We examine the impact of actual share repurchases on stock prices using several measures of price efficiency and manually collected data on U.S. repurchases. We find that share repurchases make prices more efficient and reduce idiosyncratic risk. Further analyses reveal that the effects are primarily driven by repurchases in down markets. We conclude that share repurchases help to maintain accurate stock prices by providing price support at fundamental values. We find no evidence that managers use share repurchases to manipulate stock prices when selling their equity holdings or exercising stock options.

Received June 1, 2015; accepted June 1, 2016, by Editor David Denis.

Share repurchases have become the dominant form of payout in the United States.^{1} Roughly 90% of total repurchase volume is acquired in the open market. On average, open market repurchases represent 6.8% of monthly trading volume and every tenth repurchase amounts to at least 16.5% of monthly trading volume. These numbers suggest that share repurchases can substantially influence stock prices. In line with this presumption, numerous articles in the business press have criticized buybacks for being used by managers as a costly tool to manipulate the stock price to boost their equity based compensation.^{2} The Harvard Business Review recently condensed this concern by proclaiming that “*trillions of dollars that could have been spent on innovation and job creation [...] have instead been used to buy back shares for what is effectively stock-price manipulation*”.^{3}

This paper investigates whether open market share repurchases distort market prices and undermine price efficiency. We approach this question by examining the impact of share repurchases on price efficiency and the information content of stock prices. We define “information content” as the amount of information incorporated into the stock price and “price efficiency” as the degree to which all *available* information is incorporated into the stock price. We formulate two alternative hypotheses and test them using a unique, hand-collected data set of U.S. repurchase programs; this allows us to precisely measure repurchase activity and to construct credible instruments.^{4} Contrary to public opinion, our main result is that share repurchases make prices more efficient.

Our baseline hypothesis is motivated by the business press and postulates that share repurchases increase the stock price beyond its fundamental value and consequently reduce the information content in stock prices. Managers have a strong incentive to use share repurchases to intentionally increase the stock price beyond its fundamental value, that is, to manipulate the stock price, because their compensation is at least partly based on equity. Recent empirical evidence is consistent with the notion that managers deliberately attempt to influence the stock price to increase their compensation. For example, studies show that CEOs strategically time corporate news releases (Edmans et al. 2014) and firm advertising (Lou 2014) to temporarily increase stock prices in months in which their equity vests. Further studies suggest that share repurchases might be used for the same purpose. Bonaimé and Ryngaert (2013) find that the probability of a share repurchase is highest in quarters with net insider selling. Furthermore, Fenn and Liang (2001) document a positive relationship between share repurchases and the management’s stock options, and Babenko (2009) finds that firms are more likely to initiate share repurchases when their employees hold a large stake in the firm.

Even if managers are not able to influence their compensation via buybacks directly, increasing the stock price still may be in their interest because their performance is also assessed on their ability to create shareholder value. In other words, managers might use share repurchases to keep shareholders content. Finally, many firms have large repurchase programs, which they have to execute within a certain period of time to reach payout targets. Thus, share repurchases might unintentionally increase the noise in stock prices because of their price impact. If repurchases increase the stock price beyond fundamental values, the information content in stock prices will decrease and the incorporation of market- and firm-specific information will be delayed; idiosyncratic risk will increase and price efficiency will decrease.

Our alternative hypothesis postulates that share repurchases make prices more efficient by increasing either the speed or the accuracy with which available information is incorporated into stock prices. A distinctive feature of share repurchases is that they can only incorporate positive information into the stock price because firms participate in the market as buyers of their stock. Therefore, firms can either actively initiate a trade by placing a market order, thereby directly incorporating positive information, or submit a limit order, thereby providing a lower bound for the stock price. These two alternatives provide two distinct channels via which share repurchases may increase price efficiency.

According to the first channel, share repurchases will improve the speed with which positive information is incorporated into the stock price if firms actively trade on positive information not yet reflected in the stock price. This argument builds on Hou and Moskowitz (2005), who reason that some stocks are less efficiently priced because they are less visible or neglected by investors. Firms engaging as investors in their own stock can react to other investors’ inattention and improve price efficiency by repurchasing shares.

According to the second channel, share repurchases will improve the accuracy of the stock price if firms provide price support at fundamental values. The notion of share repurchases being used to provide price support is in line with both how CFOs claim to execute their repurchase programs and empirical evidence. According to personal accounts from CFOs, at least some firms provide brokers with specific instructions that include exact price ranges and repurchase volumes. In a survey by Brav et al. 2005, CFOs name buying back at low stock prices the most popular reason to conduct share repurchases. Several empirical studies confirm the notion that valuation plays an important role in the repurchase decision (e.g., Stephens and Weisbach 1998; Dittmar 2000).

Our price support argument builds on work by Hong, Wang, and Yu (2008), who extend the model of Grossman and Miller (1988) to allow firms to intervene when the stock price drops below fundamental value because of an exogenous demand shock. In their model, firms with sufficiently large funds for share repurchases will be able to prevent the stock price from overshooting and firms will have a lower short-horizon return variance. One important implication of the argument of Hong, Wang, and Yu (2008) is that the price adjustment to new information will be less noisy because the stock price response to new, negative systematic information is bounded from below at the stock’s fundamental value. Thus, the repurchasing firm’s stock will be more efficiently priced and the idiosyncratic risk in the stock price will be lower. Note that this argument critically depends on when firms provide price support: if price support is provided above fundamental values, share repurchases will increase both price delay and idiosyncratic risk. The evidence would be consistent with the price manipulation hypothesis. Our two hypotheses are mutually exclusive, but each hypothesis might be valid for some time or some firms.

For the empirical analysis, we collect data on monthly repurchase activity from SEC filings to exploit the time-series variation in actual share repurchases. We obtain the exact numbers of monthly repurchase volumes and repurchase prices for all firms within our sample period. Our unique data set covers 6,537 repurchase programs of 2,930 U.S. firms for the period 2004–2010. Repurchase programs extend over 87,614 firm-months, including 38,155 repurchase months. In our baseline analysis, we construct a panel of monthly observations and regress a measure of the information content of stock prices on a measure of repurchases and a set of control variables.

We rely on two groups of measures of the information content of stock prices that have been applied in the context of short selling (cf. Morck, Yeung, and Yu 2000; Bris, Goetzmann, and Zhu 2007; Boehmer and Wu 2013; Saffi and Sigurdsson 2011; Phillips 2011). In several ways, share repurchases resemble short sales, just with opposite signs. Both groups of traders, firms and short sellers, are likely to be better informed and trade large amounts of stock. Like short sales, share repurchases are deemed to distort prices at the expense of market efficiency.

The first group of measures determines the delay with which prices respond to new information as proposed by Hou and Moskowitz (2005). These measures compare the explanatory power of a simple market model regression with an extended market model regression. The extended market model additionally includes five lags of the market return as explanatory variables. The intuition behind these measures is that the higher the explanatory power of the lagged market returns in the extended market model, the higher is the delay until new information is fully incorporated into prices. Hou and Moskowitz (2005) demonstrate that stocks with the highest delay face a significant return premium that can be best explained by investor neglect or inattention. If share repurchases improve speed and/or accuracy of stock prices, price delay should decrease.

The second group of measures analyzes the amount of idiosyncratic risk incorporated into the stock price. Roll (1988) points out that the extent to which a stock moves together with the market depends on the relative amounts of systematic and idiosyncratic information incorporated into the stock price. In line with Morck, Yeung, and Yu (2000) and Bris, Goetzmann, and Zhu (2007), we use the R-squared of a market model and the correlation between stock and market returns to determine the amount of idiosyncratic risk incorporated in the stock price. If share repurchases incorporate idiosyncratic information or noise (systematic information) into the stock price, the R-squared and the cross-correlation should decrease (increase).^{5}

We use two distinct measures of repurchase activity, the number of shares repurchased, scaled by shares outstanding, and the remaining volume that can be repurchased under the currently open repurchase program. The latter measure precisely captures a firm’s repurchase ability. This offers a novel way to proxy for repurchase activity: the lower the remaining repurchase volume, the lower a firm’s ability to intervene when the stock price drops below its fundamental value. As this measure is predetermined in the sense that it is fixed before the period over which we compute our efficiency measures, it allows us to exclude reverse causality.

We furthermore use firm fixed effects and time fixed effects to ensure that the results are neither driven by unobserved heterogeneity in the cross-section nor driven by unobserved macroeconomic factors. In addition, we use instruments derived from program characteristics as suggested by Hillert, Maug, and Obernberger (2016) to isolate the exogenous variation. These instruments represent the size and the month of the program and allow us to predict the execution of a program at the time of its initiation. Thereby, we ensure that predicted repurchases are entirely unrelated to future levels of price efficiency, once again eliminating reverse causality concerns.

We find that share repurchases unequivocally decrease the delay with which prices respond to new market-wide information and conclude that share repurchases make prices more efficient. Furthermore, our analysis of the R-squared and the correlation with the market reveals that share repurchases increase the synchronicity of the repurchasing firm’s stock with the market. This result implies that the relative amount of idiosyncratic risk in stock prices is lower when repurchases are higher. Therefore, the evidence is not consistent with the notion that share repurchases increase the noise in stock returns. All of these results hold regardless of how we measure repurchase activity.

Next, we refine our analysis to learn more about the channels via which repurchases increase price efficiency. We use market returns to indicate whether positive or negative systematic information comes to the market and split repurchase activity in months in which the stock market goes up and months in which the market goes down. This approach reflects our dependent variable that examines the speed and accuracy with which lagged market returns are incorporated into the stock price and builds on the insight that share repurchases decrease idiosyncratic risk. The latter finding suggests that the execution of actual share repurchases is more affected by overall market conditions than by firm-specific news. We find that repurchases increase price efficiency and decrease idiosyncratic risk, in particular in months in which the market goes down, that is, when there is new negative information. We conclude that share repurchases primarily increase the information content of stock prices by providing price support at fundamental values.

Return moment distributions strongly support the notion that firms use share repurchases to support prices at fundamental values. As argued above, if firms provide price support at fundamental values, the adjustment process to new, negative information should be less noisy, and we should see fewer extreme returns. Our finding that repurchases reduce return volatility and kurtosis is in line with this presumption.

Dittmar and Field (2015) report that many firms repurchase only a few times per year, and this raises concerns regarding the validity of our identification strategy. However, we document substantially higher repurchase frequencies after accounting for whether firms have an open repurchase program. Furthermore, we show that price efficiency increases in repurchase frequency, with continuously repurchasing firms displaying the highest improvements in price efficiency. We also conduct several additional tests to identify repurchases that are detrimental to price efficiency. We identify repurchases that take place during or before insiders sell portions of their equity holdings in the company. We also distinguish between repurchase programs for which insider ownership, outstanding stock options, or exercised stock options are high. In none of these instances do share repurchases have a detrimental effect on price efficiency. No evidence supports that share repurchases motivated by large cash-holdings harm price efficiency.

The question of whether share repurchases use and incorporate private information in the stock price is not directly addressed in this paper. However, the results are not in line with the notion that share repurchases incorporate private, firm-specific information because we observe a decrease, not an increase, in idiosyncratic risk.

We contribute to the literature in at least two ways. First, ours is the first study to examine the impact of open market share repurchases on the informational efficiency of stock prices. Hong, Wang, and Yu (2008) show that firms with a higher ability to intervene when the stock price drops below fundamental value, have lower return variances. To the best of our knowledge, no other study takes a closer look at this topic. We, therefore, provide a novel approach with which to assess the direct effects of actual share repurchases on the stock market. Second, we contribute to a growing literature that tries to understand how specific groups of investors, such as institutional traders, corporate insiders, and short sellers, affect the efficiency and information content of prices.^{6}

## 1. Theoretical Considerations

In this paper, we examine the question of whether share repurchases distort or improve market prices by looking at the impact of share repurchases on price efficiency. Price efficiency denotes the degree to which *available* information is incorporated in the stock price. In a semistrong efficient capital market, public information is considered to be available and should be incorporated into the stock price. Trading on private information does not affect the degree to which public information is incorporated into the stock price. Our study is, therefore, not tailored toward the question of whether share repurchases are based on private information. A longstanding literature exists on this question with respect to both repurchase announcements (cf. Vermaelen, 1981; Dann, 1981; Ben-Rephael, Oded, and Wohl 2013; Ikenberry, Lakonishok, and Vermaelen 1995, 2000; Peyer and Vermaelen 2009; Fu and Huang 2015) and actual repurchases (cf. Ben-Rephael, Oded, and Wohl 2013; Dittmar and Field 2015). In the following paragraphs, we discuss the implications of our study on the question of whether share repurchases use and incorporate private information. We also blend this discussion with the empirical evidence presented in studies on the managerial timing ability of share repurchases. Our overall conclusion is that our results align well with the existing literature.

Firms will incorporate private information into the stock price when their repurchase trades reveal information to the market. In this case, we would expect that the idiosyncratic risk (market correlation) in the stock price increases (decreases) because a firm’s private information will be firm specific, that is, idiosyncratic. Accordingly, the finding that share repurchases decrease (increase) idiosyncratic risk (market correlation) would be hard to reconcile with the notion of share repurchases incorporating private information. The existing literature neither confirms nor rejects this notion. Ben-Rephael, Oded, and Wohl (2013) conclude that private information is not revealed until the repurchase activity is published in the quarterly filings. Following their argument, share repurchases should incorporate little to no private information into the stock price. Dittmar and Field (2015) document positive abnormal returns in the three months following the repurchase. However, it remains unclear whether private information is incorporated into the stock price during the repurchase itself.

The literature on the managerial timing ability of actual share repurchases unanimously finds that firms buy back at prices below average market prices (cf., e.g., Ben-Rephael, Oded, and Wohl 2013; Dittmar and Field 2015). The price support argument in this study suggests that firms buy back after declines in the stock price and stabilize prices by providing a lower bound for the stock price. When firms only buy back at the lower bound of the stock price, average market prices computed over a month have to be higher than the average repurchase price in the same month. The empirical result that repurchase prices are, on average, lower than market prices is, therefore, consistent with the price support argument.

The price support argument does also not presume the use of private information. As argued above, the argument builds on the idea that firms react to a decline in the stock price and establish a lower bound for the stock price. In the model of Hong, Wang, and Yu (2008), firms react to an exogenous demand shock without having private information. In a similar spirit, Hou and Moskowitz (2005) argue that some stocks are less efficient because they are less visible or neglected by investors. As a result, publicly available information is not adequately incorporated into the stock price and prices are more noisy. Firms reacting to this neglect by repurchasing shares will improve price efficiency regardless of whether they have private information.

Finally, the price support argument does not imply managerial timing ability either. Since price support is provided after the stock price has declined, repurchase prices will be lower than preceding stock prices. However, the timing ability will still depend on whether firms buy back above or below fundamental values. If firms provide price support above fundamental values, repurchases will manipulate prices and will be followed by negative abnormal returns. If firms buy back when the stock price equals its fundamental value, repurchases will not be followed by abnormal returns. Eventually, if firms are able to buy back when the stock price drops below its fundamental value, firms command timing ability and repurchases will be followed by positive abnormal returns. Our results suggest that firms either keep prices at, or bring prices toward, their fundamental values and this implies that firms buy back either at or below fundamental values. Therefore, our results are consistent with both the presence and the lack of managerial timing ability, but not with price manipulation.

## 2. Data and Methodology

In this section, we describe the construction of the data set, our methodology, and the variables used.

### 2.1 Sample construction

New disclosure rules require firms publicly traded in the United States to publish monthly accounts of their share repurchase activity under the newly created items 2(e) of Form 10–Q and 5(c) of Form 10–K, respectively. The requirement applies to all periods ending on or after March 15, 2004, but most firms started to publish detailed accounts of their repurchase activity for the last quarter of 2003. Firms need to report the total number of shares purchased, the average price paid per share, the number of shares purchased under specific repurchase programs, and either the maximum dollar amount or the maximum number of shares that may still be purchased under these programs. Additionally, firms also have to indicate the method of repurchase (e.g., open market repurchase, accelerated share repurchase, private transaction, or tender offer). We analyze shares repurchased under an open market repurchase program, which sometimes differs slightly from the total number of shares repurchased. This difference may arise for several reasons. For example, shares may be delivered back to the issuer for the payment of taxes resulting from the vesting of restricted stock units or the exercise of stock options by employees and directors requires firms to acquire shares.

As a starting point, we obtain all ordinary shares (share codes 10 and 11) traded on the NYSE, AMEX, and NASDAQ (exchange codes 1, 2, and 3) from CRSP. This gives us 6,504 firms over the period from January 2004 to December 2010. We omit eighteen firms not available in Compustat and drop 171 firms with missing data on the central index key (cik), which is the main identifier of the SEC’s online platform Edgar. Eventually, we arrive at 6,315 firms that can be found on CRSP, Compustat, and Edgar.

