Brice Corgnet
email: corgnet@em-lyon.com

Camille Cornand
email: cornand@gate.cnrs.fr

Nobuyuki Hanaki
email: nobuyuki.hanaki@iser.osaka-u.ac.jp

NEGATIVE TAIL EVENTS, EMOTIONS & RISK TAKING

Keywords: tail events, emotions, risk JEL codes: C91, G41, D87, D91 tail events, emotions, risk JEL codes: C91, G41, D87, D91

We design a novel experiment to assess investors' behavioural and physiological reactions to negative tail events. Investors who observed, without suffering from, tail events decreased their bids whereas investors suffering tail losses increased them. However, the increase in bids after tail losses was not observed for those who exhibited no emotional arousal. This suggests that emotions are key in explaining Prospect Theory prediction of risk seeking in the loss domain.

1 Introduction "It's rarely recognized, but our trading styles are as much about our emotional management as our money management." Steenbarger (2015, p. 146).

Mainstream finance theory is designed to apply in 'normal times', that is, when asset returns fall into a standard range of values. This statement is exemplified by the use of Gaussian distributions and quadratic utility functions in portfolio theory (see e.g., [START_REF] Markowitz | Portfolio selection[END_REF][START_REF] Tobin | Liquidity preference as behavior towards risk[END_REF][START_REF] Sharpe | Capital asset prices: A theory of market equilibrium under conditions of risk[END_REF][START_REF] Lintner | Security prices, risk, and maximal gains from diversification[END_REF] and option pricing [START_REF] Black | The pricing of options and corporate liabilities[END_REF]. However, infrequent, negative tail events can easily wipe out any financial gains accumulated in normal times (e.g., [START_REF] Taleb | The Black Swan: The Impact of the Highly Improbable[END_REF]Barberis, 2013a;[START_REF] Shiller | Irrational exuberance: Revised and expanded third edition[END_REF][START_REF] Aliber | Manias, Panics, and Crashes: A History of Financial Crises[END_REF], as amply illustrated by the extreme fall in stock market indices worldwide in March 2020. As just one example, on the 16th of March 2020, the S&P500 index lost almost 12% of its value, representing the third-largest drop in the index's history and the largest daily decline in more than three decades.

Because tail events1 are rare, their occurrence will generate surprise that is a key driver of emotional arousal (see [START_REF] Joffily | Emotional valence and the free-energy principle[END_REF] and one of the six basic emotions [START_REF] Ekman | Basic emotions[END_REF].2 Such an emotional reaction can interfere with expected utility calculations, as put forth by the proponents of the 'risk-asfeelings' hypothesis [START_REF] Loewenstein | Risk as feelings[END_REF] or the 'affect heuristic' [START_REF] Slovic | The affect heuristic[END_REF]. Some studies also emphasise the potential role of emotions in explaining violations of expected utility theory (EUT) captured by prospect theory (PT) such as loss aversion and probability weighting [START_REF] Hirshleifer | Investor psychology and asset pricing[END_REF][START_REF] Sokol-Hessner | Emotion regulation reduces loss aversion and decreases amygdala responses to losses[END_REF][START_REF] Lerner | Emotion and decision making[END_REF][START_REF] Sokol-Hessner | The psychological and neural basis of loss aversion[END_REF].

Our goal is to study how the emotional arousal provoked by tail events affects subsequent investment decisions. The interplay between the cognitive assessment of prospects and emotions renders the study of investors' reaction to tail events especially challenging. Besides the role of emotions, another challenge in the study of tail events is that data are both scarce and idiosyncratic. For example, in finance, major market crashes are associated with tail events [START_REF] Sornette | Why Stock Markets Crash: Critical Events in Complex Financial Systems[END_REF], all of which possess specific characteristics [START_REF] Aliber | Manias, Panics, and Crashes: A History of Financial Crises[END_REF]. The study of the reaction of investors to tail events thus appears to require a 'tail-event factory', allowing us to produce credibly and consistently unlikely events. For this paper, we opted to develop such a device in a controlled laboratory environment, which allows us to precisely assess the emotional arousal of participants using physiological recordings (i.e., electrodermal activity) and thus the impact of emotions on the evaluation of investment prospects [START_REF] Critchley | Neural activity relating to generation and representation of galvanic skin conductance responses: a functional magnetic resonance imaging study[END_REF][START_REF] Christopoulos | The body and the brain: measuring skin conductance responses to understand the emotional experience[END_REF].

In our design, individuals have to bid repeatedly using a standard Becker, DeGroot and Marschak (1964) (BDM) mechanism for a financial asset that delivered a small positive reward (either 10/ c, 20/ c, 30/ c, 40/ c or 50/ c) in more than 99% of the cases and a large loss (1,000/ c) otherwise. The loss event was very unlikely (0.66%) but substantial enough to possibly wipe out any accumulated earnings.

To assess the drivers of individual reactions to tail events as well as to isolate the specific impact of emotions on investors' bids, we collected extensive individual information to serve as controls in our analyses. These include risk and loss attitudes as well as personality traits and cognitive skills. This led us to conduct a two-step experiment in which we first elicited individual characteristics and second conducted the tail-event experiment. To make the monetary loss associated with the tail event especially painful, we asked participants to use the fixed wage they earned in a survey from the first step (12e) for their investment decisions in the second step (see [START_REF] Thaler | Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice[END_REF][START_REF] Thaler | Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice[END_REF][START_REF] Corgnet | The effect of earned versus house money on price bubble formation in experimental asset markets[END_REF]. On this basis, it follows that investors going bankrupt in the second-step experiment would lose the money they earned in the first step.

Using model simulations with EUT and PT investors, we derive hypotheses regarding individuals' reactions to tail events in the experiment. Our first hypothesis states that investors experiencing tail events without suffering losses3 will decrease their bids after observing a tail event because they update the probability of tail events upwards. We show that this effect is especially large for those exhibiting a 'recency bias', thus relying on small samples to update the likelihood of tail events (Tversky andKahneman, 1973, 1974;[START_REF] Rabin | Inference by believers in the law of small numbers[END_REF][START_REF] Plonsky | Reliance on small samples, the wavy recency effect, and similarity-based learning[END_REF]. Relatedly, prior research has evoked the 'availability bias', according to which people estimate the probability of the occurrence of an event by the ease with which relevant instances come to mind, to explain beliefs updating of low-frequency events (e.g., Tversky andKahneman, 1973, 1974;[START_REF] Kunreuther | Disaster Insurance Protection: Public Policy Lessons[END_REF]Barberis, 2013a). One outcome is that those using the availability heuristic tend to underweight the probability of a tail event until they actually observe it, after which they tend to overweight it (e.g., Barberis, 2013a). 4 Our experimental findings support our first hypothesis, as we found participants were more likely to decrease their bids after observing, yet not suffering, a tail event compared with a non-tail event. This effect seemed more pronounced for participants exhibiting an availability bias.

Our second hypothesis proposes that PT investors suffering tail losses5 will take on more risk, thus triggering an increase in bids. Our setup is one in which losses do not materialise before the end of the experiment because, except in the case of bankruptcy, participants can always attempt to recover losses by taking on more risk (see [START_REF] Thaler | Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice[END_REF][START_REF] Garvey | Do losses linger?[END_REF][START_REF] Langer | Does commitment or feedback influence myopic loss aversion?: An experimental analysis[END_REF][START_REF] Suhonen | How do prior gains and losses affect subsequent risk taking? New evidence from individual-level horse race bets[END_REF]. Our design thus produces non-realised paper losses, which have been found to trigger risk seeking behaviour [START_REF] Imas | The Realization Effect: Risk-Taking after Realized versus Paper Losses[END_REF].

We also establish three emotion-related conjectures. In Conjecture A, we posit, along with the appraisal theory of emotions (see [START_REF] Lerner | Fear, anger, and risk[END_REF][START_REF] Lerner | Emotion and decision making[END_REF], that anger-based emotional reactions will be associated with increased risk seeking after investors have suffered tail losses. In line with this conjecture, we find strong evidence that investors showing anger-based emotional reaction to tail losses were more likely to increase their bids. More strikingly, we show that the increase in risk taking after tail losses is only observed for participants who exhibited emotional arousal. This implies that PT, which is not an emotional theory of risk, does not capture the underlying mechanisms explaining investment behaviour after tail losses. Because tail losses were substantial, subsequent investment decisions could not help participants to recoup all their losses. This implies our setup is one in which the typical 'break even' argument proposed in the literature to explain risk seeking behaviour after losses does not apply [START_REF] Shefrin | The disposition to sell winners too early and ride losers too long: Theory and evidence[END_REF][START_REF] Thaler | Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice[END_REF][START_REF] Odean | Are investors reluctant to realize their losses?[END_REF][START_REF] Shefrin | Beyond greed and fear: Understanding behavioral finance and the psychology of investing[END_REF][START_REF] Imas | The Realization Effect: Risk-Taking after Realized versus Paper Losses[END_REF][START_REF] Lo | Adaptive markets: Financial evolution at the speed of thought[END_REF].

In Conjecture B, we also put forward that fear will lead investors to decrease their bids after observing, yet not suffering, tail events. Our experimental data provide suggestive evidence for this conjecture. Finally, we did not find substantial support for Conjecture C, according to which emotions affect investors' earnings and their propensity to go bankrupt. This result could be due to the transitory impact of emotions on investors' behaviour that we observe in our experiment.

Contribution to the literature

Our paper contributes to four strands of the literature. First, our approach contrasts with previous works on tail risk (e.g., [START_REF] Rietz | The equity risk premium: A solution[END_REF][START_REF] Harvey | Conditional skewness in asset pricing tests[END_REF][START_REF] Barro | Rare disasters and asset markets in the twentieth century[END_REF][START_REF] Barro | Rare disasters, asset prices, and welfare costs[END_REF][START_REF] Bollerslev | Tails, fears, and risk premia[END_REF][START_REF] Gabaix | Variable rare disasters: An exactly solved framework for ten puzzles in macrofinance[END_REF][START_REF] Kelly | Tail risk and asset prices[END_REF][START_REF] Bollerslev | Tail risk premia and return predictability[END_REF][START_REF] Lemperiere | Risk premia: Asymmetric tail risks and excess returns[END_REF][START_REF] Andersen | The pricing of tail risk and the equity premium: evidence from international option markets[END_REF] by focusing on investors' reactions to tail events rather than on the pricing of rare events ex ante. 6 These two approaches differ because emotions experienced at the time of decision-making affect a person's evaluation of a prospect (see [START_REF] Bechara | Deciding advantageously before knowing the advantageous strategy[END_REF][START_REF] Bechara | The somatic marker hypothesis: A neural theory of economic decision[END_REF]. Furthermore, the emotional response generated by tail events is difficult to assess ex ante (e.g., [START_REF] Gilbert | Prospection: Experiencing the future[END_REF].

Second, our paper relates to the literature on risk attitudes in the loss domain. Unlike previous research studying the effect of losses on risk taking [START_REF] Thaler | Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice[END_REF][START_REF] Garvey | Do losses linger?[END_REF][START_REF] Langer | Does commitment or feedback influence myopic loss aversion?: An experimental analysis[END_REF][START_REF] Imas | The Realization Effect: Risk-Taking after Realized versus Paper Losses[END_REF][START_REF] Suhonen | How do prior gains and losses affect subsequent risk taking? New evidence from individual-level horse race bets[END_REF], we focus on tail losses, which are characterised as being both unlikely and substantial. Because tail losses are infrequent, they generate surprise and trigger negative emotions. We are thus interested in the effect of emotions on investors' reactions to tail events, hence considering the extent to which emotional arousal, as measured by electrodermal activity, can account for risk taking in the face of tail losses. While the consequentialist theories of decision-making used in the literature (such as EUT or PT) discard the role of emotions -the latter operating as inconsequential side effects of decisions [START_REF] Loewenstein | Risk as feelings[END_REF][START_REF] Loewenstein | The role of affect in decision making[END_REF][START_REF] Loewenstein | The role of emotion in economic behavior[END_REF][START_REF] Lo | Fear, greed, and financial crises: A cognitive neurosciences perspective[END_REF]-, our findings show that emotions correlate with investment decisions and are thus likely to influence them. In particular, the fact that the increase in risk taking following tail losses does not persist over time in our experiment challenges the predictions of PT with a status-quo reference point. It follows that we might be overestimating the predictive power of PT when it leads to conjectures that are similar to those of emotional theories of risk.

Third, our paper contributes to the literature linking emotions and risk attitudes. Previous research in neuroscience has shown how emotional centers of the brain, such as the nucleus accumbens, the anterior insula and the amygdala, are involved in risky decisions [START_REF] Bechara | Deciding advantageously before knowing the advantageous strategy[END_REF][START_REF] Bechara | The somatic marker hypothesis: A neural theory of economic decision[END_REF][START_REF] Camerer | Neuroeconomics: How neuroscience can inform economics[END_REF][START_REF] Kuhnen | The neural basis of financial risk taking[END_REF][START_REF] Knutson | Anticipatory affect: neural correlates and consequences for choice[END_REF][START_REF] Preuschoff | Neural differentiation of expected reward and risk in human subcortical structures[END_REF][START_REF] Preuschoff | Human insula activation reflects risk prediction errors as well as risk[END_REF][START_REF] Knutson | Neural antecedents of financial decisions[END_REF]Knutson et al., 2008). Research using physiological correlates of emotional arousal such as electrodermal and cardiovascular activity has also identified the crucial role of emotions in decision-making under risk [START_REF] Damasio | Descartes' Error: Emotion, Reason, and the Human Brain[END_REF][START_REF] Lo | The psychophysiology of real-time financial risk processing[END_REF][START_REF] Bossaerts | Emotional Engagement and Trading Performance[END_REF]. 7 In addition, according to the 'somatic marker hypothesis', emotions are necessary inputs for the cognitive evaluation of prospects, thus not making it possible to separate the cognitive and emotional drivers of a decision [START_REF] Damasio | Descartes' Error: Emotion, Reason, and the Human Brain[END_REF]. Our study contributes to this strand of the literature by studying the role emotions may play on investment decisions in the context of tail events. Our research also responds to the call of Camerer et al., (2005, p. 46) to incorporate emotions in the study of risky choices in a financial task.

Fourth, in the rare events literature (see e.g., [START_REF] Camerer | Decision processes for low probability events: Policy implications[END_REF][START_REF] Barron | Small feedback based decisions and their limited correspondence to description based decisions[END_REF][START_REF] Hertwig | Decisions from experience and the effect of rare events in risky choice[END_REF][START_REF] Erev | On the weighting of rare events and the economics of small decisions[END_REF][START_REF] Erev | From anomalies to forecasts: Toward a descriptive model of decisions under risk, under ambiguity, and from experience[END_REF][START_REF] Kunreuther | Mastering catastrophic risk: How companies are coping with disruption[END_REF], our research is the first to study investor emotional reactions to non-hypothetical negative tail events. 8 [START_REF] Kunreuther | Dynamic insurance decision-making for rare events: The role of emotions[END_REF] examine the effect of self-reported emotions on the purchasing of insurance against natural disasters in a hypothetical experiment conducted online. They show that emotions can explain changes in insurance purchasing behaviour as most participants decide to insure after observing a loss, but participants who decided to insure and observed a bad outcome did not cancel their insurance.

