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A.  Institutional Positive Feedback Trading

Quarterly changes in institutional ownership will be positively correlated with same‐quarter returns if institutional investors (noninstitutional investors) follow short‐term intraquarter positive (negative) feedback trading strategies. This explanation is consistent with theoretical models that suggest that smart investors may rationally engage in positive feedback trading strategies (e.g., Cutler, Poterba, and Summers 1990; DeLong et al. 1990; Hong and Stein 1999). Moreover, consistent with the momentum trading explanation, recent empirical studies provide evidence that institutional investors tend to purchase (sell) stocks that performed well (poorly) in the recent past (e.g., Grinblatt, Titman, and Wermers 1995; Nofsinger and Sias 1999; Wermers 1999, 2000; Cai, Kaul, and Zheng 2000; Bennett et al. 2003; Parrino et al. 2003; Sias 2004, forthcoming).4 Further evidence is provided by Odean (1998), who reports that individual investors are more likely to sell past winners than losers (i.e., negative feedback trade).

B.  Institutions’ Forecasting Intraquarter Prices

The documented correlation between quarterly changes in institutional ownership and same‐quarter returns is also consistent with the hypothesis that aggregate institutional trading has no effect on returns, but institutional investors are able to forecast intraquarter returns. Thus, stocks that institutions purchase would outperform those that they sell, and changes in institutional ownership would lead intraquarter returns. Recent studies provide evidence supporting this hypothesis in that measures of aggregate institutional demand are weakly positively correlated with subsequent returns (see Grinblatt and Titman 1989, 1993; Daniel et al. 1997; Nofsinger and Sias 1999; Wermers 1999, 2000; Chen, Jegadeesh, and Wermers 2000; Bennett et al. 2003; Parrino et al. 2003; Sias 2004, forthcoming). These results suggest that at least some of the contemporaneous quarterly correlation could be explained by institutional investors’ ability to forecast intraquarter returns. Chen, Hong, and Stein (2002) provide an alternative but similar explanation. They argue that changes in the number of mutual funds holding a security should forecast future returns because short sale constraints keep pessimistic investors’ valuations from being immediately reflected in security prices.

C.  Direct Effects of Institutional Ownership Changes

The third potential explanation is that aggregate institutional ownership changes have direct effects on security returns. Several studies find evidence that the individual trades of institutional investors have direct effects on prices. For example, Keim and Madhavan (1997) evaluate the trades for 21 institutions over a 26‐month period and find that, on average, institutional investors buy stocks at a 0.31% premium and sell stocks at 0.34% discount relative to their previous day’s close. Similarly, Chan and Lakonishok (1995) evaluate the trades of 37 investment managers over an 18‐month period and find evidence that individual institutional investors’ trades have both temporary and permanent effects. If, as the sample of trades from these studies suggest, the trades of individual institutional investors have price effects, then aggregate institutional trading will have price effects, that is, aggregate institutional trading will reflect the cumulative effect of individual institutional investor’s trades.

Return effects may be associated with aggregate institutional trading for three reasons: short‐term liquidity effects, imperfect substitution (finite elasticities), and information revealed through institutional trading. Aggregate institutional trading may have temporary liquidity effects if institutional investors’ trades require price concessions, on average, because they push liquidity providers away from their preferred inventory positions (Stoll 1978; Grossman and Miller 1988) or because liquidity providers incur a cost for processing orders (Demsetz 1968). As noted in the introduction, such liquidity effects are, by definition, temporary and therefore are unlikely to be primarily responsible for the strong positive correlation between quarterly changes in institutional ownership and same‐quarter returns. This is not to say that there are no liquidity effects associated with institutional trading, only that such effects cannot fully account for the correlation between quarterly changes in institutional ownership and same‐quarter returns.

A growing literature argues that investors view securities as imperfect substitutes (i.e., long‐term supply and demand curves have finite elasticities), and limits to arbitrage allow long‐term mispricing (Scholes 1972; Shleifer 1986; Bagwell 1991, 1992; Loderer, Cooney, and Van Drunen 1991; Lynch and Mendenhall 1997). If institutional investors purchase a security, and supply curves are upward sloping, then aggregate institutional demand will have direct effects on returns.

