Behavioral finances and prospect theory

For many decades, studies of people’s decision-making under uncertainty were guided by the expected utility theory [14]. According to this theory, economic behavior is seen as rational behavior. This hypothesis has been questioned and was challenged by [4], who proposed an alternative theory that they called prospect theory. This theory has become one of the most important tools used in behavioral finance to explain a series of biases affecting decision-making under conditions of risk.

An essential characteristic of this theory is that people taking decisions take into account changes to their wealth or wellbeing, rather than considering the final position. In other words, they evaluate changes or differences to their position considering a reference point, rather than evaluating absolute magnitudes. Thus, the context of the experience determines a reference point, and the stimuli are perceived in relation to this reference. This implies that the same level of wealth may seem to be a great deal to one person, but very little to another, depending on their current assets [4]. The value is therefore attributed to gains and losses and not to the final assets position.

Prospect theory suggests that people are risk averse in relation to gains and risk seeking in relation to losses. This means that the value function is S-shaped, being concave above the reference point and convex below it [4]. In general, the value function has the following characteristics: (i) it is defined in terms of displacements from a reference point; (ii) it is concave for gains and convex for losses; (iii) it is steeper for losses than for gains.

The concept of loss aversion emerges from this value function. According to this concept, people suffer more pain from loss than the pleasure they reap from an equivalent gain. Thus, the agent of behavioral finance judges gains and losses with relation to a reference point and so people exhibit risk-averse behavior with relation to gains and risk seeking with relation to losses. Agents are therefore loss-averse, since when faced with the possibility of a loss, they will accept risk in order not to realize the loss [15].

[4] contested the expected utility theory, showing evidence of patterns of behavior incompatible with the theory’s axioms. In other words, there is a pattern of behavior in which there is no evidence to support the expected utility theory, showing that errors are systematic and non-random. The expected utility theory is therefore inadequate in the majority of models of economic behavior [4, 12].

Theories of the personality

Economists are starting to consider aspects of the personality as relevant to economic studies. [16] demonstrate the relevance of personality to the economy. Currently, the most accepted taxonomy for definition of personality is centered on the “Big five personality traits”.

The Big Five Personality Traits is the personality model that has been most widely researched and adopted [17]. This model groups personality traits under five major factors, in order to represent personality on a wide level of abstraction. It therefore suggests that differences between individuals can be classified within these five dimensions: openness to experience, conscientiousness, extraversion, agreeableness, and neuroticism ([16], p.983).

Many different instruments containing measurement items have been developed to capture personality differences. For example, the BFI-10 comprises just 10 short sentences, each of which should be assessed by the respondent against a scale ranging from "completely disagree" to "strongly agree". The responses can be used to compute a profile in each of the five major dimensions of personality.

Each individual’s personality corresponds to a combination of the five personality traits. Thus, each person can be placed on a scale in which one personality trait will be more evident than the others. This does not imply that the other traits are not also present. Thus, participants in a sample can be classified according to the predominance of characteristics as high, moderate, or low for each major dimension of personality.

Cognitive reflection test (CRT)

Countless phenomena can be associated with greater or lesser cognitive capacity, such as preference for risk, intertemporal preference, aversion to ambiguity, etc. However, the influence of people’s different cognitive capacities on their decisions has been studied little.

According to [22], possible effects of cognitive abilities (or cognitive traits) are generally part of unexplained variance in studies that specifically analyze average behavior. However, as shown by [23], intelligence, or specific cognitive abilities, are important determinants of decision-making and should not therefore be ignored.

The Big Five model captures the majority of specific personality traits. In this paper we have operationalized intellect as a separate concept to openness to experience, which is one of the components of the Big Five. This justifies combining the cognitive reflection test (CRT) with the Big Five [24]. The CRT was presented in a study by [22] and it attempts to measure people’s cognitive capacity. It is designed to assess the capacity to substitute an impulsive, and incorrect, response with reflection that leads to the correct response. The metric used to assess the relationship between CRT results and risk preferences was based on choices between a certain gain/loss and the probability of a larger gain/loss.

Investor profile analysis

A procedure that has been adopted internationally to match investors’ investments to their risk profiles is designed to set formal standards to determine how appropriate an investment is for a customer’s risk profile. An individual’s risk profile is constructed by considering several different characteristics including their financial situation, experience with investments, risk tolerance, investment time horizon, and investment objectives, among other factors [25].

