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8/6/2019 A Study of Mutual Fund Flow and Market Return Volatility
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A Study of Mutual Fund Flow and Market Return Volatility
Charles Q. CaoDepartment of Finance
The Smeal College of Business
The Pennsylvania State University
University Park, PA 16802, USA
Tel: (814) 865-7891
Fax: (814) 865-3362
Email: charles@loki.smeal.psu.edu
and
Eric C. Chang
School of Business
The University of Hong Kong
Pokfulam Road, Hong Kong
Tel: (852) 2857-8347
Fax: (852) 2858-5614
Email: ecchang@business.hku.hk
and
Ying WangDepartment of Finance
The Smeal College of Business
The Pennsylvania State UniversityUniversity Park, PA 16802, USA
Tel: (814) 863-0486
Fax: (814) 865-3362
Email: yuw105@psu.edu
This Draft: April 2003
First Draft: May 2002
Comments are welcome. Please address all comments to the corresponding author: Eric C. Chang.
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A Study of Mutual Fund Flow and Market Return Volatility
Abstract
In this paper we investigate the impact of institutional trading on the market by
examining the daily relationship between aggregate flow into U.S. equity funds and market
volatility. We examine the relationships between market volatility and fund inflow and fund
outflow, respectively. Our empirical results show that an asymmetric concurrent relationship
between fund flow and market volatility exists: fund inflow is negatively correlated with market
volatility, whereas fund outflow is positively correlated with market volatility. We discuss
potential explanations for our results and suggest that they are consistent with the notion of
information content asymmetry between buy and sell orders.
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A Study of Mutual Fund Flow and Market Return Volatility
1. Introduction
Stock market volatility has received a great deal of attention from investors, regulators,
academics, and the press. Option traders, in particular, monitor it closely, since the value of an
option depends largely on the volatility of its underlying asset. The existing literature provides
evidence that volatility is time-varying1 and calls for a better understanding of the factors that
contribute to its variability.
The popular press often quotes practitioners to suggest that increased institutional
participation may account for large market price fluctuations. One article, previously cited in Sias
(1996), states [r]eviewing this weeks events, analysts are concluding that professional investors
simply overreacted2 The quote highlights the perception that institutional traders contribute to
stock market volatility. This view is echoed by another quote: Small investors, through their
purchase of stock mutual funds, have emerged as the major driving force that has propelled the
Dow Jones Industrial Average.3
Notwithstanding these perceptions, we know little empirically about the actual
relationship between market volatility and institutional traders, especially mutual fund traders.
Recently, academics have devoted considerable attention to theprice impactof mutual fund
trading. Chan and Lakonishok (1993, 1995, 1997), Keim and Madhavan (1997), and Jones and
Lipson (1999), for example, have examined the price effect of money inflow into a mutual fund.
In general, these studies suggest that institutional trading causes bothpermanent and temporary
price impacts.
Warther (1995, 1998) examines the relationship between aggregate cash flow into all
mutual funds and market-wide returns. These studies document a strong positive relationship
between unexpected mutual fund flow and contemporaneous stock returns. He also investigates
the lead-lag relationship between flow and returns, but he rejects both sides of feedback trading,
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arguing that security returns neither lag nor lead mutual fund flow. Although he cannot determine
causality here, he suggests a plausible causal link from flow to returns. Edelen and Warner (2001)
further address this issue using higher-frequency data. They report that aggregate unexpected
mutual fund flow is positively correlated with concurrent market returns at a daily frequency.
They also find causality from flow to returns within the day and the one-day lagged response of
aggregate flow to market returns.4
While ample empirical evidence suggests that aggregate mutual fund flow is positively
related to market returns, the relationship between aggregate mutual fund flow and market
volatility is not clear. Some indirect inferences can be drawn from studies examining the impact
of institutional trading on stock price volatility, but the evidence is inconclusive. For example,
using quarterly data, Reilly and Wachowicz (1979) examine the relationship between institutional
traders (e.g., pension funds, etc.) and stock price volatility during the period 1964-1976. They
claim that institutional trading actually reduces stock price volatility. However, several studies
suggest the opposite. For example, Sias (1996) performs cross-sectional analysis for all stocks
listed on the New York Stock Exchange (NYSE) during the period 1977-1991. He documents a
positive relationship between annual change of institutional ownership and contemporaneous
security volatility after controlling for capitalization. Using a sample of 500 stocks in the S&P
500 index, Xu and Malkiel (2003) document a positive cross-sectional relationship between the
idiosyncratic volatility of the stocks in the index and institutional ownership from 1989 to 1996.
They demonstrate that most increased idiosyncratic volatility is attributable to institutional
ownership.
These studies, however, usually focus on the micro level effect. They examine the
relationship between the level of institutional ownership of a stock and the stocks price volatility.
It is still unclear how institutional trading is related to volatility on the aggregate level
empirically.
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The focus of this paper is on the daily relationship between aggregate mutual fund flow
and market price volatility.5 We use a unique data set on daily aggregate net mutual fund flow
from February 3, 1998 to December 29, 2000, for a period of 735 days. Our flow data are from
the same source used by Edelen and Warner (2001), but over a longer period. To prevent our
results from being sensitive to the particular volatility estimator used, we use three estimators of
daily market volatility: (1) the high-frequency volatility estimated from the intraday return data of
Standard & Poor (S&P) 500 index, using the method of Andersen, Bollerslev, Diebold and Ebens
(hence ABDE, 2001), (2) the high-low volatility estimator developed by Parkinson (1980), and
(3) the implied volatility index based on the option of the S&P 100 index, which is quoted by
Chicago Board Options Exchange (CBOE).
When we use aggregate net mutual fund flow across the whole flow range to examine the
relationship, the empirical results indicate a significant negative contemporaneous volatility-flow
relationship. This implies that increases in mutual fund flow are associated with a less volatile
market.
We further examine whether the negative relationship holds for both net fund inflow and
outflow. Our further investigation is mainly motivated by two facts. First, we note the marked
asymmetry between the effects on stock prices of institutional buying and selling (Kraus and Stoll,
1972; Holthausen, Leftwich and Mayers, 1987, 1990; Gemmill, 1996, Keim and Madhavan, 1996;
and Chan and Lakonishok, 1993, 1995.) Specifically, purchases of a stock made by institutional
traders are accompanied by an increase in its price, which continues to rise after the trade. But
sells of a stock are accompanied by a drop in its price, which tends to revert to its prior level. Saar
(2001) develops a theoretical model to show how the trading strategies of money managers create
a difference between the information content of buys and sells, and hence produce a permanent
price impact asymmetry between buys and sells. In general, existing evidence suggests that the
permanent price impact of institutional trading depends on whether the initiator of a transaction is
a buyer or a seller. Since unexpected inflow (outflow) should stand proxy for subsequent
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unexpected institutional buys (sells) [Keim (1999), Edelen (1999), and Edelen and Warner
(2001)], it is natural to ask whether the flow-volatility relationship holds for inflow and outflow.
Our investigation is also motivated by the documented asymmetric relationship between
price changes and trading volume. Karpoff (1987) shows that when prices go up, volume
increases, but when prices go down, volume also increases. However, previous studies that do not
consider this asymmetry usually document a positive contemporaneous relationship between
volume and price changes. Karpoff argues that tests of the volume-price changes relationship that
do not differentiate between positive and negative price changes are misspecified because they
are based on the implicit false assumption that the relationship between volume and price changes
is monotonic. Hence we take into account flow direction to ensure that a similar problem does not
occur in our study.
An interesting finding emerges after we consider the direction of aggregate net flow. The
impact of net inflow and net outflow on the market is markedly asymmetric. We show that net
fund inflow is negatively correlated with market volatility, whereas net fund outflow is positively
correlated with market volatility.