Alternatively, due to economies of scale, institutional investors are likely to be better informed than other traders. If trading by institutional investors reveals information, then institutional trading will affect prices (Easley and O’Hara 1987; Kyle 1995). Consistent with this explanation, recent evidence suggests that institutional investors are better informed than other investors (see Sec. II.B).5 Last, a number of empirical tests suggest that information revealed through trading is primarily responsible for stock price changes (Scholes 1972; French and Roll 1986; Barclay, Litzenberger, and Warner 1990). If, in fact, information revealed through trading is the primary source of stock price changes and institutional investors are more likely to be informed than individual investors, then aggregate institutional trading will have return effects.

A.  The Covariance between Quarterly Institutional Ownership Changes and Monthly Returns

Define the continuous return over month t as r_t and the continuous return from the beginning of month A through the end of month B as r_A,B. Similarly, define the change in institutional ownership (measured as either Δnumber or Δfraction) in month t as Δ_t and the change from the beginning of month A to the end of month B as Δ_A,B. For the quarter ending in month t = 2 then, the continuous return can be written as the sum of the three monthly returns: and the quarterly change in institutional ownership given by Δ_0,2 can be written as the sum of the changes for each month: Thus, the covariance between quarterly changes in ownership and returns over the same quarter can be represented by Because covariances are linear in the arguments, we can decompose this covariance into its parts: The first, fifth, and last terms (i.e., Cov(Δ₀, r₀),Cov(Δ₁, r₁), and Cov(Δ₂, r₂)) on the right‐hand side of equation (4) are the monthly contemporaneous covariances, that is, the covariance between changes in institutional ownership in a given month and returns in that month. The second and sixth terms (i.e., Cov(Δ₁, r₀) and Cov(Δ₂, r₁)) are the lag 1‐month feedback trading terms, that is, the covariance between changes in institutional ownership in a given month and returns over the previous month. Similarly, the third term, Cov(Δ₂, r₀), measures institutional feedback trading at a 2‐month lag. Analogously, the fourth, seventh, and eighth terms (i.e., Cov(Δ₀, r₁), Cov(Δ₀, r₂), and Cov(Δ₁, r₂)), represent the covariance between monthly changes in institutional ownership and returns measured over the first or second subsequent month within the quarter.

Ideally, we would measure each term in equation (4) to estimate the relations between monthly changes in institutional ownership and returns measured over the previous, same, and following months. Unfortunately, because institutional investors are only mandated to report holdings quarterly, direct estimation is not possible. Our methodology, however, exploits the fact that we can directly estimate each “row” of equation (4). Panel A in table 3 reports these decompositions: contemporaneous (C), lag by t months (Lt), and lead (forward) by t months (Ft). As shown in the fifth row of covariances, for example, the covariance between quarterly changes in institutional ownership and returns over the first month in the quarter (Cov(Δ_0,2, r₀)) consists of a contemporaneous monthly covariance (C), a lag 1‐month covariance (L1), and a lag 2‐month covariance (L2).

Table 3 Decomposition of Covariance between Quarterly Changes in Institutional Ownership and Quarterly Returns

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We employ the additive properties of the observable covariances in the first column of table 3 to obtain an estimate of the unobservable covariances in the last column of the table. In particular, as shown in panel B of table 3, the expected value of the difference between the covariance of quarterly ownership changes and the return over the first month of the quarter (“Covariance 0” in panel A) and the covariance between quarterly ownership changes and the return over the month preceding the quarter (“Covariance −1” in panel A) is the contemporaneous covariance less the lag 3‐month covariance, Assuming (i.e., on average, monthly changes in institutional ownership are independent of returns 3 months prior), then equation (5) provides an unbiased estimate of the covariance between monthly changes in ownership and returns the same month.

By the same process, we can generate a second estimate of the covariance between monthly changes in institutional ownership and returns in the same month by taking the difference between the covariance for the last month in the quarter and the covariance for the first month following the quarter. Specifically, as shown in panel C of table 3, the “end‐of‐quarter” estimate is given by

Similarly, by taking the difference between the covariances for quarterly changes in institutional ownership and different lag returns, each quarter we can generate two estimates of each lead and lag covariance. For example, the beginning‐of‐quarter lag 1‐month covariance can be estimated as the difference between the covariance of quarterly changes in institutional ownership and returns in the month prior to the quarter (i.e., ) and the covariance between quarterly changes in institutional ownership and returns 2 months prior to the quarter (i.e., ). Analogously, we can generate a second estimate from end‐of‐quarter covariances. Specifically, the two lag 1‐month covariance estimates are given by

Similarly, the two estimates of the covariance between monthly changes in institutional ownership and returns the following month are given by

Because we generate two covariance estimates (a beginning‐of‐quarter estimate and an end‐of‐quarter estimate) from each quarter’s change in institutional ownership, the estimates are unlikely to be independent. Therefore, we average each quarter’s beginning‐ and end‐of‐quarter estimates to generate that quarter’s single covariance estimate.

