2002. 33

Mutual Shareholding and Unwinding of Mutual Shareholding

as Stockpile for Business Recovery
Nobuyuki Isagawa

Mutual Shareholding and Unwinding of Mutual Shareholding
as Stockpile for Business Recovery

Nobuyuki Isagawa
Kobe University

Abstract
Mutual Shareholding has long been a prominent future of Japanese corporate finance.
Since the 1990s, many Japanese firms have been unwinding mutual shareholdings
during the restructuring process. This paper provides a simple model in which firms
decide to practice mutual shareholding in consideration of the possibility that in the
future, they will unwind mutual shareholding. Mutual shareholding is a means of fundstockpiling in the sense that firms agree on the unwinding of mutual shareholding when
they need to raise additional funds for recovering business. In particular, mutualshareholding is an effective means of a stockpile for business recovery in the case offirms whose returns have low correlations. The present model provides several
implications with regard to mutual shareholding and the unwinding of mutualshareholding. First, the diversification effect of mutual shareholding works well, even ina risk-neutral economy. Second, when one firm is forced to unwind mutual shareholding
but the other firm does not, the unwinding of mutual shareholding is agreed upon,
because the value of the latter firm increases as the result of the recovering of theformer firm. Third, since the unwinding of mutual shareholding implies that somemember firms are forced to recover their business, the stock prices of the member firms
decrease in response to the unwinding of mutual shareholding. Nonetheless, theunwinding of mutual shareholding and business recovering remain desirable forlong-term shareholders of member firms.

1

1. Introduction

One of the most prominent features of Japanese corporate finance is the mutualshareholdings among large listed companies. Kuroki (2001) reports that mutualshareholdings observed among listed companies were about 17% of the total market
capitalization at the end of the fiscal year 1990. Several studies have focused on
explanations for why corporations choose to have mutual shareholdings. Traditionally, it
has been commonly accepted that mutual shareholdings insulate corporate managers
from interference by outside shareholders, in cases such as hostile takeovers [Sheard(1994) and Corbett (1994)]. In addition, it has been pointed out that mutualshareholdings are of benefit for risk sharing or diversification [Nakatani (1984) and
Sheard (1989)]. Berglof and Perotti (1994) have shown that mutual shareholding is aneffective mechanism of mutual control among member companies. Moreover, Osano(1996) has shown that mutual commitment caused by mutual shareholdings plays animportant role in avoiding corporate managers’ inefficient myopic investments.
During the 1990s mutual shareholdings among Japanese companies have steadily
declined. Kuroki (2001) reported that the proportion of mutual shareholdings in theoverall market declined to about 10% at the end of the fiscal year 2000. Ang andConstand (2002) also reported that the proportion of shares held by corporations andfinancial institutions tended to decrease during the 1990s in Japan. In contrast to thelarge amount of attention paid to the rationale of mutual shareholding, there has been
relatively little focus on the unwinding of mutual shareholding. Given the recent decline
in mutual shareholdings, a model of mutual shareholding in which mutual shareholdings
are rationally unwound may provide further insight into the motivations for mutualshareholding. This paper is an initial effort in this regard.
In this paper, a fund stockpiling motivation of mutual shareholding is proposed, such2

that firms have mutual shareholdings as well as unwind mutual shareholdings.
Strategies for the fund stockpiling of two firms are considered. Each of the two firms
stockpiles funds by choosing one of two optional financial strategies, namely,
cash-holding and mutual shareholding. If each of the two firms chooses cash-holding,then the firm issues a certain number of shares on the market and can thereby hold cash
until the firm needs to invest it. If both firms choose mutual shareholding, then eachfirm issues a certain number of shares to the other firm and retains mutual shareholding
until either firm needs additional funds.1
In the present model, it is assumed that the firms are required to invest additional
funds for recovering business, or for restructuring under unfavorable conditions thatcreate problems for the business. It is known to be difficult for firms facing businesstroubles to raise capital by issuing new securities. Firms must use internal funds or mustsell marketable assets to invest additional funds back into their declining business. It
appears to be plausible that firms raise funds by unwinding mutual shareholdings for therecovery of business. It is well known that, during the 1990s, many traditional Japanesecompanies restructured their operations as well as accelerated the process of theunwinding of mutual shareholdings. It has often been claimed in the business media thatfirms chose to unwind mutual shareholdings in order to raise funds for the restructuring
process. Sheard (1994) also has pointed out that the sale of securities has been acommon response of large Japanese companies facing business difficulties.
Within this framework, the present study examines the means used by firms
undergoing difficulty to stockpile the additional funds, i.e., it is considered whether
mutual shareholding or cash-holding is more beneficial. When only one firm faces bad

1

I do not consider equity finance at a time when a firm needs additional cash, because

this financial strategy is dominated by cash-holding in the model. For detail, see Section
5.1.
3

business conditions (a bad firm) and the other firm faces good business conditions (agood firm), only the bad firm needs additional funds in order to recover. The bad firm
can raise more funds compared to its fundamental value under conditions of mutualshareholding, because it can sell shares of the good firm. This effect is called the“diversification effect of mutual shareholding”. Similarly, cash-holding provides the badfirm with a relatively large amount of funds compared to its fundamental value. Since a
firm issues new shares before the business condition is realized, it can sell shares at a
price that reflects the possibility of the occurrence of favorable conditions. This effect iscalled the “self-diversification effect of cash-holding”. Assuming reasonable conditions,
it can be shown that the diversification effect of mutual shareholding is larger than thatof cash-holding. In the present case, mutual shareholding provides more funds to thebad firm than does cash-holding.
When both of the two firms face bad conditions simultaneously, mutual shareholding
provides fewer funds to the bad firm than does cash-holding. In this case, thediversification effect of mutual shareholding disappears because each bad firm has theother bad firm’s shares. In contrast, the self-diversification effect of cash-holding
remains because it does not depend on the business conditions a firm actuallyexperiences. Finally, when both firms face favorable conditions simultaneously, neitherof the firms needs to invest additional funds for the recovery of the business. In this case,mutual shareholding and cash-holding are indifferent.
Given this trade-off between mutual shareholding and cash-holding, the moredesirable means of stockpiling funds is dependent on the distribution of businessconditions that the two firms will experience. If the probability of events by which only
one firm will experience bad conditions is sufficiently larger than the probability ofevents by which both firms will experience bad conditions, then mutual shareholding isa more desirable means of stockpiling funds than is cash-holding. Both firms agree on
mutual shareholding and retain this strategy as long as neither firm experiences bad

