Attention Allocation Over the Business Cycle
 Marcin Kacperczyk? Stijn Van Nieuwerburghy Laura Veldkampz
 First version: May 2009, This version: November 2009x
 Abstract
 The invisibility of information precludes a direct test of attention allocation theories.
 To surmount this obstacle, we develop a model that uses an observable variable { the
 state of the business cycle { to predict attention allocation. Attention allocation, in
 turn, predicts aggregate investment patterns. Because the theory begins and ends with
 observable variables, it becomes testable. We apply our theory to a large information-
 based industry, actively managed equity mutual funds, and study its investment choices
 and returns. Consistent with the theory, which predicts cyclical changes in attention
 allocation, we flnd that in recessions, funds? portfolios (1) covary more with aggregate
 payofi-relevant information, (2) exhibit more cross-sectional dispersion, and (3) gener-
 ate higher returns. The results suggest that some, but not all, fund managers process
 information in a value-maximizing way for their clients and that these skilled managers
 outperform others.
 ?Department of Finance Stern School of Business and NBER, New York University, 44 W. 4th Street,
 New York, NY 10012; mkacperc@stern.nyu.edu; http://www.stern.nyu.edu/?mkacperc.
 yDepartment of Finance Stern School of Business, NBER, and CEPR, New York University, 44 W. 4th
 Street, New York, NY 10012; svnieuwe@stern.nyu.edu; http://www.stern.nyu.edu/?svnieuwe.
 zDepartment of Economics Stern School of Business, NBER, and CEPR, New York University, 44 W.
 4th Street, New York, NY 10012; lveldkam@stern.nyu.edu; http://www.stern.nyu.edu/?lveldkam.
 xWe thank Joseph Chen, Xavier Gabaix, Ralph Koijen, Matthijs van Dijk, and seminar participants at
 Stanford, Berkeley, NYU Stern, University of Vienna, Australian National University, University of Mel-
 bourne, University of New South Wales, University of Sydney, University of Technology Sydney, Erasmus
 University, University of Mannheim, Duke University, the Amsterdam Asset Pricing Retreat, the Society for
 Economic Dynamics meetings in Istanbul, the CEPR Financial Markets conference in Gerzensee, and the
 UBC Summer Finance conference for useful comments and suggestions. Finally, we thank the Q-group for
 their generous flnancial support.
\What information consumes is rather obvious: It consumes the attention of its re-
 cipients. Hence a wealth of information creates a poverty of attention, and a need
 to allocate that attention e?ciently among the overabundance of information sources
 that might consume it." Simon (1971)
 Most decision makers are faced with an abundance of available information and must choose
 how to allocate their limited attention. Recent work has shown that introducing attention
 constraints into decision problems can help explain observed price-setting, consumption, and
 investment patterns.1 Unfortunately, the invisibility of information precludes direct testing
 of whether agents actually allocate their attention in a value-maximizing way. To surmount
 this obstacle, we develop a model of investment that uses an observable variable { the state
 of the business cycle { to predict attention allocation. Attention, in turn, predicts aggre-
 gate investment patterns. Because the theory begins and ends with observable variables, it
 becomes testable. To carry out these tests, we use data on actively managed equity mutual
 funds. A wealth of detailed data on portfolio holdings and returns makes this industry an
 ideal setting in which to test the rationality of attention allocation.
 A better understanding of attention allocation sheds new light on a central question in
 the flnancial intermediation literature: Do investment managers add value for their clients?
 What makes this an important question is that a large and growing fraction of individual
 investors delegate their portfolio management to professional investment managers.2 This
 intermediation occurs despite a signiflcant body of evidence that flnds that actively man-
 aged portfolios tend to underperform passive investment strategies, on average, net of fees,
 and after controlling for difierences in systematic risk exposure.3 This evidence of negative
 average \alpha" has led many to conclude that investment managers have no skill. By devel-
 1See, for example, Sims (2003) on consumption, Ma?ckowiak and Wiederholt (2009a, 2009b) on price-
 setting and Van Nieuwerburgh and Veldkamp (2009, 2010) on investment. Klenow and Willis (2007) and
 Gabaix, Laibson, Moloche, and Weinber (2006) test whether price-setting dynamics and experimental out-
 comes are consistent with inattention theories. A related investment literature on information choice includes
 Grossman and Stiglitz (1980), Verrecchia (1982), Admati (1985), Peress (2004, 2009), Amador and Weill
 (2008), and Veldkamp (2006). While in rational inattention models, agents typically choose the precision of
 their beliefs, Brunnermeier, Gollier, and Parker (2007) solve a portfolio problem in which investors choose
 the mean of their beliefs. In models of inattentiveness, e.g. Mankiw and Reis (2002) or Gabaix and Laibson
 (2002), agents update infrequently, but do not choose to to pay more attention to some risks than others.
 2In 1980, 48% of U.S. equity was directly held by individuals { as opposed to being held through inter-
 mediaries; by 2007 that fraction has been down to 21.5%. See French (2008), Table 1. At the end of 2008,
 $9.6 trillion was invested with such intermediaries in the U.S. Of all investment in domestic equity mutual
 funds, about 85% is actively managed (2009 Investment Company Factbook). A related theoretical literature
 studies delegated portfolio management; e.g., Basak, Pavlova, and Shapiro (2007), Cuoco and Kaniel (2007),
 Vayanos and Woolley (2008), and Chien, Cole, and Lustig (2009).
 3Among many others, see Jensen (1968), Malkiel (1995), Gruber (1996), Fama and French (2008).
 1
oping a theory of managers? information and investment choices and flnding evidence for its
 predictions in the mutual fund industry data, we conclude that the data are consistent with
 a world in which a small fraction of investment managers have skill.4 However, the model is
 also consistent with the empirical literature?s flnding that skill is hard to detect, on average.
 The model identifles recessions as times when information choices lead to investment choices
 that are more revealing of skill.
 We argue that recessions and expansions imply difierent optimal attention allocation
 strategies for skilled investment managers. Difierent learning strategies, in turn, prompt
 difierent investment strategies, causing the difierential performance in recessions and expan-
 sions. Speciflcally, we build a general equilibrium model in which a fraction of investment
 managers have skill, meaning that they can acquire and process informative signals about
 the future values of risky assets. These skilled managers can observe a flxed number of
 signals and choose what fraction of those signals will contain aggregate versus stock-speciflc
 information. We think of aggregate signals as macroeconomic data that afiect future cash
  ows of all flrms, and of stock-speciflc signals as flrm-level data that forecast the part of
 flrms? future cash  ows that is independent of the aggregate shocks. Based on their signals,
 skilled managers form portfolios, choosing larger portfolio weights for assets that are more
 likely to have high returns.
 The model?s predictions fall into three categories. The flrst one relates to attention
 allocation. As in most learning problems, risks that are large in scale and high in volatility
 are more valuable to learn about. In our model, aggregate shocks are large in scale, because
 many asset returns are afiected by them, but they have low volatility. Stock-speciflc shocks
 are smaller in scale but have higher volatility. As in the data, aggregate shocks are more
 volatile in recessions, relative to stock-speciflc shocks.5 The increased volatility of aggregate
 shocks makes it optimal to devote relatively more attention to aggregate shocks in recessions
 and stock-speciflc shocks in expansions.
 The second category of predictions pertains to portfolio dispersion and helps to distin-
 guish our theory from a non-informational one. In recessions, when aggregate shocks to asset
 4The flnding that some managers have skill is consistent with a number of recent papers in the empirical
 mutual fund literature, e.g., Cohen, Coval, and P?astor (2005), Kacperczyk, Sialm, and Zheng (2005, 2008),
 Kacperczyk and Seru (2007), Koijen (2008), Baker, Litov, Wachter, and Wurgler (2009), Huang, Sialm, and
 Zhang (2009).
 5We show below that the idiosyncratic risk in stock returns, averaged across stocks, does not vary signif-
 icantly over the business cycle. In contrast, the aggregate risk averaged across stocks is almost forty percent
 higher in recessions. Consistent with this fact, Ang and Chen (2002), Ribeiro and Veronesi (2002), and
 Forbes and Rigobon (2002) document that stocks exhibit more comovement in recessions.
 2
payofis are larger in magnitude, asset payofis exhibit more comovement. Thus, any portfolio
 strategies that put (exogenously) flxed weights on assets would have returns that also co-
 move more in recessions. In contrast, when investment managers learn about asset payofis
 and manage their portfolios according to what they learn, recessionary fund returns comove
 less. The reason is that when aggregate shocks become more volatile, and less predictable,
 managers who learn about aggregate shocks end up having more heterogeneous beliefs. They
 put less weight on their common prior beliefs, which have less predictive power, and more
 weight on their heterogeneous signals. More heterogeneous beliefs in recessions generates
 more heterogeneous investment strategies and fund returns as well.
 Third, the model predicts time variation in fund performance. The average fund can only
 outperform the market if there are other, non-fund investors who underperform. Therefore,
 the model also includes unskilled non-fund investors. Due to their lack of skill, they reside
 mostly in the left tail of the return distribution. When return dispersion rises, in recessions,
 left-tail investors underperform by more and the average fund?s outperformance rises.
 We test the model?s three main predictions on the universe of actively managed U.S.
 mutual funds. To detect evidence of cyclical changes in attention, we estimate the covariance
 of each fund?s portfolio holdings with the aggregate payofi shock, proxied by innovations in
 industrial production growth. We call this covariance reliance on aggregate information
 (RAI). RAI indicates a manager?s ability to time the market by increasing (decreasing) her
 portfolio positions in anticipation of good (bad) macroeconomic news. We flnd that the
 average RAI across funds is higher in recessions. We also calculate the covariance of a fund?s
 portfolio holdings with asset-speciflc shocks, proxied by innovations in earnings. We call this
 variable reliance on stock-speciflc information (RSI). RSI measures managers? ability to pick
 stocks that subsequently experience unexpectedly high earnings. We flnd that RSI is higher
 in expansions.
 Second, we test for cyclical changes in portfolio dispersion. In recessions, we flnd a higher
 portfolio concentration, measured as the sum of squared deviations of portfolio weights from
 those of the market portfolio. When funds hold portfolios that difier more from the market,
 which is the average portfolio, they are also holding portfolios that difier more from one
 another. Also consistent with the concentration hypothesis, we flnd higher idiosyncratic risk
 in fund returns in recessions. The increased dispersion additionally appears in fund returns,
 alphas, and betas. All these are predictions of our theory. Figure 1 shows a 30% increase of
 the cross-sectional standard deviation of fund alphas in recessions for our mutual fund data.
 3
Third, we document fund outperformance in recessions.6 Risk-adjusted excess fund re-
 turns (alphas) are around 1.8 to 2.4% per year higher in recessions, depending on the specifl-
 cation. Gross alphas (before fees) are not statistically difierent from zero in expansions, but
 they are positive in recessions. Net alphas (after fees) are negative in expansions and pos-
 itive in recessions. These cyclical difierences are statistically and economically signiflcant.
 Indeed, Figure 2 shows that, over the period 1980-2005, actively managed mutual funds
 have earned 2.1% risk-adjusted excess returns (alphas) per year in recessions but only 0.3%
 in expansions. What remains for investors (net of fees) is 1.0% in recessions and -0.9% in
 expansions; the difierence of 1.9% per year is both economically and statistically signiflcant.
 Because our theory tells us how skilled managers should invest, it suggests how to con-
 struct metrics that could help us identify skilled managers. To show that skilled managers
 exist, we select the top 25 percent of funds in terms of their stock-picking ability in ex-
 pansions and show that the same group has signiflcant market-timing ability in recessions;
 the other funds show no such market-timing ability.7 Furthermore, these funds have higher
 unconditional returns. They tend to manage smaller, more active funds. By matching fund-
 level to manager-level data, we flnd that these skilled managers are more likely to attract new
 money  ows and are more likely to depart later in their careers to hedge funds. Presumably,
 both are market-based re ections of their ability. Finally, we construct a skill index based
 on observables and show that it is persistent and that it predicts future performance.
