2002. 11

Open-Market Repurchase Announcements, Actual Repurchases,
and Stock Price Behavior in Inefficient Markets<revised version of No.2001・36>
Nobuyuki Isagawa

Open-Market Repurchase Announcements, Actual Repurchases,
and Stock Price Behavior in Inefficient Markets
Abstract

In the efficient market framework, it seems difficult to explain why a firm would
actually buy back its outstanding shares after the stock price goes up in response to an
open-market repurchase announcement. We introduce the subject of market inefficiency
in a way similar to the explanation of Shleifer and Vishny (1990, 1997) and reexamine
corporate open-market repurchase strategy and stock price behavior. In contrast to
previous studies dealing with open-market repurchase signaling, we establish asignaling equilibrium without the assumption that an announcement of open-market
repurchase intention is a firm-commitment. In an inefficient market, the stock price of a
firm may be undervalued when the market is subject to temporal pessimistic noise.
Since the firm can earn capital gains by buying its outstanding shares at a bargain price,
the firm has a strong incentive to execute stock repurchases even after it makes anannouncement of repurchase intention. Empirically, our model predicts positive
performance of long-run stock returns as well as positive announcement effects
following open-market repurchase announcements.

Keywords: open-market stock repurchases, market inefficiency,
positive performance of long-run stock returns

Acknowledgement: I would like to thank Walter Novaes, Jaemin Kim, Shigeki
Sakakibara, the editors, and an anonymous reviewer for their helpful comments.
Financial support was provided by the Nomura Foundation for Social Science.

1

1.

Introduction

Stock repurchases have become an important financial policy for listing firms overthe last twenty years. As reported by Bagwell and Shoven (1989) and Grullon andMichaely (2000), open-market stock repurchasing has been the most popular method forfirms to repurchase stock. Many empirical studies, such as those of Vermaelen (1981),
Comment and Jarrell (1991), Netter and Mitchell (1989), Stephens and Weisbach (1998),
and McNally (1999), report that stock prices rise in response to open-market repurchaseannouncements. That is, open-market repurchase announcements are good news for thestock market. This is known as the signaling hypothesis for open-market stock
repurchases.1
In addition to the positive announcement effect, Ikenberry, Lakonishok, andVermaelen (1995) find that stock prices further appreciate following announcements ofopen-market repurchases.2 This phenomenon suggests that, for an announcing firm,purchase of its outstanding shares constitutes a profitable investment opportunity evenafter the stock price rises in response to the announcement of an open-market
repurchase. In fact, although firms do not necessarily need to obey their announcements,
Stephens and Weisbach (1998) report that most firms do follow through with suchannouncements.
As pointed out by Ikenberry, Lakonishok, and Vermaelen (1995), if the market

1

The signaling hypothesis could imply that a firm is undervalued because the future

operating performance of the firm is going to improve. Alternatively, a firm could
simply be inefficiently priced without implying any future improvement in operating
performance. This paper deals with both cases.
2

They report that, on average, announcing firms experience a significant positive stock

price increase of about 12 percent over the subsequent four years.
2

evaluates the worth of the stock price of a firm based on the fundamentals, thenoutstanding shares will not be profitable immediately following the market reaction to
the repurchase announcement. Thus, in the efficient market framework, it seems
difficult to explain by the signaling hypothesis why a firm would actually buy back its
outstanding shares after announcing its intention to repurchase shares. In this paper, we
attempt to reexamine corporate open-market stock repurchase strategy and stock pricebehavior when there exist both informational asymmetry and market inefficiency.
We introduce the subject of market inefficiency in a way similar to the explanationof Shleifer and Vishny (1990, 1997). In our model, pessimistic noise causes market
undervaluation of the stock price of a firm.3 Smart money is costly, so the market
misperception cannot be eliminated completely.4 A firm can make use of this market
undervaluation: by buying its outstanding shares at a bargain price and holding them
until the noise disappears, the firm can earn capital gains. There is thus an obvious
incentive for the firm to execute stock repurchases in the open market with pessimistic
noise. From the viewpoint of market efficiency, the firm provides smart money via
open-market stock repurchases. As the firm buys its own shares, demand increases andthe stock price rises. In this process, the market mispricing is partially mitigated. The
firm, however, never buys its shares to the extent that the market mispricing is

3

The assumption that the market contains noise can be supported by the empiricalfindings reported by Campbell and Kyle (1993), Redding (1996), and Morgan (1997).
Recently, Daniel, Hirshleifer, and Subrahmanyam (1998) and Barberis, Shleifer and
Vishny (1998) explored the mechanisms by which investor sentiment, based upon
psychological theory, leads to market noise.
4

