A. Trading Equilibrium with Buybacks

This section analyzes the implications of a buyback program for trading outcomes. The authorization of a buyback program at $ t=0 $ makes the firm an active participant in the market for its shares, with the manager effectively becoming another informed trader at $ t=1 $ . In this section, I assume that the manager executes buybacks with probability $ {b}_1=1 $ when firm fundamentals are high ( $ A=1 $ ) and with probability $ {b}_0\in \left[0,1\right] $ when fundamentals are low ( $ A=0 $ ). Section IV shows that such a buyback strategy is indeed optimal for a manager who maximizes a weighted combination of the firm’s stock price at $ t=1 $ and the per-share value at $ t=2 $ .Footnote ¹⁴ One interpretation of the buyback strategy is that the manager executes a fraction $ {b}_0 $ of the program in an uninformed manner—buying $ x $ shares regardless of fundamentals—and the remaining fraction $ 1-{b}_0 $ in an informed manner—buying only when fundamentals are high. Under this interpretation, $ 1-{b}_0 $ measures the informativeness of buybacks. As $ {b}_0 $ increases, the difference in the execution probabilities in good and bad states narrows, and buybacks become less informative. Buybacks are fully uninformed when $ {b}_0=1 $ : the manager buys with the same probability in good and bad states, so buybacks carry no information about fundamentals.

A buyback program changes the trading equilibrium in important ways. The following lemma characterizes the new trading equilibrium with buybacks (denoted with subscript $ B $ ):

Lemma 2. Given a stock buyback program and the manager’s buyback execution strategy $ \left({b}_1=1,{b}_0\right) $ , the equilibrium pricing rule is

(3) $$ {P}_B(q)=\left\{\begin{array}{ll}0& if\;q=-x,\\ {}\frac{\theta \left(1-\phi \right)\left(1+k\right)}{\theta \left(1-\phi \right)\left(1+k\right)+\left(1-\theta \right)\left(1+{kb}_0\right)}& if\;q=0,\\ {}\frac{\theta }{\theta +\left(1-\theta \right){b}_0}& if\;q=x,\\ {}1& if\;q=2x,\end{array}\right. $$

and the speculator buys $ x $ shares if and only if he learns that firm fundamentals are high ( $ A=1 $ ).Footnote ¹⁵

A stock buyback program introduces two economic forces to trading at $ t=1 $ . First, it affects the market’s inferences about firm fundamentals by altering the information content of the order flow. This informed execution of buybacks makes the order flow more revealing, improving price discovery and lowering informed trading profits. This competition effect is a robust feature of trading frameworks with multiple informed parties. Second, the program generates buyback profits and losses that make the firm’s per-share value more sensitive to its fundamentals. This dispersion effect is unique to the buyback setting.

1. Competition Effect

A buyback program introduces the firm’s manager as an additional informed trader who may execute buybacks in ways that affect the informativeness of the order flow. To see this clearly, consider how the market updates its beliefs about the firm’s fundamentals ( $ A $ ) based on the observed order flow ( $ q $ ): $ \hat{\theta}(q)=\mathit{\Pr}\left(A=1|q\right) $ . In the benchmark without buybacks, the market’s posterior belief is

(4) $$ {\hat{\theta}}_0(q)=\left\{\begin{array}{ll}\frac{\theta \left(1-\phi \right)}{\theta \left(1-\phi \right)+\left(1-\theta \right)}& \mathrm{if}\;q=-x,\\ {}\theta & \mathrm{if}\;q=0\\ {}1& \mathrm{if}\;q=x.\end{array}\right. $$

With buybacks, the market’s posterior belief becomes

(5) $$ {\hat{\theta}}_B(q)=\left\{\begin{array}{ll}0& \mathrm{if}\;q=-x,\\ {}\frac{\theta \left(1-\phi \right)}{\theta \left(1-\phi \right)+\left(1-\theta \right)}& \mathrm{if}\;q=0,\\ {}\frac{\theta }{\theta +\left(1-\theta \right){b}_0}& \mathrm{if}\;q=x,\\ {}1& \mathrm{if}\;q=2x.\end{array}\right. $$

One measure of market informativeness is the difference between the market’s expected posterior belief in the two fundamental states: $\Delta \hat{\theta }=\text{𝔼}[\hat{\theta }|A=1]-\text{𝔼}[\hat{\theta }|A=0]$ . A larger $ \Delta \hat{\theta} $ indicates that the order flow better discriminates between high ( $ A=1 $ ) and low fundamentals ( $ A=0 $ ), with $ \Delta \hat{\theta}=1 $ corresponding to the case where the market perfectly infers the firm’s fundamentals from the order flow. Comparing equations (4) and (5) yields the following result:

Lemma 3. Relative to the benchmark, a buyback program improves market informativeness ( $ \Delta {\hat{\theta}}_B>\Delta {\hat{\theta}}_0 $ ) if buybacks are informed ( $ {b}_0<1 $ ). The improvement increases with buyback informativeness.

When buybacks are uninformed ( $ {b}_0=1 $ ), they simply shift the distribution of the order flow—increasing it by $ x $ —across all fundamental states, as shown in Figure 1. This shift does not affect the information content of the order flow, leaving market informativeness unchanged ( $ \Delta {\hat{\theta}}_B=\Delta {\hat{\theta}}_0 $ ).

FIGURE 1Distribution of Order Flow: No Buybacks Versus Uninformed Buybacks

The upper portion of Figure 1 shows the distribution of the order flow ( $ q $ ) across different firm fundamentals ( $ A $ ) in the absence of a buyback program. The lower portion shows how uninformed buybacks ( $ 1-{b}_0=0 $ ) shift the distribution of the order flow to the right by $ x $ units in all states, leaving the informativeness of the order flow unchanged. Bracketed terms report the probabilities of the corresponding rows.

