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Journal of Financial Economics

Journal of Financial Economics 112 (2014) 213–231

0304-40http://d

☆ I amadvisorsRalph KStijn VaVanderbAndersoBerkele

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journal homepage: www.elsevier.com/locate/jfec

The price of skill: Performance evaluation by households$

Alexi SavovNew York University Stern School of Business, United States

a r t i c l e i n f o

Article history:Received 21 May 2012Received in revised form22 July 2013Accepted 4 August 2013Available online 22 November 2013

JEL classification:G11G12G23

Keywords:Mutual fund performanceActive fundsIndex fundsFund flows

5X/$ - see front matter & 2013 Elsevier B.V.x.doi.org/10.1016/j.jfineco.2013.11.005

grateful to the editor and anonymous refeGeorge Constantinides, Douglas Diamond

oijen, and to Zhiguo He, Marcin Kacperczyn Nieuwerburgh. I thank seminar participanilt Owen, Wisconsin School of Business,n, MIT Sloan, Wharton, NYU Stern, HBS, ASUy Haas, and USC Marshall.ail address: asavov@stern.nyu.edu

a b s t r a c t

Skilled investors make money off uninformed investors. By acting as intermediaries, theyprovide a hedge to the uninformed investors themselves. I present a model in whichhouseholds have imperfect information about expected returns. Non-traded incomeshocks lead them to rebalance, sometimes at the wrong time. Active funds hedge thisrisk by trading on superior information. In equilibrium, they pay off when non-tradedincome disappoints, earning a premium that makes them appear to underperformindex funds after fees. Empirical results using aggregate fund flows support the model.A corresponding asset pricing test can account for the apparent underperformance ofactive funds.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

If you were an uninformed investor, what would youdo? Choosing the right asset mix requires good knowledgeof expected returns. A lack of such knowledge can lead topoor timing, buying high and selling low. Buy-and-holdavoids this problem, but there are good reasons to trade,like outside income shocks. The alternative is to hire aprofessional. An informed fund manager corrects the poortiming of her investors by trading against the error in theirbeliefs. Her fund pays off precisely when her investorsdiscover that error. For those with no outside income,natural buy-and-hold investors, this service has limited

All rights reserved.

ree, my dissertation, Eugene Fama, andk, Alan Moreira, andts at Chicago Booth,Stanford GSB, UCLACarey, Wash U Olin,

value. But for those who buy and sell, it can be a hedgeworth a high premium. Whereas buy-and-hold investorsare best served by low-cost index funds, others maychoose active funds even if their costs are high.

I present a model of portfolio delegation in an economywith time-varying expected returns. Households learn aboutexpected returns from stock returns and economic condi-tions. Markets are incomplete so this learning is imperfect.For example, expected returns may depend on persistentshocks to non-traded income such as wages, private busi-ness, or real estate. A set of active fund managers observesthe true expected returns and trades accordingly, generatingalpha. For example, they may be able to forecast earningsmore accurately than households. In equilibrium, active fundreturns are abnormally high when household expectationsare off the mark. In particular, they are high when non-traded income disappoints. As a result, active funds attractinvestors with substantial non-traded income exposure.These investors are willing to pay a premium above andbeyond the gross alpha of their funds. This is because thevalue of active investing depends on the price of non-tradedrisk, which is not reflected in traded benchmarks. In this

A. Savov / Journal of Financial Economics 112 (2014) 213–231214

way, the model can account for the apparent underperfor-mance of active funds first noted by Jensen (1968).

The model generates several additional testable impli-cations. First, net active fund returns are countercyclical:they are high when equity risk premiums are high.1 Thisresult is consistent with the findings of Kosowski (2011)and Glode (2011), among others. In the model, in additionto non-traded income risk, active funds also load on tradedrisk, paying off when returns come in higher than antici-pated. When the price of stock market risk rises, netreturns must also rise to compensate investors. To imple-ment this mechanism, I incorporate decreasing returns toscale so that high outflows during market downturns leadto higher gross and net returns.

The model also leads to several novel implications that Iexamine in the empirical section. I derive these implicationsby connecting the household stochastic discount factor toaggregate fund flows. Income shocks cause households torevise their beliefs about expected returns and rebalancetheir portfolios. As a result, aggregate fund flows revealshocks to non-traded assets.

Consistent with the prediction that active fund inves-tors respond to shocks whereas index fund investors tendto buy and hold, I find that aggregate flows into activefunds are strongly related to contemporaneous marketreturns whereas flows into index funds are not. In themodel, both active and index fund investors are equallyinformed and both learn from stock returns, but activefunds endogenously attract investors with substantial non-traded assets who tend to rebalance.

Consistent with the prediction that mutual fund inves-tors have poor timing, I show that fund inflows predictlower market returns between six and 12 months out. Thenegative predictability is concentrated among active fundsand absent among index funds. Thus, active fund investorsare not only more likely to rebalance, they are also morelikely to do so at the wrong time, buying high and sellinglow, as predicted.

In the model, active fund managers correct the mistim-ing of their investors. I check this prediction in the data byusing fund flows to predict the returns of a strategy that islong active funds and short the market. I find that highinflows—though they predict low market returns—alsopredict high active-minus-market returns. The predictabil-ity is strongest at the three- to six-month horizon. It ispresent among active funds and absent among index funds.These results suggest that active fund managers help toundo the poor timing of their investors.

As a final exercise, I run an asset pricing test using a factorbased on aggregate fund flows that is constructed fromthe cross section of equities. In the model, controlling forthe market return, fund inflows reveal negative shocks tonon-traded income. The predicted premium on a fund-flowsfactor is therefore negative. Active funds endogenouslyprovide a hedge for non-traded risk and so their returnscovary positively with fund flows. In the data, active fundsload positively on the fund-flows factor. The estimated

1 Campbell (1999), among others, shows that equity risk premiumsare indeed higher in recessions.

premium is large and negative, and it is not subsumed bythe standard set of factors. The positive loading and negativepremium account for between 25% and over 100% of theapparent underperformance of active funds.

The empirical analysis concludes with a set of robust-ness checks and extensions, which are presented morefully in the paper's Online Appendix. Results are robust tothe exclusion of institutional funds, funds primarily soldthrough retirement plans, and small-cap and sector funds.The lagged market return negatively predicts the relativereturns of active funds versus the market, consistent withcountercyclical performance. Most of the empirical resultsextend to the universe of corporate bond funds, exceptthat it is index bond fund flows that negatively predictbond market returns.

The paper also makes a modeling contribution bypresenting a fully tractable framework that incorporatestime-varying expected returns, non-traded income risk,investor learning, and portfolio delegation. An extension ofthe model presented in Appendix B also covers the caseof multiple stocks where stock picking, not just markettiming, contributes to skill.

Among the key modeling simplifications, I assume anexogenous linear return process to make the learning problemtractable. A general equilibrium version of the model can beconstructed in the spirit of Grossman and Stiglitz (1976, 1980).However, it is important that the source of noise in prices,modeled as a reduced-form supply shock in Grossman andStiglitz (1980), be directly linked to the marginal utility ofinvestors (and not just through their portfolios). That is, theinvestors and the noise traders must be the same group; it isthe noise traders who are willing to pay a high premium foractive management. This is the key idea of the paper.

The rest of this paper proceeds with a review of theliterature in Section 2, the presentation of the model inSection 3, empirical analysis in Section 4, and concludingsentences in Section 5.

2. Related literature

This paper descends from the mutual fund performanceliterature started by Jensen (1968) and extended by Carhart(1997) and many others. Elton and Gruber (2013) summar-ize that most studies find small positive gross alphas thatare not high enough to cover fees and expenses. Fama andFrench (2010) show that a value-weighted portfolio of allequity mutual funds has a statistically significant net alphaof up to �1% per year. In light of the evidence, Gruber(1996) calls the popularity of active funds a puzzle.2 Indeed,canonical delegation models like Berk and Green (2004)predict net alphas of zero, not less than zero.

This puzzle motivates a set of recent studies. Closest tothis paper is Glode (2011). In Glode (2011), managersoptimally choose to deliver superior returns in highmarginal utility states. Model misspecification as in Roll(1977) can lead to downward-biased performance attribu-tion. Model misspecification also emerges here due tonon-traded assets, but managers have no way of allocating

2 Active mutual funds manage close to $5 trillion.

3 In this paper, managers with more private information indeedgenerate higher returns before fees, but their net returns are actuallylower as they can charge a high premium. Index funds, which have thelowest gross alpha (zero), also have the highest net alpha (also zero). Thisresult motivates the paper.

4 Edelen (1999) calculates that taking into account the liquidityservices provided by mutual funds improves their measured perfor-mance. This mechanism cannot account for the performance gapbetween active and index funds as both types provide the same liquidityservices. The cost of providing liquidity has also declined as markets have

A. Savov / Journal of Financial Economics 112 (2014) 213–231 215

alpha; it arises endogenously under asymmetric informa-tion. Micro-founding alpha in this way makes the modeldirectly testable by linking performance to shocks toperceived expected returns, which are reflected in fundflows. In other words, fund flows can be used to proxy forthe missing factor posited by Roll (1977). Active fundsprovide a natural asset class to implement this proxy.

Another point of departure from Glode (2011) concernsthe countercyclical nature of mutual fund performance. InGlode (2011), fund returns covary with the stochastic dis-count factor (SDF). Here, the covariance between fund returnsand the SDF is itself endogenously countercyclical. This meansthat fund returns are not only positively related to SDFinnovations (a return surprise effect), they are also predic-tably higher conditional on a downturn (an expected returneffect). The evidence in Kosowski (2011) and Kacperczyk, VanNieuwerburgh, and Veldkamp (accepted for publication)supports the view that net returns are predictable.

Two other recent papers that address the underper-formance puzzle are Pástor and Stambaugh (2012) andGennaioli, Shleifer, and Vishny (2012). Pástor and Stambaugh(2012) make the point that learning the full productionfunction of the active fund industry is difficult so that evena long record of underperformance need not cause theindustry to shrink. In Gennaioli, Shleifer, and Vishny (2012),investors choose funds on the basis of trust. Both mechanismsare distinct and can be viewed as complementary. Neithermakes the additional predictions derived and tested here.

A common thread among existing mutual fund theoriesis the exogenous specification of alpha. For instance, inBerk and Green (2004) alpha is an additive term in theactive fund return. As Sharpe (1991) points out, however,the net supply of gross alpha across the whole market iszero. Existing theories implicitly assume an omitted groupof investors with negative alpha. In contrast, this papertakes the point of view of the omitted group itself, whichturns out to be a natural clientele for active funds.

Other recent papers on portfolio delegation employmarket segmentation or participation constraints. Examplesinclude Vayanos and Woolley (2013), He and Krishnamurthy(2013), and Kaniel and Kondor (2013). These papers focus onthe asset pricing implications of delegation. In this paper,asset prices are given and the focus is on active versuspassive investing. To explore this margin, I necessarily allowhouseholds to trade all assets freely.

Admati and Ross (1985) point out that when activefunds trade on superior information, Jensen's alphabecomes unreliable as uncertainty about the manager'sportfolio adds to the variance of her returns. In this paper,the manager's actions add to the covariance of her returnswith household consumption. This covariance is endogen-ously negative, which biases the usual performance teststowards the appearance of underperformance.

