in any equilibrium that survives the Grossman and Perry (1986) re…nement, x = xso ( ). Suppose on the
contrary that x >
L
.
pso ( )
(x
L=n. This implies that type (v; L) will strictly prefer deviating to x
") pi (x
")
Since the price function is non-increasing, there is " > 0 such that
contradiction. We conclude x
", a
xso ( ). Suppose on the contrary that x < xso ( ). This implies
that the investor does not raise L in equilibrium by selling x. Consider a deviation where all
types other than (v; 0) deviate from x to xso ( ). Given the deviation, the market maker will
set p (xso ( )) = pso ( ). Therefore, all types who deviate raise strictly more revenue, and so
are strictly better o¤. Since pso ( ) < v type, (v; 0)’s equilibrium payo¤ is still strictly higher
than selling xso ( ) claims of the …rm. Therefore, an equilibrium with x < xso ( ) violates the
Grossman and Perry (1986) re…nement.
Next, note that in equilibrium it must be xi (v; 0) > 0 ) pi (xi (v; 0)) = v. Since xi (v; 0) = 0,
the price function given by (4) is consistent with (3) and is non-increasing. Note that (3) is
incentive compatible given (4). First, the equilibrium payo¤ of type-(v; 0) is v. Since xi > 0 )
pi (xi ) < v, type (v; 0) has no pro…table deviation. Second, since pso ( ) xso ( )
L=n and
pi (xi ) is ‡at on (0; xso ], deviating to (0; xso ] generates revenue strictly lower than L, and so is
suboptimal if
= L. Moreover, since xi > xso ( ) ) pi (xi ) = v, the investor has no optimal
deviation to xi > xso ( ), regardless of …rm value. Last, it is easy to see that xi = xso ( ) is
42
optimal for type-(v; 0). Lemma 3 in Appendix B proves that the equilibrium that is given by
Proposition 1 satis…es the Grossman and Perry (1986) re…nement.
Proof of Proposition 2.
Suppose L=n
v (1
). The investor can raise at least L by
selling only bad …rms, even if she receives the lowest possible price of v. Since the investor is
never forced to sell a good …rm, she sells a positive amount x0i > 0 from a good …rm only if
p (x0i ) = v, i.e. she does not sell x0i from a bad …rm. We …rst argue that, in any equilibrium,
xi > 0 ) p (xi ) < v. Suppose on the contrary there is x0i > 0 s.t. p (x0i ) = v, and let x0i be the
highest quantity with this property. The investor chooses not to sell x0i from a bad …rm only
if there is x00i that she chooses with strictly positive probability, where
x00i pi (x00i ) + (1
x00i ) v
x0i pi (x0i ) + (1
x0i ) v:
(24)
The above inequality requires pi (x00i ) > v. Since she sells x00i from a bad …rm with positive
probability, we have pi (x00i ) < v. Given this price, she will never sell x00i from a good …rm, contradicting pi (x00i ) > v. Therefore, she sells x0i from a bad …rm with strictly positive probability,
which contradicts p (x0i ) = v. We conclude that in any equilibrium xi > 0 ) p (xi ) < v, and so
vi = v ) xi = 0. These conditions also imply xi > 0 ) p (xi ) = v. Note that the condition on
x
e simply requires that in expectation (i.e. when the investor plays mixed strategies) she sells
enough of the bad …rms to meet her liquidity needs, given by the realization of . Last, p (0)
follows from Bayes’rule and the observation that vi = v ) xi = 0. This completes part (i).
Next, suppose v (1
) < L=n. We proceed by proving the following claims.
1. In any equilibrium there is a unique x > 0 s.t. xi (v; L) = xi (v; 0) = x. To prove this,
suppose that in equilibrium, the investor is selling x00i and x0i of a good …rm when
with strictly positive probability. Without loss of generality, suppose
x00i
>
x0i
=L
0. Since
she must be indi¤erent between x00i and x0i ,
x00i p (x00i )
x0i p (x0i ) = v (x00i
x0i ) > 0:
(25)
This condition implies that x00i generates strictly higher revenue than x0i . It also achieves
a higher payo¤:
x00i p (x00i ) + (1
x00i ) v > x0i p (x0i ) + (1
) x00i p (x00i )
43
x0i ) v
x0i p (x0i ) > v (x00i
x0i ) > 0:
Since x0i is played with positive probability, but only when vi = v, then p (x0i ) = v.
