Twin Picks: Disentangling the Determinants of Risk-Taking in Household Portfolios

 
Twin Picks: Disentangling the Determinants of Risk-Taking
        in Household Portfolios

        Laurent E. Calvet
        HEC School of Management (Greghec), Paris, France

        Paolo Sodini
        Stockholm Schools of Economics, Stockholm, Sweden

        CR 948-2011
        ISBN : 2-85418-948-5

© Groupe HEC, 78351 JOUY-EN-JOSAS CEDEX, France, 2011

ISBN : 2-85418-948-5
Twin Picks: Disentangling the Determinants
   of Risk-Taking in Household Portfolios∗
                        Laurent E. Calvet and Paolo Sodini

                                   This draft: June 2011
                                 First version: August 2009

  ∗
    Calvet: Department of Finance, HEC Paris, 1 rue de la Libération, 78351 Jouy-en-Josas, France;
and NBER, calvet@hec.fr. Sodini: Department of Finance, Stockholm School of Economics, Sveavägen
65, Box 6501, SE-113 83 Stockholm, Sweden, Paolo.Sodini@hhs.se. We received helpful comments from
Manuel Arellano, Amir Barnea, John Campbell, Jason Chen, Henrik Cronqvist, Marcus Fearnley, René
Garcia, Mariassunta Giannetti, Camelia Kuhnen, Deborah Lucas, Stefan Nagel, Jacques Olivier, Stefan
Siegel, David Thesmar, and participants at Aalto University, CEMFI, Copenhagen Business School,
EDHEC, the Einaudi Institute, the European Central Bank, HEC Paris, the London Business School,
the London School of Economics, LUISS, McGill, the Rotterdam School of Management, the Stockholm
School of Economics, Tilburg University, Université Paris-Dauphine, the University of California at
Berkeley, the University of Lugano, the University of Texas at Austin, the University of Zürich, the
2009 SAET Ischia Conference, the 2010 Annual Meeting of the American Economic Association, the
2010 University of British Columbia Summer Finance Conference, ISBIS 2010, the 2010 Econometric
Society World Congress in Shanghai, the 2010 SIFR Conference on Biology and Finance, and the 2011
Helsinki Finance Summit. We thank Statistics Sweden and the Swedish Twin Registry for providing
the data. The project benefited from excellent research assistance by Krister Ahlersten and Tomas
Thörnqvist. 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,
Riksbank, and the Wallander and Hedelius Foundation.
Abstract

This paper investigates the determinants of financial risk-taking and documents
new facts on the financial wealth elasticity of the risky share in a panel of Swedish
twins. We consider a uniquely comprehensive set of demographic and financial char-
acteristics, and use yearly twin pair fixed effects to control for genes and shared
background. Consistent with cross-sectional evidence (e.g. Carroll 2002) but in
contrast to recent panel studies, we document that financial wealth is the dominant
characteristic driving the asset allocation of individual investors. The average fi-
nancial wealth elasticity of the risky share is positive and strongly significant among
participants, which suggests that individual investors have decreasing relative risk
aversion. Furthermore, the financial wealth elasticity of the risky share itself is
heterogeneous across investors and varies strongly with characteristics; the elastic-
ity decreases with financial wealth and human capital, and increases with habit,
residential real estate, and household size. As a consequence, the elasticity of the
aggregate demand for risky assets to exogenous wealth shocks is close to, but does
not coincide with, the elasticity of a representative investor with constant relative
risk aversion. We confirm the robustness of our results by running time-differenced
instrumental variable regressions, and by controlling for zygosity, lifestyle, mental
and physical health, the intensity of communication between twins, and measures
of social interactions.
Keywords: Asset allocation, communication, genetics, habit formation, human cap-
ital, labor income, leverage, participation, risk-taking, social interactions, twin
study.
JEL Classification: C23, D14, G11.
A large body of portfolio choice theory investigates how a household’s optimal asset al-
location should depend on its main financial and demographic characteristics, including
financial wealth, real estate, human capital, labor income risk and consumption habit (e.g.
Campbell and Viceira 2002). The relation between risk-taking and financial wealth is of
primary importance, because it distinguishes the simplest constant relative risk aversion
(CRRA) specification from increasingly popular alternatives. Borrowing constraints, de-
creasing relative risk aversion (DRRA), as well as related models of habit formation and a
“capitalist” taste for wealth, all imply that richer households should invest a higher pro-
portion of their financial wealth in risky assets.1 These mechanisms also predict that the
financial wealth elasticity of the risky share should vary with household characteristics,
including financial wealth itself, which should have important implications for aggregate
risk-taking.2
       Since portfolio choice theory has major welfare and asset pricing implications, one
would like to know if its normative prescriptions are followed by investors. The empirical
household finance literature provides only partial answers to this question. The evidence
has been based until now on two types of datasets: pooled cross-sections and dynamic
panels. In cross-sections, richer and more educated investors are known to allocate a higher
fraction of financial wealth to risky assets than less wealthy or less educated households
(e.g. Calvet Campbell and Sodini, “CCS” 2007; Carroll 2002).3 In addition, the risky share
has a negative cross-sectional relation to income risk, leverage, real estate holdings, and
internal consumption habit (Cocco 2005, Flavin and Yamashita 2002, Guiso Jappelli and
Terlizzese 1996, Lupton 2002). However, it is unclear whether these characteristics, which
   1
     A positive relation between financial wealth and risk-taking originates from internal habit in Constan-
tinides (1990), external habit in Campbell and Cochane (1999), borrowing constraints in Paxson (1990),
leverage constraints and housing in Cocco (2005) and Yao and Zhang (2005), portfolio insurance in Brennan
and Schwartz (1988), or a “capitalist” taste for wealth in Carroll (2000, 2002).
   2
     The aggregate implications of investor hetorogeneity are investigated in Calvet, Grandmont and Lemaire
(2005), Constantinides (1982), Gollier (2001), Hara, Huang and Kuzmics (2007), Jouini and Napp (2007),
and Rubinstein (1974).
   3
     See Alessie, Hochguertel and van Soest (2002), Ameriks and Zeldes (2004), Banks and Tanner (2002),
Bertaut and Starr-McCluer (2002), Campbell (2006), Cohn et al. (1975), Eymann and Börsch-Supan (2002),
Friend and Blume (1975), Guiso and Jappelli (2002), King and Leape (1987, 1998), Palia, Qi and Wu (2009),
Perraudin and Sørensen (2000), and Vissing-Jorgensen (2002b).