The International Organization of Securities Commissions (IOSCO) is recognized as the global organization responsible for stock market regulation, with more than 95% of the world’s stock markets affiliated, and it publishes the major guidelines for investment matching policies. The requirements are intended to afford consumers with protection, since these products have terms, resources, and investment risks that may make them difficult to understand [26].

ANBIMA (Associação Brasileira das Entidades dos Mercados Financeiro e de Capitais) is the principal representative organization for institutions that do business in the financial and stock markets of Brazil and, in consideration of the international guidelines, has made it obligatory for institutions that sign up to its Regulatory and Best Practices Code to analyze investors’ profiles before they invest, through adoption of an Investor Profile Analysis (IPA) process. For this study, it was decided to employ the Bank of Brazil investor profile analysis questionnaire, in view of the bank’s significant role in the country’s financial sector.

Data collection

The experiment was conducted with undergraduate students from the economics and electrical engineering courses at the Federal University of Santa Catarina, during modules related to finance studies. A total of 140 students took part. Thirty-four participants were women and 106 were men. However, some of them were excluded from the study because of operational problems, leaving 137 people, and the final study sample comprised the results from 124 people, since participants who stated they already knew the answers to the CRT questionnaire were also excluded.

The questionnaire was completed online at the same time by all respondents, during an experimental session. The questionnaire comprised 5 blocks of questions. The first covered aspects relative to investor profile. Next, there were 10 questions about investment scenarios, adapted from [4], to evaluate violation of the expected utility theory, and the results were used to create a dummy variable where 1 indicates that a participant predominantly (at least 6 out of 10 questions were answered in a manner compatible with prospect theory) behaved in accordance with prospect theory, while the value 0 indicates that the participant behaved in a manner compatible with expected utility theory. The third block was made up of 10 questions from the Big Five Inventory [34]. Next were a further 8 questions from the Bank of Brazil IPA questionnaire, and, finally, 3 questions from the CRT [22].

The CRT was administered separately from the other questionnaires and all participants started to answer it at the same time, because it has a time limit of 5 minutes. Once they had completed the questionnaire, all participants started the computational investment simulation at the same time. It was stressed that participation was voluntary and did not offer any type of material incentive to the participants.

It is emphasized that before the research was carried out, the project was submitted to the Brazilian “National Information System on Research Ethics involving Human Beings” (SISNEP), whose main concern is the protection of the subjects' rights. The submission to SISNEP took place via the Plataforma Brasil site, a national and unified database of research registries involving human beings. After submission, the project was evaluated by the Human Research Ethics Committee (CEP) of the Federal University of Santa Catarina. Only after the fulfillment of all the procedures and approval of the project has the research begun.

In compliance with the requirements imposed by Resolution 466/2012 of the Brazilian National Health Council (CNS), the Free and Informed Consent Form was delivered together with the questionnaire. Only those subjects who, after reading the term, agreed, in a free and clear way, to respond to the survey participated in the research. According to the Resolution, the Term of Consent guarantees, among other things, the clarification, before and during the course of the research, on the methodology used; the freedom to give up participating in the research, in any of the stages, without any kind of penalty or loss; indemnification against any damages resulting from the research; and the confidentiality of the disclosed data in order to maintain the privacy of the respondent.

Computational investment simulation (ExpEcon)

In order to identify the respondents’ “real” behavior with relation to their preferences for assets and their appetite for risk, computational investment simulation was conducted with the aid of ExpEcon (Experimental Economics) software. This software is used to identify participants’ behavior and decisions in situations of risk [11, 12].

The assets used in the simulation were defined as those available as investment options through Bank of Brazil. Among other factors, this bank was chosen because of information contained in a classification released by ANBIMA. Their results show that Bank of Brazil tops the ranking of institutions that manage investment funds in terms of assets invested in funds. In December 2015, BB DTVM S.A had a total of R$ 591,995.8 million in assets under management in different funds, which is the largest net assets of any of the Brazilian fund managers [35]. This result illustrates the bank’s significant role in Brazil’s financial sector, justifying choosing it. Bank of Brazil investment funds were chosen with special attention to risk levels and for each risk level the fund chosen was that which had the largest net assets on the definition date, in this case, in May 2015.