Dybvig and Ross (1985) and Grinblatt and Titman (1989)also critique Jensen's alpha on the basis that delegated returnsare inherently nonlinear. Here, they are log-linear. ThoughI use the term “alpha” for expositional purposes, I judgeperformance based on the attractiveness of active funds tobuy-and-hold investors, not strictly alpha. If a buy-and-holdinvestor, someone with no exposure to (the systematiccomponent of) non-traded income, strictly prefers an index

fund to an active fund, I say that active funds appear tounderperform index funds on a buy-and-hold basis.

The mutual fund literature has also focused on condi-tional performance, specifically the countercyclical nature ofmutual fund returns. In Kacperczyk, Van Nieuwerburgh, andVeldkamp (2012), skill is in greater supply during recessionsas there is more volatility, which improves gross alpha.However, as there are no household investors, the papermakes no predictions on net alpha and does not address theunderperformance puzzle. The intuition of Berk and Green(2004) suggests that net alpha should remain at zero. In thispaper, it is the demand for skill that falls as equity riskpremiums rise, so that net performance improves, as in thedata. The two theories can therefore work side by side.

A large literature explores the cross section of skill. Berkand van Binsbergen (2012) find persistent skill before feesand expenses, as required here. Several studies delve intothe nature of skill: Kacperczyk, Sialm, and Zheng (2005),Kacperczyk and Seru (2007), and Cremers and Petajisto(2009) show that managers who have more concentratedportfolios, rely less on public signals, or depart more froma set of indexes, have higher risk-adjusted returns. Thesefindings confirm the intuition that superior information isat the heart of skill.3

Wermers (2000) and others find some evidence of stock-picking ability on the part of active mutual funds, and notmuch evidence of market-timing ability (for an exception, seeJiang, Yao, and Yu, 2007). Kacperczyk, Van Nieuwerburgh, andVeldkamp (accepted for publication) argue that funds opti-mally alternate between stock picking andmarket timing overthe business cycle. They find evidence of market timingduring downturns. Ferson and Schadt (1996) find that highinflows are associated with lower betas, as the model predicts.While the paper focuses on a one-stock model where onlymarket timing is possible, the multiple-stock extension inAppendix B introduces stock-picking. As in Kacperczyk, VanNieuwerburgh, and Veldkamp (accepted for publication), therelative contributions to performance of stock-picking andmarket-timing strategies depend on the covariance structureof stock returns and on the level and distribution of riskpremiums in the economy.

The literature on fund flows is largely focused at thefund level. Gruber (1996) shows that investors respond topast returns, whereas Zheng (1999) finds that this “smart-money” effect is short-lived. Berk and van Binsbergen(2012) use a measure of skill based on the intuition ofBerk and Green (2004) and find a stronger connectionwithflows. Edelen (1999) shows that more active mutual fundsexperience substantially higher investor turnover, consis-tent with this paper.4 As fund-level flows are largelydriven by fund-level performance, the variation that these

A. Savov / Journal of Financial Economics 112 (2014) 213–231216

papers exploit drowns out the variation exploited here,which is based on aggregate shocks. Among the fewpapers on aggregate flows, Warther (1995) finds a strongrelationship between contemporaneous returns and flows,but not much forecastability, perhaps due to a short eight-year sample that ends in 1992. More recently, Ben-Rephael,Kandel, and Wohl (2012) find that net exchanges, a subsetof total flows, have surprisingly strong forecasting power.

7 In the U.S. from 1984 to 2012, the correlation between dividendsand employee compensation is 31% quarterly and 60% annually and thecorrelation between dividends and proprietors' income is 39% quarterlyand 54% annually. Employee compensation represents 67% of totalincome and proprietors' income accounts for 9%, versus only 4% for

3. Model

I present an asset pricing model in which active mutualfunds underperform traded benchmarks net of fees. House-holds invest with active funds because fund managerspossess superior knowledge of conditional expected returns.From the household point of view, active fund returns arepositively correlated with news about risk premiums. Whenrisk premiums are countercyclical as in the data, active fundsprovide a valuable hedge against non-traded income. Inves-tors pay for this hedge in the form of low net returns.Appendix B features an extension to multiple stocks, incor-porating stock-picking skill. I develop testable hypotheses byrelating investor beliefs to aggregate fund flows.

3.1. Setup

Active trading is futile in an unpredictable setting (e.g.,roulette). Instead, consider an economy beset by persistentfluctuations (e.g., business cycles). Let yt represent log-income and write

Δytþ1 ¼ yþxtþεytþ1 ð1Þ

xtþ1 ¼ ρxtþεxtþ1; ð2Þwith ρAð0;1Þ, εy �Nð0; s2yÞ, εx �Nð0; s2x Þ, and εy ? εx forsimplicity. The persistent state variable x controls theconditional mean of income growth Δy. It also controlsrisk premiums: A single risky asset interpreted as a stockindex has an exogenous log-return5

rtþ1 ¼ r�ϕxtþεrtþ1: ð3ÞLet εr �Nð0; s2r Þ with Covðεr ; εyÞ ¼ sry and εr ? εx for sim-plicity. The parameter ϕ controls the variation of expectedreturns. The natural case to consider is ϕ40 so that riskpremiums are countercyclical as in the data. Asset pricingmodels that deliver this type of specification includeCampbell and Cochrane (1999) where the state variableis surplus consumption,6 and Santos and Veronesi (2006)where it corresponds to the relative share of traded tonon-traded income. Exogenous linear returns make thelearning problem tractable.

A one-period risk-free bond pays a constant log-return rf.

(footnote continued)evolved. To illustrate, the typical active equity fund today holds only 3%cash, down from 10% in 1990.

5 See Appendix B for a multiple-stock extension.6 In Campbell and Cochrane (1999), output follows a random walk

but surplus consumption (over which preferences are defined) evolvessimilarly to y here.

Markets are incomplete so that jCorrðεr ; εyÞjo1. To moti-vate this assumption, the return shock εr can be interpreted asa traded cash flow shock (e.g., dividend news) that is onlyimperfectly correlated with total income y. For example, non-traded income may be derived from human capital, privatebusiness, or real estate.7

Market incompleteness implies that stock returns andincome growth do not reveal the true state of the economyx, creating private demand for information and an oppor-tunity for active trading. In this way, prices are “noisy” andx serves the role of the stochastic supply by the same labelin Grossman and Stiglitz (1980).8

Households rely on returns r and income growth Δy tolearn about x,9 forming beliefs based on the innovationsrepresentation

bxtþ1 ¼ ρbxtþbεxtþ1 ð4Þ

Δytþ1 ¼ yþbxtþbεytþ1 ð5Þ

rtþ1 ¼ r�ϕbxtþbεrtþ1: ð6Þ

Throughout the paper, hats denote conditional expecta-tions under the household filtration. Since both the signalsand the state have linear dynamics, the filtered shocks arecomputed using the standard Kalman filter. The formulasare in Appendix A. I focus on the steady state of the filterfor simplicity. The steady state error dispersion

Σx ¼ limt-1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEt ½ððxt�bxtÞ2�q

ð7Þ

measures household uncertainty about the true state ofthe economy and so ϕΣx measures household uncertaintyabout expected returns. The question arises, howmuch arehouseholds willing to pay to resolve this uncertainty?

The answer depends on the price of shocks to x, whichin turn depends on the price of non-traded income shocks.This price is a free parameter due to market incomplete-ness. Let mt be the household log-stochastic discountfactor. Without loss of generality, write10

Δmtþ1 ¼m0;tþmr;tbεrtþ1þmy;t bεytþ1�bsrybs2r

!bεrtþ1

" #: ð8Þ

The composite shock in the brackets is by constructionorthogonal to the return shock. In this way, mr can becalled the price of traded risk, and my the shadow price ofnon-traded risk. Note that both mro0 and myo0 so thathouseholds dislike exposure to these shocks.

dividend income.8 The CARA-normal shocks framework of Grossman and Stiglitz

(1980) does not produce closed-form solutions once intermediaries areintroduced.

9 Additional public signals are easily accommodated as long as theydo not reveal x perfectly.

10 Note that bεx does not enter separately since it is a linearcombination of bεr and bεy (households learn about x from returns andincome).

12 More generally, if χ is log-normal, willingness to pay also depends

A. Savov / Journal of Financial Economics 112 (2014) 213–231 217

The prices of the stock and bond impose restrictions onthe coefficients of m:

1¼ Et ½eΔmtþ 1 þ rf � and 1¼ Et ½eΔmt þ 1 þ rt þ 1 �: ð9ÞSince Δm and r are log-normal,

rf ¼ �Et Δmtþ1� ��1

2 Vart Δmtþ1ð Þ ð10Þ

Et rtþ1� �þ1

2 Vart rtþ1ð Þ�rf ¼ �Covt Δmtþ1; rtþ1ð Þ: ð11ÞSubstituting for Δm into Eq. (10) gives

rf ¼ �m0;t�12

m2r;tbs2

r þm2y;t bsy�

bsrybsr

� �2" #

: ð12Þ

To maintain a constant interest rate, the mean andvariance of the stochastic discount factor must moveagainst each other so that the forces of intertemporalsmoothing and precautionary saving offset. Campbell andCochrane (1999) use an analogous construction and moti-vate it by noting that while risk premiums vary substan-tially, real interest rates are stable.

From Eq. (11), the equity premium pins down the priceof traded risk mr:

r�ϕbxtþ12 bs2

r �rf ¼ �mr;tbs2r : ð13Þ

Time-varying expected returns require a time-varyingprice of risk. Periods of low income growth x are asso-ciated with a stronger covariance between stocks andthe stochastic discount factor (or simply a more volatilestochastic discount factor), and hence a higher marketSharpe ratio.

Pricing stocks and bonds does not pin down the price ofnon-traded risk; my remains a free parameter. In fact, itcan differ across households as markets are incomplete. Itturns out that my is the key parameter for pricing activelymanaged mutual funds.

3.2. Active funds

Consider an active fund manager who knows the trueexpected return.11 For example, she might derive aninformation advantage from sophisticated analysis offinancial statements and other public sources. The cost ofthis type of analysis may be prohibitive for an individualhousehold. Given prices, a superior forecast of fundamen-tals translates directly into a superior forecast of expectedreturns (Campbell and Shiller, 1988). For this reason, I modelthe manager's expertise directly in terms of expected returnswithout any loss of generality.

The active manager opens her fund to households,investing a fraction χt40 of assets under management instocks. At the end of each period, her fund delivers a netreturn

erAtþ 1 ¼ ½erf þχtðert þ 1 �erf Þ�e� f t ð14Þ

rAtþ1 ¼ rf þ log½1þχtðert þ 1 �erf Þ�� f t : ð15Þ

11 More generally, an active fund manager will attract investors aslong as her uncertainty about expected returns is smaller than that ofhouseholds, ϕΣx.

To investors, fees and expenses ft represent a drag onreturns paid in exchange for good performance. In a modelwith explicit information production, ft would reflect thecost of acquiring information, the cost of trading, thecompetitiveness of the mutual fund industry, the need tocompensate managers for risk, and agency costs (see Berkand Green, 2004). Rather than modeling the productionof information, I focus on its resale to households andcalculate their willingness to pay. It is this willingness topay that is highlighted as a puzzle in the mutual fundliterature.