                                                     1
typically explain less than 10% of the cross-sectional variance of the risky share, are driving
the asset allocation of individual investors or are instead cross-sectional proxies for latent
traits such as ability, genes, risk aversion, or upbringing.
      Dynamic panels offer a possible solution to this identification problem because they
permit to relate time variations in a household’s risky share to time variations in financial
wealth and other characteristics while controlling for stable attributes (e.g. Chiappori
and Paiella 2008). One difficulty, however, is that the portfolio allocation dynamics may
reflect the arrival of new information and investment opportunities, and not just changes
in characteristics. The researcher also needs to control for endogeneity problems caused by
household inertia. Brunnermeier and Nagel (2008) instrument financial wealth with income
growth and inheritance receipts and find no link between wealth and risk-taking. CCS
(2009) use returns on household financial portfolios as instruments, and report instead a
positive relation between financial wealth and the risky share. The results from dynamic
panels are therefore sensitive to the validity of the instruments, and the link between
household characteristics and the risky share remains an open empirical question.
      In this paper, we consider a new estimation strategy based on the comparison of the
financial portfolios held by twins. Twin comparisons are a true and tried method for
disentangling family fixed effects from individual characteristics. They can be conducted in
a given year and do not require the use of instruments. In labor economics, twin data has
been frequently used to disentangle the relative effect of education and ability on earnings.4
A similar approach seems fruitful for household finance.5
      Our analysis is based on a high-quality and uniquely comprehensive panel containing
the disaggregated portfolios and detailed characteristics of twins in Sweden. We begin by
considering twins who both participate in risky asset markets, and regress their household
  4
     See for instance Ashenfelter and Krueger (1994), Ashenfelter and Rouse (1998), Behrman and Rosen-
zweig (2002), Behrman and Taubman (1989), Bronars and Grogger (1994), and Taubman (1976). Adoptees
are considered in the work of Björklund, Lindahl, and Plug (2006), Björklund, Jäntti, and Solon (2007),
Plug and Vijverberg (2003), and Sacerdote (2002, 2007). Other contributions on the interplay between
genetics and economics include Guiso, Sapienza, and Zingales (2009) and Murray (2002).
   5
     More generally, data on siblings can be useful in household finance, as exemplified by the work of
Grinblatt, Keloharju, and Linnainmaa (2010) on the link between IQ and stockmarket participation.

                                                  2
risky shares on yearly twin pair fixed effects and observable characteristics. The yearly
twin pair fixed effects, which are our main innovations, capture the common impact of
genes, shared background, common upbringing, expected inheritance and stock market
performance, among others, on the asset allocation of each twin.
       Financial wealth is by far the most important observable characteristic in all regressions.
The conclusions of Carroll (2002) are therefore robust to the inclusion of yearly twin pair
fixed effects. The average financial wealth elasticity of the risky share is significantly
positive and measured to be close to 02 for all the specifications and estimation methods
considered in this paper. We view this result as strong evidence that households exhibit
decreasing relative risk aversion.
       Several other characteristics are also significant. Leverage, entrepreneurship, household
size, and a measure of internal habit tend to reduce the risky share. These results are
consistent with financial theory, and confirm earlier cross-sectional evidence and the pooled
cross-sections that we estimate as a benchmark. Across specifications, human capital and
income risk are usually consistent with the predictions of portfolio choice models, but with
mixed significance levels. Educational attainment, which is positively and significantly
related to the risky share in cross-sections, becomes insignificant in the twin regressions;
risk-tolerant individuals may have a propensity to choose a high level of education, as in
Guiso and Paiella (2005),6 but education seems to have no causal impact on the risky
share.
       The adjusted 2 of the risky share regression is 19% on the set of identical and fraternal
twins, and reaches 40% on identical twins who communicate often with each other. These
estimates are large for household finance, and contrast with the 11% adjusted 2 we report
for pooled cross-sections with yearly fixed effects. Twin pair fixed effects are quantitatively
important, which we attribute both to the genetic nature of risk-taking (e.g. Barnea,
Cronqvist and Siegel 2010; Cesarini et al. 2009, 2010) and to the impact of common
background and upbringing. We do not attempt to disentangle between these explanations
   6
    Guiso and Paiella use a question from the Bank of Italy’s Survey of Household Income to estimate risk
aversion, and show that risk-tolerant investors tend to invest more in education.

                                                   3
in the paper because a growing literature in experimental psychology documents substantial
interactions between nature and nurture.7 We report, however, that communication has
a major impact on adjusted 2  suggesting that yearly twin pair fixed effects are unlikely
to be purely driven by genes. Furthermore, financial and demographic characteristics are
nearly as important as twin pair fixed effects; financial wealth and observed characteristics
explain at least 40% of the predicted variation (or 8% of the overall variation) of the risky
share in all specifications. Individual investors do not simply select a predetermined level of
the risky share, but aggressively respond to their financial and demographic circumstances,
often in accordance with the prescriptions of portfolio theory.
      Asset allocation models predict not only the level of the risky share, but also its fi-
nancial wealth elasticity. For instance, habit formation implies that the elasticity should
be decreasing with financial wealth and increasing with habit. The financial wealth elas-
ticity of the risky share can therefore be used to discriminate between utility models. To
the best of our knowledge, however, no micro-level evidence has been available until now,
presumably for lack of reliable data and identification methods. In this paper, we report
that the financial wealth elasticity of the risky share is heterogeneous across households
and sharply decreases with financial wealth. The elasticity declines from 0.3 in the bottom
wealth quartile to 0.1 in the top quartile, even when leverage and a large set of characteris-
tics are included as controls. Our various findings show that the risky share is an increasing
and concave function of financial wealth.
      The financial wealth elasticity of the risky share also decreases with human capital, but
increases with habit, residential real estate and family size. These empirical regularities
provide strong support for habit formation (Campbell and Cochrane 1999, Constantinides
1990) and nonhomothetic utility of the Stone Geary type (e.g. Carroll 2000; Wachter and
Yogo 2010). Residential real estate and family size can be viewed as commitments to
future expenditures (e.g. Chetty and Szeidl 2007, Fratantoni 2001, Grossman and Laroque
1990) or as proxies for consumption habit, which intuitively explains their impacts on the
elasticity. Until now, however, the portfolio choice literature has not directly related family
  7
      See Ridley (2003) for an overview.

