Fight Or Flight? Portfolio Rebalancing By Individual Investors

Fight Or Flight? Portfolio Rebalancing By
Individual Investors∗
Laurent E. Calvet, John Y. Campbell and Paolo Sodini
First version: March 2007
This draft: June 2008
Forthcoming in Quarterly Journal of Economics
∗Calvet: Department of Finance, Imperial College London, London SW7 2AZ, UK; Department of Fi-
nance, HEC School of Management, 78351 Jouy-en-Josas, France; and NBER, l.calvet@imperial.ac.uk.
Campbell: Department of Economics, Littauer Center, Harvard University, Cambridge, MA 02138,
USA, and NBER, john_campbell@harvard.edu. Sodini: Department of Finance, Stockholm School of
Economics, Sveavägen 65, Box 6501, SE-113 83 Stockholm, Sweden, Paolo.Sodini@hhs.se. We thank
Statistics Sweden for providing the data. We received helpful comments from Markus Brunnermeier,
René Garcia, David McCarthy, Stefan Nagel, Paolo Zaffaroni, three anonymous referees, and seminar
participants at Bergen, Boston University, the Federal Reserve Bank of Minneapolis, the Financial
Services Authority of the UK, Harvard University, Imperial College, MIT, Oxford University, Pompeu
Fabra, SIFR, the Stockholm School of Economics, the Swedish Financial Supervisory Authority, Uni-
versité Libre de Bruxelles, the University of Helsinki, the University of Venice, the Wharton School,
the 2007 Brazilian Finance Society meeting in Sao Paulo, the 2007 Summer Finance Conference in
Gerzensee, the Fall 2007 NBER Asset Pricing Meeting, and the 2008 AFA meetings in New Orleans.
The project benefited from excellent research assistance by Daniel Sunesson and Sammy El-Ghazaly.
This material is based upon work supported by the Agence Nationale de la Recherche under a Chaire
d’Excellence to Calvet, BFI under a Research Grant to Sodini, the HEC Foundation, the National Sci-
ence Foundation under Grant No. 0214061 to Campbell, Riksbank, and the Wallander and Hedelius
Foundation.

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Abstract
This paper investigates the dynamics of individual portfolios in a unique dataset
containing the disaggregated wealth of all households in Sweden. Between 1999
and 2002, we observe little aggregate rebalancing in the financial portfolio of par-
ticipants. These patterns conceal strong household-level evidence of active rebalanc-
ing, which on average offsets about one half of idiosyncratic passive variations in
the risky asset share. Wealthy, educated investors with better diversified portfolios
tend to rebalance more actively. We find some evidence that households rebalance
towards a higher risky share as they become richer. We also study the decisions to
trade individual assets. Households are more likely to fully sell directly held stocks
if those stocks have performed well, and more likely to exit direct stockholding if
their stock portfolios have performed well; but these relationships are much weaker
for mutual funds, a pattern which is consistent with previous research on the dispo-
sition effect among direct stockholders and performance sensitivity among mutual
fund investors. When households continue to hold individual assets, however, they
rebalance both stocks and mutual funds to offset about one sixth of the passive
variations in individual asset shares. Households rebalance primarily by adjusting
purchases of risky assets if their risky portfolios have performed poorly, and by
adjusting both fund purchases and full sales of stocks if their risky portfolios have
performed well. Finally, the tendency for households to fully sell winning stocks is
weaker for wealthy investors with diversified portfolios of individual stocks.
Keywords: Asset allocation, disposition effect, diversification, participation, port-
folio rebalancing.
JEL Classification: D5, D9, E3, O1.

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1. Introduction
What drives time series variations in the asset allocation of individual investors? How
do households adjust their risk exposure in response to the portfolio returns that they
experience? Are household portfolios characterized by inertia or high turnover? Fi-
nancial theory suggests a wide range of motives for active trading and rebalancing at
the household level. Realized returns on financial assets induce mechanical variations in
portfolio allocation to which an investor is passively exposed. An investor might fight
passive changes by actively rebalancing her portfolio when asset returns are expected to
be time-invariant. Changes in perceived investment opportunities, on the other hand,
might lead the investor to adopt a flight strategy that would amplify the decline in the
share of the worst-performing assets. Furthermore, trading decisions may reflect not
only asset allocation objectives, but also a disposition to hold losing and sell winning
securities (Shefrin and Statman 1985; Odean 1998).
Equilibrium considerations suggest that aggregate flows from the household sec-
tor provide limited and potentially misleading information on individual rebalancing.
