Style investing

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Journal of Financial Economics 68 (2003) 161–199
Style investing$
Nicholas Barberisa,*, Andrei Shleiferb
a Graduate School of Business, University of Chicago, Chicago, IL 60637, USA
b Department of Economics, Harvard University, Cambridge, MA 02138, USA
Received 28 November 2000; received in revised form 11 December 2001
We study asset prices in an economy where some investors categorize risky assets into
different styles and move funds among these styles depending on their relative performance. In
our economy, assets in the same style comove too much, assets in different styles comove too
little, and reclassifying an asset into a new style raises its correlation withthat style. We also
predict that style returns exhibit a rich pattern of own- and cross-autocorrelations and that
while asset-level momentum and value strategies are profitable, their style-level counterparts
are even more so. We use the model to shed light on several style-related empirical anomalies.
r 2003 Elsevier Science B.V. All rights reserved.
JEL classification: G11, G12, G14
Keywords: Style investing; Comovement; Positive feedback; Value; Momentum
1. Introduction
One of the clearest mechanisms of human thought is classification, the grouping of
objects into categories based on some similarity among them (Roschand Lloyd,
1978; Wilson and Keil, 1999). We group countries into democracies and dictator-
ships based on features of political systems within each group. We classify
$We have benefited from the comments of two anonymous referees and from discussions with John
Campbell, Doug Diamond, Eugene Fama, Edward Glaeser, Will Goetzmann, Sanford Grossman, Rafael
La Porta, David Laibson, Sendhil Mullainathan, Geert Rouwenhorst, Lawrence Summers, Jeffrey
Wurgler, and seminar participants at the University of Chicago, Harvard University, London Business
School, Princeton University, the University of Iowa, Wharton, the AFA, and the NBER.
*Corresponding author. Tel.: +1-773-834-0677; fax: +1-773-702-0458.
E-mail address: [email protected] (N. Barberis).
0304-405X/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved.

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
occupations as blue collar or white collar based on whether people work primarily
with their hands or with their heads. We put foods into categories such as proteins
and carbohydrates based on their nutritional characteristics.
Classification of large numbers of objects into categories is also pervasive in
financial markets. When making portfolio allocation decisions, many investors first
categorize assets into broad classes suchas large-cap stocks, value stocks,
government bonds, and venture capital and then decide how to allocate their funds
across these various asset classes (Bernstein, 1995; Swensen, 2000). The asset classes
that investors use in this process are sometimes called ‘‘styles,’’ and the process itself,
namely allocating funds among styles rather than among individual securities, is
known as ‘‘style investing.’’ In this paper, we analyze financial markets in which
many investors pursue style investing.
Assets in a style or class typically share a common characteristic, which can be
based in law (e.g., government bonds), in markets (e.g., small-cap stocks), or in
fundamentals (e.g., real estate). In some cases, the cash flows of assets in the same
style are highly correlated, as with automotive industry stocks, while in other cases,
suchas closed-end funds, they are largely uncorrelated. Some styles are relatively
permanent over the years (e.g., U.S. government bonds), while others come (e.g.,
small stocks) and go (e.g., railroad bonds). One reason for the appearance of a new
style is financial innovation, as when mortgage-backed securities were invented.
Another reason is the detection of superior performance in a group of securities with
a common characteristic: small stocks became a more prominent investment style
following Banz’ (1979) discovery of the small firm effect. Styles typically disappear
after long periods of poor performance, as was the case with railroad bonds.
There are at least two reasons why both institutional and individual investors
might pursue style investing. First, categorization simplifies problems of choice and
allows us to process vast amounts of information reasonably efficiently (Mullai-
nathan, 2000). Allocating money across ten asset styles is far less intimidating than
choosing among the thousands of listed securities. Second, the creation of asset
categories helps investors evaluate the performance of professional money managers,
since a style automatically creates a peer group of managers who pursue that
particular style (Sharpe, 1992). Money managers are now increasingly evaluated
relative to a performance benchmark specific to their style, such as a growth or a
value index.
These benefits of style investing are particularly attractive to institutional
investors, suchas pension plan sponsors, foundations, and endowments, who as
fiduciaries must follow systematic rules of portfolio allocation. Perhaps for this
reason, interest in style investing has grown over the years, paralleling the growth of
institutional investors. Not surprisingly, the financial services industry has responded
to the interest. Most pension fund managers, as well as some mutual fund managers
catering to the needs of individual investors, now identify themselves as following a
particular investment style, such as growth, value, or technology.1
1 As indicated earlier, we use the term ‘‘style investor’’ to refer to investors such as pension plan sponsors
who allocate funds at the style level, rather than at the individual asset level. The term can also be used in a

