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EÖTVÖS LORÁND UNIVERSITY Faculty of Education and Psychology
Ajna Uatkán
Individual risk perception and risk taking in two sequential probability games
Doctoral School of Psychology
Head of the School: Dr. Zsolt Demetrovics, professor, Eötvös Loránd University
Socialization and Psychology of Social Processes Program
Head of the Programme: Dr. Lan Anh Nguyen Luu, associate professor, Eötvös Loránd University
Supervisor: Dr. Klára Faragó, professor emerita, Eötvös Loránd University
Budapest, 2018
2 Introduction
Most economic models assume a rational decision-maker (homo economicus), who is constantly striving to maximize his utility, whose cognitive abilities are unlimited and accurate and whose attitude to risk is consistent. In real life, however, investors' perception of probability and risk management as well as their cognitive abilities usually violate the axioms of rationality.
In my dissertation, I studied individual risk-taking behavior using a computerized sequential investment simulation program. The cognitive approach I took primarily focused on how nonprofessional decision makers process information of previous outcomes (probability perception) and on the algorithms (Bayesian probability update) and on the heuristics (gambler’s fallacy) used for investment decisions.
Among various personality traits and theories, only the regulatory focus theory views risk- taking behavior by gains and losses. Therefore, I examined the effects of regulatory focus.
1. Study
Probability perception depending on the obtained information
Aim:
In the cognitive approach I aimed to explore how previous outcomes influence risk-taking in the following investment period. The risk-taking decision based on previous experiences can be primarily influenced by how individuals perceive the probability of winning. Therefore, I first examined the probability perception of individuals depending on the information they obtained about the preceding outcomes, then I investigated how much these subjective probability assessments differ from the objective probability determined by the Bayesian rule (posteriori probability)
Methods:
In the first experiment I examined the risk-taking behavior of 102 students (30% male, M = 21.3 years, SD = 3.4 years), and of 178 volunteers in the second experiment (63% male, M = 25.9 years, SD = 8.9). Participants received individual feedback on their performance and no further rewards were offered.
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We examined the risk-taking behavior of these individuals in two investment simulations, whereby individuals had to make sequential decisions, 10 times on 10 imaginary days. Participants decided about how much to buy of an unknown kind of risky share, alternating randomly over 10 imaginary days: the ‘winner’ type, with odds 2:1 of price increase vs. decrease, and the ‘loser’ type, with odds reversed. While the winner and loser shares did change randomly (50-50%) day by day, the probability of the share price increasing or decreasing remained constant: either 1/3 or 2/3 over the whole day (10 investment decisions). Such skewed distribution enabled participants to learn whether the ‘winner’ or the ‘loser’ type share was being traded throughout the 10 decision days.
Thus, investors could intuitively identify the daily type of share through the continuous immediate feedback after each investment decision. All participants encountered the same price change sequence throughout the simulation.
If the share price increased, the originally invested amount doubled; otherwise, the same amount was lost. The participants received continuous, immediate feedback on the results of their investments and the share price changes in the previous period, therefore they got an idea about the type of share they encountered (‘winner’ or ‘loser’). In the middle of the day (after 5 decisions) and at the end of the day (after 10 decisions), they assessed the probability of trading with the 'winner' share. However, these virtual days only served as barriers for the different shares because the data collection took place on one single day. The gains and losses were virtual, and the final net profit was not paid to the participants at the end of the game.
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1. Figure Process of the Investment Simulation with probability of trading with winner or loser share and probability of the share’s price changing
Note: inv= decision about the amount to be invested; guess= assessment of the probability of winner or loser share being traded; self-rate= assessment of self-performance in the simulation
Results:
We compared participants’ assessment of the probability of trading with the winner share (subjective, perceived probability) to the posterior probabilities. Investors estimated the posterior probabilities quite accurately on average, but both in the middle of the day and at the end of the day they tended to overestimate low probabilities and to underestimate high probabilities (Figure 2). The difference between the objective and subjective probabilities proved to be significant in the vast majority of the cases (17/20), mainly on the low and the high probability ranges.
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2. Figure Objective (a posteriori) and subjective probability perception (assessed probability of trading with the winner share) as a function of objective probability
Discussion:
Probability perception was tested in a dynamic learning environment where participants empirically experienced uncertainty while actively making decisions based on their previous experiences. If we plot the subjective probabilities perceived by the participants depending on the objective probabilities, we get a reverse S-shape function. This suggests that people do not linearly map probabilities, but overweight low probabilities and underweight high probabilities compared to their objective values. Although the deviation was significant, it is important to note that it was not substantial: for instance, the distinction between the type of share (winner or loser) was not affected.
