Portfolio Management Pressure ∗

Huaizhi Chen †

November 25, 2015

Abstract

This paper investigates the effect of portfolio composition management on trad-ing and return predictability. I find mutual funds, in managing their portfoliosagainst compositional changes caused by the dispersion of realized holding returns,exert a net liquidity demand on other investors. Mutual funds chase after high re-turns, but readily rebalance against large increases in their positions. The resultantasymmetric demand decreases the prices of large cap/high momentum stocks. Avalue-weighted strategy exploiting this predictability earns 2.83% (2.60% 4-factorsadjusted) returns per quarter on the largest, and supposedly most liquid and ef-ficiently priced assets in the cross section of equities; contrasting priors that thedemand channel for assets only circumstantially affect stock prices. This papermakes contributions by 1) documenting the significant consequences of portfoliomanagement by professional asset managers on stock prices, 2) identifying empir-ically how equity rebalancing is conducted across the asset management industry,and 3) explaining several puzzling facts about cross sectional equity momentum.

∗I would like to thank my advisors, Dong Lou and Christopher Polk, for their invaluable guidance,encouragement, and assistance on this project. I also thank Lauren Cohen, Daniel Ferreira, Dirk Jenter,Christian Julliard, Marcin Kacperczyk, Ian Martin, Tarun Ramadorai, Dimitri Vayanos, Michela Ver-ardo, David Webb, and seminar participants at LSE for their time and helpful comments. Any errorsare, of course, mine and mine only.†London School of Economics and Political Science, Department of Finance and the Financial Markets

Group, h.chen3@lse.ac.uk.

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1 Introduction

This paper investigates the effect of portfolio composition management by profes-

sional asset managers in the equity market. The asset management industry has become

an integral part of the financial sector. The active management provided is generally

thought to generate positive externalities- managers trade on information; the informa-

tion base trades promote price discovery and informational efficiency in the underlying

assets (French, 2008). Given a more informational efficient market, risk adjusted returns

should become less available in the cross section of assets. However portfolio manage-

ment also comes with its own constraints and biases.

I explore one important dimension in which portfolio management induces trad-

ing and cross sectional predictability as a consequence of its potential constraints and

biases. Asset managers are subject to similar constraints on portfolio diversification, and

due to common knowledge can have very similar beliefs and incentives on how portfolios

should be managed. Realized returns induce mechanical variations in portfolio weights.

How mutual funds rebalance on these variations reveals important facts about the con-

straints, beliefs, and incentives that govern these asset managers. Surprisingly, I find the

rebalancing of portfolios, against these mechanical changes in weight, is very systematic

across funds at the observable quarter-to-quarter horizon. Trades for rebalancing must

be matched to counter parties, and I find that mutual funds, in rebalancing their existing

positions, exert an aggregate liquidity demand on the largest and highest realized return

stocks. A trading strategy based on this pressure generates 2.83% per quarter returns on

the largest, and supposedly liquid and efficiently priced assets in the equity market. This

price pressure is related to past return and market capitalization characteristics, and in

consequence affects the dynamics of asset momentum in the cross section of equities. I

use the discovered portfolio management pressure to explain two puzzling facts about

cross sectional equity momentum. The underperformance of 2 to 6 month momentum,

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i.e. the echo effect, can be explained by portfolio management pressure and the momen-

tum crash of 2009 in my sample period. Furthermore, the intra-quarterly seasonality of

momentum returns, mainly its underperformance in the first half of each quarter, can

be attributed entirely to the identified price pressure.

Following the nomenclature used by previous studies, I call the reverse trading due

to return driven weight changes, portfolio rebalancing1. Several simple mechanisms can

motivate the observed predictability in portfolio management. First, investment compa-

nies have weight-based constraints in the construction of portfolios. Common constraints

include legal exposure limits on individual stock positions2, idiosyncratic positional lim-

its3, and strategies based on predefined weights on assets or sectors4. These explicit and

implicit portfolio restrictions imply the same consequence: weight changes caused by the

dispersion of the underlying returns will coincide with rebalancing against these changes.

Limits on exposures, in particular, cause trades against large increases in weights and

have limited implications on drops in positional weights. Second, benchmarking to a

tracking portfolio can also induce rebalancing trades. An asset manager trades off index

tracking with informed stock picking (Vayanos and Woolley, 2012). To maintain some

tracking to the benchmark portfolio, a manager has to actively trade against the devia-

tions in his portfolio from the benchmark. Return based weight changes, for active funds,

empirically correlate significantly and positively to deviations from my proxy of bench-

mark weights. This is not surprising in that past weights are also imperfect proxies of

benchmarking standards, if managers do benchmark. The return driven weight changes,

therefore can capture the deviation of the portfolio from benchmark weights, and induce

1See for example, Campbell, Calvet, and Sodini (2009) on the asset class rebalancing by householdinvestors.

2Declared diversified investment companies, including most equity mutual funds, closed-end funds,and some hedge funds, must with respect to 75% of their portfolio legally maintain less than 5% oftheir total asset under management in an individual position by the Investment Company Act of 1940.Endowments and insurance companies also have legal diversification requirements as well.

3A fund may limit positional exposures explicitly beyond the legal prescribed limits.4For example, a fund may follow strategies that prescribe 1/N diversification in assets. See DeMiguel,

Garlappi and Uppal (2009).

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reversal trading as a consequence of benchmarking incentives. Lastly, rebalancing can

be simply induced by the managers’ respective belief of expected returns and risks. If a

manager expects constant future returns or reversals in returns, then he would manage

his portfolio against any weight deviation caused by dispersion in returns.

The detailed granularity of the mutual fund holdings data allows me to capture

rebalancing against many different levels of return dispersion driven weight changes in a

portfolio holding. I argue that the exposure constraints in position weights are a signif-

icant reason for quarter to quarter rebalancing. For each mutual fund, the rebalancing

trades are driven mainly by positions that have increased within a portfolio, and the

biggest increases out of these positions get rebalanced the most on a fractional basis.

This empirical pattern is consistent with asset exposure constraints on portfolio man-

agement; however, it does not rule out systematic behavioral biases or unconventional

beliefs on the part of the asset manager.

In order to construct a predictor of rebalancing based trading, I follow the insight

that changes in asset weights within a portfolio are determined in part discretionarily

by the relative trading of the different positions, and in part passively by the relative

realized returns of the underlying assets. I decompose the quarter to quarter changes

in position weights into a discretionary (discret) and a passive (passive) portion5. The

passive weight change is simply the change in the weight of an asset within a portfolio

if the asset manager did not trade, or if he had simply scaled his portfolio between

quarters. The hypothetical weight of an asset within the portfolio, had the manager not

trade, can be calculated by interacting the asset’s initial weight with its gross returns

and scaling the variable so that its total in a portfolio sums to one. passive is simply the

difference between this hypothetical weight and the initial weight of a portfolio. discret

is then the total weight change between quarters subtracted by passive.

This passive weight change, in conjunction with past asset returns and initial

5The measures are the same as active and passive in Calvet, Campbell, and Sodini (2009), but asapplied to individual asset positions instead of asset classes.

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weights, forecast on average 8% of the cross sectional variation in the subsequent quar-

terly changes in asset weights for the mutual funds in my sample. I find that because

mutual funds tend to rebalance the most against their largest winners, and that the large

winner stocks tend to share characteristics such as large market capitalization and high

past returns, these rebalancing trades generate net price pressure against momentum for

the large capitalization stocks. This price pressure has two main consequences for equity

momentum. First, because the rebalancing occurs at the quarterly horizon, the rebal-

ancing pressure negates short horizon autocorrelation in stock prices. The momentum

echo effect documented in Novy-Marx (2012) can be explained by the portfolio rebalanc-

ing pressure and the momentum crash of 2009 for my sample period. Second, because

rebalancing trades by asset managers tend to occur when the underlying’s information

asymmetry is low and liquidity is high, it follows a systematic intra-quarter pattern

that increases upon information release in the underlying assets. Therefore, rebalancing

pressure promotes intra-quarterly seasonality in momentum returns. In sum, this paper

links portfolio rebalancing to asset predictability, argues that this channel is a significant

source of price pressure from the practice of portfolio management, and documents the

effect of this price pressure on equity momentum.

This study is composed of three parts. First, I establish that mutual funds re-

balance their portfolios at the observable quarter-to-quarter horizon of holding reports,

negating past return driven changes in asset weights. For each portfolio/quarter obser-

vation, I separate the change in the weight of each stock into the return driven pas-

sive change (passive) and the residual discretionary change (discret) by the investment

manager. Through the channels previously mentioned, return driven weight change can

forecast discretionary rebalancing in asset weights. To show that this forecast-ability is

observed over the quarter-to-quarter horizon, I forecast discretionary and total change

in position weights for each mutual fund per quarter. The panel average of the resul-

tant coefficients indicates that for each unit of return driven increase in the weight of

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an asset, a fund manager rebalances by discretionarily decreasing the unit by 22.77%.