 The rest of the paper is organized as follows. Section 1 lays out our model. After
 describing the setup, we characterize the optimal information and investment choices of
 skilled and unskilled investors. We show how equilibrium asset prices are formed. We derive
 theoretical predictions for funds? attention allocation, portfolio dispersion, and performance.
 Section 2 contains the empirical analysis for actively managed mutual funds and tests the
 model?s predictions. Section 3 uses the model?s insights to identify a group of skilled mutual
 funds in the data. Section 4 brie y discusses alternative explanations. While there might be
 other potential alternative explanations for each of the three main predictions of the model,
 none of the alternatives can account for all three predictions jointly.
 6Kosowski (2006), Lynch and Wachter (2007), and Glode (2008) also document such evidence, but their
 focus is solely on performance.
 7This is quite difierent from the typical approach in the literature, which has studied stock picking and
 market timing in isolation, and unconditional on the state of the economy. The consensus view from that
 literature is that there is some evidence for stock-picking ability (on average over time and across managers),
 but no evidence for market timing (e.g., Graham and Harvey (1996), Daniel, Grinblatt, Titman, and Wermers
 (1997), Wermers (2000), Kacperczyk and Seru (2007), and Breon-Drish and Sagi (2008)).
 4
1 Model
 We develop a stylized model whose purpose is to understand the optimal attention allocation
 of investment managers, its implications for asset holdings and for equilibrium asset prices.
 1.1 Setup
 We consider a three-period static model. At time 1, skilled investment managers choose how
 to allocate their attention across aggregate and idiosyncratic shocks. At time 2, all investors
 choose their portfolios of risky and riskless assets. At time 3, asset payofis and utility are
 realized. Since this is a static model, the investment world is either in the recession (R) or
 in the expansion state (E).8 Our main model holds each manager?s total attention flxed and
 studies its allocation in recessions and expansions. In Section 1.7, we allow a manager to
 choose how much capacity for attention to acquire.
 Assets The model features three assets. Assets 1 and 2 have random payofis f with
 respective loadings b1; b2 on an aggregate shock a, and face an idiosyncratic shock s1; s2.
 The third asset, c, is a composite asset. Its payofi has no idiosyncratic shock and a loading
 of one on the aggregate shock. We use this composite asset as a stand-in for all other assets
 to avoid the curse of dimensionality in the optimal attention allocation problem. Formally,
 fi = ?i + bia+ si; i 2 f1; 2g
 fc = ?c + a
 where the shocks a ? N(0;  a) and si ? N(0;  i), for i 2 f1; 2g. At time 1, the distribution of
 payofis is common knowledge; all investors have common priors about payofis f ? N(?; ?).
 Let E1, V1 denote expectations and variances conditioned on this information. Speciflcally,
 E1[fi] = ?i. The prior covariance matrix of the payofis, ?, has the following entries: ?ii =
 8We do not consider transitions between recessions and expansions, although such an extension would be
 trivial in our setting because assets are short lived and their payofis are realized and known to all investors
 at the end of each period. Thus, a dynamic model simply amounts to a succession of static models that are
 either in the expansion or in the recession state.
 5
b2i a +  i and ?ij = bibj a. In matrix notation:
 ? = bb0 a +
 2
 64
  1 0 0
 0  2 0
 0 0 0
 3
 75
 where the vector b is deflned as b = [b1 b2 1]0. In addition to the three risky assets, there
 exists a risk-free asset that pays a gross return, r.
 We model recessions as periods with higher aggregate risk, that is, the prior variance of the
 aggregate shock in recessions is higher than the one in expansions:  a(R) >  a(E). Section
 2.2 justifles this assumption by showing that aggregate risk of stocks increases substantially
 in recessions while idiosyncratic risk does not.
 Investors We consider a continuum of atomless investors. In the model, the only ex-ante
 difierence between investors is that a fraction ? of them have skill, meaning that they can
 choose to observe a set of informative signals about the payofi shocks a or si. We describe
 this signal choice problem below. The remaining unskilled investors observe no information
 other than their prior beliefs.
 Some of the unskilled investors are investment managers. As in reality, there are also
 non-fund investors, all of whom we assume are unskilled.9 The reason for modeling non-
 fund investors is that without them, the sum of all funds? holdings would have to equal the
 market (market clearing) and therefore, the average fund return would have to equal the
 market return. There could be no excess return in expansions or recessions.
 Bayesian Updating At time 2, each skilled investment manager observes signal realiza-
 tions. Signals are random draws from a distribution that is centered around the true payofi
 shock, with a variance equal to the inverse of the signal precision that was chosen at time
 1. Thus, skilled manager j?s signals are ?aj = a + eaj, ?1j = s1 + e1j, and ?2j = s2 + e2j,
 where eaj ? N(0; ?aj), e1j ? N(0; ?1j), and e2j ? N(0; ?2j) are independent of each other
 and across fund managers. Managers combine signal realizations with priors to update their
 beliefs, using Bayes? law. Asset prices are not a separate source of information. Of course,
 managers can observe asset prices and infer asset-payofi relevant information from them. But
 making that inference requires allocating attention to prices, in order to process in the infor-
 9For our results, it is su?cient that the fraction of them that are unskilled is higher than for the investment
 managers (funds).
 6
mation they contain. In other words, learning from prices requires using capacity. Whatever
 information managers choose to infer from prices is already included in the signals.
 Since the resulting posterior beliefs (conditional on time-2 information) are such that
 payofis are normally distributed, they can be fully described by posterior means, (a^j; s^ij),
 and variances, ( ^aj;  ^ij). More precisely, posterior precisions are the sum of prior and signal
 precisions:  ^?1aj =  ?1a + ??1aj and  ^?1ij =  ?1i + ??1ij . The posterior means of the idiosyncratic
 shocks, s^ij, are a precision-weighted linear combination of the prior belief that si = 0 and
 the signal ?i: s^ij = ??11j ?1j=(??1ij +  ?1i ). Simplifying yields s^ij = (1 ?  ^ij ?1i )?ij and a^j =
 (1? ^aj ?1a )?aj. Next, we convert posterior beliefs about the underlying shocks into posterior
 beliefs about the asset payofis. Let ?^j be the posterior variance-covariance matrix of payofis
 f :
 ?^j = bb0 ^aj +
 2
 64
  ^1j 0 0
 0  ^2j 0
 0 0 0
 3
 75
 Likewise, let ?^j be the vector of posterior expected payofis:
 ?^j = [?1 + b1a^j + s^1j; ?2 + b2a^j + s^2j; ?c + a^j]0 (1)
 For any unskilled manager or investor: ?^j = ? and ?^j = ?.
 Portfolio Choice Problem We solve this model by backward induction. We flrst solve
 for the optimal portfolio at time 2 and substitute in that solution into the time-1 optimal
 attention allocation problem.
 Investors are each endowed with initial wealth, W0. They have mean-variance preferences
 over time-3 wealth, with a risk aversion coe?cient ?. Let E2 and V2 denote expectations
 and variances conditioned on all information known at time 2. Thus, investor j chooses qj
 to maximize time-2 expected utility, U2j:
 U2j = ?E2[Wj]? ?
 2
 2 V2[Wj] (2)
 subject to the budget constraint:
 Wj = rW0 + q0j(f ? pr) (3)
 After having received the signals and having observed the prices of the risky assets, p, the
 7
investment manager chooses risky asset holdings, qj, where p and qj are 3-by-1 vectors.
 Asset Prices Equilibrium asset prices are determined by market clearing:
 Z
 qjdj = ?x+ x; (4)
 where the left-hand side of the equation is the vector of aggregate demand and the right-
 hand side is the vector of aggregate supply. As in the standard noisy rational expectations
 equilibrium model, the asset supply is random to prevent the price from fully revealing the
 information of informed investors. We denote the 3? 1 noisy asset supply vector by ?x + x,
 with a random component x ? N(0;  xI).
 Attention Allocation Problem At time 1, a skilled investment manager j chooses the
 precisions of signals about the payofi-relevant shocks a, s1, or s2 that she will receive at
 time 2. We denote these signal precisions by ??1aj , ??11j , and ??12j , respectively. These choices
 maximize time-1 expected utility, U1j, over the fund?s terminal wealth:
 U1j = E1
 ?
 ?E2[Wj]? ?
 2
 2 V2[Wj]
 ?
 ; (5)
 subject to two constraints.
 The flrst constraint is the information capacity constraint. It states that the sum of the
 signal precisions must not exceed the information capacity:
 ??11j + ??12j + ??1aj ? K: (6)
 Unskilled investors have no information capacity K = 0. In Bayesian updating with normal
 variables, observing one signal with precision ??1 or two signals, each with precision ??1=2,
 is equivalent. Therefore, one interpretation of the capacity constraint is that it allows the
 manager to observe N signal draws, each with precision K=N , for large N . The investment
 manager then chooses how many of those N signals will be about each shock.
 The second constraint is the no-forgetting constraint, which ensures that the chosen
 precisions are non-negative:
 ??11j ? 0 ??12j ? 0 ??1aj ? 0: (7)
 8
It prevents the manager from erasing any prior information, to make room to gather new
 information about another shock.
 1.2 Model Solution
 Substituting the budget constraint (3) into the objective function (2) and taking the flrst-
 order condition with respect to qj reveals that optimal holdings are increasing in the investor?s
 risk tolerance, precision of beliefs, and expected return on the assets:
 qj = 1??^
 ?1
 j (?^j ? pr): (8)
 Since uninformed managers and other investors have identical beliefs, ?^j = ? and ?^j = ?,
 they hold identical portfolios ??1??1(?? pr).
 Appendix S.1 utilizes the market-clearing condition (4) to prove that equilibrium asset
 prices are linear in payofis and supply shocks, and to derive expressions for the coe?cients
 A, B, and C in the following proposition:10
 Proposition 1. p = 1r (A+Bf + Cx)
 Substituting optimal risky asset holdings from equation (8) into the flrst-period objective
 (5) yields: U1j = 12E1
 h
 (?^j ? pr)?^?1j (?^j ? pr)
 i
 . Because asset prices are linear functions of
 normally distributed payofis and asset supplies, expected excess returns, ?^j?pr, are normally
 distributed as well. Therefore, (?^j?pr)?^?1j (?^j?pr) is a non-central ?2-distributed variable,
 with mean11
 U1j = 12trace(?^
 ?1
 j V1[?^j ? pr]) +
 1
 2E1[?^j ? pr]
 0?^?1j E1[?^j ? pr]: (9)
 1.3 Bridging The Gap Between Model and Data
 The following three sections explain the model?s three key predictions: attention allocation,
 dispersion in investors? portfolios, and average performance. For each prediction, we state a
 hypothesis and explain how to test it. But the payofis and quantities that have analytical
 10References denoted S are in the paper?s separate appendix, available from the authors? websites or at
 http://pages.stern.nyu.edu/~lveldkam/pdfs/mfund_KVNV_appdx.pdf
 11If z ? N(E[z]; V ar[z]), then E[z0z] = trace(V ar[z]) + E[z]0E[z], where trace is the matrix trace (the
 sum of its diagonal elements). Setting z = ?^?1=2j (?^j ? pr) delivers the result. Appendix S.1.2 contains the
 expressions for E1[?^j ? pr] and V1[?^j ? pr].
 9
expressions in a CARA-normal model do not correspond neatly to the returns and portfolio
 weights that are commonly measured in the data. To bridge this gap, we introduce empirical
 measures of attention, dispersion, and performance. These standard deflnitions of returns
 and portfolio weights have no known moment-generating functions in our model. For exam-
 ple, the asset return is a ratio of normally distributed variables. Therefore, Appendix S.2
 uses a numerical example to demonstrate that the empirical and theoretical measures have
 the same comparative statics.
