2006・2
Cross Shareholding and Unwinding of Cross Shareholding
under Managerial Entrenchment
Nobuyuki Isagawa

Cross-Shareholding and Unwinding of Cross-Shareholding
Under Managerial Entrenchment

Abstract

This paper examines corporate strategies regarding cross-shareholding and theunwinding of cross-shareholding, and presents a rationale for corporate managers to
unwind cross-shareholding from the perspective of managerial entrenchment. Whilecross-shareholding enhances managerial entrenchment, the increased agency costs
associated with managerial opportunism increase the incentives for a hostile takeover.
In order to avoid a takeover, managers have to unwind cross-shareholdings. The
unwinding of cross-shareholdings implies that managers will relinquish theirentrenchment, and thus will act to increase shareholders’ wealth in the future. The
model proposed here explains why cross-shareholdings among Japanese firms declined
during the 1990s, a decade during which the cost of takeovers decreased due to financial
market deregulation.

JEL Classification: G32, G34

1

Ⅰ. Introduction

Cross-shareholding has long been a prominent feature of Japanese corporate finance,but since the 1990s, cross-shareholdings have been declining among Japanese firms.
Kuroki (2001) reported that the proportion of cross-shareholdings in the overall market
decreased gradually in the 1990s, from about 17% at the end of 1990 to about 10% at
the end of 2000. Ang and Constand (2002) also reported that corporate and financial
institution holdings decreased in Japan during the 1990s.
Given the recent decline in cross-shareholdings, this paper provides a simple modelin which corporate managers dynamically decide to engage in cross-shareholding and,in particular, decide to liquidate cross-shareholdings. Although several studies havefocused on cross-shareholdings among Japanese firms, little attention has been paid to
the theoretical implications of the unwinding of cross-shareholdings. This paper is an
initial attempt to explore the theoretical issues surrounding the unwinding ofcross-shareholding.
In addition, this paper also contributes to the literature on cross-shareholding by
providing an analysis of corporate cross-shareholding strategies from the viewpoint ofmanagerial entrenchment. Such an entrenchment approach has recently been developedin both the empirical and theoretical corporate finance literature.1 The entrenchment
approach appears to be appropriate for analyzing large listing firms in which the
management is separated from the ownership. Most Japanese firms that havecross-shareholdings

share

this

feature.

Previous

studieshave

analyzedcross-shareholding from the viewpoint of maximizing the shareholders’ wealth, which isreferred to as the efficient approach. In the efficient approach, cross-shareholding is

1

For example, see Morck, Shleifer, and Vishny (1988), Berger, Ofek, and Yermack(1997), Zweibel (1996), Isagawa (2002), and Novaes (2003).
2

interpreted as a value-increasing financial device. Along these line, Osano (1996)
theoretically showed that cross-shareholding plays an important role in motivating themanagers of member firms to avoid inefficient myopic behavior. The model of Berglof
and Perotti (1994) demonstrated that cross-shareholding provides a reciprocal
monitoring mechanism among the member firms, and prevents managerial
opportunism.2
However, according to Ito (1992) and Morck and Nakamura (1999), one traditional
motivation for the formation of cross-shareholdings is to prevent hostile takeovers. In
the entrenchment approach, cross-shareholding enhances managerial entrenchment andinsulates corporate managers from market interference in corporate control such as
occurs in hostile takeovers. As a result, member firms attempt to maximize management
and employee utility rather than shareholders’ wealth. In the present model,
cross-shareholding is interpreted to be an entrenchment device allowing self-interested
managers to pursue their own interests. Many empirical studies appear to support the
hypothesis that cross-shareholding may dampen the disciplinary effectiveness of themarkets for corporate control, and is not desirable from the perspective of firm
profitability.3

2

Empirically, Ferris, Kumar, and Sarin (1995) and Douthett and Jung (2001)

demonstrated that the magnitude of the costs attributable to informational asymmetry is
lower for keiretsu firms than for independent firms. Since cross-shareholdings amongkeiretsu firms are tighter than those in independent firms, these results are consistent
with the hypothesis that cross-shareholding is an effective mechanism for corporate
operations.
3

Nakatani (1984), Prowse (1992), Douthett and Jung (2001), and Ang and Constand(2002) have reported that the profitability of firms in a keiretsu group is lower than thatof independent firms. Nakatani (1984) and Ang and Constand (2002) also reported that
3

The present model has several implications regarding cross-shareholding and theunwinding of cross-shareholding among Japanese firms. First, it accounts for why
Japanese firms have unwound cross-shareholdings at a time when the Japanese financial
markets have experienced substantial deregulation, resulting in a decrease in the cost of
corporate control. At first glance, it may appear strange that corporate managers decided
to unwind cross-shareholdings at a time when the costs of corporate control wererelatively low. The model provides a plausible explanation as to why these decisions
were made. Second, the present model suggests that firms tend to unwind
cross-shareholdings when their operating performance is poor. This suggestion isconsistent with the fact that Japanese firms unwound cross-shareholdings when theyexperienced very poor performance during the 1990s. The model also predicts that firm
profitability will improve following the unwinding of cross-shareholdings. Third, themodel presents the possibility that corporate managers prefer cross-shareholding toother anti-takeover devices. The diversification effect, which is a prominent feature ofcross-shareholding, distinguishes cross-shareholding from other takeover defenses, suchas self-shareholding and poison pills.