                                                4
composition or real estate to the financial wealth elasticity of the risky share, and we
provide new facts that this literature may seek to match.
   Economic theory suggests that the elasticity has key implications for the aggregate
demand for risky assets and security pricing. We use our micro estimates to compute how
the aggregate demand for risky assets responds to exogenous changes in household financial
wealth. When shocks are positive and concentrated on low and medium wealth households,
their incremental demand for risky assets is substantial because their risky shares, which
are initially low, are highly elastic. In proportional terms, aggregate risky wealth grows
almost as quickly as aggregate financial wealth. When instead the wealth shocks are
concentrated on the richest households, which have low elasticities and high initial risky
shares, aggregate risky wealth grows only slightly faster than aggregate financial wealth.
Overall, the elasticity of the aggregate demand for risky assets to a homogenous wealth
shock is estimated to be slightly above unity. Heterogeneous individual elasticities thus
imply that the aggregate demand for risky assets is close to, but does not coincide with,
the demand of a CRRA representative investor.
   We also use the twin dataset to investigate the decision to participate in risky asset
markets. The probability of owning risky assets increases with financial wealth and human
capital, and decreases with habit, leverage, and income risk. Analogous to the risky share
results, educational attainment, which is significant in the pooled regression, becomes
insignificant when we control for twin pair fixed effects. We use these results to recompute
the aggregate elasticity of the demand for risky assets when participation turnover is taken
into account.
   The paper provides a number of robustness checks. We show that our results are unlikely
to be contaminated by individual fixed effects specific to each twin in a pair, such as
differences in risk aversion. Since drinking and smoking habits have been related to risk
tolerance (e.g. Barsky et al. 1997), one strategy is to expand the regressions by including
physiological and lifestyle variables on each twin. Another strategy is to dynamically
estimate the financial wealth elasticity of the risky share by following households over

                                             5
time, excluding twin pair fixed effects from consideration.8 Under all specifications, the
elasticity has an average of about 02 and decreases with financial wealth while the impact of
other characteristics is qualitatively invariant, which indicates that individual fixed effects
are not a major source of concern. We also check that our findings are unlikely to be
driven by a reverse causality between the risky share and financial wealth by considering
an appropriate lead-lag structure. Finally, we verify that our results are robust to including
measures of social interactions; investors do not simply imitate the behavior of others but
do respond to their individual financial circumstances.
         The organization of the paper is as follows. Section I presents the Swedish twin dataset.
In Section II, we report cross-sectional and twin regressions of the risky share on financial
wealth and other characteristics. Section III investigates the empirical properties of the
financial wealth elasticity of the risky share. Section IV reports robustness checks and
dynamic estimates of the elasticity. In Section V, we investigate the participation decision
in the presence of twin pair fixed effects, and compute the aggregate financial wealth
elasticity of the risky share. Section VI concludes. An Appendix, available online (Calvet
and Sodini 2011), presents details of data construction and estimation methodology.

                                    I.   Data and Definitions

A.        The Swedish Dataset

          Swedish Twin Registry. The Swedish Twin Registry (STR), which is administered by
the Karolinska Institute in Stockholm, is the largest twin database in the world. It was
founded to study the impact of smoking and alcohol consumption on the health of Swedish
residents. The STR consists of two surveys: SALT for twins born between 1886 and 1958,
and STAGE for twins born between 1959 and 1990. The SALT survey was conducted
between March 1998 and March 2002, and STAGE between May 2005 and March 2006.
Response rates for those eligible (still alive and living in Sweden) were 65% for the 1886-
     8
   While CCS (2009) estimate an adjustment model of portfolio rebalancing, the dynamic section of this
paper focuses on a slightly more parsimonious, reduced-form specification.

                                                   6
1925 cohort, 74% for the 1926-1958 cohort, and 59.6% for the 1959-1990 cohort.
       The STR provides the zygosity of each pair (fraternal or identical),9 and the intensity
of communication between the twins. We have also obtained for each twin in SALT the
following physiological and lifestyle variables: weight, height, blood pressure, self-assessed
physical health, mental health, smoking habits, and alcohol and coffee consumption. We
refer the reader to Lichtenstein et al. (2006) and Pedersen et al. (2002) for detailed
descriptions of the STR.

Swedish Wealth Registry. The STR allows us to identify twin pairs in the Swedish Wealth
Registry, which we have used in earlier work (CCS 2007, 2009, 2009). Statistics Sweden
has a parliamentary mandate to collect highly detailed information on the household fi-
nances of all Swedish residents. The information available on each resident can be grouped
into three main categories: demographic characteristics, income, and disaggregated wealth.
       Demographic information includes age, gender, marital status, nationality, birthplace,
education, and municipality. The education variables consist of high school and post-high
school dummies.
       The income data comprises disposable income, as well as income reported by individual
source. For capital income, the database reports the interest or dividend that has been
earned on each bank account or each security. For labor income, the database reports
gross labor income and business sector.
       The wealth data includes the worldwide assets owned by the resident on December 31
of each year, including bank accounts, mutual funds and stocks. Holdings are provided
for each account or each security. The database also records debt outstanding at year end
and contributions made during the year to private pension savings. The wealth data was
collected because Sweden levied a wealth tax until 2007. In order to collect this tax, the
government assembled records of financial assets, mutual funds, and real estate down to
the individual security and property level, using statements from financial institutions that
   9
    Zygosity is determined by DNA markers or, when not available, by responses to the question: “During
your childhood, were you and your twin partner alike as two peas in a pod or not more alike than siblings
in general?”. The answer to this question has been shown to be consistent with DNA evidence in 99% of
pairs.

