Download Risk Aversion, Wealth, and Personality

Risk Aversion, Wealth, and Personality
This version: 4 Jan. 2016
BY ANDREW CONLIN, JOUKO MIETTUNEN, JUKKA PERTTUNEN, MIKKO PUHAKKA, RAULI
SVENTO*
We find estimates for absolute and relative risk aversion for individuals using stockholdings and survey
responses. The data come from combining observations from the Northern Finland Birth Cohort 1966 and the
Finnish Central Securities Depository. With stockholdings, we find decreasing absolute risk aversion and
increasing relative risk aversion. Survey responses are significantly related to real world decisions, but they
only explain a small portion of the variance in revealed preferences. We show that personality traits help
explain part of this difference – personality traits are significantly related to either survey-based measures of
risk aversion or revealed preference, but not both.
Keywords: risk aversion; personality; household behavior
JEL: D14, G11
*Conlin: Department of Finance, Oulu Business School, PO Box 4600, Oulu 90014, Finland (email: [email protected]); Miettunen: Center for Life Course
Epidemiology and Systems Medicine, University of Oulu, PO Box 5000, Oulu 90014, Finland (email: [email protected]); Perttunen: Department of
Finance, Oulu Business School, PO Box 4600, Oulu 90014, Finland (email: [email protected]); Puhakka: Department of Economics, Oulu Business School,
PO Box 4600, Oulu 90014, Finland (email: [email protected]); Svento: Department of Economics, Oulu Business School, PO Box 4600, Oulu 90014,
Finland (email: [email protected]). We thank seminar participants at the Graduate School of Finance and Oulu Business School for their comments and
suggestions. Conlin thanks the North Ostrobothnia Regional Fund of the Finnish Cultural Foundation for generous support. All authors declare that they have no
relevant or material financial interests that relate to the research described in this paper.
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‘In addition, there must come into play the diversity among men in degree of confidence in their judgment and
powers and in disposition to act on their opinions, to “venture.”’
- Frank H. Knight (1921/1971, p.269)
Risk aversion is an important parameter for decision making, both in the large and in the small. At the macro
level, risk aversion helps determine the equity risk premium, and at the individual level risk aversion determines
the level and percentage of risky asset holdings. On a daily basis, our level of risk aversion affects our decisions
over risky outcomes. Having an accurate estimate of the level and distribution of risk aversion would impact the
understanding of all the above situations. We add to the understanding of risk aversion and its measurement by
comparing estimates of individuals' risk aversion from two data sources. We also look at what personal
characteristics are related to risk aversion.
We estimate values for risk aversion from both revealed preferences (actual behavior) and from survey
responses. Our data allows us to calculate the level of risk aversion for each individual, and we find the
distribution of risk aversion across the sample. In addition to observations on gender, education, and marital
status, we have personality trait scores. We relate this detailed information on personal characteristics to risk
aversion measures. We find interesting results showing how personal characteristics influence risk behavior. As
far as we know, we are the first to explore these relationships using the combination of real-world investment
behavior, survey measures of risk aversion, and detailed personality trait scores.
We find that wealth is correlated with the amount of risky asset holdings, but not proportionately. Wealthier
individuals have greater investment portfolios than less wealthy individuals, but the average share of wealth
invested in risky assets decreases with wealth. Thus we find evidence of decreasing absolute risk aversion and
increasing relative risk aversion. Our survey measures of risk aversion allow for calculation of both absolute
and relative risk aversion. We find the same pattern in the survey as in revealed preferences - decreasing
absolute risk aversion and increasing relative risk aversion.
2
The survey answers are correlated with each other and also with revealed preferences, but the survey
measures only explain a small portion of the variation of the revealed preference measures. Rank correlations
between the survey measures are all statistically significant and range in absolute magnitude from 0.18 to 0.38.
The correlations of the survey measures with revealed preference are generally statistically significant but lower
in magnitude. We conduct principal component analysis on our four survey measures of risk aversion. We find
only one significant factor, which supports the idea of risk aversion being of a single dimension. However, the
factor scores for the first principal component only offer slight improvement over the individual survey
measures for predicting real-world behavior.
We explore personal characteristics and personality traits as the potential drivers of risk aversion. Personality
traits help explain both survey measures of risk aversion and revealed preference measures of risk aversion, but
with an interesting pattern; most of the traits that significantly predict the survey measures do not predict realworld behavior, and traits that predict real-world behavior are not good predictors of the survey measures. This
suggests that personality not only affects risk aversion directly, but can confound the measurement of risk
aversion in a survey.
Prior works that use the revealed preference method to calculate risk aversion are based on asset holdings that
were self-reported on surveys. With observations for individuals’ risky asset holdings and their wealth, and
assuming homogenous expectations, one can easily calculate the coefficient of risk aversion from power utility
or negative exponential utility. This is the approach taken by Friend & Blume (1975), Cohn, Lewellen, Lease,
and Schlarbaum (1975) and Morin and Suarez (1983). These papers generally find decreasing or constant
relative risk aversion, with the differences mainly coming from the different observations on wealth (total assets
vs. net wealth) and the treatment of housing (whether considered a risky or risk-free investment).1 More recent
works on risk aversion include Heaton and Lucas (2000) and Guiso, Haliassos, and Jappelli (2003), who look at
factors affecting the share of wealth invested in equities. Beauchamp et al. (2011) and Paravisini et al. (2010)
also explore risk aversion based on revealed preferences.
1
See Morin and Suarez (1983) for a comparison of the studies.
3
There are other studies using a representative-agent asset pricing model approach to estimate risk aversion.
Kocherlakota (1990) finds the Friend & Blume (1975) method underestimates risk aversion for a model
calibrated to actual stock market returns and consumption growth. The literature related to the equity premium
puzzle (Mehra and Prescott (1985)) is extensive. Mankiw and Zeldes (1991) use aggregate measures of
consumption to calculate risk aversion in a Consumption-CAPM framework. Other works using aggregate data
include Campbell (1996) and Vissing-Jørgensen and Attanasio (2003).
There is also an extensive literature using survey questions to estimate risk aversion. The general format of
the question presents a choice between a certain and uncertain outcome. For example, the respondent must
choose between 10€ for certain and a 50-50 chance at 0 or 20€. Binswanger (1980), Kachelmeier and Shehata
(1992), Barsky et al. (1997), Holt and Laury (2002), Kimball, Sahm, and Shapiro (2008), Dohmen et al. (2011)
and Beauchamp, Cesarini, and Johannesson (2013) have all used this general format with variation in the payoff
levels and/or probabilities of payoffs. Dohmen et al. (2011) have responses to qualitative questions via a survey
and incentivized responses to lottery questions through an experiment. They find a strong relationship between
the two measures, with the general risk question being a significant predictor of the lottery certainty equivalent.
Two papers which contain analysis similar to ours are Dorn and Huberman (2005) and Kapteyn and Teppa
(2011). Dorn and Huberman (2005) use a single ordinal measure of risk aversion and find it significantly related
to the share of wealth invested in risky assets. Kapteyn and Teppa (2011) use a combination of questions to
measure risk aversion, with one of the questions identical to what we use (the question was originally used in
Barsky et al. (1998)).
While risk aversion has been estimated before and our approach is quite similar, we offer a unique
contribution to the literature in terms of data and results. Our register data reflect official stockholdings, not
survey responses. Our survey questions for risk aversion allow us to calculate point estimates for absolute and
relative risk aversion, in addition to simple ordinal values. The personality data we use is measured at the
subscale (i.e. trait facet) level, providing a more detailed look at the relationship between personality and risk
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aversion than studies using only higher-order personality traits. This detailed personality data helps to explain
some of the differences between the survey and revealed preference measures of risk aversion.
The rest of the paper is structured as follows: Section I explains how we calculate revealed preference risk
aversion and describes our survey questions in detail. Section II presents our data sources and descriptive
statistics. Section III presents results for the relationship between risk aversion and wealth, and the relationship
between the survey and revealed preference measures. Section IV shows how personality affects the measures
of risk aversion. Section V concludes.
I. MEASURING RISK AVERSION
We use both revealed preferences and survey responses to measure risk aversion. The revealed preference
method requires observations on the individual’s level of stockholdings and wealth. Assuming that the
individual has invested the optimal amount in stocks, one can easily calculate the individual’s cardinal level of
risk aversion. The survey questions obtain cardinal or ordinal levels of risk aversion. We describe both methods
below.
Revealed Preference approach
One can find a closed-form approximation for the degree of risk aversion if one starts from power utility and
assumes one risky asset and one risk-free asset. The full derivation is in the Appendix A. The main idea is that
an individual will chose the percentage(x) of his wealth (W), to invest in the risky asset in order to maximize his
expected utility of final wealth. The remainder of this wealth (1-x) is invested in the risk-free asset. The utility
function is
(1)
with
W 1
u (W ) 
1 
degree of relative risk aversion. The solution for relative risk aversion is
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(2)

