Master Thesis in Economics, 30 credits Degree Project in Economics
Spring term 2020
Irrational individuals and inefficient markets
A quantitative study of factors’ impact on individuals’ risk willingness
Tom Ekelund
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Acknowledgement
I would like to express my gratitude towards my supervisor Tomas Sjögren, at the Institution of Economics, for his guidance during the beginning of my work.
Sincerely, Tom Ekelund
2020-06-05
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Abstract
While conventional academic finance highlights theories within modern portfolio theory such as the Capital Asset Pricing Model, the emerging field of behavioral finance tries to develop these theories by incorporating psychological elements into the equation. Furthermore, an extensively discussed phenomenon is individuals’ risk willingness. Accordingly, this thesis dissects said risk willingness to better understand what affects it. For this analysis, a Partial Proportional Odds Model is performed via the usage of individuals who answered the ‘Survey of Household Economics and Decision-making’ back in 2018. Altogether, several factors are discovered to have a highly significant impact on individuals’ risk willingness – were the results are in line with Tversky and Kahneman’s (1992) Prospect Theory. Conclusively, suggestions on future research is presented based on implications that occurred.
Keywords: risk willingness, rationality, behavioral finance, partial proportional odds model,
ordered logit, survey data
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Table of Contents
1. Introduction ... 1
2. Purpose ... 2
2.1 Formulating the problem... 2
3. Literature review ... 3
3.1 Why behavioral finance? ... 3
3.2 Qualitative factors affecting risk-willingness... 4
3.2.1 Perceived risk and person-centered characteristics ... 4
3.2.2 Situational characteristics ... 5
3.2.3 Emotions mediating investment decisions ... 5
4. Methodology... 7
4.1 Discrete choice data ... 7
4.2 Ordered, Generalized and –Partial Proportional Odds logit models... 7
5. Data ... 10
5.1 Response variable ... 10
5.2 Explanatory variables ... 11
5.2.1 Person-centered variables ... 11
5.2.2 Situational variables ... 17
6. Results... 20
6.1 Intuition on how to interpret the model ... 20
6.2 The final model ... 21
6.2.1 Factors increasing risk willingness... 22
6.2.2 Factors decreasing risk willingness ... 22
6.2.3 Insignificant factors ... 23
7. Discussion ... 24
7.1 Factors in accordance with previous research ... 24
7.2 Factors with more debatable results ... 25
7.3 Factors considered as situational ... 27
8. Conclusion ... 29
8.1 Suggestions for future research ... 30
9. References ... 31
Appendix A ... 37
Appendix B ... 38
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1. Introduction
Efficient markets with rational individuals are two fundamental assumptions economists tend to make in standard investment theory, where investors look to always act in a manner that maximizes their expected return (Chaudhary, 2013). Yet, the field of behavioral finance provides several research arguing otherwise. Individuals are not always rational and markets are not always working as one might like - the reason being we are human and decisions tend to originate from emotions, and emotions are not rational (Chaudhary 2013; Ricciardi & Simon, 2000). Thus, behavioral finance immediately challenges standard investment theory where decisions tend to be motivated through expectation-type mathematics (Cheng, 2019). For instance, modern portfolio theory would explain decisions with mean-variance analysis through the Capital Asset Pricing Model (CAPM) from Sharpe (1964) and Lintner (1965). Here, one assumes the investor only cares about two elements; highest expected return given a certain level of risk or the least risk given a certain level of expected return (Markowitz, 1952).
Arguably, these theories provide a homogenous outcome without acknowledging investors’
individual risk preferences – which seems to be of utmost interest when explaining investment
behavior. Therefore, a thesis on what factors that affects individuals’ risk willingness would
appear to be interesting since there seems to be more complexity to investment choices than
what the applied models suggests.
2. Purpose
The purpose of this thesis is to examine what factors, and to what extent, they affect individuals’
risk willingness. Subsequently, the predicted risk willingness will be incorporated into Cheng’s (2019) model to conclude the absolute perceived risk-willing utility for gains and losses respectively. Altogether, the results in this paper will be in line with Tversky and Kahneman’s (1992) argument around prospect theory – where preferences toward gains and losses differ.
Essentially, losses loom larger than equivalent gains.
2.1 Formulating the problem
Which parameters affects individuals’ absolute perceived risk-willing utility for both gains and losses?
| P (𝑈
𝑟𝑖𝑠𝑘−𝑤𝑖𝑙𝑙𝑖𝑛𝑔,𝑔𝑎𝑖𝑛𝑠) | = [| E(𝑃𝑎𝑦𝑜𝑓𝑓
𝑔𝑎𝑖𝑛𝑠) |] (𝑅𝑤), where Rw > 0 (1)
| P (𝑈
𝑟𝑖𝑠𝑘−𝑤𝑖𝑙𝑙𝑖𝑛𝑔,𝑙𝑜𝑠𝑠𝑒𝑠) | = [| E(
𝑃𝑎𝑦𝑜𝑓𝑓𝑙𝑜𝑠𝑠𝑒𝑠𝑅𝑤
)|] , where Rw > 0 (2)
Equations (1) and (2) exhibit Cheng’s (2019) model where the author argues that the absolute
perceived risk-willing utility for gains and losses are functions of the absolute values of
expected gains ( | E(𝑃𝑎𝑦𝑜𝑓𝑓
𝑔𝑎𝑖𝑛𝑠) | ) and losses ( | E(𝑃𝑎𝑦𝑜𝑓𝑓
𝑙𝑜𝑠𝑠𝑒𝑠)|), and an investor’s risk
willingness (𝑅𝑤) which is always positive. The equations state that, the more risk-willing an
individual is, the greater the perceived utility for gains is, and the lower the perceived utility for
losses is (could be interpreted as one cares less about losses) – even for the same risk preference
and expected magnitude of gains and losses. The main objective in this thesis is to examine the
effect of the factors that affect Rw.
3. Literature review
Several sources have contributed to this thesis, mostly consisting of journals and books. Yet, Cheng’s (2019) published article in the ‘Journal of Behavioral Finance’ together with profound research from Professor Richard Williams (2006, 2011, 2016, 2019) have provided the fundamental base of this paper.