                                                   7
were verified by taxpayers.
       All tax returns are filed individually in Sweden since the tax code does not allow the
possibility of joint filing. In particular, each resident declares the fraction of the household’s
assets that it owns. Statistics Sweden provides a household identification number for
each resident, which allows us to group residents by living units.10 Because financial
theory suggests that investment decisions should be studied at the family level, the results
presented in this paper are based on households with an adult twin during the 1999-2002
period. In unreported work, we have verified that our main results are qualitatively similar
on the subsample of twins living alone.
       Throughout the paper, we group households with an adult twin into pairs, and conduct
our investigation on the set of pairs for which all characteristics are available. We impose
no constraint on the risky asset market participation status of these households, but require
that both households in a pair satisfy the following financial requirements at the end of
each year. First, disposable income must be at least 1,000 Swedish kronor ($113) each
year. Second, the value of all financial assets must be no smaller than 3,000 kronor ($339).
Third, the household head, defined as the individual with the highest income, must be at
least 25 years old.

B.      Definitions and Construction of Variables

We will use the following definitions throughout the paper. Cash consists of bank account
balances and money market funds. Risky financial assets include directly held stocks and
risky mutual funds. For every household , the risky portfolio is defined as the portfolio of
risky financial assets. We measure financial wealth  at date  as the sum of holdings in
cash, risky financial assets, capital insurance products, and directly held bonds, excluding
from consideration illiquid assets such as real estate or consumer durables, and defined
contribution retirement accounts. Also, our measure of wealth  is gross financial wealth
and does not subtract mortgage or other household debt. Residential real estate consists of
  10
    In order to protect privacy, Statistics Sweden provided us with a scrambled version of the household
identification number.

                                                   8
primary and secondary residences, while commercial real estate consists of rental, industrial
and agricultural property. The leverage ratio is defined as a household’s total debt divided
by the sum of its financial and real estate wealth.
   The risky share  is the proportion of risky assets in the household’s portfolio of
cash and risky financial assets. A participant is a household with a positive risky share.
A variety of habit formation models imply that the risky share is effected by lagged values
of consumption, either by the household itself or by a peer group. Since we do not observe
individual consumption, we proxy the internal habit of household  at date  by its average
disposable income in years  − 2  − 1 and , excluding private pension savings from
consideration. Similarly, we proxy the external habit by the three-year average household
income in household 0 s municipality. The twin sample is excluded from the households
sampled in each peer group.
   We define the gender index of economic power as the share of the household’s gross
financial and real estate wealth owned by adult men. The gender index ranges between
zero and one. It is close to unity if gross wealth is primarily controlled by men.

Human Capital. We estimate the labor income specification used in Cocco, Gomes and
Maenhout (2005):
                            ln( ) =  + 0  +   +  

where  denotes real income in year ,  is a household fixed effect,  is a vector of
characteristics,   is an idiosyncratic permanent component, and  is an idiosyncratic
temporary shock distributed as N (0 2 ). The permanent component   follows the
random walk:
                                      =  −1 +   

where   ∼ N (0  2 ) is the shock to permanent income in period . The Gaussian
innovations  and   are white noise and are uncorrelated with each other at all leads
and lags.
   We estimate the income process of each household on its yearly series between 1993

                                               9
and 2002 by following the procedure of Carroll and Samwick (1997). Let  denote
the difference between the income growth, ln( −1 ) and the fitted value, 0 ( −
−1 ) We measure the systematic risk in income by computing the beta coefficient  
of the innovation  relative to historical excess returns on the risky portfolio. Detailed
descriptions of the labor income specification and estimation methodology are provided in
the appendix.
     Expected human capital is defined by:

                                   
                                   X                 E (+ )
                                          +                
                                   =0
                                                      (1 + )

where  denotes the difference between 100 and the age of household  at date , and
 + denotes the probability that the household head  is alive at  +  conditional
on being alive at  We make the simplifying assumption that no individual lives longer
than 100. The survival probability is estimated using the life table provided by Statistics
Sweden. The interest rate is set equal to  = 3% per year. We have verified that our results
are strongly robust to alternative choices of .
     We use the following variables throughout the remainder of the paper: (a) expected
human capital expressed in year  prices; (b) the variance of the transitory component of
real income,  2 ; (c) the variance of the permanent component of real income,  2 ; and
(d) the beta of income growth relative to the risky portfolio,   .

C.    Summary Statistics

In the remainder of this section and in sections II to IV, we consider pairs in which both
twins participate in risky asset markets. The participation decision is investigated in section
V.

                               [Insert Table 1 about here]

     Table I reports summary statistics for the set of participating twins, as well as for a
random sample from the population of participating households. For the twin sample, the

                                                10
education, entrepreneur and unemployment dummies refer to the twin in the household,
while all other characteristics are computed at the household level. Our estimates of in-
come risk, which are based on the Carroll and Samwick (1997) OLS regressions, can take
negative values, as has been observed in U.S. data (e.g. Campbell and Viceira 2002, ch.
7). To facilitate international comparisons, we convert all financial quantities into U.S.
dollars. Specifically, the Swedish krona traded at $0.1127 at the end of 2002, and this fixed
conversion factor is used throughout the paper. A household in the twin sample selects on
average a slightly higher risky share, has slightly higher financial and real estate wealth,
is slightly more educated, is more likely to be unemployed and is less leveraged than the
average Swedish household. Differences in the means across the two samples are modest,
except for the leverage ratio. The correlation of characteristics within twin pairs is positive,
ranging from 3% for permanent income risk to 48% for human capital.
   In the Appendix, we report summary statistics separately for identical and fraternal
twins. Pairwise correlations are generally higher for identical twins, which suggests that
the risky share and characteristics may have a genetic component. We also report the
results of an ACE decomposition, an additive model of genetic effects that has been widely
employed in medicine and is now starting to be used in household finance (e.g. Barnea,
Cronqvist and Siegel 2010; Cesarini et al. 2009, 2010). The cross-sectional variance of
a characteristic is decomposed into a genetic component, a common component, and an
idiosyncratic component, which are assumed to be uncorrelated and are conveniently es-
timated using the pairwise correlations of identical and fraternal twins. The risky share,
financial wealth and most characteristics have a substantial genetic component according
to ACE. We interpret this result with caution, however, since ACE does not take into
account interactions between nature and nurture.