The portfolio choice χt generally depends on the trueexpected return and so it cannot be made public in realtime. Households could potentially infer χt with a one-period lag from ex post fund returns. This would curtail(though not eliminate) the information advantage of fundmanagers, and for this reason I preclude it in the house-hold learning problem. To motivate this assumption, con-sider adding an unpriced disturbance to a fund's returnthat reflects unmodeled aspects of the manager's tradingstrategy. Such a disturbance would have no effect on themain results and is safely left out. In practice, funds investin many securities using diverse strategies and it isimpossible to infer their actions from a single ex postreturn (see the multiple-stock version of the model inAppendix B).

3.2.1. Negative net alphaFrom the point of view of households, active funds

represent an additional asset available for trading. As such,they must be priced by the household stochastic discountfactor m:

1¼ Et ½eΔmtþ 1 þ rAt þ 1 � ð16Þ

1¼ Et ½eΔmtþ 1 ðerf þχtðertþ 1 �erf ÞÞe� f t �: ð17ÞSuppose that χt is log-normal under public informationwith Et ½χt � ¼ 1 so that households expect their managers tobe fully invested in stocks. Then willingness to pay ft isgiven by12

ef t �1¼ eCovt ðlog χt ;Δmt þ 1Þ½eCovt ðlog χt ;rt þ 1Þ �1�: ð19ÞA linearization provides a more intuitive version of thisformula:

f t � ½1þCovtðlog χt ;Δmtþ1Þ� Covtðlog χt ; rtþ1Þ: ð20ÞHouseholds' willingness to compensate active managershas two components. The second arises from the ability toanticipate stock returns, Covtðlog χt ; rtþ1Þ. I call this com-ponent gross alpha.

The first component relates to the timing of activefund returns. From the point of view of households, theportfolio choice of the active manager adds a layer ofuncertainty. This uncertainty is necessarily systematic asit is correlated with news about the true state of the

on a fund's average risk exposure

ef t �1¼ eEt log χt½ �þ 12 Vart log χtð ÞþCovt log χt ;Δmt þ 1ð Þ eCovt ðlog χt ;rt þ 1 Þ �1

h i:

ð18Þ

Fig. 1. The active fund return and the stochastic discount factor. Thisfigure illustrates the return of the active fund RA ¼ er

A in excess of theindex R¼ er , and the stochastic discount factor Δm as a function of thefiltered return and income shocks bεr and bεy . The active return is givenby Eqs. (14) and (22). The stochastic discount factor is given by Eq. (8).(The various parameters are set to η¼ 1, rf¼0, ρ¼ 0:9, ϕ¼ :5, sx ¼ 0:05,sy ¼ 0:1, sr ¼ 0:2, sry ¼ 0, mr ¼ �0:2, my ¼ �1.)

A. Savov / Journal of Financial Economics 112 (2014) 213–231218

economy. The compensation of the active manager there-fore depends on the pricing of this uncertainty as capturedby the term Covtðlog χt ;Δmtþ1Þ. From Eq. (19), householdsare willing to pay active managers more than their grossalpha whenever

Covtðlog χt ;Δmtþ1Þ40; ð21Þ

that is, when active funds provide a hedge. In this case,they will appear to underperform traded benchmarks. AsI show below, this turns out to be the natural case toconsider.

The covariance in Eq. (21) is a function of the portfoliopolicy χ. The particular form of χ generally depends on themanager's preferences and any agency frictions that ariseunder delegation. However, as long as the manager isconcerned with maximizing fee income, χ will be increas-ing in the expected stock return, and this is what is neededhere. Given that, as Admati and Pfleiderer (1990) point out,the precise functional form of the manager's policy issecondary as households can manipulate their fund alloca-tion to achieve a desired overall exposure.13 With this inmind, I consider a convenient example for χ to convey theintuition of the model:

χt ¼ e�ηt ðxt �bxt Þ=Σx

� ��η2t =2: ð22Þ

This policy can be motivated as an approximation to theoptimal strategy of a manager with CRRA preferencesmaximizing end-of-period wealth.14 Recall from Eq. (3)that expected returns are decreasing in x so χ is indeedincreasing in expected returns. Also, χ is log-normal withmean one as required by Eq. (19). The parameter ηt40controls the aggressiveness with which managers trade onprivate information. I assume ηt is public (in Pástor andStambaugh, 2012, it is not).

Fig. 1 illustrates the resulting active fund return. Inpanel A, a strategy long active funds and short the indexpays off whenever returns are high and income is low, orreturns are low and income is high.15 This is because withϕ40, returns and income have opposing exposures to x.At the same time, the stochastic discount factor, shown inpanel B, is high when both income and returns are low. Ifthe price of non-traded shocks my is high enough (i.e., if mis steep enough in y), then the high active fund payoff inthe low-income-high-return state is a valuable hedge, asshown below.

To formalize the intuition of Fig. 1 and calculate theresulting active fund compensation, substitute Eq. (22)

13 More precisely, when only a stock and bond are traded, house-holds can undo any linear transformation of the fund's portfolio policy.The coefficients can be time-varying. In continuous time with no jumps,nonlinear transformations can also be undone.

14 Suppose the manager's relative risk aversion coefficient is γt.Campbell and Viceira (2002) show that the optimal portfolio policycan be approximated as χt � Et rtþ1

� �þ 12s

2r �rf

� �=γts

2r � rþ 1

2 s2r �rf

� �=

�γts

2r �1Þþeð1=γts

2r ÞðEt ½rt þ 1 �� r Þ . This matches the reduced-form expression in

Eq. (22) up to a constant.15 Merton (1981) shows that trading skill generates a payoff that

resembles an option straddle (buy low, sell high). Fig. 1 confirms thisresult.

into (19) using (Eqs. (5) and 6):

ef t �1¼ eηt ½ϕmr;t �ð1þϕbsry=bs2r Þmy;t �Σx ½eηt ðϕΣxÞ �1�: ð23Þ

Gross alpha depends on the amount of private informationΣx that the active manager possesses, its importance ϕ forexpected returns, and the aggressiveness ηt with whichfund assets are deployed.

Net alpha, on the other hand, depends on the price ofnon-traded risk my. From Eq. (23), if non-traded risk is notpriced, my¼0, net alpha cannot be negative since the priceof traded risk mr is negative. In this case, high expectedreturns (low x) are good news.

The opposite is true when expected returns are highduring bad times as in the data. In this case, the price ofnon-traded risk is negative, myo0. If jmyj is large enoughand csry 40 (as in the data) so that

my;t 4 ϕ

1þϕbs rybs2r

0BB@1CCAjmr;t j; ð24Þ

A. Savov / Journal of Financial Economics 112 (2014) 213–231 219

net alpha will also be negative. Intuitively, Eq. (24) saysthat net alpha is negative whenever the net effect of lowincome growth x is negative: the bad news about lowerincome growth must more than offset the good newsabout future investment returns.

Recall that individual households can differ in theirshadow prices of non-traded risk since markets areincomplete. Therefore, an investor with no non-tradedincome exposure strictly prefers an index fund over anactive fund with a negative net alpha. Buy-and-holdinvestors are strictly better off with index funds, whereasinvestors with substantial non-traded income risk formthe natural clientele of active funds.

Eqs. (19) and (23) suggest that the net performance ofactive funds can be used to infer the price of non-tradedrisk my. In Section 3.3 below, I show how aggregate fundflows can be used to identify the time series of shocks tonon-traded income, which offers a potential response tothe critique of Roll (1977) and a test of the model.

16 For example, with CRRA investors with risk aversion γ, thestochastic discount factor is �γΔctþ1. The exposure mr is approximatedby the household's total wealth share in stocks multiplied by �γ. (Whennon-traded income is correlated with returns, an adjustment is made forthe non-traded income share of wealth.) See the Online Appendix.

3.2.2. Countercyclical performanceThe evidence suggests that net mutual fund alphas

increase during downturns (Moskowitz, 2000; Kosowski,2011; Glode, 2011). Eq. (23) provides a mechanism: if as xfalls the price of traded risk mr increases faster in magni-tude than the price of non-traded risk my, willingness topay for active fund delegation falls. When this is the case,high expected stock returns reflect a particularly highdistaste for stock market risk. By betting in the directionof future returns, active fund managers amplify this risk,leading investors to demand higher net returns. Formally,using Eqs. (13), (23), and bsry40, countercyclical perfor-mance requires

∂my;t

∂bx o ϕ2=bs2r

1þϕbsrybs2r

: ð25Þ

This condition is satisfied in the model of Santos andVeronesi (2006) where it is the share of non-traded incomethat drives risk premiums, which makes the prices of tradedand non-traded income risk move in opposite directions. Itis also likely to be satisfied in stochastic volatility modelswhere the volatility of stocks rises by more than thevolatility of non-traded income during downturns, perhapsbecause stocks represent a claim with embedded leverage.

In practice, mutual funds rarely change their feesthough they sometimes offer waivers and discounts. Morecommonly, funds suffer large outflows during downturns.Coupled with a decreasing returns-to-scale technology(e.g., Berk and Green, 2004), outflows raise net returnswithout lowering fees.

To implement this mechanism, suppose that theaggressiveness η with which funds trade is decreasing inassets under management A:

ηt ¼ ηðAtÞ; η′o0: ð26Þ

For the purposes of this paper, the diseconomies can beeither at the fund level as found by Chen, Hong, Huang,and Kubik (2004) or at the industry level as in Pástorand Stambaugh (2012). With a fixed fee, f t ¼ f , Eq. (23)

becomes

ef �1¼ eηðAt Þ½ϕmr;t �ð1þϕbs ry=bs2r Þmy;t �Σx ½eηðAt ÞðϕΣxÞ �1�: ð27Þ

In a market downturn, as mr becomes more negative,mutual funds become riskier, which raises their requirednet returns. Since fees remain fixed, funds see investoroutflows, which raises their gross returns to restoreequilibrium. The model with decreasing returns to scalepredicts that a rise in Sharpe ratios leads to both fundoutflows and higher net returns.

3.3. Testing the model with fund flows

A direct test of the model requires identifying shocks tonon-traded assets and relating them to market returns andactive fund returns. In this section, I show how to useaggregate fund flows to proxy for beliefs and, by extension,income shocks. This connection forms the basis for theempirical tests that follow.

The household stochastic discount factor in Eq. (8)relates expected returns to risk exposures. Eq. (13) showsthat high expected returns (low bx) correspond to a highcovariance with the stochastic discount factor (a morenegative mr). Intuitively, when expected returns are high,households keep a larger fraction of their wealth in stocks.The portfolio model in the Online Appendix links portfolioweights and stochastic discount factor exposures in moredetail.16 For present purposes, note that portfolios canadjust via either flows or capital appreciation. The goalhere is to show that flows identify shocks to beliefs bxholding x fixed, i.e., shocks to household error, which inturn are driven by income shocks.