Shleifer and Vishny (1990, 1997) and Shleifer (2000, Chapter 1) stress that smart

money seems to be costly in the real world. Pontiff (1996) provides empirical findingsthat support the idea of costly smart money.
3

eliminated completely, because the firm cannot earn capital gains by doing so.
In contrast to previous papers dealing with open-market repurchase signaling, suchas those of Ofer and Thakor (1987), Constantinides and Grundy (1989), and McNally(1999), we do not assume that a firm has to follow through on its announcement of an
intention to repurchase its shares on the open market. Ikenberry and Vermaelen (1996)
say that the irrevocability assumption of open-market repurchase announcements is notrealistic. In practice, open market repurchase announcements provide firms with an
option to buy back their outstanding shares but do not commit firms to do so.5
On the other hand, as pointed out by Stephens and Weisbach (1998) and Grullon andMichaely (2000), although firms are not required to announce their intention to
repurchase shares on the open market, the announcement is interpreted as a safe harboragainst stock price manipulation. We incorporate this idea into our model as follows.
While an announcing firm can buy back any number of shares up to a relatively large
proportion of its outstanding shares, the number of shares that a firm can buy backwithout making a repurchase announcement is restricted to a relatively small proportionof shares. We assume that if a firm repurchases a large proportion of its shares without
making an announcement, the firm will be suspected of stock price manipulation or
insider trading and a deadweight cost will be imposed on the firm.
The above setting establishes a signaling equilibrium in which a high-quality firmchooses to make an open-market repurchase announcement and a low-quality firmchooses not to announce. In the equilibrium, the high-quality firm makes anannouncement in order to buy back a large number of shares at a bargain price caused

5

Ikenberry and Vermaelen (1996) insist that open-market repurchase programs areuseful for firms because the programs expand the firms’ investment opportunity sets bygiving management an additional investment opportunity, that is, to purchase the firms’
own shares.
4

by pessimistic noise. On the other hand, the low-quality firm does not announce its
intention and buys back a small number of shares at a price lower than its fundamental
value. By mimicking the low-quality firm, the high-quality firm can buy back its sharesat a lower price than it can on the equilibrium path, because the market believes that a
non-announcing firm is a low-quality firm. However, since the high-quality firm canbuy back only a small number of shares without making a repurchase announcement,
the capital gains the high-quality firm could earn is smaller than what it could earn on
the equilibrium path. If the low-quality firm mimics the high-quality firm, then it loses
the opportunity to earn capital gains, because the market believes that an announcing
firm is a high-quality firm.
It should be stressed that the high quality firm has an intense incentive to actually
buy back its outstanding shares following an announcement of repurchase intention
even though the announcement is not a firm commitment. This is one contribution of
our paper. As argued just above, an announcing firm can enjoy capital gains byrepurchasing its shares at a bargain price if markets are not completely efficient.
Capital gains earned by the announcing firm results in the positive performance oflong-run stock returns. Thus, our signaling model predicts both positive announcement
effects and long-run positive performance of stock returns associated with open-market
repurchase announcements. This type of prediction of positive long-run performance,
which is consistent with the empirical finding of Ikenberry, Lakonishok, and Vermaelen(1995), has not been investigated theoretically. This is another contribution of our paper.
The central motivation considered in this paper is that actual repurchases may be
inconsistent with the efficient market if the only reason for repurchasing shares issignaling. There are, however, some reasons for repurchasing shares that have nothing
to do with signaling. One of the most cited reasons is the tax advantage of stock
repurchases relative to cash dividends (e.g., Talmor and Titman, 1990; Bagwell andShoven, 1991; Grullon and Michaely, 2000). Since we do not incorporate tax payment,5there is no tax-related reason for the firm to buy back its shares in our model. The free
cash flow hypothesis introduced by Jensen (1986) posits that the firm makes thedecision to execute stock repurchases (or pay dividends) in order to avoid managerial
overinvestment. There is no such problem in our model because we assume that theobjective of the firm is to maximize the future stock price. We repeat that, in our model,
the motivation for repurchase is the undervaluation of the stock price caused bypessimistic noise.
The remainder of this paper is organized as follows. In the next section, we present
our model. In section 3, we analyze corporate open-market repurchase strategy andmarket behavior. In section 4, we examine stock price behavior and show some of theempirical implications of our model. In section 5, we address some remaining points ofrelevance to the model, and in section 6, we conclude the paper.

2.

The Model

date-0date-1date-2date-3Firm knows its type

SignalInterim cash flow

Terminal cash flow

Pessimistic noise{Repurchase, No-Repurchase}

Actual repurchase

Informational asymmetry
and noise disappear

Figure 1. Time Line

Figure 1 summarizes the sequence of events and decisions over four dates. There arethree types of participants in the model: a firm, noise traders, and smart traders. For
simplicity, we assume that all participants are risk-neutral, and the interest rate is zero.
We consider the case of an all-equity firm whose objective is to maximize its stock
price at the terminal date (date-3). For example, when a manager of the firm has an