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
The growing importance of style investing points to the usefulness of assessing its
effect on financial markets and security valuation. This paper presents a simple
model that allows for such an assessment. The model combines style-based portfolio
selection strategies of investors with a plausible mechanism for how these investors
choose among styles. Specifically, we assume that many investors allocate funds
based on relative past performance, moving into styles that have performed well in
the past, and financing this shift by withdrawing funds from styles that have
performed poorly. We also assume that these fund flows affect prices.
These simple assumptions generate a number of empirical predictions, some
already available in the theoretical literature, others entirely new. In our model, style
investing generates common factors in the returns of assets that happen to be
grouped into the same style. These return factors can be completely unrelated to
common factors in cash flows (they exist even if there is no common component to
underlying cash flows) and can be accompanied by higher average returns for reasons
that have nothing to do with risk. When an asset is reclassified into a new style, it
comoves more with that style after reclassification than before, even if the cash-flow
covariance matrix is unchanged. And while style investing increases the correlation
between assets in the same style, it lowers the correlation between assets in different
We also predict a richstructure of style return autocorrelations: positive own-
autocorrelations and negative cross-autocorrelations in the short run, and with the
opposite signs in the long run. The predictions about own-autocorrelations are
shared with earlier models, while those about cross-autocorrelations are more unique
to our framework. Moreover, while asset-level momentum and value strategies are
profitable in our model, as in other models, we make the additional prediction that
style-level momentum and value strategies can be as profitable or even more
profitable than their asset-level counterparts.
Our predictions about time-series autocorrelations reflect the fact that in our
economy, investment styles follow a specific life cycle. The birth of a style is often
triggered by good fundamental news about the securities in the style. The style then
matures as its good performance recruits new funds, further raising the prices of
securities belonging to the style. Finally, the style collapses, either because of
arbitrage or because of bad fundamental news. Over time, the style can be reborn.
We use our model to shed light on a number of puzzling empirical facts. Among
other phenomena, we address the common factors in small stock and value stock
returns that appear unrelated to common factors in cash flows (Fama and French,
1995), the performance of the small stock investment style over time, the poor
returns of value stocks in 1998 and 1999 despite good earnings (Chan et al., 2000),
and patterns of comovement when stocks are added to indices such as the S&P 500.
(footnote continued)
related, but distinct sense to describe money managers who restrict themselves to picking stocks from
within a specific asset style. While both uses of the term are common in practice, in this paper ‘‘style
investor’’ refers only to the investors providing the funds and not to the money managers they hire.