As flows involve trade between investors, and sincehouseholds are relatively uninformed, consider the sto-chastic discount factor λ of an informed investor, one whoobserves the underlying shocks:

Δλtþ1 ¼ λ0;tþλr;tεrtþ1þλy;t εytþ1�

srys2r

� �εrtþ1

�þλx;tε

xtþ1:

ð28ÞIn equilibrium, both informed and uninformed investorsmust be marginal in the stock market:

r�ϕxtþ12 s

2r �rf ¼ �λr;ts2r ð29Þ

r�ϕbxtþ12 bs2

r �rf ¼ �mr;tbs2r : ð30Þ

Thus, we can relate the error in household beliefs x�bx todifferences in stochastic discount factor exposures:

ϕ xt�bx� �¼ λr;ts2r �mr;tbs2r þ1

2 s2r �bs2r

� : ð31Þ

Since the volatilities are constant, a shock to householderror x�bx must be met by a change in relative exposuresλr;ts2r �mr;tbs2

r . By contrast, a shock to bx that leaves x�bxfixed, i.e., a true shock to expected returns, leaves the

Fig. 2. The time series of fund flows. “Flow” is net cash flow (sales minusredemptions) divided by the previous month's assets. The econometrictests of the paper use the de-trended series, “Flow ex 12-mo MA”,obtained by subtracting a 12-month moving average. Data shown arefrom Morningstar, January 1990 to January 2013, matching the avail-ability of returns. Gray bands indicate NBER recessions.

Table 1Summary statistics.

Means, standard deviations, autocorrelations, and observation countsfor key variables. Using fund-level data on net cash flows and returns,I aggregate all funds in a given category into a single value-weightedfund. “All” is comprised of all U.S. equity mutual funds. “Active” and“Index” are for the subsets of active and index funds, respectively. “Flow”

is the ratio of net cash flows (sales minus redemptions) over last month'stotal assets, expressed in percent. To remove time trends, I subtract a12-month moving average from each month's flow (see Fig. 2). Returnsare in percent per month. Monthly data from Morningstar, January 1990to January 2013.

Mean St. dev. Autocorr. N

All �0.03 0.53 0.43 277Flows Active �0.03 0.54 0.41 277

Index �0.05 1.08 0.32 277

All 0.74 4.48 0.12 277Returns Active 0.74 4.50 0.12 277

Index 0.79 4.34 0.06 277

A. Savov / Journal of Financial Economics 112 (2014) 213–231220

difference between exposures unchanged even as theirlevels change. We can interpret the former shock as a flowfrom one group to the other (one group raises its exposurewhile the other reduces it) and the latter as a compensat-ing price change (both groups bid prices up or downwithout trading). As in Grossman and Stiglitz (1980),incomplete information precludes optimal risk sharing.

The connection between belief shocks and flows leads toa connection between non-traded income and flows. Con-sider a positive transitory shock to non-traded income,εy40. By optimal filtering, households raise their expecta-tions, bx goes up: households anticipate high income growthand lower stock returns. As the true x is unchanged, x�bx islower. By Eq. (31), λrs2r �mrbs2

r is also lower, so mr risesrelative to λr (becomes less negative). Thus, householdexposure to stocks declines, leading to outflows. A negativeincome shock analogously leads to inflows.

A positive return shock εr40 also leads to inflows by asimilar argument. Thus, flows are negatively correlatedwith non-traded income and positively correlated withstock returns. It is therefore necessary to control formarket exposure when constructing a fund-flows factor.

The information structure of the model effectivelyassumes that fund flows are not publicly observable, atleast not in real time. This assumption can be micro-founded by adding a layer of unpriced idiosyncratic shocksto household income, left out here for simplicity. Thesewould make the flows of individual households uninforma-tive about aggregate shocks without changing the stochas-tic discount factor. This is a necessary condition for avoidingthe no-trade theorem of Glosten and Milgrom (1985).

Since active funds attract investors with substantial non-traded income, it is their flows that should reveal non-traded shocks while also responding to contemporaneousstock returns. As they are related to household error, theyshould negatively predict subsequent stock returns. Theyshould also predict relatively high active fund returns, asactive managers take the other side. Since income shocksand flows move in opposite directions, the premium on afund-flows risk factor should be negative (at least aftercontrolling for correlation with the market). Active fundsshould load positively on this factor in a way that accountsfor their apparent underperformance. I test all these pre-dictions in the next section.

4. Empirical results

In this section, I test the predictions of the model usingmutual fund flows. After documenting the buy-and-holdunderperformance puzzle, I examine the relationshipbetween flows and contemporaneous market returns, flowsand future market returns, and flows and future active-minus-market returns. I then construct a flows-based factorthat according to the model mimics shocks to non-tradedassets and use it to price active and index funds. The sectionconcludes with some robustness checks and extensions.

4.1. Data and preliminary results

I use monthly data on fund flows and returns fromMorningstar. I consider U.S. equity open-end mutual funds

from January 1989 to January 2013 (no index funds reportmonthly flows prior to 1989). The data are reported at theshare-class level. I aggregate all share classes on a value-weighted basis into three aggregated “funds”: all funds,active funds, and index funds. All analysis takes place atthis aggregated level. Whereas fund-level flows are drivenby the search for skill in the cross section (Chevalier andEllison, 1997; Sirri and Tufano, 1998), aggregate flowsreflect aggregate shocks, as in the model.

I calculate flows as net cash flows (also called dollarflows) over lagged total net assets. Fig. 2 plots the timeseries of aggregate flows. A downward trend reveals aslowdown in the growth rate of the mutual fund sector.Since returns are stationary, I remove this trend by sub-tracting a 12-month moving average. I use de-trended flowsin all tests, which limits the final sample to 277 monthlyobservations between January 1990 and January 2013.

Table 1 shows descriptive statistics for the key vari-ables, flows and returns. Flows are moderately persistentwith a half-life of about 25 days. A typical month seesflows on the order of a half a percent of total assets. Indexfund flows are more volatile, a result concentrated in thefirst half of the sample when index funds are relatively

Fig. 3. Cumulative flows and expected returns. “12-mo cum flow extrend” is the sum of all flows over the past 12 months net of a linear timetrend; “p–d ratio” is the 12-month trailing price–dividend ratio of the S&P500. The return “12-mo RA�RM is the return on a strategy long theaggregate active mutual fund portfolio and short the market portfolio.Data are from Morningstar, January 1990 to January 2013. Gray bandsindicate NBER recessions.

A. Savov / Journal of Financial Economics 112 (2014) 213–231 221

small. The average monthly returns of index funds are fivebasis points higher than active funds before adjustingfor risk.

Fig. 3 looks at the relationship between the size of theactive fund sector and returns. In the model with decreas-ing returns to scale, times of high risk premiums areassociated with outflows and hence higher net returns.17

Panel A of Fig. 3 plots 12-month cumulative fund flows netof a linear time trend against the market price–dividendratio, a proxy for expected returns. The second half of thesample shows a strong positive relationship betweencumulative flows and the price–dividend ratio, as pre-dicted. In the first half, when the mutual fund sector issmall and growing at a faster pace, this relationship is notevident, though it remains clear that the sector contractsduring recessions, when risk premiums are high.

Panel B of Fig. 3 looks at decreasing returns to scale byplotting past cumulative flows (on a reversed axis) againstfuture active fund returns in excess of the market. The twoseries have a sample correlation of �29% (Newey-West t-stat of 1.63). Visually, the co-movement between the twoseries is strongest in the mid-to-late 1990s and thefinancial crisis of 2008. Overall, Fig. 3 offers some supportto the decreasing returns-to-scale channel, which is stan-dard in the literature (Berk and Green, 2004; Pástor and

17 In the absence of decreasing returns to scale, net returns must riseby another mechanism such as fee waivers or greater skill.

Stambaugh, 2012). Chen, Hong, Huang, and Kubik (2004)offer direct evidence.

4.2. Main results

Table 2 confirms the well-documented starting premiseof the paper: active mutual funds underperform standardbenchmarks, whereas index funds do not. The averagefund underperforms by 0.07% to 0.10% per month, or 0.84%to 1.20% per year. These numbers are consistent with Famaand French (2010). Active funds tend to overweight smallstocks, which lowers their three-factor alphas. Althoughthe CAPM alphas are not statistically significant, the three-and four-factor alphas are significant at the 95% confidencelevel for both the total and active aggregated funds.

By contrast, index funds have tiny alphas of 70:01%,never more than half a standard error from zero. Indexfunds load more heavily on large stocks as many explicitlyseek to replicate the S&P 500 index. Perhaps surprisingly,index funds also appear to load positively on the valuefactor and slightly negatively on the momentum factor.Overall, Table 2 demonstrates that active funds underper-form traded benchmarks by about as much as theirexpense ratios (which range between 0.85% and 1% peryear over 1990 to 2006 according to French, 2008).

4.2.1. Flows and returnsTurning to the core predictions of the model, Table 3

shows that active fund flows are strongly related tocontemporaneous market returns, whereas index fundflows are not. I place the market return on the left sideof the regression to run a horse race between active andindex fund flows on the right. Overall, a one-standarddeviation inflow is associated with a 1.8% higher marketreturn, and this relationship is significant at the 1% level.The middle columns of Table 3 show that the effect isconcentrated among active funds, which have a coefficient4.5 times that of index funds. Whereas the stand-alonecoefficient on index fund flows is also highly significant, itdrops by a factor of seven and falls within a standard errorfrom zero when active fund flows are included in theregression. By contrast, the coefficient on active fund flowsis undiminished. Looking at R2, market returns account for16% of the variation in active flows versus only 3% forindex flows.

The results of Table 3 are consistent with the predic-tions of the model, where active funds attract investorswho are more likely to rebalance due to outside income.These investors rely on market returns to learn aboutexpected returns. As a result, they respond strongly tocurrent market returns (they also respond to non-tradedincome shocks).

Table 4 shows results from regressions of future stockmarket returns on current flows. I include the marketprice–dividend ratio as an additional forecasting variablein some specifications since households in the modelcondition on prices. The top panel of Table 4 shows thataggregate flows negatively forecast market returns at thesix- and 12-month horizons. (The point estimates arenegative but insignificant at the three-month horizon.) Aone-standard deviation monthly inflow is associated with

Table 2Mutual fund performance.

This table compares the after-fee performance of active and index mutual funds. “All” is the return on a value-weighted portfolio of all U.S. equity mutualfunds. “Active” is for active funds and “Index” is for index funds. The alphas are in percent per month (e.g., �0.07 is negative seven basis points per month).Mkt�Rf is the excess market return, “SMB” and “HML” are the Fama-French size and book-to-market factors, and MOM is the momentum factor. Monthlydata from Morningstar, January 1990 to January 2013. Three, two, and one stars denote significance at the 1%, 5%, and 10% levels, respectively.

All Active Index

α �0.07 �0.09nn �0.10nn �0.08 �0.09nn �0.10nn �0.01 �0.01 0.01(0.05) (0.04) (0.04) (0.05) (0.05) (0.05) (0.04) (0.02) (0.02)

Mkt�Rf 0.99nnn 0.98nnn 0.98nnn 0.98nnn 0.98nnn 0.98nnn 0.96nnn 1.00nnn 0.99nnn

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)

SMB 0.09nnn 0.08nnn 0.10nnn 0.10nnn �0.18nnn �0.18nnn

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)

HML 0.02n 0.03n 0.02 0.03 0.04nnn 0.03nnn

(0.01) (0.01) (0.02) (0.02) (0.01) (0.02)

MOM 0.00 0.01 �0.02nnn

(0.01) (0.01) (0.01)

R2 97% 97% 97% 97% 97% 97% 97% 97% 97%N 277 277 277 277 277 277 277 277 277

Table 3Fund flows and contemporaneous returns.

