wayne e. ferson* - university of southern californiaferson/papers/flowfinal.pdf · systematic...

112 Int. J. Portfolio Analysis and Management, Vol. 1, No. 2, 2012

Copyright © 2012 Inderscience Enterprises Ltd.

The factor structure of mutual fund flows

Wayne E. Ferson* Marshall School of Business, University of Southern California, 3670 Trousdale Parkway Suite 308, 90089-0804, Los Angeles, CA, USA E-mail: [email protected] *Corresponding author

Min S. Kim Level 3, Australian School of Business, University of New South Wales, 2052, Sydney, NSW, Australia E-mail: [email protected]

Abstract: Common factors in mutual fund flows explain significant fractions of annual and quarterly flows to individual US mutual funds. The factors are persistent and correlated with financial market conditions and macroeconomic variables. We find evidence that the common factors in investor flows are forward looking, although subject to frictions. The systematic components of flows differ substantially across funds according to funds’ ‘flow betas’. High-performing funds’ common factor flows bear an option-like relation to the aggregate sector flows, suggesting a new dimension in the incentives of fund managers. High flow beta funds offer low subsequent returns, consistent with adverse price pressure effects.

Keywords: mutual fund flows; common flow factors; flow beta; asymptotic principal components; fire sales.

Reference to this paper should be made as follows: Ferson, W.E. and Kim, M.S. (2012) ‘The factor structure of mutual fund flows’, Int. J. Portfolio Analysis and Management, Vol. 1, No. 2, pp.112–143.

Biographical notes: Wayne E. Ferson is the Ivadelle and Theodore Johnson Chair of Banking and Finance at Marshall School of Business, University of Southern California and a Research Associate of the National Bureau of Economic Research.

Min S. Kim is an Assistant Professor of Finance at the University of New South Wales.

1 Introduction

The determinants of the flows of money into mutual funds are important to understand for macroeconomic, microeconomic, financial economic and practical reasons. This

The factor structure of mutual fund flows 113

paper studies the factor structure of mutual fund flows. Like asset returns and liquidity, the flows of money into mutual funds have common components and idiosyncratic components.1 The common factor components of flows concentrate the relation of flows to macroeconomic variables, and we find several strong relations between those flows and the macroeconomy. The sensitivity of funds’ flows to common flow factors (flow betas) reflect the needs of funds to buy and sell securities at the same time, and are shown to be related to the funds’ subsequent return performance.

Previous studies have extracted common factors from mutual fund returns (e.g., Elton et al., 1999; Brown et al., 2004) but less is known about the common factors in mutual fund flows. Goetzmann et al. (2008) study factors in a small sample of daily fund flows during 18 months of 1998–1999. We focus on quarterly and annual flows for a large sample of stock, bond and money market funds during 1981–2009. We find that the systematic components of fund flows represent significant fractions of the time variation in individual fund flows. In a statistical factor analysis the first few factors capture more than 40% of the variance for equity and bond funds and slightly less for money market funds.

The common factors in mutual fund flows respond strongly to macroeconomic conditions.2 Economic variables explain almost 40% of the variance of the first equity fund flow factor, and the adjusted R-squares for bond funds and money funds are 37% and 30%, respectively. While the common flow factors are correlated with measures of investor sentiment, multiple regressions reveal that the simple correlation to sentiment proxies for relations to the fundamental macroeconomic and financial market variables.

Lagged flows also bear a predictive relation to the future values of several variables representing economic conditions, suggesting that in the aggregate fund investors do not simply chase the past (performance), but also look to expected future economic conditions. In particular, flows have predictive power for future economic growth and interest rates. The common factors in mutual fund flows are themselves predictable, displaying significant and complex autocorrelation structure with substantial persistence.

There is substantial variation across individual mutual funds in the sensitivity of their flows to common flow factors. Funds’ ‘flow betas’ describe this sensitivity.3 We model flow betas as functions of the characteristics of a fund including its size, age, expense ratio and recent return performance. We find that equity funds’ flow betas are asymmetric. Funds with recent high return performance have lower flow betas when the aggregate flow is negative and higher flow betas when the flow is positive. Thus, higher-performing funds’ common factor flows bear an option-like relation to the aggregate sector flows.

We find that equity funds with higher flow betas given large sector outflows offer lower subsequent return 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. This effect is related to the ‘fire sales’ phenomenon studied by Coval and Stafford (2007), who examine the individual stocks held by funds experiencing large negative total flows. Our analysis is not at the stock level but at the fund level, and concentrates on the systematic component of flows.

The rest of the paper is organised 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. Section 5 concludes and offers suggestions for future research.

114 W.E. Ferson and M.S. Kim

2 Data and methods

We study data for 1981–2009 from Morningstar on open-ended US equity, bond and taxable money market funds. We use Morningstar’s fund classifications. The equity funds exclude balanced funds, asset allocation funds, and index funds as identified by Morningstar from the funds’ prospectuses. The bond funds exclude municipal bond funds, and the money market funds exclude tax-exempt funds.4 The percentage flows of new money are defined in the usual way as:

( )[ ]1 11 ,− −= − +it it it it itF TNA TNA r TNA (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.5

2.1 Factor extraction methods

We decompose the fund flows into systematic and fund-specific or idiosyncratic components using a factor model:

1 , ( ) 0, ( ) 0,TF a YB u E u E u Y′ ′= + + = = (2)

where F is a T × N matrix of flows for T periods on N funds, Y is a T × K matrix of common flow factors, B is a K × 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, where E(uu′/N) is assumed to have 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 × 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 compared with traditional factor analyses or principal components based on the N × N covariance matrix, because there are many mutual funds with short time series, so N is large compared to T. Leaving out the funds 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 starts with the common factors extracted separately for each sector. Let xis be the ith orthonormal eigenvector from sector s. The eigenprojection matrix Σ Σ ( )i s is isx x′ 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 realisation 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.6

2.2 Factor extraction results

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, 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.

We examine the ratios of the adjacent ordered eigenvalues for the equity, bond and money market sectors. As is common in applications of factor analysis, 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 six to eight factors may be important for equity fund flows. Rolling estimation suggests a smaller number, typically three equity flow factors. The ratios for bond funds 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 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. The informal eigenvalue analysis likely overstates the number of common factors because the flows and their common factors are autocorrelated.

We combine the first six common equity flow factors with three bond and two money fund flow factors to examine common factors across the sectors. This approach produces a maximum of eleven non-zero eigenvalues, and the smallest estimated eigenvalue is often very close to zero. We examine the first ten raw eigenvalues. Given that the eigenprojection matrix Σ Σ ( )i s is isx x′ 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 sector-specific 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 orthonormalised. 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 an idealised step function we expect a smoothed graph in practice and that is what we find (figures are available by request). The analysis suggests that there is at least one factor that is common across all three sectors (eigenvalue above 2.0), and as many as four more with two sectors in common (eigenvalues above 1.0).


3 Empirical results for flow factors

3.1 Seasonality

Kamstra et al. (2010) study seasonality in monthly fund flows. Quarterly fund flow data have seasonal patterns. Table 1 summarises regressions of individual fund flows on four dummy variables for the quarter of the year. The seasonal patterns are not strong in the sense of high R-squares, but are often statistically significant. The mean adjusted R-squares of the regressions are between 6% and 14% for the three fund sectors, and the 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, consistent with Kamstra et al. (2010), 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 our analyses, including the previously described factor extraction. 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. 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 3,303 0.071 0.330 –0.923 –0.305 –0.049 0.024 0.182 0.638 0.950

Bond 1,722 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 3,303 0.025 (0.061) 0.029 (0.060) 0.019 (0.059) 0.015 (0.058)

Bond 1,722 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)

Notes: 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.


Table 1 Seasonality in quarterly fund flows and common factor correlations (continued)

(C) Correlations among the first factors

Equity Bond Money Goyal et al. (2008)

Annual Equity 1 Bond 0.075 1 (0.767) Money 0.132 –0.192 1 (0.601) (0.446) Combined 0.724 –0.173 0.336 1 Sectors (0.001) (0.493) (0.173) Quarterly Equity 1 Bond 0.321 1 (0.007) Money 0.221 0.006 1 (0.068) (0.963) Combined 0.729 0.003 0.431 1 Sectors ( < .0001) (0.978) (0.000)

Notes: 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.

3.2 Summary statistics

Since the factor analysis only identifies common factors to within a rotation, we scale the first common factor so that the flow beta of a value-weighted portfolio of funds in the sector on that 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 larger peaks and troughs, although sometimes with different amplitudes. This suggests that the first factors may be roughly interpreted as reflecting the aggregate sector flows.

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% to 73%) and has moderate positive correlation with money fund flows (34% to 43%) in quarterly data but has insignificant correlations with bond fund flows.


3.3 The explanatory power of common factors for individual funds’ flows

We run regressions for the flows of individual funds on the common factors over time and examine the cross-sectional distributions of the adjusted R-squares, including the values at various fractiles of the distributions (tables are available by request). On average the first 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, the common factors explain a significant fraction of equity mutual fund flows. The 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% to 10% and six factors deliver 18% to 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 in part, significant heterogeneity in the ‘flow betas’, or the loadings of the funds’ flows on the common flow factors.

3.4 Economic variables, financial market variables and flow factors

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 sentiment. Details about these data are provided in the Appendix, Table A1.

Goetzmann et al. (2008) extract factors from daily flow data over an 18-month sample, 1998–1999 and argue that ‘behavioural’ factors reflecting investor sentiment are important in mutual fund flows. Ben-Rephael et al. (2011) use flows between bond and stock funds as a measure of investor sentiment. We examine changes in two indexes for investor sentiment. The first is from Baker and Wurgler (2006) (BW), and the second is the Michigan consumer confidence index.

Table 2 presents simple correlations of the annual first common flow factors from each sector, and the first overall factor, on contemporaneous values of the 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 negative relation to volatility is consistent with Ederington and Golubeva (2009). The first bond flow factor is positively related to the slope of the term structure and stock market volatility, but negatively correlated with the change in the Baker-Wurgler sentiment index and the level of the short-term treasury rate. The correlations to market volatility and sentiment make sense as a ‘flight to quality’ phenomenon. The difference between the stock and bond fund sector flows is strongly positively related to changes in sentiment and negatively related to stock market volatility. When the stock market is volatile and sentiment is pessimistic investors reduce equity fund purchases and increase bond fund purchases (see also Chalmers et al., 2011; Ben-Rephael et al., 2011).


Table 2 Correlations of the first common factors with macroeconomic and financial market variables in annual data

(A) E

quity

fund

s (B

) Bon

d fu

nds

(C) M

oney

mar

ket

(D) G

oyal

et a

l. (2

008)

ρ p

valu

e

ρ p

valu

e

ρ p

valu

e

ρ p

valu

e

ΔMic

higa

n se

ntim

ent

0.39

0.

04

0.

25

0.32

–0.4

4 0.

07

0.

27

0.28

ΔB

W se

ntim

ent

0.08

0.

68

–0

.69

0.00

–0.1

3 0.

63

–0

.02

0.94

In

flatio

n –0

.04

0.84

–0.2

7 0.

28

–0

.50

0.03

–0.0

6 0.

82

Exch

ange

0.

39

0.04

–0.1

1 0.

66

0.

53

0.02

0.62

0.

01

Indu

stria

l pro

duct

ion

grow

th

0.31

0.

10

–0

.08

0.76

–0.5

0 0.

03

0.

48

0.04

D

ispo

sabl

e in

com

e gr

owth

0.

03

0.87

–0.0

9 0.

72

–0

.24

0.33

0.31

0.

22

TBill

0.

11

0.57

–0.7

1 0.

00

0.

07

0.78

0.59

0.

01

AA

A

0.23

0.

23

–0

.12

0.64

0.13

0.

62

0.

61

0.01

B

AA

0.

17

0.38

0.00

0.

99

0.

54

0.02

0.45

0.

06

AA

A –

Tbi

ll 0.

20

0.31

0.80

0.