(1  r ) r 1
 r2 x
where x = share of wealth invested in the risky asset, = the risk-free rate,  r = the excess return on the risky
asset, and  r2 = the variance of the risky asset’s return.
We can also use negative exponential utility, retaining the assumption of one risky and one risk-free asset
(3)
1
u (W )   eW

in which case the solution is
(4)

r
 xW
2
r
We assume homogenous expectations. We simplify further by assuming the risk-free rate to be zero. Since we
are assuming homogeneous expectations, the ratio of expected excess return to variance for the risky asset is the
same for all individuals. We simply set this ratio to one. (This is actually a reasonable estimate. Assuming an
excess return of 6% and standard deviation of 24.5% would lead to a ratio of one.) Thus, our measure of relative
risk aversion is equal to the inverse of the share of wealth invested in stocks. Our measure of absolute risk
aversion is equal to the inverse of the euro amount invested in stocks.
Survey based measures of risk aversion
From our survey, we have four questions to measure risk aversion. Two of the questions allow us to calculate
a coefficient of risk aversion by asking directly for the individual’s willingness to pay for a lottery; the first
question makes no reference to wealth, while the second question implies an endowment of 10,000€. The other
two questions allow us to sort our subjects into ordinal categories of risk aversion. One of these questions asks
for choices over lotteries, while the other asks about one’s general willingness to take risks.
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Our first question, which we call lottery, asks (originally in Finnish): “You have the chance to participate,
upon paying a fee, in a game that offers a 50% chance to win 10,000€ and a 50% chance to get nothing. What is
the maximum amount you are willing to pay to participate?” It is clear that the more a person is willing to pay
to play the game the less risk averse he is. A response equal to 5000 implies risk neutrality and a response
greater than 5000 implies risk seeking preference. For a person who provides a response greater than 0, it must
be the case that
0.5 *U (W0  10000  P)  0.5 *U (W0  P)  U (W0 )
(5)
If we assume power utility (as in equation (1)) and have an observation for the individual’s level of wealth,
we are able to calculate the coefficient of relative risk aversion. We acknowledge that an individual may exhibit
narrow framing (evaluating the gamble in isolation, without incorporating it with overall wealth - see e.g.
Barberis et al. (2006)), thus we also use household income and personal income as reference values in the utility
function. If we assume negative exponential utility (eq. 3), we are able to find the coefficient of absolute risk
aversion.
The second question, which we call risky investment, poses the following situation: “You just won 10000€.
You quickly get an offer from a trustworthy bank: you can double your investment in two years, but there is an
equally likely probability that you could lose half of the investment over the same period. How much would you
invest?” Like the lottery question, the more a person is willing to invest, the less risk averse he is. Using power
utility, we can calculate relative risk aversion. We can also calculate absolute risk aversion by using negative
exponential utility.
The third question, which we call risky job, is a three step problem. The text reads (originally in
Finnish):
Imagine the following situation. You are your household’s only source of income. You
have to choose between two equally good jobs. In the safe Job A, your monthly after-tax
salary will be 2800€ for the rest of your life. In the risky Job B, you have a 50-50 chance at
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receiving a higher monthly after-tax salary for the rest of your life, and a 50-50 chance at
receiving a lower monthly after-tax salary for the rest of your life. In the table below,
circle either Job A or Job B for each of the three cases.
Monthly Salary
Monthly Salary
Job A 2800€
or Job B
Job A 2800€
or Job B
Job A 2800€
or Job B
50-50 chance at:
5600€ or 2240€
50-50 chance at:
5600€ or 2460€
50-50 chance at:
5600€ or 1900€
Respondents must answer all 3 parts – they must accept or reject the gamble for each level of the losing
outcome. The more safe choices one takes, the more risk averse the individual is. We do not use inconsistent
answers (e.g. someone who rejects the gamble when the losing payoff is 2460, but accepts the gamble when the
losing payoff is 1900). For this question, we code the answers by the number of gambles rejected. Thus the
range is 0-3, with those who reject all the gambles (coded as 3) being the most risk averse.
We call the fourth question general risk. The question simply asks (translated from Finnish) “In general, are
you fully willing to take risks or do you avoid taking risks?” The response is scaled from 0 (not at all willing to
take risks) to 10 (fully willing to take risks). In our analysis, we reverse the scale so that higher numbers reflect
more risk aversion.
There is precedent for all four of the questions in the literature. The lottery question has been used by Guiso
and Paiella (2008). The risky investment question has been used by Halko et al. (2012) and. The general risk
question has been used in Dohmen et al. (2011) and Halko et al. (2012). The risky job question has been in
Barsky et al. (1997), Kimball et al. (2008), and Kapteyn and Teppa (2011). A similar question in Dohmen et al.
(2010) has a multiple price list of 20 rows, where respondents choose between a safe option and a lottery in
each row; the lottery is the same across rows, while the safe option increases in value across rows. We did not
offer any payouts based on the survey responses.
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II. DATA AND DESCRIPTIVE STATISTICS
The data come from combining Northern Finland Birth Cohort 1966 data (NFBC), Finnish Central Securities
Depository (FCSD) data, and income data for the year 2012 from the Finnish Tax Administration. We get our
socioeconomic data and survey-based risk aversion measures from the NFBC, and the stock holding
information from the FCSD.2
Northern Finland Birth Cohort 1966
The NFBC started by gathering information on more than 12 000 babies born in 1966 in the provinces of
Oulu and Lapland, in northern Finland. The cohort covers approximately 95% of all babies born in the two
provinces in 1966. The project has periodically conducted follow-up studies, with the most recent study taking
place in 2012. In addition to clinical examinations for physical health, the studies also collect data on a wide
range of socioeconomic and psychological variables. We use data collected in 2012, when the cohort members
were 46 years old. Our four questions for risk aversion (described in Section I) were part of this survey. We
have observations on gender, marital status, and educational attainment. We have self-reported values for net
wealth and household income. For net wealth, respondents were asked to sum the values of their assets (house,
autos, vacation homes, forest land, investments, etc.) and subtract all debts. The questions about household
wealth and household income come before the questions on risk aversion in the survey, so we cannot rule out
that these questions primed the respondents to think about their overall wealth when answering the risk aversion
questions. The responses for the lottery and risky investment question are quite low (see Table 2); it is difficult
to imagine that the response would have been lower if we had not asked for wealth and income first.
The NFBC data also contain personality trait scores, as measured by the Temperament and Character
Inventory (TCI, version IX) of Cloninger et al. (1993). This personality model has been used to predict stock
2
NFBC survey respondents must give permission to use their answers in research. They also give permission to combine their survey answers with other official
register data.
9
market participation (Conlin et al. (2015)) and the decision to be self-employed (Ekelund et al. (2005)). The
TCI has four temperament traits: novelty seeking, harm avoidance, reward dependence, persistence. 3 We briefly
describe the traits here. Higher novelty seeking is exemplified by active behavior seeking excitement and
reward. Harm avoidance is reflected by passively avoiding harmful situations. Reward dependence is a measure
of how much one seeks the praise and comfort of others. Persistence measures the ability to stay focused on
achieving one's goals. From the descriptions of the traits (and their respective subscales), novelty seeking is
likely to be negatively related to risk aversion and harm avoidance is likely to be positively related to harm
avoidance. Reward dependence and persistence have less-clear interpretations for their relationships with risk