                                              11
II.   What Drives the Risky Share?

A.    Theoretical Motivation

      We briefly review some of the main implications of portfolio choice theory for the risky
share of a utility-maximizing agent. When the agent has constant relative risk aversion
                                                                    ∗ =  (  )
(CRRA) and is financially unconstrained, the target risky share is     

where   is the agent’s coefficient of relative risk aversion, and  and   are, respectively,
the portfolio’s Sharpe ratio and standard deviation of excess returns.
     By contrast, if the agent has decreasing relative risk aversion, the optimal risky share
increases with financial wealth. DRRA is frequently modelled by including a subsistence
level in the CRRA utility function, as in the Stone Geary specification and closely re-
lated models of habit formation (Campbell and Cochrane 1999) and the “capitalist spirit”
(Carroll 2000). The optimal risky share is then of the form:
                                                  µ             ¶
                                            ∗          
                                   =       1−                                         (1)
                                                        

where  is a subsistence level or habit, and  is a positive constant. In the internal
habit model of Constantinides (1990) and the external habit specification of Campbell
and Cochrane (1999),   represents the cost of supporting the habit over an infinite
horizon. The risky share (1) has the following testable implications.

Implication 1. The risky share increases with financial wealth.

Implication 2. The risky share decreases with the subsistence level or habit  

In the rest of the paper, we do not attempt to distinguish between subsistence and habit,
and we will generically refer to  as the habit parameter.
     The financial wealth elasticity of the risky share is defined as:

                                                    ln( )
                                          =                                               (2)
                                                      

                                                   12
where  = ln( ) denotes the household’s log financial wealth. The elasticity   has
important implications for the aggregate demand for risky assets and asset pricing models,
as will be seen in Section IV. The elasticity   is zero for a CRRA investor facing no
market frictions.
   When the risky share satisfies (1), its financial wealth elasticity is:

                                                    
                                 =            =                                      (3)
                                         1 −     −  

where  =    denote the present value of the cost of maintaining the habit
relative to financial wealth.

Implication 3. The financial wealth elasticity of the risky share is positive, decreases with
financial wealth, and converges to zero when financial wealth is large.

Implication 4. The financial wealth elasticity of the risky share increases with habit

   Many other mechanisms can theoretically affect risk-taking, such as background risk,
real estate holdings, family composition, borrowing constraints, and other market frictions.
We will review the predictions of these theories as we discuss the results of our regressions
in the next sections.
   Testing the predictions of portfolio choice models is in principle complicated by the fact
that households have heterogeneous preferences. Table I and the ACE decomposition in the
appendix confirm that consistent with earlier studies, twins have closer preferences than
two randomly selected households. This proximity has multiple origins, such a common
genetic make-up, communication between twins and shared family background, among
many others. We will now use the twin dataset to analyze the empirical determinants of
risk-taking while controlling for their common pair fixed effects.

                                                  13
B.    Financial Wealth and Variance Decomposition

      For every twin pair  we specify the risky share of twin  0 s household,  ∈ {1 2} at
date  by:

                          ln(1 ) =  + 1 +  0 1 + 1                  (4)

                          ln(2 ) =  + 2 +  0 2 + 2 

The intercept  is a fixed effect specific to twin pair  in year . It captures the common
impact of time, stock market performance, genes, shared background, common upbringing,
and expected inheritance, among others, on the twin’s risky shares. The elasticity  is
assumed to be the same for all households. In Section III, we will consider a more flexible
specification in which the financial wealth elasticity of the risky share can vary across pairs.

                                 [Insert Table II about here]

     In Panel A of Table II, we report the within estimates of the linear panel (4) computed
on the set of all twins. The financial wealth elasticity of the risky share  is highly significant
and estimated at 0196 in the absence of controls (first set of columns), 0224 when we
include real estate, leverage, human capital, income risk and habit (second set of columns),
and 0223 when we add demographic characteristics (third set). As a benchmark, we also
run regressions with yearly fixed effects  on the same set of households (fourth set of
columns). The regressions reveal that there is a strong and stable positive link between
financial wealth and the risky share. Since we control for the leverage ratio, this relation
cannot be attributed to cash-in-advance constraints alone, and indicates that households
exhibit decreasing relative risk aversion. In Sections III and IV, we will provide further
evidence that financial wealth has a causal impact on the risky share and its elasticity. For
expositional convenience, we will discuss the impact of characteristics other than financial
wealth in section II.C.
     The predicted variation 2 =  ( +  +  0  ) (ln  ) denotes the
fraction of the cross-sectional variation of the log risky share explained by twin pair fixed

                                                  14
effects, financial wealth, and other characteristics. The adjusted 2 coefficient of the
panel regression (4) consistently estimates 2  It is equal to 180% when financial wealth is
the only characteristic, and 191% when all characteristics are included. These estimates
are high for households finance regressions and improve on the 115% adjusted 2 of the
pooled cross-section. These findings provide a first indication that twin pair fixed effects
are quantitatively important.
       In Panel B of Table II, we report the following decomposition of the predicted variation:

                                     2 = 2 + 2 +  2 + 2 + 2                                             (5)

where  2  2  and  2 denote, respectively, the contributions of twin pair fixed effects,
financial wealth, and other characteristics. The decomposition also includes two cross-
terms: the rescaled covariance of twin pair fixed effects and observable characteristics,
   and the rescaled covariance of financial wealth with other characteristics,   .11
       The contribution of the twin pair fixed effect,  2  ranges from 91% to 96% across
specifications. Twin pair fixed effects are thus important and explain the high adjusted
2 of twin regressions. The contribution of observable characteristics,  2 + 2  + 2  is
nearly equal to the contribution of the yearly twin pair fixed effects, ranging from 69% in
the first set of columns to 91% in the third set of columns. Thus, while genetic and other
family fixed effects are important, individual financial circumstances also play a major
role in explaining the risk-taking behavior of households, as will be further investigated in
section II.D.
       Financial wealth is by far the most important observable characteristic. As can be
seen in the second and third set of columns, its contribution  2 to the cross-sectional
  11
    Specifically, we write 2 =  ( ) (ln  )  2 =  ( ) (ln  )  2 =
 ( 0  ) (ln  ) and define the cross-terms by  =  ( ;  +  0  ) (ln  )
and  =  ( ;  0  ) (ln  ) Since the regression residuals

                                   = ln( ) −  −  0  =  + 

satisfy (1 ; 2 ) =  ( ) we estimate 2 by the ratio of the sample pairwise covariance of the
regression residuals to the sample variance of the risky share. We estimate 2 , 2  and  by their sample
equivalents, and infer from (5) an estimate of the covariance  .

                                                             15
variance of the risky share is close to 90%, while the contribution of all the other observable
characteristics,  2 , ranges between 12% and 16%. Furthermore, the cross-terms are quite
small, and to save space will not be reported in the next tables. Thus, twin pair fixed
effects and financial wealth contribute almost equally to the cross-sectional variation of
the risky share, and largely dominate the contribution of other characteristics. Several
characteristics other than financial wealth are nonetheless significant, as is now discussed.

C.    Impact of Characteristics Other Than Financial Wealth

      We now analyze the investment impact of observable characteristics other than finan-
cial wealth, as reported in Panel A of Table II.

Real Estate Wealth and Leverage. Residential real estate is not significantly related to the
risky share in twin pair fixed effects regressions (second and third set of columns). From
a theoretical perspective, residential real estate plays an ambiguous role, since it is both
a hedge against future rental costs and a speculative investment. Neither effect dominates
empirically in the presence of yearly twin pair fixed effects.
     Moreover, when we consider only yearly fixed effects (last set of columns), we obtain
that households with substantial residential real estate holdings tend to also select large
risky shares. The twin and cross-sectional regressions thus yield contrasting results on
the link between housing and financial risk. One possible interpretation is that residential
real estate acts a cross-sectional proxy for risk tolerance. A complementary view is that
residential real estate and financial investments are strongly tied to upbringing. Investors
who were born in wealthy families and grew up in a “culture of ownership” may have
a stronger propensity to hold risky financial and residential real estate assets than other
investors.
     The commercial real estate wealth elasticity of the risky share is −0005 which is of the
opposite sign as and about 40 times smaller than the financial elasticity . This link holds
under both types of fixed effects. Unlike residential real estate, commercial real estate
holdings crowd out investment in risky financial assets, as in the models of Cocco (2005),

                                              16
Flavin and Yamashita (2002), and Yao and Zhang (2005).
   Indebted households select conservative portfolios, whether or not one controls for twin
pair fixed effects. This result confirms both portfolio choice theory (e.g. Grossman and Vila
1992, Paxson 1990, Teplá 2000) and earlier cross-sectional evidence (e.g. Guiso, Jappelli,
and Terlizzese 1996). A leveraged household worries that it may be unable to borrow in
the future and may incur a severe reduction in consumption, which encourages it to adopt
a more conservative asset allocation.

Human Capital and Income Risk. Expected human capital has a positive but insignificant
coefficient in the presence of yearly twin pair fixed effects. The theoretical models of Bodie,
Merton and Samuelson (1992), Cocco, Gomes and Maenhout (2005), and Wachter and Yogo
(2010) indicate that if future income can be viewed, at least partly, as a nontraded bond,
households with substantial human capital may tilt their financial portfolios toward risky
financial assets. We find weak support for this mechanism in Table II, possibly because
of measurement error. We will see that the human capital coefficient becomes larger and
more significant when we consider only identical twins.
   Income risk has a negative relation to the risky share. In the twin regressions, the coef-
ficient of transitory income risk is significant at the 10% level, while permanent income risk
is insignificant. In the pooled cross-sections, the income risk coefficients are also negative
and strongly significant, consistent with Palia, Qi and Wu (2009) and Vissing-Jørgensen
(2002b).
   A high beta of household income relative to the risky portfolio return is associated
with a high risky share, but the coefficient is insignificant. The effect of beta remains
insignificant if we exclude permanent and transitory income risk from the set of regressors,
or if we regress risky share only on financial wealth and the beta coefficient. Table II thus
provides weak confirmation of the findings of Massa and Simonov (2006).
   Entrepreneurs tend to invest less aggressively than the rest of the population, as in
Heaton and Lucas (2000). As theory suggests, private business risk tends to crowd out
financial risk in household portfolios. Unemployed residents tend to invest less aggressively

                                             17
in the stock market, consistent with their high liquidity needs and earnings uncertainty
compared to the rest of the population.

Habit. The measure of internal habit has a negative impact on the risky share: households
with higher average income (a proxy for own consumption habit) are less prone to financial
risk. Lupton (2002) obtained a similar result in a U.S. cross-section, the 1994 Panel Study
of Income Dynamics. Overall, the financial wealth and internal habit coefficients are both
consistent with Implications 1 and 2 of habit formation models even when one controls for
yearly twin pair fixed effects.12
       The external habit coefficient is insignificant, suggesting that income differences across
Swedish municipalities provide only limited explanations for differences in asset allocation.
Our results are based on a short history and should be interpreted with caution. External
habit-formation models are primarily used to explain time series variations in asset returns
and risk premia, not the cross-section of the risky share.
       The estimates of Table II can be readily interpreted in the context of habit formation
models. Since the average elasticity  is about 02 we infer from (3) that the present value
of maintaining the habit relative to financial wealth,  , is approximately (1 + ) ≈ 16
Since average financial wealth represents about 32 of three-year average disposable income
(Table I), the habit also amounts to about 16 × 32 = 14 of disposable income. Overall,
the present value of maintaining the habit over an infinite horizon represents about one
sixth of financial wealth and one quarter of disposable income.