FIGURE 1 Long description

The chart is divided into two horizontal panels. The top panel, labeled No Buybacks, lists three rows for A equals 0 and A equals 1, each with bracketed probabilities in red. For A equals 0, the probability is open bracket 1 minus theta close bracket, and order flow q is negative x or 0. For A equals 1, the first row has probability open bracket theta times open parenthesis 1 minus phi close parenthesis close bracket, and order flow q is negative x or 0. The second A equals 1 row has probability open bracket theta phi close bracket, and order flow q is 0 or x. Dotted lines connect each probability to its corresponding order flow value. The bottom panel, labeled Uninformed Buybacks, repeats the same three rows for A with identical probabilities, but the order flow q values are shifted rightward: for A equals 0, q is 0 or x; for the first A equals 1 row, q is 0 or x; for the second A equals 1 row, q is x or 2 x. Dotted lines again connect each probability to its new order flow values, illustrating a uniform rightward shift in order flow across all states.

In contrast, informed buybacks ( $ 1-{b}_0>0 $ ) make the order flow more revealing of firm fundamentals. As illustrated in Figure 2, informed buybacks are more likely to shift the order flow distribution rightward when firm fundamentals are high ( $ A=1 $ ) than when they are low ( $ A=0 $ ). This state-contingent shift makes high-order flows more indicative of high fundamentals, and low-order flows more indicative of low fundamentals. The more informative the buybacks (i.e., higher $ 1-{b}_0 $ ), the greater the improvement in market informativeness.

FIGURE 2Distribution of Order Flow: No Buybacks Versus Informed Buybacks

The upper portion of Figure 2 shows the distribution of the order flow ( $ q $ ) across different firm fundamentals ( $ A $ ) in the absence of buybacks. The lower portion illustrates how informed buybacks improve the informativeness of the order flow by shifting the distribution of the order flow to the right more when the firm’s fundamentals are high ( $ A=1 $ ) than when they are low ( $ A=0 $ ). Bracketed terms report the probabilities of the corresponding rows.

FIGURE 2 Long description

The table is divided into two sections. The upper section, labeled No Buybacks, lists three rows for firm fundamentals: A equals 0 with probability one minus theta, A equals 1 with probability theta times open parenthesis one minus phi close parenthesis, and A equals 1 with probability theta phi. Each row connects by dotted lines to order flow q values: minus x, 0, and x. The lower section, labeled Informed Buybacks, has four rows: A equals 0 with probability open bracket one minus theta close bracket times open bracket one minus b sub 0 close bracket, A equals 0 with probability open bracket one minus theta close bracket b sub 0, A equals 1 with probability theta times open parenthesis one minus phi close parenthesis, and A equals 1 with probability theta phi. These connect to order flow values minus x, 0, x, and 2 x. Dotted lines indicate how probabilities map to order flow outcomes, with more mass shifted to higher order flow values under Informed Buybacks, especially when A equals 1.

Informed buybacks that closely track the firm’s fundamentals erode the speculator’s informational advantage by making the order flow more revealing. In other words, informed buybacks compete against the speculator’s informed trades.

These results parallel the classic literature on competing informed traders (e.g., Admati and Pfleiderer (Reference Admati and Pfleiderer1988), Holden and Subrahmanyam (Reference Holden and Subrahmanyam1992), Foster and Viswanathan (Reference Foster and Viswanathan1993), and Back et al. (Reference Back, Cao and Willard2000)), where additional informed parties enhance price informativeness and compress existing traders’ profits. However, a crucial distinction emerges: in conventional models, informed traders use private accounts and personally bear their trading gains and losses. While their activities alter the firm’s ownership composition, they do not directly affect per-share value.Footnote ¹⁶ Consequently, the competition effect completely captures the impact of introducing an additional informed trader.

In my framework, however, the additional informed trader is the manager acting on behalf of the firm. Her buyback trades affect not only the information content of order flow but also the distribution of per-share value through realized trading gains and losses—introducing the novel dispersion effect analyzed next.

2. Dispersion Effect

Buyback activity generates trading gains and losses that accrue to the firm’s remaining shareholders. Consequently, with buybacks, the firm’s per-share value at $ t=2 $ becomes $ V=A+T $ , where $ A $ represents the fundamental payoff from the firm’s assets and $ T $ captures the per-share gains and losses from the firm’s trading activity.

The impact of buybacks on the firm’s per-share value at $ t=2 $ depends on whether its shares are under- or overvalued at $ t=1 $ . When fundamentals are high relative to the market-clearing price at $ t=1 $ ( $ A>{P}_B $ ), the firm buys back undervalued shares, generating trading gains that increase per-share value at $ t=2 $ from $ A $ to $ {V}_H $ (i.e., $ T>0 $ ):

(6) $$ {V}_H=\frac{\overset{\mathrm{fundamentals}}{\overbrace{A}}-\overset{\mathrm{cost}\ \mathrm{of}\ \mathrm{buybacks}}{\overbrace{xP_B}}}{\underset{\mathrm{remaining}\ \mathrm{shares}}{\underbrace{1-x}}}=A\hskip1em +\underset{\mathrm{buyback}\ \mathrm{trading}\ \mathrm{gain}\left({T}_G\right)}{\underbrace{k\left(A-{P}_B\right)}}>A, $$

where $ k=\frac{x}{1-x} $ is the scale of the buyback program. Conversely, when fundamentals are low relative to the market-clearing price at $ t=1 $ ( $ A<{P}_B $ ), the firm buys back overvalued shares, generating trading losses that decrease per-share value at $ t=2 $ from $ A $ to $ {V}_L $ (i.e., $ T<0 $ ):