00

0.

00

1.00

–0.3

1 0.

21

BA

A –

AA

A

–0.2

2 0.

25

0.

22

0.39

0.62

0.

01

–0

.40

0.10

M

arke

t ret

urn

0.30

0.

12

–0

.25

0.32

–0.3

8 0.

12

0.

42

0.08

M

arke

t vol

atili

ty

–0.4

5 0.

01

0.

46

0.05

0.38

0.

12

–0

.44

0.07

M

arke

t ret

urn

– Tb

ill

0.28

0.

14

–0

.18

0.46

–0.4

0 0.

10

0.

38

0.12

D

/P –

Tre

asur

y10y

ear

–0.2

9 0.

13

0.

42

0.08

–0.1

0 0.

69

–0

.68

0.00

D

/P

0.20

0.

31

0.

02

0.94

0.35

0.

16

–0

.08

0.76

Not

es: T

he sa

mpl

e co

rrel

atio

n be

twee

n th

e fir

st c

omm

on fa

ctor

s and

the

mac

roec

onom

ic a

nd fi

nanc

ial v

aria

bles

are

den

oted

as ρ

. The

p-v

alue

s are

com

pute

d us

ing

th

e t-d

istri

butio

n w

ith (T

– 2

) deg

ree

of fr

eedo

m fo

r the

stat

istic

(T –

2)1/

2 ([(ρ

2 ) / (1

– ρ

2 )])1/

2 whe

re T

is th

e nu

mbe

r of t

ime

perio

ds. T

he fa

ctor

s are

ext

ract

ed

usin

g as

ympt

otic

prin

cipa

l com

pone

nts a

naly

sis o

n fu

nd fl

ows.

Pane

l (D

) use

s the

Goy

al e

t al.

(200

8) m

etho

d. T

he M

ichi

gan

sent

imen

t ind

ex is

the

cons

umer

co

nfid

ence

inde

x fro

m th

e U

nive

rsity

of M

ichi

gan,

and

ΔM

ichi

gan

sent

imen

t is t

he c

hang

e in

the

log

of th

e in

dex.

ΔB

W se

ntim

ent i

s the

cha

nge

in th

e va

riabl

e co

nstru

cted

in B

aker

and

Wur

gler

(200

6). I

nfla

tion

is th

e ch

ange

in lo

g of

the

cons

umer

pric

e in

dex.

Exc

hang

e ra

te is

the

chan

ge in

log

of th

e m

ajor

fore

ign

exch

ange

inde

x. In

dust

rial p

rodu

ctio

n gr

owth

is th

e ch

ange

in lo

g of

the

inde

x fro

m F

eder

al R

eser

ve B

ank

of S

t. Lo

uis E

cono

mic

(FR

ED) d

ata.

Dis

posa

ble

inco

me

grow

th is

the

chan

ge in

log

of d

ispo

sabl

e pe

rson

al in

com

e pe

r cap

ita fr

om F

RED

. Mar

ket v

olat

ility

and

retu

rn a

re th

e st

anda

rd d

evia

tion

and

the

retu

rn o

n S&

P500

inde

x re

spec

tivel

y, w

hich

are

obt

aine

d us

ing

its d

aily

dat

a. D

/P ra

tio is

the

divi

dend

to p

rice

ratio

of t

he v

alue

wei

ghte

d C

RSP

inde

x. T

Bill

is th

e yi

eld

on

the

thre

e-m

onth

trea

sury

bill

. Tre

asur

y10y

ear i

s the

yie

ld o

n th

e te

n-ye

ar tr

easu

ry b

ond.

The

sam

ple

perio

d is

ann

ual,

from

198

1 to

200

9 fo

r US

equi

ty fu

nds a

nd

from

199

2 to

200

9 fo

r US

bond

fund

s and

US

mon

ey m

arke

t fun

ds.


Table 3 Regressions of common factors on macroeconomic and financial market variables

(A) E

quity

fund

sec

tor:

firs

t flo

w fa

ctor

f1 (a

nnua

l)

f1 (q

uart

erly

)

mod

el1

mod

el2

mod

el3

mod

el4

mod

el1

mod

el2

mod

el3

mod

el4

ΔM

ichi

gan

sent

imen

t

0.15

3

0.03

1

0.

028

–0

.003

(2

.098

)

(0.2

92)

(2.0

48)

(–

0.25

0)

ΔB

W s

entim

ent

0.

014

–0

.078

–0

.075

–0.0

16

(0.0

16)

(–

0.06

8)

(–0.

176)

(–0.

044)

In

flat

ion

–0.0

75

–1.0

36

0.

028

–0

.075

–0

.126

–0.3

70

(–

0.39

7)

(–1.

486)

(0.0

21)

(–

0.39

7)

(–0.

611)

(–1.

736)

E

xcha

nge

rate

0.

110

0.32

3

0.29

3

0.11

0 0.

102

0.

064

(2

.157

) (2

.101

)

(1.5

58)

(2

.157

) (1

.690

)

(1.4

54)

Dis

p in

com

e gr

owth

0.

070

–1.6

97

–0

.991

0.07

0 –0

.106

–0.1

93

(0

.473

) (–

1.96

3)

(–

0.92

0)

(0

.473

) (–

0.73

5)

(–

1.51

0)

IP g

row

th

0.

214

0.

219

0.01

8

0.01

7

(0

.818

)

(0.8

75)

(1.9

25)

(1

.545

) M

arke

t vol

atili

ty

–6.1

82

–5.0

68

–0

.596

–0

.910

(–1.

786)

(–

1.94

5)

(–

1.50

0)

(–2.

473)

M

kt. –

Tbi

ll re

t.

0.

074

0.10

8

0.03

1 0.

038

(1

.373

) (1

.755

)

(1.7

22)

(2.2

30)

BA

A –

AA

A

–0.0

31

–2.5

64

–0

.350

–0

.747

(–0.

017)

(–

0.57

0)

(–

1.00

7)

(–1.

631)

A

AA

– T

bill

2.22

2 2.

347

0.

407

0.45

9

(1.9

60)

(2.1

88)

(2

.256

) (2

.710

) D

p ra

tio –

T-1

0yr

–0.4

67

0.11

3

–0.3

29

–0.3

81

(–

1.05

1)

(0.0

67)

(–

3.94

1)

(–2.

965)

R

2 0.

332

0.40

30.

438

0.64

20.

054

0.08

5 0.

389

0.44

0A

djus

ted

R2

0.22

0 0.

215

0.31

6 0.

360

0.

019

0.02

9 0.

361

0.37

3

Not

es: T

he d

epen

dent

var

iabl

es a

re th

e co

mm

on fa

ctor

s ex

trac

ted

usin

g a

prin

cipa

l com

pone

nts

anal

ysis

on

fund

flow

s fo

r a g

iven

sec

tor.

Pan

el (D

) com

bine

s se

ctor

s us

ing

the

Goy

al e

t al.

(200

8) m

etho

d. T

he in

depe

nden

t var

iabl

es a

re th

e m

acro

var

iabl

es a

nd fi

nanc

ial v

aria

bles

as

liste

d in

the

firs

t col

umn.

ΔM

ichi

gan

sent

imen

t is

the

chan

ge o

f the

log

of th

e M

ichi

gan

sent

imen

t ind

ex a

s su

rvey

ed b

y th

e U

nive

rsity

of M

ichi

gan.

ΔB

W s

entim

ent i

s th

e ch

ange

in th

e va

riab

le c

onst

ruct

ed in

B

aker

and

Wur

gler

(200

6). I

nfla

tion

is th

e ch

ange

in lo

g of

the

cons

umer

pri

ce in

dex.

Exc

hang

e ra

te is

the

chan

ge in

log

of th

e m

ajor

fore

ign

exch

ange

inde

x. IP

gr

owth

is th

e ch

ange

in lo

g of

US

indu

stri

al p

rodu

ctio

n. D

isp

inco

me

grow

th is

the

chan

ge in

log

of p

erso

nal d

ispo

sabl

e in

com

e pe

r cap

ita. M

arke

t vol

atili

ty a

nd

retu

rn a

re th

e st

anda

rd d

evia

tion

and

the

retu

rn o

n S&

P500

inde

x re

spec

tivel

y, w

hich

are

obt

aine

d us

ing

its d

aily

dat

a. d

/p ra

tio is

the

divi

dend

to p

rice

ratio

of t

he

valu

e w

eigh

ted

CR

SP in

dex.

Tbi

ll is

the

yiel

d on

the

thre

e-m

onth

trea

sury

bill

. T-1

0yr

is th

e yi

eld

on th

e te

n-ye

ar tr

easu

ry b

ond.

The

tabl

e re

port

s th

e co

effi

cien

t es

timat

es a

nd th

eir t

-rat

ios,

whe

re th

e st

anda

rd e

rror

s ar

e N

ewey

-Wes

t est

imat

es w

ith tw

o la

gs fo

r ann

ual d

ata

and

five

lags

for q

uart

erly

dat

a. T

he s

ampl

e in

clud

es U

S eq

uity

mut

ual f

unds

, US

bond

fund

s, a

nd U

S m

oney

mar

ket f

unds

that

hav

e at

leas

t 5 m

illio

n do

llars

of a

sset

s un

der

man

agem

ent a

t the

beg

inni

ng o

f th

e pe

riod

s an

d ar

e at

leas

t one

-yea

r old

. The

sam

ple

peri

od is

from

198

0 Q

1 to

200

9 Q

4 fo

r US

equi

ty fu

nds

and

from

199

1 Q

1 to

200

9 Q

4 fo

r US

bond

fund

s an

d U

S m

one y

mar

ket f

unds

.


Table 3 Regressions of common factors on macroeconomic and financial market variables (continued)

(B

) Bon

d fu

nd s

ecto

r: fi

rst t

wo

flow

fact

ors

f1 (q

uart

erly

) f2

(qua

rter

ly)

mod

el1

mod

el2

mod

el3

mod

el4

mod

el1

mod

el2

mod

el3

mod

el4

ΔM

ichi

gan

sent

imen

t

–0.0

22

–0

.018

0.

279

–0

.085

(–

0.84

2)

(–

0.79

4)

(1.4

63)

(–

0.76

6)

ΔB

W s

entim

ent

–0

.023

–0.0

14

0.04

4

–0.0

36

(–2.

579)

(–2.

611)

(0

.615

)

(–1.

213)

In

flatio

n –0

.129

–0

.414

–0.3

54

1.

927

0.03

7

–1.5

93

(–

0.47

5)

(–0.

911)

(–1.

041)

(0.8

75)

(0.0

21)

(–

0.91

4)

Exc

hang

e ra

te

0.05

5 0.

171

0.

171

0.

855

0.89

1

0.51

0

(0.7

41)

(2.2

49)

(2

.920

)

(2.0

51)

(2.2

98)

(1

.805

) D

isp

inco

me

grow

th

–0.0

83

–0.2

63

–0

.221

2.14

2 0.

727

–0

.227

(–0.

452)

(–

1.52

7)

(–

1.36

1)

(1

.347

) (0

.426

)

(–0.

344)

IP

gro

wth

–0.0

08

–0

.005

0.

201

0.

199

(–0.

344)

(–0.

261)

(1

.763

)

(1.8

52)

Mar

ket v

olat

ility

0.

886

0.87

9

–5.8

16

–7.8

72

(1

.706

) (1

.863

)

(–1.

379)

(–

2.27

2)

Mkt

. – T

bill

ret.

0.00

4 0.

004

0.

253

0.44

4

(0.2

00)

(0.1

93)

(1

.746

) (4

.192

) B

AA

– A

AA

–1

.407

0.

677

–5

.460

–2

3.06

0

(–2.

740)

(0

.583

)

(–1.

338)

(–

4.04

1)

AA

A –

Tbi

ll

0.

657

0.52

5

–0.4

40

0.15

0

(3.0

36)

(2.5

24)

(–

0.37

7)

(0.1

84)

Dp

ratio

– T

-10y

r

–0

.085

–0

.189

–2.4

76

–1.6

59

(–

0.44

8)

(–0.