Ⅱ. An Entrenchment Model

There are two all-equity firms, firm a and firm b. Each firm is run by a single
entrenched manager (the incumbent manager). The number of outstanding shares ofeach firm is normalized to one. Without a loss of generality, it is assumed that neither

independent firms have higher growth rates than keiretsu firms. Nakatani (1984), Brown,
Soybel, and Stickney (1994), along with Gibson (2000), have argued that the averagecompensation for employees of keiretsu firms exceeds that for employees of
independent firms.
4

firm has any initial financial slack. All participants are risk-neutral, and the interest rate
is zero.
The sequence of events and decisions, described in Figure Ⅰ, are as follows. At
date-0, each incumbent manager makes a decision about cross-shareholding. If bothmanagers agree on cross-shareholding, then each firm issues n shares to the other firm.
In the current model, the optimal number of shares issued for cross-shareholding is notconsidered. Instead, as described in Berglof and Perotti (1994) and Osano (1996), it isassumed that each firm holds an n/(1+n)≡α (0<α<1/2) fraction of the other firm’s sharesas a cross-shareholding.
[Figure Ⅰ]

At date-1, it is commonly revealed whether the product market condition for eachfirm is good (state G) or bad (state B). Although this paper formally discusses the casein which each of the two firms face a different state, cases in which both firms
experience the same state would be analyzed similarly. Hereafter, event (B, G) isdefined as the date-1 situation, in which firm a faces state B and firm b faces state G.
Similarly, firm a faces state G and firm b faces state B in event (G, B).
At date-2, each manager chooses the firm’s operating strategy. There are two possible
strategies that the incumbent manager could pursue, strategy M or strategy S. Strategy
M gives the incumbent manager private benefits, but decreases the shareholders’ wealth.
In contrast, strategy S increases the shareholders’ wealth, but gives no private benefits tothe incumbent manager.
At date-3, each firm’s operating return is realized. The operating return depends on
both the state of the firm at date-1 and the strategy undertaken at date-2. Let Xi denotethe operating return conditional on strategy M being undertaken in state i∈{G, B}, andlet Yi denote the operating return conditional on strategy S being undertaken in statei∈{G, B}. Let us define Δi≡Yi-Xi. It is assumed that5

0 < Δ G < Δ B < (2 − α )Δ G .

(1)In assumption (1), Δi>0 (i=G, B) indicates that strategy S generates a larger returnthan strategy M in both states. In this sense, strategy S is more desirable for theshareholders than strategy M, regardless of the state realization. The second inequality,
ΔG<ΔB, indicates that the difference between the return generated by strategy S and thatgenerated by strategy M is larger in state B than in state G. This implies that theshareholders’ loss due to managerial opportunism (agency cost) in state G is less thanthat in state B. Therefore, as long as strategy M is undertaken, state G is desirable for theshareholders. The last inequality is assumed for a technical reason that is mentioned
below.
An incumbent manager acts in her own interest, in conflict with the shareholders’wealth. She derives utility both from being in the managerial position until the final date
(date-3) and completing strategy M. An incumbent manager does not have any utility if
she is replaced in a takeover. For an incumbent manager, to undertake strategy M
without a takeover is the best outcome, and to undertake strategy S without a takeover isthe second best outcome. To be replaced in a takeover is the worst outcome (i.e., theutility of the manager is zero).
The takeover stage occurs every time the firm makes a new decision. As described by
Zweibel (1996), a takeover succeeds if its value is larger than its cost. The value of atakeover is given by the difference between the target firm’s current stock price and theprice conditional upon a takeover being launched.4 The cost of a takeover depends onwhether cross-shareholding exists or not. Cross-shareholding enhances an incumbent
manager’s entrenchment, which presents additional costs in the event of a takeover. A

4Since a potential raider can collect one share at the most under conditions ofcross-shareholding (the remaining n shares are held by the other firm), the value of atakeover is calculated for one share (stock price).
6

