FinancialInstitutionsCenter

Why Are Mutual Fund Flow andMarket Returns Related? Evidencefrom High-Frequency Data

byRoger M. EdelenJerold B. Warner

99-01

THE WHARTON FINANCIAL INSTITUTIONS CENTER

The Wharton Financial Institutions Center provides a multi-disciplinary research approach tothe problems and opportunities facing the financial services industry in its search forcompetitive excellence. The Center's research focuses on the issues related to managing riskat the firm level as well as ways to improve productivity and performance.

The Center fosters the development of a community of faculty, visiting scholars and Ph.D.candidates whose research interests complement and support the mission of the Center. TheCenter works closely with industry executives and practitioners to ensure that its research isinformed by the operating realities and competitive demands facing industry participants asthey pursue competitive excellence.

Copies of the working papers summarized here are available from the Center. If you wouldlike to learn more about the Center or become a member of our research community, pleaselet us know of your interest.

Anthony M. SantomeroDirector

The Working Paper Series is made possible by a generousgrant from the Alfred P. Sloan Foundation

Roger M. Edelen is at The Wharton School, University of Pennsylvania,1

Philadelphia, PA 19104, edelen@wharton.upenn.edu

Jerold B. Warner is at The William E. Simon Graduate School of Business Administration,University of Rochester, Rochester, NY 14627, warner@ssb.rochester.edu

We have received helpful comments from Mike Barclay, Craig MacKinlay, David Musto,Bill Schwert, Jay Shanken, Rob Stambaugh, Nick Souleles, and workshop participants atRochester and Wharton. We gratefully acknowledge financial support from the WhartonFinancial Institutions Center, and thank Don Keim, Tony Santomero, and Carl Wittnebertfor assistance. We also appreciate the excellent research assistance of Peter Wysocki.

Why Are Mutual Fund Flow and Market Returns Related?Evidence from High-Frequency Data 1

November 1998

Abstract: We study the relation between market returns and unexpected aggregate flow intoU.S. equity funds, using semi-weekly and daily flow data. The reaction of flow and return --whether it be one reacting to the other, or both reacting to a third factor -- is fast and strong.The flow-return relation is mainly concurrent, but flow also follows returns with a one-day lag.The lagged response of flow indicates either a common response of both returns and flow tonew information, or positive feedback trading. Additional tests suggest that the concurrentrelation reflects flow driving returns.

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1. Introduction and summary

This paper examines the relation between stock market returns and aggregate flow

into U.S. equity mutual funds, using semi-weekly and daily flow data for a large sample

of funds. Previous research on this relation has used monthly flow data (Warther (1995,

1998)). The major finding using monthly data is a strong positive concurrent relation

between stock market returns and unexpected aggregate cash inflow into equity mutual

funds.

Several economic hypotheses link market returns and investors’ asset allocation

decisions. Flow into mutual funds could drive stock returns, for example, if it conveys

information about changes in cash flow expectations or the market risk premium, or if

flow causes temporary price pressure (Warther (1998)). The direction of causality could

be the reverse, however, if fund investors chase returns and follow positive feedback

trading strategies (DeLong, Shleifer, Summers, and Waldmann (1990)). Finally, there

could be no causal relation between flow and return, but a common response of both flow

and returns to new information (Brennan and Cao (1996)) could produce the observed

correlation.

Each of these hypotheses is consistent with a concurrent association between flow

and returns at a monthly frequency. Since the hypotheses are not mutually exclusive, all

could act jointly and cause the monthly correlation. High-frequency data potentially yield

more powerful tests because these hypotheses make different predictions about the lead

and lag relation of flow and returns within the month (Warther (1995, 1998), Froot,

O’Connell and Seasholes (1998), Goetzmann and Massa (1998)). Whether the monthly

concurrent relation in fact breaks down at semi-weekly or daily frequency is an

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unresolved empirical issue. Even if the high-frequency relation is concurrent, we argue

that this can still help distinguish the various hypotheses.

Our tests confirm the usefulness of a high-frequency analysis. We show that flow

responds to returns, or the information driving returns. We also show that returns

respond to flow.

Our main empirical finding is that the reaction of flow and return -- whether it be

one reacting to the other, or both reacting to a third factor -- is fast and strong. The high

frequency flow-return relation is mainly concurrent, with flow also following returns

almost exclusively at a one-day lag. The one day lag of flow relative to returns supports

the hypothesis of a joint response to information, with an immediate return response and

a flow response that is completed by the following day. The lagged relation also supports

the hypothesis that flow responds to returns with positive feedback trading. Both of these

explanations require flow to respond to events surprisingly quickly. These hypotheses

cannot easily explain the concurrent daily relation, however. They require an even more

rapid (i.e., intraday) response of flow, but none is detected by our tests. For example, a

day’s (close to close) flow is unrelated to returns from the previous close to the open.

The concurrent relation is consistent with the hypothesis that flow drives returns.

Tests using intraday return data support this interpretation: returns late in the day predict

daily flow far better than those early in the day. For example, there is a strong correlation

between a day’s flow and the return in the final two hours of trading, but there is no

correlation between a day’s flow and the return in the first hour of trading. This pattern is

predicted if flow drives returns, but seems inconsistent with flow responding to

information or to returns.

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In other tests of the hypothesis that flow drives returns we do not find supporting

evidence. If flow influences returns, then this influence could carry over to the next day,

because a day’s flow is not generally known until the following day. Purchase and

redemption requests are processed by the fund’s transfer agent; this processing only

begins after the market closes and the results are not reported back to the fund until the

following morning. We find no correlation between the day’s flow and the next day’s

return, or the close to open component of the next-day return. Further, unexpected flows

are not associated with subsequent market price reversals, as would be predicted if flows

exert temporary price pressure. We argue that this failure to find any association between

flow and the next-day return could reflect the low power of these tests.

The various findings are not sensitive to our test procedures. We account for turn

of the month effects in both flow and index returns. We address timing and accuracy

issues inherent in using high-frequency flow data. Moreover, our results are unchanged

with alternative estimation techniques, such as vector autoregression, non-linear, or

system-of-equations procedures.

Section 2 discusses the sources and properties of our flow data; further details of

mutual fund reporting procedures are given in the Appendix. Section 3 presents the

paper’s main results using semi-weekly data. Section 4 conducts further tests using daily

flow data, coupled with both daily and overnight return data. Section 5 provides a more

detailed analysis using intraday return data. Section 6 discusses the interpretation of our

results. Section 7 gives the conclusions.

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2. Aggregate mutual fund flow

2.1 Data sources

Most of the paper’s data on fund flow is from Mutual Fund Trim Tabs (MFTT),

published by Trim Tabs Financial Services of Santa Rosa, California. Twice per week,

usually Tuesday and Friday, MFTT reports aggregate net flow (inflow minus outflow) for

a sample of approximately 500 U.S. equity funds. The sample period is from April 11,

1994 through July 27, 1998, and there are 446 half-week observations on aggregate net

flow ( henceforth, “flow” ).

Coverage. The MFTT sample contains 16.5% (by number of funds) and 20% (by

net assets) of all U.S. equity mutual fund assets covered by the Investment Company

Institute (ICI). The sample includes over 90 fund families. From its sample’s flow and

the historic relation with ICI flow, MFTT also provides subscribers with an estimate of

aggregate ICI flow, but we only use the actual MFTT flow. Since (at the monthly level)

the correlation between MFTT flow and ICI flow over the sample period is .72, MFTT

flow contains significant information about overall fund activity.

