The factor structure of mutual fund flows

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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

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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.

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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 1

]

−1,

= − +

it it it it it

F 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:

1T , ( ) 0, ( ) 0,

F= 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 Σi s (x xis is′) 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

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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 Σi s(x xis is′) 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).

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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.

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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.

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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).

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

(A ) Equ it y f unds (B ) Bo nd fund s (C ) Money mar ke t (D ) Goyal et a l. ( 2008 ) ρ p va lu e ρ p va lu e ρ p va lu e ρ p va lu e Δ Mic hig an se nti m en t 0.3 9 0. 04 0.2 5 0.3 2 –0 .4 4 0.0 7 0.2 7 0. 28 Δ BW se nt im en t 0.0 8 0. 68 –0 .69 0.0 0 –0 .1 3 0.6 3 –0. 02 0. 94 Inf la tion –0. 04 0. 84 –0 .27 0.2 8 –0 .5 0 0.0 3 –0. 06 0. 82 Exch an ge 0. 39 0. 04 –0 .1 1 0. 66 0. 53 0. 02 0 .62 0. 01 Ind ust ria l p ro du ct io n g row th 0.3 1 0. 10 –0 .08 0.7 6 –0 .5 0 0.0 3 0.4 8 0. 04 D is posa ble in co m e g ro w th 0.0 3 0. 87 –0 .09 0.7 2 –0 .2 4 0.3 3 0.3 1 0. 22 T B il l 0. 11 0. 57 –0 .7 1 0. 00 0. 07 0. 78 0 .59 0. 01 AA A 0. 23 0. 23 –0 .1 2 0. 64 0. 13 0. 62 0 .61 0. 01 BAA 0. 17 0. 38 0. 00 0 .99 0. 54 0 .02 0. 45 0. 06 A A A – T bi ll 0.2 0 0. 31 0.8 0 0.0 0 0. 00 1.0 0 –0. 31 0. 21 BA A – A A A –0. 22 0. 25 0.2 2 0.3 9 0. 62 0.0 1 –0. 40 0. 10 Ma rk et re turn 0.3 0 0. 12 –0 .25 0.3 2 –0 .3 8 0.1 2 0.4 2 0. 08 Ma rk et v ola ti li ty –0. 45 0. 01 0.4 6 0.0 5 0. 38 0.1 2 –0. 44 0. 07 Ma rk et re turn – T bi ll 0.2 8 0. 14 –0 .18 0.4 6 –0 .4 0 0.1 0 0.3 8 0. 12 D /P – T re as ury 10 ye ar –0. 29 0. 13 0.4 2 0.0 8 –0 .1 0 0.6 9 –0. 68 0. 00 D/ P 0. 20 0. 31 0. 02 0 .94 0. 35 0 .16 –0 .0 8 0. 76 No tes : T he s am pl e co rr ela tio n be tw ee n th e f ir st co mm on f act or s an d th e m acr oe co no m ic an d fin an ci al var iab le s ar e d en ot ed a s ρ . T he p -v alu es ar e co m pu ted u si ng the t -d is tr ib ut io n w ith ( T – 2) de gr ee o f fr ee dom f or t he s ta ti st ic ( T – 2) 1/2 ([ ( ρ 2) / ( 1 – ρ 2)] ) 1/2 wh er e T is th e nu m ber o f t im e p er io ds. T he f act or s ar e ex tr act ed us in g as ym pt ot ic p rin cip al c om po nen ts an al ys is o n fu nd f lo w s. P anel ( D ) u ses th e G oyal et a l. ( 200 8) m eth od . Th e M ic higan se nt im ent i nde x is th e c on sum er co nf id en ce i nd ex f ro m th e U ni ve rsi ty o f M ich igan , an d Δ M ich igan s en tim en t is th e c han ge i n th e lo g of th e i nd ex. Δ BW se nt im en t i s t he ch an ge i n t he var iab le co ns tr uc ted i n Baker an d Wu rg le r ( 200 6) . I nf lati on is th e ch an ge in lo g o f th e co ns um er p ri ce i nd ex . E xch an ge r ate i s th e ch an ge in lo g o f t he majo r f oreign ex ch an ge index . Indu st ri al p ro du ct ion g row th is the cha ng e i n l og o f the ind ex f rom Fe de ra l Re se rv e Ba nk o f St. L ou is E co nom ic (FRE D ) da ta . Disp os able in co m e gr ow th is th e ch an ge in log o f d is po sab le pe rs on al in co m e p er cap it a f ro m F R ED . M ar ket vo la ti lit y an d r et ur n ar e th e st an dar d de vi at io n and th e r et ur n on S& P5 00 index re sp ec tiv el y, w hi ch ar e ob ta in ed us ing it s d ai ly da ta . D /P r at io is th e d iv id en d to pr ic e r ati o of the v alue w ei gh ted CRS P in de x. T B il l is th e y ield o n th e t hr ee -m on th tr ea su ry b ill . Tr eas ur y1 0y ea r is th e y ield o n th e t en -y ear tr ea su ry b on d. Th e s am ple p er iod is ann ual, f ro m 1 98 1 to 20 09 f or U S e qu ity f unds a nd fr om 1 992 to 2 00 9 f or US b on d f und s an d US m one y mar ket f un ds .