Consider for instance an economy in which households own all financial assets. If the
aggregate value of risky securities falls, the average share of risky assets in household
portfolios must necessarily fall as well. Thus, the average individual investor cannot
fight aggregate variations in equity returns. When households have heterogeneous port-
folios, however, there could still be substantial rebalancing at the individual level. For
instance, it is an open question whether households with higher passive losses tend to
buy or sell risky assets.
The empirical investigation of household rebalancing therefore requires high-quality
and comprehensive micro data. Traditional datasets do not meet these requirements and
have unsurprisingly led to conflicting answers on household behavior. Surveys, which
have been widely used in the household finance literature, only report the allocation
of household financial wealth into broad asset classes (e.g. Bilias, Georgarakos and
Haliassos 2005). They permit the analysis of changes in the share of risky assets in
the financial portfolio, but not the computation of active and passive changes. Thus,
surveys cannot tell us whether households attempt to offset passive variations in their
risky share.
Account datasets, such as 401k and brokerage accounts, present a partial view of fi-
nancial wealth and do not permit the computation of the risky share. Research based on
discount brokerage accounts finds evidence of intense trading activity (e.g. Odean 1999;
Barber and Odean 2000), while substantial inertia is observed in 401k accounts (e.g.
Agnew, Balduzzi and Sunden 2003; Ameriks and Zeldes 2004; Choi, Laibson, Madrian
and Metrick 2002, 2004; Madrian and Shea 2001). These seemingly contradictory re-
sults may result from a selection bias in account datasets. For example, households may
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choose a discount broker precisely because they are (over)confident in their ability to
process information and intend to engage in high-frequency trading. And households
may trade less actively in retirement accounts than in other accounts that they control.
The Swedish dataset used in Calvet, Campbell, and Sodini (2007, henceforth “CCS
2007”) allows us to overcome these issues. We assembled data supplied by Statistics
Sweden into a panel covering four years (1999-2002) and the entire country (about
4.8 million households). The information available on each resident is systematically
compiled by financial institutions and corporations, and includes demographic charac-
teristics, wealth portfolio, and income. Our administrative dataset is therefore more
reliable than self-reported datasets, such as surveys. The wealth information is highly
disaggregated and provides the worldwide assets owned by the resident at the end of a
tax year. All financial assets held outside retirement accounts are reported, including
bank accounts, mutual funds and stocks. However the database does not report the
exact date of a sale nor information on asset purchases.
In CCS (2007) we found that household portfolios of risky assets have important
idiosyncratic exposure, accounting for just over half the variance of return for the median
household. While underdiversification causes only modest welfare losses for most of the
population ex ante, the realized returns on household portfolios are heterogeneous ex
post. In this paper we exploit this cross-sectional variation to analyze the determinants
of portfolio rebalancing. The Swedish dataset is well suited for such an investigation
because we can compute the risky share of every household and decompose its changes
into passive and active components.
Our main results are the following. First, we study the dynamics of the risky asset
share among participating households. The equal-weighted share of household financial
wealth invested in risky assets fell from 57% in 1999 to 45% in 2002, a decline that
implies very weak active rebalancing by the Swedish household sector as a whole in
response to the equity bear market of the early 2000’s.
In striking contrast to this
aggregate result, individual households actively rebalanced their portfolios in response to
their own returns. Household-level regressions show that on average, active rebalancing
compensates about one half of idiosyncratic passive variations in the risky share.
We estimate a partial adjustment model for the risky share, with heterogeneous
adjustment speeds, and find that financially sophisticated households holding well di-
versified portfolios adjust more rapidly towards their target risky share. We also find
some evidence that the target risky share increases when households become richer,
consistent with theories of declining relative risk aversion, portfolio insurance, or habit
formation (Brennan and Schwartz 1988; Campbell and Cochrane 1999; Carroll 2000,
2002; Constantinides 1990; Dybvig 1995).
Second, we study patterns of entry to and exit from risky financial markets.
The
overall stock market participation rate increased slightly between 1999 and 2002.
At
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the microeconomic level, household demographics influence entry and exit as one would
expect: financially sophisticated households, with greater income, wealth, and educa-
tion, are more likely to enter, and less likely to exit. We are able to go beyond this
familiar result to see how portfolio characteristics influence exit decisions. We find that
households with initially more aggressive investment strategies are generally less likely
to exit, although poorly diversified households and those with extremely high initial
risky shares are slightly more likely to exit. If we consider mutual funds and directly
held stocks as separate asset classes, we find that households are slightly more likely
to exit mutual fund holding when their mutual funds have performed badly, but much
more likely to exit direct stockholding when their stocks have performed well.