(7) $$ {V}_L=\frac{\overset{\mathrm{fundamentals}}{\overbrace{A}}-\overset{\mathrm{cost}\ \mathrm{of}\ \mathrm{buybacks}}{\overbrace{xP_B}}}{\underset{\mathrm{remaining}\ \mathrm{shares}}{\underbrace{1-x}}}=A\hskip1em -\underset{\mathrm{buyback}\ \mathrm{trading}\ \mathrm{loss}\;\left({T}_L\right)}{\underbrace{k\left({P}_B-A\right)}}<A. $$

Unlike the trades of speculators, buybacks tend to increase the firm’s per-share value when its fundamentals are high ( $ A=1 $ ) and decrease the firm’s per-share value when its fundamentals are low ( $ A=0 $ ). As a result, buybacks amplify the sensitivity of the firm’s per-share value to its fundamentals—the dispersion effect. Footnote ¹⁷

To quantify this effect, consider the dispersion in the firm’s expected per-share value between good ( $ A=1 $ ) and bad ( $ A=0 $ ) states: $ \Delta V=E\left[V|A=1\right]-E\left[V|A=0\right] $ . In the benchmark without buybacks, this measure simply equals the fundamental spread in asset payoffs: $ \Delta {V}_0=1 $ . With buybacks, the dispersion becomes

(8) $\Delta V_B=(1+\underset{={\overline{T}}_G\ge 0}{\underbrace{\text{𝔼}\left[T|A=1\right]}})-(0+\underset{=-b_0{\overline{T}}_L\le 0}{\underbrace{\text{𝔼}\left[T|A=0\right]}})=\Delta V_0+{\overline{T}}_G+b_0{\overline{T}}_L,$

where $ {\overline{T}}_G $ and $ {\overline{T}}_L $ are the magnitudes of the expected trading gains and losses from executing buybacks when the firm’s fundamentals are high ( $ A=1 $ ) and low ( $ A=0 $ ), respectively.

Lemma 4. Relative to the benchmark, a buyback program strictly increases the dispersion of the firm’s per-share value ( $ \Delta {V}_B>\Delta {V}_0 $ ). The dispersion in per-share value decreases with the informativeness of buybacks $ \left(\frac{\mathrm{\partial \Delta }{V}_B}{\partial {b}_0}>0\right) $ .

Buybacks increase the dispersion of the firm’s per-share value: they tend to raise per-share value when fundamentals are high and reduce it when fundamentals are low. Less informed buybacks amplify value dispersion through two channels. First, they incur larger trading losses in bad states ( $ A=0 $ ), further suppressing value. Second, they make the order flow less informative, which increases the profitability of good-state buybacks, further boosting value in good states ( $ A=1 $ ).

The competition effect of buybacks improves market informativeness and reduces information asymmetry about the firm’s fundamentals among market participants. The dispersion effect works in the opposite direction—the increased sensitivity of the firm’s per-share value to its fundamentals makes any residual private information more valuable for trading. These changes have important economic consequences, as they determine both the efficiency of market prices and the distribution of trading gains between the speculator and the firm’s shareholders.

B. Speculator’s Profits

This section explores how buybacks shape trading outcomes, focusing on the speculator’s expected trading profits. Because these gains come at the expense of shareholders with liquidity needs, they are essential for evaluating how buybacks affect shareholder welfare.

To begin, consider the following measure of price discovery: $ \Delta P=\unicode{x1D53C}\left[P|A=1\right]-\unicode{x1D53C}\left[P|A=0\right] $ . It captures how much market prices differ across fundamental states, with higher values indicating that prices better reflect the firm’s underlying value. In the benchmark without buybacks, price discovery coincides with market informativeness because the firm’s per-share value only depends on the fundamental payoff of its assets ( $ A $ ): $ \Delta {P}_0=\Delta {\hat{\theta}}_0 $ . With buybacks, price discovery involves learning both about fundamentals and about buyback trading gains, which are jointly determined.

At first glance, this result may seem puzzling. The analysis in Section III.A.2 shows that less informed buybacks generate more dispersion in per-share value, suggesting that prices should also diverge more across fundamental states. However, price discovery depends not only on the actual dispersion of per-share value, but also on what the market can infer from the order flow. Section III.A.1 shows that less informed buybacks decrease the information content of the order flow. This effect dominates, and a more informed execution of buybacks improves price discovery.

Recall that $ {q}_S $ denotes the speculator’s order. His expected trading profit can be expressed as

(9) $\Pi =\text{𝔼}\left[q_S\left(V-P\right)\right]=Cov\left(q_S,V-P\right)-\text{𝔼}\left[q_S\right]\text{𝔼}\left[V-P\right]=Cov\left(q_S,V-P\right),$

where the last equality follows from the market-clearing condition ( $ \unicode{x1D53C}\left[V-P\right]=0 $ ). The speculator profits to the extent that his trades covary positively with the deviation of per-share value from price—that is, he gains by buying when the firm’s shares are undervalued and abstaining when they are overvalued.

