NBER WORKING PAPER SERIES
DO WEALTH FLUCTUATIONS GENERATE TIME-VARYING RISK AVERSION?
MICRO-EVIDENCE ON INDIVIDUALS' ASSET ALLOCATION
Markus K. Brunnermeier
Stefan Nagel
Working Paper 12809
http://www.nber.org/papers/w12809
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
December 2006
We thank John Campbell, Darrell Duffie, Mark Gertler, Francisco Gomes, Joy Ishii, Frank de Jong,
Christian Julliard, Martin Lettau, Chris Malloy, Filippos Papakonstantinou, Jonathan Parker, Jacob
Sagi, Ken Singleton, Ilya Strebulaev, Annette Vissing-Jorgensen, Yihong Xia, Motohiro Yogo, two
anonymous referees, and seminar participants at the CEPR Meetings in Gerzensee, the Five-Star Conference
at NYU, HECER Helsinki, Humboldt University Berlin, IAEEG Trier, London School of Economics,
the Stanford-Berkeley joint Finance seminar, and UC Irvine for useful comments. Brunnermeier acknowledges
financial support from the National Science Foundation and the Alfred P. Sloan Foundation. The views
expressed herein are those of the author(s) and do not necessarily reflect the views of the National
Bureau of Economic Research.
© 2006 by Markus K. Brunnermeier and Stefan Nagel. All rights reserved. Short sections of text, not
to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including
© notice, is given to the source.
Do Wealth Fluctuations Generate Time-varying Risk Aversion? Micro-Evidence on Individuals'
Asset Allocation
Markus K. Brunnermeier and Stefan Nagel
NBER Working Paper No. 12809
December 2006
JEL No. G11
ABSTRACT
We use data from the PSID to investigate how households' portfolio allocations change in response
to wealth fluctuations. Persistent habits, consumption commitments, and subsistence levels can generate
time-varying risk aversion with the consequence that when the level of liquid wealth changes, the
proportion a household invests in risky assets should also change in the same direction. In contrast,
our analysis shows that the share of liquid assets that households invest in risky assets is not affected
by wealth changes. Instead, one of the major drivers of households' portfolio allocation seems to be
inertia: households rebalance only very slowly following inflows and outflows or capital gains and
losses.
Markus K. Brunnermeier
Princeton University
Department of Economics
Bendheim Center for Finance
Princeton, NJ 08540
and NBER
markus@princeton.edu
Stefan Nagel
Stanford University
Graduate School of Business
518 Memorial Way
Stanford, CA 94305
and NBER
nagel_stefan@gsb.stanford.edu
1 Introduction
A growing number of studies in macroeconomics and …nance propose models in which
agents’ relative risk aversion is time-varying. The most popular approach is to use
habit-formation preferences, in particular di¤erence habits, which imply that felicity is
a function of consumption minus a habit. In asset pricing, di¤erence-habit models have
some success in reproducing the mean and counter-cyclicality of asset return risk premia
found in the data (Constantinides (1990); Bakshi and Chen (1996); Campbell and
Cochrane (1999)). In macroeconomics, habits help to jointly match stylized facts about
asset returns and the business cycle (see, e.g., Jermann (1998); Boldrin, Christiano,
and Fisher (2001)). An alternative approach focuses on consumption commitments,
which can have e¤ects similar to those of di¤erence habits, in particular, similar time-
variation in relative risk aversion (Chetty and Szeidl (2005)).
While habit preferences
1
seem to help in matching aggregate data, little is known
yet about whether the predictions of habit-formation models also …t with microdata.
Mehra and Prescott (2003), for example, point out that it is not clear whether investors
actually have the huge time varying counter-cyclical variations in risk aversion postu-
lated by models like Campbell and Co chrane (1999). One of the key implications of
di¤erence habits is that individuals’relative risk aversion should vary with wealth, in
contrast to models with constant relative risk aversion (CRRA). An increase in wealth,
for example, should lead to a temporary decrease in relative risk aversion. This is an
important, but so far untested prediction. In this paper, we provide evidence on this
question from microdata on how households allocate their wealth between risky and
riskless assets.
To clarify the implications of di¤erence habits for asset allocation, we start by study-
ing a simple discrete-time model of portfolio choice. The issues are most transparent if
we take the view that with CRRA preferences— i.e., without habit— the investor would
have su¢ ciently low risk aversion so that she would invest most of her liquid wealth in
risky assets. If we now introduce a di¤erence habit, this increases the desire to hold
riskless assets. Their primary role is to provide su¢ cient …nancial resources to ensure
that future consumption can always be kept above the level of the habit. Hence, opti-
mal riskless asset holdings are tied to the slow-moving habit level and thus relatively
…xed. But liquid wealth ‡uctuates, due to capital gains, income, and consumption. As
a result, when liquid wealth increases, the optimal share of risky assets in the liquid
wealth portfolio increases, and vice versa. E¤ectively, relative risk aversion varies with
wealth.
We test this prediction with household-level panel data from the Panel Study of
1
In the following we often speak, for ease of reference, somewhat loosely of "habit preferences" or
"habit formation", but we mean di¤erence habits (or subsistence levels, or consumption commitments
that lead to similar e¤ects), which lead to time-varying risk aversion. But we exclude ratio habits of
the type used by Abel (1990), because they imply constant relative risk aversion.