4business conditions. However, when either firm experiences bad conditions, the badfirm is required to unwind mutual shareholding in order to raise cash and recoverbusiness. The good firm agrees on the unwinding of mutual shareholding, because therecovery of the bad firm has the effect of increasing the value of the shares held by thegood firm, resulting in an increase in the good firm’s value. When both firms experiencebad conditions under mutual shareholding, each bad firm sells the other firm’s sharesand invests the funds raised in this manner into its own faltering business. Thus, in thepresent model, firms choose mutual shareholding while considering the possibility of
the unwinding of mutual shareholding.
The diversification effect of mutual shareholding discussed in this paper is somewhat
different from the traditional diversification effect pointed out by Nakatani (1984).
Traditionally, the diversification effect has been conceived within a framework
assuming that mutual shareholding plays a role in stabilizing the returns of member
firms, such that it is a desirable option for risk-averse investors who cannot easily
diversify their portfolios due to market frictions. The diversification effect discussed inthis paper indicates the possibility that firms facing difficulty can raise large amount offunds for recovery by the unwinding of mutual shareholding. In this model, arisk-averse economy is not assumed, and the diversification effect described in thispaper is not dependent on risk-aversion. Instead, the diversification effect depends on
the idea that firms can recover or improve their faltering business by investing
additional funds into the business, and mutual shareholding may provide more funds
than other financial instruments such as cash-holding. Sheard (1994, ch.7) informallypoints out that mutual shareholding provides member firms with a form of insurance
against financial failure. The present model explicitly shows that mutual shareholding
actually plays an important role in fund stockpiling; by these means, firms can theninvest more funds into their faltering business than could utilizing other financial
instruments.

5

The remainder of this paper is organized as follows. In Section 2, a model ofstockpiling funds for business recovery is presented. In Section 3, the value of stockpile
for business recovery is examined, considering both mutual shareholding andcash-holding. In Section 4, the value of mutual shareholding and that of cash-holding
are compared. Then, the issue is addressed regarding the conditions under which mutualshareholding is a more desirable means of stockpile for business recovery than is
cash-holding. In Section 5, various remaining points and implications of the model areconsidered. Section 6 provides concluding remarks.

2. A Model of Stockpile for Business Recovery

In this model, there are two firms, firm a and firm b. At the beginning, each of thetwo firms issues one share outstanding, and has one existing asset. All participants arerisk-neutral, and the interest rate is zero.
The asset-in-place of each firm generates stochastic return. If the external conditionof a firm is good (state G), then the asset-in-place generates a high return, X. If theexternal condition is bad (state B), then the asset-in-place generates a low return, Y,
where Y<X. In state B, however, the firm has the opportunity for recovery. That is, if thefirm facing state B were in a position to quickly invest additional funds, C, into its
business, then the total return generated from the asset-in-place would increase toY+(1+r)C, where r>0 is the recovery rate. It can be interpreted that C is the funds
invested into the firm’s faltering business to recover the business. Thus, in the current
model, a firm can recover its performance by investing new funds into the business in atimely fashion in response to the crisis. With regard to the recovery rate, it is assumed
that 0<r<1. In addition, the return in state B never exceeds the return in state G.
There are two means for firms to prepare funds for business recovery. Each firm canissue n shares to the market in advance and keep raised cash in hand; this is refereed to6

as “cash-holding”. Alternatively, each firm can issue n shares to the other firm inadvance, that is, “mutual shareholding”. Whether or not a firm prefers mutualshareholding to cash-holding is dependent on the amount of funds the firm can utilize
when in crisis. Here, equity finance just following the realization of state B is not taken
into account, because of the requirement of a swift investment of cash into the business.
Since the execution of equity finances requires several weeks in the real world, the firm
may lose an investment opportunity which requires the swift investment of cash. In
addition, as will be addressed later, the equity finance conditional for the realization ofstate B is dominated by cash-holding in the current setting.

date-0date-1date-2stock issue

state realization {Good , Bad}mutual shareholding

investment for recovery

or cash-holding

unwinding of shareholding

return realization

Figure 1. Sequence of Events and Decisions

The formal sequence of events and decisions, described in Figure 1, is as follows. At
date-0, each firm chooses cash-holding or mutual shareholding. If the two firms agree
on mutual shareholding, then they exchange n shares with each other and maintain theother firm’s shares until date-1. Let us define α=n/(1+n). In the case of mutualshareholding, each firm holds α fraction of the other firm’s equity. It is assumed that0<α<1/2. On the other hand, if both firms choose cash-holding, each firm issues nshares to the market and keep raised funds in hand.
At date-1, the true state is publicly realized. For both firms, the prior probability ofstate G is 1/2, and that of state B is 1/2. The date-0 values of both firms are identical, sothat it is natural to assume that the two firms exchange the same fraction of equity from7

each other. However, it should be noted that it is not required that both firms always
experience the same state at date-1. It is possible that each firm faces a different state.
Hereafter, event (G, B) is referred to as the date-1 situation, in which firm a faces state
G and firm b faces state B. Event (B, G), event (G, G), and event (B, B) indicate similar
situations. Let us indicate the probability of event (G, G) by θGG, the probability ofevent (G, B) by θGB, the probability of event (B, G) by θBG, and the probability of event(B, B) by θBB. Since θGG+θGB=1/2, θBG+θBB=1/2, θGG+θBG=1/2, and θGB+θBB=1/2, then

θGG=θBB and θGB=θBG hold in the current setting.
As mentioned earlier, a firm experiencing state B must invest new funds into thebusiness in order to recover. If mutual shareholding was chosen at date-0, a firm
experiencing state B can raise funds swiftly by selling the other firm’s shares to themarket. This is the case of involving the unwinding of mutual shareholding, which isagreed upon because the recovery of the bad firm’s business increases the value of bad
firm’s shares held by the other firm, resulting in an increase in the total value of theother firm. If cash-holding was chosen at date-0, then a firm experiencing state B can
use the funds raised at date-0.
Then, at date-2, the total returns of the two firms are realized. Since there is no
informational asymmetry, in the case of mutual shareholding, the total return of a firm
experiencing state G is not dependent on whether or not it sells the other firm’s shares.