3.1 Why behavioral finance?
As briefly mentioned in the introduction section, the field of behavioral finance tries to provide reasons for irrational behavior of investors – thus combining both financial and psychological theory into one, mutual field of studies (Weber, 1999). Moreover, according to behavioral experts, investors do not perform as rational and perfect as the classical school of financial theory suggests. Therefore, advocates of behavioral finance try to explain this lack of information – the irrationality of investors – by incorporating psychological aspects to the contemporary theories of finance. (Naveed et al., 2014) Arguably, this irrationality could be interpreted as risk behavior in terms of finance and decision-making. This interpretation of irrational behavior provides an opportunity to investigate the underlying factors affecting risk- willingness for individuals – which is the fundamental basis of this paper.
Cheng (2019), dissects the standard risk preferences economists tend to assume; risk averse, risk neutral and risk venturous. The author argues that, from a behavioral perspective, said three categories may not be adequate to explain the wide spectra of individual risk preferences.
Therefore, a continuum of risk-willingness is constructed to give some intuition to the context
- at one end of the spectra there is absolute risk aversion and at the other end there is absolute
risk venture. Between both ends, there are infinite levels of risk preferences giving room for all
possible constructions. The reason behind this continuum being that every individual that holds
a portfolio has subconsciously integrated risk preferences that are not strictly risk averse nor
risk venturous. If an investor holds a portfolio, asset A will certainly be either riskier or not
riskier than asset B – thus, more complex risk preferences may be more realistic. Cheng (2019)
concludes his reasoning regarding risk preferences by stating that to understand risky behavior,
one should not focus on the amount of risk an individual is taking, but rather on an individual’s
willingness to assume risk. Arguably, since risk-willingness seems to be more complex than
the above stated three categories (risk averse, risk neutral and risk venturous), it further strengthens the motives to examine it.
3.2 Qualitative factors affecting risk-willingness
Previous research suggests numerous factors affect risk-willingness, both complex and simple.
Cheng (2019), provides a summary on the subject matter and divides the factors into three categories. Firstly, perceived risk and person-centered characteristics such as gender, age and education etc. Secondly, situational characteristics such as one’s history entering a decision.
Finally, and perhaps the most significant and complex one; emotions.
3.2.1 Perceived risk and person-centered characteristics
Person-centered characteristics such as gender, age, personality (temperament, trust etc.), wealth and competencies all together construct individuals’ perception toward risk (Weber et al., 2002). Furthermore, previous research claim that individuals’ perception of risk is easily mistaken for their preference of risk (Cooper et al., 1988). To distinguish the two, the authors argue that just because a certain individual sees risk from a different perspective than another individual, does not conclude that that individual is more risk-willing nor risk-averse. An intuitive example of this phenomenon is to consider two university graduates, A and B.
Graduate A aspirers to become an entrepreneur while graduate B contends to build a solid career with an established company. The question seems to be whether A is more risk-willing than B.
Cooper et al., (1988) demonstrates that it is graduate A’s optimistic perception (and thus A’s personal attributes) of risk that distinguish the two, and not the risk-willingness per say.
Furthermore, if an individual perceives that the risk at hand is controllable and hence
manageable, irrespective of it being illusory or realistic – the perceived risk will be at a lower
level, and not necessarily the risk-preference (March & Shapria, 1987). Arguably, this
distinction may be difficult to capture and translate into relevant variables. However, it could
also be argued that individuals’ perception toward risk is the fundamental base concerning risk-
willingness for that one individual. Additionally, financial securities could be considered as
strictly objective and does not take individual risk perception into account when labeling a
certain asset “risky”. Therefore, person-centered characteristics will be included in the
empirical analysis of this paper.
3.2.2 Situational characteristics
Depending on an investor’s history, such as whether the investor comes from a winning streak or a losing streak can also influence the risk-willingness, concluding that that risky decisions are circumstantial (Cheng, 2019). Supporting theory states that individuals’ risk-willingness is highly domain specific and thus not strictly risk averse/venturous across different situations (Weber et al., 2002). Moreover, personality psychologists argue that individuals are consistent in their risk behavior and explains this continuity by highlighting person-centered characteristics (Bromiley & Curley, 1992). In contrast, experimental psychologists challenge the consistency of personal attributes by emphasizing that situational factors deal greater influence on risk taking (Khaneman & Tversky, 1979; Slovic, 1972). Consequently, efforts to unite the two perspectives have been made since both views have their virtues and empirical support. This resulted in an integrated standpoint where both situational characteristics and person-centered characteristics jointly influence risk-taking (Sitkin & Weingart, 1995).
Conclusively, situational characteristics affect risk-willingness and will therefore also be included in the empirical analysis of this thesis.
3.2.3 Emotions mediating investment decisions
There is a wide range of research emphasizing the power of emotions in relation to decisions.
Lowenstein et al., (2001) provide an overview of the matter where emotions can be divided into two categories; immediate and anticipated.
Firstly, the former differs substantially from the latter in terms of exposing themselves as true emotions experienced exactly during the decision at hand. Regardless if the immediate emotion experienced is connected to the decision or not, it can still provide a powerful impact – especially if the emotion is intense. Intense emotions even tend to bias the actual probability of the possible outcome to great extents. Individuals with fear of flying may choose to drive to a destination rather than flying, solely based on an emotion of fear of crashing, even though statistics argue the opposite (Keltner & Lerner as cited in Fiske et al., 2010). It could be argued that immediate emotions, related or not, have substantial effects on decisions.
Secondly, anticipated emotions can be described as feelings not experienced directly. Instead,
they are expectations of how oneself will feel once gains or losses associated with the decision
at hand are experienced (Lowenstein et al., 2001). The authors continue their reasoning by
illustrating anticipated emotions in different scenarios. One scenario being an investor who
imagines losing a small amount of money will focus on the possible loss investment, rather than
steering focus toward the amount already owned. Another scenario, and closely related, is a process referred to as counterfactual comparison. Said process occurs when individuals compare a possible outcome of a decision with what one could have had, rather than to what one already had. Arguably, one’s current mindset entering a decision will affect it, diminishing the ability to be objective and thus rational.