well-known interpretation of cross-shareholding is that a hostile takeover tends to be
more problematic and/or expensive when the target firm engages in cross-shareholding,because the shares in cross-shareholdings are rarely transacted.5 Formally, the cost of atakeover is E if the target firm’s shares are held by another firm; otherwise the cost is
zero. Cross-shareholding increases the cost of a takeover by E.
If a takeover succeeds, then a new manager replaces the incumbent manager. A new
manager acts in the interest of the shareholders and always undertakes strategy S at
date-2. If a new manager is employed after strategy M has already been undertaken,
then she can change the firm’s strategy to strategy S from strategy M. In such a situation,
however, the firm has to bear additional costs to change the operating strategy becauseof the difficulty of reversing the investment. Alternatively, the firm loses the opportunity
to earn money during the period in which the strategy is switched.
Formally, a switching cost, Z>0, is required to change the firm’s operation to strategy
S from strategy M. Since the switching cost decreases the value of the firm, the date-2
value of a takeover decreases, too. In the sense that the incumbent manager can make atakeover less valuable (more difficult) by investing in strategy M, the managerial
investment decision is in itself an entrenchment device, as pointed out by Shleifer and
Vishny (1989) and Noe and Rebello (1997).
It should be noted that, at the date-1 takeover stage, it is possible that a takeover will
succeed for one firm j, but not for the other firm k (j≠k). In this case, a new manager is

5

Ito (1992) and Morck and Nakamura (1999) mentioned that one traditional motivation

for the formation of cross-shareholdings is to prevent hostile takeovers. Theoretically,
Stulz (1988) has shown that an increase in the fraction of shares controlled bymanagement decreases the probability that a hostile takeover will occur. In the current
model, it is assumed that the incumbent manager can (indirectly) control a fraction ofher firm’s shares by maintaining the cross-shareholding.
7

hired for firm j, and acts in order to maximize the shareholders’ wealth. The new
manager can reconsider the cross-shareholding between date-1 and date-2 (See FigureⅠ). If the new manager of firm j decides to liquidate the firm k shares, then an
additional takeover stage will occur for firm k before date-2. The liquidation ofcross-shareholding may change the value of a takeover of firm k.

Ⅲ. Cross-Shareholding and the Unwinding of Cross-ShareholdingThis

section

shows

that

corporate

managers

dynamicallychangefirms’

cross-shareholding strategies in response to the product market conditions. It is assumed
that
ΔG < E < Δ B .

(2)

If the cost of a takeover is too large, that is if ΔB<E is satisfied, then the market forcorporate control does not work well under conditions of cross-shareholding. In suchsituations, the incumbent manager will always maintain cross-shareholding andundertake strategy M. Conversely, if the cost of a takeover is too small, that is if E<ΔG issatisfied, then the cross-shareholding will not play an entrenchment role to prevent
pressures from the market for corporate control. In such situations, the incumbent
manager has no incentive to possess cross-shareholding, and will always undertake
strategy S.
For the switching cost of Z, it is assumed thatΔ B − E < Z < (1 − α )Δ G .

(3)

It follows from the third inequality of assumption (1) that ΔB-E<(1-α)ΔG holds for E
satisfying (2). The first inequality in (3), which is equivalent to ΔB<E+Z, means that atakeover will not succeed at date-2 under conditions of cross-shareholding once strategy

8M has been undertaken. The second inequality means that a takeover will succeed at
date-2 without cross-shareholding, even though strategy M has been undertaken.
For the following analysis, it is useful to show how to calculate the stock price of a
firm under conditions of cross-shareholding. Let Fj denote the expected operating returnof firm j∈{a, b}, and let Pj denote the stock price of firm j∈{a, b}. Since firm a has nshares of firm b under conditions of cross-shareholding, the total value of the assets
owned by firm a is Fa+nPb. Since firm a issues 1+n shares,
P a = ( F a + nP b ) /(1 + n) .

(4)

Similarly,
P b = ( F b + nP a ) /(1 + n) .

(5)

By solving (4) and (5) and using n/(1+n)≡α, the stock price of firm j undercross-shareholding is given by
P j = ( F j + α F k ) /(1 + α ) , j , k ∈ {a, b}, j ≠ k .

(6)Note that equations (4) and (5) are satisfied when both of the two firms decide toliquidate the cross-shareholding. The stock price of firm j∈{a, b} just after theunwinding of cross-shareholding is given by equation (6).

Managerial Investment Decision
Suppose that firm a faces state B and firm b faces state G, that is, event (B, G) occurs
at date-1. The results in event (G, B) are symmetric. First, consider what takes place at
date-2 under conditions of cross-shareholding. Let P2a(M, M; h) denote the date-2 stock
price of firm a when cross-shareholding exists and when strategy M is undertaken byboth firms. It follows from (6) that9

P2 a ( M , M ; h) =X B +α XG
.
1+ α

(7)

Note that the date-2 value of a takeover for firm a is maximized when both firms
change their operating strategies from strategy M to strategy S. Let P2a(S, S) denote thedate-2 stock price of firm a, provided that both firms decided to change their strategies.
It follows from (4), (5), and (6) that, regardless of whether cross-shareholding ismaintained or not,P2 ( S , S ) =a

YB + αYG
−Z.
1+α

(8)

The date-2 takeover value for firm a in the above case is denoted by V2a(M, M; h).
Then, the following relation is obtained.
V2 a ( M , M ; h) ≤ P2 a ( S , S ) − P2 a ( M , M ; h) =Δ B + αΔ G
− Z < ΔB − Z .
1+ α