Combined with (25), this implies p (x00i ) = v. Recall that pi (xi (v; 0)) = v. Therefore,
the investor cannot sell xi (v; ) of a bad …rm. This in turn implies pi (xi (v; )) = v for
2 f0; Lg, and so her payo¤ from selling a bad …rm is always v in equilibrium. This
creates a contradiction, since when
x00i v + (1
= 0, she can sell x00i > 0 of a bad …rm and obtain
x00i ) v > v. We conclude that, in any equilibrium, there is a unique x such that
the investor sells x of each good …rm when
Since v (1
= L.
) < L=n, it must be x > 0. We denote pi (x) = p. Since the investor sells
x of a good …rm with positive probability, p > v. We argue that, in any equilibrium, if
= 0 then she sells x of every bad …rm. Suppose she sells a di¤erent quantity. Recall
that pi (xi (v; 0)) = v implies that she does not sell xi (v; 0) of a bad …rm in equilibrium.
Since xi (v; 0) 6= x and xi (v; 0) 6= xi (v; 0), we must have pi (xi (v; 0)) = v, which yields a
payo¤ of v. This creates a contradiction since she has strict incentives to deviate and sell
x of a bad …rm, thereby obtaining a payo¤ above v. Note that this implies that p < v.
2. In any equilibrium, either xi (v; L) = x w.p. 1, or xi (v; L) = 1 w.p. 1, where x is de…ned
as in Claim 1. To prove this, note that the investor cannot sell xi (v; 0) of a bad …rm in
equilibrium. Therefore, if xi (v; L) 6= x, then pi (xi (v; L)) = v. Suppose xi (v; L) 6= x and
xi (v; L) < 1. Then, she can always deviate to fully selling a bad …rm, and not selling
some good …rms, to keep revenue constant. Her payo¤ from selling a bad …rm is no lower
(since she previously received v for each bad …rm), but by not selling some good …rms,
for which she previously received xp + (1
x) v < v, she increases her payo¤. Therefore,
xi (v; L) 2 fx; 1g. Suppose the investor chooses xi (v; L) = 1 with probability strictly
between zero and one. Therefore, p (1) = v < p, and the investor chooses xi (v; L) = 1
with strictly positive probability only if xp < min fL=n; xp + (1
) vg. That is, it
must be that by selling x from all …rms, she cannot raise revenue of at least L, and
by selling x of all good …rms and 1 of all bad …rms, she can raise strictly more. This,
however, implies the investor cannot be indi¤erent between 1 and x, thereby proving that
either xi (v; L) = x w.p. 1, or xi (v; L) = 1 w.p. 1, as required.
3. If in equilibrium xi (v; L) = 1 and x < 1 then L=n < v and x = xco ( ), as given by (7).
To prove this, since xi (v; L) = 1 and vi = v ) xi < 1, pi (1) = v. Moreover, given claims
1 and 2, and by Bayes’rule, p is given by pco ( ), as given by (8). Suppose
= L. Since
pco ( ) > v, the investor chooses xi (v; L) = 1 only if the revenue from selling x from all
44
…rms is strictly smaller than L and also the revenue from selling x of all good …rms and
1 from all bad …rms, i.e.
xpco ( ) < min f(1
)v + xpco ( ) ; L=ng , xpco ( ) < min fv; L=ng :
Intuitively, we require xpco ( ) < v, since the investor receives xpco ( ) by partially selling
x of a bad …rm for price pco ( ), and v by fully selling a bad …rm for price v. In equilibrium,
she would only fully sell a bad …rm if doing so raises more revenue.
We now prove that (1
)v + xpco ( ) = L=n, i.e. fully selling bad …rms and selling x
of good …rms raises exactly L. We do so in two steps. We …rst argue that this strategy
cannot raise more than L, i.e.