 Speciflcally, our empirical measures use conventional deflnitions of asset returns, portfolio
 returns, and portfolio weights. Risky asset returns are deflned as Ri ? fipi ?1, for i 2 f1; 2; cg,
 while the risk-free asset return is R0 ? 1+r1 ?1 = r. We deflne the market return as the value-
 weighted average of the individual asset returns: Rm ? P3i=1 wmi Ri, where wmi ? piq
 j
 iP3
 i=1 piqji
 .
 Likewise, a fund j?s return is Rj ?P3i=0 wjiRi, where wji ? piq
 j
 iP3
 i=0 piqji
 . It follows that end-of-
 period wealth (assets under management) equals beginning-of-period wealth times the fund
 return: W j = W j0 (1 +Rj).
 1.4 Hypothesis 1: Attention Allocation
 Each skilled manager (K > 0) solves for the choice of signal precisions ??1aj ? 0 and ??11j ? 0
 that maximize her time-1 expected utility (9). The choice of signal precision ??12j ? 0 is
 implied by the capacity constraint (6). A robust prediction of our model is that it becomes
 relatively more valuable to learn about the aggregate shock, a, when the prior aggregate
 variance increases, that is, in recessions.
 Proposition 2. If the aggregate shock variance is not too high ( a ? 1), then the marginal
 value of additional capacity K devoted to learning about the aggregate shock is increasing in
 the aggregate shock variance: @2U=@K@ a > 0.
 The proofs of this and all further Propositions are in Appendix S.1. Intuitively, in most
 learning problems, investors prefer to learn about large shocks that are an important com-
 ponent of the overall asset supply, and volatile shocks that have high prior payofi variance.
 Aggregate shocks are larger in scale, but are less volatile than stock-speciflc shocks. Re-
 cessions are times when aggregate volatility increases, which makes aggregate shocks more
 valuable to learn about. As a result, in recessions, skilled investment managers allocate
 a relatively larger fraction of their attention to learning about the aggregate shock. The
 converse is true in expansions. The parameter restriction  a < 1, is a su?cient, but not nec-
 10
essary condition. Of the seven terms in expected utility, six can be signed without parameter
 restrictions and one requires this restriction to be positive.
 Appendix S.2 presents a detailed numerical example in which parameters are chosen to
 match the observed volatilities of the aggregate and individual stock returns in expansions
 and recessions. For our benchmark parameter values, all skilled managers exclusively allocate
 attention to idiosyncratic shocks in expansions. In contrast, the bulk of skilled managers
 learn about the aggregate shock in recessions (87%, with the remaining 13% equally split
 between shocks 1 and 2). Thus, managers may want to reallocate their attention over the
 business cycle.
 We have verifled that similarly large swings in attention allocation occur for a wide range
 of parameters. The result breaks down when assets become very asymmetric so that one
 learning decision is dominant in recessions and expansions. For example, if the average
 supply of the composite asset, ?xc, is too large relative to the supply of the individual asset
 supplies, ?x1 and ?x2, the aggregate shock will be so valuable to learn about that all skilled
 managers will want to learn about it all the time. Similarly, if the aggregate volatility,  a,
 is too low, then nobody ever wants to learn about the aggregate shock.
 Investors? optimal attention allocation decisions are re ected in their portfolio holdings.
 In recessions, skilled investors predominantly allocate attention to the aggregate payofi shock,
 a. They use the information they observe to form a portfolio that covaries with a. In times
 when they learn that a will be high, they hold more risky assets whose returns are increasing
 in a. This positive covariance can be seen from equation (8) in which q is increasing in ?^j
 and from equation (1) in which ?^j is increasing in a^j, which is further increasing in a. The
 positive covariances between the aggregate shock and funds? portfolio holdings in recessions,
 on the one hand, and between idiosyncratic shocks and the portfolio holdings in expansions,
 on the other hand, directly follow from optimal attention allocation decisions switching over
 the business cycle. As such, these covariances are the key moments that enable us to test
 the attention allocation predictions of the model.
 We deflne a fund?s reliance on aggregate information, RAI, as the covariance between its
 portfolio weights in deviation from the market portfolio weights, wji ?wmi , and the aggregate
 payofi shock, a:
 RAIjt =
 1
 N
 NX
 i=1
 (wjit ? wmit )(at+1); (10)
 where N is the number of individual assets. The subscript t on the portfolio weights and the
 subscript t + 1 on the aggregate shock signify that the aggregate shock is unknown at the
 11
time of portfolio formation. In our static model, time t is period 2 and time t + 1 is period
 3. Relative to the market, a fund with a high RAI overweighs assets that have high (low)
 sensitivity to the aggregate shock in anticipation of a positive (negative) aggregate shock
 realization and underweighs assets with a low (high) sensitivity.
 RAI is closely related to measures of market-timing ability. Timing measures how a
 fund?s holdings of each asset, relative the market, covary with the systematic component of
 the stock return:
 Timingjt =
 1
 N
 NX
 i=1
 (wjit ? wmit )(flit+1Rmt+1); (11)
 where fli measures the covariance of asset i?s return, Ri, with the market return, Rm, divided
 by the variance of the market return. The object fliRm measures the systematic component
 of returns of asset i. The time subscripts indicate that the systematic component of the
 return is unknown at the time of portfolio formation. Before the market return rises, a fund
 with a high Timing ability overweighs assets that have high beta. Likewise, it underweighs
 assets with a high beta in anticipation of a market decline.
 To conflrm that RAI and Timing accurately represent the model?s prediction that skilled
 investors allocate more attention to the aggregate state in recessions, we resort to a numer-
 ical simulation. Appendix S.2 details the procedure and the construction of the empirical
 measures. For brevity, we only discuss the comparative statics in the main text. The simu-
 lation results show that RAI and Timing are higher for skilled investors in recessions than
 they are in expansions. Because of market clearing, not all investors can time the market.
 Unskilled investors have negative timing ability in recessions. When the aggregate state a is
 low, most skilled investors sell, pushing down asset prices, p, and making prior expected re-
 turns, (?? pr), high. Equation (8) shows that uninformed investors? asset holdings increase
 in (? ? pr). Thus, their holdings covary negatively with aggregate payofis, making their
 RAI and Timing measures negative. Since no investors learn about the aggregate shock in
 expansions, RAI and Timing are close to zero for both skilled and unskilled. When averaged
 over all funds (including both skilled and unskilled funds but excluding non-fund investors),
 we flnd that RAI and Timing are higher in recessions than in expansions.
 When skilled investment managers allocate attention to stock-speciflc payofi shocks, si,
 information about si allows them to choose portfolios that covary with si. We deflne re-
 liance on stock-speciflc information, RSI, which measures the covariance of a fund?s portfolio
 12
weights of each stock, relative to the market, with the stock-speciflc shock, si:
 RSIjt =
 1
 N
 NX
 i=1
 (wjit ? wmit )(sit+1) (12)
 How well the manager can choose portfolio weights in anticipation of future asset-speciflc
 payofi shocks is closely linked to her stock-picking ability. Pickingjt measures how a fund?s
 holdings of each stock, relative to the market, covary with the idiosyncratic component of
 the stock return:
 Pickingjt =
 1
 N
 NX
 i=1
 (wjit ? wmit )(Rit+1 ? fliRmt+1) (13)
 A fund with a high Picking ability overweighs assets that have subsequently high idiosyn-
 cratic returns and underweighs assets with low subsequent idiosyncratic returns. In our
 simulation, we flnd that skilled funds have positive RSI and Picking ability in expansions,
 when they allocate their attention to stock-speciflc information. Unskilled investors have
 negative Picking in expansions for the same reason that they have negative Timing in re-
 cessions: Price  uctuations induce them to buy when returns are low and sell when returns
 are high. Across all funds, the model predicts lower RSI and Picking in recessions.
 1.5 Hypothesis 2: Dispersion
 A second, more fundamental question is whether investment managers are processing infor-
 mation at all. One prediction that speaks directly to that question is portfolio dispersion.
 In recessions, as aggregate shocks become more volatile, the idiosyncratic shocks to assets?
 payofis account for less of the variation, and the comovement in stock payofis rises. Since
 asset payofis comove more, the payofis to all investment strategies that put flxed weights on
 assets should also comove more.
 When investment managers are processing information, this prediction is reversed. To
 see why, consider the Bayesian updating formula for the posterior mean of asset payofis. It
 is a weighted average of the prior mean ? and the signals ?jf ? N(f;??), where each is
 weighted by their relative precision:
 E[f j?] = ???1 + ??1?
 ??1 ???1?+ ??1? ?
 ? (14)
 In recessions, when the variance of the aggregate shock  a rises, the prior beliefs about asset
 payofis are more uncertain, ? rises, and ??1 falls. This makes the weight on prior beliefs
 13
? decrease and the weight on the signal ? increase. The prior ? is common across agents,
 while the signal ? is heterogeneous. When agents weight their heterogeneous signals more,
 their resulting posterior beliefs become more heterogeneous. More disagreement about what
 asset payofis will be results in more heterogeneous portfolios and portfolio returns.
 Thus, the model?s second prediction is that in recessions, the cross-sectional dispersion in
 funds? investment strategies and returns rises. The following Proposition shows that funds?
 portfolio returns, q0j(f ? pr), display higher cross-sectional dispersion when aggregate risk is
 higher, in recessions.
 Proposition 3. If the average manager has su?ciently low capacity, ?K <  ?1a , then an
 increase in aggregate risk,  a, increases the dispersion of funds? portfolios E[(qj? ?q)0(qj? ?q)0],
 and their portfolio returns E[((qj ? ?q)0(f ? pr))2], where ?q ?
 R qjdj.
 As before, the parameter restriction is su?cient, but not necessary.
 To connect our model to the data, we use several measures of portfolio dispersion, com-
 monly used in the empirical literature. The flrst one is the sum of squared deviations of fund
 j?s portfolio weight in asset i at time t from the average fund?s portfolio weight in asset i at
 time t, summed over all assets:
 Concentrationjt =
 NX
 i=1
 ?wjit ? wmit
 ?2 (15)
 We label this measure Concentration because, as any Herflndahl index, it is a measure
 of portfolio concentration. Cross-sectional dispersion and concentration are two sides of
 the same coin. Because markets must clear, funds cannot all hold concentrated portfolios
 without dispersion across their portfolios. Our numerical example shows that Concentration
 is higher for all funds in recessions than it is in expansions. This increase is driven entirely
 by the informed; the uninformed are all holding the exact same portfolio because of common
 prior beliefs.
 Because more concentrated portfolios are less diversifled, the model predicts that a skilled
 fund?s returns contain higher idiosyncratic risk in recessions.12 We deflne idiosyncratic port-
 12The terminology idiosyncratic risk is slightly misleading in our context. In fact, the portfolio is not
 riskier as skilled managers obtain information which reduces risk. They optimally trade ofi the beneflts
 from information against the costs of a reduction in diversiflcation. The standard CAPM equation does not
 capture this tradeofi because it does not condition on what the manager knows.
 14
folio risk as the residual standard deviation,  j", from a CAPM regression for fund j:
 Rjt = fij + fljRmt +  j""jt (16)
 In the simulation, skilled funds take on more idiosyncratic risk than the unskilled ones, and
 more so in recessions than in expansions. As a result, idiosyncratic risk, our second measure
 of portfolio dispersion, is higher in recessions than it is in expansions for all funds.