3. The Value of Business Recovery

3.1. The Value of Mutual Shareholding

In this subsection, the issue addressed is the amount of funds that a firm can invest
into its faltering business when the two firms choose mutual shareholding at date-0.
First, consider a situation in which firm a faces state B and firm b faces state G (event8(B, G)). In this event, only firm a needs to invest additional funds into its falteringbusiness in order to recover the business. Let Pj1 denote the date-1 stock price of thefirm j∈(a, b). Since firm a injects nPb1 into its business, the total value of assets of firm
a is given by Y+nPb1(1+r). On the other hand, the value of total assets of firm b is given
by X+nPa1. Therefore,

Y + nPb (1 + r )
,
1+ n
1

Pa =
1

(1)

X + nPa
.
Pb =
1+ n
1

1

(2)

By using α=n/(1+n) and solving these two equations, the following equations are
obtained:
Pa ( B, G; mh) =(1 − α )[Y + α (1 + r ) X ],1 − (1 + r )α 2

(3)

Pb ( B, G; mh) =(1 − α )[ X + αY ],1 − (1 + r )α 2

(4)

1

1

where Pj1(B, G; mh) represents the date-1 stock price of firm j∈(a, b) under mutualshareholding in event (B, G). In this case, firm a can invest nPb1(B, G; mh) into its
business, and creates the value of rnPb1(B, G; mh). This is the value of businessrecovery under the condition of mutual shareholding. Note that the denominator of (3)and (4), 1-(1+r) α2, is positive because r<1 and α<1/2.
By calculating the difference between Y and (4), the following equation is obtained:(1 − α )[ X + αY ](1 − α )( X − Y ) + rα 2Y
−
=
Y
> 0.
1 − (1 + r )α 2
1 − (1 + r )α 2

(5)The numerator consists of two positive components. The first positive component,(1-α)(X-Y), is derived from the fact that a bad firm possesses shares of the other firm
facing a good state. This effect is the diversification effect. The second component, rα2Y,

9

comes from the fact that a firm can recover business. This effect is the recovery effect.
When one firm faces a bad state and the other firm faces a good state, both thediversification effect and the recovery effect increase the amount of funds that a firm
facing a bad state can invest into its business, resulting in an increase in the value of the
firm.
The above argument can be applied when event (G, B) occurs. In this event, thedate-1 stock price of firm a is given by the right hand of equation (4), and that of firm b
is given by the right hand of equation (3). The value of mutual shareholding as stockpile
for business recovery, given by rnPa1(G, B; mh), is equal to rnPb1(B, G; mh).
Next, consider the situation in which both of the two firms face state B (event (B, B)).
In this event, both firms must invest additional funds into their business by unwinding
mutual shareholding. Then,
Y + nPb (1 + r )
,
1+ n

(6)

Y + nPa (1 + r )
.
Pb =
1+ n

(7)

1

Pa =
1

1

1

It follows from (6) and (7) that the date-1 stock price of firm j∈(a, b) underconditions of mutual shareholding in event (B, B), denoted by Pj1(B, B; mh), is given by

Pa ( B, B; mh) = Pb ( B, B; mh) =1

1(1 − α )Y.
1 − α − αr(8)Since both firm a and firm b face bad states, no diversification effect exists in (8). On
the other hand, there exists a recovery effect, by which the amount of raised funds
exceeds Y. In this case, the value of mutual shareholding is given by rnPa1(B, B;mh)+rnPb1(B, B; mh), because both of the two firms attempt to recover business.
Finally, when both of the two firms face state G (event (G, G)), neither firm has toinvest additional funds into its business. In this case, it is easy to demonstrate that the10stock price of firm j is equal to X under mutual shareholding conditions.

3.2. The Value of Cash-Holding

The two firms can choose cash-holding to stockpile funds instead of mutualshareholding. In the case of cash-holding, a firm issues n shares at date-0, and maintainthe raised cash for the recovery of business at date-2. The date-0 stock price of firmj∈{a, b} under cash-holding is represented by Pj0(ch). The total amount of funds thatfirm j can use for recovery is then nPj0(ch). Since the value of the assets of firm j instate G is X+nPj0(ch), that in state B is Y+(1+r)nPj0(ch), and each state is realized with aprobability of 1/2,
(1 / 2)[ X + nPj (ch) + Y + (1 + r )nPj (ch)]0Pj (ch) =
0

0

1+ n

.

(9)

By solving (9) with respect to Pj0(ch),Pj (ch) =0(1 − α )(1 / 2)( X + Y ) (1 − α )( X + Y )=.
1 − α − (rn / 2)
2 − 2α − αr

(10)

The denominator is positive because r<1 and α<1/2.
As in the case of mutual shareholding, the value of (10) is larger than Y, that is,
Pj (ch) − Y =0(1 − α )( X − Y ) + rαY> 0.
2 − 2α − αr(11)

The first positive term in the numerator can be interpreted as a kind of diversification
effect. Since issuance of new shares precedes the state realization, the value of a shareof the firm includes the possibility of a high return, X. For the firm actually facing a badstate, cash-holding provides more funds than its fundamental value, Y; this is theself-diversification effect. The second positive term is derived from the recovery effect.
When only one of two firms faces state B, the firm invest nPj0(ch) into its faltering

11business and creates the value of rnPj0(ch), which is the value of cash-holding. On theother hand, when both of the two firms face state B, the value of cash-holding is givenby 2rnPj0(ch).
Recall that it is assumed that a return in state B never exceeds a return in state G. This
assumption is formalized as
X + nPj (ch) > Y + (1 + r )nPj (ch) .
0

0

(12)

By plugging (10) into (12) and solving the equation,(1 − α − αr ) X > (1 − α )Y(13)

is obtained. Therefore, the recovery rate, r, must satisfy the requirement that 0<r<min{1,(1-α)(X-Y)/αX}.