(1
)v + xpco ( )
(26)
L=n:
Suppose not. Then, the investor has “slack”: she can deviate by selling only x " instead
of x from each good …rm, while still meeting her liquidity need. Since prices are nonincreasing, pi (x
")
pco ( ), and so for small " > 0, she still raises at least L. Her
payo¤ is strictly higher since she sells less from the good …rms. We next argue that this
strategy cannot raise less than L, i.e.
(1
)v + xpco ( )
(27)
L=n:
Suppose not. If the strategy did not raise L, then it must be that v
(1
)v + xpco ( ),
i.e. the alternative strategy of fully selling her entire portfolio raises even less revenue.
Therefore, v
xpco ( ), which contradicts xpco ( ) < v. Intuitively, if fully selling a …rm
for v raises less revenue than selling x of a …rm for pco ( ) ; then the investor would not
pursue the strategy of fully selling bad …rms. Combining (26) and (27) yields
(1
)v + xpco ( ) = L=n
as required, implying x = xco ( ), and xco pco ( ) < v implies L=n < v as required.
4. If in equilibrium xi (v; L) = x then v
1
+1
L=n, p = pso ( ) and x = xso =n. To
prove this, since prices are monotonic, we must have xp
the investor deviates by selling x
L=n. Otherwise, if
= L
" instead of x from a good …rm. For small " > 0,
45
she can raise the same amount of revenue and sell less from the good …rms. Note that
xi (v; L) = x ) p = pso ( ). Suppose on the contrary that such an equilibrium exists and
L=n < v
1
+1
:
We argue that there is an optimal deviation to fully selling all bad …rms, and selling
x0 from good …rms, for some x0 2 (0; x]. Since
L=n
v
<
1
+1
< 1, she can always
raise at least L by selling all …rms. Therefore, it must be xpso ( ) = L=n. Moreover,
pso ( ) > v ) x < 1. Since x is an equilibrium, xp (x) < L=n for any x < x. Let
x0 =
Note that L=n
(1
L=n
(1
)v
pso ( )
) v > 0 implies x0 > 0 and xpso ( ) = L=n < v implies x0 < x. By
deviating to fully selling all bad …rms and selling only x0
x from all good …rms, the
revenue raised is at least L. This deviation generates a higher payo¤ if and only if
x0 pso ( ) + (1
x0 ) v + (1
Using xpso ( ) = L=n, x0 =
v
1
+1
L=n
) v > xpso ( ) + (1
L=n (1 )v
,
pso ( )
and pso ( ) = v +
x) ( v + (1
+1
) v)
, we obtain L=n <
, which implies that this deviation is optimal, a contradiction. We conclude that
v
1
+1
as required. Intuitively, if the shock were smaller, the investor would
retain more of good …rms. For the same reasons as in the benchmark, x = xso =n.
Consider part (ii). We show that if v (1
) < L=n < v then the speci…ed equilibrium
indeed exists. First note that L=n < v ) xco ( ) < 1. Second, note that the prices in (8)
are consistent with the trading strategy given by (7). Moreover, the pricing function in (8)
is non-increasing. Third, we show that given the price function in (8), the investor’s trading
strategy in (7) is indeed optimal. Suppose
= 0. Given (8), the investor’s optimal response is
vi = v ) xi = 0 and vi = v ) xi = xco ( ), as prescribed by (7). Suppose
= L. Given (8),
the investor’s most pro…table deviation involves selling xco from each bad …rm, and the least
amount of a good …rm, such that she raises at least L. However, recall that by the construction
of xco ( ), (1
)v + xco ( ) pco ( ) = L=n. Also note that L=n < v ) xco ( ) pco ( ) < L=n.
Therefore, the most pro…table deviation generates a revenue strictly lower than L, and hence
is suboptimal. This concludes part (ii).
Consider part (iii). We show that if v
1
+1
46
L=n then the speci…ed equilibrium indeed
exists. The proof is as described by Proposition 1, where xso is replaced by xso =n. The only
exception is that we note that as per the proof of Claim 4, the condition v
guarantees that, if
1
+1
L=n
= L, the investor has no pro…table deviation. The proof that the investor
has no pro…table deviation when
= 0 is the same as in the proof of part (ii) above.