We argue that our findings are consistent with evidence in two lines of research. First,
Harris and Raviv (1993), Shalen (1993) and Delong, Shleifer, Summers and Waldman (1990a)
demonstrate that informed trades are useful in helping adjust prices to new information. However,
the presence of a substantial portion of uninformed investors, and hence their trades, may increase
market price volatility. Second, Chan and Lakonishok (1993, 1995), Keim and Madhavan (1995)
and Saar (2001) all argue that there is a difference in the information content of mutual fund
managers buying and selling orders: buys tend to convey more information than sells. They
argue that mutual fund managers devote substantial resources to gathering and analyzing
information and make decisions based on their private information. To maximize trading
performance, they search for information about stocks regardless of whether they are in their
portfolios, in order to buy stocks with favorable prospects. However, due to restrictions on the use
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of leverage and short sells, their sells are limited to the assets they already own. If individual
investors tend to redeem fund shares more in a down market, the liquidity demand would result in
an asymmetry whereby mutual fund managers trading on selling stocks contains less information
than their trading on buying stocks. The asymmetric relationship between market volatility and
fund flow documented in our paper is consistent with the asymmetric information content
argument.
The remainder of the paper is organized as follows. In Section 2 we review stabilization
and destabilization arguments pertaining to the impact of institutional trading on the stock market.
In Section 3 we discuss our mutual flow data and volatility measures. In Section 4 we present our
main results using daily data. In section 5 we discuss possible explanations for the asymmetric
relationship. Section 6 concludes the paper.
2. Potential effects of institutional trading on market volatility
Existing literature offers mixed views on whether the increasing presence of institutional
trading in the financial market stabilizes or destabilizes financial asset prices. One of the
difficulties in addressing this issue is the absence of a benchmark for normal price volatility. Most
existing financial theories deal with asset price determination rather than volatility. In particular,
the aim of valuation theories is to offer paradigms on how to rationally determine the fundamental
value of financial assets, but taking asset price volatilities and/or co-variabilities as exogenously
given.
Since a normal level of volatility is neither empirically observable nor theoretically
determinable, whether or not a particular market force has impacted price volatility can only be
indirectly inferred. In general, any market forces that tend to drive a financial assets price
temporarily away from its fundamental value have been viewed as destabilizing factors, and vice
versa. The rationale is straightforward. In a competitive market, any disequilibrium cannot be
sustainable in the long run. Therefore, in the subsequent market correction process, a relatively
large price change in absolute value is bound to occur and results in a higher volatility than it
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would be the case without such a market force. In this section, we review several views that imply
that institutional trading may either affect or correlate with stock price volatility.
2.1. Herding and positive-feedback trading
Lakonishok, Shleifer, and Vishny (1992) argue that institutions may destabilize stock
prices and increase market volatility through herding or positive-feedback trading. Herding
occurs when money managers trade in the same direction at the same time withoutnecessarily
focusing on fundamental values. Positive-feedback trading occurs when money managers chase
winners and sell losers without regard to fundamental values.6 Scharfstein and Stein (1990) favor
the first view, arguing that money managers are typically evaluated against each other, not some
absolute standard. To minimize the chance of becoming an outlier, money managers have
incentives to follow the trading patterns of others rather than responding to their private
information. Herding, motivated by this agency problem, may therefore amplify exogenous stock
price shocks.7
However, Lakonishok, Shleifer, and Vishny (1992), Bikhchandani, Shilfer, and Welch
(1992), and Hirshleifer, Subrahmanyam, and Titman (1994) argue that if, for example,
institutional investors are better informed than individual investors, they will probably herd to
undervalued stocks but away from overvalued stocks. Their trading actually moves prices toward
rather than away from equilibrium values8. Chopra, Lakonishok, and Ritter (1992), Lakonishok,
Shleifer, and Vishney (1994), and Brennan (1995) all suggest that institutional investors are more
likely to behave rationally than individual investors.
The empirical evidence in regard to this phenomenon is mixed. Sias and Starks (1997)
demonstrate that the returns on portfolios dominated by institutional investors lead returns on
portfolios dominated by individual investors. Wermers (1999) investigates the impact of mutual
fund herding on stock prices, and shows that stocks bought by herds outperform stocks sold by
herds. Both findings are consistent with the conjecture that managers herd on new information on
fundamentals and help to speed up the information incorporation process. Nofsinger and Sias
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(1999) show that analyses of post-herding returns provide no evidence that institutional herding is
irrational. This is consistent with the hypothesis that institutional investors, at the margin, are
better informed than other investors. However, Dennis and Strickland (2002) argue that earlier
studies using quarterly or annual ownership data may not reveal herding that occurs over a shorter
time interval. To circumvent this problem, they perform cross-sectional tests to investigate the
relationship between ownership structure and returns of firms on event days when the absolute
value of market return exceeds 2%. They find that a firms abnormal return on event days is
related to the percentage of institutional ownership. They conclude that the evidence is consistent
with the positive feedback behavior on the part of some institutions, particularly mutual and
pension funds, which may drive asset prices away from their true values.
2.2. Investors preference
Some scholars, although without asserting a causal relation, have inferred either a
positive or a negative contemporaneous relationship between volatility and institutional trading
based on institutional traders preferences. Kothare and Laux (1995), for example, predict a
positive relation on the ground that institutional investors are attracted to more volatile stocks.
Badrinath, Gay, and Kale (1989) and Arbel, Carvell, and Strebel (1983), however, suggest that
institutional traders are prudent and more likely to avoid riskier (and typically smaller) stocks;
they are thus associated with decreased volatility. Gompers and Metrick (2001) also suggest that
large institutions, compared with other investors, prefer to invest in large, more liquid stocks.
It is fair to say that existing theories offer no definitive conclusion about whether
institutional trading is associated with either increased or reduced volatility. Therefore, we must
appeal to empiricism to determine the relationship between institutional trading and market
volatility.
3. Data and volatility measurement
3.1. Mutual fund flow data
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We use data on daily net mutual fund flow from Trim Tabs (TT) financial services of
Santa Rosa, CA. TT furnished us with the daily data on net asset values (NAVs) and total net
assets (TNAs) for a sample of over 800 mutual funds9. The sampling period was from February 2,
1998, to December 29, 2000. The data include equity funds and bond funds, which represent
approximately 15% and 12% respectively of the total funds covered by the Investment Company
Institute(ICI). TT also provided us with daily net fund flow (new subscription less redemptions)
based on the following formula:
1
1
=t
ttttNAV
TNANAVTNAFlow . (1)
3.1.1. Fund classification and aggregation
Since we want to explore the relationship between aggregate mutual fund flow and U.S.
stock market volatility, our focus in this paper is on domestic equity mutual funds. Therefore, we
isolate domestic equity funds from other funds. We then match the whole sample with those in
the Center for Research in Security Prices (CRSP) survivor-bias free U.S. mutual fund database
and classify the funds by the investment objectives. Like Warther (1995), we classify mutual
funds by ICI category10 and include the funds with the following investment objectives in our
sample: aggressive growth (AG), growth and income (GI), long-term growth (LG), sector funds
(SF), total return (TR), utility funds (UT), income (IN) and precious metals (PM).11 The final
sample contains 411 domestic equity mutual funds.
3.1.2. Data filter
TT advised us that its data are prone to errors such as interchanged digits and digit
transposition, because the data are collected by hand.12 Thus, we need to filter NAVs and TNAs
before aggregating the daily U.S. equity mutual fund flow data. We use the same two filters as
employed in Chalmers, Edelen, and Kadlec (hence CEK, 2001) to eliminate potential data error in
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NAV and TNA series13. After the filtering, we calculate the net flow on the basis of these two
series.