4. Mutual Shareholding versus Cash-holding

In this section, mutual shareholding and cash-holding are compared from theperspective of stockpile for business recovery. First, event (B, G) is compared. Undermutual shareholding conditions, firm a can invest nPb1(B, G; mh) into its falteringbusiness for recovery. On the other hand, under cash-holding conditions, firm a caninvest nPj0(ch) into its business. Let us define ∆BG=nPb1(B, G; mh)-nPj0(ch). If ∆BG is
positive (negative), then firm a can stockpile more (less) funds by mutual shareholding
than it can by cash-holding. It follows from (4) and (10) that
∆ BG =(1 − α )[(1 − α − αr ) X − (1 − α )Y ].
(1 − α 2 − α 2 r )(2 − 2α − αr )(14)

From the assumption of (13), it can be concluded that ∆BG is positive. That is, inevent (B, G), firm a can invest more funds into its business by choosing mutualshareholding than by choosing cash-holding. The reason for this can be explained as
12

follows. Since α<1/2 and r<1, the coefficient of X is positive. This implies that thediversification effect of mutual shareholding is larger than the self-diversification effectof cash-holding; this result is derived from the fact that, under mutual shareholding, a
bad firm can sell shares of the other good firm. With regard to the recovery effect, thefollowing is obtained:∂∆ BG− α 2 (1 − α ) f ( X , Y ,α , r )=<0,∂r(1 − α 2 − α 2 r ) 2 (2 − 2α − αr ) 2

(15)

where
f ( X , Y ,α , r ) = X ((1 − α ) 3 + 2α 2 r − 2α 3 r − α 3 r 2 ) + Y (1 − α )(1 + 2α − 3α 2 − 2α 2 r ) > 0 .
The inequality follows from α<1/2 and r<1. Since ∆BG decreases with r, the recovery
effect of mutual shareholding is smaller than that of cash-holding. 2 Under theassumption of (13), the diversification effect is more important than the recovery effect,
because the recovery rate is restricted to be small.
The same result holds in event (G, B). That is, ∆GB=nPb1(G, B; mh)-nPj0(ch), which isequal to ∆BG, is positive.
Next, consider in event (B, B). The arguments in the previous section maintain thatfirm j∈{a, b} can invest nPj1(B, B; mh) into its faltering business under mutualshareholding conditions, whereas it can invest nPj0(ch) into its business under2

The intuition for this is as follows. Since the probability of the occurrence of state B is

1/2, the sensitivity of the ex-ante stock price to an increase in the recovery rate is also
approximately 1/2. On the other hand, since each of the two firms has α fraction of theother firm’s equity under mutual shareholding, the sensitivity of the good firm’s stock
price to an increase in the recovery rate is approximately α<1/2. Thus, the amount ofcash that a bad firm can raise under cash-holding is more (positively) sensitive to anincrease in the recovery rate than is the amount it can raise by mutual shareholding.
13

cash-holding conditions. Let us define ∆BB=nPj1(B, B; mh)-nPj0(ch). It follows from (8)and (10) that
∆ BB =− α [(1 − α − αr ) X − (1 − α )Y ].
(1 − α − αr )(2 − 2α − αr )(16)

The condition (13) ensures that ∆BB is negative. The negative coefficient of X means thatthe diversification effect of mutual shareholding is smaller than the self-diversification
effect of cash-holding. This result is due to the fact that the diversification effect ofmutual shareholding disappears in such an event.
The results of ∆GB=∆BG>0 and ∆BB<0 state that there is a trade-off between mutualshareholding and cash-holding. Although mutual shareholding is more beneficial thancash-holding when each firm faces a different state, cash-holding outperforms mutualshareholding when both firms face the same state B. Which is more beneficial, mutualshareholding or cash-holding, depends on the distribution of the occurrence of event. In
order to examine which strategy is preferable for stockpiling cash, the ex-ante efficiencyof mutual shareholding, denoted by Emh, and that of cash-holding, denoted by Ech, aredefined below.
E mh = θ GB rnPb ( B, G; mh) + θ BG rnPa (G , B; mh) + θ BB rn{Pa ( B, B; mh) + Pb ( B, B; mh)} ,
1

1

1

1

E ch = θ GB rnPa (ch) + θ BG rnPb (ch) + θ BB rn{Pa (ch) + Pb (ch)} .
0

0

0

0

The ex-ante efficiency of mutual shareholding, Emh, is given by the expected value ofrecovery when both firms agree on mutual shareholding at date-0. Similarly, the ex-ante
efficiency of cash-holding, Ech, is given by the expected value of recovery under
cash-holding conditions. Taking into consideration that θGG=θBB, θGB=θBG, Pa1(G, B;mh)=Pb1(B, G; mh), Pa1(B, B; mh)=Pb1(B, B; mh), and Pa0(ch)=Pb0(ch), the following is
obtained:
E mh = 2r[θ BG nPb ( B, G; mh) + θ BB nPb ( B, B; mh)] ,
1

1

14

(17)

E ch = 2r[θ BG nPa (ch) + θ BB nPa (ch)] .
0

0

(18)

Therefore,
E mh − E ch = 2r (θ BG ∆ BG − θ BB ∆ BB ) .

(19)

Mutual shareholding is agreed upon at date-0 when Emh>Ech holds. It follows from
(14) and (16) thatθ BG
1 − α 2 − α 2r
E mh > E ch ⇔>.
θ BB (1 − α )(1 − α − αr )(20)

On the other hand, cash-holding is chosen at date-0 when
E mh < E ch ⇔θ BG
1−α 2 −α 2r<.
θ BB (1 − α )(1 − α − αr )(21)

When Emh=Ech, mutual shareholding and cash-holding are indifferent. Now, thefollowing proposition can be obtained.