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Posteriori P Assessed P weighting function
6 2. Study
Negative recency in an asymmetrical investment simulation.
Failing despite knowing
Aim:
People tend to misinterpret random events in statistical terms (Oskarsson et al., 2009; Falk et al., 2009; Nickerson, 2002). Two, rather contradicting heuristics can serve as the base for such misinterpretations. In the prediction of consecutive random events, positive recency stands for people believing in the continuation of positive series, while negative recency (NR) for the interruption of such series. The latter is also called as the gambler’s fallacy: when we do not believe that the same outcome of a series can continue for long time and that the longer it lasts, the greater chance it has of coming to an end.
Most of previous research (Leopard, 1978; Ball, 2012) has focused on exploring risk-taking behavior after binary random events with symmetric probabilities (1:1 odds). Gambler’s fallacy was proven to be present both in real life (Sundali and Croson, 2006, Clotfelter and Cook, 1993) and in laboratory experiments (Bar-Hillel and Wagenaar, 1991; Burns and Corpus, 2004; Sun and Wang, 2010). I explored whether negative recency arises in an asymmetric random sequential setup. Owing to the apparent odds (2:1) in this setting, negative recency is more pronounced, rather perceptible and turns out to be severely maladaptive. Therefore, I would expect no or at least fewer individuals to follow negative recency in such a setting.
Methods:
Participants applied to take part in the simulation by filling out an online questionnaire. I asked applicants about their online trading, poker, strategic games and sports betting behaviors and their formal statistics and probability theory studies.
To analyze the risk-taking behavior of the individuals, I measured how much money participants were willing to invest in the simulation. The interpretation was straightforward: the more they invested, the more risk they took. I analyzed correlations between invested amounts, the length of positive and negative runs (number of consecutive identical price changes), and the posteriori probability of trading with the 'winner' type share. The first correlation captures the effect of the belief in the run continuing or reversing, and the second one is considered as an indicator of
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economically rational decision making. Negative correlation with signed run length implies negative recency: once participants are faced with several price decreases, they will increase their investment, but after several price increases they will take fewer risks.
Results:
The risk-taking behavior of the majority of the participants was not particularly irrational.
Half of them invested approximately in line with the rational model (r>0.27). 12 participants (7%) invested contrary to the normative model.
10 paticipants’ investments in the first and 50 participants’ investments in the second experiment correlated negatively with the signed run length, which indicates that they believed in the principle of negative recency. In the second experiment, of these, 13 lost all their money before the end of the simulation.
We found no gender, age or education differences between those who followed the heuristic of negative recency and those who did not; nor was there any difference in how many courses they completed in statistics or probability theory, or in the use of online trading or strategic games.
There was a weak relationship between engaging in poker (rs=-0.26, p< .05) and sports betting (rs=-0.21, p< .05) and negative recency. Those who were more susceptible to negative recency played more poker or bet more on sports than those who were not.
There was no significant difference between those who showed the fallacy of negative recency and the rest (p> .05) in the assessment of the probability of trading with the winner type of share. As this group was not less accurate estimating the type of shares, the differences in risk- taking strategy between these groups could not be explained by different assessment abilities.
Discussion:
In the current context of the simulation, despite the perceivable asymmetric probabilities, negative recency was present in 10% and 28% of the participants in the two experiments respectively. These participants were aware of their chances, yet still behaved irrationally, which implies that the law of small number (Tversky and Kahneman, 1971) overruled the dominant winning strategy. In the second experiment, 13 participants out of the NR group lost all their money before the end of the simulation, which highlights the detrimental consequences of negative recency, which can result in severe losses or reduced gains. Education in or knowledge of statistics
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and probability theory did not stop participants from behaving according to this heuristic, which is in line with the findings of Tversky and Kahneman (1971), Engländer (1999) and Williams and Connolly (2006).
The relationship with poker and sports betting raises further questions: Are people who like games of chance more prone to misinterpreting random chance events, and to holding unsupported beliefs about randomness? Is acting in line with the gambler's fallacy not a cognitive mistake, but a proof of unsuccessful inhibitory functions?
Due to its simplicity and short-term feature, this investment simulation most likely differs from the real process of investing, it rather resembles gambling. Can people avoid the gambler’s fallacy if they consider their activity as investing, rather than gambling?
Financial, behavioral and perceptual effects are difficult to separate in the analysis. The break-even effect, namely taking more risks to regain previous losses, could be eliminated by allowing the short position of the shares. It would be worth repeating the experiment with real money and introducing the so-called short position.
3. Study
Regulatory focus in the risk-taking process
Aim:
Higgins’s (1997) regulatory focus theory distinguishes promotion and prevention-focused aspirations depending on whether a person focuses on gains or losses. Both the theory and some previous empirical research reveals a relationship between regulatory focus in the risk-taking process and efficiency, however, it has not yet been studied in the context of sequential individual investment behavior.