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
Of the two assumptions underlying our predictions—investors’ policy of
allocating funds at the style level and their doing so based on relative past
performance—neither has received much prior attention in the theoretical literature.
The closest papers to our own are De Long et al. (1990a) and Hong and Stein (1999),
in which investors allocate across assets based on absolute past performance. Neither
of these papers studies the effect of classifying assets into styles, nor the effect of
relative rather than absolute performance-chasing.2
In Section 2, we construct a simple model of style investing. Section 3 develops
some of the intuition that lies behind the model’s predictions. In Section 4, we lay out
the model’s implications in a series of formal propositions. Section 5 analyzes two
specific kinds of styles—indices and price-dependent styles—in more detail. Section 6
2. A model of style investing
2.1. Assets and styles
We consider an economy with2n risky assets in fixed supply and a riskless asset,
cash, in perfectly elastic supply and with zero net return. Following Hong and Stein
(1999), we model risky asset i as a claim to a single liquidating dividend Di;T to be
paid at some later time T : The eventual dividend equals
Di;T ¼ Di;0 þ ei;1 þ ? þ ei;T ;
where Di;0 and ei;t are announced at time 0 and time t; respectively, and where
et ¼ ðe1;t; y; e2n;tÞ0BNð0; SDÞ; i:i:d: over time:
The price of a share of risky asset i at time t is Pi;t and the return on the asset between
time t À 1 and time t is3
DPi;t ¼ Pi;t À Pi;tÀ1:
We assume that, to simplify their decision-making, some investors in the economy
group the risky assets into a small number of categories, which we refer to as styles,
and express their demand for risky assets at the level of these styles. In other words, a
style is a group of risky assets that some investors do not distinguish between when
formulating their demand.
To test any predictions that emerge from a model of style investing, it is important
to have a concrete way of identifying styles. One way of doing this is to look at the
products that mutual and pension fund managers offer clients. If money managers
are responsive to their clients, they will create products that correspond to the
categories those clients like to use. The fact that many money managers offer funds
2 Empirical work on styles has advanced more rapidly than theoretical work on the topic. Recent
contributions to the empirical literature include Brown and Goetzmann (1997, 2001) and Chan et al.
3 For simplicity, we refer to the asset’s change in price as its return.

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
that invest in small-cap stocks suggests that ‘‘small stocks’’ is a style in the minds of
many investors. Large stocks, value stocks, growthstocks, and stocks with
in a
particular industry, country, or index are then also all examples of styles.
We build a simple model of style investing. There are two styles, X and Y ; and
each risky asset in the economy belongs to one, and only one, of these two styles.
Risky assets 1 through n are in style X while n þ 1 through 2n are in style Y : For
now, we assume that this classification is permanent, so that the composition of the
two styles is the same in every time period. It may be helpful to think of X and Y as
‘‘old economy’’ stocks and ‘‘new economy’’ stocks, say.4
As a measure of the value of style X at time t; we use PX;t; the average price of a
share across all assets in style X ;
1 X
PX;t ¼
The return on style X between time t À 1 and time t is
DPX;t ¼ PX;t À PX;tÀ1:
Although our model does not require it, we restrict attention to simple cash-flow
covariance structures. In particular, we suppose that the cash-flow shock to an asset
has three components: a market-wide cash-flow factor which affects assets in both
styles, a style-specific cash-flow factor which affects assets in one style but not the
other, and an idiosyncratic cash-flow shock specific to a single asset. Formally, for
iAX ;
ei;t ¼ c f
M M;t þ cS X ;t þ
1 À c2
and for jAY ;
ej;t ¼ c f
M M;t þ cS Y ;t þ
1 À c2
where fM;t is the market-wide factor, fX;t and fY;t are the style-specific factors, and fi;t
and fj;t are idiosyncratic shocks. The constants cM and cS control the relative
importance of the three components. Each factor has unit variance and is orthogonal
to the other factors, so that 81; i ¼ j;
 cov ei;t; ej;t ¼
c2 þ c2 ; i; j in the same style; iaj;
: c2 ; i; j in different styles:
In words, all assets have a cash-flow news variance of one, the pairwise cash-flow
correlation between any two distinct assets in the same style is the same, and the
pairwise cash-flow correlation between any two assets in different styles is also the
4 More generally, a given security may belong to multiple overlapping styles. A small bank stock witha
low price-earnings ratio may be part of a small stock style, a financial industry style, and a value style. A
model capturing suchoverlaps can be constructed and would yield similar but less transparent predictions.