B.  Correlation Decomposition

Because institutional ownership increases over time (figs. 1 and 2), the covariance of changes in institutional ownership and returns also increases over time. Thus, although the covariance estimates given in equations (5)–(10) are appropriate for a given quarter, the lack of covariance stationarity makes aggregation of the estimates over time problematic. To overcome this issue, we “normalize” the covariance estimates each quarter by dividing by that quarter’s cross‐sectional standard deviations of quarterly returns and changes in institutional ownership.12 Note that because our goal is to estimate the portion of the quarterly correlation attributed to monthly comovement, we normalize the monthly covariance estimate by the standard deviation of quarterly ownership changes and returns. Hence, we refer to these estimates as normalized covariances rather than estimated correlations.13 The normalized estimates of the relation between monthly changes in institutional ownership and returns the same month (analogous to eqq. [5] and [6]), for example, are given by:

C.  Decomposing Monthly Covariances by Investor Type and Investor Size

Our data partition institutional investors into five groups: bank trust departments, insurance companies, mutual funds, independent investment advisers, and others. Therefore, the total change in the institutional ownership for a stock over any period is simply the sum of the changes in each of the five categories. As before, denote the total change in institutional ownership from the beginning of month A to the end of month B as Δ_A,B. Similarly denote the change in ownership by bank trust departments, insurance companies, mutual funds, independent investment advisers, and others over the same period as ΔB_A,B, ΔI_A,B, ΔM_A,B, ΔD_A,B, and ΔO_A,B, respectively. Then the covariance between the total change in institutional ownership (Δ_A,B) and returns over the same period is given by Dividing the right‐ and left‐hand sides of equation (13) by the cross‐sectional standard deviations of quarterly changes in institutional ownership and quarterly returns allows us to partition the correlation between quarterly changes in institutional ownership and returns the same quarter to each investor group:

Moreover, because the quarterly change in total institutional ownership is simply the sum of the quarterly changes by investor type, each term in any covariance equation can be partitioned by investor type. The estimates of the contemporaneous monthly covariance between changes in ownership by bank trust departments and returns analogous to equations (5) and (6), for example, are given by

The same method can be used to partition the correlation (and estimates of shorter‐term covariances) between institutional demand and returns the same quarter by investor size. Specifically, rather than partitioning managers by type, we divide managers into large (total portfolio value greater than the median manager’s portfolio value) and small (total portfolio value less than median manager’s portfolio value) managers each quarter and use the methods described in the previous paragraphs to determine the roles of large and small managers.

D.  Generating an Unbiased Estimate

Equations (5) and (6) provide unbiased estimates of the covariance between monthly changes in institutional ownership and returns the same month if changes in institutional ownership are independent of returns 3 months prior (i.e., ) and 3 months following (i.e., ). This will not be the case, however, if institutional investors engage in momentum or contrarian trading based on returns 3 months previous (i.e., and , respectively). Similarly, changes in institutional ownership will not be independent of returns 3 months forward if institutions forecast prices 3 months forward (i.e., ) or if institutional trading temporarily affects prices and this impact is reversed (at least in part) in the third month following the trading (i.e., ). Henceforth, we refer to these terms as, “decomposition error terms” (e.g., Cov(L3) in eq. [5] or Cov(F3) in eq. [6]).