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Table 3 Regressions of common factors on macroeconomic and financial market variables (A ) E q u ity f u nd secto r: f irst fl o w f a cto r f1 ( a n nu al ) f1 ( q u a rterly) mo d el1 mo d el2 mo d el 3 mo d el4 m ode l1 m o d el2 m ode l3 m o de l4 Δ Mic h ig an s ent im en t 0.1 5 3 0 .0 31 0.0 28 –0. 0 03 (2 .0 9 8 ) (0 .2 9 2 ) (2 .04 8 ) (– 0 .2 50 ) Δ BW s enti m en t 0.0 1 4 – 0 .0 78 –0. 0 75 –0. 0 16 ( 0 .0 1 6 ) (– 0. 06 8) (– 0. 17 6) (– 0. 04 4) In fl at ion –0. 0 75 –1. 0 36 0 .0 28 –0. 0 75 –0. 1 26 –0. 3 70 ( – 0. 39 7) (– 1. 48 6) (0 .0 21) (–0. 39 7) (– 0. 61 1) (– 1. 73 6) Ex ch an ge r at e 0 .1 1 0 0.3 2 3 0 .2 93 0.1 1 0 0.1 02 0.0 6 4 (2 .1 5 7 ) (2 .1 0 1 ) (1 .5 5 8 ) (2 .1 5 7 ) (1 .69 0 ) (1 .4 5 4 ) D is p i n co m e g row th 0 .0 7 0 –1. 6 97 – 0 .9 91 0.0 7 0 –0. 1 06 –0. 1 93 ( 0 .4 73) (– 1. 96 3) (– 0. 92 0) (0 .4 73 ) (– 0. 73 5) (– 1. 51 0) IP g row th 0.2 1 4 0 .2 19 0.0 18 0.0 1 7 (0 .8 1 8 ) (0 .8 7 5 ) (1 .92 5 ) (1 .5 4 5 ) Ma rk et v o la ti li ty –6. 18 2 – 5 .0 68 –0 .5 96 –0. 9 10 (–1. 78 6) (– 1. 94 5) (– 1 .50 0) (– 2. 47 3) Mk t. – T b il l r et . 0.0 74 0 .1 08 0 .0 3 1 0.0 3 8 (1 .37 3 ) (1 .7 5 5 ) (1 .7 2 2 ) (2 .2 3 0 ) BA A – A A A –0. 03 1 – 2 .5 64 –0 .3 50 –0. 7 47 (–0. 01 7) (– 0. 57 0) (– 1 .00 7) (– 1. 63 1) A A A – T b il l 2.2 22 2 .3 47 0 .4 0 7 0.4 5 9 (1 .96 0 ) (2 .1 8 8 ) (2 .2 5 6 ) (2 .7 1 0 ) D p ra ti o – T -10y r –0. 46 7 0 .1 13 –0 .3 29 –0. 3 81 (–1. 05 1) (0 .0 67) (– 3 .94 1) (– 2. 96 5) R 2 0 .3 3 2 0.4 0 3 0 .4 38 0 .6 4 2 0 .0 54 0.0 85 0 .3 8 9 0.4 4 0 Ad ju st ed R 2 0 .2 2 0 0.2 1 5 0.3 16 0 .3 60 0.0 1 9 0.0 29 0 .3 6 1 0.3 7 3 No te s: T h e d ep en d en t va ri ab les are th e co mm o n f acto rs e xtra ct ed u sin g a p rin ci p al co m p o n en ts an al ysis o n f u n d f lo w s fo r a g iven se ct o r. P an el (D) co m b in es se cto rs u sin g th e G o ya l e t a l. (2 0 08 ) m et h o d. T h e i nd ep en d en t variab les ar e t h e m acro va ri ab les an d f in an cial va ri ab les as list ed in t he f irst co lu m n . Δ Mi ch ig an sen ti m en t is t h e ch an ge o f th e l o g o f t h e Mi ch ig an sen ti m en t in d ex as s u rv ey ed b y th e Un iv ersi ty o f Mi ch ig an . Δ BW se n ti m en t is th e ch an ge i n th e v ariab le co n st ru cted i n Bak er an d W u rg ler (2 0 0 6) . I n fl ati o n is th e ch an ge i n l o g o f th e co ns u m er p rice in d ex. Exc h an ge ra te is th e ch an ge i n l o g o f t h e m ajor f o re ig n e xc h an ge inde x. I P gr o w th i s th e ch an ge in lo g o f US in du st rial p ro d u ct io n . Di sp i n co me gro w th is t h e c h an ge in l o g o f p erso n al d isp o sab le i n co m e p er ca p ita. Mark et vo la ti lity an d retu rn are t h e stan d ard d eviati on an d t h e retu rn o n S & P 5 00 i n d ex r esp ec ti ve ly , w h ic h a re o b tai n ed u sin g it s d ai ly d ata. d /p rat io is t h e di vi de nd t o pr ic e r at io of t h e va lu e weigh ted CRS P i n d ex. T b il l is t h e y ie ld o n th e th ree -m o n th tr easu ry b il l. T -1 0 yr is th e y iel d o n t h e ten -y ea r t rea su ry b on d . Th e t ab le r ep o rt s t h e co eff ici en t es ti m ates an d th ei r t-r at io s, w h ere th e stand ar d e rro rs are New ey -We st esti m ates w ith t w o l ags fo r an n u al d ata an d f iv e l ags fo r q u art er ly d ata. T h e sa m p le in cl ud es U S e q ui ty m u tu al f unds , U S bo nd f u n d s, a n d U S m o ne y m ar ke t fu nds t h at ha ve a t le as t 5 m ill io n d o ll ar s o f a ss ets unde r m ana ge m en t a t the be gi nni n g of th e p eri o d s an d are at least on e-y ear o ld . T h e sa m p le p eri o d is f ro m 1 9 80 Q 1 t o 20 09 Q4 f o r US eq ui ty f u n d s a n d f ro m 1 9 91 Q1 t o 20 09 Q 4 f o r US bo n d f unds an d U S m one y m ar ke t f u nds .