550)

(–2.

147)

(–

1.05

7)

R2

0.02

2 0.

253

0.33

4 0.

537

0.

080

0.11

7 0.

636

0.68

5 A

djus

ted

R2

–0.0

40

0.16

9 0.

281

0.43

1

0.02

3 0.

017

0.60

7 0.

613

Not

es: T

he d

epen

dent

var

iabl

es a

re th

e co

mm

on fa

ctor

s ex

trac

ted

usin

g a

prin

cipa

l com

pone

nts

anal

ysis

on

fund

flow

s fo

r a g

iven

sec

tor.

Pane

l (D

) com

bine

s se

ctor

s us

ing

the

Goy

al e

t al.

(200

8) m

etho

d. T

he in

depe

nden

t var

iabl

es a

re th

e m

acro

var

iabl

es a

nd fi

nanc

ial v

aria

bles

as

liste

d in

the

firs

t col

umn.

ΔM

ichi

gan

sent

imen

t is

the

chan

ge o

f the

log

of th

e M

ichi

gan

sent

imen

t ind

ex a

s su

rvey

ed b

y th

e U

nive

rsity

of M

ichi

gan.

ΔB

W s

entim

ent i

s th

e ch

ange

in th

e va

riab

le c

onst

ruct

ed in

B

aker

and

Wur

gler

(200

6). I

nfla

tion

is th

e ch

ange

in lo

g of

the

cons

umer

pri

ce in

dex.

Exc

hang

e ra

te is

the

chan

ge in

log

of th

e m

ajor

fore

ign

exch

ange

inde

x. IP

gr

owth

is th

e ch

ange

in lo

g of

US

indu

stri

al p

rodu

ctio

n. D

isp

inco

me

grow

th is

the

chan

ge in

log

of p

erso

nal d

ispo

sabl

e in

com

e pe

r cap

ita. M

arke

t vol

atili

ty a

nd

retu

rn a

re th

e st

anda

rd d

evia

tion

and

the

retu

rn o

n S&

P500

inde

x re

spec

tivel

y, w

hich

are

obt

aine

d us

ing

its d

aily

dat

a. d

/p ra

tio is

the

divi

dend

to p

rice

ratio

of t

he

valu

e w

eigh

ted

CR

SP in

dex.

Tbi

ll is

the

yiel

d on

the

thre

e-m

onth

trea

sury

bill

. T-1

0yr i

s th

e yi

eld

on th

e te

n-ye

ar tr

easu

ry b

ond.

The

tabl

e re

port

s th

e co

effi

cien

t es

timat

es a

nd th

eir t

-rat

ios,

whe

re th

e st

anda

rd e

rror

s ar

e N

ewey

-Wes

t est

imat

es w

ith tw

o la

gs fo

r ann

ual d

ata

and

five

lags

for q

uart

erly

dat

a. T

he s

ampl

e in

clud

es U

S eq

uity

mut

ual f

unds

, US

bond

fund

s, a

nd U

S m

oney

mar

ket f

unds

that

hav

e at

leas

t 5 m

illio

n do

llars

of a

sset

s un

der m

anag

emen

t at t

he b

egin

ning

of

the

peri

ods

and

are

at le

ast o

ne-y

ear o

ld. T

he s

ampl

e pe

riod

is fr

om 1

980

Q1

to 2

009

Q4

for U

S eq

uity

fund

s an

d fr

om 1

991

Q1

to 2

009

Q4

for U

S bo

nd fu

nds

and

US

mon

e y m

arke

t fun

ds.



(C) M

oney

mar

ket s

ecto

r: fi

rst t

wo

flow

fact

ors

f1 (q

uart

erly

) f2

(qua

rter

ly)

mod

el1

mod

el2

mod

el3

mod

el4

mod

el1

mod

el2

mod

el3

mod

el4

ΔM

ichi

gan

sent

imen

t

–0.0

65

–0

.019

0.

163

0.

285

(–1.

779)

(–0.

667)

(0

.833

)

(1.2

20)

ΔB

W s

entim

ent

0.

005

–0

.004

0.

007

–0

.032

(0

.678

)

(–0.

566)

(0

.202

)

(–1.

068)

In

flat

ion

–0.1

71

–0.9

05

–0

.716

–0.2

41

–2.2

87

–1

.425

(–0.

649)

(–

2.06

8)

(–

2.03

7)

(–

0.12

1)

(–0.

745)

(–0.

416)

E

xcha

nge

rate

0.

182

0.17

4

–0.0

15

–0

.465

0.

097

–0

.490

(1.7

07)

(1.9

78)

(–

0.22

9)

(–

0.99

7)

(0.2

16)

(–

1.03

8)

Dis

p in

com

e gr

owth

–0

.140

–0

.009

–0.2

03

5.

613

1.62

6

0.79

3

(–0.

406)

(–

0.04

3)

(–

1.32

5)

(1

.802

) (1

.176

)

(0.5

35)

IP g

row

th

–0

.004

–0.0

29

0.42

0

0.36

0

(–

0.11

4)

(–

1.02

3)

(2.5

33)

(2

.450

) M

arke

t vol

atili

ty

0.75

5 0.

579

5.

254

3.28

7

(1.3

27)

(0.9

90)

(1

.801

) (0

.974

) M

kt. –

Tbi

ll re

t.

–0

.114

–0

.094

0.05

9 –0

.175

(–3.

492)

(–

3.24

6)

(0

.431

) (–

1.70

7)

BA

A –

AA

A

–0.3

09

–2.7

87

–1

1.20

6 –7

.529

(–0.

464)

(–

1.80

8)

(–

2.31

1)

(–1.

036)

A

AA

– T

bill

–0.1

60

–0.1

06

–1

.115

–1

.039

(–0.

802)

(–

0.57

1)

(–

1.72

7)

(–1.

926)

D

p ra

tio –

T-1

0yr

(0.2

31)

(0.3

32)

(0

.887

) (1

.029

)

(–2.

738)

(–

1.59

5)

(–

1.54

3)

(–2.

257)

R

2 0.

073

0.11

2 0.

376

0.38

9

0.20

9 0.

131

0.25

0 0.

289

Adj

uste

d R

2 0.

015

0.01

2 0.

327

0.25

0

0.16

0 0.

032

0.19

1 0.

126

Not

es: T

he d

epen

dent

var

iabl

es a

re th

e co

mm

on fa

ctor

s ex

trac

ted

usin

g a

prin

cipa

l com

pone

nts

anal

ysis

on

fund

flow

s fo

r a g

iven

sec

tor.

Pane

l (D

) com

bine

s se

ctor

s us

ing

the

Goy

al e

t al.

(200

8) m

etho

d. T

he in

depe

nden

t var

iabl

es a

re th

e m

acro

var

iabl

es a

nd fi

nanc

ial v

aria

bles

as

liste

d in

the

firs

t col

umn.

ΔM

ichi

gan

sent

imen

t is

the

chan

ge o

f the

log

of th

e M

ichi

gan

sent

imen

t ind

ex a

s su

rvey

ed b

y th

e U

nive

rsity

of M

ichi

gan.

ΔB

W s

entim

ent i

s th

e ch

ange

in th

e va

riab

le c

onst

ruct

ed in

B

aker

and

Wur

gler

(200

6). I

nfla

tion

is th

e ch

ange

in lo

g of

the

cons

umer

pri

ce in

dex.

Exc

hang

e ra

te is

the

chan

ge in

log

of th

e m

ajor

fore

ign

exch

ange

inde

x. IP

gr

owth

is th

e ch

ange

in lo

g of

US

indu

stri

al p

rodu

ctio

n. D

isp

inco

me

grow

th is

the

chan

ge in

log

of p

erso

nal d

ispo

sabl

e in

com

e pe

r cap

ita. M

arke

t vol

atili

ty a

nd

retu

rn a

re th

e st

anda

rd d

evia

tion

and

the

retu

rn o

n S&

P500

inde

x re

spec

tivel

y, w

hich

are

obt

aine

d us

ing

its d

aily

dat

a. d

/p ra

tio is

the

divi

dend

to p

rice

ratio

of t

he

valu

e w

eigh

ted

CR

SP in

dex.

Tbi

ll is

the

yiel

d on

the

thre

e-m

onth

trea

sury

bill

. T-1

0yr i

s th

e yi

eld

on th

e te

n-ye

ar tr

easu

ry b

ond.

The

tabl

e re

port

s th

e co

effi

cien

t es

timat

es a

nd th

eir t

-rat

ios,

whe

re th

e st

anda

rd e

rror

s ar

e N

ewey

-Wes

t est

imat

es w

ith tw

o la

gs fo

r ann

ual d

ata

and

five

lags

for q

uart

erly

dat

a. T

he s

ampl

e in

clud

es U

S eq

uity

mut

ual f

unds

, US

bond

fund

s, a

nd U

S m

oney

mar

ket f

unds

that

hav

e at

leas

t 5 m

illio

n do

llars

of a

sset

s un

der m

anag

emen

t at t

he b

egin

ning

of

the

perio

ds a

nd a

re a

t lea

st o

ne-y

ear o

ld. T

he s

ampl

e pe

riod

is fr

om 1

980

Q1

to 2

009

Q4

for U

S eq

uity

fund

s an

d fr

om 1

991

Q1

to 2

009

Q4

for U

S bo

nd fu

nds

and

US

mon

e y m

arke

t fun

ds.



(D) G

oyal

et a

l. (2

008)

: fir

st tw

o flo

w fa

ctor

s

f1 (q

uart

erly

) f2

(qua

rter

ly)

mod

el1

mod

el2

mod

el3

mod

el4

mod

el1

mod

el2

mod

el3

mod

el4

ΔM

ichi

gan

sent

imen

t

0.01

2

–0.0

04

–0.1

96

–0

.070

(1

.326

)

(–0.

627)

(–

1.40

0)

(–

0.53

2)

ΔB

W s

entim

ent

0.

002

–0

.003

–0

.020

–0.0

72

(0.6

81)

(–

1.64

0)

(–0.

502)

(–1.

764)

In

flat

ion

0.09

6 –0

.112

–0.1

77

–0

.976

–3

.755

–3.5

45

(0

.613

) (–

0.75

2)

(–

1.56

8)

(–

0.43

6)

(–1.

714)

(–1.

738)

E

xcha

nge

rate

0.

089

0.09

6

0.03

8

0.81

7 1.

348

0.

566

(3

.256

) (3

.268

)

(2.3

95)

(1

.431

) (1

.963

)

(1.0

02)

Dis

p in

com

e gr

owth

0.

224

0.09

5

–0.0

11

–3

.320

–3

.045

–3.8

78

(2

.015

) (1

.011

)

(–0.

268)

(–1.

774)

(–

1.29

3)

(–

2.11

4)

IP g

row

th

0.

014

0.

011

0.03

8

–0.0

73

(2.0

77)

(1

.670

)

(0

.281

)

(–0.

516)

M

arke

t vol

atili

ty

–0.1

66

–0.3

41

0.

577

–1.3

16

(–

0.73

1)

(–1.

914)

(0.1

24)

(–0.

290)

M

kt. –

Tbi

ll re

t.

0.

001

0.01

1

–0.2

95

–0.3

79

(0

.120

) (1

.555

)

(–1.

413)

(–

2.36

8)

BA

A –

AA

A

–0.2

99

–1.1

79

7.

915

–14.

154

(–

1.35

1)

(–2.

551)

(1.5

10)

(–1.

255)

A

AA

– T

bill

0.00

0 0.

026

–0

.609

–0

.734

(0.0

02)

(0.4

55)

(–

0.27

2)

(–0.

387)

D

p ra

tio –

T-1

0yr

–0.3

68

–0.3

62

–0

.362

–1

.890

(–4.

989)

(–

3.47

4)

(–

0.21

3)

(–0.

726)

R

2 0.

139

0.18

9 0.

686

0.70

6

0.13

1 0.