Design

We designed an incentivised experiment that allows us to observe participants' reactions to tail events. We invited participants for a two-step study. In the first step, participants earned money by responding to a survey regarding various psychological and cognitive characteristics (Section 3.3), and in the second step participants played a repeated investment task while physiological measures were recorded (Sections 3.1 al., 2017;[START_REF] Andersen | The pricing of tail risk and the equity premium: evidence from international option markets[END_REF]. For example, [START_REF] Bollerslev | Tails, fears, and risk premia[END_REF] created an 'Investor Fears index' by estimating the risk associated with jumps or discontinuities in the pricing of options, and showed that pricing fear of tail events using their index could account for a substantial part of the equity premium puzzle. Using firm-level prices instead of option prices, [START_REF] Kelly | Tail risk and asset prices[END_REF] also found that tail risk had a substantial impact on asset prices. 7 Electrodermal activity has been linked to the brain activation of emotional centers such as the amygdala [START_REF] Boucsein | Electrodermal activity[END_REF]. 8 While she does not study the role of emotions, Payzan-LeNestour (2018) also developed a tail-event software in order to analyse individuals' ability to learn whether they were facing an environment in which tail losses were either frequent (16% of the time) or rare (1% of the time). and 3.2). We collected our data in two separate waves of 15 sessions each (see Section 3.4).

Investment task

We elicited the willingness to pay of participants for an asset involving a tail risk using the BDM method. At the beginning of each of the 300 periods, participants had to bid for a financial asset that delivered a small positive reward (either 10/ c, 20/ c, 30/ c, 40/ c or 50/ c) in 99.34% of cases and a large loss (1,000/ c) otherwise. The bid (any integer between 0 and 50) in each period was compared with a price (also an integer) randomly drawn from a uniform distribution between 1 and 50. If the bid of participants was greater than the price, they paid the price and received the asset; otherwise, they did not purchase the asset.

At the end of each period, a feedback screen informed participants about the reward from the financial asset, the earnings for the current period as well as the cumulated earnings. Cumulated earnings were equal to the initial endowment, which was equal to the fixed wage of the first step (1,200/ c), plus and minus any gains or losses from buying the asset in previous periods.

The tail event was highly unlikely (0.66%) but triggered losses that were as large as 83.3% of the fixed wage of the first step. As a result, participants would typically go bankrupt when suffering a tail event twice. The trade-off in selecting the probability of the tail event occurring is that it must be high enough to ensure most participants would experience it, while rare enough to be qualified as a tail event. Although no formal definition regarding the frequency of tail events exists, we opted for picking a value less than 1% (0.66%), which is smaller than typical experiments studying the pricing of tail risk. 9 To make the monetary loss associated with the tail event especially meaningful, we asked participants to invest the fixed wage they earned in the first step during the investment task. In addition, participants were given a loan of 1,000/ c for liquidity reasons, which had to be repaid at the end of the experiment. 10 This loan ensured that participants would have sufficient cash to bid for the asset even after incurring tail losses, thus allowing us to study investors' reaction to tail events while abstracting from potential liquidity constraints. However, if the current wealth of participants (including the loan) was no longer sufficient to repay the loan, they would go bankrupt. In that case, participants could no longer purchase the asset and had to wait until the end of the session while provided with Internet access. Investors who went bankrupt lost the fixed wage they earned in the first step and were only rewarded with a 5-euro show-up fee. 11 Because participants can lose all their endowment when a tail event occurs, participants might believe the experimenter is purposefully engineering the draws to ensure tail events would occur, thus reducing participants' earnings and lowering the cost of the experiment. To make it clear to the participants that the sequence of draws was random and thus unpredictable, we adopted the following hand-run procedure. Before participants read the instructions, we showed them a transparent box containing 302 tokens of six different colours, each of which was associated with a payoff for the asset (blue = 10/ c, red = 20/ c, orange = 30/ c, green = 40/ c, purple = 50/ c, yellow = -1,000/ c). There were 60 tokens of each colour, except just the two yellow tokens. Once everyone had seen the tokens, we told participants we were taking a picture of the box that would be displayed on their screens during the experiment. 12 By observing this picture during the experiment, participants could form an estimate of the frequency of occurrence of each token (see screenshot in Online Appendix I.4). The distribution of tokens was thus not fully known by participants to allow for learning during the experiment. 9 Existing studies usually consider higher tail frequencies of 1%, 5% or 10% (e.g., [START_REF] Barron | Small feedback based decisions and their limited correspondence to description based decisions[END_REF][START_REF] Hertwig | Decisions from experience and the effect of rare events in risky choice[END_REF][START_REF] Erev | On the weighting of rare events and the economics of small decisions[END_REF][START_REF] Erev | From anomalies to forecasts: Toward a descriptive model of decisions under risk, under ambiguity, and from experience[END_REF]. For an early survey on choices with low probability, high-consequence events and their impact on policymaking, see [START_REF] Camerer | Decision processes for low probability events: Policy implications[END_REF]. [START_REF] Camerer | Do biases in probability judgment matter in markets? Experimental evidence[END_REF] and [START_REF] Kluger | Are judgment errors reflected in market prices and allocations? Experimental evidence based on the Monty Hall problem[END_REF] review the biases involved in such choices as well as their impact on markets. 10 This design feature is inspired by Plott andSunder (1982, 1988). 11 There is limited liability in our experiment because bankrupt participants did not repay the loan in full. On average, they repaid about 75% of its value.

12 Actually, a photograph of the box was taken prior to the first experimental session so that the picture displayed on participants' screens was exactly the same in all sessions. We did not tell participants that we showed the same picture of the box in all the sessions. This omission was not consequential because the composition of the box was indeed the same across sessions. Showing the same picture across sessions facilitated the comparison across sessions and eliminated unnecessary noise related to the reshuffling of the tokens or the quality of the picture in each day.

In the first wave, one participant, the picker, was randomly selected and escorted to a separate room. We asked the picker to put all the tokens in the transparent box into an opaque bag and draw the tokens with replacement. The picker entered the token draws on a computer and on a separate sheet of paper in real time. The picker signed this sheet of paper upon completion of the task, and it was then shown to all other participants at the end of the experiment to ensure the additional credibility of the procedure. The picker did not know the instructions for the investment task to avoid any cheating attempts or any retaliation by peers. 13 The picker was paid a fixed amount of 15e, but incurred a 5-euro penalty if the task was not completed within one hour to ensure timely completion of the experiment. 14 During the task, one of the experimenters closely monitored the picker to ensure they followed the procedure.

In the second wave, we told participants that 15 pickers had been randomly selected in fifteen previous experimental sessions. We explained the role of the picker, as previously described. At the beginning of each session of the second wave, a participant was randomly selected to choose a number between 1 and 15 in order to select the sequence of draws from the fifteen previous (first wave) experimental sessions. We ensured that a sequence of draws could not be selected in more than one session so that the exact same sequence of draws was used in both waves.

Of the thirty sessions we conducted, we had an average of two tail events per session including two sessions without any tail event and eight sessions with four. 15 The distribution of tail events for each session is shown in Figure A.1 in the Appendix.

Measurement of emotions

Our experimental design allowed us to assess precisely the emotional arousal (i.e., the magnitude of an emotional response) of participants using physiological tools measuring electrodermal activity during the investment task [START_REF] Critchley | Neural activity relating to generation and representation of galvanic skin conductance responses: a functional magnetic resonance imaging study[END_REF][START_REF] Boucsein | Electrodermal activity[END_REF][START_REF] Christopoulos | The body and the brain: measuring skin conductance responses to understand the emotional experience[END_REF]. This emotional arousal is a manifestation of the basic emotion of surprise [START_REF] Ekman | Basic emotions[END_REF]) and as such is deprived of positive or negative valence.

One of the experimenters placed electrodes on each participant's second phalanx (palmar surface) of the index and middle fingers of the non-dominant hand using a Velcro strap and isotonic gel. 16 Another experimenter checked the quality of the recordings before the experiment could start. Setting up the physiological equipment took 20 minutes on average. After a stimulus is observed, the electrodermal activity needs time to rise and this is referred to as latency (see Figure A.2 in the Appendix for the typical shape of an event-related electrodermal activity). Latency is on average about 4 seconds. In the following seconds, the signal rises until it reaches a peak. In the absence of further stimulation, the signal recovers its baseline (pre-stimulus) level. In our setup, we recorded electrodermal responses to two types of stimuli: i) a decision is made and ii) the earnings for the period are shown on the screen. We define these two measurements as decision and feedback arousal, respectively. 17 To ensure sufficient time elapsed between stimuli, we inserted a four-second waiting screen after a decision was made and after the receipt of the end-of-period feedback. A timer on the screen indicated the time participants had to enter a price using a cursor. If participants did not enter a price on the screen and validate their decision on time, the number indicated by the cursor was selected.

To prompt participants to make a decision each period, the default value on the cursor was 50. 18 Our metric of interest is the amplitude of the signal as computed using the Matlab routine developed in [START_REF] Joffily | Electrodermal activity (EDA) toolbox[END_REF] electrodermal activity toolbox, which is equal to the peak of the physiological response measured in microsiemens. [START_REF] Breaban | Emotional state and market behavior[END_REF] considered an alternative physiological measure of emotions in a standard experimental asset market with bubbles [START_REF] Smith | Bubbles, crashes, and endogenous expectations in experimental spot asset markets[END_REF] by assessing traders' emotional state (happiness, surprise, anger, disgust, sadness or fear) using face-reading software. As an alternative to physiological measurements of emotions, surveys are most commonly used. For example, [START_REF] Kunreuther | Dynamic insurance decision-making for rare events: The role of emotions[END_REF] elicited emotions releasing questionnaires to participants in a hypothetical insurance-purchasing experiment conducted online.

In contrast to [START_REF] Breaban | Emotional state and market behavior[END_REF] and [START_REF] Kunreuther | Dynamic insurance decision-making for rare events: The role of emotions[END_REF], we did not use facereading software or survey measures to elicit the valence of emotions during the investment task. Our first concern was methodological. Although very appealing in identifying emotions, face-reading techniques have been challenged by emotion scholars (e.g., [START_REF] Keltner | Understanding multimodal emotional expressions: Recent advances in Basic Emotion Theory[END_REF][START_REF] Barrett | Emotional expressions reconsidered: Challenges to inferring emotion from human facial movements[END_REF][START_REF] Martinez | The promises and perils of automated facial action coding in studying children's emotions[END_REF]Pollack et al., 2019). Beyond technical aspects impeding the precise identification of emotions, these studies have emphasised that emotions do not necessarily involve distinct facial expressions. 19 Although the use of surveys to elicit emotional valence is widespread in the extant literature (e.g., [START_REF] Crawford | The Positive and Negative Affect Schedule (PANAS): Construct validity, measurement properties and normative data in a large non-clinical sample[END_REF][START_REF] Barrett | Emotional expressions reconsidered: Challenges to inferring emotion from human facial movements[END_REF], for practical reasons we did not consider this option as we did not want the elicitation of emotional valence to interfere with the behaviour in the investment task and with our physiological recordings. This is a pressing issue because allocating time for participants to express their emotions may have the unintended effect of venting emotions, thus altering investment decisions (e.g., [START_REF] Bushman | Does venting anger feed or extinguish the flame? Catharsis, rumination, distraction, anger, and aggressive responding[END_REF][START_REF] Xiao | Emotion expression in human punishment behavior[END_REF][START_REF] Bolle | Vendettas[END_REF][START_REF] Dickinson | Emotion venting and punishment in public good experiments[END_REF]. 20 More generally, manipulation checks following the standard use of surveys can bring unintended consequences and act not only as measures, but also as sheer interventions [START_REF] Hauser | Are Manipulation Checks Necessary?[END_REF]. In the emotion literature, a growing number of studies have shown that putting emotions into words ("affect labeling") dampens individual physiological responses to emotional experiences (see [START_REF] Lieberman | Searching for Implicit Emotion Regulation[END_REF], for a review). Finally, eliciting emotional valence throughout the investment task would have lengthened an already long experiment.

Nonetheless, eliciting the valence of emotions in addition to its arousal is crucial for pinning down a specific emotion as widely accepted in the emotion literature [START_REF] Bradley | Measuring emotion: the self-assessment manikin and the semantic differential[END_REF][START_REF] Adolphs | Emotions are Functional States that Cause Feelings and Behavior[END_REF]Lang and Bradley, 1998). In our experimental setup, the valence of emotions following tail losses is unambiguously negative. 21 However, within the set of basic emotions characterised by high arousal and negative valence, we cannot distinguish between fear and anger. 22 To distinguish between fear and anger, emotion scholars have emphasised the approach-avoidance dimension. Fear triggers an avoidance response whereas anger promotes an approach response (see [START_REF] Davidson | Approach-withdrawal and cerebral asymmetry: emotional expression and brain physiology: I[END_REF][START_REF] Elliot | Approach-avoidance motivation and emotion: Convergence and divergence[END_REF][START_REF] Ellsworth | Maladaptive Emotions Are Inseparable From Inaccurate Appraisals[END_REF]. In our context, fear responses triggered by tail losses will prompt investors to avoid future losses by lowering their bids in an attempt to limit their exposure to tail-event risk. By contrast, anger will promote an appetite for risk and lead to an increase in bids [START_REF] Elliot | Approach-avoidance motivation and emotion: Convergence and divergence[END_REF][START_REF] Engelmann | Emotions can Bias Decision-Making Processes by Promoting Specific Behavioral Tendencies[END_REF].

In the second wave of sessions, we included a post-experiment questionnaire (see Appendix I.5) in which we asked participants about the emotion (anger, fear, joy, and sadness) they felt when they faced a tail event and when they incurred tail losses. This allowed us to assess emotional valence without interfering with 18 Participants did not make a timely decision in only 1.84% of the cases. 19 For example, an expression of joy could also be interpreted as one of sadness depending on the context. An emotion, such as anger, could also lead to different facial expressions, smiling or scowling, depending on the context or the person. In certain cases, emotions are not facially expressed because of emotional regulation strategies leading to the suppression of emotions [START_REF] Matsumoto | Facial expressions of emotion[END_REF]. It is thus not surprising that two recent meta-analyses have shown that identifying emotions with face-reading techniques lack reliability [START_REF] Duran | Do emotions result in their predicted facial expressions? A meta-analysis of studies on the link between expression and emotion[END_REF][START_REF] Barrett | Emotional expressions reconsidered: Challenges to inferring emotion from human facial movements[END_REF]. In particular, based on 37 studies, [START_REF] Barrett | Emotional expressions reconsidered: Challenges to inferring emotion from human facial movements[END_REF] show that identifying fear using face-reading techniques performs no better than chance. 20 This effect is also recognised in the case of traders instructed to regularly report their emotions in a journal to better regulate their influence [START_REF] Steenbarger | Trading Psychology 2.0: From best practices to best processes[END_REF].

21 When tail events are observed but not suffered, both negative and positive valence could be triggered, such as fear and joy (hope).

