Risk aversion: measurement, determinants and financial
decisions
Tim van den Bosch
",∗, supervised by Dr. Artūrus Juodis
"" Faculty of Economics and Business, University of Groningen, The Netherlands
ARTICLE INFO ABSTRACT
JEL classifications: D14 D80 D81 Keywords: Risk aversion Household finance
This paper studies risk aversion using a demographically representative sample of the Dutch population from the Longitudinal Internet Studies for the Social sciences (LISS) panel. Using a measure of risk aversion based on incentivised lottery questions, the relationship between several demographic factors and risk aversion is analysed. Subsequently, the effect of risk aversion on financial household decisions is examined. This paper finds that gender and age are significantly positively correlated with risk aversion, while income and wealth are significantly negatively correlated with risk aversion. Furthermore, this paper finds that risk aversion increases the likelihood of holding a savings account and decreases the likelihood of holding risky assets. Furthermore, risk aversion is positively correlated with the amount of savings and negatively correlated with the share of financial assets allocated to risky assets. This paper finds no significant relationship between risk aversion and holding decision nor the amount of debt and mortgages.
∗ Corresponding author at: Faculty of Economics and Business, student number s2353326,
Nettelbosje 2, 9747 AE Groningen, NL.
2 1. Introduction
Risk and uncertainty play a role in almost every important economic decision. Consequently, understanding individual attitudes towards risk is intimately linked to the goal of understanding and predicting economic behaviour. In this respect, risk aversion may well be the most fundamental pattern of preference that economists use to explain heterogeneity in individual behaviour under uncertainty (Guiso and Paiella, 2004). Risk aversion has been used to explain a wide range of differences in individual behaviour, including those observed in household financial portfolio decisions. Important financial household decisions, including stock market participation, debt accumulation and savings decisions, are found to be influenced by risk aversion. (Donkers and van Soest 1999; Shum and Faig, 2006; Puri and Robinson, 2007; Brown, 2013)
Since risk aversion is a key driver of individual financial behaviour, the determinants of risk aversion have been widely studied. Empirical studies have identified a wide range of individual characteristics, such as gender, age, education, income and wealth that are all correlated with risk attitudes (see Outreville, 2014 for an overview).
3 In experimental economic studies, problems regarding the measurement instrument can be overcome. In experimental design, a lottery based incentive compatible measure of risk aversion can be obtained (e.g. Eckel and Grossman, 2008 and Croson an Gneezy, 2009). However, the samples of these experiments are limited due to cost and effort to administer. Consequently, they are mostly administered on a convenience samples. This results in serious sample limitations, making the results non-generalizable and possibly biased, due to sample selection. Furthermore, information on financial decisions of participants is often not obtained in these experimental settings. Hence, the influence of the obtained risk aversion measure on financial decisions outside the experimental setting cannot be analysed.
This paper sets out to determine whether previous results are correct or that these shortcomings in measurement instruments or data set employed, have resulted in possible biased estimators of both the determinants of risk aversion and the influence of risk aversion on financial decisions.
The contribution of this paper is twofold. Firstly, this paper overcomes aforementioned problems of previous research in terms of measurement instrument employed and data set used by using a measure of risk aversion based on incentivised lottery questions conducted among a large demographically representative sample. Using this measure of risk aversion this paper examines the demographic factors influencing risk aversion and the influence of risk aversion on financial household decisions. Secondly, this paper examines the effect of risk aversion on a wide range of financial decisions, where previous research has had a selective focus on household decisions, mostly limited to stock market participation and share of financial assets invest in risky assets. This paper examines numerous financial household decisions, including savings and the accumulation of debt. Thereby this paper contributes to understanding of the effects of risk attitudes on individuals’ financial decisions. Based on the aforementioned, the research question is twofold:
Which individual characteristics are correlated to risk aversion?
To what extent is risk aversion a determinant of financial portfolio choices?
Correctly assessing the factors influencing risk aversion and the relationship between risk aversion and financial portfolio decisions leads to a better understanding of heterogeneity in individual financial behaviour. This has become of increasing importance since the financial crisis. Following the financial crisis, the Financial Service Authorities (FSA) and other regulatory institutions have issued new guidance consolidation regarding the assessment of client’s risk attitudes that must carefully be taken into account by financial advisors.1 Hence,
increasing regulatory scrutiny has resulted in the need for financial advisors to assess client’s willingness to take risk more closely than ever.
4 This paper finds that gender, higher education and wealth are significantly positively correlated with risk aversion while income is significantly negatively correlated with risk aversion. Subsequently, this paper finds that risk aversion increases the likelihood of holding a savings account and risky assets. Furthermore, this paper finds that risk aversion is positively correlated with the amount of savings and negatively correlated with the share of financial assets allocated to risky assets. No significant relationship between risk aversion and holding decision nor the amount of debt is found.
The remainder of this paper is structured as follows: section 2 gives an overview of the individual characteristics that influence risk aversion, the influence of risk aversion on financial household decisions and the relevant literature on the measure of risk aversion. Section 3 explains the research framework and hypothesis coming forth from the literature. Section 4 explains the methodology employed in this paper. In section 5 the results of the empirical regression are discussed. In section 6 the limitations of this study are considered, after which final conclusions are drawn in section 7.
2 Literature review
This section will first give an overview of risk aversion and individual characteristics that have been found to be correlated with risk aversion.2 Secondly, an overview of previous
studies regarding the effect of risk aversion on individuals’ financial behaviour is provided.3
Thirdly, an overview of the academic discussion regarding the measure of risk aversion used in empirical research is presented.
2.1 Demographics and risk aversion
Individuals respond differently to identical risky situations. In this reaction risk aversion, is the tendency to prefer a certain but possibly less desirable outcome over an uncertain but potentially greater outcome (Boyl, et al., 2012). Risk aversion is regarded to be a key determinant of individuals’ financial decision making. Hence, the determinants of risk attitudes of individuals are of interested to those examining household portfolios (Bajtelsmit et al., 2001). Empirical literature seeks to find observable variables that explain variation in risk aversion between individuals and finds that these differences can partially be explained by individuals’ demographics. Typical covariates used to explain these variations include socio-demographic characteristics (age, race, gender, marital status) as well as resources available to the individual (wealth and income) (see Outreville, 2014 for an overview).