 The higher dispersion across funds? portfolio strategies translates into a higher cross-
 sectional dispersion in fund returns. We look at dispersion in the funds? abnormal returns,
 Rj ? Rm, CAPM alphas, fij from equation (16), and CAPM betas, flj. To facilitate com-
 parison with the data, we deflne the dispersion of variable X as the average over funds of
 jXj ? ?Xj. The notation ?X denotes the equally weighted cross-sectional average across all
 investment managers (excluding the other investors). Our numerical results show a higher
 dispersion of fund abnormal returns, alphas, and betas.
 1.6 Hypothesis 3: Performance
 The third prediction of the model is that the average performance of investment managers
 is higher in recessions than it is in expansions. The following Proposition shows that skilled
 funds? abnormal portfolio returns, deflned as their portfolio return, q0j(f ? pr), minus the
 market return, ?q0(f ? pr), are higher when aggregate risk is higher, that is, in recessions.
 Proposition 4. If some managers are uninformed, ? < 1, but all informed managers learn
 about aggregate risk, and the average manager has su?ciently low capacity, ?K <  ?1a ,
 then an increase in aggregate risk,  a, increases the expected proflt of an informed fund,
 E[(qj ? ?q)0(f ? pr)], where ?q ?
 R qjdj.
 Because asset payofis are more uncertain, recessions are times when information is more
 valuable. Therefore, the advantage of the skilled over the unskilled increases in recessions.
 This informational advantage generates higher (risk-adjusted) excess returns for informed
 managers. In equilibrium, market clearing dictates that alphas average to zero across all
 investors. However, because our data only include mutual funds, our model calculations
 similarly exclude non-fund investors. Since investment managers are skilled or unskilled,
 while other investors are only unskilled, an increase in the skill premium implies that the
 average manager?s alpha rises in recessions. The same argument holds for the abnormal
 return.
 15
Our numerical simulations conflrm that abnormal returns and alphas, deflned as in the
 empirical literature, and averaged over all funds, are higher in recessions than in expansions.
 Skilled investment managers have positive excess returns, while the uninformed ones have
 negative excess returns. Aggregating across skilled and unskilled funds results in higher
 average alphas in recessions, the third main prediction of the model.
 1.7 Endogenous Capacity Choice
 So far, we have assumed that skilled investment managers choose how to allocate a flxed
 information-processing capacity, K. We now extend the model to allow for skilled managers
 to add capacity at a cost C (K).13 We draw three main conclusions. First, the proofs of
 Propositions 2-4 hold for any chosen level of capacity K, below an upper bound, no mat-
 ter the functional form of C. Endogenous capacity only has quantitative, not qualitative
 implications. Second, because the marginal utility of learning about the aggregate shock is
 increasing in its prior variance (Proposition 2), skilled managers choose to acquire higher ca-
 pacity in recessions. This extensive-margin efiect amplifles our benchmark intensive-margin
 results. Third, the degree of ampliflcation depends on the convexity of the cost function,
 C (K). The convexity determines how elastic equilibrium capacity choice is to the cyclical
 changes in the marginal beneflt of learning. Appendix S.2.4 discusses numerical simulation
 results from the endogenous-K model; they are similar to our benchmark results.
 2 Evidence from Equity Mutual Funds
 Our model studies attention allocation over the business cycle, and its consequences for
 investors? strategies. We now turn to a speciflc set of investment managers, mutual fund
 managers, to test the predictions of the model. The richness of the data makes the mutual
 fund industry a great laboratory for this test. In principle, similar tests could be conducted
 for hedge funds, other professional investment managers, or even individual investors.
 2.1 Data
 Our sample builds upon several data sets. We begin with the Center for Research on Security
 Prices (CRSP) survivorship bias-free mutual fund database. The CRSP database provides
 13We model this cost as a utility penalty, akin to the disutility from labor in business cycle models. Since
 there are no wealth efiects in our setting, it would be equivalent to modeling a cost of capacity through the
 budget constraint. For a richer treatment of information production modeling, see Veldkamp (2006).
 16
comprehensive information about fund returns and a host of other fund characteristics, such
 as size (total net assets), age, expense ratio, turnover, and load. Given the nature of our
 tests and data availability, we focus on actively managed open-end U.S. equity mutual funds.
 We further merge the CRSP data with fund holdings data from Thomson Financial. The
 total number of funds in our merged sample is 3,477.
 In addition, for some of our exercises, we map funds to the names of their managers using
 information from CRSP, Morningstar, Nelson? Directory of Investment Managers, Zoominfo,
 and Zabasearch. This mapping results in a sample with 4,267 managers. We also use the
 CRSP/Compustat stock-level database, which is a source of information on individual stocks?
 return, market capitalization, book-to-market ratio, momentum, liquidity, and standardized
 unexpected earnings (SUE). We use changes in monthly industrial production as a proxy for
 aggregate shocks. Industrial production is seasonally adjusted; the data are from the Federal
 Reserve Statistical Release.
 Finally, we measure recessions using the deflnition of the National Bureau of Economic
 Research (NBER) business cycle dating committee. The start of the recession is the peak of
 economic activity and its end is the trough. Our aggregate sample spans 312 months of data
 from January 1980 until December 2005, among which 38 are NBER recession months (12%).
 In robustness analysis, we consider several alternative recession indicators (see Section 2.6).
 2.2 Recessions Are Periods of Higher Aggregate Risk
 Before testing our main hypotheses, we present empirical evidence for the main assumption
 in our model: Recessions are periods in which individual stocks contain more aggregate risk.
 Table 1 shows that an average stock?s aggregate risk increases substantially in recessions
 whereas the change in idiosyncratic risk is not statistically difierent from zero. The table
 uses monthly returns for all stocks in the CRSP universe. For each stock and each month, we
 estimate a CAPM equation based on a twelve-month rolling-window regression, delivering
 the stock?s beta, flit , and its residual standard deviation,  i"t. We deflne the aggregate risk of
 stock i in month t as jflit mt j and its idiosyncratic risk as  i"t, where  mt is formed monthly as
 the realized volatility from daily return observations. Panel A reports the results from a time-
 series regression of the aggregate risk averaged across stocks (Columns 1 and 2) and of the
 idiosyncratic risk averaged across stocks (Columns 3 and 4) on the NBER recession indicator
 variable.14 The aggregate risk is one-third higher in recessions than it is in expansions (0.69
 14The reported results are for equally weighted averages. Unreported results conflrm that value-weighted
 averaging across stocks delivers the same conclusion.
 17
versus 0.48), an economically and statistically signiflcant difierence. In contrast, the stock?s
 idiosyncratic risk is essentially identical in expansions and in recessions. The results are
 similar whether one controls for other aggregate risk factors (Columns 2 and 4) or not
 (Columns 1 and 3). Panel B reports estimates from panel regressions of a stock?s aggregate
 risk (Columns 1 and 2) or idiosyncratic risk (Columns 3 and 4) on the recession indicator
 variable, Recession, and additional stock-speciflc control variables including size, book-to-
 market ratio, and leverage. The panel results conflrm the time-series flndings.
 2.3 Testing Hypothesis 1: Attention Allocation
 We begin by testing the flrst and most direct prediction of our model, that skilled investment
 managers reallocate their attention over the business cycle. Learning about the aggregate
 payofi shock in recessions makes managers choose portfolio holdings that covary more with
 the aggregate shock. Conversely, in expansions their holdings covary more with stock-speciflc
 information. To this end, we estimate the following regression model:
 Attentionjt = a0 + a1Recessiont + a2Xjt + ?jt ; (17)
 where Attentionjt denotes a generic attention variable, observed at month t for fund j.
 Recessiont is an indicator variable equal to one if the economy in month t is in recession, as
 deflned by the NBER, and zero otherwise. X is a vector of fund-speciflc control variables,
 including the fund age (natural logarithm of age in years since inception, log(Age)), the
 fund size (natural logarithm of total net assets under management in millions of dollars,
 log(TNA)), the average fund expense ratio (in percent per year, Expenses), the turnover
 rate (in percent per year, Turnover), the percentage  ow of new funds (deflned as the ratio
 of TNAjt ? TNAjt?1(1 + Rjt ) to TNAjt?1, Flow), and the fund load (the sum of front-end
 and back-end loads, additional fees charged to the customers to cover marketing and other
 expenses, Load). Also included are the fund style characteristics along the size, value, and
 momentum dimensions.15 To mitigate the impact of outliers on our estimates, we winsorize
 15The size style of a fund is the value-weighted score of its stock holdings? percentile scores calculated
 with respect to their market capitalizations (1 denotes the smallest size percentile; 100 denotes the largest
 size percentile). The value style is the value-weighted score of its stock holdings? percentile scores calculated
 with respect to their book-to-market ratios (1 denotes the smallest B/M percentile; 100 denotes the largest
 B/M percentile). The momentum style is the value-weighted score of a fund?s stock holdings? percentile
 scores calculated with respect to their past twelve-month returns (1 denotes the smallest return percentile;
 100 denotes the largest return percentile). These style measures are similar in spirit to those deflned in
 Kacperczyk, Sialm, and Zheng (2005) and Huang, Sialm, and Zhang (2009).
 18
Flow and Turnover at the 1% level.
 We estimate this and most of our subsequent regression speciflcations using pooled (panel)
 regression and calculating standard errors by clustering at the fund and time dimensions.
 This approach addresses the concern that the errors, conditional on independent variables,
 might be correlated within fund and time dimensions (e.g., Moulton (1986) and Thompson
 (2009)). Addressing this concern is especially important in our context since our variable of
 interest, Recession, is constant across all fund observations in a given time period. Also,
 we demean all control variables so that the constant a0 can be interpreted as the level of
 the attention variable in expansions, and a1 indicates how much the variable increases in
 recessions.
 The flrst attention variable we examine is reliance on aggregate information, RAI, as in
 equation (10). We proxy for the aggregate payofi shock with the innovation in log industrial
 production growth.16 A time series for RAIjt is obtained by computing the covariance of the
 innovations and each fund j?s portfolio weights using twelve-month rolling windows. Our
 hypothesis is that RAI should be higher in recessions, which means that the coe?cient on
 Recession, a1, should be positive.
 Our estimates of the parameters appear in Table 2. Column 1 shows the results for a
 univariate regression. In expansions, RAI is not difierent from zero, implying that funds?
 portfolios do not comove with future macroeconomic information in those periods. In reces-
 sions, RAI increases. Both flndings are consistent with the model. The increase amounts
 to ten percent of a standard deviation of RAI. It is measured precisely, with a t-statistic of
 3. To remedy the possibility of a bias in the coe?cient due to omitted fund characteristics
 correlated with recession times, we turn to a multivariate regression. Our flndings, presented
 in Column 2, remain largely unafiected by the inclusion of the control variables.
 Next, we repeat our analysis using funds? reliance on stock-speciflc information (RSI)
 as a dependent variable. Using equation (12), the RSI metric is computed in each month
 t as a cross-sectional covariance across the assets between the fund?s portfolio weights and
 flrm-speciflc earnings shocks.17 In the model, the fund?s portfolio holdings and its returns
 covary more with subsequent flrm-speciflc shocks in expansions. Therefore, our hypothesis
 16We regress log industrial production growth at t+1 on log industrial production growth in month t, and
 use the residual from this regression. Because industrial production growth is nearly i.i.d, the same results
 obtain if we simply use the log change in industrial production between t and t+ 1.
 17We regress earnings per share in a given quarter on earnings per share in the previous quarter (earnings
 are reported quarterly), and use the residual from this regression. Suppose month t and t + 3 are end-of-
 quarter months. Then RSI in months t, t+ 1, and t+ 2 are computed using portfolio weights from month t
 and earnings surprises from month t+ 3.
 19
is that RSI should fall in recessions, meaning that a1 should be negative.
