The Factor Structure of Mutual Fund Flows

by Wayne Ferson

Min S. Kim

March 3, 2011

* Ferson is the Ivadelle and Theodore Johnson Chair of Banking and Finance and a Research Associate of the National Bureau of Economic Research, Marshall School of Business, University of Southern California, 3670 Trousdale Parkway Suite 308, Los Angeles, CA. 90089-0804, ph. (213) 740-5615, ferson@marshall.usc.edu, www-rcf.usc.edu/~ferson/. He would like to acknowledge the hospitality of the Center for Financial Innovation and Stability at the Federal Reserve Bank of Atlanta. Kim is Assistant Professor of Finance at the University of New South Wales, Level 3, Australian School of Business, UNSW, Sydney, Australia 2052, +61-2-9385-5984, min.kim@unsw.edu.au, www-scf.usc.edu/~minskim/. We are grateful to Jeff Wurgler for access to data and to Rich Evans and participants at the 2009 Financial Research Association Early Ideas Session for helpful comments.

The Factor Structure of Mutual Fund Flows ABSTRACT Common flow factors explain significant fractions of annual and quarterly flows to US mutual funds. Common flow factors are highly autocorrelated and are correlated with financial market yields, macroeconomic variables, investor confidence and market volatility at various leads and lags. The systematic components of flows differ across funds according to funds’ “flow betas.” Equity fund flow betas depend on past performance and fund characteristics, such as size, age and expense ratios. High flow beta funds offer significantly lower subsequent returns. Decomposing mutual fund flows into common and idiosyncratic components also generates new insights about the “flow-performance” relation in equity funds first observed by Ippolito (1992) and the “smart money” effect in fund flows first documented by Gruber (1996).

1. Introduction

The determinants of the flows of money into mutual funds are important to understand for

macroeconomic, microeconomic, financial economic and practical reasons. From a macroeconomic

perspective mutual funds capture a substantial fraction of consumer savings, affect the allocation of

that capital, and are likely to be a key factor in retirement outcomes for many households. Money

market funds are key lenders in the repurchase markets, important in funding fixed-income broker-

dealer operations and for implementing Federal Reserve policy. From a microeconomic perspective,

fund flows are a window into individuals' investment decisions. Financial economists study mutual

fund flows for insights about fund managers' incentives, investor behavior and the efficiency of

financial markets. The flows of moneys in and out of mutual funds may affect prices in financial

markets. Finally, mutual fund managers care deeply about fund flows, as their compensation is

linked to flows through the levels of assets under management.

Like asset returns and liquidity, the flows of money into mutual funds have common

components and fund-specific or idiosyncratic components.1 This paper explores mutual fund flows

from this perspective. Previous studies have extracted common factors from mutual fund returns (e.g.

Elton, Gruber and Blake (1999) and Brown, Goetzmann and Grinblatt (2004)) but less is known about

the common factors in mutual fund flows. Goetzmann, Massa and Rouwenhorst (2008) study factors

in a small sample of daily fund flows during 18 months of 1998-99. We focus on quarterly and annual

flows for a large sample of stock, bond and money market funds during 1981-2009. Decomposing the

flows into common and idiosyncratic components generates a number of new insights.

The systematic components of fund flows represent significant fractions of the

variation in individual fund flows over time. In a statistical factor analysis the first common factor

captures about 11% of the variance of percentage flows for US equity funds during 1981-2009, and the

first six factors capture more than 43%. For bond funds the figures are in a similar range, and slightly

lower for money market funds.

1 Common factors in stock returns have been explored since King (1966) and common factors in liquidity since

2

The common factor in percentage equity fund flows are related to contemporaneous

values of macroeconomic and financial market variables such as aggregate stock market returns,

consumer confidence, the value of the US dollar and the growth rate of industrial production and

stock market volatility. A time-series regression of the first equity factor on a collection of a dozen

contemporaneously measured macroeconomic and financial variables produces an adjusted R-

squared of 39%. For bond funds we get 37% and for money funds, 30%. While the finance literature

finds it difficult to explain much of the variance in financial asset prices using macroeconomic

variables, the common factors in mutual fund flows respond strongly to macroeconomic conditions.2

We examine the predictability of the common factors in mutual fund flows. The flow factors display

significant and complex autocorrelation structure with substantial persistence, and some relation to

lagged macroeconomic and financial market variables. In the sample, we find adjusted R-squares

exceeding 60% in regressions predicting flow factors for bond funds, using lagged flows and

economic variables, and the R-squares are about 25% for equity funds and 13% for money market

funds. Lagged flows also bear a predictive relation to future values of variables that represent

economic conditions, suggesting that in the aggregate, fund investors do not simply chase the past

(performance), but look to expected future economic conditions.

Common flow factors are closely related to sector-wide flows. Value-weighted and

equal-weighted flows for each fund sector (stock, bond and money market) have correlations with the

first common statistical factors in that sector of at least 76% annually and 55% quarterly. Thus, the

first common factor may be roughly interpreted as the sector-wide flow.

There is substantial variation across individual mutual funds in the sensitivity of their

flows to the common flow factors. The “flow betas” that describe this sensitivity may be roughly

interpreted as the marginal “market share” of new sector flows that a fund receives. We find that

flow betas depend on characteristics of a fund such as its size, age, expense ratio and recent return

Chordia, Roll and Subrahmanyam (2000). 2 Other studies have observed that aggregate mutual fund flows are related to economic conditions. See for example, Warther (1995) and Chalmers, Kaul and Phillips (2007).

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performance. Equity fund flow betas are also asymmetric. High-performing funds have lower flow

betas when the aggregate flow is negative. Thus, when flows are strong, high performing funds

increase their market share and when there are negative sector flows, their market share loss is

smaller than funds with weaker recent return performance. High-performing funds’ common factor

flows bear an option-like relation to the aggregate flows.

We find that equity funds with higher flow betas on large sector outflows offer lower

subsequent performance. Such funds have to sell assets when other funds in the sector are selling.

The difference between the average returns of the high and low quintile of equity funds, sorted

quarterly on the lagged flow beta on sector outflows, is 23-30 basis points per month and significant

after adjustment for standard return factors. This effect adds a new dimension to the “fire sales”

phenomenon studied by Coval and Stafford (2007), who examined the individual stocks held by funds

experiencing large negative total flows.

Studying the common and idiosyncratic components of funds’ flows refines our

understanding of other stylized facts in the mutual fund literature. One is the “flow-performance”

relation documented by Ippolitto (1992), Sirri and Tufano (1998) and Chevalier and Ellison (1997).

Here we find that common and idiosyncratic flows behave differently in flow-performance

regressions, and these differences are related to changes in the overall relation over time. A second

application is the "smart money" effect of Gruber (1996), who finds that new money flows into US

equity mutual funds earn higher returns than existing shareholders. We find that this effect, to the

extent that it exists in our data, is concentrated in the common factor component of fund flows.

The rest of the paper is organized as follows. Section 2 describes our data and

empirical methods. Section 3 presents the analysis of fund flows and their common factors. In Section

4 we examine the relation between flow betas and fund performance and summarize the implications

of common and idiosyncratic flows for the flow-performance relation and smart money effects.

Section 5 concludes and offers suggestions for future research.

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2. Data and Methods

We study data for 1980-2009 from Morningstar on US Equity funds, bond funds and taxable money

market funds. We use Morningstar's fund classifications. The Equity funds exclude balanced funds,

asset allocation funds, closed-end funds and index funds identified by Morningstar from the funds'

prospectuses. The bond funds exclude closed-end and municipal bond funds, and the money market

funds exclude tax-exempt funds.

We subject the funds to a number of screens. To minimize incubation and the

associated back-fill bias (e.g. Evans, 2010) we exclude funds that had less than $5 million in total net

assets at the end of the previous year, and we exclude the first year for each new fund. We also

exclude funds for the year in which they record an extreme flow observation (less than -100% or

greater than 500%). This leaves us with a total of 28,078 fund years, where the number of equity funds

is 183 in 1981, rising to 2,046 in 2009. For bond funds and money market funds, the number of fund

years is 15,801 and 9,774, respectively (data start from 1992). Table A.2 in the Appendix provides

summary statistics for the mutual fund sample.

The percentage flows of new money are defined in the usual way as:

Fit = [TNAit - TNAit-1(1+rit)]/TNAit-1, (1)

where TNAit represents the total net assets of fund i at time t and rit is the reported return for the

period from t-1 to t. We use annual and quarterly flows.3

Figure 1 presents time-series plots of (value and equally-weighted) aggregate flows for

the three fund sectors. Broadly speaking, the series appear stationary, but display some persistent

multi-year swings (we examine the autocorrelations below). For example, money market fund flows

3 When mutual funds merge, the calculation in (1) is adjusted for the effects of the merger to avoid the appearance of spurious flow to the acquirer. Given a merger the selling fund dies and we reduce the buying fund’s reported, newly-combined TNAt by TNAs,t-1(1+rst)f, where s indicates the selling fund, rst is the selling fund’s return for the period during which the merger took place and f is the fraction of the period prior to the recorded merger date.

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recover from a negative position around 2005 and increase until around 2008, declining through the

end of the sample. Bond fund flows turn negative in the 1990s and the year 2000, then rise

dramatically from 2005 to the end of the sample on an equally-weighted basis, but the value-weighted

(and total dollar) flows turn briefly negative during 2003-2004 and 2008-2009. Equity fund flows

appear to trend downward since the 1990s, but remain positive on an equally-weighted basis. The

total dollar flows to equity funds turn negative during 2002-2003 and from mid-2007 to 2008. These

figures suggest that there have been periods where flows move across market sectors, such as the late

1990s, and also periods of inflows and outflows for the whole industry, such as in 2003.

2.1 Factor Extraction Methods

We decompose the fund flows into systematic and fund-specific or idiosyncratic

components using a factor model:

F = 1Ta' + YB + u, E(u)=0, E(u'Y)=0, (2)

where F is a T x N matrix of flows for T periods on N funds, Y is a T x K matrix of common flow

factors, B is a K x N matrix of factor loadings, a is an N-vector of intercepts, 1T is a T-vector of ones

and u is the idiosyncratic residual. The residuals are assumed to be idiosyncratic in the sense that

E(uu’/N) has bounded eigenvalues as N goes to infinity, while E(FF’/N) has K unbounded

eigenvalues. Connor and Korajczyk (1986) provide conditions under which the first K eigenvectors of

(FF'/N) converge to the common factors, Y, to within a K x K rotation, as N goes to infinity. We use

these scaled eigenvectors as the common factors in mutual fund flows.

The Connor and Korajczyk approach to factor extraction is attractive here, compared

with traditional factor analyses or principal components based on the N x N covariance matrix. There

are many mutual funds with short time series, so N is large compared to T. The T x T matrix (FF'/N)

is therefore more tractable, and it makes more sense to rely on N-asymptotics. Leaving out the funds

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with missing data could create sample selection biases. Fortunately, Connor and Korajczyk (1988)

show that we can use their approach with missing data, by simply averaging over the available funds

for each date-pair corresponding to an element of the FF' matrix. The result is K factor time series of

length T, with no missing observations.

We extract fund flow factors separately for equity, bond and money market funds, but

we are also interested in common factors across the market sectors. To this end we use the approach

advocated by Goyal, et al (2008). This approach starts with the common factors extracted separately

for each sector. Let xis be the i-th orthonormal eigenvector from sector s. The eigenprojection matrix

ΣiΣs (xis xis’) is formed and its principal components are extracted. This allows for common factors

that may be sector-specific or shared across sectors.

The factor extraction assumes that the factor loading matrices are fixed over time. This

may not be true, and we find strong evidence for time-varying "flow betas." To avoid internal

inconsistency we estimate the common factors using a conventional rolling estimation scheme. Here

we take rolling overlapping subsamples with T=12 years (or T=48 quarters), extract the eigenvectors

and associate the last value of the common factor realization in each subsample with the last period in

the subsample. We roll the whole procedure forward to obtain a time series of common factors that

are not forward looking and admit that the loadings may be time varying.4

2.2 Factor Extraction Results

We examine Scree plots (Cattell, 1966) of the eigenvalues. Here we look for a number K

such that the next smaller eigenvalue drops off dramatically. A number of formal tests are available

(see Connor and Korajczyk (1993) and Brown, 1989). In the context of an approximate factor structure

we should see that the pervasive eigenvectors have exploding eigenvalues as N gets large, so the

number of eigenvalues below any finite cutoff point is an N-consistent estimator (e.g., Bai and Ng

4 Fund flows might represent fertile grounds for future work using dynamic factor models. However, as the results of our two approaches are similar, we resist putting the additional structure on the data.

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(2002), Onatski (2006)). Ahn and Horenstein (2009) propose a test based on the ratios of adjacent

ordered eigenvalues which exploits this feature of an approximate factor structure.

The ratios of the adjacent ordered eigenvalues are plotted in Figure 2 for the equity,

bond and money market sectors. In the left-hand panels the full 1981-2009 sample is used for equity

funds (1992-2009 for bond and money funds). In the right-hand panels we present the averages for

the rolling subsamples.5 We evaluate these figures informally. As is common in applications of factor

analysis on stock returns, the first factor appears to dominate in most cases, and we see a big spike at

K=1. But there are peaks that suggest that 6-8 factors may be important for equity fund flows. Rolling

estimation suggests a smaller number, typically three equity flow factors. The ratios for bond funds in

Panel B suggest four dominant factors in annual data, and five in quarterly data, but maybe only one

in the rolling estimation. For money market funds the graphs in Panel C suggest one, or at most three

common factors.

It makes sense that rolling estimation indicates a smaller number of common factors. It

is well-known that a factor model for returns with time-varying betas can generate an unconditional

model with fixed betas and more factors (e.g. Cochrane (1996), Jagannathan and Wang, 1996). A

similar phenomenon likely occurs for fund flows.

2.3 Factors Common across Sectors

The analysis combining the sectors is summarized in Figure 3. Here we combine the

six common equity flow factors with three bond and two money fund flow factors. The approach thus

produces a maximum of eleven nonzero eigenvalues, and the smallest estimated eigenvalue is often

very close to zero. This generates a spike in the last eigenvalue ratio, which we interpret as spurious.