6executive option expired at date-3, she cares about the date-3 stock price.6 Initially, thefirm has one outstanding share and no cash. The firm generates an interim cash flow,
C>0, at date-2, which is its resources for stock repurchases. In addition, the firm
generates a terminal cash flow, Vt>0, at date-3. The terminal cash flow depends on thequality of the firm, t∈{h, l}, where h means high quality and l means low quality. The
terminal cash flow of the high-quality firm is larger than that of the low-quality firm,that is Vh>Vl. In this paper, we analyze the case of Vh-Vl≤2C. The reverse case can beanalyzed in a similar way.
There is an informational asymmetry regarding the quality (type) of the firm. At
date-0, the firm knows its type but the market (noise traders and smart traders) does not.
The market knows only the distribution over types; the probability of a firm being ahigh-quality type is θ (0<θ<1) and that of it being a low-quality type is 1-θ. This
informational asymmetry is resolved at date-3. All other parameters are equal between
the two types.
The structure of the market is similar to that described by Shleifer and Vishny (1990,
1997). At date-0, noise traders experience a pessimistic shock, S>0, which will persist
until date-3. As a reflection of the pessimistic noise, the date-0 demand schedule ofnoise traders is given by [θVh+(1-θ)Vl+C-S]/P0, where P0 is the market price at date-0. It
can be interpreted that noise traders underestimate the firm value to the extent of themagnitude of the pessimistic shock, S. For the sake of simplicity, we assume that themagnitude of the pessimistic shock is smaller than the difference between the terminal
cash flows of the two types. That is,S ≤ V h − V l ≤ 2C .7

6(1)

Jolls (1998) reports that executive options play an important role in explaining stock

repurchase behavior.
7

As will be shown later, S≤Vh-Vl ensures that a low-quality firm does not buy back its
7In this paper, we do not formally model the mechanism by which noise traders
underestimate the firm value, but rather use the reduced demand schedule describedabove. Recent articles, such as those of Barberis, Shleifer, and Vishny (1998) and
Daniel, Hirshleifer, and Subrahmanyam (1998), provide mechanisms by which investor
sentiment, based upon psychological theory, leads to market misperception. For
example, if traders have a representative heuristic or are overconfident, then they tend tounderestimate the firm value just after observing a negative surprise. One can imagine ascenario in which the firm experiences an unexpected negative earning surprise prior todate-0, resulting in underestimation by the noise traders. This scenario seems to beconsistent with the fact that firms tend to make open-market repurchase announcements
after an abnormal stock price decline.8, 9The total amount of cash that smart traders invest in the stock of the firm at date-0 is
B0, and the date-0 demand schedule of smart traders is given by B0/P0. Since the stock
price is determined by the market clearing condition that the aggregate demand must be
equal to the unit supply, the date-0 stock price of the firm is given by

P0 = θV h + (1 − θ )V l + C − S + B0 .

(2)shares when the market believes that the firm is a high-quality firm. Also, S≤2C ensuresthat the optimal amount of dollars the firm uses for repurchases is less than the interim
cash flow, C.
8

Under this scenario, many firms tend to announce an open-market repurchaseprogram after systematic pessimistic shock appears. One example of systematic
pessimistic shock may be the crash of 1987. It is well known that many firms
announced open-market repurchase programs in the first few months after the crash.
9

In the efficient market framework, Isagawa (2000) provides a signaling model inwhich a firm chooses to make an announcement of open-market repurchase after it
experiences a stock price decline.
8Note that the stock price of the firm is undervalued unless smart traders invest too much.
Then, the firm has an incentive to repurchase its outstanding shares.
At date-1, knowing the pessimistic shock of noise traders, the firm decides whether
or not it will announce an open-market stock repurchase at date-2. Let j∈{a, n}represent a message sent by the firm, where a means an announcement and n means noannouncement. It should be stressed that the firm does not need to follow through on its
repurchase announcement. It is also possible that the firm buys back its shares without
making an announcement. As described just below, however, the number of shares thefirm can buy back without making an announcement is restricted to a small proportionof its outstanding shares.
Just after receiving a message j∈{a, n}, both noise traders and smart traders update
their demand schedules. Let V(j) denote the noise traders’ assessment of the terminal
cash flow of the firm conditional on a message j. The demand schedule of noise traderschanges to [V(j)+C-S]/P1(j), and the demand schedule of smart traders changes to
B1(j)/P1(j), where P1(j) is the date-1 stock price of the firm conditional on a message j. It
follows from the market clearing condition that the date-1 stock price is given by
P1 ( j ) = V ( j ) + C − S + B1 ( j ) ,j∈{a, n}.