The MFTT sample has been roughly constant over the sample period, although a

few changes have taken place. For example, in 1997 the Fidelity family of funds was

added. Later, our tests address asset base changes by scaling a half-week’s flow by the

beginning of period asset base.

Timeliness. MFTT is quite timely. A feature emphasized by Trim Tabs is that the

sample includes only those funds which reliably provide total assets based on daily

updates.1 The sequence of events surrounding MFTT reports can be summarized as

1 According to the Trim Tabs website, this determination of reliability is made “after much digging andquestioning”.

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follows. Trim Tabs receives its data electronically (by fax or e-mail) from each fund’s

customer service or public relations department on the morning of the report date, and

then aggregates the data and sends out MFTT to subscribers (usually electronically) in

the afternoon. The flow reported by MFTT is for flow from 4 P.M. (Eastern time) on the

day before the previous report date to 4 P.M. on the day before the report date. Thus,

flow reported on Tuesday is for the immediately preceding Friday-Monday half-week

(i.e., Thursday 4 P.M. through Monday 4 P.M.), and flow reported on Friday is for the

immediately preceding Tuesday-Thursday half-week (i.e., Monday 4 P.M. through

Thursday 4 P.M.).

Since early 1998, Trim Tabs has also reported flow on a daily basis (Daily Liquidity

Trim Tabs/Heads Up Alert). Later in the paper we analyze these data as well. Although

the funds sampled and sequence of events surrounding a report does not change with

daily flow, at such high frequencies the timing and accuracy of the reported flow

becomes even more critical. For example, there are issues of settlement, check-clearing,

and transfer agent record-keeping. In the Appendix, we discuss further details of mutual

fund accounting and reporting conventions and Trim Tabs procedures; our general

conclusion is that these considerations do not change the paper’s inferences.

2.2 Properties of semi-weekly flow

General characteristics. Table 1 and Figure 1 describe the flow data. Dollar flow

for each half-week is divided by the number of trading days, and expressed as a

percentage of the asset base at the beginning of the half-week; alternative scaling

procedures had no effect on the paper’s results.

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Scaled per day flow over the four-year sample period is on average positive. From

Panel A of Table 1, the mean daily flow for Friday-Monday half weeks is .0346%,

compared to .0289% for Tuesday-Thursday half-weeks. The difference is not statistically

significant. This daily flow implies an annual growth rate in assets of about 8% per year.

In addition to positive flow, market returns over this period exceeded .08% per day

(20%/year), and the MFTT asset base increased from $145 to $493 billion. From Figure

1, flow varies gradually over time, and there appear to be calendar time effects. For

example, the first half of 1996 displays consistently higher than average flow.

Within-month effects. From Panel B of Table 1, flow at the turn-of-the month is

higher than flow during the month. Specifically, flow for half-weeks at the turn of the

month (i.e., the first two and the last half-week) averages .039%, compared to .027% for

midmonth (i.e., all other half-weeks) flow. The t-statistic for the difference is 3.1. These

within month effects could reflect different growth patterns for different types of mutual

fund accounts, for example if retirement account (e.g., 401(k)) flow has been higher than

other types, and is concentrated around month end.

Autocorrelations. Panel C shows the time-series properties of flow. Although flow

is not highly predictable, there is information in past flow that is relevant for future flow.

There is statistically significant negative autocorrelation at lag one, but significant

positive autocorrelation at lags three, five, six, eight, ten, and eleven. None of the

autocorrelations exceed .2, however. The largest autocorrelations are at lags three and

eight.

The negative autocorrelation at lag one increases our confidence that the Trim Tabs

flows are timely. There is a common component to individual fund flows (Edelen

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(1998)). If MFTT reported flow were one or more days out of date for some funds,

positive autocorrelation at lag one would occur; why the autocorrelation coefficient is

negative is unclear, however. The positive autocorrelation at lag eight is not surprising

because flow is higher at the turn of the month, and there are approximately eight half-

weeks per month. There is no serial dependence from one turn of the month to another,

however. Although not reported in Panel C, the correlation between flows at the turn of

the month and at the previous turn of the month is positive but not significantly different

from zero. The correlation between mid-month and lagged midmonth flows is .55, and

between turn-of-the month and lagged midmonth flows is .48.

Returns. Table 1 also describes the semi-weekly returns. We use NYSE Index

returns because they are available throughout the sample period. From Panel B, turn of

the month returns over the sample period are statistically significantly higher than

midmonth returns. Moreover, from Panel C there is measurable autocorrelation in NYSE

Index returns over this time period. The autocorrelation at lag two is -.18 and statistically

significant. Similar autocorrelation is also observed for the CRSP Value-Weighted Index

(from 1994 through 1997), although it disappears with longer sample periods. For both

indices, there is negative autocorrelation in the underlying daily returns at lag four. Our

later tests incorporate both turn-of-the month and time-series autocorrelations in returns.

Using this information about return predictability help assure correct inferences about

return-flow relations.

2.3 Expected flow models

To separate expected from unexpected flow components, we investigated a variety

of alternative models. Table 2 summarizes the results. Panel A shows results for several

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autoregressive moving average models (ARMA). The choice of models is motivated by

the flow autocorrelations shown in Table 1. Because these autocorrelations extend to lag

11, the structure of the models is not always parsimonious. Panel B shows results with

simpler representations which are not restricted to an ARMA structure.

From Panel A, ARMA models explain between 1% and 13% of the variation in

flow. The explanatory power of these models increases with the number of

autoregressive terms. Model 3, which incorporates the seven significant autocorrelations

from Table 1, yields the highest R-squared. Although not reported in the Table, a

qualitatively similar picture to Panel A emerges with other ARMA models. For example,

we also modeled the significant negative autocorrelation at lag one as a first order

moving average process.

In Panel B, we employ various mean values of lagged flow to capture

autocorrelation at long lags. In addition, we incorporate turn of the month effects in flow

with a dummy variable (month_end) equal to one if the half-week period is the first,

second, or last of the month. Model 6 in Panel B seems to work best. In the paper’s tests,

we use predicted and residual values from model 6 to represent expected and unexpected

flow. This model incorporates a turn-of-the-month dummy, one lag of flow, and the mean

of flow at lags three through eight. Figure 2 shows unexpected flows from this model.

The R-squared is slightly higher than for the ARMA models, and the unexpected flow

series has desirable properties. Most of the autocorrelation is purged (not reported); none

of the first twelve autocorrelations exceed .1 in absolute value. The signs appear random

and only two autocorrelations (at lags four and nine) are statistically significant. As a

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further check, we examined turn of the month effects for the unexpected flows, but no

such effects were found (not reported).

3. The relation between market returns and flow: semi-weekly results

3.1 Return-flow regressions

Table 3 shows the relation between market returns and concurrent and lagged

values of expected and unexpected flow. The column 1 regression includes only a month

end dummy (month_end) and the return lagged two periods. These two variables, which

capture predictability due to the time-series and within month properties of the return

series, jointly explain about 4% of the variation in returns.

Unexpected flow. From columns 2 through 4, there is a strong concurrent relation

between returns and unexpected flow. The coefficient on unexpected flow in column 2 is

5.72 (t = 11.0), and the regression R-squared is .245. This coefficient seems

economically significant. The coefficient implies that a one standard deviation shock to a

half-week’s flow (.047%) is associated with a .27% (or .5 standard deviation) per day

market return. The finding of a strong concurrent relation with semi-weekly data

reinforces Warther’s (1995) similar finding with monthly data. The relation remains

largely concurrent at high frequency. This result implies that the monthly

contemporaneous relation reported in Warther is not driven by feedback-trading in which

returns over a period of several days cause subsequent high flow over the next several

days. Thus, high-frequency data narrows the range of economic hypotheses that are

consistent with the data.