The first personal characteristic that has been widely studied in this context is gender. The majority of empirical literature finds that men are less risk averse than women in both laboratory experiments and field studies (Eckel and Grossman, 2008; Croson and Gneezy,
5 2009). Men are more likely to engage in risky behaviour and are found to be more risk tolerant than women (Riley and Chow, 1992; Bajtelsmit, 2001). This also holds for financial risk tolerance, as men are more likely to be willing to take substantial financial risk (Yao and Hanna, 2005). The result holds across different contexts and cultural environments. Similar results have been found in the Netherlands, Israel, Taiwan and Germany. (Hartog et al., 2002; Cohen and Einav, 2007; Lin, 2009; Dohmen et al., 2011)
Age is also a factor commonly associated with risk aversion. Cohen and Einav (2007) find a non-linear U-shaped relationship between age and risk aversion. This relationship indicates that aversion first decreases and then increases over the lifecycle of an individual. Riley and Chow (1992) and Halek and Eisenhauer (2001) find similar results which show that after the age of 65 the decrease slows down and risk aversion starts to increase again.
Several studies have examined the effects of education on risk aversion. The majority of studies examining the relationship between individual characteristics and risk aversion, find a negative relationship. This indicates that a higher level of education corresponds with a lower level of risk aversion (Riley and Chow, 1992; Lin, 2009; Dohmen et al., 2011). A possible explanation is those investors are less willing to engage in transactions in which they lack understanding (Anber et al., 2010). This explanation is supported by research examining financial knowledge, which find that higher levels of financial knowledge are associated with a lower level of risk aversion (Grable, 2000).
The relationship between health and risk aversion is rather novel, but multiple papers find a significant relationship between health and risk aversion. Decker (2016) finds that health shocks can influence individuals’ level of risk aversion. Individuals with increased health risk are less willing to assume additional financial risk (Rosen and Wu, 2004). By contrast, risk averse persons are less likely to engage in unsafe health behaviour such as smoking cigarettes and hence may have better health (Anderson and Mellor, 2008; Hatfield and Fernandes, 2009). The causality link thus remains unclear.
Marital status is also linked to risk aversion. Single respondents exhibit lower levels of risk aversion (Grable, 2016). The majority of empirical literature finds that marital status is significantly related to risk aversion. Results indicate that single individuals are less risk averse than their married counterparts (Riley and Chow, 1992; Bajtelsmit, 2001; Hartog et al., 2002; Lin, 2009). Although it can be argued that marital status affects the level of risk aversion, it can also be argued that risk aversion affects individual’s life style choices. Spivey (2006) e.g. finds that risk averse individuals take shorter time to get married.
6 employment positions with a high likelihood of stability, but limited opportunity for advancement (Cramer et al., 2002).
2.2 Risk aversion and financial decisions
Risk aversion is a pattern of preference used by economist to explain differences in individual behaviour. Some classical models on portfolio decision-making even assume that an individual’s investment choice is solely based on the risk reward trade-off with risk aversion as only parameter (e.g. Merton 1969; and Gollier, 2001). Risk aversion is no longer seen as the only factor influencing financial decision making, as a large stream of studies indicate that investment decisions are also driven by other factors e.g. financial literacy and health (Rosen and Wu 2011; Rooij et al 2011). However, risk aversion remains to be identified as an important determinant of individuals’ financial decisions (Boyle, et al., 2012).
The role of risk aversion in financial decision-making has been most extensively examined in context of the holding and allocation decision of risky investments. From the point of view of standard portfolio theory, the amount a person is willing to invest, depends on their degree of risk aversion. In this theory, more risk averse investors hold safer portfolio’s (Gollier, 2001). Risk averse investors are thereby expected to forgo relatively higher expected returns for more certain returns with lower variability.
In this respect, the stock market participation decision has received the most academic interest. This concerns individuals’ overall decision whether to invest in risky assets; equity, mutual funds, options or bonds. The main body of literature finds that the probability of holding stock is smaller for those with a high degree of risk aversion. For example, Dimmock and Kouwenberg (2010) find a significant negative relationship between risk aversion and decision to hold risky assets. The main body of literature find a significant negative effect of stock risk aversion on stock market participation. However, Guiso et al. (2008a) find little predictive power of risk aversion for financial risk taking.
Risk aversion has not only been examined in the light of the overall decision of holding an asset, but also in the light of the allocation decisions. Prior empirical literature finds that higher levels of risk aversion are associated with lower shares of financial assets allocated to the stock market (Shum and Faig, 2006; Puri and Robinson, 2007; Donkers and van Soest, 1999). This indicates that both the holding decision as the allocation decision in terms of risky assets are influenced by risk aversion.
7 which is subject to significant risk. Among others, these risks stem from possible unemployment and changes in real wages. Hence, risk aversion of an individual will potentially play a key role in the decision to acquire debt. Intuitively, one predicts that risk aversion is negatively correlated with both the an individual is, the lower the likelihood an individual holds debt and the amount held will be, if there is a probability that one is unable to repay this debt in the future.
Crook (2001) is among the few that does examine the relationship between risk aversion and debt. Results from this study indicate a negative relationship between the risk aversion and the demand for debt. Brown (2013) finds similar results using household level data drawn from the United States, indicating that risk aversion is inversely associated with the amount of secured, unsecured and total debt accumulated at the household level. However, Donkers and Van Soest (1999) examine the height mortgages, using Dutch household data, and find no significant relationship between risk aversion between risk aversion and the height of the mortgages. Hence, current literature is inconclusive on the relationship between risk aversion and the accumulation of debt.
2.3 Financial risk aversion measure
Multiple methods have been employed to measure individuals’ risk aversion. Previous researches have used objective measures, self-reported scales, lottery election questions, gambling behaviour and even televisions shows to construct measures of risk aversion. However, these employed measures have been subject to several shortcomings. The advantages and disadvantages of the different measures will be discussed below.