To build intuition, consider the limiting case with $ \phi \to 1 $ , where the speculator is almost always informed. Recall that the speculator buys ( $ {q}_S=x $ ) if and only if he learns that firm fundamentals are high ( $ A=1 $ ). In this case, the speculator almost always observes fundamentals, so his order ( $ {q}_S $ ) is nearly perfectly correlated with $ A $ , implying that

(10) $$ \Pi =\unicode{x1D53C}\left[{q}_S\left(V-P\right)\right]= x Cov\left(A,V-P\right)= x\theta \left(1-\theta \right)\left(\Delta V-\Delta P\right). $$

and

(11) $$ {\Pi}_B-{\Pi}_0= x\theta \left(1-\theta \right)\left[\left(\Delta {V}_B-\Delta {V}_0\right)-\left(\Delta {P}_B-\Delta {P}_0\right)\right]. $$

This decomposition in equation (11) reveals the tension between the two effects of buybacks. The competition effect improves price discovery ( $ \Delta {P}_B>\Delta {P}_0 $ ), compressing the speculator’s informational advantage. The dispersion effect increases the spread in per-share value across fundamental states ( $ \Delta {V}_B>\Delta {V}_0 $ ), making his private information about firm fundamentals more valuable for trading. Buybacks reduce the speculator’s expected trading profit relative to the benchmark if and only if the competition effect dominates the dispersion effect.

In the more general case with $ \phi \in \left(0,1\right) $ , the speculator is not always informed. As a result, his trades are not perfectly correlated with firm fundamentals, and the expression for his expected trading profit does not decompose cleanly into value dispersion and price discovery components. Intuitively, what matters is how value and prices vary across the speculator’s trading decisions, not just across fundamental states. Nevertheless, the same economic forces apply: the dispersion effect raises the stakes for informed trading, while the competition effect erodes the speculator’s informational advantage. The following proposition formalizes these results:

An immediate implication of Proposition 1 is that uninformed buybacks ( $ {b}_0=1 $ ) unambiguously increase the speculator’s expected trading profits. Uninformed buybacks maximize the dispersion effect while contributing nothing to the competition effect. The speculator benefits from the increased value dispersion without facing any additional competition for trading profits.

The results in this section characterize how buybacks affect the speculator’s expected trading profits, which, in turn, reveal how they affect the aggregate payoffs of the firm’s existing shareholders. For this analysis, the level of informed speculation ( $ \phi $ ) affects the magnitude of changes but not the qualitative conclusions. However, when analyzing how buybacks affect different types of shareholders, the level of informed speculation becomes qualitatively important as well. Section III.C explores these welfare implications.

C. Heterogeneous Shareholder Welfare

A central concern in the literature is that informed buybacks transfer wealth from outside shareholders to insiders—a phenomenon Fried (Reference Fried2013) calls “insider trading via the firm” (see also Barclay and Smith (Reference Barclay and Smith1988), Fried (Reference Fried2005), Buffa and Nicodano (Reference Buffa and Nicodano2008), and Babenko, Tserlukevich, and Wan (Reference Babenko, Tserlukevich and Wan2020) for similar arguments). The mechanism underlying this wealth transfer is not insider status per se, but rather that insiders typically hold their shares until firm value is realized, whereas outside shareholders may need to sell beforehand to satisfy liquidity needs. Hence, this section examines how a buyback program affects shareholders with different exposures to liquidity shocks.

So far, the analysis has been agnostic about how the firm’s ownership is structured. To connect to the literature on wealth transfers between insiders and outside shareholders, I consider two types of investors who initially own the firm: liquidity-exposed and liquidity-insulated, denoted with superscript $ E $ and $ I $ , respectively. Liquidity-exposed shareholders own a fraction $ x $ of the firm; their liquidity needs at $ t=1 $ are the source of noise trade in the model.Footnote ¹⁸ Liquidity-insulated shareholders own the remaining $ 1-x $ shares and hold their position until $ t=2 $ . These two groups represent the extremes of liquidity exposure. The payoffs of shareholders with intermediate exposures can be obtained as convex combinations of the payoffs of these two groups, providing insight into heterogeneous welfare effects—including for insiders and outside shareholders as conventionally defined.

In the benchmark, the firm’s expected per-share value at $ t=2 $ equals $ \theta $ , the expected fundamental payoff of its assets. The expected payoff of liquidity-insulated shareholders is $ {U}_0^I=\left(1-x\right)\theta $ . The expected payoff of liquidity-exposed shareholders is $ {U}_0^E= x\theta -{\Pi}_0 $ . Because of their liquidity needs at $ t=1 $ , the speculator’s trading profits come at their expense.

With buybacks, the firm’s expected per-share value at $ t=2 $ becomes $ \theta +\unicode{x1D53C}\left[T\right] $ , where $ \unicode{x1D53C}\left[T\right] $ is the expected per-share trading gains of its buyback program. The expected payoff of liquidity-insulated shareholders becomes $ {U}_B^I=\left(1-x\right)\left(\theta +\unicode{x1D53C}\left[T\right]\right) $ .

An informed manager who executes buybacks based on her private information about firm fundamentals earns trading profits in expectation: she is more likely to buy back shares when they are undervalued than when they are overvalued. The more buybacks reflect the manager’s private information, the larger the expected profits from buybacks.

Because the firm’s liquidity-insulated shareholders hold their shares until $ t=2 $ , they avoid adverse-selection trading costs at $ t=1 $ . Instead, they benefit from the trading gains generated by informed buybacks. Lemma 6, therefore, implies that liquidity-insulated shareholders are always weakly better off with a buyback program, strictly so if buybacks are informed ( $ {b}_0<1 $ ). This result echoes a concern emphasized by Barclay and Smith (Reference Barclay and Smith1988) and others in the literature: informed buybacks benefit those who hold their shares until firm fundamentals are revealed at the expense of those who may need to sell earlier. This traditional perspective implies that liquidity-exposed shareholders prefer less informed buybacks to limit this wealth transfer. Whether this conclusion holds, however, depends on the prevalence of informed speculation ( $ \phi $ ) in the market.