Framing effects are another area which connects emotions to decisions. Studies suggests that if individuals are exposed with a benchmark, they are much more likely to decide closer to that benchmark, even if it is completely irrelevant. This phenomenon is referred to as anchoring (Tversky & Khaneman, 1974). The authors also explain the fundamentals of another framing effect; availability. This rule of thumb helps to explain risk related behavior and the decisions that comes together with it. Individuals tend to exaggerate recent, vivid occurrences and buy insurance for them, even if the probability for said occurrence is low. Arguably, decisions may easily be framed to steer individuals into certain directions – which ultimately could make the decisions biased.
Related to framing effects, other previous research suggests that individuals employ two different “behavioral systems” when exposed to decisions; surveillance and/or disposition (Marcus et al., 2000; MacKuen et al., 2005). Findings suggest that negative emotions, such as anxiety, tend to shelter individuals from framing effects since negative emotions alerts the surveillance system. Subsequently in return, the surveillance system interrupts our habitual routines and engages our thoughts – ultimately leading to more contemplation and less intuition (Marcus et al., 2000). However, and quite controversially, both negative and positive emotions such as anger or enthusiasm, can generate aversion to apprehend information since these feelings triggers the disposition system. Altogether, decisions taken under the influence of the disposition system tend to be more vulnerable to framing effects (MacKuen et al., 2005).
Druckman & McDermott (2008) provide a diplomatic summary of the above stated controversy
by stating that emotions clearly influence both tendencies to take risks, as well as the impact
framing effects have on risky decisions – emotions may either amplify or depress the framing
effect. Conclusively, one may appreciate that emotions are heterogeneous and complex factors
that might be difficult to incorporate in an empirical model. Therefore, such variables will be
excluded in the empirical analysis of this paper.
4. Methodology
Several different regressions were computed in the process to achieve the most valid and parsimonious model. Ultimately, the final model proposed to predict risk-willingness in this thesis is a Partial Proportional Odds model (a case of generalized ordered logit). The regressions are estimated in the program STATA.
4.1 Discrete choice data
To address individuals’ risk propensity accordingly, the dependent variable ‘risk-willingness’
is constructed to fit the characteristics of discrete choice data. Stock & Watson (2014) state that a discrete choice variable indicate that the variable can adopt numerous unordered or ordered qualitative values. In this paper, the dependent variable has three different ordered categories;
an individual can have low, medium or high risk-willingness. Furthermore, these three possible outcomes all depend on certain qualitative factors (Stock & Watson, 2014), which in this analysis appear as person-centered and- situational characteristics
1. Additionally, the authors recommend that discrete choice data models are reasonable to interpret through principles of utility, where usage of logit or probit models are considered attractive. Accordingly, Hawley and Fujii (1993) employed ordered logit models to investigate effects of net worth and individual characteristics on risk-willingness, whereas Sung & Hanna (1996) employed an ordered probit on factors affecting households’ risk tolerance. Therefore, this thesis will take one method into consideration that both fits the attributes of Stock & Watson’s (2014) reasoning, as well as being in line with Hawley and Fujii’s (1993) and Sung & Hanna’s (1996) model – a Partial Proportional Odds model.
4.2 Ordered, Generalized and –Partial Proportional Odds logit models
Before intuition regarding the Partial Proportional Odds model commences, a dissection on its progenitor – the ordered logit, is presented. Previous research interprets an ordered logit model as an extension of a normal logistic regression model where the dependent variable is categorical with discrete outcomes. Consequently, when outcome variables are ordinal rather than continuous, the general approach is to employ an ordered logit as the analytical method (Williams, 2016). Other scholars support this reasoning by stating that an ordered logit is
1Each characteristic is explained in detail in section 5, Data.
employed when one desires to predict the probability of each response level (McCullagh, 1980;
Gray et al., 2006). In this thesis, said response levels appear as low, medium and high risk- willingness for individuals. However, while the ordered logit may seem as the obvious choice of method, generalized ordered logits are often a superior alternative. This since generalized ordered logits have the benefits of being less restrictive than standard ordered logits and more parsimonious than models that neglect the ordering of the categories altogether, such as multinomial logits (Williams, 2016). Furthermore, for an ordered logit to prove useful and valid, it requires a certain condition to be fulfilled – the Proportional Odds Assumption.
Essentially, this assumption states that every explanatory variable has the same effect on the odds of moving to a higher order category everywhere along the scale (Nerlove & Press, 1973).
Williams (2016) supports this theory by arguing that if the assumption is met, all corresponding coefficients ought to be the same across all the logistic regressions. Arguably, while an ordered logit seems like an attractive method in theory, it seems to fail quite often in practice. This opinion is strengthened by Williams (2016) who demonstrates that researchers often fail to explain why the ordered logit was indeed inadequate. The author also highlights that scholars tend to overlook the useful insights the generalized ordered logit can provide compared to the ordered logit (given the Proportional Odds Assumption being violated). As previously stated, the proposed model in this thesis is a Partial Proportional Odds model – a variant of a Generalized Ordered logit. Different features of the three cases of Ordered logits are displayed in table 1.
Table 1, characteristics of the different ordered logits
OLM: Ordered Logit model PPOM: Partial Proportional Odds model GOLM: Generalized Ordered Logit model
Subsequently, the PPOM relaxes the Proportional Odds Assumption only for those explanatory
variables that violate the assumption – providing a less parsimonious model than the OLM but
a more accurate model than the GOLM (Soon, 2010; Williams, 2016). Ultimately, the question
seems to be whether the Proportional Odds Assumption is met or not. Usually, a Brant test is
computed which compares slope coefficients of the J-1 binary logits implied in the ordered
model. Here, the null hypothesis indicates no difference in the coefficients between the
cumulative logits and thus a non-significant result is desirable (Long & Freese, 2013).