(3)

At date-2, an interim cash flow is realized and the firm decides on the amount ofcash it will use to repurchase shares. Let K(j; t)≥0 denote the amount of cash used bytype t∈{h, l} following the date-1 message j∈{a, n}. Throughout the paper, the externalfinancing problem is assumed away. 10 If the firm makes an announcement ofrepurchase intention, it can then invest any dollars up to the interim cash flow amount,10

Vermaelen (1981) says that open-market repurchases are mainly financed withinternal funds. Furthermore, in our model, the optimal amount of dollars that the firmuses for repurchasing following an announcement is less than the interim cash flow, C,
under the condition of S≤2C. For more on this point, see section 3.
9that is, K(a; t)≤C. On the other hand, the amount of dollars that the firm can use for
repurchasing without announcement is restricted to D<C, that is, K(n; t)≤D<C. We
assume that if the firm uses more than D dollars to buy back its shares without
announcement, then it will be suspected of stock price manipulation or insider trading
and a deadweight cost will be imposed on the manager of the firm. Without loss ofgenerality, we assume that repurchased shares are redeemed.
The date-2 demand schedule of noise traders conditional on a message j is[V(j)+C-S]/P2(j), and that of smart traders is B2(j)/P2(j). In addition, the firm of type t
repurchases K(j; t)/P2(j) shares. Therefore, the date-2 stock price of the firm conditionalon a message j is given by
P2 ( j ) = V ( j ) + C − S + B2 ( j ) + K ( j; t ) ,j∈{a, n}, t∈{h, l}.

(4)

At date-3, the terminal cash flow of the firm is publicly realized, and bothinformational asymmetry and the pessimistic noise disappear. After realizing the true
value of the firm, noise traders correct their assessment on the firm value so that theundervaluation disappears.11 Since the number of outstanding shares is 1-K(j; t)/P2(j)and the residual cash is Vt+C-K(j; t), the date-3 stock price of the firm is given by
V t + C − K ( j; t ) P2 ( j )[V t + C − K ( j; t )]P3 ( j; t ) ==, j∈{a, n}, t∈{h, l}.
1 − K ( j; t ) / P2 ( j )V ( j ) + C − S + B2 ( j )(5)The objective of the firm is to maximize the date-3 stock price, so the firm chooses a

11

Alternatively, we can consider the situation in which noise traders gradually correct

their pessimistic assessment on the firm value. Daniel, Hirshleifer, and Subrahmanyam(1998) show that mispricing caused by overconfidence is partially corrected whenpublic information arrives. In our model, public information arrives at date-1(repurchase announcement) and date-2 (actual repurchases). Although it is necessary toassume S0>S1>S2 under this scenario (St is the magnitude of date-t pessimistic shock),
the results will not essentially change.
10

pair of {j, K} that maximizes (5). By plugging (4) into (5) and differentiating (5) withrespect to K(j; t), we obtain the following lemma.

Lemma 1. Let us definef ( j; t ) = [V t − V ( j ) + S − B2 ( j )] / 2 .
Suppose that f( j ;t)≥0. Then, the date-3 stock price, P3(j; t), increases with K(j; t) whenK(j; t)<f(j; t) and decreases with K(j; t) when K(j; t)> f(j; t).

Lemma 1 says that, for any B2(j), the optimal amount of dollars the firm invests in its
shares is given by f(j; t).

In order to incorporate the market inefficiency into the model, we assume that smart
traders are competitive and incur a cost, R>0, to take per dollar position for one period(between two dates). As argued by Shleifer and Vishny (1990, 1997) and Shleifer (2000),
most professional smart traders do not manage their own money in the real world. Since
smart traders have to finance outside money, transaction costs caused by theimperfections in the money market are required. In addition, as shown by Shleifer and
Vishny (1997), the agency relationship between smart traders (fund managers) and theirfund providers may result in an agency cost on smart traders. It should be stressed thatthe misperception of noise traders is quickly and completely eliminated in the case of
rational smart traders who can take any position without cost. In contrast to smart
traders, the firm does not need to pay an additional cost for purchasing its sharesbecause it uses only internal funds.12

12

The idea of costly smart money is the central argument of market inefficiency(Shleifer (2000, p.13)). This assumption also holds when the individual smart trader isrisk-averse and there exists uncertainty with regard to the firm value (fundamental risk)
11

Under the above assumption of costly smart money, smart traders decide to take a
non-zero position (B≠0) if and only if the gross return per dollar position exceeds R, or
the rate of return exceeds R-1. The competition among smart traders ensures that thegross return for one period is equal to R or the rate of return is equal to R-1 wheneversmart traders take a non-zero position. To ensure that the date-2 total demand of smart
traders is strictly positive in the equilibrium, we assume that
1 < R < 1 + (V h − V l ) / 2(V l + C ) .

(6)

The second inequality requires that the cost of smart traders is not too large. When thecost is too large, smart traders will not take any position even if the stock price ismispriced. Since the third term is strictly larger than 1, there exists an R that satisfies(6).

3. Corporate Open-Market Repurchase Strategy

In this section, we consider signaling equilibria in which the high-quality firmchooses to make an announcement of repurchase intention and the low-quality firmchooses not to announce. In particular, we focus our attention on the equilibrium inwhich the noise traders’ assessment of the terminal cash flow, V(j), is correct, that is,
V(a)=Vh and V(n)=Vl.
First, let us consider the equilibrium path following a repurchase announcement(j=a). Here, we analyze the case in which the date-2 position of smart traders is strictly
positive (B2(a)>0).13 In this case, we have two conditions to solve the equilibrium B2(a)and noise process (noise trader risk). The assumption that the cost incurred on the firm
is lower than the cost incurred on smart traders is also persuasive in such a risk-averse
setting because the individual investor is likely to be more risk-averse than the firm.
13

If B2(a)=0, the following analysis is somewhat simplified, but the essence of the12and K(a; h). One is the condition of smart traders, that is, smart traders have to earn R
dollars per dollar investment. This condition is given by P3(a; h)=RP2(a). The othercondition requires that the high-quality firm maximizes its date-3 stock price. Fromlemma 1, this condition is given by K(a; h)= f(a; h). By solving these two equations, we
can obtain the following proposition.