Figure 3 shows the first ten raw eigenvalues, which are more informative for this analysis. Given that

the eigenprojection matrix ΣiΣs (xis xis’) is constructed with unit weights on the eigenvectors its

eigenvalues have a special interpretation. The number of eigenvalues equal to 1.0 is the number of

5 We also examined the individual rolling estimation results but did not find any notable trends.

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sector-specific common factors. If two sectors share a common factor it will be “double counted” and

its eigenvalue is 2.0. Similarly, a factor common across all three sectors produces an eigenvalue equal

to 3.0.

Of course, estimation error affects these calculations. Measurement error reduces the

eigenvalues, on the assumption that the true and measured eigenvectors are both orthonormalized.

Under these assumptions imperfect correlation across sectors means that a factor common across two

sectors has an eigenvalue of (1+ρ)<2, where ρ is the correlation. Thus, instead of the idealized step

function we expect a smoothed graph in practice and that is what we find in figure 3. Figure 3

suggests that there is at least one factor that is common across all three sectors, and one or two more

with two sectors in common.

3. Empirical Results for Flow Factors

In this section we first deal with seasonality in quarterly fund flows and illustrate the common flow

factors. We then explore the relation of the common flow factors to contemporaneous macroeconomic

and financial variables. Third, we explore predictive relations involving the common flow factors.

Fourth, we examine the determinants of funds’ flow betas.

3.1 Seasonality

Quarterly fund flow data may have seasonal patterns. Table 1 summarizes regressions

of individual fund flows on four dummy variables for the quarter of the year. The seasonal patterns

are not strong, but often statistically significant. The mean adjusted R-squares of the regressions are

between 6% and 14% for the three fund sectors; highest in the money fund sector. The distributions

of the R-squares across funds are slightly skewed to the right, with the medians between 2% and 7%.

The extreme 5% right-tail values are greater than 50%. The coefficients in Panel B show that equity

flows are larger in the first half of the year, while money fund flows are negative in the second quarter

and largest in the fourth quarter on average. We use a seasonally-adjusted quarterly flow series in all

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of our analyses, including the factor extraction described above. For each fund the quarterly

seasonally-adjusted flow is the sample mean flow for that fund plus the residuals of the dummy

variable regression for that fund.

3.2 Time Series Plots and Summary Statistics

Figure 4 shows the annual time-series of the first common factors for each sector and

the first overall common factor. These may be compared to the aggregate flows depicted in Figure 1.

Since the factor analysis only identifies common factors to within a rotation, we scale the first

common factors so that the beta of a value-weighted portfolio of funds on the factor is equal to 1.0.

The first common factors display a great deal of similarity to the aggregate sector flows, picking up

most of the peaks and troughs, although sometimes with different amplitudes. This foreshadows

results below that suggest the first factors well represent the sector aggregates.

Panel C of Table 1 presents the simple correlations among the first factors in each sector and

the first overall common factor. The overall factor is highly correlated with the first factor in equity

fund flows (72%-73%) and has moderate positive correlation with money fund flows (34-43%) in

quarterly data but bears little correlation to bond fund flows.

3.3 The Explanatory Power of Common Factors for Individual Funds’ Flows

Table 2 summarizes the adjusted R-squares, regressing the flows of individual funds on

the common factors over time. Each fund's regression uses all of the flow data for that fund, provided

at least K+3 observations are available when K factors are in the regression. The means of the

adjusted R-squares taken across all of the funds are shown for various values of K, as well as other

statistics of the cross-sectional distributions, including the values at various fractiles of the

distributions.

Panel A of Table 2 presents the results for equity funds. The average R-squares have an

interpretation similar to the communalities in a traditional factor analysis. On average the first

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common factor explains about 11% of the variance of annual flows and 8% of the seasonally-adjusted

quarterly flows. With six factors the R-squares increase to about 43% annually and 30% quarterly.

Given that the mean R-squared of the seasonal-adjustment regression is about 7%, the overall R-

squares at the quarterly and annual frequencies are similar. Thus, common factors explain a

substantial fraction of equity mutual fund flows. Panel B presents the results for bond funds and

panel C, for money market funds. These regressions show similar R-squares for the bond funds and

slightly smaller for the money market funds, where one factor delivers an average R-squared of 8%-

10% and six factors deliver 18%-44%.

There is substantial dispersion across funds in the R-squares. For example, the cross-

sectional standard deviation of the R-squares on the first factor is at least two or three times the mean

value in each sector. These differences in R-squares reflect the significant heterogeneity in “flow

betas,” or the loadings of the funds’ flows on the common flow factors.

Panel D of Table 2 summarizes the R-squares for the pooled sample of funds, regressed

on the overall common factors extracted using the Goyal et al (2008) technique. The results for

quarterly and annual flows are similar. Using one factor the average R-squared is 9.9% and with six

factors it is 32.4%. The interquartile range with six factors covers 39.8%-60.3%, and more than 5% of

the funds have an adjusted R-squared of 90% or greater with six factors in annual data. Thus, the

common factors in flows are important and the relative importance of common factors differs

substantially across funds.

3.4 Economic Variables, Financial Market Variables and Flow Factors

In this section we examine the relation between fund flow factors and

contemporaneous values of macroeconomic and financial market variables. There may be common

factors in mutual fund flows because many investors are affected by the state of the macroeconomy

and business conditions in similar ways, or because investors respond to financial market information

in similar ways. We examine measures of the macroeconomy, financial markets and investor

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sentiment. The macroeconomic variables include the growth of personal disposable income,

industrial production, inflation and an index of the relative value of the US dollar against major

trading partners. The financial market variables include stock market volatility, the excess returns of

stocks over bonds, a short-term Treasury bill rate, yield spreads of AAA corporate bonds over

Treasuries, of BAA over AAA bonds, and the difference between the value-weighted dividend yield

and the yield on a 10-year US Treasury Bond. Details about these data are provided in the Appendix,

tables A.1 and A.3.

Goetzmann et al (2008) extract factors from daily flow data over an 18-month sample,

1998-1999 and argue that "behavioral" factors reflecting investor sentiment are important in mutual

fund flows. To investigate this directly we include the index of investor sentiment from Baker and

Wurgler (2006) as an explanatory variable. We also include the change in the Michigan consumer

confidence index.

Table 3 presents simple correlations of the annual first common flow factors from each

sector, and the first overall factor, on contemporaneous values of economic and financial variables.

We find that the first factor in percentage equity fund flows is positively related to the change in the

Michigan sentiment index, the value of the US dollar and industrial production growth, and

negatively related to stock market volatility. The first bond flow factor is positively related to the slope

of the term structure and stock market volatility, but negatively correlated with the level of the short-

term Treasury rate. The correlations to market volatility and sentiment make sense as a “flight to

quality” phenomenon. When the stock market is volatile and sentiment is pessimistic investors

reduce equity fund purchases and increase bond fund purchases. Bonds earn higher average returns

when the slope of the term structure is steep, so the correlation with term spreads is consistent with

bond fund flows systematically chasing the higher expected returns.

The first money market flow factor is positively related to the value of the dollar, the

credit spread and the yield on BAA corporate bonds, and negatively related to consumer confidence,

inflation, and industrial production growth. These correlations generally make intuitive sense.

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Investor flows into money market funds are high when consumer sentiment is pessimistic, real output

is down and interest rates are high. The opposite signs of the correlations for money market and

equity fund flows reflect the fact that flows cross between stock, bond and money markets. At the

same time, the value of the US dollar is positively related to stock and money fund flows, indicating

common factors that work in the same direction across the sectors.

Common factors spanning the sectors should be captured in the overall common flow

factors. Column D of Table 3 presents the correlations of the first overall common factor and finds

strong correlations with the macroeconomic and financial market variables. Industrial output, the

value of the US dollar, financial market yields and stock market volatility all present significant and

often strong correlations.

Table 4 presents the results of multiple regressions for the common factors on

contemporaneous values of the explanatory variables. Panels A-C present results for the equity, bond

and money market flow factors and panel D presents regressions for the overall common factors.

Four regression models are presented in each case: one isolates the macroeconomic variables and a

second brings in the measures of consumer confidence and sentiment. A third isolates the financial

market variables and a fourth model combines the variables.

Significant fractions of the variance in the sector flow factors are related to the

macroeconomic variables. Previous studies have a hard time associating much of the variance in stock

returns to macroeconomic variables (e.g., Roll 1988). In contrast, Panel A of Table 4 shows that the

macro variables produce an adjusted R-square of 22% for the first equity fund flow factor in annual

data. The financial market variables do not dominate the macro variables in the annual regressions,

and both sets of variables contribute significantly to the explained variance of the combined model.

In quarterly flows the macroeconomic variables deliver smaller R-squares, which could be related to

the larger measurement errors in quarterly macro data, and the financial market variables provide

most of the explanatory power at the quarterly frequency. The combined regression models produce

adjusted R-squares near 40% for the first equity factor at either frequency. The R-squares are slightly

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higher for the third factor (not tabulated), which seems to be more strongly related to the financial

market variables. The R-squares are generally smaller for higher ordered factors.

The explanatory variables are correlated (their correlations are displayed in the

Appendix Table A.3), so the t-ratios of the multiple regressions help discover which variables survive

on a partial correlation basis. Stock market volatility and the credit spread emerge as important

variables for annual equity fund flows. The BW sentiment index, stock market returns, inflation and

the dividend yield spread also survive in quarterly data, but the signs on sentiment and the dividend

yield spread are counterintuitive in the quarterly data.

The multiple regressions for the bond fund flows are summarized in Panel B of Table 4.

Because of the shorter sample period (1991-2009) we present multiple regressions for the quarterly

flows only, and present results for the first two factors. The adjusted R-squares of the combined

models exceed 37% for the first factor and 64% for the second factor. The first quarterly bond fund

flow factor bears little relation to the macro variables or sentiment with the exception of inflation and

the exchange rate, and appears to be largely driven by interest rate spreads. The second factor in

contrast is significantly related to the BW investor sentiment index (with a negative sign) as well as

financial market variables including stock market volatility and the dividend yield spread.

Panel C of Table 4 presents the regressions for the first two money market fund sector

flow factors, again using quarterly data. The full models have the smallest R-squares of the three

sectors, but are still significant at almost 30% for the first factor. The first factor is mainly driven by

financial market variables, with little relation to the macro variables. The first factor is positively

related to stock market volatility and negatively-related to sentiment, contemporaneous stock market

returns and the dividend yield spread. The second factor, however, is positively related to industrial

production growth. Panel D of Table 4 examines regressions for the overall common factors that

combine the three fund sectors. Again only quarterly data are used. Both the macro and financial

market variables capture significant fractions of the flow variance, but the financial variables

dominate. The financial market yields, inflation, exchange rates and the BW sentiment index (again,

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with a negative sign) show the strongest relations. The combined models’ R-squares exceed 65% for

the firstfactor, but only reach 18% for the second factor. Thus, the common factors extracted from

mutual fund flows are strongly related to economic conditions.

3.5 Predicting Flow Factors

Several previous studies examine the predictability of mutual fund flows, but do not

break the flows down into their systematic and idiosyncratic parts. Table 5 presents the first eight

autocorrelations of the first common flow factors; Panel A with annual data and Panel B with

quarterly data. To ensure that the factor extraction itself induces no look-ahead bias we use factors

extracted with the rolling method in all of the subsequent analysis in Section 3. The table shows that

the common factors have interesting autocorrelation structure. In annual data, the first order

autocorrelations of the first factor are 0.73 for equity fund flows, 0.43 for bond funds and almost 0.80

for the overall common factor. The first money fund flow factors show much smaller autocorrelation.

Higher ordered factors also have high autocorrelations. There seems to be a lot of persistence in

percentage flow factors. In some cases an AR(1) with a positive coefficient might be a good

approximation, but in others the autocorrelation structure appears more complex, with sign switches

over the periodogram. The quarterly data presents even larger autocorrelations in many cases. This

rich autocorrelation structure indicates significant predictability based on lagged flows.

While the autocorrelations of the flow factors are substantial, the largest value in the

table is less than 0.92. This suggests that the lagged flows may be used as predictors in regressions,

reported below, without undue concerns about spurious regression bias. Ferson, Sarkissian and

Simin (2003) find that these issues arise mainly with autocorrelations larger than 0.95.

Table 6 presents regressions that attempt to predict the first common flow factors using

lagged predictor variables. The predictor variables include the own-lagged flow factors and the

lagged values of all the variables that were measured contemporaneously in Table 4, and we

summarize the results with time-series regressions over the full sample period. Four regressions

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models are presented, similar to Table 4.

Panel A of Table 6 presents the regressions for equity fund flows, both annual and

quarterly data. The results for the annual regressions are stronger. The regressions suggest

predictability in the flows related to lagged macro variables (mainly, the exchange rate and disposable

income growth) and financial market variables (mainly, market volatility and interest rates). There is

little predictive relation using the lagged investor sentiment indexes. The adjusted R-squares of the

combined models are about 25% both in the annual and the quarterly data. Thus, the common

components of equity mutual fund flows are characterized by substantial predictability over time,

much of it attributed to the relationships with macro and financial conditions.

Ferson and Warther (1996) find that the first differences of aggregate monthly flows

into equity mutual funds may be predicted during 1968-1990 using lagged short term interest rates

and dividend yields, but they do not include macro variables or other lagged flows in the models. We

find significant t-statistics for the annual equity fund flow on the lagged market volatility index and

the lagged term slope, but not on the lagged dividend yield, and the adjusted R-squares of the model

isolating financial market variables is 26% in annual data. In quarterly data only market returns

appear as significant predictors in the model isolating financial market variables, and the adjusted R-

squared of this model is only 11%. However, none of the financial market variables, excepting the

exchange rate, remain significant in the combined model that includes the lagged flows in the

quarterly data.

Panel B presents the predictability regressions for bond funds, using quarterly data

beginning in 1992. Like in the equity funds in quarterly data, lagged flows are main predictors. The

combined model does feature significant t-ratios on the consumer sentiment and the credit spread.

The combined model’s adjusted R-squared is 64%.

Panel C presents the regressions for quarterly money fund flows, where the combined

model produces a smaller adjusted R-square of 13%. The market return survives with a t-ratio of -1.7.

Unlike the case of equity fund flows and bond fund flows and consistent with the relatively low

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autocorrelations in Table 5, the lagged money fund flows do not deliver much predictive power in the

combined model.