8 Another, more valid measure, is a risk tolerance scale. A widely used form of such a risk tolerance scale is self-reported risk tolerance, which is used as a measure of an individuals’ self-assessed willingness to accept risk (Hanna, 2001). A high score on the scale is associated with a low level of risk aversion. It remains questionable whether the use of survey questions is a comprehensive method for measuring risk aversion. Various factors including self-serving bias, inattention and strategic motives could cause respondents to distort their reported risk attitudes (for a discussion see Camerer and Hogarth, 1999). Furthermore, since survey questions are not incentive compatible, economists are sceptical whether self-reported personal attitudes and traits are useful for predicting real life behaviour (Ding et al., 2010). Another problem with this measure is that the self-assed measure of risk aversion is often based on a single-item question that not necessarily reveals individuals’ risk preference.
The Survey of Consumer Finances (SCF) contains such a question and is widely used in empirical research because it is one of the only direct measures of risk aversion attitudes for a demographically representative sample asked in national surveys to consumers in the U.S. (Grable, 2016). The question asked in the SCF is as follows:
“Which of the following statements on this page comes closest to the amount of financial risk that you are willing to take when you save or make investments?”
1. Take substantial financial risk expecting to earn substantial returns
2. Take above average financial risks expecting to earn above average returns 3. Take average financial risks expecting to earn average returns
4. Not willing to take any financial risks.
This single item may not be a good measure of risk aversion (Chen and Finke 1996). The answers to this question are clearly influenced by personal beliefs of the respondent about what “substantial”, “above average” and “average” financial risks mean. The item is closely linked to investment choice attitude, which not only captures risk aversion (Grable and Lytton, 2001). Moreover, the question does not distinguish between risk aversion and risk perception, because it is asked through a self-assessment question. This could result in a measure of risk aversion that ‘does not necessarily reveal pure preferences’ (Hanna and Chen (1997). Hence, self-reported measures of risk aversion suffer from significant shortcomings.
9 measure obtained through hypothetical lottery payoffs is an indicator of an individuals’ actual risk aversion, however may significantly differ from the level of risk aversion observed in real life situations.
A fourth alternative used to measure risk aversion, overcomes the problem of the lack of monetary incentives by constructing a measure of risk aversion from actual choices made by individuals. Bombardini and Trebbi (2012) employ such a method and base their measure of risk aversion on an Italian television show. Another example of such a measure is that of Cohen and Einav (2007) who construct their measure of risk aversion on the basis of deductibles in insurance contacts. The outcomes are then used to check whether previously found factors argued to influence risk aversion still hold for actual decisions made by individuals. Since actual money is involved in the game show and insurance contracts, the outcomes are not subject to the incentive distortion of hypothetical survey questions. This is not without cost, because individuals’ wealth and other relevant variables are unobserved in these studies. Furthermore, the samples are not a representation of the population, which makes generalization of findings difficult. Additionally, some of these studies require strong assumptions on individuals believes e.g. the probability of an accident as in the research of Cohen and Einav (2007).
The last alternative instrument to measure risk aversion stems from experimental economic research. In economic experiments, problems regarding measurement construction can be overcome. Experimental studies could thus provide the most reliable measures of risk aversion, because the experiment can be incentivised and objectively assessed. In these studies risk aversion is measured through incentivised lottery questions. Participants are presented with choices between a certain and uncertain payoff. However, the samples for which this measure of risk aversion is obtained are limited. Since this technique is costly and difficult to perform with a large representative sample, studies of significant scale can hardly are rare. In experimental psychology and economic literature, the data sets are typically small and possibly biased, due to sample selection This makes that the results found are often not generalizable to the entire population. For example, Ding et al. (2010) construct their risk aversion measure based on lottery election questions with monetary payoffs, but only among a limited convenience sample of 121 students. Furthermore, in these experimental settings information on financial decisions of participants is often not obtained, which limits the possibility of examining the effect of risk aversion on financial decision making outside the experimental setting.
3. Research framework and hypotheses
10 aversion hold, when employing an improved measure of risk aversion. Subsequently, the predictive power of the measure of risk aversion for financial household decisions is evaluated. Previous research has had a selective focus on household decisions, mostly limited to stock market participation decision. Households however make a wide range of financial decisions. Therefore, this paper examines numerous financial household decisions, including the accumulation of debt and savings. This paper conducts two analyses. The first analysis examines the relationship between individual characteristics and risk aversion. The second analyses the relationship between risk-aversion and financial household decisions both in terms of holding as the allocation decision of financial asset/debt classes.
3.1 Hypotheses socio-demographic factors and risk aversion
Several individual characteristics have been identified to affect risk aversion, as discussed in the literature review. The factors that have gained the most support in the literature are age, gender, marital status, wealth, income, type of employment and education. Gender is an important factor that affects risk aversion, as women are more are found to be more risk averse than men (Eckel and Grossman, 2008). Age is another factor associated with risk aversion and seems to exhibit a non-linear relationship. This indicates that age first decreases and after the age of 65 increases risk aversion (Cohen and Einav, 2007). Education is also correlated with risk aversion, as education is found to have a negative relationship with risk aversion (Dohmen et al., 2011). Furthermore, singles are found to be less risk averse, marriage is therefore expected to be positively related to risk aversion (Lin, 2009). The relationship between risk aversion and being self-employed is expected to be negative (Hartog et al., 2002). Based on relationships found in previous empirical literature the first hypothesis is:
%&: Male, age, single, higher educated, self-employed, good health, income and wealth are significantly negatively correlated with risk aversion.
3.2 Hypotheses risk aversion and financial risky decisions
11 %': Risk aversion is significantly positively correlated to the probability of having savings and the amount of savings.
%(: Risk aversion is significantly negatively correlated to the probability of having a risky asset and the share invest in risky assets.