However, since this paper’s analysis is based on survey data
2, a Wald test is preferable and more accurate. Accordingly, one estimates a Generalized Ordered logit (an unconstrained model where no predictors are required to meet the Proportional Odds Assumption) and then test whether the coefficients of the variables in the J-1 equations are all equal (Williams, 2019).
In the first extreme case, the OLM, the cumulative probabilities are usually expressed as:
𝑃(𝑌 ≤ 𝑚|𝑋) = 𝐹(𝜏
𝑚− 𝑋𝛽) for m = 1, 2…, J (3)
where 𝜏 are the cutpoints and 𝛽 indicates the same set of coefficients for each outcome level.
In the second extreme case, the GOLM, the cumulative probabilities are usually expressed as:
𝑃(𝑌 ≤ 𝑚|𝑋) = 𝐹(𝛼
𝑚− 𝑋𝛽
𝑚) for m = 1, 2…, J (4)
where 𝛼 are the cutpoints and 𝛽
𝑚indicates different sets of coefficients for each outcome level.
Finally, in the third case, the PPOM, the cumulative probabilities can be displayed as:
𝑃(𝑌 ≤ 𝑚|𝑋) = 𝐹(𝛼
𝑚− 𝑋
1𝛽
1+ 𝑋
2𝛽
2+ 𝑋
3𝛽
3𝑚) for m = 1, 2…, J (5)
where 𝛼 are the cutpoints and 𝛽
1and 𝛽
2are fixed for each outcome whereas 𝛽
3𝑚coefficients can vary by m outcomes.
Conclusively, when taking above stated information into account and adopting it to fit the survey data used in the analysis, the proposed method of choice in this thesis is the Partial Proportional Odds model/PPOM.
2The survey data characteristics are explained in section 5, Data.
5. Data
The Survey of Household Economics and Decision-making (SHED) is a cross-national study that has been conducted by the Federal Reserve every year across the United States since 2013.
For this analysis, the most recent 2018 SHED survey data is used (The Federal Reserve, 2019).
The study has 11.316 respondents, of which 11.316 (100%) had complete data for the variables used in this analysis. Since individuals have unequal probability of selection, sampling weights should be, and are used (Williams, 2016).
5.1 Response variable
Respondents were asked where on a scale they would place themselves regarding the following question: “On a scale from zero to ten, where zero is not at all willing to take risks and ten is very willing to take risks, what number would you be on the scale?” The possible responses were ranging from ‘0 = Not at all willing to take risks’ to ’10 = Very willing to take risks’ and every number in-between. This is the response variable in this analysis. However, according to Sung & Hanna (1996) and Williams (2016), multivariate analysis of all eleven response levels may not be meaningful since some categories have too few respondents. Conclusively, multivariate analysis may be more appropriate when combining levels to create fewer response categories with more respondents in each group. With more substantial response levels, multivariate analysis may provide more useful insights. Therefore, in this thesis, the dependent variable is divided into three different categories where respondents constitute new response levels. Firstly, respondents answering 0, 1, 2, and 3 compose level 1 (low risk willingness).
Secondly, respondents answering 4, 5, and 6 constitute level 2 (medium risk willingness).
Finally, respondents answering 7, 8, 9, and 10 create level 3 (high risk willingness.
5.2 Explanatory variables
Several independent variables are included in the empirical analysis to predict individuals’ risk- willingness. Discussions regarding each variable’s relevance will be presented, as well as the anticipated effect on risk willingness. Subsequently, the degree of exogeneity to avoid endogeneity problems in the model, will also be discussed (Stock & Watson, 2014). Firstly, the person-centered characteristics will be presented. Secondly, the situational characteristics.
Table 2 and 3 provide a summary of the predictors used in the final model.
5.2.1 Person-centered variables
Table 2, descriptive summary of predictors considered as person-centered
5.2.1.1 Female
The general opinion tends to assume that women are more risk averse than men. This opinion is supported by several previous research that all conclude that men are more inclined to take risk than women (Sundheim, 2013; Mather & Lighthall, 2012). Accordingly, the hypothesis for this regressor is in unison with previous research – that women are less risk-willing than men.
Furthermore, one’s gender is not decided within the model and is therefore considered strictly exogenous.
5.2.1.2 RacialMinority
In the United States, the racial majority are whites. Therefore, every other race is considered as a racial minority in the US (United States Census Bureau, 2020a). Although empirical research lack in explaining the impact race has on risk-willingness, scholars agree that culture affects it (Sitkin and Weingart, 1995; Weber et al., 2002; March & Shapria, 1987). Yet, Yao et al., (2005) found that non-whites are less likely to take minor financial risk but more likely to take substantial financial risk. However, this paper does not revolve around financial risk- willingness per say, but general risk-willingness. Nevertheless, it could be argued that non- whites’ general risk-willingness is difficult to prophesy. Still, the hypothesis for this predictor is that non-whites are less risk-willing than whites – solely based on whites’ higher median income (United States Census Bureau, 2020b). Moreover, one’s ethnical background is not decided within the model and is therefore considered strictly exogenous.
5.2.1.3 Age
Continuous variables can with advantage be constructed as categorical for a more interesting and isolated result (Williams, 2016). So, the independent variable ‘Age’ in this paper adopts this reasoning (see table 2). Furthermore, most of the empirical evidence that tries to shed light on the potential link between age and risk behavior are cross-sectional data, where results indicated a negative relationship (Barsky et al., 1997; Donkers et al., 2001; Dohmen et al., 2011). While this can prove useful insights, Dohmen et al., (2017) argue that observing age and risk attitude is better performed via usage of panel data. So, by observing panel data, the authors found that risk-willingness declined with age even here but with difficulties to observe a pattern for younger ages. Arguably, panel data is a superior method when investigating age and risk.
However, since previous cross sectional research provides roughly the same results, there is no
reason to neglect age as a factor affecting risk-willingness in this paper either. Thus, the
hypothesis for ‘Age’ is in line with previous research that risk-willingness decline when individuals gets older. Also, one’s age is not decided within the model and is therefore exogenous.