Proposition 1. The two firms agree upon mutual shareholding when (20) holds,

whereas the two firms choose cash-holdings when (21) holds.

Note that (1-α2-α2r)/(1-α)(1-α-αr)>1. Thus, condition (20) requires that θBG>θBB.
That is, mutual shareholding is agreed upon only when the probability of event (B, G) isrelatively large compared to the probability of event (B, B). Intuitively, in such asituation, the diversification effect of mutual shareholding works well to stockpile cash.
On the other hand, when (21) holds, the diversification effect of cash-holding functions
well.33Note that in event (B, B), mutual shareholding has no diversification effect while

cash-holding does have a diversification effect.
15

5. Discussion and Implications

5.1. Equity Finance in the Bad StateSo far, equity finance conditional on state B being realized (hereafter, “equity
finance”) has not been considered for two reasons. First, since the execution of equity
finance frequently requires several weeks, a bad firm may lose its opportunity torecovery. Second, in the current setting, equity finance is dominated by cash-holding.
That is, the total amount funds raised by equity finance just following the staterealization (equity finance) is less than that raised by equity finance prior to the staterealization (cash-holding). A formal argument follows regarding this point.
Suppose that a firm j∈{a, b} issues n shares and raises cash after it experienced state
B. The date-1 stock price of firm j experiencing state B can be denoted by Pj1(ef). Since
the total rerun of the firm is Y+nPj1(ef)(1+r) and the total number of shares is 1+n,Pj1(ef) has to satisfy
Y + nPj (ef )(1 + r )1

Pj (ef ) =
1

1+ n

.

(22)

By comparing (22) with (5) (or (6)), Pj1(ef) is equal to Pj1(B, B; mh). That is,
Pj (ef ) =1(1 − α )Y.
1 − α − αr(23)Furthermore, ∆BB<0 implies that Pj1(ef)<Pj0(ch). Thus, the amount of funds raised byequity finance is always less than that raised by cash-holding. Therefore, neither firmchooses equity finance just following the state realization.

Proposition 2. In the current setting, equity finance conditional on state B being

16

realized is dominated by cash-holding.

5.2. Diversification Effect of Mutual Shareholding

As introduced in Section 1, it has been traditionally pointed out that one advantage ofmutual shareholding is to stabilize member firms’ returns though asset diversification.
Some empirical studies, such as those of Nakatani (1984) and Douthett and Jung (2001),
have reported that Keiretsu firms experience more stable returns than do non-Keiretsu
firms. Since mutual shareholdings among Keiretsu firms are tighter than non-Keiretsu
firms, mutual shareholding is an instrument of diversification.
However, it should be noted that in a situation in which investors can diversify theirportfolios by themselves, the traditional diversification effect of mutual shareholding is
not important per se. In other words, the diversification effect alone is not a motivation
for mutual shareholding in a risk-neutral economy. In contrast, the diversification effectdiscussed in this paper plays an important role for cash stockpiling even in a risk-neutral
setting, because both the diversification effect and the recovery effect are considered
together.
Under mutual shareholding conditions, it is possible for a firm facing bad businessconditions (a bad firm) to sell shares of the other firm. In particular, when the other firm
faces good business conditions (a good firm), the value of a good firm is higher thanthat of the bad firm. In such an event, the bad firm can raise more funds for recovery bymutual shareholding than by cash-holding. In the current model, the diversification
effect of mutual shareholding is economically important because it affects themagnitude of business recovery. As shown in the previous section, the more likely eachof the two firms are to experience a different state, the better the diversification effect ofmutual shareholding will work. Mutual shareholding is desirable among firms whose
returns have low correlation. The present model suggests that the lower the correlation17

is between the returns of member firms, the more effective the diversification effect ofmutual shareholding will be for business recovery.
Sheard (1994, ch.7) maintains that the advantage of mutual shareholding does notappear to be to stabilize the returns of member firms, but rather to provide the member
firms with a form of insurance against financial failure. By incorporating the recovery
effect into the diversification effect, the present model formally demonstrates this point.

5.3. Unwinding of Mutual Shareholding for Business Recovery

One of contributions of this paper is to explicitly analyze the unwinding of mutualshareholding. In this model, mutual shareholding is unwound when at least one of two
firms experiences bad business conditions. For such a firm, the unwinding of mutualshareholding is an effective financial instrument for raising funds required to recover or
restructure the business.
As reported by Kuroki (2001) and Ang and Constand (2002), mutual shareholdings
among Japanese firms have been declining since the 1990s. It is well known thatJapanese firms have been progressively restructuring since the 1990s. The businesspress has often indicated that Japanese firms unwound mutual shareholdings in order toraise capital for restructuring; it has also been suggested that Japanese banks intended tounwind mutual shareholdings in order to raise capital in preparation for bad debt. In
addition, Sheard (1994) has pointed out that the sale of securities has been a common
response of large Japanese companies facing difficulties. Thus, although there havebeen few empirical studies focusing on the reason why mutual shareholdings among
Japanese firms have declined, it is be possible to argue that firms abandoned mutualshareholding when they faced more profitable investment opportunities; in particular,
the unwinding of mutual shareholdings provided firms the additional funds for recovery

18

or restructuring when the firms were experiencing difficulty.4
In the present model, mutual shareholding is unwound when at least one firm faces
difficulty and therefore requires additional funds for recovery. There is no conflict
between member firms with regard to the unwinding of mutual shareholding. Whenboth of the two firms are confronted with bad business conditions, each firm sells theother firm’s shares and invests the raised funds into more profitable options than mutualshareholding, that is, they focus on business recovery. When only one of the two firms
experiences bad business conditions, this bad firm has to unwind mutual shareholding inorder to raise funds for recovery. The other good firm agrees to unwind mutualshareholding, because the recovery of the bad firm will increase the value of the badfirm’s shares held by the good firm, resulting in an increase in the value of the goodfirm. Thus, in the present model, firms rationally choose to unwind mutual shareholding
in order to achieve recovery, and they choose to engage in mutual shareholding whileconsidering the possibility of the unwinding of mutual shareholding.