To see why, note that buybacks present a more complex trade-off for liquidity-exposed shareholders because they affect two wealth transfers: one to liquidity-insulated shareholders and another to the speculator. With buybacks, the expected payoff of liquidity-exposed shareholders is

(12) $$ {U}_B^E=\underset{\mathrm{fundamental}\ \mathrm{payoff}}{\underbrace{x\theta}}-\underset{\mathrm{transfer}\ \mathrm{to}\ \mathrm{liquidity}\hbox{-} \mathrm{insulated}\ \mathrm{shareholders}}{\underbrace{\left(1-x\right)\unicode{x1D53C}\left[T\right]}}-\underset{\mathrm{transfer}\ \mathrm{to}\ \mathrm{speculator}}{\underbrace{\Pi_B.}} $$

The first term ( $ x\theta $ ) is the fundamental value of the liquidity-exposed shareholders’ stake. The second term ( $ \left(1-x\right)\unicode{x1D53C}\left[T\right] $ ) reflects a wealth transfer to liquidity-insulated shareholders, who capture a fraction of the expected buyback gains without incurring trading costs. The final term ( $ {\Pi}_B $ ) is the wealth transfer to the speculator, whose informed trades profit at the expense of liquidity-exposed shareholders. One can interpret the last two terms as the reduction in the expected payoff of liquidity-exposed shareholders due to illiquidity.

More informative buybacks have two opposing effects on this payoff. They increase the wealth transfer to liquidity-insulated shareholders, but also decrease the wealth transfer to the speculator. In general, the net effect is ambiguous and can be nonmonotonic.

(13) $$ \frac{\partial {U}_B^E}{\partial {b}_0}=-\left(1-x\right)\underset{<0}{\underbrace{\frac{\partial \unicode{x1D53C}\left[T\right]}{\partial {b}_0}}}-\underset{>0}{\underbrace{\frac{\partial {\Pi}_B}{\partial {b}_0}}}\gtrless 0. $$

However, we can characterize the effects when informed speculation ( $ \phi $ ) is sufficiently rare or sufficiently prevalent. When informed speculation is sufficiently rare, liquidity-exposed shareholders face limited adverse-selection trading costs in the benchmark, so the benefit of reducing the speculator’s profits is small. In this case, the wealth transfer to liquidity-insulated shareholders dominates, and liquidity-exposed shareholders prefer less informative buybacks.

This result aligns with the conventional view in the literature, which abstracts from informed speculation and concludes that liquidity-exposed shareholders prefer less informed buybacks to limit the wealth transfer to liquidity-insulated shareholders, such as insiders. Proposition 2 shows that this conclusion holds when informed speculation is sufficiently rare—including the limiting case of $ \phi \to 0 $ implicitly assumed in many prior studies.

When informed speculation is sufficiently prevalent, the opposite can occur. Liquidity-exposed shareholders face substantial adverse-selection costs in the benchmark, so the benefit from reduced speculator profits can more than offset the wealth transfer to liquidity-insulated shareholders.

Proposition 3 suggests that the firm can use informed buybacks to protect its liquidity-exposed shareholders from adverse-selection trading costs, consistent with the findings of Wiggins (Reference Wiggins1994), who documents that the adverse-selection component of the bid–ask spread tends to widen before the authorization of a buyback program and narrow afterward. More recently, Hillert, Maug, and Obernberger (Reference Hillert, Maug and Obernberger2016) conclude that “the information content of repurchases is not associated with a deterioration of liquidity […] higher information content seems to be associated with improvements and not with deterioration in liquidity at the time repurchases were executed.”

The preceding analysis might suggest that uninformed buybacks are benign—they minimize wealth transfers to insiders while avoiding the complications of informed execution. They are not:

At first glance, Corollary 1 may seem puzzling. Uninformed buybacks—which are always executed regardless of firm fundamentals—neither make nor lose money in expectation. Why should they harm liquidity-exposed shareholders?

The crux of the result is that the speculator’s informed trading induces a correlation between the liquidity trades of liquidity-exposed shareholders and the profitability of buybacks. The presence of informed speculative trading ( $ \phi >0 $ ) results in an equilibrium pricing rule that increases with order flow even when buybacks are uninformed. When liquidity-exposed shareholders sell to meet liquidity needs, they simultaneously reduce their stake in the firm and push down the price at which buybacks are executed. Consequently, they are less likely to retain shares in states where buybacks generate gains. Even though uninformed buybacks break even in expectation, liquidity-exposed shareholders receive a disproportionately small share of the gains and bear a disproportionately large share of the losses. This correlation causes liquidity-exposed shareholders to incur net losses from uninformed buybacks. Such a channel is absent in conventional models without buybacks, where informed speculation affects only the price at which liquidity-exposed shareholders sell, not the per-share value of the shares they retain.

The stock buyback literature often emphasizes how informed buybacks can hurt liquidity-exposed shareholders (e.g., Barclay and Smith (Reference Barclay and Smith1988), Brockman and Chung (Reference Brockman and Chung2001), Buffa and Nicodano (Reference Buffa and Nicodano2008), Fried (Reference Fried2013), and Babenko et al. (Reference Babenko, Tserlukevich and Wan2020)). This conventional view suggests that firms could protect them by committing not to use the manager’s private information when executing buybacks. The analysis in this section shows that this view is incomplete. While informed buybacks do transfer wealth to liquidity-insulated shareholders, uninformed buybacks are not a neutral alternative. They subject liquidity-exposed shareholders to additional adverse-selection costs arising from the speculator’s informed trades. In fact, when informed speculation is sufficiently prevalent, informed buybacks can actually benefit liquidity-exposed shareholders by reducing the speculator’s profits (Proposition 3). The desirability of informed versus uninformed buybacks thus depends critically on the level of informed speculation already present in the market.