This table shows the correlation between fund flows and contempora-neous market returns. Flows are measured as net cash flows over laggedassets, net of a 12-month moving average. “All flow” are the percentageflows of a value-weighted portfolio of all U.S. equity mutual funds. “Activeflow” and “Index flow” are for value-weighted portfolios of all activefunds and index funds, respectively. RM is the CRSP value-weightedmarket return in the same month as the fund flows. Newey-Weststandard errors with 12 lags. Monthly data from Morningstar, January1990 to January 2013. Three, two, and one stars denote significance at the1%, 5%, and 10% levels.

RMt

Constant 0.91nnn 0.91nnn 0.86nnn 0.91nnn

(0.27) (0.27) (0.30) (0.27)

All flowt 3.38nnn

(0.59)

All flowt 3.37nnn 3.28nnn

(0.58) (0.66)

Index flowt 0.76nnn 0.10(0.18) (0.19)

R2 16% 16% 3% 16%N 277 277 277 277

A. Savov / Journal of Financial Economics 112 (2014) 213–231222

a 1.8% lower return over the next six months (significant atthe 10% level) and a 2.5% lower return over the next year(significant at the 5% level). These magnitudes are on theorder of half the sample equity premium. Conditioning ona public signal like the price–dividend ratio does not affectthe forecasting power of flows, as predicted. Nevertheless,the price–dividend ratio is a strong predictor, which showsthat the information contained in fund flows is distinct.

The remaining panels of Table 4 show that the fore-casting power of fund flows is concentrated among activefunds. The forecasting coefficients for active fund flows arevery close to the aggregate numbers, whereas the coeffi-cients on index fund flows are three to 20 times smaller.They are also insignificant in all but one specification,where they come in with a t-stat of 1.78. The last panel of

Table 4 shows that in a horse race between active andindex funds, active fund flows retain the magnitude oftheir forecasting coefficients, whereas those of index fundstend to change sign. Active fund flows retain their sig-nificance at the 12-month horizon but not at the six-month horizon.

The evidence in Tables 3 and 4 suggests that active fundinvestors rebalance their portfolios in a systematic way:they buy in response to contemporaneous market returnsthat are reversed in subsequent months. In the model,households that have this tendency—due to imperfectinformation and outside income shocks—optimally investwith active funds, even at a high premium as activemanagers undo their poor timing.

Table 5 brings together the actions of investors andfund managers by showing that high inflows, though theypredict lower market returns, also predict high active fundreturns relative to the market. The table regresses thefuture returns of a strategy that is long mutual funds andshort the market on current fund flows. The top panelshows that a one-standard deviation inflow is associatedwith a 0.28% higher active-minus-market return over thenext three months (significant at the 1% level) and a 0.46%higher return over the next six months (also significant atthe 1% level). The point estimates are large but insignif-icant at the 12-month horizon. Curiously, the statisticalsignificance of the results in Table 5 is concentrated at aslightly shorter (though overlapping) horizon than inTable 4. However, the point estimates increase similarlywith horizon in both tables.

As before, the forecasting power of flows is concen-trated among active funds: the coefficients on active fundflows are nearly the same in magnitude and significance tothe aggregate numbers, whereas the coefficients on indexfund flows are about five times smaller and never muchmore than one standard error from zero. In a horse race(bottom panel), active fund flows retain their forecastingpower whereas index fund flows become even weaker andoften flip sign, as predicted.

Table 4Predicting market returns with fund flows.

Regressions of future market returns on current flows. Flows are net cash flows over lagged assets, net of a 12-month moving average. “All flow” is for avalue-weighted portfolio of all U.S. equity mutual funds. “Active flow” and “Index flow” are for value-weighted portfolios of active and index funds,respectively. RM is the return on the market portfolio from CRSP over a 3-, 6-, and 12-month horizon. p–d is the 12-month trailing market price–dividendratio. Newey-West standard errors with 12 lags. Monthly data from Morningstar, January 1990 to January 2013. Three, two, and one stars denotesignificance at the 1%, 5%, and 10% levels.

RMtþ1;tþ3 RM

tþ1;tþ6 RMtþ1;tþ12

All fund flows

Constant 2.53nnn 20.68nnn 5.07nnn 44.77nn 10.71nnn 99.88nnn

(0.87) (9.63) (1.71) (17.61) (3.20) (28.32)

All flowt �0.89 �0.89 �3.41n �3.40n �4.80nn �4.79nn

(1.22) (1.25) (1.93) (1.85) (2.41) (2.09)

ðp�dÞt �4.64n �10.15nn �22.63nnn

(2.48) (4.58) (7.47)

R2 0% 3% 2% 9% 2% 18%

Active fund flows

Constant 2.53nnn 20.63nn 5.08nnn 44.60nn 10.71nnn 99.03nnn

(0.87) (9.63) (1.71) (17.61) (3.20) (28.28)

Active flowt �0.91 �0.89 �3.30n �3.25n �4.95nn �4.83nn

(1.25) (1.28) (1.91) (1.86) (2.43) (2.13)

ðp�dÞt �4.63n �10.10nn �22.57nnn

(2.48) (4.58) (7.46)

R2 0% 3% 2% 9% 2% 18%

Index fund flows

Constant 2.56nnn 20.74nn 5.11nnn 46.00nnn 10.85nnn 100.19nnn

(0.87) (9.49) (1.70) (17.51) (3.21) (28.81)

Index flowt 0.08 �0.03 �0.87 �1.11n �0.21 �0.73(0.33) (0.35) (0.74) (0.62) (1.08) (0.83)

ðp�dÞt �4.65n �10.45nn �22.84nnn

(2.44) (4.54) (7.58)

R2 0% 3% 1% 8% 0% 16%

Active and index fund flows

Constant 2.54nnn 20.44nn 5.07nnn 45.19nn 10.75nnn 98.70nnn

(0.87) (9.48) (1.72) (17.66) (3.21) (28.46)

Active flowt �1.16 �1.04 �3.09 �2.81 �5.71nn �5.08nn

(1.44) (1.48) (1.91) (1.96) (2.80) (2.48)

Index flowt 0.31 0.18 �0.26 �0.54 0.93 0.30(0.42) (0.45) (0.73) (0.66) (1.22) (0.98)

ðp�dÞt �4.58n �10.26nn �22.48nnn

(2.47) (4.59) (7.53)

R2 0% 3% 2% 9% 3% 18%

N (all panels) 274 274 271 271 265 265

A. Savov / Journal of Financial Economics 112 (2014) 213–231 223

4.2.2. Asset pricing with flowsOverall, Tables 3–5 suggest that active fund investors

are more likely than index fund investors to buy ahead oflow market returns, and that active funds offer protectionagainst this bad timing. According to the model, the valueof this timely service can raise the compensation of fundmanagers above their gross alpha. This value depends onthe premium for non-traded income risk. The modelshows that non-traded income shocks are reflected inthe investment flows of mutual fund investors: A posit-ive non-traded income shock conditional on the market

return is associated with lower expected returns, andtherefore fund outflows. This result suggests that fundflows can serve as an inverse proxy for non-traded incomeshocks in an asset pricing framework. The premium on anaggregate flow factor should be negative.

To test this prediction, I estimate the premium of afund-flows factor in the cross section of equities, whichis independent of mutual funds. To construct the factor,I value-weight all stocks in CRSP into double-sortedquintiles based on their univariate betas with respect tothe market return and the time series of aggregate fund

Table 5Predicting active-minus-market returns with fund flows.

Regressions of future active fund returns in excess of the market oncurrent flows. Flows are net cash flows over lagged assets, net of a 12-month moving average. “All flow” is for a value-weighted portfolio of allU.S. equity mutual funds. “Active flow” and “Index flow” are for value-

weighted portfolios of active and index funds, respectively. RA�RM is thereturn on a strategy long the value-weighted active fund portfolio andshort the market over a 3-, 6-, and 12-month horizon. p�d is the 12-month trailing market price–dividend ratio. Newey-West standard errorswith 12 lags. Monthly data from Morningstar, January 1990 to January2013. Three, two, and one stars denote significance at the 1%, 5%, and 10%levels.

ðRA�RMÞtþ1;tþ3 ðRA�RMÞtþ1;tþ6 ðRA�RMÞtþ1;tþ12

All fund flows

Constant �0.23 �1.34 �0.48 �2.68 �1.10 �8.40(0.18) (2.33) (0.37) (4.59) (0.77) (7.96)

All flowt 0.54nnn 0.54nnn 0.87nnn 0.87nnn 0.90 0.90(0.19) (0.19) (0.33) (0.32) (0.63) (0.59)

ðp�dÞt 0.28 0.56 1.87(0.60) (1.17) (2.02)

R2 3% 4% 3% 4% 1% 3%

Active fund flows

Constant �0.23 �1.32 �0.48 �2.63 �1.10 �8.35(0.18) (2.32) (0.37) (4.57) (0.76) (7.94)

Active flowt 0.54nnn 0.54nnn 0.86nn 0.86nnn 0.89 0.89(0.20) (0.19) (0.34) (0.33) (0.64) (0.60)

ðp�dÞt 0.28 0.55 1.85(0.59) (1.17) (2.02)

R2 3% 4% 3% 4% 1% 3%

Index fund flows

Constant �0.24 �1.47 �0.49 �2.90 �1.12 �8.57(0.19) (2.45) (0.39) (4.78) (0.78) (8.24)

Index flowt 0.10 0.10 0.17 0.18 0.10 0.14(0.09) (0.08) (0.17) (0.16) (0.27) (0.27)

ðp�dÞt 0.31 0.61 1.91(0.62) (1.22) (2.09)

R2 0% 1% 0% 1% 0% 2%

Active and index fund flows

Constant �0.23 �1.31 �0.48 �2.65 �1.10 �8.30(0.18) (2.28) (0.37) (4.51) (0.76) (7.95)

Active flowt 0.55nn 0.54nn 0.86nn 0.85nn 0.98 0.93(0.23) (0.22) (0.43) (0.41) (0.76) (0.73)

Index flowt �0.01 �0.01 �0.01 0.01 �0.10 �0.05(0.11) (0.10) (0.21) (0.19) (0.32) (0.33)

ðp�dÞt 0.28 0.56 1.84(0.58) (1.15) (2.02)

R2 3% 4% 3% 4% 1% 3%

N (all panels) 274 274 271 271 265 265

Table 6Aggregate flows as a risk factor.

Pricing of the aggregate fund flows risk factor FLO. FLO is constructedfrom the returns of 25 double-sorted portfolios. Each stock in CRSP isassigned full-sample univariate betas with respect to the market returnand the time series of aggregate fund flows (net of a 12-month movingaverage). Each month, stocks are sorted into value-weighted portfoliosbased on the quintile of their market and flow betas. FLO is a portfoliothat is long the five high-flow beta quintiles and short the five low-flowbeta quintile portfolios. Panel A displays correlations between FLO andstandard risk factors. Panel B runs time-series regressions of FLO on theother factors. All returns are in percent per month (e.g., �0.83 is minus83 basis points per month). Data are monthly from Morningstar, January1990 to January 2013. Three, two, and one stars denote significance at the1%, 5%, and 10% levels.