We use web crawlers to download all 10-Q and 10-K filings filed between January 1, 2004 and March 31, 2011. In total we obtain 96,203 10-Qs and 34,589 10-Ks and use textual analysis programs to extract the repurchase data from these filings. To ensure the quality of our data, we manually check and correct all observations. We are left with 376,843 firm-month observations, including more than 20,000 firm-months with missing CRSP data because firms are no longer or are not yet listed on AMEX, NASDAQ, or NYSE at the time of the repurchase.

The initial data set includes 9,100 repurchase programs. We drop 167 programs with unknown announcement date; 1,587 programs, which were started before 2004; and a further 50, which were announced after 2010. Next, we exclude 144 programs, because they are not executed in the open-market and a further 615 programs with an unlimited or variable volume, because program size is one of our instruments and needs to be determined. After these screening procedures, we end with 6,537 repurchase programs, of which half remain active until they have been completed; that is, they have no fixed expiration date.^{7}

In the last step, we add data from I/B/E/S and TAQ and eliminate all firms that do not have an open repurchase program in at least one month between 2004 and 2010. After deleting all observations for which the variables used in the baseline analysis are not available, we end with a final data set including 2,930 repurchasing firms and 158,471 firm months. These firms have 6,537 programs that extend over 87,614 firm-months, and firms conduct share repurchases in 38,155 of these firm-months.

### 2.2 Research design and definition of variables

Our generic specifications regress a measure of price efficiency or information content on a measure of repurchase activity and a range of controls:

Here, $${\it Efficiency}$$ is a measure of price delay and $${\it IdiosyncraticRisk}$$ denotes *R-squared* or *Market correlation*. $${\it Rep}$$ denotes either *Repurchase intensity* or *Remaining volume*. *Repurchase intensity* is defined as the number of shares repurchased in a month, divided by the number of shares outstanding at the end of the previous month. *Remaining volume* is defined as the number of shares that still can be bought under the current program at the beginning of month *t* scaled by shares outstanding at the beginning of the program. $${\it Control}$$ refers to the control variables, $$\mu$$ is a time-invariant firm fixed effect and $$\eta$$ is a month fixed effect.

*Repurchase intensity* precisely captures the activity of firms in the stock market. However, *Repurchase intensity* also might be the outcome of current, partly unobserved market conditions. For example, if firms step in to prevent a mispricing of their stock, we will only observe the outcome of the firm’s effort to prevent the mispricing. A realistic outcome of the firm’s trading activity, therefore, is, that the observed price efficiency is kept at a level similar to the one in previous months. In this setting, *Repurchase intensity* will be endogenously determined by the unobserved counterfactual level of price efficiency, that is, the level of mispricing in absence of share repurchases. Meanwhile, the actual effect of share repurchases on price efficiency is reflected in the difference between the observed outcome and the unobserved counterfactual outcome. As a consequence, contemporaneous *Repurchase intensity* and observed price efficiency will not be correlated, or they will be negatively correlated if repurchases cannot fully prevent a mispricing of the stock. Therefore, concerns of endogeneity and reverse causality are high when firms provide price support to prevent a mispricing of their stock.

We tackle this problem from three different angles. In our first specification, we predict exogenous *Repurchase intensity* using two instruments proposed by Hillert, Maug, and Obernberger (2016): the announced program size and the distance between the current month and the program starting month. *Program size* denotes the maximal number of shares that may be purchased under a particular program and is scaled by the number of shares outstanding. If the program volume is reported in US dollars we divide the maximal dollar volume that may be repurchased under the program by the firm’s market capitalization. The size of the program is fixed before the execution begins in order to ensure that the size of the program is exogenous with respect to future variations in our dependent variables. We can use neither the realized size of the program nor the remaining portion of the program as instruments, because both depend on firms’ actual repurchase behavior and are therefore endogenously determined. Hillert, Maug, and Obernberger (2016) show that *Program size* has a positive impact on repurchases. *Program month* denotes the number of calendar months since the announcement of the repurchase program. The motivation is that the period for which the program has been active is not influenced by the subsequent within-firm variation of our dependent variables. Hillert, Maug, and Obernberger (2016) demonstrate that firms frontload the execution of their programs, and hence *Program month* has a negative impact on realized repurchases. Taken together, these program characteristics allow us to prescribe the execution of a program at its beginning to the future. Thereby, we ensure that predicted repurchases are not related to future levels of price efficiency, a fact critical to our identification strategy.

In our second specification, we lag *Repurchase intensity* by one period and thereby circumvent the reverse causality problem. In our third specification, we use *Remaining volume* as a measure of the ability to conduct repurchases. The advantage of *Remaining volume* over *Repurchase intensity* is that it is predetermined and therefore not potentially driven by reverse causality: price efficiency and returns over month *t* cannot affect the remaining repurchase volume at the beginning of month *t*. Meanwhile, the remaining repurchase volume should proxy very well for a firm’s ability to buy back amounts of shares large enough to put information into prices. Also, note that *Remaining volume* is not driven by prior returns (cf. Table 3).

Name | Definition | Source | Unit |
---|---|---|---|

Acquiror | 1 if firm is currently (time between announcement and end of the offer) bidding for another company | SDC | Binary |

Amihud | Monthly average of daily Amihud illiquidity ratio | CRSP | Ratio |

Analysts | Number of analysts (ln) | IBES | Unit |

Book to market | Book value equity / market cap, winsorized at 1% | Comp. | Ratio |

Book value equity | Common equity (Compustat item: ceqq) | Comp. | Million |

Cash | Cash and short-term investments (Compustat item: cheq) | Comp. | Million |

Change in short interest | Change in short interest at month end scaled by shares outstanding | Comp. | Ratio |

Delay | Price efficiency measure constructed as the ratio of the R$$^2$$ estimates of the extended market model and the base model | CRSP | Ratio |

Coefficient-based delay | Price efficiency measure constructed as the ratio of the lag-weighted sum of the coefficients of the lagged market returns relative to the sum of all coefficients | CRSP | Ratio |

Deviation from $\$$ 30 | Absolute difference between the stock price and $\$$ 30 (ln) | CRSP | Unit |

Dividends | Total dividends (Compustat item: dvt) | Comp. | Million |

EBITDA | Operating income before depreciation (Compustat item: oibdpq) | Comp. | Million |

Governance | Governance Index of Gompers, Ishii, and Metrick (2003) | ISS | Unit |

Insider ownership | Shares held by insiders scaled by shares outstanding | Exec. | Ratio |

Institutional ownership | Shares held by institutions scaled by shares outstanding | TR Inst. Holdings | Ratio |

Leverage | (Total asset - book value equity) / (total asset - book value equity + market cap) | Comp./CRSP | Ratio |

Market cap | Monthly average of daily market capitalization (ln) | CRSP | Million |

Market correlation | Correlation between daily stock return and contemporaneous market return | CRSP | Unit |

Net insider trading | Insider buying minus insider selling scaled by market cap | TR Insider Data | Ratio |

Options exercised | Number of shares obtained by option exercises of coporate insiders in the respective month scaled by shares outstanding | TR Insider Data | Ratio |

Options outstanding | Outstanding options scaled by shares outstanding | Comp. | Ratio |

Program month | Difference between current month and month before start of the repurchase program plus 1 (ln) | SEC | Unit |

Program size (scaled) | Size of the repurchase program scaled by shares oustanding as of the beginning of the program | SEC | Ratio |

Relative spread | Monthly average of intraday relative spread, time-weighted (ln) | TAQ | Ratio |

Remaining volume | Remaining volume at the beginning of the months that can be repurchased under the program scaled by shares outstanding | SEC | Ratio |

Repurchase volume | Dollar volume of shares repurchased during the month | SEC | Million |

Repurchase dummy | 1 if repurchase transaction takes place | SEC | Binary |

Repurchase intensity | Number of shares repurchased during the month divided by the number of shares outstanding at the last trading day of the previous month | SEC/CRSP | Ratio |

Repurchase intensity (TV) | Number of shares repurchased during the month divided by the number of shares traded over the current month | SEC/CRSP | Ratio |

Return | Monthly stock return | CRSP | Unit |

Return > 0 | Monthly stock return if positive, else zero | CRSP | Unit |

Return < 0 | Monthly stock return if negative, else zero | CRSP | Unit |

R-squared | R-squared estimate of the market model | CRSP | Ratio |

Shares outstanding | Number of shares outstanding at last trading day of month | CRSP | Million |

Target | 1 if firm is currently (time between announcement and end of the offer) a target of another company | SDC | Binary |

Total assets | Total assets (Compustat item: atq) (ln) | Comp. | Million |

Trading volume (scaled) | Monthly total trading volume excluding repurchases scaled by shares outstanding | CRSP | Ratio |

Turnover | Trading volume scaled by market cap | CRSP | Ratio |

Volatility | Standard deviation of daily returns over one month (ln) | CRSP | Unit |

Name | Definition | Source | Unit |
---|---|---|---|

Acquiror | 1 if firm is currently (time between announcement and end of the offer) bidding for another company | SDC | Binary |

Amihud | Monthly average of daily Amihud illiquidity ratio | CRSP | Ratio |

Analysts | Number of analysts (ln) | IBES | Unit |

Book to market | Book value equity / market cap, winsorized at 1% | Comp. | Ratio |

Book value equity | Common equity (Compustat item: ceqq) | Comp. | Million |

Cash | Cash and short-term investments (Compustat item: cheq) | Comp. | Million |

Change in short interest | Change in short interest at month end scaled by shares outstanding | Comp. | Ratio |

Delay | Price efficiency measure constructed as the ratio of the R$$^2$$ estimates of the extended market model and the base model | CRSP | Ratio |

Coefficient-based delay | Price efficiency measure constructed as the ratio of the lag-weighted sum of the coefficients of the lagged market returns relative to the sum of all coefficients | CRSP | Ratio |

Deviation from $\$$ 30 | Absolute difference between the stock price and $\$$ 30 (ln) | CRSP | Unit |

Dividends | Total dividends (Compustat item: dvt) | Comp. | Million |

EBITDA | Operating income before depreciation (Compustat item: oibdpq) | Comp. | Million |

Governance | Governance Index of Gompers, Ishii, and Metrick (2003) | ISS | Unit |

Insider ownership | Shares held by insiders scaled by shares outstanding | Exec. | Ratio |

Institutional ownership | Shares held by institutions scaled by shares outstanding | TR Inst. Holdings | Ratio |

Leverage | (Total asset - book value equity) / (total asset - book value equity + market cap) | Comp./CRSP | Ratio |

Market cap | Monthly average of daily market capitalization (ln) | CRSP | Million |

Market correlation | Correlation between daily stock return and contemporaneous market return | CRSP | Unit |

Net insider trading | Insider buying minus insider selling scaled by market cap | TR Insider Data | Ratio |

Options exercised | Number of shares obtained by option exercises of coporate insiders in the respective month scaled by shares outstanding | TR Insider Data | Ratio |

Options outstanding | Outstanding options scaled by shares outstanding | Comp. | Ratio |

Program month | Difference between current month and month before start of the repurchase program plus 1 (ln) | SEC | Unit |

Program size (scaled) | Size of the repurchase program scaled by shares oustanding as of the beginning of the program | SEC | Ratio |

Relative spread | Monthly average of intraday relative spread, time-weighted (ln) | TAQ | Ratio |

Remaining volume | Remaining volume at the beginning of the months that can be repurchased under the program scaled by shares outstanding | SEC | Ratio |

Repurchase volume | Dollar volume of shares repurchased during the month | SEC | Million |

Repurchase dummy | 1 if repurchase transaction takes place | SEC | Binary |

Repurchase intensity | Number of shares repurchased during the month divided by the number of shares outstanding at the last trading day of the previous month | SEC/CRSP | Ratio |

Repurchase intensity (TV) | Number of shares repurchased during the month divided by the number of shares traded over the current month | SEC/CRSP | Ratio |

Return | Monthly stock return | CRSP | Unit |

Return > 0 | Monthly stock return if positive, else zero | CRSP | Unit |

Return < 0 | Monthly stock return if negative, else zero | CRSP | Unit |

R-squared | R-squared estimate of the market model | CRSP | Ratio |

Shares outstanding | Number of shares outstanding at last trading day of month | CRSP | Million |

Target | 1 if firm is currently (time between announcement and end of the offer) a target of another company | SDC | Binary |

Total assets | Total assets (Compustat item: atq) (ln) | Comp. | Million |

Trading volume (scaled) | Monthly total trading volume excluding repurchases scaled by shares outstanding | CRSP | Ratio |

Turnover | Trading volume scaled by market cap | CRSP | Ratio |

Volatility | Standard deviation of daily returns over one month (ln) | CRSP | Unit |

The table describes all control variables and some repurchase variables. For each variable the table reports the definition, the data source, and the unit of measurement. Variables denoted with (ln) are expressed as natural logarithms.

By including firm fixed effects, time fixed effects, and lagged dependent variables, we avoid results driven by unobserved heterogeneity in the cross-section, macro-factors, and between-month “efficiency-timing”. Even if the start of a repurchase program depended on the current efficiency of the stock, the lagged dependent variable would control for currently high or low levels of efficiency. To ensure that the results are not driven by announcement effects, we additionally control for the month in which the repurchase program begins.

#### 2.2.1 Measures of price delay and idiosyncratic risk.

To measure price efficiency, we use two variants of the delay measure suggested by Hou and Moskowitz (2005). The delay measure quantifies how fast and how accurately new information is incorporated into prices by assessing the explanatory power of lagged returns in an extended market model relative to a simple market model. We estimate the measures as in Boehmer and Wu (2013) or Phillips (2011) using daily returns. Therefore, we estimate the following models for each firm and each month:

Here, $$r_{i,t}$$ denotes the return of firm $$i$$ on day $$t$$; $$r_{m,t}$$ denotes the market return on day $$t$$; and $$r_{m,t-n}$$ denotes the market return $$n$$ days prior to day $$t$$. If all new information was immediately incorporated into a firm’s stock price, this will be reflected in the coefficient for the contemporaneous market return $$\beta_{i}^{0}$$, while the coefficients for the lagged market returns $$\beta_{i}^{n}$$ will be equal to zero. However, if the incorporation of new information into prices is delayed, then the coefficients for the lagged market returns $$\beta_{i}^{n}$$ will be different from zero and the extended market model consequently will have a higher explanatory power than the base model. We use five lags to include all trading days within one week.

The first delay measure suggested by Hou and Moskowitz (2005) is the ratio of the R-squared estimates of the two models:

The higher the price efficiency of stock, and consequently the faster new information is incorporated into prices, the smaller is the difference in explanatory power between base model and extended market model. Thus, as price efficiency increases, the *Delay* measure decreases.

The second delay measure is based on the coefficients of the two regressions. This delay measure is constructed as the ratio of the lag-weighted sum of the absolute coefficients of the lagged market returns relative to the sum of all coefficients, scaled by the standard errors of the coefficients:

As for *Delay, Coefficient-based delay* also decreases with higher degrees of price efficiency, that is,$$\,$$faster information incorporation, as the explanatory power of the coefficients of the lagged market returns decreases.

To measure the amount of idiosyncratic information incorporated into stock prices, we determine the degree of comovement (synchronicity) of individual stock returns with the market return. In line with Morck, Yeung, and Yu (2000) and Bris, Goetzmann, and Zhu (2007), we use the R-squared of a market model and the correlation between stock and market returns. We estimate *R-squared* and *Market correlation* using daily returns for each month. We use the R-squared of the model in Equation (3).

#### 2.2.2 Further variables.

For a measure of the relative spread, we use the NYSE TAQ database to extract the necessary intraday transaction data. For each trade we assign the prevailing bid and ask quotes valid at least one second before the trade took place. If there is more than one transaction in a given second, the same bid and ask quotes are matched to all of these transactions. If there is more than one bid and ask quote in a given second, we assume that the last quote in the respective second is the prevailing quote.^{8} We only consider the NBBO (National Best Bid and Offer) quotes.^{9} We calculate the quote midpoint as the average of the prevailing bid and ask quotes. *Relative spread* is defined as time-weighted average of the difference between the prevailing ask and the prevailing bid quote, divided by the quote midpoint price.

### 2.3 Descriptive statistics

Table 2 provides descriptive statistics for all variables used in the analysis. As we exclusively analyze within-firm variation in repurchases, we exclude nonrepurchasing firms. Our sample covers 158,471 firm months, including 38,155 repurchase months.