A. Insider-Aligned Board

Because the buyback program generates weakly positive expected trading gains (Lemma 6), insiders benefit from buybacks. Hence, an insider-aligned board always authorizes, implying that restrictions on authorization come from outside shareholder influence.

B. Aggregate Payoff Maximization

Suppose the board maximizes the aggregate payoff of all existing shareholders. Proposition 1 implies a cutoff rule: authorize if and only if buybacks are anticipated to be sufficiently informed ( $ {b}_0^{\ast }<{\overline{b}}_0 $ ). Proposition 5 then suggests that authorization is more likely when expected firm fundamentals ( $ \theta $ ) are higher, informed speculation ( $ \phi $ ) is less prevalent, and market conditions support larger buyback programs ( $ k $ ).

The intuition follows from the manager’s execution incentives. Higher expected fundamentals and larger programs make bad-state buybacks more costly, increasing the anticipated informativeness of buybacks. Greater liquidity (lower $ \phi $ ) reduces the price impact of order flow, limiting the manager’s ability to inflate the interim stock price with bad-state buybacks. These factors increase the likelihood that the anticipated informativeness of buybacks exceeds the authorization threshold.

These predictions align with documented patterns of buyback activity. The procyclical nature of authorizations, as documented by Jagannathan, Stephens, and Weisbach (Reference Jagannathan, Stephens and Weisbach2000) and Dittmar and Dittmar (Reference Dittmar and Dittmar2008), is consistent with firms authorizing when expected fundamentals are high. Notably, this prediction concerns ex ante expectations at the time of authorization, not ex post realizations—firms authorize when they expect fundamentals to be strong, which differs from the undervaluation hypothesis that firms repurchase when they believe their stock is currently underpriced. The empirical finding that firms with more liquid shares are more likely to authorize buyback programs (Brockman, Howe, and Mortal (Reference Brockman, Howe and Mortal2008)) is consistent with the liquidity prediction.

C. Proportional Representation

Suppose the board authorizes a buyback program if the proportion of the firm’s existing shareholders who benefit exceeds a threshold $ \tau \in \left(0,1\right) $ . For instance, the majority rule corresponds to a threshold of $ \tau =0.5 $ . The authorization decision then depends on ownership composition ( $ s $ ), the prevalence of informed speculation ( $ \phi $ ), and the anticipated informativeness of buybacks ( $ {b}_0^{\ast } $ ).

When outside shareholder ownership is low ( $ s<\tau $ ), insiders determine the outcome. Here, the authorization follows the insider-aligned case, so the board authorizes the buyback program.

When outside shareholder ownership is high ( $ s\ge \tau $ ), their preferences become pivotal. If informed speculation is rare, outside shareholders lose from any buyback program. Uninformed buybacks amplify adverse-selection costs, increasing the wealth transfer to the speculator. Informed buybacks are even worse—the wealth transfer to insiders dominates the reduction in speculator profits. Authorization fails when informed speculation is sufficiently rare, as both uninformed and informed buybacks harm outside shareholders in this case.Footnote ²¹

If informed speculation is prevalent, the situation is more nuanced. Uninformed buybacks remain harmful—and are, in fact, more damaging because the wealth transfer to the speculator is larger. However, sufficiently informed buybacks can benefit outside shareholders: the reduction in speculator profits offsets the wealth transfer to insiders.Footnote ²² Authorization passes if anticipated execution is sufficiently informed. There is a subtle tension: more prevalent informed speculation (higher $ \phi $ ) makes reducing the speculator’s trading profits more valuable to outside shareholders—but simultaneously reduces buyback informativeness (Proposition 5), thereby weakening the competition effect that delivers this reduction.

When informed speculation is rare, firms with dispersed ownership face a conflict: insiders prefer authorization, but outside shareholders—who may constitute the majority—are harmed by any buyback program. This conflict can lead to two types of inefficiency. Insiders may push through authorization over outside shareholders’ objections, transferring wealth to themselves without providing offsetting benefits for outside shareholders. Outside shareholders may block authorization, forgoing informed buybacks that would have increased aggregate shareholder payoffs. When informed speculation is prevalent, this tension eases: outside shareholders can benefit from sufficiently informed buybacks, aligning their preferences with insiders. The welfare implications of buyback authorization thus depend not only on governance, but also on market conditions that determine how buybacks are executed.

A. Buyback Disclosure

The baseline model assumes that the market only observes the aggregate order flow. In practice, however, regulators have sought to expand the disclosure requirements of buyback activity. For instance, in 2004, the SEC began requiring firms to report monthly buyback activity in their quarterly filings. In 2023, the SEC adopted rules mandating reports of daily buyback activity, though these rules were subsequently vacated by the courts. The policy rationale for enhanced disclosure centers on the adverse-selection problem: insiders may use the manager’s informational advantage to execute buybacks in a way that transfers wealth from outside shareholders to themselves.