168

0.16

5 0.

339

Adj

uste

d R

2 0.

085

0.09

8 0.

661

0.63

8

0.07

6 0.

074

0.09

8 0.

188

Not

es: T

he d

epen

dent

var

iabl

es a

re th

e co

mm

on fa

ctor

s ex

trac

ted

usin

g a

prin

cipa

l com

pone

nts

anal

ysis

on

fund

flow

s fo

r a g

iven

sec

tor.

Pane

l (D

) com

bine

s se

ctor

s us

ing

the

Goy

al e

t al.

(200

8) m

etho

d. T

he in

depe

nden

t var

iabl

es a

re th

e m

acro

var

iabl

es a

nd fi

nanc

ial v

aria

bles

as

liste

d in

the

first

col

umn.

ΔM

ichi

gan

sent

imen

t is

the

chan

ge o

f the

log

of th

e M

ichi

gan

sent

imen

t ind

ex a

s su

rvey

ed b

y th

e U

nive

rsity

of M

ichi

gan.

ΔB

W s

entim

ent i

s th

e ch

ange

in th

e va

riab

le c

onst

ruct

ed in

B

aker

and

Wur

gler

(200

6). I

nfla

tion

is th

e ch

ange

in lo

g of

the

cons

umer

pri

ce in

dex.

Exc

hang

e ra

te is

the

chan

ge in

log

of th

e m

ajor

fore

ign

exch

ange

inde

x. IP

gr

owth

is th

e ch

ange

in lo

g of

US

indu

stri

al p

rodu

ctio

n. D

isp

inco

me

grow

th is

the

chan

ge in

log

of p

erso

nal d

ispo

sabl

e in

com

e pe

r cap

ita. M

arke

t vol

atili

ty a

nd

retu

rn a

re th

e st

anda

rd d

evia

tion

and

the

retu

rn o

n S&

P500

inde

x re

spec

tivel

y, w

hich

are

obt

aine

d us

ing

its d

aily

dat

a. d

/p ra

tio is

the

divi

dend

to p

rice

ratio

of t

he

valu

e w

eigh

ted

CR

SP in

dex.

Tbi

ll is

the

yiel

d on

the

thre

e-m

onth

trea

sury

bill

. T-1

0yr i

s th

e yi

eld

on th

e te

n-ye

ar tr

easu

ry b

ond.

The

tabl

e re

ports

the

coef

ficie

nt

estim

ates

and

thei

r t-r

atio

s, w

here

the

stan

dard

err

ors

are

New

ey-W

est e

stim

ates

with

two

lags

for a

nnua

l dat

a an

d fi

ve la

gs fo

r qua

rter

ly d

ata.

The

sam

ple

incl

udes

US

equi

ty m

utua

l fun

ds, U

S bo

nd fu

nds,

and

US

mon

ey m

arke

t fun

ds th

at h

ave

at le

ast 5

mill

ion

dolla

rs o

f ass

ets

unde

r man

agem

ent a

t the

beg

inni

ng o

f th

e pe

riods

and

are

at l

east

one

-yea

r old

. The

sam

ple

peri

od is

from

198

0 Q

1 to

200

9 Q

4 fo

r US

equi

ty fu

nds

and

from

199

1 Q

1 to

200

9 Q

4 fo

r US

bond

fund

s an

d U

S m

one y

mar

ket f

unds

.


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 changes in consumer confidence, to inflation, and to the growth rate of industrial production growth. These correlations generally make intuitive sense. Investor flows into money market funds are high when consumer sentiment is pessimistic, real output growth is low 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. Chalmers et al. (2011) also find that investor flows are lower for money market funds and higher for stock funds when indicators associated with an improving economy are higher. At the same time, the value of the US dollar is positively related to stock fund and money fund flows, indicating that there are 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, and as Column D of Table 2 shows, this concentrates the relation with fundamental variables even more strongly. The correlations of the first overall common factor with the macroeconomic and financial market variables are strong. Industrial output, the value of the US dollar, financial market yields and stock market volatility all present significant and often strong correlations. However, there is no significant relation to the investor sentiment measures.

Table 3 presents the results of multiple regressions for the common factors on contemporaneous values of the variables. The goal here is to see if some of the variables subsume others. The explanatory variables are correlated, so the t-ratios of the multiple regressions are useful to discover which variables survive on a partial correlation basis. Stock market volatility and credit spreads emerge as important variables for annual equity fund flows. Stock market returns, inflation and the dividend yield spread survive in quarterly data. However, the sentiment indexes do not survive the combined model at either frequency. Thus, the significant simple correlations of flows to changes in the investor sentiment indexes appear to be a proxy for mutual correlations with more fundamental variables.

The multiple regressions for the bond fund flows are summarised in Panel B of Table 3. Because of the shorter sample period (1992–2009) we present multiple regressions for the first two factors and quarterly flows only. The first factor bears little relation to the macro variables, with the exception of the exchange rate, but is positively associated with the term spread, and has a counterintuitive negative coefficient on the change in the BW sentiment index. The second factor is strongly negatively related the credit spread, unlike the first, suggesting that the higher order factors are picking up differences in style within the bond fund sector.

Panel C of Table 3 presents the regressions for the first two money fund flow factors, again using quarterly data. The first factor is mainly associated with financial market variables, excepting a negative relation with inflation. The second factor, however, is positively related to industrial production growth. Panel D of Table 3 examines regressions for the overall common factors across the three fund sectors, again in quarterly data. Both the macro and financial market variables capture significant fractions of the flow variance, but the financial market variables contribute the larger share. The market yields and exchange rates show the strongest relations. There is no significant


relation to the sentiment indexes. Panel D confirms the overall impression that the common factors in mutual fund flows are strongly related to fundamental economic and financial market conditions, and once those are included in the regressions, there is little relation to sentiment indexes.

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. 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. 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, almost 0.80 for the overall common factor, but much smaller for the first money fund flow factor. Higher ordered factors also have high autocorrelations, including the money fund factors. While the autocorrelations are substantial, all are below 0.92. This suggests that the lagged flows may be used as predictors in regressions without undue concerns about spurious regression bias. Ferson et al. (2003) find that these issues arise mainly with autocorrelations larger than 0.95. Similarly, the lagged stochastic regressor bias studied by Stambaugh (1999) should not be a serious concern.

Table 4 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 the variables from Table 3. We summarise the results with time-series regressions over the full sample period. Four regressions models are presented, similar to Table 3. The annual regressions suggest predictability in the flows related to lagged macro variables (mainly, the exchange rate and past disposable income growth) and financial market variables (mainly, market volatility and the term spread). Jank (2011) also finds that equity fund flows are related to variables that have been used to predict equity market risk premiums. 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 characterised by substantial predictability over time, much of it associated with past macroeconomic and financial market 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. Model 3 in Table 4 appears consistent with these findings. Chalmers et al. (2011) find that economic activity, a term spread and the volatility of interest rates can predict monthly net fund flows. We find in quarterly data that the exchange rate and the lagged flows capture most of the explanatory power.

Panel B of Table 4 presents the predictability regressions for bond funds, using the quarterly data beginning in 1992. Like in the equity funds in quarterly data, lagged flows are main predictors, and the combined model’s adjusted R-squared is 64%. The combined model does feature significant t-ratios on the Michigan sentiment index and the credit spread.


Table 4 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

–0.035 –0.277 0.021 –0.024 ΔMichigan

sentiment (–0.405) (–1.426) (0.641) (–0.728) –0.022 –0.030 –0.001 0.001 ΔBW

sentiment (–1.573) (–1.355) (–0.211) (0.376) –0.922 –1.450 –0.690 –0.254 –0.862 –0.899 Inflation

(–1.568) (–1.452) (–0.404) (–0.488) (–1.818) (–1.767) 0.270 0.415 0.098 0.122 0.175 0.221 Exchange

rate (1.786) (1.868) (0.457) (1.292) (2.111) (3.055) –1.584 –1.566 0.291 0.078 –0.264 –0.264 Disp income

growth (–1.723) (–1.936) (0.264) (0.305) (–1.045) (–1.254) 0.761 0.458 0.544 –0.028 –0.021 –0.042 IP growth

(2.638) (1.028) (0.678) (–1.096) (–0.741) (–1.273) –7.999 –7.576 –0.622 –0.523 Market

volatility (–2.298) (–1.027) (–1.264) (–1.247) 0.061 –0.112 0.058 –0.012 Mkt –

Tbill return (0.713) (–1.089) (1.817) (–0.271) –1.176 –4.328 –0.748 0.780 BAA –

AAA (–0.587) (–0.837) (–1.253) (1.040) 2.472 1.539 0.301 0.091 AAA –

Tbill (2.636) (1.071) (1.476) (0.483) 0.136 –0.956 –0.147 0.181 Dp ratio –

T-10yr (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

Notes: The standard errors are Newey-West estimates with two lags for annual data and five 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.


Table 4 Regressions of the first factors on lagged macro and financial variables (continued)

(B) First bond fund flow factor

Quarterly f1(t + 1)

model1 model2 model3 model4

ΔMichigan sentiment –0.043 –0.055 (–1.766) (–3.771) ΔBW 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 growth –0.101 –0.143 0.054

(–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 – Tbill 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




(C) First money market fund flow factor

Quarterly f1(t + 1)


ΔMichigan sentiment –0.003 –0.012

(–0.455) (–1.372)

ΔBW 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 growth 0.042 –0.011 –0.043

(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)

Mkt – Tbill return 0.006 –0.017

(0.501) (–1.705)

BAA – AAA –0.174 –0.291

(–0.858) (–0.895)

AAA – Tbill –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




(D) First overall common factor

Quarterly f1(t + 1)


ΔMichigan sentiment –0.008 0.011 (–0.602) (0.800) ΔBW 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 growth 0.048 0.090 0.038 (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 – Tbill –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


Panel C of Table 4 presents the predictive regressions for the quarterly money fund flows, where the combined model produces a smaller adjusted R-square of 13%. Unlike


the case of equity and bond fund flows, and consistent with their relatively low autocorrelations, the lagged money fund flows do not deliver as much predictive power in the combined model. This makes sense if the autocorrelations and a substantial part of the predictability for the other types of fund flows reflect frictions, because the frictions are likely smaller in money market funds. For example, there are no embedded capital gains or load fees in money market funds.

Panel D summarises 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, the exchange rate, credit and term spreads, and especially the l 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. Even if it is largely driven by frictions, to the extent that aggregate investor behaviour as reflected in fund flows can be predicted, this behaviour 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 the question is also interesting. Is there information in fund flows that is predictive for future economic and financial market conditions? Table 5 examines whether the first factors can forecast the macroeconomic and financial variables. We regress the macroeconomic and financial market variables on their own lagged values and on the lagged flow factors. The 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 on the lagged flow factor and its t-ratio, indicating the marginal predictive ability of the flow for the economic variable’s AR(1) residuals.

Table 5 suggests that lagged flow factors bear a predictive relation to several of the variables. Equity and bond fund flow factors predict changes in the Michigan sentiment index. There is also significant predictive ability for industrial production growth, exchange rates, some interest rate spreads, and market volatility. The predictive relations also appear significant in the quarterly regressions, where ten of the 48 coefficient sport t-ratios larger than 2.0. The overall common factor predicts output and income growth in annual data, and several interest rates at both frequencies. Jank (2011) also finds that US equity mutual fund flows predict future industrial output and income growth. These results suggest that investors, at least in the aggregate flows, may not simply be irrationally chasing the past (performance) as some authors have suggested (e.g., Sapp and Tiwari, 2004; Frazzini and Lamont, 2006). The aggregate behaviour seems to anticipate future economic and financial market conditions.


Table 5 Regressions of macroeconomic and financial variables on their own lags and lagged common fund flow factors

(A) E

quity

f1 (1

981–

2009

) (B

) Equ

ity f1

(199

2–20

09)

(C) B

ond

f1 (1

992–

2009

) (D

) Mon

ey m

arke

t f1

(199

2–20

09)

Coe

ff.