Third, we explore decisions to adjust positions in individual stocks and mutual
funds.
We begin by examining decisions to fully sell positions.
We find that the
absolute value of the return on a stock or fund has a positive effect on the probability
that a household will sell it.
This effect is much stronger for stocks with positive
returns (winners) than for stocks with negative returns (losers), but the asymmetry
is much weaker for mutual funds.
We allow portfolio and household characteristics
to influence the strength of these return effects, and find that wealthy investors with
diversified portfolios of individual stocks have a weaker propensity to dispose of winning
stocks and a stronger propensity to dispose of losers.
We also estimate a rebalancing model for positions that are not fully sold. We find
that the passive change in the share of a stock or mutual fund in the risky portfolio
does explain the active change, but the effect is weaker than we found when we treated
all risky assets as a homogeneous asset class.
Instead of a rebalancing coefficient of
one half, we obtain coefficients of about one sixth which are only slightly greater for
stocks than for mutual funds.
Thus the difference in household decisionmaking with
respect to stocks and mutual funds shows up primarily in full sales rather than in partial
rebalancing decisions.
Finally, we investigate the relation between asset-level trading decisions and port-
folio rebalancing. Households primarily rebalance by using a small number of trading
strategies. When a household is unlucky in the sense that its risky portfolio performs
worse than average, rebalancing is mostly driven by adjustments in purchases of risky
assets. Conversely, when the household is lucky in the sense that its risky portfolio per-
forms better than average, the household rebalances primarily by adjusting full sales of
stocks and purchases of mutual funds.
Both our entry and exit results, and our results on asset-level trading decisions,
are consistent with two branches of the literature. The disposition effect, that investors
hold losing stocks and sell winning stocks, has been documented using account data
on direct stockholdings by Odean (1998) and many others; Frazzini (2006), Goetzmann
and Massa (2008), and Grinblatt and Han (2005) present evidence that this behavior
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may contribute to momentum in stock returns. The literature on mutual fund flows, on
the other hand, finds evidence of performance chasing by individual investors (Chevalier
and Ellison 1997; Frazzini and Lamont 2007; Gruber 1996; Ippolito 1992; Ivkovic and
Weisbenner 2007a; Sirri and Tufano 1998). We find similar patterns using different data
and a different approach for classifying stocks and funds as losers or winners. Dhar and
Zhu (2006) have recently found that households with higher self-reported income are
less prone to the disposition effect in stock trading; our results are broadly consistent
with this, although we find that wealth and portfolio diversification are more relevant
than income in predicting the strength of the disposition effect.
The organization of the paper is as follows. In Section 2 we present some basic facts
about the evolution of risk-taking among Swedish households in the period 1999-2002.
In Section 3, we assess the magnitude of active rebalancing by decomposing household-
level portfolio variations into their passive and active components. In Section 4, we
estimate a partial adjustment model of portfolio risk and use it to ask which types of
households adjust their portfolios more rapidly. This section also asks whether increases
in financial wealth increase households’ desired risk exposure. Section 5 explores entry
and exit decisions and asset-level rebalancing in relation to the disposition effect.
In
Section 6, we link households’ asset-level decisions to their rebalancing strategies. Sec-
tion 7 concludes. An Appendix available online (Calvet, Campbell, and Sodini 2008)
presents details of data construction and estimation methodology.
2. How Has Risk-Taking Changed Over Time?
2.1. Data Description and Definitions
Swedish households pay taxes on both income and wealth. For this reason, the national
Statistics Central Bureau (SCB), also known as Statistics Sweden, has a parliamentary
mandate to collect highly detailed information on the finances of every household in
the country. We compiled the data supplied by SCB into a panel covering four years
(1999-2002) and the entire population of Sweden (about 4.8 million households). The
information available on each resident can be grouped into three main categories: de-
mographic characteristics, income, and disaggregated wealth.
Demographic information includes age, gender, marital status, nationality, birth-
place, education, and place of residence. The household head is defined as the individ-
ual with the highest income. The education variable includes high school and post-high
school dummies for the household head.
Income is reported by individual source. For capital income, the database reports the
income (interest, dividends) that has been earned on each bank account or each security.
For labor income, the database reports gross labor income and business sector.
The panel’s distinguishing feature is that it contains highly disaggregated wealth
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information. We observe the worldwide assets owned by each resident on December
31 of each year, including bank accounts, mutual funds and stocks. The information
is provided for each individual account or each security referenced by its International
Security Identification Number (ISIN). The database also records contributions made
during the year to private pension savings, as well as debt outstanding at year end and
interest paid during the year.