Finally, part (iv) follows from claims 1-4.
A.2
Proofs of Section 2
We now move to the proofs of the statements in Section 2. Some of these proofs use auxiliary
Lemma 4 in Appendix B.28
Proof of Lemma 1. For separate ownership, see the proofs of Proposition 4. For common
ownership, recall that in equilibrium,
2 arg max
2[0;1]
( ; ), where
( ; ) is de…ned in
Lemma 4. Since all …rms are ex-ante identical, the investor will necessarily monitor the mass
of n
…rms with the lowest monitoring costs. That is, the investor will monitor …rm i if and
only if e
ci
F
1
( ), as required.
Proof of Proposition 4. We solve for the investor’s monitoring threshold. Note that even
if she chooses
6=
itoring probability
, she still faces the prices in (4), where the market maker anticipates mon. Therefore, as in the proof of Proposition 1, the investor has incentives
to follow the trading strategy in (3). She thus chooses vi = v if and only if
where from Proposition 1,
28
e
ci =n
Vso (v;
8
<v +
Vso (vi ; ) =
:v
)
xso ( )
(pso
n
xso ( )
(v
n
Vso (v;
( )
v)
(28)
);
if vi = v
:
(29)
pso ( )) if vi = v:
In the proof of Lemma 4 and in the proofs below, we seemingly ignore the cost K the investor incurs when
she does not satisfy her shock. This is without loss of generality. The Grossman and Perry (1986) re…nement
ensures that, if in equilibrium v +
L=n (i.e. total portfolio value exceeds L, the region in which our main
results hold), the investor sells exactly enough to satisfy her liquidity needs. Moreover, it also implies that, if in
equilibrium v +
< L=n, the investor sells her entire portfolio if she su¤ers a shock, and fully sells (retains)
the bad (good) …rms if she does not su¤er a shock. In this case, the investor incurs the cost K whenever she
su¤ers a shock. She is unable to avoid this by monitoring more: since her monitoring is unobserved by the
market makers, it does not a¤ect the prices she receives upon selling, and so will not allow her to meet the
liquidity need.
47
This holds if and only if
e
ci =n
v
e
ci =n
e
ci =n
xso ( )
(v pso ( ))
n
xso ( )
1
1
n
+1
voice ( )
xso ( )
(pso ( )
n
v
,
Thus, the cuto¤ in any equilibrium must satisfy c =n =
and hence, cso;voice must solve c =n =
c,
voice
voice
v) ,
voice
( ). In equilibrium,
= F (c ),
(F (c )), as required. Note that as a function of
(F (c )) is strictly positive and bounded from above. Therefore, a strictly positive
solution always exists. If
29
solution is unique.
v (1
0, then
)
voice
(F (c )) is decreasing in c and so the
Note that since Vso (vi ; ) is derived from Proposition 1, the equilibrium
is characterized by Proposition 1, where
is given by
so;voice .
The comparative statics are
proven in Appendix B.
We prove the result in three parts. First, suppose v
Proof of Proposition 5.
L=n.
Based on Proposition 2, the equilibrium must be type-(iii). Based on part (iii) of Lemma 4,
the monitoring threshold must solve c =
voice
(F (0)) =
) and
(1
voice
(1) =
voice
(F (c )). Note that
L=n
minf v+
(1
voice
(F (c)) is continuous,
; 1g), and hence, by the intermediate
value theorem, a solution always exists. Given a threshold that satis…es c =
(F (c )), by
voice
construction there is a type-(iii) equilibrium with this threshold.
Second, suppose L=n
is smaller than
F ( )). Based on Lemma 4, in any equilibrium the threshold
v (1
. Therefore, L=n
), and from Proposition 2, the equilibrium
v (1
must be type-(i). From part (i) of Lemma 4, and since L=n
F
1
1
L=n
v
, we have c =
v (1
F ( )) )
1
. By construction, there is a type-(i) equilibrium with such a
threshold.