Proposition 1. Suppose2( R − 1)(V h + C ) /(2 R − 1) < S ≤ V h − V l .

(7)Then, in the equilibrium,
B2 (a ) = S − 2( R − 1)(V h + C ) /(2 R − 1) > 0 ,(8)

K (a; h) = ( R − 1)(V h + C ) /(2 R − 1) .

(9)Under (6), there exists an S that satisfies (7).
Proof: See Appendix.

In the proposed equilibrium, the high-quality firm has an intense incentive to buyback its shares on the market after it makes an announcement of repurchase intention,
because the firm can earn capital gains by repurchasing its outstanding shares at abargain price. To see this, by plugging (8) and (9) into (4) and (5) and rearranging, thedate-2 and date-3 stock prices following an announcement are given by
P2 (a ) = V h + C − ( R − 1)(V h + C ) /(2 R − 1) ,(10)

P3 (a; h) = V h + C + ( R − 1) 2 (V h + C ) /(2 R − 1) = RP2 (a) .

(11)Equation (10) means that the date-2 stock price of the high-quality firm is lower
than its fundamental value, Vh+C. Equation (11) means that the date-3 stock price ishigher than Vh+C. The term of (R-1)2(Vh+C)/(2R-1) in (11) represents capital gains
obtained by a stock repurchase at date-2. It can be easily shown that the date-3 stock

results will not change.
13

price is equal to Vh+C if the high-quality firm does not buy back its shares. Note that
P3(a)=RP2(a) holds because of the condition of smart traders.
Since the demand of the high-quality firm for its shares is strictly positive (K(a;h)>0), the undervaluation caused by the pessimistic noise is partly mitigated at date-2.
In this sense, it can be interpreted that an open-market stock repurchase is a supply ofsmart money. The firm does not provide sufficient money to bring the stock price to its
fundamental value, however, because it loses the opportunity for capital gains by doingso.
Next, we consider the equilibrium path following no announcement. In this case, thetotal amount of dollars that the low-quality firm can use for repurchasing is restricted up
to D. For analytical simplicity, we suppose that D is so small that the firm always uses
D for repurchasing. Formally, we assume that0 ≤ D ≤ ( R − 1)(V l + C ) / 2 R ≡ D * .

(12)

The following proposition characterizes the date-2 total demand of the low-quality firm
and that of smart traders conditional on the absence of a repurchase announcement(j=n).

Proposition 2. Suppose (12) is satisfied. Then, in the equilibrium,

K (n; l ) = D ,(13)

B2 (n) = S − [( R − 1)(V l + C ) + D] / R > 0 .

(14)

Proof. See Appendix.

It follows from (13) and (14) that the date-2 and date-3 stock prices following noannouncement are given by
P2 (n) = V l + C − ( R − 1)(V l + C − D) / R ,(15)

P3 (n; l ) = V l + C + ( R − 1) D = RP2 (n) .

(16)

14

Since the date-2 stock price is undervalued (P2(n)<Vl+C), the low-quality firm also has
an incentive to buy back its shares even though it does not make an announcement ofrepurchase intention. The term of (R-1)D in the equation (16) represents capital gains
generated from stock repurchasing.
In order to establish the proposed equilibrium, we have to show that both types offirms have no incentive to deviate from the equilibrium strategy. It is easy to show thatthe low-quality firm never chooses to make an announcement. To see this, note that
P2 (a ) = V h + C − S + B2 (a) > V l + C .
The inequality follows from (1) and (8). Since the date-2 stock price following anannouncement is larger than its fundamental value, repurchasing any shares results in acapital loss at date-3. Therefore, the low-quality firm never buys its shares if it makes anannouncement. It should be stressed that an announcement of repurchase intention is nota firm commitment in our model. As a result,P3 (a; l ) = V l + C < V l + C + ( R − 1) D = P3 (n; l ) .

(17)

Thus, the low-quality firm has no incentive to deviate from the equilibrium strategy.
By choosing not to make an announcement, the high-quality firm faces a tradeoff.
That is, while the high-quality firm can buy back its shares at a lower price than it canon the equilibrium path, the amount of dollars it can use for repurchasing is restricted toD. If D is so small that the capital gains is smaller than the capital gains possible on theequilibrium path, then the high-quality firm does not deviate from the equilibrium
strategy. In fact, we can obtain the following Lemma.

Lemma 2. Let us defineg ( D) ≡ D[ R(V h + C − D) /(V l + C − D) − 1] , 0≤D<Vl+C.