We will refer to the following asset classes throughout the paper. Cash consists
of bank account balances and money market funds. Stocks refer to direct holdings
only. Risky mutual funds are classified as either bond funds or equity funds. The latter
category is broadly defined to include any fund that invests a fraction of its assets in
stocks; that is, balanced funds are counted as equity funds.1 Risky assets include stocks
and risky mutual funds.
Following CCS (2007), we measure a household’s total financial wealth as the sum of
its holdings in these asset classes, excluding from consideration illiquid assets such as real
estate or consumer durables, defined contribution retirement accounts, capital insurance
products that combine return guarantees with risky asset holdings, and directly held
bonds.
Also, our measure of wealth is gross wealth and does not subtract mortgage
or other household debt.
CCS (2007) summarize the relative magnitudes of all these
components of Swedish household balance sheets.
A participant is a household whose financial wealth includes risky assets. In Table
1A, we report summary statistics on the assets held by participating households. To
facilitate international comparisons, we convert all financial quantities into US dollars.
Specifically, the Swedish krona traded at $0.1127 at the end of 2002, and this fixed
conversion factor is used throughout the paper. The aggregate value of risky holdings
declined by about one half during the bear market. Between 1999 and 2002, household
stockholdings fell from $62 to $30 billion, and fund holdings from $53 to $29 billion.
Cash, on the other hand, increased from $49 to $57 billion over the same period.
In the same panel we also report aggregate statistics on stock and fund holdings com-
piled by the SCB and by the Swedish mutual fund association, Fondbolagens Förening
(FF).2 The official statistics are incomplete because the SCB does not specifically report
the aggregate cash holdings of participants and the FF series only start in 2000. The
aggregate estimates obtained with our dataset closely match available official statistics.
In the Appendix, we also match quite closely official aggregate statistics on flows into
stocks and mutual funds. The aggregate flow into an asset class is generally quite mod-
est and never exceeds a few percentage points of the total household wealth invested in
1 The managers of balanced funds periodically rebalance their holdings of cash and risky assets to
maintain a stable risky share. We do not try to measure this form of rebalancing, but treat balanced
funds like any other mutual funds, assuming that they have stable risk characteristics.
2 These statistics can be downloaded at www.scb.se and www.fondbolagen.se.
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the class. Thus, the strong reduction in aggregate risky holdings reported in Table 1A
primarily results from price movements and not from large outflows from the household
sector.
Following CCS (2007), we define the following variables for each household h. The
complete portfolio contains all the stocks, mutual funds and cash owned by the house-
hold. The risky portfolio contains stocks and mutual funds but excludes cash. The
risky share wh,t at date t is the weight of the risky portfolio in the complete portfolio.
Since the risky share is model-free, we use it extensively throughout the paper. The
household’s risky portfolio is also characterized by its standard deviation σh,t, and by
its systematic exposure βh,t and Sharpe ratio Sh,t relative to a global equity benchmark,
the MSCI World Index. The definition and estimation of these quantities are discussed
in the Appendix.
The results presented in this paper are based on households that exist throughout
the 1999-2002 period. We impose no constraint on the participation status of these
households, but require that they satisfy the following financial requirements at the
end of each year. First, disposable income must be strictly positive and the three-year
rolling average must be at least 1,000 Swedish kronor ($113). Second, financial wealth
must be no smaller than 3,000 kronor ($339). For computational convenience, we have
selected a random panel of 100,000 households from the filtered population. Unless
stated otherwise, all the results in the paper are based on this fixed subsample, and
unreported work confirms the strong robustness of the reported estimates to the choice
of alternative subsamples.
2.2. Cross-Sectional Dynamics of Participation and Risk-Taking
Household participation in risky asset markets increased from 61% to 65% between 1999
and 2002, as is reported in Table 1B. The inflow is equal to 20% of nonparticipating
households, or about 8% of the entire population. The outflow is 7% of participants,
or about 4% of the entire household population. These patterns are consistent with
the “participation turnover” documented for US data (Hurst, Luoh and Stafford 1998,
Vissing-Jorgensen 2002b). In Section 5, we will further investigate the microeconomic
and portfolio determinants of entry and exit.
In studying rebalancing in the next two sections, we focus in each year on the large
group of households that maintain participation in risky asset markets throughout the
year.
Between 1999 and 2002, the equal-weighted average risky share wh,t of these
households fell from 57% to 45% (Table 1B). As illustrated in Figure 1A, this lower
mean reflects a downward shift in the cross-sectional distribution of wh,t, which is most
pronounced in the tails.