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Lagged flow and price-pressure. The column 2 regression provides no support for

the price-pressure hypothesis at any frequency longer than a day. To examine this

hypothesis, the column 2 regression include two lags of unexpected flow. If high

unexpected flow causes temporary price pressure, there should be high returns, but these

returns should subsequently be reversed. Thus, there should be a negative relation

between returns and lagged unexpected flow. From column 2, however, the regression

coefficients on past flow are not significant. The regression in column 3 includes four

(rather than two) lags of unexpected flow, but the results are unchanged. The only

evidence consistent with price pressure is the significant coefficient on lag two

unexpected flow in the column 4 regression, but the significance disappears when a

month-end dummy and lagged return variables are included in the regression.

These results are not entirely surprising. The case for temporary price pressure

associated with individual trades is somewhat ambiguous. Keim and Madhavan (1995)

and Chan and Lakonishok (1993) examine the price pressure hypothesis using data on the

sign, size, and time of individual block trades. Even with such precise data, there is some

difficulty in identifying temporary price pressure. Keim and Madhavan examine the

trades of a small-stock manager and find evidence of a price reversal (from the time of

the trade to the next-day close) on the order of 50% of the initial price reaction to a stock

sale. However, they find a price continuation after stock purchases. Chan and

Lakonishok detect a similar pattern.

Our finding of no support for price pressure at an aggregate, macro level

complements these papers. Let us make the (strong) assumption that the price effects of

flow are similar to the price effects documented in these papers, and consider a mapping

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of the individual-trade results into our study. A flow shock of one standard deviation

implies a $1.1 billion shock to per-day trading activity, if that shock is fully invested.

During the time period of our sample, the average daily trading volume on the NYSE and

NASDAQ in dollar terms was about $15 billion. Thus, even if flow causes a price

reversal similar to that found in the aforementioned papers, the shock to volume seems

relatively small, making reversals all the more difficult to detect.

Expected flow. Concurrent expected flow is not significant in Table 3. Given

market efficiency, this is not a surprising result. Further, the use of OLS in Table 3

overstates the statistical significance of expected (but not of unexpected) flow because

the independent variables are generated regressors (Pagan (1984, Theorem 7) and

Warther (1995, fn. 5)), that is, predicted and residual values of flow from the Table 2

regressions

3.2 Flow-return regressions

Table 4 reports the relation between flow and lagged market returns. As a starting

point, the regression in column 1 repeats the results from Panel B of Table 2, and

includes only those lagged flow variables that are significant predictors of current flow.

The regression in column 2 then adds lagged unexpected market returns, defined as the

difference between the return and the expected return conditional on past returns and the

time of month.

Past returns as flow predictors. Table 4 contains evidence that past returns can

predict flow. First, returns lagged one half-week are a positive predictor of flow. The t-

statistic on the coefficient for the previous half-week’s return is 3.6. These findings

contradict Warther’s conclusion that there is no positive relation between flows and

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lagged returns. This observed relation between flow and lagged returns is consistent with

a common reaction of flow and return to new information, but with flow acting less

quickly. The relation is also consistent with positive feedback trading by investors.

From Table 4, there is also evidence that flow is negatively related to returns at

longer lags. The coefficient on the mean return from half-weeks -3 through –8 is -.033

(t = –3.1). The existence of this “contrarian” feedback effect at longer lags is consistent

with but much stronger than evidence presented in Warther (1995, p. 227). The joint

effect of all lagged returns in predicting flow is still not strong, however. The flow-return

regression R-squared increases from .13 in column 1 to .17 in column 3.

The dependence of flow on concurrent returns in Table 4 mirrors the concurrent

relation in the Table 3 regressions. The concurrent unexpected flow association with a

one standard deviation (.053%) unexpected return is 0.020% (0.4 standard deviations).

When the various lagged flow-return relations are considered, the cumulative unexpected

flow associated with a one standard deviation unexpected return is 0.013%. These

figures seem economically significant. Given that $2.4 trillion was invested in equity

mutual funds in 1997, they imply an inflow of $312 million in response to a one standard

deviation unexpected return.

Estimation issues. The results in Tables 3 and 4 show that both returns and flow are

correlated with lagged returns. This has potential implications for our estimation

procedures. First, unexpected flows in Table 3 do not condition on past returns and thus

contain an expected component that should have a regression coefficient of zero. Thus,

the regression coefficient on unexpected flow is biased downward and understates the

relation between returns and unexpected (conditional on past return) flow. Second,

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disturbance terms of the return-flow equation (Table 3) and flow-return equation (Table

4) will be correlated, and inferences from the separate regressions could be affected. To

address this second issue, we have reestimated the Table 3 and 4 relations using a

seemingly unrelated regression (SUR) procedure to take into account the joint

dependence of flow and returns, and a two-stage least squares procedure to address

potential simultaneous equation biases. In addition, we estimated the relations using

vector autoregression. None of our conclusions change, and to save space the results are

not reported.

Other variations on our procedures were also tried in an effort to provide sharper

tests of economic hypotheses. For example, we investigated the Table 4 linear

specification in more detail, and found that the response coefficient of flow to lagged

return did not depend on the size or sign of returns. We also examined whether the Table

3 and 4 flow-return relations differed for the turn of the month. Turn of the month slope

dummies in the regressions were insignificantly different from zero.

4. Further tests: daily and overnight data

Overview. Daily market returns are available throughout the sample period. In

addition, in early 1998 Trim Tabs began to report daily flow. Overnight return data are

available for this latter period. The tests in this Section study the relation between semi-

weekly flow and daily returns (Section 4.1), daily flow and daily returns (Section 4.2),

and daily flow and overnight returns (Section 4.3).

The concurrent relation between return and flow applies even with a one-day

observation period. Daily flow is also strongly positively related to returns lagged one

day. These findings are consistent with returns and flow reacting to information, but with

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flow acting less quickly. The results are also consistent with feedback trading. A day’s

flow is uncorrelated with the previous overnight return, however. This suggests that the

response of flow to information or to returns is too slow to explain the daily concurrent

flow-return relation, and that the daily concurrent relation is because flow drives returns.

Further evidence supporting each of these two points is presented in Section 5, which

provides a more detailed analysis using intraday return data.

4.1 Semi-weekly flow and daily returns

Table 5 shows the regression relation between a half-week’s flow and the returns on

individual days in the same and the previous half-week. As in Table 4, the return

variable in the regression is the difference between the actual return and the predicted

return. Daily returns over the sample period show significant autocorrelation, at least at

lags two and four, and we use a linear regression with five lags of daily returns to predict

returns.

From Table 5, flow in a half-week is positively related to returns on the last day of

the previous half-week. From column 2, the regression coefficient on returns lagged one

day is .023 (t=10.1), almost as large as the coefficient of .032 (t=13.7) on returns for the

first day of the half-week. A half-week’s flow is only weakly related to returns on the

last day of that half-week. Jointly, these two findings would be expected if flow follows

returns with a one day lag; further evidence on this issue is examined using daily flow

data in the next subsection. From column 1, the expected flow model in Table 2 coupled

with lagged returns jointly explain 23.6% of the variation in flow. From column 2,

including contemporaneous returns roughly doubles this figure, to 47.4%.

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In results not presented, we regressed the return on the first day of the next half-

week on the semi-weekly flow and found no evidence of a relation. This indicates no

evidence of an influence of flow on returns.