Some funds may send one-day-old data or partially updated data (with updated NAVs but
not reflecting the days fund-share transactions) to TT. However, Edelen and Warner (2001)
suggest that TT include the funds in their sample only if the funds can reliably provide up-to-date
daily NAVs. They employ various tests to reject the hypothesis that TT reports one-day-old
data14. They caution that merely adjusting the fund's data by one day can result in severe
classification errors. For this reason, Edelen and Warner (2001) make no adjustments to their data
based on concern of data timeliness and argue that their decision would only strengthen their
papers main conclusion: that flow-motivated trade has an aggregate price impact.
Goetzmann, Ivkovic, and Rouwenhorst (hence GIR, 2001) also examine the reporting
practices of each international fund in their sample. They compare TTs fund data with that in the
CRSP mutual fund database. They identify 88 of 116 funds in their sample that report appropriate
TNAs and 3 that report one-day-lagged TNAs. Data for the remaining 25 funds were either too
noisy to allow for a determination or were not available for 1998. GIR conclude that the
overwhelming majority of the funds in their sample follow the proper practice of reporting post-
flow TNAs. Moreover, they point out that the results obtained under the assumption that all 116
funds report timely data and those obtained from the 91 funds with clearly identifiable reporting
practice are very similar. As a result, they only report results based on the whole sample.
Taken together, previous studies suggest that in general TT reports timely data on mutual
fund flow. Therefore, like Edelen and Warner (2001) and GIR (2001), we make no adjustments to
fund flow data in this research.
3.1.3. Properties of daily aggregate mutual fund flow
The dollar value of the TT asset base varied dramatically from 340 to 810 billion during
our three-year sample period. Therefore, we normalize flow by expressing it as a percentage of
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5-minute returns.16 They argue that the estimators thus constructed are, in theory, both free of
measurement error and model free.
Following ABDE (2001), We construct the five-minute return series of Standard and
Poor (S&P) 500 index from the logarithmic difference between the prices recorded at or
immediately before the corresponding five-minute interval. We obtain the intraday transaction-
level data from Tick Data, Inc.17 As pointed out by ABDE (2001), the use of fixed discrete time
interval and the inherent bidask spread could induce the negative serial correlation in the
return series and thus systematically bias the volatility measure. Therefore, much as ABDE
(2001) did, we estimate an MA (1) model for the five-minute return series for the whole sample
to remove the potential negative serial correlation. Consistent with ABDE (2001), we find that the
estimated moving-average coefficient is 0.09818 with a t-value of 23.8. Then we construct the
high-frequency volatility estimator
=
+=
/1
1
2
, )(i
ittHigh r (2)
so that tHigh, denotes daily market volatility based on high-frequency data on day t, is the
observation interval length (e.g., five minutes), 1/ is the number of observation intervals in one
trading day (e.g., 79 five-minute intervals per day), and+itr is the intraday de-meaned MA(1)-
filtered five-minute S&P 500 index returns in interval on day t.
Two additional measures of daily market volatility are used to check the robustness of the
results. The first is the extreme value estimator developed by Parkinson (1980), which is defined
as
)/ln(601.0, tttHL LH= (3)
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whereHtandLt, respectively, are the highest and lowest index prices on day t. The daily high and
low S&P 500 prices are obtained from the Reuters Database.
The second measure is the implied volatility of an option on a market index. The Chicago
Board Options Exchange (CBOE) began to quote a daily implied volatility index ( VIX ) based on
the option of the S&P 100 index in 1986. Our sample begins on February 2, 1998, and ends on
December 29, 2000.
3.2.2. Properties and correlations of volatility estimators
Summary statistics for alternative daily volatility estimators are shown in Table 2. Two
observations merit discussion here. First, Panel A shows that all three volatility estimators exhibit
substantial positive autocorrelation. Thus, we should control for this autocorrelation in our later
tests. Second, implied volatility ( VIX ) is on average higher than volatility estimated from high-
frequency intraday data ( High ) and high-low volatility ( HL ). But, from the correlations shown
in Panel B, we can see that these three volatility estimators are highly correlated. The time series
of three volatility estimators are depicted in Figure 2.19
4. Empirical Results
4.1. Daily flow-return relationships
Edelen and Warner (2001) document a daily relationship between aggregate equity
mutual fund flow and NYSE composite index returns during the period February 1998 to June
1999. Our data on flow come from the same source as theirs, but differ from theirs in that we do
not have aggregate equity mutual fund flow. Instead, TT furnished us with daily data on NAVs,
TNAs, and flow for a sample of about 800 funds. We then aggregated the domestic equity fund
flow on our own and normalized the flow by dividing it by the previous days TNAs. Thus, in this
section, we use data over a longer period to replicate their flow-return-relationship test. The
purpose of this test is twofold: (1) to validate our self-constructed flow data and (2) to extend
their tests to a more recent period.
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We employ the same expected-unexpected flow decomposition that Edelen and Warner
(2001) use to accomplish our replication flow-return-relationship tests. Edelen and Warner argue
that, given the substantial persistence in the flow series20 and the strong dependence of flow on
lagged returns21, it is necessary to explicitly separate expected and unexpected flow. Also, many
previous studies [e.g., Warther (1995, 1998) and Edelen and Warner (2001)] have pointed out that
returns correlate only with the unexpected component of flow but not with expected flow.
We use three sample periods: (1) a whole period from February 1998 to December 2000,
(2) the identical sample period (i.e., February 1998 to June 1999) used in Edelen and Warner
(2001), and (3) a second sub-period from July 1999 to December 2000. All three sample periods
produce qualitatively the same results, although the result based on the more recent sub-period is
slightly weaker than that based on the first sub-period. For brevity, we report only the results in
Table 3, based on the whole period.
Table 3 is divided into two panels. Panel A reports the results of examining the
dependence of fund flows on returns and past flows, and Panel B reports the dependence of
returns on fund flows.
In Panel A, daily flow is regressed on lagged flow and concurrent and lagged returns. As
in Edelen and Warner (2001), usually several different lag values of independent variables are
used in the regressions. Columns 1 and 2 of Panel A indicate that flow is closely related to lagged
flow and lagged return, which is consistent with Edelen and Warner (2001). Their main focus is
the concurrent flow-return relationship, which is shown in Column 3. We confirm that their
results hold in an extended period and document a significantly positive concurrent flow-return
relationship (coefficient 0.009 with a t-value of 2.01) after controlling for lagged flow and lagged
returns.
In Panel B, returns are regressed on concurrent and lagged flow using both the raw series
and the expected-unexpected flow series. Column 4 presents the regression of returns on
concurrent and lagged raw flow. Columns 5 and 6 show the regression of returns on expected and
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unexpected flow. Expected daily flow is taken from the fitted values of model 2 in Panel A, and
unexpected flow is actual minus expected. Again, we confirm the main finding of Edelen and
Warner (2001) in this extended sample period. In particular, Column 6 shows that returns are
positively related to contemporaneous unexpected flow (coefficient 0.629 with a t-value of 2.01)
but not to expected flow (coefficient 0.459 with a t-value of 1.01).
4.2. Regression of volatility on aggregate flow
The main focus of this paper is to investigate the concurrent daily volatility-flow
relationship. In this subsection we first present our regression specifications, discuss the
dependent and independent variables used, and then report the main empirical results. To examine
the relationship between market volatility and aggregate mutual fund flows, our regression
specifications take the following forms:
t
i
itHighittHigh LnFlowLn +++= =
3
1
,10, )()( (4a)
t
i
itHighittHigh LndownUpFlowLn ++++= =
3
1
,210, )(_)( (4b)
t
i
itHighitttHigh LnTVdownUpFlowLn +++++= =
3
1
,3210, )(_)( (4c)
wheretHigh, is the daily volatility estimator based on high-frequency data on day t, tFlow is the
aggregate net mutual fund flow on day t, downUp_ is a dummy variable equal to one when the
market return is positive and equal to zero otherwise, and tTV is the market turnover rate on day t.