Panel D summarizes the regressions for the first overall common factor. The

predictability appears substantial, with an adjusted R-square of 82% in the combined quarterly model

and significant coefficients for BW sentiment, exchange rate, industry production growth, interest rate

spreads, and especially the lagged flows. Thus, the future values of the common factors in mutual

fund flows are persistent and significantly predictable based on current economic conditions.

The significant predictability in common flow factors has a number of implications. To

the extent that aggregate investor behavior as reflected in fund flows can be predicted, this behavior

can be anticipated by policy makers as a function of economic conditions and recent flows. This

might be useful in planning the deployment of regulatory and supervisory resources, for example.

For the mutual fund industry and individual funds, the ability to predict future sales should be useful

for planning marketing strategies, managing cash inventories and forming investment strategy.

Research on financial market efficiency can exploit predictability, as for example, market prices

should respond differently to the expected and unexpected components of fund flows. Finally, the

predictability in common flow factors informs our empirical specifications in the analysis below.

3.6 The Predictive Content of Flows

While the predictability of common flow factors is interesting, the flip side of that

question is also interesting. Is there information in fund flows that is predictive for future economic

and financial market conditions? Table 7 examines whether the first factors can forecast the

macroeconomic and financial variables. We regress the macroeconomc and financial market

variables on their own lagged values and on the lagged flow factors. Panels A, B, C and D use a single

lagged sector flow factor on the right had side, Panel E uses the three sector flows together and Panel

F uses the overall common flow factor. The table reports the coefficient on the lagged flow, its

Newey-West (1980) standard error (using 3 lags for annual data and 6 lags for quarterly data), and the

17

adjusted R-squares of the multiple regressions. These R-squares are sometimes quite high when the

dependent variable is a highly persistent yield or yield spread, so our main interest is the coefficient

and standard error of the lagged flow factor, indicating the marginal predictive ability of the flow for

the economic variable’s AR(1) residuals.

Table 7 suggests that lagged flow factors bear a predictive relation to several of the

variables. In particular, equity and bond fund flow factors predict innovations in the Michigan

sentiment index. There is also significant predictive ability for industrial production growth,

exchange rates, some interest rate spreads, and market volatility. These results suggest that investors,

as reflected in the aggregate flows, may not simply be irrationally chasing the past (performance) as

some authors have believed (e.g., Sapp and Tiwari (2004) and Frazzini and Lamont (2006)). Their

behavior is actually predictive of future economic and financial market conditions.

3.7 Models of Flow Betas

Individual funds' “unconditional” loadings on the common factors have large cross-

sectional variation. For example, the average beta of annual equity fund flows on the first common

factor is about 0.95, but the standard deviation is higher than 3.4. More than 65% of individual funds’

have positive flow betas on the first factor, half of which are significant at the 5% significance level.

As the common factors in fund flows are important, the cross-sectional variation motivates a deeper

analysis of the structure of funds’ flow betas.

We estimate models that allow the flow betas to vary over time and with fund

characteristics. Specifically, using panel data, we estimate:

Fit = ai + G'Xit-1 + Σj (boj + Bj Xit-1) Yjt + uit, (3)

where (boj + Bj Xit-1) is the linear approximation for fund i's flow beta as a function of its predetermined

characteristics, Xit-1 and uit is a regression error. This is similar to the models for equity returns

18

discussed in Rosenberg and Marathe (1979) and Ferson and Harvey (1997). For fund characteristics,

we use fund age, size, the fund family size, the fund’s monthly return volatility over the past two

years, the lagged fund flow and expense ratios as the characteristics. The lagged performance is

measured as a fractional ranking (a number between zero and 1.0) of the average return over the past

year. We also include year or/and fund dummies, considering that uit may include time and fund

fixed effects.

The regression estimates, standard errors and p-values for equity fund flows are

presented in Table 8. The regression models shown in panels (A) through (D) differ in terms of fixed

effects and a focus on retail versus institutional share classes. The coefficients, Bj, on the

characteristics interacted with the flow factors describe the flow betas and the same characteristics

variables appear in the intercept, in the G'Xit-1 term. We include six equity fund flow factors in the

regression but present only the coefficients for the first factor in the table. The G coefficients, shown in

the bottom part of the table, describe relations between fund flows and these characteristics, similar to

what has been documented in previous studies. Previous studies find that young, small, more

expensive and less volatile funds, and funds in larger families, attract more flows other things equal.

Lagged performance enters the flow regression positively and sometimes nonlinearly, although the

coefficient on the squared performance changes with the specification.

There is strong evidence that for retail share classes, flow betas are functions of the

lagged fund characteristics and are time-varying with the funds’ recent performance. The regressions

in Table 8 also show that for retail share classes, young funds, expensive funds and funds with higher

recent flows are more sensitive to the first common flow factor. In particular, flow betas are positive

functions of the lagged performance. Since the flow betas on the first factor roughly represent the

marginal market share of a fund in the sector flows, the coefficients on the squared performance

suggest that some of the nonlinearity in the relation of funds’ flows to past performance is captured in

the flow beta or market share.

A striking finding in Table 8 is the difference between the results for institutional retail

19

share classes. We find virtually no evidence that the flow betas for institutional share classes are

functions of the lagged characteristics or recent performance. There is some relation to lagged

performance in the intercept term. The R-squares also show that the regressions explain less of the

variance of flows for the institutional share classes. To the extent that institutional flows are driven

by defined-contribution retirement accounts, these flows are likely to vary less with economic

conditions, and it makes sense that the response to aggregate flows are insensitive to short term

changes in fund performance or characteristics.

We also find evidence that flow betas for retail share classes are asymmetric, differing

when the aggregate flow is positive or negative. The models allowing for asymmetry are presented

in Table 9. Here we use a piece-wise estimation around zero value of the common flow factor. We

find that the difference between the coefficient estimates on the positive and the negative flow factor

is significant for retail share classes. The effects are interesting, and are illustrated in Figure 5. Here

we graph the fitted fund flow against the aggregate flow factor for retail funds with performance in

the top 25% and bottom 25% of the lagged performance figures. The other variables in the regression

that interact with the flow factor are set equal to their sample means and the variables in the intercept

terms are ignored. The flow betas for the low-performance funds are positive in both regions, but

with smaller slopes when the aggregate flow is positive. Thus, when the aggregate flow is positive

the poorly performing funds get a smaller marginal market share than their share of the loss when the

aggregate flow is negative. The flow betas of the high-performance funds actually change sign,

turning negative when the aggregate flow is negative. Thus, the relations between the fitted and

aggregate flows appear option-like. The high-performing funds appear to be long a straddle on the

aggregate flows, so their expected flows would be enhanced when the aggregate flow is more volatile.

The low-performance funds have flows that appear to be short a put option on the aggregate: when

the aggregate flow is negative they take the brunt of the loss in market share.

4. Applications

20

Using our models of funds’ flow betas and the implied decomposition of fund flows into common

factor and idiosyncratic components, we pursue three applications. First we explore the relation

between flow betas and subsequent fund performance. Then, we revisit the well known flow-

performance relation and the so-called smart money effect.

4.1 Fund Flow Betas and Fund Performance

We conjecture that funds with larger flow betas might deliver relatively poor

performance. Such funds have more pressure to sell their holdings when other funds are selling, and

may realize depressed selling prices at such times. Edelin (1999) finds evidence that equity fund

trades made in response to flows are less profitable than are discretionary trades. The price effect

should be more pronounced relative to the systematic component of flows.

Table 10 summarizes an exercise where we sort equity mutual funds each quarter

according to estimates of their flow betas and examine the subsequent performance of the funds. The

table reports percentage monthly excess returns over the Treasury Bill rate and various alphas for

portfolios of funds formed based on their flow betas on the first common factor for equity mutual

fund flows. At the end of each quarter, t, from 1984 Q3 to 2009 Q3, flow betas on the first factor are

estimated by rolling panel regressions using the data up to that quarter. The factors are estimated

using principal components analysis and data up to the quarter t. The coefficient estimates from the

panel regression, and the fund characteristics in the quarter t, are used to estimate betas on the first

factor for quarter t. Funds are ranked and grouped into five portfolios from low to high according to

the beta estimates. The portfolios of funds are equally-weighted in Panel (A) and TNA-weighted in

Panel (B). The portfolios are rebalanced and the whole procedure is rolled forward every quarter. We

examine the monthly returns on the portfolios in the following quarter following portfolio formation.

Using the time series of returns for the five quintile portfolios we estimate the performance of the

portfolios as the average excess returns over the risk-free rate, the CAPM alpha, the Fama-French

three-factor alpha or the Carhart four-factor alpha. Table 10 reports the estimates, their standard

21

errors and p-values. High - Low is the high flow beta minus the low beta portfolio. The sample

period is from 1982 to 2009 and the first panel regression uses data up to 1983 Q3. The standard errors

are Newey-West estimates with 4 lags.

The first panel of Table 10 shows that high flow-beta funds earn lower average returns

than low flow-beta funds. When the flow betas from Table 8 are used the difference in raw returns is

only 1.4 basis points per month and is not significant. The differences in the alphas are larger, as

much as 13 basis point for the CAPM alphas, but are not significant. However, Table 9 shows that

flow betas are asymmetric and when we allow for asymmetries the effects are stronger. The next

three panels allow for different flow beta functions on three factors, corresponding to aggregate flows

greater than or less than about one standard deviation of the aggregate flow factor. (The flow values

are greater than 0.01 or less than 0.007.) We include a third factor for aggregate flows in between

those tail areas. This exercise reveals that the poor relative performance of high flow-beta funds is

concentrated using the low-aggregate-flow betas. Here the difference between the low and high flow-

beta funds is 24 basis points, which significant at the 10% level. The CAPM and FF3 alpha difference

are larger and significant at the 2% levels. Controlling for Momentum with the Carhart four-factor

model, however, the 17 basis point difference in alphas is not statistically significant. In Panel B the

TNA-weighted portfolios produce similar results.6

4.2 The Flow-Performance Relation

We use the fitted values from the panel regressions in Tables 8 and 9 to decompose the

flows for a given US equity mutual fund into two components. The systematic flow is the fitted flow

beta, (boj + Bj Xit-1) from equation (3), multiplied by the common flow factor, Yjt and summed across the

six common equity flow factors. The idiosyncratic flow is the total net percentage flow for fund i

6 We have also examined annual flows and flow factors with annually rebalanced fund portfolios, where the first panel regression uses data for 1982-1991 and the results are evaluated during 1992-2009. Using the flow betas from Table 8 the raw return difference between low and high flow-beta funds is 14 basis points per month and the CAPM and FF3 alphas are significant at the 5% level for TNA weighted portfolios. The difference are smaller for the equally-weighted portfolios and none of the other differences are significant.

22

minus the common factor part.

We revisit the classical flow-performance relationship documented in the literature

using the two components of flows. Our goal is to distinguish between the responses of idiosyncratic

flows and systematic flows to past performance. Given that most of the literature looks at retail

investors' money flows into equity mutual funds, we restrict our analysis to equity fund flows. We

also look separately at institutional and retail share classes.

We find, but do not report in the tables, that the two components of fund flows appear to

respond differently to past fund performance. Both components are positively related to lagged

performance but the coefficient for the common part is about three times as large on average. The

common part of flows has a weak negative relation to the squared past performance, while the

idiosyncratic part has a positive relation on average. Furthermore, the relation of the idiosyncratic

part of flows to lagged performance and the other control variables is relatively stable in subsamples,

whereas the common factor component presents less stable relations. Kim (2011) finds that the flow

performance relation changes around the year 2000 from a convex relation in the earlier years to a

linear or even concave relation after 2000. Our results suggest that it is the common factor component

of flows driving these changes, while the relation of the idiosyncratic part of flows to past

performance remains convex and stable during the sample. Thus, the decomposition into common

and idiosyncratic flow factors helps to dissect the dynamics of the flow performance relation.

4.3 The Smart Money Effect

Gruber (1996) and Zheng (1999) find that funds with money inflows subsequently

perform better during the next quarter than funds with outflows. Sapp and Tiwari (2004) confirm

these findings, but note that the differences are not significant when adjusted for Momentum using

the Carhart four-factor model. We replicate these exercises with our data and find similar results.

The smart money effect is stronger when the portfolios weighted according to fund flows are

rebalanced quarterly than when held for a year. However, when we use the two components of fund

23

flows we find that the smart money effect, to the extent that it exists, is concentrated in the common

factor part of funds’ flows. We find little relation using the idiosyncratic flows. This reinforces the

interpretation that the smart money effect has less to do with investors picking out idiosyncratically

good funds, and more with systematic factors such as momentum.

5. Conclusions

The determinants of the flows of money into mutual funds are important to understand, as mutual

funds are significant in consumer savings, and as a window into individuals' investment decisions,

fund manager's incentives and the efficiency of financial markets. This paper explores mutual fund

flows, decomposing the flows into their common factors and idiosyncratic components, and modeling

funds’ “flow betas,” or the sensitivity of their flows to common flow factors.

The systematic components of fund flows capture significant fractions of the variation

in individual fund flows over time. Unlike asset market prices, which the finance literature finds

difficult to explain, the common factors in mutual fund flows respond strongly to macroeconomic

conditions. The common flow factors are also predictable, displaying significant and complex

autocorrelation structure and relations to lagged macroeconomic and financial market variables.

Lagged flows also bear a predictive relation to future economic conditions, suggesting that in the

aggregate fund investors do not simply chase the past (performance), but look to the future in their

investment decisions.

There is substantial variation across individual mutual funds in the sensitivity of their

flows to the common flow factors. These flow betas may be roughly interpreted as the marginal

market share of new sector flows that a fund receives. We find that flow betas can be modeled as

functions of the characteristics of a fund such as its size, age, expense ratio and recent return

performance. These functions are asymmetric. High-performing funds have lower or even negative

flow betas when the aggregate flow is negative. Thus, when flows are strong, high performing funds

increase their market share and when there are negative sector flows, funds with weaker recent return

24

performance lose the most market share.

Equity funds with higher flow betas on large sector outflows offer lower subsequent

performance. Such funds have to sell assets when other funds in the sector are selling. This adds a

new dimension to the “fire sales” phenomenon studied by Coval and Stafford (2007), who examined

the individual stocks held by funds experiencing large negative total flows.

Studying the common and idiosyncratic components of funds’ flows refines our

understanding of other stylized facts in the mutual fund literature. One is the “flow-performance”

relation documented by Ippolitto (1992), Sirri and Tufano (1998) and Chevalier and Ellison (1997).