(18)

Then, there exists D**∈(0, Vl+C) such thatg ( D ** ) = ( R − 1) 2 (V h + C ) /(2 R − 1) .

(19)

15

Suppose that0 ≤ D ≤ min{D * , D ** } ,(20)

where D* is given by (12) and D** is given by (19). Then,P3 (a; h) ≥ P3 (n; h) .

(21)

Proof. See Appendix.

As shown in the Appendix, g(D) represents capital gains that the high-quality firm
can earn by choosing no announcement. On the other hand, from equation (11), we
know that (R-1)2(Vh+C)/(2R-1) represents capital gains that the firm can earn by making
an announcement. Since g(D) increases with D, the condition (20) ensures that thecapital gains the high-quality firm can earn by choosing an announcement is larger thanwhat the firm can earn by choosing no announcement. The high-quality firm thenchooses to make an announcement under (20).
From the above arguments, under a set of parameters (Vh, Vl, C, S, R, D) thatsatisfies (1), (6), (7), and (20), the proposed signaling equilibrium exists.

Proposition 3. There exists a signaling equilibrium in which the high-quality firm makes
an announcement of open-market repurchase intention and the low-quality firm does notmake such an announcement.

In our model, the high-quality firm chooses to make an announcement of
open-market repurchase intention in order to buy back a relatively large number ofshares. On the other hand, the low-quality firm chooses not to announce an intention to
repurchase shares because it cannot earn any capital gain following such anannouncement.

4. Stock Price Behavior and Empirical Implications

16

In this section, we examine stock price behavior in the equilibrium and show someof the empirical implications of our analysis. The following proposition characterizes
date-0 and date-1 stock prices.

Proposition 4. In the proposed equilibrium,
P1 (a ) = P2 (a) / R = P3 (a, h) / R 2 ,(22)

P1 (n) < P0 < P1 (a ) .

(23)

Proof. See Appendix.

It follows from (23) that, in the proposed equilibrium, the stock price goes up in
response to a repurchase announcement (P0<P1(a)). This is consistent with the typicalempirical results of the immediate positive stock price reaction to open-market
repurchase announcements.
In addition, the equation (22) shows that the date-2 stock price of the high-quality
firm is larger than the date-1 stock price (P1(a)<P2(a)), and the date-3 stock price islarger than the date-2 price (P2(a)<P3(a; h)). That is, our model predicts that the stock
price continues to go up gradually subsequent to an announcement of an open-market
repurchase program. This prediction is consistent with the empirical findings reported
by Ikenberry, Lakonishok, and Vermaelen (1995). Thus, our model can explain both thepositive return at the announcement of a repurchase intention and the long-run positive
return observed subsequent to the announcement.
In our model, the long-run stock return subsequent to an open-market repurchaseannouncement is given by[ P3 (a; h) − P1 (a)] / P1 (a ) = R 2 − 1 .

(24)Note that the magnitude of the pessimistic noise does not directly affect the long-run

17

return. This is the result from the condition of competition among smart traders.
The long-run return represented in (24) increases with a cost R of smart traders.
Pontiff (1996) argues that costs of smart traders include both transaction costs such as
brokerage fees, market impact costs, and bid-ask spreads, and holding costs such as
borrowing costs, opportunity costs due to a margin requirement of short-sale proceeds,
and risk exposure from imperfectly hedged positions. Our model then predicts that themagnitude of the long-run abnormal performance following open-market repurchaseannouncements has positive relationships with these costs.14
With regard to actual repurchases of an announcing firm, the equation (9) implies
that the amount of dollars the firm uses for repurchasing increases with its interim cash
flows. Stephens and Weisbach (1997) find that share repurchases of firms are positively
related to their cash flows. This evidence is consistent with our prediction. The size ofthe repurchase program given by (9) also increases with R, as does the long-run return(see above). That is, given C and Vh, both the size of the repurchase program and thelong-run return increase when R increases. In this sense, our model predicts a positive
relationship between the repurchase size and the long-run performance.15
Finally, in contrast to previous studies, our model suggests that a non-announcing
firm may buy back its outstanding shares on the market. It is difficult to examine
whether or not firms actually buy back their shares on the open market without making
a repurchase announcement. However, from the viewpoint of the institutions, firms are
not required to announce their intention to make open-market stock repurchases.