22 Sadness and disgust are not relevant to this situation and they are, unlike tail events, usually associated with low levels of emotional arousal (See Figure 1). Figure 1 (adapted from [START_REF] Russell | A circumplex model of affect[END_REF][START_REF] Russell | Multidimensional scaling of emotional facial expressions: similarity from preschoolers to adults[END_REF][START_REF] Posner | The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology[END_REF] represents the six basic emotions [START_REF] Ekman | Expression and the nature of emotion[END_REF][START_REF] Ekman | Basic emotions[END_REF] defined as a function of the three previously discussed dimensions of emotion: arousal, valence and approach-avoidance. 23To complement our electrodermal recordings as well as our ex post self-assessment emotion questionnaire and assess the approach-avoidance dimension of emotions following tail losses, we elicited the temperament (henceforth, emotional traits) of our participants, used in the literature as a complementary procedure to identify certain emotions [START_REF] Tomarken | Resting frontal brain asymmetry predicts affective responses to films[END_REF][START_REF] Barrett | Discrete emotions or dimensions? The role of valence focus and arousal focus[END_REF][START_REF] Colombetti | Appraising valence[END_REF][START_REF] Scherer | What are emotions? And how can they be measured?[END_REF]. We conducted these tests in the first step (see Section 3.3 for details), so that they did not interfere with the investment task. In particular, these scores allowed us to assess a person's proneness to emotions such as anger, fear or hope [START_REF] Ashton | The HEXACO-60: A short measure of the major dimensions of personality[END_REF]. Although these scores were not elicited during the investment task, they provided us with valuable information regarding whether an emotionally aroused participant experiences fear or anger.24 This is the case because there is a close connection between personality traits and emotions, as put forth by Shiner (2018, p. 62): "(...) temperament-based personality traits are the clearest manifestation of individual differences in emotion (...)". An emotional trait can both increase one's attention to an emotional stimulus as well as lower the physiological threshold above which the emotion is expressed [START_REF] Shackman | The psychological and neurobiological bases of dispositional negativity[END_REF]. Thus, a person with a fearful (anger-prone) emotional trait is more likely to exhibit fear (anger) when facing a negative event [START_REF] Rothbart | Becoming who we are: Temperament and personality in development[END_REF][START_REF] Chen | Temperament and personality[END_REF][START_REF] Shiner | Personality as lasting individual differences in emotions[END_REF]. It is also important to note that emotional traits, especially in relation to fear, hope and anger, are shaped early in life and tend to be stable over time and across contexts (e.g., [START_REF] Buss | Temperament (PLE: Emotion): Early developing personality traits[END_REF][START_REF] Shiner | Personality as lasting individual differences in emotions[END_REF].

Survey

In the first step, we collected extensive individual information regarding -depending on the wave of sessions -risk, loss and ambiguity attitudes, emotional traits, cognitive skills, Bayesian updating, gambling fallacy scores, and demographic data. We also elicited estimations of the percentage of yellow and orange tokens in the photograph of the box of tokens that was displayed on participants' screens during the investment task in the second step. An English language translation of the 13 blocks of tests, along with the descriptive statistics, are reported in Online Appendix I.1. 25

Protocol

Data were collected in two distinct waves. A total of 171 participants were recruited through ORSEE [START_REF] Greiner | Subject pool recruitment procedures: Organizing experiments with ORSEE[END_REF] for a total of 30 sessions. 26 All tasks were computerised. Half of the participants were male and the average participant was 21.65 years of age.

The first wave of data collection occurred between November 2018 and February 2019. All the sessions were conducted in the laboratory. The two steps of the experiments took place on two different days, referred to as Day 1 and Day 2. We invited 154 participants, of whom 109 showed up on Day 1, from a participant pool of more than 2,500 students in Lyon, France. To limit attrition, participants were only paid the show-up fee (5e) at the end of the Day 1 sessions and thus needed to come back on Day 2 to collect their Day 1 earnings, which consisted of a fixed wage of 12e and a variable amount of pay depending on their decisions in some of the tests (4.6e on average). On Day 2, 83.5% of the participants that completed Day 1 again showed up. 27 We conducted a total of 15 sessions on Day 2, 11 of which were with six investors and the remainder with five investors, which amounted to a total of 86 decision makers. Day 1 sessions lasted for one hour and Day 2 sessions for 3.5 hours. Average earnings for the two-day experiment were 38e, including a 5-euro show-up fee for each day.

The second wave of data collection took place in April 2022. The second wave of experiments was preregistered using 'AsPredicted' (#92456). 28 Step 1 was shortened (see subsection 3.3) and conducted online. The first step lasted 20 minutes on average. Only participants who completed step 1 could participate in step 2. At the end of step 2, we added a post-experiment questionnaire eliciting participants' emotions when facing tail events (as described in subsection 3.2 above and presented in Online Appendix I.5) and an incentivised comprehension questionnaire for the BDM procedure (see Online Appendix I.6). We recruited 85 participants from the same participant pool as in the first wave. 29 We conducted a total of 15 sessions, 2 of which were with seven investors, 6 with six and the remaining sessions with five investors. 30 Step 2 lasted for 3 hours. Participants were paid for steps 1 and 2 only at the end of step 2. Average earnings for 25 In the first wave, we conducted tests of Blocks 1 to 12. In the second wave, we implemented the survey online and selected the following subset of blocks to keep the average completion time to 20 minutes: risk aversion in the gain domain (Block 2), estimation of tokens (Block 5), loss aversion (Block 8), availability heuristic 1 & 2 (Blocks 7 and 10), questions 5, 11, 17, 21, 23, 29 35, 41, 45, 47, 53, 59, 69, 93 of the personality test (Block 3), and demographic data (Block 12). We added a gambling fallacy test (Block 13).

26 Due to the technical complexity of setting up the physiological tool, we conducted one session at a time except for six instances in the second wave in which we conducted two sessions at a time.

27 People who did not come back to Day 2 sessions were not significantly different from those who came back in terms of demographics (gender and age), risk and loss aversion, and cognitive ability (CRT and Bayesian updating score) (all Rank Sum Tests p-values > 0.10). This is somehow not so surprising given that we recruited from a relatively homogeneous population of students. Out of the 91 returning participants, 86 played the role of investors whereas five were assigned the role of pickers. The remaining 10 pickers were recruited separately for Day 2 sessions. 28 Available at : https://aspredicted.org/74hd2.pdf. We pre-registered our design, hypotheses and analyses based on the working paper version of the current manuscript (see [START_REF] Corgnet | Negative Tail events, emotions and risk taking[END_REF]. 29 We thus doubled our original sample size from 86 to 171 observations. We end up with a unique sample of physiological and behavioural data that largely surpasses the standard sample size in related experiments (n = 40) (see Christopoulos et al., 2019, p. 402). 30 To be more precise, in one of the sessions, one participant arrived late and was assigned to a separate session. Yet, from the point of view of this participant, the experiment unfolded as he or she was part of the main session, to which other participants were assigned, since he or she faced exactly the same sequence of draws. steps 1 and 2 were 32e, including a 5-euro show-up fee for completing step 2. 31 , 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 Wave 2 15 85 2 groups of 7 6 groups of 6 7 groups of 5

Same as wave 1

Testable predictions

To derive hypotheses regarding investors' reaction to tail events, in Section 4.1 we present a model that encompasses EUT and PT specifications. In Section 4.2, we propose three conjectures regarding the moderating role of emotions in the face of tail events. These conjectures reflect the exploratory nature of our study which is due to the absence of a commonly-accepted model of emotions in decision theory.

Model & hypotheses for emotionless investors

We assume that each investor i chooses their bid b i t in period t given their belief B i c,t regarding the probability that colour c is drawn in period t, where c ∈ {0, 1, 2, 3, 4, 5} and c = 5 stands for the yellow colour (that is, the tail event). An investor i selects a bid to maximise the following utility function:

b i * t = argmax b i t ∈[0,50] b i t r t =1 1 50 5 c=0 B i c,t u i (w i t -r t + v(c), R i t ) + 50 r t =b i t +1 1 50 u i (w i t , R i t ),
where v(c) is the payoff associated with drawing colour c. The variable r t refers to the random integer (drawn uniformly between 1 and 50) used in the BDM mechanism that determines whether the investor purchases the asset or not. We also denote by w i t the accumulated level of wealth of investor i up to period t and by R i t ≥ 0 the reference wealth in period t. We then consider the following power utility function, which has extensive empirical support (e.g., [START_REF] Stott | Cumulative prospect theory's functional menagerie[END_REF]:

u i (w i t , R i t ) =          (w i t -R i t ) α i , if w i t ≥ R i t -λ i -max w i t , 0 -R i t α i , otherwise (1)
where α i > 0 characterises risk attitudes and the term max w i t , 0 appears in lieu of w i t because of the limited liability of the participants in our experiment. In the EUT framework, both the loss aversion parameter (λ i ) and the reference wealth (R i t ) are set to zero. In the PT framework, we assume λ i > 1. We consider that the reference wealth is determined by the original level of wealth (w i 0 ) which, in our experiment, can be set equal to the fixed wage earned on Day 1 (1,200/ c). 32 To determine how investors update their beliefs, we rely on Bayes' rule, further motivated by the findings of [START_REF] Payzan-Lenestour | Can people learn about 'black swans'? Experimental evidence[END_REF], which showed that people use Bayesian updating in an environment in which they learn about the likelihood of tail events. In particular, we assume a conjugate prior for the multinomial distribution associated with the probability of occurrence of each colour. The conjugate prior for the multinomial distribution is the Dirichlet distribution, Dir(η i 0 , η i 1 , η i 2 , η i 3 , η i 4 , η i 5 ), where η i c η i represents the prior for the probability of occurrence of colour c and η i = 5 c=0 η i c captures the overall weight assigned to the prior probabilities. We denote the sample evidence regarding the probability of the occurrence of the respective colours until period t by s i t = 5 c=0 t j=1 ρ i t-j s c,j , where s c,j is a dummy variable that takes a value of one if colour c is observed in period j and otherwise zero. We introduce the parameter ρ i ∈ [0, 1] so as to capture recency bias in the probability updating of investor i. Perfect Bayesian updating corresponds to ρ i = 1, in which case all past realizations are used in updating the subjective belief. However, investors may rely on small samples for updating their beliefs (ρ i < 1). 33 In our model, the recency and availability biases are closely related because they both lead people to overweight the occurrence of tail events after observing them. The belief of investor i in period t is thus computed as follows:

B i c,t = 1 η i + s i t         η i c + t j=1 ρ i t-j s c,j         . ( 2
)
We simulate our model using the parameters of the experiments. 34 In the model simulations reported below, we assume the prior belief of the tail event, which we denote π i = η i 5 η i , is 1% while the weight on the prior η i is 100, and investors believe all remaining payoffs are equally likely. 35 Furthermore, we consider the case of a risk-averse EUT investor (α i = 0.75) and a PT investor with λ i = 2.0 [START_REF] Tversky | Advances in prospect theory: Cumulative representation of uncertainty[END_REF] and α i = 0.75, unless otherwise noted. We conduct numerous robustness checks where we consider alternative parameter values of our model (i.e., α i , λ i , π i , η i ). These results confirm the findings summarised in each hypothesis. 36 Figure 2 shows the dynamics of bids around the tail event for three values of ρ for PT investors with α = 0.75, λ = 2.0 (top) and EUT investors with α = 0.75 (bottom). The results for those investors who suffered the tail loss are shown in red dashed line, while the results for those who did not suffer a tail loss are shown in blue solid.

Our model implies that observing the tail event will lead investors to update their beliefs about its occurrence upwards compared with a case in which they observe no tail event. When tail events are observed without being suffered, they tend to depress bids, regardless of whether we consider PT or EUT investors (see solid blue lines in Figure 2). The decrease in bids also appears to be magnified by the presence of recency bias (ρ i < 1). 37 This leads to our first hypothesis. 32 Our approach consists of assuming that attitudes toward tail events are captured by value functions. Under PT, an alternative interpretation of attitudes toward tail events would be to consider distortion of a probability weighting function. 33 There is mounting evidence that people rely on small samples and overweight salient information (Tversky andKahneman, 1973, 1974;[START_REF] Rabin | Inference by believers in the law of small numbers[END_REF][START_REF] Plonsky | Reliance on small samples, the wavy recency effect, and similarity-based learning[END_REF]. 34 To generate the simulated dynamics of the bids before and after observing the tail event, we use payoff sequence 2 from our experiment in which four tail events occurred (see Figure A.1). We report the dynamics of the bids around the first tail event in period 49 (the remaining three are in periods 147, 179 and 257). The reason for choosing the first tail event is that the simulated investors have not yet accumulated much wealth, so that suffering the tail event will put them in the loss domain (their wealth level will be below 1,200). In addition, investors will not go bankrupt because they are facing the tail event for the first time in this case. The random draw (r t ) for the BDM mechanism also follows the realised sequence of the experimental sessions, except for period 49. We set r 49 = 50 to simulate the case where the tail event is observed but not suffered, and r 49 = 1 for the case where the tail event is suffered. 35 In step 1 survey, the median prior belief of participants regarding the occurrence of a tail event was 1.2%. 36 The results of these additional simulations are available in Online Appendix II. 37 Note that in the three upper panels of Figure 2, the decrease in bids is limited when ρ is low because bids hit the lower bound after PT Investors ρ = 1.0 ρ = 0.5 ρ = 0.0 t-5 t-4 t-3 t-2 t-1 Tail Event Hypothesis 1. Tail Events and Bids Investors that observe but do not suffer a tail event are more likely to reduce their bids compared with investors that observe a non-tail event. This effect is especially pronounced for investors with a high level of recency or availability bias.

Dashed red lines of Figure 2 display the evolution of bids for the case in which a risk-averse (α i = 0.75) investor observed the tail event and incurred its loss. Under EUT, the decline in wealth which follows tail losses causes the limited liability assumption to bind, thus partly offsetting the depressing effect of updated beliefs on bids (see bottom center and bottom left panels of Figure 2). More strikingly, under PT, investors that incurred tail losses tend to become more risk seeking as they are dragged into the loss domain [START_REF] Kahneman | Prospect theory: An analysis of decision under risk[END_REF][START_REF] Tversky | Advances in prospect theory: Cumulative representation of uncertainty[END_REF][START_REF] Imas | The Realization Effect: Risk-Taking after Realized versus Paper Losses[END_REF]. This leads them to increase rather than decrease their bids after suffering a tail event. The top three panels of Figure 2 shows that PT investors are more likely to increase their bids after experiencing a tail than a non-tail event. This leads us to our second hypothesis.

Hypothesis 2. Tail Losses and Bids Investors suffering a tail event are more likely to increase their bids compared with investors experiencing a non-tail event. This effect is especially pronounced for loss-averse investors.

These first two hypotheses capture the reaction of investors to tail events in the absence of emotional considerations. We now turn to the moderating role of emotions on risk taking.