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
The results we derive later do not require that styles be associated with cash-flow
factors. However, if the purpose of styles is to simplify decision-making, it is
plausible that investors might create them by grouping together assets with similar
2.2. Switchers
There are two kinds of investors in our model, ‘‘switchers’’ and ‘‘fundamental
traders.’’ The investment policy of switchers has two distinctive characteristics. First,
they allocate funds at the level of a style. Second, how much they allocate to each
style depends on that style’s past performance relative to other styles. In other words,
each period, switchers allocate more funds to styles with better than average
performance and finance these additional investments by taking funds away from
styles with below average performance. To capture this, we write their demand for
shares of asset i in style X at time t as

NS ¼
ykÀ1 DPX;tÀk À DPY;tÀk
X ;t;
X þ
where AX and y are constants with0oyo1: Symmetrically, switcher demand for
shares of asset j in style Y at time t is

NS ¼
ykÀ1 DPY;tÀk À DPX;tÀk
Y ;t:
Y þ
In words, when deciding on their time t allocation, switchers compare style X’s
and style Y’s return between time t À 2 and time t À 1; between time t À 3 and time
t À 2; and so on, with the most recent past being given the most weight. They then
move funds into the style with the better prior record, buying an equal number of
shares of each asset in that style and reducing their holdings of the other style. The
fact that their demand for all assets within a style is the same underscores our
assumption that they allocate funds at the style level and do not distinguish among
assets in the same style. The parameter y determines how far back they look when
comparing the past performance of styles and hence, the persistence of their flows.
AX and AY can be thought of as their average long-run demand for styles X and Y ;
respectively, from which they deviate based on the styles’ relative performance.5
We think of the relative performance feature in Eqs. (9) and (10) as arising from
extrapolative expectations, whereby switchers think that future style returns will be
similar to past style returns, combined with switchers’ reluctance to let their
allocations to the broadest asset classes – cash, bonds, and stocks – deviate from
preset target levels. Put differently, this second condition means that while switchers
are quite willing to move between different equity styles, they are much less willing to
5 The strategies in Eqs. (9) and (10) are not self-financing. Rather, we assume that switchers are endowed
with sufficient resources to fund their strategies. This allows us to abstract from issues which are not our
main focus here – the long-run survival of switchers, for example – and to concentrate on understanding
the behavior of prices when switchers do play a role in setting them.

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
change their overall allocation to equities. Institutional investors in particular try to
keep their allocations to the three broadest asset classes close to predetermined
targets (Swensen, 2000).
The intuition for how extrapolative expectations and target allocation levels
combine to give the allocations in Eqs. (9) and (10) is straightforward. Holding
everything else constant, an increase in DPX;tÀ1; the most recent past return for old
economy stocks, leads switchers to forecast higher returns on that style in the future
and hence to increase their demand for it at time t: However, since they want to keep
their overall allocation to equities unchanged, they have to sell shares of new
economy stocks, style Y : Therefore, DPX;tÀ1 has an opposite effect on NS in Eq. (9)
and NS in Eq. (10), making demand a function of relative past performance.6
Extrapolative expectations can themselves be motivated by a cognitive bias that
leads investors to put more weight on past returns than they should when forecasting
future returns. For example, people often estimate the probability that a data set is
generated by a certain model by the degree to which the data is representative or
reflects the essential characteristics of the model (Tversky and Kahneman, 1974). A
style which has had several periods of high returns is representative of a style with a
high true mean return, which may explain why impressive past returns raise some
investors’ forecasts of future returns.
The same behavior can also stem from agency considerations. An institutional
investor, suchas the sponsor of a defined benefit plan, may move into styles with
good past performance and out of styles withpoor performance simply became such
strategies are easier to justify ex-post to those monitoring their actions.
Although there is still relatively little work analyzing data on institutional fund
flows, the available research supports the idea that investors move funds towards
styles withstrong past performance. Choe et al. (1999) and Froot et al. (2001), for
example, show that foreign institutional investors tend to buy into countries with
good recent stock market performance.
In reality, investors have many styles to choose from, not just two. Even with
many styles, though, the two-style formulation in Eqs. (9) and (10) remains relevant.
When an investor pours money into a style he deems attractive, he may finance this
by withdrawing funds from just one other style, rather than from many others. One
reason for this is transaction costs. In terms of withdrawal fees and time spent, it is
likely to be less costly to take $10 million away from one money manager than to
take $1 million away from ten of them.
Another, potentially more important, reason is that there is often a natural
candidate style to withdraw funds from, namely a style’s twin style. Many styles
come in natural pairs. Stocks witha highvalue of some characteristic constitute one
style, and stocks with a low value of the same characteristic, the twin. Value stocks
and growth stocks are a simple example. When an investor moves into the growth
style, the value style is a tempting source of funds. First, because of the way twins are
6 The appendix in Barberis and Shleifer (2000) shows more formally how extrapolative expectations
combined witha constraint on asset class allocations leads to demand functions like those in Eqs. (9)
and (10).