Third, suppose v (1
F ( )) < L=n < v. We …rst analyze which equilibria are sustain-
able in this range, and then compare the e¢ ciency of the sustainable equilibria. Starting
with the …rst step, we prove that if v (1
F ( )) < L=n < v, there always exists a type-(ii)
equilibrium where the monitoring threshold is given by part (ii) of Lemma 4, i.e. the largest
solution of c =
voice
(F (c )). In particular, it is su¢ cient to show that c =
has a solution such that F
1
1
L=n
v
< c (which is equivalent to v (1
29
voice
) < L=n). In-
For the comparative statics we restrict attention to stable equilibria, i.e. ones for which n
crosses the 45-degree line from above.
48
(F (c ))
voice
(F (c ))
1
deed, when c = F
1
c =F
L=n
v
1
voice (F (c )) =
h
L=n
v
1
)
then
voice
. Since v (1
(F (c )) =
F ( )) < L=n, then
(F (c )) > F 1 1 L=n
. Furthermore, when F (c ) = 1 then
v
i
< 1, since F (c ) =
= 1. Since voice (F (c )) is continuous
voice
L=n
v+
1
in c , by the intermediate value theorem, a solution strictly greater than F
1
L=n
v
1
always
exists. By construction, there is a type-(ii) equilibrium with such a threshold.
We now move to the e¢ ciency comparison. We …rst show that, for v (1
F ( )) < L=n < v,
any type-(i) equilibrium is less e¢ cient than
Based on Lemma 4, if
n a type-(ii) equilibrium.
o
L=n
the equilibrium is type-(i), then c = min
; F 1 (1
) . However, v (1 F ( )) < L=n
v
1
implies c = F
L=n
)
v
(1
< cii .
Next, consider type-(iii) equilibria. When L=n < v, such equilibria exhibit x p = L=n,
where p = v +
. Therefore, whenever these equilibria exist,
+1
voice
Note that
voice
( )>
2
1
L=n
41
1
+
+
voice
v
1
1
( )
L=n
v (1
v+(
:
))
( ) if and only if
v (1
(1
+
1
1
)
)+
3
+
5 >
+
v
v (1
v+(
1
v+(
L=n
v (1
))
(30)
L=n < v:
))
Also note that
1
1
1
v
v+
Therefore, if
+
+
1
+
v
v (1
v+(
))
,
v
v+
:
, then (30) always holds, which implies that the most e¢ cient equilibrium
is type-(ii). In this case, y = y = v. In other words, whenever a type-(ii) equilibrium exists
(i.e. v (1
F ( )) < L=n < v), it is the most e¢ cient equilibrium.
Suppose
<
v
v+
. Note that (30) is equivalent to
( )=
Note that min
2
h
v
+v
v
+v
( ) < 0. Also, recall v (1
i
1
ii
49
v L=n
v
( ) < 0, where
1
,
v
+v
v
+v
v L=n
v
) < L=n. Therefore, it is su¢ cient to focus
on v (1
^>
v L=n
v
1v
^=
2
v L=n
v
) < L=n ,
such that
0,
( )
v
+v
L=n
v
v L=n
v
< . It can be veri…ed that
< 0. Therefore, there is
^ where ^ is the largest root of
!
1
1v
+
2
v
+v
v
u
L=n u
t
v
v
+v
1
v
+v
( ), given by
!2
+4
1
v
+v
v
+v
v
(31)
Note that a type-(iii) equilibrium requires
1
+1
v
where
v L=n
v
<
1
1+ v
L=n
L=n
< L=n ,
. Also note that
1
1+
< F ( ) in both a type-(ii) and type-(iii) equilib1
rium. Therefore, the relevant range is
<
L=n
v L=n
1+ v
F ( ). This interval is non-empty if
L=n
L=n
and only if
v
1+
Note that v (1
F ( )) <
< L=n ,
F( )
1 F( )
v
1+ 1
L=n 1 F ( )
< :
L=n
F( )
v
for all . Since
F( )
F( )
v
v+
<
if L=n <
v
1+ 1
F( )
v
F ( ) v+
, the most
e¢ cient equilibrium is type-(ii). This establishes the existence of y, the threshold below which
a type-(ii) equilibrium is most e¢ cient.