4.2 Daily flow and daily returns

Table 6 basically repeats the analysis of Table 5, but uses daily rather than semi-

weekly flows regressed against daily returns. From Table 6, the use of daily flow data

does not alter the impression of a strong contemporaneous relation between flow and

return. The coefficient on return is .052 (t=3.8). This coefficient is actually lower than

the coefficient of .087 (t=5.9) on return lagged one day. Again, return predicts flow with

a one-day lag. Returns lagged two or more days do not appear significant in the

regression.

In Table 7, daily returns are regressed against unexpected flow. The estimate of

daily expected flow is based on a regression of flow against flow lagged one day, return

lagged one day, and expected per day flow given the time-series model for half-week

flow. This procedure explicitly conditions expected flow on lagged returns. Returns are

still strongly positively related to concurrent unexpected flow. The slope coefficient on

concurrent flow in column 2 is 2.40 (t=3.6). A concurrent daily return-flow relation is

also reported, for index funds, by Goetzmann and Massa (1998). Their sample consists

of only three funds, however, and the relation they find is weaker.

The Table 7 regressions also provide a direct test of the hypothesis that flow

contains information that is relevant for returns. This hypothesis is discussed in detail in

Warther (1995, 1998). The hypothesis is consistent with the practitioner view that

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investor sentiment affects the market, and the economic literature in which changes in

investors’ demand to hold equity can change the level of the stock market.

A fund’s flow for a day (from 4 P.M. the previous day to 4 P.M. on the day) is

generally not known, even by the fund’s manager or transfer agent, until some time that

evening or the next morning. Further, aggregate fund flow is not reported by Trim Tabs

until the following afternoon. Thus, actual aggregate flow for the day could contain

information which is relevant for returns but which is not known at the market close on

this day. Under this ‘processing lag’ hypothesis, a day’s flow should be correlated with

the next day’s return. From Table 7, however, there is no such correlation. This result is

at odds with the proposition that fund flow contains information. We caution that the

test’s power depends on the assumption that the current day’s flow has a significant

unpredictable component as of 4 P.M. Although (as discussed in the Appendix) this is a

highly plausible assumption, the power of the test is unknown.

Finally, Table 7 also provides evidence of whether the positive return-flow relation

occurs because mutual fund flow exerts temporary price pressure. The regressions in

columns 2 and 3 include four lags of flow. None of the slope coefficients on lagged flow

are significant. Thus, it does not appear that recent high unexpected flow results in lower

current returns, as would be expected under a temporary price pressure hypothesis.

Similar results apply using the Russell 2000, a small stock index (not reported). The

failure to find a correlation between flow and the subsequent-day return is consistent with

two offsetting factors acting simultaneously: a positive correlation induced by a reporting

lag, and a negative correlation induced by a reversal of the concurrent relation. This

conjecture requires an unlikely coincidence in the magnitude of the two effects. The

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alternative hypothesis, that neither reporting lags nor temporary price pressures are at

work, seems more plausible.

4.3 Daily flow and overnight returns

Tick data on the S&P 500 cash index from the Futures Industry Institute allows us

to refine the Table 7 tests by using close to open returns. For example, if the joint

hypothesis of flow driving returns coupled to a one-day lag in the processing of flow is

correct, then the positive correlation between flow and next-day returns that it implies

should predominate in the close-to-open return. There seems little doubt that fund

managers know the previous day’s flow by the subsequent open. In results not presented,

we find that the correlation between a day’s flow and the next-day return is

insignificantly different from zero using either subsequent close-to-open or subsequent

open-to-close returns. Thus, we again reject the joint hypothesis of flow driving returns

and a processing lag, or the temporary price pressure hypothesis.

Using overnight returns, it is also of interest to repeat the Table 6 flow-return

regression. If the concurrent daily relation occurs because flow reacts to information or

returns, then one expects the day’s flow to be positively correlated with the day’s

overnight (i.e., from previous close to open) returns. In fact, as discussed in the next

section, there is no evidence of a correlation. This suggests that the reaction of flow to

returns and/or the information driving returns does not take place within the day.

Because overnight volatility is low, indicating that there is relatively little news, this test

is not conclusive and the more detailed intraday analysis of the next section is required.

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5. Intraday returns

Partitioning the day’s return into non-trading (close to open) and trading (open to

close) components results in an extreme asymmetry in the information flow (return

volatility). We address this by using extended measures of overnight returns (i.e.,

intraday break points).

Table 8 presents the analysis of intraday returns. The variable FIRST_HR is the

return from the previous close to 10:30 A.M.; the variable AFTER_FIRST is the return

from 10:30 A.M. to the close; the variable HALFDAY1 is the return from the previous

close to 12:00 P.M.; and the variable HALFDAY2 is the return from 12:00 P.M. to the

close. Panel A suggests that extended overnight returns (close to 10:30 A.M.) yield an

approximate match of “overnight/morning” volatility with “afternoon” volatility. For

example, the standard deviations of the return from close to 10:30 A.M. and the return

from 10:30 A.M. to close are 53.7 and 66.3, respectively.

Panel B presents a regression analysis of daily flow on returns over the various

intervals. In all regressions, the previous day’s flow is included as in Table 6. Also, all

regressions include the previous day’s return decomposed into two terms representing the

return from 4:00 P.M. two days earlier to 10:30 A.M. the previous day (FIRST_HRt-1),

and the return from 10:30 A.M. the previous day to 4:00 P.M. the previous day

(AFTER_FIRSTt-1).

Intraday flow reaction to information/returns. The column 2 regression employs

the 10:30 A.M. break point. The correlation between the day’s flow and this measure of

extended overnight returns is insignificantly different from zero (t-statistic = .6). This

stands in contrast to the correlation with the previous day’s 10:30 A.M. to close return

19

and, moreover, the previous day’s extended overnight return (t-statistics 6.1 and 2.3,

respectively). These results suggest that the flow response (to information or returns) is

too slow to explain the daily concurrent flow-return relation.

If the same-day flow-return association were the result of a joint reaction of flow

and returns to information, or a result of return chasing, then the correlation between flow

and same-day extended overnight returns should be at least as strong as the correlation

with same-day 10:30 A.M. to close return. Given the greater reaction time (time to trade

before close) available with extended overnight returns, one would expect the correlation

with extended overnight returns to be stronger. In fact, the reverse appears to be true.

While the coefficient on extended overnight returns is .012 with a t-statistic of .6, the

coefficient on returns from 10:30 A.M. to close is .067, with a t-statistic of 4.5.

One could argue that return-chasers have an affinity for reacting to the day’s

afternoon returns relative to extended overnight returns, or that information relevant to

asset allocation accrues only in the afternoon (despite the common tendency of macro-

economic announcements to occur in the morning). While there may be grounds for the

former (as discussed in Section 6), the latter can be ruled out by the fact that the

correlation between flow and the previous morning’s return is strong, indicating that

investors do react to extended overnight returns, just not on the same day.

Flow driving returns. The strong positive correlation between the day’s flow and

afternoon returns is very much consistent with mutual fund flows having a causal affect

on market returns. Given the fund’s difficulty in conducting a preliminary assimilation of

the day’s fund-share transactions into a meaningful flow estimate (see the Appendix), it

makes sense to perform such a task only later in the day when it counts the most. Thus,

20

one expects fund managers’ trading in response to flow, which in turn causes the flow

figure to be reflected in the market price, to occur later in the day.