(9)

The last inequality follows from assumption (1). Since ΔB-Z<E holds under assumption(3), no takeover succeeds for firm a. By using a similar argument, it can be shown that atakeover will not succeed for firm b at date-2. These results show that under conditionsof cross-shareholding both incumbent managers undertake strategy M at date-2.
Next, consider the managers’ investment decision without the entrenchment ofcross-shareholding at date-2. Suppose that the manager of firm b undertakes strategy M.
Note that each firm has already sold the other firm’s shares. Let P2b(M; u) denote thedate-2 stock price of firm b provided that strategy M is undertaken withoutcross-shareholding, and let P1 denote the selling price of the firm a shares. Then,P2b ( M ; u ) =X G + nP1
.
1+ n

(10)

On the other hand, the date-2 stock price, provided that the firm’s operating strategy
would be changed to strategy S, denoted by P2b(S; u), is given by

10

P2b ( S ; u ) =YG + nP1
−Z .
1+ n

(11)

Note that the switching cost Z is required in this equation. The date-2 takeover value forfirm b in the above case is denoted by V2b(M, u). Then, the following relation is
obtained:V2b ( M ; u ) = P2b ( S ; u ) − P2b ( M ; u ) =ΔG− Z = (1 − α )Δ G − Z > 0 .
1+ n

(12)

The last inequality follows from (3). Since the cost of a takeover is zero withoutcross-shareholding, the manager of firm b is replaced by the date-2 takeover if sheundertakes strategy M without cross-shareholding. By using a similar argument, it canbe shown that a takeover will succeed for firm a without cross-shareholding at date-2.
Predicting this result, the incumbent manager never undertakes strategy M oncecross-shareholding is unwound.

Takeover Strategies of the Market for Corporate Control
This subsection analyzes what takes place at the date-1 takeover stage underconditions of cross-shareholding. Since each of the two firms faces a different state, it ispossible that a takeover succeeds for one firm but does not succeed for the other firm.
The following Lemma shows that both firms undertake strategy S in such situations.

Lemma 1. Both firms will undertake strategy S if a takeover succeeds for either firm at

date-1.

Proof. See Appendix.

In the following analysis, it is assumed that there are two potential raiders. One raider

11

(hereafter raider a) watches for an opportunity to execute of a takeover of firm a, andthe other raider (raider b) watches for the same opportunity for firm b. Each raider
makes the takeover decision independently. Lemma 2 below characterizes theequilibriumoutcomesofthedate-1

takeover

stage

under

conditionsofcross-shareholding, which is dependent on the magnitude of the cost of a takeover, E.
Let us defineδ=

Δ B + αΔ G
.
1+ α

(13)

Lemma 2. Suppose that event (B, G) is realized, and cross-shareholding is maintainedat date-1. When δ<E<ΔB is satisfied, no takeover occurs. When (ΔG+αΔB)/(1+α)<E<δ
is satisfied, a takeover occurs for only firm a. When ΔG<E<(ΔG+αΔB)/(1+α) is satisfied,a takeover occurs for both firms.

Proof. See Appendix.

Lemma 2 says that when the cost of a takeover is relatively large (δ<E<ΔB), no
takeover occurs under conditions of cross-shareholding. In this case, neither of the two
managers ever sells the other firm’s shares in order to maintain the cross-shareholding.
On the other hand, when the cost of a takeover is relatively small (ΔG<E<δ), at least
one manager will be replaced by the date-1 takeover if cross-shareholding is maintained.
This would be the worst possible outcome for the incumbent manager of the target firm.

Managerial Strategies regarding Cross-Shareholding
In order to avoid a takeover, an incumbent manager of the target firm has to commit
to undertaking strategy S by unwinding the cross-shareholding and relinquishing her

12entrenchment. The results given in the previous subsection show that the unwinding ofcross-shareholding is a credible signal that both firms will choose strategy S. Predictingthat strategy S will be undertaken, there is no reason for raiders to launch a takeover at
date-1. Thus, the targeted manager can avoid a hostile takeover by dissolving
cross-shareholding.
To dissolve cross-shareholding, the targeted manager has to make the other manager
liquidate her cross-held shares. As shown in the next Lemma, the targeted manager canunwind cross-shareholding by selling her own shares of the other firm on the market.
More precisely, the decision of one manager to sell the other firm’s shares makes it
optimal for the other manager to do the same.

Lemma 3. When ΔG<E<δ is satisfied, the manager can unwind the cross-shareholding

by selling the other firm’s shares on the market.

Proof. See Appendix.

When ΔG<E<δ is satisfied, the target manager wants to liquidate thecross-shareholding. Lemma 3 says that, in such situations, cross-shareholding is
unwound as a result of individual rationality.
When δ<E<ΔB is satisfied, no takeover occurs under conditions of cross-shareholding.
It is optimal for both incumbent managers to maintain cross-shareholding and toundertake strategy M at date-2. These results are summarized in the following
Proposition.