If changes in institutional ownership are not independent of returns 3 months previous or 3 months forward, we can still generate unbiased estimates of the monthly contemporaneous covariance as long as changes in institutional ownership are independent of returns at some point in the past and at some point in the future. Specifically, we can add a second difference to the estimate to move the decomposition error term further from the quarter. Consider, for example, adding the covariance between the return for month (“Covariance −3” in table 3) and the quarterly change in institutional ownership and subtracting the covariance between the return for month (“Covariance −4” in table 3) and the quarterly change in institutional ownership to equation (5). As shown in panel D of table 3, the expected value of the “first difference” given in equation (5) plus this “second difference” yields

Similarly, we can add a “second difference” to the end‐of‐quarter estimate (eq. [6]) to move the decomposition error term further from the quarter. Specifically, as shown in panel E of table 3, the “two‐difference” end‐of‐quarter estimate of the monthly contemporaneous covariance is given by Thus, if changes in institutional ownership are independent of the monthly return 6 months prior (i.e., ) and 6 months following (i.e., ), then equations (17) and (18) provide unbiased estimates of the covariance between monthly changes in institutional ownership and returns the same month. Again, however, if changes in institutional ownership are not independent of returns 6 months prior or post, we can further improve the estimate by adding as many differences as needed to reach the point where changes in institutional ownership are independent of lead and lag returns. Two costs, however, are associated with each additional difference. First, additional differences have the potential to add noise to our estimates. For example, if the covariance between quarterly changes in institutional ownership and lag returns reflects both momentum trading and a noise component, then additional differences may add noise to our estimates. Second, additional terms require a longer time series of data to be included in the sample (e.g., eqq. [5] and [6] require returns from 1 month prior [ ] to 1 month following [ ] the quarterly change in institutional ownership, while eqq. [17] and [18] require returns from 4 months prior [ ] to 4 months following [ ] the quarterly change in institutional ownership).

In this study, we focus on lead and lag estimates up to 12 months following and 12 months previous. Thus, to generate unbiased estimates we must determine (1) the point at which changes in institutional ownership become independent of lead and lag returns and (2) the numbers of differences needed to reach that point. To address the first issue, we must determine at what point changes in institutional ownership become independent of returns. Although we cannot directly estimate the normalized decomposition error term (e.g., Cov(L3)/(σ(Δ_0,2)σ(r_0,2) in eq. [11]), we can estimate the average sum given by as the covariance between the quarterly change in institutional ownership and monthly returns 3 months prior to the beginning of the quarter divided by the cross‐sectional standard deviations of quarterly changes in institutional ownership and quarterly returns, that is, . Similarly, although we cannot directly estimate the decomposition error term from equation (12) (i.e., Cov(F3)/[σ(Δ_0,2)σ(r_0,2)]), we can estimate the average sum given by as the normalized covariance between the quarterly change in institutional ownership and returns 3 months following the end of the quarter, that is, Cov(Δ_0,2, r₅)/[σ(Δ_0,2)σ(r_0,2)].

Table 4 reports the time‐series averages of the normalized cross‐sectional covariances based on quarterly changes in institutional ownership and returns measured over each of the previous 15 months, each of the 3 months within the quarter, and each of the 15 months following the quarter. The second column shows that these estimates include covariances from lag 17 months (Cov(L17)) to lead 17 months (Cov(F17)). The third and fourth columns in table 4 report the mean estimate and associated t‐statistic (based on Newey and West [1987] standard errors with four lags), respectively, based on Δnumber. Similarly, the last two columns report the mean estimate and associated t‐statistic, respectively, based on Δfraction.

Table 4 Average Normalized Covariance between Quarterly Changes in Institutional Ownership and Contemporaneous, Lead, and Lag Monthly Returns

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The results in table 4 reveal that normalized covariances are large and differ significantly from zero during the same quarter as the change in institutional ownership (i.e., months , 1, and 2) for both measures. Lag normalized covariances tend to be positive and large (relative to lead normalized covariances), but they decay rapidly as one moves further from the quarter. Lead normalized covariances are substantially smaller than lag covariances, which suggests that end‐of‐quarter estimates are likely to be less biased than beginning‐of‐quarter estimates. Beyond a 14‐month lag (i.e., ) or a 14‐month lead (i.e., ), the normalized covariances do not, in general, differ significantly from zero. Thus, the results in table 4 suggest that estimates with lead or lag return decomposition error terms beyond 14 months (i.e., greater than Cov(F14) or Cov(L14)) should yield unbiased estimates.