Panel A: Pairwise factor correlations with FLO

Mkt�Rf SMB HML MOM

FLO 0.10 0.53 �0.26 �0.08

Panel B: Time-series regressions of FLO

(1) (2) (3) (4)

Constant �0.83n �0.92nn �0.94nn �0.76nn

(0.43) (0.43) (0.37) (0.37)

Mkt�Rf 0.16n �0.08 �0.16n

(0.10) (0.09) (0.09)

SMB 1.07nnn 1.09nnn

(0.12) (0.12)

HML �0.23n �0.30nnn

(0.12) (0.12)

MOM �0.21nnn

(0.07)

R2 0% 1% 29% 31%N 276 276 276 276

A. Savov / Journal of Financial Economics 112 (2014) 213–231224

flows. The flow factor FLO is the return on a strategy longthe five quintiles with high flow betas and short the fivequintiles with low flow betas (this approach reduces thecorrelation between FLO and the market return).

Table 6 explores the distribution and pricing of FLO.Panel A shows that FLO has a weak positive 10% correlation

with the market (by construction) and a strong 53%correlation with the size factor. The correlation is a weaker�26% with value and an insignificant �8% with momen-tum. These results suggest that small stocks are morelikely to have high returns in months with high fundinflows, making them a potential hedge for non-tradedshocks in the context of the model.

Panel B of Table 6 considers the pricing of FLO. FLO has asample average return of �0.83% per month (t-stat 1.93),suggesting a negative premium, as expected. Importantly,this premium is not subsumed by the other factors.Controlling for the correlation between FLO and the market,the flow premium grows in magnitude to �0.92% and issignificant at the 5% level. Adding the size and value factorsstrengthens it further to �0.94% (5% significance). Momen-tum tapers the premium to �0.76% without affectingits statistical significance. As FLO has by far its largestloading on size, a negative average return despite a positivesize premium bolsters the evidence for a negative flowpremium.

The next step is to check whether the negative flowpremium can help price mutual funds. Since FLO wasobtained from equity returns, it offers an independenttest. For this exercise, I construct the returns of a portfolio

Table 7Asset pricing with flows.

Results from an asset pricing test using the aggregate fund flows riskfactor FLO. FLO is constructed from the returns of 25 value-weightedportfolios, double-sorted according to their univariate betas with respectto the market and aggregate fund flows. FLO is a portfolio that is long thefive high-flow beta quintiles and short the five low-flow beta quintileportfolios. The table presents alphas and betas from time-series regres-sions of the return on an active-minus-index long-short portfolio strategy

RA�RI on FLO and standard risk factors. All returns are in percent permonth (e.g., �0.07 is minus seven basis points per month). Data aremonthly fromMorningstar, January 1990 to January 2013. Three, two, andone stars denote significance at the 1%, 5%, and 10% levels.

RA�RI

Alpha �0.07 0.02 �0.09n �0.06 �0.11nn �0.08(0.08) (0.07) (0.05) (0.05) (0.05) (0.05)

FLO 0.09nnn 0.03nnn 0.03nnn

(0.01) (0.01) (0.01)

Mkt�Rf 0.03nn 0.02 �0.02n �0.02 �0.01 �0.01(0.02) (0.02) (0.01) (0.01) (0.01) (0.01)

SMB 0.28nnn 0.25nnn 0.28nnn 0.24nnn

(0.02) (0.02) (0.02) (0.02)

HML �0.01 �0.01 �0.01 0.00(0.02) (0.02) (0.02) (0.02)

MOM 0.03nn 0.03nnn

(0.01) (0.01)

R2 1% 3% 53% 55% 54% 56%N 276 276 276 276 276 276

Table 8Fund flows and contemporaneous returns, robustness.

This table shows the correlation between fund flows and contempora-neous market returns under four robustness specifications. For bench-mark results and methodology, see Table 3, column 4. “No retirement”excludes funds flagged as “available for retirement plan” in Morningstar;“No institutional” excludes funds flagged as institutional; and “No small-cap & sector” excludes funds flagged as small-cap, defined as primarilyinvesting in stocks with market capitalization below $1 billion, or assector funds; “Bond funds” is for corporate bond mutual funds. Monthlydata from Morningstar, January 1990 (January 1992 for bond funds) toJanuary 2013. Three, two, and one stars denote significance at the 1%, 5%,and 10% levels.

RMt

No No No small-cap Bondretirement institutional & sector funds

Constant 0.91nnn 0.92nnn 0.92nnn 0.61nnn

(0.27) (0.27) (0.27) (0.08)

Active flowt 3.20nnn 3.31nnn 3.28nnn 0.51nnn

(0.64) (0.61) (0.74) (0.11)

Index flowt 0.15 0.07 0.14 0.06(0.81) (0.16) (0.21) (0.07)

R2 16% 17% 14% 14%N 277 277 277 253

18 At the same time, the model predicts that investors with stableincome flows, natural buy-and-hold-investors, are optimally attracted toindex funds, so this observation can be interpreted as a prediction.

19 A priori, one might expect institutional clients to favor either indexor active funds. For example, they might be more informed, which wouldsuggest index funds, or since many are in reality wealthy individuals,they might have significant non-traded assets (e.g., private business),which would lead them towards active funds.

20 An alternative is to only include large-cap funds, which Morningstardefines as primarily investing in stocks with market capitalization over $8billion. Results are similar to those excluding small-cap stocks. Therelationship between flows and contemporaneous returns is unaffected.

A. Savov / Journal of Financial Economics 112 (2014) 213–231 225

long active funds and short index funds. I run time-seriesregressions of this long-short portfolio on the risk factors.

The results of the pricing test are in Table 7. The active-minus-index fund portfolio has a highly significant posi-tive beta of 0.09 with respect to FLO in an augmentedCAPM specification. In other words, active funds outper-form index funds in months in which mutual fund inflowsare high, even after controlling for the market return. TheFLO beta falls to 0.03 when the size factor is added, but itremains significant at the 1% level. The positive FLO betaarises in the model: active funds perform relatively wellwhen non-traded income disappoints and expectedreturns are revised higher, leading to inflows. As predicted,this correlation remains even conditional on the marketreturn.

The intercepts in Table 7 show that including FLOimproves the measured performance of active funds. Inthe augmented CAPM specification, the alpha flips from�0.07% to 0.02% per month. The three- and four-factoralphas increase from �0.09% and �0.11% to �0.06% and�0.08%. In all cases, the alphas are not statisticallysignificant once FLO is included. Thus, depending on thespecification, the fund-flows factor accounts for between25% and over 100% of the apparent underperformance ofactive funds.

It is possible that this result understates the effect ofnon-traded shocks if the cross section of equities does notfully reveal these shocks. Nevertheless, the results suggestthat fund flows are picking up important shocks experi-enced by household investors.

4.3. Robustness

Tables 8–10 examine the robustness of the main resultsof the paper with respect to variation in the underlyingsample of funds. A full set of tables is available in theOnline Appendix that accompanies the paper. Tables 8–10also present results for bond funds, which are discussedseparately in Section 4.4.

The first robustness check excludes funds flagged as“available for retirement” in Morningstar. Index fundsreceive substantial flows through retirement plans on apre-determined basis, which could potentially account fortheir distinct flow dynamics.18

The second robustness check excludes funds flagged asinstitutional. The goal here is to determine whether thedocumented differences in the flow dynamics of index andactive funds are correlated with differences in institutionalversus retail clienteles.19

The third robustness check excludes small-cap funds(defined by Morningstar as funds that primarily invest instocks with market capitalization under $1 billion), andsector funds.20 Many index funds explicitly target the S&P500, a large-cap index. Removing small-cap and sector

Table 9Predicting market returns with fund flows, robustness.

Regressions of future market returns on current flows under four robustness specifications. For benchmark results and methodology, see Table 4. “Noretirement funds” excludes funds flagged as “available for retirement plan” in Morningstar; “No institutional funds” excludes funds flagged as institutional;and “No small-cap & sector funds” excludes funds flagged as small-cap (defined as primarily investing in stocks with market capitalization below $1 billion)or as sector funds; “Bond funds” is for corporate bond mutual funds. Monthly data from Morningstar, January 1990 (January 1992 for bond funds) toJanuary 2013. Three, two, and one stars denote significance at the 1%, 5%, and 10% levels.

RMtþ1;tþ3 RM

tþ1;tþ6 RMtþ1;tþ12

No retirement funds

Constant 2.54nnn 20.37nn 5.07nnn 45.16nn 10.75nnn 98.63nnn

(0.87) (9.59) (1.72) (17.65) (3.21) (28.41)

Active flowt �1.21 �1.09 �3.08 �2.80 �5.73nn �5.11nn

(1.41) (1.44) (1.92) (1.96) (2.80) (2.49)

Index flowt 0.38 0.26 �0.27 �0.54 0.98 0.37(0.38) (0.40) (0.73) (0.67) (1.22) (0.98)

ðp�dÞt �4.56n �10.25nn �22.46nnn

(2.47) (4.59) (7.51)

R2 1% 3% 2% 9% 3% 18%

No institutional funds

Constant 2.54nnn 20.46nn 5.06nnn 45.23nn 10.76nnn 98.10nnn

(0.87) (9.48) (1.72) (17.63) (3.19) (28.37)

Active flowt �0.96 �0.85 �2.87 �2.62 �5.70nn �5.15nn

(1.43) (1.47) (1.91) (1.97) (2.45) (2.20)

Index flowt 0.26 0.14 �0.20 �0.47 1.33 0.75(0.48) (0.49) (0.73) (0.68) (1.13) (0.93)

ðp�dÞt �4.58n �10.27nn �22.33nnn

(2.45) (4.59) (7.50)

R2 0% 3% 2% 9% 3% 18%

No small-cap & sector funds

Constant 2.53nnn 20.42nn 5.05nnn 45.11nnn 10.74nnn 98.76nnn

(0.87) (9.51) (1.72) (17.46) (3.20) (28.35)

Active flowt �1.27 �1.12 �3.46n �3.12 �5.68n �4.93n

(1.62) (1.67) (2.08) (2.13) (2.97) (2.72)

Index flowt 0.31 0.18 �0.23 �0.52 0.86 0.22(0.44) (0.45) (0.74) (0.66) (1.24) (1.00)

ðp�dÞt �4.57n �10.24nn �22.50nnn

(2.45) (4.54) (7.49)

R2 0% 3% 2% 9% 2% 18%

Bond funds

Constant 1.78nnn �0.65 3.59nnn �1.52 7.20nnn �5.16(0.31) (1.22) (0.59) (2.52) (1.08) (5.07)

ðActive flowÞt 0.20 0.22 0.61n 0.62 0.37 0.34(0.23) (0.25) (0.37) (0.39) (0.49) (0.47)

ðIndex flowÞt �0.17nn �0.12 �0.49nnn �0.37nn �0.83nnn �0.54nnn

(0.08) (0.09) (0.15) (0.15) (0.24) (0.20)

Yieldt 0.40nn 0.84nn 2.02nn

(0.20) (0.41) (0.79)

R2 1% 4% 4% 11% 4% 20%

A. Savov / Journal of Financial Economics 112 (2014) 213–231226

Table 10Predicting active-minus-market returns with fund flows, robustness.

Regressions of future active fund returns in excess of the market on current flows under four robustness specifications. For benchmark results andmethodology, see Table 5, panel 4. “No retirement funds” excludes funds flagged as “available for retirement plan” in Morningstar; “No institutional funds”excludes funds flagged as institutional; and “No small-cap & sector funds” excludes funds flagged as small-cap (defined as primarily investing in stockswith market capitalization below $1 billion) or as sector funds; “Bond funds” is for corporate bond mutual funds. Monthly data from Morningstar, January1990 to January 2013. Three, two, and one stars denote significance at the 1%, 5%, and 10% levels.