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Table 3 Regressions of common factors on macroeconomic and financial market variables (continued) (B ) Bond fu nd s ec tor: f ir st tw o flo w f a ct or s f1 ( q uar te rl y) f2 ( quarte rl y) mo d el1 mo d el2 mo d el3 mo d el4 mo d el 1 mo d el 2 mo d el 3 mo d el 4 Δ M ic h ig an se n tim en t –0. 0 22 –0. 0 18 0.2 7 9 – 0 .0 85 (–0. 8 42) (–0. 7 94) (1.4 6 3 ) (– 0. 76 6 ) Δ B W s enti m en t –0. 0 23 –0. 0 14 0.0 4 4 – 0 .0 36 (–2. 5 79) (–2. 6 11) (0.6 1 5 ) (– 1. 21 3 ) In fl ation –0. 12 9 –0. 4 14 –0. 3 54 1.9 2 7 0.0 3 7 – 1 .5 93 (–0. 47 5) (–0. 9 11) (–1. 0 41) (0.8 7 5 ) (0.0 2 1 ) (– 0. 91 4 ) E xc h an ge ra te 0. 055 0. 171 0. 171 0.8 5 5 0.8 9 1 0.5 1 0 (0.7 41) (2.2 49) (2.9 20) (2.0 5 1 ) (2.2 9 8 ) (1.8 05 ) D isp inc o m e gr o w th –0. 08 3 –0. 2 63 –0. 2 21 2.1 4 2 0.7 2 7 – 0 .2 27 (–0. 45 2) (–1. 5 27) (–1. 3 61) (1.3 4 7 ) (0.4 2 6 ) (– 0. 34 4 ) IP g row th –0. 0 08 –0. 0 05 0.2 0 1 0.1 9 9 (–0. 3 44) (–0. 2 61) (1.7 6 3 ) (1.8 52 ) Ma rk et v o la tility 0.8 86 0.8 79 – 5 .8 16 – 7 .8 72 (1. 706) (1. 863) (– 1. 37 9 ) (– 2. 27 2 ) M kt. – T b ill r et. 0. 004 0. 004 0.2 5 3 0.4 4 4 (0.2 00) (0.1 93) (1.7 4 6 ) (4.1 92 ) B A A – A A A –1. 4 07 0. 677 – 5 .4 60 –23 .0 60 (–2. 7 40) (0. 583) (– 1. 33 8 ) (– 4. 04 1 ) AA A – T b ill 0.6 57 0.5 25 – 0 .4 40 0.1 5 0 (3. 036) (2. 524) (– 0. 37 7 ) (0.1 84 ) D p ra tio – T -10 yr –0. 0 85 –0. 1 89 – 2 .4 76 – 1 .6 59 (–0. 4 48) (–0. 5 50) (– 2. 14 7 ) (– 1. 05 7 ) R 2 0. 022 0. 253 0. 334 0. 537 0.0 8 0 0.1 1 7 0.6 3 6 0.6 8 5 Ad ju st ed R 2 –0. 04 0 0. 169 0. 281 0. 431 0.0 2 3 0.0 1 7 0.6 0 7 0.6 1 3 No te s: T h e d ep en d en t v ar iab le s are t h e co mm o n f acto rs ext ra ct ed u si n g a p ri n ci p al co m p o n en ts an aly si s o n f u n d f lo w s fo r a gi ve n s ec tor. P ane l (D ) c o m b in es se ct o rs using the G o ya l et a l. (200 8) m ethod . T h e in de pe nd en t v aria b le s ar e the m ac ro v aria b le s an d f ina nc ia l v aria b le s a s lis te d in t he f irs t co lu m n . Δ Mic h ig an se n tim en t is t h e ch an ge o f t h e lo g o f t h e Mi ch ig an sen ti m en t in d ex as su rv ey ed b y t h e Un iv ers it y o f Mi ch ig an . Δ B W s enti m en t is the c h an ge in the v ar ia b le c ons tr u cte d in B ak er a nd W u rg le r ( 2 006 ). I n fl ation is th e c h an ge i n l o g of the c o ns u m er pr ic e inde x. E xc h an ge ra te is the c h an ge in log of t h e m ajor fore ig n e xc h an ge inde x. I P gr o w th is the c h an ge in lo g of US ind u st ria l pr oduc ti on. D isp i n co me g ro w th is the c h an ge in l o g of pe rs ona l dis pos ab le i n co m e pe r c ap ita . Ma rk et v o la tili ty a nd re tur n a re t h e st an da rd d ev ia tio n a n d t h e re tur n on S& P50 0 i n de x re sp ec tiv el y, w h ic h ar e obta in ed us ing i ts da ily da ta . d/ p ra tio is t h e di vi de nd t o pric e ra tio of the va lue we ig hte d CR S P i n de x. T b il l is the y ie ld o n the thre e-m onth tr ea sur y bill. T -10y r is the y ie ld on th e te n-y ea r tr ea su ry b o n d . T h e t ab le rep o rt s th e co ef fi ci en t es ti m ate s a n d the ir t-ra ti o s, w h er e the sta nda rd er rors a re N ew ey -We st e sti m ate s w ith tw o la gs f o r annua l da ta a nd fi ve la gs f or qua rte rl y da ta . T h e s am p le inc lu d es U S e q uity m u tua l fu nds , U S bo nd f u n d s, a nd U S m o n ey m ark et f u n d s t h at ha ve a t le as t 5 m il lio n d o lla rs of a ss ets unde r m ana ge m ent a t the be gi nni ng of the pe ri ods an d ar e at le as t on e-ye ar o ld . T h e s am p le pe riod is f ro m 198 0 Q 1 to 2 0 09 Q 4 f o r U S e q ui ty f unds a nd f rom 19 91 Q 1 to 20 09 Q 4 f o r U S bo nd f u n d s an d US m o n ey m ar ke t f u nds .