The total decrease in the position is by 25.27%. The explanatory power of the regressed

variables is significant: they explain on average 8% of the total variation in future weight

changes. Further decompositions separate positive deviations from negative deviations,

and a proxy of benchmark deviations from residual return driven deviation. These de-

compositions indicate that positive return driven deviations, specifically large passive

increases in weight, are the main drivers of rebalancing and that benchmark deviations

and residual deviations both have predictive power on rebalancing. Rebalancing trades

don’t appear to be absorbed by other mutual fund investors, and instead are absorbed

by other market participants. I show that the aggregated share weighted average passive

deviation for each stock (passive) has predictive power on its holding by the aggregation

of all mutual funds. One standard deviation of this variable indicates a 12-basis point

increase in the proportion of a stock that is held by the entire equity fund universe,

and more than 20-basis point increase in the proportion held by all institutions. This

indicates that the main counter parties to portfolio rebalancing trades are non-reporting

entities such as institutions without significant holdings and retail investors.

Second, I investigate the impact of these trades on stock returns. Value-weighted

Fama Macbeth regressions indicate passive has predictability on stock returns at the

quarterly horizon. Because passive is related to past 3 month returns, this predictability

is strong and significant only after controlling for past return characteristics, and remains

significant after controlling for many other stock characteristics. This predictability is

stronger in the later sample periods, when the asset management industry is larger.

The price pressure related to passive generates positive quarterly returns which revert

at longer holding horizons. Strategies sorted on momentum or passive alone hide the

two effects that occur through the quarter; the negative price pressure from rebalancing

by portfolio managers, and the positive cross sectional momentum. I follow up on two

immediate implications from portfolio management pressure. The first implication is

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that the underperformance of 2 to 6 sorting month momentum as documented in Novy

Marx 2012 can be partially explained by the short term portfolio rebalancing. Value-

weighted Fama Macbeth regressions indicate that after controlling for passive and the

momentum crash of 2009, 2 to 6 month performance becomes a significant predictor

of future returns in my sample period. The second implication is that the seasonality

in momentum returns can be attributed to the seasonality of portfolio rebalancing by

funds. Since rebalancing trades require counterparties, managers time their trades to

minimize costs from information asymmetry and the lack of market liquidity. I use a high

frequency dataset of institutional trades, Ancerno, to pin down the timing of rebalancing

by asset managers and find that institutional trades in general occur more during the first

half of each quarter, and that rebalancing tend to occur predominantly after a stock’s

earning announcement when informed trading and market liquidity is at its highest. The

long short portfolio and passive return factor constructed in the next section subsumes

the underperformance of momentum returns during this intra-quarterly period.

Lastly, I examine the intra-quarterly price pressure from rebalancing trades in

detail. I find that one standard deviation increase in the passive variable indicates

0.52% higher returns in the underlying stock during the dates before the last 10% of

the S&P500 constituents make their earnings announcements each quarter. A value-

weighted portfolio holding the bottom decile and shorting the top decile of passive large

cap stocks earns 2.83% raw and (2.60% adjusted) returns during this period. The highest

decile portfolio earned an average of 0.32% (-0.95% adjusted) return while the lowest

decile earned 3.15% (1.65% adjusted). The cumulative returns around individual firm’s

quarter earnings announcements indicate that most of the return predictability occurs

during and after the release of earnings information into the market. This is also when

market liquidity and informational symmetry for the underlyings are at their highest,

and when assets managers time their trades. The predictability from passive is strong

even after adjusting for contemporaneous standardized unexpected earnings (SUE). In

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fact, price pressure from portfolio management by asset managers affects the largest and

supposedly most efficiently priced assets in the equity market; contrasting the standard

priors that the demand channel for assets only circumstantially affect prices.

2 Related Literature

One of the first mentions (See also Tobin 1958, 1969) of the channel through which

an appreciating financial asset affects the relative prices of other securities in a portfolio

is in Milton Friedman and Anna Schwartz’s 1963 magnum opus, The Monetary History

of the United States. In it, the authors state ”It seems plausible that both nonbank and

bank holders of redundant balances will turn first to securities comparable to those they

have sold... as they seek to purchase these they will tend to bid up the prices of those

issues...” To paraphrase, the free cash balances from the sale of an appreciating asset,

in their case treasuries, ends up triggering the bidding up of other related securities. In

an effect, the hypothesis is a price pressure channel of investor demand. Despite the

pedigree, this channel, which proposes a relationship of assets within the same portfolio,

has lacked micro level support in the literature, and has never been applied to the cross

section of equity assets. One reason for this may be that this channel is difficult to

disentangle from other channels of asset spillover, especially in the bond market, where

asset substitutability is inherently linked by the term structure of expectations and micro

portfolio level data is scant. Another reason is that the portfolio channel may not have

been important prior to the growth of asset management institutions in the financial

sector. This paper presents evidence from the equity markets to validate the hypothesis

that portfolio qualities do affect relative prices.

This paper follows the steps of two prior studies on the portfolio balancing by

investors. Calvet, Campbell and Sodini (2009) study the household rebalancing of stocks,

mutual funds, and bonds using a detailed comprehensive household dataset. Hau and

Rey (2010) track the global mutual fund flows, foreign/domestic equity returns, and

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exchange rates in a VAR and discovers a pattern consistent with rebalancing flows. This

current paper joins them in documenting the active rebalancing of portfolios by investors

against the pressures of cross sectional price changes. However, distinct from the previous

studies, the current study reveals the timing and aggregate price impact of this behavior

and explores institutional constraint channels for this rebalancing. Unlike the household

investors in Calvet, Campbell and Sodini (2009), the institutional investors in aggregate

exhibit rebalancing over time, and this induces price pressure on the underlyings. I

further document the link between the portfolio rebalancing channel and the relative

returns of assets. In terms of the mechanism, my evidence supports the hypothesis that

individual exposure constraints, at least for institutions, are likely a large part of the

reason for rebalancing trades.

This paper is also related to the literature that connects trading pressure, par-

ticularly from mutual funds, to stock returns. A starting point is Shleifer (1983), which

documents a significant price effect on the inclusion and exclusion of stocks from a stock

index. A strand of price pressure literature that involve mutual funds includes Coval and

Stafford (2007) and Lou (2012) who study mutual fund trading in the presence of asset

flows, which induces fund buying and selling. The linkage from prices to mutual fund

can be seen in further works that include Greenwood and Thesmar (2011) who study

fund ownership structure and underlying stock returns and Anton and Polk (2014) that

study the reversal of correlated positive movement between assets held under the same

mutual funds. A classic paper by Gompers and Metrick (2001) documents increase in

returns to large capitalization stocks between 1980 and 1996. This occurred along side

institutional growth and the accompanying institutional demand for large cap stocks.

An implicit assumption of this literature is that the change the underlying asset dynam-

ics is driven by investment flows in and out of intermediary institutions. A missing piece

in this literature is the how these funds trade in response to the changes in the relative

price levels of its holdings. This response is, on the existing holdings, for the most part

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orthogonal to flows in and out of each fund. In presence of positive flow, a fund can

rebalance by simply purchasing its relatively low return assets without selling any of its

high return assets. Surprisingly, this response is predictable, and economics significant

for the largest equity assets.

This paper is also related to the seasonality of stock returns found in the finance

literature. Ritter (1988), and Ritter and Chopra (1989) study the turn of the year effects

in which low capitalization stocks have higher returns than high capitalization stocks

during the January of each year. Ritter and Chopra (1989) argues that shifts in risks

cannot explain this phenomenon and that portfolio rebalancing, potentially related to

accounting incentives, is the most consistent hypothesis for this effect. The phenomenon

reported in this paper is distinct from size related effects in the cross section of asset

prices. In fact, the rebalancing pricing pressure by the asset management industry

exists after controlling for size, is the strongest among the largest capitalized stocks in

the market, and is mainly driven outside of the first quarter of the year.

Lastly, this paper contributes to the literature by clarifying the empirical behavior

of momentum and institutional demand for assets. Jegadeesh and Titman (1993) first

described momentum returns, motivated by technical analysis by industry practitioners.

Prior research on mutual fund behavior includes Grinblatt, Titman, and Wermer (1995),

who document return chasing behavior by mutual fund managers. Koijen and Yogo

(2015) recently found mean-reversion in institutional demands for the characteristics of

book equity, equity to asset, and profitability as determinants of portfolio weights. They

find that predictability from this reversion in characteristics demand is most pronounced

for the smallest stocks, which are a priori most illiquid assets. This paper instead looks

directly at the reversion in portfolio weights as determined by passive dispersion of

constituent returns, and find that this rebalancing liquidity demand generates significant

predictability on the largest and supposedly most liquid assets in the equity market.

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3 Data

The standard CDA/Spectrum mutual fund holdings dataset is used for the mutual

fund portfolio holdings. This is matched to the CRSP Mutual Fund data using links

provided by Wharton Data Services. The holdings data is observed at the quarterly

frequency and is compiled from both mandatory SEC filings and voluntary disclosures.

Funds that report prior to the end of the quarter are assumed to have held the same

portfolio at the quarter end date. To separate out the index funds, I drop funds that

have the words “INDX”, “IDX”, or “INDEX” in their names. Although some funds had

reported at semi-annual frequency prior to mandatory changes in 2003, the majority of

funds voluntarily report holdings at the quarterly even prior to these changes. The vari-

ables constructed and the tests conducted are done on quarterly reporting portfolios.