aversion. For a detailed explanation of the traits and subscales, see Cloninger et al. (1994). For a more in-depth
look at the traits and subscales relationship with economic behavior, please see Conlin et al. (2015). Appendix
B has a table listing the traits and their respective subscales.
Finnish Central Securities Depository
The Finnish Central Securities Depository (FCSD) has the official records for holdings of securities registered
in Finland. The data includes stocks traded on the Nasdaq OMX in Helsinki, and equity structured products. We
look at the investor's holdings in 2010. For most investors in our sample, we observe their holdings on the last
trading day of the year. For those few investors that sell all of their holdings before the end of the year, we take
their holdings for the last available date. Equity structured products are securities issued by banks that are the
equivalent of holding an index fund and a European put. The structured product holdings are valued at 1000€
per contract, which is the “normal” guaranteed value at maturity. In our sample 183 people owned structured
products, and of these 112 did not own any exchange-traded shares. We eliminate portfolios with a value less
than 250€.
We do not have data on mutual fund holdings. Keloharju et al. (2012) show that the smallest investors hold
stocks and risky mutual funds (balanced funds and equity funds) in a roughly 1-2 ratio, while the largest
3
The TCI has four temperament traits and three character traits (self-directedness, cooperativeness, and self-transcendence). We do not have data on the character
traits, so we do not discuss them further.
10
investors hold roughly twice as much in stocks as in risky mutual funds. If this pattern would hold for our
sample, it would imply a flattening of the relationship of both absolute and relative risk aversion with wealth
compared to what we find now. Our results below show that while the magnitude of the relationship between
risk aversion and wealth would likely be dampened by including mutual funds, it almost certainly would not be
eliminated. Keloharju et al. (2012) also show that the probability of owning mutual funds is essentially flat (just
over 60%) over the entire distribution of wealth. We have no reason to believe this pattern does not hold for our
sample.
Descriptive Statistics
Table 1 presents descriptive statistics for the socioeconomic variables. Since we are looking at both revealed
preference and survey measures of risk aversion, we focus on those cohort members who own equities and/or
equity structured products. After eliminating investment accounts with a value less than 250€, we are left with a
sample of 922 individuals. We report two measures of income, household income and personal income.
Household income is self-reported on the NFBC survey. Gross personal income is from 2012 Finnish Tax
Authority records. We see the household income reported on the survey is roughly twice as large as the personal
income figures we get from the tax office, most likely reflecting the preponderance of two-income households.
Negative values reported for wealth were changed to missing. Since we are looking at only those individuals
who have investment portfolios, it is not surprising that we find large values for wealth. Also the proportion of
respondents with a university degree (46%) and the percentage of females (38%) align with previous findings
regarding education and gender being positively and negatively related to investor status, respectively (Guiso et
al. (2003)).
TABLE 1. DESCRIPTIVE STATISTICS FOR SOCIOECONOMIC VARIABLES.
Inc.House
Inc.Pers
Wealth
Female
University
Married
N
828
911
786
922
871
922
Mean
89462
48618
391484
0.38
0.46
0.61
Median
78000
40675
250000
0
0
1
Std Dev
87389
38705
971217
0.49
0.50
0.49
Min
0
0
1000
0
0
0
Max
1020000
563936
20000000
1
1
1
Note: Inc.House is household income. Inc.Pers is gross personal income. Wealth is net wealth. Inc.House and Wealth are self-reported on the survey.
Inc.Pers is from 2012 Finnish Tax Authority records. Female, university, and married are indicator variables.
11
In Table 2 we present the descriptive statistics for our measures of risk aversion and the investors' portfolios.
People respond differently to the lottery and risky investment questions. The median value for betting on the
lottery question is only 100€, while the median value for the risky investment question is 2750€. These values
indicate a high degree of risk aversion. When using wealth as the reference value in the utility function we find
very high values for relative risk aversion. The values for relative risk aversion come down when we use
household income as the reference value; the values fall further when we use personal income as the reference
value. The pattern of falling relative risk aversion as the reference value is changed is not surprising – most
individuals exhibit the following relationship: wealth > household income > personal income. The values for
risk aversion are still quite high, though. The median value for relative risk aversion using the risky investment
question and personal income as the reference value is 15, while the mean is 371.
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TABLE 2. DESCRIPTIVE STATISTICS FOR RISK AVERSION MEASURES.
N
Mean
Median
Std Dev
Minimum
Maximum
Lottery
865
487.14
100
965.19
0
8000
Risky investment
856
3168.40
2750
2847.60
0
10000
General risk
870
4.19
4
2.22
0
10
Risky job
811
1.26
1
0.98
0
3
Lot.wealth
753
12542.26
1110
62186.28
-82
1275392
Lot.inc.house
788
3671.51
451.5
14151.48
-29.5
207945
Lot.inc.pers
802
1932.79
277.25
6815.88
-24
77374
Lot.ara
825
0.04315
0.00693
0.12851
-0.00033
1.38629
Rinv.wealth
612
2478.96
69.5
26914.27
2.5
447527.5
Rinv.inc.house
578
659.90
23.5
6445.07
2.5
91430.5
Rinv.inc.pers
655
370.93
15
3788.93
2
67249.5
Rinv.ara
659
0.01
0
0.07
0
0.96
Investment
922
24801.90
6000
61100.28
250.00
703405.30
Share Invested
786
0.133
0.030
0.698
0.0001
18.300
Note: Lottery and Risky investment are the survey responses, in €, to the respective questions. Risky job is the number of gambles rejected in the risky job
question. General risk is response to the general risk question (reversed so higher numbers indicate higher risk aversion). Lot.wealth, Lot.inc.house, and
Lot.inc.pers are the coefficients of relative risk aversion from the lottery question when using wealth, household income, and personal income, respectively,
as the reference level in the power utility function. The same pattern holds for Rinv.wealth, Rinv.inc.house., and Rinv.inc.pers. Lot.ara and Rinv.ara are the
coefficients of absolute risk aversion calculated from the negative exponential utility function. Investment is the portfolio value in euros. Share invested is
Investment divided by net wealth.
In contrast to the lottery and risky investment questions, the risky job and general risk questions show more
reasonable responses. The mean response for the general risk question is about 4, indicating a greater
willingness to take risks than avoid risks. The median response for the risky job question is 1, indicating that
more than half of the respondents rejected only the riskiest gamble (or even accepted it).
We
next
present
the
distributions
of
the
survey
responses
in
Figure
1
panels
A-D.
13
FIGURE 1. DISTRIBUTIONS OF SURVEY RESPONSES.
Note: The panels show the distributions of survey responses. The lottery and risky investment responses are in euros. Higher values for general risk reflect greater risk
aversion. Risky job is the number of risky job offers rejected, so higher values reflect greater risk aversion.
For the lottery and risky investment question, we see how clustered the answers are. There are only 40 unique
responses for the lottery question, and only 28 for the risky investment question. These counts include responses
of 0. Without prompting, respondents seem to be drawn to round numbers. Even though these two questions
exhibit this type of answer clustering, the responses still help predict real world behavior (as shown in Section
III). The general risk question and risky job question show a more evenly distributed profile of responses.
For the lottery question, there are 57 non-responses. Of these people, 55 also did not respond to the risky
investment question. In total there are 66 non-responses to the risky investment question. Thus, most of the nonresponses to these two questions are from the same individuals. These individuals also provided few responses
for the general risk and risky job questions – 6 responses and 2 responses, respectively. We do not interpret
14
non-response as zero; non-responses on a question are left out of analyses including that question, while zeroresponses are used where appropriate.
Panel A. Absolute risk aversion
Panel B. Share of wealth invested
FIGURE 2. DISTRIBUTION OF REVEALED PREFERENCE RISK AVERSION.