Here we find that common and idiosyncratic flows behave differently in flow-performance

regressions, and these differences are related to changes in the overall relation over time. A second

application is the "smart money" effect of Gruber (1996), who finds that new money flows into US

equity mutual funds earn higher returns than existing shareholders. We find that this effect is

concentrated in the common factor component of fund flows. We believe that future research

comparing common and idiosyncratic fund flows should lead to further significant refinements of our

understanding.

25

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Table 1. Seasonality in quarterly fund flows and common factor correlations

(A) Distributions of adjusted R2 of time-series OLS regressions of individual quarterly fund flows on quarterly dummies

Sector N mean std p1 p5 p25 p50 p75 p95 p99

equity 3303 0.071 0.330 -0.923 -0.305 -0.049 0.024 0.182 0.638 0.950

bond 1722 0.058 0.322 -1.033 -0.287 -0.041 0.029 0.162 0.553 0.881

money market 757 0.137 0.266 -0.423 -0.106 -0.001 0.068 0.208 0.694 0.944

(B) Quarterly mean flows

Sector N Q1 (std err) Q2 (std err) Q3 (std err) Q4 (std err)

Equity 3303 0.025 (0.061) 0.029 (0.060) 0.019 (0.059) 0.015 (0.058)

Bond 1722 0.030 (0.075) 0.028 (0.074) 0.033 (0.072) 0.020 (0.071)

money market 757 0.027 (0.052) -0.005 (0.050) 0.016 (0.051) 0.034 (0.052)

(C) Correlations among the first factors

Annual quarterly

equity Bond Money Goyal et al equity bond money Goyal et al

Equity 1 equity 1

Bond 0.075 1 bond 0.321 1

(0.767) (0.007)

Money 0.132 -0.192 1 money 0.221 0.006 1

(0.601) (0.446) (0.068) (0.963)

Combined sectors

0.724 -0.173 0.336 1 Combined sectors

0.729 0.003 0.431 1

(0.001) (0.493) (0.173) (<.0001) (0.978) (0.000)

*Note: The dependent variables in Panel (A) are the quarterly percentage net money flows into individual funds that have at least 5 million dollars of assets under management at the beginning of the period and are at least one-year old. The independent variables are four quarterly dummies (without the intercept). The table reports sample means, standard deviations and percentiles of the adjusted R squares. "pn" is the value above which (100-n) percent of the estimates lie, where n is the number of funds. Panel (B) reports the average of individual-fund coefficients on the dummy variables and the average standard errors. Panel (C) reports sample correlations of the first flow factors for the different sectors. The quarterly sample period is from 1980 Q1 to 2009 Q4 for US equity funds and from 1991 Q1 to 2009 Q4 for US bond funds and US money market funds.

29

Table 2. Distributions of adjusted R2 of time-series regressions of individual fund flows on common factors.

(A) equity funds

factors up to mean Std p1 p5 p25 p50 p75 p95 p99

annual f1 0.105 0.369 -0.976 -0.468 -0.095 0.036 0.331 0.769 0.953

f2 0.250 0.404 -0.887 -0.336 -0.014 0.239 0.529 0.897 0.989

f3 0.335 0.426 -0.974 -0.324 0.071 0.360 0.654 0.933 0.994

f4 0.372 0.451 -1.124 -0.342 0.130 0.421 0.693 0.956 0.997

f6 0.427 0.477 -1.254 -0.403 0.215 0.524 0.772 0.958 0.994

f10 0.558 0.425 -1.028 -0.213 0.400 0.669 0.841 0.983 1.000

quarterly f1 0.080 0.186 -0.245 -0.138 -0.034 0.019 0.170 0.456 0.656

f2 0.188 0.274 -0.734 -0.187 0.014 0.159 0.362 0.666 0.825

f3 0.207 0.402 -2.098 -0.245 0.043 0.212 0.431 0.739 0.875

f4 0.255 0.383 -1.003 -0.266 0.068 0.262 0.492 0.785 0.896

f6 0.296 0.382 -1.038 -0.290 0.101 0.320 0.542 0.817 0.914

f10 0.379 0.396 -1.071 -0.201 0.178 0.428 0.642 0.874 0.965

(B) bond funds

factors up to mean Std p1 p5 p25 p50 p75 p95 p99

annual f1 0.106 0.347 -0.924 -0.401 -0.073 0.023 0.311 0.772 0.990

f2 0.198 0.454 -1.324 -0.545 -0.075 0.175 0.514 0.902 0.988

f3 0.279 0.478 -1.430 -0.410 -0.017 0.314 0.644 0.931 0.994

f4 0.346 0.444 -0.862 -0.389 0.045 0.397 0.711 0.942 0.998

f6 0.439 0.475 -1.085 -0.427 0.216 0.543 0.794 0.963 0.998

f10 0.532 0.503 -1.197 -0.384 0.351 0.689 0.865 0.973 0.999

quarterly f1 0.122 0.203 -0.192 -0.087 -0.014 0.044 0.214 0.575 0.765

f2 0.199 0.247 -0.405 -0.113 0.023 0.154 0.361 0.655 0.825

f3 0.240 0.282 -0.520 -0.148 0.049 0.219 0.439 0.709 0.883

f4 0.273 0.307 -0.498 -0.159 0.080 0.265 0.479 0.749 0.909

f6 0.329 0.327 -0.684 -0.112 0.131 0.336 0.554 0.803 0.966

f10 0.379 0.352 -0.731 -0.087 0.196 0.399 0.616 0.844 0.956

30

(C) money market funds

factors up to mean Std p1 p5 p25 p50 p75 p95 p99

annual f1 0.097 0.262 -0.697 -0.184 -0.059 0.025 0.237 0.608 0.872

f2 0.192 0.328 -0.684 -0.235 -0.026 0.166 0.402 0.762 0.944

f3 0.223 0.365 -0.789 -0.248 -0.007 0.242 0.464 0.774 0.950

f4 0.263 0.372 -0.580 -0.285 0.002 0.269 0.547 0.868 0.949

f6 0.318 0.437 -0.974 -0.411 0.049 0.377 0.638 0.907 0.972

f10 0.442 0.488 -1.156 -0.570 0.199 0.576 0.823 0.961 0.997

quarterly f1 0.083 0.143 -0.196 -0.043 -0.007 0.039 0.127 0.366 0.658

f2 0.120 0.171 -0.207 -0.049 0.008 0.081 0.190 0.463 0.670

f3 0.144 0.218 -0.237 -0.049 0.022 0.101 0.236 0.546 0.835

f4 0.149 0.213 -0.301 -0.061 0.028 0.113 0.258 0.510 0.724

f6 0.182 0.236 -0.285 -0.081 0.050 0.155 0.301 0.568 0.877

f10 0.225 0.230 -0.488 -0.075 0.090 0.204 0.369 0.602 0.815

(D) All funds

factors up to mean Std p1 p5 p25 p50 p75 p95 p99

annual f1 0.099 0.330 -0.933 -0.327 -0.081 0.028 0.280 0.723 0.975

f2 0.150 0.391 -0.961 -0.446 -0.089 0.119 0.398 0.805 0.983

f3 0.214 0.446 -1.156 -0.453 -0.059 0.206 0.537 0.880 0.995

f4 0.258 0.456 -1.317 -0.499 0.013 0.290 0.585 0.903 0.987

f6 0.324 0.516 -1.456 -0.488 0.074 0.414 0.677 0.923 0.996

f10 0.455 0.525 -1.444 -0.540 0.263 0.609 0.813 0.958 0.995

quarterly f1 0.093 0.275 -0.892 -0.200 -0.017 0.033 0.180 0.623 0.977

f2 0.147 0.244 -0.457 -0.133 0.002 0.099 0.269 0.597 0.874

f3 0.185 0.269 -0.519 -0.141 0.022 0.145 0.333 0.657 0.899

f4 0.210 0.298 -0.701 -0.157 0.039 0.182 0.385 0.692 0.914

f6 0.255 0.311 -0.616 -0.178 0.061 0.237 0.459 0.757 0.918

f10 0.299 0.353 -0.786 -0.150 0.096 0.301 0.526 0.799 0.950

*Note: The dependent variable is the percentage net flows to individual funds. The table reports the means, standard deviations, and percentiles of the adjusted R squares. The notation pn denotes the R-squared value above which (100-pn)% of the funds’ Rquares lie. The sample period is from 1980 Q1 to 2009 Q4 for US equity funds and from 1991 Q1 to 2009 Q4 for US bond funds and US money market funds.

31

Table 3. Correlations of the first common factors with macroeconomic and financial market variables in annual data

(A) equity funds (B) bond funds (C) money market (D) Goyal et al (2008)

ρ p value ρ p value ρ p value ρ p value

∆Michigan sentiment 0.39 0.04 0.25 0.32 -0.44 0.07 0.27 0.28

BW sentiment -0.11 0.58 -0.17 0.54 0.23 0.41 0.04 0.88

Inflation -0.04 0.84 -0.27 0.28 -0.50 0.03 -0.06 0.82

Exchange 0.39 0.04 -0.11 0.66 0.53 0.02 0.62 0.01

industrial production growth 0.31 0.10 -0.08 0.76 -0.50 0.03 0.48 0.04

disposable income growth 0.03 0.87 -0.09 0.72 -0.24 0.33 0.31 0.22

TBill 0.11 0.57 -0.71 0.00 0.07 0.78 0.59 0.01

AAA 0.23 0.23 -0.12 0.64 0.13 0.62 0.61 0.01

BAA 0.17 0.38 0.00 0.99 0.54 0.02 0.45 0.06

AAA – Tbill 0.20 0.31 0.80 0.00 0.00 1.00 -0.31 0.21

BAA – AAA -0.22 0.25 0.22 0.39 0.62 0.01 -0.40 0.10

market return 0.30 0.12 -0.25 0.32 -0.38 0.12 0.42 0.08

market volatility -0.45 0.01 0.46 0.05 0.38 0.12 -0.44 0.07

market return – Tbill 0.28 0.14 -0.18 0.46 -0.40 0.10 0.38 0.12

D/P - Treasury10year -0.29 0.13 0.42 0.08 -0.10 0.69 -0.68 0.00

D/P 0.20 0.31 0.02 0.94 0.35 0.16 -0.08 0.76

*Note: The sample correlation between the first common factors and the macroeconomic and financial variables are denoted as ρ. The p-values are computed using the t-distribution with (T-2) degree of freedom for the statistic (T-2)1/2 ([(ρ2)/(1-ρ2)])1/2 where T is the number of time periods. The factors are extracted using asymptotic principal components analysis on fund flows. Panel (D) uses the Goyal et al (2008) method. The Michigan sentiment index is the consumer confidence index from the University of Michigan, and ∆Michigan sentiment is the change in the log of the index. BW sentiment is the variable constructed in Baker and Wurgler (2006). Inflation is the change in log of the consumer price index. Exchange rate is the change in log of the major foreign exchange index. Industrial production growth is the change in log of the index from Federal Reserve Bank of St. Louis Economic data (FRED). Disposable income growth is the change in log of disposable personal income per capita from FRED. Market volatility and return are the standard deviation and the return on S&P500 index respectively, which are obtained using its daily data. D/P ratio is the dividend to price ratio of the value weighed CRSP index. TBill is the yield on the 3-month Treasury bill. Treasury10year is the yield on the 10-year Treasury bond. The sample period is annual, from 1981 to 2009 for US equity funds and from 1992 to 2009 for US bond funds and US money market funds.

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Table 4. Regressions of Common Factors on Macroeconomic and Financial Market Variables

(A) Equity fund sector: first flow factor

f1 (annual) f1 (quarterly)

model1 model2 model3 model4 model1 model2 model3 model4

∆Michigan Sentim. 0.166 0.043 0.027 -0.007

(2.107) (0.386) (1.909) (-0.524) BW sentiment -0.025 -0.014 -0.001 -0.004

(-1.782) (-0.833) (-0.482) (-2.244) Inflation -0.802 -0.993 -0.365 -0.075 -0.136 -0.446

(-1.592) (-1.521) (-0.225) (-0.397) (-0.649) (-2.144) Exchange rate 0.370 0.434 0.322 0.110 0.112 0.075

(2.445) (2.337) (1.638) (2.157) (1.746) (1.809) Disp income growth -1.074 -1.355 -0.962 0.070 -0.085 -0.159

(-1.420) (-1.857) (-0.869) (0.473) (-0.650) (-1.297) IP growth 0.586 0.129 0.165 0.014 0.017 0.016

(2.295) (0.633) (0.686) (1.596) (1.780) (1.419) Market volatility -6.179 -4.754 -0.596 -0.844

(-1.786) (-1.963) (-1.500) (-2.679) Mkt. – Tbill Ret. 0.074 0.088 0.031 0.035

(1.373) (1.370) (1.722) (2.011) BAA-AAA -0.031 -2.322 -0.349 -0.669

(-0.017) (-0.645) (-1.007) (-1.505) AAA-T bill 2.221 2.117 0.407 0.446

(1.960) (1.987) (2.256) (2.822) Dp ratio-T - 10yr -0.467 -0.299 -0.329 -0.469

(-1.051) (-0.157) (-3.941) (-3.523)

R2 0.332 0.472 0.438 0.656 0.054 0.089 0.389 0.465

adjusted R2 0.220 0.305 0.316 0.385 0.019 0.032 0.361 0.401

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(B) Bond fund sector: first two flow factors

f1 (quarterly ) f2 (quarterly)

model1 model2 model3 model4 model1 model2 model3 model4

∆Michigan Sentim. -0.026 -0.022 0.281 -0.090

(-1.153) (-1.128) (1.366) (-0.888) BW sentiment 0.001 0.000 -0.035 -0.032

(0.112) (-0.154) (-1.555) (-4.785) Inflation -0.129 -0.795 -0.579 4.335 3.513 1.090

(-0.475) (-1.920) (-1.731) (1.623) (1.912) (0.888) Exchange rate 0.055 0.150 0.176 0.725 0.649 0.282

(0.741) (1.528) (2.850) (1.903) (2.007) (1.145) Disp income growth -0.083 -0.240 -0.186 2.257 1.274 0.347

(-0.452) (-1.072) (-0.866) (1.653) (0.969) (0.670) IP growth 0.005 0.007 0.004 0.021 -0.065 0.004