This conclusion is supported in all regressions in Table 8, but most strongly in the

column 3 regression, which includes the return in the last two hours of trading. Using

this return, there remains a very strong correlation with the day’s flow. It seems very

unlikely that flow reacts to the return in the last hours of trading, but to no other return; or

that flow jointly reacts to information affecting late afternoon returns, but to no other

return-causing information. In contrast, it is quite likely that fund managers who trade on

their (partially) observed flow do so late in the afternoon.

6. Empirical results: further interpretation and issues

Our high frequency analysis shows that flow follows returns with a one day lag.

Difficulties in distinguishing between alternative explanations for the lagged flow

response are considered below.

6.1 New information as a driver of returns and flow

Returns and flow could move together in response to new information that is

relevant for valuation. This type of story is given structure in the dynamic rational

expectations model of Brennan and Cao (1996). In this model, mutual fund investors are

relatively uninformed about the distribution of returns on the risky asset. When value-

relevant information about the risky asset is publicly released, relatively informed

investors already hold a different fraction of the asset in their portfolios to profit from the

information. After news is released, the severity of the information asymmetry lessens.

Mutual fund investors are net buyers (sellers) in response to public release of good

(news); informed investors take the other side of these trades. The model’s predicted

21

positive correlation between returns and flow reflects uninformed investors’ rational

response to a lessening of information asymmetries. Investors respond to information

which is correlated with returns.

Although the model does not explicitly predict that flow will lag returns, Brennan

(1998) argues that a lag of several days is consistent with information driving returns and

flow, if there are some investors who do not stay attuned to the latest news. This

argument accords well with the one day lag in flow. However, the intraday evidence that

flow drives returns is a puzzle under this story, as it is inconsistent with the model’s

assumption that fund investors are relatively uninformed. Flow should not drive returns

unless some fund investors have private information, or there is temporary price pressure

associated with exogenous flow shocks.

6.2 Feedback trading

In the Brennan and Cao model, the predicted positive relation between flow and

returns does not represent positive feedback trading or “return chasing”. Further, it can

be rational for uninformed investors to chase returns, if these returns are a sufficient

statistic for public information releases. For these reasons, even explicit feedback trading

by investors does not cause rejection of the hypothesis that the one-day lag in flow is

explained by information driving both flow and return.

There is another situation in which positive feedback trading can make sense for

mutual fund investors (see DeLong, Shleifer, Summers, and Waldmann (1990) for

examples in other contexts). If some stocks react slowly to economic news then a fund’s

portfolio return during the day will be positively autocorrelated. Trading in the direction

of fund returns – particularly late-afternoon returns – then allows fund investors a profit

22

opportunity if there is one-day positive autocorrelation. In principle, this could explain a

concurrent late-afternoon return-flow relation. This cannot easily explain the observed

one-day lag in flow, however. Positive return index autocorrelation is strong at a one-day

lag but apparently nonexistent at longer lags (over our sample period, even the first-order

autocorrelation is insignificant). Thus, trading fund shares after 4 P.M. based on today’s

return would not be profitable, as these transactions take place at the fund’s closing price

at 4 P.M. on the following trading day.

7. Conclusions

Our analysis of high frequency flow data presents a more detailed picture of the

relation between flow and returns than previously available. The concurrent relation

between flow and return continues to exist. Further, it is clearly evident from our data

that flow also follows returns.

With the available data, however, we cannot conclusively determine the source of

the lagged relation of flow to returns. Whether some of this response is due to return

chasing that is unrelated to information remains unclear. Moreover, the exact mechanism

by which flow drives return within the trading day is not well understood.

23

Appendix: Mutual fund accounting & Trim Tabs’ data-collection procedures

The discussion in this appendix is based on interviews with dozens of mutual fund

managers, accountants, fund-accounting consultants, transfer agents, the Investment

Company Institute operations division, and the official publication of the American

Institute of Certified Public Accountants regarding Generally Accepted Accounting

Principals (GAAP) for the investment management industry.

A. The process

Receipt of flow. Orders for a purchase or sale of fund shares take a variety of

different forms, and are received by a variety of different agents. Orders can be wire

transfers, telephone transfers, or in writing. Orders can be sent to the fund or the transfer

agent. The primary function of the transfer agent is to carry out the task of assimilating

all orders into a single statement of the fund’s flow.

Processing of flow. In principle, the transfer agent could assimilate the orders

continuously, so that the fund manager could be given a good estimate of the total flow

from all sources that obtains at his fund prior to the 4 P.M. close of trading (all times

Eastern). However, our discussions with fund managers, transfer agents, and other

knowledgeable sources indicate that this is very difficult to achieve in practice, given the

many different paths that an order can take. For reasons of efficiency, transfer agents

execute their task in batches, with no accounting done between batches. This practice is

universal, with the batching almost always being daily with processing beginning at 4

P.M. and continuing overnight. We are aware of no funds that employ continuous

24

processing of the transfer agent’s tasks.2 Thus, while the fund manager probably does

have some knowledge of the day’s flow at that fund prior to the close of trading, this

knowledge is typically far from complete.

Reporting at the fund level. By law, when a fund receives a “good” order from an

investor, the order must be executed at the next calculated net asset value (NAV).3 NAV

is typically calculated only once a day, after the market closes, using closing prices and

the shares outstanding as of the close of business on the preceding day.4 Thus, a flow

figure can be calculated only after NAV has been calculated.

When is the flow figure known? After the NAV is calculated it is reported to the

National Association of Security Dealers (NASD) and the transfer agent. This must occur

by 5:50 P.M. The transfer agent then processes all orders for share purchases and sales

using this NAV to determine the change in the fund’s receivables, payables, and cash on

the one hand, and the change in shares outstanding on the other hand. This processing

occurs overnight, with the numbers reported back to the fund manager and entered into

the fund’s balance sheet the next morning (generally by 7:30 – 8 A.M.). Once the updated

balance sheet is received, the flow for the previous day is calculated as the change in the

balance of the shareholder equity account (i.e., share purchases minus sales).

Thus, the fund manager is not aware of the official day t flow until early in the

morning on day t+1. This is referred to as “t plus one” accounting and is standard

2 Several of the major fund families indicated that they are currently trying to put together systems toproduce preliminary aggregation figures prior to the market close, but that these systems are not in place asof 1998. This is confirmed by discussion with the major software producers who indicated that they aredeveloping the systems but that their implementation has not yet been achieved.3 While there is some flexibility as to what constitutes a good or bona fide request, it generally includeschecks and applications received (even though the check is not yet cleared or the application not yetprocessed). Until the check is cleared, it is booked as a receivable.

25

industry practice. It is specifically provided for in the 1970 Amendment to the Investment

Company Act.5 This accounting practice is quite separate from the issue of check

settlement. Settlement typically occurs on day t+3 to t+5, at which point a receivable

(payable) is converted to a change in cash. In particular, checks received though not yet

cleared are incorporated into flow at the time of receipt.

Reporting of aggregate flow. Trim Tabs receives a report of the fund’s total assets

by fax or email from the fund’s customer service department (typically) or public

relations department (less frequently). This information arrives between 9 A.M. and noon

on day t+1. Since the fund has by this time received it’s report from the transfer agent,

this data most likely reflects day t flow. Thus, in spite of the common industry practice of

using t+1 accounting, there is no structural reason to expect timing errors in the Trim

Tabs data.

B. Tests

Nevertheless, the possibility exists that timing errors resulting from t+1 accounting

arise. Given our finding of a one-day lag in the flow correlation with returns, the exact

timing of these data is critical. Therefore, we examine the matter empirically. Using a

variety of tests we reject the conjecture that t+1 accounting introduces one-day reporting

delay errors in the Trim Tabs data.