I had numerous hypothesizes regarding risk assessment, risk-taking behavior and efficiency:
1. a. People with a stronger chronic promotion focus tend to believe that they estimate correctly when trading with the winner share. 1. b. With stronger chronic promotion focus, people are more likely to overestimate the probability of trading with the winner share (Kluger, Stephan, Ganzach,
& Hershkovitz, 2004, Higgins and Tykocinski, 1992). 2. With a higher chronic promotion focus, people are more risk prone: their risk aversion rate is lower (Zou and Scholer, 2016). 3. With a
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higher chronic promotion focus, participants over assess their performance, meaning they think they perform better in the simulation (Hazlett, Molden, & Sackett, 2011). 4. With a higher chronic promotion focus, participants do perform better in the investment simulation (Markman, Baldwin,
& Maddox, 2005). 5. Participants with a higher chronic promotion focus not only expect better results but would only be satisfied with them. 6. Participants with a higher chronic promotion focus are more cheerful, and participants with a higher chronic prevention focus are more relaxed after the simulation (Higgins, 1997).
Methods:
We examined risk assessment, risk-taking behavior, subjective performance, objective efficiency and aspiration of 71 and 178 individuals in a sequential investment simulation and compared them based on their chronic regulatory focus orientation. To assess regulatory focus, Regulatory Focus Questionnaire (RFQ) and General Regulatory Focus Measure (GRFM) were registered. The amount of money people were willing to invest served as the measure of absolute risk taking. I also derived the parameter of risk-taking propensity from the investment behavior.
The relationship between the degree of risk-taking and the promotion and prevention focus sub- scales was analyzed 1) by the absolute measure of risk (the invested amount) and 2) the relative measure (the risk avoidance parameter). The objective efficiency was indicated by the absolute and the relative (compared to the risk-taken) profit of the participants. Risk perception was operationalized as the assessed probability of trading with the winner share. To test the relationships, I conducted structural equations modeling (SEM).
Results and discussion:
We did not find any significant association between the invested amount and the regulatory focus with either of the questionnaires. There was a weak correlation between the derived risk- taking propensity and the RFQ promotion (β = -0.287) and the GRFM prevention (β = 0.266) sub- scales. More promotion-focused participants were more risk-prone, while more prevention-focused participants were more risk-averse, while making investment decisions.
We found a moderate relationship between subjective self-performance, objective efficiency and the regulatory focus, but there seemed to be no significant association between risk perception, and the regulatory focus. Based on the results of the GRFM, it seems that promotion-focused
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participants were objectively more efficient (β = 0.189), while the results on the RFQ indicated that they rated their own performance (subjectively) higher (β = 0.275). According to the RFQ, promotion-focused individuals had higher expectations of their future results and felt happier and more relaxed after the simulation. The results suggest that the regulatory focus merges two constructs: the pursuit of ideals and duties (RFQ) and the motivational bases of seeking gains and avoiding losses (GRFM).
General discussion:
The investment simulation presented in this dissertation allows us to gain a better understanding of an essential economic psychological process: how previous independent price changes in asymmetrical (1:2 odds) consecutive random events influence risk-taking. Furthermore, the design of the experiment allows us to identify those individuals who are susceptible to negative recency, or in other words the gambler’s fallacy; as well as to measure to what extent they are prone to it. This research is unique, given that it is the first empirical investigation that examines asymmetric binary events in sequential decision-making, moreover the design enables rational normative behavior to be contrasted with actual risk-taking.
In the cognitive approach I aimed to explore how previous outcomes influence risk-taking in the following investment period. In the first study I examined the probability perception dependent on the obtained information, and to what extent the assessed probability differs from the posterior probability. In the second study I examined the effect of economically rational decision-making and of heuristics (gambler’s fallacy) in an asymmetrical investment situation.
Based on the first two studies, we can conclude that people behave essentially rationally.
Nevertheless, both the probability perception on average and the risk-taking behavior of a notable part of the participants differed from the normative expectations. Assessed probabilities do not coincide completely with objective probabilities. The probability of trading with the winner share was overestimated in the low, while was underestimated in the high probability ranges.
The risk-taking behavior of the majority of the people was not particularly irrational. Half of them invested according to the economic rational model to some extent. However, despite the substantially asymmetrical setup, 10% in the first and 28% in the second experiment followed maladaptive investment strategies giving rise to the negative recency effect. This is surprising
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because, while in a symmetrical setting the gambler's fallacy is only an erroneous belief but does not necessarily lead to losses (the chances of winning are not reduced), but it is explicitly irrational and harmful in this asymmetrical setting due to the increased chances of losing. Even though participants were aware of the type of share being traded, they still made a financially disadvantageous choice. In the second experiment, more than half of them went bankrupt.