Proposition 1. Suppose that event (B, G) is realized. When δ<E<ΔB is satisfied,cross-shareholding is maintained, and both firms undertake strategy M. When ΔG<E<δ
is satisfied, cross-shareholding is unwound, and both firms undertake strategy S.

13

In event (G, G), in which both firms experience the good condition at the same time,
it follows from (6) that the takeover value is given by ΔG. Since the takeover value issmaller than its cost, E (at date-1) and E+Z (at date-2), no takeover occurs underconditions of cross-shareholding. Then, both incumbent managers maintaincross-shareholding and undertake strategy M.
When event (B, B) occurs, cross-shareholding is unwound at date-1. The following
scenario is likely. Suppose that cross-shareholding is maintained and strategy M has
been undertaken at date-2. It follows from (6) that the date-2 value of a takeover isgiven by ΔB, which is smaller than its cost, E+Z. Then, the incumbent manager will
undertake strategy M without fear of being replaced.
In contrast to event (G, G), however, the incumbent manager is replaced by the date-1
takeover under the conditions of cross-shareholding, because the value of a takeover, ΔB,
is larger than its cost, E, at date-1. In order to avoid a takeover, the incumbent manager
decides to unwind the cross-shareholding. The unwinding of cross-shareholding is acredible signal that the manager will choose strategy S.

Formation of Cross-Shareholding
Given the above results, this subsection shows that the two firms agree on
cross-shareholding at date-0. Suppose that event (G, G) occurs with probability θGG,
event (B, B) occurs with probability θBB, event (G, B) occurs with probability θGB, andevent (B, G) occurs with probability θBG.

Proposition 2. Both incumbent managers agree on cross-shareholding at date-0.

Proof. See Appendix.

14

Under the current setting, two firms possess cross-shareholdings at the beginning of
the process. In response to the external conditions, they decide whether to maintain the
cross-shareholding or to unwind the cross-shareholding. Although cross-shareholding
and the unwinding of cross-shareholding can both help prevent a hostile takeover, themechanisms by which they accomplish this are different. On the one hand,cross-shareholding helps prevent a takeover by increasing the cost of the takeover. On
the other hand, the unwinding of cross-shareholding helps prevent a takeover bydecreasing the value of the takeover.

Ⅳ. Implications

Costs of Corporate Control and the Unwinding of Cross-Shareholding
Cross-shareholdings among Japanese firms declined during the 1990s. During thesame period, Japanese financial markets experienced substantial deregulation, resulting
in a decrease in the cost of corporate control. Among the series of deregulations thattook place, the one that most affected the potential of corporate control was probably
the liberalization of commissions on stock transactions. In 1994, commissions on stocktransactions over 1 billion yen were freed, and in 1998, those on transactions over 50
million yen were freed. In 1999, fixed brokerage commissions were freed on stocktransactions of all amounts. The liberalization of commissions on equity transactions
directly lowered the cost of takeovers. In addition, many other restrictions on thefinancial markets were removed during the Japanese “Big Bang”. According to anargument presented by Gibson (2000, p.309), Big Bang deregulation could push theJapanese financial system in the right direction by focusing on strengthening corporate
governance. Thus, in the 1990s, it was becoming easier for outside shareholders to exert
corporate control through financial markets.
At first glance, it may appear strange that corporate managers decided to unwind
15

cross-shareholdings at a time when the costs of corporate control were relatively low.
The current model provides a plausible explanation as to why these decisions were
made. That is, entrenched managers have no choice but to unwind cross-shareholdings(i.e., relinquish their entrenchment) in order to keep their positions when the cost of atakeover is smaller than the value of a takeover. As shown in Section Ⅲ, the unwindingof cross-shareholding is a commitment by managers that they will not pursue their own
interests at the expense of the shareholders’ wealth. This commitment decreases thevalue of a takeover, so that no takeover occurs and managers can retain their positions.
Thus, the present model suggests that the lower the cost of a takeover, the more
frequently cross-shareholdings are unwound.
To represent this point formally, let us introduce the cost of a takeover withoutcross-shareholding, represented by C.6 First, suppose that both 0<C<ΔG and ΔB<C+E
are satisfied. Since the cost of the takeover, C+E, is larger than the maximum value ofthe takeover, ΔB, no takeover occurs under conditions of cross-shareholding.7 In suchsituations, both incumbent managers always maintain cross-shareholding, and choose
strategy M at date-2.
Next, suppose that the deregulation of financial markets decreases C to the extent that

δ<C+E<ΔB is satisfied. The results in Section Ⅲ show that, under such parameters,
cross-shareholding is unwound in event (B, B). Furthermore, if C decreases to a levelsuch that ΔG<C+E<δ is satisfied, then cross-shareholding is unwound in three events (G,B), (B, G), and (B, B). As the cost of a takeover decreases, cross-shareholding is likely
to be gradually unwound. This scenario seems to be consistent with the fact thatcross-shareholdings among Japanese firms have declined at a time when the
deregulation of financial markets has been promoted.