The downward shift in the risky share translates into a downward shift in complete
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portfolio risk. We illustrate in Figure 1B how the standard deviation of the complete
portfolio, wh,tσh,t, varies with the risky share wh,t. The relation is almost linear and
has similar slopes in all years. Consistent with this finding, we verify in the Appendix
that the standard deviation of the risky portfolio, σh,t, has a stable cross-sectional
distribution over time and is almost a flat function of the risky share.3
These results imply that Swedish households adjust their overall risk exposure pri-
marily by scaling up or down their risky portfolio, passively or actively, rather by altering
its composition. This justifies our emphasis on modelling wh,t in the next two sections.
3. Passive and Active Rebalancing of the Risky Share
3.1. Decomposition of the Risky Share
The change in a household’s risky share is partly determined by the household’s active
trades and partly by the returns on its risky securities. For instance, the risky share
tends to mechanically fall in a severe bear market. For this reason, we now decompose
the change in the risky share between year t and year t + 1, wh,t+1 −wh,t, into a passive
change, driven by the returns on risky assets, and an active change resulting from
household rebalancing decisions. This decomposition is empirically meaningful because
of the comprehensive individual asset information available in our dataset.
The passive risky return 1+rh,t+1 is the proportional change in value of a household’s
risky portfolio if the household does not trade risky assets during the year. It is easily
computed from the initial risky portfolio and asset returns. Let w∗
denote the share
h,j,t
of asset j (1 ≤ j ≤ J) in the risky portfolio. If the investor does not trade between date
t and date t + 1, the risky portfolio value at t + 1 is its value at t times its gross return
1 + rh,t+1 = PJ w∗ (1+r
j=1
h,j,t
j,t+1). We compute returns rj,t+1 excluding dividends, as is
appropriate if households consume dividends rather than reinvesting them, but we verify
in the Appendix that our empirical results are essentially unchanged when dividends
are included in returns.
The passive risky share is the risky share at the end of the year if the household
does not trade risky assets during the year.
It is a function of the initial risky share
and the passive risky return:
wp
= ωp(w
h,t+1
h,t; rh,t+1),
where
w(1 + r)
ωp(w; r) ≡
.
w(1 + r) + (1 − w)(1 + rf)
3 Of course, the stability of average σh,t across risky share bins does not imply that all households
own the same risky portfolio. We will indeed show in Section 3 that there is substantial heterogeneity
in individual portfolio returns.
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The passive change is the change in the risky share during the year if the household
trades no risky assets during the year:
Ph,t+1 = wph,t+1 − wh,t.
It is equal to zero if the investor is initially invested exclusively in cash (wh,t = 0) or
exclusively in risky assets (wh,t = 1). The passive change is a hump-shaped function of
the initial share if r > rf , as investors presumably expect, but a U-shaped function of
the initial share if r < rf , as in our data from the bear market of 2000—2002.
The active change in the risky share, Ah,t+1 = wh,t+1 − wp , is the movement in
h,t+1
the risky share that does not result mechanically from realized returns and thus reflects
portfolio rebalancing. The total change in the risky share can be written as the sum of
the active and passive changes:
wh,t+1 − wh,t = Ph,t+1 + Ah,t+1.
We will also use the analogous decomposition in logs:
ln(wh,t+1) − ln(wh,t) = ph,t+1 + ah,t+1,
where ph,t+1 = ln(wp
)
) respectively
h,t+1
− ln(wh,t) and ah,t+1 = ln(wh,t+1) − ln(wph,t+1
denote the active and passive changes in logs.
These decompositions treat changes in riskless asset holdings, caused by saving,
dissaving, or dividends received on risky assets, as active rebalancing. An alternative
approach would be to calculate the passive risky share that would result from house-
hold saving or dissaving, assumed to take place through accumulation or decumulation
of riskless assets, in the absence of any trades in risky assets. This alternative decom-
position is attractive to the extent that households build up and run down their riskless
balances for liquidity reasons that are unrelated to their investment policies.
We do
not pursue this alternative decomposition further here, but in our structural model of
active rebalancing we do allow for a white noise error that may capture high-frequency
savings effects.
3.2. Rebalancing Regressions
Changes in a household’s risky share tend to be strongly affected by the initial level of
the risky share. One reason for this is purely mechanical: the total change wh,t+1 −wh,t
is bounded between −wh,t and 1 − wh,t in the presence of short sales and leverage
constraints. In addition, there may be behavioral reasons, including sluggish rebalancing
and high-frequency variation in riskless balances, why the risky share may be subject
to transitory shocks and gradual reversion to a long-term mean.
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