The decision to acquire debt is a major financial decision involving significant risks and uncertainty in terms of the repayment obligations that originate from the accumulation of debt. Therefore, individuals’ risk aversion will potentially be an important determinant of the decision to acquire debt. Intuitively, one predicts that the more risk averse an individual is, the lower the probability is that individual holds debt. Furthermore, the amount of debt is also expected to be lower for more risk averse individuals (Brown, 2013). Hence, the following hypotheses:
%): Risk aversion is significantly negatively correlated to the probability of having debt and
the amount of debt
%*: Risk aversion is significantly negatively correlated to the probability of having a mortgage and the height of the mortgage.
4. Data and methodology 4.1 Data
The data used in this paper is obtained from the LISS panel. The LISS panel is an internet panel managed by CentERdata, which is affiliated with Tilburg University. The LISS panel consists of approximately 4,500 households, comprising 7,000 individuals. The LISS panel is a representative sample, in terms of observable background characteristics, of the Dutch population. The panel is based on a true probability sample of households drawn from the population register. Households that do not have a computer or internet connection are provided with one in order to be able to participate. Individuals within the sample participate in monthly Internet surveys. The respondents of the LISS panel are reimbursed for completing the questionnaires four times a year, which allowed for incentivised monetary payments to participants in the experiment.
The random subsample invited to participate in the experiment was stratified to reflect the population. In total 2,792 subjects participated in the study, used to obtain the risk aversion measure. The usage of the LISS data set is limited 2010, since the questionnaire regarding the specific measure of risk aversion employed in this paper was only conducted once.
12 and demographic information of the participants of the questionnaire was gathered prior to the experiment.
4.1.1. Data set construction
The data set employed in this paper is constructed by merging data obtained in separate questionnaires. The questionnaires are merged on the basis of a unique indicator. Subsequently, individuals with missing values for any of the dependent or independent variables are dropped. Lastly, only the variables covered in the analysis are kept for brevity reasons. An overview of the variables employed in this paper found Table A4 in the Appendix. This leads to data set consisting of 2.443 observations.
4.2 Methodology
The following section describes the employed research methods and is divided into three parts. The first describes the construction of the risk aversion measure, which will be used as dependent variable and as a determinant of financial decisions. The second part defines the specification of the OLS regression used to measure the influence of individual characteristics on risk aversion and subsequently defines the probit and the tobit model used to examine the effect of risk aversion on individuals’ financial decisions. The third part discussed the usage of marginal effects for ease of interpretation.
4.2.1 Measure of risk aversion
The risk aversion measure employed in this paper is obtained by letting participants make five choices between a sure payoff and a risky lottery. A list of the choices is given in Table 1 below.
Table 1. List of choices lottery
Notes: *** indicates significant difference from random choice between left and right option at 1% level, binominal test two-sided.
The subjects were presented with one choice at a time. The choices were ordered with increasing payoffs for the certain payoff choice. The choice was given between a lottery that paid 65 or 5 with equal probabilities, and a sure payoff that differed per trial. The sure payoff varied from 20 to 40, increasing with steps of 5. Subjects did not learn of the outcomes of the
Sure payoff Risky lottery Instances sure payoff is chosen (%)
Riskav 1 20 65 or 5 50.21
Riskav 2 25 65 or 5 58.81***
Riskav 3 30 65 or 5 69.48***
Riskav 4 35 65 or 5 78.71***
13 lotteries during the experiment and no indifferent option was provided. To control for the presentation of choices, the presentation was counterbalanced. For half of the participants the relative lottery payoffs increased, while for the other half the payoffs ascended.
The questionnaire is incentivised by monetary payoffs based on the decisions the subjects make in the experimental task and are paid accordingly. The outcome based on the choices the individual made was paid out in 1 out of 10 times. The individual was notified of this possibility at the start of the experiment. This random selection of participants’ real payoffs is observed in multiple large-scale studies with the general public (Von Gaudecker et al., 2011). This random selection is preferred over a downscale of the payoffs, because it leads to stronger incentives (Abdellaoui et al., 2011).
The measure of risk aversion is equal to the number of instances in which a subject chooses the sure pay off over the risky one. The more certain payoff options chosen by participant, the greater the assumed level of risk aversion. The risk aversion measure thus ranges from zero, indicating choosing the uncertain payoff in all instances to five, indicating to prefer the certain payoff in all instances.
Table 2. Number of risk averse choices
Number of risk averse choices Risk attitude Number of observations
0 Risk loving 214
1 Risk loving/risk neutral 159
2 Risk neutral/risk averse 341
3 Risk averse 405
4 Risk averse 319
5 Risk averse 1005
It is interesting to observe that there is a relatively large number of participants that in none of the offered choices prefer the uncertain payoff over the certain payoff and therefore in all five instances chose the certain option.
4.2.2 Regression analysis
14 aversion measure is treated as continuous. Therefore, OLS regression is used to examine the relationship between demographic factors and risk aversion. A robustness check compares both options. The following econometric model is derived to examine the effect of individual characteristics on risk aversion:
+,- = / + 1- ∗ 2-+ ℇ
-Where +,-, takes on a value between zero and five depending on the number of
certain choices of individual i. 2- is the set of explanatory variables previously found to have
a significant effect on risk aversion: gender, age, age squared, marital status, self-employed, education, self-assessed health status, logarithm of income and logarithm of wealth. 1- is the corresponding coefficient testing the influence of the variables and ℇ- the error term.
Secondly, the influence of risk aversion on financial holding decisions is analysed using a binary holding variable. The dependent variable 4- is binary, this means the variable can only have two outcomes. The two possible outcomes are holding or not holding a specific debt/asset class, respectively denoted as one and zero. The advantage measuring economic behaviour using binary variables is that they are presumably measured with little error because they do not suffer from a self-reporting bias (Campbell et al., 2009). Since the dependent variable is binary, linear regression analysis is unfit to examine the relationship between risk aversion and the holding decision. If one would still use linear regression, an adaption of the model would be required. However, a better alternative to overcome this problem is using a probit model. The purpose of this model is to estimate the probability that an individual with particular characteristics will or will not hold a certain debt/asset class. A series of probit models is estimated. The specification of the model is denoted below:
%∗ - = 1&2-+ 5 -%- = 6 1 89 % ∗> 0 0 <=ℎ?@A8B? With %∗
- being a latent variable, 2- vector representing the set of individual 8´s observable
characteristics affecting portfolio allocation. Unobservable characteristics are captured by 5-, which is assumed to be normally distributed and %- being the observed binary response variable representing holding or not holding a certain asset/debt class. For each set of 1&
coefficients, the likelihood of each %- is calculated. The maximum likelihood estimation technique is used to estimate probit parameters. maximum likelihood estimation focuses on choosing parameter estimates that yield the highest probability of obtaining the observed sample %-.