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
defined, there is no overlap between them. Second, it is easy to succumb to the
mistaken belief that since a style and its twin are defined as opposites, their returns
will also be ‘‘opposite’’: if prospects for the growth style are good, prospects for the
value style must be bad.
2.3. Fundamental traders
The second investor type in our model is fundamental traders. They act as
arbitrageurs and try to prevent the price of each asset from deviating too far from its
expected final dividend.
We assume that, at the start of each period, fundamental traders have CARA
preferences defined over the value of their invested funds one period later. Our
justification for giving them a short horizon is drawn from Shleifer and Vishny
(1997), who argue that if investors are not sophisticated enough to understand a
money manager’s strategies, they will use short-term returns as a way of judging his
competence and withdraw funds after poor performance. The threat of this
happening forces arbitrageurs to take a short-term view.
Fundamental traders therefore solve
max EFðÀexp½ÀgðW
t þ N 0t
tþ1 À PtÞÞŠÞ;
Nt ¼ ðN1;t; y; N2n;tÞ0;
Pt ¼ ðP1;t; y; P2n;tÞ0;
and where Ni;t is the number of shares allocated to risky asset i; g governs the degree
of risk aversion, EF denotes fundamental trader expectations at time t; and W
t is
time t wealth.
If fundamental traders assume a Normal distribution for conditional price
changes, optimal holdings NF are given by
NF ¼

1Þ À PtÞ;
V F ¼ varFðP
tþ1 À PtÞ;
withthe F superscript in V F again denoting a forecast made by fundamental traders.
2.4. Prices
Given fundamental trader expectations about future prices, which we discuss
shortly, prices are set as follows. The fundamental traders serve as market makers
and treat the demand from switchers as a supply shock. If the total supply of the 2n
assets is given by the vector Q; Eq. (14) implies
Pt ¼ EFðP
tþ1Þ À gV F

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
where NS ¼ ðNS ;
Þ0: In contrast to switchers, who form expectations of
1;t y; N S
future prices based on past prices, fundamental traders are forward looking and base
price forecasts on expectations about the final dividend. One way they may do this is
to roll Eq. (16) forward iteratively, setting
T Þ ¼ EF
T Þ ¼ DT À1;
where Dt ¼ ðD1;t; y; D2n;tÞ0: This leads to
Pt ¼ Dt À gV FðQ À NSÞ À EF
gV F ðQ À NS Þ:
Suppose that fundamental traders set
V F ¼ V ; 8t;
where V has the same structure as the cash-flow covariance matrix SD; so that V ij; its
ði; jÞthelement, is given by
8 s2; i ¼ j
V ij ¼
1; i; j in the same style; iaj
: s2r ; i; j
in different styles
and also that they set
¼ %
N :
Eq. (21) means that while fundamental traders recognize the existence of a supply
shock due to switchers, they are not sophisticated enough to figure out its time series
properties. They simply lean against the shock, preventing it from pushing prices too
far away from expected cashflows.
Our assumptions imply
Pt ¼ Dt À gV ðQ À NSÞ À ðT À t À 1ÞgV ðQ À %
N Þ:
Dropping the non-stochastic terms, we obtain
Pt ¼ Dt þ gVNS:
For the particular form of V conjectured by fundamental traders, this simplifies
further. Up to a constant, the price of an asset i in style X is
X ;t
i;t ¼ Di;t þ gs2ð1 À r þ