 Columns 3 and 4 of Table 2 show that the average RSI across funds is positive in
 expansions and substantially lower in recessions. The efiect is statistically signiflcant at the
 1% level. It is also economically signiflcant: RSI decreases by approximately ten percent
 of one standard deviation. Overall, the data support the model?s prediction that portfolio
 holdings are more sensitive to aggregate shocks in recessions and more sensitive to flrm-
 speciflc shocks in expansions.
 Next, we examine market-timing, Timingjt , and stock-picking ability, Pickingjt , deflned
 in equations (11) and (13). The beneflt of using these variables is that they have an exact
 analog in the model. In contrast, for RAI and RSI, we need to take a stance on the empirical
 proxy for the aggregate and idiosyncratic shocks. The stock betas, fli, in Timing and Picking
 are computed using the twelve-month rolling-window regressions of stock excess returns on
 market excess returns.
 Columns 5 and 6 of Table 2 show that the average market-timing ability across funds
 increases signiflcantly in recessions. In turn, we flnd no evidence of market timing in ex-
 pansions. Since expansion months make up the bulk of our sample, this result is consistent
 with the literature which fails to flnd evidence for market timing, on average. However, we
 flnd that market timing is positive and statistically difierent from zero in recessions. The
 increase is 25 percent of a standard deviation of the Timing measure, which is economically
 meaningful. Likewise, Columns 7 and 8 show that stock-picking ability deteriorates substan-
 tially in recessions, again consistent with the theory. The reduction in recessions is about 20
 percent of a standard deviation of the Picking measure.
 Table S.5 performs several robustness checks. First, we compute an alternative RAI
 measure, in which the aggregate shock is proxied by surprises in non-farm employment
 growth, another salient macroeconomic variable, instead of industrial production growth.
 Second, we compute an alternative RSI measure in which earnings surprises are deflned as
 the residual from a regression of earnings per share in a given year on earnings per share
 in that same quarter one year earlier (instead of one quarter earlier), as in Bernard and
 Thomas (1989). Third, to check the market-timing results, we also study the R2 from a
 CAPM regression at the fund level, as in equation (16). It measures how the funds? excess
 returns (as opposed to their portfolio weights) covary with the aggregate state, as measured
 by the market?s excess return. All the results are similar to our benchmark result, and in
 the case of employment growth, are estimated even more precisely.
 To further understand how funds improve their market timing in recessions, we conduct
 20
several exercises. We flnd they increase their cash holdings, reduce their holdings of high-
 beta stocks, and tilt their portfolios towards more defensive sectors. Tables S.6, S.7, and S.8
 present the results; a more detailed discussion is in Appendix S.3.1.
 2.4 Testing Hypothesis 2: Dispersion
 The second prediction of the model is that heterogeneity in fund investment strategies and
 portfolio returns rises in recessions. To test this hypothesis, we estimate the following re-
 gression speciflcation, using various return and investment heterogeneity measures, denoted
 as Dispersionjt , the dispersion of fund j at month t.
 Dispersionjt = b0 + b1Recessiont + b2Xjt + ?jt ; (18)
 The deflnitions of Recession and other control variables mirror those in regression (17). Our
 coe?cient of interest is b1.
 We begin by examining dispersion in investment strategies. The results are in Table
 3. Our flrst measure is a fund?s portfolio Concentration, deflned in equation (15). Funds
 whose holdings deviate more from the S&P 500 portfolio, and therefore from other investors,
 have higher levels of portfolio concentration; they pursue more active investment strategies.
 In contrast, when all funds hold the market portfolio, average concentration and portfo-
 lio dispersion are zero. The results, in Columns 1 and 2, indicate an increase in average
 Concentration across funds in recessions. The increase is statistically signiflcant at the 1%
 level. It is also economically signiflcant: The value of stock concentration in recessions goes
 up by about 15% of a standard deviation.
 An alternative way to assess a fund?s concentration level is to look at its degree of idiosyn-
 cratic risk. A more concentrated portfolio carries more idiosyncratic risk,  j", according to
 the CAPM regression (16). Columns 3 and 4 show that the idiosyncratic volatility increases
 in recessions. The increase is highly signiflcant, statistically and economically. One concern
 with the CAPM-based measure of idiosyncratic risk is that it might not capture the possi-
 bility that some fund returns load on passive factors besides the market return. Therefore,
 we recompute idiosyncratic volatility, controlling for a fund?s exposure to size (SMB), value
 (HML), and momentum (UMD) factors. The resulting Recession coe?cient in a univariate
 regression is 0.347 and the intercept is 1.189. Controlling for fund characteristics changes
 the coe?cients by 1% or less.
 Since dispersion in fund strategies should generate dispersion in fund returns, we next
 21
look for evidence of higher return dispersion in recessions. To measure dispersion in return
 variable X, we use the absolute deviation between fund j?s value and the equally weighted
 cross-sectional average, jXjt ? X tj, as the dependent variable in (18). Columns 5 and 6
 of Table 3 present the results for the dispersion in the funds? CAPM alphas, which are
 obtained from twelve-month rolling-window regressions of fund excess returns on market
 excess returns. Comparing the slope b1 to the intercept b0, we flnd a 50% dispersion increase
 in recessions. The efiect is measured precisely. Columns 7 through 8 show that using four-
 factor alphas in place of CAPM alphas does not change the result. Finally, Columns 9
 and 10 show that the CAPM-beta dispersion also increases by about 30% in recessions,
 as investment managers take difierent directional bets in their investment strategies. The
 increased dispersions in abnormal returns, alphas, and betas are all consistent with the
 predictions of our model.
 Table S.9 (in the Appendix) considers additional measures of portfolio and return disper-
 sion. For example, we show that managers shift their investment styles more in recessions,
 consistent with more active portfolio management. Their funds also exhibit greater industry
 concentration in recessions. Next, we show that the dispersion of fund returns minus the
 market return nearly doubles in recessions. In unreported results, we obtain similar results
 for the dispersion of CAPM alpha and betas that are calculated by estimating their depen-
 dence on the aggregate dividend-price ratio, the term spread, the short-term interest rate,
 and the default spread, in one full-sample regression (Avramov and Wermers 2006). Finally,
 we study the dispersion in the information ratio, deflned as the ratio of the CAPM alpha to
 the CAPM residual volatility. These results further strengthen the evidence of the increased
 dispersion in recessions.
 2.5 Testing Hypothesis 3: Performance
 The third prediction of our model is that recessions are times when information allows funds
 to earn higher average risk-adjusted returns, on average. We evaluate this hypothesis using
 the following regression speciflcation:
 Performancejt = c0 + c1Recessiont + c2Xjt + ?jt (19)
 where Performancejt denotes the fund j?s performance in month t using previously in-
 troduced measures of abnormal fund returns, CAPM, three-factor, and four-factor alphas.
 Recession and the control variables, X, are deflned as before. All returns are expressed net
 22
of management fees. Our coe?cient of interest is c1.
 Table 4, Column 1, shows that the average fund?s net return is 3bp per month less
 than the market return in expansions, but it is 34bp per month higher in recessions. This
 difierence is highly statistically signiflcant and becomes even larger (42bp), after we control
 for fund characteristics (Column 2). Similar results (Columns 3 and 4) obtain when we use
 the CAPM alpha as a measure of fund performance, except that the alpha in expansions
 becomes negative. When we use alphas based on the three-factor and four-factor models,
 the recession return premium diminishes (Columns 5 through 8). But in recessions, the
 four-factor alpha still represents a non-trivial 1% per year risk-adjusted excess return, 1.6%
 higher than the -0.6% recorded in expansions (signiflcant at the 1% level).
 The cross-sectional regression model allows us to include a host of fund-speciflc control
 variables, making use of rich panel data. But because performance is measured using past
 twelve-month rolling-window regressions, a given observation for the dependent variable can
 be classifled as a recession when some or even all of the remaining eleven months of the
 window are expansions. To verify the robustness of our results, we also employ a time-series
 approach. In each month, we form the equally weighted portfolio of funds and calculate
 its net return, in excess of the risk-free rate. We then regress this time series of fund
 portfolio returns on Recession and common risk factors. We adjust standard errors for
 heteroscedasticity and autocorrelation (Newey and West 1987). Table S.10 shows that our
 previous results remain largely unchanged.
 Our results are robust to alternative performance measures. Table S.11 uses gross fund
 returns and alphas. In unreported results, we also use the information ratio (the ratio of
 the CAPM alpha to the CAPM residual volatility) as a performance measure. It increases
 sharply in recessions. Finally, we flnd similar results when we lead alpha on the left-hand
 side by one month instead of using a contemporaneous alpha. All results point in the same
 direction: Outperformance clusters in periods of recessions.
 2.6 Identifying Recessions
 So far, we have measured the state of the business cycle using an indicator variable based
 on the NBER deflnition of recessions. While this choice seems quite natural in light of its
 salience as an indicator of observed economic activity, it sufiers from two potential prob-
 lems. First, the information on NBER recessions is available only after the recession has
 already started. Second, measuring business cycles using a discrete variable contains less
 information than using a continuous counterpart. To address these concerns, we conflrmed
 23
our results using various contemporaneous recession indicators such as a dummy for negative
 real consumption growth, or, alternatively, for the 25% lowest stock market returns. We also
 assessed the robustness of our results using the Chicago Fed National Activity Index (CF-
 NAI), a continuous and contemporaneous indicator of the strength of economic activity, as
 our independent variable. Table S.12 shows that the results on performance are, if anything,
 stronger than those for our baseline measure. The other two hypotheses, on RAI/RSI and
 on dispersion, also hold for the CFNAI, but are omitted for brevity.
 Another question is whether recession is the right conditioning variable. Since a key
 feature of recessions is high payofi volatility, we could replace the recession indicator with a
 dummy variable for high payofi volatility. The latter equals one in months with the highest
 volatility of aggregate earnings growth.18 As predicted by the theory, we flnd that RAI,
 dispersion, and performance all rise in high volatility months, while RSI falls. For illustration,
 Table S.13 describes the performance results. Yet, we prefer to think of attention allocation
 as a cyclical phenomenon and believe that using our current deflnition of recession is more
 suitable, for the following reasons. First, it allows us to make contact with the existing
 macroeconomics literature on rational inattention, e.g., Ma?ckowiak and Wiederholt (2009a,
 2009b). Second, our data suggests that attention allocation is more of a cyclical phenomenon:
 Cyclical attention reallocation is more pronounced than volatility-based attention allocation.
 Third, periods of low and high economic activity are common knowledge whereas measuring
 earnings volatility requires paying close attention to aggregate earnings data, which our
 theory predicts not all managers choose to do. A downturn in economic activity has such
 wide-ranging implications for investors, and as a binary variable, is so easy to learn, that
 knowing about the start or end of a recession is almost inescapable.
 3 Using Theory and Data to Identify Skilled Managers
 Our analysis so far shows that the data are consistent with the three main predictions
 of the model. This suggests we can use it to identify skilled investment managers. In
 particular, we exploit the model?s prediction that skilled managers display market-timing
 ability in recessions and stock-picking ability in expansions. We deflne market-timing and
 stock-picking ability as in equations (11) and (13). Since the funds? portfolio holdings in
 each stock are observed at most quarterly, we assume that funds use buy-and-hold strategies
 18We chose the volatility cutofi such that 12% of months are selected, the same fraction as NBER recession
 months.
 24
in non-disclosure periods. In these periods, the portfolio weights, wjit, would only vary to
 the extent that market prices vary.
 3.1 The Same Managers Do Switch Strategies
 We flrst test the prediction that the same investment managers with stock-picking ability in
 expansions display market-timing ability in recessions. To this end, we flrst identify funds
 with superior stock-picking ability in expansions: For all expansion months, we select all
 fund-month observations that are in the highest 25% of the Pickingjt distribution. We form
 an indicator variable Skill Picking (SPj 2 f0; 1g) that is equal to 1 for the 25% of funds (884
 funds) with the highest fraction of observations in the top, relative to the total number of
 observations (in expansions) for that fund. Then, we estimate the following pooled regression
 model, separately for expansions and recessions:
 Abilityjt = d0 + d1SP jt + d2Xjt + ?jt ; (20)
 where Ability denotes either Timing or Picking. X is a vector of previously deflned control
 variables. Our coe?cient of interest is d1.