ðRA�RMÞtþ1;tþ3 ðRA�RMÞtþ1;tþ6 ðRA�RMÞtþ1;tþ12

No retirement funds

Constant �0.23 �1.33 �0.48 �2.70 �1.11 �8.39(0.18) (2.26) (0.37) (4.47) (0.76) (7.86)

Active flowt 0.55nn 0.55nn 0.87nn 0.86nn 1.03 0.98(0.24) (0.22) (0.43) (0.41) (0.75) (0.72)

Index flowt �0.03 �0.02 �0.01 0.00 �0.14 �0.08(0.11) (0.10) (0.21) (0.19) (0.31) (0.32)

ðp�dÞt 0.28 0.57 1.86(0.58) (1.14) (2.00)

R2 3% 4% 3% 4% 2% 4%

No institutional funds

Constant �0.24 �1.19 �0.49 �2.51 �1.12 �7.99(0.17) (2.26) (0.36) (4.46) (0.73) (7.83)

Active flowt 0.53nn 0.52nn 0.83nn 0.82nn 0.85 0.81(0.22) (0.21) (0.40) (0.39) (0.70) (0.68)

Index flowt �0.06 �0.05 �0.07 �0.06 �0.19 �0.14(0.11) (0.10) (0.20) (0.20) (0.31) (0.33)

ðp�dÞt 0.24 0.52 1.76(0.58) (1.14) (2.00)

R2 3% 4% 3% 4% 1% 3%

No small-cap & sector funds

Constant �0.25n �0.99 �0.53n �2.18 �1.19n �7.05(0.15) (1.85) (0.30) (3.63) (0.61) (6.41)

Active flowt 0.41n 0.41nn 0.64n 0.63n 0.90 0.85(0.22) (0.21) (0.39) (0.37) (0.73) (0.73)

Index flowt �0.01 �0.01 �0.01 0.00 �0.16 �0.12(0.09) (0.09) (0.17) (0.16) (0.28) (0.29)

ðp�dÞt 0.19 0.42 1.50(0.47) (0.92) (1.61)

R2 2% 2% 2% 3% 1% 4%

Bond funds

Constant �0.23 1.29n �0.49n 2.01 �0.99n 3.39(0.15) (0.74) (0.28) (1.32) (0.51) (2.61)

ðActive flowÞt 0.14 0.13 0.00 �0.01 0.25 0.26(0.12) (0.12) (0.10) (0.11) (0.22) (0.21)

ðIndex flowÞt 0.07 0.03 0.16nn 0.10 0.27nn 0.17(0.05) (0.05) (0.07) (0.08) (0.12) (0.14)

Yieldt �0.25nn �0.41n �0.72n

(0.12) (0.21) (0.43)

R2 2% 7% 2% 9% 4% 14%

A. Savov / Journal of Financial Economics 112 (2014) 213–231 227

A. Savov / Journal of Financial Economics 112 (2014) 213–231228

funds checks whether differences in the portfolios of indexand active funds are related to the main results of thepaper.21

Table 8 reproduces the contemporaneous return regres-sions in Table 3, last column. In each robustness specification,active fund flows are strongly correlated with contempora-neous market returns, whereas index fund flows are not. Thecoefficients are very close to the benchmark results and thestatistical significance is identical.

Table 9 reproduces the market return forecastingregressions in Table 4, last panel. In all cases, as in thebenchmark results, active flows are significant negativepredictors of the market return at the 12-month horizon.Statistical significance is reduced to the 10% level whensmall-cap and sector funds are excluded but in this case,the six-month forecast gains in significance. As expected,index fund flows have no forecasting power.

Table 10 reproduces the active-minus-market returnforecasting regressions in Table 5, last panel. Active fundflows are strong positive predictors of the excess return ofactive funds versus the market at the three- and six-monthhorizons across all robustness specifications. The coeffi-cients are generally significant at the 5% level, falling to10% in some specifications when small-cap and sectorfunds are excluded. Once again, index fund flows haveno forecasting power. The magnitudes are close to thebenchmark estimates.

The Online Appendix also contains results for fore-casting models that condition on the lagged marketreturn. The results from the market-forecasting regres-sion become a bit weaker, whereas the active-minus-market forecasting regression becomes stronger. Thelagged market return is a significant negative predictorof the active-minus-market return, consistent with coun-tercyclical performance. The premium on FLO is some-what larger following a market downturn, consistentwith a higher volatility of non-traded income or riskaversion. In a conditional asset pricing model, FLO has abigger impact on mutual fund performance, but statisticalpower is reduced.

4.4. Bond funds

In a final extension of the empirical analysis, I examinethe universe of corporate bond funds. The key challenge inmapping bond funds into the framework of the paper isthe nature of bonds as an intermediate asset class in termsof risk. In the model, risky and risk-free asset flows arenegatively correlated and so they predict returns in oppo-site directions. Nevertheless, at nearly $1 trillion in assets,bond funds represent an important asset class.

The Online Appendix documents the existence of anunderperformance puzzle among bond funds, though it isabout one-third smaller than among equity funds (active

(footnote continued)The coefficient estimates for predicting the market return and the active-minus-market return come in significant at the 10% level.

21 Within the model, an active fund bias towards small stocks couldbe due to greater uncertainty about their expected returns or a hedgingdemand by investors with substantial non-traded assets.

bond funds underperform index bond funds by four toseven basis points per month versus six to ten for equityfunds). These results are consistent with the literature(Blake, Elton, and Gruber, 1993).

The last column of Table 8 shows that the flows ofactive bond funds are strongly correlated with contem-poraneous market returns, as with equity funds. Thecoefficients are quite a bit smaller but the statisticalsignificance is just as high due to smaller standard errors.

The last panel of Table 9 shows that in contrast toequity funds, it is index bond fund flows that negativelypredict market returns. The forecasting coefficients aresmall but the statistical significance is high. These resultssuggest that index bond fund investors are not attainingthe high buy-and-hold returns of their funds. Non-tradedincome shocks generate this bad timing in the model, butthe matching between funds and investors mitigates it.

In the active-minus-market forecasting regressionspresented in Table 10, neither active nor index bond fundflows are good predictors. In the full set of tables in theOnline Appendix, active bond fund flows come in signifi-cantly in specifications without index funds, as they do inthe benchmark results.

Interestingly, the flows into bond and equity indexfunds are highly correlated at 40% versus only 12%for bond and equity active funds. This suggests a possibleexplanation for the predictability results: Index fundinvestors appear to treat bond and equity funds similarly,going in and out of both at the same time, whereas activefund investors do not. This could happen if active fundinvestors perceive bonds to be closer to the model's risk-free asset, perhaps because they are less risk averse. Arelated possibility is that if expected bond returns arestable, bond fund flows might be primarily driven bydevelopments in other markets.

The Online Appendix also contains analogs to the assetpricing results in Tables 6 and 7. For consistency, I examinethe pricing power of the equity-based fund-flows factorFLO in the context of bond funds. As with equities, FLOretains its robust negative premium against a set of bond-market factors that includes the returns of the aggregatebond market, a high-yield strategy, a term-premiumstrategy, and a Treasury index. Interestingly, FLO loadsstrongly on the high-yield index.

Like active equity funds, active bond funds also loadstrongly on FLO. Adding FLO to an asset pricing modelnarrows the performance gap between active and indexbond funds by between one and five basis points permonth. Since the gap is narrower to begin with, the effectis somewhat smaller and less significant than for equityfunds.

5. Conclusion

Roll (1977) points out that non-traded assets create anomitted variables problem in asset pricing. If econometri-cians lack full information, then likely so do households.By hiring an active portfolio manager, they can hedge therisk of being wrong. This risk must exist widely and it mustbe at least in part systematic in order for active trading tobe profitable in the first place. This makes it expensive to

A. Savov / Journal of Financial Economics 112 (2014) 213–231 229

hedge; expensive enough to make active funds appear tounderperform passive index funds net of fees.

The data suggest that active fund investors rebalancetheir portfolios in a way that is systematically relatedto market returns, whereas index fund investors do not.Active fund investors are more likely to buy (sell) ahead oflow (high) market returns. Active fund managers help toundo this effect and, depending on the specification, thepremium for this service can account for the apparentunderperformance of active mutual funds.

In this paper, I study mutual fund performance fromthe household point of view. Consider the portfolio pro-blem of a household that just got richer, perhaps thanks toa pay raise, a booming business, or house price apprecia-tion: Is now a good time to buy stocks? What is the currentexpected return? And what if the future is not so brightafter all? For some investors, like those with no outsideincome, these questions never arise and they are better offbuying and holding low-cost index funds. For everyoneelse, there are active funds.

Appendix A. The Kalman filter

The state-space system can be summarized as

xtþ1 ¼ ρxtþεxtþ1 ð32Þ

Δytþ1 ¼ yþxtþεytþ1 ð33Þ

rtþ1 ¼ r�ϕxtþεrtþ1: ð34ÞHouseholds update their beliefs by running the populationregression

xtþ1�ρbxt ¼ LtΔytþ1�ðyþbxtÞrtþ1�ðr�ϕbxtÞ

" #þυtþ1: ð35Þ

The orthogonality condition gives

Lt ¼ Et ðxtþ1�ρbxtÞ Δytþ1�ðyþbxtÞrtþ1�ðr�ϕbxtÞ

" #′

" #ð36Þ

� EtΔytþ1�ðyþbxtÞrtþ1�ðr�ϕbxtÞ

" #Δytþ1�ðyþbxtÞrtþ1�ðr�ϕbxtÞ

" #′

" #�1

: ð37Þ

Let Σ2x;t ¼ Et ½ðxt�bxtÞ2� represent the variance of the error in

household beliefs about x. Evaluating,

Lt ¼ ρΣ2x;t ½1 �ϕ�

Σ2x;tþs2y �ϕΣ2

x;tþsry

�ϕΣ2x;tþsry ϕ2Σ2

x;tþs2r

24 35�1

: ð38Þ

The error variance evolves according to

Σ2x;tþ1 ¼ Etþ1½ðxtþ1�bxtþ1Þ2� ð39Þ

Σ2x;tþ1 ¼ Etþ1 ρðxt�bxtÞþεxtþ1�Lt

ðxt�bxtÞþεytþ1

�ϕðxt�bxtÞþεrtþ1

" # !224 35 ð40Þ

Σ2x;tþ1 ¼ ρ�Lt

1�ϕ

" # !2

Σ2x;tþLt

s2y sry

sry s2r

" #L′tþs2x ð41Þ

with initial condition Σ2x;0. The steady state is given by the

solution to

Σ2x ¼ ρ�L

1�ϕ

" # !2

Σ2x þL

s2y sry

sry s2r

" #L′þs2x ð42Þ

L¼ ρΣ2x ½1 �ϕ�

Σ2x þs2y �ϕΣ2

x þsry

�ϕΣ2x þsry ϕ2Σ2

x þs2r

" #�1

: ð43Þ

Appendix B. Multiple stocks

I consider an extension of the model with multiplerisky assets to allow for stock picking in addition to markettiming. There are N stocks with returns stacked insidert ¼ ½r1t r2t ⋯ rNt �′ given by

rtþ1 ¼ r�ϕxtþεrtþ1 ð44Þ

xtþ1 ¼ ρxtþεxtþ1; ð45Þwhere r is an N�1 vector, and ϕ and ρ are scalars. Letεr �Nð0;srs′rÞ and εx �Nð0; sxs′xÞ with εr ? εx as before.The risk-free rate is rf. Total log-output y is given by

Δytþ1 ¼ yþ1′xtþεytþ1; ð46Þwith εy �Nð0; s2yÞ. For simplicity, suppose εy ? εx. Aggre-gate growth is composed of growth in N sectors, onlypartly reflected in the N risky assets. Markets remainincomplete and returns are not fully revealing.