5.2.1.4 HighEdu
As displayed in table 2, this thesis interprets high education as individuals with a bachelor’s degree or higher. Subsequently, Sung & Hanna (1996) as well as Hawley & Fujii (1993), both demonstrates that risk-willingness increases with higher education. Another perspective is adopted by Cooper & Zhu (2014), who conclude that higher education does in fact increase households’ risk-propensity, but via the means of increased income. Arguably, speculations regarding multicollinearity may arise between income and education. Yet, both variables will be included in the analysis due to previous research and subsequently excluded if the correlation is too problematic.
3As to the degree of exogeneity, simultaneity could be apparent if one’s risk tolerance affects the choice of education, and not vice versa. However, since respondents of the SHED chose their current risk tolerance when their level of education already was fixed, this thesis proposes that ‘HighEdu’ could be interpreted as exogenous. Conclusively, the hypothesis for this predictor is in line with previous research; that higher education increases the risk- willingness.
5.2.1.5 Student
Yurtkoru et al., (2014) examined students’ intentions to choose an entrepreneurial path, thus translating this entrepreneurial feature as risk-venturous. Furthermore, they compared students from private and state universities. Their findings suggest that private university students are more prone to risk than state university students. In this thesis however, students are not divided into different categories, since the objective of this variable is to see whether there is a difference in risk propensity solely on being a student. Therefore, due to lack of previous research in the area, this variable is more of an explorative kind. Still, the hypothesis for this predictor is that being a student decreases risk-willingness since it could be argued that students may want to “secure” future income. However, this reasoning may unfortunately generate simultaneity since risk propensity affects the choice of being a student, and not the other way
3See Appendix A for correlation matrix.
around. Thus, caution with the interpretation should be taken since endogeneity problems may occur.
5.2.1.6 Income
Income is a commonly used factor to explain risk behavior. Both Shaw (1996) and Hawley &
Fujii (1993) found that increasing income is positively correlated with higher risk-willingness.
However, Shaw (1996) continues her reasoning by connecting higher income with higher education, thus explaining a portion of the increased risk propensity. Still, as stated previously when discussing ‘HighEdu’, future engagement regarding excluding one of the variables will be considered only after tests for multicollinearity. Additionally, deliberation regarding exogeneity is coherent with the reasoning around ‘HighEdu’; individuals who participated in the SHED have arguably had their income for a while when there and then deciding the degree of risk-willingness. Thus, concluding that ‘Income’ is decided outside of the model.
The hypothesis for this variable are in line with Shaw’s (1996) results; that higher income increases individuals’ risk-willingness.
5.2.1.7 TotalSavings
This explanatory variable summarizes a household’s approximate savings and investments. In Sung & Hanna’s (1996) ordered probit model, they distinguish savings and investments into liquid assets (savings, checking and- money market accounts) and non-liquid assets (solely assets from financial investments). The authors conclude that both higher liquid, and higher non-liquid assets increases households’ risk-willingness. Notably, non-liquid assets (financial investments) affected risk-willingness with greater magnitude than liquid assets (i.e. savings accounts) Conclusively, the hypothesis for ‘TotalSavings’ is in line with previous research stating that increased total savings (both investments and savings in this paper) increase individuals’ risk-willingness. Arguably, since individual’s total savings were given at the time they answered the SHED, worries concerning simultaneity and thus endogeneity may be dismissed.
5.2.1.8 InvKnow
The respondents in the SHED were asked: “Considering a long-time period (for example 10 or
20 years), which asset described below normally gives the highest returns?” The respondents
who answered “Stocks” were correct, and this is how this dummy variable were constructed;
values of 1 = basic investment knowledge (individuals who answered “Stocks”). Although one might recognize that this variable is subjective, it will still be included in the empirical analysis due to curiosity reasons. Nonetheless, Satti et al., (2013) demonstrates that investors’ with less financial knowledge are more risk-averse than investors with more financial knowledge. The hypothesis for this predictor is in line with their results; “better” financial knowledge increases individuals’ risk-willingness. Arguably, since financial knowledge may be viewed as a personal trait, ‘InvKnow’ is considered as exogenous.
5.2.1.9 Status
The respondents in the SHED were asked: “Imagine a ladder showing where people stand in the United States. At the top are people who are the best off. At the bottom are people who are the worst off. Where would you place yourself on this ladder?” Subsequently, the respondents could choose any number between 0 (worst off) and 10 (best off). This thesis interprets this variable as self-perceived social status. Arguably, social status could be connected to wealth, career and overall success – perhaps resulting in high correlation between ‘Income’ and
‘HighEdu’. However, Woo et al., (2008) conducted a study on self-perceived social status, education, income and occupation. Their findings suggest that even though individuals’
education, income and occupation were ranked low, they could still consider themselves as highly ranked in terms of social status. Arguably, Woo’s et al., (2008) findings support the decision to include ‘Status’ in the model since higher perceived social status does not necessarily equal greater wealth and success. Perhaps instead, social status can be explained in terms of satisfaction with one’s social life i.e. friends and family – regardless of it being illusory or realistic. Conclusively, the hypothesis for ‘Status’ is left undecided due to the complexity of its characteristics. Finally, as a personal characteristic, ‘Status’ is interpreted as exogenous.
5.2.1.10 Trust
The relationship between risk and trust is often related in theory. Yet, this relationship is
troublesome and scholars tend to separate trust in different ways. Firstly, as perception which
is also known as subjective trust. Secondly, as the actions resulting from the subjective trust –
behavioral trust (Das & Teng, 2004). The authors also claim that an individual’s perception of
trust is the mirror of perceived risk. For example, a risk averse individual who trusts another
risk venturous individual blindly, will act as that individual does in risky decisions, irrespective
of the actual risk magnitude in that certain decision – since the risk averse individual perceives
the risk in the same way as the risk venturous individual does. Arguably, the relationship between trust and risk is a complex one, concluding in a more explorative starting point. The hypothesis is therefore undecided. As to exogeneity, ‘Trust’ should be taken with caution since it is unclear whether trust affects risk-willingness or vice versa.