The number of differences needed to reach at least a 15‐month lead or a 15‐month lag is a function of the particular lead or lag being estimated. Because we use monthly data in partitioning the quarterly results, each additional difference for every month increases the decomposition error term by 3 months. As a result, we can generate estimates that have 15‐month decomposition error terms only for one in 3 months. Thus, we use the number of differences needed to generate decomposition error terms of 15, 16, or 17 months. Specifically, the number of differences needed to generate a 15‐, 16‐, or 17‐month decomposition error term for the beginning‐of‐quarter estimate of lag month X (where X is negative for lead values) is solved by determining

Similarly, the number of differences needed for the end‐of‐quarter estimate of lag month X is solved by determining Thus, for example, the lag 8‐month estimate (i.e., Cov(L8)) requires three differences for the beginning‐of‐quarter estimate (eq. [19]) and eight differences for the end‐of‐quarter estimate (eq. [20]). One to nine differences are need to solve equations (19) and (20) for the lag 12‐month to lead 12‐month estimates that are the focus of our study. These estimates require returns up to 15 months prior to the quarter and 15 months following the quarter. As discussed in the Section III, we therefore require firms to have complete return data available for the 15 months prior to, and the 15 months following, the quarterly change in institutional ownership to be included in the sample.

A.  Monthly Estimates

As noted above (see eq. [4]), the contemporaneous quarterly correlation consists of three normalized contemporaneous monthly covariances, two normalized lag 1‐month covariances, one normalized lag 2‐month covariance, two normalized lead 1‐month covariances, and one normalized lead 2‐month covariance. Because the quarterly correlation contains three normalized monthly contemporaneous covariances, we estimate the contribution of the normalized monthly contemporaneous covariance to the quarterly covariance as three times the estimated normalized monthly contemporaneous covariance. (Multiplying these estimates by a constant does not affect the t‐statistics.) Moreover, because the correlation between the quarterly change in institutional ownership and same‐quarter returns is simply the covariance divided by the standard deviations of each, three times the normalized covariance estimate is an estimate of the portion of the quarterly correlation attributed to price movements that occur the same month as the change in institutional ownership. Similarly, because there are two lag 1‐month covariances and two lead 1‐month covariances, the 1‐month lead and 1‐month lag contributions are given as two times the normalized estimates.

The 85 quarters of data yield a total of 84 quarterly correlations and estimates of normalized lead, contemporaneous, and lag monthly covariances. The first row in table 5 reports the time‐series average of the 84 cross‐sectional correlations between Δnumber and returns the same quarter. The other columns in the first row partition this correlation by investor type (next five columns; see eq. [14]) and by investor size (last two columns). The estimated portion of the quarterly correlation due to correlation between monthly changes in institutional ownership and returns the same month is reported in the middle row of panel A (second column). The first column reports the fraction of the quarterly correlation accounted for by the comovement between monthly changes in institutional ownership and returns the same month, that is, the number in the “Total” column divided by the number in the first row of that column. Similarly, the remaining rows report estimates from 2 months prior to 2 months forward (last row). The t‐statistics (reported in parentheses) are computed from the time series of the 84 quarterly estimates and are based on Newey and West (1987) standard errors with four lags. Panel B repeats the analysis based on Δfraction.

Table 5 Monthly Partitioning of Correlation between Quarterly Changes in Institutional Ownership and Continuous Returns

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The estimates reported in panel A of table 5 suggest that the relation between monthly Δnumber and returns the same month accounts for 115% of the quarterly correlation (statistically significant at the 1% level). The results also provide evidence that price effects associated with institutional trading have a temporary liquidity component—the relation between monthly Δnumber and returns the following month accounts for, on average, −25% of the quarterly correlation (statistically significant at the 1% level).

The other columns in the middle row of table 5 (panel A) report monthly contemporaneous comovement apportioned to each investor type and by manager size. Similar to the results for institutional investors in aggregate, the contemporaneous relation is by far the dominant source of the quarterly correlation for each type of institutional investor. The partitioned monthly contemporaneous estimate differs significantly (at the 1% level or better) from zero for each of the five investor types and for each of the two investor size categories. The estimated fraction of the quarterly correlation attributed to each investor group accounted for by that investor group’s contemporaneous monthly comovement (i.e., the numbers in the middle row of panel A divided by the numbers in the top row in panel A) ranges from 101% for mutual funds to 123% for unclassified institutions. The results in panel B, based on Δfraction, are largely consistent with those reported in panel A (based on Δnumber). Specifically, the relation between monthly Δfraction and contemporaneous monthly returns primarily drives the correlation between quarterly Δfraction and returns the same quarter.