Mean | Median | SD | SD (within) | 1st Perc. | 99th Perc. | N | |
---|---|---|---|---|---|---|---|

Dependent variables | |||||||

Delay | 0.504 | 0.465 | 0.306 | 0.253 | 0.032 | 1.000 | 158,471 |

Coefficient-based delay | 1.973 | 1.940 | 0.630 | 0.566 | 0.705 | 3.482 | 158,471 |

R-squared | 26.84% | 22.17% | 22.62% | 18.53% | 0.01% | 81.21% | 158,471 |

|Market correlation| | 0.456 | 0.471 | 0.246 | 0.197 | 0.010 | 0.901 | 158,471 |

Repurchase measures | |||||||

Repurchase volume (mill.) | 12.8 | 0.0 | 97.9 | 82.6 | 0.0 | 286.4 | 158,471 |

Repurchase intensity | 0.16% | 0.00% | 0.55% | 0.53% | 0.00% | 2.58% | 158,471 |

Repurchase intensity (TV) | 1.64% | 0.00% | 5.71% | 5.25% | 0.00% | 29.22% | 158,471 |

Remaining volume | 4.54% | 2.05% | 6.77% | 3.77% | 0.00% | 33.46% | 158,471 |

Repurchase measures in repurchase months | |||||||

Repurchase volume (mill.) | 49.3 | 5.1 | 167.3 | 121.9 | 0.0 | 740.7 | 38,155 |

Repurchase intensity | 0.68% | 0.38% | 0.96% | 0.81% | 0.00% | 4.56% | 38,155 |

Repurchase intensity (TV) | 6.81% | 3.33% | 10.01% | 7.47% | 0.00% | 53.07% | 38,155 |

Remaining volume | 6.90% | 4.84% | 7.22% | 3.85% | 0.00% | 36.62% | 38,155 |

Program descriptives | |||||||

Program month | 16 | 12 | 14.02 | 9.37 | 1 | 67 | 6,537 |

Program size (scaled) | 6.59% | 5.27% | 4.86% | 3.66% | 0.47% | 25.11% | 6,537 |

Control variables | |||||||

Acquisition dummy | 0.096 | 0 | 0.295 | 0.268 | 0 | 1 | 158,471 |

Analysts | 7.001 | 5 | 6.839 | 2.266 | 0 | 28 | 158,471 |

Book to market | 0.655 | 0.527 | 0.580 | 0.393 | -0.172 | 3.385 | 158,471 |

Cash to assets | 16.9% | 8.5% | 19.1% | 7.1% | 0.1% | 78.3% | 158,471 |

Change in short interest | 0.0% | 0.0% | 1.2% | 1.2% | -0.2% | 3.6% | 146,397 |

Deviation from $\$$ 30 | 18.4 | 15.9 | 39.2 | 15.2 | 0.3 | 70.9 | 158,471 |

Dividends to assets | 0.92% | 0.00% | 2.03% | 1.14% | 0.00% | 13.54% | 158,471 |

EBITDA to assets | 0.027 | 0.026 | 0.035 | 0.021 | -0.078 | 0.124 | 158,471 |

Governance | 9.256 | 9 | 2.556 | 0.372 | 4 | 15 | 68,014 |

Insider ownerhsip | 5.24% | 2.59% | 7.89% | 3.73% | 0.15% | 45.14% | 86,746 |

Institutional ownership | 61.3% | 67.8% | 29.3% | 9.3% | 38.2% | 100.0% | 146,397 |

Leverage | 0.435 | 0.376 | 0.290 | 0.092 | 0.022 | 0.974 | 158,471 |

Market cap (mill.) | 4796.7 | 629.0 | 17456.4 | 4284.0 | 11.6 | 84770.3 | 158,471 |

Net insider trading | -0.07% | 0.00% | 0.87% | 0.86% | -1.33% | 0.37% | 154,753 |

Options exercised | 0.08% | 0.00% | 0.26% | 0.25% | 0.00% | 1.59% | 158,471 |

Options outstanding | 8.77% | 7.07% | 13.13% | 7.36% | 0.00% | 32.50% | 151,863 |

Relative spread | 0.77% | 0.17% | 1.75% | 1.05% | 0.02% | 9.17% | 158,471 |

Return | 0.008 | 0.004 | 0.144 | 0.144 | -0.354 | 0.420 | 158,471 |

Target dummy | 0.004 | 0.000 | 0.064 | 0.064 | 0.000 | 0.000 | 158,471 |

Total assets (mill.) | 10582.6 | 904.4 | 83539.8 | 23738.2 | 17.8 | 139280.4 | 158,471 |

Trading volume (scaled) | 0.189 | 0.131 | 0.307 | 0.260 | 0.003 | 0.996 | 158,471 |

Volatility | 0.028 | 0.022 | 0.022 | 0.020 | 0.006 | 0.111 | 158,471 |

Mean | Median | SD | SD (within) | 1st Perc. | 99th Perc. | N | |
---|---|---|---|---|---|---|---|

Dependent variables | |||||||

Delay | 0.504 | 0.465 | 0.306 | 0.253 | 0.032 | 1.000 | 158,471 |

Coefficient-based delay | 1.973 | 1.940 | 0.630 | 0.566 | 0.705 | 3.482 | 158,471 |

R-squared | 26.84% | 22.17% | 22.62% | 18.53% | 0.01% | 81.21% | 158,471 |

|Market correlation| | 0.456 | 0.471 | 0.246 | 0.197 | 0.010 | 0.901 | 158,471 |

Repurchase measures | |||||||

Repurchase volume (mill.) | 12.8 | 0.0 | 97.9 | 82.6 | 0.0 | 286.4 | 158,471 |

Repurchase intensity | 0.16% | 0.00% | 0.55% | 0.53% | 0.00% | 2.58% | 158,471 |

Repurchase intensity (TV) | 1.64% | 0.00% | 5.71% | 5.25% | 0.00% | 29.22% | 158,471 |

Remaining volume | 4.54% | 2.05% | 6.77% | 3.77% | 0.00% | 33.46% | 158,471 |

Repurchase measures in repurchase months | |||||||

Repurchase volume (mill.) | 49.3 | 5.1 | 167.3 | 121.9 | 0.0 | 740.7 | 38,155 |

Repurchase intensity | 0.68% | 0.38% | 0.96% | 0.81% | 0.00% | 4.56% | 38,155 |

Repurchase intensity (TV) | 6.81% | 3.33% | 10.01% | 7.47% | 0.00% | 53.07% | 38,155 |

Remaining volume | 6.90% | 4.84% | 7.22% | 3.85% | 0.00% | 36.62% | 38,155 |

Program descriptives | |||||||

Program month | 16 | 12 | 14.02 | 9.37 | 1 | 67 | 6,537 |

Program size (scaled) | 6.59% | 5.27% | 4.86% | 3.66% | 0.47% | 25.11% | 6,537 |

Control variables | |||||||

Acquisition dummy | 0.096 | 0 | 0.295 | 0.268 | 0 | 1 | 158,471 |

Analysts | 7.001 | 5 | 6.839 | 2.266 | 0 | 28 | 158,471 |

Book to market | 0.655 | 0.527 | 0.580 | 0.393 | -0.172 | 3.385 | 158,471 |

Cash to assets | 16.9% | 8.5% | 19.1% | 7.1% | 0.1% | 78.3% | 158,471 |

Change in short interest | 0.0% | 0.0% | 1.2% | 1.2% | -0.2% | 3.6% | 146,397 |

Deviation from $\$$ 30 | 18.4 | 15.9 | 39.2 | 15.2 | 0.3 | 70.9 | 158,471 |

Dividends to assets | 0.92% | 0.00% | 2.03% | 1.14% | 0.00% | 13.54% | 158,471 |

EBITDA to assets | 0.027 | 0.026 | 0.035 | 0.021 | -0.078 | 0.124 | 158,471 |

Governance | 9.256 | 9 | 2.556 | 0.372 | 4 | 15 | 68,014 |

Insider ownerhsip | 5.24% | 2.59% | 7.89% | 3.73% | 0.15% | 45.14% | 86,746 |

Institutional ownership | 61.3% | 67.8% | 29.3% | 9.3% | 38.2% | 100.0% | 146,397 |

Leverage | 0.435 | 0.376 | 0.290 | 0.092 | 0.022 | 0.974 | 158,471 |

Market cap (mill.) | 4796.7 | 629.0 | 17456.4 | 4284.0 | 11.6 | 84770.3 | 158,471 |

Net insider trading | -0.07% | 0.00% | 0.87% | 0.86% | -1.33% | 0.37% | 154,753 |

Options exercised | 0.08% | 0.00% | 0.26% | 0.25% | 0.00% | 1.59% | 158,471 |

Options outstanding | 8.77% | 7.07% | 13.13% | 7.36% | 0.00% | 32.50% | 151,863 |

Relative spread | 0.77% | 0.17% | 1.75% | 1.05% | 0.02% | 9.17% | 158,471 |

Return | 0.008 | 0.004 | 0.144 | 0.144 | -0.354 | 0.420 | 158,471 |

Target dummy | 0.004 | 0.000 | 0.064 | 0.064 | 0.000 | 0.000 | 158,471 |

Total assets (mill.) | 10582.6 | 904.4 | 83539.8 | 23738.2 | 17.8 | 139280.4 | 158,471 |

Trading volume (scaled) | 0.189 | 0.131 | 0.307 | 0.260 | 0.003 | 0.996 | 158,471 |

Volatility | 0.028 | 0.022 | 0.022 | 0.020 | 0.006 | 0.111 | 158,471 |

This table provides descriptive statistics for the repurchase variables used, for the dependent variables, and for the control variables for firms that had an open repurchase programs at some point between 2004 and 2010. Additionally, the table provides information on the repurchase variables in repurchase months and on the repurchase programs. The repurchase variables and the control variables are defined in Table 1. We report the arithmetic mean, the median, the standard deviation (SD), the within-firm standard deviation (SD within), the 1st percentile, and the 99th percentile of the distribution for each variable. None of the variables is expressed in natural logarithms. Within-firm variation is calculated from a regression of the respective variable on firm fixed effects.

Both measures of price delay exhibit similar means and medians, and this indicates that both variables are not skewed. *Delay* is strictly defined between 0 and 1, and *Coefficient-based delay* ranges between 0 and 5. In both cases, the mean and median are close to the midpoint of these ranges. *R-squared* and the *Market correlation* are also defined between 0 and 1. Both measures exhibit similar means and medians. We use the absolute values of *Market correlation* in all of our analyses.

The average *Repurchase volume* over 38,155 repurchase months is

## 3. Empirical Analysis

We start the empirical analysis with a discussion of the determinants of our repurchase variables, *Repurchase intensity* and *Remaining volume*. In the following sections, we test our main hypotheses and examine the robustness of our results.

### 3.1 Analysis of share repurchase variables

The purpose of the analysis of our repurchase variables, *Repurchase intensity* and *Remaining volume*, is threefold. First, we establish the relevance of our instruments, *Program month* and *Program size.* Second, we discuss whether lagged *Repurchase intensity* is a good proxy for contemporaneous *Repurchase intensity*. Third, we examine additional drivers of repurchase activity.^{10} To analyze repurchase activity, we use specifications similar to the ones presented in Section 2.2 and regress a measure of repurchase activity on program characteristics and control variables. The results are reported in Table 3.

Dependent variable: | Repurchase intensity | Repurchase intensity | Remaining volume |
---|---|---|---|

(1) | (2) | (3) | |

Method: | OLS | OLS | OLS |

Repurchase intensity$$_{t-1}$$ | 0.2001^{***} | ||

(16.45) | |||

Program month$$_{t}$$ (ln) | -0.0006^{***} | -0.0005^{***} | -0.0070^{***} |

(-12.47) | (-12.08) | (-13.51) | |

Program size$$_{t}$$ | 0.0316^{***} | 0.0260^{***} | 0.8628^{***} |

(16.16) | (15.37) | (39.13) | |

Options exercised$$_{t}$$ | 0.0159^{**} | 0.0214^{***} | 0.0002 |

(2.03) | (2.76) | (0.01) | |

Net insider trading$$_{t}$$ (scaled) | -0.0110^{***} | -0.0103^{***} | 0.0093 |

(-2.96) | (-2.99) | (1.22) | |

Options outstanding$$_{t}$$ | 0.0005^{*} | 0.0004^{*} | -0.0020 |

(1.94) | (1.87) | (-0.95) | |

Return$$_{t-1}$$ > 0 | 0.0001 | 0.0001 | -0.0008 |

(0.60) | (0.58) | (-0.88) | |

Return$$_{t-1}$$ < 0 | -0.0034^{***} | -0.0034^{***} | 0.0015 |

(-10.32) | (-10.41) | (0.98) | |

Book to market$$_{t-3}$$ | 0.0002^{***} | 0.0002^{***} | -0.0001 |

(3.34) | (3.03) | (-0.06) | |

Total assets$$_{t-3}$$ (ln) | 0.0009^{***} | 0.0009^{***} | 0.0008 |

(8.72) | (9.62) | (0.58) | |

Cash to assets$$_{t-3}$$ | 0.0015^{***} | 0.0014^{***} | 0.0127^{***} |

(4.14) | (4.62) | (2.80) | |

EBITDA to assets$$_{t-3}$$ | 0.0009 | 0.0006 | -0.0123 |

(1.03) | (0.74) | (-1.30) | |

Dividends to assets$$_{t-3}$$ | -0.0008 | -0.0009 | 0.0473^{*} |

(-0.41) | (-0.56) | (1.93) | |

Leverage$$_{t-3}$$ | -0.0048^{***} | -0.0041^{***} | 0.0024 |

(-13.03) | (-13.65) | (0.53) | |

Acquiror dummy$$_{t}$$ | -0.0004^{***} | -0.0003^{***} | 0.0005 |

(-5.39) | (-4.86) | (1.13) | |

Target dummy$$_{t}$$ | -0.0004 | -0.0003 | 0.0005 |

(-1.61) | (-1.10) | (0.35) | |

Relative spread$$_{t-1}$$ (ln) | -0.0000 | 0.0001^{*} | 0.0004 |

(-0.13) | (1.83) | (0.62) | |

Constant | -0.0042^{***} | -0.0034^{***} | 0.0071 |

(-6.43) | (-6.30) | (0.88) | |

$$R^2$$ (within firm) | 0.061 | 0.102 | 0.563 |

Observations | 134,081 | 133,869 | 134,428 |

Firm FE and month FE | Y | Y | Y |

Dependent variable: | Repurchase intensity | Repurchase intensity | Remaining volume |
---|---|---|---|

(1) | (2) | (3) | |

Method: | OLS | OLS | OLS |

Repurchase intensity$$_{t-1}$$ | 0.2001^{***} | ||

(16.45) | |||

Program month$$_{t}$$ (ln) | -0.0006^{***} | -0.0005^{***} | -0.0070^{***} |

(-12.47) | (-12.08) | (-13.51) | |

Program size$$_{t}$$ | 0.0316^{***} | 0.0260^{***} | 0.8628^{***} |

(16.16) | (15.37) | (39.13) | |

Options exercised$$_{t}$$ | 0.0159^{**} | 0.0214^{***} | 0.0002 |

(2.03) | (2.76) | (0.01) | |

Net insider trading$$_{t}$$ (scaled) | -0.0110^{***} | -0.0103^{***} | 0.0093 |

(-2.96) | (-2.99) | (1.22) | |

Options outstanding$$_{t}$$ | 0.0005^{*} | 0.0004^{*} | -0.0020 |

(1.94) | (1.87) | (-0.95) | |

Return$$_{t-1}$$ > 0 | 0.0001 | 0.0001 | -0.0008 |

(0.60) | (0.58) | (-0.88) | |

Return$$_{t-1}$$ < 0 | -0.0034^{***} | -0.0034^{***} | 0.0015 |

(-10.32) | (-10.41) | (0.98) | |

Book to market$$_{t-3}$$ | 0.0002^{***} | 0.0002^{***} | -0.0001 |

(3.34) | (3.03) | (-0.06) | |

Total assets$$_{t-3}$$ (ln) | 0.0009^{***} | 0.0009^{***} | 0.0008 |

(8.72) | (9.62) | (0.58) | |

Cash to assets$$_{t-3}$$ | 0.0015^{***} | 0.0014^{***} | 0.0127^{***} |

(4.14) | (4.62) | (2.80) | |

EBITDA to assets$$_{t-3}$$ | 0.0009 | 0.0006 | -0.0123 |

(1.03) | (0.74) | (-1.30) | |

Dividends to assets$$_{t-3}$$ | -0.0008 | -0.0009 | 0.0473^{*} |

(-0.41) | (-0.56) | (1.93) | |

Leverage$$_{t-3}$$ | -0.0048^{***} | -0.0041^{***} | 0.0024 |

(-13.03) | (-13.65) | (0.53) | |

Acquiror dummy$$_{t}$$ | -0.0004^{***} | -0.0003^{***} | 0.0005 |

(-5.39) | (-4.86) | (1.13) | |

Target dummy$$_{t}$$ | -0.0004 | -0.0003 | 0.0005 |

(-1.61) | (-1.10) | (0.35) | |

Relative spread$$_{t-1}$$ (ln) | -0.0000 | 0.0001^{*} | 0.0004 |

(-0.13) | (1.83) | (0.62) | |

Constant | -0.0042^{***} | -0.0034^{***} | 0.0071 |

(-6.43) | (-6.30) | (0.88) | |

$$R^2$$ (within firm) | 0.061 | 0.102 | 0.563 |

Observations | 134,081 | 133,869 | 134,428 |

Firm FE and month FE | Y | Y | Y |

The table presents OLS regressions of *Repurchase intensity* and *Remaining volume* on *Returns*, instruments, and control variables. All variables are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

In Columns (1) and (2), we analyze *Repurchase intensity*. The program characteristics *Program month* and *Program size*, which we use as instruments for repurchases, are highly significant and in line with Hillert, Maug, and Obernberger (2016). The coefficient on *Program month* is negative, indicating that repurchase activity is highest at the beginning of the program. The positive coefficient on *Program size* is also in line with what one would expect: *Repurchase intensity* is higher when program size is larger.