Suppose
v
If
<
=F(
v
v+
, then
voice
voice
L=n 1 F ( )
<
L=n
F( )
( )), is unique. Therefore, the equilibrium with
(
1
1+
and
<
v
v+
;^
L=n
v L=n
)
1
In Lemma 5 in Appendix B we show that ^
iii
v
v+
1+ v
L=n
L=n
<
iii
v
+v
1
<
iii
50
+
1
iii
given by the solution of
is most e¢ cient if and only if
. Therefore,
v
iii v L=n
+
iii ,
iii :
, i.e.
v
+v
(32)
:
( ) is a decreasing function, and so
max
if ^ <
<
:
iii
is most e¢ cient only
v
:
L=n
Note that limL=n!v
iii
> 0 = limL=n!v ^. By continuity, there is y 2 [y; v) such that, if
L=n > y, the most e¢ cient equilibrium is type-(iii). This completes the proof.
Proof of Corollary 1. Recall from Proposition 5 that
cco;voice =
8
>
>
>
<
if L=n
v (1
F ( ))
(33)
maxfcii ; ciii g if v (1 F ( )) < L=n < v
>
>
>
:c
if v L=n:
iii
It is straightforward to see that
voice
( ) and
voice
( ) are decreasing in L=n. Our focus on
stable equilibria implies that cii and ciii are decreasing in L=n. Therefore, max fcii ; ciii g is
> max fcii ; ciii g
also decreasing in L=n. Finally, note that
globally decreasing in L=n.
ciii . Therefore, cco;voice is
The second statement follows directly from Proposition 5, the observation that cco;voice =
cso;voice when n = 1 and cco;voice = ciii , where cso;voice is the largest solution of c =n =
voice
(F (c )) :
Proof of Proposition 6. Suppose L > 0. Let cso (n; L) be a solution of c = n
that constitutes a stable equilibrium (i.e., n
under separate ownership. Note that n
voice
voice
(F (c ))
(F (c )) crosses the 45 degree line from above)
(F ( )) is strictly increasing in n. Therefore,
cso (n; L) locally increases in n as well. Since for a given c we have limn!1 n
limn!1 cso (n; L) = 1 as well. In addition, cso (1; L) <
that if n > n then the smallest solution of c = n
cco;voice
voice
voice
voice
(F (c )) = 1,
. It follows that there is n > 1 such
(F (c )) is strictly greater than
. Since
, if n > n then any equilibrium under separate ownership is strictly more e¢ cient
than any equilibrium under common ownership. This completes part (i).
Consider part (ii). Since
of c = n
voice
voice
(F (c )) <
, there is n (L) > 1 such that the largest solution
(F (c )), denoted cso (n; L), is strictly smaller than
n (L) satis…es cso (n (L) ; L) =
part (i) shows that c =
Therefore, if L=n
v (1
if n < n (L). Note that
. In any equilibrium under common ownership, Lemma 4
if L=n
v (1
F ( )) then c =
), and Proposition 5 shows that
F ( ).
in any equilibrium under common ownership.
Since an equilibrium under common ownership always exists according to Proposition 5, we
conclude that if n < n (L) and L
v (1
F ( )), any equilibrium under common ownership is
strictly more e¢ cient than any equilibrium under separate ownership. Therefore, there exists
L
v (1
F ( )) as required.
51
Proof of Proposition 7. Given threshold c and number of …rms n, the investor’s net payo¤
under separate and common ownership, respectively, are
Note that
co;voice
so;voice
(n; c) = n (v + F (c) )
F (c) E [ci jci < c]
co;voice
(n; c) = n (v + F (c) )
nF (c) E [ci jci < c] :
(1; c) =
so;voice
have a unique maximum at
(1; c) for any …xed c, that
and n
co;voice
(n; c) and
so;voice
(n; c)
respectively, and that in any equilibrium cso;voice
and
cco;voice < n . Moreover, under the conditions of part (ii) of Proposition 6, cso;voice < cco;voice
under any equilibrium of common and separate ownership.