6

In the previous analysis, it is implicitly assumed that C=0.

7

The value of a takeover is maximized in event (B, B).
16

Firm Characteristics and the Unwinding of Cross-Shareholding
In the present model, cross-shareholding is likely to be unwound by a firm facing
state B, in which the agency costs of managerial opportunism are relatively large. If allother things are equal, the profitability of a firm decreases as the agency costs increase.
Thus, the model implies that a firm with low profitability will tend to have a stronger
incentive to unwind cross-shareholding than a firm with high profitability. Japanesefirms experienced a sharp decline in their profitability during the 1990s. It can beargued that, in addition to the decrease in the cost of takeovers, low profitability forced
Japanese firms to unwind cross-shareholdings during this period.
Regarding the relationship between managerial entrenchment and the unwinding ofcross-shareholding, Proposition 1 implied that managers with low E tend to unwind
cross-shareholdings more often than managers with high E. Berger, Ofek, and Yermack(1997) suggest several characteristics of managerial entrenchment, including the lengthof a manager’s career in the firm, managerial ownership, board composition, and so on.
The current model then predicts that cross-shareholding will tend to be unwound by amanager who has a short career in the firm and who owns a small fraction of the firm’sshares. Nissan Motors’ Revival Plan is a good example of this scenario. The current
CEO, Carlos Ghosn, decided to dissolve the traditional keiretsu and sell the shares ofkeiretsu firms just after joining Nissan as CEO. Cross-shareholding will also tend to be
unwound by a firm that has a relatively large number of outside directors.
The present model also suggests that firm profitability will improve following theunwinding of cross-shareholding. The unwinding of cross-shareholding is a signal thatthe manager relinquishes her entrenchment and will act in support of the shareholders’wealth in the future.

Cross-Shareholding as an Anti-Takeover Device
17This subsection compares cross-shareholding and self-shareholding in terms of theireffectiveness as an anti-takeover device. Suppose that the incumbent manager of firm a
can use self-shareholding as an anti-takeover device by holding an α fraction of her own
firm’s shares. By using an argument similar to that used in Section Ⅲ, it can be shownthat the manager maintains self-shareholding in state G, but relinquishes it in state B.
Therefore, if the manager of firm a chooses self-shareholding, then she can achieve herbest outcome, undertaking strategy M without a takeover, with a probability of θGG+θGB.
On the other hand, if the manager chooses cross-shareholding, then she can achieve thebest outcome with a probability of θGG+θGB+θBG when δ<E<ΔB is satisfied, and with aprobability of θGG when ΔG<E<δ is satisfied. Cross-shareholding is a betteranti-takeover device in the case of δ<E<ΔB, and self-shareholding is a better one in thecase of ΔG<E<δ.
In order to examine why cross-shareholding is a better anti-takeover device thanself-shareholding in the case of δ<E<ΔB, suppose that event (B, G) is realized at date-1.
While the manager of firm a must give up self-shareholding to commit to undertaking
strategy S, she can undertake strategy M under conditions of cross-shareholding. This isbecause the value of the date-1 takeover under conditions of cross-shareholding,(ΔB+αΔG)/(1+α), is smaller than that under self-shareholding, ΔB. In other words, thestock price under cross-shareholding is larger than that under self-shareholding. The
manager of firm a can avoid an extreme stock price decline by investing in the shares offirm b.
This effect can be interpreted as the diversification effect, which is a prominent
featureofcross-shareholding.

8The

diversification

effectdistinguishes

cross-shareholding from other takeover defenses, such as those of self-shareholding and

8

Nakatani (1984) and Douthett and Jung (2001) have found that keiretsu firms perform

in a more stable manner than independent firms.
18poison pills. It is reasonable to assume that the lower the correlation between theoperating performances of the two firms, the larger the diversification effect will be.
The above argument suggests that cross-shareholding is a desirable anti-takeover device
in situations in which the diversification effect works well.

Ⅴ. Conclusion

This paper proposes a motivation for corporate management to possesscross-shareholdings and, in particular, to unwind cross-shareholdings. Whilecross-shareholding enhances managerial entrenchment and insulates corporate
management from the potential threat of a takeover, the increased agency costs
associated with managerial entrenchment increase the incentives for a hostile takeover.
In particular, when the cost of a takeover is relatively small compared to its value,
maintaining cross-shareholdings leads to managerial opportunistic behavior, and ahostile takeover can then occur. In order to avoid a takeover, corporate management
must commit to not behaving opportunistically by unwinding cross-shareholdings.
Since the unwinding of cross-shareholdings is a credible signal that management will
pursue shareholders’ wealth in the future, the stock price of a firm will increase, and atakeover will not occur.
The present model has several implications. First, it accounts for why Japanese firms
have unwound cross-shareholdings at a time when the Japanese financial markets haveexperienced substantial deregulation, which resulted in a decrease in the cost of
corporate control. Second, the model predicts that firms tend to unwind
cross-shareholdings when they experience poor performance, and that firm profitability
will improve following this unwinding. The current model also predicts thatcross-shareholdings will tend to be unwound by a manager who has a short career and asmall fraction of the firm’s equity. Third, the model gives insights into what conditions

19

must exist for entrenched managers to choose cross-shareholdings over otheranti-takeover devices. The diversification effect, which is a prominent feature ofcross-shareholding, is an important factor in this choice.
[2006.2.9

742]

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Keiretsu, Journal of Financial Economics 36, 259-284.