(0.351) (0.394) (0.225) (0.115) (-0.515) (0.050) Market volatility 0.886 0.877 -8.048 -6.111

(1.706) (1.718) (-3.845) (-3.183) Mkt – Tbill return 0.004 0.004 0.303 0.462

(0.200) (0.155) (2.171) (5.041) BAA-AAA -1.407 1.151 -3.224 -12.002

(-2.740) (0.928) (-1.110) (-4.468) AAA-T bill 0.657 0.567 0.315 0.642

(3.036) (2.455) (0.450) (1.334) Dp ratio-T - 10yr -0.085 -0.175 -3.448 -3.362

(-0.448) (-0.437) (-4.136) (-3.450) R2 0.022 0.114 0.334 0.488 0.115 0.165 0.774 0.708

adjusted R2 -0.040 0.014 0.281 0.371 0.060 0.071 0.756 0.642

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(C) Money market sector: first two flow factors

f1 (quarterly ) f2 (quarterly)

model1 mode;2 model3 model4 model1 model2 model3 model4

∆Michigan Sentim. -0.056 -0.027 0.213 0.263

(-1.575) (-0.821) (1.121) (1.149) BW sentiment 0.004 -0.009 0.024 -0.019

(0.806) (-1.978) (1.510) (-1.176) Inflation -0.171 -0.795 -0.782 -0.241 -2.020 -1.931

(-0.649) (-1.915) (-1.880) (-0.121) (-0.727) (-0.605) Exchange rate 0.182 0.157 -0.011 -0.465 -0.024 -0.473

(1.707) (2.214) (-0.159) (-0.997) (-0.058) (-0.954) Disp income growth -0.140 -0.020 -0.245 5.613 1.584 0.766

(-0.406) (-0.093) (-1.559) (1.802) (1.120) (0.556) IP growth -0.012 -0.004 -0.037 0.279 0.439 0.360

(-0.366) (-0.104) (-1.179) (1.577) (2.653) (2.417) Market volatility 0.755 0.932 5.254 3.996

(1.327) (1.855) (1.801) (1.234) Mkt – Tbill return -0.114 -0.111 0.059 -0.211

(-3.492) (-3.138) (0.431) (-1.941) BAA-AAA -0.309 -2.361 -11.206 -5.882

(-0.464) (-1.598) (-2.311) (-0.946) AAA-T bill -0.160 -0.148 -1.115 -1.056

(-0.802) (-0.830) (-1.727) (-2.175) Dp ratio-T - 10yr -0.632 -0.831 -1.369 -2.911

(-2.738) (-2.394) (-1.543) (-2.340) R2 0.073 0.123 0.376 0.429 0.209 0.154 0.250 0.289

adjusted R2 0.015 0.023 0.327 0.298 0.160 0.058 0.191 0.126

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(D) All sectors: first two overall common factors

f1 (quarterly ) f2 (quarterly)

model1 model2 model3 model4 model1 model2 model3 model4

∆Michigan Sentim. 0.013 -0.007 -0.190 -0.115

(1.336) (-1.134) (-1.376) (-0.907) BW sentiment 0.000 -0.003 0.005 -0.036

(0.068) (-3.292) (0.154) (-1.586) Inflation 0.095 -0.070 -0.228 -0.976 -4.056 -4.670

(0.613) (-0.491) (-2.140) (-0.436) (-1.954) (-2.166) Exchange rate 0.089 0.097 0.041 0.817 1.304 0.604

(3.256) (4.148) (2.198) (1.431) (1.963) (1.047) Disp income growth 0.224 0.092 -0.019 -3.320 -3.032 -3.907

(2.015) (1.013) (-0.478) (-1.774) (-1.267) (-1.886) IP growth 0.011 0.012 0.010 -0.127 0.057 -0.068

(1.211) (1.676) (1.677) (-0.672) (0.442) (-0.492) Market volatility -0.166 -0.236 0.577 0.047

(-0.731) (-1.689) (0.124) (0.011) Mkt – Tbill return 0.001 0.006 -0.295 -0.447

(0.120) (0.654) (-1.413) (-2.378) BAA-AAA -0.298 -0.986 7.915 -10.665

(-1.351) (-2.441) (1.510) (-1.023) AAA-T bill 0.000 0.020 -0.609 -0.739

(0.002) (0.346) (-0.272) (-0.380) Dp ratio-T - 10yr -0.368 -0.449 -0.362 -3.009

(-4.989) (-3.959) (-0.213) (-1.019) R2 0.139 0.181 0.686 0.719 0.131 0.167 0.165 0.332

adjusted R2 0.085 0.089 0.661 0.655 0.076 0.072 0.098 0.179

36

*Note: The independent variables are the common factors extracted using a principal components analysis on fund flows for a given sector. Panel (D) combines sectors using the Goyal et al (2008) method. The independent variables are the macro variables and financial variables as listed in the first column. ∆Michigan sentim is the change of the log of the Michigan sentiment index as surveyed by the University of Michigan. BW sentiment is the variable constructed in Baker and Wurgler (2006). Inflation is the change in log of the consumer price index. Exchange rate is the change in log of the major foreign exchange index. IP growth is the change in log of US industrial production. Disp income growth is the change in log of personal disposable income per capita. Market volatility and return are the standard deviation and the return on S&P500 index respectively, which are obtained using its daily data. d/p ratio is the dividend to price ratio of the value weighted CRSP index. T bill is the yield on the 3-month Treasury bill. 10yr is the yield on the 10-year Treasury bond. The tables report the coefficient estimates and their t-ratios, where the standard errors are Newey-West estimates with 2 lags for annual data and 5 lags for quarterly data. The sample includes US equity mutual funds, US bond funds, and US money market funds that have at least 5 million dollars of assets under management at the beginning of the periods and are at least one-year old. The sample period is from 1980 Q1 to 2009 Q4 for US equity funds and from 1991 Q1 to 2009 Q4 for US bond funds and US money market funds.

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Table 5. Autocorrelations of Common Flow Factors

(A) annual factors

lag1 Lag2 Lag3 lag4 lag5 lag6 lag7 lag8

Equity

factor 1 0.731 0.519 0.404 0.213 0.063 0.072 -0.131 -0.161

(0.000) (0.006) (0.041) (0.307) (0.770) (0.744) (0.560) (0.487)

factor 2 0.806 0.634 0.405 0.228 0.074 0.050 0.059 0.098

(0.000) (0.000) (0.040) (0.272) (0.733) (0.822) (0.793) (0.673)

factor 3 -0.246 -0.395 -0.556 -0.634 -0.579 -0.441 -0.199 0.154

(0.207) (0.041) (0.003) (0.001) (0.003) (0.035) (0.375) (0.505)

factor 4 0.558 0.146 -0.175 -0.275 -0.379 -0.404 -0.158 0.160

(0.002) (0.466) (0.393) (0.183) (0.068) (0.056) (0.484) (0.488)

Bond

factor 1 0.431 -0.277 -0.456 -0.401 -0.267 -0.063 0.043 0.153

(0.085) (0.300) (0.087) (0.155) (0.378) (0.846) (0.900) (0.674)

factor 2 0.839 0.460 0.338 0.285 0.463 0.480 0.060 -0.195

(0.000) (0.073) (0.218) (0.323) (0.111) (0.114) (0.860) (0.589)

factor 3 0.300 0.234 0.226 0.143 -0.051 -0.514 -0.840 -0.515

(0.242) (0.382) (0.419) (0.626) (0.869) (0.088) (0.001) (0.128)

Money

factor 1 -0.051 -0.131 -0.004 -0.270 -0.305 -0.141 0.213 -0.657

(0.845) (0.628) (0.988) (0.350) (0.311) (0.661) (0.529) (0.039)

factor 2 0.540 0.278 0.256 0.426 0.452 0.374 0.010 0.243

(0.025) (0.298) (0.356) (0.129) (0.121) (0.230) (0.976) (0.500)

Combined sectors

factor 1 0.798 0.599 0.484 0.497 0.461 0.417 0.269 0.549

(0.000) (0.014) (0.067) (0.071) (0.113) (0.178) (0.424) (0.101)

(B) quarterly factors

lag1 Lag2 Lag3 lag4 lag5 lag6 lag7 lag8

Equity

factor 1 0.824 0.710 0.696 0.654 0.580 0.498 0.524 0.507

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

factor 2 0.919 0.850 0.802 0.723 0.645 0.550 0.486 0.419

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

factor 3 0.103 0.201 0.231 0.279 0.300 0.355 0.387 0.454

(0.282) (0.034) (0.015) (0.003) (0.002) (0.000) (0.000) (0.000)

factor 4 0.880 0.795 0.766 0.718 0.636 0.575 0.502 0.433

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

bond

factor 1 0.854 0.693 0.519 0.257 0.134 0.040 -0.068 -0.105

(0.000) (0.000) (0.000) (0.039) (0.292) (0.753) (0.601) (0.421)

factor 2 0.883 0.826 0.761 0.722 0.679 0.662 0.598 0.536

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

factor 3 0.091 0.174 0.307 0.384 0.410 0.477 0.455 0.433

(0.461) (0.160) (0.012) (0.002) (0.001) (0.000) (0.000) (0.000)

money

factor 1 0.394 0.384 0.322 0.101 0.112 -0.018 0.044 0.030

(0.001) (0.001) (0.008) (0.423) (0.377) (0.887) (0.735) (0.820)

factor 2 -0.194 0.531 -0.028 0.398 -0.056 0.250 -0.034 0.259

38

(0.114) (0.000) (0.822) (0.001) (0.659) (0.048) (0.792) (0.044)

Combined sectors

factor 1 0.917 0.903 0.886 0.862 0.834 0.807 0.769 0.748

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

*Note: The autocorrelations ρ are shown with p-values in parentheses, calculated assuming that (T-2)1/2 ([(ρ2)/(1-ρ2)])1/2 is distributed according to the t-distribution with (T-2) degree of freedom where T is the number of time periods. The common factors are extracted using a principal components analysis on fund flows for funds in the given sector. The combined sector factors use the Goyal et al (2008) method. The sample includes US equity mutual funds, US bond funds, and US money market funds that have at least 5 million dollars in assets under management at the beginning of the period and are at least one-year old. The sample periods are from 1980 to 2009 for equity funds and from 1991 to 2009 for bond funds and money market funds.

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Table 6. Regressions of the first factors on lagged macro and financial variables

(A) First Equity Fund Flow Factor

Annual f1(t+1) Quarterly f1(t+1) model1 model2 model3 model4 model1 model2 model3 model4 ∆Michigan -0.035 -0.277 0.021 -0.024 Sentiment (-0.405) (-1.426) (0.641) (-0.728) BW sentiment -0.022 -0.030 -0.001 0.001 (-1.573) (-1.355) (-0.211) (0.376) Inflation -0.922 -1.450 -0.690 -0.254 -0.862 -0.899 (-1.568) (-1.452) (-0.404) (-0.488) (-1.818) (-1.767) Exchange rate 0.270 0.415 0.098 0.122 0.175 0.221 (1.786) (1.868) (0.457) (1.292) (2.111) (3.055) Disp income -1.584 -1.566 0.291 0.078 -0.264 -0.264 growth (-1.723) (-1.936) (0.264) (0.305) (-1.045) (-1.254) IP growth 0.761 0.458 0.544 -0.028 -0.021 -0.042 (2.638) (1.028) (0.678) (-1.096) (-0.741) (-1.273) Market volatility -7.999 -7.576 -0.622 -0.523 (-2.298) (-1.027) (-1.264) (-1.247) Mkt- Tbill return 0.061 -0.112 0.058 -0.012 (0.713) (-1.089) (1.817) (-0.271) BAA-AAA -1.176 -4.328 -0.748 0.780 (-0.587) (-0.837) (-1.253) (1.040) AAA-T bill 2.472 1.539 0.301 0.091 (2.636) (1.071) (1.476) (0.483) Dp ratio - T-10yr 0.136 -0.956 -0.147 0.181 (0.225) (-0.536) (-0.942) (0.967) f1 (t) 0.748 0.455 (1.206) (3.527) f1 (t-1) -0.568 -0.130 (-1.196) (-1.164) f1 (t-2) 0.311 0.149 (1.170) (1.022) R2 0.256 0.304 0.395 0.708 0.040 0.122 0.148 0.353 adjusted R2 0.126 0.084 0.258 0.255 0.004 0.068 0.108 0.249

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(B) First Bond Fund Flow Factor

Quarterly f1(t+1) model1 model2 model3 model4 ∆Michigan Sentim. -0.043 -0.055 (-1.766) (-3.771) BW sentiment 0.003 0.003 (0.693) (1.473) Inflation -0.174 -0.538 -0.116 (-1.270) (-1.834) (-0.769) Exchange rate 0.037 0.065 0.024 (0.729) (0.836) (0.478) Disp income -0.101 -0.143 0.054 Growth (-0.636) (-0.634) (0.388) IP growth 0.001 -0.008 -0.005 (0.035) (-0.469) (-0.317) Market volatility 0.066 -0.384 (0.135) (-1.135) Mkt – Tbill return -0.027 0.011 (-1.333) (0.686) BAA-AAA -0.064 1.841 (-0.082) (2.386) AAA-T bill 0.198 -0.007 (0.929) (-0.075) Dp ratio -T-10yr -0.037 -0.216 (-0.146) (-1.843) f1 (t) 0.799 (5.824) f1 (t-1) -0.028 (-0.148) f1 (t-2) -0.122 (-1.241) R2 0.031 0.098 0.081 0.729 adjusted R2 -0.030 -0.004 0.007 0.641

41

(C) First Money market Fund Flow Factor

Quarterly f1(t+1) model1 model2 model3 model4 ∆Michigan -0.003 -0.012 Sentiment (-0.455) (-1.372) BW sentiment 0.000 -0.001 (-0.209) (-0.787) Inflation 0.010 -0.027 -0.183 (0.111) (-0.290) (-1.605) Exchange rate 0.002 0.040 0.018 (0.074) (1.511) (0.773) Disp income 0.042 -0.011 -0.043 growth (0.768) (-0.179) (-0.565) IP growth 0.009 0.001 -0.001 (0.857) (0.103) (-0.145) Market volatility -0.130 -0.399 (-0.775) (-2.835) Mk – Tbill return 0.006 -0.017 (0.501) (-1.705) BAA-AAA -0.174 -0.291 (-0.858) (-0.895) AAA-T bill -0.011 -0.032 (-0.207) (-0.697) Dp ratio-T - 10yr -0.034 -0.076 (-0.487) (-0.973) f1 (t) -0.218 (-1.410) f1 (t-1) 0.189 (1.139) f1 (t-2) 0.098 (0.702) R2 0.019 0.050 0.170 0.345 adjusted R2 -0.043 -0.058 0.103 0.131