Conjectures on the moderating role of emotions

We consider several mechanisms by which emotions can influence investors' reactions to tail events by affecting either their utility or their beliefs. To that end, we focus on the basic emotions studied by Ekman observing a tail event. In the cases in which bids do not hit the lower bound after observing a tail event, the recency bias magnifies the decrease in bids for loss-averse investors (see panel (b) in Figure II.1.3 in the Online Appendix II). (1999). As explained in Section 3.2, in our setup, tail losses constitute an unambiguous instance of a negative event, and in that case, the only basic emotions that are relevant are anger and fear. When tail events are observed yet not suffered, emotions of both negative and positive valence could be triggered, such as fear and hope. Section 4.2.1 is dedicated to anger, while Section 4.2.2 focuses on fear. In Section 4.2.3, we complement our analyses of emotions by studying their potential impact on bankruptcy and financial gains. (2000, p. 107) argues that investors are prone to 'get-evenitis', which is defined as "the difficulty people experience in making peace with their losses", that leads them to take on more risks [START_REF] Garvey | Do losses linger?[END_REF]. This behaviour is also key to explaining the disposition effect whereby investors are reluctant to sell stocks at a loss [START_REF] Shefrin | The disposition to sell winners too early and ride losers too long: Theory and evidence[END_REF][START_REF] Odean | Are investors reluctant to realize their losses?[END_REF]. 38 The inability of investors to make peace with their losses is likely to be driven by an emotional reaction to losses [START_REF] Steenbarger | Trading Psychology 2.0: From best practices to best processes[END_REF][START_REF] Lo | Adaptive markets: Financial evolution at the speed of thought[END_REF]. In particular, sudden losses are likely to upset investors which, in turn, would prevent them from making peace with their losses, thus promoting risk-seeking behaviours [START_REF] Lerner | Fear, anger, and risk[END_REF][START_REF] Fessler | Angry men and disgusted women: An evolutionary approach to the influence of emotions on risk taking[END_REF][START_REF] Habib | Fear and anger have opposite effects on risk seeking in the gain frame[END_REF][START_REF] Lerner | Emotion and decision making[END_REF]Ferrer et al., 2016;[START_REF] Engelmann | Emotions can Bias Decision-Making Processes by Promoting Specific Behavioral Tendencies[END_REF]. 39 We thus posit that an emotional reaction to tail losses, particularly anger, will make it difficult for investors to make peace with their losses, leading to an increase in bids. This leads us to Conjecture A.

Anger and losses

Shefrin

Conjecture A. Anger and Tail Losses Anger-prone investors will be more likely to increase their bids after suffering tail losses compared with those who are not.

It follows from Conjecture A that one of the key features of PT, risk seeking in the loss domain, may only arise because losses trigger anger. The empirical success of PT [START_REF] Barberis | Thirty years of prospect theory in economics: A review and assessment[END_REF] could thus hinge upon its ability to indirectly capture emotional reactions to risky prospects [START_REF] Loewenstein | Risk as feelings[END_REF]. Relatedly, [START_REF] Sokol-Hessner | Emotion regulation reduces loss aversion and decreases amygdala responses to losses[END_REF][START_REF] De Martino | Amygdala damage eliminates monetary loss aversion[END_REF] have established a connection between brain emotional centers, such as the amygdala, and loss aversion.

In Online Appendix III, we introduce emotions into the model of Section 4.1. To capture the role of anger, in Online Appendix III.1 we allow for the reference wealth R i t to be a weighted average of the previous reference and current wealth levels, the weight on the previous reference wealth level depending on whether the investor is in the loss (ω -) or in the gain (ω + ) domain:

R i t =        ω i -R i t-1 + (1 -ω i -)w i t if w i t < R i t-1 ω i + R i t-1 + (1 -ω i + )w i t otherwise.
We assume that this weight is higher in the loss than in the gain domain (ω -≥ ω + ) capturing the idea that investors are more reluctant to adjust their reference wealth level to accumulated losses than gains. Simulations of the model are in line with Conjecture A.

Fear

We have thus far considered the effect of emotional arousal on investors' utility leaving aside its effect on beliefs. However, emotions also likely influence beliefs [START_REF] Lopes | Between hope and fear: The psychology of risk[END_REF][START_REF] Charness | When optimal choices feel wrong: A laboratory study of bayesian updating, complexity, and affect[END_REF][START_REF] Shefrin | Behavioralizing finance[END_REF]. In [START_REF] Lopes | Between hope and fear: The psychology of risk[END_REF], beliefs are distorted by the emotions of fear and hope, where fear increases the weight associated with the least favorable events and hope increases the weight associated with the most favorable events (see also, e.g., [START_REF] Rottenstreich | Money, kisses,and electric shocks: On the affective psychology of risk[END_REF]. This view is consistent with other major theories on the role of emotions in decision-making, including appraisal theory (see Lerner and Keltner, 38 Well known cases of traders such as Nick Leeson and Jérôme Kerviel who increased their positions instead of exiting the market after incurring considerable losses have also been interpreted as examples of 'get-evenitis' (see [START_REF] Lo | Adaptive markets: Financial evolution at the speed of thought[END_REF].

39 [START_REF] Taleb | The Black Swan: The Impact of the Highly Improbable[END_REF] provides a vivid description of traders' anger reactions to tail losses.

2001; [START_REF] Lerner | Emotion and decision making[END_REF] and mood-congruence theory, according to which people would more easily recall events more consistent with their current mood [START_REF] Blaney | Affect and memory: a review[END_REF][START_REF] Matt | Mood-congruent recall of affectively toned stimuli: A meta-analytic review[END_REF][START_REF] Watkins | Mood-congruent memory in depression: Emotional priming or elaboration?[END_REF][START_REF] Mayer | Mood-congruent memory and natural mood: New evidence[END_REF][START_REF] Watkins | Unconscious mood-congruent memory bias in depression[END_REF][START_REF] Koszegi | Fragile self-esteem[END_REF]. Empirical and experimental evidence has also shown that fear tends to trigger risk-averse (see [START_REF] Lerner | Fear, anger, and risk[END_REF][START_REF] Cohn | Evidence for countercyclical risk aversion: An experiment with financial professionals[END_REF][START_REF] Lerner | Emotion and decision making[END_REF][START_REF] Andrade | Bubbling with excitement: An experiment[END_REF][START_REF] Guiso | Time varying risk aversion[END_REF][START_REF] Breaban | Emotional state and market behavior[END_REF][START_REF] Van Well | Relief from incidental fear evokes exuberant risk taking[END_REF][START_REF] Wake | The influence of fear on risk taking: a meta-analysis[END_REF] 40 and cautious [START_REF] Raghunathan | All negative moods are not equal: Motivational influences of anxiety and sadness on decision making[END_REF] behaviours. 41 Positive feelings tend to lead to more optimistic beliefs [START_REF] Isen | The effect of positive feelings on risk taking: When the chips are down[END_REF][START_REF] Johnson | Affect, generalization, and the perception of risk[END_REF] and increased risk taking [START_REF] Bassi | O sole mio: an experimental analysis of weather and risk attitudes in financial decisions[END_REF][START_REF] Kaplanski | Do happy people make optimistic investors?[END_REF][START_REF] Breaban | Emotional state and market behavior[END_REF]. 42 This leads us to the following conjecture.

Conjecture B. Fear and Tail Events i) Fearful investors will be more likely to decrease their bids after observing, yet not suffering, a tail event compared with non-fearful investors.

ii) Fearful investors will also be less likely to increase their bids after suffering tail losses compared with non-fearful investors.

In Online Appendix III.2, we extend the model of Section 4.1 to account for the effect of fear associated with tail events on investors' beliefs. Fear is captured by an excessive weight attributed to the tail event when updating beliefs (in comparison to the benchmark model without emotions presented in Section 4.1). Simulations are in line with Conjecture B.

Emotional arousal, bankruptcy and earnings

Conjectures A and B suggest that emotions are likely to influence investors' reactions to tail events. As a result, emotional reactions might affect the likelihood of investors going bankrupt, which in turn will affect their earnings.

Conjecture A posits that anger-prone investors exhibiting high levels of emotional arousal bid aggressively after observing tail losses. Because these investors tend to place high bids, they are more likely to go bankrupt. It follows that anger should impact investors' wealth negatively when bankruptcy is possible, which is when at least two tail events occur. By contrast, when tail events are few and bankruptcy is not an eventuality, then anger should not significantly affect investors' wealth.

Finally, Conjecture B emphasises that fearful investors tend to bid conservatively. We thus expect that they will be less likely to go bankrupt. Fearful investors bid low and thus often fail to buy the asset and collect the corresponding payoffs. This is why fear should lead to an overall decrease in investors' wealth. We summarise our predictions regarding bankruptcy and earnings in Conjecture C.

Conjecture C. Emotions, Bankruptcy and Earnings i) Anger-prone investors will be more likely to go bankrupt and will earn less than those that are not when tail events are frequent.

ii) Fearful investors will be less likely to go bankrupt and will also earn less than those that are not fearful.

Simulations of the model with emotions reported in Online Appendix III.3 are in line with Conjecture C. 40 The meta-analysis of Marini (2020) also provides support to the negative relationship between fear and risk-seeking behaviour, although to a small extent. 41 Similarly, anxiety leads people to focus their attention on threat-related stimuli [START_REF] Eysenck | Trait anxiety, defensiveness, and the structure of worry[END_REF][START_REF] Derakshan | Interpretive biases for one's own behavior and physiology in high-trait-anxious individuals and repressors[END_REF] and become more risk averse [START_REF] Kuhnen | Asymmetric learning from financial information[END_REF]Knutson, 2005, 2011;Knutson et al., 2008). In a recent experimental study, [START_REF] Van Well | Relief from incidental fear evokes exuberant risk taking[END_REF] also show that decreasing anxiety by relieving people from a possible aversive electric shock tends to increase risk taking. 42 Finance researchers have also assessed the effect of mood on stock markets [START_REF] Saunders | Stock prices and Wall Street weather[END_REF][START_REF] Hirshleifer | Good day sunshine: Stock returns and the weather[END_REF][START_REF] Kamstra | Winter Blues: A SAD Stock Market Cycle[END_REF]Baker andWurgler, 2006, 2007;[START_REF] Edmans | Sports sentiment and stock returns[END_REF][START_REF] Kaplanski | Sentiment and stock prices: the case of aviation disasters[END_REF][START_REF] Goetzmann | Weather-induced mood, institutional investors, and stock returns[END_REF][START_REF] Hirshleifer | Mood beta and seasonalities in stock returns[END_REF].

Figure 3: Median Bids Five Periods Before and After a Tail Event Occurred. The series in red dashed (blue) represent the case in which the random BDM number at time t was less (more) than 10 (40), in which case tail losses were (not) suffered 94.2% (96.7%) of the times.

Results

Hypotheses 1&2 (Tail events, tail losses and bids)

We start by testing Hypotheses 1 and 2, thus considering the response of investors to tail events in cases in which they incurred and did not incur tail losses. In our experiment, the occurrence of a tail event is exogenous, but the likelihood of incurring tail losses is not. Indeed, investors who bid high values are more likely to buy the asset and thus incur losses when a tail event occurs compared to those who bid low values. We thus face selection issues when assessing the distinct impact of tail events on bidding behaviour when losses are suffered and when they are not. For example, risk-seeking investors are more likely to bid high values and incur tail losses. Note that these selection issues are not a concern in our model simulations because we use a representative agent.

To tackle selection issues, we use the exogenous variation in random BDM numbers (between 1 and 50) drawn each period to compare situations in which the BDM number is very low, in which case investors are almost certain to buy regardless of their risk attitudes, and very high, in which case investors are almost certain not to buy the asset. We know that for a BDM number lower than 10 (20) people bought the asset in 94.2% (87.5%) of the cases in our experiment. We also know that for a BDM number higher than 40 (30) people did not buy the asset in 96.7% (92.4%) of the cases. To test Hypotheses 1 and 2 while eliminating selection issues, we can thus compare the response of investors who faced a tail event when the BDM number was low and when it was high. Following our pre-registered plan, we will consider 10 and 20 (30 and 40) as the two upper (lower) bounds for low (high) BDM numbers.

Figure 3 presents median bids five periods before and after a tail event occurred for the case in which the random BDM number at time t was less than 10 or more than 40. We observe that, in line with Hypotheses 1 and 2, bids increased (decreased) after investors experienced a tail event along with a BDM number lower than 10 (higher than 40), in which case 97.1% (93.9%) of the investors bought (did not buy) the asset and thus incurred (did not incur) tail losses. 43In our statistical analysis, we define BDM10-and BDM20-(BDM30+ and BDM40+) as dummy variables that take value one if the BDM number drawn in a given period was less (more) than 10 and 20 (30 and 40). In regression (1) of Table 2, we compare the impact of tail events on investors' bids when the BDM number was less than 10 and when it was more than 40. This effect is captured by the interaction term ('Tail Event × BDM-Dummy'). In this first regression, we use 40% of our data because 60% of the periods are such that a random BDM number was between 10 and 40. In regression (2), for the sake of robustness, we replicate the analysis for a broader sample (80% of our data) by considering BDM numbers that were either less than 20 or more than 30. However, the broader sample provides a slightly noisier test of our hypotheses because in 6.1% (10.0%) of the cases people facing the low (high) BDM number did not buy (bought) the asset. In all our regressions, we also included individual characteristics to control for any remaining differences between investors that could explain their bidding behaviour, such as, gender, availability bias, risk and loss attitudes (see Online Appendix I.1 for detailed descriptions of these variables). We also introduce participants' current wealth levels as a regressor to control for potential limited liability effects that could foster risk taking (see Moffatt, 2015, p. 89). There is limited liability in our experiment because bankrupt participants repaid on average 80% of the loan value. Finally, following the recommendation in Cameron and Triverdi (2010), we use AR(1) errors in all bid regressions to control for the autocorrelation in the error term that is due to the high level of inertia in investors' bidding behaviour.

In line with Hypothesis 1, the 'Tail Event Dummy' is negative and marginally significant in both regressions of Table 2 showing that experiencing a tail event when the random BDM number was high, in which case almost all investors did not buy the asset, decreased bids in the next period.

In line with the second part of Hypothesis 1, we show that the 'Tail Event Dummy' in Table 3 (regressions (1) and ( 4)) is negative and significant for investors with a level of availability bias above the median whereas it is not significant for those with an availability bias below the median (regressions (2) and ( 5)). We measure the availability bias using two of the tests in our Day 1 session, as adapted from Tversky and

Wealth -21×10 -4 * * * -25×10 -4 * * * -22×10 -4 * * * -19×10 -4 * * * -25×10 -4 * * * -21×10 -4 * * * (4×10 -4 ) (4×10 -4 ) (3×10 -4 ) (2×10 -4 ) (2×10 -4 ) (1×10 -4 )
Number of Tail Events -2.027 * * * -1.045 * * * -1.620 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 * * * p< 0.01, * * p< 0.05, * p< 0.1 Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression Table IV.4 in the Online Appendix for more details. [START_REF] Tversky | Judgment under uncertainty: Heuristics and biases[END_REF]. We define the availability bias index as the sum of the standardised scores on the two measures. 44 We also define the 'High Availability Dummy' as taking a value of one when an investor's availability bias is above the median of all investors' scores. Furthermore, the interaction term 'Tail Event × High Availability Dummy' is negative though non-significant in regression (3) and marginally significant in regression (6).