(S.E

.) Ad

j. R2

Coe

ff.

(S.E

.) Ad

j. R2

Coe

ff.

(S.E

.) Ad

j. R2

Coe

ff.

(S.E

.) Ad

j. R2

Ann

ual

ΔM

ichi

gan

sent

imen

t 0.

787

(0.3

65)

0.04

3

0.49

5 (0

.328

) –0

.026

0.83

2 (0

.384

) 0.

092

0.

411

(0.3

56)

–0.0

13

In

flatio

n 0.

011

(0.0

34)

–0.0

36

0.

013

(0.0

26)

–0.0

62

–0

.022

(0

.019

) –0

.048

–0.0

28

(0.0

27)

–0.0

24

Ex

chan

ge

0.40

8 (0

.239

) 0.

030

0.

167

(0.2

50)

–0.0

53

–0

.704

(0

.252

) 0.

266

–0

.017

(0

.179

) –0

.066

IP g

row

th

0.39

4 (0

.111

) 0.

180

0.

358

(0.1

71)

0.08

7

0.10

1 (0

.119

) –0

.049

–0.0

14

(0.0

75)

–0.0

66

In

com

e gr

owth

0.

101

(0.0

73)

0.08

6

0.03

0 (0

.070

) –0

.054

0.04

9 (0

.034

) –0

.020

–0.0

03

(0.0

39)

–0.0

66

Tb

ill

0.10

7 (0

.120

) 0.

017

0.

162

(0.0

95)

0.13

2

–0.1

38

(0.0

38)

0.13

5

–0.0

65

(0.0

73)

–0.0

04

B

AA

0.

115

(0.0

95)

0.03

7

0.06

4 (0

.037

) 0.

084

–0

.009

(0

.030

) –0

.063

0.02

5 (0

.048

) –0

.022

AA

A

0.14

0 (0

.092

) 0.

089

0.

104

(0.0

47)

0.24

0

0.00

2 (0

.039

) –0

.067

0.01

5 (0

.049

) –0

.054

BA

A –

AA

A

–0.0

25

(0.0

15)

0.03

0

–0.0

40

(0.0

21)

0.07

1

–0.0

11

(0.0

15)

–0.0

53

0.

009

(0.0

09)

–0.0

52

A

AA

– T

bill

0.03

3 (0

.053

) –0

.021

–0.0

58

(0.0

80)

–0.0

23

0.

140

(0.0

26)

0.28

3

0.08

1 (0

.040

) 0.

094

M

arke

t ret

urn

0.18

2 (0

.557

) –0

.035

0.90

6 (0

.853

) –0

.008

–0.1

81

(0.6

77)

–0.0

63

0.

263

(0.3

63)

–0.0

57

M

arke

t vol

atili

ty

–0.0

39

(0.0

12)

0.16

1

–0.0

53

(0.0

16)

0.21

9

0.00

8 (0

.014

) –0

.059

0.03

8 (0

.007

) 0.

218

Qua

rterly

ΔM

ichi

gan

sent

imen

t –0

.179

(0

.069

) 0.

053

–1

.640

(1

.017

) 0.

031

0.

567

(0.3

83)

–0.0

03

–0

.042

(0

.367

) –0

.015

Infla

tion

0.00

1 (0

.005

) –0

.009

0.12

6 (0

.067

) 0.

014

–0

.055

(0

.031

) –0

.002

0.00

2 (0

.038

) –0

.015

Exch

ange

–0

.028

(0

.026

) –0

.002

0.31

7 (0

.388

) –0

.007

–0.0

52

(0.2

50)

–0.0

15

0.

290

(0.1

73)

0.01

8

IP g

row

th

–0.0

02

(0.0

37)

–0.0

09

0.

583

(0.7

58)

–0.0

08

0.

094

(0.2

32)

–0.0

15

–0

.073

(0

.358

) –0

.015

Inco

me

grow

th

–0.0

02

(0.0

06)

–0.0

08

–0

.018

(0

.130

) –0

.015

–0.0

09

(0.0

47)

–0.0

15

0.

020

(0.0

45)

–0.0

13

Tb

ill

–0.0

40

(0.0

32)

0.02

1

0.11

0 (0

.275

) –0

.011

–0.3

71

(0.1

78)

0.08

4

0.27

6 (0

.159

) 0.

099

B

AA

–0

.067

(0

.028

) 0.

082

0.

194

(0.0

88)

0.03

9

0.13

6 (0

.107

) 0.

045

0.

181

(0.0

60)

0.20

7

AA

A

–0.0

65

(0.0

25)

0.09

2

0.25

8 (0

.110

) 0.

061

0.

129

(0.1

12)

0.02

8

0.16

8 (0

.082

) 0.

136

B

AA

– A

AA

–0

.002

(0

.005

) –0

.006

–0.0

64

(0.0

41)

0.00

3

0.00

6 (0

.045

) –0

.015

0.01

3 (0

.033

) –0

.012

AA

A –

Tbi

ll –0

.025

(0

.015

) 0.

039

0.

148

(0.2

55)

–0.0

04

0.

500

(0.1

43)

0.27

3

–0.1

08

(0.1

05)

0.01

3

Mar

ket r

etur

n –0

.125

(0

.075

) 0.

022

–1

.030

(0

.814

) 0.

001

0.

266

(0.5

96)

–0.0

13

–0

.099

(0

.817

) –0

.014

Mar

ket v

olat

ility

0.

010

(0.0

05)

0.03

7

–0.0

42

(0.0

71)

–0.0

10

0.

039

(0.0

70)

–0.0

05

0.

033

(0.0

37)

–0.0

01

Not

es: T

he d

epen

dent

var

iabl

es a

re m

acro

econ

omic

and

fina

ncia

l var

iabl

es a

s lis

ted

in th

e fir

st c

olum

n. T

he in

depe

nden

t var

iabl

es a

re la

gged

dep

ende

nt v

aria

bles

and

the

lagg

ed v

alue

of t

he c

omm

on fl

ow fa

ctor

s in

mut

ual f

unds

, ext

ract

ed u

sing

a pr

inci

pal c

ompo

nent

s ana

lysi

s on

fund

flow

s for

the

indi

cate

d se

ctor

. Pan

el F

use

s the

G

oyal

et a

l. (2

008)

met

hod.

The

tabl

es re

port

the

coef

ficie

nt e

stim

ates

and

thei

r New

ey-W

est (

1980

) sta

ndar

d er

rors

usi

ng tw

o la

gs fo

r ann

ual d

ata

five

lags

for

quar

terly

dat

a. T

he sa

mpl

e pe

riods

are

from

198

1 Q

4 to

200

9 Q

4 fo

r equ

ity fu

nds a

nd fr

om 1

992

Q4

to 2

009

Q4

for b

ond

fund

s and

mon

ey m

arke

t fun

ds a

s sta

ted

in th

e pa

rent

hese

s.


Table 5 Regressions of macroeconomic and financial variables on their own lags and lagged common fund flow factors (continued)

(E) E

quity

f1 (1

992–

2009

) Bo

nd f1

(199

2–20

09)

Mon

ey m

arke

t f1

(199

2–20

09)

(F) O

vera

ll co

mm

on fa

ctor

(199

2–20

09)

Coe

ff.

(S.E

.)

Coe

ff.

(S.E

.)

Coe

ff.

(S.E

.) Ad

j. R2

Coe

ff.

(S.E

.) Ad

j. R2

Ann

ual

ΔMic

higa

n se

ntim

ent

0.45

1 (0

.373

)

0.78

3 (0

.398

)

0.40

7 (0

.401

) 0.

046

0.

093

(0.7

25)

–0.0

66

In

flatio

n 0.

013

(0.0

25)

–0

.022

(0

.018

)

–0.0

27

(0.0

29)

–0.1

56

–0

.007

(0

.051

) –0

.066

Exch

ange

0.

240

(0.2

18)

–0

.722

(0

.209

)

0.01

5 (0

.184

) 0.

185

0.

537

(0.2

21)

0.01

3

IP g

row

th

0.35

0 (0

.190

)

0.07

7 (0

.090

)

–0.0

02

(0.1

10)

–0.0

43

0.

449

(0.2

43)

0.07

3

Dis

p in

com

e gr

owth

0.

025

(0.0

80)

0.

047

(0.0

38)

–0

.003

(0

.039

) –0

.167

0.18

3 (0

.053

) 0.

202

Tb

ill

0.17

3 (0

.069

)

–0.1

48

(0.0

29)

–0

.053

(0

.060

) 0.

322

0.

327

(0.0

76)

0.40

1

BA

A

0.06

7 (0

.039

)

–0.0

15

(0.0

14)

0.

028

(0.0

44)

0.02

0

0.13

3 (0

.047

) 0.

314

A

AA

0.

106

(0.0

49)

–0

.006

(0

.018

)

0.02

0 (0

.040

) 0.

150

0.

189

(0.0

48)

0.52

1

BA

A –

AA

A

–0.0

39

(0.0

21)

–0

.008

(0

.013

)

0.00

8 (0

.011

) –0

.051

–0.0

57

(0.0

26)

0.08

9

AA

A –

Tbi

ll –0

.066

(0

.045

)

0.14

2 (0

.025

)

0.07

3 (0

.034

) 0.

403

–0

.138

(0

.089

) 0.

073

M

arke

t ret

urn

0.95

8 (0

.865

)

–0.2

63

(0.7

85)

0.

312

(0.4

81)

–0.1

40

1.

094

(1.0

35)

–0.0

17

M

arke

t vol

atili

ty

–0.0

51

(0.0

12)

0.

010

(0.0

10)

0.

036

(0.0

11)

0.40

6

–0.0

32

(0.0

39)

–0.0

08

Qua

rterly

ΔM

ichi

gan

sent

imen

t –1

.729

(1

.054

)

0.67

3 (0

.468

)

–0.0

78

(0.3

54)

0.01

9

0.33

1 (0

.734

) –0

.014

Infla

tion

0.13

5 (0

.066

)

–0.0

63

(0.0

29)

0.

005

(0.0

37)

0.00

1

0.03

4 (0

.090

) –0

.013

Exch

ange

0.

335

(0.3

80)

–0

.097

(0

.230

)

0.29

6 (0

.181

) –0

.002

0.90

2 (0

.379

) 0.

041

IP

gro

wth

0.

573

(0.7

85)

0.

068

(0.2

60)

–0

.074

(0

.359

) –0

.039

0.55

8 (0

.519

) –0

.010

Dis

p in

com

e gr

owth

–0

.016

(0

.132

)

–0.0

10

(0.0

48)

0.

021

(0.0

45)

–0.0

43

0.

106

(0.0

70)

–0.0

03

Tb

ill

0.16

9 (0

.226

)

–0.4

06

(0.1

56)

0.

293

(0.1

69)

0.19

6

1.37

4 (0

.242

) 0.

485

B

AA

0.

183

(0.0

89)

0.

110

(0.0

85)

0.

177

(0.0

57)

0.28

0

0.39

7 (0

.164

) 0.

174

A

AA

0.

248

(0.1

05)

0.

101

(0.0

91)

0.

164

(0.0

80)

0.21

7

0.70

8 (0

.145

) 0.

462

B

AA

– A

AA

–0

.065

(0

.041

)

0.00

9 (0

.042

)

0.01

3 (0

.034

) –0

.024

–0.3

11

(0.1

07)

0.33

7

AA

A –

Tbi

ll 0.

079

(0.1

56)

0.

507

(0.1

40)

–0

.129

(0

.107

) 0.

295

–0

.666

(0

.254

) 0.

173

M

arke

t ret

urn

–1.0

76

(0.8

36)

0.

338

(0.6

66)

–0

.117

(0

.827

) –0

.026

2.55

2 (1

.101

) 0.

067

M

arke

t vol

atili

ty

–0.0

46

(0.0

81)

0.

039

(0.0

66)

0.

031

(0.0

38)

–0.0

17

–0

.258

(0

.142

) 0.