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(D) First Overall common factor

Quarterly f1(t+1) model1 model2 model3 model4 ∆Michigan. -0.008 0.011 Sentiment (-0.602) (0.800) BW sentiment 0.006 0.002 (2.862) (2.278) Inflation -0.167 -0.186 -0.032 (-1.488) (-1.073) (-0.302) Exchange rate 0.078 0.078 0.042 (1.841) (2.042) (2.579) Disp income 0.048 0.090 0.038 Growth (0.424) (0.691) (0.672) IP growth -0.005 -0.003 -0.010 (-0.494) (-0.274) (-1.668) Market volatility 0.594 0.033 (2.006) (0.175) Mkt – Tbill return 0.010 -0.006 (0.659) (-0.598) BAA-AAA 0.647 -0.791 (1.437) (-2.276) AAA-T bill -0.384 -0.201 (-4.754) (-4.765) Dp ratio-T - 10yr -0.240 0.099 (-2.192) (1.408) f1 (t) 0.363 (2.541) f1 (t-1) 0.002 (0.013) f1 (t-2) 0.275 (2.270) R2 0.119 0.286 0.503 0.867 adjusted R2 0.063 0.205 0.463 0.824

*Note: The dependent variables are the first common factors extracted using principal components analysis on fund flows for the indicated fund sector. Panel (D) combines the sectors using the Goyal et al (2008) method. The independent variables are the lagged macroeconomic and financial variables, and lagged factors as listed in

43

the first column. The tables report the coefficient estimates and t-ratios, where the standard errors Newey-West estimates with 2 lags for annual data and 5 lags for quarterly data. The sample periods are from 1981 Q4 to 2009 Q4 for equity funds and from 1992 Q4 to 2009 Q4 for bond funds and money market funds.

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Table 7. Regressions of Macroeconomic and Financial Variables on their own lags and lagged Common Fund Flow Factors

(A) equity f1 (B) equity f1 (C) bond f1 (D) money market f1

(1981-2009) (1992-2009) (1992-2009) (1992-2009)

coeff (s.e.) adj R2 coeff (s.e.) adj R2 Coeff (s.e.) adj R2 coeff (s.e.) adj R2

Annual

∆Michigan sentiment 0.787 (0.365) 0.043 0.495 (0.328) -0.026 0.832 (0.384) 0.092 0.411 (0.356) -0.013

Inflation 0.011 (0.034) -0.036 0.013 (0.026) -0.062 -0.022 (0.019) -0.048 -0.028 (0.027) -0.024

Exchange 0.408 (0.239) 0.030 0.167 (0.250) -0.053 -0.704 (0.252) 0.266 -0.017 (0.179) -0.066

IP growth 0.394 (0.111) 0.180 0.358 (0.171) 0.087 0.101 (0.119) -0.049 -0.014 (0.075) -0.066

income growth 0.101 (0.073) 0.086 0.030 (0.070) -0.054 0.049 (0.034) -0.020 -0.003 (0.039) -0.066

Tbill 0.107 (0.120) 0.017 0.162 (0.095) 0.132 -0.138 (0.038) 0.135 -0.065 (0.073) -0.004

BAA 0.115 (0.095) 0.037 0.064 (0.037) 0.084 -0.009 (0.030) -0.063 0.025 (0.048) -0.022

AAA 0.140 (0.092) 0.089 0.104 (0.047) 0.240 0.002 (0.039) -0.067 0.015 (0.049) -0.054

BAA-AAA -0.025 (0.015) 0.030 -0.040 (0.021) 0.071 -0.011 (0.015) -0.053 0.009 (0.009) -0.052

AAA-Tbill 0.033 (0.053) -0.021 -0.058 (0.080) -0.023 0.140 (0.026) 0.283 0.081 (0.040) 0.094

market return 0.182 (0.557) -0.035 0.906 (0.853) -0.008 -0.181 (0.677) -0.063 0.263 (0.363) -0.057

market volatility -0.039 (0.012) 0.161 -0.053 (0.016) 0.219 0.008 (0.014) -0.059 0.038 (0.007) 0.218

Quarterly

∆Michigan sentiment -0.179 (0.069) 0.053 -1.640 (1.017) 0.031 0.567 (0.383) -0.003 -0.042 (0.367) -0.015

Inflation 0.001 (0.005) -0.009 0.126 (0.067) 0.014 -0.055 (0.031) -0.002 0.002 (0.038) -0.015

Exchange -0.028 (0.026) -0.002 0.317 (0.388) -0.007 -0.052 (0.250) -0.015 0.290 (0.173) 0.018

IP growth -0.002 (0.037) -0.009 0.583 (0.758) -0.008 0.094 (0.232) -0.015 -0.073 (0.358) -0.015

income growth -0.002 (0.006) -0.008 -0.018 (0.130) -0.015 -0.009 (0.047) -0.015 0.020 (0.045) -0.013

Tbill -0.040 (0.032) 0.021 0.110 (0.275) -0.011 -0.371 (0.178) 0.084 0.276 (0.159) 0.099

BAA -0.067 (0.028) 0.082 0.194 (0.088) 0.039 0.136 (0.107) 0.045 0.181 (0.060) 0.207

AAA -0.065 (0.025) 0.092 0.258 (0.110) 0.061 0.129 (0.112) 0.028 0.168 (0.082) 0.136

BAA-AAA -0.002 (0.005) -0.006 -0.064 (0.041) 0.003 0.006 (0.045) -0.015 0.013 (0.033) -0.012

AAA-Tbill -0.025 (0.015) 0.039 0.148 (0.255) -0.004 0.500 (0.143) 0.273 -0.108 (0.105) 0.013

market return -0.125 (0.075) 0.022 -1.030 (0.814) 0.001 0.266 (0.596) -0.013 -0.099 (0.817) -0.014

market volatility 0.010 (0.005) 0.037 -0.042 (0.071) -0.010 0.039 (0.070) -0.005 0.033 (0.037) -0.001

45

(E) equity f1 bond f1 money market f1 (F) Overall Common Factor

(1992-2009) (1992-2009) (1992-2009) (1992-2009)

coeff (s.e.) Coeff (s.e.) Coeff (s.e.) adj R2 Coeff (s.e.) adj R2

Annual

∆Michigan sentiment 0.451 (0.373) 0.783 (0.398) 0.407 (0.401) 0.046 0.093 (0.725) -0.066

Inflation 0.013 (0.025) -0.022 (0.018) -0.027 (0.029) -0.156 -0.007 (0.051) -0.066

Exchange 0.240 (0.218) -0.722 (0.209) 0.015 (0.184) 0.185 0.537 (0.221) 0.013

IP growth 0.350 (0.190) 0.077 (0.090) -0.002 (0.110) -0.043 0.449 (0.243) 0.073

disp income growth 0.025 (0.080) 0.047 (0.038) -0.003 (0.039) -0.167 0.183 (0.053) 0.202

Tbill 0.173 (0.069) -0.148 (0.029) -0.053 (0.060) 0.322 0.327 (0.076) 0.401

BAA 0.067 (0.039) -0.015 (0.014) 0.028 (0.044) 0.020 0.133 (0.047) 0.314

AAA 0.106 (0.049) -0.006 (0.018) 0.020 (0.040) 0.150 0.189 (0.048) 0.521

BAA-AAA -0.039 (0.021) -0.008 (0.013) 0.008 (0.011) -0.051 -0.057 (0.026) 0.089

AAA-Tbill -0.066 (0.045) 0.142 (0.025) 0.073 (0.034) 0.403 -0.138 (0.089) 0.073

market return 0.958 (0.865) -0.263 (0.785) 0.312 (0.481) -0.140 1.094 (1.035) -0.017

market volatility -0.051 (0.012) 0.010 (0.010) 0.036 (0.011) 0.406 -0.032 (0.039) -0.008

Quarterly

∆Michigan sentiment -1.729 (1.054) 0.673 (0.468) -0.078 (0.354) 0.019 0.331 (0.734) -0.014

Inflation 0.135 (0.066) -0.063 (0.029) 0.005 (0.037) 0.001 0.034 (0.090) -0.013

Exchange 0.335 (0.380) -0.097 (0.230) 0.296 (0.181) -0.002 0.902 (0.379) 0.041

IP growth 0.573 (0.785) 0.068 (0.260) -0.074 (0.359) -0.039 0.558 (0.519) -0.010

disp income growth -0.016 (0.132) -0.010 (0.048) 0.021 (0.045) -0.043 0.106 (0.070) -0.003

Tbill 0.169 (0.226) -0.406 (0.156) 0.293 (0.169) 0.196 1.374 (0.242) 0.485

BAA 0.183 (0.089) 0.110 (0.085) 0.177 (0.057) 0.280 0.397 (0.164) 0.174

AAA 0.248 (0.105) 0.101 (0.091) 0.164 (0.080) 0.217 0.708 (0.145) 0.462

BAA-AAA -0.065 (0.041) 0.009 (0.042) 0.013 (0.034) -0.024 -0.311 (0.107) 0.337

AAA-Tbill 0.079 (0.156) 0.507 (0.140) -0.129 (0.107) 0.295 -0.666 (0.254) 0.173

market return -1.076 (0.836) 0.338 (0.666) -0.117 (0.827) -0.026 2.552 (1.101) 0.067

market volatility -0.046 (0.081) 0.039 (0.066) 0.031 (0.038) -0.017 -0.258 (0.142) 0.141

*Note: The dependent variables are macroeconomic and financial variables as listed in the first column. The independent variables are lagged dependent variables and the lagged value of the common flow factors in mutual funds, extracted using a principal components analysis on fund flows for the indicated sector. Panel (F) uses the Goyal et al (2008) method. The tables report the coefficient estimates and their Newey West (1980) standard error using 2 lags for annual data 5 lags for quarterly data. The sample periods are from 1981 Q4 to 2009 Q4 for equity funds and from 1992 Q4 to 2009 Q4 for bond funds and money market funds as stated in the parentheses.

46

Table 8. Flow Beta Models for Equity Funds on the first Flow Factor (Six Common Flow Factors are included)

(A) retail share classes (B) institutional share classes

estimate s.e p-value estimate s.e p-value

f1*lagperformance 0.670 0.224 0.003

-0.484 0.728 0.507

f1*lagperformance^2 2.354 0.848 0.006

4.170 2.756 0.130

f1*lag2 performance 0.016 0.225 0.944

-0.854 0.742 0.250

f1*lagage -0.196 0.114 0.086

0.056 0.359 0.877

f1*lagsize 0.055 0.065 0.398

0.718 0.212 0.001

f1*lagexp 84.956 17.312 0.000

112.334 79.131 0.156

f1*lagvol 4.090 6.567 0.533

2.298 21.805 0.916

f1*lagfamily size 0.057 0.043 0.186

0.011 0.124 0.929

f1*lagflow 1.436 0.129 0.000

0.002 0.437 0.997

f1 -13.749 5.915 0.020

-16.150 13.493 0.231

lagperformance 0.334 0.017 0.000

0.384 0.042 0.000

lagperformance^2 0.266 0.064 0.000

0.344 0.160 0.032

lag2 performance 0.175 0.017 0.000

0.284 0.043 0.000

lagage -0.074 0.020 0.000

-0.072 0.061 0.241

lagsize -0.177 0.006 0.000

-0.222 0.013 0.000

lagexp -3.208 1.987 0.106

-0.790 7.085 0.911

lagvol -1.202 0.561 0.032

-1.947 1.488 0.191

lagfamily size 0.046 0.008 0.000

0.124 0.018 0.000

lagflow 0.065 0.011 0.000

0.087 0.025 0.000

adjusted R^2 0.335

0.277

fixed effect time and fund time and fund

*Note: The dependent variable is the net flow into an equity fund in calendar year t. The independent variables are the first common factor for year t (f1), fund performance and characteristics in the year t-1, fund performance in t-2, and interaction terms between the first common factor and the fund variables as listed in the first column. The independent variables also include a constant, the common factors from f2 to f6 and their interaction terms with the fund variables (not presented). The tables report the coefficient estimates, their standard errors and p-values. The standard errors in (A) and (C) are clustered by year and (B) and (D) by year and fund. Performance is measured as the ranking based on lagged annual returns divided by the number of sample funds in each period. Age is the log of the years since the inception date of fund or the first date that the fund return data is available if earlier. Size is the log of TNA of a fund divided by the average TNA of equity mutual funds, including index funds. Expense ratio is the expense ratio for the most recent fiscal year as reported in the fund prospectus and does not include load fees. Volatility is the standard deviation of the monthly return of a fund over the last two years. Family size is the log of size of the family divided by the average size of families. Size of a family is the sum of the total net assets of the funds belonging to the same advisor. The sample period is from 1982 to 2009.