 Table 5, Column 3, conflrms that SP funds are signiflcantly better at picking stocks in
 expansions, after controlling for fund characteristics. This is true by construction. The main
 point, however, is that these same SP funds are also good at market timing in recessions.
 This result is evident from the recession-based market-timing regression in Column 2, in
 which the coe?cient on SP is statistically signiflcant at the 5% level. Finally, we note that
 the funds in SP do not exhibit superior market-timing ability in expansions (Column 1) nor
 superior stock-picking ability in recessions (Column 4), which conflrms that SP funds switch
 strategies.
 Having identifled a subset of skilled funds based on their time-varying investment strate-
 gies, the model predicts that this group should outperform the unskilled funds not only in
 recessions but also in expansions. Table 6 compares the unconditional performance of the
 SP portfolio to that composed of all other funds. After controlling for various fund char-
 acteristics, the CAPM, three-factor, and four-factor alphas are 70-90 basis points per year
 higher for the SP portfolio, a difierence that is statistically and economically signiflcant.
 In Panel A of Table 7, we further compare the characteristics of the funds in the Skill-
 Picking portfolio to those not included in the portfolio. We note several salient difierences.
 First, funds in SP are on average younger (by flve years). Second, they have less wealth
 25
under management (by $400 million), suggestive of decreasing returns to scale at the fund
 level, as in Berk and Green (2004) and Chen, Hong, Huang, and Kubik (2004). Third,
 they tend to charge higher expenses (by 0.26% per year), suggesting rent extraction from
 customers for the skill they provide. Fourth, they exhibit much higher turnover rates (about
 130% per year, versus 80% per year for other funds), consistent with their more active-
 management styles. Fifth, they receive higher in ows of new assets to manage, consistent
 with their superior performance, and presumably a market-based re ection of their skill.
 Sixth, the SP funds tend to hold more concentrated portfolios, with fewer stocks and higher
 stock-level and industry-level Herflndahl concentration. Seventh, their betas deviate more
 from their peers suggesting a strategy with difierent systematic risk exposure. Finally, they
 rely signiflcantly more on aggregate information. Taken together, these flndings begin to
 paint a picture of what a typical skilled fund looks like.
 To what extent can observable characteristics predict skill (SP )? Table S.14 reports the
 estimates from a linear-probability regression model of the SP indicator on fund character-
 istics, such as age, TNA, expenses, and turnover. The regression R2 equals 14%. Including
 attributes that our theory links to skilled managers, such as stock and industry concen-
 tration, beta deviation, and RAI, increases the R2 to 19%. Table 7, Panel B, examines
 manager characteristics. SP fund managers are 2.6% more likely to have an MBA, are one
 year younger, and have 1.7 fewer years of experience. Interestingly, they are much more
 likely to depart for hedge funds later in their careers, suggesting that the market judges
 them to have superior skills.
 The existence of skilled mutual funds with cyclical learning and investment strategies is
 not a fragile result. First, the results continue to hold if we change the cutofi levels for the
 inclusion in the SP portfolio. Second, we show that the top 25% RSI funds in expansions have
 higher RAIs in recessions and higher unconditional alphas (Tables S.15 and S.16). Third,
 we verify our results using Daniel, Grinblatt, Titman, and Wermers (1997)?s deflnitions of
 market timing (CT) and stock picking (CS). Finally, we reverse the sort, to show that funds
 in the top 25% of market-timing ability in recessions, have statistically higher stock-picking
 ability in expansions and higher unconditional alphas (Tables S.17 and S.18).
 3.2 Creating a Skill Index
 If one is going to use the model to identify skilled investment managers, it is important that
 she can identify these managers in real time, without looking at the full sample of the data.
 To this end, we construct a Skill Index that is informed by the main predictions of our model
 26
that attention allocation and investment strategies change over the business cycle. We deflne
 the Skill Index as a weighted average of Timing and Picking measures, in which the weights
 we place on each measure depend on the state of the business cycle:
 Skill Indexjt(z) = w(zt)Timingjt + (1? w(zt))Pickingjt ; with zt 2 fE;Rg:
 We demean Timing and Picking, divide each by its standard deviation, and set w(R) =
 0:8 > w(E) = 0:2 (the exact number is not crucial).
 Subsequently, we examine whether the time-t Index can predict future fund performance,
 measured by the CAPM, three-factor, and four-factor alphas one month (and one year)
 later. Table 8 shows that funds with a higher Skill Index have on average higher alphas.
 For example, when Skill Index is zero (its mean), the alpha is -4bp per month. However,
 when the Skill Index is one standard deviation (0.83%) above its mean, the alpha is 1.1%
 (four-factor) or 2.4% (CAPM) higher per year. The three most right columns show similar
 predictive power of the Skill Index for one-year ahead alphas. As a robustness check, we
 construct a second skill index based on RAI and RSI instead of Timing and Picking.
 A one-standard-deviation increase in this skill index increases one-month-ahead alphas by
 0.3-0.5% per year, a statistically signiflcant efiect (Table S.19).
 A large literature investigates whether measures of skill persist through time (e.g., Carhart
 (1997), Brown and Goetzmann (1995)). To investigate whether the skill we identify exhibits
 persistence, we sort funds into quintiles based on their values of the Skill Index. We then
 track the Skill Index of the funds in each quintile over the next twelve months. Figure 3
 shows a substantial amount of skill persistence, which is slowly declining over time. One
 interesting observation is that the best funds display the most persistence, which is in con-
 trast with most of the literature, which usually flnds persistence among the worst but not
 the best funds.
 4 Alternative Explanations
 We brie y explore other candidate explanations. The flrst alternative is that no skill exists.
 In that case, all the recession efiects in fund returns would have to arise mechanically from
 the properties of asset returns. To rule this out, we calculate means, volatilities, alphas,
 betas, and idiosyncratic volatilities of individual stock returns, in the same way as we do it
 for mutual fund returns. None of these moments difier between expansions and recessions
 (except for higher volatility of asset returns in recessions, our driving force). Using a simu-
 27
lation, we verify that a mechanical mutual fund investment policy that randomly selects 50,
 75, or 100 stocks cannot produce the observed counter-cyclical fund returns.
 Second, we consider labor market explanations. In recessions, fund managers? labor-
 market options deteriorate. Not only do their assets under management and therefore their
 wages shrink, they are also less likely to get promoted or picked ofi by a hedge fund and more
 likely to get flred or demoted (Table S.20). In a model with risk-averse investment managers
 who are compensated based on their relative performance, larger downsides and smaller
 upsides would make optimal investment choices more conservative and less dispersed. To
 see why, imagine that a manager implements a small deviation from the strategy of all other
 managers; then she has an approximately 50% chance of underperforming. If fewer than 50%
 of managers are flred, following peers is better. The opposite is true in expansions: There is
 a lot of upside and little downside, giving managers incentives to gamble and deviate from
 the pack, in an attempt to get promoted. This explanation counterfactually generates higher
 portfolio dispersion in expansions. While labor market considerations may be important to
 understand many aspects of the behavior of mutual fund managers, the above argument
 suggests that they cannot account for the dispersion patterns we document.
 Another labor-market explanation could be that the quality of fund managers improves
 during recessions because better fund managers survive (or self-select) into the mutual fund
 industry in such periods. We flnd no evidence for such an efiect. Table S.21 shows no difier-
 ence between the age, educational background or experience of our managers in recessions
 versus expansions.
 Fourth, Glode (2008) argues that funds outperform in recessions because their investors?
 marginal utility is highest in such periods. While complementary to our explanation, his
 work remains silent on what strategies investment managers pursue to achieve this difier-
 ential performance, and hence on our flrst and second hypothesis. In sum, while various
 explanations can account for some of the facts, we conclude that they cannot account for all
 facts jointly.
 5 Conclusion
 Do investment managers add value for their clients? The answer to this question matters for
 problems ranging from the discussion of market e?ciency to a practical portfolio advice for
 households. The large amount of randomness in flnancial asset returns makes it a di?cult
 question to answer. The multi-billion investment management business is flrst and foremost
 28
an information-processing business. We model investment managers not only as agents
 making optimal portfolio decisions, but also as ones who optimally allocate a limited amount
 of attention or information-processing capacity. Since the optimal attention allocation varies
 with the state of the economy, so do investment strategies and fund returns. As long as a
 subset of investment managers can process information about future asset payofis, the model
 predicts a higher covariance of portfolio holdings with aggregate information, more dispersion
 in returns across funds, and a higher average outperformance, in recessions. We observe these
 patterns in investments and returns of actively managed U.S. mutual funds. Hence, the data
 are consistent with a world in which some investment managers have skill, but that skill is
 often hard to detect. Recessions are times when difierences in performance are magnifled
 and skill is easier to detect.
 Beyond the mutual fund industry, a sizeable fraction of GDP now comes from industries
 that produce and process information. Increasing access to information through the internet
 has made the problem of how to best allocate a limited amount of information-processing
 capacity even more relevant. While information choices have consequences for real outcomes,
 they are often poorly understood because they are di?cult to measure. By predicting how
 information choices are linked to observable variables (such as the state of the economy) and
 by tying information choices to real outcomes (such as portfolio investment), we show how
 models of information choices can be brought to the data. This information-choice-based
 approach could be useful in examining other information-processing sectors of the economy.
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Figure 1: Cross-Sectional Distribution of Outperformance
 This flgure shows the cross-sectional distribution in recessions (red) and in expansions (blue) of the four-factor alpha for the
 mutual funds in our sample. The data are from CRSP and are available monthly from January 1980 until December 2005.
 ?40 ?30 ?20 ?10 0 10 20 30 40 50 60
 0
 0.01
 0.02
 0.03
 0.04
 0.05
 0.06
 0.07
 0.08
 4?factor alpha (in % per year)
 Recession
 Boom
 Figure 2: Investment Performance in Recessions vs. Expansions
 This flgure shows four-factor alphas for all domestic equity mutual funds. They are obtained by, flrst, regressing fund returns
 in excess of the risk-free rate on the market return in excess of the risk-free rate, the return on a portfolio that is long in small
 flrms and short in large flrms (SMB), the return on a portfolio that is long in value flrms and short in growth flrms (HML), and
 the return on a portfolio that is long in winners and short in losers (UMD) in twelve-month rolling-window regressions. The
 fund alpha is the intercept of that regression. In a second step, we regress the fund alphas on a recession indicator variable in
 a panel regression, controlling for other fund characteristics. The intercept of that regression is the alpha in expansions, the
 sum of the coe?cient on the dummy and the intercept is the alpha in recessions. We annualize monthly alphas by multiplying
 them by twelve. The data are from CRSP and available monthly from January 1980 until December 2005.
 0 1 2 2.5
 Alphas, 4?factor model, in percent per year
 Equally weighted
  
Net ? Boom
  Net ? Recession
 Gross ? Boom
 Gross ? Recession
 34
Figure 3: Skill Index Persistence
 In a given month, all funds are ranked into quintiles based on their Skill Index, deflned as Skill Indexjt (z) = w(zt)Timingjt +
 (1?w(zt))Pickingjt ; with zt 2 fE;Rg. Skill Index is standardized cross-sectionally to have mean zero and standard deviation
 one. We then compute and plot the Skill Index of the funds in each quintile in the subsequent twelve months. The data cover
 the period from January 1980 until December 2005.