5.2.1.11 Mortgage
The predictor ‘Mortgage’ separates households with mortgages or loans to all other household situations. While previous research deems the variable as a relevant tool to predict risk willingness, it’s effect remain ambiguous due to lack of significance (Sung & Hanna, 1996). In this paper, the hypothesis for ‘Mortgage’ is that individuals that currently have a house mortgage or personal loan – have lower risk willingness than those who do not have a mortgage or loan. Simply because of a preconception where debt may equal more caution. Moreover, it could be argued that individuals who are more risk averse tend to avoid personal debt to a greater extent than others – ultimately stating that one’s risk propensity affects whether you have a mortgage or loan and not the other way around, leading to endogeneity. However, it could also be argued that mortgages are a necessity for the majority when it comes to purchasing a home, regardless of one’s risk propensity since we simply cannot afford it otherwise.
Conclusively, ‘Mortgage’ may also be interpreted as exogenous and will therefore be included in the empirical analysis of this paper.
5.2.1.12 Unemployed
Attempts to demonstrate the relationship between risk willingness and unemployment is
nothing new within empirical research. Diaz-Serrano & O’Neill (2004) found that being
unemployed increases the probability of having a low risk willingness. However, their result is
in contrast with the traditional job search model that suggests that more risk averse individuals
have shorter unemployment spells (Feinberg, 1977). The hypothesis for ‘Unemployed’ in this
paper is in line with the traditional job search model – where being unemployed increases the
probability of having high risk willingness. One supporting argument is that more risk averse
individuals may be more willing to accept lower wages, just for the sake of being employed
and have a secure income. Nonetheless, caution should be taken with the interpretation of this
predictor since it could be argued that one’s risk willingness affects employment status and not
vice versa. Still, due to its common appearance in previous research ‘Unemployed’ will be
included in the final model.
5.2.1.13 SelfEmployed
As with unemployment, trying to connect self-employment to risk willingness is no new phenomena either. Scholars are unanimous in that being self-employed increases the probability of having a higher risk willingness (Sung & Hanna, 1996; Brown et al., 2007). Accordingly, the hypothesis for this predictor is in line with previous research since starting an own business can be considered as risky behavior. However, self-employment may be considered as an obvious variable in terms of endogeneity since choosing the entrepreneurial route is an action originating from one’s risk propensity and not vice versa.
Despite possible endogeneity issues, self-employment is often related to explaining risk behavior in previous research, and this stirs curiosity whether the data used in this paper also aligns with earlier discoveries. Thus, ‘SelfEmployed’ will be included in the final model.
5.2.1.14 Newborn
Since no previous research on the subject matter was found, the independent variable
‘Newborn’ which indicates that the household consists of at least one infant between 0-12 months, is an explorative kind. The hypothesis for this variable is that individuals with infants may act more cautious and responsible to not jeopardize accommodation and future income.
Therefore, it is believed that the probability of high risk willingness decreases when individuals gets a newborn. Arguments supporting exogeneity is that propagation is a natural instinct, and can therefore not be affected by one’s risk propensity. Instead, getting children may change one’s view on risk, concluding that ‘Newborn’ may be considered as exogenous.
5.2.2 Situational variables
Regarding the predictors, it could be argued that there is a fine line between what could be
interpreted as person-centered or situational. This thesis tries to distinguish the two types by
stating a sudden, unexpected circumstance as a criterion for a predictor to be considered as
situational. Furthermore, in empirical research, attempts to explain risk willingness with
situational variables seems like an unobserved area. Here, one might acknowledge this as a
progressive attempt which can be enhanced in future research. Additionally, motives for these
predictors are subjective and is not supported by any research. Hence, they all appear in an
explorative sense. Since these variables origin from unpredicted circumstances, strict
exogeneity is assumed and is therefore not discussed.
Table 3, descriptive summary of predictors considered as situational
5.2.2.1 EmergencyThreeMonths
The respondents in the SHED were asked: “Have you set aside emergency or rainy day funds that would cover your expenses for 3 months in the case of sickness, job loss, economic downturn, or other emergencies?” Said situation may be interpreted as a sudden circumstance and is thus considered as situational. The hypothesis for this variable is uncertain, and it divides the respondents into two groups – individuals with enough savings and individuals with not enough savings. Moreover, the underlying reason one belongs to the latter group may differ.
Perhaps the individual in question does everything in its ability to save but still cannot manage to get by, or perhaps the individuals is reckless and irresponsible. The objective with this predictor is to observe if there is a pattern between this certain circumstance and individuals’
risk willingness.
5.2.2.2 CantPayBill
The respondents in the SHED were asked: “Which best describes your ability to pay all of your bills in full this month?” To this they could either answer “Can’t pay some bills” or “Able to pay all bills”. Despite this situation may not be considered as sudden or unexpected, one can interpret it as something not recurrent. Thus, it may describe one’s current situation and not one’s usual situation. The hypothesis for this variable is that individuals with “difficult months”
is less risk venturous.
5.2.2.3 LostWork
The respondents in the SHED were asked a yes or no question: “Think about any job in the past 12 months not just your main job last month. In the past 12 months, have you gotten laid off or fired from a job?” Arguably, getting laid off/fired could be interpreted as something out of the ordinary and is thus considered as circumstantial. The hypothesis for this predictor is that individuals who lost their employment, may develop an ambition to achieve something new, thus leading to increased risk willingness.
5.2.2.4 NeighborhoodSaftey
The respondents in the SHED were asked: “How satisfied are you with the safety of your neighborhood?” The answers could range between five levels of satisfaction. However, to create more substantial categories, said five levels were combined into two – either you are satisfied, or you are not. Arguably, one’s neighborhood can change in perceived safety depending on various happenings such as; murders, accidents, natural disasters, gang activity etc. The hypothesis for this predictor is that individuals who are satisfied with their current neighborhood situation are more risk willing. Perhaps the fact that these individuals do not need to worry about everyday danger encourages other areas such as more risk taking.