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Table 3 Regressions of common factors on macroeconomic and financial market variables (continued) (C ) Mo n ey m a rket s ect o r: f ir st t w o flo w fa ct o rs f1 ( quarte rly ) f2 (q uar te rly ) m o de l1 m ode l2 m ode l3 m o d el4 m o de l1 m ode l2 m o de l3 m o d el 4 Δ M ic h ig an s entim en t –0. 06 5 –0. 0 19 0.1 63 0 .2 85 (–1. 77 9) (–0. 6 67 ) (0 .8 33) (1 .2 20) Δ B W s en ti m en t 0 .0 05 –0. 0 04 0.0 07 –0. 0 32 ( 0 .6 78) (–0. 5 66 ) ( 0 .2 02) (–1. 0 68) In fl at io n –0. 1 71 –0. 90 5 –0. 7 16 –0. 2 41 –2. 28 7 –1. 4 25 (–0. 6 49) (–2. 06 8) (–2. 0 37 ) (–0. 1 21 ) (–0. 74 5) (–0. 4 16) E xc h an ge r ate 0.1 8 2 0 .1 74 –0. 0 15 –0. 4 65 0.0 97 –0. 4 90 (1.7 07 ) (1 .9 78) (–0. 2 29 ) (–0. 9 97 ) (0 .2 16) (–1. 0 38) D is p inc o m e g row th –0. 1 40 –0. 00 9 –0. 2 03 5. 61 3 1.6 26 0 .7 93 (–0. 4 06) (–0. 04 3) (–1. 3 25 ) (1. 802 ) (1 .1 76) (0 .5 35) IP g row th –0. 00 4 –0. 0 29 0.4 20 0 .3 60 (–0. 11 4) (–1. 0 23 ) (2 .5 33) (2 .4 50) Ma rk et v o la tility 0.7 5 5 0.5 7 9 5.2 5 4 3 .2 87 (1.3 2 7 ) (0.9 90 ) (1.8 0 1 ) (0 .9 74) M kt. – T b ill re t. – 0 .1 14 –0. 0 94 0.0 5 9 –0. 1 75 (– 3. 49 2) (–3. 2 46 ) (0.4 3 1 ) (–1. 7 07) B A A – A A A – 0 .3 09 –2. 7 87 –11 .2 06 –7. 5 29 (– 0. 46 4) (–1. 8 08 ) (– 2 .31 1) (–1. 0 36) A A A – T b il l –0 .1 60 – 0 .10 6 – 1 .1 15 – 1 .03 9 (– 0. 80 2) (–0. 5 71 ) (– 1 .72 7) (–1. 9 26) D p r atio – T -10y r (0.2 3 1 ) (0.3 32 ) (0.8 8 7 ) (1 .0 29) (– 2. 73 8) (–1. 5 95 ) (– 1 .54 3) (–2. 2 57) R 2 0.0 7 3 0 .1 12 0.3 7 6 0. 38 9 0. 20 9 0.1 31 0.2 5 0 0 .2 89 Ad ju st ed R 2 0.0 1 5 0 .0 12 0.3 2 7 0. 25 0 0. 16 0 0.0 32 0.1 9 1 0 .1 26 No te s: T h e d ep en d en t v ar iab le s are t h e co m m o n f act o rs ext ra ct ed u si n g a p ri n ci p al co m p o n ent s an al ysi s o n f u n d f lo w s fo r a g iven sec to r. P an el ( D ) co m b in es sect o rs us ing t h e G o ya l et a l. (200 8) m etho d. T h e in de pe nd en t v aria b le s a re th e m ac ro v aria b le s a n d f ina nc ia l va ria b le s a s liste d in t h e f ir st co lu m n . Δ Mic h ig an s entim en t is t h e ch an ge o f th e lo g o f th e Mich ig an s en ti m en t i n d ex as su rv ey ed b y t h e Un iv er si ty o f Mi ch ig an . Δ BW s enti m en t is th e ch an ge in th e v ar ia b le c onstr uc te d i n Bak er an d W u rg le r (2 0 0 6). I n fl at io n i s th e ch an ge in l o g o f th e co nsu m er p ri ce i n d ex. E xch an ge rat e i s t h e ch an ge i n lo g o f t h e m ajo r f o rei gn ex ch an ge i n d ex. I P gr ow th is the c h an ge in l o g of US ind u st ri al p ro duc ti on. Dis p i n co m e g ro w th is the c h an ge in l o g o f pe rs o n al dis pos ab le i n co m e p er c ap ita . Ma rk et v o la tility a n d re turn a re t h e s ta n da rd de vi atio n a nd t h e re tu rn on S& P50 0 i nde x re spe ctiv el y, w h ic h a re ob ta in ed u sing its da ily da ta . d/ p r at io is t h e d iv id end to p ric e ra tio o f the va lue we ig h te d CR S P i nde x. T b il l is the y ie ld o n the thre e-m o n th tr ea su ry bill. T -10y r is the y ie ld on the te n-y ea r tr ea su ry bo n d . T h e t ab le rep o rt s t h e co ef fi ci en t es ti m ate s a nd the ir t-ra ti os , w h er e the s ta nda rd e rrors a re Ne w ey -We st e sti m ate s w ith tw o la gs f o r an nua l da ta a nd f iv e la gs f or q u ar te rl y da ta . T h e sa m p le in cl ud es U S e q uity m u tua l f unds, U S bo nd f u n d s, a nd U S m o ne y m ar ke t fu n d s t h at ha ve a t le as t 5 m illion d o lla rs of a ss ets und er m ana ge m ent a t th e be gi nni ng of th e p eri o d s an d ar e at l east o n e-ye ar o ld . T h e sa m p le p er io d is f ro m 1 9 80 Q 1 to 2 0 09 Q4 fo r US eq ui ty f u n d s an d f ro m 1 9 91 Q1 t o 20 09 Q 4 f o r U S bo nd f u nds an d U S m one y m ar ke t f unds.