The data used for simulations are real financial data from the 2006 to 2014. Half-yearly closing data were used, for which the percentage change in the asset in the corresponding 6-month period was considered. Thus, for example, period 1 of the simulator corresponds to the percentage variation of the asset in the period from January to June 2006, year 2 of the simulator corresponds to the percentage change from July to December 2006. Year 3 corresponds to the percentage change of January to June 2007 and so on. These data can be found at: https://figshare.com/s/d64e31241357afa8b950

The participants were not informed what period in time the data were from, they were only told that the data were real historic data on the assets involved. The deposit account profitability used was the six-monthly mean interest rate and was taken from the Central bank’s information system (SISBACEN), while profitability figures for Bank of Brazil investment funds were taken from the six-monthly variation per unit for each fund, taken from the Brazilian securities commission database (Comissão de Valores Mobiliários–CVM)

This approach to operationalization of the experiment was intended to make the simulation realistic, using historical profitability and interest data for the investment funds and deposit account. The objective of the simulation is to observe whether each participant chooses higher or lower risk assets to invest in, in order to approximate their "real" investor profile.

As input to the experimental system, all assets started period 1 with a value equal to R$ 1,000.00 and, for each subsequent year, historical real profitability was added to the initial value, thus demonstrating the evolution of the asset over the years. What was sought with this operationalization of the experiment is to make the simulation real, using real profitability data.

The participants were instructed to manage a financial investment portfolio over 18 periods. Price variations for the first 3 periods were displayed and used to provide a basis for initial investment decisions. Participants were not informed about the future performance of the assets.

The characteristics of each of the assets used in the simulation are shown in Table 1:

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Table 1. Characteristics of assets used in the investment simulation.

https://doi.org/10.1371/journal.pone.0214062.t001

The results of portfolios were analyzed in order to capture participants’ risk profiles and thus identify their asset preferences. In this study, it was decided to employ the weighted mean of assets held in the portfolio in the last three periods during which the agent bought or sold assets. This was used to classify agents into one of three risk profiles. These risk profiles resulting from the investment simulation using ExpEcon were used to populate a variable, termed Simulator_Profile, which would be used as the dependent variable for the logistic regression model. According to the portfolio they are holding at the end of the simulation, each participant is allocated a risk profile and a number to represent it, which is the dependent variable in the model (Dummy). The low risk profile is coded with the value 1, the moderate risk profile with value 2, and the daring risk profile is coded as 3.

Data analysis

An ordered logistic regression model was used to achieve the study objective. Table 2 contains a description of each of the variables used in this stage of the study:

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Table 2. Descriptions of study variables.

https://doi.org/10.1371/journal.pone.0214062.t002

The logistic regression model assumes that the response variable exhibits a natural order of options. The model employs an index, with a single multinomial variable that is inherently ordered [36, 37].

According to [37], the model is constructed by starting from the same form as a multinomial logit model: (1) In which, y* is not observed. What is observed is Where μ_s is an unknown parameter, to be estimated from β. The probabilities are therefore as follows: (2) (3) (4) (5)

For probabilities to take positive values, necessarily

The function Φ(.) is a notation used for the standard normal distribution. As with other logistic regression models, the regressors’ marginal effects on the probabilities are not equal to the coefficients. However, the sign of the regression parameter can be interpreted as an increase or not of the ordered variable. Thus, if β_j is positive, then an increase in x_ij necessarily reduces its probability of being in the lowest category (y_i = 1) and increases the probability of being in the highest category [36].

However, according to [37], the marginal effects of the variables can be obtained from, for example, the following probabilities: (6) (7) (8)

Since the model does not illustrate a linear relationship between variables, the coefficients obtained from ordered logistic regression should not be interpreted as a direct increase of the probability. According to [37] and [36], the signs of the coefficients are unequivocal. However, it is necessary to interpret the coefficients with caution. They should be interpreted considering their marginal effects.

Ordered logistic regression model

An ordered logit model was used to evaluate behavioral and personality variables that possibly have an impact on the risk profile in “real” environments. The dependent ordered variable, the Simulator_Profile, corresponds to the 3 risk levels extracted from the investment simulation: Low, Moderate, and High risk. Analyses of the results are conducted by comparing these different categories. Thus, the coefficient is calculated maintaining the other categories constant. The initial results are shown in Table 4.

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Table 4. Ordered logistic regression model.

https://doi.org/10.1371/journal.pone.0214062.t004

Table 1 contains five different ordered logistic regression models. Each one shows the results of including additional variables and model 5 has the greatest explanatory power (R² is 62.2%) and will therefore be adopted for subsequent analyses. It was found that the statistically significant variables were Mean IPA, CRT Profile, Mean Prospect, and OpennessExpDummy. The β obtained in the regression reflects the impact of changes on the probability of X, but the results are best interpreted by calculating the exact values of the probabilities [37].