In line with Hypothesis 2, 'Tail Event Dummy × BDM-' is positive and significant in both regressions in Table 2 showing that when the BDM number is low and investors are almost always buying the asset, tail events tend to increase bids. In line with Hypothesis 2, Table 4 shows that the increase in bids after incurring tail losses tends to be stronger for investors who are loss averse than for those who are not. This is the case because the coefficient 'Tail Event × BDM-Dummy' is positive and significant for investors with a loss aversion index above the median (see regressions ( 1) and ( 4)) whereas it is not significant for those with a loss aversion index below the median (see regressions ( 2) and ( 5)). The loss aversion index is measured as the number of times a participant chose the option involving a smaller loss in the loss aversion test administered in step 1 (see [START_REF] Brink | The effects of risk preference and loss aversion on individual behavior under bonus, penalty, and combined contract frames[END_REF]. Furthermore, the triple interaction coefficient 'Tail Event × BDM-× High Loss Aversion Dummy' is positive in regressions ( 3) and ( 6), and marginally significant in the latter.

In Online Appendix IV.1 to IV.3, we conducted additional robustness checks. First, we used directional changes instead of bid value as dependent variable in line with our pre-registered plan. Second, as a final robustness check (not pre-registered), we used instrumental variable panel regressions as an alternative technique to alleviate endogeneity issues. 45 The findings in Tables 2 and4 replicate consistently. For Table 3, results are qualitatively similar but fail to reach statistical significance when considering directional changes and BDM numbers below 10 and above 40, and when using an instrumental variable panel regression.

Overall, these results are in line with Hypotheses 1 and 2. More precisely, we can summarise them as follows.

Result 1 -There is support for Hypothesis 1 according to which investors observing tail events without suffering tail losses tend to decrease their bids. There is also some evidence for the second part of Hypothesis 1 according to which the former effect is stronger for investors who exhibit higher levels of availability bias.

Result 2 -There is support for Hypothesis 2 according to which tail losses tend to increase investors' bids. There is also evidence for the second part of Hypothesis 2 according to which the former effect is stronger for investors who exhibit higher levels of loss aversion.

We have thus far ignored the possible moderating role of emotions in explaining investors' reactions to tail events. We study these effects by testing Conjectures A to C.

Empirical measurement of emotions

In this section, we conduct empirical tests to validate our measurement of emotions. To assess whether investors were emotionally aroused by an event, we evaluated their electrodermal activity using standard physiological techniques (see Section 3.2). Recall that we refer to decision (feedback) arousal as the physiological reaction, as measured by electrodermal activity, immediately after an investor has made a decision (at the end of the period when learning whether a tail event occurred and whether tail losses were incurred).46 We define a 'Decision Arousal Dummy' ('Feedback Arousal Dummy') as taking a value of one in a given period if an investor exhibited decision (feedback) arousal. 47 We also compute a baseline feedback (decision) arousal index that sums the number of times an investor had been aroused after feedback (at the time a decision is made), which is the case when the 'Feedback Arousal Dummy' takes a value of one. We compute this index on the first five periods so as to ensure that no tail event had yet occurred in any session. 48 We show that emotional arousal is indeed responsive to surprise, which in our setup follows from observing a tail event (see Figure A.3 in the Appendix). This effect is significant for feedback arousal although decision arousal in the subsequent period is not significantly impacted by the tail event (see 'Tail Event Dummy' in Regressions ( 3) and ( 4) in Table A.1 in the Appendix). This suggests the emotional impact of tail events is transitory. 49 The interaction term 'Tail Event Dummy × BDM-' is positive in regressions ( 1) and ( 2). Yet the coefficient is marginally significant in (1) and non-significant in (2). That is, incurring tail losses slightly increases the emotional arousal associated with tail events. In sum, we observe an emotional response to tail events in the current period whether tail losses are incurred or not.

Wealth -18×10 -4 * * * -26×10 -4 * * * -22×10 -4 * * * -15×10 -4 * * * -27×10 -4 * * * -21×10 -4 * * * (3×10 -4 ) (4×10 -4 ) (3×10 -4 ) (2×10 -4 ) (3×10 -4 ) (1×10 -4 ) Number of Tail Events -1.571 * * * -1.698 * * * -1.619 * * * -1.540 * * * -1.742

Conjecture A (Emotional arousal, anger and tail losses)

According to Conjecture A, the increase in bids following tail losses is more pronounced for investors exhibiting an emotional reaction to tail events. In Table 5, we replicate our regression analysis of Table 4 to consider whether loss-averse investors increased their bids out of feedback arousal. We start by showing that the interaction term 'Tail Event × BDM-Dummy' is positive when loss averse investors exhibited feedback arousal in the previous period (i.e., 'Feedback Arousal Dummy' equals one) (see regressions ( 2) and ( 5)) whereas it is negative otherwise (see regressions ( 1) and ( 4)). The triple interaction effect 'Tail Event × BDM-× Feedback Arousal Dummy' in regressions ( 3) and ( 6) is positive and significant. This shows that loss-averse investors who exhibited feedback arousal were more likely to increase their bids as a result of tail losses than those who did not exhibit any feedback arousal. These findings are consistent with Conjecture A.

To test Conjecture A further, we need to identify whether feedback arousal is associated with anger. To that end, as part of the second wave of data collection, we added a post-experiment questionnaire in which we asked participants about emotional valence when they faced a tail event (see Online Appendix I.5). More specifically, we asked participants how much (1-Not at all 2-A little 3-Moderately 4-Very much 5-Very much) they felt one of four relevant emotions (anger, fear, joy, and sadness) when incurring tail losses. 50 Our results clearly show, in line with the underlying mechanism in Conjecture A, that anger is the dominant emotion when tail losses are incurred. The modal response of participants was that they felt 'Very much' anger after incurring tail events. By comparison, the modal response was 'A little' for sadness and 'Not at all' for fear and joy. Almost half the participants reported feeling no fear at all after incurring tail losses.

Furthermore, we use the HEXACO anger personality scale [START_REF] Ashton | The HEXACO-60: A short measure of the major dimensions of personality[END_REF] completed by participants during step 1 to evaluate whether a person was especially prone to exhibit anger after incurring tail losses. We categorised as anger-prone those participants scoring above the median in the anger facet of personality 51 and as not anger-prone those scoring below. We defined the 'Anger Dummy' as taking a value of one for investors categorised as anger-prone and a value of zero otherwise. This procedure helped 47 Overall, the 'Decision Arousal Dummy' ('Feedback Arousal Dummy') takes a value of one in 22.2% (22.9%) of cases. Arousal is detected using the Matlab routine developed in Joffily's (2018) electrodermal activity toolbox, which is based on estimating the peak and amplitude of the physiological response measured in microsiemens. 48 The earliest tail event appeared in period 7. 49 Note that conducting similar regressions for feedback arousal in the next period also shows no effect of the tail event, p-values = 0.959 and 0.654 for 'Tail Event Dummy.' 50 Our post-experiment questionnaire was programmed so that only those who incurred tail losses during the experiment answered this question. 51 Cronbach's alpha = 0.65. For wave 2 sessions, step 1 was performed online, which might have lowered the reliability of the scale. Indeed, Cronbach's alpha is 0.86 for wave 1, while it is 0.52 for wave 2. us identify the specific emotion associated with feedback arousal without interfering with the choice experiment. Our approach was thus to assess whether investors categorised as anger-prone were especially likely to increase their bids as a result of the feedback arousal generated by tail losses.

Wealth -17×10 -4 * * * -26×10 -4 * * * -18×10 -4 * * * -15×10 -4 * * * -19×10 -4 * * * -15×10 -4 * * * (4×10 -4 ) (8×10 -4 ) (3×10 -4 ) (2×10 -4 ) (5×10 -4 ) (2×10 -4 ) Number of Tail Events -1.646 * * * -1.434 * * * -1.588 * * * -1.601 * * * -1.320
In Table 6, we replicate our regression analysis of Table 5 (regressions (3) and(6)) to consider whether feedback arousal increased investors' bids out of anger. We thus examine whether the triple interaction 'Tail Event × BDM-× Feedback Arousal Dummy' is more pronounced for people who are anger-prone. We find that the triple interaction is positive for anger-prone investors (see regressions ( 1) and ( 4)) and significantly so in regression (4). For investors who are not anger-prone, the triple interaction is never significant and negative in regression (5). In regressions (3) and(6) of Table 6, we observe that the interaction term 'Tail Event × BDM-× Feedback Arousal × Anger Dummy' is positive and significantly so in regression ( 6). This stresses that the increase in bids following tail losses in the presence of feedback arousal tends to be more pronounced for anger-prone investors.

We assessed the robustness of our findings to alternative specifications (see Online Appendix IV.4 and IV.5.) using directional changes instead of bid value as dependent variable and instrumental variable regressions. All the findings in Tables 5 and6 are robust to these alternative specifications except for the instrumental variable regression associated with Table 5 (see Table IV.12) for which we do not observe a significant effect of feedback arousal on the increase in bids. 52We summarise our findings below.

Result A -There is support for Conjecture A according to which anger-prone investors emotionally aroused by tail losses are more likely to increase their bids than investors who are not anger-prone.

Conjecture B (Fear and tail events)

Conjecture Bi states that emotional arousal triggered by tail events is likely to affect investor decisions even in cases in which they avoid tail losses. This is because tail events may impact beliefs. The logic underlying Conjecture Bi is in line with the fact that investors showed an emotional reaction to tail events whether they entailed tail losses or not (see Figure A.3

in the Appendix).

To test Conjecture Bi, we follow the same approach as for testing Conjecture A relying on the HEXACO personality test [START_REF] Ashton | The HEXACO-60: A short measure of the major dimensions of personality[END_REF]. We characterise investors as fearful when they scored above the median participants' scores in the fear personality facet. 53 We define the 'Fear Dummy' as taking a value of one for investors categorised as fearful and a value of zero otherwise.

Because Conjecture Bi refers to a situation in which tail losses are not incurred, we focus on the sign and significance of the variable 'Tail Event × Feedback Arousal Dummy', which captures the effect of being emotionally aroused by observing a tail event when the BDM was high, that is when BDM10-(BDM20-) was equal to 0 in regressions (1) to (3) (( 4) to ( 6)) in Table 7. We observe that 'Tail Event × Feedback Arousal Dummy' is positive and significant for investors who are not fearful (see regressions (1) and ( 4)), and negative (see regressions (2) and ( 5), significantly so for regression (5)), for investors who are fearful. Furthermore, the triple interaction 'Tail Event × Feedback Arousal × Fear Dummy' is negative and significant in regressions (3) and ( 6) showing that when BDM numbers were high and investors were unlikely to buy the asset, tail events decreased subsequent bids for fearful investors who were aroused. Our results support Conjecture Bi and are in line with the meta-analysis of [START_REF] Wake | The influence of fear on risk taking: a meta-analysis[END_REF] and [START_REF] Marini | 20 years of emotions and risky choices in the lab: A meta-analysis[END_REF] showing the negative relationship between fear and risk-seeking behaviour. However, robustness checks using directional changes as dependent variable and instrumental variables panel regressions do not confirm our results. We should also note that unlike the case of tail losses in which anger was the dominant emotion, our post-experiment questionnaire shows that joy rather than fear was the predominant emotion as 73.8% of investors reported experiencing a very high or extreme level of joy when facing a tail event without incurring losses. Yet, a substantial proportion of people reported exhibiting fear. In particular, 41% of investors reported exhibiting at least some moderate level of fear in that scenario, and 23% reported a very high or extreme level of fear. Only 6.6% (9.8%) reported exhibiting at least some moderate level of anger (sadness) in that scenario. We summarise our findings as follows.

(4.009) Wealth -12×10 -4 ** -21×10 -4 *** -18×10 -4 *** -13×10 -4 *** -17×10 -4 *** -15×10 -4 *** (6×10 -4 ) (4×10 -4 ) (3×10 -4 ) (3×10 -4 ) (2×10 -4 ) (2×10 -
(3.029) Wealth -23×10 -4 *** -21×10 -4 *** -22×10 -4 *** -24×10 -4 *** -18×10 -4 *** -21×10 -4 *** (4×10 -4 ) (4×10 -4 ) (3×10 -4 ) (2×10 -4 ) (2×10 -4 ) (1×10 -
Result Bi -There is suggestive evidence for Conjecture Bi according to which fearful investors emotionally aroused when observing, yet not suffering, tail events are more likely to decrease their bids than non-fearful investors.

To test Conjecture Bii, we consider the impact of tail events when losses are incurred. In Table 7, this is captured, as in Tables 5 and6, by the interaction 'Tail Event × BDM-× Feedback Arousal Dummy'. In Table 7, this triple interaction is negative for investors who are not fearful (see regressions ( 1) and ( 4)) and positive and significant for those who are fearful (see regressions ( 2) and ( 5)). The difference in reaction of fearful and non-fearful investors is captured by the interaction term 'Tail Event × BDM-× Feedback Arousal × Fear Dummy' in regressions ( 3) and ( 6), which is positive and significant. These findings contrast with Conjecture Bii because fearful investors who are emotionally aroused tend to increase their bids after incurring tail losses compared to non-fearful investors. This might not be surprising given that our post-experiment questionnaire on emotions shows that only 14.3% of participants reported a more than moderate level of fear after incurring tail losses. The predominant emotion was anger rather than fear. It follows that the positive effect of fear could partly be due to a positive correlation between fear and anger (see [START_REF] Zhan | Distinctive effects of fear and sadness induction on anger and aggressive behavior[END_REF][START_REF] Zhan | The neural basis of fear promotes anger and sadness counteracts anger[END_REF][START_REF] Wager | A Bayesian model of category-specific emotional brain responses[END_REF].

Result Bii -There is no evidence for Conjecture Bii according to which fearful investors emotionally aroused when suffering tail losses are less likely to increase their bids than nonfearful investors.

Conjecture C (Emotional arousal, bankruptcy and earnings)

As stated in Conjecture C, the emotional reactions of investors might influence their likelihood of going bankrupt and their earnings.

However, Table A.2 in the Appendix does not provide support for Conjecture Ci. The coefficient for 'BFA × Anger Dummy' is not significant in regression (1), thus implying that anger-prone investors are not significantly more likely to go bankrupt when their baseline feedback arousal (BFA) levels are high. By contrast with Conjecture Ci, the coefficient for 'BFA × Anger × Number of Tail Events' is not significant in regression (2) so that the negative effect of baseline feedback arousal on anger-prone investors' earnings does not significantly increase when tail events are numerous. Regarding Conjecture Cii, the coefficient for 'BFA × Fearful Dummy' is negative yet not significant in regression (1). This shows that fearful investors are not significantly less likely to go bankrupt. In regression (2), the coefficient for 'BFA × Fear × Number of Tail Events' is positive yet not significant so that fear does not significantly increase investors' earnings as the number of tail events increases.

Result C -Fear and anger do not significantly impact investors' earnings and their likelihood to go bankrupt.