4 This has no effect on the determination of NAV. The NAV resulting from this calculation is exactly theexchange rate necessary to ensure that no dilution or accretion occurs with the subsequent exchange ofshares for cash.5 t+1 accounting is not consistent with generally accepted accounting principals (GAAP). GAAP requiresthat end-of-year numbers be adjusted back one day to reflect the reality of the transactions. The data used inthis study are not from official, audited financial statements and are not subjected to GAAP.

26

B.1. The relative accuracy of day t and day t+1 reported flow

Mutual funds must file a semi-annual report with the Securities and Exchange

Commission (SEC) that includes the fund’s total assets and shares outstanding (Form N-

30D). This report must be in conformance with GAAP, and thus reflect the true balance

sheet as of the close of business on the last day of the fiscal period (i.e., include the flow

on that last day in contradiction to t+1 accounting).6 We have daily data on the

individual-fund assets reported to Trim Tabs for the period Feb. 2, 1998 through July 7,

1998. We compare Trim Tabs’ individual-fund reported assets for the last day of the

fiscal period (EOP) to the (correct) number reported to the SEC, and similarly compare

Trim Tabs’ reported assets for the first day of the next fiscal period (BONP) to the correct

number.

The metric of interest is the absolute value of the difference in the two total asset

figures (Trim Tabs versus SEC), divided by the SEC figure. The average absolute error

using the Trim Tabs reported EOP figure is 0.31%. The average absolute error using the

Trim Tabs BONP figure is 0.89%. Thus, the reported figure is far more accurate than the

next-day reported figure. This suggests that the Trim Tabs data does not suffer from a

one-day reporting lag resulting from the ubiquitous use of t+1 accounting. If the Trim

Tabs data were one day late, the BONP total assets should be closer to the SEC figure.

B.2. Correlation patterns in the data

Nevertheless, in some cases the Trim Tabs BONP figure is closer to the audited

number than the EOP figure (25% of the time). This fact is consistent with two

hypotheses. It could indicate that some funds (e.g., 25%) systematically report a one-day

6 Of course, the filing typically doesn’t occur for another couple of months, so there is no difficulty withbackdating the numbers.

27

late number to Trim Tabs, or it could be that other reporting noise is a factor in both the

EOP and BONP data.

Systematic late reporting by some funds. Because of t+1 accounting, it is plausible

that the total assets figure that some funds report to Trim Tabs (on, for example, Tuesday

morning) does not reflect the net inflows of the previous day. As a result, flow

calculations from the reported total assets do not correspond to flow as of the previous

day (e.g., Monday), but rather the day before that (e.g., Friday). In that case, even if the

only correlation between actual daily flow and market returns is concurrent (e.g., only

Friday’s actual flow is correlated with Friday returns), we will observe a correlation

between next-day reported flow and returns (e.g. Monday reported flow is correlated with

Friday returns). If such reporting errors were present in the data, the BONP figure would

on occasion be closer to the audited figure than the EOP figure.

Other reporting errors. There are many possible sources of noise in the EOP and

BONP data, including simple factors like transposing digits, reading the wrong line from

the Balance Sheet, etc., and more formal factors like subsequent changes to the Balance

Sheet due to auditor restatement7. Other reporting noise would cause the BONP figure to

be closer than the EOP figure on occasion, even if all funds report a timely figure.

However, random reporting errors would not produce a correlation between flow and

lagged returns.

Tests of these alternative hypotheses. Two observed patterns in the data cause us to

reject the ‘systematic late reporting’ hypothesis in favor of the ‘other reporting noise’

7 Recall that the SEC filing is not due until three months after the period ends. There are countlesssituations which could cause the concurrent (t+1) unaudited books to be restated to conform to GAAP.

28

hypothesis. First, the first-order autocorrelation in the Trim Tabs sample is significantly

negative for both the daily and the semi-weekly flow series. There is a strong common

(systematic) component to flow (Edelen, 1998). Given this common component, the

‘systematic late reporting’ hypothesis implies positive first-order autocorrelation in the

flow data.

Second, the error in the EOP Trim Tabs figure is positively correlated with the

error in the BONP Trim Tabs figure (the correlation is 0.31 with a p-value of 0.04). The

‘systematic late reporting’ hypothesis implies that the EOP error and the BONP error

should be negatively correlated across observations. For example, under the first

hypothesis, when the BONP error is small it is because the next-day total assets is the

correct EOP figure. That being the case, the reported EOP figure is for the wrong day and

thus exhibits a relatively large error. Conversely, when the BONP error is large, under the

‘systematic late reporting’ hypothesis it must be because the BONP figure corresponds to

the wrong day. That means that the fund is reporting on a timely basis, making the EOP

figure accurate. In short, one error is large if and only if the other is small.

Therefore, we conclude that the tendency for the Trim Tabs BONP figure to

sometimes be closer to the SEC figure is simply due to other noise and causes no bias in

our estimate of the correlation between flow and lagged returns.

29

References

Brennan, M. and H. Cao, 1996, Information, trade, and derivative securities, Review ofFinancial Studies, Vol. 9, No. 1, 163-208.

Brennan, M., 1998, Discussion: Has the rise of mutual funds increased marketinstability?, Brookings-Wharton Papers on Financial Services, 263-267.

Chan, L. and J. Lakonishok, 1993, The behavior of stock prices around institutionaltrades, Journal of Financial Economics, 33, 173-200.

DeLong, J., A. Shleifer, L. Summers, and R. Waldman, 1990, Positive feedbackinvestment strategies and destabilizing rational speculation, Journal of Finance, 379-395.

Edelen, R., 1998, Investor flows and the assessed performance of open-end mutual funds,Journal of Financial Economics, Forthcoming.

Froot, K., P. O’Connell, and M. Seasholes, 1998, The portfolio flows of internationalinvestors, NBER Working paper.

Goetzmann, W. and M. Massa, 1998, Index funds and stock market growth, YaleUniversity Working paper.

Keim, D. and A. Madhavan, 1996, The upstairs market for large-block transactions:Analysis and measurement of price effects, Review of Financial Studies, 9, pp. 1-36.

Pagan, A., 1984, Econometric issues in the analysis of regressions with generatedregressors, International Economic Review, 25 (Feb.), 221-247.

Warther, V., 1995, Aggregate mutual fund flows and security returns, Journal ofFinancial Economics, 39, 209-235.

Warther, V., 1998, Has the rise of mutual funds increased market instability?, Brookings-Wharton Papers on Financial Services, 239-262.

30

Table 1. Aggregate Equity Mutual Fund FlowFlow (inflows minus outflows) is reported semi-weekly by Trim Tabs Financial Services. Flow is usuallyfor either Friday-Monday (Thursday 4 P.M. to Monday 4 P.M.) or Tuesday-Thursday (Monday 4 P.M. toThursday 4 P.M.). Flow for each half-week is scaled by the assets at the beginning of the period, dividedby the number of days in the period. Returns are the average daily return over the half-week. Flow andNYSE Index return are expressed in basis points (i.e., 1.00 = .01%) per day.Time period: 4/11/94 - 7/27/98 (446 observations)Sample: 500 U.S. Equity Funds.