5.2.2.5 HouseQuality
The respondents in the SHED were asked: “How satisfied are you with the overall quality of
your housing?” As with ‘NeighborhoodSaftey’, the answers could range between five levels of
satisfaction. Even here, said five levels were combined into two to create more substantial
categories. Either one is satisfied with one’s housing situation or not. Arguably, individuals do
not necessary live in the same accommodation their entire lives. Therefore, one’s current
housing situation could be interpreted as situational and not forever. The hypothesis for this
variable is undecided and thus the objective is to see whether a pattern can be observed.
6. Results
Technical discussions regarding confirmation of the Proportional Odds Assumption and its appropriate Wald test is found in Appendix B. Thus, this section’s objective is to interpret the explanatory variables’ different effects on individuals’ risk willingness.
6.1 Intuition on how to interpret the model
The format used to interpret the coefficients for all predictors are expressed in odds ratios.
Since the response variable (risk willingness) has three possible values (low, medium and high) the PPOM will have two sets of odds ratios, or more technically expressed, J-1 cumulative logits (Williams, 2016). In this thesis, the first set of odds ratios contrasts the “Low risk willingness”
category with the “Medium and –high risk willingness” categories. That is, the odds ratios in the first set imply the probability of an individual having Low risk willingness as opposed to the remaining two categories (medium and high). Similarly, the second set contrasts the “Low and –medium risk willingness” categories with the “High risk willingness” category. Note that odds ratios greater than 1, imply that higher values of an explanatory variable increase the probability that an individual is in a higher category of risk willingness than the current one.
Odds ratios less than 1, imply that higher values of an explanatory variable increase the probability of being in the current or a lower risk willing category (Williams, 2006).
Altogether, the model estimates 29 odds ratios; 25 in the first set (Low vs Medium, High) and four in the second set (Low, Medium vs High), see table 4. Variables in red rows (‘Female’,
‘RacialMinority’, ‘TotalSavings’-category “$500k-$999.9k” and ‘Unemployed’) all violate the Proportional Odds assumption which makes them appear in set number two as well, but with different odds ratios. The PPOM thus allows the odds ratios of these four variables to vary across the J-1 equations (Soon, 2010).
4Accordingly, the other variables do not violate said assumption which make their odds ratios constant throughout all cumulative logits.
4Had a standard OLM been estimated, there would only be 25 estimated odds ratios since they would have been assumed to be the same across the J-1 equations for all predictors.
Had a GOLM been estimated, there would have been 25x2=50 estimated odds ratios since there would be a different set of odds ratios for all J-1 equations.
6.2 The final model
Table 4 shows different effects on risk willingness for the predictors.
5Most of them had significant effects (see highlighted variables), except for ‘ages 30-44’, ‘HighEdu’, ‘Student’,
‘total savings $50k-$99.9k’, ‘Mortgage’, ‘CantPayBill’ and ‘HouseQuality’.
Table 4, Partial Proportional Odds Model for individuals’ risk willingness
* Significance level 10% ** Significance level 5% *** Significance level 1%
5 Variables in red rows all violate the Proportional Odds Assumption.
6.2.1 Factors increasing risk willingness
Several highly significant and positive effects (odds ratios greater than 1) on risk willingness stand out. Individuals with higher income and/or self-perceived good investment knowledge are more likely to take higher risk. Additionally, individuals with greater self-perceived social status and/or less trust issues are also more positive towards risky behavior, as with those who are self-employed and/or have newborns. Furthermore, those who got laid off/fired during the past 12 months are also more likely to express higher risk propensity. Lastly, non-whites and most of the total savings-categories also expressed positive odds ratios, however with somewhat different features than the rest. As for non-whites, the variable does not fulfill the Proportional Odds Assumption which provides two different estimates. So, when observing the two odds ratios of 1.196 and 1.428 respectively, one can conclude that non-whites are more likely to express high risk willingness – with an increasing magnitude.
6Finally, the rigid pattern of
‘TotalSavings’ indicates that, the higher the total savings – the greater the probability is to take higher risk.
6.2.2 Factors decreasing risk willingness
As opposed to above stated variables who increased the probability of risk willingness, numerous predictors also displayed significant and negative effects (odds ratios less than 1) on risk willingness. Individuals who economically, would not muster the next three months in case of an emergency, is less likely to take risk than those who would manage. Or, expressed more technical – if one goes from managing three months in case of an emergency to not manage, the odds of medium and high risk willingness versus low risk willingness is 0.868 times lower given all the other variables are held constant. Moreover, on a 10% significance level, individuals who are satisfied with the safety of their neighborhood are also less likely to express risky behavior. Regarding ‘Age’, one can observe a significant negative pattern from the ages 45-59 – as one gets older, the risk propensity decreases. Finally, both variables ‘Female’ and
‘Unemployed’ violates the Proportional Odds Assumption, generating two different estimates each. Consequently, females are less likely to take on risks than males. With estimates of 0.737 and 0.587 between sets indicating an increased magnitude of less risk willingness. Unemployed individuals also reveal less tendencies to take risks, displaying a significant result to be more
6The first set shows that non-whites are 1.196 times more likely to express medium or high risk willingness than low risk willingness. The second set shows that non-whites are 1.428 times more likely to express high risk willingness than a low or medium risk willingness.
likely to have low risk willingness versus medium and high risk willingness. However, the second estimate of 1.058 falls short from statistical significance (Low, Medium vs High).
6.2.3 Insignificant factors
Statistically insignificant variables also provide insights. Seemingly, having a higher academic education and/or being a student do not provide any significant conclusions regarding individuals’ risk willingness. The same goes for having a mortgage or personal loans, not being able to pay all bills the current month and being satisfied with one’s current housing situation.
Evidently, all these factors fall short from describing risky behavior.
7. Discussion
When reflecting over the results, both intuitive and surprising effects occurred. Some variables will be discussed more thoroughly than others and this is solely due to subjective reasons originating from interest and curiosity. Regarding the person-centered characteristics, most of the results were in line with previous research. These results will be discussed first. Secondly, the personal attributes with more peculiar and debatable results are presented. Lastly, the situational variables considered as explorative are discussed.