The subscripts indicate the days lagged.
The dependent variable in these regressions is the natural logarithm of the daily volatility
estimator based on high-frequency data on day t ( )( ,tHighLn ). As mentioned, we have
constructed three estimators of volatility. For brevity, we use the high-frequency volatility
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estimator to present our main results and use the high-low-volatility and implied-volatility index
as a robustness check.
A discussion of the independent variables and their expected relationships with the
dependent variable are as follows:
Aggregate mutual fund flow ( tFlow ). The coefficient on tFlow is the main focus of
this subsection, since this coefficient reflects the concurrent volatility-flow
relationship.
Lagged values of the natural logarithm of market volatility ( )( , itHighLn ). We
include these values in our tests to account for persistence in market volatility (see,
e.g., Bollerslev, Chou, and Kroner, 1992). Without including them as controlling
regressors, there will be a positive bias on any included regressor that covaries with
lagged volatilities. Thus, the estimation process will be biased and will incorrectly
reflect the concurrent relationship between volatility and flow. Since existing
evidence suggests that high volatility is often followed by high volatility and vice
versa (see, e.g., Bollerslev, Chou, and Kroner, 1992), we expect the coefficients on
these lag values to be significantlypositive. The number of lagged differences to be
included (i.e., the value of maximum i) is determined by the standard t-test of
significance on the last lagged difference term.
Up_down. This is a dummy variable equal to one when the market return is positive
and equal to zero otherwise. Existing literature (see, e.g., Campbell, Koedijk, and
Kofman, 2002) suggests that bear markets are associated with higher volatility than
bull markets. Cox and Ross (1976) and Christie (1982), among others, document a
negative correlation between market returns and volatility. Therefore, it is possible
that the flow-volatility relationship thus gained in regression (4a) is only a spurious
result of the positive flow-return relationship documented by Edelen and Warner
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(2001). We include this dummy variable in regressions (4b and 4c) to determine
whether meaningful changes occur after we control for changes in the volatility when
the market is up that are not related to volatility to flow sensitivity. If the flow-
volatility relationship still holds after we control for this dummy variable, we then
have reason to believe that the concurrent daily flow-volatility relationship does not
simply derive from the positive correlation between daily flow and returns. We
expect the coefficient on this dummy variable to be negative.
Market turnover rate ( tTV ). This rate is defined as the daily trading volume divided
by shares outstanding at the end of the previous day. It is well known that trading
volume is positively related to volatility [See, e.g., Karpoff (1987)]. We thus include
TVt as a control variable in some versions of the tests22. Accordingly, we expect the
estimated coefficient to be positively significant.
Table 4 presents the main results of our volatility-to-flow-sensitivity tests. Results based
on regressions (4a), (4b) and (4c) are reported in Columns 1, 2 and 3, respectively. Our discussion
focuses on Model (4c). As indicated, the sign of estimated coefficients on the controlling
variables are all consistent with the existing finance literature. First, the results confirm that
market volatility persists over time [see, e.g., Bollerslev, Chou, and Kroner (1992)], with all
coefficients on the lagged volatilities positively significant. Second, the coefficient of 0.11 on
the Up_down dummy (with t-statistics of 6.1) suggests that bear markets are associated with
higher volatility than bull markets. This result is consistent with the finding in Campbell, Koedijk,
and Kofman (2002). Third, the coefficient on the turnover rate is significantly positive (with t-
statistics of10.32).
More important for our analysis, however, is the coefficient on tFlow for all three
columns. The coefficients remain negatively significant in all three cases (t-values = - 4.75, -4.50
and 5.60, respectively). The negative and significant coefficient on flow implies that increased
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aggregate fund flow is associated with decreased market volatility. The results also indicate that
adding the dummy term and the turnover rate does not materially affect the flow coefficient.
4.3. Regression of volatility on aggregate net inflow and outflow
The finding that the concurrent relationship between volatility and flow is negative
suggests that the larger the fund cash flow, the less volatile the market. However, as Table 1
shows, of the 735 observations of aggregate net flow data, 416 are positive and 319 are negative.
In other words, 43% of the trading days over Feb. 3, 1998 to Dec. 29, 2000, collectively, involve
cash flowing out of rather than into the equity mutual funds. In this section, we further investigate
the question of whether the above result holds for aggregate net inflow and outflow, respectively.
Our further investigation is motivated by two facts. First, existing studies document that
block purchases have a larger permanent price impact than block sales. Specifically, trades
induced by block transactions and institutional traders impact prices in an asymmetric manner.
Whereas prices go up on buys and down on sells of block trading, they tend to revert after sells
but remain high after buys. In other words, the market seems to react differently to buy and sell
orders23. Saar (2001) develops a theoretical model showing that trading strategies of mutual fund
managers could make buy orders convey more information than sell orders. Therefore,
equilibrium prices should adjust more for buys than for sells. Since unexpected inflow (outflow)
could stand proxy for subsequent unexpected institutional buys (sells) [Keim (1999), Edelen
(1999), and Edelen and Warner (2001)], it is natural to ask whether inflow and outflow will have
different effects on market volatility.
Second, Karpoff (1987) offers a review of the relationship between trading volume and
price changes and presents a model that suggests an asymmetric concurrent relationship between
volume and price changes in financial markets. He points out that, as the V shape in Figure 3
illustrates, there exists a positive relationship between volume and positive price changes and a
negative relationship between volume and negative price changes. Moreover, he argues that tests
on linear relationships between volume and price changes per se will yield positive correlations,
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as indicated by the slope of the dotted line that connects the midpoints of the two sides of the Vin
Figure 3. Morgan (1976), Rogalski (1978), Harris (1986, 1987), and Richardson, Sefcik, and
Thompson (1987) all document such a positive concurrent relationship between volume and price
changes. However, Karpoff (1987) asserts that tests of the volume-price change relationship that
do not differentiate between positive and negative price changes could be misspecified, since they
may be based on the implicit false assumption that the relationship between volume and price
changes is monotonic.
Our investigation of the volatility-fund flow relationship bears some similarities with that
of the volatility-flow relationship. While price changes can be either positive or negative, volume
can never be negative. Similarly, while flow can be either positive (net inflow) or negative (net
outflow), market volatility is always positive. Moreover, our previous models are also based on
the implicit assumption that the volatility-flow relationship is functional and/or monotonic. Thus,
it seems reasonable to take into account the direction of flow to see if any asymmetric volatility-
flow relationship exists.
To examine the impact of inflow and outflow respectively on market volatility, we
introduce two dummy variables ( 1D and 2D ) to differentiate between inflow and outflow. 1D is
defined as 1 when aggregate net flow is positive and as 0 otherwise, and2D is defined as 1
when aggregate net flow is negative and as 0 otherwise. We then construct two new variable
series, namely tInflow and tOutflow , with these two dummy variables. Specifically, we multiply
the tFlow series in the previous models (Regressions (4a)-(4c)) by 1D to derive the new
t
Inflow series. Similarly, we multiply thet
Flow series by2
D to derive the newt
Outflow
series. Note, however, that we actually obtain the absolute value of outflow whentFlow is
multiplied by2D , but, for brevity, we refer to it as outflow henceforth.