While the distribution for absolute risk aversion looks "good" in Panel A, with almost half of the respondents
are in the lowest tranche, it is worth noting that this lowest trance contains portfolios in the range 6667€ 703405€. In Panel B, we see that the share of wealth invested in stocks is generally very low. For the 786
15
people who reported a value for wealth, we see that 75% of them have 12% or less of their wealth invested in
stocks. As a reminder, we use the inverse of the share of wealth invested as our measure of relative risk
aversion; thus 75% of our sample has a coefficient of relative risk aversion of at least 8.33. The median share of
wealth invested is 3%, corresponding to a relative risk aversion value of 33.33. Because both of the distributions
have such long right tails, we use logs of these values in our analyses.
III. RESULTS
We start by showing the relationship between risk aversion and wealth, for both the revealed preferences and
for the survey measures. We see in Figure 3 Panel A that individuals who report larger wealth generally have
larger portfolios. The line represents the fitted value for the OLS regression of ln(investment) on ln(wealth).
The slope is 0.34, p-value < 0.001, R2 = 0.05. This is clear evidence of declining absolute risk aversion wealthier people invest more in risky assets. The “vertical streaks” in the plot are due to people reporting the
same level of net wealth (e.g. 200,000€). We see very few points with investment value greater than net wealth,
indicating no obvious under-reporting of wealth.
Panel A. ln(investment) plotted against ln(wealth).
Panel B. ln(share invested) plotted against ln(wealth)
FIGURE 3. INVESTMENT AND WEALTH
Note: The line in each panel represents the simple OLS regression line.
16
In Panel B, we see a clearly downward sloping relationship between the share of wealth invested and wealth
(OLS regression, slope = -0.59, p-value < 0.001, R2 = 0.12). The wealthier individuals have a lower percentage
of their wealth invested in stocks, on average. This is evidence of increasing relative risk aversion. Figure 3
nicely shows how wealthier people generally have larger portfolios (decreasing ARA), but a smaller percentage
of their wealth is invested in stocks (increasing RRA). The figure nicely supports the hypotheses of increasing
RRA and decreasing ARA originally stated in Arrow (1963). We stress that these are cross-sectional data, so we
cannot say anything about how an individual might change her investment portfolio if her wealth changed. All
we can say is that wealthier individuals have larger portfolios, but their portfolios represent a smaller fraction of
their wealth. Across individuals, we have decreasing ARA and increasing RRA (by the Arrow-Pratt definitions,
and by assuming that the share invested is the optimal share).
How are the survey responses related to wealth? Figure 4 plots the responses to the four survey questions
against log wealth. Panels A and B show the responses to the lottery and risky investment questions (in euros),
respectively. For these two panels, the positive relationship between the response and wealth implies risk
aversion decreases with wealth; wealthier individuals are willing to bet more.
17
Panel A. Lottery, in euros
Panel B. Risky investment, in euros
Panel C. General risk
Panel D. Risky job (number of gambles rejected)
FIGURE 4. SURVEY RESPONSES AND WEALTH
Note: The survey response is on the vertical axis and ln(wealth) on the horizontal axis.
In Panels C. and D. we see a similar pattern; wealthier people are less risk averse. Wealthier people are more
willing to take risks in general (higher numbers for general risk represent greater risk aversion) and they are
more willing to accept the risky job gambles (higher numbers of gambles rejected represent greater risk
aversion) than less wealthy individuals. As discussed in Section I, net wealth may not be the appropriate
reference value to use in utility function when calculating relative risk aversion over the lottery and risky
investment gambles. When contemplating these gambles, an individual may think in terms relative to income
instead of relative to wealth. Figure 5 plots the survey responses against personal income. We see patterns
nearly identical to those in Figure 4.
18
Panel A. Lottery, in euros
Panel B. Risky investment, in euros
Panel C. General risk
Panel D. Risky job (number of gambles rejected)
FIGURE 5. SURVEY RESPONSES AND PERSONAL INCOME
Note: The survey response is on the vertical axis and ln(inc.pers) on the horizontal axis.
How well do the survey answers predict actual behavior?
We see above that wealthier people are less risk averse, both in real world behavior and their survey answers.
While the nature of the relationship between risk and wealth holds between the survey and the world, how close
are these measures in magnitude? Do the survey responses accurately predict real world behavior? We start by
looking rank correlations between the measures, in Table 3.
19
TABLE 3. RANK CORRELATION MATRIX
RRA
ARA
ARA
Wealth
Inc.Pers
Lottery
Risky.inv
Gen.risk
0.834***
(<.0001)
Wealth
Inc.Pers
Lottery
Risky.inv
Gen.risk
Risky.job
0.296***
-0.209***
(<.0001)
(<.0001)
0.028
-0.083**
0.193***
(0.432)
(0.012)
(<.0001)
-0.036
-0.123***
0.122***
0.214***
(0.320)
(0.000)
(0.001)
(<.0001)
-0.050
-0.114***
0.096***
0.154***
0.359***
(0.163)
(0.001)
(0.008)
(<.0001)
(<.0001)
0.079**
0.108***
-0.114***
-0.056
-0.204***
-0.182***
(0.028)
(0.002)
(0.001)
(0.102)
(<.0001)
(<.0001)
0.020
0.111***
-0.173***
-0.244***
-0.263***
-0.269***
0.379***
(0.590)
(0.002)
(<.0001)
(<.0001)
(<.0001)
(<.0001)
(<.0001)
Note: ARA (RRA) is absolute (relative) risk aversion calculated from stockholdings. Inc.Pers is personal income from the Finnish Tax Authority. Lottery,
Risky.inv, Gen.risk, and Risky.job are the responses to the survey questions about risk taking. ***, **,* indicate significance at the 1%, 5%, and 10% level,
respectively. p-values in parentheses below the correlations.
The relationships evident in Figure 4 are borne out here – decreasing absolute risk aversion and increasing
relative risk aversion. The correlations between wealth and all of our risk aversion measures have the correct
sign and are statistically significant. The survey responses are significantly correlated with ARA but not RRA;
only the general risk question has a significant correlation with RRA. Interestingly, general risk is the only
survey response not significantly correlated with personal income. Personal income is significantly correlated
with one’s willingness to take monetary gambles, but less so with willingness to take risks in general.
Thus far we have presented evidence that the survey based measures of risk aversion are related to real-world
measures of risk aversion, but we have not said anything about how well the survey measures predict actual
behavior. We next parameterize the relationship, looking at how well the survey based measures predict actual
risk aversion. We use a simple OLS regression of the form
(6)
ln( RAi )    1Survi   s X i  ei
where ln(RAi) is the log of ARA or RRA, Survi is the survey-based measure of risk aversion, and Xi is a vector
of controls. We calculate relative (absolute) risk aversion by using power (negative exponential) utility for the
20
lottery and risky investment questions. For these two questions we calculate three values of relative risk
aversion by using either wealth, household income, or personal income as the reference value in the utility
function. All six distributions have long right tails (3 for lottery, 3 for risky investment) so we use logs of these
values in the regressions. For the general risk and risky job variables, we simply enter the value in the equation.4
The control variables are ln(wealth) along with indicator variables for gender, marital status, and education.
Table 4 presents the results when we use RRA as the dependent variable. Of the four survey measures, the
risky investment question produces the best results. It is interesting that the relative risk aversion values for the
lottery and risky investment questions using personal income are not statistically significant; the value of the
bets relative to an individual’s income has essentially no relationship with the share of wealth invested in
stocks. The general risk variable is significant at just the 10% level, but not when controls are added. The risky
job question shows no significant relationship with relative risk aversion. Wealth is positively related to relative
risk aversion. Females have higher relative risk aversion than males, and being married is associated with higher
RRA. The coefficient on the university dummy variable is negative across the board, but it is statistically
significant in only one the models.
We see a common pattern across all models in Table 4 when controls are added – the coefficient on the