1
Income Dynamics (PSID), covering a period of about 20 years. We …rst examine how
changes in liquid wealth a¤ect stock market participation. We …nd that changes in
liquid wealth have a signi…cant positive e¤ect on the probability of stock market entry
and a negative e¤ect on the probability of exit. While this is consistent with time-
varying risk aversion if there are some …xed per-period cost of participation, similar
e¤ects also arise with CRRA preferences. Thus, these tests cannot discriminate between
habit models and models with CRRA preferences.
Unlike for the participation decision, we …nd that changes in liquid wealth essen-
tially play no role in explaining changes in asset allocation for households that partici-
pate in the stock market. We regress the change in proportion of liquid assets invested
in risky assets on the change in liquid wealth and …nd that the positive e¤ect predicted
by di¤erence-habit models is absent. If anything, the e¤ect is slightly negative (but
economically tiny). This is not the result of low statistical power— our coe¢ cients are
quite precisely estimated. Thus, the asset allocation results favor the CRRA model.
Our regressions control for a broad set of household characteristics, including vari-
ables related to the life-cycle and time dummies to eliminate aggregate e¤ects and focus
on cross-sectional variation. We also pay attention to measurement error. We obtain
similar results when we instrument changes in wealth with independently measured
income growth and inheritances, albeit with somewhat lower precision. Moreover, we
also show, theoretically, that it doesn’t matter whether the liquid wealth change is
anticipated, as long as the anticipated change is not entirely riskless. What matters is
that optimal riskless asset holdings are relatively …xed in the short-run, because they
are tied to the habit level, and thus any ‡uctuation in current liquid wealth, whether
previously anticipated or not, leads to a change in the risky asset share.
One possible explanation for the lack of a contemporaneous e¤ect of wealth changes
on asset allocation is that households’asset allocation is governed by inertia. When
capital gains and losses arise, they are not rebalanced, and when in- and out‡ows arise,
they a¤ect mostly the riskless asset (cash) balances. With infrequent or delayed adjust-
ment, the …rst e¤ect would lead to a positive, the latter e¤ect to a negative relationship
between changes in liquid wealth and the liquid risky asset share. Indeed, we …nd that
inertia seems to be the dominant factor determining changes in asset allocation. The
PSID data on purchases and sales of risky assets allows us to reconstruct, approxi-
mately, how the portfolio allocation would look like if households had not bought or
sold risky assets between successive interview dates (assuming that all in- and out‡ows
a¤ect only cash balances). We …nd that actual portfolio allocations are quite close.
The data on purchases and sales are surely noisy and probably a¤ected by forgotten
trades, but the strength of the inertia e¤ect seems to be too big to be just the result
of measurement error.
Given that there seems to be strong inertia, we then check whether a positive
e¤ect of liquid wealth changes on portfolio shares might appear if we allow for slow
adjustment. We regress future changes in the risky asset share on past changes in
2
wealth and …nd a small positive e¤ect. But in terms of economic magnitudes it is
again a very small e¤ect, and it is statistically weak.
Taken together, our …ndings suggest that relative risk aversion does not vary with
wealth changes in the way postulated by habit-formation models. The large variations
in relative risk aversion induced by wealth changes that these theories predict are
evidently absent from microdata. At least with respect to the relationship between
asset allocation and wealth, our evidence suggests that constant relative risk aversion
is a good description of microeconomic behavior. But the CRRA model cannot explain
the large inertia in households’portfolio shares either.
Our evidence on household asset allocation ties in well with some recent work
that …nds it hard to reconcile habit preferences and microdata along other dimensions
of households’ economic choices. Dynan (2000) …nds no evidence that household-
level consumption growth exhibits the patterns predicted by internal habit-formation
models. Gomes and Michaelides (2003) study a life-cycle model of consumption and
portfolio choice and …nd that the introduction of habit formation makes it more di¢ cult
to match empirical regularities in microdata. A recent paper by Sahm (2006) examines
relative risk aversion measures elicited from responses to hypothetical gamble questions
in the Health and Retirement Study and …nds no e¤ect of wealth changes on changes
in relative risk aversion. The …ndings in these studies contrast with Lupton (2003)
who …nds a negative relationship between past consumption levels and current risky
asset holdings, including businesses and real estate, which he argues is consistent with
habit formation, and Ravina (2005), who …nds support for habit formation in credit
card purchases data. The results in our (…rst-di¤erences) regressions are also consistent
with earlier evidence that the cross-sectional relationship between the level of the risky
asset share (Heaton and Lucas (2000); Guiso, Haliassos, and Jappelli (2003)) or elicited
relative risk aversion measures (Barksy, Juster, Kimball, and Shapiro (1997)) and the
level of wealth is essentially ‡at among households that participate in the stock market.
The paper is organized as follows. Section 2 presents a simple portfolio choice
model with habit preferences, our methodology, and the data. Section 3 reports our
main results. In Section 4 we discuss the implications of our results.
2 Theory and Methodology
2.1 Model of Asset Allocation with Habits
We develop a simple model of portfolio choice that illustrates how relative risk aversion
can be time-varying when agents’ preferences exhibit di¤erence habits, subsistence
levels, or similar features. Let time be discrete and consider a single agent with in…nite
horizon. The agent’s wealth at time t is denoted W
t
and is measured before time t
consumption, C
t
. There are two securities the agent can invest in: a risky asset, with
return R
t
and a riskfree asset with constant return R
f
. At time t the agent chooses C
t
3