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Next, we replace the tFlow series in regressions (4a)-(4c) with these two new series,
tInflow and tOutflow , on the right-hand sides of the regressions. In addition, we include the
lagged values of market volatility, the downUp_ dummy variable defined before, and market
turnover rate ( tTV ) as controlling variables in our tests. Our regression specifications take the
following forms:
t
i
itHighitttHigh LnOutflowInflowLn ++++= =
3
1
,210, )()( (5a)
t
i
itHighitttHigh LndownUpOutflowInflowLn +++++= =
3
1
,3210, )(_)( (5b)
t
i
itHighi
ttttHigh
Ln
TVdownUpOutflowInflowLn
++
++++=
=
3
1
,
43210,
)(
_)(
(5c)
Table 5 presents the results of estimating the revised models. In Column 1, the natural
logarithm of daily volatility is regressed on inflow and outflow respectively after controlling for
the persistence of volatility. In Column 2, we further control for the downUp_ dummy variable,
as previously discussed. We also include the market turnover rate in Column 3 as an explanatory
variable.
The results in Table 5 confirm that relationships between volatility and control variables
remain unchanged, as documented in Table 4. Specifically, significant and positive coefficients
are found on lagged volatilities and market turnover rate while significant and negative
coefficients on the downUp_ dummy variable are documented.
The most important results, however, are the coefficients on tInflow and tOutflow . The
three columns in which these coefficients are shown display a consistent pattern of significantly
negative coefficients on tInflow and significantly positive coefficients on tOutflow . For
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example, Column 1 shows that market volatility is negatively correlated with aggregate net cash
flow into mutual funds with t-statistics of 3.32 and positively correlated with aggregate outflow
(actually the absolute value of outflow, as mentioned) with t-statistics of 2.39. These results do
not materially change even after controlling for the impact of market returns and trading volume
on market volatility.
Table 5 reveals an interesting finding: an asymmetric concurrent correlation between
volatility and flow, depending on the direction of flow. We find that fund inflow is negatively
related to market volatility, and that fund outflow is positively related to market volatility. That is,
the larger the aggregate cash flow into the mutual funds, the less volatile the market. On the other
hand, the larger the aggregate cash flow out of the mutual funds, the more volatile the market. We
illustrate this asymmetry in Figure 4.
The slopes of solid lines in Figure 4 roughly illustrate the asymmetric relationship
between volatility and fund flows. Moreover, the slope of the dotted line that connects the
midpoints of the two solid lines ofVin the figure suggests that a negative correlation is likely to
be detected when the volatility-flow relationship is examined across a whole spectrum of flow
range. This is in fact the case; as indicated in Table 4, we detect significantly negative concurrent
relationships between volatility and flow.
4.4. Robustness tests
4.4.1. Tests of outliers
Our sample covers 411 U.S. equity mutual funds, including funds with various
investment objectives such as aggressive growth and precious metals. The fund flow patterns are
diversified. For example, whereas average flows of funds with the investment objectives of AG,
GI, LG, and SF are positive, average flows of funds including TR, UT, IN, and PM are negative
(see Panel A of Table 1). We perform robust tests to ensure that the results based on aggregate
fund flows are not driven by a few outliers.
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To test this possibility, we construct a new variable, dispersion rate ( tDR ), as follows:
t
ttt
T
NMDR
= (6)
where Mtrefers to the number of funds whose flow on day tis positive,Ntis the number of funds
whose flow on day tis negative, and Ttis the total number of funds on day t.
Table 6 shows the summary statistics ofDR. Among 735 observations of DR, 250
observations are positive with the mean of 0.119, and 485 are negative with the mean of 0.177.
In addition, the correlation between flow and the DR variable across the whole time period is 0.63.
We perform similar tests onDR to examine whether any outliers induce this asymmetric
volatility-flow relationship. First, we introduce two new dummy variables:3D is defined as 1
when tDR is positive and as 0 otherwise; 4D is defined as 1 when tDR is negative and as 0
otherwise. Next, we construct two new series, pDRt_ and nDRt_ , with these two dummy
variables. Specifically, pDRt_ is tDR multiplied by 3D , and nDRt_ is tDR multiplied by
4D . The models are specified as follows:
t
i
itHighitttHigh LnnDRpDRLn ++++= =
3
1
,210, )(__)( (7a)
t
i
itHighitttHigh LndownUpnDRpDRLn +++++= =
3
1
,3210, )(___)( (7b)
t
i
itHighi
ttttHigh
Ln
TVdownUpnDRpDRLn
++
++++=
=
3
1
,
43210,
)(
___)(
. (7c)
The results are shown in Table 7. In Column 1, we regress natural logarithm of volatility
on positive tDR and absolute value of negative tDR respectively, after controlling for the
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persistence of volatility. In Column 2, we also control for the downUp_ dummy variable.
Turnover rate is included in Column 3 as a controlling variable.
The results confirm the asymmetric pattern reported in Table 5. Specifically, there is a
negative relationship between concurrent volatility and positive dispersion rate, and there is a
positive relationship between concurrent volatility and absolute value of negative dispersion rate.
The results imply that a day where a higher number of mutual funds experience net inflow is
more likely to be one of a lower market volatility.
4.4.2. Alternative volatility estimators
In this section, we repeat our tests using two previously discussed alternative volatility
estimators: high-low volatility and implied volatility index. We report the results in Table 8.24
Table 8 illustrates that the results using two alternative volatility estimators are similar to
the previously presented results.25 In both cases, we find that fund inflow is negatively related to
market volatility and fund outflow is positively related to market volatility. We conclude that our
finding of an asymmetric relationship between volatility and flow is not driven by the particular
volatility estimator used.
4.4.3. Sub-time periods tests
We also divide our sample period into two sub-time periods: one from February 1998 to
June 199926 and the other from July 1999 to December 2000. We then replicate all the tests for
the two periods.27 Table 9 presents the results.
The results are largely consistent with our previous results. For example, we obtain
inflow estimates of 33.4 with the tstatistic of 2.94 and 38.1 with the tstatistic of 2.83 for
two sub-time periods. At the same time, the outflow estimates during two sub-time periods are
25.5 with the tstatistic of 1.93 and 63.1 with the tstatistic of 2.33, respectively.
4.4.4. Other tests
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We perform two additional tests. First, we include global equity (GE) and balanced funds
(BL) in our sample to check whether the results are sensitive to these specific types of fund.
Second, we repeat the analysis, excluding the December data from our sample, to check the
dividend effect. Our data providers advised us that determining flow in the presence of dividends
is pure guesswork because mutual funds do not handle distributions in a uniform manner. Since
most distributions happen in December, for the sake of a robustness check, we re-estimate our
models by discarding December data from the sample to see whether a nontrivial change occurs.
In both cases, we find that the results remain qualitatively the same28.5. Discussion
In this section we attempt to offer an explanation for the documented asymmetric
relationship between volatility and mutual fund flows. We first establish a link between market
volatility and the information content of a trade. We then discuss a possible asymmetry in the
information content between the trades that induce an average aggregate fund inflow and fund
outflow.
Harris and Raviv (1993) and Shalen (1993) demonstrate that the presence of a substantial
portion of uninformed investors in the markets, and hence their trades, may increase market price
volatility. They show that a wider dispersion of beliefs (that is, a wider dispersion of expectations
in the current and preceding rounds of trade) creates excess price variability relative to
equilibrium value. In particular, Shalen (1993) points out that uninformed (or less-informed)
investors have difficulty interpreting the noisy signals of price change. They cannot differentiate
between short-term random liquidity demand and overall fundamental changes in supply and
demand. This could result in a general discrepancy in the true price embodied in revealed
information. Moreover, uninformed investors tend to revise their beliefs more frequently than
their informed counterparts after new information becomes publicly available, resulting in the
slower disappearance of price fluctuations from their trading. In these ways, uninformed investors
(and hence their trades) are more likely to overreact to fundamental price movements, which lead
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to increased price volatility. Informed trades, however, are arguably useful in helping adjust
prices to new fundamentals, and thus are immune from these problems.