Brown, P., V. Soybel, and C. Stickney, 1994, Comparing U.S. and Japanese Corporate
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Douthett, E.，and K. Jung, 2001, Japanese Corporate Groupings (Keiretsu) and theInformativeness of Earnings, Journal of International Financial Management andAccounting 12, 133-159.

Ferris, S., R. Kumar, and A. Sarin, 1995, The Role of Corporate Groupings inControlling Agency Conflicts: The Case of Keiretsu, Pacific-Basin Finance Journal 3,
319-335.

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Gibson, M., 2000, Big Bang Deregulation and Japanese Corporate Governance: A
Survey of the Issues, in T. Hoshi and H. Patrick ed., Crisis and Change in the Japanese
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Ito, T., 1992, The Japanese Economy, MIT Press.

Kuroki, F., 2001, The Present Status of Unwinding of Cross-shareholding: The Fiscal
2000 Survey of Cross-shareholding, NLI Research Paper No. 157, NLI ResearchInstitute.

Morck, R., and M. Nakamura, 1999, Banks and Corporate Control in Japan, Journal of
Finance 54, 319-339.

Morck, R., A. Shleifer, and R. Vishny, 1988, Management Ownership and Market
Valuation: An Empirical Analysis, Journal of Financial Economics 20, 293-315.

Nakatani, I., 1984, The Economic Role of Financial Corporate Grouping, in M. Aoki ed.,Economic Analysis of the Japanese Firm, Elsevier, New York.

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21Osano, H., 1996, Intercorporate Shareholdings and Corporate Control in the JapaneseFirm, Journal of Banking and Finance 20, 1047-1068.

Prowse, S., 1992, The Structure of Corporate Ownership in Japan, Journal of Finance
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Shleifer, A., and R. Vishny, 1989, Management Entrenchment, The Case ofManager-Specific Investment, Journal of Financial Economics 25, 123-139.

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22

Appendix

Proof of Lemma 1. Consider what takes place if the incumbent manager of firm a isreplaced in a takeover, but the manager of firm b is still in control after date-1. From theresults given in the previous subsection, the manager of firm b will undertake strategy
M if her entrenchment is maintained. In order to increase the shareholders’ wealth, the
new manager of firm a will sell the firm b shares between date-1 and date-2. As a result,the manager of firm b has no entrenchment, so that she cannot but undertake strategy S
at date-2. By using a similar argument, it can be concluded that if one of the two
managers is replaced, then both firms will undertake strategy S at date-2.

Proof of Lemma 2. As shown by Lemma 1, if either manager is replaced, then both

firms will undertake strategy S at date-2. In such cases, the stock price of firm a justfollowing a takeover is given by Pa=(YB+nPb)/(1+n), and that of firm b is given by
Pb=(YG+nPa)/(1+n). By solving these equations, the stock price of firm a is
(YB+αYG)/(1+α) and that of firm b is (YG+αYB)/(1+α). If both of the managers are
replaced in takeovers at date-1, then both firms will undertake strategy S. It can beshown easily that, in this case, the stock price of firm a is (YB+αYG)/(1+α), and that offirm b is (YG+αYB)/(1+α).
If no takeover occurs at date-1, then both incumbent managers undertake strategy M
under conditions of cross-shareholding. In this case, it follows from (6) that the stock
price of firm a is (XB+αXG)/(1+α), and that of firm b is (XG+αXB)/(1+α). Therefore, thetakeover value for firm a is given by (ΔB+αΔG)/(1+α), and that for firm b is given by(ΔG+αΔB)/(1+α).
Figure Ⅱ presents a date-1 payoff matrix of the two raiders under conditions of23

cross-shareholding. The first term in each cell represents a payoff of raider a, and thesecond term is a payoff of raider b. It is assumed that the raider obtains the net value ofthe takeover (the takeover value minus its cost) if he launches a takeover; otherwise heobtains zero. By using Figure Ⅱ, the date-1 takeover strategies are analyzed.

[Figure Ⅱ](ⅰ). When δ<E<ΔB is satisfied, the cost of a takeover is always larger than its value.

In this case, no takeover will occur at date-1 under conditions of cross-shareholding.
Both incumbent managers maintain cross-shareholdings and undertake strategy M at
date-2.
(ⅱ). When (ΔG+αΔB)/(1+α)<E<δ is satisfied, the takeover value for firm a is larger

than its cost, but the takeover value for firm b is smaller than its cost. In this case, atakeover will occur for firm a.
(ⅲ). When ΔG<E<(ΔG+αΔB)/(1+α) is satisfied, a takeover is successful for both
firms. Each of the two raiders launches a takeover simultaneously.