47

Table 9. Asymmetric Flow Beta Regressions (six factors are included in the model)

(A) retail share classes (B) institutional share classes

estimate s.e pvalue

estimate s.e Pvalue

f1 positive*lagperformance 2.728 0.383 0.000

1.873 1.241 0.131

f1 negative*lagperformance -8.884 1.481 0.000

-8.991 3.974 0.024

f1 positive*lagperformance^2 0.120 1.459 0.934

-0.727 4.639 0.875

f1 negative*lagperformance^2 12.534 5.534 0.024

22.310 14.589 0.126

f1 positive*lag2 performance 0.667 0.390 0.088

0.237 1.259 0.850

f1 negative*lag2 performance -2.766 1.517 0.068

-5.270 4.025 0.190

f1 positive*lagage -0.275 0.149 0.064

-0.228 0.516 0.658

f1 negative*lagage 0.720 0.578 0.213

1.050 1.495 0.483

f1 positive*lagsize -0.397 0.102 0.000

0.387 0.357 0.278

f1 negative*lagsize 1.939 0.340 0.000

1.845 0.939 0.050

f1 positive*lagexp 89.583 25.870 0.001

221.694 135.214 0.101

f1 negative*lagexp 19.543 94.826 0.837

-361.513 414.201 0.383

f1 positive*lagvol -7.847 9.531 0.410

-32.141 37.200 0.388

f1 negative*lagvol 57.399 33.498 0.087

114.100 106.384 0.284

f1 positive*lagfamily size 0.303 0.068 0.000

0.197 0.216 0.362

f1 negative*lagfamily size -1.050 0.231 0.000

-0.733 0.642 0.254

f1 positive -21.527 8.306 0.010

1.949 0.675 0.004

f1 negative -13.300 6.373 0.037

-6.268 1.773 0.000

lagperformance 0.140 0.033 0.000

0.255 0.080 0.001

lagperformance^2 0.472 0.128 0.000

0.653 0.305 0.032

lag2 performance 0.114 0.034 0.001

0.208 0.082 0.011

lagage -0.076 0.021 0.000

-0.036 0.065 0.587

lagsize -0.144 0.009 0.000

-0.208 0.018 0.000

lagexp -3.995 2.589 0.123

-8.833 9.530 0.354

lagvol -0.412 0.736 0.576

-0.020 1.911 0.992

lagfamily size 0.027 0.009 0.002

0.116 0.020 0.000

lagflow -0.051 0.019 0.007

-0.018 0.039 0.648

adjusted R^2 0.344

0.280

fixed effect time and fund time and fund

*Note: The table is the same as Table 8 except that the terms with lagged performance are allowed to have asymmetric estimates around zero (piecewise linear specification). See the note for Table 8 for variable descriptions. The sample period is from 1982 to 2009.

48

Table 10. The Performance of Quarterly-rebalanced portfolios of funds formed by betas on the first factor for equity fund flows

(A) Equally-weighted portfolio of funds

excess return CAPM alpha FF alpha Carhart alpha

estimate s.e. p-value estimate s.e. p-value estimate s.e. p-value estimate s.e. p-value

beta on f1

Low 0.525 0.240 0.029 0.010 0.047 0.827 -0.031 0.045 0.497 -0.025 0.046 0.586 1 0.528 0.251 0.036 -0.014 0.040 0.726 -0.038 0.039 0.334 -0.041 0.040 0.300 2 0.551 0.263 0.037 -0.016 0.042 0.702 -0.023 0.039 0.549 -0.036 0.039 0.359 3 0.528 0.279 0.060 -0.071 0.055 0.194 -0.050 0.038 0.191 -0.066 0.039 0.088

High 0.511 0.302 0.092 -0.125 0.083 0.130 -0.070 0.054 0.198 -0.092 0.055 0.092 High – Low -0.014 0.118 0.903 -0.136 0.105 0.197 -0.039 0.075 0.598 -0.068 0.075 0.371

beta on f1>0.01

Low 0.500 0.286 0.081 -0.059 0.061 0.334 -0.067 0.062 0.276 -0.010 0.064 0.000 1 0.507 0.285 0.076 -0.062 0.043 0.148 -0.067 0.039 0.090 -0.052 0.045 0.249 2 0.549 0.283 0.053 -0.025 0.047 0.599 -0.027 0.036 0.458 -0.043 0.041 0.289 3 0.511 0.287 0.077 -0.064 0.063 0.310 -0.062 0.046 0.177 -0.106 0.046 0.023

High 0.575 0.293 0.050 -0.007 0.074 0.923 0.011 0.060 0.851 -0.050 0.060 0.409 High – Low 0.075 0.102 0.459 0.052 0.104 0.620 0.079 0.096 0.415 -0.039 0.090 0.660

beta on -0.007< f1<0.01

Low 0.517 0.268 0.055 -0.012 0.071 0.870 -0.061 0.058 0.294 -0.060 0.065 0.351 1 0.525 0.275 0.057 -0.021 0.058 0.713 -0.055 0.047 0.244 -0.055 0.052 0.292 2 0.520 0.281 0.065 -0.047 0.043 0.274 -0.051 0.034 0.143 -0.059 0.040 0.139 3 0.536 0.296 0.071 -0.058 0.055 0.295 -0.028 0.038 0.454 -0.053 0.041 0.196

High 0.544 0.314 0.084 -0.078 0.071 0.271 -0.016 0.048 0.730 -0.033 0.053 0.535 High – Low 0.027 0.107 0.799 -0.066 0.108 0.541 0.044 0.076 0.561 0.028 0.083 0.739

beta on f1<-0.007

Low 0.569 0.279 0.042 0.110 0.083 0.182 0.083 0.066 0.209 0.003 0.066 0.964 1 0.512 0.283 0.072 0.039 0.064 0.544 0.014 0.051 0.776 -0.028 0.052 0.592 2 0.458 0.290 0.116 -0.028 0.057 0.621 -0.046 0.047 0.328 -0.062 0.050 0.222 3 0.420 0.304 0.169 -0.087 0.050 0.083 -0.097 0.043 0.026 -0.073 0.048 0.128

High 0.331 0.349 0.344 -0.239 0.086 0.006 -0.222 0.076 0.004 -0.168 0.084 0.047 High – Low -0.238 0.140 0.091 -0.349 0.136 0.011 -0.305 0.121 0.012 -0.171 0.116 0.142

49

(B) Size-weighted portfolio of funds

excess return CAPM alpha FF alpha Carhart alpha

estimate s.e. p-value estimate s.e. p-value estimate s.e. p-value estimate s.e. p-value

beta on f1

Low 0.577 0.237 0.016 0.076 0.062 0.222 0.009 0.051 0.866 0.028 0.052 0.593 1 0.505 0.253 0.047 -0.043 0.039 0.271 -0.058 0.037 0.116 -0.063 0.037 0.091 2 0.540 0.268 0.045 -0.041 0.038 0.282 -0.016 0.036 0.649 -0.020 0.037 0.591 3 0.424 0.292 0.147 -0.200 0.062 0.001 -0.133 0.045 0.003 -0.148 0.046 0.001

High 0.416 0.320 0.195 -0.246 0.106 0.021 -0.137 0.076 0.073 -0.167 0.077 0.030 High – Low -0.161 0.169 0.339 -0.322 0.153 0.037 -0.145 0.108 0.181 -0.195 0.109 0.076

beta on 0<f1

Low 0.527 0.280 0.061 -0.023 0.054 0.663 -0.040 0.052 0.444 0.013 0.053 0.799 1 0.487 0.281 0.084 -0.079 0.036 0.029 -0.078 0.034 0.025 -0.090 0.035 0.010 2 0.546 0.290 0.060 -0.040 0.053 0.454 -0.025 0.050 0.623 -0.066 0.051 0.204 3 0.497 0.295 0.093 -0.097 0.071 0.171 -0.071 0.060 0.238 -0.139 0.058 0.018

High 0.541 0.311 0.083 -0.067 0.092 0.469 -0.009 0.086 0.914 -0.135 0.078 0.084 High – Low 0.014 0.133 0.915 -0.043 0.128 0.734 0.031 0.119 0.795 -0.148 0.106 0.163

beta on -0.007< f1<0

Low 0.537 0.266 0.044 0.019 0.083 0.817 -0.057 0.061 0.352 -0.041 0.068 0.550 1 0.526 0.274 0.055 -0.015 0.065 0.814 -0.066 0.049 0.178 -0.073 0.054 0.178 2 0.463 0.287 0.108 -0.112 0.036 0.002 -0.098 0.036 0.007 -0.108 0.037 0.004 3 0.471 0.308 0.127 -0.138 0.064 0.031 -0.082 0.052 0.117 -0.113 0.049 0.021

High 0.457 0.330 0.168 -0.192 0.102 0.062 -0.078 0.067 0.251 -0.099 0.068 0.149 High – Low -0.081 0.160 0.615 -0.211 0.168 0.209 -0.020 0.105 0.846 -0.058 0.111 0.602

beta on f1<-0.007

Low 0.579 0.271 0.034 0.128 0.085 0.136 0.088 0.068 0.194 0.000 0.070 0.998 1 0.572 0.283 0.045 0.103 0.065 0.111 0.084 0.058 0.153 0.001 0.057 0.988 2 0.435 0.287 0.130 -0.044 0.045 0.328 -0.056 0.040 0.167 -0.092 0.041 0.025 3 0.439 0.293 0.136 -0.058 0.045 0.198 -0.044 0.042 0.294 -0.030 0.041 0.467

High 0.270 0.343 0.433 -0.288 0.092 0.002 -0.260 0.079 0.001 -0.173 0.084 0.040 High – Low -0.309 0.154 0.045 -0.416 0.158 0.009 -0.348 0.125 0.006 -0.173 0.125 0.168

Note: The table reports monthly excess returns (%) over the Treasury Bill rate and alphas (%) for portfolios of funds formed based on betas on the first common factor for equity mutual fund flows. At the end of each quarter from 1984 Q3 to 2009 Q3, flow betas on the first factor are estimated by rolling panel regressions using the data up to that quarter. The panel regression varies in two ways: (1) the linear specification for the first factor f1; and (2) a piecewise linear specification with three factors, defined as {f1>0.1,-0.007<f1 <0.1 and f1< -0.007}. The sample

50

mean flow minus the standard deviation of f1 is about -0.007. The coefficient estimates obtained from the panel regression, fund characteristics in the quarter t and the first factor are used to estimate betas on the first factor. The first factor is estimated using the principal component analysis and the data up to the quarter t. Funds are ranked and grouped into five portfolios from low to high according to the beta estimates for year t. The portfolios of funds are size-weighted in Panel (A) and equally-weighted in Panel (B). The portfolios are rebalanced every quarter. We use monthly returns on the portfolios in the following quarter and estimate the performance of these portfolios as the average excess returns over the risk-free rate, CAPM alphas, Fama-French three-factor alphas and Carhart four-factor alphas. The table reports the estimates, standard errors and their p-values. High - Low reports the estimates on the High minus Low portfolios. Numbers in bold represent significance at a 10% level. The sample period is from 1982 to 2009 and the first panel regression uses data up to 1983 Q3. The standard errors Newey-West estimates with 4 lags.

51

Appendix. A.1 Macroeconomic and Financial variables Table A.1

variable definition source

∆Michigan sentiment change in log of the University of Michigan Consumer Sentiment Federal Reserve Bank of St. Louis Economic data (FRED)

Inflation change in log of the Consumer Price Index of all items Federal Reserve Bank of St. Louis Economic data (FRED)

Exchange change in log of the major foreign exchange index (trade-weighted) Federal Reserve Bank of St. Louis Economic data (FRED)

IP growth change in log of the Industrial Production Index Federal Reserve Bank of St. Louis Economic data (FRED)

disp income growth change in log of the Disposable Personal Income Federal Reserve Bank of St. Louis Economic data (FRED)

Tbill Three-month Treausry Bill rate (Secondary market rate) Federal Reserve Bank of St. Louis Economic data (FRED)

T-10yr 10-Year Treasury Constant Maturity Rate Federal Reserve Bank of St. Louis Economic data (FRED)

BAA Moody's Seasoned Baa Corporate Bond Yield Federal Reserve Bank of St. Louis Economic data (FRED)

AAA Moody's Seasoned Aaa Corporate Bond Yield Federal Reserve Bank of St. Louis Economic data (FRED)

market return Return on the S&P500 index WRDS

market volatility Standard deviation of return on the S&P500 index WRDS

d/p ratio Dividend to price ratio of the value weighted CRSP index WRDS

BW sentiment Sentiment index updated by Eq. (2) in Baker and Wurgler (2006) Jeffrey Wurgler

*Note: The table contains the precise definitions and the sources used for the data on macroeconomic and financial market variables.