1 X
¼ Di;t þ
ykÀ1 DPX;tÀk À DPY;tÀk ;
f ¼
gs2ð1 À r þ

N. Barberis, A. Shleifer / Journal of Financial Economics 68 (2003) 161–199
and the price of an asset j in style Y is

1 X
Pj;t ¼ Dj;t þ
ykÀ1 DPY;tÀk À DPX;tÀk :
We study equilibria in which fundamental traders’ choices of V and %
Eqs. (19) and (21) are reasonable, in that they lead, through Eq. (22), to prices for
which the conditional covariance matrix of returns actually is V ; and for which
unconditional mean switcher demand actually is %
N : Suchequilibria exist for a wide
range of values of the exogeneous parameters SD; AX ; AY ; y; and g:
In a world withonly fundamental traders,
Pt ¼ Dt:
We refer to this as the fundamental value of the assets and denote it PÃ:
Eq. (23) shows that fundamental traders are unable to push prices back to
fundamental values. Their short one-period horizon forces them to worry about
shifts in switcher sentiment and makes them less aggressive in combating mispricing,
a mechanism originally suggested by De Long et al. (1990b). Their inability to wipe
out the influence of noise traders is consistent with the substantial body of empirical
evidence indicating that uninformed demand shocks influence security prices (Harris
and Gurel, 1986; Shleifer, 1986; Kaul et al., 2000; Lamont and Thaler, 2003).
Moreover, if we think of switchers as institutions chasing the best-performing style,
our model is consistent with evidence that demand shifts by institutions in particular
influence security prices (Gompers and Metrick, 2001).
Even if we included more sophisticated arbitrageurs in our model – arbitrageurs
who understand the form of the demand function in Eq. (9) – they might exacerbate
rather than counteract the mispricing. This is the finding of De Long et al. (1990a),
who consider an economy with positive feedback traders similar to our switchers, as
well as arbitrageurs. When an asset’s price rises above fundamental value, the
arbitrageurs do not sell or short the asset. Rather, they buy it, knowing that the price
rise will attract more feedback traders next period, leading to still higher prices, at
which point the arbitrageurs can exit a profit. Since sophisticated arbitrageurs may
amplify rather than counteract the effect of switchers, we exclude them from our
simple model.
2.5. Parameter values
In section 4, we prove some general propositions about the behavior of asset prices
in our economy. To illustrate some of these propositions, we use a numerical
implementation of Eqs. (24) and (26) in which the exogeneous parameters SD; AX ;
AY ; y; and g are assigned specific values.
From Eq. (8), the cash-flow covariance matrix is completely determined by cM
and c
S : We set cM
0:25 and cS
0:5; which gives


Document Outline

  • Style investing
    • Introduction
    • A a model of style investing
      • Assets and styles
      • Switchers
      • Fundamental traders
      • Prices
      • Parameter values
    • Competition among styles
      • Impulse response functions
      • Discussion
    • The behavior of asset prices
      • Comovement within styles
      • Comovement across styles
      • Own- and cross-autocorrelations
      • Asset-level momentum and value strategies
      • Style-level momentum and value strategies
    • Special styles
    • Conclusion
    • Appendix
    • A
    • References