Proof of Lemma 3. Suppose that the manager of firm a wants to dissolve thecross-shareholding with firm b. Consider what happens if the manager of firm b
continues to hold firm a shares, when the manager of firm a liquidates firm b shares. In
this case, the entrenchment of the manager of firm b is lost, so that firm b will always
undertake strategy S. On the other hand, the entrenchment of the manager of firm aremains, so that firm a will undertake strategy M if no takeover occurs. If a takeover offirm a occurs, then the new manager of firm a will undertake strategy S. If a takeover offirm b occurs, then the new manager of firm b will liquidate the firm a shares before
date-2. As a result, firm a will undertake strategy S because the manager of firm a loses
her entrenchment. Thus, the managerial opportunism of firm a can be disciplined by a24

takeover of firm b as well as a takeover of firm a.
It follows from the above arguments that the stock price of firm a conditional on atakeover being launched for at least one firm, Pa(t), is given by {YB+nP0}/(1+n), where
P0 represents the selling price of firm b shares. On the other hand, the current stock
price of firm a without a takeover, Pa(n), is given by {XB+nP0}/(1+n). The takeovervalue for firm a is then given by Pa(t)-Pa(n)=ΔB/(1+n)=(1-α)ΔB, and the takeover cost is
E as long as firm b keeps its firm a shares.
Since firm b always undertakes strategy S, the stock price of firm b conditional on atakeover being launched for either firm, Pb(t), is given by {YG+nPa(t)}/(1+n), and thatwithout a takeover, Pb(n), is given by {YG+nPa(n)}/(1+n). The value of a takeover forfirm b is then given by n{Pa(t)-Pa(n)}/(1+n)=α(1-α)ΔB. Note that the takeover value forfirm b is dependent on the managerial opportunism of firm a. The cost of a takeover iszero for firm b, because firm a has already sold its form b shares.

[Figure Ⅲ]

Figure Ⅲ presents a payoff matrix of the two raiders in the above case. The firstterm in each cell represents a payoff of raider a, and the second term is a payoff ofraider b. It follows from Figure Ⅲ that to launch a takeover is a dominant strategy forraider b. That is, the incumbent manager of firm b is replaced in a takeover as long as
she keeps her firm a shares. In order to avoid a takeover, the manager of firm b
rationally decides to liquidate her shareholding of firm a. As a result, thecross-shareholding is completely unwound.
By using similar arguments, it can be shown that the manager of firm b can liquidate
cross-shareholding with firm a by selling firm a shares on the market.

25

Proof of Proposition 2. Let V0j denote the date-0 value of a takeover of firm j∈{a, b}.

When ΔG<E<δ is satisfied, both incumbent managers undertake strategy M in event (G,G), and strategy S in the other three events. The date-0 takeover increases the firm’svalue only when event (G, G) occurs. Then the date-0 takeover value for firm j is given
by θGGΔG. Since 0<V0j=θGGΔG<E holds underΔG<E<δ, a takeover cannot succeed undercross-shareholding. On the other hand, without cross-shareholding, a takeover can
succeed because its cost is zero. Therefore, both managers must agree on
cross-shareholding in order to avoid a takeover at date-0.
When δ<E<ΔB is satisfied, both incumbent managers undertake strategy S in event (B,B) and strategy M in the other three events. Then, for firm a,
V0 a = θGG Δ G + θ BG

Δ B + αΔ G
Δ + αΔ B+ θGB G< (1 − θ BB )δ < E .
1+ α
1+ α

(14)

Similarly, 0<V0b<E holds for firm b. For reasons similar to those given for the above
case, both managers agree on cross-shareholding at date-0.

26

date-0date-1date-2state realization

date-3return realization

shareholding

shareholding

decision about strategy

takeover stage

takeover stage

takeover stage

new manager’s decision (if replaced)takeover stage

FigureⅠ. Sequence of Events and Decisions

27

Raider b (state G)
TakeoverTakeover(ΔB+αΔG)/(1+α)－E =δ－E

(ΔB+αΔG)/(1+α)－E =δ－E

(ΔG+αΔB)/(1+α)－E

Raider a (state B)
No Takeover

No takeover000(ΔG+αΔB)/(1+α)－E

0FigureⅡ. Raiders’ Payoff Matrix at Date-1 under Cross-shareholding

Raider b (state G)
TakeoverTakeover(1-α)ΔB－E(1-α)ΔB－E

α (1-α)ΔB

Raider a (state B)
No Takeover

No takeover000α (1-α)ΔB

0FigureⅢ. Raiders’ Payoff Matrix at Date-1 Takeover Stage
when Firm a Sold Firm b Shares but Firm b Holds Firm a Shares28