Panel A. Flow and returns within the week

mean median std. dev. mean median std. dev.

tues-thur flow 2.89 3.10 5.22 tues-thur returns 8.68 14.50 62.0fri-mon flow 3.46 3.10 4.14 fri-mon returns 8.32 13.65 42.1

t-statistic for difference in means: 1.0 -0.0

Panel B. Flow and returns within the month

The first half-week of a month is defined as the first whose days all occur during the month. The last half-week begins within the month, but can include days from the next month (32 of 51 months). Observationsare labeled “period 8” only if there is another period following in the month. Otherwise, the observation islabeled “last”. Turn of month flow refers to the average flow in the first, second, and last half-week, andmidmonth flow is the average flow in all other half-weeks.

Half-week: first 2 3 4 5 6 7 8 last All

Flow

mean 3.6 3.9 2.4 2.8 3.2 2.6 3.1 1.8 4.1 3.2std. dev. 4.3 6.2 4.2 4.4 4.6 4.1 5.2 5.3 4.2 4.7

Flow mean std. dev. Return mean std. dev.

Turn of month 3.9 2.7 Turn of month 16.0 53.3midmonth 2.7 1.9 midmonth 4.6 53.2t-statistic for difference in means: 3.1 t-statistic for difference in means: 2.2_____________________________________________________________________________________Panel C. Autocorrelations of flow and of returns

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

Flow -.12* .06 .19* -.01 .17* .09 .07 .18* -.03 .13* .12* .01Returns -.03 -.18* .00 .08 .05 -.12 -.04 .10 -.01 -.09 -.00 -.05

*significant at .05 level, one-tailed test

31

Table 2. Expected Mutual Fund Flow

Each column indicates a separate model for expected flow. Panel a is restricted to autoregressive modelsand panel b presents more general regressions. Models are estimated using flow reported semi-weekly byTrim Tabs Financial Services. Flow for each half-week is scaled by the assets at the beginning of the periodand divided by the number of days in the period. Month_end is an indicator variable taking the value 1 ifthe observation is the first, second, or last period of the month, 0 otherwise. The p-value is for residualautocorrelation (12 lags). t-statistics in parenthesis.Time period: 4/11/94 - 7/27/98 (446 observations)Sample: 500 U.S. Equity Funds

Panel A. ARMA models Panel B. Regression models

1 2 3 4 5 6

AR(1) -0.12 -0.14 -0.16 intercept 0.00011 0.00006 0.00008(-2.6) (-3.0) (-3.6) (2.33) (1.20) (1.87)

AR(3) 0.20 0.14 Month_end 0.00012 0.00015 0.00015(4.3) (3.0) (2.45) (3.29) (3.29)

AR(5) 0.17 0.13 flowt-1 -0.21 -0.21(3.6) (2.8) (-4.60) (-4.69)

AR(6) 0.09 flowt-2 -0.26 (1.9) (-0.56)

AR(8) 0.11 mean flow: (2.4)

AR(10) 0.10 pdt-1 thru pdt-8 0.51 (2.2) (4.43)

AR(11) 0.09 pdt-3 thru pdt-8 0.69 0.78(1.8) (5.69) (7.31)

pdt-9 thru pdt-13 0.19(1.65)

Forecast R2 0.013 0.094 0.128 R2 0.050 0.131 0.130

p-value 0.00 0.06 0.44 p-value 0.00 0.34 0.42

32

Table 3. OLS Regressions: Returns on Flow

Each column indicates a separate model for returns. Return (NYSE Composite Index) and flow (Trim TabsFinancial Services) observations are semi-weekly. Flow for each half-week is scaled by the assets at thebeginning of the period and divided by the number of days in the period. Returns are the average dailyreturn over the half-week. These data are then fit to regression model 6 of Table 2. The fitted values fromthis regression are denoted EFLOW and the residuals are denoted UFLOW. Month_end is an indicatorvariable taking the value 1 if the observation is the first, second, or last period of the month, 0 otherwise. t-statistics in parenthesis.Time period: 4/11/94 - 7/27/98 (446 observations)Sample: 500 U.S. Equity Funds

1 2 3 4

intercept 0.0006 0.0006 0.0006 0.0003(2.0) (1.2) (1.2) (0.5)

EFLOWt 0.18 0.12 2.05 (0.1) (0.1) (1.6)

UFLOWt 5.72 5.66 5.68(11.0) (10.7) (10.7)

UFLOWt-1 -0.25 -0.27 0.23(-0.4) (-0.4) (0.4)

UFLOWt-2 -0.23 -0.17 -1.32(-0.4) (-0.3) (-2.4)

UFLOWt-3 0.16 (0.3)

UFLOWt-4 -0.17 (-0.3)

Month_end 0.0012 0.0012 0.0012(2.3) (2.5) (2.5)

returnt-2 -0.18 -0.17 -0.18(-3.9) (-3.6) (-3.7)

adjusted R2 0.040 0.245 0.239 0.217

33

Table 4. OLS Regressions: Flow on Returns

Each column indicates a separate model for flow. Flow (Trim Tabs Financial Services) and return (NYSEComposite Index) observations are semi-weekly. Flow for each half-week is scaled by the assets at thebeginning of the period and divided by the number of days in the period. Returns are the average dailyreturn over the half-week. Returns are fit to the following regression model

ttt ereturnbendmonthbareturn +++= −221 _

and the residual denoted URET. The regressor “URET, pdt-3 thru pdt-8” is the sum of these six average dailyflows. Month_end is an indicator variable taking the value 1 if the observation is the first, second, or lastperiod of the month, 0 otherwise. t-statistics in parenthesis.Time period: 4/11/94 - 7/27/98 (446 observations)Sample: 500 U.S. Equity Funds

1 2 3 4 5

intercept 0.00008 0.00006 0.00004 0.00005 0.00010(1.87) (1.73) (1.0) (1.4) (2.6)

Month_end 0.00015 0.00014 0.00015 0.00014 0.00014(3.29) (3.2) (3.4) (3.7) (3.6)

flowt-1 -0.21 -0.28 -0.30 -0.30 -0.28(-4.69) (-5.5) (-6.0) (-6.8) (-6.3)

mean flow, 0.78 0.87 0.98 0.96 0.80pdt-3 thru pdt-8 (7.31) (7.8) (8.5) (9.3) (8.6)

URET t 0.038 0.038 (11.0) (10.9)

URET t-1 0.016 0.017 0.019 0.018 (3.6) (3.8) (4.8) (4.6)

URET t-2 -0.001 (-0.2)

URET t-3 -0.001 (-0.2)

URET t-4 -0.009 (-2.2)

URET t-5 -0.001 (-0.2)

URET, pdt-3 thru pdt-8 -0.006 -0.006 (-3.1) (-3.5)

adjusted R2 0.130 0.154 0.168 0.350 0.333

34

Table 5. OLS Regressions: Semi-weekly Flow on Daily Returns

Each column indicates a separate model for flow. Flow (Trim Tabs Financial Services) observations aresemi-weekly and return (NYSE Composite Index) observations are daily, except for the regressor listed as“return, pd t-3 thru t-8,” which is the sum of the average daily returns over 6 semi-weekly periods. Theremaining return regressors are from the autoregressive model

tj

jtjt ereturnbareturn ++= ∑=

−

5

1

.