In Column (2), we add the lagged dependent variable to assess its fit for use as a proxy for repurchase activity. Using a noisy measure of an independent variable causes attenuation, which biases the coefficient estimate toward zero. Thus, if lagged *Repurchase intensity* was a weak proxy for contemporaneous *Repurchase intensity*, it would be harder for us to obtain significant results. In the regression analysis of *Repurchase intensity* depicted in Column (2), the lagged dependent variable has a positive coefficient of 0.2. As we control for firm fixed effects that already pick up the average effect of *Repurchase intensity*, the impact of lagged *Repurchase intensity* appears to be economically highly significant. In line with this observation, the explanatory power of the model (excluding the variation already explained by the fixed effects) increases from 6% to 10% when including the lagged dependent variable. We conclude that lagged *Repurchase intensity* is the best predictor we have at our disposal.

For *Repurchase intensity*, the results on the controls match well with the results from the existing literature. Our results confirm earlier studies on the relation between compensation of employees and executives and actual share repurchases (Fenn and Liang 2001; Babenko 2009; Bonaimé and Ryngaert 2013): *Options exercised* has a positive impact on repurchases. Furthermore, repurchases are higher when corporate insiders sell their stock (see *Net insider trading*) or when employees hold many stock options in the firm (see *Options outstanding*). In line with earlier literature (cf., e.g., Stephens and Weisbach 1998; Dittmar 2000), we find that *Repurchase intensity* is driven by lagged negative returns, whereas lagged positive returns have no statistically significant impact. Firms also buy back more when their book-to-market ratio is higher, suggesting that valuation is factored in the repurchase decision. This result is in line with the notion that managers buy back when they consider the firm’s stock price to be low. Jensen (1986) and Stephens and Weisbach (1998) find that firms tend to repurchase more shares if they have stronger cash flows. Coefficients on *EBITDA to assets* come in with the right sign, but lack statistical significance. Once *Cash to assets* has been controlled for*, EBITDA to assets* does not impact share repurchases. Dividends seem to have no impact on repurchases, consistent with the notion that firms view repurchases as complements to dividends rather than as substitutes. Dittmar (2000) shows that firms use repurchases to increase leverage, consistent with our result that firms with higher leverage conduct fewer repurchases. The dummy variable *Acquiror* indicates acquiror status in a takeover and has a negative impact on repurchases. The dummy variable *Target* indicates target status in a takeover attempt and equals one from the time of the announcement until the completion or cancellation of the takeover. Bagwell (1991) develops a theoretical model to show that repurchases may serve as a takeover defense, and Dittmar (2000) confirms the prediction of the model empirically. However, we do not find significant results. *Repurchase intensity* is driven by liquidity as indicated by the lagged relative spread.^{11}

In Column (3), we analyze *Remaining volume*, which denotes the number of shares that can be repurchased at the beginning of the month scaled by shares outstanding as of the beginning of the program. In this specification, most of the controls remain insignificant when controlling for *Program size*, which accounts for more than 50% of the variation in *Remaining volume*. Most importantly, the coefficients on lagged returns for *Remaining volume,* which is determined at the beginning of the month, are insignificant. Thus, the number of shares that still can be repurchased under the currently active program is not affected by prior returns. No such relationship exists because firms can always add an additional repurchase program when needed. *Remaining volume*, therefore, has two major advantages over *Repurchase intensity*. First, it is fixed at the beginning of the month, allowing us to exclude reverse causality in the subsequent analyses. Second, as *Remaining volume* is not driven by prior returns, comovement of this variable and our measures of efficiency (which are likely to be driven by lagged returns) are much less of a concern. The coefficients on *Cash to assets* and *Dividends to assets* are positive and statistically significant, indicating that higher cash and higher propensity to pay out dividends increase the volume that can be repurchased in the next quarter.

In

in the , we check the robustness of our results by estimating a Tobit model like in Dittmar (2000). The results are qualitatively similar. In particular, the coefficients on lagged*Repurchase intensity*,

*Program size*, and

*Program month*exhibit the correct sign and high statistical significance.

### 3.2 Share repurchases and price efficiency

Table 4 reports the results on the impact of actual repurchases on price efficiency. We analyze *Delay* and *Coefficient-based delay* in Columns (1) to (3) and Columns (4) to (6), respectively. In Columns (1) and (4), we predict *Repurchase intensity* using *Program size* and *Program month* as instruments. For both models, we cannot reject the overidentifying restrictions.^{12} We test for underidentification by using the statistic proposed by Kleibergen and Paap (2006). Their test is for the rank of a matrix, and, in our case, it checks the rank of the matrix of reduced-form coefficients and tests whether the instruments are sufficient to identify the endogenous variables. We can reject the null hypothesis of underidentification for all of our models. The Stock-Yogo test on the weak-instrument bias always rejects the hypothesis that the bias exceeds 5% of the bias from OLS (not tabulated). Furthermore, the instruments are statistically significantly different from zero and have the predicted signs as shown in Table 3: higher *Program size* implies higher *Repurchase intensity*, and a later *Program month* implies lower *Repurchase intensity*. We therefore conclude that the models are correctly specified. In Columns (2) and (5), we proxy for *Repurchase intensity* by using *Repurchase intensity* of the previous month. In Columns (3) and (6), we use *Remaining volume* as a measure of a firm’s ability to use share repurchases to intervene in the stock market

Dependent variable: | Delay | Coefficient-based delay | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{{\it Repurchase} \: {\it intensity}}_{t}$$ | -2.8020^{***} | -4.5158^{**} | ||||

(-2.91) | (-2.31) | |||||

Repurchase intensity$$_{t-1}$$ | -0.6429^{***} | -1.2656^{***} | ||||

(-5.49) | (-4.72) | |||||

Remaining volume$$_{t}$$ | -0.0612^{***} | -0.1240^{***} | ||||

(-2.66) | (-2.63) | |||||

Delay$$_{t-1}$$ | 0.0875^{***} | 0.0868^{***} | 0.0867^{***} | |||

(26.68) | (26.64) | (26.63) | ||||

Coefficient-based | 0.0298^{***} | 0.0296^{***} | 0.0295^{***} | |||

$$\quad$$ delay$$_{t-1}$$ | (10.57) | (10.57) | (10.56) | |||

Return$$_{t-1}$$ > 0 | -0.0160^{**} | -0.0119^{*} | -0.0118^{*} | -0.0223 | -0.0170 | -0.0168 |

(-2.28) | (-1.70) | (-1.68) | (-1.38) | (-1.06) | (-1.04) | |

Return$$_{t-1}$$ 0 | -0.0893^{***} | -0.0812^{***} | -0.0806^{***} | -0.1671^{***} | -0.1524^{***} | -0.1511^{***} |

(-8.64) | (-8.16) | (-8.10) | (-7.28) | (-6.80) | (-6.74) | |

Program initiation$$_{t}$$ | 0.0352^{***} | 0.0277^{***} | 0.0256^{***} | 0.0651^{***} | 0.0509^{***} | 0.0468^{***} |

(7.44) | (8.16) | (7.49) | (6.42) | (6.75) | (6.15) | |

Market cap$$_{t-1}$$ (ln) | -0.0320^{***} | -0.0334^{***} | -0.0336^{***} | -0.0573^{***} | -0.0594^{***} | -0.0597^{***} |

(-10.16) | (-10.66) | (-10.72) | (-9.05) | (-9.44) | (-9.51) | |

Book to market$$_{t-3}$$ | 0.0183^{***} | 0.0174^{***} | 0.0172^{***} | 0.0319^{***} | 0.0305^{***} | 0.0302^{***} |

(6.37) | (6.09) | (6.03) | (5.31) | (5.09) | (5.03) | |

Volatility$$_{t-1}$$ (ln) | -0.0437^{***} | -0.0442^{***} | -0.0442^{***} | -0.0783^{***} | -0.0787^{***} | -0.0788^{***} |

(-21.36) | (-21.53) | (-21.57) | (-17.67) | (-17.73) | (-17.79) | |

Analysts$$_{t-1}$$ (ln) | -0.0087^{***} | -0.0094^{***} | -0.0096^{***} | -0.0183^{***} | -0.0196^{***} | -0.0199^{***} |

(-3.03) | (-3.24) | (-3.31) | (-3.05) | (-3.23) | (-3.29) | |

Relative Spread$$_{t-1}$$ (ln) | 0.0392^{***} | 0.0392^{***} | 0.0396^{***} | 0.0674^{***} | 0.0676^{***} | 0.0683^{***} |

(18.64) | (18.65) | (18.85) | (14.38) | (14.40) | (14.57) | |

Deviation from $\$$ 30$$_{t-1}$$ | 0.0029^{***} | 0.0029^{***} | 0.0029^{***} | 0.0056^{***} | 0.0057^{***} | 0.0057^{***} |

(2.83) | (2.84) | (2.85) | (2.59) | (2.63) | (2.65) | |

Trading volume$$_{t-1}$$ | 0.0119^{***} | 0.0125^{***} | 0.0126^{***} | 0.0132^{**} | 0.0144^{**} | 0.0147^{**} |

$$\quad$$ (scaled) | (4.41) | (4.63) | (4.70) | (2.12) | (2.36) | (2.42) |

Change in short | -0.0224 | -0.0321 | -0.0447 | -0.0657 | -0.0528 | -0.0776 |

$$\quad$$ interest$$_{t-1}$$ | (-0.41) | (-0.61) | (-0.84) | (-0.57) | (-0.46) | (-0.67) |

Institutional | -0.0815^{***} | -0.0853^{***} | -0.0846^{***} | -0.0846^{***} | -0.0898^{***} | -0.0883^{***} |

$$\quad$$ ownership$$_{t-3}$$ | (-7.20) | (-7.50) | (-7.43) | (-3.78) | (-4.00) | (-3.94) |

Constant | 0.7138^{***} | 0.7176^{***} | 2.2576^{***} | 2.2652^{***} | ||

(32.70) | (32.86) | (51.04) | (51.17) | |||

$$R^2$$ (within firm) | 0.131 | 0.149 | 0.149 | 0.094 | 0.112 | 0.112 |

Observations | 155,573 | 156,718 | 156,718 | 155,556 | 156,700 | 156,700 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 1.15 | 0.98 | ||||

Hansen’s J (p-value) | 28.43% | 32.22% | ||||

Kleibergen-Paap (test) | 319.8 | 319.2 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% |

Dependent variable: | Delay | Coefficient-based delay | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{{\it Repurchase} \: {\it intensity}}_{t}$$ | -2.8020^{***} | -4.5158^{**} | ||||

(-2.91) | (-2.31) | |||||

Repurchase intensity$$_{t-1}$$ | -0.6429^{***} | -1.2656^{***} | ||||

(-5.49) | (-4.72) | |||||

Remaining volume$$_{t}$$ | -0.0612^{***} | -0.1240^{***} | ||||

(-2.66) | (-2.63) | |||||

Delay$$_{t-1}$$ | 0.0875^{***} | 0.0868^{***} | 0.0867^{***} | |||

(26.68) | (26.64) | (26.63) | ||||

Coefficient-based | 0.0298^{***} | 0.0296^{***} | 0.0295^{***} | |||

$$\quad$$ delay$$_{t-1}$$ | (10.57) | (10.57) | (10.56) | |||

Return$$_{t-1}$$ > 0 | -0.0160^{**} | -0.0119^{*} | -0.0118^{*} | -0.0223 | -0.0170 | -0.0168 |

(-2.28) | (-1.70) | (-1.68) | (-1.38) | (-1.06) | (-1.04) | |

Return$$_{t-1}$$ 0 | -0.0893^{***} | -0.0812^{***} | -0.0806^{***} | -0.1671^{***} | -0.1524^{***} | -0.1511^{***} |

(-8.64) | (-8.16) | (-8.10) | (-7.28) | (-6.80) | (-6.74) | |

Program initiation$$_{t}$$ | 0.0352^{***} | 0.0277^{***} | 0.0256^{***} | 0.0651^{***} | 0.0509^{***} | 0.0468^{***} |

(7.44) | (8.16) | (7.49) | (6.42) | (6.75) | (6.15) | |

Market cap$$_{t-1}$$ (ln) | -0.0320^{***} | -0.0334^{***} | -0.0336^{***} | -0.0573^{***} | -0.0594^{***} | -0.0597^{***} |

(-10.16) | (-10.66) | (-10.72) | (-9.05) | (-9.44) | (-9.51) | |

Book to market$$_{t-3}$$ | 0.0183^{***} | 0.0174^{***} | 0.0172^{***} | 0.0319^{***} | 0.0305^{***} | 0.0302^{***} |

(6.37) | (6.09) | (6.03) | (5.31) | (5.09) | (5.03) | |

Volatility$$_{t-1}$$ (ln) | -0.0437^{***} | -0.0442^{***} | -0.0442^{***} | -0.0783^{***} | -0.0787^{***} | -0.0788^{***} |

(-21.36) | (-21.53) | (-21.57) | (-17.67) | (-17.73) | (-17.79) | |

Analysts$$_{t-1}$$ (ln) | -0.0087^{***} | -0.0094^{***} | -0.0096^{***} | -0.0183^{***} | -0.0196^{***} | -0.0199^{***} |

(-3.03) | (-3.24) | (-3.31) | (-3.05) | (-3.23) | (-3.29) | |

Relative Spread$$_{t-1}$$ (ln) | 0.0392^{***} | 0.0392^{***} | 0.0396^{***} | 0.0674^{***} | 0.0676^{***} | 0.0683^{***} |

(18.64) | (18.65) | (18.85) | (14.38) | (14.40) | (14.57) | |

Deviation from $\$$ 30$$_{t-1}$$ | 0.0029^{***} | 0.0029^{***} | 0.0029^{***} | 0.0056^{***} | 0.0057^{***} | 0.0057^{***} |

(2.83) | (2.84) | (2.85) | (2.59) | (2.63) | (2.65) | |

Trading volume$$_{t-1}$$ | 0.0119^{***} | 0.0125^{***} | 0.0126^{***} | 0.0132^{**} | 0.0144^{**} | 0.0147^{**} |

$$\quad$$ (scaled) | (4.41) | (4.63) | (4.70) | (2.12) | (2.36) | (2.42) |

Change in short | -0.0224 | -0.0321 | -0.0447 | -0.0657 | -0.0528 | -0.0776 |

$$\quad$$ interest$$_{t-1}$$ | (-0.41) | (-0.61) | (-0.84) | (-0.57) | (-0.46) | (-0.67) |

Institutional | -0.0815^{***} | -0.0853^{***} | -0.0846^{***} | -0.0846^{***} | -0.0898^{***} | -0.0883^{***} |

$$\quad$$ ownership$$_{t-3}$$ | (-7.20) | (-7.50) | (-7.43) | (-3.78) | (-4.00) | (-3.94) |

Constant | 0.7138^{***} | 0.7176^{***} | 2.2576^{***} | 2.2652^{***} | ||

(32.70) | (32.86) | (51.04) | (51.17) | |||

$$R^2$$ (within firm) | 0.131 | 0.149 | 0.149 | 0.094 | 0.112 | 0.112 |

Observations | 155,573 | 156,718 | 156,718 | 155,556 | 156,700 | 156,700 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 1.15 | 0.98 | ||||

Hansen’s J (p-value) | 28.43% | 32.22% | ||||

Kleibergen-Paap (test) | 319.8 | 319.2 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% |

The table presents OLS and GMM regressions of *Delay* and *Coefficient-based delay* on either *Repurchase intensity* or *Remaining volume* and control variables. The dependent variable is *Delay* in specifications (1)-(3) and *Coefficient-based delay* in specifications (4)-(6). In specifications (1) and (4) the repurchase variables are instrumented using *Program size* and *Program month*. Instrumented variables are in italics and marked with a circumflex. In specifications (2) and (5) the repurchase variables are included as predetermined values. The repurchase variables and the control variables are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions. The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The table reports the test statistics and the *p*-values for both tests.