The lack of support for Conjecture C could be due to the transitory impact of emotions on investors' behaviour. As shown in Figure 3, unlike the predictions of PT with a status-quo reference point, the increase in risk taking following tail losses does not persist over time. This implies that the predictions of PT with an exogenous reference point cannot explain the data. However, PT could accommodate the transient impact of emotions when the reference point quickly adapts to the new wealth level as in the models considered in Section 4.2. In these models (see Online Appendix III), we show that depending on the exact parameters, the impact of tail events could be persistent or not. The simulation results that led to Conjecture C relied on average estimates across the full parameter grid. These simulations were characterised by a persistent impact of tail events that impacted investors' bankruptcy rates and earnings.

By contrast, our data seem to emphasise the transitory nature of the effect of tail events. In Table A.3 in the Appendix, we added regression analyses showing that the increase in bids following a tail event that is suffered in the previous period (see positive and significant coefficient for 'Tail Event × BDM10-Dummy in t-1') is offset by a similar decrease in bids four periods later (see negative and significant coefficient for 'Tail Event × BDM10-Dummy in t-5'). The coefficients for 'Tail Event × BDM10-Dummy in t-1' and 'Tail Event × BDM10-Dummy in t-5' are not statistically different (p-value for the coefficients test = 0.973 [0.988] for regression (1) [(2)]).

Our results suggest that PT can only explain our findings if it is envisioned as a theory of emotions. Understanding this fact is key to model the reference point so that it reflects the transitory nature of emotional reactions to large losses. In the next section, we investigate this claim further by comparing various versions of PT that differ in how reference points are set.

A comparison of alternative models

Transitory effect of tail losses

The simulations reported in Figure 2 show that our basic PT model with a fixed reference point cannot explain the transitory effect of tail losses. By contrast, the anger-based PT model presented in Section 4.2.1 can produce, depending on parameters, a transitory effect of tail losses (see Online Appendix III). This transitory effect is similar in length (five periods) to the one observed in our experiment when the weight assigned to the previous reference point in case of losses is around 0.25 and the reference point adjusts immediately in the case of gains. This corresponds to a case in which people adjust their reference point relatively quickly in the face of losses so that five periods after tail losses have been incurred, the weight assigned to the pre-tail losses reference point is only 0.1%.

Model fitting

If our anger-based PT model can capture unique features of the data, it should perform well compared to other models in a fitting exercise. The fitting procedure is described in Online Appendix V. For each participant, we select the best model among the 9 specifications in column (1) of Table 8 using the Akaike Information Criterion. Column (2) of Table 8 report the number and percentage of participants for which this model is the best fit.

We show that, in line with our previous observations, the models that fit the data best are PT with variable reference points. These models provide the best fit for 71.4% of the participants, and are characterised, on average, by substantial loss aversion (λ = 1.57), concave utility (α = 0.52) and the presence of an availability bias (ρ = 0.58). The models that assume gains and losses lead to the same level of adjustment of the reference point to current wealth levels (ω -= ω + < 1, see models 5 and 6) provide the best fit for 42.7% of the participants. For these participants, the average level of sluggishness of the reference point (ω) is estimated to be only 0.10 on average. The models that assume an anger-based reference point adjustment (ω -> ω + , see models 7 and 8 and Section 4.2.1) provide the best fit for 28.7% of the participants. These models estimate, on average, that ω -= 0.72 and ω + = 0.13. It follows that for the participants whose behavioural data are best fitted by anger-based models, the adjustment of the reference point is very sluggish when incurring tail losses while not being so in the case of gains. On average, these participants adjust their reference point so that five periods after tail losses have been incurred, the weight assigned to the pre-tail losses reference point is still 19.3%.

To validate further the interpretation of the anger-based PT model, we categorise participants as 'Angerbased PT' if their behavioural data were best fitted by one of the two anger-based PT models, and use this dummy variable in our previous analyses. In Table A.4 in the Appendix, we replicate the findings reported in Table 6. As in Table 6, we find that the interaction term 'Tail Event × BDM-× Feedback Arousal × Angerbased PT Dummy' is positive and significant in regression (6) while not being significant in regression ( 3). Yet, we do not report a substantial positive correlation between 'Anger-based PT Dummy' and 'Anger Dummy' (ρ l = 0.013, p-value = 0.866).

Discussion

Even though tail events are rare, their impact can be massive, as exemplified by the decline in stock markets worldwide in March 2020. Because tail events are, by definition, surprising, they are especially likely to trigger a strong emotional response. Our research developed a novel tail-event experimental design that allowed us to examine investors' behavioural and physiological responses to tail events.

We found that investors who suffered tail losses tended to increase their bids subsequently whereas those who observed the tail event without suffering losses decreased their bids. Furthermore, we showed that tail events produced a dramatic emotional reaction. In particular, the increase in bids observed when loss-averse investors suffered tail losses was substantially larger for those prone to anger and emotionally aroused by tail events.

Our findings contribute to the literature on emotions and risk taking by establishing a relationship between emotions and investment behaviour. Extending previous research showing that anger increases risk taking (see [START_REF] Lerner | Fear, anger, and risk[END_REF][START_REF] Lerner | Emotion and decision making[END_REF], we demonstrate, in the context of an incentivised investment task, that substantial losses can trigger an anger-related emotional response that fosters risk seeking.

At a theoretical level, our results suggest that one key implication of PT, that is risk-seeking in the loss domain, crucially hinges upon the emotional arousal of decision makers. However, PT is not an emotion theory, and the basic theory with a fixed reference point cannot account for the transitory effect of tail events observed in our experiment. We thus see our anger-based PT model, which features a variable reference point that adjusts slowly to current wealth levels when incurring losses, as a first step in incorporating emotions in reference-dependence models.

Identifying whether PT or emotional theories of risk explain investment behaviour is also practically relevant. If emotions play a critical role in triggering risk seeking after substantial losses, we should be cautious in implementing strategies, such as stop-loss orders, that might upset traders and lead them to increase risk taking in unrelated investment decisions. In the same vein, the popular practice that consists in switching a trader's position to another trader in case of losses [START_REF] Camerer | Behavioral Economics: Past, Present, Future[END_REF]) might fail to tame risk seeking because it does not tame anger. If emotions rather than the 'break even' effect explain risk seeking after substantial losses, then venting emotions might be an appealing solution (e.g., [START_REF] Bushman | Does venting anger feed or extinguish the flame? Catharsis, rumination, distraction, anger, and aggressive responding[END_REF][START_REF] Xiao | Emotion expression in human punishment behavior[END_REF][START_REF] Bolle | Vendettas[END_REF][START_REF] Dickinson | Emotion venting and punishment in public good experiments[END_REF].

Overall, our study highlights that the relationship between emotions and decision-making is multifaceted. Emotions of the same valence, such as anger and fear, can have divergent effects on investors' behaviour. It follows that any attempt by financial authorities to regulate investors' emotions could backfire. Because our work offers specific insights on the type of emotions triggered by tail events and on their impact on investors' decisions, it might prompt policy makers to reflect further on the emotional consequences of new regulations in times of distress.

Future research could build on our experimental paradigm to consider the impact of various tail-event regulations in alleviating or nurturing emotions such as fear, hope or anger. For example, circuit breakers might promote risk-averse or risk-seeking strategies depending on whether they induce fear or anger. 11 (6.4%) EUT with availability bias (ρ = 1) 9 (5.3%) PT with no availability bias (ρ = 1) with fixed reference point (ω -= ω + = 1) 5 (2.9%) PT with availability bias (ρ < 1) with fixed reference point (ω -= ω + = 1) 4 (2.3%) PT with no availability bias (ρ = 1) with variable reference point (ω -= ω + < 1) 31 (18.1%) PT with availability bias (ρ < 1) with variable reference point (ω -= ω + < 1) 42 (24.6%) PT with no availability bias (ρ = 1) with variable anger-based reference point (ω -> ω + ) 20 (11.7%) PT with availability bias (ρ < 1) with variable anger-based reference point (ω -> ω + ) 29 (17.0%)

A Appendix

Wealth -60×10 -6 43×10 -6 10×10 -6 -10×10 -6 (44×10 -6 ) (41×10 -6 ) (41×10 -6 ) (36×10 -6 )
Period -14×10 -4 * * * -12×10 -4 * * * -23×10 -5 -30×10 -5 (4×10 -4 ) (4×10 -4 ) (39×10 -5 ) (34×10 < 0.001 < 0.001 < 0.001 < 0.001 a: In the second wave of data collection, we have not elicited hopeful personality for the sake of reducing the length of the questionnaire, which was conducted online. Our new approach was to elicit the valence of emotions (anger, fear, joy and sadness) in a survey conducted at the end of the experiment. Baseline decision arousal index is defined as BFA except that it uses recordings for decision arousal instead of feedback arousal. We control for decision arousal because the literature on the 'somatic marker hypothesis' has suggested it affects one's likelihood of going bankrupt in gambling tasks (see [START_REF] Bechara | Deciding advantageously before knowing the advantageous strategy[END_REF][START_REF] Bechara | The somatic marker hypothesis: A neural theory of economic decision[END_REF]. Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression Table IV.21 in the Online Appendix for more details.

(3.364) Wealth -28×10 -4 *** -19×10 -4 ** -22×10 -4 *** -26×10 -4 *** -19×10 -4 *** -21×10 -4 *** (5×10 -4 ) (3×10 -4 ) (3×10 -4 ) (3×10 -4 ) (2×10 -4 ) (1×10 -

I Instructions

Sentences in italics are for the readers and not shown to participants.

I.1 SPECIFIC INSTRUCTIONS FOR PARTICIPANTS IN STEP 1 (on screen)

Welcome.

Thank you for participating in this experiment.

Please turn off your phone. It is forbidden to talk to other participants throughout the session. If at any time during the session you need help, press the red button on the left of your desk or raise your hand, we will immediately come to answer your questions in private.

You have registered to participate in two experimental sessions.

During this first experimental session, we ask you to perform a series of tests on the computer.

You will be paid to do these tests. This payoff will be added to your total earnings at the end of the second experimental session.

In this first part, you will answer 12 blocks of questions.

Please answer the following questions as best as you can.

Calculators, paper and pen are not allowed.

Block 1 Bayesian updating

Following [START_REF] Charness | The origin of the winner's curse: A laboratory study[END_REF] we use the following test to assess participants' Bayesian skills. Consider two machines placed on either side of a large production room in a factory, left side (L) and right side (R). Both machines produce rings of good or poor quality. Each ring coming from the machine on the left (L) has a 50% chance of being of good quality and a 50% chance of being of poor quality. Each ring from the right machine (R) has a 75% chance of being of good quality and a 25% chance of being of poor quality.

In each of the next four questions, you will observe a few rings produced by one of the two machines (L or R). You will be asked how likely it is that these rings were produced by the left-hand machine (L). You will receive 50/ c for each correct answer.

Question 1. You are looking at a good quality ring. How likely do you think it is that this ring was produced by the machine on the left (L) (select your answer below)? (correct answer: 40%) The Bayesian updating score corresponds to the number of correct answers. Recall that this Block is only performed on the first wave of sessions.

Block 2

Risk aversion

Following [START_REF] Holt | Risk aversion and incentive effects[END_REF] we use the following risk aversion test.

For each line of the table presented on the following screen, indicate whether you prefer option A or option B.

Note that there is a total of 10 lines in the table, but only one line will be randomly selected to compute your payoffs. As all lines are equally likely to be selected for the computation of your payoffs, you should attribute the same importance to each of your decisions.

At the end of the experiment, a number between 1 and 10 will be randomly selected by the computer. This number will determine which line will be used to compute your payoffs. Your payoff for the selected line thus depends on the option that you will have chosen for this line: option A or option B. To finalise the computation of your payoffs, a second number between 1 and 10 will also be randomly selected by the computer.

• For example, if the first number selected by the computer is 3, this indicates that line 3 will be chosen for the computation of your payoffs. If for this line you have chosen option A, you will earn 2 euros if the second number randomly selected by the computer is 1, 2 or 3. If the second selected number is 4, 5, 6, 7, 8, 9 or 10, you will earn 1.60 euros.

• For example, if the first number selected by the computer is 5, this indicates that line 5 will be chosen for the computation of your payoffs. If for this line you have chosen option B, you will earn 3.85 euros if the second number randomly selected by the computer is 1, 2, 3, 4 or 5. If the second selected number is 6, 7, 8, 9 or 10, you will earn 0.10 euros.

Once on the decision screen, you can always come back to the present instructions screen by clicking on Instructions. The risk aversion score is the number of safe choices. This Block is performed for the two waves of sessions. We conducted a Wilcoxon signed-rank test to compare the individual risk aversion scores of participants from wave 1 to those of participants from wave 2. We do not find any statistical difference between the two waves (p-value = 0.0926).

Block 3

Personality test

Basic information and materials for the HEXACO Personality Inventory-Revised [START_REF] Ashton | The HEXACO-60: A short measure of the major dimensions of personality[END_REF], a test that assesses the six major dimensions of personality (Honesty-Humility, Emotionality, eXtraversion, Agreeableness (versus Anger), Conscientiousness, Openness to Experience) is made available by Kibeom Lee and Michael C. Ashton at http://hexaco.org/hexaco-inventory. We used the following 60-item version of the test. For each statement, participants answered using a 5-level Likert scale from strongly disagree (1) to strongly agree (5).

1 I would be quite bored by a visit to an art gallery.

2 I plan ahead and organise things, to avoid scrambling at the last minute.

3 I rarely hold a grudge, even against people who have badly wronged me.

4 I feel reasonably satisfied with myself overall. 5 I would feel afraid if I had to travel in bad weather conditions. 6 I wouldn't use flattery to get a raise or promotion at work, even if I thought it would succeed. 7 I'm interested in learning about the history and politics of other countries. 8 I often push myself very hard when trying to achieve a goal. 9 People sometimes tell me that I am too critical of others. 10 I rarely express my opinions in group meetings. 11 I sometimes can't help worrying about little things.

12 If I knew that I could never get caught, I would be willing to steal a million dollars.

13 I would enjoy creating a work of art, such as a novel, a song, or a painting.

14 When working on something, I don't pay much attention to small details.

15 People sometimes tell me that I'm too stubborn. 16 I prefer jobs that involve active social interaction to those that involve working alone. 17 When I suffer from a painful experience, I need someone to make me feel comfortable.

18 Having a lot of money is not especially important to me.

19 I think that paying attention to radical ideas is a waste of time. 20 I make decisions based on the feeling of the moment rather than on careful thought.

21 People think of me as someone who has a quick temper.

22 On most days, I feel cheerful and optimistic.

I feel like crying when I see other people crying.

I think that I am entitled to more respect than the average person is.

If I had the opportunity, I would like to attend a classical music concert.

When working, I sometimes have difficulties due to being disorganised.

My attitude toward people who have treated me badly is "forgive and forget". I feel that I am an unpopular person.

When it comes to physical danger, I am very fearful.

If I want something from someone, I will laugh at that person's worst jokes. I've never really enjoyed looking through an encyclopedia.

I do only the minimum amount of work needed to get by. I tend to be lenient in judging other people.

In social situations, I'm usually the one who makes the first move. I worry a lot less than most people do.