15 (Betraut and Starr-McClue, 2002). This model treats the decisions to hold a certain asset/debt class as dependent on the monetary amount. Including or excluding the censored observations in a normal OLS, will result in biased and inconsistent estimates. Tobit models, however, provide consistent estimates while exploiting all available data, including information related to the censored observations. Due to certain fixed cost regarding the debt or asset classes (e.g. stock market participation costs), the amount of a certain asset/debt class are expected to be dependent on a threshold, under which zero amounts are unobserved. If, however the decision to hold an asset/debt class is independent on the amount of this asset or liability class, the two-part model is preferred. The two-step model consists of a binary probit model as the first step. In the second step a continuous linear regression is estimated, conditional on having that asset/debt class. A robustness check compares both options. Alternatively, a Heckman selection model, which is a version of the two-part model, would be fit to analyse the influence of risk aversion on the amounts held in the different asset/debt classes. However, for the Heckman selection model the covariates explaining two decisions cannot be exactly the same. This method is not employed in this paper since the existence of an excluded variable that influences holding decision and the amount held is difficult to find in this setting of research.
In order to examine the influence of risk aversion on amounts, momentary values of the debt/asset classes are used. All monetary values have been standardized using logarithm in order to normalise the skewness and kurtosis.4 The Tobit model is formalised as:
log (GH∗
-) = 1&2- + 5
-log (GH-) = log (GH∗
-) if log( GH∗-) > 0
log (GH-) = 0 <=ℎ?@A8B?
With log (GH-) being the logarithm of the monetary value of the certain asset/debt class of
individual 8, log (GH∗
-) the corresponding untruncated latent variable, / is the intercept and
1& is the coefficient of the covariate of interest. 2- is a set of control variables that has been put forward by literature to influence these financial decisions, 1& is the corresponding
coefficient testing the influence of these control variables. Finally, 5- is the error term.
Again, a tobit model is used in order to analyse the influence of risk aversion on share of financial asset invested in risky assets. In order to do so, the share of risky assets is first determined. Investments in shares, bonds, mutual funds and options are added and divided by the value of net financial assets. Again, the tobit model is applied to analyse the effect of risk aversion. The Tobit model assessing this relationship is formalised as:
J+∗
- = 1&∗ 2- + 5
-J+- = J+∗
- if J+∗- > 0
4 In order to deal with zero values of the debt/asset classes, one is added to each series.
(3.3)
16 J+- = 0 <=ℎ?@A8B?
With J+- being the share of financial assets invested in risky assets of individual 8.
Independent variables are equal to the aforementioned model. If the share of risky assets would be truncated into the [0,1] interval, the share of risky assets could have been modelled using a fractional response model. However, such a truncation is questionable since values below zero and above one are possible in case of short selling or leveraging.
4.2.3 Marginal effects
The probit model estimates the impact of independent variables on the dependent variable. These results indicate the significance and sign, but shows no easy interpretable order of magnitude. To interpret the resulting coefficients properly, the marginal effect of a coefficient is therefore calculated. The marginal effects of a variable in a probit model how the probability of obtaining an outcome of %- = 1 will alter (increase or decrease) as a result
of a unit change in a specific independent variable, while keeping all other variables at their mean values. Therefore, marginal effects are reported in the main body of this paper to show the expected instantaneous change in the dependent variable as a function of a change in a certain explanatory variable, while keeping all other covariates constant.
5. Analysis
5.1 Descriptive statistics
Table 3 gives an overview of the summary statistics of the dependent variables. Focussing on financial asset classes, approximately 89% of the individuals within the sample hold a saving account. This is in line with the national average of 78%. Remarkably, the population can be considered as comparably risk averse on average. The mean risk aversion of an individual is approximately 3.405, with more than two safe choices indicating risk aversion. Mortgage numbers are also in line with the national average of approximately 60%. The number of people with credit card debt in the sample is 3.59%. The number of households with shares 16.8% is inline with the Dutch national average of 21.7% (CBS, 2012)
Table 3. Summary statistics dependent variables
Mean Standard
deviation Min. Max.
Number of observations
Risk aversion 3.421 1.670 0 5 2,443
Holding savings account 0.889 0.314 0 1 2,443
Log savings account 14.401 9.369 0 25.332 2,443
Holding risky assets 0.156 0.363 0 1 2,443
Log share risky assets 0.104 0.234 0 5 2,443
Holding debt 0.108 0.310 0 1 2,443
17
Holding mortgage 0.802 0.398 0 1 684
Log mortgage 11.557 1.208 0 16.916 549
Table 4 presents summary statistics for the independent variables. The mean age of the population is 49.24, which is considerably higher than the actual mean age in the Netherlands of 42.7 (OECD, 2015). The positive skewness towards older participants can be partly attributed to construction of our sample in which only participants in the age of 16 and over can participate. Another remark can be made concerning the self-employment rate, which is 4.94% in our sample, while the national average is around 16,8% (OECD, 2015). This can be due to definition differences. Higher education 29.7% is also in line with national average of 28% (CBS, 2012). Also the number of individuals with a mortgages, 63.2% is comparable to the national average of 59.2% (Eurostat 2014). The mean height of the mortgage is in the sample is 217,818 euros. This in line with the national average of 210.000 euros (Hypotheken Data Netwerk, 2010).
Table 4. Summary statistics independent variables
Mean Standard
deviation Min. Max.