Next, we offer three arguments that suggest that, on average, mutual fund inflow may
contain better information than outflow. The first argument comes from the joint nature of fund
flow decisions by individual investors and fund managers. To buy or redeem mutual fund shares
is basically an exclusive decision made by individual investors. However, mutual fund money
managers proactive trading strategies (e.g., market timing, stock selection) may also play a
crucial role in determining the timing of fund flow. Therefore, it is fair to say that the timing and
the magnitude of fund flow into and out of the market are generally determined jointly by
individual investors and fund managers. However, mutual funds are required by law to entertain
share redemption requests by individual investors on a daily basis. The obligation to
accommodate the liquidity, as pointed out by Edelen (1999), forces mutual fund managers to
engage at times in a substantial amount of uninformed trading. A large fund outflow day could be
a day characterized by substantial redemption on the part of individual investors. It is expected
that the relative decision role fund managers play on such a day is less significant than that on a
normal day. We hence argue that, on average, mutual fund inflow contains better information
than outflow does.
Chan and Lakonishok (1993) offer the second argument on the difference in institutional
trades information content. They argue that since an institutional investor typically does not
hold the market portfolio, the choice of a particular issue to sell, out of the limited alternatives in
a portfolio, does not necessarily convey negative information. Rather, the stocks that are sold may
already have met the portfolios objectives, or there may be other mechanical rules, unrelated to
expectations about future performance, for reducing a position. As a result, there are many
liquidity-motivated reasons to dispose of a stock. In contrast, the choice of one specific issue to
buy, out of the numerous possibilities on the market, is likely to convey favorable firm-specific
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news. Implied in this argument also is the suggestion that institutions buy orders convey more
information than their sell orders
Saar (2001) develops a model which provides the third argument that the trading strategy
of mutual fund managers creates a difference between the information content of buys and sells.
The asymmetry is mainly driven by two factors: (1) portfolio managers ability to gather, analyze,
and optimally use private information and (2) a set of trading constraints (e.g., restriction on the
use of leverage and short sells) that portfolio managers face. In particular, fund managers profit-
maximizing trading strategies propel them to search for information about stocks not in their
portfolios in order to buy stocks with favorable information, as well as about stocks already in
their portfolios, in order to sell stocks whose price is expected to drop or on which there is no
special information. Saar (2001) argues that such a dynamic strategy creates a difference between
the information content of buys and sells, if the market knows that institutional investors are
informed investors about the prospects of stocks29.
Our findings of an asymmetric concurrent volatility-flow relationship are consistent with
the differences of information content of mutual fund managers buying and selling behavior
discussed above. When individual investors buy mutual fund shares, large sums of cash flow into
mutual funds and induce mutual fund managers to invest money in a diversified portfolio. As
pointed out by Saar (2001), mutual fund managers devote substantial resources to gathering and
analyzing private information and to makingselection and timingdecisions based on their
research departments predictions and recommendations. These trades on average contribute to
adjusting prices to new fundamentals. We thus expect to see a negative relationship between
market volatility and aggregate mutual fund flow. That is consistent with our finding that higher
fund inflow is associated with a less-volatile market.
In contrast, when individual investors redeem mutual fund shares, large sums of money
exit the mutual funds. As mentioned previously, mutual funds are subject to some operational
constraints (Saar, 2001). For example, use of leverage is restricted, and short sells are forbidden.
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Hence fund managers are forced to sell stocks from their portfolios to satisfy the liquidity
requirement of individual investors more often than they are forced to buy stocks. Such less-
informed trades may drive the prices away from the assets fundamental values. This is also
consistent with our findings: the greater the aggregate mutual fund outflow, the more volatile the
market. In a word, we link the impact of individual investors and mutual fund managers in a
unified framework and provide a possible explanation for our findings.
6. Conclusion
In this study, we use daily data to directly investigate the concurrent relationship between
aggregate mutual fund flow and market volatility. Our high-frequency data enable us to conduct
rigorous tests that offer new evidence. The study sheds light on the impactof institutional trading
on the market and should be important to investors, practitioners, academics, and regulators.
Our initial evidence suggests a significantly negative contemporaneous relationship
between volatility and aggregate net mutual fund flow across the whole flow range. However, we
gain additional insight into this issue by separating net inflow and outflow data. An important
finding emerges after we take into account the direction of aggregate net flow: there is a marked
asymmetry between the impact of inflow and the impact of outflow on the market. Increases in
aggregate net inflow are associated with a less-volatile market, while increases in aggregate net
outflow are associated with more-volatile market.
We discuss the possible explanations for our findings of an asymmetric concurrent
volatility-flow relationship and suggest the joint roles played by individual investors and mutual
fund managers in the market. Our results are consistent with the differences of information
content of mutual funds buys and sells.
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Endnotes
1For example, based on monthly observations, Schwert (1989) reports that stock volatility varied
substantially during the period 18571987. Using daily return data, Haugen, Talmor, and Torous (1991)document a large variation in volatility during the period 18971988. Wood, McInish, and Ord (1985),
among others, examine intraday market returns and show that market volatility is high at the beginning and
the end of the trading day.
2 See Wall Street Journal (WSJ), July 21, 1995, p. A1.
3 See WSJ, February 26, 1993, p. C1.
4 However, unlike Warther (1995), who finds a high correlation (R2=55%) between monthly flow and
returns, they show that variation in aggregate flow accounts for only 3% of the variation of daily market
index returns, thus providing limited evidence for the common view that mutual fund flow causes
movement of security prices.
5 Warther (1998) does question whether increased mutual fund flow leads to increased market instability,
but he provides no empirical evidence that directly addresses the flow-volatility-relationship question.
6See also De Long, Shleifer, Summers, and Waldmann (1990a).
7 Investors who follow either of these trading strategies can be included in the class of noise traders
proposed by Delong, Shleifer, Summers and Waldmann (1990b). They show that the unpredictability ofnoise traders beliefs creates excessive risk, resulting, in turn, in a significant divergence of stock prices
from fundamental values
8 Lakonishok, Shleifer, and Vishny (1992) also caution that herding and positive-feedback trading
phenomena per se do not necessarily destabilize the market. Institutions might appear to irrationally herd if
they all react to the same fundamental information in time or if they all counter the same irrational moves inindividual investor sentiment.
9 TNA is the current market value of all the funds assets minus its liabilities. NAV is the price per share atwhich shares are redeemed; it is defined as TNA divided by the total number of shares outstanding.
10 Refer toICI Mutual Fund Factbook, 2001, pp. 36.
11 Unlike Warther, we exclude international equities funds from our sample, given that we are concerned
with U.S. domestic equity market volatility. This is also consistent with Edelen and Warner (2001).
However, it is debatable whether global equity (GE) and balanced (BL) funds should be included in our
sample, since GE funds invest in both U.S. and international equities, and BL funds invest in a mix ofequity securities and bonds. Hence we will perform a robustness check by including GE and BL funds to
see if the results are, in particular, sensitive to them.
12 Greene and Hodges (2002), Goetzmann, Ivkovic, and Rouwenhorst (2001), and Chalmers, Edelen, and
Kadlec (2001) also address this issue.
13The first is a five-standard-deviation filter intending to eliminate outliers due to typos. The second is a
filter designed to catch potential false reversals. For details, please see CEK (2001).
14 Although they cannot reject the partially updated data hypothesis, they also note that the tests power is
limited by the availability of semiannual Security Exchange Commission (SEC) reports. Furthermore, even
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if a fund shows a one-day reporting lag based on comparisons of SEC and TT data, it is unclear whether
there is also a one-day lag for all other days.