 1 2 3 6 12
 ?0.1
 ?0.08
 ?0.06
 ?0.04
 ?0.02
 0
 0.02
 0.04
 0.06
 0.08
 Months
 Skill Inde
 x 1
  
 
bottom quintile
 Q2
 Q3
 Q4
 top quintile
 35
Table 1: Individual Stocks Have More Aggregate Risk in Recessions
 For each stock i and each month t, we estimate a CAPM equation based on twelve months of data (a twelve-
 month rolling-window regression). This estimation delivers the stock?s beta, flit , and its residual standard
 deviation,  i"t. We deflne stock i?s aggregate risk in month t as
 flflflit mt
 flfl and its idiosyncratic risk as  i"t, where
  mt is formed as the realized volatility from daily return observations. Panel A reports the results from a
 time-series regression of the aggregate risk averaged across stocks, 1N
 PN
 i=1
 flflflit mt
 flfl, in Columns 1 and 2, and
 of the idiosyncratic risk averaged across stocks, 1N
 PN
 i=1  i"t, in Columns 3 and 4 on Recession. Recession isan indicator variable equal to one for every month the economy is in a recession according to the NBER, and
 zero otherwise. In Columns 2 and 4 we include several aggregate control variables: We regress the portfolio
 (net) return in excess of the risk-free rate on Recession and a set of four risk factors: the market excess
 return (MKTPREM), the return on the small-minus-big portfolio (SMB), the return on the high-minus-low
 book-to-market portfolio (HML), the return on the up-minus-down momentum portfolio (UMD). The data
 are monthly and cover the period 1980 to 2005 (309 months). Standard errors (in parentheses) are corrected
 for autocorrelation and heteroscedasticity. Panel B reports results of panel regressions of the aggregate
 risk of an individual stock,
 flflflit mt
 flfl, in Columns 1 and 2 and of its idiosyncratic risk,  i"t, in Columns 3
 and 4 on Recession. In Columns 2 and 4 we include several flrm-speciflc control variables: the log market
 capitalization of the stock, log(Size), the ratio of book equity to market equity, B ?M , the average return
 over the past year, Momentum, the stock?s leverage, Leverage, measured as the ratio of book debt to book
 debt plus book equity, and an indicator variable, NASDAQ, equal to one if the stock is traded on NASDAQ.
 All control variables are lagged one month. The data are monthly and cover all stocks in the CRSP universe
 for the period 1980 to 2005. Standard errors (in parentheses) are clustered at the stock and time dimensions.
 (1) (2) (3) (4)
 Aggregate Risk Idiosyncratic Risk
 Panel A: Time-Series Regression
 Recession 0.213 0.207 0.058 0.016
 (0.120) (0.118) (1.018) (1.016)
 MKTPREM -0.678 -1.865
 (0.487) (3.043)
 SMB 1.251 12.045
 (0.593) (4.293)
 HML 0.015 9.664
 (0.842) (8.150)
 UMD -0.684 -1.112
 (0.372) (3.888)
 Constant 0.475 0.484 13.229 13.196
 (0.030) (0.031) (0.286) (0.276)
 Observations 309 309 309 309
 Panel B: Pooled Regression
 Recession 0.212 0.253 0.064 0.510
 (0.058) (0.057) (0.493) (0.580)
 Log(Size) -0.029 -1.544
 (0.004) (0.037)
 B-M Ratio -0.160 -2.691
 (0.012) (0.086)
 Momentum 0.029 2.059
 (0.021) (0.177)
 Leverage -0.095 -1.006
 (0.015) (0.119)
 NASDAQ 0.150 1.937
 (0.017) (0.105)
 Constant 0.447 0.442 12.641 12.592
 (0.015) (0.015) (0.122) (0.144)
 Observations 1,312,216 1,312,216 1,312,216 1,312,216
 36
Table 2: Attention Allocation
 The dependent variables are funds? reliance on aggregate information (RAI), funds? reliance on stock-speciflc
 information (RSI), funds? market-timing ability (Timing), and funds? stock-picking ability (Picking). A fund
 j?s RAIjt is deflned as the (twelve-month rolling-window time-series) covariance between the funds? holdings
 in deviation from the market (wjit ?wmit ) in month t and changes in industrial production growth between t
 and t+1. A fund j?s RSIjt is deflned as the (across stock) covariance between the funds? holdings in deviation
 from the market (wjit ? wmit ) in month t and changes in earnings growth between t and t + 1. Timing is
 deflned as follows: Timingjt =
 PN
 i=1(wjit?wmit )(flitRmt+1) and Pickingjt =
 PN
 i=1(wjit?wmit )(Rit+1? flitRmt+1),where the stocks? flit is measured over a twelve-month rolling window. RAI, RSI, Timing, and Pickingare all multiplied by 10,000 for ease of readability. Recession is an indicator variable equal to one for every
 month the economy is in a recession according to the NBER, and zero otherwise. Log(Age) is the natural
 logarithm of fund age. Log(TNA) is the natural logarithm of a fund total net assets. Expenses is the fund
 expense ratio. Turnover is the fund turnover ratio. Flow is the percentage growth in a fund?s new money.
 Load is the total fund load. The last three control variables measure the style of a fund along the size,
 value, and momentum dimensions, calculated from the scores of the stocks in their portfolio in that month.
 They are omitted for brevity. All control variables are demeaned. Flow and Turnover are winsorized at the
 1% level. The data are monthly and cover the period 1980 to 2005. Standard errors (in parentheses) are
 clustered at the fund and time dimensions.
 (1) (2) (3) (4) (5) (6) (7) (8)
 RAI RSI Timing Picking
 Recession 0.011 0.011 -0.682 -0.696 0.140 0.139 -0.144 -0.146
 (0.004) (0.004) (0.159) (0.150) (0.070) (0.068) (0.047) (0.047)
 Log(Age) -0.002 0.423 0.006 0.004
 (0.001) (0.060) (0.006) (0.004)
 Log(TNA) -0.001 -0.173 0.000 -0.003
 (0.000) (0.029) (0.004) (0.003)
 Expenses -0.330 88.756 1.021 -0.815
 (0.244) (11.459) (1.280) (0.839)
 Turnover -0.004 -0.204 0.007 0.017
 (0.001) (0.053) (0.013) (0.010)
 Flow -0.008 1.692 -0.001 0.058
 (0.010) (0.639) (0.078) (0.088)
 Load 0.017 -9.644 0.033 0.156
 (0.023) (1.972) (0.180) (0.131)
 Constant -0.001 -0.001 3.084 3.086 0.007 0.007 -0.010 -0.010
 (0.001) (0.001) (0.069) (0.070) (0.024) (0.024) (0.018) (0.018)
 Observations 224,257 224,257 166,328 166,328 221,306 221,306 221,306 221,306
 37
Table 3: Dispersion in Funds? Portfolio Strategies and Returns
 The dependent variables are Concentration, Idio V ol, and jXjt ? ?Xtj, where Xjt is the CAPM Alpha,
 4 ? Factor Alpha, or CAPM Beta, and ?X denotes the (equally weighted) cross-sectional average.
 Concentration for fund j at time t is calculated as the Herflndahl index of portfolio weights in stocks
 i 2 f1; ? ? ? ; Ng in deviation from the market portfolio weights PNi=1(wjit ? wmit )2 ? 100. Idio V ol is the
 idiosyncratic volatility from a twelve-month rolling-window CAPM regression at the fund level. The CAPM
 alpha (and four-factor alpha) and the CAPM beta are obtained from twelve-month rolling-window regressions
 of fund-level excess returns on excess market returns (and returns on SMB, HML, and MOM). Recession
 is an indicator variable equal to one for every month the economy is in a recession according to the NBER,
 and zero otherwise. Log(Age) is the natural logarithm of fund age. Log(TNA) is the logarithm of a fund
 total net assets. Expenses is the fund expense ratio. Flow is the percentage growth in a fund?s new money.
 Turnover is the fund turnover ratio. Load is the total fund load. The last three control variables measure
 the style of a fund along the size, value, and momentum dimensions, calculated from the scores of the stocks
 in their portfolio in that month. They are omitted for brevity. All control variables are demeaned. Flow
 and Turnover are winsorized at the 1% level. The data are monthly and cover the period 1980 to 2005.
 Standard errors (in parentheses) are clustered at the fund and time dimensions.
 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
 Concentration Idio Vol CAPM Alpha 4-Factor Alpha CAPM Beta
 Recession 0.205 0.147 0.348 0.359 0.275 0.298 0.140 0.150 0.082 0.083
 (0.027) (0.026) (0.127) (0.104) (0.054) (0.050) (0.028) (0.025) (0.015) (0.014)
 Log(Age) 0.203 -0.181 -0.045 -0.011 -0.009
 (0.028) (0.017) (0.004) (0.002) (0.002)
 Log(TNA) -0.179 0.039 0.017 -0.006 0.003
 (0.014) (0.012) (0.002) (0.001) (0.001)
 Expenses 28.835 54.365 9.468 8.58 5.460
 (4.860) (2.806) (0.658) (0.468) (0.235)
 Turnover -0.092 0.358 0.050 0.059 0.020
 (0.025) (0.023) (0.004) (0.003) (0.001)
 Flow 0.122 0.196 0.315 0.242 0.022
 (0.104) (0.174) (0.053) (0.032) (0.017)
 Load -1.631 -5.562 -1.123 -0.420 -0.444
 (0.907) (0.490) (0.095) (0.070) (0.042)
 Constant 1.525 1.524 2.103 2.104 0.586 0.585 0.497 0.497 0.229 0.229
 (0.024) (0.022) (0.071) (0.068) (0.018) (0.016) (0.009) (0.008) (0.006) (0.006)
 Observations 230,185 230,185 227,159 227,159 226,745 226,745 226,745 226,745 227,159 227,159
 38
Table 4: Fund Performance: Cross-Section Approach
 The dependent variables are funds? Abnormal Return, CAPM Alpha, 3 ? Factor Alpha, and 4 ? Factor
 Alpha. All are obtained from twelve-month rolling-window regressions of fund-level excess returns on excess
 market returns for the CAPM alpha, additionally on the SMB and the HML factors for the three-factor
 alpha, and additionally on the UMD factor for the four-factor alpha. The abnormal return is the fund return
 minus the market return. Recession is an indicator variable equal to one for every month the economy is
 in a recession according to the NBER, and zero otherwise. Log(Age) is the natural logarithm of fund age.
 Log(TNA) is the natural logarithm of a fund total net assets. Expenses is the fund expense ratio. Flow
 is the percentage growth in a fund?s new money. Turnover is the fund turnover ratio. Load is the total
 fund load. The last three control variables measure the style of a fund along the size, value, and momentum
 dimension, calculated from the scores of the stocks in their portfolio in that month. They are omitted for
 brevity. All control variables are demeaned. Flow and Turnover are winsorized at the 1% level. The data
 are monthly and cover the period 1980 to 2005. Standard errors (in parentheses) are clustered at the fund
 and time dimensions.