survey measure drops, and the R-squared increases dramatically. This is due to the inclusion of wealth as an
explanatory variable. We calculate RRA from the share of wealth invested, so it is not surprising that including
wealth on the right hand side leads to a large R-squared and lower significance for the survey measures. A
simple way to work around this issue is to look at absolute risk aversion. We present the results of OLS
regressions of revealed preference absolute risk aversion on the survey measures of risk aversion in Table 5.
4
We do not use the risky job responses to estimate a risk aversion parameter as in Barsky et al. (1998) or Sahm et al. (2007). Those papers had responses from
multiple waves of the survey, allowing them to estimate a true risk aversion parameter and a noise parameter from the responses. We have only one response from each
individual, thus the risky job responses can only be mapped to a range for relative risk aversion. Choosing the lower bound or midpoint of the range would not change
the scale or variation of the responses very much.
21
TABLE 4. REVEALED PREFERENCE RRA AND SURVEY MEASURES OF RISK AVERSION
Panel A.
ln(lot.wealth)
0.16
(5.76)
0.14
(4.68)
ln(lot.inc.house)
0.08
(2.84)
0.05
(1.76)
ln(lot.inc.pers)
0.04
(1.39)
0.04
(1.27)
general risk
0.05
(1.69)
ln(wealth)
female
married
university
intercept
N. observations
R-squared
Panel B.
ln(rinv.wealth)
2.38
(11.39)
730
0.04
0.22
(3.5)
0.39
(3.08)
0.47
(3.8)
-0.05
(-0.43)
2.13
(9.27)
704
0.08
3.06
(16.22)
722
0.01
0.56
(8.4)
0.51
(4.36)
0.25
(2.03)
-0.18
(-1.56)
-4.00
(-5)
697
0.15
3.33
(18.05)
713
0.00
0.56
(8.3)
0.54
(4.62)
0.24
(1.99)
-0.17
(-1.54)
-3.87
(-4.73)
689
0.14
0.19
(3.07)
ln(rinv.inc.house)
0.07
(1.07)
-0.05
(-1.03)
ln(rinv.inc.pers)
0.03
(0.47)
0.00
(0.03)
risky job
0.00
(0.05)
ln(wealth)
female
married
university
intercept
N. observations
R-squared
3.36
(26.43)
722
0.00
2.53
(9.16)
604
0.04
0.04
(1.59)
0.56
(8.5)
0.54
(4.94)
0.27
(2.29)
-0.21
(-1.91)
-3.86
(-4.81)
745
0.15
0.53
(3.91)
0.56
(4.16)
-0.11
(-0.86)
2.21
(8.16)
583
0.09
3.33
(14.43)
544
0.00
0.60
(7.33)
0.54
(4.18)
0.32
(2.23)
-0.07
(-0.57)
-4.02
(-4.25)
526
0.17
3.44
(18.6)
600
0.00
0.54
(7.1)
0.63
(5.04)
0.35
(2.58)
-0.23
(-1.81)
-3.46
(-3.89)
579
0.15
3.55
(35.6)
724
0.00
Note: The table is split into Panels A and B because of its size. The dependent variable in these OLS regressions is log(RRA), the log of relative risk
aversion calculated from investment portfolios and wealth. The main explanatory variables are the risk aversion measures from the NFBC survey. For the
lottery and risky investment question, the variable names reflect the reference value (wealth, household income, personal income) used in the utility
function. Female, married, and university are indicator variables. t-statistics (in parentheses) are calculated from heteroskedasticity-corected standard errors.
0.04
(0.63)
0.57
(8.41)
0.55
(4.91)
0.29
(2.33)
-0.18
(-1.61)
-3.88
(-4.78)
697
0.16
22
TABLE 5. REVEALED PREFERENCE ARA AND SURVEY MEASURES OF RISK AVERSION
ln(lot.ara)
0.13
(4.51)
0.06
(2.06)
ln(rinv.ara)
0.07
(1.22)
-0.04
(-0.81)
general risk
0.08
(3.36)
0.05
(2.15)
risky job
0.18
(3.3)
ln(wealth)
female
married
university
intercept
N. observations
R-squared
-8.15
(-55.47)
813
0.03
-0.32
(-4.99)
0.50
(4.26)
0.26
(2.1)
-0.17
(-1.51)
-4.90
(-6.43)
715
0.09
-8.28
(-17.22)
659
0.00
-0.36
(-4.99)
0.61
(4.73)
0.36
(2.61)
-0.27
(-2.1)
-5.04
(-5.27)
591
0.10
-9.14
(-75.33)
870
0.01
-0.33
(-5.26)
0.53
(4.83)
0.26
(2.17)
-0.22
(-1.94)
-5.25
(-6.82)
757
0.09
-9.02
(-97.74)
811
0.01
0.07
(1.16)
-0.33
(-5.04)
0.55
(4.89)
0.29
(2.29)
-0.19
(-1.62)
-5.17
(-6.61)
708
0.08
Note: The dependent variable in these OLS regressions is log(ARA), the log of absolute risk aversion calculated from investment portfolios. The main
explanatory variables are the risk aversion measures from the NFBC survey. Lot.ara (rinv.ara) is the coefficient of absolute risk aversion from negative
exponential utility for the lottery (risky investment) question. Female, married, and university are indicator variables. t-statistics (in parentheses) are
calculated from heteroskedasticity-corected standard errors.
When using absolute risk aversion, we see that lottery, general risk, and risky job are all significant predictors
of revealed preference absolute risk aversion. Only the risky investment question is not significant. Wealth has a
negative and significant coefficient, as expected. As a reminder, absolute risk aversion is decreasing with
portfolio size. Females have higher ARA, as do married individuals. University education is negatively related
to risk aversion, but the statistical significance varies across the models.
In Table 4 and Table 5 we see that there is a relationship between the survey measures and actual behavior,
but the relationships are not very strong. In an attempt to increase explanatory power we could put all four
survey measures in the same regression model, but this is troublesome – they should represent the same
underlying construct, and we know the variables are correlated with each other (see Table 3). We thus run
principal components analysis on the four survey measures, simply using the raw scores for each variable
(Kapteyn and Teppa (2011) used this approach on a set of ordinal measures of risk aversion). Thus we include
responses of zero for the lottery and risky investment question in this analysis, whereas these zero-responses
were excluded from the regressions in Tables 4 and 5 (it is impossible to calculate a value for risk aversion
when the amount gambled is zero). The analysis produces one principal component with an eigenvalue of 1.83.
The other three principal components have eigenvalues less than one. The factor pattern is: lottery (-0.637);
23
risky investment (-0.673); general risk (0.667); risky job (0.722). The negative signs for the weights of lottery
and risky investment are correct; higher values for the lottery and risky investment question reflect lower risk
aversion, while higher values for the general risk and risky job questions reflect higher risk aversion.
We find the factor scores for each individual, and we call this RAfactor. As this variable is based on the raw
scores of the survey responses, it is more like a measure of absolute risk aversion than relative risk aversion. We
thus see how well the RAfactor variable is able to predict revealed preference ARA. The OLS regression results
are in Table 6.
TABLE 6. REVEALED PREFERENCE ARA AND COMPOSITE SURVEY RISK AVERSION
RAfactor
0.30
(5.26)
ln(wealth)
Female
Married
University
Intercept
N. observations
R-squared
-8.78
(-162.01)
793
0.04
0.15
(2.53)
-0.31
(-4.82)
0.47
(4.03)
0.29
(2.31)
-0.19
(-1.61)
-5.24
(-6.79)
696
0.09
Note: The dependent variable in these OLS regressions is log(ARA), the log of absolute risk aversion calculated from investment portfolios. The main
explanatory variable is RAfactor, the factor score of the first principal component of the four survey measures of risk aversion in the NFBC survey. Female,
married, and university are indicator variables. t-statistics (in parentheses) are calculated from heteroskedasticity-corrected standard errors.
We find a significant effect for the RAfactor, robust to the inclusion of the controls. The variable, however,
does not explain much more of the variation in revealed preference ARA than the individual survey measures
used in Table 5. The R-squared only increases to 0.04 from 0.03. The respondents were consistent in answering
the four survey questions, evidenced by the single significant principal component. But even accounting for this
consistency does not help explain much of the variation in actual behavior.
IV. PERSONALITY AND RISK AVERSION
Conlin et al. (2015) show how personality traits are related to stock market participation. In that paper, the
subscales extravagance, sentimentality, and harm avoidance have large negative effects on stock market
24
participation, while there are positive effects for the subscales exploratory excitability, impulsiveness,
dependence and persistence. In this paper we look at the effects of personality on risk aversion, conditional on
being a stock market participant.
We have so far shown that the survey responses are statistically significant predictors of real-world behavior,
but most of the variation in actual behavior is left unexplained. Here we show that personality may help to
explain part of this difference. Table 7 has the OLS results for our risk aversion measures regressed on the TCI
personality traits and controls. Panel A has the personality traits alone, and Panel B has the personality traits and
controls for wealth, gender, marital status, and university education. The first five columns on the left side of
the table have the survey measures, and the three columns on the right side of the table have the revealed
preference measures and wealth. We include the model with wealth as the dependent variable because it helps