I supplement the holdings information with the Ancerno/Abel Noser data on

institutional trading to investigate the timing of rebalancing trades. Large institutions

such as brokerages, insurance companies, and pension funds, submit the stock transac-

tions by their asset managers to the Ancerno/Abel Noser Corporation for trading cost

analysis. Each trade is linked to a unique account code (clientmgrcode). Two data

filters are used. Since most of the calculations are based on the relative intra-quarter

trades per stock, I ensure that each trade observation used comes from firms that were

first observed prior to the beginning and last observed after the end of that quarter in

the whole sample. I also drop funds that have the words “INDX”, “IDX”, “INDEX”,

or “BANK” appearing in the either name of the specific account or that of the specific

manager. After applying data filters, the data sums to about 300 billion dollars of trade

volume each quarter and spans 376,200 different accounts from January 2000 to Decem-

ber 2010. See Puckett and Yan (2011) for a more detailed discussion of the data and its

selection issues. To calculate the dollar volumes for various trades, I use the prices from

the last quarter.

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I link the Ancerno database to the CDA/Spectrum quarter-to-quarter mutual

fund holdings to produce a combined dataset of trades and holdings using a simple

procedure. I regress each change in asset positions against the aggregate trades of each

fund in Ancerno per the quarter against the change in each quarter/portfolio set in CDA

spectrum. If the coefficient is significantly positive (t > 10) and explains over 90% of the

variation in the portfolio data, then I call the match successful. At the end of the process,

I obtain matching of about 2800 portfolio/quarter sets between the two databases from

2000 to 2010. An inspection of the Ancerno fund and CDA/Spectrum portfolio names

indicates that the matches are reasonable.

Stock returns, prices, and other stock related characteristics come from the CRSP

database. Tests forecasting future returns are done with common stocks traded on

AMEX, NYSE, and NASDAQ exchanges. The standard Size/Momentum portfolio re-

turns, as well as the usual cross sectional factors, are taken from Ken French’s website.

Quarterly earnings announcement dates for the S&P500 constituents are obtained

from the Compustat database. Standardized Unexpected Earnings (SUE) is calculated

using the code provided by WRDS on quarterly earnings announcements.

4 Portfolio Rebalancing

There are many reasons to observe portfolio rebalancing against return driven

changes in asset weights. I motivate and explore three reasons in particular. First, if a

fund has specific weight based constraints, return driven increases of individual positions

due to outperformance must be met with trades to offload these positions. For example, if

a portfolio manager specifies that each of his individual position should be constrained at

5% of the fund’s total value then he is more likely to sell an asset with large weights after

it had experience high returns. Higher the passive increase in weight, the more he will

have to discretionarily sell shares. Investment companies classified as diversified legally

have to limit individual positions to less than 5% of the total asset under management;

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these diversified companies include most equity funds, closed-ended funds, and holding

companies. Second, benchmarking by active funds requires rebalancing over time- as

a particular stock picks change their weight in a portfolio due to realized returns, the

fund manager will have to rebalance in order for the portfolio to not deviate too far

from a particular benchmarks. I show that the dispersion of asset returns tend to be

correlated with deviation from a proxy benchmark index. Following Koijen and Yogo

(2015), I compare the fund composition to a market cap weighted index of the universe

of stocks that were held by the fund over the past 3 years. I decompose the return

driven change in weights to the difference between the return driven weight and the

benchmark weight and the difference between the benchmarket weight and the initial

weight. I show that both portions forecast negatively the weight changes in the position

in the next quarter; consistent with possible benchmarking. Lastly and importantly,

if asset managers have particular beliefs on expected returns; such beliefs may induce

rebalancing against passive weight changes. For example, if the manager believes that

returns and risks are constant, then he would resist any change to portfolio composition

brought about by realized returns. I explore the consistency of these channels later in

this section.

Regardless of the reasons, the major symptom of many types of portfolio manage-

ment is that changes in weight brought by realized returns will be met with rebalancing

through discretionary selling and buying. Whether this occurs in the observable quarter-

to-quarter frequency, whether this results in forecast-able patterns of portfolio adjust-

ments, and whether this form of rebalancing accounts for a significant portion of trading

are empirical questions, relevant to understanding the impact of these financial interme-

diaries on assets. To begin answering them, I separate the passive weight changes from

the discretionary changes made by the portfolio managers. If a manager didn’t trade

discretionarily and only scaled his existing holdings between the two periods, the weight

difference in the portfolio would be entirely passive.

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Let fund j have stocks {w1,j,t, . . . , wi,j,t, . . . , wI,j,t}. For each component in a

portfolio j, I separate changes in the weight of stock i to that by discretion of the

manager and that by return dispersion.

wi,j,t+1 − wi,j,t︸ ︷︷ ︸Total Change (total)

= wi,j,t+1 − wi,j,t+1︸ ︷︷ ︸Discretionary Change (discret)

+ wi,j,t+1 − wi,j,t︸ ︷︷ ︸Passive Change (passive)

where

wi,j,t+1 =wi,j,t(1 + ri,t)∑N

n=1wn,j,t(1 + rn,t)

is the predicted weight of stock i in portfolio j from the dispersion of returns.

The variable passivei,j,t is assigned as the passive return driven change for each

stock i in portfolio j between quarters t to t+1. Another interpretation of this variable

is simply the interaction of the scaled individual stock return and its weight within a

portfolio minus the initial weight.

I regress positional changes between t+1 to t+2 for each portfolio/quarter sample

collection on passivei,j,t along with initial weight and the stock’s scaled return. The

major reason for choosing the left handside variables as changes in weights rather than

buying and selling is that this paper is mainly concerned with portfolio management.

Given that asset managers experience persistent inflow and outflows, direct buying and

selling of assets inherit induced effects of capital constraints. The regression coefficients

are collected in a panel and averaged similar to a Fama Macbeth procedure. I find

that the return driven changes are negative predictors of discretionary and total weight

changes in the subsequent quarter. This effect is complementary to return chasing

by mutual fund managers. Quarterly returns predict weight increases while passivei,j,t

predicts weight decreases (Table 2a). Consistent with the existing literature, these results

indicate that while mutual funds ‘chase’ returns, they do so for the smaller and new

positions.

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The table also indicates that for their existing positions, mutual funds have histor-

ically managed to rebalance their positions. For a single position, a unit of passive weight

change is met with 22.4% (t=15.46) discretionary decrease, and a 25.1% (t=10.32) to-

tal decrease. A second set of coefficient averages are reported in columns 5 to 8. The

weighted average is based on the quarterly fraction of total mutual fund assets held

by each individual portfolio. The magnitudes of the rebalancing coefficients decrease

to 15.26 % (t=8.25) and 17.68% (t=5.61) respectively, indicating that larger funds re-

balance less intensely than smaller funds. The three variables used in the regression

explain about 8% of the total variation in the quarterly changes in position weights.

This set of results concludes that that mutual funds on average exhibit significant rebal-

ancing behavior and this behavior explains significant variation of the quarter-to-quarter

changes in portfolio compositions. I include regression with further lags of the passive

in the appendix (Table A3). The forecasting power of passive is the strongest at the

quarter-to-quarter horizon; rebalancing as predicted by longer lags is very marginal.

To further explore the channels for portfolio rebalancing, I decompose the variable

passivei,j,t in a few reasonable fashions. First because most constraints are prescribed

upper limits on positions, funds should react more toward weight increases and less

toward weight decreases. I separate return driven changes into increases and decreases

and carry the same analysis in Table 3.

wi,j,t+1 − wi,j,t︸ ︷︷ ︸passive

= (wi,j,t+1 − wi,j,t) · 1(wi,j,t+1 > wi,j,t)︸ ︷︷ ︸passive+

+ (wi,j,t+1 − wi,j,t) · 1(wi,j,t+1 ≤ wi,j,t)︸ ︷︷ ︸passive−

We observe that the main drivers of the rebalancing trades are positions that have

appreciated. The negative side of the passive weight changes have small to no statistical

significance. Because the data on mutual fund holdings is so large and granular, I am

able to separate passivei,j,t even further. I plot the fund size weighted coefficients for

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regressions of discretionary change in weights against further separation of the variable

passivei,j,t in Figure 1. I find that the reversal coefficients are the strongest for large

positive return driven weight changes. This is consistent of the position constraint

channel for portfolio rebalancing. Simple beliefs on constant returns and risk, and direct

benchmarking to asset weights would not generate this asymmetry.

Second in table 3, I also separate the return driven changes into a portion that

contains the difference between benchmark weights6 and a residual difference.

wi,j,t+1 − wi,j,t︸ ︷︷ ︸passive

= (wi,j,t+1 − bi,j,t+1)︸ ︷︷ ︸Benchmark Deviation (bench dev)

+ (bi,j,t+1 − wi,j,t)︸ ︷︷ ︸Residual Deviation (res dev)

Here bi,j,t+1 is a proxy benchmark weight constructed using past 3 year stock level

holding. Both Bench Dev and Res Dev have negative predictive power over future

weight position adjustments. The difference between benchmark weight and return

driven weight in a position is positively correlated with the total return driven weight

change (ρ = 0.10).