In sum, the results presented in table 5 suggest that the correlation between quarterly changes in institutional ownership and returns the same quarter primarily arises from the comovement between monthly changes in institutional ownership and returns the same month. Moreover, the negative normalized covariance for lead monthly returns suggests that the price impact associated with institutional trading has a temporary liquidity component. To examine intramonth effects of aggregate institutional trading, we next extend our analysis to weekly partitioning.

B.  Weekly Estimates

Finer partitioning allows us to better isolate the relative importance of return effects associated with aggregate institutional trading versus very short‐term (i.e., intramonth) momentum trading or price forecasting. The cost, however, is that the analysis is limited to two estimates each quarter regardless of the interval because the partitioning methodology generates two normalized covariance estimates each quarter (a beginning‐of‐quarter estimate and an end‐of‐quarter estimate). In the case of weekly data, for example, we generate two estimates of the weekly contemporaneous normalized covariance each quarter. Because there are 12 weekly contemporaneous covariances each quarter, we estimate the total contribution of the weekly contemporaneous covariances to the quarterly correlation as 12 times the average weekly contemporaneous covariance estimate divided by the cross‐sectional standard deviations of quarterly changes in institutional ownership and same‐quarter returns. Greater extrapolation, however, results in a noisier estimate.

The number of trading days in any quarter over our sample period ranges from 61 to 64 days. We define the first “weekly” return of the quarter as the first five trading days of the quarter.14 We similarly define 11 other weekly returns, for a total of 12 weekly returns each quarter.15 We then estimate the normalized covariance between weekly changes in institutional ownership and returns using formulas analogous to equations (11) and (12).16 Similarly, we estimate the portion of the correlation between quarterly changes in institutional ownership and returns the same quarter attributed to the comovement between weekly changes in institutional ownership and returns the same week as 12 times the normalized weekly contemporaneous covariance. We estimate analogous contributions for 3 weeks prior and 3 weeks following. We limit the weekly analysis to 3 weeks in each direction to maintain reasonable table sizes and because these estimates capture the relation between monthly changes in institutional ownership and returns the same month. The reader may refer to the previous section for analysis of lead and lag monthly relations.

Panel A in table 6 reports the weekly estimates based on Δnumber, while panel B reports estimates based on Δfraction. The results in table 6 suggest that the positive correlation between quarterly changes in institutional ownership and returns the same quarter is primarily driven by the relation between weekly changes in institutional ownership and returns the same week. Specifically, the middle row of panel A (panel B) reports that the estimated weekly contemporaneous comovement accounts for 141% (153%) of the correlation between Δnumber (Δfraction) and same‐quarter returns (both estimates differ from zero at the 1% level). The results in table 6 also reveal evidence that weekly changes in institutional ownership are inversely related to returns the following week, providing further evidence of a temporary liquidity component.17

Table 6 Weekly Partitioning of Correlation between Quarterly Changes in Institutional Ownership and Continuous Returns

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C.  Is the Contemporaneous Relation Driven by Information or Finite Elasticities?

The results in this section suggest that the correlation between quarterly changes in institutional ownership and returns the same quarter is primarily driven by the price impact associated with institutional trading. As noted in the introduction, institutional trades may have a permanent contemporaneous effect on returns if either (1) information is revealed through institutional trading or (2) institutional investors face finite elasticities when buying or selling. We generate two tests to differentiate between these explanations. First, we hypothesize that if the relation is driven by finite elasticities, then returns should be more strongly related to Δfraction than Δnumber. That is, if institutions demand a lot of shares, for whatever reason (information or noise), and the price impact of institutional trading is driven by finite elasticities, then returns should move with net institutional order flow.

Second, we demonstrate that although small managers play a relatively minor role in determining institutional order flow, they play a much larger role in determining Δnumber. Moreover, we find evidence that both small and large institutional investors are likely to be better informed than other investors (e.g., individual investors). Thus, we hypothesize that if the contemporaneous relation between institutional demand and returns is driven by finite elasticities, then the fraction of the correlation attributed to small institutions should be relatively minor because small institutions play a minor role in determining institutional order flow imbalance. Alternatively, if information revealed through trading primarily drives the correlation between institutional demand and contemporaneous returns, then the portion of the correlation attributed to small managers should be similar to the portion of the Δnumber attributed to small institutions.