141

Not

es: T

he d

epen

dent

var

iabl

es a

re m

acro

econ

omic

and

fina

ncia

l var

iabl

es a

s lis

ted

in th

e fir

st c

olum

n. T

he in

depe

nden

t var

iabl

es a

re la

gged

dep

ende

nt v

aria

bles

and

the

lagg

ed v

alue

of t

he c

omm

on fl

ow fa

ctor

s in

mut

ual f

unds

, ext

ract

ed u

sing

a pr

inci

pal c

ompo

nent

s ana

lysi

s on

fund

flow

s fo

r the

indi

cate

d se

ctor

. Pan

el F

use

s the

G

oyal

et a

l. (2

008)

met

hod.

The

tabl

es re

port

the

coef

ficie

nt e

stim

ates

and

thei

r New

ey-W

est (

1980

) sta

ndar

d er

rors

usi

ng tw

o la

gs fo

r ann

ual d

ata

five

lags

for

quar

terly

dat

a. T

he sa

mpl

e pe

riods

are

from

198

1 Q

4 to

200

9 Q

4 fo

r equ

ity fu

nds a

nd fr

om 1

992

Q4

to 2

009

Q4

for b

ond

fund

s and

mon

ey m

arke

t fun

ds a

s sta

ted

in th

e pa

rent

hese

s.


3.7 Models of flow betas

Individual funds’ loadings on the common flow factors have large cross-sectional variation, as the correlations in Table 2 suggest. This cross-sectional variation motivates a deeper analysis of the flow betas. We estimate models that allow the flow betas to vary over time and with fund characteristics. Specifically, using panel data, we estimate:

( )1 1Σ ,it i it j oj j it jt itF a G X b B X Y u− −′ ′= + + + + (3)

where 1( )oj j itb B X −′+ 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 models for equity returns discussed in Rosenberg and Marathe (1979) and Shanken (1990). The common component of a fund’s flow is captured in regression (3) by the common factors, Yjt, and the flow betas, 1( ).oj j itb B X −′+ When Xit–1 includes the fund’s past performance, the associated part of ai + G′Xit–1 is essentially a classical ‘flow-performance’ regression, following Sirri and Tufano (1998) or Chevalier and Ellison (1997) for the idiosyncratic component of flows.7

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. 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 dummies in the regressions. We distinguish between retail and institutional share classes in the regressions.

The regression estimates, standard errors and p-values for equity fund flow betas are presented in Table 6. 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. Previous studies of the flow-performance relation for equity funds find that young, small, more expensive and less volatile funds, and funds in larger families, attract more flows other things equal. Table 6 is consistent with these findings for the idiosyncratic flows. Lagged performance enters the regression positively and non-linearly, indicating a positive concave relation for the idiosyncratic flows, similar to previous work that uses the total flows. The coefficient in flow betas on the squared performance is only marginally significant, suggest that non-linearity in the flow performance relation is largely driven by the idiosyncratic component of flows.

A striking finding in Table 6 is the difference between the results for institutional and retail share classes. We find virtually no evidence that the flow betas for institutional share classes are functions of the lagged characteristics or recent performance. The idiosyncratic flow performance relation is similar to that of the retail share classes, with the exception of an insignificant relation to fund age and a marginally significant non-linear term in the lagged performance. The R-squares also show that the regression explains a smaller fraction of the variance of flows for the institutional share classes. To the extent that institutional flows are driven by defined-contribution retirement accounts, the 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.


Table 6 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 1.125 0.228 0.000 –0.168 0.754 0.824 f1*lagperformance^2 1.636 0.852 0.055 4.003 2.852 0.160 f1*lag2 performance 0.243 0.228 0.286 –0.436 0.768 0.570 f1*lagage –0.089 0.084 0.288 0.127 0.258 0.624 f1*lagsize –0.176 0.058 0.002 0.204 0.197 0.301 f1*lagexp 56.436 14.768 0.000 47.965 72.398 0.508 f1*lagvol –1.055 5.967 0.860 –6.145 20.678 0.766 f1*lagfamily size 0.191 0.037 0.000 0.087 0.113 0.440 f1*lagflow 0.783 0.124 0.000 –0.546 0.444 0.219 f1 –12.302 5.234 0.019 –13.585 11.371 0.232 lagperformance 0.348 0.017 0.000 0.369 0.041 0.000 lagperformance^2 0.306 0.063 0.000 0.284 0.156 0.069 lag2 performance 0.155 0.017 0.000 0.254 0.042 0.000 lagage –0.033 0.007 0.000 –0.010 0.016 0.530 lagsize –0.032 0.004 0.000 –0.044 0.010 0.000 lagexp –0.836 1.125 0.458 3.443 4.502 0.444 lagvol –0.737 0.422 0.081 –2.952 1.247 0.018 lagfamily size 0.016 0.003 0.000 0.022 0.007 0.001 lagflow 0.189 0.010 0.000 0.195 0.022 0.000

Adjusted R2 0.236 0.157 Fixed effect Time Time

Notes: 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 are clustered by 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.


Table 7 Asymmetric flow beta regressions (six factors are included in the model)

(A) Retail share classes (B) Institutional share classes

Estimate S.E. p-value Estimate S.E. p-value

f1 positive*lagperformance 2.395 0.393 0.000 1.917 1.294 0.138 f1 negative*lagperformance –4.666 1.502 0.002 –7.416 4.040 0.066 f1 positive*lagperformance^2 –0.640 1.490 0.667 1.111 4.804 0.817 f1 negative*lagperformance^2 12.051 5.634 0.032 14.876 14.937 0.319 f1 positive*lag2 performance 0.506 0.402 0.208 0.003 1.312 0.998 f1 negative*lag2 performance –0.682 1.553 0.661 –2.285 4.112 0.578 f1 positive*lagage –0.297 0.143 0.038 0.441 0.473 0.351 f1 negative*lagage 0.901 0.554 0.104 –0.815 1.511 0.590 f1 positive*lagsize –0.611 0.100 0.000 –0.190 0.347 0.584 f1 negative*lagsize 1.616 0.350 0.000 1.462 0.968 0.131 f1 positive*lagexp 67.617 25.298 0.008 155.969 133.180 0.242 f1 negative*lagexp –30.223 94.447 0.749 –438.816 429.376 0.307 f1 positive*lagvol –11.874 9.401 0.207 –52.102 37.084 0.160 f1 negative*lagvol 40.809 32.746 0.213 140.372 107.536 0.192 f1 positive*lagfamily size 0.433 0.067 0.000 0.275 0.214 0.199 f1 negative*lagfamily size –0.852 0.238 0.000 –0.649 0.667 0.330 f1 positive*lagflow 2.454 0.211 0.000 1.613 0.695 0.020 f1 negative*lagflow –7.267 0.826 0.000 –7.395 1.799 0.000 f1 positive –13.013 7.539 0.084 –3.963 16.576 0.811 f1 negative –10.614 5.532 0.055 –14.870 13.010 0.253 lagperformance 0.230 0.034 0.000 0.268 0.080 0.001 lagperformance^2 0.516 0.129 0.000 0.461 0.304 0.130 lag2 performance 0.131 0.035 0.000 0.224 0.082 0.006 lagage –0.014 0.012 0.266 –0.018 0.030 0.534 lagsize 0.001 0.008 0.902 –0.026 0.016 0.113 lagexp –2.427 2.147 0.258 –5.774 8.108 0.476 lagvol 0.136 0.708 0.847 –0.322 1.871 0.863 lagfamily size –0.003 0.005 0.531 0.010 0.012 0.404 lagflow 0.033 0.019 0.079 0.081 0.037 0.030

Adjusted R2 0.245 0.160 Fixed effect Time Time

Notes: The table is the same as Table 6 except that the interaction terms with the first factor have asymmetric estimates around the first factor equal to zero (piecewise linear specification). See the note for Table 6 for variable descriptions. The sample period is from 1982 to 2009.


Figure 1 The first common equity flow factor and the average flows into groups formed by performance ranking (see online version for colours)

First factor and average flow

Notes: 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.

We find evidence that flow betas for retail share classes are asymmetric, differing when the aggregate flow is positive or negative. Models allowing for asymmetry are presented in Table 7. Here we use a piece-wise estimation around a 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 illustrated in Figure 1. Here we graph the fitted fund flow against the aggregate flow factor for retail funds with performance in the top 30% and bottom 30% 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 percentage flow than 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.

4 Applications

4.1 Fund flow betas and fund performance

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 realise


depressed selling prices at such times. On the up side, there may be buying pressure effects. Coval and Stafford (2007) and Zhang (2009) find that funds with large outflows face poor performance, which is attributed to price pressure in the stocks they sell. Edelen (1999) finds evidence that equity fund trades made in response to flows are less profitable than are discretionary trades. Any price effect of non-discretionary trades should be more pronounced when driven by the systematic component of flows, when other funds are trading in the same direction.

Table 8 summarises 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 equity 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 regression using the data up to that quarter. The factors are estimated using rolling principal components on data up to quarter t. The coefficient estimates from the panel regression and the fund characteristics in 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 and the subsequent performance is evaluated. The portfolios of funds are equally-weighted in Panel A and TNA (size) 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 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 8 reports the performance estimates, their standard errors and p-values. High-low is the high flow beta minus the low flow beta portfolio. The sample period for performance is from 1984 to 2009. The standard errors are Newey-West estimates with four lags.

The first panel of Table 8 shows that high flow-beta funds earn lower subsequent average returns than low flow-beta funds, but the differences are less than 14 basis points per month and not statistically significant. However, flow betas are asymmetric as a function of sector flow levels, and when we allow for asymmetries in Table 8 the effects are stronger. In the lower three panels of the table we allow for different flow beta functions depending on the levels of the aggregate sector flows. Flows greater than, less than or within about one standard deviation of the aggregate flow factor are dummied out. This exercise reveals that the poor relative performance of high flow-beta funds is concentrated in betas on low sector flows. This is consistent with a stronger price pressure effect in sales than in purchases. The difference between the excess returns of the low and high flow-beta funds on sector outflows is 24 basis points per month and significant at the 10% level. Using the CAPM and FF3 alphas the differences are also monotonic across the quintiles and the high-low differences are significant at the 2% level. Controlling for momentum with the Carhart four-factor model, the high flow beta funds conditional on large sector outflows have significant negative performance. However, the 17 basis point difference in the high-low alpha is not statistically significant. In Panel B the TNA-weighted portfolios produce similar results.8 In summary, we find that equity funds whose flows are more sensitive to large sector outflows experience inferior subsequent return performance.


Table 8 The performance of quarterly-rebalanced portfolios of funds formed by betas on the first factor for equity fund flows

(A)

Equ

ally

-wei

ghte

d po

rtfo

lio o

f fun

ds

Exc

ess

retu

rn

CA

PM

alp

ha

FF

alp

ha

Car

hart

alp

ha

Est

imat

e S.

E.

p-va

lue

Est

imat

e S.

E.

p-va

lue

Est

imat

e S.

E.

p-va

lue

Est

imat

e S.

E.

p-va

lue

Bet

a on

f1

Low

0.

525

0.24

00.

029

0.

010

0.04

70.

827

–0.0

310.

045

0.49

7

–0.0

25

0.04

60.

586

1

0.52

8 0.

251

–0.0

14

–0

.014

0.04

0–0

.038

–0.0

380.

039

–0.0

41

–0

.041

0.

040

0.30

0

2 0.

551

0.26

3–0

.016

–0.0

160.

042

–0.0

23–0

.023

0.03

9–0

.036

–0.0

36

0.03

90.

359

3

0.52

8 0.

279

–0.0

71

–0

.071

0.05

5–0

.050

–0.0

500.

038

–0.0

66

–0

.066

0.

039

0.08

8

Hi g

h 0.

511

0.30

2–0

.125

–0.1

250.

083

–0.0

70–0

.070

0.05

4–0

.092

–0.0

92

0.05

50.

092

H

i gh-

low

–0

.014

0.