A.3
Proofs of Section 3
Suppose in equilibrium under ownership structure
Proof of Lemma 2.
the market believes that the manager works w.p.
vi = v his expected utility is R + !P
utility is R + !P
v;
! P
v;
v;
P
2 fso; cog
. From (18), if the manager chooses
e
ci , and if he chooses vi = v his expected
v;
. Therefore, he chooses vi = v if and only if e
ci
.
c
R
R+
Proof of Proposition 8. In equilibrium, the market and the investor believe the manager
follows threshold c . Given (3) and (4), the manager expects the price to be Pso (vi ; F (c )) if
he chooses vi . Therefore, he chooses vi = v if and only if
R + !Pso (v; F (c ))
e
ci
(34)
R + !Pso (v; F (c )) ;
where Pso (vi ; ) is explicitly given in the proof of Proposition 3. In equilibrium, c must solve
(20). Using the explicit formulation of Pso (vi ; ), (20) is equivalent to c =
that
exit
( ) is decreasing in
exit
(F (c )). Note
and is bounded from above and below. Therefore, a solution
always exists and is unique. The equilibrium is characterized by Proposition 1, where
given by
so;exit .
is
The comparative statics are proven in Appendix B.
Proof of Proposition 9. First, suppose v
L=n. Based on Proposition 2, any equilibrium
is type-(iii). Therefore, cco;exit = cso;exit in this range. Similar to the proof of Proposition 2
part (iii) and Proposition 8, such an equilibrium indeed exists.
Second, suppose v 1
ii;exit
< L=n < v. Based on Proposition 2, any equilibrium is
52
either type-(ii) or type-(iii). Consider a type-(ii) equilibrium. The manager has incentives to
choose vi = v if and only if
R + ! [ pco ( ) + (1
Using pco ( ) = v +
solve c =
exit
+(1
)(1
)
) v]
e
ci
R + ! [ v + (1
, we obtain vi = v , e
ci
(35)
) pco ( )] :
). Therefore, c must
exit (
(F (c )). Similar to the proof of Proposition 2 part (ii), if
=
ii;exit
then
indeed an equilibrium with these properties indeed exists. By de…nition of cii;exit , such an
equilibrium is more e¢ cient than any other type-(ii) equilibrium. Moreover, simple algebra
shows that
exit
( )>
exit
( ), and so cii;exit > cso;exit . That is, an equilibrium with
=
ii;exit
is more e¢ cient than any equilibrium with the properties of part (iii). Finally, to show that
an equilibrium with
=
ii;exit
is more e¢ cient than any type-(i) equilibrium, note that based
on part (i) of Proposition 2, the threshold of the alternative equilibrium must satisfy L=n
v (1
). However, since by assumption v 1
ii;exit
< L=n, it follows that
<
ii;exit ,
that is, the alternative equilibrium must be less e¢ cient.
Third, suppose L=n
v 1
ii;exit
. We argue that a type-(i) equilibrium exists. If
true, then this equilibrium is more e¢ cient than any type-(ii) or type-(iii) equilibrium. We
argue that the following strategies are an equilibrium: the manager’s working threshold is
c
= minfR
where
R+
1
L=n
)g,
v
(1
the investor’s trading strategy is
8
>
>
0
>
<
x (vi ; ) = 1 w.p. 1
>
>
>
:1
=
and prices are
!; F
8
>
<0
if vi = v
and 0 otherwise if vi = v and
if vi = v and
if R
1
>
:1
1
L=n
v
!
R R+!
F
1 (1
8
<v +
pi (xi ) =
:v
L=n
v )
F (c
R+
!