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Table 3 Regressions of common factors on macroeconomic and financial market variables (continued) (D ) G o ya l e t al . (2 008): fi rs t t w o flow f a ct or s f1 ( quar te rl y) f2 ( quar te rl y) m ode l1 m ode l2 m ode l3 m ode l4 m ode l1 m ode l2 m ode l3 m ode l4 Δ Mic h ig an s ent im en t 0. 012 –0. 00 4 –0. 19 6 –0 .0 70 (1. 326) (–0. 62 7) (–1. 40 0) (–0 .53 2) Δ B W s enti m en t 0. 002 –0. 00 3 –0. 02 0 –0 .0 72 (0. 681) (–1. 64 0) (–0. 50 2) (–1 .76 4) In fl at ion 0. 09 6 –0. 11 2 –0. 17 7 –0. 97 6 –3. 75 5 –3 .5 45 (0. 61 3 ) (–0. 75 2) (–1. 56 8) ( –0. 43 6) (–1. 71 4) (–1 .73 8) E xc h an ge r ate 0. 08 9 0. 096 0.0 38 0. 817 1.3 48 0.5 66 (3. 25 6 ) (3. 268) (2 .3 95) (1. 431) ( 1 .9 63) (1 .0 02) D is p i n co m e gr ow th 0. 22 4 0. 095 –0. 01 1 –3. 32 0 –3. 04 5 –3 .8 78 (2. 01 5 ) (1. 011) (–0. 26 8) ( –1. 77 4) (–1. 29 3) (–2 .11 4) IP g row th 0. 014 0.0 11 0.0 38 –0 .0 73 (2. 077) (1 .6 70) (0 .2 81) (–0 .51 6) Ma rk et v o la ti lity –0. 16 6 –0. 34 1 0.5 77 –1 .3 16 (–0. 73 1) (–1. 91 4) (0 .1 24) (–0 .29 0) Mk t. – T b il l re t. 0.0 01 0.0 11 –0. 29 5 –0 .3 79 (0 .1 20) (1 .5 55) (–1. 41 3) (–2 .36 8) B A A – A A A –0. 29 9 –1. 17 9 7.9 15 –14 .1 54 (–1. 35 1) (–2. 55 1) (1 .5 10) (–1 .25 5) A A A – T b ill 0.0 00 0.0 26 –0. 60 9 –0 .7 34 (0 .0 02) (0 .4 55) (–0. 27 2) (–0 .38 7) D p r ati o – T -1 0 yr –0. 36 8 –0. 36 2 –0. 36 2 –1 .8 90 (–4. 98 9) (–3. 47 4) (–0. 21 3) (–0 .72 6) R 2 0. 13 9 0. 189 0.6 86 0.7 06 0. 131 0.1 68 0.1 65 0.3 39 Ad ju st ed R 2 0. 08 5 0. 098 0.6 61 0.6 38 0. 076 0.0 74 0.0 98 0.1 88 N o te s: T h e de pe nde nt v aria b le s a re the c o m m on fa ct ors e xtr ac te d us ing a pr inc ip al c o m pone nt s a n al ys is on fund f low s fo r a g iv en se ct o r. P an el ( D ) c o m b in es se ct o rs us ing t h e G o ya l e t a l. (200 8) m ethod . T h e in de pe nd en t va ri ab le s a re the m ac ro v ar ia b le s and fi na nc ia l v ar ia b le s a s l is te d in th e f ir st c o lum n . Δ Mi ch ig an sen ti m en t is t h e ch an ge of the l o g of the Mi ch ig an s entim en t inde x as s u rv ey ed b y t h e Univ er sity o f Mic h ig an . Δ BW s ent im en t is the c h an ge in th e va ri ab le c ons tr uc te d in B ak er a nd W u rg le r (2006 ). I n fl ation is t h e ch an ge i n l o g of t h e co ns um er pri ce inde x. E xc h an ge r ate i s the c h an ge in log of the m ajor for eig n ex ch an ge ind ex . IP gr ow th is the c h an ge i n log o f U S i n du stri al pr oduc ti on. D is p i n co m e g ro w th is the c h an ge in lo g of pe rs ona l dis pos ab le i n co m e pe r c apit a. Ma rk et v o la ti lity a nd re tur n a re t h e st anda rd de vi at io n a n d t h e re tur n on S& P 5 00 i nde x re sp ec tiv el y, w h ic h a re obta ine d us in g its da il y da ta . d/ p r at io is t h e di vi de nd t o pr ic e r at io of the va lue w eig hte d CRS P i nde x. T b il l i s the y ie ld on th e thr ee -m onth tr ea su ry bill. T -10y r is the y ie ld on the t en-ye ar tr ea sur y bo nd. T h e ta ble r epor ts the c o ef fi ci en t es ti m ate s a nd the ir t-ra ti os , w h er e the s ta nda rd e rror s a re N ew ey -W es t e sti m ate s w ith tw o la gs f o r annua l da ta a nd f iv e la gs f o r qua rt er ly da ta . T h e sa m p le inc lu d es U S e q uity m u tu al f unds , U S bo nd f unds , and U S m one y m ar ke t funds t h at ha ve a t le as t 5 m ill ion d o lla rs of a ss ets unde r m an ag em ent a t the be gi nni ng of the pe ri ods a nd a re a t le as t on e-ye ar old. T h e s am p le pe ri od is f rom 198 0 Q 1 to 2 0 09 Q 4 fo r U S e q ui ty f unds a nd f rom 19 91 Q 1 to 20 09 Q 4 f o r U S bo nd f unds and U S m one y m ar ke t f unds .