Number of observations
Risk aversion 3.421 1.670 0 5 2,443
Female 0.528 0.499 0 1 2,443
Age (10 years) 4.934 1.780 1.600 9.100 2,443
Age (10 years) squared 27.513 17.278 2.560 82.81 2,443
Higher education 0.291 0.454 0 1 2,443
Married 0.575 0.494 0 1 2,443
Self-employed 0.043 0.205 0 1 2,443
Health status (1 = worst, 5 = best) 3.133 0.765 1 5 2,443
Log income 7.146 0.733 3.689 11.657 2,443
Log wealth 15.09 9.175 0.693 26.023 2,282
5.2 Regression results
In the following section the regression results are presented. Firstly, the relationship between individual characteristics and risk aversion is analysed using an OLS model. Secondly, the relationship between risk aversion and financial household decision is explored. The holding decision is examined using a probit model. Subsequently, the influence of risk aversion on the amount held of a certain asset/debt class or share of financial assets allocated to the stock market is analysed using a tobit model. Marginal effects are reported throughout the main body of the paper. The probit and tobit model regression coefficients are reported in the Table A7 and A8 in the Appendix.
18 First, the relationship between individual characteristics and risk aversion is analysed. The first specification includes two individual characteristics: gender and age. These characteristics are exogenous with respect to individual risk aversion and behaviour and thus allow to give a causal interpretation of the correlations found5. The second specification also
includes individual characteristics: education, marital status, health and self-employment. A potential problem with adding these variables is that they may be endogenous. This means that although it can be argued that these factors may influence ones’ level of risk aversion, it can also be argued that ones’ level of risk aversion affects these life choices. Hence, any correlations found in the analyses should therefore be carefully interpreted with respect to causality.
Table 5. The effect of individual characteristics on risk aversion
Specifications 1-3 are OLS regressions. The sample consists of data from the 2010 wave of the LISS Panel. The dependent variable, risk aversion ranges from zero to five, dependent on the number of risk averse choices of an individual. Higher education is a dummy that takes on the value of one if the respondent has completed the corresponding educational degree. Married is a dummy variable that takes on the value of one if the respondent is married. Health is self-reported on a scale from zero to five, where five represents excellent health. Self-employed is a dummy that takes on the value of one if the respondent is self-employed. Logarithmic values of income and wealth have been taken in order to normalize them. t-values are based on heteroscedasticity robust (White) s.e. in parenthesis; *,**,*** represent significance at the 10%, 5% and 1% levels, respectively.
Risk aversion (1) (2) (3) Female 0.416*** 0.430*** 0.347*** (6.18) (6.35) (4.16) Age (10 years) -0.191* -0.296*** -0.124 (-1.95) (-2.69) (-0.83)
Age (10 years) squared 0.015 0.011** 0.002
(1.52) (2.21) (0.82) Higher education 0.074 0.156* (0.99) (1.77) Married 0.203** 0.106 (2.54) (1.20) Health 0.025 0.035 (0.57) (0.69) Self-employed -0.174 -0.199 (-0.97) (-1.01) Log income -0.145** (-2.32) Log wealth 0.008* (1.88)
5 Note, however, the caveat that age could potentially be endogenous. Individuals that are more risk
19
Constant 3.709*** 3.757*** 4.208***
(17.55) (13.22) (9.03)
Observations 2,443 2,443 1,894
R-squared 0.019 0.022 0.024
Table 5 shows the results of the OLS regression analysing the drivers of individual level risk aversion. A comparison of the results in columns one to three shows that the coefficients for gender is virtually unchanged and remains statistically significant when including the most extensive specification. The results indicate that women are more risk averse than men. Being female as opposed to male, increases risk aversion by 0.347 to 0.416 depending on the specification of the model. This result is in line with previous literature which finds that woman are more risk averse than men (Niessen and Ruenzi, 2007; Jianakoplos and Bernasek, 1998; Eckel and Grossman, 2008; Croson and Gneezy, 2009).
With respect to age, the results are significant in the first and second specification. A non-linear measure of age is found to be significant in the second specification. The results suggest that as individuals get older, their level of risk aversion decreases. Only in the second column the results indicate a non-linear relationship. At an early age, risk aversion decreases faster than at later age. This U-shaped relationship found, is in line with previous research of Cohen and Einav (2007). However, in the third specification that includes measures of income and wealth, age and the non-linear measure of age are no longer significant. This indicates no significant relationship between age and risk aversion. A possible explanation might be that the effect of age is attributable to income and wealth that in general increases over the lifetime. Hence, the results on age are inconclusive.
Income is significantly negatively related to risk aversion, while wealth is found to be significantly positively related to risk aversion. The result that income is negatively related to risk aversion, is surprising since one expects that high income or wealth levels may increase the willingness to takes risks because they cushion the impact of bad realisations. Although causal interpretations are inadvisable, it is interesting to note that correlation between wealth and risk aversion progresses in the predicted direction, indication that more wealthy individuals are more willing to take risks.
Contrary to expectations, a large number of independent variables have little explanatory value in individual risk aversion. Education is only found to be significant in the third specification. Marital status is only found to be significant in the second specification.
Self-employment is significant in the second specification, however is no longer statistically significant when additional income and wealth repressors are included. Thus, %& is only partly corroborated.
20 decrease 0.431 in a person risk aversion. Overall the part of variance between individuals’ in their respective risk aversion that can be explained through individual characteristics is small. Only 2.4% in the most comprehensive model. Although the explanatory power of the model is limited, this is in line with previous research (Lin, 2009). This indicates that demographic factors are only partly able to explain an individuals’ level of risk aversion.
5.2.2 Robustness check with ordered probit and binary probit regressions
Rather than interpreting the number of risk averse choices as continuous variables, all regressions are also analysed using ordered probity models and a binary probit classification. In the binary probit classification, risk aversion as the dependent variable, takes a value of one if individuals take above two risk averse choices and zero otherwise. In both classifications similar quantitative results are found in terms of significance and robust coefficients. Results based on these alternative estimation methods can be found Table A5 and A6 in the Appendix.