118

–0.1

36

–0

.136

0.10

5–0

.039

–0.0

390.

075

–0.0

68

–0

.068

0.

075

0.37

1B

eta

on f

1 >

0.0

1

L

o w

0.50

0 0.

286

0.08

1

–0.0

590.

061

0.33

4–0

.067

0.06

20.

276

–0

.010

0.

064

0.00

0

1 0.

507

0.28

5–0

.062

–0.0

620.

043

–0.0

67–0

.067

0.03

9–0

.052

–0.0

52

0.04

50.

249

2

0.54

9 0.

283

–0.0

25

–0

.025

0.04

7–0

.027

–0.0

270.

036

–0.0

43

–0

.043

0.

041

0.28

9

3 0.

511

0.28

7–0

.064

–0.0

640.

063

–0.0

62–0

.062

0.04

6–0

.106

–0.1

06

0.04

60.

023

H

i gh

0.57

5 0.

293

–0.0

07

–0

.007

0.07

40.

011

0.01

10.

060

–0.0

50

–0

.050

0.

060

0.40

9

Hi g

h-lo

w

0.07

5 0.

102

0.05

2

0.05

2 0.

104

0.07

90.

079

0.09

6–0

.039

–0.0

39

0.09

00.

660

Bet

a on

–0.

007

< f

1 <

0.0

1

L

o w

0.51

7 0.

268

0.05

5

–0.0

120.

071

0.87

0–0

.061

0.05

80.

294

–0

.060

0.

065

0.35

1

1 0.

525

0.27

5–0

.021

–0.0

210.

058

–0.0

55–0

.055

0.04

7–0

.055

–0.0

55

0.05

20.

292

2

0.52

0 0.

281

–0.0

47

–0

.047

0.04

3–0

.051

–0.0

510.

034

–0.0

59

–0

.059

0.

040

0.13

9

3 0.

536

0.29

6–0

.058

–0.0

580.

055

–0.0

28–0

.028

0.03

8–0

.053

–0.0

53

0.04

10.

196

H

i gh

0.54

4 0.

314

–0.0

78

–0

.078

0.07

1–0

.016

–0.0

160.

048

–0.0

33

–0

.033

0.

053

0.53

5

Hi g

h-lo

w

0.02

7 0.

107

–0.0

66

–0

.066

0.10

80.

044

0.04

40.

076

0.02

8

0.02

8 0.

083

0.73

9B

eta

on f

1 <

–0.

007

Lo w

0.

569

0.27

90.

042

0.

110

0.08

30.

182

0.08

30.

066

0.20

9

0.00

3 0.

066

0.96

4

1 0.

512

0.28

30.

039

0.

039

0.06

40.

014

0.01

40.

051

–0.0

28

–0

.028

0.

052

0.59

2

2 0.

458

0.29

0–0

.028

–0.0

280.

057

–0.0

46–0

.046

0.04

7–0

.062

–0.0

62

0.05

00.

222

3

0.42

0 0.

304

–0.0

87

–0

.087

0.05

0–0

.097

–0.0

970.

043

–0.0

73

–0

.073

0.

048

0.12

8

Hi g

h 0.

331

0.34

9–0

.239

–0.2

390.

086

–0.2

22–0

.222

0.07

6–0

.168

–0.1

68

0.08

40.

047

H

igh-

low

–0

.238

0.

140

–0.3

49

–0

.349

0.

136

–0.3

05

–0

.305

0.

121

–0.1

71

–0

.171

0.

116

0.14

2

Not

es: T

he ta

ble

repo

rts

mon

thly

exc

ess

retu

rns

(%)

over

the

trea

sury

bil

l rat

e an

d al

phas

(%

) fo

r po

rtfo

lios

of

fund

s fo

rmed

bas

ed o

n be

tas

on th

e fi

rst c

omm

on f

acto

r fo

r eq

uity

mut

ual f

und

flow

s. A

t the

end

of

each

qua

rter

fro

m 1

984

Q3

to 2

009

Q3,

flo

w b

etas

on

the

firs

t fa

ctor

are

est

imat

ed b

y ro

llin

g pa

nel r

egre

ssio

ns u

sing

th

e da

ta u

p to

that

qua

rter

. The

pan

el r

egre

ssio

n va

ries

in tw

o w

ays:

1

the

line

ar s

peci

fica

tion

for

the

firs

t fac

tor

f1

2 a

piec

ewis

e li

near

spe

cifi

cati

on w

ith

thre

e fa

ctor

s, d

efin

ed a

s {f

1 >

0.0

1, –

0.00

7 <

f1

< 0

.01

and

f1 <

–0.

007}

.

T

he s

ampl

e m

ean

flow

min

us th

e st

anda

rd d

evia

tion

of

f1 is

abo

ut –

0.00

7. T

he c

oeff

icie

nt e

stim

ates

obt

aine

d fr

om th

e pa

nel r

egre

ssio

n, f

und

char

acte

rist

ics

in

the

quar

ter

t and

the

firs

t fac

tor

are

used

to e

stim

ate

beta

s on

the

firs

t fac

tor.

The

fir

st f

acto

r is

est

imat

ed u

sing

the

prin

cipa

l com

pone

nt a

naly

sis

and

the

data

up

to th

e qu

arte

r t.

Fun

ds a

re r

anke

d an

d gr

oupe

d in

to f

ive

port

foli

os f

rom

low

to h

igh

acco

rdin

g to

the

beta

est

imat

es f

or y

ear

t. T

he p

ortf

olio

s of

fun

ds a

re

equa

lly-

wei

ghte

d in

Pan

el A

and

val

ue (

TN

A)-

wei

ghte

d in

Pan

el B

. The

por

tfol

ios

are

reba

lanc

ed e

very

qua

rter

. We

use

mon

thly

ret

urns

on

the

port

foli

os

in th

e fo

llow

ing

quar

ter

and

esti

mat

e th

e pe

rfor

man

ce o

f th

ese

port

foli

os a

s th

e av

erag

e ex

cess

ret

urns

ove

r th

e ri

sk-f

ree

rate

, CA

PM

alp

has,

Fam

a-F

renc

h

thre

e-fa

ctor

alp

has

and

Car

hart

fou

r-fa

ctor

alp

has.

The

tabl

e re

port

s th

e es

tim

ates

, sta

ndar

d er

rors

and

thei

r p-

valu

es. H

igh-

low

rep

orts

the

esti

mat

es o

n th

e hi

gh

min

us lo

w p

ortf

olio

s. T

he s

ampl

e pe

riod

is f

rom

198

2 to

200

9 an

d th

e fi

rst p

anel

reg

ress

ion

uses

dat

a up

to 1

984

Q3.

The

sta

ndar

d er

rors

New

ey-W

est e

stim

ates

w

ith

four

lags

.


Table 8 The performance of quarterly-rebalanced portfolios of funds formed by betas on the first factor for equity fund flows (continued)

(B)

Size

-wei

ghte

d po

rtfo

lio

of fu

nds

Exc

ess

retu

rn

CA

PM

alp

ha

FF

alp

ha

Car

hart

alp

ha

Est

imat

e S.

E.

p-va

lue

Est

imat

e S.

E.

p-va

lue

Est

imat

e S.

E.

p-va

lue

Est

imat

e S.

E.

p-va

lue

Bet

a on

f1

Low

0.

577

0.23

70.

016

0.

076

0.06

20.

222

0.00

90.

051

0.86

6

0.02

8 0.

052

0.59

3

1 0.

505

0.25

30.

047

–0

.043

0.

039

0.27

1–0

.058

0.03

70.

116

–0

.063

0.

037

0.09

1

2 0.

540

0.26

80.

045

–0

.041

0.

038

0.28

2–0

.016

0.03

60.

649

–0

.020

0.

037

0.59

1

3 0.

424

0.29

20.

147

–0

.200

0.

062

0.00

1–0

.133

0.04

50.

003

–0

.148

0.

046

0.00

1

Hi g

h 0.

416

0.32

00.

195

–0

.246

0.

106

0.02

1–0

.137

0.07

60.

073

–0

.167

0.

077

0.03

0

Hi g

h-lo

w

–0.1

61

0.16

90.

339

–0

.322

0.

153

0.03

7–0

.145

0.10

80.

181

–0

.195

0.

109

0.07

6B

eta

on f

1 >

0.0

1

L

ow

0.52

7 0.

280

0.06

1

–0.0

23

0.05

40.

663

–0.0

400.

052

0.44

4

0.01

3 0.

053

0.79

9

1 0.

487

0.28

10.

084

–0

.079

0.

036

0.02

9–0

.078

0.03

40.

025

–0

.090

0.

035

0.01

0

2 0.

546

0.29

00.

060

–0

.040

0.

053

0.45

4–0

.025

0.05

00.

623

–0

.066

0.

051

0.20

4

3 0.

497

0.29

50.

093

–0

.097

0.

071

0.17

1–0

.071

0.06

00.

238

–0

.139

0.

058

0.01

8

Hi g

h 0.

541

0.31

10.

083

–0

.067

0.

092

0.46

9–0

.009

0.08

60.

914

–0

.135

0.

078

0.08

4

Hi g

h-lo

w

0.01

4 0.

133

0.91

5

–0.0

43

0.12

80.

734

0.03

10.

119

0.79

5

–0.1

48

0.10

60.

163

Bet

a on

–0.

007

< f

1 <

0.0

1

L

ow

0.53

7 0.

266

0.04

4

0.01

9 0.

083

0.81

7–0

.057

0.06

10.

352

–0

.041

0.

068

0.55

0

1 0.

526

0.27

40.

055

–0

.015

0.

065

0.81

4–0

.066

0.04

90.

178

–0

.073

0.

054

0.17

8

2 0.

463

0.28

70.

108

–0

.112

0.

036

0.00

2–0

.098

0.03

60.

007

–0

.108

0.

037

0.00

4

3 0.

471

0.30

80.

127

–0

.138

0.

064

0.03

1–0

.082

0.05

20.

117

–0

.113

0.

049

0.02

1

Hi g

h 0.

457

0.33

00.

168

–0

.192

0.

102

0.06

2–0

.078

0.06

70.

251

–0

.099

0.

068

0.14

9

Hi g

h-lo

w

–0.0

81

0.16

00.

615

–0

.211

0.

168

0.20

9–0

.020

0.10

50.

846

–0

.058

0.

111

0.60

2B

eta

on f

1 <

–0.

007

Low

0.

579

0.27

10.

034

0.

128

0.08

50.

136

0.08

80.

068

0.19

4

0.00

0 0.

070

0.99

8

1 0.

572

0.28

30.

045

0.

103

0.06

50.

111

0.08

40.

058

0.15

3

0.00

1 0.

057

0.98

8

2 0.

435

0.28

70.

130

–0

.044

0.

045

0.32

8–0

.056

0.04

00.

167

–0

.092

0.

041

0.02

5

3 0.

439

0.29

30.

136

–0

.058

0.

045

0.19

8–0

.044

0.04

20.

294

–0

.030

0.

041

0.46

7

Hi g

h 0.

270

0.34

30.

433

–0

.288

0.

092

0.00

2–0

.260

0.07

90.

001

–0

.173

0.

084

0.04

0

Hig

h-lo

w

–0.3

09

0.15

4 0.

045

–0

.416

0.

158

0.00

9

–0.3

48

0.12

5 0.

006

–0

.173

0.

125

0.16

8

Not

es: T

he ta

ble

repo

rts

mon

thly

exc

ess

retu

rns

(%)

over

the

trea

sury

bil

l rat

e an

d al

phas

(%

) fo

r po

rtfo

lios

of

fund

s fo

rmed

bas

ed o

n be

tas

on th

e fi

rst c

omm

on f

acto

r fo

r eq

uity

mut

ual f

und

flow

s. A

t the

end

of

each

qua

rter

fro

m 1

984

Q3

to 2

009

Q3,

flo

w b

etas

on

the

firs

t fa

ctor

are

est

imat

ed b

y ro

llin

g pa

nel r

egre

ssio

ns u

sing

th

e da

ta u

p to

that

qua

rter

. The

pan

el r

egre

ssio

n va

ries

in tw

o w

ays:

1

the

line

ar s

peci

fica

tion

for

the

firs

t fac

tor

f1

2 a

piec

ewis

e li

near

spe

cifi

cati

on w

ith

thre

e fa

ctor

s, d

efin

ed a

s {f

1 >

0.0

1, –

0.00

7 <

f1

< 0

.01

and

f1 <

–0.