I would never accept a bribe, even if it were very large.

People have often told me that I have a good imagination.

I always try to be accurate in my work, even at the expense of time.

I am usually quite flexible in my opinions when people disagree with me.

The first thing that I always do in a new place is to make friends. I can handle difficult situations without needing emotional support from anyone else. I would get a lot of pleasure from owning expensive luxury goods.

I like people who have unconventional views.

I make a lot of mistakes because I don't think before I act.

Most people tend to get angry more quickly than I do.

Most people are more upbeat and dynamic than I generally am. I feel strong emotions when someone close to me is going away for a long time.

I want people to know that I am an important person of high status.

I don't think of myself as the artistic or creative type.

People often call me a perfectionist. 6 51 Even when people make a lot of mistakes, I rarely say anything negative. 52 I sometimes feel that I am a worthless person.

53 Even in an emergency I wouldn't feel like panicking. 54 I wouldn't pretend to like someone just to get that person to do favors for me.

55 I find it boring to discuss philosophy. 56 I prefer to do whatever comes to mind, rather than stick to a plan. 57 When people tell me that I'm wrong, my first reaction is to argue with them.

58 When I'm in a group of people, I'm often the one who speaks on behalf of the group. 59 I remain unemotional even in situations where most people get very sentimental. 60 I'd be tempted to use counterfeit money, if I were sure I could get away with it. This test was not incentivised and yielded no earnings. This block is performed for the two waves of sessions. We conducted a Wilcoxon signed-rank test to compare the individual anger, fear and emotionality scores from wave 1 and wave 2. We do not find any statistical difference between the two waves (respective p-values are equal to 0.3728, 0.6439 and 0.5606).

Box I Box C

Block 4

Ambiguity aversion

This test is based on [START_REF] Dimmock | Ambiguity attitudes in a large representative sample[END_REF]. The instructions are given here for a 2-colour ambiguity aversion test; we conducted two other similar tests for 10 colours and 100 colours.

In this game, you can choose between Box I and Box C, both containing 100 balls, which can be either yellow or purple. One ball will be taken from the box you have chosen. You will earn 1 euro if a purple ball is picked.

For Box C, you can select the exact percentage of purple balls (p) and yellow balls (1-p) it contains. This percentage between 0 and 100% (p) must be chosen so that you are indifferent to picking a ball from Box I or picking a ball from Box C.

Box I also contains yellow and purple balls, but the percentages of balls of the two colours are not known in advance. All in all, the two boxes contain 100 balls of two different colours (yellow and purple). However, the percentage of yellow and purple balls for Box C (Known) is chosen by yourself in advance, whereas this percentage is unknown and will remain unknown for Box I (Unknown).

Your decision is to choose the percentage of purple balls in Box C (p) so that you are indifferent between picking a ball from Box I and picking a ball from Box C. In this game, the computer will randomly choose a percentage between 1 and 100 (called r) to calculate your payoffs. Each integer between 1 and 100 has the same chance of being selected so that each number has a 1 in 100 chances of being selected.

• If the randomly selected percentage (r) is less than the percentage of purple balls (p) you chose for Box C then a ball will be drawn from Box I to calculate your payoffs.

• If the randomly selected percentage (r) is greater than or equal to the percentage of purple balls (p) you selected for Box C then one ball will be drawn from Box C to calculate your payoffs.

You will earn 1 euro if a purple ball is drawn and 0 euro if another colour is drawn.

Choose the percentage of purple balls in Box C (p) so that you are indifferent between picking a ball from Box I and picking a ball from Box C: . CONFIRM?

A pop-up opens if participants do not try several values.

This test was incentivised. The average earning is 0.84 euro (minimum earning: 0 euro; maximum earning: 3 euros).

Table I.4: Distribution of Scores in the Ambiguity Aversion Test

Percentage choice [0,10( [10,20( [20,30( [30,40( [40,50( [50,60( [60,70( [70,80( [80,90( [90, The ambiguity aversion test score is the average of a participant's chosen values across the three versions of the test. That is the 2-colour version described above along with the 10-and 100-colour versions.

This Block is performed only for the first wave of sessions.

Block 5

Estimation of tokens

In order to have an idea about the participants' prior belief on the distribution of tokens, we asked them to estimate the proportion of an orange and a yellow token.

Estimation of orange tokens

On the following screen, you will see a photograph with tokens of several colours. We ask you to estimate the percentage of orange tokens. Enter a percentage with one decimal (ex: 5.0% or 4.2%). If your answer is correct (up to 0.1%), you will receive 50/ c. You will have 15 seconds to answer. Click on the OK button once ready.

Your estimation of orange tokens: .

Table I.5: Distribution of Estimations for the Orange Token

Estimation of orange tokens [0,10( [10,20( [20,30( [30,40( [40, This test is performed for the two waves of sessions. We conducted a Wilcoxon signed-rank test to compare the individual estimation of orange tokens by participants from wave 1 to those by participants from wave 2. We do not find any statistical difference between the two waves (p-value = 0.2069).

Estimation of yellow tokens

On the following screen, you will see a photograph with tokens of several colours. We ask you to estimate the percentage of yellow tokens. Enter a percentage with one decimal (ex: 5.0% or 4.2%). If your answer is correct (up to 0.1%), you will receive 50/ c. You will have 15 seconds to answer. Click on the OK button once ready.

Your estimation of yellow tokens: . This test is performed for the two waves of sessions. We conducted a Wilcoxon signed-rank test to compare the individual estimation of yellow tokens by participants from wave 1 to those by participants from wave 2. We cannot reject the fact that the two samples come from the same population (p-value = 0.3728). This two-estimation test was incentivised. The average earning is 0.09 euro (minimum earning: 0 euro; maximum earning: 0.5 euro). Note that the photograph used for the test is the same as the one shown on participants' screen in step 2.

Block 6

Extended Cognitive Reflection Test (CRT)

We administered the extended (seven-question) version of the CRT in which the original three questions [START_REF] Frederick | Cognitive reflection and decision making[END_REF] are augmented with four additional questions developed and validated by [START_REF] Toplak | Assessing miserly information processing: An expansion of the cognitive reflection test[END_REF]. Our measure of cognitive reflection is given by the total number of correct answers (from 0 to 7). Participants had 5 minutes in total to complete the CRT.

Taken from [START_REF] Frederick | Cognitive reflection and decision making[END_REF]:

1 A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?

cents [Correct answer: 5 cents; intuitive answer: 10 cents] 2 If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

minutes [Correct answer: 5 minutes; intuitive answer: 100 minutes]

3 In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? days The CRT score corresponds to the number of correct answers to the seven questions. This Block is only performed on the first wave of sessions.

[

Block 7

Availability heuristic 1

Based on [START_REF] Tversky | Judgment under uncertainty: Heuristics and biases[END_REF], we asked the 5 following questions (answers were computed using the following website in French: https://www.listesdemots.net), for which participants had 25 seconds to answer. This test intended to measure the availability bias of participants, that is whether participants make judgments about the likelihood of an event based on how easily an example, instance, or case comes to mind.

In a French language dictionary: 1 Are there more words where the letter I appears first or third?

What is your estimate of the ratio of words where the letter I appears first to words where the letter I appears third (a ratio of 1 means that there are as many words where the letter I appears first and where the letter I appears first or third):

[true ratio: 0.59] The score corresponds to the number of correct answers to the first question of each of the 5 groups of 2 questions. This block is performed for the two waves of sessions. We conducted a Wilcoxon signed-rank test to compare the individual estimation of yellow tokens by participants from wave 1 to those by participants from wave 2. We cannot reject the fact that the two samples come from the same population (p-value = 0.6002).

2

Block 8

Loss aversion

Following [START_REF] Brink | The effects of risk preference and loss aversion on individual behavior under bonus, penalty, and combined contract frames[END_REF] we use the following loss aversion test.

For this task, your potential losses will be subtracted from your total gains in the various tests.

For each line in the table on the following screen: please indicate whether you prefer option A or option B. Even if the table has a total of 10 rows, only one row will be randomly selected for the calculation of your gains or losses. Since all lines are likely to be selected for the calculation of your gains or losses, you must give equal weight to each of your decisions. At the end of the experiment, a number between 1 and 10 will be randomly selected by the computer. This number will determine which line will be used to calculate your gains or losses. The computer will randomly select a second number between 1 and 6 to determine the exact amount of your gains or losses.

Example:

You have chosen one option (A or B) for each of the ten rows in the table. Next, the computer randomly selects row 7 to be used to calculate your gains and losses.

-If you selected option A for line 7, then you will lose 2.40 euros if the second number chosen by the computer at random is 1, 2 or 3. If the second number chosen by the computer is 4, 5 or 6 you will win 5.00 euros.

-If you selected option B for line 7, then you will lose 1.00 euro if the second number chosen by the computer at random is 1, 2 or 3. If the second number chosen by the computer is 4, 5 or 6 you will win 1.00 euro. This block is performed for the two waves of sessions. We conducted a Wilcoxon signed-rank test to compare the individual loss aversion scores of participants from wave 1 to those of participants from wave 2. We cannot reject the fact that the two samples come from the same population (p-value = 0.0616).

Decision

Block 9

Reactance scale

Following [START_REF] Hong | Refinement of the Hong psychological reactance scale[END_REF], we asked participants to evaluate on a scale from 1 to 5 (1 = Strongly agree, 2 = Agree, 3 = Neither agree nor disagree, 4 = Disagree, 5 = Strongly disagree), the extent to which they agree or disagree with the following 11 statements54 :

1. Regulations trigger a sense of resistance in me.

2. I find contradicting others stimulating.

3. When something is prohibited, I usually think that's exactly what I am going to do. 4. I consider advice from others to be an intrusion.

5. I become frustrated when I am unable to make free and independent decisions. 6. It irritates me when someone points out things which are obvious to me. 7. I become angry when my freedom of choice is restricted.

8. Advice and recommendations induce me to do just the opposite. 9. I resist the attempts of others to influence me. 10. It makes me angry when another person is held up as a model to follow. 11. When someone forces me to do something, I feel like doing the opposite.

This test was not incentivised and yielded no earnings.

Table I.9: Distribution of Reactance Score

Reactance score [0,10( [10,20( [20,30( [30,40( [40, The score is computed as the ratio of correct answers involving famous names to the total of correct answers. This block is performed for the two waves. We conducted a Wilcoxon signed-rank test to compare the individual score of participants from wave 1 to those of participants from wave 2. We cannot reject the fact that the two samples come from the same population (p-value = 0.1645).

Block 11 Eyes gaze test

Following [START_REF] Bruguier | Exploring the nature of 'trader intuition[END_REF][START_REF] De Martino | In the mind of the market: Theory of mind biases value computation during financial bubbles[END_REF], we administered the Theory of Mind (ToM) test [START_REF] Baron-Cohen | Another advanced test of theory of mind: Evidence from very high functioning adults with autism or asperger syndrome[END_REF] to assess participants' theory of mind skills. In this task, participants looked at images of people's eyes and had to choose one of four feelings that best described the mental state of the person whose eyes were shown. Our ToM score is defined as the number of correct answers to the 36-question test.

Here is an example of one of the 36 questions in the test of [START_REF] Baron-Cohen | Another advanced test of theory of mind: Evidence from very high functioning adults with autism or asperger syndrome[END_REF]:

This test was not incentivised and yielded no earnings.

This test was performed only in the first wave of sessions and for reasons of comparability with other treatments involving markets and which are not studied in this paper. We do not make use of the results of this test since it is not relevant for the purpose of the paper. We do not report descriptive statistics for this test.

Block 12 Demographic data

We asked participants about a few demographic questions: age, gender, diploma, grades, socio-professional category, colour blindness, number of previous participation in experimental sessions, mother tongue.

Block 13

Gambling fallacy test

This test is taken from [START_REF] Corgnet | What makes a good trader? On the role of intuition and reflection on trader performance[END_REF]. Consider a wheel divided into 100 equal parts labelled with the numbers 1 to 100. Each year we spin this wheel and the arrow has an equal probability of stopping on each part numbered 1 to 100. On the next screen, you will be asked to make one prediction at a time for each of the 10 turns of the wheel that will be performed. This prediction concerns the part of the wheel on which the arrow will stop: part R between 1 and 55 (inclusive) or part B between 56 and 100 (inclusive). For the payoffs, we will randomly take one of your 10 predictions so that it is in your interest to always make the best possible prediction.

For the randomly selected prediction (between 1 and 10) you will receive 50 cents if it is correct; otherwise you will receive 0 cent. Once you have made your decision, click on the "Spin the Wheel" button. Once the wheel has spun and selected a number, you will move on to the next prediction. Note that to simplify the appearance of the wheel, it is only divided into 2 parts (R and B).

Enter your prediction below and click on "Spin the Wheel". The arrow will fall on the part:

• R • B
Of the wheel.

This test was incentivised. The average earning is 0.24 euro (minimum earning: 0 euros; maximum earning: 0.5 euro). This block is only performed in the second wave of sessions. ----------------------------------------------You are 7 people participating in this experiment. Among the 7 participants, one of you has been randomly chosen to perform a different task from the other 6 participants. This participant does not know the task that the other 6 participants will perform during this experiment. Specific instructions for the randomly selected participant You are the selected participant. You have been selected to perform a different task from the other 6 participants.

Distribution of Colour R Choices in the Gambling Fallacy Task

Your task is to:

-put all the tokens in an opaque bag; -pick a token from the bag, tick the colour of the token on your computer screen, tick the colour of the token on the sheet of paper in front of you, put the token back into the opaque bag (so that the contents of the bag always remains the same), mix the tokens, and again pick a token from the bag, tick the colour of the token on your computer screen, tick the colour of the token on the sheet of paper, put the token back in the bag, mix the tokens, and so on until you have drawn a total of 300 tokens;

-to sign the sheet of paper at the end of your task.

Your earnings consist of a fixed amount of 15 euros. If you do not complete your task in an hour, or if you make a mistake (i.e., tick the wrong colour), you will only be paid 10 euros. You will be under the supervision of an experimenter at all times.

It is expected that you will take an average of 10 seconds to pull a token, tick the colour of the token on your computer, tick the colour on the sheet of paper, mix the tokens. A timer on the computer will tell you if you are on time.

Specific instructions for the other participants

You are not the participant selected to draw the tokens.

The task of the randomly selected participant is:

-to put all the tokens in an opaque bag;

-to pick a token from the bag, tick the colour of the token on the computer screen, tick the colour of the token on a sheet of paper, put the token back into the opaque bag (so that the content of the bag always remains the same), mix the tokens, and again pick a token from the bag, tick the colour of the token on the computer screen, tick the colour of the token on the sheet of paper, put the token back in the bag, mix the tokens, and so on until he or she draws 300 tokens in total;

-to sign the sheet of paper at the end of the task.

The participant selected to draw the tokens will be paid 15 euros for the task if he or she finishes on time, i.e., in one hour. A timer will be displayed on the screen to help this participant find the right pace.

Your task: You will play for 300 periods.