5.2.3 Influence of risk aversion on financial decisions
This following, will analyse how risk aversion and individual characteristics affect financial portfolio decisions by conducting a probit and tobit regressions. In order to examine whether the measure is useful for explaining and predicting financial decisions of individuals, in terms of both statistical and economic significance. In Table 6 and 7, the financial decision of the individual is the dependent variable. The presence of an asset/debt class is examined, followed by the amount or share of net financial assets in the respective asset/debt class. The regression table includes two specifications for both decisions regarding each asset/liability class. The first of the specifications includes exogenous control variables, these consist of risk aversion, gender and age. The second specification includes more, possible endogenous, control variables, education, marital status, health, self-employment, income and wealth.
5.2.4 Influence of risk aversion on financial assets
Table 6 reports the marginal effects of the probit model and tobit model regression results. Looking at savings in column one and two of Table 6, one finds that risk aversion is positively related to the probability of holding a savings account. A unit change in the level of risk aversion leads to a 0.8 percentage point higher probability of holding a savings account. This result is in line with previous results which indicate a negative relationship between risk aversion and stock market participation (Donker and Van Soest, 1999; Shum and Faig, 2006; Guiso et al., 2008; Kapteyn and Teppa, 2011).
21 approximately 13.6 percentage point. The results show that both the decision to hold savings, as the amount of savings, is significantly influenced by risk aversion. Hence, %' is confirmed. The fifth and sixth column of Table 6, shows the results regarding risky assets. The results indicate that risk aversion is negatively correlated with likelihood of holding risky assets. The marginal effects show that a unit increase in the level of risk aversion leads to approximately 0.7 percentage point lower probability of holding risky assets. The latter remains significant in the more elaborate specification of the model. Not only the holding decisions is negatively influenced by risk aversion, but also the share of financial assets allocated to risky assets is negatively related to risk aversion as indicated in seventh and eighth column of Table 6. Shum and Faig (2006) and Guiso et al. (2008) find similar results that also indicate that risk aversion and share of financial assets allocated to risky assets are negatively related. The theoretical rational behind this is that risk averse people forgo risky investments for more certain asset allocation. Consequently, %( is corroborated.
In general, it can be stated that risk aversion is more important when examining the amounts held in a certain asset class than the probability of holding a certain asset class. In other words, risk aversion plays a larger role in the allocation decision, rather than the decision of individuals to hold certain asset classes.
With respect to the control variables, the results show the importance of including these variables. Gender, income and education are of significant influence. Furthermore, female and higher education are in the majority of specifications is highly significant. Being female is negatively associated with holding an asset class and the amount or share. Contrary, higher education has a positive relationship with both the holding decisions and the amount or share of the respective assets classes. The relationship between income and financial decisions indicates a positive impact similar to that of education.
5.2.4 Influence of risk aversion on debt and mortgage
Table 6. Savings, risky assets and risk aversion
Specifications (1)-(2) and (5)-(6) are probit regressions. Specifications (3)-(4) and (7)-(8) are tobit regressions truncated at zero. The sample consists of data from the 2010 wave of the LISS Panel. Risk aversion ranges from zero to five, dependent on the number of certain choices of an individual. Higher education is a dummy that takes on the value of one if the respondent has completed the corresponding educational degree. Married is a dummy variable that takes on the value of one if the respondent is married. Health is self-reported on a scale from zero to five, where five represents excellent health. Self-employed is a dummy that takes on the value of one if the respondent is self-employed. Logarithmic value of income and savings been taken in order to normalize them. t-values are based on heteroscedasticity robust (White) s.e. in parenthesis; *,**,*** represent significance at the 10%, 5% and 1% levels, respectively.
(1) (2) (3) (4) (5) (6) (7) (8)
Holding savings Log savings Holding risky assets Share risky assets
M.E. M.E. M.E. M.E. M.E. M.E. M.E. M.E.
23
Table 7. Debt, mortgage and risk aversion
Specifications (1)-(2) and (5)-(6) are probit regressions. Specifications (3)-(4) and (7)-(8) are tobit regressions truncated at zero. The sample consists of data from the 2010 wave of the LISS Panel. Risk aversion ranges from zero to five, dependent on the number of certain choices of an individual. Higher education is a dummy that takes on the value of one if the respondent has completed the corresponding educational degree. Married is a dummy variable that takes on the value of one if the respondent is married. Health is self-reported on a scale from zero to five, where five represents excellent health. Self-employed is a dummy that takes on the value of one if the respondent is self-employed. Logarithmic value of income, debt and mortgage has been taken in order to normalize them. t-values are based on heteroscedasticity robust (White) s.e. in parenthesis; *,**,*** represent significance at the 10%, 5% and 1% levels, respectively.
(1) (2) (3) (4) (5) (6) (7) (8)
Holding debt Log debt Holding mortgage Log Mortgage
M.E. M.E. M.E. M.E. M.E. M.E. M.E. M.E.
Briefly examining the control variables, the results indicate that age is an important determinant of both the decisions to acquire debt and the amount of debt accumulated. This is remarkable, since one expects that the for consumption purposes the liquidity shortage would be at the beginning of a person’s life cycle, while the results indicate that older people are more likely to have debt as well as a larger amount of debt.
Looking at mortgages in column five and six of Table 7, the marginal effects of the probit model reveal no significant influence of risk aversion on the holding decision. Also, no significant influence in terms of amount held is found. Theoretically the level of risk aversion should be negatively related to both the decision to take on a mortgage and the amount of mortgage accumulated, since the ability to repay the mortgage is uncertain. However, this relationship is not significant. These results are in line with findings of Donkers and van Soest (1999) that also find no significant relationship between risk aversion and the amount of mortgage held by an individual. A possible explanation might be that since mortgages are secured debt, the probability of not being able to repay and therefore the uncertainty surrounding this decision is limited. Additionally, the decision to acquire a mortgage may be driven by other factors. In the Netherlands interest on mortgages, is fully tax-deductible and capital gains on housing are not taxed at all. Consequently, having a mortgage and the amount of mortgage may be primarily motivated by fiscal reasons (Donkers and van Soest, 1999).