An important caveat, however, is that the act of rebalancing requires that in

aggregate asset managers trade with other investors because returns and weights are

correlated per stock across portfolios. Appreciated assets have to be sold to investors

outside of the asset managers. I find that these rebalancing trades are not absorbed by

the mutual fund or the asset management industry. Table 2b regresses the difference

of the proportion of stock shares held by the sum of all mutual funds each quarter

against past 3-month returns, lagged average passive change in weight, and lagged share-

weighted average weights in a portfolio. While the overall industry exhibit strong return

chasing behavior based on past returns, this behavior severely decreases for high average

weight and high return shares. One standard deviation of passive forecasts a 12 basis

6Since the true tracking benchmark is unobservable for each fund, I construct proxy indices usingmarket cap weighing of the universe of stocks that the fund had invested in the past 3 years.

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point decrease in the total proportion of a stock held by all mutual funds and a 20 basis

point decrease in the proportion held by all institutions (untabulated). These results

indicate that high average weights and high return driven deviations in weights forecast

net decreases in the proportion of shares held by asset managers. The largest rebalancing

trades have to be absorbed by retail investors and non-reporting institutions.

Next, I investigate the pricing effects of these rebalancing trades.

5 Predictability and Echo

Following the hypothesis that collective portfolio management induces trading and

consumption of liquidity from outside investors, I use the passive and passive+7 variable

calculated in the previous section to forecast returns. Because passive is generated on

past 3 month returns and portfolio weights, it is generally correlated to past return

characteristics. Description of the variable, and its correlation to past returns is given

in the panel b of table 1.

At quarterly horizons, passive forecasts negative returns in large cap and high

past return stocks. Table 4 shows value-weighted Fama Macbeth regressions of quarterly

stock returns with passive and passive+. The forecasting power of passive is significant

once controlling for past 3 month returns, and is greater in magnitude after 20008. One

standard deviation of passive forecasts 50 basis points returns between 1990 and 2013,

and 64 basis point between 2000 and 2013.

One immediate observation from table 4 is that 3-month past returns positively

forecast future returns once I control for the rebalancing related price pressures. Be-

cause the observable rebalancing tend to be at the quarterly horizons, it may very well

attenuate momentum based predictability using past performances measured at similar

horizons. I explore this hypothesis further to explain the echo effect documented in

7passive+ is simply the share weighted average of passive+.8The results remain qualitatively the same after kicking out sample periods such as 2009 with the

momentum crash.

17

Novy-Marx (2012). In Table 5, I regress forward quarter returns on passive, passive+,

past 1 month returns, past 2 to 6 month returns, past 7 to 12 month returns, and various

controls. I find that controlling for the rebalancing variables increase the magnitude and

power of 2 to 6 month past stock performance in forecasting future quarterly returns.

In fact, the main drivers that result in the insignificance of 2 to 6 month returns are

rebalancing based price pressure and the momentum crash of 2009. Once controlling for

the two factors, 2 to 6 month past performance significantly forecast quarterly returns

at the quarterly portfolio formation intervals. Predictive strategy based only past per-

formance or passive alone hide the two effects that occur; the negative price pressure

from rebalancing by portfolio managers, and the positive cross sectional momentum.

I plot the cumulative Fama Macbeth return coefficients from one standard devi-

ation of passive returns in figure 2. The results indicate that the forecasting power of

passive is predominant in the first 1 to 2 month holding period. The cumulative return

reverses during the second quarter, completing its reversal by months 6 to 8. I also plot

the intra-quarterly cumulative return from holding a simple long short portfolio based

on passive for large capitalization stocks in figure 3. The long (short) portfolio is based

on the bottom (top) decile of passive sorted stocks with capitalization great than the

80th percentile of firms in the NYSE. The gap between the two portfolios accumulated

over the quarter constitutes a very peculiar pattern. In fact, this is similar to patterns

observed in size sorted momentum portfolios in figure 4. Figure 4 includes the average

intra quarter cumulative daily returns of 2-12 momentum sorted on size, rebalanced at

month end, between Q1 1990 and Q4 1999 (top), and Q1 2000 and Q4 2013 (bottom).

Table A1a (A1b) shows the long-short returns of portfolios sorted on size and 12-

month momentum (size and short-term reversal) from January 1990 to December 2013

and January 2000 to December 2013. On average, the long-short momentum portfolios

have had negative returns during January, April, July, and October; while most of their

portfolio returns come at the end of the quarter. The largest size momentum portfolio,

18

in particular, experienced the largest negative returns during this intra-quarter period.

This effect is not apparent in the periods from 1970 to 1990 or from 1950 to 1970 (Table

A2a). As documented in the literature, for much of its history, momentum effects tend

to be more concentrated in smaller and more illiquid stocks. However, as I document in

the most recent era, the dispersion of momentum returns became concentrated mainly

in the largest and ideally most liquid stocks of the market rather than in the small ones.

A very similar pattern can be observed for short-term reversal portfolios in table A2b.

Momentum based portfolios, for large cap stocks, perform negatively in the first halve

of the quarter and positively in the second halve. I investigate the hypothesize that the

timing of rebalancing based trades is the cause of this seasonality in the subsequent

section.

6 Rebalancing Seasonality and the Seasonality

of Momentum

To examine the timing of rebalancing trades in detail, I examine the intra-quarter

variation in the trading intensity of my sample of asset managers. A guiding hypothesize

is that asset managers tend to trade to rebalance more at times when information is

released into the market. This is when informational asymmetry is low and trading on

public information is the highest.

I use the Ancerno database to explicitly identify trades by professional asset

managing institutions. I filter the data in 2 ways. First, observations of a portfolio in

the quarters where the fund is first observed or is last observed are deleted from the

sample. Second, observations with the words ‘INDX’, ‘IDX’, ‘INDEX’, and ‘BANK’ in

their reported names are eliminated to drive out index funds and banks.

I then aggregate the buy and sell orders from all accounts each month using lagged

quarter prices from CRSP. The fraction of buys and sells in each month relative to

19

that of the entire quarter is then calculated for the data period. The subsample of

institutions have different trading schedules than the aggregate market. Figure A1 panels

A and B plot the average monthly dollar fraction of quarterly buys and sells. Evidently,

more trades come in January, April, July, and October when compared to the rest

of the quarter. This effect is very apparent when comparing money managers to the

aggregated equity volume in Panel C. On average, institutional managers trade more

intensely during these periods than the other market participants. In fact, these trades

do not cancel out within the money management sector. More net trades between money

managers and other market participants occur during these months, panel D. Statistical

tests of the difference are presented in the appendix Table A4. Since these months tend

to accompany earnings releases by firms, I hypothesize that more rebalancing trades

follow individual firm’s information release.

The matched dataset of individual ancerno reported trading managers to CDA/Spectrum

mutual fund holdings is used to test this hypothesis. The description of the matching

procedure is placed in the data section. I examine the shares bought and sold for each

stock as a fraction of existing holdings by the matched managers. Table 6, panel a shows

that a majority of selling and buying of this total fraction as driven by passive comes in

during the earnings announcement date and the 10 days following. On the returns level,

this period also coincide with significant return predictability in the underlying stock,

not seen in the days before the earnings (panel b).

To examine the cumulative effect of rebalancing trades on stock prices, I simply

examine the cumulative effect of rebalancing trades between the start of the quarter

and when a majority of earnings releases end. Intra-quarterly cumulative returns, from

the first trading day of the quarter to the day before the last 10% of the S&P con-

stituents make their announcements, are regressed cross-sectionally by value-weighted

Fama Macbeth on lagged passive. The second stage coefficient averages are reported in

Table 7. The variable passive subsumes the negative predictability of the past return

20

characteristics. We observe that a majority of the total quarterly returns predictabil-

ity by passive, from table 3, comes in during this interval. The univariate regression

on passive alone, shows that one standard deviation of passive implies about 49 basis

points of return on the underlying. This effect is stronger between 2000 and 2013, and

robust to the exclusion of the ‘Momentum Crash’ in 2009. I form intra-quarterly long

short portfolios based on the ranking sorting of passive to quantify the economic mag-

nitudes of a portfolio strategy based on front running the portfolio management trades.

The long short portfolios are created by first sorting on size using NYSE breakpoints,

and then for each size quintile, and going long/short the bottom/top quintile of passive

sorted stocks. The returns of these long short portfolios are reported in table 8 with

various factor adjustments. This table indicates that the firms that tend to drive this

predictability are the firms with market caps greater than 80% of the firms in the NYSE.

The largest and supposed most liquid firms are the most affected by the portfolio ad-

justment pressures. As documented in figure 3 and table 8, the highest passive portfolio

has had zero to negative returns until the last thirds of the quarter, while the lowest

passive portfolio experienced almost 3% returns. This price pressure does not come at

an individual quarter, and is spread out across the year; see panel b of table 8.

Finally, I use the portfolio rebalancing pressure to explain the underperformance of

the standard (2-12) momentum factor (UMD) returns during the announcement season.

I create a loser minus winner (LMW) factor whose returns are based off of the decile

sorted portfolios in the previous section (bottom 10% minus the top 10%). In table 9, I

find that the UMD returns each quarter before the last 10% of the S&P500 constituents

make their earnings announcements are increased by adjusting for the passive portfo-

lio. The unadjusted intra-quarter return of UMD from Q1 1990 to Q4 2013 is -0.34%

(t=-0.46). After adjusting for the standard 3 factors, the return is increased to 0.35%

(t=0.53). After incorporating the LMW factor, the 4 factors adjusted return of UMD

is increased to 1.28% (t=2.22). This is expected as most of the underperformance by

21

UMD is caused by the large capitalization portfolios (See Appendix table A1a).