to show whether the effect on relative risk aversion is due more to the effect on the size of the portfolio or the
effect on wealth.5
A clear pattern emerges in the results. With few exceptions, the personality trait scores are significant
predictors of either survey-based measures of risk aversion or revealed preference measures, but not both. In
Panel A, impulsiveness, disorderliness, worry/pessimism and persistence are significantly related to survey
measures, but show no relationship with revealed preference measures. These variables retain their significance
in Panel B except worry/pessimism, which drops out when controls are added. Exploratory excitability has a
significant effect on the general risk and risky job responses, and it also has a significant effect on RRA.
Extravagance shows a large positive effect on risk aversion for both survey and revealed preference measures in
Panel A, but the effect on the survey measures is no longer significant in Panel B. Sentimentality has a large
positive effect on risk aversion for both survey and revealed preference measures, and its effects are robust to
the inclusion of controls. Fear of uncertainty is positively related to risk aversion for the survey measures when
no controls are included in the regression. The negative coefficient on fear of uncertainty for RRA seems to
5
As explained in Section I, ARA = 1/investment and RRA = 1/(investment/wealth). Thus we have ln(RRA) = ln(wealth) - ln(ARA).
25
come from its negative relationship with wealth; fear of uncertainty shows no relationship with portfolio size
.
For the controls, wealth is negatively related to risk aversion for the survey responses and real world
behavior. Females are more risk averse across the board. Married individuals show greater risk aversion for
only the general risk question on the survey, but being married has a large effect on real world behavior –
married individuals have greater absolute risk aversion and greater relative risk aversion. Married people report
higher wealth (not surprisingly, as the survey asks for household wealth) but they also have smaller investment
portfolios. While a university degree is negatively related to the lottery, risky investment, and risky job
measures, it is not a significant predictor of the general risk measure. University education is also positively
related to wealth, but not to absolute or relative risk aversion.
What is the significance of this overall pattern of the personality traits’ effects across the survey and revealed
preference measures? The pattern suggests personality traits affect the way people answer the risk aversion
questions in an interesting way. Exploratory excitability leads to more willingness to take risks in general and a
willingness to take the "new" risky job, but it does not affect the willingness to take monetary gambles in the
survey. The trait impulsiveness seems to respond to the 10000€ endowment of the risky investment question,
but the trait does not affect the willingness to bet on the lottery question. Individuals with higher disorderliness
scores are more willing to make monetary gambles in the survey, but do not see themselves as generally more
willing to take risks in general. People with high persistence scores are driven to achieve their goals, and they
are willing to take some risks along the way. This willingness to take risks, though, is not reflected in the level
of wealth or size of the investment portfolio.
Worry/pessimism and fear of uncertainty are positively related to general risk aversion and lower risky
investment values, but show no relation to the lottery question; people with higher worry/pessimism and fear of
uncertainty may be less afraid of taking small gambles than they are of losing what they already have. 6 Lower
6
The overall lower level of risk aversion in the risky investment question compared to the lottery question could be a result of the "house money" effect of Thaler
and Johnson (1990). Individuals who express lower risk aversion on lottery than the risky investment could be subject to an "endowment effect" (Kahneman et al.
(1990)). With only the two questions, we are unable to distinguish between the two effects.
26
fear of uncertainty has been shown to be positively related to the decision to be self-employed (Ekelund et al.
(2005)). Being an entrepreneur likely entails putting some of your wealth at risk, a quite different matter from a
willingness to take small gambles. It is interesting to find that while fear of uncertainty has a negative effect on
wealth, it is not related to the amount invested.
Two traits that have robust effects on revealed preference are likely reflective of behaviors that have a
cumulative impact on wealth and investment in risky assets. People with high extravagance scores have a
preference for spending over saving; this leads to both lower wealth accumulation and smaller investment
portfolios. Higher scores for attachment and dependence are common for more social people, and being social is
likely to increase stock market participation (Hong et al. (2005)). Conlin et al. (2015) showed the effect of
dependence on stock market participation was stronger among those more likely to be stock market participants
- people with university degrees and managerial level occupations.
Sentimentality shows a large effect for the lottery, general risk, and risky job questions, and it also has a large
effect on the both ARA and RRA. The effects are robust to the inclusion of controls. Sentimentality is an
interesting trait in that it is very difficult to make a priori predictions for the trait's relationship with economic
behavior. People who cry at movies, are moved by poetry, and like pleasing others (examples taken from the
TCI questionnaire) have higher scores on sentimentality. These types of behavior are not related to any
economic interpretation of risk aversion, yet sentimentality has a strong relationship with risk aversion - both in
the survey and in the real world.
27
TABLE 7. RISK AVERSION AND PERSONALITY TRAITS
Panel A. No Controls
Exp Excitability NS1
Impulsiveness NS2
Extravagance NS3
Disorderliness NS4
Worry/pess HA1
Fear of uncert HA2
Shyness HA3
Fatigability HA4
Sentimentality RD1
Attachment RD3
Dependence RD4
Persistence P
Intercept
n. obs
r-squared
RAfactor
-0.094**
(-1.96)
-0.166***
(-4.085)
0.110**
(2.493)
-0.117***
(-2.936)
0.081*
(1.751)
0.131***
(2.725)
-0.002
(-0.045)
-0.024
(-0.52)
0.158***
(4.117)
0.008
(0.187)
-0.043
(-1.222)
-0.144***
(-3.719)
0.135***
(3.680)
669
0.19
Lottery
10.034
(0.21)
15.722
(0.381)
-93.198**
(-2.306)
121.156***
(3.045)
-17.785
(-0.448)
-41.769
(-0.8)
-60.682
(-1.418)
45.596
(1.179)
-145.956***
(-3.956)
-0.608
(-0.014)
76.100**
(2.142)
53.279
(1.353)
397.385***
(11.943)
726
0.06
Risky.inv
29.894
(0.226)
278.149**
(2.329)
-326.984***
(-2.683)
289.944**
(2.437)
-256.920**
(-2.012)
-255.384*
(-1.698)
142.919
(1.088)
23.135
(0.171)
-121.802
(-1.105)
-22.961
(-0.183)
148.253
(1.415)
241.965**
(2.157)
2907.058***
(26.317)
718
0.07
Gen.risk
-0.360***
(-3.465)
-0.365***
(-4.027)
0.109
(1.132)
-0.065
(-0.769)
0.211**
(2.036)
0.175*
(1.743)
0.025
(0.236)
0.022
(0.208)
0.240***
(2.908)
-0.064
(-0.716)
0.018
(0.225)
-0.246***
(-2.913)
4.391***
(51.001)
730
0.17
Risky.job
-0.110**
(-2.29)
-0.122***
(-3.038)
0.024
(0.564)
-0.058
(-1.574)
-0.002
(-0.049)
0.134***
(2.865)
-0.035
(-0.728)
-0.002
(-0.033)
0.116***
(2.954)
0.053
(1.287)
0.009
(0.23)
-0.109***
(-2.769)
1.336***
(32.832)
686
0.11
Ln(ARA)
-0.04
(-0.5)
-0.002
(-0.03)
0.344***
(4.991)
-0.035
(-0.583)
-0.031
(-0.41)
0.002
(0.024)
-0.01
(-0.141)
0.047
(0.626)
0.243***
(3.85)
0.018
(0.265)
-0.139**
(-2.251)
-0.073
(-1.177)
-8.596***
(-138.948)
756
0.06
Ln(RRA)
-0.170**
(-1.993)
0.059
(0.775)
0.242***
(3.058)
-0.03
(-0.434)
0.028
(0.328)
-0.134
(-1.565)
-0.049
(-0.598)
-0.062
(-0.685)
0.268***
(3.974)
0.140*
(1.929)
-0.056
(-0.762)
0.002
(0.024)
3.635***
(51.303)
664
0.06
Ln(wealth)
-0.065
(-1.271)
0.023
(0.522)
-0.125***
(-2.708)
0.007
(0.179)
0.007
(0.127)
-0.107**
(-2.003)
-0.021
(-0.39)
-0.073
(-1.33)
0.013
(0.293)
0.114***
(2.781)
0.091**
(2.147)
0.068
(1.448)
12.293***
(259.741)
664
0.05
Note: The table shows OLS regression results of risk aversion on personality. The left five columns have the survey based measures as
dependent variables. RAfactor is the factor score for the first principal component of the four survey measures. Lottery and Risky.inv
are the answers from the survey, including responses of zero (for these two columns, positive coefficients represent decreased risk
aversion). The right three columns have the revealed preference measures and wealth as dependent variables. ln(ARA) and ln(RRA)
are the logs of absolute and relative risk aversion. The personality trait scores are normalized to mean zero and standard deviation of
one. Panel A has only the personality trait scores. In Panel B, female, married, and university are indicator variables. t-statistics (in