14

In his empirical work, Pontiff (1996) uses the inverse of the stock price of a firm andmarket equity value as transaction cost proxies, and the short-term interest rate anddividend yield as holding cost proxies.
15

Since we do not calculate P0, we cannot show any relationship between the

repurchase size and the announcement period return.
18

5. Discussions

There are several additional points worth discussing. First, in our model, an
open-market stock repurchase is superior to cash dividends. Suppose that the firmchooses to distribute all the interim cash flow, C, as cash dividends in place of stock
repurchases. By choosing cash dividends, the firm loses the opportunity to earn capitalgains, because the firm cannot purchase its outstanding shares at a bargain price. In thatcase, the date-3 stock price following the distribution of cash dividends is lower thanthat following stock repurchases. There is an obvious incentive for the firm to substitutestock repurchases for cash dividends when its stock price is undervalued. Conversely,
the firm tends to choose cash dividends when its stock price is overvalued. The firm
incurs capital losses if it buys backs overpriced shares.
Next, the above results still hold when interim cash flow is uncertain or when
pessimistic noise disappears before date-2 stochastically. Suppose that the firm
generates an interim cash flow, C>0, with probability p (0<p<1), and generates no cash
flow with probability 1-p. In this case, the firm buys back its shares with only
probability p. With positive probability 1-p, the firm refrains from purchasing its shareseven after it makes an announcement of repurchase intention.16 In a situation where thepessimistic noise is random, the firm executes a repurchase only when the stock price isundervalued by the pessimistic noise. The firm has no incentive to buy back its
outstanding shares unless the market is subject to pessimistic noise.
This argument shows the advantage of open-market repurchases over tender offers.
In contrast to open-market repurchases, the firm must follow through after its tender

16

Even if external funds are available for the firm, it has no incentive to raise externalfunds for repurchasing when the financing cost is equal to R.
19

offer announcement. Suppose that the firm incurs additional cost to raise external funds
as smart traders do. Having made a tender offer, the firm has to incur the cost whenneither interim cash flow nor pessimistic noise persists. On the other hand, the firm does
not have to pay this cost under an open-market stock repurchase program. Thus, in thecurrent model, an open-market repurchase is more desirable than a tender offer. Thisadvantage of an open-market repurchase comes from its flexibility. Ikenberry andVermaelen (1996) and Stephens and Weisbach (1998) stress the flexibility of
open-market stock repurchases.
The results of the paper may hold when the firm considers the date-1 stock price inaddition to the date-3 stock price. Suppose that the objective function of the firm is

αP1 ( j ) + (1 − α ) P3 ( j; t ) ,(25)

where α (0<α <1) is the weight on the date-1 stock price. It immediately follows from
P1(n)<P1(a) and P3(n; h)<P3(a; h) thatαP1 (n) + (1 − α ) P3 (n; h) < αP1 (a) + (1 − α ) P3 (a; h) .

(26)

Thus, the high-quality firm chooses to make an announcement.
In order to ensure that the low-quality firm chooses not to announce, we must placean additional restriction on α such thatαP1 (a ) + (1 − α ) P3 (a; l ) ≤ αP1 (n) + (1 − α ) P3 (n; l ) .

(27)

In this way, it might be shown that the results still hold when the firm attends to thedate-2 stock price in addition to the date-1 and date-3 stock prices.
Finally, the arguments developed in this paper may still hold when informational
asymmetry exists with regard to interim cash flow rather than terminal cash flow. The
low-quality firm, which has relatively small interim cash flow, has no incentive toannounce an open-market repurchase intention since the firm has to repurchase its
shares at a higher price at date-2. However, if the low-quality firm does not announce, it
may still earn capital gains as a result of the pessimistic noise. The high-quality firm,
which has relatively large interim cash flow, should continue to announce in order to20

earn capital gains from purchasing a relatively large number of shares. This argument
implies that announcing firms have relatively higher cash flows than non-announcing
firms.

6. Conclusion

In this paper, we reexamined open-market stock repurchases under the condition ofboth informational asymmetry and market inefficiency. The market is inefficient in thesense that smart traders are costly so that the mispricing caused by noise traders is notcompletely removed. The firm makes use of this market mispricing. In particular, whenthe market undervalues the stock of the firm, the firm can enjoy capital gains byrepurchasing its outstanding shares at a bargain price. Thus, in our model, the firm has
an intense incentive to actually buy back its shares following an announcement ofrepurchase intention even though the announcement is not a firm commitment.
Capital gains that the firm can earn through open-market repurchase activity cause
the positive performance of long-run stock returns. Our model predicts that the stock
price will continues to increase even after it rises in response to an announcement.
These predictions are consistent with typical empirical findings.

Appendix

Proof of Proposition 1. We claim that P3(a; h)≥P2(a) and 0≤B2(a)≤S hold as follows.
From (5), if P3(a; h)<P2(a), then K(a; h)+B2(a)>S must hold. This means that at least
one of K(a; h) and B2(a) is strictly positive. However, the firm and smart traders nevertake long positions, because long positions result in a capital loss at date-3. Therefore,
P3(a; h)≥P2(a), in which case taking short positions at date-2 does not generate capitalgains at date-3. Therefore, B2(a)≥0. Again, from (5), P3(a; h)≥P2(a) means B2(a)≤S.

21

It follows from (1) and Lemma 1 that
K (a; h) = [ S − B2 (a )] / 2 ≤ C .

(a. 1)

Since smart traders have to earn R dollars per dollar investment,
P3 (a; h) = RP2 (a) ⇔ V h + C − K (a; h) = R[V h + C − S + B2 (a)] .