We have already shown in table 2 that returns are more strongly related to Δnumber than Δfraction, suggesting that information revealed through trading primarily drives the correlation.18 Specifically, the average correlation between Δnumber and same‐quarter returns is 95% greater than the correlation between Δfraction and same‐quarter returns (statistically significant at the 1% level).19

As an alternative test of the relative strength of the relations between contemporaneous returns and the two measures of changes in institutional holdings, we estimate cross‐sectional regressions of contemporaneous quarterly returns on both variables. To allow direct comparison of the estimated coefficients, we standardize (i.e., rescale to zero mean, unit variance) both the dependent and independent variables.20 The average coefficients from the 84 cross‐sectional regressions and associated t‐statistics (in parentheses, based on the 84 estimates and Newey‐West standard errors with four lags) are

According to the t‐statistics, both coefficients differ significantly from zero at the 1% level. In addition, the average R² is 11.51%. The standardized coefficients reveal that a one standard deviation increase in the fraction of shares held by institutional investors is associated with a 0.0886 standard deviation larger quarterly return, while a one standard deviation increase in the number of institutional investors is associated with a 0.2894 standard deviation larger quarterly return. Although the average coefficients for both independent variables differ significantly from zero, the average coefficient associated with Δnumber is over three times the average coefficient associated with Δfraction. Moreover, a paired t‐test of the hypothesis that the coefficients are equal is rejected at the 1% level ( ). In sum, the stronger relation between returns and Δnumber than Δfraction is most consistent with the hypothesis that institutional trading affects returns because such trading reveals information.

We next partition institutional investors into two equal‐size groups (each quarter)—large institutions (those with portfolio values greater than the median manager’s portfolio value) and small institutions (those with portfolio values less than the median manager’s portfolio value). As noted in the introduction, we hypothesize that both small and large managers are likely to be better informed than other investors (also see discussion in Sec. II.B). To test this hypothesis, we compute Δnumber and Δfraction for small and large managers.21 We then compute the cross‐sectional correlation between both measures of institutional demand (Δnumber and Δfraction) for both small and large managers and returns the following quarter. Consistent with the hypothesis that both small and large managers are better informed than other investors, Δnumber for both small and large institutions is positively correlated with subsequent quarter returns (statistically significant in both cases at the 5% level).22

We next examine the relative roles of small and large managers in determining Δfraction and Δnumber. Specifically, we measure the role of small and large managers by partitioning Δnumber (or Δfraction) by manager size, for example, the fraction of Δnumber due to large (small) managers for security i in quarter t is the change in the number of large (small) institutions divided by the total change in the number of institutions for security i in quarter t. We similarly compute the proportion of Δfraction attributed to small and large managers.23 We then average these estimates across securities each quarter and then across quarters. Not surprisingly, small managers play a relatively small role in determining Δfraction—averaging only 8% (i.e., large managers account for 92% of Δfraction, on average). Small managers, however, play a more important role in determining Δnumber—accounting for, on average, 22% of Δnumber (i.e., large managers account for 78% of Δnumber, on average).

Given that small managers appear to be better informed than non‐13(f) (e.g., individual) investors but play a relatively minor role in determining institutional order flow imbalance (Δfraction), we hypothesize that if the contemporaneous relation between institutional demand and returns is driven by finite elasticities, then the fraction of the correlation attributed to small institutions should be relatively minor for both measures of institutional demand (Δfraction and Δnumber). Alternatively, if information revealed through trading primarily drives the correlation between institutional demand and contemporaneous returns, then the fraction of the correlation between Δnumber and contemporaneous returns attributed to small managers should be similar to the portion of Δnumber attributed to small institutions.

Next, we partition the correlation between quarterly returns and both measures of institutional demand into the portion accounted for by small managers and the portion accounted for by large managers (using the method analogous to eq. [14]). In addition, we estimate the portion of the correlation attributed to changes that occur the same month and lead and lag months within the quarter. Results are reported in the last two columns of table 5.