The linearity of the signals (returns and income) andthe state imply the optimality of the Kalman filter. Thehousehold information filtration has the formbx tþ1 ¼ ρbx tþbεxtþ1 ð47Þ

Δytþ1 ¼ yþ1′bx tþbεytþ1 ð48Þ

rtþ1 ¼ r�ϕbx tþbεrtþ1: ð49ÞLet the steady state error covariance matrix be Σ′

xΣx ¼limt-1 Et ½ðxt�bx tÞðxt�bx tÞ′�. The stochastic discount factorhas the form

Δmtþ1 ¼m0;tþm′r;tbεrtþ1þmy;t ½bεytþ1�ðbsybs′

rÞðbsrbs′rÞ�1bεrtþ1�:

ð50ÞThe vector mr contains the risk prices of the N tradedassets and my is the price of non-traded income risk. No-arbitrage requires

1¼ Et ½eΔmtþ 1 þ rf � and 1¼ Et ½eΔmtþ 1 þ rtþ 1 �: ð51ÞThe risk-free rate fixes the level of the stochastic discountfactor:

rf ¼ �m0;t�12 m′

r;t bsrbs′r

� mr;tþm2

y;tbs2y 1�bs ′

rðbsrbs′rÞ�1bsr

� h i:

ð52ÞThe expected returns of the N stocks pin down the pricesof the traded shocks:

r�ϕbx tþ12 diag bsrbs ′

r

� �rf ¼ � bsrbs ′

r

� mr;t : ð53Þ

As in the one-stock case, the price of non-traded risk my

remains a free parameter.

A. Savov / Journal of Financial Economics 112 (2014) 213–231230

Consider an active fund manager who knows thetrue state vector x and invests accordingly. For example,consider the portfolio weight vector χ t ¼ ½χ1t χ2t ⋯ χNt �′given by

χ t ¼1Ne�ηt ðΣ′

xΣxÞ � 1=2ðxt �bx t Þ�η2t =2: ð54Þ

Households expect their managers to be fully invested inthe equally weighted market portfolio. Managers usetheir private information to overweight undervaluedstocks. This strategy combines market timing and stockpicking. Stock picking tends to dominate when house-holds have an accurate estimate of the average expectedreturn but not of any one stock's expected return. Thissituation arises if the volatility of aggregate income is lowbut idiosyncratic (or sector) volatility is high. This result issimilar to Kacperczyk, Van Nieuwerburgh, and Veldkamp(2012) where managers rationally stock-pick in booms andmarket-time during downturns when aggregate volatilityis high.

Pricing the active mutual fund gives

ef t �1¼ ∑N

i ¼ 1eCovt ðlog χit ;Δmt þ 1Þ½eCovt ðlog χ it ;r

itþ 1Þ �1�: ð55Þ

A fund that trades in N assets is priced as a portfolio offunds that each trade in one asset. Evaluating,

ef t �1¼ 1N1′eηt ðΣ′

xΣxÞ1=2 ½ϕmr;t �ð1þϕðbsrbs ′r Þ � 1bsrbsyÞmy;t � 1′eηtϕ diagðΣ′

xΣxÞ1=2 �1h i

: ð56Þ

Looking across stocks, higher expected returns (low mir)

contribute to higher net returns as in the time series. Atthe same time, stocks with more uncertain expectedreturns (high ðΣ′

xΣxÞii) contribute to lower net returns.Overall, the multiple-stock extension of the model

incorporates stock picking in addition to market timing.When aggregate uncertainty is high, market timingbecomes more profitable but required net returns are highso fund compensation is relatively low. By contrast, stockpicking is most profitable when there is lots of dispersionin expected returns across stocks.

Appendix C. Supplementary material

Supplementary data associated with this article can befound in the online version at http://dx.doi.org/10.1016/j.jfineco.2013.11.005.

References

Admati, A.R., Pfleiderer, P., 1990. Direct and indirect sale of information.Econometrica 58, 901–928.

Admati, A.R., Ross, S.A., 1985. Measuring investment performance in arational expectations equilibrium model. J. Bus. 58, 1–26.

Ben-Rephael, A., Kandel, S., Wohl, A., 2012. Measuring investor sentimentwith mutual fund flows. J. Financ. Econ. 104, 363–382.

Berk, J.B., van Binsbergen, J.H., 2012. Measuring managerial skill in themutual fund industry. NBER Working Paper No. 18184.

Berk, J.B., Green, R.C., 2004. Mutual fund flows and performance inrational markets. J. Polit. Econ. 112, 1269–1295.

Blake, C.R., Elton, E.J., Gruber, M.J., 1993. The performance of bond mutualfunds. J. Bus. 66, 371–403.

Campbell, J., Viceira, L., 2002. Strategic Asset Allocation: Portfolio Choicefor Long-term Investors. Oxford University Press, USA.

Campbell, J.Y., 1999. Asset prices, consumption, and the business cycle. In:Taylor, J., Woodford, M. (Eds.), Handbook of Macroeconomics, vol. 1,North Holland, Amsterdam, pp. 1231–1303. (Chapter 19).

Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: a consumption-based explanation of aggregate stock market behavior. J. Polit. Econ.107, 205–251.

Campbell, J.Y., Shiller, R.J., 1988. The dividend–price ratio and expecta-tions of future dividends and discount factors. Rev. Financ. Stud. 1,195–228.

Carhart, M.M., 1997. On persistence in mutual fund performance.J. Finance 52, 57–82.

Chen, J., Hong, H., Huang, M., Kubik, J., 2004. Does fund size erode mutualfund performance? The role of liquidity and organization. Am. Econ.Rev. 94, 1276–1302.

Chevalier, J., Ellison, G., 1997. Risk taking by mutual funds as a responseto incentives. J. Polit. Econ. 105, 1167–1200.

Cremers, K.M., Petajisto, A., 2009. How active is your fund manager? Anew measure that predicts performance. Rev. Financ. Stud. 22,3329–3365.

Dybvig, P.H., Ross, S.A., 1985. Differential information and performancemeasurement using a security market line. J. Finance 40, 383–399.

Edelen, R., 1999. Investor flows and the assessed performance of open-end mutual funds. J. Financ. Econ. 53, 439–466.

Elton, E.J., Gruber, M.J., 2013. Mutual funds. In: Constantinides, G.M.,Harris, M., Stulz, R.M. (Eds.), Handbook of the Economics of Finance,vol. 2B. , North Holland, Amsterdam, pp. 1011–1061. (Chapter 15).

Fama, E.F., French, K.R., 2010. Luck versus skill in the cross-section ofmutual fund returns. J. Finance 65, 1915–1947.

Ferson, W.E., Schadt, R.W., 1996. Measuring fund strategy and perfor-mance in changing economic conditions. J. Finance 51, 425–461.

French, K.R., 2008. Presidential address: the cost of active investing.J. Finance 63, 1537–1573.

Gennaioli, N., Shleifer, A., Vishny, R., 2012. Money doctors. NBER WorkingPaper No. 18174.

Glode, V., 2011. Why mutual funds underperform. J. Financ. Econ. 99,546–559.

Glosten, L.R., Milgrom, P.R., 1985. Bid, ask and transaction prices in aspecialist market with heterogeneously informed traders. J. Financ.Econ. 14, 71–100.

Grinblatt, M., Titman, S., 1989. Portfolio performance evaluation: oldissues and new insights. Rev. Financ. Stud. 2, 393–421.

Grossman, S.J., Stiglitz, J.E., 1976. Information and competitive pricesystems. Am. Econ. Rev. 66, 246–253.

Grossman, S.J., Stiglitz, J.E., 1980. On the impossibility of informationallyefficient markets. Am. Econ. Rev. 70, 393–408.

Gruber, M.J., 1996. Another puzzle: the growth in actively managedmutual funds. J. Finance 51, 783–810.

He, Z., Krishnamurthy, A., 2013. Intermediary asset pricing. Am. Econ. Rev.103, 732–770.

Jensen, M.C., 1968. The performance of mutual funds in the period1945–1964. J. Finance 23, 389–416.

Jiang, G., Yao, T., Yu, T., 2007. Do mutual funds time the market? Evidencefrom portfolio holdings. J. Financ. Econ. 86, 724–758.

Kacperczyk, M., Seru, A., 2007. Fund manager use of public information:new evidence on managerial skills. J. Finance 62, 485–528.

Kacperczyk, M., Sialm, C., Zheng, L., 2005. On the industry concentrationof actively managed equity mutual funds. J. Finance 60, 1983–2011.

Kacperczyk, M., Van Nieuwerburgh, S., Veldkamp, L., 2012. Rationalattention allocation over the business cycle. NBER Working PaperNo. 15450.

Kacperczyk, M., Van Nieuwerburgh, S., Veldkamp, L. Time-varying fundmanager skill. J. Finance, http://dx.doi.org/10.1111/jofi.12084, acceptedfor publication.

Kaniel, R., Kondor, P., 2013. The delegated Lucas tree. Rev. Financ. Stud. 26,929–984.

Kosowski, R., 2011. Do mutual funds perform when it matters most toinvestors? U.S. mutual fund performance and risk in recessions andexpansions. Q. J. Finance 1, 607–664.

Merton, R.C., 1981. On market timing and investment performance. I. Anequilibrium theory of value for market forecasts. J. Bus. 54, 363–406.

Moskowitz, T.J., 2000. Mutual fund performance: an empirical decom-position into stock- picking talent, style, transactions costs, andexpenses: discussion. J. Finance 55, 1695–1703.

Pástor, L., Stambaugh, R.F., 2012. On the size of the active managementindustry. J. Polit. Econ. 120, 740–781.

Roll, R., 1977. A critique of the asset pricing theory's tests. Part I: on pastand potential testability of the theory. J. Financ. Econ. 4, 129–176.

Santos, T., Veronesi, P., 2006. Labor income and predictable stock returns.Rev. Financ. Stud. 19, 1–44.

A. Savov / Journal of Financial Economics 112 (2014) 213–231 231

Sharpe, W.F., 1991. The arithmetic of active management. Financ. AnalystsJ. 47, 7–9.

Sirri, E.R., Tufano, P., 1998. Costly search and mutual fund flows. J. Finance53, 1589–1622.

Vayanos, D., Woolley, P., 2013. An institutional theory of momentum andreversal. Rev. Financ. Stud. 26, 1087–1145.

Warther, V.A., 1995. Aggregate mutual fund flows and security returns.J. Financ. Econ. 39, 209–235.

Wermers, R., 2000. Mutual fund performance: an empirical decomposi-tion into stock-picking talent, style, transactions costs, and expenses.J. Finance 55, 1655–1695.

Zheng, L., 1999. Is money smart? A study of mutual fund investors' fundselection ability. J. Finance 54, 901–933.