 (1) (2) (3) (4) (5) (6) (7) (8)
 Abnormal Return CAPM Alpha 3-Factor Alpha 4-Factor Alpha
 Recession 0.342 0.425 0.337 0.404 0.043 0.073 0.107 0.139
 (0.056) (0.058) (0.048) (0.047) (0.034) (0.028) (0.041) (0.032)
 Log(Age) -0.031 -0.036 -0.028 -0.039
 (0.009) (0.008) (0.006) (0.006)
 Log(TNA) 0.046 0.033 0.009 0.012
 (0.005) (0.004) (0.003) (0.003)
 Expenses -1.811 -2.372 -7.729 -7.547
 (1.046) (0.945) (0.782) (0.745)
 Turnover -0.023 -0.044 -0.074 -0.065
 (0.016) (0.010) (0.010) (0.008)
 Flow 2.978 2.429 1.691 1.536
 (0.244) (0.172) (0.097) (0.096)
 Load -0.809 -0.757 -0.099 -0.335
 (0.226) (0.178) (0.131) (0.141)
 Constant -0.027 -0.033 -0.059 -0.063 -0.059 -0.060 -0.050 -0.052
 (0.027) (0.026) (0.025) (0.024) (0.020) (0.018) (0.023) (0.021)
 Observations 226,745 226,745 226,745 226,745 226,745 226,745 226,745 226,745
 39
Table 5: Same Funds with Stock-Picking Ability in Expansions Have Market-
 Timing Ability in Recessions
 We divide all fund-month observations into Recession and Expansion subsamples. Recession is an indicator
 variable equal to one for every month the economy is in a recession according to the NBER, and zero
 otherwise; Expansion is equal to one every month the economy is not in recession. The dependent variables
 are our measure of a fund?s market timing, Timingjt , and our measure of the fund?s stock-picking ability,
 Pickingjt . They are deflned as follows: Timingjt =
 PN
 i=1(wjit ? wmit )(fliRmt+1) and Pickingjt =
 PN
 i=1(wjit ?
 wmit )(Rit+1?fliRmt+1). Skill P icking is an indicator variable equal to one for all funds whose Picking measure
 in Expansion is in the highest 25th percentile of the distribution, and zero otherwise. Log(Age) is the natural
 logarithm of fund age. Log(TNA) is the natural logarithm of a fund total net assets. Expenses is the fund
 expense ratio. Flow is the percentage growth in a fund?s new money. Turnover is the fund turnover ratio.
 Load is the total fund load. The last three control variables measure the style of a fund along the size,
 value, and momentum dimensions, calculated from the scores of the stocks in their portfolio in that month.
 They are omitted for brevity. All control variables are demeaned. Flow and Turnover are winsorized at
 the 1% level. The data are monthly and cover the period 1980 to 2005. Standard errors (in parentheses) are
 clustered at the fund and time dimensions.
 (1) (2) (3) (4)
 Market Timing Stock Picking
 Expansion Recession Expansion Recession
 Skill Picking 0.000 0.017 0.056 -0.096
 (0.004) (0.009) (0.004) (0.017)
 Log(Age) 0.009 -0.025 -0.001 0.029
 (0.002) (0.006) (0.002) (0.007)
 Log(TNA) -0.001 0.005 0.000 -0.023
 (0.001) (0.003) (0.001) (0.003)
 Expenses 0.868 1.374 -1.291 -4.434
 (0.321) (1.032) (0.376) (1.378)
 Turnover 0.009 -0.011 0.017 -0.006
 (0.003) (0.007) (0.004) (0.012)
 Flow 0.056 -0.876 0.138 -0.043
 (0.024) (0.112) (0.037) (0.093)
 Load 0.094 -0.076 0.131 0.615
 (0.049) (0.151) (0.055) (0.195)
 Constant 0.016 0.059 -0.021 -0.148
 (0.001) (0.004) (0.001) (0.005)
 Observations 204,330 18,354 204,330 18,354
 40
Table 6: Unconditional Performance of \Skill-Picking" Funds
 We divide all fund-month observations into Recession and Expansion subsamples. Expansion equals one
 every month the economy is not in recession according to the NBER, and zero otherwise. We deflne the stock
 picking ability of a fund as Pickingjt =
 PN
 i=1(wjit ? wmit )(Rit+1 ? fliRmt+1). Skill Picking, SP , is an indicator
 variable equal to one for all funds whose Picking measure in Expansion is in the highest 25th percentile of
 the distribution, and zero otherwise. The dependent variables are the CAPM alpha, three-factor alpha, or
 four-factor alpha of the mutual fund, obtained from a twelve-month rolling-window regression of a fund?s
 excess returns before expenses on a set of common risk factors. Log(Age) is the natural logarithm of fund
 age. Log(TNA) is the natural logarithm of a fund?s total net assets. Expenses is the fund expense ratio.
 Flow is the percentage growth in a fund?s new money. Turnover is the fund turnover ratio. Load is the total
 fund load. The last three control variables measure the style of a fund along the size, value, and momentum
 dimensions, calculated from the scores of the stocks in their portfolio in that month. They are omitted for
 brevity. All control variables are demeaned. Flow and Turnover are winsorized at the 1% level. The data
 are monthly and cover the period 1980 to 2005. Standard errors (in parentheses) are clustered at the fund
 and time dimensions.
 (1) (2) (3)
 CAPM Alpha 3-Factor Alpha 4-Factor Alpha
 Skill Picking 0.076 0.056 0.064
 (0.040) (0.021) (0.018)
 Log(Age) -0.039 -0.028 -0.038
 (0.008) (0.006) (0.006)
 Log(TNA) 0.032 0.013 0.014
 (0.005) (0.004) (0.004)
 Expenses 4.956 0.627 0.241
 (1.066) (0.793) (0.739)
 Turnover -0.009 -0.047 -0.041
 (0.014) (0.012) (0.009)
 Flow 2.579 1.754 1.602
 (0.173) (0.102) (0.101)
 Load -0.744 -0.090 -0.289
 (0.214) (0.136) (0.145)
 Constant 0.057 0.038 0.049
 (0.017) (0.015) (0.018)
 Observations 227,183 227,183 227,183
 41
Table 7: Comparing \Skill-Picking" Funds to Other Funds
 We divide all fund-month observations into Recession and Expansion subsamples. Expansion equals one
 every month the economy is not in recession according to the NBER, and zero otherwise. We deflne the
 stock picking ability of a fund as Pickingjt =
 PN
 i=1(wjit?wmit )(Rit+1? fliRmt+1). Skill P icking is an indicator
 variable equal one for all funds whose Picking measure in Expansion is in the highest 25th percentile of
 the distribution, and zero otherwise. Panel A reports fund-level characteristics. Age is the fund age in
 years. TNA is the fund?s total net assets. Expenses is the fund expense ratio. Turnover is the fund
 turnover ratio. Flows is the fund?s net in ow of new assets to manage. Concentration is the concentration
 of the fund?s portfolio, measured as the Herflndahl index of portfolio weights in deviation from the market
 portfolio?s weights. Stock Number is the number of stocks in the fund?s portfolio. Industry is the industry
 concentration of the fund?s portfolio, measured as the Herflndahl index of portfolio weights in a given industry
 in deviation from the market portfolio?s weights. Beta Deviation is the absolute difierence between the fund?s
 beta and the average beta in its style category. RAI is the manager reliance on aggregate information, deflned
 as the R-squared from the regression of the fund?s portfolio returns on contemporaneous changes in industrial
 production. Panel B reports manager-level characteristics. MBA equals one if the manager obtained an
 MBA degree, and zero otherwise. Ivy equals one if the manager graduated from an Ivy League institution,
 and zero otherwise. Age is the fund manager age in years. Experience is the fund manager experience in
 years. Gender equals one if the manager is a male and zero if the manager is female. Hedge Fund equals one
 if the manager ever departed to a hedge fund, and zero otherwise. SP1? SP0 is the difierence between the
 mean values of the groups for which Skill P icking equals one and zero, respectively. The data are monthly
 and cover the period 1980 to 2005. p? values measure statistical signiflcance of the difierence.
 Skill Picking = 1 Skill Picking = 0 Difierence
 Mean Stdev. Median Mean Stdev. Median SP1-SP0 p-value
 Panel A: Fund Characteristics
 Age 10.01 8.91 7 15.20 15.34 9 -5.19 0.000
 TNA 621.13 2027.04 129.60 1019.45 4024.29 162.90 -398.32 0.002
 Expenses 1.48 0.47 1.42 1.22 0.47 1.17 0.26 0.000
 Turnover 130.41 166.44 101.00 79.89 116.02 58.00 50.52 0.000
 Flows 0.22 7.39 -0.76 -0.07 6.47 -0.73 0.300 0.008
 Concentration 1.68 1.60 1.29 1.33 1.50 0.99 0.35 0.000
 Stock Number 90.83 110.20 68 111.86 187.13 69 -21.03 0.000
 Industry 8.49 7.90 6.39 5.37 7.54 3.54 3.12 0.000
 Beta Deviation 0.18 0.38 0.13 0.13 0.23 0.10 0.05 0.000
 RAI 4.13 5.93 1.82 2.77 3.97 1.26 1.37 0.000
 Panel B: Fund Manager Characteristics
 MBA 42.09 49.37 0 39.49 48.88 0 2.60 0.128
 Ivy 25.36 43.51 0 27.94 44.87 0 -2.57 0.205
 Age 53.02 10.42 50 54.11 10.06 52 -1.08 0.081
 Experience 26.45 10.01 24 28.14 10.00 26 -1.69 0.003
 Gender 90.89 28.77 100 90.50 29.31 100 0.39 0.681
 Hedge Fund 10.43 30.57 0 6.12 23.96 0 4.31 0.000
 42
Table 8: Skill Index Predicts Performance
 The dependent variable is the fund?s cumulative CAPM, three-factor, or four-factor alpha, calculated from a
 twelve-month rolling regression of observations in month t+2 in the three left columns and in month t+13
 in the three most right columns. For each fund, we form the following skill index in month t. Skill Indexjt =
 w(zt)Timingjt + (1 ? w(zt))Pickingjt ; zt 2 fExpansion;Recessiong, w(Recession)=0.8 > w(Expansion) =
 0.2, where Timingjt = 1N
 PN
 i=1(wjit ? wmit )(fliRmt+1) and Pickingjt = 1N
 PN
 i=1(wjit ? wmit )(Rit+1 ? fliRmt+1).
 Picking and Timing are normalized so that they are mean zero and have a standard deviation of one over
 the full sample. Log(Age) is the natural logarithm of fund age. Log(TNA) is the natural logarithm of a
 fund total net assets. Expenses is the fund expense ratio. Flow is the percentage growth in a fund?s new
 money. Turnover is the fund turnover ratio. Load is the total fund load. The last three control variables
 measure the style of a fund along the size, value, and momentum dimensions, calculated from the scores of
 the stocks in their portfolio in that month. They are omitted for brevity. All control variables are demeaned.
 Flow and Turnover are winsorized at the 1% level. The data are monthly and cover the period 1980 to
 2005. Standard errors (in parentheses) are clustered at the fund and time dimensions.
 (1) (2) (3) (4) (5) (6)
 One Month Ahead One Year Ahead
 CAPM Alpha 3-Factor Alpha 4-Factor Alpha CAPM Alpha 3-Factor Alpha 4-Factor Alpha
 Skill Index 0.239 0.118 0.107 0.224 0.104 0.106
 (0.044) (0.022) (0.019) (0.031) (0.025) (0.014)
 Log(Age) -0.034 -0.024 -0.036 -0.019 -0.009 -0.024
 (0.009) (0.006) (0.007) (0.008) (0.005) (0.006)
 Log(TNA) 0.026 0.010 0.011 -0.016 -0.018 -0.011
 (0.005) (0.004) (0.004) (0.003) (0.003) (0.003)
 Expenses -2.977 -7.063 -7.340 -5.793 -9.093 -9.308
 (1.620) (1.004) (0.957) (1.578) (0.917) (0.887)
 Turnover -0.010 -0.047 -0.039 -0.001 -0.041 -0.036
 (0.016) (0.014) (0.010) (0.016) (0.014) (0.010)
 Flow 2.409 1.664 1.519 0.237 0.210 0.227
 (0.151) (0.097) (0.095) (0.119) (0.086) (0.071)
 Load -0.762 -0.093 -0.313 -0.683 0.213 -0.044
 (0.233) (0.144) (0.157) (0.225) (0.129) (0.149)
 Constant -0.030 -0.055 -0.041 -0.043 -0.070 -0.056
 (0.024) (0.018) (0.021) (0.024) (0.019) (0.022)
 Observations 219,338 219,338 219,338 187,668 187,668 187,668
 43