15 Statistics on flow data are consistent with Edelen and Warner (2001).
16
ABDL (2001) justify using a sampling frequency of five minutes, stating that this amount of time is longenough to avoid most measurement errors and short enough to avoidmicrostructure biases.
17 Tick Data, Inc. provided tick-by-tick data on 1500 U.S. equities, 60 futures, and 7 most popular cash
indices. We refer the interested reader to www.tickdata.com for a more complete description of the actualdata and the method of data capture.
18 The negative serial correlation may suggest the spurious dependence induced by non-synchronous
trading and bid-ask bounce effects.
19 To save space, we present our results mainly by using high-frequency volatility. Also, to prevent our
inferences from being sensitive to the particular estimators used, we repeat all the analyses with the high-
low-volatility and implied-volatility index time series.
20 Table 1, Panel A shows that flow is highly predictable.
21 This is shown in Table 3, Panel A.
22 Edelen and Warner (2001) suggest that unexpected flow should stand proxy for subsequent unexpected
institutional trading volume. Edelen (1999) documents a positive relationship between gross flow (half of
the sum of inflow and outflow) and trading volume; however, he argues that a positive relationship betweennet flow (inflow minus outflow) and trading volume does not necessarily follow.
23 See, for example, Kraus and Stoll (1972), Holthausen, Leftwich and Mayers (1987, 1990), Chan and
Lakonishok (1993), Gemmill(1996), and Keim and Madhavan (1996)
24 For brevity, we only show the results for the most comprehensive models.
25 Nevertheless, the results are slightly weaker than those using high-frequency volatility.
26 The time period is consistent with that used in Edelen and Warner (2001).
27 For brevity, we only show the most comprehensive models using high-frequency volatility.
28 To save space, these results are not reported.
29 Keim and Madhavan (1995) also suggest that the information content of buys is greater than that of sells:Following a buy decision, institutional traders can choose among various potential assets; however, their
sells are limited to the assets they already own, owing to the short sells restriction. Keim and Madhavan
(1997) also show that trading costs for buyer-initiated trades exceed seller-initiated trades, and their
findings are consistent with the differences between the information content of buys and sells.
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Table 1
Summary statistics for daily mutual fund flow
Our data on daily flow (new subscriptions less redemptions), NAVs, and TNAs come from TT financial
services of Santa Rosa, CA. We match the whole sample of about 850 mutual funds in TT with those in theCRSP survivor-bias-free U.S. mutual fund database and classify the mutual funds by the investment
objectives defined by ICI. Included in our sample of all U.S. equity funds are funds from aggressive growth
to precious metals. We apply two filters described in detail in the main text, the absolute-value filter and thereversal filter, to the TNA and NAV series, and we aggregate the two series. Flow is defined as the one-day
percentage change in aggregate TNAs less the one-day percentage change in aggregate NAVs.
Distributions are not accounted for in these data.
Time period: 2/3/9812/29/00 (735 observations)Sample: 411 U.S. equity funds
Panel A. Univariate statistics and autocorrelations of fund flow
AutocorrelationsFund
investment
objective
Mean
(b.p.)
Median
(b.p.)
Std. dev.
(b.p.)
Std.err
of mean
(b.p.) Lag1 Lag2 Lag5
Aggressivegrowth
4.54 3.54 25.6 0.95 -0.023* -0.144* 0.094
Growth and
income1.33 1.11 8.9 0.33 -0.193* 0.051 0.129*
Long-term
growth3.63 2.57 23.3 0.86 -0.065* -0.310* 0.003
Sector funds 3.44 1.33 40.0 1.48 -0.223* -0.075* -0.012
Total return -4.44 -4.35 18.2 0.67 -0.076* 0.031 0.122*
Utility funds -1.91 -2.97 38.0 1.41 -0.361* 0.009* 0.041
Income -1.68 -2.18 13.0 0.48 -0.076* 0.071 0.140*
Precious
metals-4.77 -21.3 198.0 7.33 -0.147* -0.237* -0.034
All U.S. equity
funds2.94 1.63 15.6 0.58 -0.091* -0.227* 0.060
Panel B. Univariate statistics of aggregate net inflow and outflow
Obs. Mean (b.p.) Median (b.p.)Std. dev.
(b.p.)
Std. err of
mean (b.p.)
Aggregate net
inflow416 11.83 9.00 12.8 0.63
Aggregate net
outflow319 -8.62 -6.69 10.5 0.59
* Significant at 0.05 level, two-tailed test.
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Table 2
Summary statistics for alternative volatility estimators
Panel A shows the univariate statistics and autocorrelations of market high-frequency volatility ( High ),
high-low volatility ( HL ), and implied volatility ( VIX ). High is calculated from S&P 500 index five-
minute intraday returns using the estimator of ABDL (2001) and ABDE (2001). HL is calculated usingthe methods of Parkinson (1980). VIX is the implied volatility index based on the option of the S&P 100
index quoted by the CBOE. Panel B shows the correlations of these three volatility estimators. t-statisticsare in parentheses.
Time period: 2/3/9812/29/00 (735 observations)
Panel A. Univariate statistics and autocorrelations of volatility estimators
Autocorrelations
Mean (%)Median
(%)Std.dev.
(%)Std.err. ofmean (%)
Lag 1 Lag 2 Lag 3
High 16.3 15.2 6.8 0.25 0.624* 0.525* 0.480*
HL 15.6 14.0 8.2 0.30 0.368* 0.349* 0.286*
VIX 25.7 24.7 5.1 0.19 0.931* 0.877 0.832
Panel B. Correlations of volatility estimators
High HL VIX
High 1.0000
HL 0.8059*
(
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Table 3
Contemporaneous relationships between returns and flow
In Panel A, daily flow (Flowt) is regressed on current and past observations of market returns of the NYSEindex (Returnt-i) and past observations of flow (Flowt-i). In Panel B, daily returns of the NYSE index are
regressed on concurrent and lagged daily flow in Column 4 and on concurrent and lagged unexpected daily
flow (Uflowt-i) and concurrent expected daily flow (Eflowt) in Columns 5 and 6. Expected daily flow istaken from Panel A, Column 2. Unexpected flow is actual minus expected. The subscripts indicate the days
lagged. t-statistics are in parentheses.Time Period: 2/3/9812/29/00(735 observations)
Sample: 411 U.S. Equity funds
Panel A. Flow dependence on returns and past flow
1 2 3
Coefficient on:
Intercept0.00031*
(6.2)
0.00031*
(8.2)
0.00030*
(8.1)
Returnt-
-
-
-
0.009*
(2.01)
Returnt-1 0.068*(15.1)0.069*(15.6)
0.066*(15.1)
Returnt-2-0.036*
(-5.9)
-0.035*
(-8.0)
-0.038*
(-8.5)
Returnt-3-0.010
(-1.87)
-0.009
(-1.67)
-
-
Flowt-1-
-
-0.077*
(-2.11)
-0.077*
(-2.12)
Flowt-2--
-0.220*(-6.03)
-0.225*(-6.18)
R2 28.5% 32.3% 33.3%Panel B. Returns dependence on flow
Raw flow 4 Exp.-Unexp. flow 5 6
Coefficient on: Coefficient on:
Intercept0.00012
(0.25)Intercept
0.00043
(0.01)
0.00013
(1.07)
Flowt0. 317*(1.97)
Uflowt0. 663*(2.48)
0.629*(2.01)
Flowt-10.021
(0.08)Uflowt-1
0.006
(0.02)
-
-
Flowt-2-0.038
(-0.14)Uflowt-2
0.273
(0.81)
-
-
Flowt-3-0.00002
(-0.00)
Uflowt-3-0.325
(-1.03)
-
-Flowt-4
-0.119(-0.44)
Uflowt-4-0.089(-0.28)
--
Flowt-50.115
(0.43)Uflowt-5
0.166
(0.52)
-
-
Eflowt0.483
(0.98)
0.459
(1.01)
R2 1.0% 2.3% 1.9%
* Significant at 0.05 level, two-tailed test.