We find that repurchases unequivocally decrease price delay, regardless of which specification and measure of price delay we use. In Column (1), an increase by one within-firm standard deviation in *Repurchase intensity* decreases *Delay* by 0.0227 percentage points ($$=0.0081\times-2.8020$$, where $$-2.8020$$ is the coefficient on *Repurchase intensity* from Table 4), which corresponds to 4.88% of median *Delay* ($$=0.0227/0.465$$, where 0.465 is the median of *Delay* obtained from Table 2). Boehmer and Wu (2013) document a lower effect of shorting on price delay. In their Model 2 in Table 3, which includes time and firm fixed effects, a one-standard-deviation increase in shorting (0.068), reduces delay by 2.49% ($$=(0.160\times0.068)/0.437$$, where 0.160 is the coefficient on shorting and 0.437 is the median delay).^{13}Saffi and Sigurdsson (2011) report that a “one-standard-deviation increase in lending supply is associated with a decrease in [delay] of 0.097 standard deviations.” In our case, which only considers within-firm variation, a one-standard-deviation increase in *Repurchase intensity* reduces *Delay* by 0.090 standard deviations.

The coefficient on lagged *Repurchase intensity* in Column (2) is lower by a factor of 4.4 compared with Column (1), which could indicate that lagged *Repurchase intensity* is a more noisy measure of contemporaneous repurchases and, therefore, the coefficient estimate might suffer from an attenuation bias. In Column (3), an increase by one within-firm standard deviation in *Remaining volume* decreases *Delay* by 0.0023 percentage points ($$=0.0377\times-0.0612$$, where $$-0.0612$$ is the coefficient on *Remaining volume* from Table 4), which corresponds to 0.50% of median *Delay* ($$=0.0023/0.465$$, where 0.465 is the median of *Delay* obtained from Table 2). For *Coefficient-based delay*, GMM diagnostics, coefficients, test statistics, and economic significance are qualitatively similar.

In conclusion, our results suggest that share repurchases increase the speed and accuracy with which information is incorporated into the stock price. We conclude that repurchases lead to both higher price efficiency and higher information content of stock prices. The evidence is not consistent with the notion that share repurchases are used to manipulate share prices, as in this case we should observe higher price delay.

The coefficients for the control variables are reasonable and mostly in line with the prior literature. We observe in all specifications that *Delay* decreases with size, analyst coverage, and liquidity. This result is in line with the results of Hou and Moskowitz (2005), Saffi and Sigurdsson (2011), and Phillips (2011). The coefficient on *Book to market* indicates that *Delay* is lower when stocks are valued higher. Phillips (2011) reports the same sign when analyzing the change in price delay.^{14} However, his results are mostly not statistically different from zero. For the dummy variable indicating the initiation month, the coefficient is significantly positive. This is plausible considering that the initiation of a repurchase program is associated with abnormal returns (cf., e.g., Peyer and Vermaelen 2009). We observe that *Delay* decreases with higher *Volatility*. Phillips (2011) reports a similar result for an analysis of the change in delay. Again, his results are not statistically different from zero. An increase in short interest decreases *Delay*, which is, for example, documented in Boehmer and Wu (2013). Surprisingly, we are not able to document a statistically significant relationship between changes in short interest and price delay. In

*Trading volume*is positive and statistically significant, but we would have expected a negative coefficient as reported by Boehmer and Wu (2013). In in the , we demonstrate that this result is driven by the other liquidity controls. We obtain the expected coefficient when we exclude all other liquidity controls and conclude that the variation in

*Trading volume*positively associated with delay is already picked up by these other liquidity controls. Finally, higher institutional ownership is associated with lower price delay as documented in Boehmer and Kelley (2009).

### 3.3 Share repurchases and idiosyncratic risk

In the previous section we looked at the speed with which information is incorporated into stock prices. In this section, we take another perspective and analyze the impact of share repurchases on the relative amounts of idiosyncratic risk and systematic risk. If firms manipulate prices or incorporate firm-specific information, idiosyncratic risk should go up. If firms provide price support as suggested by Hong, Wang, and Yu (2008), idiosyncratic risk should go down. We use the same research design as in Section 3.2 and analyze *R-squared* and *Market correlation* in Columns (1) to (3) and Columns (4) to (6) of Table 5, respectively.

Dependent variable: | R-squared | |Market correlation| | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{{\it Repurchase} \: {\it intensity}}_{t}$$ | 1.7350^{**} | 2.0315^{***} | ||||

(2.41) | (2.65) | |||||

Repurchase intensity$$_{t-1}$$ | 0.4569^{***} | 0.5377^{***} | ||||

(5.46) | (6.19) | |||||

Remaining volume$$_{t}$$ | 0.0407^{**} | 0.0481^{***} | ||||

(2.33) | (2.59) | |||||

R-squared$$_{t-1}$$ | 0.1423^{***} | 0.1418^{***} | 0.1417^{***} | |||

(37.32) | (37.38) | (37.36) | ||||

|Market correlation|$$_{t-1}$$ | 0.1220^{***} | 0.1216^{***} | 0.1215^{***} | |||

(34.23) | (34.39) | (34.37) | ||||

Program initiation$$_{t}$$ | -0.0309^{***} | -0.0255^{***} | -0.0240^{***} | -0.0319^{***} | -0.0262^{***} | -0.0245^{***} |

(-8.89) | (-10.81) | (-10.09) | (-8.56) | (-10.12) | (-9.37) | |

Market cap$$_{t-1}$$ (ln) | 0.0221^{***} | 0.0227^{***} | 0.0228^{***} | 0.0242^{***} | 0.0249^{***} | 0.0250^{***} |

(9.83) | (10.10) | (10.14) | (9.74) | (10.05) | (10.09) | |

Book to market$$_{t-3}$$ | -0.0128^{***} | -0.0127^{***} | -0.0126^{***} | -0.0126^{***} | -0.0123^{***} | -0.0122^{***} |

(-6.47) | (-6.43) | (-6.38) | (-5.64) | (-5.51) | (-5.46) | |

Analysts$$_{t-1}$$ (ln) | 0.0032 | 0.0038^{*} | 0.0040^{*} | 0.0060^{***} | 0.0068^{***} | 0.0070^{***} |

(1.56) | (1.83) | (1.90) | (2.63) | (2.96) | (3.03) | |

Relative spread$$_{t-1}$$ (ln) | -0.0273^{***} | -0.0271^{***} | -0.0274^{***} | -0.0278^{***} | -0.0276^{***} | -0.0279^{***} |

(-17.75) | (-17.67) | (-17.88) | (-16.73) | (-16.57) | (-16.79) | |

Deviation from $\$$ 30$$_{t-1}$$ | -0.0030^{***} | -0.0031^{***} | -0.0031^{***} | -0.0030^{***} | -0.0030^{***} | -0.0030^{***} |

(-3.90) | (-3.90) | (-3.91) | (-3.66) | (-3.66) | (-3.67) | |

Trading volume$$_{t-1}$$ (scaled) | 0.0068 | 0.0066 | 0.0065 | 0.0044 | 0.0041 | 0.0040 |

(1.63) | (1.59) | (1.57) | (1.06) | (1.01) | (0.98) | |

Change in short interest$$_{t-1}$$ | -0.0137 | -0.0105 | -0.0018 | 0.0444 | 0.0478 | 0.0582 |

(-0.36) | (-0.28) | (-0.05) | (1.09) | (1.18) | (1.44) | |

Institutional ownership$$_{t-3}$$ | 0.0285^{***} | 0.0314^{***} | 0.0309^{***} | 0.0581^{***} | 0.0612^{***} | 0.0607^{***} |

(3.61) | (3.97) | (3.91) | (6.67) | (7.01) | (6.94) | |

Constant | -0.0500^{***} | -0.0526^{***} | 0.0877^{***} | 0.0847^{***} | ||

(-3.39) | (-3.55) | (5.34) | (5.15) | |||

$$R^2$$ (within firm) | 0.231 | 0.246 | 0.246 | 0.185 | 0.201 | 0.201 |

Observations | 155,569 | 156,715 | 156,715 | 155,574 | 156,720 | 156,720 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 0.89 | 0.91 | ||||

Hansen’s J (p-value) | 34.47% | 34.06% | ||||

Kleibergen-Paap (test) | 316.8 | 316.5 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% |

Dependent variable: | R-squared | |Market correlation| | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{{\it Repurchase} \: {\it intensity}}_{t}$$ | 1.7350^{**} | 2.0315^{***} | ||||

(2.41) | (2.65) | |||||

Repurchase intensity$$_{t-1}$$ | 0.4569^{***} | 0.5377^{***} | ||||

(5.46) | (6.19) | |||||

Remaining volume$$_{t}$$ | 0.0407^{**} | 0.0481^{***} | ||||

(2.33) | (2.59) | |||||

R-squared$$_{t-1}$$ | 0.1423^{***} | 0.1418^{***} | 0.1417^{***} | |||

(37.32) | (37.38) | (37.36) | ||||

|Market correlation|$$_{t-1}$$ | 0.1220^{***} | 0.1216^{***} | 0.1215^{***} | |||

(34.23) | (34.39) | (34.37) | ||||

Program initiation$$_{t}$$ | -0.0309^{***} | -0.0255^{***} | -0.0240^{***} | -0.0319^{***} | -0.0262^{***} | -0.0245^{***} |

(-8.89) | (-10.81) | (-10.09) | (-8.56) | (-10.12) | (-9.37) | |

Market cap$$_{t-1}$$ (ln) | 0.0221^{***} | 0.0227^{***} | 0.0228^{***} | 0.0242^{***} | 0.0249^{***} | 0.0250^{***} |

(9.83) | (10.10) | (10.14) | (9.74) | (10.05) | (10.09) | |

Book to market$$_{t-3}$$ | -0.0128^{***} | -0.0127^{***} | -0.0126^{***} | -0.0126^{***} | -0.0123^{***} | -0.0122^{***} |

(-6.47) | (-6.43) | (-6.38) | (-5.64) | (-5.51) | (-5.46) | |

Analysts$$_{t-1}$$ (ln) | 0.0032 | 0.0038^{*} | 0.0040^{*} | 0.0060^{***} | 0.0068^{***} | 0.0070^{***} |

(1.56) | (1.83) | (1.90) | (2.63) | (2.96) | (3.03) | |

Relative spread$$_{t-1}$$ (ln) | -0.0273^{***} | -0.0271^{***} | -0.0274^{***} | -0.0278^{***} | -0.0276^{***} | -0.0279^{***} |

(-17.75) | (-17.67) | (-17.88) | (-16.73) | (-16.57) | (-16.79) | |

Deviation from $\$$ 30$$_{t-1}$$ | -0.0030^{***} | -0.0031^{***} | -0.0031^{***} | -0.0030^{***} | -0.0030^{***} | -0.0030^{***} |

(-3.90) | (-3.90) | (-3.91) | (-3.66) | (-3.66) | (-3.67) | |

Trading volume$$_{t-1}$$ (scaled) | 0.0068 | 0.0066 | 0.0065 | 0.0044 | 0.0041 | 0.0040 |

(1.63) | (1.59) | (1.57) | (1.06) | (1.01) | (0.98) | |

Change in short interest$$_{t-1}$$ | -0.0137 | -0.0105 | -0.0018 | 0.0444 | 0.0478 | 0.0582 |

(-0.36) | (-0.28) | (-0.05) | (1.09) | (1.18) | (1.44) | |

Institutional ownership$$_{t-3}$$ | 0.0285^{***} | 0.0314^{***} | 0.0309^{***} | 0.0581^{***} | 0.0612^{***} | 0.0607^{***} |

(3.61) | (3.97) | (3.91) | (6.67) | (7.01) | (6.94) | |

Constant | -0.0500^{***} | -0.0526^{***} | 0.0877^{***} | 0.0847^{***} | ||

(-3.39) | (-3.55) | (5.34) | (5.15) | |||

$$R^2$$ (within firm) | 0.231 | 0.246 | 0.246 | 0.185 | 0.201 | 0.201 |

Observations | 155,569 | 156,715 | 156,715 | 155,574 | 156,720 | 156,720 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 0.89 | 0.91 | ||||

Hansen’s J (p-value) | 34.47% | 34.06% | ||||

Kleibergen-Paap (test) | 316.8 | 316.5 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% |

The table presents OLS and GMM regressions of *R-squared* and *Absolute market correlation* on either *Repurchase intensity* or *Remaining volume* and control variables. The dependent variable is *R-squared* in specifications (1)-(3) and *Market correlation* in specifications (4)-(6). In specifications (1) and (4) the repurchase variables instrumented using *Program size* and *Program month*. Instrumented variables are in italics and marked with a circumflex. In specifications (2) and (5) the repurchase variables are included as predetermined values. The repurchase variables and the control variables are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions. The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The table reports the test statistics and the *p*-values for both tests.

In Column (1), we estimate a GMM-IV model of *R-squared* using *Program size* and *Program month* as instruments. As in the previous analysis, we can reject the hypothesis of underidentification, that the instruments are weak, and that the bias exceeds the OLS bias by more than 5%. The results corroborate that share repurchases decrease idiosyncratic risk: An increase by one within-firm standard deviation in *Repurchase intensity* increases *R-squared* by 0.0141 points ($$=0.0081\times1.7350$$, where 1.7350 is the coefficient on *Repurchase intensity* from Column (1) in Table 5), which corresponds to 6.34% of median *R-squared* ($$=0.0141/0.2217$$, where 0.2217 is the median of *R-squared* obtained from Table 2).

We confirm this result in Column (2), where we again use a predetermined variable instead of a contemporaneous instrumented one. For the reasons discussed above, the coefficients are, however, again much lower. For *Remaining volume*, the impact is qualitatively the same but is much less pronounced. For a within-firm standard deviation increase in *Remaining volume*, *R-squared* is higher by 0.0019 points ($$=0.0385 \times 0.0407$$, where 0.0407 is the coefficient on *Remaining volume* from Column (2) in Table 5), which corresponds to 0.71% ($$=0.0016/0.2217$$) of median *R-squared*. In Columns (4) to (6), we repeat the analysis with a measure of synchronicity, *Market correlation*. GMM diagnostics, coefficients, test statistics, and economic significance are in the same ballpark as for *R-squared*.

Most of our controls come in with the expected sign. In line with Roll (1988), Hutton, Marcus, and Tehranian (2009), Piotroski and Roulstone (2004), and Ferreira and Laux (2007), larger firms have higher *R-squared,* suggesting that noise is lower in these firms. *R-squared* also increases in the number of analysts that can be interpreted in a similar way. The results in the literature for the impact of valuation measured by *Book to market* are mixed (cf. Hutton, Marcus, and Tehranian 2009; Ferreira and Laux 2007). We obtain a negative coefficient, which we find difficult to interpret. Liquidity measures are, in general, associated with higher *R-squared* and lower idiosyncratic risk (cf. Bris, Goetzmann, and Zhu 2007). Our results are in line with this result from the literature. For *Trading volume*, we do not find significant results. As outlined in Section 3.2, other liquidity measures already control for the effect, and removing these measures leads to significant results. Bris, Goetzmann, and Zhu (2007) find that changes in short interest reduce *R-squared*. We cannot confirm this result for our specification, but respecifying the model as in

Since share repurchases increase the synchronicity between the stock and the market, the evidence is not consistent with the notion that share repurchases increase the amount of noise or that share repurchases incorporate private information in the stock price.

### 3.4 Do firms incorporate positive information or provide price support at fundamental values?

So far, we have established that share repurchases improve the efficiency of stock prices and reduce idiosyncratic risk. More still can be learned about the mechanism that brings about this effect. As outlined in the Introduction, share repurchases can increase price efficiency in two ways. First, firms can trade on the basis of positive public information not yet incorporated in the stock price. Following this argument, firms recognize that, in the light of new information, their shares should be worth more, and, accordingly, they buy shares until prices reach fundamental values. Second, firms can improve the accuracy with which negative public information is incorporated into the stock price by using share repurchases to prevent prices from dropping below (diverging from) fundamental values.

Each of the two aforementioned mechanisms has distinct empirical predictions. If firms incorporate positive public information into the stock price, we should observe increases in price efficiency in months with positive news. If firms help to price negative public information more accurately by establishing a lower bound at the fundamental value, we should observe increases in price efficiency when there is negative news. For the empirical analysis, we use the market return over the current month to determine whether positive news or negative news come to the market and split our repurchase variables in months in which the market goes up and months in which the market goes down. This approach reflects our dependent variable that examines the speed and accuracy with which lagged market returns are incorporated into the stock price and builds on the insight that idiosyncratic risk is lower when repurchases are higher.

We use the same specification as presented in Tables 4 and 5 with the only distinction being that we split up our repurchase variable. We interact our measure of repurchase activity with dummy variables, indicating whether the stock market went up or down. We do not include level variables in this specification because they are collinear with other included variables: *Repurchase intensity* is collinear with the vector *Repurchase intensity**x**Up market* and *Repurchase intensity**x Down market*. Dummy variables for up markets or down markets are furthermore collinear with time fixed effects.