parentheses) are calculated from heteroskedasticity-corrected standard errors. *, **, and *** represent statistical significance at the
10%, 5%, and 1% levels, respectively. Coefficients significant at the 10% level or better are colored in red (green) for the survey
(revealed preference) to highlight the pattern of significance.
28
TABLE 7. RISK AVERSION AND PERSONALITY TRAITS
Panel B. Controls added.
Exp Excitability NS1
Impulsiveness NS2
Extravagance NS3
Disorderliness NS4
Worry/pess HA1
Fear of uncert HA2
Shyness HA3
Fatigability HA4
Sentimentality RD1
Attachment RD3
Dependence RD4
Persistence P
ln(wealth)
Female
Married
University
Intercept
n. obs
r-squared
RAfactor
-0.099**
(-2.14)
-0.165***
(-3.918)
0.05
(-1.127)
-0.13***
(-3.326)
0.045
(-0.96)
0.067
(-1.326)
0.042
(-0.932)
-0.011
(-0.247)
0.084**
(-2.081)
0.006
(-0.143)
0.022
(-0.598)
-0.116***
(-2.978)
-0.12***
(-3.823)
0.532***
(-7.151)
0.035
(-0.489)
-0.161**
(-2.278)
1.371***
(-3.686)
593
0.28
Lottery
22.187
(-0.444)
9.38
(-0.203)
-46.015
(-1.028)
118.48***
(-2.798)
-5.211
(-0.12)
15.14
(-0.262)
-90.395*
(-1.926)
45.065
(-1.076)
-89.553**
(-2.335)
0.187
(-0.004)
31.075
(-0.816)
27.578
(-0.654)
73.273**
(-2.534)
-443.924***
(-6.479)
53.111
(-0.691)
192.722***
(-2.709)
-405.084
(-1.182)
641
0.11
Risky.inv
8.734
(-0.064)
282.633**
(-2.262)
-193.629
(-1.491)
333.992***
(-2.683)
-182.661
(-1.346)
-186.923
(-1.164)
65.025
(-0.472)
-10.823
(-0.077)
36.417
(-0.301)
-13.55
(-0.105)
-24.75
(-0.225)
159.49
(-1.342)
221.139**
(-2.086)
-912.178***
(-3.958)
-182.377
(-0.789)
397.765*
(-1.801)
631.432
(-0.495)
634
0.1
Gen.risk
-0.431***
(-3.985)
-0.387***
(-4.128)
0.088
(-0.904)
-0.05
(-0.584)
0.168
(-1.56)
0.109
(-1.059)
0.082
(-0.769)
0.026
(-0.245)
0.177**
(-2.08)
-0.116
(-1.269)
0.08
(-0.956)
-0.232***
(-2.638)
-0.134*
(-1.72)
0.759***
(-4.467)
0.376**
(-2.306)
0.178
(-1.12)
5.345***
(-5.661)
641
0.23
Risky.job
-0.093*
(-1.895)
-0.11***
(-2.599)
-0.022
(-0.477)
-0.073**
(-1.952)
-0.027
(-0.562)
0.089*
(-1.793)
-0.006
(-0.123)
0.006
(-0.129)
0.078*
(-1.776)
0.048
(-1.123)
0.031
(-0.772)
-0.097**
(-2.411)
-0.12***
(-3.361)
0.267***
(-3.157)
-0.031
(-0.4)
-0.134*
(-1.765)
2.723***
(-6.331)
605
0.15
Ln(ARA)
-0.096
(-1.174)
0.035
(-0.512)
0.274***
(-3.721)
-0.007
(-0.108)
0.007
(-0.083)
-0.1
(-1.266)
-0.021
(-0.29)
0.001
(-0.017)
0.235***
(-3.562)
0.024
(-0.342)
-0.127**
(-1.911)
-0.044
(-0.708)
-0.337***
(-5.034)
0.363***
(-2.919)
0.349***
(-2.779)
-0.195
(-1.628)
-4.81***
(-6.02)
643
0.13
Ln(RRA)
-0.142*
(-1.68)
0.053
(-0.706)
0.197**
(-2.442)
-0.008
(-0.115)
0.015
(-0.171)
-0.166*
(-1.884)
-0.042
(-0.523)
-0.035
(-0.392)
0.244***
(-3.374)
0.08
(-1.096)
-0.073
(-0.998)
-0.004
(-0.062)
Ln(wealth)
-0.07
(-1.351)
0.027
(-0.615)
-0.117**
(-2.508)
-0.002
(-0.044)
0.012
(-0.229)
-0.099*
(-1.788)
-0.032
(-0.608)
-0.055
(-0.991)
0.013
(-0.286)
0.083**
(-2.014)
0.081*
(-1.888)
0.06
(-1.251)
0.359**
(-2.468)
0.574***
(-4.266)
-0.058
(-0.443)
3.139***
(-21.901)
643
0.09
-0.007
(-0.07)
0.339***
(-3.661)
0.207**
(-2.484)
11.991***
(-122.576)
643
0.08
Note: The table shows OLS regression results of risk aversion on personality. The left five columns have the survey based measures as
dependent variables. RAfactor is the factor score for the first principal component of the four survey measures. Lottery and Risky.inv
are the answers from the survey, including responses of zero (for these two columns, positive coefficients represent decreased risk
aversion). The right three columns have the revealed preference measures and wealth as dependent variables. ln(ARA) and ln(RRA)
are the logs of absolute and relative risk aversion. The personality trait scores are normalized to mean zero and standard deviation of
one. Panel A has only the personality trait scores. In Panel B, female, married, and university are indicator variables. t-statistics (in
parentheses) are calculated from heteroskedasticity-corrected standard errors. *, **, and *** represent statistical significance at the
10%, 5%, and 1% levels, respectively. Coefficients significant at the 10% level or better are colored in red (green) for the survey
(revealed preference) to highlight the pattern of significance.
V. CONCLUSION
We estimate risk aversion from survey responses and from revealed preferences. The data come from the
Northern Finland Birth Cohort 1966 survey conducted in 2012 and from the official register of stockholdings of
29
the Finnish Central Securities Depository. From the NFBC survey, we have responses to four questions of
various types: the standard lottery question with fixed probabilities and fixed payoffs (as in Guiso and Paiella
(2008)); an investment question with fixed probabilities and relative payoffs (as in Halko et al. (2012)); a
question with fixed probabilities and fixed payoffs framed in terms of lifetime income (as in Barsky et al.
(1998)); and a simple question asking for general willingness to take risks (as in Dohmen et al. (2011)). The
FCSD data contain the value of stockholdings for shares registered in Finland.
We find the respondents to be fairly consistent in their expression of risk aversion in the survey questions,
with rank correlations ranging from 0.18 to 0.38. We also run principal component analysis on the four
questions and we find a single significant factor. For the revealed preferences we find decreasing absolute risk
aversion and increasing relative risk aversion; these are cross-sectional measures and we are unable to say
anything about how risk aversion might change in response to changes in wealth at the individual level. We find
the survey measures to be statistically significant predictors of real-world behavior, but the survey measures
only explain a small fraction of the variation in the revealed preference measures.
The variation left unexplained in the revealed preferences is not indicative of mismeasurement or poorly
defined concepts. Using the size of the portfolio and the share of wealth invested in risky assets as measures of
risk aversion come directly from expected utility theory. Even abstracting from expected utility theory, one can
hardly argue that the size of the risky investment portfolio and the share of wealth invested in risky assets do not
represent risk aversion in some sense. Our survey measures are simple and straightforward measures of risk
aversion, and have been used in the literature previously. It is thus difficult to argue that we are not capturing
risk aversion.
We find that personality traits may help explain the difference between the survey measures and the revealed
preference measures. Certain personality traits have a large influence on the survey responses, but have no
discernible effect on revealed preferences. There are also traits that have significant effects on revealed
preferences without showing a corresponding effect on the survey measures. The implication is that the traits
related to revealed preferences (extravagance, sentimentality, attachment, dependence) likely reflect behaviors
30
that have a cumulative effect over time. The traits that are significant predictors of mainly survey measures
(exploratory excitability, impulsiveness, disorderliness, worry/pessimism, persistence) seem to affect behavior
for actions that do not have cumulative effects, at least when measured by wealth and size of the investment
portfolio.
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33
Appendix A
CRRA functions
We present a simple decision problem (a standard portfolio problem) of an investor. He can invest in two
assets: a risky security and a riskless security. The goal of this exercise is to measure the attitude towards risk
by this investor. We want to relate his risk behavior to observables so that we can obtain a direct measure for
risk aversion for a particular investor. For that purpose we assume that the investor has the constant relative risk
aversion (CRRA) utility function, i.e.
A.1
W 1
u (W ) 
.
1 
We assume   0 and   1 . When   1 , the preferences are logarithmic.
We first proceed with a general utility function, u (W ) with assumptions u' (W )  0 and u' ' (W )  0 . With a
slight abuse of notation we denote by W the initial wealth of an investor. He can invest in a risky asset, the net
return of which is stochastic and is denoted by ~
r . The density function of the return is f (r~) . We assume that
the riskless return is r . The share of initial wealth invested in a risky asset is denoted by x . The final wealth of
the investor will thus be
A.2
~
W  (1  r )(1  x)W  (1  ~
r ) xW  (1  r )W  (~
r  r ) xW .
The standard portfolio problem is then
A.3
(SPP)
~
max
~
r  r ) xW .
Eu (W ) s.t. W  (1  r )W  (~
x
The first-order condition is
A.4
Eu'(1  r )W  (~
r  r ) xW (~
r  r )W   0 .
By cancelling out W it is
A.5
Eu'(1  r )W  (~
r  r ) xW (~
r  r )  0 .
Since the utility function is strictly concave the second-order condition,
34
A.6