Education. The high school and post-high variables are insignificant in the twin regressions.
These results sharply contrast with the strong cross-sectional correlation between education
and the risky share reported in the last set of columns of Table II and in CCS 2007. We infer
that educational attainment acts as a cross-sectional proxy for latent traits such as ability
and upbringing that are also associated with higher risk-taking. Risk-tolerant individuals
may have a propensity to choose both high levels of education and aggressive financial
  12
    Furthermore, given that we proxy habit with average income, the internal habit coefficient may be due
to cash on hand effects, as in Haliassos and Bertaut (1995) and Haliassos and Michaelides (2002).

                                                  18
portfolios, but education has no direct bearing on the risky share.
   Our results confirm two earlier studies. In a dynamic panel investigation, Christiansen,
Joensen and Rangvid (2008) provide evidence that conditional on stockmarket participa-
tion, no field of study at the university level has a causal impact on direct stockholdings.
Guiso and Paiella (2005) use an experimental question from the Bank of Italy’s Survey of
Household Income to estimate risk aversion, and show that risk-tolerant investors tend to
invest more in education. Their explanation is that the risk of failure is an impediment
to education investment, which is less pronounced for risk-tolerant individuals. The twin
study confirms that the causal relation between educational attainment and the risky share
is either weak or difficult to measure.

Family Size and Gender. Large households select a conservative asset allocation, consistent
with the substantial background risk caused by the random needs of the members of a
large family. A complementary interpretation is that larger households behave like poorer
households of smaller size, as in household equivalence scale models of consumption (e.g.
Calvet and Comon 2003; Deaton, 1974; Jorgenson and Slesnick 1987; Lewbel and Pendakur
2008; Prais and Houthakker 1955).
   Households in which men control a large share of financial wealth have a tendency to
select a slightly lower risky share than households with more evenly distributed assets. In
unreported work, we obtain that male-dominated households invest a higher share of their
risky portfolios directly in stocks. These results are in line with the evidence that gender
differences in risk taking vary with the gamble payoff structure and the type of task (e.g.
Croson and Gneezy 2008, Feng and Seasholes 2007, Haliassos and Bertaut 1995).

   In contrast to the fragmentary data used in earlier research, the Swedish dataset allows
us to simultaneously measure the relation between the risky share and a large number
of household characteristics. As in Carroll (2002), the risky share is substantially larger
for households with higher financial wealth, and is by far the most significant regressor.
Leveraged households with commercial property, a large family size, or a high habit, tend to
select conservative asset allocations. Educational attainment, which is significantly related

                                             19
to the risky share in the cross-section, is insignificant in the twin regression.

D.    Zygosity, Communication and Random Matching

      We now report complementary evidence on link between the risky share and observable
characteristics.

Identical Twins. The pairwise correlation of the risky share is substantially higher for
identical twins than for fraternal twins. In Table III, we reestimate the yearly twin pair
regressions on the subsample of identical twins. The adjusted 2 is in the 24%−25% range,
as compared to the 18% − 19% range obtained with all twins. The explanation is that the
contribution of yearly twin pair fixed effects is almost twice as high for identical twins
(2 ≈ 16%) as for all twins ( 2 ≈ 9%). The financial wealth elasticity of the risky share
is nearly the same in the subsample of identical twins as in the sample of all twins, and is
strongly significant. Human capital, which has an insignificant positive coefficient in Table
II, has a substantially higher and significant estimate with identical twins. Table III thus
confirms and strengthens our earlier results.

                              [Insert Table III about here]

Communication. The frequency of communication between twins can potentially have an
important impact on their financial decisions. For instance, the insignificant education
coefficients in Table II can be interpreted as evidence that educational attainment does not
impact risk-taking, or alternatively that twins communicate frequently enough to overcome
education differences. Communication may also contribute to the twin pair fixed effect,
along with genes, upbringing and expected inheritance, among others.

                              [Insert Table IV about here]

     In Table IV, we separately reestimate our regressions on the set of twins who commu-
nicate often with each other and the set of twins who communicate rarely. The regression
coefficients reported for both groups are very similar to the ones reported in Table III.

                                              20
Thus, individual twins do not simply mimic each other’s behavior but respond to their
own economic and financial circumstances, whether or not they communicate often with
each other.
   The adjusted 2 is twice as high for frequently communicating twins as for infrequent
communicators. The increase in the fixed effects  2 is the main contributor to this increase
in explanatory power. The adjusted reaches 40% for identical twins who communicate
frequently, which is high value for a household finance regression.
   Another striking observation is that when twins communicate rarely with each other,
the 2 coefficient is nearly the same for identical twins as for all twins. The intensity of
communication has of course a genetic component, but if communication and genes are im-
perfectly correlated, our findings suggest that the twin pair fixed effect is also substantially
driven by communication.

Random Matching. In the appendix, we reestimate (4) on a panel of randomly matched
pairs in order to check that the results of Table II are not statistical artifacts. Random pairs
produce coefficients that are very similar to the yearly fixed effects coefficients obtained
with actual pairs. In particular, education variables are strongly significant. The adjusted
2 declines to 13% (compared to 19% with actual twins in the presence of all character-
istics) and the contribution of the fixed effect 2 hovers around 25% across specifications
(compared to 95% with actual twins). The estimates of 2 are of the same order as the
contribution of yearly fixed effects and are substantially smaller than the values obtained
with properly matched twins. These findings confirm the empirical importance of yearly
twin pair fixed effects in the actual dataset.

   In the above analysis, we have not controlled for individual fixed effects that are specific
to each twin in a pair, such as differences in risk aversion. We will provide a detailed
treatment of this issue in Section IV.

                                                21
III.      What Drives the Financial Wealth Elasticity of the Risky Share?

        Several leading portfolio choice theories predict that the financial wealth elasticity of
the risky share should vary with wealth and other household characteristics. For instance,
in a habit formation model, the elasticity increases with habit and decreases with financial
wealth, as was reviewed in Section II.A. To the best of our knowledge, however, the em-
pirical relation between household characteristics and the financial wealth elasticity of the
risky share has not been documented until now, presumably for lack of reliable data and
identification techniques.