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Table 4
Regressions of high-frequency volatility on flow
Daily high-frequency volatility (ln(tHigh ,
)) is regressed on concurrent aggregate domestic equity fund
flow in Column 1, after controlling for the persistence of volatility. Column 2 controls for a dummy
variable ( downUp_ ). Column 3 also controls for market turnover rate ( tTV ) in addition to downUp_ .
tHigh , is calculated from S&P 500 index five-minute intraday returns using the estimator of ABDL (2001)
and ABDE (2001). downUp_ is defined as 1 when the S&P 500 daily return is positive and as 0
otherwise. tTV is the daily trading volume scaled by shares outstanding at the end of the previous day. The
subscripts indicate the days lagged. t-statistics are in parentheses.
Time period: 2/3/9812/29/00 (735 observations)
Sample: 411 U.S. Equity funds
1 2 3
Coefficient on:
Intercept -0.389*(-6.56)
-0.318*(-5.38)
-1.049*(-11.68)
Flowt-31.530*(-4.75)
-29.228*(-4.50)
-34.099*(-5.60)
downUp_ --
-0.120*(-6.00)
-0.114*(-6.08)
TVt-
-
-
-
88.165*
(10.32)
Ln(1, tHigh
) 0.395*(10.94)
0.404*
(11.44)
0.339*
(10.09)
Ln(2, tHigh
) 0.236*(6.10)
0.240*
(6.33)
0.036*
(5.88)
Ln(3, tHigh
) 0.157*(4.36)
0.150*
(4.27)
0.128*
(3.89)
Adj R2 48.14% 50.52% 56.80%
* Significant at 0.05 level, two-tailed test.
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Table 5
Regressions of high-frequency volatility on aggregate net inflow and outflow
Daily high-frequency volatility (ln(tHigh ,
)) is regressed on concurrent aggregate net inflow ( tInflow )
and outflow ( tOutflow ) in Column 1, after controlling for the persistence of volatility. Column 2 controls
for a dummy variable ( downUp_ ). Column 3 also controls for market turnover rate ( tTV ) in addition to
downUp_ .tHigh ,
is calculated from S&P 500 index five-minute intraday returns using the estimator of
ABDL (2001) and ABDE (2001). tInflow and tOutflow are two series representing net inflow and net
outflow, respectively. downUp_ is defined as 1 when the S&P 500 daily return is positive and as 0
otherwise. tTV is the daily trading volume scaled by shares outstanding at the end of the previous day. The
subscripts indicate the days lagged. t-statistics are in parentheses.Time period: 2/3/9812/29/00 (735 observations)
Sample: 411 U.S. Equity funds
1 2 3
Coefficient on:
Intercept-0.389*
(-6.45)
-0.315*
(-5.23)
-1.296*
(-13.83)
tInflow -31.647*
(-3.32)
-31.215*
(-3.35)
-36.819*
(-4.37)
tOutflow 31.335*
(2.39)
25.934*
(2.02)
28.035*
(2.42)
downUp_ -
-
-0.121*
(-6.01)
-0.115*
(-6.32)
TVt--
--
110.740*(12.85)
Ln(1, tHigh
) 0.395*(10.93)
0.404*
(11.43)
0.317*
(9.70)
Ln(2, tHigh
) 0.236*(6.09)
0.240*
(6.33)
0.200*
(5.82)
Ln(3, tHigh
) 0.157*(4.36)
0.150*(4.27)
0.127*(3.99)
Adj R2 48.07% 50.46% 59.61%
* Significant at 0.05 level, two-tailed test.
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Table 6
Dispersion rate statistics
Dispersion rate ( tDR ) is calculated by dividing the difference between the number of funds with positive
flow and the number of funds with negative flow on day tby the total number of funds on the same day.
Statistics of PDRt_ ( 0>tDR ) and NDRt_ ( 0
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Table 7
Regression of high-frequency volatility on dispersion rate
Daily high-frequency volatility (ln(tHigh ,
)) is regressed on positive ( PDRt_ ) and negative dispersion
rate ( NDRt_ ) in Column 1, after controlling for the persistence of volatility. Column 2 controls for a
dummy variable ( downUp_ ). Column 3 also controls for market turnover rate ( tTV ) in addition to
downUp_ .tHigh ,
is calculated from S&P 500 index five-minute intraday returns using the estimator of
ABDL (2001) and ABDE (2001). PDRt_ and NDRt_ are positive and negative tDR , respectively,
where tDR is calculated by dividing the difference between the number of funds with positive flow and
the number of funds with negative flow on day tby the total number of funds on the same day.
downUp_ is defined as 1 when the daily S&P 500 return is positive and as 0 otherwise. tTV is the daily
trading volume scaled by shares outstanding at the end of the previous day. The subscripts indicate the days
lagged. t-statistics are in parentheses.Time period: 2/3/9812/29/00 (735 observations)
1 2 3
Coefficient on:
Intercept-0.517*
(-8.24)
-0.443*
(-7.13)
-1.306*
(-13.72)
PDRt_ -0.380*
(-2.36)
-0.362*
(-2.31)
-0.235#
(-1.63)
NDRt_ 0.493*
(4.99)
0.500*
(5.20)
0.496*
(5.44)
downUp_ --
-0.125*
(-6.40)
-0.121*
(-6.72)
TVt-
-
-
-
98.612*
(11.35)
Ln(1, tHigh
) 0.357*(9.90)
0.365*
(10.39)
0.298*
(9.04)
Ln(2, tHigh
) 0.233*(6.20)
0.238*(6.51)
0.195*(5.73)
Ln(3, tHigh
) 0.159*(4.52)
0.152*(4.43)
0.134*(4.24)
Adj R2 50.42% 53.01% 60.08%
* Significant at 0.05 level, two-tailed test
# Significant at 0.10 level, two-tailed test
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Table 8
Dependence of high-low volatility and implied volatility on aggregate net inflow and outflow
Controlling for the persistence of volatility, a dummy variable ( downUp_ ), and market turnover rate
( tTV ), daily high-low volatility (Ln( tHL , )) and implied volatility (Ln( tVIX, )) are regressed on
concurrent aggregate net inflow ( tInflow ) and outflow ( tOutflow ) in Column 1 and Column 2,respectively.
tVIX, is calculated using the methods of Parkinson (1980).
tVIX, is the implied volatility
index based on the option of the S&P 100 index quoted by the CBOE. tInflow and tOutflow are two
series representing net inflow and outflow, respectively. downUp_ is defined as 1 when the S&P 500
daily return is positive and as 0 otherwise. tTV is the daily trading volume scaled by shares outstanding at
the end of the previous day. The subscripts indicate the days lagged.Time period: 2/3/9812/29/00 (735 observations)
Sample: 411 U.S. Equity funds
1 2
Ln(tHL ,) Ln(
tVIX,)
Estimate t-value Estimate t-value
Intercept -1.535* -11.97 -0.034# -1.67
tInflow -39.671* -3.03 -4.835* -2.69
tOutflow 48.481* 2.71 4.066# 1.82
downUp_ -0.160* -5.68 -0.085* -22.96
TVt 114.305* 9.20 3.885* 2.34
Ln( 1t ) 0.151* 4.43 0.950* 90.32
Ln( 2t ) 0.237* 7.00 - -
Ln( 3t ) 0.133* 3.94 - -
Adj R2 34.70% 94.02%
* Significant at 0.05 level, two-tailed test.# Significant at 0.10 level, two-tailed test.
8/
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