In relation to the chronic regulatory focus analysis, we can conclude that regulatory focus impacts self-confidence in risk-taking and risk-taking propensity in winning situations (when expected gains exceed expected losses) but does not directly influence the absolute level of risk- taking. The regulatory focus did not alter probability perception over the entire probability range.
In economic decision making, past outcomes have considerable impact on consecutive risk- taking behavior. Understanding decision-making distortions and heuristics may facilitate the elimination of undesirable losses and omitted gains resulting from such maladaptive risk-taking behavior.
References (without self-citations):
Ball, C. T. (2012). Not all streaks are the same: Individual differences in risk preferences during runs of gains and losses. Judgment and Decision Making, 7(4), 452-461.
Bar-Hillel, M., & Wagenaar, W. A. (1991). The perception of randomness. Advances in applied mathematics, 12(4), 428-454.
Burns, B. D., & Corpus, B. (2004). Randomness and inductions from streaks:“Gambler’s fallacy”
versus” hot hand “. Psychonomic bulletin & review, 11(1), 179-184.
Clotfelter, C. T., & Cook, P. J. (1993). The “gambler's fallacy” in lottery play. Management science, 39(12), 1521-1525.
Engländer, T. (1999). Viaskodás a bizonytalannal: a valószínűségi ítéletalkotás egyes pszichológiai problémái. Budapest: Akadémiai Kiadó.
Falk, R., Falk, R., & Ayton, P. (2009). Subjective patterns of randomness and choice: Some consequences of collective responses. Journal of Experimental Psychology: Human Perception and Performance, 35(1), 203.
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Hazlett, A., Molden, D. C., & Sackett, A. M. (2011). Hoping for the best or preparing for the worst?
Regulatory focus and preferences for optimism and pessimism in predicting personal outcomes. Social Cognition, 29(1), 74-96.
Higgins, E. T. (1997). Beyond pleasure and pain. American psychologist, 52(12), 1280.
Higgins, T., & Tykocinski, O. (1992). Seff-Discrepancies and Biographical Memory: Personality and Cognition at the Level of Psychological Situation. Personality and social psychology bulletin, 18(5), 527-535.
Kluger, A. N., Stephan, E., Ganzach, Y., & Hershkovitz, M. (2004). The effect of regulatory focus on the shape of probability-weighting function: Evidence from a cross-modality matching method. Organizational Behavior and Human Decision Processes, 95(1), 20-39.
Leopard, A. (1978). Risk preference in consecutive gambling. Journal of Experimental Psychology: Human Perception and Performance, 4(3), 521-528.
Markman, A. B., Baldwin, G. C., & Maddox, W. T. (2005). The interaction of payoff structure and regulatory focus in classification. Psychological Science, 16(11), 852-855.
Nickerson, R. S. (2002). The production and perception of randomness. Psychological review, 109(2), 330.
Oskarsson, A. T., Van Boven, L., McClelland, G. H., & Hastie, R. (2009). What's next? Judging sequences of binary events. Psychological bulletin, 135(2), 262-285.
Sun, Y., & Wang, H. (2010). Gambler's fallacy, hot hand belief, and the time of patterns. Judgment and Decision Making, 5(2), 124-132.
Sundali, J., & Croson, R. (2006). Biases in casino betting: The hot hand and the gambler's fallacy.
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Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological bulletin, 76(2), 105-110.
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. science, 185(4157), 1124-1131.
Williams, R. J., & Connolly, D. (2006). Does learning about the mathematics of gambling change gambling behavior? Psychology of Addictive Behaviors, 20(1), 62-68.
Zou, X., & Scholer, A. A. (2016). Motivational Affordance and Risk-Taking Across Decision Domains. Personality and social psychology bulletin, 0146167215626706.
13 List of publications forming basis of the dissertation:
Uatkán, A. (2015). Empirical analysis of risk-taking in a sequential investment simulation. Spring Wind 2015 Conference book, 1(4), 139-150.
Uatkán, A., Faragó, K. (2016). The relationship between regulatory focus and risk taking.
Empirical results of an investment simulation. Tavaszi Szél 2016 Konferenciakötet.
Uatkán, A., Ruzsa, G., Faragó, K. (in press). Regulation focus and risk-taking in a sequential investment simulation. Applied Psychology.
Uatkán, A., Ruzsa, G., Faragó, K. (in press). Regulation focus, risk perception and efficiency in a sequential investment simulation. Applied Psychology.