5.4. Market Response to Unwinding of Mutual Shareholding

Next, stock price behavior following the unwinding of mutual shareholding is
examined. It is assumed that informational asymmetry exists between firms and thestock market with regard to the firms’ external conditions. That is, the firms are awareof their true business conditions, but the market is not. In addition, it is assumed that4

To the best of my knowledge, the Fuji Research Institute Corporation (1993) is the

only comprehensive empirical research center that has focuses on what Japanese
corporate managers thought about mutual shareholdings; a questionnaire was used toanalyze their options. It was in fact reported that about 2/3 of the firms in the sample(n=1175) worried about low returns from shares held as mutual shareholdings.
19

firms do not have access to any other means of raising funds for recovery. In such asituation, the unwinding of mutual shareholding is a signal that the external conditionsof the firm are unfavorable.
Consider a situation in which condition (20) is satisfied such that the two firms agree
upon mutual shareholding at date-0. Suppose that both firm a and firm b face badbusiness conditions. Since both firms wish to recover business, both firms agree on theunwinding of mutual shareholding and they sell their holding shares of the other firm;
this type of unwinding of mutual shareholding can be referred to as “bilateral
unwinding”. Both firms have no incentive to continue shareholding, because they lose
profitable investment opportunities by doing so. In order to maximize the long-term
shareholders’ wealth, both firms relinquish mutual shareholding, even though their stock
prices will decline in the short-term. Stock price declines, dependent upon mutualshareholdings being unwound, are ensured by the assumption that returns under bad
conditions will be smaller than returns under good conditions.
Next, suppose that firm a faces bad business conditions, but firm b faces goodbusiness conditions. In this case, firm a sells its holding shares of firm b in order to raise
funds required to recover business. For the same reason as that given above, firm a has
no incentive not to sell shares of firm b. On the other hand, firm b has no incentive tosell its holding shares of firm a. The explanation for this phenomenon is as follows. If
firm b sells its holding shares of firm a, then the market realizes that both firms face badbusiness conditions. Since the stock price of firm b is undervalued compared to its fairvalue, the total amount of cash that firm a is able to raise decreases, resulting in adecrease in the total value of firm b. In order to avoid this risk, firm b will retain its
shares of firm a or it will postpone selling them. This can be interpreted as a “unilateral
unwinding” of mutual shareholding, or as “one-sided shareholding”. Thus, a model withasymmetric information provides insights regarding the timing of the unwinding of
mutual shareholding. When both firms face good business conditions, neither firm has

20

an incentive to unwind mutual shareholdings.
The following proposition summarizes the arguments discussed above.

Proposition 3. There exists a signaling equilibrium at which the bilateral unwinding of

mutual shareholding indicates that both firms face bad business conditions
simultaneously, and the unilateral unwinding of mutual shareholding indicates that only
one firm faces bad business conditions. Although in both cases, stock prices decline
following the unwinding of mutual shareholding, the magnitude of the stock pricedecline that occurs after the bilateral unwinding is larger than that following theunilateral unwinding.

Financial market practitioners often argue that the unwinding of mutual shareholdings
will lead to a decline in the stock price due to an excess supply of shares. Although thepresent model also predicts that an unwinding of mutual shareholding will lead to a
stock price decline, the reason for this decline is not excess supply. In the present model,
the unwinding of mutual shareholding is a signal that the business conditions of therespective firms are unfavorable, so that the firms are forced to raise additional cash forrecovery. The unwinding of mutual shareholding is desirable for long-term
shareholders.

6. Conclusions

Mutual shareholding has long been a prominent strategy in Japanese corporate
finance. However, since the 1990s, mutual shareholdings among Japanese firms havebeen unwound. In this paper, a simple model is outlined in which firms choose mutualshareholding while considering the possibility that they will at some point in the future
unwind mutual shareholdings. In the model, mutual shareholding is a means of21

stockpiling funds in the sense that when firms face bad business conditions, they canraise the funds required for recovery by selling the holding shares (unwinding mutualshareholding). This model reflects the well-known fact that many Japanese firms
restructured their operations during the 1990s, and that they accelerated the unwindingof mutual shareholdings during that period.
The present study compared mutual shareholding and cash-holding (holding cashraised by equity finance) from the perspective of stockpile for business recovery, anddemonstrated that mutual shareholding is superior to cash-holding when the correlation
between the returns of the firms is low. In such cases, firms appear to agree on mutualshareholding, and they continue with mutual shareholding as long as their businesses
are healthy. However, when at least one of the member firms experiences difficulty, themutual shareholdings are unwound. Thus, in the present model, firms dynamically havemutual shareholdings, and then unwind such shareholdings in response to particular
unfavorable business conditions.
The present model has several implications regarding mutual shareholding and theunwinding of mutual shareholding. First, in this model, the diversification effect ofmutual shareholding functions well, even in a risk-neutral economy. When one firm
faces bad business conditions (a bad firm), but the other firm faces good businessconditions (a good firm), the bad firm can sell its holding shares of the good firm. Then,the bad firm can raise additional funds in an amount that exceeds its fundamental value
in order to recover. The diversification effect of the mutual shareholding plays animportant role in business recovery in this model.
Second, the present model suggests that the unwinding of mutual shareholding isagreed upon, even when only one firm faces bad business conditions. In such a situation,
the bad firm has to discontinue with mutual shareholding in order to raise funds
required to recover its business. The other good firm that does not require funds agrees
to an unwinding of mutual shareholdings, because the recovery of the bad firm will22

increase the value of the bad firm’s shares that are still held by the good firm, resulting
in an increase in the value of the good firm.
Third, by incorporating asymmetric information, the present model predicts that an
unwinding of mutual shareholding will decrease the prices of member firms stocks,
because unwinding of this sort is a signal that at least one member firm is undergoingdifficulty. Although the unwinding of mutual shareholding will decrease the stock prices
of member firms, the recovery of the bad firm following the unwinding of mutualshareholding is desirable for the long-term shareholders in member firms. The present
model also provides new insight into the timing of the unwinding of mutualshareholding.
[2002.12.9 637]

ReferencesAng, J., and R. Constand, 2002, The Portfolio Behavior of Japanese Corporations’Stable Shareholders, Journal of Multinational Financial Management 12, 89-106.