(a. 2)In the equilibrium, K(a; h) and B2(a) must satisfy (a. 1) and (a. 2) simultaneously. Bysolving them, we can obtain (8) and (9). It is clear that B2(a)>0 under (7).
The remaining point is to show that there exists an S that satisfies (7). Note that
(V h − V l ) − 2( R − 1)(V h + C ) /(2 R − 1) = [(V h − V l ) − 2( R − 1)(V l + C )] /(2 R − 1) > 0 .
The inequality follows from (6). Therefore, there exists an S that satisfies (7).

Proof of Proposition 2. By applying (a. 2) to this case, we obtain
B2 (n) = S − [( R − 1)(V l + C ) + K (n; l )] / R ≤ S − ( R − 1)(V l + C ) / R .

(a. 3)The inequality follows from K(n; l)≥0. Then,[ S − B2 (n)] / 2 ≥ ( R − 1)(V l + C ) / 2 R = D * ,(a. 4)

It follows from Lemma 1, (12), and (a. 4) that
K (n; l ) = min{D, [ S − B2 (n)] / 2} = D .

(a. 5)

By plugging K(n; l)=D into the first equation of (a. 3), we can obtain (14). Furthermore,2( R − 1)(V h + C ) /( 2 R − 1) − [( R − 1)(V l + C ) + D] / R= [2 R ( R − 1)(V h − V l ) + ( R − 1)(V l + C ) − 2 RD + D] /( 2 R − 1) R > 0(a. 6)

holds under (12). From (a. 6), (8), and (14), B2(n)>B2(a)>0.

Proof of Lemma 2. It follows from Lemma 1 and (14) that, under D≤D*, the amount of
dollars that the high-quality firm uses for repurchasing is given by
K (n; h) = min{D, [V h − V l + S − B (n)] / 2} = D .

(a. 7)

Then, the date-3 stock price of the high-quality firm following no announcement is
Vh +C −D
P3 (n; h) == V h + C + g ( D) ,(a. 8)
1 − D / P2 (n)22whereg ( D) ≡ D[ R(V h + C − D) /(V l + C − D) − 1] .

(a. 9)

Note that g(D) is strictly increasing and is continuous with D for 0≤D<Vl+C. Sinceg(0)=0 and g(D)→∞ as D→Vl+C, there exists a D**∈(0, Vl+C) that satisfies (19). From(11) and (a. 8), we see that the high-quality firm does not deviate from the equilibrium
strategy if and only if
P3 (a; h) ≥ P3 (n; h) ⇔ g ( D ** ) = ( R − 1) 2 (V h + C ) /(2 R − 1) ≥ g ( D) .

(a. 10)Since g(D) is strictly increasing with D, g(D)≤g(D**) for 0<D≤D**. Therefore, (a. 10)
holds for D such that 0≤D≤min{D*, D**}. There exists D such that 0≤D≤min{D*, D**}because 0≤D* and 0<D**.

Proof of Proposition 4. First, we consider P1(a). If B1(a)<0, then P1(a)<Vh+C-S<P2(a).
The second inequality follows from (7). This means that smart traders lose their moneyby taking a short position. If B1(a)=0, then P1(a, B1(a)=0)<RP2(a). The inequality
follows from (7). This means that smart traders can earn capital gains larger than R by
taking a long position. Therefore, B1(a)>0. In this case, B1(a) is determined by thecondition of P1(a, B1(a))=RP2(a). By solving this equation, we can obtain
B1 (a ) = S − 2( R − 1)(V h + C ) /(2 R − 1) > 0 .
The inequality follows from (7). Then, (22) holds in the equilibrium.
Next, we show that P1(n)<P1(a). Suppose that P1(n)≥P1(a). In this case, B1(n)>S
holds because
B1 (n) − S > B1 (n) − S − B1 (a) ≥ B1 (n) − (V h − V l ) − B1 (a) = P1 (n) − P1 (a ) ≥ 0 .
Since P1(n, B1(n)>S)>Vi+C>P2(n), smart traders incur capital loss by taking such a large
long position. Therefore, P1(n)<P1(a).
Finally, consider the relationship between P0 and P1(j). It follows from (2), (3), andB1(a)>0 that B0>0 has to hold when P1(a)≤P0. Since P1(n)<P1(a)≤P0, smart traders incur23

capital loss by taking such a long position at date-0. Therefore, P0<P1(a). It also follows
from (2), (3), and B1(n)≥0 that B0<0 has to hold when P0≤P1(n). Note that we can show
B1(n)≥0 by using an argument similar to that for B1(a). Since P0≤P1(n)<P1(a), thisdate-0 short position brings capital loss to smart traders. Therefore, P1(n)<P0.
[2002.5.16 615]

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26

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27

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
Katsuhiko Kokubu

2001･10

2001･25

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

3／2001The 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(in Japanese)

Environmental Reporting of Japanese companies

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(in Japanese)

8／2001

Discussion Paper
No.

2001･26
2001･27

AuthorTomomi 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 Accounting of Japanese companies
Elementary 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―

Date(in Japanese)

8／20019／2001(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