The coefficients on j=2 and 4 are significant in this sample. The residuals from this regression are referredto as unexpected returns. DAY_RETt-k is the unexpected return on the day k days before the beginning ofthe semiweekly period of flow (the dependent variable). FIRST_RET is the unexpected return on the firstday of the semi-weekly period of flow. LAST_RET is the unexpected return on the last day of the semi-weekly period of flow. Month_end is an indicator variable taking the value 1 if the observation is the first,second, or last period of the month, 0 otherwise. t-statistics in parenthesis.Time period: 4/11/94 - 7/27/98 (446 observations)Sample: 500 U.S. Equity Funds

1 2 3

intercept 0.00009 0.00010 0.00010(2.3) (2.9) (2.9)

Month_end 0.00010 0.00006 0.00006(2.3) (1.8) (1.8)

flowt-1 -0.19 -0.21 -0.21(-3.3) (-4.4) (-5.1)

mean flow, pdt-3 thru pdt-8 0.86 0.88 0.90(7.5) (9.3) (9.6)

FIRST_RET 0.032 0.032(13.7) (13.7)

LAST_RET 0.003 0.003(1.5) (1.4)

DAY_RETt-1 0.019 0.023 0.022(7.0) (10.1) (10.1)

DAY_RETt-2 -0.007 -0.005 -0.005(-1.9) (-1.8) (-1.8)

DAY_RETt-3 -0.003 -0.003(-0.9) (-0.9)

DAY_RETt-4 -0.003 -0.001(-1.1) (-0.2)

return, pdt-3 thru pdt-8 -0.004 -0.005 -0.05 (-2.0) (-3.3) (-3.3)

adjusted R2 0.236 0.474 0.475

35

Table 6. OLS Regressions: Daily Flow on Daily Returns

Each column indicates a separate model for flow. Flow (Trim Tabs Financial Services) and return (NYSEComposite Index) observations are daily. The return regressors are from the autoregressive model

tj

jtjt ereturnbareturn ++= ∑=

−

5

1

.

The coefficients on j=2 and 4 are significant in this sample. The residuals from this regression are referredto as unexpected returns. DAY_URETt-k is the unexpected return on the day k days before the dependentvariable observation. DAY_URETt-k through t-8 is the cumulative unexpected return over days t-3 through t-8.t-statistics in parenthesis.Time period: 2/2/98 - 7/27/98 (114 observations)Sample: 500 U.S. Equity Funds

1 2 3

intercept 0.00009 0.00010 0.00009(0.8) (0.9) (0.9)

DAY_URETt 0.052 0.055(3.8) (4.1)

DAY_URETt-1 0.088 0.087 0.089(5.6) (5.9) (6.3)

DAY_URETt-2 -0.016 -0.017(-0.8) (-1.0)

DAY_URET t-3 through, t-8 -0.005 -0.008 -0.009(-0.9) (-1.4) (-1.7)

DAY_FLOWt-1 -0.24 -0.24 -0.29(-2.2) (-2.3) (-3.4)

DAY_FLOWt-2 -0.05 -0.05(-0.5) (-0.6)

DAY_FLOWt-3 -0.11 -0.06(-1.3) (-0.8)

DAY_FLOWt-4 -0.08 -0.04(-0.9) (-0.5)

adjusted R2 0.243 0.332 0.340

36

Table 7. OLS Regressions: Daily Returns on Daily Flow

Each column indicates a separate model for returns. Flow (Trim Tabs Financial Services) and return(NYSE Composite Index) observations are daily. The daily flow data is transformed into an unexpectedflow with the following regression (observations are daily in this regression)

ttttt ereturnbEFLOWbflowbaflow ++++= −− 12211 ,

where EFLOWt is the expected flow from the semi-weekly model (Table 2, column 6) for the semi-weeklyperiod which holds day t. The residuals from this regression are denoted DAY_UFLOW. t-statistics inparenthesis.Time period: 2/2/98 - 7/27/98 (114 observations)Sample: 500 U.S. Equity Funds

1 2 3

intercept 0.0012 0.0009 0.0010(1.7) (1.4) (1.5)

DAY_RETt-1 0.044 0.057(0.4) (0.6)

DAY_RETt-2 0.061 0.11(0.6) (1.1)

DAY_RETt-3 -0.096 -0.05(-0.9) (-0.5)

DAY_RETt-4 -0.208 -0.22 -0.21(-2.1) (-2.3) (-2.2)

DAY_UFLOWt 2.40 2.39(3.6) (3.7)

DAY_UFLOWt-1 -0.03 -0.13 0.07(-0.0) (-0.2) (0.1)

DAY_UFLOWt-2 0.17 0.25 0.52(0.2) (0.4) (0.8)

DAY_UFLOWt-3 -1.45 -0.86 -0.88(-2.0) (-0.8) (-1.4)

DAY_UFLOWt-4 -0.42 -0.56 -0.55(-0.6) (-0.8) (-0.8)

adjusted R2 0.058 0.142 0.151

37

Table 8. Intraday returns

Flow (Trim Tabs Financial Services) observations are daily. Returns are for the S&P 500 cash index fromthe Futures Industry Institute. Observations on returns are intraday. All times are Eastern. The marketopens at 9:30 A.M and closes at 4:00 P.M.Time period: 2/2/98 - 7/27/98 (114 observations)Sample: 500 U.S. Equity Funds

Panel A. Summary statisticsThe mean and standard deviation statistics are for the return over the indicated interval.

Period Beginning End Regressor label mean std. dev. (units = 0.01%)

Previous day, 4:00 P.M. 9:30 A.M. ONITE 0.6 4.9Previous day, 4:00 P.M. 10:30 A.M. FIRST_HR 6.1 53.7Previous day, 4:00 P.M. 12:00 P.M. HALFDAY1 5.5 64.59:30 P.M. 4:00 P.M. INTRADAY 9.0 88.510:30 P.M. 4:00 P.M. AFTER_FIRST 3.5 66.312:00 P.M. 4:00 P.M. HALFDAY2 4.1 58.82:00 P.M. 4:00 P.M. LAST_2HR 2.9 46.0

Panel B. RegressionsThe dependent variable is the unexpected one-day observation of flow as in Table 6. DAY_UFLOWt-1 is theprevious day value of the dependent variable. The regressors are intraday returns described in Panel A.Each column indicates a separate model for daily flow. t-statistics in parenthesis.

1 2 3 4

intercept -0.00019 -0.00013 -0.00013 -0.00015(-1.9) (-1.3) (-1.2) (-1.5)

DAY_UFLOWt-1 -0.314 -0.350 -0.326 -0.345(-3.7) (-4.2) (-3.7) (-4.0)

FIRST_HRt-1 0.045 0.045 0.046 0.047(2.2) (2.3) (2.3) (2.4)

AFTER_FIRSTt-1 0.098 0.101 0.108 0.103(6.0) (6.1) (6.0) (5.7)

ONITEt 0.036 0.012 0.014(0.2) (0.6) (0.7)

INTRADAY t 0.046 0.067(3.8) (4.5)

FIRST_HRt 0.012 0.014(0.6) (0.7)

AFTER_FIRSTt 0.067(4.5)

LAST_2HRt 0.069(3.0)

HALFDAY1t 0.035(2.0)

HALFDAY2t 0.058(3.3)

adjusted R2 0.344 0.392 0.331 0.366

FIGURE 1: Semi-weekly flow as reported by Trim Tabs, scaled by assets managed and the number of days in the period

FIGURE 2: Unexpected semi-weekly flow from a time-series model (Table 2, column 6)

flow per day (semiweekly data)

-0.15%

-0.10%

-0.05%

0.00%

0.05%

0.10%

0.15%

May

-94

Aug

-94

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-94

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95M

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97M

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-98

inflow per day

Unexpected flow from time-series model

-0.15%

-0.10%

-0.05%

0.00%

0.05%

0.10%

0.15%

May

-94

Aug

-94

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95M

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97M

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unexpectedinflow

per day