Berglof, E., and E. Perotti, 1994, The Governance Structure of the Japanese Financial
Keiretsu, Journal of Financial Economics 36, 259-284.

Corbett, J., 1994, An Overview of the Japanese Financial System, in N. Dimsdale and
M. Prevezer, ed., Capital Market and Corporate Governance, Oxford University Press,
Oxford.

Douthett, E.，and K. Jung, 2001, Japanese Corporate Groupings (Keiretsu) and theInformativeness of Earnings, Journal of International Financial Management andAccounting 12, 133-159.

23

Fuji Research Institute Corporation, 1993, Research Report of Main Bank and Cross
Shareholding, (in Japanese).

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.

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

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

Sheard, P., 1989, The Japanese General Trading Company as an Aspect of Interfirm
Risk-Sharing, Journal of Japanese and International Economies 3, 308-322.

Sheard, P., 1994, Interlocking Shareholdings and Corporate Governance, in Aoki M, and
R. Dore, eds., The Japanese Firm: the Sources of Competitive Strength, Oxford
University Press.

24

Discussion Paper
No.
2001･1

AuthorTakashi Hatakeda
Nobuyuki Isagawa

2001･2Michiyasu Nakajima
Takeshi Mizuguchi
Katsuhiko Kokubu
Yasushi Onishi
Koji Okubayashi

2001･3
2001･4

2001･5
2001･6
2001･7

2001･8

2001･9Katsuhiko Kokubu
Akihiro Noda
Yasushi Onishi
Tomomi Shinabe
Kunio Miyashita
Akinobu Sakashita
KOKUBU,
Katsuhiko
NASHIOKA, ErikoDAIKUHARA, Rie
KOKUBU,
Katsuhiko
KURASAKA,
TomokoShuzo Murata

2001･11

Makoto Yano
Fumio Dei
Mahito Okura

2001･122001･13

Mahito Okura
Shuzo Murata

2001･14

Koji Okubayashi
Toshinori Takashina

2001･15
2001･16

Takuji Hara
Shuzo Murata

2001･17

Norio Kambayashi

2001･18
2001･19
2001･20

Yuichi Fukuta
Kazuhiro Tanaka
Kentaro Nobeoka
Kazuhiro Tanaka

2001･21

Mahito Okura

2001･22
2001･23

Kazuhiro Tanaka
Mahito Okura

2001･24

Katsuhiko Kokubu
Akihiro Noda
Yasushi Onishi
Tomomi Shinabe
Akira Higashida

2001･10

Title
Stock Price Behavior Surrounding Repurchase
Announcements:
Evidence from Japan
Material Flow Cost Accounting of IMU (October 2000)

Date
1／2001(in Japanese)

1／2001

Japanese Manufacturers Without Factories:
Cases of Sony, Matsushita, Misumi, People
Determinants of Environmental Report Publicationin Japanese Companies

1／2001

Logistics Strategy of Japanese Port Management
Issues and Method of Organizational Culture Studies:
Functionalism Approach
Environmental Accounting in Japanese Companies as ofNovember 2000

(in Japanese)

2／20013／2001(in Japanese)

3／20012／2001

Corporate Environmental Accounting: A Japanese
Perspective

The Comparative Study of Japanese & U.S. Companies(6) The Health & Long Term Care-The Management
Education
A Trade Model with Vertical Production Chain andCompetition Policy in the Downstream Sector
Risk Classification: A Study of the Tradeoff between
Quantity and Quality of Insured
Is the Separating Equilibrium Really Desirable?
The Comparative Study of Japanese & U.S. Companies(5) The Conflict Among Companies
Research Report on the relations between there-employment process and former job career at thecompulsory retirement of workers of a firm
The Social Shaping of Medicines
The Comparative Study of Japanese & U.S. Companies(7) Toward Restructuring Japanese Corporations
Cultural influences on IT usage among workers:a UK-Japanese comparison
A Test for Rational Bubbles in Stock Prices
Toward the Effective Reform of Japanese Corporate
Governance
Structural Changes in Top Management―The Effect ofCorporate Governance Reform in Japan
In the Separating Equilibrium Really Desirable ?
―revised version of No.2001･12―
Introduction to Corporate Governance
The Role of Some Insurance Contracts in a Subjective
Equilibrium Model with Observable Effort
Environmental Disclosure of Japanese companies

3／2001(in Japanese)

4／2001

12／2000(in Japanese)

5／2001(in Japanese)(in Japanese)

5／20016／2001(in Japanese)

7／2001(in Japanese)(in Japanese)

7／20017／20017／2001(in Japanese)

7／20017／2001(in Japanese)

7／2001(in Japanese)

8／2001(in Japanese)(in Japanese)

8／20018／2001(in Japanese)

8／2001

Discussion Paper
No.
2001･25

2001･26
2001･27

AuthorKatsuhiko Kokubu
Tomomi Shinabe
Akira Higashida
Yasushi Onishi
Akihiro Noda
Katsuhiko Kokubu
Eriko Nashioka
Masakazu Takagi

2001・28 Mahito Okura
2001・29 Atsushi Takao

2001・30 Mahito Okura
2001・31 Masakazu Takagi
2001・32 Norio Kambayashi
Harry Scarbrough2001・33 Fumitoshi Mizutani
Shuji Uranishi
2001・34 Mahito Okura

2001・35 Tsutomu Harada
2001・36 Nobuyuki Isagawa

2001・37 Nobuyuki Isagawa
2002・1

Nobuyuki Isagawa

2002・2

Nobuyuki Isagawa

2002・3Mahito Okura

2002・4

Elmer Sterken
Ichiro Tokutsu
Mahito Okura
Mahito Okura
Nobuyuki Isagawa
Koji Okubayashi
Toshinori Takashina