For example, it is possible that, for a unit increase (from 0 to 1) in mean participant risk, calculated from their responses to the IPA questionnaire, it is expected that the probability of the participant being on a higher risk tolerance level would increase, since the respective coefficient in the fifth model is positive. This is assuming that the other variables all remain constant. This result is coherent, since both measures assess individuals’ risk tolerance.

The results for the impact that cognitive capacity has on the risk profile indicate that an increase in the number of correct answers to the CRT questionnaire (indicating greater cognitive capacity), triggers a reduction in the probability of greater risk taking. These results with relation to the CRT contradict findings reported by [22]. His study confirmed the hypothesis that participants with higher levels of education and intelligence exhibit higher risk tolerance, finding that in the domain of gains a group with High CRT was willing to risk more and to risk larger sums. [29] also reported similar findings, indicating that people with greater cognitive capacity were significantly more willing to take risks in lottery experiments.

In contrast, when [22] evaluated risk taking in the domain of losses, he found that the group that scored high on the CRT sought less risk and were more willing to accept a guaranteed loss than a probability of a loss with lower expected value. In this case, in the domain of losses, the results observed by [22] are in agreement with those observed in the present study. Similarly, [10] revealed that the relationship between risk tolerance and cognitive capacity is non-linear. They state that people classified as at the two extremes of cognitive ability, i.e., those with low cognitive capacity and those with elevated cognitive capacity have greater risk tolerance.

The results for the variable Mean_Prospect, which represents violation or compliance with expected utility theory, revealed an inverse relationship. In other words, as an individual changes from 0 to 1 (compatible with prospect theory) there is a reduction in willingness to accept risk. This result is compatible with the certainty effect. According to [4], people tend to choose certain gains over probable results, indicating loss aversion.

The OpennessExpDummy variable reflects high, medium, or low scores for this characteristic in personality dimensions. A unit increase in this variable is expected to be related to an increase in the probability that the individual will accept higher levels of risk. These results for the dimension openness to experience are in line with results observed in a study by [8], who reported that this personality trait has an inverse relationship with risk aversion, indicating that people who have the characteristics creativity and novelty seeking are willing to take greater risks. These results also point in the same direction suggested by [21], that risk tolerance is directly related with the dimension openness to experience. Thus, high scores for openness to experience indicate greater risk propensity.

Starting from these initial results, since it is known that the estimations of logistic regression models do not directly reflect marginal responses, as in the traditional method of ordinary least squares, it is necessary to analyze the marginal coefficients of each explanatory variable on the basis of the mean values for the sample. This estimation method makes it possible to calculate the marginal effects separately for each alternative (Table 5).

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Table 5. Marginal effects of the ordered logit model for risk taking.

https://doi.org/10.1371/journal.pone.0214062.t005

Observing the marginal results of ordered logit regression model 5, the first finding of note is that for the Low risk tolerance level from the investment simulation, none of the variables were significant. In other words, they are not determinants of consolidation of the risk-averse profile. In contrast, for the moderate and daring profiles, the variables already discussed in relation to the results shown in Table 2 were significant.

Thus, taking the CRT profile first, it is understood that an increase in the number of correct answers on the cognitive reflection test reduced the probability of respondents exhibiting a daring risk profile on the simulator by 0.810 percentage points. However, an increase in the number of correct answers on the CRT increased the probability of participants exhibiting a moderate risk profile on the simulator by 0.807 percentage points. This confirms that, in the setting analyzed, individuals with high cognitive capacity tended not to take excessive risk in investment decisions but were not conservative and rather had a moderate profile. This result is in line with descriptions by [7], who pointed out that the relationship between these two variables is non-linear.

With relation to IPA profiles, it was found that an increase in the level of risk allocated by the IPA increased the probability that respondents would exhibit a daring risk profile on the investment simulator by 4.745 percentage points, which is coherent, since both measures provide a risk profile. With regard to the variable representing violation or compliance with expected utility theory, it was observed that an increase in compliance with prospect theory reduced the probability that respondents would behave in a risk-seeking manner in their investment decisions on the simulator by 0.934 percentage points, confirming the existence of the certainty effect and risk aversion in unstable conditions [4]. Finally, it was also of note that of the five personality traits investigated, only openness to experience proved relevant to the risk profile, where an increase in this characteristic increased the probability that individuals would exhibit a daring risk profile by 0.176 percentage points, confirming the prevailing literature [8, 21].