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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

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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.

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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.

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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}

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Table 4 Regressions of the first factors on lagged macro and financial variables (continued) (C) First money market fund flow factor

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}

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Table 4 Regressions of the first factors on lagged macro and financial variables (continued) (D) First overall common factor

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

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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.

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

(A ) E qu it y f1 (1 98 1– 20 09 ) (B ) E qu it y f1 (1 99 2– 20 09 ) (C ) B on d f1 (1 99 2– 20 09 ) (D ) Mo ne y m ar ke t f 1 (1 99 2– 20 09 ) C oeff. ( S.E.) Adj. R 2 C oe ff. ( S.E.) Adj. R 2 C oeff. ( S.E .) Adj. R 2 C oe ff. ( S.E.) A dj. R 2 A nn ua l Δ M ichig an s entim en t 0.7 87 (0 .3 65 ) 0.0 43 0.4 95 ( 0.3 28 ) –0 .0 26 0.8 32 (0 .3 84 ) 0.0 92 0.4 11 (0.3 56) –0.01 3 In fl ation 0.0 11 (0 .0 34 ) – 0. 03 6 0.0 13 (0 .0 26 ) – 0. 06 2 –0 .0 22 (0 .0 19 ) –0 .0 48 –0 .0 28 (0.0 27) –0.02 4 Ex ch an ge 0.4 08 (0 .2 39 ) 0.0 30 0.1 67 ( 0.2 50 ) –0 .0 53 –0 .7 04 (0 .2 52 ) 0.2 66 –0 .0 17 (0.1 79) –0.06 6 IP gr ow th 0.3 94 (0 .1 11 ) 0.1 80 0.3 58 (0 .1 71 ) 0.0 87 0.1 01 (0 .1 19 ) –0 .0 49 –0 .0 14 (0.0 75) –0.06 6 In co m e gr ow th 0.1 01 (0 .0 73 ) 0.0 86 0.0 30 (0 .0 70 ) –0 .0 54 0.0 49 (0 .0 34 ) –0 .0 20 –0 .0 03 (0.0 39) –0.06 6 T bill 0.1 07 (0 .1 20 ) 0.0 17 0.1 62 ( 0.0 95 ) 0.1 32 –0 .1 38 (0 .0 38 ) 0.1 35 –0 .0 65 (0.0 73) –0.00 4 BA A 0.1 15 (0 .0 95 ) 0.0 37 0.0 64 ( 0.0 37 ) 0.0 84 –0 .0 09 (0 .0 30 ) –0 .0 63 0.0 25 (0.0 48) –0.02 2 AA A 0.1 40 (0 .0 92 ) 0.0 89 0.1 04 (0 .0 47 ) 0.2 40 0.0 02 (0 .0 39 ) –0 .0 67 0.0 15 (0.0 49) –0.05 4 BA A – A A A –0 .0 25 (0 .0 15 ) 0.0 30 –0 .0 40 (0 .0 21 ) 0.0 71 –0 .0 11 (0 .0 15 ) –0 .0 53 0.0 09 (0.0 09) –0.05 2 AA A – T bill 0.0 33 (0 .0 53 ) –0 .0 21 –0 .0 58 (0 .0 80 ) –0 .0 23 0.1 40 (0 .0 26 ) 0.2 83 0.0 81 (0.0 40) 0.0 94 Ma rk et r eturn 0.1 82 (0 .5 57 ) – 0. 