Table 6 presents the results for price delay in panel A and idiosyncratic risk in panel B. The coefficient estimates on the interaction terms have the same sign as in the previous analyses. In up markets, most of the coefficient estimates are statistically insignificant or marginally significant, and their size decreases by about 50%. In down markets, however, the size of the coefficient estimates increases by a factor of two to three relative to the results in Tables 4 and 5. In panel A Column (1), a down-market repurchase of the size of median *Repurchase intensity* decreases *Delay* by 0.0365 points, which corresponds to 7.86% of median *Delay*. In panel B Column (1), a down-market repurchase of the size of median *Repurchase intensity* increases *R-squared* by 0.0294 points, which corresponds to 13.26% of median *R-squared*. For the GMM model of *R-squared*, we have to reject the null hypothesis that the model is correctly specified (Hansen J test) at the 10% level. However, in Column (4), we cannot reject the same model for *Market correlation*, for which we obtain results in the same order of magnitude. The results provide a consistent picture regardless of which measure of efficiency or specification we use: share repurchases decrease price delay and idiosyncratic risk in months in which the stock market goes down, that is, when negative information comes to the market.

Dependent variable: | Delay | Coefficient-based delay | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{\it Rep. \; intensity}_{t}$$ | -1.4623 | -2.1348 | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-1.28) | (-0.91) | ||||

$$\widehat{\it Rep. \; intensity}_{t}$$ | -4.5103^{***} | -7.1483^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (-4.42) | (-3.24) | ||||

Rep. intensity$$_{t-1}$$ | -0.3315^{**} | -0.5418 | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-2.22) | (-1.61) | ||||

Rep. intensity$$_{t-1}$$ | -1.0563^{***} | -2.2267^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (-6.19) | (-5.90) | ||||

Rem. volume$$_{t}$$ | -0.0415^{*} | -0.0929^{*} | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-1.69) | (-1.86) | ||||

Rem. volume$$_{t}$$ | -0.0884^{***} | -0.1671^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (-3.55) | (-3.11) | ||||

$$R^2$$ (within firm) | 0.130 | 0.149 | 0.149 | 0.094 | 0.112 | 0.112 |

Observations | 156,713 | 156,718 | 156,718 | 156,695 | 156,700 | 156,700 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 2.33 | 3.11 | ||||

Hansen’s J (p-value) | 31.11% | 21.08% | ||||

Kleibergen-Paap (test) | 318.0 | 316.9 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% | ||||

Wald (up - down) (test) | 10.14 | 11.48 | 6.76 | 5.08 | 13.09 | 3.06 |

Wald (up - down) (p-value) | 0.15% | 0.07% | 0.94% | 2.42% | 0.03% | 8.04% |

B. The influence of repurchases on R-squared and absolute market correlation in up and down markets | ||||||

Dependent variable: | R-squared | |Market correlation| | ||||

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{\it Rep. \; intensity}_{t}$$ | -0.0948 | 0.6820 | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-0.12) | (0.76) | ||||

$$\widehat{\it Rep. \; intensity}_{t}$$ | 3.6301^{***} | 3.5997^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (4.46) | (4.40) | ||||

Rep. intensity$$_{t-1}$$ | 0.0548 | 0.2069^{*} | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (0.54) | (1.89) | ||||

Rep. intensity$$_{t-1}$$ | 0.9909^{***} | 0.9770^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (7.59) | (7.63) | ||||

Rem. volume$$_{t}$$ | 0.0186 | 0.0324^{*} | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (1.03) | (1.65) | ||||

Rem. volume$$_{t}$$ | 0.0712^{***} | 0.0699^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (3.64) | (3.50) | ||||

$$R^2$$ (within firm) | 0.228 | 0.246 | 0.246 | 0.183 | 0.202 | 0.201 |

Observations | 156,710 | 156,715 | 156,715 | 156,715 | 156,720 | 156,720 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 4.76 | 1.88 | ||||

Hansen’s J (p-value) | 9.27% | 38.98% | ||||

Kleibergen-Paap (test) | 314.9 | 314.7 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% | ||||

Wald (up – down) (test) | 24.25 | 34.52 | 12.79 | 15.12 | 22.69 | 6.59 |

Wald (up – down) (p-value) | 0.00% | 0.00% | 0.04% | 0.01% | 0.00% | 1.03% |

Dependent variable: | Delay | Coefficient-based delay | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{\it Rep. \; intensity}_{t}$$ | -1.4623 | -2.1348 | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-1.28) | (-0.91) | ||||

$$\widehat{\it Rep. \; intensity}_{t}$$ | -4.5103^{***} | -7.1483^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (-4.42) | (-3.24) | ||||

Rep. intensity$$_{t-1}$$ | -0.3315^{**} | -0.5418 | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-2.22) | (-1.61) | ||||

Rep. intensity$$_{t-1}$$ | -1.0563^{***} | -2.2267^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (-6.19) | (-5.90) | ||||

Rem. volume$$_{t}$$ | -0.0415^{*} | -0.0929^{*} | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-1.69) | (-1.86) | ||||

Rem. volume$$_{t}$$ | -0.0884^{***} | -0.1671^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (-3.55) | (-3.11) | ||||

$$R^2$$ (within firm) | 0.130 | 0.149 | 0.149 | 0.094 | 0.112 | 0.112 |

Observations | 156,713 | 156,718 | 156,718 | 156,695 | 156,700 | 156,700 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 2.33 | 3.11 | ||||

Hansen’s J (p-value) | 31.11% | 21.08% | ||||

Kleibergen-Paap (test) | 318.0 | 316.9 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% | ||||

Wald (up - down) (test) | 10.14 | 11.48 | 6.76 | 5.08 | 13.09 | 3.06 |

Wald (up - down) (p-value) | 0.15% | 0.07% | 0.94% | 2.42% | 0.03% | 8.04% |

B. The influence of repurchases on R-squared and absolute market correlation in up and down markets | ||||||

Dependent variable: | R-squared | |Market correlation| | ||||

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{\it Rep. \; intensity}_{t}$$ | -0.0948 | 0.6820 | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (-0.12) | (0.76) | ||||

$$\widehat{\it Rep. \; intensity}_{t}$$ | 3.6301^{***} | 3.5997^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (4.46) | (4.40) | ||||

Rep. intensity$$_{t-1}$$ | 0.0548 | 0.2069^{*} | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (0.54) | (1.89) | ||||

Rep. intensity$$_{t-1}$$ | 0.9909^{***} | 0.9770^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (7.59) | (7.63) | ||||

Rem. volume$$_{t}$$ | 0.0186 | 0.0324^{*} | ||||

$$\quad$$$$\times$$ Up market$$_{t}$$ | (1.03) | (1.65) | ||||

Rem. volume$$_{t}$$ | 0.0712^{***} | 0.0699^{***} | ||||

$$\quad$$$$\times$$ Down market$$_{t}$$ | (3.64) | (3.50) | ||||

$$R^2$$ (within firm) | 0.228 | 0.246 | 0.246 | 0.183 | 0.202 | 0.201 |

Observations | 156,710 | 156,715 | 156,715 | 156,715 | 156,720 | 156,720 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 4.76 | 1.88 | ||||

Hansen’s J (p-value) | 9.27% | 38.98% | ||||

Kleibergen-Paap (test) | 314.9 | 314.7 | ||||

Kleibergen-Paap (p-value) | 0.00% | 0.00% | ||||

Wald (up – down) (test) | 24.25 | 34.52 | 12.79 | 15.12 | 22.69 | 6.59 |

Wald (up – down) (p-value) | 0.00% | 0.00% | 0.04% | 0.01% | 0.00% | 1.03% |

The table presents OLS and GMM regressions of *Delay* and *Coefficient-based delay* (panel A), and *R-squared* and *Absolute market correlation* (panel B) on *Repurchase intensity* or *Remaining volume,* interaction terms of dummy variables identifying up and down markets and the repurchase variables, and control variables (untabulated). The controls are the same as in Table 4, respectively Table 5. In the GMM specifications, the repurchase variables are instrumented using *Program size* and *Program month*. The repurchase variables and the control variables are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions. The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The Wald statistic tests for differences between the coefficients on up-market and down-market repurchases. The table reports the test statistics and the *p*-values for these tests.

Our results for up markets suggest weak evidence in favor of the information incorporation channel, and this warrants further examination. First, we test whether the coefficients obtained for up markets and down markets are not only economically but also statistically significantly different from each other (see bottom of Table 6). We find that the differences are statistically significant for all variables and all specifications, mostly at the 1% level. Furthermore, note that our setup cannot entirely rule out that price support is driving the positive effects in up markets because we use the return over the full month to split repurchase activity into up and down markets, whereas we use daily returns to compute our price delay measures. If an up-market month includes a down-market period during which firms provide price support, we will observe a positive effect of share repurchases on price efficiency in up markets, too. To examine this possibility, we exclude from “up markets” those months for which more than one-third of the daily market returns are negative. We name the new up market dummy *Steady up market* and report the results in

*Steady up market*and repurchases are much lower than the coefficient estimates for up market repurchases in Table 6 and lose their statistical significance in all specifications. Thus, share repurchases do not improve price efficiency in those up-market months for which the information incorporation effect should be strongest.

In Table 7, we analyze the effect of share repurchases on stock return moment distributions (volatility and kurtosis). According to our interpretation of the above reported results, firms prevent prices from diverging from their fundamental values. Consequently, extreme negative values of stock returns should become less frequent, and, therefore, volatility and kurtosis should be lower when firms buy back shares. We again utilize the research design discussed above. The results strongly support the price stability argument. Volatility is lower, and kurtosis is smaller. In

of the , we further analyze the effect of share repurchases on volatility in up markets and down markets using the empirical set-up of Table 6. If the observed, positive effect on the efficiency measures in up markets stemmed from actively incorporating information, volatility should increase in up markets because incorporating (positive) information should go in hand with an increase in volatility. Meanwhile, note that even when the stock market as a whole goes up, the individual stock price may still drop below its fundamental value because of negative idiosyncratic shocks to the stock price. Furthermore, our earlier results suggest that firms provide price support to short down-market periods within up-market months. If firms provide price support during negative idiosyncratic shocks or short down-market periods, volatility also will be lower in up markets. Table A7 reports that stock repurchases decrease volatility in both up markets and down markets, and this is therefore further evidence that price support at fundamental values is driving our results. We conclude that the results obtained in up markets are not fully consistent with the information incorporation channel and might be better explained by the price support hypothesis.Dependent variable: | Volatility (ln) | Kurtosis (ln) | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{\it Repurchase \: intensity}_{t}$$ | -14.4293^{***} | -2.0354^{*} | ||||

(-7.93) | (-1.85) | |||||

Repurchase intensity$$_{t-1}$$ | -1.4424^{***} | -0.6724^{***} | ||||

(-7.99) | (-3.73) | |||||

Remaining volume$$_{t}$$ | -0.3187^{***} | -0.0541^{*} | ||||

(-7.40) | (-1.96) | |||||

Volatility$$_{t-1}$$ (ln) | 0.3087^{***} | 0.3097^{***} | 0.3091^{***} | |||

(53.93) | (52.41) | (52.53) | ||||

Kurtosis$$_{t-1}$$ (ln) | -0.0288^{***} | -0.0302^{***} | -0.0302^{***} | |||

(-10.01) | (-10.61) | (-10.62) | ||||

Return$$_{t-1}$$ > 0 | -0.0480^{***} | -0.0660^{***} | -0.0658^{***} | -0.0215^{**} | -0.0196^{*} | -0.0194^{*} |

(-3.39) | (-4.51) | (-4.51) | (-1.98) | (-1.80) | (-1.79) | |

Return$$_{t-1}$$ < 0 | -0.6106^{***} | -0.5726^{***} | -0.5694^{***} | -0.0682^{***} | -0.0634^{***} | -0.0628^{***} |

(-33.99) | (-32.72) | (-32.58) | (-4.86) | (-4.58) | (-4.54) | |

Program initiation$$_{t}$$ | 0.1116^{***} | 0.0618^{***} | 0.0533^{***} | 0.0687^{***} | 0.0612^{***} | 0.0593^{***} |

(13.79) | (11.84) | (9.94) | (10.73) | (11.55) | (11.10) | |

Market cap$$_{t-1}$$ (ln) | -0.0958^{***} | -0.1012^{***} | -0.1024^{***} | -0.0252^{***} | -0.0264^{***} | -0.0266^{***} |

(-14.75) | (-15.15) | (-15.31) | (-7.39) | (-7.71) | (-7.75) | |

Book to market$$_{t-3}$$ | 0.0447^{***} | 0.0415^{***} | 0.0406^{***} | 0.0133^{***} | 0.0123^{***} | 0.0121^{***} |

(6.85) | (6.22) | (6.14) | (3.86) | (3.55) | (3.50) | |

Analysts$$_{t-1}$$ (ln) | 0.0152^{***} | 0.0154^{***} | 0.0151^{***} | 0.0045 | 0.0043 | 0.0041 |

(2.69) | (2.68) | (2.63) | (1.39) | (1.31) | (1.25) | |

Relative spread$$_{t-1}$$ (ln) | 0.0771^{***} | 0.0843^{***} | 0.0849^{***} | -0.0021 | -0.0017 | -0.0013 |

(15.97) | (17.14) | (17.27) | (-0.78) | (-0.64) | (-0.50) | |

Deviation from $\$$ 30$$_{t-1}$$ | 0.0020 | 0.0013 | 0.0014 | -0.0008 | -0.0007 | -0.0007 |

(1.07) | (0.68) | (0.75) | (-0.61) | (-0.59) | (-0.59) | |

Trading volume$$_{t-1}$$ | 0.0278^{***} | 0.0238^{***} | 0.0242^{***} | -0.0076 | -0.0076 | -0.0074 |

$$\quad$$ (scaled) | (3.48) | (3.03) | (3.07) | (-1.57) | (-1.55) | (-1.53) |

Change in short | 0.9591^{***} | 0.9603^{***} | 0.9270^{***} | -0.0095 | -0.0084 | -0.0213 |

$$\quad$$ interest$$_{t-1}$$ | (10.63) | (10.86) | (10.59) | (-0.13) | (-0.11) | (-0.28) |

Institutional | 0.0391^{*} | 0.0398^{*} | 0.0433^{**} | -0.0124 | -0.0136 | -0.0130 |

$$\quad$$ ownership$$_{t-3}$$ | (1.88) | (1.88) | (2.05) | (-1.01) | (-1.11) | (-1.06) |

Constant | -1.6007^{***} | -1.5876^{***} | 1.6635^{***} | 1.6672^{***} | ||

(-34.77) | (-34.54) | (69.43) | (69.59) | |||

$$R^2$$ (within firm) | 0.523 | 0.541 | 0.541 | 0.006 | 0.024 | 0.024 |

Observations | 155,571 | 156717 | 156,717 | 155,566 | 156,712 | 156,712 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 0.03 | 0.88 | ||||

Hansen’s J (p-value) | 86.11% | 34.92% | ||||

Kleibergen-Paap (test) | 318.9 | 318.9 | ||||

Kleibergen-Paap | 0.00% | 0.00% | ||||

$$\quad$$ (p-value) |

Dependent variable: | Volatility (ln) | Kurtosis (ln) | ||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Method: | GMM | OLS | OLS | GMM | OLS | OLS |

$$\widehat{\it Repurchase \: intensity}_{t}$$ | -14.4293^{***} | -2.0354^{*} | ||||

(-7.93) | (-1.85) | |||||

Repurchase intensity$$_{t-1}$$ | -1.4424^{***} | -0.6724^{***} | ||||

(-7.99) | (-3.73) | |||||

Remaining volume$$_{t}$$ | -0.3187^{***} | -0.0541^{*} | ||||

(-7.40) | (-1.96) | |||||

Volatility$$_{t-1}$$ (ln) | 0.3087^{***} | 0.3097^{***} | 0.3091^{***} | |||

(53.93) | (52.41) | (52.53) | ||||

Kurtosis$$_{t-1}$$ (ln) | -0.0288^{***} | -0.0302^{***} | -0.0302^{***} | |||

(-10.01) | (-10.61) | (-10.62) | ||||

Return$$_{t-1}$$ > 0 | -0.0480^{***} | -0.0660^{***} | -0.0658^{***} | -0.0215^{**} | -0.0196^{*} | -0.0194^{*} |

(-3.39) | (-4.51) | (-4.51) | (-1.98) | (-1.80) | (-1.79) | |

Return$$_{t-1}$$ < 0 | -0.6106^{***} | -0.5726^{***} | -0.5694^{***} | -0.0682^{***} | -0.0634^{***} | -0.0628^{***} |

(-33.99) | (-32.72) | (-32.58) | (-4.86) | (-4.58) | (-4.54) | |

Program initiation$$_{t}$$ | 0.1116^{***} | 0.0618^{***} | 0.0533^{***} | 0.0687^{***} | 0.0612^{***} | 0.0593^{***} |