7 Conclusion

The growth of the dedicated asset management industry represents a major struc-

tural change in the financial markets. Coinciding with this change is an increase in the

cross sectional dispersion and in the seasonality of momentum. I argue that this change

is due to the asset management practices and constraints spread across the industry.

The dispersion therefore is expected in part because past returns are imprecise signals

of how much managers have to respond in rebalancing their portfolios. Because dedi-

cated asset managers are asymmetric in the rebalancing of asset positions, there is an

active pressure against high weight high past-return stocks at the rebalancing horizons.

The active rebalancing of portfolios generates a net pricing pressure against high return

large capitalization stocks from the mutual fund industry. Contrasting priors that the

institutional demand channel only circumstantially affect stock prices, I show that this

pricing pressure is significant on the largest and supposedly liquid stocks in the cross

section of equities. This mechanism also explains two puzzling facts about the dynamics

of cross sectional momentum. The first is the echo effect in Novy-Marx (2012) and the

second is the intra-quarter seasonality of momentum returns.

22

8 References

[1] Ang, Brandt and Denison, 2014, Review of the Active Management of the Norwegian

Government Pension Fund Global, Working Paper.

[2] Anton and Polk, 2013, Connected Stocks, Journal of Finance, Forthcoming.

[3] Calvet, Campell and Sodini, 2009, Fight or Flight? Portfolio Rebalancing by Indi-

vidual Investors, Quarterly Journal of Economics, 124(1), 301-348.

[4] Coval and Stafford, 2007, Asset Fire Sales (and Purchases) in Equity Markets, Jour-

nal of Financial Economics, 86, 479-512.

[5] Daniel and Moskowitz, 2014, Momentum Crashes, Unpublished Working Paper, Uni-

versity of Chicago.

[6] DeMiguel, Garlappi and Uppal, 2009, Optimal Versus Naive Diversification: How

Inefficient is the 1/N Portfolio Strategy?, Review of Financial Studies, 22(5), 1915-

1953.

[7] French, Ken, 2008, The Cost of Active Investing, The Journal of Finance, 63, 1537-

1573.

[8] Gompers and Metrick, 2001, Institutional Investors and Equity Prices, Quarterly

Journal of Economics, 116(1), 229-259.

[9] Greenwood and Thesmar, 2011, Stock Price Fragility, Journal of Financial Eco-

nomics, 102(3), 471-490.

[10] Greenwood and Vayanos, 2013, Bond Supply and Excess Bond Returns, Review of

Financial Economics, Forthcoming.

23

[11] Grinblatt, Titman and Wermer, 1995, Momentum Investment Strategies, Portfolio

Performance, and Herding: A Study of Mutual Fund Behavior, American Economic

Review, 85, 1088-1105.

[12] Hau and Rey, 2008, Global Portfolio Rebalancing Under the Microscope, Unpub-

lished Working Paper, London Business School.

[13] Jegadeesh and Titman, 1993, Returns to Buying Winners and Selling Losers: Im-

plications for Stock Market Efficiency, Journal of Finance, 48, 65-91.

[14] Koijen and Yogo, 2015, An Equilibrium Model of Institutional Demand and Asset

Prices, Unpublished Working Paper, London Business School.

[15] Lou, Dong, 2012, A Flow-Based Explanation For Return Predictability, Review of

Financial Studies, 25, 3457-3489.

[16] Puckett and Yan, 2011, The Interim Trading Skills of Institutional Investors, The

Journal of Finance, 66(2), 601-633.

[17] Shleifer, Andrei, 1958, Do Demand Curves for Stocks Slope Down?, The Journal of

Finance, 41(3), 579-590.

[18] Tobin, James, 1958, Liquidity Preference as Behavior Toward Toward Risk, Review

of Economic Studies, 25, 124-131.

[19] Tobin, James, 1969, A General Equilibrium Approach to Monetary Theory, Journal

of Money, Credit, and Banking, 1, 15-29.

[20] Vayanos and Woolley, 2012, An Institutional Theory of Momentum and Reversal,

Working Paper, London School of Economics.

24

Panel A Summary Statistics

Mean Std Min 25 P. Median 75 P. Max N

N. of Account

Per Quarter 8,550 14,069 3,649 6,748 8,550 19,966 53,510 44

N. of Trades Per

Account/Qtr 279 10,415 1 11 24 69 3839056 697807

Dollar Value of

Buy Trade 161,421 1,390,599 0.19 1,632 8,470 50,611 4,000,000,000 109,210,492

Dollar Value of

Sell Trade 168,576 1,357,989 0.08 1,494 8,344 50,560 2,406,170,000 108,250,017

Total Sum of

Quarter's Buys 305 B 71 B 191 B 238 B 311 B 350 B 488 B 44

Total Sum of

Quarter's Sells 314 B 78 B 207 B 244 B 305 B 366 B 474 B 44

Qtrs Observed

Per Account 6.97 5.23 1 4 6 8 44 100,155

Panel B Correlation Statistics

Mean Median Std Ret(1,1) Ret(1,3) Ret(2,6) 𝑝𝑎𝑠𝑠𝑖𝑣𝑒

Ret(1,1) 1.06% 0.43% 16.5% 1

Ret(1,3) 3.69% 1.66% 31% 0.52 1

Ret(2,6) 6.31% 2.50% 46% 0.03 0.49 1

𝑝𝑎𝑠𝑠𝑖𝑣𝑒 0.00% 0.00% 1.88% 0.29 0.50 0.26 1

9 Tables and Figures

Table 1. Summary Statistics on Ancerno

This table records the summary statistics of the Ancerno Database used in this study.Trades from the starting quarter and ending quarter of individual accounts are drop.Furthermore, accounts with words ‘INDEX,’ ‘INDX,’ ‘IDX’, or ‘BANK’ in either theaccount or manager names are dropped. The data cover January 2000 to December2010.

25

Equal Weighted Coefficients Value Weighted Coefficients

discreti,j,t+1 totali,j,t+1 discreti,j,t+1 totali,j,t+1

passivei,j,t -0.159 -0.224 -0.170 -0.251 -0.114 -0.155 -0.126 -0.179

(-16.82) (-15.55) (-8.77) (-10.39) (-8.25) (-8.52) (-5.83) (-6.61)

wghti,j,t

-0.124

-0.126

-0.107

-0.108

(-30.77)

(-27.43)

(-23.48)

(-22.15)

sret(1,3) i,j,t

0.110

0.125

0.067

0.075

(7.19)

(6.47)

(5.98)

(5.82)

Avg rsquared 0.028 0.076 0.035 0.080 0.027 0.078 0.034 0.081

Qtr 96 96 96 96 96 96 96 96

Table 2. Rebalancing on Portfolio and Aggregated Levels

Panel a. This panel reports Fama Macbeth regressions of discretionary changes in weight(discret) and total change in weight (total) against lagged return driven passive changein weight (passive), initial weight (wght), and 3 month returns scaled by total holdingsreturn (sret). The first stage coefficients are obtained by regressing for each portfo-lio/quarter subsample, requiring at least 20 degrees of freedom per regression. Thecoefficients are then pooled into a panel and averaged. Columns 1 through 4 computethe equal weight averages, and columns 5 through 8 compute the averages as weightedby the fraction of the fund’s total net asset value to the aggregate mutual fund net assetvalue for that quarter. The standard errors are clustered quarterly. All right hand sideregression variables are winsorized at 2.5% to 97.5% level per portfolio/quarter. Thesample is from Q1 1990 to Q4 2013.

26

Change in Prop Held by Mutual Funds at t+1

Weighted Least Squares

1990 to 2013 1990 to 1999 2000 to 2013

𝑝𝑎𝑠𝑠𝑖𝑣𝑒 𝑖,𝑡 -0.001 0.001 -0.001

(-6.37) (-2.97) (-5.87)

𝑤𝑔ℎ𝑡 𝑖,𝑡 -0.061 -0.062 -0.061

(-3.32) (-2.16) (-2.49)

𝑟𝑒𝑡(1,3)𝑖,𝑡 0.008 0.010 0.007

(7.12) (5.33) (4.81)

Qtrs 96 40 56

Panel b. This panel reports Fama Macbeth regressions of the change (difference) inproportion of stocks held (Shares in Mutual Funds/Total Shares Outstanding) betweenquarters. The right hand side regression variables are winsorized at 2.5% to 97.5%. Theleft hand side variable is winsorized at 1% and 99% level per quarter to level off extremeobservations. The first stage coefficients are obtained by weighted least squares basedoff of the stock’s market cap at the end of past June. The sample is from Q1 1990 toQ4 2013.