007}

.

T

he s

ampl

e m

ean

flow

min

us th

e st

anda

rd d

evia

tion

of

f1 is

abo

ut –

0.00

7. T

he c

oeff

icie

nt e

stim

ates

obt

aine

d fr

om th

e pa

nel r

egre

ssio

n, f

und

char

acte

rist

ics

in

the

quar

ter

t and

the

firs

t fac

tor

are

used

to e

stim

ate

beta

s on

the

firs

t fac

tor.

The

fir

st f

acto

r is

est

imat

ed u

sing

the

prin

cipa

l com

pone

nt a

naly

sis

and

the

data

up

to th

e qu

arte

r t.

Fun

ds a

re r

anke

d an

d gr

oupe

d in

to f

ive

port

folio

s fr

om lo

w to

hig

h ac

cord

ing

to th

e be

ta e

stim

ates

for

yea

r t.

The

por

tfol

ios

of f

unds

are

eq

uall

y-w

eigh

ted

in P

anel

A a

nd v

alue

(T

NA

)-w

eigh

ted

in P

anel

B. T

he p

ortf

olio

s ar

e re

bala

nced

eve

ry q

uart

er. W

e us

e m

onth

ly r

etur

ns o

n th

e po

rtfo

lios

in

the

foll

owin

g qu

arte

r an

d es

tim

ate

the

perf

orm

ance

of

thes

e po

rtfo

lios

as

the

aver

age

exce

ss r

etur

ns o

ver

the

risk

-fre

e ra

te, C

AP

M a

lpha

s, F

ama-

Fre

nch

th

ree-

fact

or a

lpha

s an

d C

arha

rt f

our-

fact

or a

lpha

s. T

he ta

ble

repo

rts

the

esti

mat

es, s

tand

ard

erro

rs a

nd th

eir

p-va

lues

. Hig

h-lo

w r

epor

ts th

e es

tim

ates

on

the

high

m

inus

low

por

tfol

ios.

The

sam

ple

peri

od is

fro

m 1

982

to 2

009

and

the

firs

t pan

el r

egre

ssio

n us

es d

ata

up to

198

4 Q

3. T

he s

tand

ard

erro

rs N

ewey

-Wes

t est

imat

es

wit

h fo

ur la

gs.


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 them into common factors and idiosyncratic components, and modelling funds’ ‘flow betas’, or the sensitivity of their flows to common flow factors. We study 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 capture significant fractions of the variation in individual fund flows over time. Unlike asset market prices, 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, likely reflecting frictions, and are also related to lagged macroeconomic and financial market variables. Lagged flows 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. Simple correlations of the common flow factors to measures of investor sentiment seem to proxy for relations to fundamental macroeconomic and financial market variables.

There is substantial variation across individual mutual funds in the sensitivity of their flows to the common flow factors. We model flow betas as functions of the characteristics of a fund and find that these betas 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 share and when there are negative sector flows, funds with weaker recent return performance lose the most. This option-like relation in the flows adds a new dimension to the incentives of mutual fund managers.

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. We believe that future research comparing common and idiosyncratic fund flows should lead to further significant refinements of our understanding of mutual funds and investor behaviour. Examples where this decomposition may prove interesting for future work include the flow-performance relation of Sirri and Tufano (1998) and Chevalier and Ellison (1999) and the ‘smart money’ effect of Gruber (1996) and Zheng (1999).

Acknowledgements

Wayne E. Ferson would like to acknowledge the hospitality of the Center for Financial Innovation and Stability at the Federal Reserve Bank of Atlanta. Min S. Kim would like to acknowledge financial support from 2011 Australian School of Business Research Grant. The authors are grateful to Jeff Wurgler for access to data and to Rich Evans, Chun Yang Hwang, Mitch Warachka and participants at the 2009 Financial Research Association Early Ideas Session, the First Asian Alliance Meeting, and the 2011 Asian Finance Meeting for helpful comments.


References Ahn, S.C. and Horenstein, A. (2009) ‘Eigenvalue ratio test for the number of factors’, Working

paper, Arizona State University. Bai, J. and Ng, S. (2002) ‘Determining the number of factors in approximate factor models’,

Econometrica, Vol. 70, No. 1, pp.191–221. Baker, W. and Wurgler, J. (2006) ‘Investor sentiment and the cross-section of stock returns’,

Journal of Finance, Vol. 61, No. 4, pp.1645–1680. Ben-Rephael, A., Kandel, S. and Wohl, A. (2011) ‘Measuring investor sentiment with mutual fund

flows’, Journal of Financial Economics, forthcoming. Brown, S.J., Goetzmann, W. and Grinblatt, M. (2004) ‘Positive portfolio factors’, Yale School of

Management working papers, Yale School of Management. Chalmers, J., Kaul, A. and Phillips, B. (2011) ‘The wisdom of crowds: mutual fund investors’

aggregate asset allocation decisions’, Working paper. Chevalier, J. and Ellison, L. (1997) ‘Risk taking by mutual funds as a response to incentives’,

Journal of Political Economy, Vol. 105, No. 6, pp.1167–1200. Chordia, T., Roll, R. and Subrahmanyam, A. (2000) ‘Commonality in liquidity’, Journal of

Financial Economics, Vol. 56, No. 1, pp.3–28. Cochrane, J.H. (1996) ‘A cross-sectional test of an investment-based asset pricing model’, Journal

of Political Economy, Vol. 104, No. 3, pp.572–621. Connor, G. and Korajczyk, R. (1986) ‘Performance measurement with the arbitrage pricing theory:

a new framework for analysis’, Journal of Financial Economics, Vol. 15, No. 3, pp.373–394. Connor, G. and Korajczyk, R. (1988) ‘Estimating pervasive factors with missing observations’,

Working paper. Coval, J. and Stafford, E. (2007) ‘Asset fire sales (and purchases) in equity markets’, Journal of

Financial Economics, Vol. 86, No. 2, pp.479–512. Duan, Y. (2010) ‘Fund flow betas and the cross-section of stock returns’, Working paper. Edelen, R.M. (1999) ‘Investor flows and the assessed performance of open-end mutual funds’,

Journal of Financial Economics, Vol. 53, No. 3, pp.439–466. Ederington, L. and Golubeva, E. (2009) ‘Evidence on investor behavior from aggregate stock

mutual fund flows’, Working paper. Elton, E.J., Gruber, M.J. and Blake, C.R. (1999) ‘Common factors in fund returns’, European

Financial Review, Vol. 3, No. 1, pp.1–23. Evans, R. (2010) ‘Mutual fund incubation’, Journal of Finance, Vol. 65, No. 4, pp.1581–1611. Ferson, W. and Warther, V.A. (1996) ‘Evaluating fund performance in a dynamic market’,

Financial Analysts Journal, Vol. 52, No. 6, pp.20–28. Ferson, W.E., Sarkissian, S. and Simin, T.T. (2003) ‘Spurious regressions in financial economics?’,

Journal of Finance, Vol. 58, No. 4, pp.1393–1414. Frazzini, A. and Lamont, O. (2006) ‘Dumb money: mutual fund flows and the cross-section of

stock returns’, Journal of Financial Economics, Vol. 88, No. 2, pp.299–232. Goetzmann, W., Massa, M. and Rouwenhorst, G. (2008) ‘Behavioral factors in mutual fund flows’,

Yale School of Management working paper. Goyal, A., Pérignon, C. and Villa, C. (2008) ‘How common are common return factors across the

NYSE and NASDAQ?’, Journal of Financial Economics, Vol. 90, No. 3, pp.252–271. Gruber, M. (1996) ‘Another puzzle: the growth in actively managed mutual funds’, Journal of

Finance, Vol. 51, No. 3, pp.783–810. Jagannathan, R. and Wang, Z. (1996) ‘The conditional CAPM and the cross-section of expected

returns’, Journal of Finance, Vol. 51, No. 1, pp.3–53. Jank, S. (2011) ‘Mutual fund flows, expected returns, and the real economy’, CFR working paper,

No. 11-04.


Kamstra, M.J., Kramer, L.A., Levi, M.D. and Wermers, R.R. (2010) ‘Seasonal asset allocation: evidence from mutual fund flows’, Working paper.

Kim, M.S. (2012) ‘Commonality in mutual fund flows and its implications’, Working paper, University of New South Wales.

King, B.F. (1966) ‘Market and industry factors in stock price behavior’, Journal of Business, Vol. 39, No. 1, pp.139–190.

Onatski, A. (2006) ‘Determining the number of factors from empirical distribution of eigenvalues’, Working paper, Columbia University.

Rosenberg, B. and Marathe, V. (1979) ‘Tests of capital asset pricing hypotheses’, in H. Levy (Ed.): Research in Finance, Vol. 1, CT-JAI Press Inc., Greenwich.

Sapp, T. and Tiwari, A. (2004) ‘Does stock return momentum explain the ‘smart money’ effect?’, Journal of Finance, Vol. 59, No. 6, pp.2605–2622.

Shanken, J. (1990) ‘Intertemporal asset pricing: an empirical investigation’, Journal of Econometrics, Vol. 45, Nos. 1–2, pp.99–120, Elsevier.

Sirri, E.R. and Tufano, P. (1998) ‘Costly search and mutual fund flows’, Journal of Finance, Vol. 53, No. 5, pp.1589–1622.

Stambaugh, R.F. (1999) ‘Predictive regressions’, Journal of Financial Economics, Vol. 54, No. 3, pp.375–421.

Warther, V.A. (1995) ‘Aggregate mutual fund flows and security returns’, Journal of Financial Economics, Vol. 39, Nos. 2–3, pp.209–235.

Zhang, H. (2009) ‘Asset fire sales, liquidity provision, and mutual fund performance’, Working paper, University of Texas.

Zheng, L. (1999) ‘Is money smart?: a study of mutual fund investors’ fund selection ability’, Journal of Finance, Vol. 54, No. 3, pp.901–933.

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

in liquidity since Chordia et al. (2000). 2 Other studies have observed that aggregate mutual fund flows are related to economic

conditions. See for example, Warther (1995), Chalmers et al. (2011), Jank (2011) and Ben-Raphael et al. (2011).

3 Duan (2010) examines betas of equity fund returns on aggregate fund flows and calls these ‘flow betas’. Our flow betas are the betas of a fund’s flow on the common factor flows.

4 We subject the funds to a number of screens. To minimise 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 where the data begin in 1992, the number of fund years is 15,801 and 9,774, respectively.

5 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.

6 Fund flows might represent fertile grounds for future work using dynamic factor models. 7 See Kim (2012) for an analysis of the flow performance relation that distinguishes between

common and idiosyncratic flows.


8 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.

Appendix

Table A1 Macroeconomic and financial variables

Variable Definition Source

ΔMichigan sentiment

Change in log of the University of Michigan consumer sentiment

Federal Reserve Bank of St. Louis Economic data (FRED)

ΔBW sentiment Change in the sentiment index updated by equation (2) in Baker and Wurgler (2006)

Jeff Wurgler

Inflation Change in log of the consumer price index of all items


Exchange Change in log of the major foreign exchange index (trade-weighted)


IP growth Change in log of the industrial production index


Disp income growth Change in log of the disposable personal income


Tbill Three-month treasury bill rate (secondary market rate)


T-10yr Ten-year treasury constant maturity rate


BAA Moody’s seasoned Baa corporate bond yield


AAA Moody’s seasoned Aaa corporate bond yield


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

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

wayne e. ferson* - university of southern californiaferson/papers/flowfinal.pdf · systematic...

Documents