03 5 0.9 06 (0 .8 53 ) – 0. 00 8 –0 .1 81 (0 .6 77 ) –0 .0 63 0.2 63 (0.3 63) –0.05 7 Ma rk et v ola tility –0 .0 39 (0 .0 12 ) 0.1 61 –0 .0 53 (0 .0 16 ) 0.2 19 0.0 08 (0 .0 14 ) –0 .0 59 0.0 38 (0.0 07) 0.2 18 Q ua rt er ly Δ M ichig an s entim en t –0 .1 79 (0 .0 69 ) 0.0 53 –1 .6 40 (1 .0 17 ) 0.0 31 0.5 67 (0 .3 83 ) –0 .0 03 –0 .0 42 (0.3 67) –0.01 5 In fl ation 0.0 01 (0 .0 05 ) –0 .0 09 0.1 26 ( 0.0 67 ) 0.0 14 –0 .0 55 (0 .0 31 ) –0 .0 02 0.0 02 (0.0 38) –0.01 5 Ex ch an ge –0 .0 28 (0 .0 26 ) – 0. 00 2 0.3 17 (0 .3 88 ) – 0. 00 7 –0 .0 52 (0 .2 50 ) –0 .0 15 0.2 90 (0.1 73) 0.0 18 IP gr ow th –0 .0 02 (0 .0 37 ) – 0. 00 9 0.5 83 (0 .7 58 ) – 0. 00 8 0.0 94 (0 .2 32 ) –0 .0 15 –0 .0 73 (0.3 58) –0.01 5 In co m e gr ow th –0 .0 02 (0 .0 06 ) – 0. 00 8 –0 .0 18 (0 .1 30 ) – 0. 01 5 –0 .0 09 (0 .0 47 ) –0 .0 15 0.0 20 (0.0 45) –0.01 3 T bill –0 .0 40 (0 .0 32 ) 0.0 21 0.1 10 ( 0.2 75 ) –0 .0 11 –0 .3 71 (0 .1 78 ) 0.0 84 0.2 76 (0.1 59) 0.0 99 BA A –0 .0 67 (0 .0 28 ) 0.0 82 0.1 94 ( 0.0 88 ) 0.0 39 0.1 36 (0 .1 07 ) 0.0 45 0.1 81 (0.0 60) 0.2 07 A A A –0 .0 65 (0 .0 25 ) 0 .0 92 0. 25 8 ( 0. 110 ) 0 .0 61 0.1 29 (0 .1 12 ) 0.0 28 0.1 68 (0.0 82) 0.1 36 BA A – A A A –0 .0 02 (0 .0 05 ) –0 .0 06 –0 .0 64 (0 .0 41 ) 0.0 03 0.0 06 (0 .0 45 ) –0 .0 15 0.0 13 (0.0 33) –0.01 2 AA A – T bill –0 .0 25 (0 .0 15 ) 0.0 39 0.1 48 ( 0.2 55 ) –0 .0 04 0.5 00 (0 .1 43 ) 0.2 73 –0 .1 08 (0.1 05) 0.0 13 Ma rk et r eturn –0 .1 25 (0 .0 75 ) 0.0 22 –1 .0 30 (0 .8 14 ) 0.0 01 0.2 66 (0 .5 96 ) –0 .0 13 –0 .0 99 (0.8 17) –0.01 4 Ma rk et v ola tility 0.0 10 (0 .0 05 ) 0.0 37 –0 .0 42 (0 .0 71 ) –0 .0 10 0.0 39 (0 .0 70 ) –0 .0 05 0.0 33 (0.0 37) –0.00 1 No te s: T he de pe nd en t var iab le s ar e macr oeco no m ic an d fi na nc ia l var iab le s as l is te d i n th e f ir st co lu m n. T he in de pe nd en t var iab les ar e l ag ged d ep en den t v ari ab le s and th e la gg ed v al ue o f t he co mm on f lo w fact or s i n m ut ual f un ds, ext ract ed u sin g a pr in ci pa l co m po ne nt s a nal ys is o n f un d fl ow s fo r t he in di cat ed s ect or . P an el F u ses th e G oy al et al . (2 00 8) m et ho d. T he tab les rep or t t he co ef fi ci en t est im at es an d t hei r New ey -W est ( 19 80 ) st an da rd er ro rs u si ng t w o la gs f or annu al data f iv e la gs f or qu ar ter ly d ata . T he s am ple pe ri od s a re f ro m 1 98 1 Q 4 to 2 00 9 Q 4 f or e qu ity f und s a nd f rom 19 92 Q 4 to 2 00 9 Q 4 fo r bo nd f und s a nd m on ey m ar ket fu nd s as s tat ed in t he p ar en th es es.