(13.79) | (11.84) | (9.94) | (10.73) | (11.55) | (11.10) | |

Market cap$$_{t-1}$$ (ln) | -0.0958^{***} | -0.1012^{***} | -0.1024^{***} | -0.0252^{***} | -0.0264^{***} | -0.0266^{***} |

(-14.75) | (-15.15) | (-15.31) | (-7.39) | (-7.71) | (-7.75) | |

Book to market$$_{t-3}$$ | 0.0447^{***} | 0.0415^{***} | 0.0406^{***} | 0.0133^{***} | 0.0123^{***} | 0.0121^{***} |

(6.85) | (6.22) | (6.14) | (3.86) | (3.55) | (3.50) | |

Analysts$$_{t-1}$$ (ln) | 0.0152^{***} | 0.0154^{***} | 0.0151^{***} | 0.0045 | 0.0043 | 0.0041 |

(2.69) | (2.68) | (2.63) | (1.39) | (1.31) | (1.25) | |

Relative spread$$_{t-1}$$ (ln) | 0.0771^{***} | 0.0843^{***} | 0.0849^{***} | -0.0021 | -0.0017 | -0.0013 |

(15.97) | (17.14) | (17.27) | (-0.78) | (-0.64) | (-0.50) | |

Deviation from $\$$ 30$$_{t-1}$$ | 0.0020 | 0.0013 | 0.0014 | -0.0008 | -0.0007 | -0.0007 |

(1.07) | (0.68) | (0.75) | (-0.61) | (-0.59) | (-0.59) | |

Trading volume$$_{t-1}$$ | 0.0278^{***} | 0.0238^{***} | 0.0242^{***} | -0.0076 | -0.0076 | -0.0074 |

$$\quad$$ (scaled) | (3.48) | (3.03) | (3.07) | (-1.57) | (-1.55) | (-1.53) |

Change in short | 0.9591^{***} | 0.9603^{***} | 0.9270^{***} | -0.0095 | -0.0084 | -0.0213 |

$$\quad$$ interest$$_{t-1}$$ | (10.63) | (10.86) | (10.59) | (-0.13) | (-0.11) | (-0.28) |

Institutional | 0.0391^{*} | 0.0398^{*} | 0.0433^{**} | -0.0124 | -0.0136 | -0.0130 |

$$\quad$$ ownership$$_{t-3}$$ | (1.88) | (1.88) | (2.05) | (-1.01) | (-1.11) | (-1.06) |

Constant | -1.6007^{***} | -1.5876^{***} | 1.6635^{***} | 1.6672^{***} | ||

(-34.77) | (-34.54) | (69.43) | (69.59) | |||

$$R^2$$ (within firm) | 0.523 | 0.541 | 0.541 | 0.006 | 0.024 | 0.024 |

Observations | 155,571 | 156717 | 156,717 | 155,566 | 156,712 | 156,712 |

Firm FE | Y | Y | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y | Y | Y |

Hansen’s J (test) | 0.03 | 0.88 | ||||

Hansen’s J (p-value) | 86.11% | 34.92% | ||||

Kleibergen-Paap (test) | 318.9 | 318.9 | ||||

Kleibergen-Paap | 0.00% | 0.00% | ||||

$$\quad$$ (p-value) |

The table presents OLS and GMM regressions of *Volatility* and *Kurtosis* on either *Repurchase intensity* or *Remaining volume* and control variables. The dependent variable is *Volatility* in specifications (1)-(3) and *Kurtosis* in specifications (4)-(6). In specifications (1) and (4) the repurchase variables are instrumented using *Program size* and *Program month*. Instrumented variables are in italics and marked with a circumflex. In specifications (2) and (5) the repurchase variables are included as predetermined values. The repurchase variables and the control variables are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. The Hansen-J statistic tests for the validity of the overidentifying restrictions. The Kleibergen-Paap test is for underidentification and tests for the full rank of the reduced-form coefficient matrix following Kleibergen and Paap (2006). The table reports the test statistics and the *p*-values for both tests.

To further distinguish our hypothesis that firms react to market-wide shocks from the hypothesis that firms react to firm-specific information, we use value-weighted SIC-2 industry returns instead of market returns to compute our dependent variables and redo the analysis presented in Table 6. The rationale here is that industry returns better reflect information relevant for the firm, and this makes it more likely that firms actively trade and incorporate it. In the

in , we provide the results of these analyses. In panels A and B, we replicate the analyses of Sections 3.2 and 3.3, and in panels C and D, we replicate the analysis of this section using SIC-2 industry returns as proxies for whether positive news or negative news comes to the market. While all of the results go into the same direction, they are much weaker, both from an economic and a statistical perspective.^{15}Most importantly, the coefficients on the up market interactions do not systematically gain economic or statistical significance. In the (), we further investigate whether firms incorporate idiosyncratic positive information by analyzing the post-earnings announcement drift (PEAD) in the context of share repurchases. Also in this setup, we do not find evidence in this regard.

This section provides strong evidence for the notion that share repurchases provide price support and prevent the stock price from dropping below its fundamental value. As a consequence, share repurchases make prices more accurate and thus more efficient when new negative information arrives at the market. In line with this argument, share repurchases decrease volatility and kurtosis. While we cannot reject the notion that firms actively incorporate positive information into the stock price, we find the evidence presented in this regard weak, both from a statistical and an economic perspective, and better aligned with the price support hypothesis.

### 3.5 OLS results for contemporaneous repurchases

In Table 8, we estimate the OLS coefficients for contemporaneous *Repurchase intensity* and *Repurchase dummy*, a variable that indicates firm months with repurchase activity. As discussed in Section 2.2, we can expect that the coefficient on contemporaneous *Repurchase Intensity* has a positive bias if firms step in to prevent a mispricing of their stock. In this scenario, contemporaneous *Repurchase intensity* might be positively correlated with *Delay*. A variable more exogenous than *Repurchase intensity* is a dummy variable indicating a month in which share repurchases take place because reverse causality will rather effect the size of the repurchase than the decision to repurchase. The results in Table 8, panels A and B confirm this conjecture. For all efficiency measures, the coefficient on *Repurchase intensity* is not statistically significantly different from zero. Meanwhile, the coefficients on the dummy variable come in with the predicted sign and are highly statistically significant: Price efficiency is higher in months in which repurchases take place.

A. Contemporaneous repurchase intensity | ||||
---|---|---|---|---|

Dependent variable: | Delay | Coeff.-based delay | R-squared | |Market correlation| |

(1) | (2) | (3) | (4) | |

Repurchase intensity$$_{t}$$ | 0.0606 | -0.0635 | -0.0347 | -0.0082 |

(0.52) | (-0.25) | (-0.41) | (-0.09) | |

$$R^2$$ (within firm) | 0.150 | 0.112 | 0.246 | 0.202 |

Observations | 155,987 | 155,970 | 155,983 | 155,988 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

B. Contemporaneous repurchase dummy | ||||

Repurchase dummy$$_{t}$$ | -0.0067^{***} | -0.0124^{***} | 0.0032^{**} | 0.0040^{***} |

(-3.51) | (-2.99) | (2.30) | (2.66) | |

$$R^2$$ (within firm) | 0.150 | 0.112 | 0.246 | 0.202 |

Observations | 155,987 | 155,970 | 155,983 | 155,988 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

C. Contemporaneous repurchase dummy in up and down markets | ||||

Rep. dummy$$_{t}$$ x Up market$$_{t}$$ | -0.0033 | -0.0048 | -0.0017 | 0.0004 |

(-1.39) | (-0.95) | (-1.00) | (0.23) | |

Rep. dummy$$_{t}$$ x Down market$$_{t}$$ | -0.0121^{***} | -0.0233^{***} | 0.0105^{***} | 0.0095^{***} |

(-4.98) | (-4.22) | (5.70) | (5.05) | |

$$R^2$$ (within firm) | 0.149 | 0.112 | 0.246 | 0.201 |

Observations | 156,718 | 156,700 | 156,715 | 156,720 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

A. Contemporaneous repurchase intensity | ||||
---|---|---|---|---|

Dependent variable: | Delay | Coeff.-based delay | R-squared | |Market correlation| |

(1) | (2) | (3) | (4) | |

Repurchase intensity$$_{t}$$ | 0.0606 | -0.0635 | -0.0347 | -0.0082 |

(0.52) | (-0.25) | (-0.41) | (-0.09) | |

$$R^2$$ (within firm) | 0.150 | 0.112 | 0.246 | 0.202 |

Observations | 155,987 | 155,970 | 155,983 | 155,988 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

B. Contemporaneous repurchase dummy | ||||

Repurchase dummy$$_{t}$$ | -0.0067^{***} | -0.0124^{***} | 0.0032^{**} | 0.0040^{***} |

(-3.51) | (-2.99) | (2.30) | (2.66) | |

$$R^2$$ (within firm) | 0.150 | 0.112 | 0.246 | 0.202 |

Observations | 155,987 | 155,970 | 155,983 | 155,988 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

C. Contemporaneous repurchase dummy in up and down markets | ||||

Rep. dummy$$_{t}$$ x Up market$$_{t}$$ | -0.0033 | -0.0048 | -0.0017 | 0.0004 |

(-1.39) | (-0.95) | (-1.00) | (0.23) | |

Rep. dummy$$_{t}$$ x Down market$$_{t}$$ | -0.0121^{***} | -0.0233^{***} | 0.0105^{***} | 0.0095^{***} |

(-4.98) | (-4.22) | (5.70) | (5.05) | |

$$R^2$$ (within firm) | 0.149 | 0.112 | 0.246 | 0.201 |

Observations | 156,718 | 156,700 | 156,715 | 156,720 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

The table presents OLS regressions of *Delay*, *Coefficient-based delay*, *R-squared*, and *Absolute market correlation* on contemporaneous repurchase variables and control variables. The dependent variable is *Delay* in specification (1), *Coefficient-based delay* in (2), *R-squared* in (3), and *Absolute market correlation* in (4). In panel A *Repurchase intensity* is included as repurchase variable. Panel B includes *Repurchase dummy* and panel C includes *Repurchase dummy* interacted with dummy variables identifying up and down markets. The controls are the same as in Table 4, respectively Table 5. Repurchase variables and controls are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

In panel C, we split *Repurchase dummy* into up markets and down markets like in earlier analyses. Consistent with the evidence presented earlier, the effect of repurchases on price efficiency and idiosyncratic risk is only present in down markets.

### 3.6 Attempts to identify repurchases that harm price efficiency or increase idiosyncratic risk

So far, we have restricted our analysis to the impact of within-firm variation in repurchase activity on price efficiency. Furthermore, we have focused on specifications that identify the exogenous variation in share repurchases and determine its impact on price efficiency. Taken together, these measures ensure that the hurdle for rejecting the null hypothesis, which states that share repurchases have no impact on price efficiency, is high. Meanwhile, one concern about our research design is that it is too strict to identify harmful effects caused by a subset of firms or repurchases.

In this section, we employ a research design that both substantially reduces the hurdle for rejecting the null hypothesis and singles out potentially harmful subsets of repurchases. We adjust our identification strategy along three dimensions. First, we use contemporaneous *Repurchase Intensity* and thereby include its potentially endogenous variation. Second, we exclude firm fixed effects to allow heterogeneity in the cross-section to drive our results. Third, we interact *Repurchase intensity* with dummy variables indicating subsets of repurchases that are more likely to have a detrimental effect on price efficiency. Using a similar research design as in Section 3.4, we split *Repurchase intensity* in two groups: *Repurchase intensity {** Interaction variable} and *Repurchase intensity * (1- Interaction variable)*. In this specification, we test the null hypothesis of the groups’ share repurchases having no impact on our dependent variables. As pointed out in Section 3.4, we cannot include *Repurchase intensity* as a level variable because it would be collinear with the included interaction terms.

Table 6 presents the results. In Columns (1) to (4), we identify share repurchases where corporate insiders would profit most from a manipulation of the stock price. In Column (1), we interact *Repurchase intensity* with *Net insider selling*, which is equal to one if *Net insider trading* is negative and zero otherwise. Our coefficient of interest, the interaction of *Net insider selling* and *Repurchase intensity*, is not statistically different from zero. This result also holds for defining *Net Insider Selling* over the following month or over the following three months (results not tabulated). Splitting *Repurchase intensity* in two groups according to whether insider ownership (Column 2), outstanding options (Column 3), or options exercised (Column 4) are above or below the median at program inception does also not produce any significant results. At the bottom of Table 6, we also test whether the effects for high and low groups are statistically significantly different from each other. We do not obtain any significant results.

If firms are forced to conduct (large) share repurchases within a short period of time, these share repurchases could harm price efficiency. For example, firms with huge piles of cash on their balance sheets might not be able to align their repurchase activity with the liquidity of their stock and therefore cause prices to increase. As a result, share repurchase trades might move prices away from fundamental values. Using a research design where we split *Research intensity* at the median of *Cash to assets* at the beginning of the program does, however, not provide any evidence for this conjecture (see Column 5). In

*Cash to assets*of the previous quarter as an instrument for

*Repurchase intensity*to examine this issue from a different angle. Again, an increase in

*Repurchase intensity*due to an increase in

*Cash to assets*does not significantly impact our efficiency measures.

In Column (6), we group repurchases according to the quality of corporate governance measured by the Governance Index of Gompers, Ishii, and Metrick (2003). A high governance firm has an above median GIM index at the inception of the program. Once again, we do not obtain significant results.

In

of the , we modify the above specifications: We use the 75th percentile to define our high and low groups in panel A; we add firm fixed effects in panel B; we lag*Repurchase intensity*in panel C; and we exchange

*Repurchase intensity*for

*Repurchase dummy*in panel D. However, none of these modifications help us to identify harmful repurchases. We conclude that, if any, only a very small subset of repurchases intentionally harm price efficiency. We only report the results for

*Delay*and

*R-squared*but we obtain similar results for all other measures.

### 3.7 Cross-sectional differences in repurchase frequency

Dittmar and Field (2015) point out the substantial heterogeneity in repurchasing frequency across both firms and time. The authors group firms every year into infrequent, moderate, and frequent repurchasers, according to whether firms buy back in no more than four months, between five and eight months, and at least nine months, respectively. In their sample, half of repurchasing firms repurchase four times or less in a year and only roughly 20% of firms repurchase nine times or more in a year. We obtain similar numbers for our data set. In the light of these results, this section is dedicated to discuss the validity of both instrumented *Repurchase intensity* and lagged *Repurchase intensity* as proxies for exogenous *Repurchase intensity*. Furthermore, we utilize the heterogeneity in repurchasing frequency among firms to refine our identification strategy.

If firms repurchase infrequently and spread their repurchases randomly, lagged *Repurchase intensity* might not be a good estimator of exogenous *Repurchase intensity*. To evaluate this concern, we take a look at the probability of a repurchase taking place conditional on a repurchase having taken place in the previous month. For our data set, we find that 71% of months following a repurchase month have repurchase activity. Restricting this analysis to infrequently repurchasing firms, we obtain a conditional probability of 51%. Thus, although repurchase frequency is different among firms, even for infrequently repurchasing firms there is a high probability that a repurchase month is followed by another repurchase month because repurchases cluster.

Repurchase frequency is also a major concern for the conceptual validity of our instruments. If infrequently repurchasing firms distort price efficiency, the very noisy estimates of *Repurchase intensity* for infrequently repurchasing firms might not be able to pick up on these effects. Here, it is important to note that share repurchases are predicted within active programs. Considering active programs instead of calendar years, changes the repurchase frequency statistics substantially. Now, only 39% of firms repurchase infrequently and 32% repurchase frequently. Thus, the majority of firms repurchases at least five times in the 12 months after the start of the program. Furthermore, infrequently repurchasing firms only represent 8,737 repurchase months of the total of 38,177 repurchase months.