F
1
(1
)+(1
F (c )
) (1 F (c
= L;
L=n
)
v
;
otherwise
L=n
v
(36)
=0
))
if xi = 0
(37)
(38)
if xi > 0:
If the above equilibrium indeed exists, note that it is must be the most e¢ cient equilibrium
among all type-(i) equilibria, and hence the most e¢ cient equilibrium. To understand why, …rst
53
note that if c
R + ! then the equilibrium exhibits maximum governance, and hence,
=R
by de…nition, no other equilibrium is strictly more e¢ cient. However if c
v (1
1
=F
(1
F (c )) = L=n. Therefore, any other type-(i) equilibrium must satisfy L=n
and hence,
F (c ), which implies that threshold c
L=n
)
v
then
v (1
),
is more e¢ cient.
We now prove that the above equilibrium indeed exists. First note that the prices in
this equilibrium follow from the investor’s trading strategy and the application of Bayes’rule.
Second, given these prices, the investor’s trading strategy is optimal. Indeed, note that L=n
v (1
F (c )), and so the investor can satisfy her liquidity needs by selling only bad …rms.
Since xi > 0 ) pi = v, the investor has strict incentives to fully retain good …rm, and weak
incentives to sell bad …rms. The manger works if and only if
e
ci
R + !pi (0)
R
R + ! (1
(1
)
) (pi (0)
R + ! [ v + (1
) ( pi (0) + (1
) v)] ,
e
ci
v)
Using the explicit form of pi (0) as given above, the manager works if and only if
R
R + ! (1
(1
)
F (c )
F (c ) + (1
) (1
)
F (c ))
H ( ;c )
where
H ( ; c) = R
is a continuous function of
R+!
required. Second, suppose R
R+
R+
!
1
F
1
!>F
v 1
solution of cii;exit =
F cii;exit . Therefore,
ii;exit
F
1
(1
(1
) cii;exit
L=n
)
v
L=n
)
H 1; F 1 (1
v
L=n
H 1; F 1 (1
)
v
F
+1
F (c)
< F
<
54
1
> 0. There are two
1
L=n
))
v
(1
exit
< F
e
ci
L=n
) then H (0; c ) = R R + ! , as
v
L=n
) and note that H (1; c) < exit (F (c))
v
1
F (1 L=n
), where cii;exit is the largest
v
(1
for all c. Recall, L=n
exit
F (c) 1
1
and c, and it strictly decreases in , when
cases to consider. First, if R
exit
1
1
!
e
ci ,
(1
F
F
1
(1
L=n
):
v
L=n
)
v
)
Also note that
1
H 0; F
(1
L=n
)
v
=R
R+!
>F
1
L=n
):
v
(1
Therefore,
H 1; F
1
L=n
)
v
(1
<F
1
L=n
) < H 0; F
v
(1
1
L=n
) ;
v
(1
and by the intermediate value theorem, there is ^ 2 (0; 1) such that H ^; F
F
1
L=n
).
v
(1
B
H@
1
1
1
implying that
R R+!
1
L=n
)
v
=
!
F
L=n
v
1 (1
;F
L=n
L=n
)
v
1
(1
v
1
L=n C
)A = F
v
1
(1
L=n
);
v
2 (0; 1) as required.
Proof of Proposition 10.
!; F
(1
Since H ( ; c) is decreasing in , ^ is unique. Finally, one can verify that
0
1
1
L=n
v
First, for L=n
v(1
ii;exit ),
cco;exit = minfR
g, which is decreasing in L=n. Note also at L=n = v(1
implies that cco;exit = F
1
1
L=n
v
=F
1
(
ii;exit )
ii;exit ),
R+
this
= cii;exit . Furthermore, cii;exit is constant
in L=n. Altogether, this implies that cco;exit is continuous and weakly decreasing in L=n for
L=n < v. Note that for v
exit (
) >
exit (
L=n, cco;exit = cso;exit , which is constant in L=n. Finally, since
) for all , cco;exit = (F (cco;exit )) >
decreasing in c, it implies that cso;exit such that
exit (F (cco;exit )).
exit (F (cso;exit ))
Since
exit (F (c))
is
= cso;exit is strictly less than
cco;exit . This con…rms that cco;exit is decreasing in L=n, and that cco;exit > cso;exit for v < L=n.
That cco;exit = cso;exit for v
L=n trivially shows that cuto¤ is identical under common and
separate ownership for such values of L=n. This complete the proof.
55