2002・5
2002・6
2002・7
2002・8

2002・9Hajime Shimizu

2002・10 Nobuyuki Isagawa
2002･11

Nobuyuki Isagawa

Title
Environmental Reporting of Japanese companies(in Japanese)

Date
8／2001

Environmental Accounting of Japanese companies(in Japanese)

8／2001Elementary Study of East Asian Corporate andManagement System
Vertical Differentiation in the Insurance Market
A Study on the Penetration Process of Modern Insurance
by Evolutionary Economics―Why do the Modern
Insurance and the Premodern Mutual Society coexist?―
An Essay in the Economics of Post-loss Minimisation:
An Analysis of the Effectiveness of the Insurance Law
and Clauses
Co-operation between Hanshin(Osaka-Kobe) Area andSouth-east Asia-Finding business opportunities of mutual
benefits
Cultural influences on IT use amongst factory managers：
A UK-Japanese comparison
The Post Office vs. Parcel Delivery Companies：
Competition Effects on Costs and Productivity
An Essay in the Economics of Post-loss Minimisation:
An Analysis of the Effectiveness of the Insurance Law
and Clauses―revised version of No.2001・30―
An Examination of IT Paradox in Japan
Open-Market Repurchase Announcements, Actual
Repurchases, and Stock Price Behavior in Inefficient
markets
Corporate Financial Strategy and Stock Price Behavior ina Noise Trader Model with Limited Arbitrage
Cross Holding of Shares, Unwinding Cross Holding of
Shares, and Managerial
Entrenchment
A Theory of Stock Price Behavior following Repurchase
Announcements
An Equilibrium Analysis of the Insurance Market
with Vertical Differentiation
What are the determinants of the number of bankrelations of Japanese firms?
Review Article：Adverse Selection in Insurance Market
Welfare Effect of Firm Size in Insurance Market
Does Investment Horison Affect Investment Strategy ?
Research Report of Careers and Employment Process ofWorkers over 60 years old :a Case of a Japnaese
Manufacturing Company
On the Existence of Tax Equilibrium : Incomplete Market
with Capital Income Tax
Cost of Financial Distress and Debt Restructuring :Debt Forgiveness and Equity-for-Debt Swap
Open-Market Repurchase Announcements, Actual
Repurchases, and Stock Price Behavior in Inefficient
Markets―revised version of No.2001･36―

9／2001(in Japanese)(in Japanese)

9／20019／20019／2001(in Japanese)

9／2001

10／2001
10／2001
11／2001(in Japanese)

11／2001
12／2001
12／2001(in Japanese)

1／ 2002(in Japanese)

1／ 20022／20023／2002(in Japanese)(in Japanese)(in Japnaese)

3／20023／20023／20024／2002(in Japnaese)

4／2002(in Japnaese)

4／20025／2002

Discussion Paper
No.
2002･12

AuthorKenji Kutsuna
Richard Smith

2002・13 Kunio Miyashita
2002・14 Hajime Shimizu
2002・15 Hajime Shimizu
2002・16 Koji Okubayashi
2002・17 Fumitoshi Mizutani
Shuji Uranishi
2002・18 Kazuhisa Otogawa
2002・19 Atsuo Takenaka
2002・20 Tsuneo Nakano

2002・21 Tsuneo Nakano
2002・22 Fumitoshi Mizutani
Shuji Uranishi
2002・23 Atsushi Takao
Mahito Okura
2002・24 Fumitoshi Mizutani
2002・25 Fumitoshi Mizutani
Takuya Urakami
2002・26 Yasuyuki Miyahara
2002・27 Nobuyuki Isagawa
2002・28 Mitsutoshi Hirano

2002・29 Atsushi Takao
2002・30 Yasuhiro Shimizu
2002・31 Hideki Murakami

2002・32 Atsushi Takao

2002・33 Nobuyuki Isagawa

Title
Why Does Book Building Drive Out Auction Methodsof IPO Issuance?
Evidence and Implications from Japan
International Logistics and Modal Choice
Incomplete markets with capital income tax and public
goods
On the possibility of Pareto improving of tax-equilibrium
China-Japan Comparison of Work Organization
The Post Office vs. Parcel Delivery Companies:
Competition Effects on Costs and Productivity―revised version of No.2001･33―
Earnings Forecast and Earnings Management of JapaneseInitial Public Offerings Firms
The Classification of Foreign R&D Units
The Dutch East India Company and its Corporate
Governance―revised version of No.2000･40―
The British East India Company and its Corporate
Governance
Privatization Effects on TFP Growth and Capital
Adjustments
Some Notes on the Privatization of Postal Life Insurancein JapanPrivately Owned Railways’ Cost Function, Organization
Size and Ownership
A Private-Public Comaprison of Bus Service Operators
Principal-Multiagent Relationships with Costly
Monitoring
Unwinding of Cross Shareholding under Managerial
Entrenchment
Contingency Model for Personnel Grading System―Issues on Design and Management for Qualification
System and Job Grading System―
On the Emergency Effect of the late FUKUZAWA,
Yukichi in Introducing of Modern Insurance into Japan
Amortization of Intangible Assets before Newark
Morning Ledger
An Economic Analysis of Duopolistic Competition
between Gulliver and Dwarf airlines:
The case of Japanese Domestic Air Markets
Simulation Model to Consider the Penetration of Modern
Insurance in Japan −Confirmation of Emergence andPhase Transition of New Japanese Risk-Bearing System
by Evolutional Economics
Mutual Shareholding and Unwinding of Mutual
Shareholding as Stockpile for Business Recovery

Date
5／2002(in Japnaese)(in Japnaese)

6／20026／20026／20027／20027／20028／2002(in Japanese)(in Japanese)

8／20028／2002(in Japanese)

8／20028／2002(in Japanese)

9／20029／20029／2002
10／2002
10／2002(in Japanese)

11／2002(in Japanese)

11／2002(in Japanese)

11／2002
11／2002(in Japanese)

12／2002

12／2002