This section analyzes how buyback disclosures affect the trading equilibrium. Specifically, I assume that the market observes both the aggregate order flow ( $ q $ ) and the firm’s buyback order ( $ {q}_B $ ) before setting prices—a scenario I refer to as the pretrade buyback disclosure regime (denoted with superscript $ D $ ). The speculator does not observe the firm’s buyback order prior to submitting his order. As in Section III.A, I assume that the manager’s buyback strategy is ( $ 1,{b}_0 $ ).Footnote ²³

Let $ {\theta}_x $ and $ {\theta}_0 $ be the market’s posterior belief about firm fundamentals conditional on observing $ {q}_B=x $ and $ {q}_B=0 $ , respectively. Because the manager always executes buybacks when firm fundamentals are high, the absence of disclosed buybacks ( $ {q}_B=0 $ ) fully reveals that firm fundamentals are low: $ {\theta}_0=0 $ . In this case, the market-clearing price equals zero for all order flows.

In contrast, the disclosure of buybacks ( $ {q}_B=x $ ) indicates that firm fundamentals are more likely to be high: $ {\theta}_x=\frac{\theta }{\theta +\left(1-\theta \right){b}_0}\ge \theta $ , strictly so when buybacks are informed ( $ {b}_0<1 $ ). In this case, the trading equilibrium is isomorphic to the one characterized in Lemma 2, with $ {\theta}_x $ replacing $ \theta $ and buybacks occurring with certainty. Hence, given buybacks ( $ {q}_B=x $ ), the equilibrium pricing rule is

(16) $$ {P}_B^D(q)=\left\{\begin{array}{ll}0& \mathrm{if}\;q=-x,\\ {}\frac{\theta_x\left(1-\phi \right)}{\theta_x\left(1-\phi \right)+\left(1-{\theta}_x\right)}& \mathrm{if}\;q=0,\\ {}{\theta}_x& \mathrm{if}\;q=x,\\ {}1& \mathrm{if}\;q=2x.\end{array}\right. $$

As before, the speculator buys $ x $ shares if and only if he learns that firm fundamentals are high (A = 1).

With pretrade disclosure, the market always observes whether buybacks are occurring. As a result, the manager has no informational advantage vis-à-vis the market, and the buyback program cannot generate positive expected trading profits. Lemma 7 implies that pretrade buyback disclosure eliminates the wealth transfer from outside shareholders to insiders studied in Section III.C. This result is consistent with arguments in the literature that pretrade disclosure prevents insiders from profiting at the expense of outside shareholders (e.g., Fried (Reference Fried2005)).

However, this analysis is incomplete in the presence of informed speculative trading ( $ \phi >0 $ ). Lemma 4 establishes that buybacks also induce a dispersion effect that increases the value of any remaining informational advantage held by the speculator. As a result, even with pretrade disclosure, the economic consequences of buybacks still depend on their informativeness:

Buybacks continue to generate two opposing effects in the pretrade buyback disclosure regime. First, buybacks convey information to the market—though under this regime, information transmission occurs directly through disclosure rather than indirectly through order flow. This competition effect erodes the speculator’s informational advantage. Second, buybacks increase the dispersion in per-share value across fundamental states. This dispersion effect makes the speculator’s private information more valuable for trading. Consequently, buybacks decrease the speculator’s expected trading profit if and only if they are sufficiently informed.

Because disclosure eliminates the wealth transfer to insiders, the expected payoff of the firm’s outside shareholders depends solely on the transfer to the speculator: $ {U}_B^{DO}= x\theta -{\Pi}_B^D $ . Consequently, they strictly prefer more informed buybacks: $ \frac{\partial {U}_B^{DO}}{\partial {b}_0}=-\frac{\partial {\Pi}_B^D}{\partial {b}_0}<0 $ .

Thus far, I have taken the manager’s strategy as given. The following demonstrates that the pretrade disclosure regime also affects the manager’s optimal buyback strategy:

The crux of Proposition 7 is that pretrade disclosure increases the sensitivity of the interim stock price to buybacks. If the manager does not buy back shares, the market infers that firm fundamentals are low ( $ A=0 $ ), and the stock price falls. Hence, she faces stronger incentives to execute buybacks when firm fundamentals are low, resulting in a less informed buyback strategy.

These results have nuanced policy implications. Pretrade disclosure eliminates wealth transfers from outside shareholders to insiders, but it does not eliminate the speculator’s trading profits. Outside shareholders, therefore, still prefer more informed buybacks to limit their losses to the speculator. However, disclosure itself reduces the informativeness of buybacks: by punishing nonexecution—the market infers low fundamentals when no buyback is disclosed—the regime strengthens the manager’s incentive to buy back overvalued shares. The net effect of mandatory disclosure on outside shareholder welfare, therefore, depends on whether the benefit of eliminating the wealth transfer to insiders outweighs the cost of reduced buyback informativeness.

B. Other Frictions Affecting Buyback Strategy

The baseline model assumes that the manager executes buybacks to maximize $ \unicode{x1D53C}\left[\omega P+V\right] $ , a weighted combination of the firm’s $ t=1 $ stock price ( $ P $ ) and its $ t=2 $ per-share value ( $ V $ ). Under this objective, the manager always executes buybacks when she learns that fundamentals are high ( $ A=1 $ ) because doing so strictly increases both the stock price and per-share value. Because the manager is perfectly informed about firm fundamentals and faces no additional constraints, she executes good-state buybacks with certainty.