Not surprisingly, given the minor role small managers play in determining institutional order flow imbalance (Δfraction), we find that small managers account for relatively little (approximately 5%) of the correlation between Δfraction and returns the same quarter.24 Consistent with the information explanation, however, small managers account for 23% of the correlation between Δnumber and returns the same quarter (nearly matching the 22% of Δnumber accounted for by small managers). Moreover, for both small and large managers, the relation between institutional demand and returns the same month (middle row) primarily drives the quarterly correlation.

In short, the results in this section are most consistent with the hypothesis that information revealed through trading drives the contemporaneous relation between institutional demand and stock returns. Specifically, returns are more strongly related to Δnumber than institutional order flow imbalance (Δfraction), and although small managers account for little of the institutional order flow imbalance, they account for a substantial portion of the correlation between Δnumber and same‐quarter returns.

A.  Potential Bias due to Window Dressing

Our method implicitly assumes that the covariance between changes in institutional ownership and lead or lag returns is independent of the calendar date. For example, equation (5) assumes that the expected value of the covariance between changes in ownership the last month in quarter t and returns in the first month in the quarter (Cov_t(Δ₂, r₀)) equals the expected value of the covariance between changes in ownership the second month in a quarter and returns 1 month prior to the quarter (Cov_t(Δ₁, r₋₁)). In other words, we are assuming that the covariance between portfolio changes in December of a given year and returns in October is equal, on average, to the covariance between portfolio changes in November of that year and returns in September. Similarly, our method implicitly assumes that changes in ownership (Δnumber or Δfraction) have the same means across months. One might expect these assumptions to be violated if institutional investors have a tendency to “window dress” at the end of each quarter.

We address the potential window‐dressing bias in several ways. First, the limited evidence supporting the window‐dressing hypothesis suggests that it occurs only at the turn of the year (see, e.g., Lakonishok et al. 1991). Therefore, we repeat the analyses in tables 5–8 excluding estimates garnered from both the first and last quarters of the year. Our results remain similar to those that include all quarters. For example, the monthly contemporaneous normalized covariance based on Δnumber accounts for 118% of the quarterly correlation when excluding the first and fourth quarters and 115% of the quarterly correlation when including all quarters.

Second, this potential bias is likely to be less important as we move to a finer partitioning of the data. If institutional investors window dress only in the last week in the quarter, the potential bias remains. To the extent that institutional investors begin to window dress in the second week prior to the end of the quarter, the potential bias is diminished.

In sum, although institutional window dressing has the potential to bias our estimates, our results remain intact when we exclude the turn‐of‐the‐year period, and the potential bias is likely to be less important as our partitioning moves to a finer interval (e.g., less important for weekly estimates than monthly estimates).

B.  Trade Discreteness

Because aggregate institutional ownership data are available only on a quarterly basis, we exploit the linear properties of covariances to infer the shorter‐term relations between aggregate institutional trading and returns. Thus, we do not know when, exactly, the change in ownership occurs. For a given security, it is possible that the entire change in ownership occurs the first day of the quarter, the last day in the quarter, or somewhere in between. Because our analyses are cross‐sectional, however, this should not seriously bias our estimates unless the change in ownership occurs systematically across all securities on the same day. Given that institutional investors account for 70% of trading volume (Schwartz and Shapiro 1992), it is unlikely that the change in ownership occurs on a given day or even a few days.

Nonetheless, to ensure that our results are not sensitive to such potential patterns, we repeat the analysis in table 5 for small, medium, and large stocks (stocks are sorted into three equal‐size groups each quarter based on market capitalization) separately. We hypothesize that because institutions account for most of the trading volume of medium and large stocks, changes in institutional ownership are more likely to be spread out over the quarter. Thus, if our results are systematically biased by the discreteness in changes in institutional ownership, then the small stock analysis should differ substantially from the medium and large stock analysis.

The analysis by firm size (not reported to conserve space) reveals little evidence that discreteness of ownership changes affects our results. Specifically, the six contemporaneous estimates (small, medium, and large stocks based on Δnumber and Δfraction) are statistically significant (at the 1% level) and account for a minimum of 105% of the quarterly correlation (Δfraction for medium stocks) to a maximum 140% of the quarterly correlation (Δfraction for small stocks).31 In sum, the estimates by firm size suggest that the relation between quarterly changes in institutional ownership and same‐quarter returns is primarily driven by the price impact of institutional trading.