27

Equal Weighted Coefficients Value Weighted Coefficients

discreti,j,t+1 totali,j,t+1 discreti,j,t+1 totali,j,t+1

passive+i,j,t -0.361

-0.417

-0.271

-0.316

(-17.75)

(-13.22)

(-10.20)

(-8.12)

passive-i,j,t -0.067

-0.071

-0.014

-0.029

(-4.33)

(-2.59)

(-0.78)

(-1.02)

bench_devi,j,t -0.181

-0.197

-0.156

-0.185

(-19.16)

(-11.12)

(-12.56)

(-8.21)

res_devi,j,t

-0.147

-0.163

-0.090

-0.110

(-15.25)

(-9.06)

(-7.61)

(-5.16)

wghti,j,t -0.116 -0.119 -0.115 -0.120 -0.101 -0.087 -0.100 -0.088

(-30.61) (-26.90) (-24.54) (-22.17) (-21.98) (-20.06) (-18.96) (-18.23)

sret(1,3)i,j,t 0.001 0.000 0.001 0.000 0.001 0.000 0.001 0.000

(6.10) (3.05) (6.15) (2.59) (5.36) (1.58) (5.25) (1.22)

Avg Adj Rsq 0.082 0.094 0.088 0.096 0.083 0.093 0.087 0.095

Num Qtrs 96 96 96 96 96 96 96 96

Table 3. Rebalancing Channels

This table reports Fama Macbeth regressions of discretionary changes in weight (discret)and total change in weight (total) against lagged return driven positive return drivenchange in weight (passive+), negative return driven change (passive−), benchmark de-viation (bench dev), residual deviation (res dev), initial weight (wght), and 3 monthreturns scaled by total holdings return (sret). The first stage coefficients are obtainedby regressing for each portfolio/quarter subsample, requiring at least 20 degrees of free-dom per regression. The coefficients are then pooled into a panel and averaged. Columns1 through 4 compute the equal weight averages, and columns 5 through 8 compute theaverages as weighted by the fraction of the fund’s total net asset value to the aggregatemutual fund net asset value for that quarter. The standard errors are clustered quar-terly. All right hand side regression variables are winsorized at 2.5% to 97.5% level perportfolio/quarter. The sample is from Q1 1990 to Q4 2013.

28

Forw

ard

t+

1 Q

uart

erly

Ret

urn

s

1990 t

o 2

013

2000 to

2013

1990 t

o 2

013

2000 to

2013

𝑝𝑎𝑠𝑠𝑖𝑣𝑒

-0

.063

-0.5

27

-0.5

00

-0.2

73

-0.7

59

-0.6

35

(-0.3

1)

(-2.5

2)

(-2.7

9)

(-0.9

6)

(-2.8

4)

(-2.5

1)

𝑝𝑎𝑠𝑠𝑖𝑣𝑒+

-0.1

05

-0.4

14

-0.4

18

-0.4

15

-0.9

22

-0.6

30

(-0.4

9)

(-1.9

9)

(-2.3

7)

(-1.4

6)

(-3.2

5)

(-2.4

6)

Ret

(1,3

)

0.9

96

0.6

76

1.0

39

0.6

31

0.6

94

0.5

17

1.1

56

0.5

51

(1.4

2)

(1.3

1)

(1

.16)

(0.8

7)

(1

.17)

(1.1

7)

(1

.33)

(0.8

3)

Log(B

M)

-0

.002

0.0

00

-0.0

02

0.0

00

(-

0.5

6)

(-0.0

1)

(-0.6

0)

(-0.0

2)

Log(M

E)

-0

.003

-0.0

06

-0.0

02

-0.0

05

(-

1.9

7)

(-3.7

2)

(-1.4

1)

(-3.0

7)

Inst

Ow

n

-0.0

01

0.0

04

0.0

00

0.0

06

(-

0.1

2)

(0.3

7)

(0.0

6)

(0.5

3)

Idio

Vol

-0

.599

-0.8

87

-0.4

74

-0.7

11

(-

1.5

6)

(-1.7

4)

(-1.2

4)

(-1.3

9)

Turn

over

0.0

04

0.0

01

0.0

04

0.0

01

(2

.13)

(0.5

7)

(2.2

9)

(0.7

0)

Q

trs

96

96

96

56

56

56

96

96

96

56

56

56

Tab

le4.

Qu

arte

rly

Ret

urn

For

ecas

ted

bypassive

Th

ista

ble

reco

rds

the

valu

ew

eigh

ted

Fam

aM

acb

eth

regr

essi

ons

ofto

tal

qu

arte

rly

retu

rns

onpassive,passive+

an

dva

riou

sco

ntr

ols

incl

ud

ing

pas

t3

mon

thre

turn

s,lo

gb

ook

tom

arke

t,lo

gm

arke

teq

uit

y,in

stit

uti

onal

own

ersh

ip,

idio

syn

crati

cvo

lati

lity

,an

d12

mon

thtu

rnov

er.

Th

em

arke

tca

pit

aliz

atio

nis

bas

edgi

ven

atth

een

dof

last

Ju

ne.passive

isst

an

dard

ized

by

its

un

con

dit

ion

alst

and

ard

dev

iati

on.

All

righ

th

and

sid

ere

gres

sion

vari

able

sar

ew

inso

rize

dat

2.5%

and

97.5

%ea

chqu

arte

r.T

he

sam

ple

per

iod

isfr

omQ

119

90to

Q4

2013

and

Q1

2000

toQ

420

13.

29

Value Weight Fama Macbeth With Next Quarter’s Return

1990 to 2013

No 2009

passive

-0.321

-0.367

(-2.36)

(-2.69)

passive

-0.367

-0.411

(-2.59)

(-3.00)

Ret(1,1) -0.287 0.044 0.047 -0.256 0.112 0.111

(-0.97) (0.14) (0.15) (-0.82) (0.34) (0.32)

Ret(2,6) 0.190 0.481 0.544 0.492 0.823 0.879

(0.51) (1.11) (1.31) (1.37) (2.01) (2.24)

Ret(7,12) 0.949 0.924 0.959 1.024 1.010 1.045

(2.38) (2.28) (2.39) (2.54) (2.46) (2.58)

Log(BM) -0.086 -0.033 -0.025 0.092 0.139 0.153

(-0.19) (-0.08) (-0.06) (0.24) (0.38) (0.42)

Log(ME) -0.322 -0.328 -0.264 -0.322 -0.321 -0.254

(-1.65) (-1.68) (-1.37) (-1.58) (-1.59) (-1.27)

InstHolding -0.371 -0.335 -0.247 -0.502 -0.443 -0.362

(-0.54) (-0.49) (-0.36) (-0.65) (-0.59) (-0.47)

Idiovol -0.786 -0.831 -0.722 -0.817 -0.855 -0.738

(-2.51) (-2.61) (-2.29) (-2.39) (-2.50) (-2.19)

Turnover12 0.294 0.306 0.311 0.254 0.269 0.275

(2.16) (2.33) (2.40) (1.77) (1.92) (2.00)

Qtrs 96 96 96 92 92 92

Table 5. The Echo Effect

This table examines the relationship between rebalancing and the horizons of past per-formances used to predict future returns. The columns records Fama Macbeth regressioncoefficients of passive and various different controls against foward one quarter returns.The variables passive and passive+ increase the power of past 2 to 6 months returnsin positively predicting future returns. If avoiding the momentum crash period of 2009,2 to 6 month momentum becomes almost as strong as 7 to 12 month momentum on avalue weighted basis. The table is consistent with the results in Novy-Marx 2012. Italso suggests that portfolio rebalancing and the 2009 momentum crash are the two mainfactors that contribute underperformance of 2 to 6 month momentum in this sampleperiod.

30

Trading of Total Shares Held by Matched

Ancerno Funds around Earnings

Announcement Date at t+1

All (0,10) All (0,10)

passive -0.017 -0.013

(-1.62) (-2.16)

passive

-0.018 -0.017

(-2.08) (-3.13)

Ret(1,3) (0.07) 0.056 (0.07) 0.061

(3.60) (4.19) (3.67) (5.12)

SUE 0.096 0.142 0.108 0.133

(0.49) (1.19) (0.55) (1.11)

Log(BM) 0.042 0.030 0.041 0.028

(4.85) (5.31) (4.82) (5.08)

Log(ME) -0.159 -0.160 -0.158 -0.159

(-21.18) (-22.13) (-21.65) (-22.45)

InstOwn -0.271 -0.277 -0.277 -0.279

(-7.80) (-14.28) (-7.98) (-14.42)

Idiovol 0.024 0.019 0.027 0.021

(2.82) (2.83) (3.22) (3.19)

Turnover -0.012 -0.012 -0.012 -0.011

(-3.41) (-4.08) (-3.03) (-3.64)

Qtrs 44 44 44 44

Table 6. Earnings Season Trading

Panel a. This panel runs value-weighted Fama Macbeth regression on trading by passiveand passive+ along with various different controlling predictors. The left hand sidevariable is the fraction of held shares bought and sold over the whole quarter and overthe 11 days including and after the earnings announcement by the matched ancernoasset managers; the variable is caped at -100% to 100%. It is regressed against passiveand passive+ along with various controls. The sample period is from 2000 to 2010. Allthe right hand side variables are winsorized at 2.5% and 97.5% levels. The regressionindicates that the majority of rebalancing by these funds occurs during and immediatelyafter the earnings announcements of the firms.