However, many frictions can prevent the manager from executing buybacks when fundamentals are high. The manager may have imperfect information about fundamentals, limiting her ability to identify good states. Financing constraints may leave the manager without the resources to buy back shares. Regulatory constraints and blackout periods may restrict trading windows. This section extends the analysis of Section III.A to accommodate these possibilities, characterizing equilibrium outcomes for a more general buyback strategy ( $ {b}_1,{b}_0 $ ), with $ {b}_1\ge {b}_0 $ .Footnote ²⁴

Here, the manager does not always buy back shares when firm fundamentals are high ( $ {b}_1<1 $ ). As a result, informativeness has two dimensions: the probability of good-state buybacks ( $ {b}_1 $ ) and the probability of bad-state buybacks ( $ {b}_0 $ ). For a given $ {b}_0 $ , increasing $ {b}_1 $ increases informativeness; for a given $ {b}_1 $ , decreasing $ {b}_0 $ increases informativeness. The baseline model fixes $ {b}_1=1 $ and captures informativeness by varying $ {b}_0 $ :

The results in Lemma 8 follow from how the buyback strategy shapes market inferences. When the manager buys more aggressively in good states (higher $ {b}_1 $ ), large positive order flows become stronger signals of high firm fundamentals ( $ A=1 $ ). Conversely, when she buys more in bad states (higher $ {b}_0 $ ), she adds noise that makes large positive order flows less indicative of high firm fundamentals. As in the baseline model, Lemma 8 implies that uninformed buybacks ( $ {b}_1={b}_0=b $ ) weakly decrease market informativeness, strictly so if $ b<1 $ . Effectively, uninformed buybacks inject additional noise into trading without improving the information contained in order flows.

The dispersion effect is more nuanced in this setting. Recall that the dispersion in the firm’s expected per-share value between good ( $ A=1 $ ) and bad ( $ A=0 $ ) states is given by $ \Delta V=E\left[V|A=1\right]-E\left[V|A=0\right] $ . In the benchmark without buybacks, this dispersion simply equals the fundamental spread in asset payoffs: $ \Delta {V}_0=1 $ . With buybacks, the dispersion becomes

(17) $\Delta V_B=(1+\underset{=b_1{\overline{T}}_G\ge 0}{\underbrace{\text{𝔼}\left[T|A=1\right]}})-(0+\underset{=-b_0{\overline{T}}_L\le 0}{\underbrace{\text{𝔼}\left[T|A=0\right]}})=\Delta V_0+b_1{\overline{T}}_G+b_0{\overline{T}}_L,$

where $ {\overline{T}}_G $ and $ {\overline{T}}_L $ are the magnitudes of the expected trading gains and losses from executing buybacks when the firm’s fundamentals are high ( $ A=1 $ ) and low ( $ A=0 $ ).

The buyback strategy ( $ {b}_0,{b}_1 $ ) affects the dispersion through two channels: a direct trading channel and an indirect spillover channel. The following decomposition reveals an asymmetry—dispersion unambiguously increases with bad-state buybacks but can either increase or decrease with good-state buybacks:

(18) $$ \frac{\mathrm{\partial \Delta }{V}_B}{\partial {b}_0}=\underset{\mathrm{Trading}}{\underbrace{\left({\overline{T}}_L+{b}_0\frac{\partial {\overline{T}}_L}{\partial {b}_0}\right)}}+\underset{\mathrm{Spillover}}{\underbrace{\left({b}_1\frac{\partial {\overline{T}}_G}{\partial {b}_0}\right)}}>0 $$

and

(19) $$ \frac{\mathrm{\partial \Delta }{V}_B}{\partial {b}_1}=\underset{\mathrm{Trading}}{\underbrace{\left({\overline{T}}_G+{b}_1\frac{\partial {\overline{T}}_G}{\partial {b}_1}\right)}}+\underset{\mathrm{Spillover}}{\underbrace{\left({b}_0\frac{\partial {\overline{T}}_L}{\partial {b}_1}\right)}}\gtrless 0. $$

More bad-state buybacks (higher $ {b}_0 $ ) increase dispersion through both the direct trading and the indirect spillover channels. First, they deepen expected buyback losses, reducing per-share value when fundamentals are weak. Second, they make the order flow less informative, lowering the expected market-clearing price in good states ( $ A=1 $ ) and increasing the profitability of good-state buybacks ( $ {\overline{T}}_G $ ). Consequently, bad-state buybacks unambiguously increase dispersion.

In contrast, more buybacks in good states (higher $ {b}_1 $ ) have a more nuanced effect on dispersion. The direct trading channel works as before—good-state buybacks expand expected gains, enhancing per-share value when firm fundamentals are high and increasing dispersion. However, the indirect spillover channel now features a countervailing force—good-state buybacks make the order flow more informative, lowering the expected market-clearing price in bad states and limiting the losses from bad-state buybacks ( $ {\overline{T}}_L $ ). The trading channel dominates when the buyback program size is large (high $ k $ )—increasing expected trading profits—or when bad-state buybacks are rare (low $ {b}_0 $ )—making the spillover effect less relevant:

These two effects—competition reducing the speculator’s informational advantage and dispersion raising the stakes of informed trading—jointly determine the speculator’s expected trading profit:

The effect of bad-state buybacks ( $ {b}_0 $ ) on speculator profit is unambiguous. More bad-state buybacks reduce market informativeness and increase value dispersion, both of which benefit the speculator. The effect of good-state buybacks ( $ {b}_1 $ ) is more nuanced. They strengthen the competition effect, eroding the speculator’s informational advantage. However, they can also amplify value dispersion due to the trading profits they generate. When the buyback program is not too large ( $ k<1 $ ), the competition effect dominates.Footnote ²⁵

Despite this nuance, the overall message is unchanged: uninformed buybacks benefit the speculator at shareholders’ expense. When $ {b}_1={b}_0<1 $ , buybacks amplify value dispersion while injecting noise that worsens market informativeness. The core insight from the baseline model—that uninformed buybacks harm shareholders by increasing the speculator’s profits—extends to this more general setting with two dimensions of buyback informativeness.