E u' '(1  r )W  (~
r  r ) xW (~
r  r )2W  0 ,
is automatically fulfilled.
We next proceed by considering a Taylor expansion of the utility function around (1  r)W . We first
obtain
A.7
u'(1  r )W  (~
r  r ) xW   u'(1  r )W   u' '(1  r )W (~
r  r ) xW  .
Equation (A.4) can now be approximated by
A.8
Eu'(1  r )W   u' '(1  r )W (~
r  r ) xW (~
r  r)  0 .
Since (1  r)W is non-stochastic we can re-express (6) as
A.9
 u ' ' (1  r )W (1  r )W  (~

r  r )  ~
u ' (1  r )W E 1 
x  ( r  r )  0 ,

u ' (1  r )W 
 1  r 


and of course as
A.10
 u ' ' (1  r )W (1  r )W  (~

r  r )  ~
E 1 
x  ( r  r )  0 .

u ' (1  r )W 
 1  r 


Suppose now the utility function is of the CRRA type as in equation (1) above. Then
A.11

u ' ' (1  r )W (1  r )W
 .
u ' (1  r )W 
Now we can express (10) as
A.12


 (~
r  r )  ~


E 1   
x  (r  r )  0 .


 1  r 


Taking expectations we get
A.13

E (~
r  r) 
E (~
r  r )2 x  0 .
1 r
r  r )2 (=  r2 ) is the variance of excess return. It
E (~
r  r ) (= r ) is the mean of the excess return and E (~
finally follows from (11)
35
A.14

(1  r ) r 1
.
 r2
x
Given the data on r ,  r2 , and, in particular, a person’s share of risky investments, the aversion to risk can be
computed from (12) for each investor.
Suppose the riskless return is close to zero, the excess return around 6%, the standard deviation around
30%, and the share of risky investments out of wealth around one half. We compute the person’s relative risk
aversion coefficient to be around 1.33 (=.06/((.09)(.5)). Suppose the share is 0.67, then   1 , i.e. this investor
has (almost) logarithmic preferences. If x  1/ 10 , then   6.67 .
CARA functions
For the sake of comparison we also consider the case of utility function, where the absolute risk aversion
measure,  u' ' (W ) / u' (W ) , is constant. The utility function then is
A.15
u (W )  
1

eW .
To ease the notation we assume that r  0 , and that the risky rate is normally distributed, i.e. ~
r ~ N ( r ,  r2 ) .
Now we can write the standard portfolio problem (SPP) as follows
A.16
(~
r   r ) 2 


max   1  (W  ~r xW )  1
2 r2  ~
 e
e
(SPPA)

  2
dr .
x   
 r


By rewriting we get the objective function as
  W (1 ~r x )  ( ~r  2r ) 2  
1 1
2 r   ~
e 

dr





  r 2



A.17
Now, in particular, consider the exponent
A.18
(~
r r )2
EXP  W (1  ~
r x) 
.
2
2 r
36
We compute
2~
2
~ 2 2 ~
r r  r
r
EXP  2 r W  2 r r2xW
2
2
A.19
.
r
We concentrate on the numerator
A.20
NUM  2 2W  2 2~
r xW  ~
r 2  2 ~
r  2
r
r
r
r
Rewriting we get
A.21


NUM  ~
r 2  2~
r     2 xW    2  2 2W .
r
r
r
 r

Completing the square we get
A.22



2

2
NUM  ~
r 2  2~
r     2 xW       2 xW       2 xW    2  2 2W .
r
r
r
r
r
 r

 r

 r

This can be then expressed as
A.23

2


NUM  ~
r  (    2 xW )   2  2 2W      2 xW  2 .
r
r
r
r
r


 r

We can plug this back into the original objective function to get
A.24
   ~r  (  r  r2 xW ) 2   r2  2 r2W  r  r2 xW 2  

2 r2
1
1
 


e
d~
r.





  r 2





We can separate this expression as
 1   r  2 r W 2r  r xW 
 e
2 r
 

2
A.25
2
2
2
 1

  2
 r
Consider the term
A.26
1
 r 2
   ~r  (  r 2r2 xW )  2  
2 r

  ~
dr
 e 




   ~r  (  r 2r2 xW )  2  
2 r

  ~
dr .
 e 




37
in the above expression. The integrand is clearly a density function for the normal distribution with
mean  r   r2 xW and variance  r2 . Thus the expression (25) equals unity. We have been able to “reduce” the
original optimization problem to
A.27
max  1 
 e
x  


 r2  2 r2W   r  r2 xW
2 r2
 
2
.


2
To maximize the expression we need to make the term  r  r2 xW  as small as possible, i.e. equal to zero. This
yields
A.28
r   r2 xW  0 .
Thus we get
A.29

r
 xW
2
r
.
In contrast to the result with CRRA utility functions, this condition holds precisely.
38
Appendix B
Table B.1
The table lists the higher-order traits and subscales of the Temperament and Character Inventory (Cloninger et al. (1993)).
Persistence was originally a subscale of reward dependence, and thus it has no subscales. Persistence also had the label R2
when it was a subscale of reward dependence; thus there is no missing reward dependence subscale. The commonly used
labels are included after the trait/subscale name.
Higher-Order Trait
Novelty Seeking NS
Subscale
Exploratory Excitability NS1
Impulsiveness NS2
Extravagance NS3
Disorderliness NS4
Harm Avoidance HA
Worry/pessimism HA1
Fear of uncertainty HA2
Shyness HA3
Fatigability HA4
Reward Dependence RD
Sentimentality RD1
Attachment RD3
Dependence RD4
Persistence P