31

Returns Earnings Announcement Date

Cret(-11,-1) Cret(0,10) Cret(-11,-1) Cret(0,10)

passive 0.036 0.001 -0.322 -0.227

(0.49) (0.01) (-4.95) (-2.28)

passive

0.075 0.046 -0.349 -0.215

(1.04) (0.66) (-5.66) (-2.61)

Ret(1,3) 0.000

-0.003

-0.001

-0.004

(-0.18)

(-1.63)

(-0.57)

(-1.98)

Log(BM) 0.001

-0.001

0.001

-0.001

(0.87)

(-0.85)

(0.99)

(-1.12)

Log(ME) 0.000

0.000

0.000

0.000

(1.12)

(-0.47)

(1.00)

(0.20)

Idiovol 0.001

-0.004

0.060

-0.321

(0.57)

(-2.88)

(0.48)

(-2.48)

InstOwn -0.002

0.009

-0.002

0.010

(-0.68)

(2.31)

(-0.69)

(2.59)

Turnover 0.003

0.000

0.003

0.001

(3.67)

(0.50)

(3.79)

(0.65)

Qtrs 96 96 96 96 96 96 96 96

Panel b. This panel records Fama Macbeth regressions on cumulative returns aroundthe earnings announcement dates. passive and passive+ are standardized by theirunconditional standard deviation. Much of the forecasting power comes directly at theannouncement date and the several trading days after that. All right hand side regressionvariables are winsorized at 2.5% and 97.5% each quarter. The sample period is from Q11990 to Q4 2013.

32

Intra Quarter Return at t+1 (1990 to 2013)

passive -0.489 -0.554 -0.612

(-3.23) (-3.20) (-4.23)

passive -0.456 -0.335 -0.480

(-3.00) (-2.18) (-3.67)

Ret(1,3) 0.019 0.086 -0.467 -0.271

(0.04) (0.21) (-1.02) (-0.75)

Log(BM) -0.001 -0.001

(-0.38) (-0.42)

Log(ME) 0.000 0.001

(0.41) (1.15)

InstOwn 0.003 0.004

(0.44) (0.67)

IdioVol -0.384 -0.265

(-1.27) (-0.86)

Turnover 0.005 0.005

(3.03) (3.18)

Qtrs 96 96 96 96 96 96

Table 7. Earnings Season Return Predictbility

This table regresses the cumulative returns of stocks held between the first day of thequarter and before the last 10% of the S&P 500 stocks make their earnings announce-ment. The control variables are standard and same as in the previous sections. passiveand passive+ are standardized by their unconditional standard deviation. All the righthand side variables are winsorized at 2.5% and 97.5% levels.

33

Returns on portfolios sorted by size and passive

LS (D - U)

Raw 3 Factors Adjusted 4 Factors Adjusted

1990-2013 2000-2013 1990-2013 2000-2013 1990-2013 2000-2013

Size 1 0.001 0.005 -0.004 0.002 -0.003 -0.002

(0.09) (0.48) (-0.67) (0.26) (-0.45) (-0.19)

Size 2 0.014 0.021 0.008 0.017 0.010 0.012

(1.70) (1.55) (1.02) (1.48) (1.50) (1.27)

Size 3 0.017 0.026 0.008 0.022 0.011 0.015

(1.55) (1.46) (0.76) (1.40) (1.33) (1.18)

Size 4 0.021 0.027 0.011 0.022 0.014 0.015

(1.84) (1.49) (1.08) (1.43) (1.72) (1.22)

Size 5 0.028 0.039 0.024 0.036 0.026 0.033

(3.80) (3.53) (3.31) (3.62) (4.20) (3.61)

Raw Returns on size and passive Split by Quarters

LS (D - U)

Q1 Q2 Q3 Q4

1990-

2013

2000-

2013

1990-

2013

2000-

2013

1990-

2013

2000-

2013

1990-

2013

2000-

2013

Size 1 0.008 -0.001 0.008 0.024 -0.011 -0.007 -0.003 0.004

(0.48) (-0.05) (0.74) (1.45) (-1.33) (-0.59) (-0.17) (0.16)

Size 2 0.012 0.004 0.018 0.034 0.004 0.012 0.024 0.033

(0.73) (0.16) (1.15) (1.35) (0.40) (0.80) (1.00) (0.86)

Size 3 -0.012 -0.018 0.043 0.077 0.002 0.004 0.035 0.043

(-0.82) (-0.82) (1.54) (1.67) (0.17) (0.19) (1.33) (0.96)

Size 4 -0.008 -0.022 0.041 0.062 0.013 0.020 0.038 0.047

(-0.52) (-0.89) (1.56) (1.39) (0.90) (1.01) (1.27) (1.01)

Size 5 0.015 0.019 0.040 0.066 0.029 0.040 0.030 0.032

(1.18) (1.16) (2.03) (2.16) (2.58) (2.42) (1.92) (1.40)

Table 8. Earnings Season Portfolio Returns Sorted on Size and passive

Panel a. This panel records long short raw and adjusted returns from portfolios sortedon size and passive. The Long Short portfolio is calculated using the lowest decile (D)minus the highest decile (U) of passive. Market cap values and the size breakpoints arefrom the end of last June. The size breakpoints follow the Fama and French and usespercentile cutoff values from the NYSE stock exchange.

Panel b. This panel records long short raw from portfolios sorted on size and passive(the average past quarter return driven weight change cross all mutual funds for eachstock) separated by the 4 quarters. The Long Short portfolio is calculated using thelowest decile (D) minus the highest decile (U) of passive. Market cap values and thesize breakpoints are from the end of last June. The size breakpoints follow the Famaand French and uses percentile cutoff values from the NYSE stock exchange.

34

Intra Quarter UMD Return at t

Intercept -0.003 0.003 0.015

(-0.46) (0.53) (2.54)

,i tM ktrf -0.527 -0.346

(-5.25) (-3.81)

,i tSM B 0.013 0.054

(0.09) (0.42)

,i tHML -0.291 -0.204

(-2.09) (-1.71)

LMWi ,t

-0.479

(-5.98)

Qtrs 96 96 96

Table 9. Momentum Returns through the Earnings Season

This table relates the intra-quarter returns of (2,12) Momentum factorsto portfolio re-balancing pressure from 1990 to 2013. The intra-quarter period is from the beginningto before the last 10% of the S&P 500 constituents make their quarterly earnings an-nouncements. The losers minus winners (LMW) portfolio is constructed by holdingbottom decile and shorting the top decile of passive sorted stocks from the top quintilein NYSE breakpoint stocks.

35

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

-3 -2 -1 1 2 3

Coefficients of Piece-wise Passive

Discretionary Change in Weight Total Change in Weight

Figure 1. Rebalancing Coefficients for Piece-Wise Separation of passive

This plot contains the averaged coefficients on variables generated on passive as regressedagainst total change in weight and discretionary change in weight. The variable passive,for each observation in each portfolio quarter set, is separated into 6 pieces based onhow far the value is away from 0 as measured by its standard deviation in that portfolioquarter set. For example, -3 is defined as passive · 1(passive <= −2 · std(passive)),-2 is defined as passive · 1(−2 · std(passive) < passive <= −std(passive)), and so on.These variables by definition adds up to passive. We observe a clear non-linear patternin rebalancing intensity- most of the rebalancing predictability is on the largest winningportfolios.

36

-0.006

-0.004

-0.002

0

0.002

0 1 2 3 4 5 6 7 8

Cu

mu

lati

ve R

etu

rn P

er

1 S

td o

f P

assi

ve

Months After Starting Period

Figure 2. Return Predictability of passive

Cumulative coefficients from the Fama Macbeth regression of forward returns for onestandard deviation of the passive variable. The sample period is from 1990 to 2013.The controls for the regression are lagged 3 month returns, book to market ratio, laggedmarket capitalization, idiosyncratic volatility, percentage institutional ownership, andturnover.

37

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61

Cu

mu

lati

ve R

etu

rns

Trading Days Into the Quarter

Passive Sorted Portfolios from 1990 to 2013 (Top Quintile NYSE)

Bottom Decile

Top Decile

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61

Cu

mu

lati

ve R

etu

rns

Trading Days Into the Quarter

Passive Sorted Portfolios from 2000 to 2013 (Top Quintile NYSE)

Bottom Decile

Top Decile

Figure 3. Return Patterns for the Long Short passive sorted portfolios.

This figure records the portfolio returns of the top decile and the bottom decile ofpassive sorted portfolios for the higest size quintile size portfolios (i.e. stocks whosemarket caps are greater than 80% of the firms in the NYSE). The top panel recordsthe returns from 1990 to 2013, whereas the bottom panel records from 2000 to 2013. Avisible gap starts early in the quarter and closes into the end of the quarter. The gap isthe largest around the middle of each quarter.

38

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.07

0.09

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58

Cu

mu

lati

ve R

etu

rn

Trading Days Into the Quarter

Intra Quarter LS Momentum Returns Q1 1990 to Q4 1999

Size 1 LS

Size 3 LS

Size 5 LS

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58

Cu

mu

lati

ve R

etu

rn

Trading Days Into the Quarter

Intra Quarter LS Momentum Returns Q1 2000 to Q1 2014

Size 1 LS

Size 3 LS

Size 5 LS

Figure 4. Return Patterns for Momentum and Size Sorted Portfolios.

This figure records the return patterns for the momentum and size sorted portfolios fromQ1 1990 to Q4 1999 (top) and Q1 2000 to Q4 2013 (bottom). Size 1 is the smallest cap,while size 5 is the largest quintile of NYSE breakpoint equities. The LS portfolio foreach size quintile is constructed using the edge momentum quintiles. All the data usedto construct the figures come from Ken French’s website.

39

Table A1. Momentum and Reversal Seasonality

Panel a. Momentum portfolio returns (25 portfolios) sorted by size. Each long short portfolio is

calculated using the top quintile (U) return minus the bottom quintile (D) return.