Also for mortgage the results indicate that age is no significant determinant of the amount of mortgage an individual holds. This while intuitively one expects that over-time an individual makes repayments on their mortgage and hence the amount of mortgage and age are negatively correlated. However, again this result may be attributable to the fiscal policy in the Netherlands, which until recently made it lucrative not to make payoffs on your mortgage (Vandevyvere and Zenthöfer, 2012).
5.2.5 Robustness check with a two-step model
25 6. Discussion
Like any other study, this study has its weaknesses and is subject to certain limitations. Hence, the data, methodologies employed and results found in this study will be assessed in this chapter. Finally, suggestions for future research are presented.
The data set used in this research has limitations. The first limitation is that the measure of risk aversion is only obtained in a single wave study. Hence, this limits the possibility to track individuals’ risk aversion over time. This limits the possibilities that result from the usage of longitude data, given that other variables included in the research are measured in multiple waves. This limitation could be overcome if risk aversion was assumed to be constant over time for individuals. However, research of Guiso et al. (2014) indicates that risk aversion is not stable over time. They find that risk aversion increases substantially after the financial crisis of 2008. This indicates that life events can significantly influence individuals’ risk aversion and it is therefore not possible to assume that risk aversion is constant.
Additionally, the LISS data is obtained through surveys and the quality of the LISS data therefore depends on the willingness of individuals to participate and the accuracy of their answers when they participate. Hence, the data possible suffers from selection bias, non-response and panel conditioning. Furthermore, values of several socio-demographic factors like income and wealth come primarily from self-surveys that are notorious subject to potential large measurement errors (Hanna, 2001). Hence, the quality of the data could be improved if the reported wealth measure and other monetary measures were cross-checked with administrative data.
Furthermore, risk aversion is included in the regression for financial decisions since it is a function of the other explanatory variables that are already included as factors associated with risk aversion, implying that risk aversion is not exogenous. The reason to include risk aversion is that not all the determinants of risk aversion are known. The determinants that are included explain only 2.4% of the variation in risk aversion. Hence, risk aversion seems to be only partially endogenous.
In terms of risk aversion measure, the payoff stakes employed in this paper, were relatively small. The measure of risk aversion is partly dependent on the way participants are incentivised. Since intuitively higher stakes make subjects more risk averse, it would be interesting to examine whether participants make more risk averse choices for higher stakes. This would provide insight in the relationship between risk aversion and monetary incentives. Another caveat is that the risky lottery employed in this paper only involves gains and thus may only proxy imperfectly for the risk aversion to lotteries that involve both gains and losses, such as stock market gambles.
26 gender and age affect an individual´s degree of risk aversion and financial decisions. For other variables, the direction of causality is difficult to determine. The relationship between risk aversion and characteristics like type of employment, marital status, health status and education is not as clear (Outreville, 2014). While it can be argued that these factors may influence one’s level of risk aversion, it can also be argued that one’s level of risk aversion affects these life choices. For example, it can be argued that investors that are self-employed are less risk averse, but also that people that are less risk averse choose to be self-employed. Even though the risk of reverse causality and omitted variables is minimised by including a large set of control variables, any correlations found in the analyses should be carefully interpreted with respect to causality. This limitation can be overcome by i.e. an instrumental variable. Without the inclusion of such an instrumental variable, the results should merely be interpreted as well estimated correlations.
The results indicate that the relationship between risk aversion and the accumulation of debt is insignificant. This result can be influenced by the inability of this study to differentiate between secured and unsecured debt, except for mortgages. Since secured debt is surrounded with less uncertainty the effect of risk aversion might differ, although Brown (2013) find no difference between secured and unsecured debt. This limitation comes forth from the data, which does not allow to distinguish secured and unsecure debt.
7. Conclusion
Theory of choice under uncertainty, implies that risk preferences of individuals strongly affects individuals’ choices. Hence, differences in risk aversion between individuals should be an important factor in explaining observed differences in individuals’ decisions. The measure of risk aversion in practice has however come with shortcoming. This paper overcomes these problems by employing a measure of risk aversion based on incentivised lottery questions for a demographically representative sample. Using this measure of risk aversion, both demographic factors influencing risk aversion and the influence of risk aversion on financial household decisions are analysed.
First, the relationship between several individual characteristics and risk aversion is analysed. This paper finds that gender and wealth are significantly positively correlated with risk aversion while income is significantly negatively correlated with risk aversion.
Subsequently, the effect of risk aversion on financial choices made under uncertainty is examined. For the decisions regarding the financial assets side, risk aversion is found to be a significant determinant for household financial decisions.
27 risky assets. These results are in line with theory and previous empirical research (Donkers and van Soest, 1999; Shum and Faig, 2006; Puri and Robinson, 2007). Risk averse individuals are less likely to take risky financial decisions and when they do they will allocate less of their financial assets to risky investments and more to the less risky, savings account. In general, it can be said that risk aversion is more important when examining the amounts held in a certain asset/debt class than the probability of holding them. In other words, risk aversion plays a larger role in deciding how much to invest, rather than whether to hold risky assets at all.
Contrary to previous research of Brown (2013), this paper does not find a significant relationship between risk aversion and the decision to accumulate debt. Although this decision to accumulate debt is surrounded with uncertainty, no significant relationship between risk aversion and debt accumulation is found. This may be the result of the underlying motivation to acquire debt, the inability of this paper to distinguish between secured and unsecured debt or Dutch fiscal policy.
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Appendix
Table A1. Overview of risk aversion determinants literature
Study Measure Monetary incentives Context/country Variables
Current Lottery to gain Yes Dutch household survey Gender (+)
Riley and Chow (1992) Objective N.A. US household survey Age (+/-), education (-), female (+),
race, marital status (-) Bajtelsmit, Bernseak and
Jianakoplos (2001)
Objective N.A. US household survey Age (+), female (+),education (-), Race,
marital status (-)
Eckel and Grossman (2008) Lottery to gain No US laboratory experiment Female (+)
Lin (2009) Objective N.A. Household survey, Taiwan Female (+), age (+/-), education (-),
marital status (-), family size (-)
Croson and Gneezy (2009) Lottery to gain Yes US laboratory experiment Female (+)