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

(E ) Equity f1 ( 199 2– 20 09 ) B on d f 1 (1 99 2– 20 09) M one y m ar ke t f1 ( 19 92 –2 00 9) (F ) O ve rall co m m on fac tor ( 199 2– 20 09 ) C oe ff. ( S.E.) C oe ff. ( S.E .) C oe ff. ( S.E .) A dj. R 2 C oe ff. ( S.E.) A dj. R 2 A nnu al Δ Mic hig an s entim en t 0.4 51 (0.3 73 ) 0.7 83 (0. 398) 0.4 07 (0.4 01 ) 0.0 46 0.0 93 (0 .7 25) –0. 06 6 Inf la tion 0.0 13 (0.0 25 ) –0. 02 2 (0. 018) –0. 02 7 (0.0 29 ) –0. 15 6 –0 .0 07 (0 .0 51) –0. 06 6 Ex ch an ge 0.2 40 (0.2 18 ) –0. 72 2 (0. 209) 0.0 15 (0.1 84 ) 0.1 85 0.5 37 (0 .2 21) 0. 013 IP gr ow th 0.3 50 (0.1 90 ) 0.0 77 (0. 090) –0. 00 2 (0.1 10 ) –0. 04 3 0.4 49 (0 .2 43) 0. 073 D is p inc om e gr ow th 0.0 25 (0.0 80 ) 0.0 47 (0. 038) –0. 00 3 (0.0 39 ) –0. 16 7 0.1 83 (0 .0 53) 0. 202 T bi ll 0.1 73 (0.0 69 ) –0. 14 8 (0. 029) –0. 05 3 (0.0 60 ) 0.3 22 0.3 27 (0 .0 76) 0. 401 BA A 0.0 67 (0.0 39 ) –0. 01 5 (0. 014) 0.0 28 (0.0 44 ) 0.0 20 0.1 33 (0 .0 47) 0. 314 AAA 0. 10 6 (0 .0 49 ) –0 .0 06 (0 .01 8) 0. 02 0 ( 0. 04 0) 0 .15 0 0. 18 9 (0 .0 48 ) 0. 52 1 BA A – A A A –0 .0 39 (0.0 21 ) –0. 00 8 (0. 013) 0.0 08 (0.0 11 ) –0. 05 1 –0 .0 57 (0 .0 26) 0. 089 AAA – T bill –0 .0 66 (0.0 45 ) 0.1 42 (0.0 25) 0.0 73 (0.0 34 ) 0.4 03 –0 .1 38 (0 .0 89) 0.0 73 Ma rk et re turn 0.9 58 (0.8 65 ) –0. 26 3 (0. 785) 0.3 12 (0.4 81 ) –0. 14 0 1.0 94 (1 .0 35) –0. 01 7 Ma rk et v ola tility –0 .0 51 (0.0 12 ) 0.0 10 (0.0 10) 0.0 36 (0.0 11 ) 0.4 06 –0 .0 32 (0 .0 39) –0. 00 8 Qu arter ly Δ Mic hig an s entim en t –1 .7 29 (1.0 54 ) 0.6 73 (0. 468) –0. 07 8 (0.3 54 ) 0.0 19 0.3 31 (0 .7 34) –0. 01 4 Inf la tion 0.1 35 (0.0 66 ) –0. 06 3 (0. 029) 0.0 05 (0.0 37 ) 0.0 01 0.0 34 (0 .0 90) –0. 01 3 Ex ch an ge 0.3 35 (0.3 80 ) –0. 09 7 (0. 230) 0.2 96 (0.1 81 ) –0. 00 2 0.9 02 (0 .3 79) 0. 041 IP gr ow th 0.5 73 (0.7 85 ) 0.0 68 (0. 260) –0. 07 4 (0.3 59 ) –0. 03 9 0.5 58 (0 .5 19) –0. 01 0 D is p inc om e gr ow th –0 .0 16 (0.1 32 ) –0. 01 0 (0. 048) 0.0 21 (0.0 45 ) –0. 04 3 0.1 06 (0 .0 70) –0. 00 3 T bi ll 0.1 69 (0.2 26 ) –0. 40 6 (0. 156) 0.2 93 (0.1 69 ) 0.1 96 1.3 74 (0 .2 42) 0. 485 BA A 0.1 83 (0.0 89 ) 0.1 10 (0. 085) 0.1 77 (0.0 57 ) 0.2 80 0.3 97 (0 .1 64) 0. 174 AAA 0. 24 8 (0 .1 05 ) 0. 10 1 ( 0.09 1) 0. 16 4 ( 0. 08 0) 0 .21 7 0. 70 8 (0 .1 45 ) 0. 46 2 BA A – A A A –0 .0 65 (0.0 41 ) 0.0 09 (0. 042) 0.0 13 (0.0 34 ) –0. 02 4 –0 .3 11 (0 .1 07) 0. 337 AAA – T bill 0.0 79 (0.1 56 ) 0.5 07 (0.1 40) –0. 12 9 (0.1 07 ) 0.2 95 –0 .6 66 (0 .2 54) 0.1 73 Ma rk et re turn –1 .0 76 (0.8 36 ) 0.3 38 (0. 666) –0. 11 7 (0.8 27 ) –0. 02 6 2.5 52 (1 .1 01) 0. 067 Ma rk et v ola tility –0 .0 46 (0.0 81 ) 0.0 39 (0.0 66) 0.0 31 (0.0 38 ) –0. 01 7 –0 .2 58 (0 .1 42) 0.1 41 N ote s: T he de pe nd en t v aria ble s a re m ac roe conom ic a nd fi na nc ia l v aria ble s a s l iste d in th e f irs t c olu m n. T he inde pe nd en t v aria bl es ar e l agg ed d ep en den t vari ab les and th e la gg ed v alu e of the c om m on f lo w f ac tors in m utua l f unds, e xtra ct ed u si ng a pri nc ipa l c om pone nts a na ly sis on f und f low s fo r the in di cat ed s ec to r. P an el F u ses t he G oy al et a l. (2008 ) m ethod. T he ta bl es re port t he c oe ff ic ie nt es ti m ate s an d t he ir N ew ey -W es t (19 80) s ta nda rd er rors us ing tw o l ag s fo r a nn ua l d at a fi ve la gs fo r qu ar te rly da ta . T he s am ple pe riod s ar e fr om 19 81 Q 4 t o 2 00 9 Q 4 f or eq uity f und s an d f ro m 199 2 Q 4 to 2 00 9 Q 4 f or b on d fu nd s a nd m on ey m ar ket f un ds as st at ed in t he p ar en th eses .

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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 Σ 1 ,

it i it j oj j it jt it

F =a +G X′ − + b +B X′ − Y +u (3)

where (boj+B X′j it−1) is the linear approximation for fund i’s flow beta as a function of

its predetermined characteristics, Xit–1 and uit is a regression error. This is similar to

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, (boj+B X′j it−1). 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.