Dependent variable: | Delay | |||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Interaction variable: | Net insider | High insider | High options | High insider | High cash | High governance |

selling | ownership | outstanding | options exercised | |||

Interaction variable$$_{t}$$ | 0.0066^{***} | -0.0151^{***} | 0.0090^{***} | -0.0134^{***} | 0.0121^{***} | -0.0183^{***} |

(3.31) | (-4.09) | (2.98) | (-5.03) | (4.20) | (-4.19) | |

Rep. intensity$$_{t}$$ * Interaction variable$$_{t}$$ | -0.0525 | 0.2496 | -0.0925 | 0.2367 | 0.0947 | 0.2050 |

(-0.25) | (1.20) | (-0.50) | (1.41) | (0.55) | (0.68) | |

Rep. intensity$$_{t}$$ * (1 - Interaction variable$$_{t}$$) | 0.1582 | -0.0262 | 0.0989 | 0.0644 | -0.1381 | -0.0508 |

(1.06) | (-0.13) | (0.61) | (0.38) | (-0.79) | (-0.25) | |

High -Low | -0.2106 | 0.2758 | -0.1914 | 0.1724 | 0.2328 | 0.2558 |

(-0.84) | (0.94) | (-0.78) | (0.74) | (0.96) | (0.70) | |

$$R^2$$ | 0.355 | 0.218 | 0.355 | 0.355 | 0.355 | 0.214 |

Observations | 152,210 | 84,487 | 155,987 | 155,987 | 155,987 | 67,606 |

Firm FE | N | N | N | N | N | N |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Dependent variable: | R-squared | |||||

(1) | (2) | (3) | (4) | (5) | (6) | |

Interaction variable: | Net insider | High insider | High options | High insider | High cash | High governance |

selling | ownership | outstanding | options exercised | |||

Interaction variable$$_{t}$$ | -0.0057^{***} | 0.0100^{***} | -0.0094^{***} | 0.0083^{***} | -0.0108^{***} | 0.0160^{***} |

(-3.95) | (3.30) | (-4.28) | (4.28) | (-5.11) | (4.26) | |

Rep. intensity$$_{t}$$ * Interaction variable$$_{t}$$ | 0.1181 | -0.1408 | 0.0894 | -0.1113 | -0.0309 | -0.0879 |

(0.79) | (-0.88) | (0.66) | (-0.88) | (-0.25) | (-0.36) | |

Rep. intensity$$_{t}$$ * (1 - Interaction variable$$_{t}$$) | -0.1869^{*} | 0.0299 | -0.0971 | -0.1568 | 0.0403 | 0.0045 |

(-1.71) | (0.18) | (-0.80) | (-1.31) | (0.32) | (0.03) | |

High - Low | 0.3051^{*} | -0.1707 | 0.1865 | 0.0454 | -0.0712 | -0.0924 |

(1.72) | (-0.75) | (1.04) | (0.27) | (-0.41) | (-0.32) | |

$$R^2$$ | 0.429 | 0.328 | 0.429 | 0.429 | 0.429 | 0.325 |

Observations | 152,206 | 84,486 | 155,983 | 155,983 | 155,983 | 67,603 |

Firm FE | N | N | N | N | N | N |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Dependent variable: | Delay | |||||
---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | |

Interaction variable: | Net insider | High insider | High options | High insider | High cash | High governance |

selling | ownership | outstanding | options exercised | |||

Interaction variable$$_{t}$$ | 0.0066^{***} | -0.0151^{***} | 0.0090^{***} | -0.0134^{***} | 0.0121^{***} | -0.0183^{***} |

(3.31) | (-4.09) | (2.98) | (-5.03) | (4.20) | (-4.19) | |

Rep. intensity$$_{t}$$ * Interaction variable$$_{t}$$ | -0.0525 | 0.2496 | -0.0925 | 0.2367 | 0.0947 | 0.2050 |

(-0.25) | (1.20) | (-0.50) | (1.41) | (0.55) | (0.68) | |

Rep. intensity$$_{t}$$ * (1 - Interaction variable$$_{t}$$) | 0.1582 | -0.0262 | 0.0989 | 0.0644 | -0.1381 | -0.0508 |

(1.06) | (-0.13) | (0.61) | (0.38) | (-0.79) | (-0.25) | |

High -Low | -0.2106 | 0.2758 | -0.1914 | 0.1724 | 0.2328 | 0.2558 |

(-0.84) | (0.94) | (-0.78) | (0.74) | (0.96) | (0.70) | |

$$R^2$$ | 0.355 | 0.218 | 0.355 | 0.355 | 0.355 | 0.214 |

Observations | 152,210 | 84,487 | 155,987 | 155,987 | 155,987 | 67,606 |

Firm FE | N | N | N | N | N | N |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

Dependent variable: | R-squared | |||||

(1) | (2) | (3) | (4) | (5) | (6) | |

Interaction variable: | Net insider | High insider | High options | High insider | High cash | High governance |

selling | ownership | outstanding | options exercised | |||

Interaction variable$$_{t}$$ | -0.0057^{***} | 0.0100^{***} | -0.0094^{***} | 0.0083^{***} | -0.0108^{***} | 0.0160^{***} |

(-3.95) | (3.30) | (-4.28) | (4.28) | (-5.11) | (4.26) | |

Rep. intensity$$_{t}$$ * Interaction variable$$_{t}$$ | 0.1181 | -0.1408 | 0.0894 | -0.1113 | -0.0309 | -0.0879 |

(0.79) | (-0.88) | (0.66) | (-0.88) | (-0.25) | (-0.36) | |

Rep. intensity$$_{t}$$ * (1 - Interaction variable$$_{t}$$) | -0.1869^{*} | 0.0299 | -0.0971 | -0.1568 | 0.0403 | 0.0045 |

(-1.71) | (0.18) | (-0.80) | (-1.31) | (0.32) | (0.03) | |

High - Low | 0.3051^{*} | -0.1707 | 0.1865 | 0.0454 | -0.0712 | -0.0924 |

(1.72) | (-0.75) | (1.04) | (0.27) | (-0.41) | (-0.32) | |

$$R^2$$ | 0.429 | 0.328 | 0.429 | 0.429 | 0.429 | 0.325 |

Observations | 152,206 | 84,486 | 155,983 | 155,983 | 155,983 | 67,603 |

Firm FE | N | N | N | N | N | N |

Month FE | Y | Y | Y | Y | Y | Y |

Controls | Y | Y | Y | Y | Y | Y |

The table presents OLS regressions of *Delay* and *R-squared* on dummy variables, interaction terms of contemporaneous *Repurchase intensity* with the dummy variables, and control variables (untabulated). The controls are the same as in Table 4 and Table 5 respectively. The repurchase variables and the control variables are defined in Table 1. The dependent variable is *Delay* in panel A and *R-squared* in panel B. *Net insider selling* is a dummy variable indicating net insider selling in the respective month. *High insider ownership*, *High options outstanding*, *High cash*, and *High governance* are dummy variables equal to 1 if the respective firm characteristic at the beginning of the program is above the median of all programs. *High insider options excercised* is a dummy variable equal to 1 if the aggregated sum of insider options exercised over the whole program duration is above the median of all programs. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

The differences in repurchasing frequency also allow for a refinement of our identification strategy. In Table 10, we follow Dittmar and Field (2015) and group repurchasing firms every year into three categories according to their repurchase frequency (infrequent, moderate, frequent). Each of the three categories is identified by a dummy variable. Thus, we use firm-years without repurchase activity as our baseline category. We would expect that the efficiency gain is strongest for high frequency firms and lowest for low frequency firms. Our results corroborate our expectations. In Columns (1) and (2), we observe that price delay is lower in repurchasing years regardless of repurchase frequency. Furthermore, price delay is lower, the more frequent repurchases take place. In Columns (3) and (4), we observe the same pattern for measures of idiosyncratic risk and synchronicity. Note, however, that idiosyncratic risk is not significantly lower when firms repurchase infrequently.

Dependent variable: | Delay | Coeff.-based delay | R-squared | |Market correlation| |
---|---|---|---|---|

(1) | (2) | (3) | (4) | |

Method: | OLS | OLS | OLS | OLS |

Infrequent$$_{t}$$ | -0.0059^{***} | -0.0082^{**} | 0.0006 | 0.0025 |

(-2.70) | (-1.77) | (0.37) | (1.46) | |

Moderate$$_{t}$$ | -0.0126^{***} | -0.0211^{***} | 0.0046^{**} | 0.0074^{***} |

(-4.53) | (-3.48) | (2.25) | (3.35) | |

Frequent$$_{t}$$ | -0.0172^{***} | -0.0211^{***} | 0.0066^{**} | 0.0102^{***} |

(-4.52) | (-2.60) | (2.19) | (3.28) | |

$$R^2$$ (within firm) | 0.149 | 0.112 | 0.246 | 0.201 |

Observations | 156,718 | 156,700 | 156,715 | 156,720 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

Dependent variable: | Delay | Coeff.-based delay | R-squared | |Market correlation| |
---|---|---|---|---|

(1) | (2) | (3) | (4) | |

Method: | OLS | OLS | OLS | OLS |

Infrequent$$_{t}$$ | -0.0059^{***} | -0.0082^{**} | 0.0006 | 0.0025 |

(-2.70) | (-1.77) | (0.37) | (1.46) | |

Moderate$$_{t}$$ | -0.0126^{***} | -0.0211^{***} | 0.0046^{**} | 0.0074^{***} |

(-4.53) | (-3.48) | (2.25) | (3.35) | |

Frequent$$_{t}$$ | -0.0172^{***} | -0.0211^{***} | 0.0066^{**} | 0.0102^{***} |

(-4.52) | (-2.60) | (2.19) | (3.28) | |

$$R^2$$ (within firm) | 0.149 | 0.112 | 0.246 | 0.201 |

Observations | 156,718 | 156,700 | 156,715 | 156,720 |

Firm FE | Y | Y | Y | Y |

Month FE | Y | Y | Y | Y |

Controls | Y | Y | Y | Y |

The table presents OLS regressions of *Delay, Coefficient-based delay,**R-squared* and *Absolute market correlation* on dummy variables for different repurchase frequency categories. The dummy variables are defined as in Dittmar and Field (2015). *Infrequent* is one if a firm conducts repurchases in four or fewer months in a calendar year and zero otherwise. *Moderate* is one if a firm conducts repurchases in five to eight months in a calendar year and zero otherwise. *Frequent* is one if a firm conducts repurchases in nine or more months in a calendar year and zero otherwise. The controls are the same as in Table 4, respectively Table 5. All variables are defined in Table 1. Standard errors are clustered at the firm level. *t*-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

### 3.8 Robustness tests

In this section we evaluate our results with respect to repurchase frequency, discuss alternative measures of price efficiency, and present our baseline analysis excluding the financial market crisis.

#### 3.8.1 Alternative measures of price efficiency.

In this section, we discuss alternative measures of price efficiency. To the extent that these measures are feasible within the context of our analysis, we use them to check the robustness of our results.

Variance ratios have a long history as measures of price efficiency dating back to, at least, Lo and MacKinlay (1988). Variance ratios are often estimated for annual or even longer periods and compare, for example, the variance of weekly returns to the variance of monthly returns (cf., e.g., Saffi and Sigurdsson 2011; Griffin, Kelly, and Nardari 2010). Since the analyses in this paper compile daily observations into monthly efficiency measures, a sensible variance ratio would have to relate daily return variances to weekly return variances. For estimating weekly variance ratios, we face the problem that we would have to rely on only four observations since a month has only four weeks. Thus, we are not able to obtain meaningful variance ratios.

Some studies, for example, Ferreira and Laux 2007, use idiosyncratic volatility as an alternative measure of idiosyncratic risk. We define idiosyncratic volatility as the variance of the residual of a simple market model regression and find results which are consistent with our earlier findings: when repurchases are high, idiosyncratic volatility is low (see

of the ).Phillips (2011) proposes an adjusted version of *Delay* for which lagged market returns are substituted by market adjusted stock returns. He argues that this measure captures the speed with which idiosyncratic information is incorporated in the stock price. We find that this measure and *Delay* are highly correlated (correlation coefficient: 0.88) and using idiosyncratic price delay instead of *Delay* yields similar results (See

There are several price efficiency measures that are computed for each trading day using intraday data (cf., e.g., Boehmer and Wu, 2013). To integrate these measures into our analyses, we have to average these daily measures over all trading days in a month. Therefore, intraday data do not necessarily allow for a more precise measurement of the effect of share repurchases on price efficiency. In

of the , we provide results using the autocorrelation of changes in stock prices as our dependent variable.^{16}All of our major results are robust to this measure.

#### 3.8.2 Share repurchases, price efficiency, and previous levels of price efficiency.

In

of the , we investigate whether the impact of share repurchases on price efficiency depends on the general level of price efficiency of the respective stock. If firms would dampen the investor inattention or neglect, the effect should be less pronounced, the more efficient a stock is. Our finding that firms in the highest efficiency tercile do not further increase their levels of price efficiency by repurchasing shares is in line with this presumption.#### 3.8.3 Price support and the financial market crisis.

To ensure that our main results of Table 6 are not driven by the financial market crisis, we exclude all observations from September 2008 to March 2009 and redo the analysis of Section 3.4. Our results are also robust to restricting the data set in this way (see

of the ).## 4. Conclusion

In this paper, we examine the impact of share repurchases on price efficiency and the information content of stock prices. The evidence is neither consistent with the notion that share repurchases incorporate private information into the stock price nor with the notion that share repurchases increase the noise in stock returns. The evidence is consistent with the notion that share repurchases increase the accuracy with which negative information is incorporated into the stock price. We conclude that share repurchases increase the price efficiency of stock prices by providing price support at fundamental values.

We thank Jacopo Bizzotto, Dion Bongaerts, Thomas Boulton, Philipp Geiler, Alexander Hillert, Thomas Keusch, Olga Lebedeva, Mike Mao, Stefan Ruenzi, Christoph Schneider, Michael Ungeheuer, and Patrick Verwijmeren for advice on this project and seminar participants at the 12th Corporate Finance Day, 12th International Paris Finance Meeting, Copenhagen Business School, Erasmus University Rotterdam, German Finance Association Conference 2014, Georgia State University, IFABS Oxford Corporate Finance Conference 2015, and University of Mannheim for fruitful discussions and helpful comments. We are especially grateful to Ernst Maug for many valuable comments and suggestions. Pascal Busch received financial support from the Rudolph von Bennigsen-Foerder-Foundation and the Graduate School of Economic and Social Sciences of the University of Mannheim. Supplementary data can be found on *The Review of Financial Studies* web site.

## References

*R*, and crash risk.

^{2}^{2}.

^{1}cf., for example, Skinner (2008) and Grullon and Michaely (2004). Based on hand-collected data from SEC filings and data from CRSP, we estimate the total payout between 2004 and 2010 to amount to

^{2}For example, “The Buyback Boondoggle,” Bloomberg Business. http://www.bloomberg.com/bw/magazine/content/09_34/b4144096907029.htm. “Why Stock Buybacks Are More Harmful than You Think,” MoneyMorning. http://moneymorning.com/2013/01/23/why-stock-buybacks-are-more-harmful-than-you-think/.

^{3}William Lazonick, “Profits without Prosperity,” Harvard Business Review, September 2014.

^{4}In 2003, the Securities and Exchange Commission adopted amendments to Rule 10b-18 that mandate the publication of monthly share repurchases under the quarterly filings with the SEC. Before 2004, studies analyzing actual U.S. stock repurchases had to use proxies for the number of shares bought back derived from CRSP and Compustat (for example, Stephens and Weisbach 1998, Dittmar 2000). See Banyi, Dyl, and Kahle (2008) for an exhaustive overview on studies using proxies from CRSP and Compustat and the reliability of these measures.

^{5}Notably, we can infer from these measures whether the idiosyncratic or the systematic component of the stock price is affected by share repurchases. If the idiosyncratic component is affected, this might be due to private information or public, firm-specific information, but price manipulation (noise) will also increase idiosyncratic risk.

^{7}No regulatory rules require a repurchase program to expire. Stephens and Weisbach (1998) report average program completion rates of 54.10%, 68.70%, and 73.80% for one, two, and three years after the program announcement. Bonaimé (2012) finds an average completion rate of 72.57% eight quarters after the quarter of the program announcement. The average completion rates in our sample are 45.53%, 53.17%, and 59.31%. The lower average completion rates in our sample are partly attributable to the decline in repurchase activity during the financial crisis. Precrisis completion rates are four to eight percentage points higher.

^{8}Henker and Wang (2006) consider this procedure to be more appropriate compared with the classical Lee and Ready (1991) five-second rule. Bessembinder (2003) tries zero to thirty-second delays in increments of five seconds and does not find any differences in the results.

^{10}Note also that the determinants of actual share repurchases are related to, but not equivalent to, the determinants of repurchase program announcements. For example, liquidity plays a much bigger role in executing repurchase programs than in deciding on a repurchase program.

^{11}For a thorough discussion of the relationship between share repurchases and stock liquidity for a U.S. sample, see Hillert, Maug, and Obernberger (2016).

^{12}The Hansen J-statistic for the test of overidentifying restrictions cannot reject the null that the model is correctly specified.

^{13}Note that Boehmer and Wu (2013) compute “plain” standard deviations, whereas we compute within-firm standard deviations. For our sample, “plain” standard deviations are about 20% larger. Therefore, the economic magnitude of our results is biased downwards relative to the one reported by Boehmer and Wu (2013).

^{15}One reason for the generally weaker results might be that industry-specific information is ex ante (i.e., without share repurchases) more accurately priced because it is easier to assess the relevance of the information for the single stock, and therefore overshooting is less likely. In other words, the pricing error of industry-specific information is ex ante much lower than the pricing error of market-wide information.

^{16}We obtain data on the autocorrelation of absolute changes in stock prices from the Market Mircostructure Database of the Financial Markets Research Center at Vanderbilt University.