                                      [Insert Table V about here]

       In Table V, we consider the extended specification:

                                ln( ) =  +   +  0  +                             (6)

where   is the elasticity of pair  in date .13 In the first set of columns, we classify twin
pairs annually into quartiles of the average log financial wealth  = (1 + 2 )2, and
report the elasticity of the risky share in each quartile. We do not consider characteristics
other than financial wealth and do not allow time variations in the elasticity of a given
quartile. The measured elasticity is 029 in the lowest financial wealth quartile, 022 in the
second quartile, 015 in the third quartile, and 010 in the top quartile. The elasticity is
therefore a decreasing function of financial wealth. In the second set of columns of Table
V, we also include all the other characteristics as controls. The elasticity increases slightly
in each quartile compared to the previous specification, and remains a strongly decreasing
function of financial wealth.
       We next specify the elasticity as a linear function of log financial wealth and other
characteristics:
                                             =  0 +  1  +  0                                       (7)
  13
    Equation (6) is a direct implication of the specification ln( ) =  +    +  0  +  .
Ashenfelter and Rouse (1998) consider a similar approach to modeling heterogeneity in the context of labor
economics.

                                                          22
where  denotes the average vector of characteristics in pair . The variables  and 
are demeaned year by year. Specification (7) implies:

                 ln( ) =  + (0 +  1  +  0  ) +  0  +     (8)

which can be conveniently estimated.

                                  [Insert Table VI about here]

   In the first set of columns of Table VI, we estimate a version of (8) in which the financial
wealth elasticity of the risky share is driven only by log financial wealth and log internal
habit. We focus on the internal habit because our measure of external habit is noisy and
less significant in previous tables. The elasticity is a decreasing function of financial wealth
and an increasing function of habit, which confirms Implications 3 and 4 of habit formation
models. The first result is consistent with the bin regressions in Table V, while the second
result is new to Table VI.
   We interpret the regression coefficients by loglinearizing (3) around ln( ) :

                       ¡            ¢     h                     i    h                     i
         ≈ ̄ −  1  − ¯ +  1 ln( ) − ln( ) + 1 ln( ) − ln( ) 

where  1 = ̄2 ln( )  Since ̄ ≈ 02 we infer that  1 ≈ 024 By regression (1) of Table
VI, the coefficient of financial wealth and habit are −010 and 014, respectively. These
estimates are approximately the negative of each other, and their magnitudes are about half
of the predicted theoretical values. Our analysis represents of course a rough assessment
of habit formation, since our measures of habit and financial wealth are contaminated by
measurement error and nonlinearities have been ignored.
   In the second set of columns of Table VI, we allow the elasticity to depend on the
full set of demographic and financial characteristics. The elasticity decreases with financial
wealth and human capital, and increases with residential real estate. Family size impacts
negatively the risky share itself and positively its elasticity. Consistent with the household
equivalence scales literature, large households behave like poorer households of smaller

                                                      23
size. A complementary explanation is that family size and residential real estate proxy for
internal habit, which would explain their positive impact on   in the second set of columns
as well as the positive coefficient of internal habit reported in the first set of columns.
     In the Appendix, we investigate the relation between the elasticity   and the propen-
sity to take risk. We reestimate the twin regression when the set of explanatory variables
of   includes the twin pair fixed effect  obtained from the regression reported in Table
VI. The coefficient of  is negative and significant: households with a high propensity to
take risk tend to have a small financial wealth elasticity of the risky share.
     The financial wealth elasticity of the risky share is therefore heterogeneous across house-
holds, and tends to strongly decrease with financial wealth. The next section examines the
robustness of these results to alternative specifications, and Section V derives their impli-
cations for the aggregate demand for risky assets.

                                IV.    Robustness Checks

A.    Age

      It is sometimes suggested that genetic effects matter less with age. In the Appendix, we
classify twin pairs by age and reestimate the twin regressions in each group. The financial
wealth elasticity of the risky share remains significantly positive and close to 0.2 for all
groups, and we cannot reject that the null hypothesis that the elasticity is constant with
age. The effect of other characteristics is generally robust, albeit with lower significance
due to the smaller group sizes. Furthermore, the beta of income growth relative to the
risky portfolio return,    is significant and positively related to risk-taking for investors
between 35 and 45, and is insignificant in the other three age groups.

B.    Measurement Error

      Financial wealth and the risky share are observed with measurement error. For in-
stance, there are high-frequency variations in cash balances at the end of the year, which
are partly unrelated to the asset allocation of the financial portfolio. For this reason, we

                                               24
consider the instrumental variable estimation of the twin specification (4).
     We begin with a few definitions. The passive risky return  is the proportional change
in value of a household’s risky portfolio if the household does not trade risky assets during
the year. Similarly, passive financial wealth is the financial wealth the household has if it
does not trade, save or dissave during the year. Formally the log of passive financial wealth
is defined as:
                                
                                = (−1  −1     )

where
                     (    ) = ln {[(1 + ) + (1 − )(1 +  )] } 

In Table VII, we instrument log financial wealth with log passive financial wealth. In the
first set of columns, the average elasticity  is estimated to be 028, which is slightly higher
than the 022 values reported in earlier tables. In the second set of columns of Table VII,
we reestimate the elasticity  in every financial wealth quartile. Consistent with Section
III, the measured elasticity strongly decreases with financial wealth, and the impact of
other characteristics is qualitatively unchanged. Internal habit now has a strongly negative
coefficient.

                              [Insert Table VII about here]

     In the Appendix, we also consider the instrumental variable estimation of the linear
elasticity specification (8). The internal habit coefficient is measured to be larger and more
significant than in Table VI. Overall, the results of Sections II and III hold even more
strongly when we control for measurement error in financial wealth

C.    Reverse Causality between the Risky Share and Financial Wealth

      We have hitherto viewed the positive cross-sectional correlation between financial
wealth and risk-taking as evidence that richer households tend to select a higher risky
share. An alternative interpretation is that at the end of the bull market of the nineties,
investors with high equity investments happened to have larger financial wealth than other

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