7.1 Factors in accordance with previous research
Several authors all conclude that females are less prone to risk than males (Sundheim, 2013;
Mather & Lighthall, 2012). The result in this paper is no exception. Subsequently, authors have tried to explain why this is a unanimous phenomenon. Buss (2003) extends Trivers’ (1972) evolutionary analysis of parental investment. The authors emphasize the difference in physical investment (for humans: nine months pregnant versus a few seconds) between females and males when producing an offspring. Apparently, this disparity may generate stronger maternal instincts than their paternal counterparts – which then is related to risk propensity in terms of females’ tendencies to act more careful and nurturing (Buss, 2003). However, it could be argued that the field of psychology provides a more nuanced standpoint. By recalling Druckman &
McDermott’s (2008) theory about how emotions can either amplify or depress tendencies to take risk, one might conclude that females are more vulnerable to feelings associated with reducing risky behavior, and therefore depresses their risk willingness more.
Age is another variable that is consistent with previous theory in the sense that as we get older, our risk propensity decreases (Barsky et al., 1997; Donkers et al., 2001; Dohmen et al., 2011).
One interesting observation from table 4 however, is the fact that the younger age categories fall short from significance. This is in line with Dohmen et al., (2017) findings who also found difficulties to observe a pattern for younger years. Arguably, risk behavior for adolescents and young adults seem to be less predictable than for their elders. Naturally, one can appreciate that as we get older, our propensity and eagerness to “experience new things” may decline.
Income, total savings and investment knowledge may all be sorted into one common
denominator – finance. Evidently, higher values of said factors all increase one’s attitude
towards risk (Shaw, 1996; Hawley & Fujii, 1993; Sung & Hanna, 1996; Satti et al., 2013). This paper provides no exception to its progenitors and can confidently state that one’s financial situation matters in relation to risk. Arguably, better financial conditions may provide more spontaneous actions and less contemplation in decisions – resulting in a riskier attitude.
Obviously, mortgage and personal loans are related to finance as well, but not in the sense of wealth but rather in the sense of debt. Nonetheless, Sung & Hanna (1996) tried to prove a relationship between home owners with mortgages and their risk willingness with no success.
Unfortunately, this thesis also falls short from significance regarding mortgages. Perhaps it could be argued that for the majority, taking a mortgage at some point in life is a necessity, and thus not related to one’s risk propensity at all since it is somewhat inevitable.
Self-employed individuals seem to express high risk willingness. The results in this paper are in accordance with previous findings (Sung & Hanna, 1996; Brown et al., 2007). Arguably, entrepreneurs tend to exhibit various proactive characteristics such as courage, spontaneity and ambition – which may all be related to higher risk tolerance. Yet, concerning financial investments, it could also be argued that it would be more reasonable for a self-employed to tolerate less risk than an otherwise similar individual who was not self-employed. Presumably, income from self-employment ought to vary more than income from wages, providing a more uncertain life situation. However, said argument rely on rationality – which individuals are not.
7.2 Factors with more debatable results
The remaining results regarding personal attributes lack support from previous research.
Arguably, these attributes provided more controversial and perhaps less intuitive results. Take
‘RacialMinority’ for example, the results in this paper opposes the hypothesis and suggest that non-whites are more likely to express high risk willingness at the 1% significance level.
Although with vague support from scholars who rather argue that culture affects risk, and not race per say (Sitkin and Weingart, 1995; Weber et al., 2002; March & Shapria, 1987).
Controversially, one might argue that culture translates into race. Yet, as the world gets more globalized, different cultures gets more blended and integrated, arguing against said translation.
Still, the results in this thesis are certain – non-whites are more likely to express high risk
propensity, with increasing magnitude. The question seems to be why this is the case. While
the hypothesis stated that non-whites ought to be less risk willing due to lower median income
(poorer financial condition translates into lower risk propensity), perhaps it is the opposite in relation to race. Arguably, non-whites’ perspective on the relation between wealth and risk may differ from non-whites. Conclusively, these results provide opportunities for future research within the subject since there still appear to be uncertainties whether the results are reasonable.
Both ‘Status’ and ‘Trust’ have complex relationships to risk, and scholars have approached the relations in different ways, with different results. However, previous research consists of theoretical research whereas this thesis provides empirical research on the matter. Hence, these results may serve as a foundation for future research within the subjects. Evidently, individuals who believes they have a greater social status are more prone to risk, as with those who have less trust issues. Arguably, the field of psychology seems appropriate when attempting to explain why this is the case. Since Woo et al., (2008) demonstrated that self-perceived social status could be regarded as higher due to illusory reasons, it could be argued that individuals who ranks themselves higher in terms of status, interprets risk differently – perhaps in an underestimated manner. Thus, exposing as high risk willingness in the eyes of others, when in fact, their self-perceived risk willingness is lower. Regarding trust, debates whether the relation with risk is inverse is apparent. However, if Das & Teng’s (2004) theory that “one’s perception of trust is the mirror of perceived risk” is true, one might recognize that individuals with less trust issues, may trust risk venturous individuals and subsequently act as they do in risky decisions – perhaps explaining why higher trust may increase risk willingness.
The variable ‘Unemployed’ displays controversial characteristics. Scholars disagree whether being unemployed affects risk propensity positively or negatively. Moreover, the hypothesis in this paper agreed with Feinberg’s (1977) theory about the job search model – indicating higher risk willingness for unemployed individuals. However, the result in this thesis is in line with Diaz-Serrano & O’Neill’s (2004) findings which suggest that being unemployed decreases risk willingness. Notably, the empirical findings in table 4 displays that being unemployed change its affect between sets, however insignificant in the latter.
7Apparently, risk and unemployment provide a complex relationship with uncertain conclusions. Ultimately, these uncertainties may be further explored in future research to achieve a more decisive standpoint.
7’Unemployed’ change its affect between Low vs Medium, High and Low, Medium vs High going from 0.834 to 1.058.