Momentum (2 to 12 Month Returns)

LS (U - D)

1st of Quarter Ignoring Jan Rest of Quarter

1990-2013 2000-2013 1990-2013 2000-2013 1990-2013 2000-2013

Size 1 -0.008 -0.015 0.006 -0.004 0.016 0.009

(-0.90) (-1.14) (0.75) (-0.31) (3.80) (1.34)

Size 2 -0.003 -0.014 0.000 -0.013 0.012 0.007

(-0.43) (-1.07) (-0.01) (-0.86) (2.85) (1.19)

Size 3 -0.006 -0.016 -0.004 -0.015 0.011 0.010

(-0.73) (-1.38) (-0.49) (-1.14) (2.60) (1.56)

Size 4 -0.008 -0.017 -0.005 -0.015 0.013 0.014

(-0.96) (-1.40) (-0.52) (-1.06) (2.74) (1.87)

Size 5 -0.011 -0.027 -0.005 -0.019 0.013 0.018

(-1.39) (-2.47) (-0.59) (-1.67) (2.98) (2.78)

Panel b. Short-Term Reversal portfolio returns (25 portfolios) sorted by size. Each long short portfolio

is calculated using the bottom quintile (U) return minus the top quintile (D) return.

Reversal (1 Month Returns)

LS (D - U)

1st of Quarter Ignoring Jan Rest of Quarter

1990-2013 2000-2013 1990-2013 2000-2013 1990-2013 2000-2013

Size 1 0.022 0.024 0.008 0.011 -0.005 -0.005

(3.27) (2.33) (1.33) (1.24) (-1.56) (-0.97)

Size 2 0.015 0.020 0.010 0.014 -0.001 -0.003

(2.73) (2.31) (1.56) (1.51) (-0.44) (-0.60)

Size 3 0.016 0.018 0.012 0.014 -0.003 -0.004

(3.01) (2.26) (1.95) (1.52) (-0.82) (-0.81)

Size 4 0.008 0.015 0.003 0.007 -0.003 -0.006

(1.43) (1.78) (0.47) (0.74) (-0.83) (-1.07)

Size 5 0.013 0.023 0.009 0.019 -0.004 -0.005

(2.21) (2.65) (1.33) (1.83) (-1.21) (-0.88)

10 Appendix

40

Table A2. Momentum and Reversal Seasonality (Continued)

Panel a. Momentum portfolio returns (25 portfolios) sorted by size at other holding periods. Each long

short portfolio is calculated using the top quintile (U) return minus the bottom quintile (D) return.

Momentum (2 to 12 Month Returns)

LS (U - D)

1st of Quarter Ignoring Jan Rest of Quarter

1970-1990 1950-1970 1970-1990 1950-1970 1970-1990 1950-1970

Size 1 0.004 0.000 0.023 0.016 0.023 0.015

(0.57) (-0.06) (4.54) (3.42) (7.20) (5.50)

Size 2 0.012 0.008 0.022 0.019 0.016 0.012

(2.17) (1.64) (3.98) (4.34) (5.24) (4.75)

Size 3 0.013 0.011 0.019 0.019 0.013 0.012

(2.34) (2.55) (3.07) (3.92) (3.84) (4.60)

Size 4 0.006 0.008 0.014 0.014 0.013 0.013

(0.98) (1.67) (2.09) (2.69) (3.72) (5.25)

Size 5 0.006 0.006 0.009 0.012 0.008 0.011

(0.93) (1.38) (1.30) (2.26) (1.84) (4.25)

Panel b. Short-term Reversal portfolio returns (25 portfolios) sorted by size at other holding periods.

Each long short portfolio is calculated using the top quintile (U) return minus the bottom quintile (D)

return.

Reversal (1 Month Returns)

LS (U - D)

1st of Quarter Ignoring Jan Rest of Quarter

1970-1990 1950-1970 1970-1990 1950-1970 1970-1990 1950-1970

Size 1 0.025 0.022 0.007 0.005 0.004 0.009

(4.21) (4.76) (1.52) (1.41) (1.71) (4.62)

Size 2 0.018 0.012 0.010 0.002 0.008 0.006

(3.75) (3.58) (2.11) (0.68) (3.12) (3.00)

Size 3 0.014 0.010 0.011 0.005 0.009 0.008

(3.37) (3.56) (2.34) (1.43) (3.82) (3.97)

Size 4 0.011 0.009 0.008 0.004 0.010 0.009

(2.59) (3.12) (1.78) (1.13) (3.79) (4.98)

Size 5 -0.003 0.004 -0.005 0.000 0.005 0.006

(-0.67) (1.09) (-1.03) (0.12) (1.38) (2.63)

41

Equal Weighted Coefficients Value Weighted Coefficients

𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑡+1,𝑖,𝑗 𝑡𝑜𝑡𝑎𝑙𝑡+1,𝑖,𝑗 𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑡+1,𝑖,𝑗 𝑡𝑜𝑡𝑎𝑙𝑡+1,𝑖,𝑗

𝑝𝑎𝑠𝑠𝑖𝑣𝑒𝑡,𝑖,𝑗 -0.131 -0.142 -0.105 -0.121

(-16.33) (-8.65) (-12.15) (-6.88)

𝑝𝑎𝑠𝑠𝑖𝑣𝑒𝑡−1,𝑖,𝑗 -0.021 -0.005 -0.046 -0.019

(-1.40) (-0.22) (-3.02) (-0.75)

𝑤𝑔ℎ𝑡𝑡,𝑖,𝑗 -0.088 -0.108 -0.058 -0.072

(-45.40) (-5.49) (-33.91) (-5.58)

𝑠𝑟𝑒𝑡𝑡,𝑖,𝑗 0.116 0.052 0.120 0.064

(5.43) (4.76) (4.65) (5.24)

Avg Adj Rsq 0.087 0.098 0.091 0.108

Port/Qtr 133803 133803 133803 133803

Num Qtrs 96 96 96 96

Table A3. Portfolio Trading With More Lags

This additional panel follows table 2, but includes additional control, passivet−1,i,j asfurther lagged predictor of rebalancing trades. The first stage coefficients are obtained byregressing for each portfolio/quarter subsample, requiring at least 20 degrees of freedomper regression. The coefficients are then pooled into a panel and averaged. Most of theforecasting power of passive on changes in weight is from the one quarter horizon. Thepower of the additional lag seems marginal. The right hand side regression variables arewinsorized at 2.5% to 97.5% level per portfolio/quarter. The sample is from Q1 1990 toQ4 2013.

42

S&P 500 Trade Intensity by Money Managers

2000 to 2010 2000 to 2005 2006 to 2010

Sell Buy Sell Buy Sell Buy

Average Start of Quarter

Relative Adjusted Volume 0.359 0.360 0.364 0.362 0.354 0.358

Average Rest of Quarter Relative

Adjusted Volume 0.321 0.320 0.318 0.319 0.323 0.321

Diff 0.038 0.040 0.046 0.043 0.031 0.037

(6.48) (7.02) (5.92) (6.02) (3.24) (3.96)

Number of Start of Quarter

Months 44 44 24 24 20 20

Number of Rest of Quarter

Months 88 88 48 48 40 40

Table A4. Monthly Trading by Aggregate Asset Managers

Panel a. This panel presents the fraction of each quarter’s buy and sells (share tradedmultiplied by last quarter prices) in the months at the start of the quarter versus themonths in the rest of the quarter. The average January, April, July, and October relativetrades are reported in the top row, while the rest of the quarter months’ relative tradesare reported in the second row. The pooled t-score for the difference in fractions isreported.

43

Fraction Buy/Sell versus Aggregate S&P Volume in

Start of Qtr

2000 to 2010 2000 to 2005 2006 to 2010

Sell Buy Sell Buy Sell Buy

Relative Money Manager

Sells/Buys in 0.359 0.360 0.364 0.362 0.354 0.358

Relative S&P Volume 0.348 0.348 0.351 0.351 0.344 0.344

Diff 0.011 0.013 0.013 0.011 0.010 0.014

(3.59) (4.59) (3.96) (3.64) (1.65) (2.99)

Number of Start of Quarter

Months 44 44 24 24 20 20

Panel b. This panel compares the relative trade fractions of beginning month of eachquarter in the money manager trades to the relative volume of the S&P aggregate. Thepooled t-score for the difference in fractions is reported.

44

0.27

0.32

0.37

1 2 3 4 5 6 7 8 9 10 11 12

(A) Buys SP500

0.27

0.32

0.37

1 2 3 4 5 6 7 8 9 10 11 12

(B) Sells SP500

0.27

0.32

0.37

1 2 3 4 5 6 7 8 9 10 11 12

(C) SP500 Volume

0.27

0.32

0.37

1 2 3 4 5 6 7 8 9 10 11 12

(D) Absolute Net Trades of SP500

Figure A1. Monthly Seasonal Trading Pattern of Institutional Managers.

This figure records the seasonal pattern of Institutional Managers trades. Panel A plotsthe relative fraction of each month over each quarter’s total buys from the Ancernodatabase. Panel B plot the relative fraction of each month over each quarter’s totalsells. Panel C plots the same account from the aggregate S&P 500 volume. Panel Dplots the fraction of each month’s net un-cancelled buys and sells over quarter.

45