52

Table A.2. Descriptive statistics (A) equity funds

Flow net assets ($B) return

year N mean median p1 p99 std mean median std mean median std

1981 183 0.056 -0.038 -0.226 1.464 0.274 0.189 0.062 0.319 -0.012 -0.012 0.090

1982 190 0.089 -0.051 -0.630 3.260 0.550 0.174 0.062 0.286 0.267 0.257 0.124

1983 196 0.341 0.075 -0.411 3.480 0.716 0.211 0.083 0.332 0.215 0.217 0.075

1984 215 0.079 -0.007 -0.404 1.249 0.419 0.261 0.114 0.373 -0.016 -0.015 0.096

1985 236 0.147 -0.048 -0.463 3.117 0.645 0.255 0.103 0.387 0.284 0.287 0.066

1986 267 0.219 -0.011 -0.515 3.923 0.726 0.308 0.121 0.502 0.144 0.145 0.064

1987 310 0.054 -0.018 -0.389 1.069 0.287 0.345 0.112 0.690 0.012 0.018 0.075

1988 344 -0.058 -0.106 -0.582 1.185 0.384 0.310 0.100 0.561 0.153 0.156 0.081

1989 390 0.092 -0.063 -0.515 3.081 0.577 0.289 0.082 0.595 0.255 0.254 0.088

1990 432 0.052 -0.025 -0.527 1.391 0.347 0.328 0.087 0.745 -0.066 -0.055 0.072

1991 448 0.251 0.035 -0.571 3.470 0.689 0.296 0.077 0.686 0.384 0.346 0.154

1992 498 0.326 0.107 -0.600 3.752 0.736 0.432 0.120 0.955 0.093 0.086 0.076

1993 554 0.269 0.046 -0.612 3.545 0.678 0.512 0.149 1.193 0.129 0.128 0.076

1994 649 0.143 0.013 -0.884 2.841 0.561 0.620 0.145 1.885 -0.014 -0.012 0.049

1995 752 0.219 0.033 -0.622 3.272 0.656 0.541 0.127 1.419 0.312 0.313 0.081

1996 852 0.244 0.073 -0.637 2.962 0.628 0.718 0.168 1.923 0.192 0.195 0.061

1997 952 0.251 0.057 -0.724 3.325 0.692 0.885 0.185 2.465 0.243 0.260 0.093

1998 1108 0.159 0.012 -0.673 3.002 0.581 1.046 0.193 3.094 0.142 0.142 0.151

1999 1264 0.125 -0.054 -0.802 3.594 0.721 1.174 0.187 3.787 0.280 0.205 0.305

2000 1379 0.174 -0.006 -0.728 3.682 0.679 1.401 0.216 4.482 -0.001 -0.013 0.155

2001 1488 0.164 0.004 -0.528 2.942 0.561 1.279 0.219 4.045 -0.086 -0.105 0.153

2002 1656 0.100 -0.017 -0.450 1.782 0.437 1.059 0.199 3.391 -0.220 -0.222 0.089

2003 1673 0.211 0.026 -0.660 3.503 0.694 0.827 0.170 2.765 0.337 0.310 0.114

2004 1806 0.118 -0.016 -0.684 2.324 0.530 1.063 0.216 3.704 0.125 0.121 0.060

2005 1899 0.122 -0.045 -0.702 2.966 0.626 1.184 0.235 4.378 0.072 0.068 0.048

2006 1967 0.091 -0.057 -0.657 2.748 0.567 1.242 0.245 4.891 0.126 0.131 0.057

2007 2115 0.049 -0.056 -0.680 1.985 0.499 1.381 0.275 5.646 0.070 0.062 0.094

2008 2209 0.013 -0.055 -0.429 1.650 0.359 1.451 0.272 6.322 -0.386 -0.385 0.072

2009 2046 0.033 -0.084 -0.747 2.368 0.526 0.887 0.171 3.888 0.319 0.304 0.119

all 28078 0.126 -0.023 -0.645 2.865 0.580 0.991 0.183 3.895 0.084 0.106 0.232

53

(B) bond funds

Flow net assets ($B) return

year N mean median p1 p99 std mean median std mean median std

1992 408 0.314 0.164 -0.576 3.522 0.669 0.483 0.129 1.154 0.078 0.066 0.045

1993 468 0.189 0.078 -0.710 2.838 0.561 0.547 0.175 1.204 0.105 0.093 0.052

1994 593 -0.099 -0.120 -0.882 1.256 0.324 0.533 0.162 1.163 -0.032 -0.032 0.036

1995 674 0.014 -0.081 -0.808 2.233 0.516 0.400 0.115 0.893 0.157 0.161 0.057

1996 748 0.092 -0.042 -0.603 2.824 0.564 0.423 0.121 0.974 0.054 0.040 0.056

1997 766 0.099 -0.013 -0.712 2.714 0.539 0.443 0.121 1.033 0.082 0.084 0.038

1998 803 0.165 0.050 -0.650 2.238 0.495 0.489 0.122 1.171 0.061 0.069 0.053

1999 858 0.018 -0.058 -0.636 1.912 0.404 0.543 0.140 1.373 0.004 -0.002 0.054

2000 847 -0.050 -0.124 -0.760 1.851 0.445 0.554 0.145 1.516 0.066 0.088 0.074

2001 807 0.212 0.047 -0.668 3.069 0.633 0.558 0.154 1.750 0.061 0.070 0.038

2002 849 0.247 0.065 -0.660 3.820 0.694 0.628 0.190 2.108 0.068 0.077 0.053

2003 857 0.129 -0.010 -0.686 2.395 0.532 0.800 0.231 2.892 0.083 0.042 0.089

2004 912 0.031 -0.053 -0.818 2.049 0.473 0.867 0.253 3.054 0.050 0.040 0.036

2005 923 0.001 -0.075 -0.762 1.641 0.408 0.901 0.263 3.251 0.022 0.020 0.026

2006 947 -0.012 -0.072 -0.726 1.609 0.388 0.909 0.240 3.589 0.054 0.044 0.028

2007 958 0.051 -0.032 -0.712 2.153 0.448 1.000 0.253 3.943 0.048 0.054 0.040

2008 986 0.069 -0.071 -0.687 3.098 0.616 1.142 0.273 4.583 -0.063 -0.028 0.137

2009 966 0.232 0.042 -0.710 3.351 0.720 1.100 0.256 5.171 0.172 0.118 0.167

all 15801 0.099 -0.029 -0.704 2.588 0.556 0.701 0.177 2.726 0.062 0.058 0.094

(C) money market funds

Flow net assets ($B) return

year N mean median p1 p99 std mean median std mean median std

1992 141 0.065 -0.058 -0.453 2.571 0.468 0.818 0.322 1.309 0.032 0.033 0.005

1993 222 0.075 -0.039 -0.399 2.764 0.531 0.886 0.322 1.590 0.025 0.025 0.004

1994 422 0.133 0.022 -0.605 3.091 0.573 0.907 0.343 1.882 0.033 0.035 0.007

1995 475 0.165 0.083 -0.566 1.809 0.417 0.920 0.337 1.975 0.047 0.053 0.011

1996 481 0.152 0.082 -0.779 1.723 0.415 1.074 0.395 2.402 0.042 0.047 0.010

1997 517 0.176 0.082 -0.596 2.165 0.491 1.209 0.421 2.732 0.044 0.049 0.010

1998 549 0.248 0.165 -0.422 2.029 0.442 1.394 0.481 3.151 0.043 0.048 0.010

1999 557 0.136 0.039 -0.611 2.138 0.498 1.746 0.567 4.008 0.040 0.044 0.010

2000 566 0.090 0.039 -0.641 1.661 0.419 2.205 0.607 5.213 0.050 0.056 0.012

2001 578 0.180 0.086 -0.525 1.967 0.459 2.570 0.671 6.341 0.032 0.035 0.007

2002 620 0.016 -0.032 -0.589 1.168 0.349 3.149 0.718 8.166 0.012 0.012 0.003

54

2003 611 -0.086 -0.116 -0.788 1.020 0.345 3.027 0.703 8.990 0.006 0.006 0.002

2004 616 -0.073 -0.090 -0.804 0.822 0.259 2.447 0.594 5.557 0.008 0.008 0.002

2005 595 0.018 -0.013 -0.731 1.202 0.312 2.344 0.567 5.246 0.024 0.025 0.005

2006 585 0.081 0.032 -0.733 1.539 0.384 2.624 0.603 5.987 0.040 0.043 0.008

2007 573 0.184 0.121 -0.723 1.961 0.456 3.174 0.675 8.032 0.041 0.044 0.009

2008 596 0.228 0.048 -0.833 3.927 0.722 3.806 0.844 9.290 0.020 0.020 0.005

2009 590 -0.190 -0.236 -0.801 1.474 0.386 5.491 1.173 12.660 0.002 0.002 0.002

all 9774 0.089 0.012 -0.689 1.967 0.468 2.323 0.554 6.464 0.031 0.030 0.019

*Note: The sample consists of mutual funds that have at least 5 million assets under management at the beginning of the periods and are at least one-year old. The sample period is from 1980 Q1 to 2009 Q4 for US equity funds and from 1991 Q1 to 2009 Q4 for US bond funds and US money market funds.

Table A.3. Autocorrelations of the macroeconomic and financial variables

Annual Quarterly

lag1 lag2 lag3 lag1 lag2 lag3

∆Michigan sentiment -0.096 -0.271 -0.069 -0.205 -0.082 0.029

(0.621) (0.163) (0.733) (0.025) (0.378) (0.756)

BW sentiment 0.611 0.229 0.169 0.918 0.833 0.720

(0.001) (0.272) (0.430) (0.000) (0.000) (0.000)

BW sentiment change -0.038 -0.442 -0.041 0.019 0.165 0.034

(0.856) (0.031) (0.852) (0.848) (0.088) (0.729)

inflation 0.527 0.303 0.155 0.232 0.126 0.151

(0.003) (0.117) (0.440) (0.011) (0.172) (0.105)

exchange rate 0.343 0.108 0.036 0.191 0.055 0.113

(0.068) (0.584) (0.858) (0.037) (0.551) (0.227)

disp income growth 0.095 -0.034 -0.087 -0.194 0.177 -0.051

(0.624) (0.864) (0.666) (0.035) (0.055) (0.587)

IP growth 0.084 -0.051 -0.277 -0.774 0.644 -0.779

(0.665) (0.797) (0.161) (0.000) (0.000) (0.000)

market volatility 0.433 -0.057 -0.200 0.576 0.372 0.258

(0.019) (0.771) (0.317) (0.000) (0.000) (0.005)

market return -0.041 0.028 -0.017 0.104 0.025 -0.039

(0.833) (0.887) (0.933) (0.260) (0.786) (0.676)

Tbill 0.853 0.590 0.487 0.958 0.923 0.885

(0.000) (0.001) (0.010) (0.000) (0.000) (0.000)

market return - Tbill -0.100 0.002 -0.050 0.167 0.071 0.003

(0.607) (0.993) (0.804) (0.070) (0.446) (0.978)

AAA 0.901 0.909 0.907 0.980 0.959 0.931

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

BAA 0.914 0.921 0.898 0.982 0.960 0.932

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

BAA-AAA 0.402 0.355 0.249 0.883 0.732 0.593

(0.031) (0.064) (0.211) (0.000) (0.000) (0.000)

AAA-Tbill 0.424 -0.188 -0.469 0.845 0.748 0.635

(0.022) (0.339) (0.014) (0.000) (0.000) (0.000)

dp ratio - 10yr 0.839 0.729 0.718 0.936 0.888 0.861

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

*Note: The table reports the autocorrelation of the variables listed in the first column. Inflation is the change in log of the consumer price index. Exchange rate is the change in log of the major foreign exchange index. Michigan sentiment index is the consumer confidence index as surveyed by the University of Michigan, and ∆Michigan sentiment is the change of the log of the index. BW sentiment is the variable constructed in Baker and Wurgler (2006) and BW sentiment change is its first difference. IP growth is the change in log of the industry production. Market volatility and return are the standard deviation and the return on S&P500 index respectively, which are obtained using its daily data. dp ratio is the dividend to price ratio of the value weighed CRSP index. 10yr is the yield on the 10-tear Treasury bond. The sample period is from 1980 Q1 to 2009 Q4 except for BW sentiment and BW sentiment change, which are from 1980 Q1 to 2006 Q4.

56

Figure 1. Equally weighted and value weighted fund flows over time

(A) equally weighted fund flows

1985 1990 1995 2000 2005

equity funds

1995 2000 2005

bond funds

1995 2000 2005

money market funds

1995 2000 2005

all funds

flow

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

flow

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

(B) value weighted fund flows

1985 1990 1995 2000 2005

equity funds

1995 2000 2005

bond funds

1995 2000 2005

money market funds

1995 2000 2005

all funds

flow

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

flow

-0.2

0

0.2

0.4

-0.2

0

0.2

0.4

Note: The figures plot annual equally weighted fund flows and value-weighted fund flows for each sector of U.S.

57

mutual funds: (A) US equity mutual funds, (B) US bond funds, (C) US money market funds, and (D) all funds including (A) to (C). Value-weighted fund flows aer weighted based on the total net assets at the beginning of the period. The sample period is 1981 to 2009 for (A) and (D) and from 1992 to 2009 for (B) and (C). The vertical shaded bars indicate recession periods according to the National Bureau of Economic Research.

58

Figure 2. Eigenvalue ratios (A) equity funds

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5annual flow (full)

(i

) /

(i+

1)

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5rolling

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5quarterly flow (full)

(i

) /

(i+

1)

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5rolling

(B) bond funds

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5annual flow (full)

(i

) /

(i+

1)

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5rolling

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5quarterly flow (full)

(i

) /

(i+

1)

2 4 6 8 101

1.1

1.2

1.3

1.4

1.5rolling

59

(C) money market funds

2 4 6 8 101

1.2

1.4

1.6

1.8

2annual flow (full)

(i

) /

(i+

1)

2 4 6 8 101

1.2

1.4

1.6

1.8

2rolling

2 4 6 8 101

1.2

1.4

1.6

1.8

2quarterly flow (full)

(i

) /

(i+

1)

2 4 6 8 101

1.2

1.4

1.6

1.8

2rolling

*Note: The figures plot the ratios of eigenvalues obtained from principal components analysis. The sample period is from 1981 to 2009 (annual) and from 1981 Q4 to 2009 Q4 (quarterly) for equity fund flows and from 1992 to 2009 (annual) and from 1992 Q4 to 2009 Q4 (quarterly) for bond fund flows, money market flows. The “full” method uses the whole sample period and the rolling method uses overlapping rolling samples of 12 years or 48 quarters. The sample includes the net flows of individual funds that have at least 5 million dollars in assets under management at the beginning of the period and are at least 1-year old.

60

Figure 3. Eigenvalues obtained using the Goyal et al. (2008) eigenprojection method to combine sectors

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3annual

(i)

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3quarterly

(i)

i

*Note: The eigenvalues of the matrix formed as the sum of the combined eigenprojections from each sector (equity, bond, and money market fund flows). For equity funds we use the first six factors, for bond funds the first three factors, and for money market funds the first two factors. Quarterly flows are residual flows after regressing net flows on quarterly dummies (without the intercept). The sample period is from 1992 to 2009 (annual) and from 1992 Q4 to 2009 Q4 (quarterly). The sample includes the net flows of individual funds that have at least 5 million dollars in assets under management at the beginning of the period and are at least 1-year old.

61

Figure 4. The first common factors

(A) full method

1985 1990 1995 2000 2005

equity fund factor

1995 2000 2005

bond fund factor

1995 2000 2005

money market fund factor

1995 2000 2005

Goyal et al factor

f1

-0.1

0

0.1

0.2

0.3

-0.1

0

0.1

0.2

0.3

f1

-0.1

0

0.1

0.2

0.3

-0.1

0

0.1

0.2

0.3

(B) rolling method

1985 1990 1995 2000 2005

equity fund factor

1995 2000 2005

bond fund factor

1995 2000 2005

money market fund factor

1995 2000 2005

Goyal et al factor

f1

-0.1

0

0.1

0.2

0.3

-0.1

0

0.1

0.2

0.3

f1

-0.1

0

0.1

0.2

0.3

-0.1

0

0.1

0.2

0.3

Note: The figures plot the first common factor extracted using principal components analysis or the Goyal et al

62

(2008) method. The “full” examples use the whole sample period and “rolling” uses overlapping rolling samples of 12 years or 48 quarters. The factor is scaled so that the value-weighted sector flows have the coefficient estimate on the factor equal to one. The sample period is 1981 to 2009 for the equity sector and from 1992 to 2009 for the others. The vertical shaded bars indicate recession periods as defined by the National Bureau of Economic Research.

63

Figure 5. The first common equity flow factor and the average flows into groups formed by performance ranking

Note: The top figure plots the first common equity factor and the average flows into each group formed based on lagged performance (return relative to the CSRP VW index) ranking. Group 1 is the lowest group and 3 is the highest group. Similarly, the bottom figure plots the first common equity factor and the average betas of each group. Group 2 is not shown. The data period is from 1981 to 2009.