Each period, your task is to decide how much you are willing to pay for a lottery that gives you the following payoffs (which may be negative) depending on the colour of the token drawn by the randomly selected participant:

• Blue: 10 cents The outcome of the lottery in one period is independent of the outcome of the lottery in another period: in each period a new token is drawn into the bag which has strictly the same content in each period. Remember that the randomly selected participant who draws the tokens must pick the token from the bag, tick the colour of the token on the computer, tick the colour on a sheet of paper, put the token back into the opaque bag, so that the content of the bag always remains the same, mix the tokens, and again pull a token into the bag, tick the colour of the token on the computer, tick the colour on the sheet of paper, put the token back in the bag, mix the tokens and so on, until it does so for a total number of 300 tokens.

Your task:

To make your decisions, you will use the fixed amount of 12 euros (1200 cents) that you were attributed to answer the tests during the first experimental session. This initial endowment is intended both to allow you to pay the lottery and to deal with the possibility of a yellow token being drawn. The earnings for each period are added to this initial endowment.

In addition, we make you a loan of 10 euros (1000 cents) for liquidity reasons, which you will repay at the end of the experiment.

If your endowment is no longer sufficient to cover the actual occurrence of a yellow token, you will no longer be able to participate in the experiment and you will only earn your variable payoffs acquired during the tests as well as 5 euros for showing-up.

You can select on your screen any price between 0 and 50 cents up to which you would be willing to buy the lottery.

The computer randomly selects an integer from 1 to 50.

If the price you indicate is greater than or equal to the number selected by the computer, then you buy the lottery for the price equal to the number selected by the computer.

If the price you indicate is strictly lower than the number selected by the computer, then you keep your endowment and do not buy the lottery.

Each period, your payoff, if you actually buy the lottery, is given by: Lottery payoff -price paid to purchase the lottery Your total earnings over the 300 periods are given by: 1200 cents of fixed wage earned in step 1 + (lottery payoff -price you paid to buy the lottery) × 300 periods + variable earnings in step 1 + 5 euros of show-up fee.

Example 1

You have entered a price of 28 at which you are ready to buy the lottery.

The computer randomly selects between 1 and 50 the number 12. In this case, the price you have indicated is higher than the selected number, so you buy the lottery for 12 cents that corresponds to the number selected by the computer. This lottery will give you:

• 10 cents if the token drawn is blue, in which case your payoff for this period is -2 cents (10-12).

• 20 cents if it is red, in which case your payoff for this period is 8 cents (20-12).

• 30 cents if it is orange, in which case your payoff for this period is 18 cents (30-12).

• 40 cents if it is green, in which case your payoff for this period is 28 cents (40-12).

• 50 cents if it is purple, in which case your payoff for this period is 38 cents (50-12).

• -1,000 cents if it is yellow, in which case your payoff for this period is -1012 cents (-1000-12).

Example 2

You have entered a price of 21 and the computer randomly selects between 1 and 50 the number 43.

In this case, the price you have indicated is lower than the selected number, so you will not buy the lottery.

In this case, your payoff is 0 for this period.

Information:

At the end of each period, you will be informed about the token that has been drawn, your payoff for the lottery, as well as your available cash which is equal to your initial endowment (2200 cents) plus or minus the accumulated gains and losses for buying (or not) the lottery.

You will also be able to see this information at the bottom of your screen for all periods before the current period.

At the end of the experiment, if you wish, you can have a look at the sheet of paper signed by the participant who drew the tokens. This will allow you to check that the sequence of drawn tokens is correct.

Decision-making time:

To ensure that the experiment is completed on time, we expect you to make your decision within 10 seconds in each period.

Note that you can take a little more time at the beginning of the experiment and that you are expected to make your decisions more quickly over time.

You are given 30 seconds in the first period and 20 seconds in the second period.

From the third period onwards, you will have 10 seconds to make your decision. A timer on the screen will indicate the time you have to enter a price using the cursor and validate your decision. If you do not enter a price on the screen and validate your decision in time, the number indicated by the cursor will be selected.

II Robustness checks for hypotheses

The results of sensitivity analyses for each hypothesis will be provided below. In line with our first four hypotheses, we first focus on the change in bids as a result of observing or suffering a tail event. Let ∆b = b τ+1b τ , where τ is the period in which the first tail event was observed.

II.1 Hypothesis 1

Our robustness checks vary (1) the prior probability for the tail event (π), (2) the weight for the prior (η), and (3) the degree of risk and loss aversion (α and λ).

Figure II.1.1 shows the relationship between ∆b and the prior for the tail event, π, in case risk-averse investors observed the tail event without suffering tail losses, under EUT with α = 0.75 (panel (a)) and PT with α = 0.75 and λ = 2.0 (panel (b)). In each panel, four combinations of weights for the prior (η, 100 (thin) vs. 300 (thick)) and the recency bias (ρ i , 1.0 (solid) vs. 0.5 (dashed)) are considered. Thus in the figure, a thin solid line stands for (η, ρ i ) = (100, 1.0), a thick dashed line for (η, ρ i ) = (300, 0.5), etc.

Two observations can be derived from Figure II.1.1. First, the magnitude of the drop in bids is smaller when η = 300 (thick lines) than when η = 100 (thin lines) for both values of ρ i , regardless of the value of π. ∆b is negative for this set of parameters which shows the robustness of Hypothesis 1 according to which bids tend to decrease after a tail event has been observed yet not suffered. This is straightforward: the higher the weight of the prior, the smaller is the impact of the tail event on the bid. Second, the magnitude of changes in bids, |∆b|, is larger for ρ i = 0.5 (dashed lines) than for ρ i = 1.0 (solid lines) for both values of η, although the differences are smaller for η = 300. Thus, Hypothesis 1 is robust to variations in the weights on the prior and in the value of the prior probability of the tail event, while holding the preference parameters constant. For EUT investors (panel (a)), the magnitude of the change in bids |∆b|, is larger for ρ i = 0.5 (dashed line) than for ρ i = 1.0 (solid) for all the four values of α considered. For PT investors, |∆b| is larger for ρ i = 0.5 (dashed line) than for ρ i = 1.0 (solid line) for α = 0.75 and 1.0, but not necessarily so for the other values of α (panel (b)). Furthermore, for PT investors, |∆b| is larger for ρ i = 0.5 (dashed line) than for ρ i = 1.0 (solid line) for λ = 1.0 or 1.5, but not for the larger value of λ (panel (c)). These observations suggest that, for some range of parameters, the model does not support the second part of Hypothesis 1. But this is due to bids reaching the lower bound (i.e., zero) after the tail event, as one can observe in Figure II.1.3 that shows that PT investors with small values of α or high values of λ (panels (a), (c), and (d)) may respond to the tail event by bidding zero afterwards. But because their pre-tail event levels are low, especially when there is a recency bias (ρ i = 0.5), |∆b| values can become smaller for investors with recency bias (ρ i = 0.5) than those without ρ i = 1.0 contrary to Hypothesis 1.

(a) α = 0.25, λ = 1.0 (b) α = 0.75, λ = 1.0 �-� �-� �-� �-� ���� ����� �+� �+� �+� �+� �+� ���� � �� �� �� �� ��� �-� �-� �-� �-� ���� ����� �+� �+� �+� �+� �+� ���� � �� �� �� �� ��� (c) α = 0.25, λ = 2.0 (d) α = 0.75, λ = 2.0 �-� �-� �-� �-� ���� ����� �+� �+� �+� �+� �+� ���� � �� �� �� �� ��� �-� �-� �-� �-� ���� ����� �+� �+� �+� �+� �+� ���� � �� �� �� �� ���

II.2 Hypothesis 2

As for Hypothesis 1, we vary (1) the prior probability for the tail event (π), (2) the weight for the prior (η), and (3) degree of risk and loss aversion (α and λ). In each panel, four combinations of weights for the prior (η, 100 (thin) vs. 300 (thick)) and the recency bias (ρ i , 1.0 (solid) vs. 0.5 (dashed)) are considered.

Two observations can be derived from Figure II.2.1. First, bids increase after PT investors suffer from the tail event, and the magnitude of the increase tends to be larger when ρ i = 0.5 (dashed line) than when ρ i = 1.0 (solid line). Second, even EUT investors can increase their bids as a result of suffering the tail event, which is due to the limited liability. Now we fix η = 100 and π = 0.01 and vary α and λ. For EUT investors (panel (a)), bids decrease less when risk aversion decreases (i.e., the larger α). For PT investors, bids increase less for a larger α and a smaller λ. In addition, for PT investors, except when α = 1.0 and λ = 1.0, the increase in bids is larger for ρ i = 0.5 (dashed line) than for ρ i = 1.0 (solid line). ∆b is positive for a large set of parameters which shows the robustness of Hypothesis 2 according to which bids tend to increase after a tail event has been observed and suffered.

III Model with emotions III.1 Anger and losses

In PT, investors can attenuate risk seeking in the loss domain by swiftly adjusting their reference level of wealth to the new circumstances. We consider the following specification of the dynamics of the reference wealth level:

R i t =          ω i -R i t-1 + (1 -ω i -)w i t if w i t < R i t-1 ω i + R i t-1 + (1 -ω i + )w i t otherwise
where R i 0 = w i 0 = 1, 200 being the initial endowment of investors in the experiment. The investor's reference wealth level evolves as a weighted average of the previous reference and current wealth level. However, we allow the weight placed on the previous reference wealth level (ω i -and ω i + ) to depend on whether the investor is in the loss domain, i.e., w i t < R i t-1 or not. Note that when ω i -= ω i + = 1, the reference wealth level remains constant at the initial wealth level as assumed in the main model of Section 4.1. When ω i -= ω i + = 0, the reference wealth level is immediately adjusted to the new wealth level regardless of whether the investor has suffered a loss.

In our formulation, ω i

-captures the reluctance of investors to make peace with their losses. Whenever 0 ≤ ω i -< 1, investors partly adjust their reference wealth level to reflect their current wealth. In particular, when ω i -= 0, investors suffering tail losses immediately adjust their reference wealth to the current level of wealth thus 'making peace with their losses'. This will prevent investors from exhibiting risk-seeking behaviour immediately after incurring tail losses. 55 The parameter ω i + captures investors' reluctance to adjust their reference wealth level in the face of gains. We assume ω i -≥ ω i + , that is, investors are more reluctant to adjust their reference wealth level to accumulated losses than to gains.

In Figure III.1.1, we simulate the bids around the tail event for a PT investor (λ i = 2.0 and α i = 0.75) who adjust reference level immediately in the gain domain (ω i + = 0.0) but may not do so in the loss domain. We consider four values of ω i -0.0 (top), 0.25 (second row), 0.5 (third row), and 1.0 (bottom). With ω i -= 0.0, the investors immediately 'make peace with their losses' while they never do so with ω i -= 1.0. The top panel shows that with ω i -= 0.0, investors tend to decrease their bids even after tail losses have been suffered. By contrast, when investors do not adjust their wealth level to losses (i.e., ω i -= 1.0), their bids increase after tail losses and continue to stay at high level. For ω i -= 0.25 (the second row), we observe the increase in bids after suffering from the tail loss is temporary. After three periods, the bids starts to decline in this case.

III.2 Fear and hope

We extend our main model to account for the effect of fear and hope associated with tail events on investor beliefs. In order to separate the effect of tail events on beliefs from that on preferences, we consider only investors that have observed but not suffered the tail event. 56 The emotional weight assigned to the tail event is captured by variable s 5,j in the beliefs equation (2), which takes value µ > 0 when the tail event is observed in period j and zero otherwise. The case µ > 1 (0 < µ < 1) captures fear (hope) because it gives an excessive (insufficient) weight to the tail event compared with the emotionless investor (µ = 1) when updating beliefs. In our setup, hopeful investors are those that feel relief when observing the tail event without incurring tail losses.

The top panels of Figure III.2.1 show that PT investors that are fearful (µ = 4 and µ = 2) are more likely to decrease their bids than investors that experience hope (µ = 0.2 and µ = 0.25) as a result of observing the tail event. 57 Emotional arousal is also likely to have an impact on beliefs when tail losses are suffered, leading to increased pessimism [START_REF] Kuhnen | Asymmetric learning from financial information[END_REF]. This effect could potentially counterbalance the increase in bids captured in Hypothesis 2. In particular, if emotional arousal after tail losses triggers fear rather than anger, we would expect tail losses to prompt a decrease rather than an increase in bids [START_REF] Lerner | Emotion and decision making[END_REF]. The 55 This sluggish adjustment of the reference level of wealth bears some resemblance with the model in [START_REF] Barberis | Prospect theory and asset prices[END_REF]. However, in our model, the adjustment process applies to the reference wealth level directly and not to the loss-aversion parameter.

56 Although this separation is clear in our model because fear and hope only affect beliefs, [START_REF] Kuhnen | The influence of affect on beliefs, preferences, and financial decisions[END_REF] have shown that emotions, such as anxiety, can also decrease the preference for risk. 57 The effect of hope and fear on bids after tail events are observed, yet not suffered, is more pronounced when investors suffer from a recency bias (i.e., ρ i = 0.5) as is shown in panel (a) in

III.3 Emotional arousal, bankruptcy and earnings

We analyse the effect of varying ω -and µ on the likelihood of bankruptcy and final earnings, holding ω + = 0.0 while changing the other parameters in our simulated model. 58 We summarise our regression results in Table III.1.

Conjecture A shows that anger-prone investors exhibiting high levels of emotional arousal bid aggressively after observing tail losses. Because these investors tend to place high bids, they are more likely to go bankrupt, as confirmed by the positive and significant coefficients of ω -in columns ( 2) and (3) in Table III.1. It follows that anger impacts investor wealth negatively when bankruptcy is possible, which is 58 We keep ω + = 0.0 constant while varying ω -because, in our model, it is the best way to capture the impact of anger. We have used the following set of parameter values: π i ∈ {0.005, 0.0075, 0.01, 0.0125}; η i ∈ {50, 100, 300}; α i ∈ {0.25, 0.5, 0.75, 1}; λ ∈ {1.0, 1.5, 2.0, 2.5}; ρ i ∈ {0, 0.25, 0.5, 0.75, 1}; µ i ∈ {0.25, 0.5, 1, 2, 4}, and ω i -∈ {0, 0.5, 1}. For each of the 15 sequences of the realizations of the colour of the tokens during the experiment, we generate 25 sequences of prices for the lottery. Thus, for each possible set of parameter values, we run 375 simulations. In each simulation, we collect data on average bids, the occurrence of bankruptcy and on final earnings. For each possible number of tail events (0, 1, 2, 3 and 4) and set of parameter values, we then take the average of these variables across the 375 simulations. These values provide the data points in our regression analyses. For the bankruptcy regressions, we only consider cases in which the number of tail events is at least equal to two. Given the parameters of our experiment, this is the number of tail events required to observe bankruptcy.

when at least two tail events occur (see column ( 5)). By contrast, when tail events are few and bankruptcy is not an eventuality, then anger does not significantly affect investor wealth (see column ( 4)).

Finally, Conjecture B shows that fearful investors bid conservatively. We thus expect that they will be less likely to go bankrupt, which is confirmed by the negative and significant coefficients of µ in columns ( 2) and (3) in Table III.1. Fearful investors bid low (see column (1)) and thus often fail to buy the asset and collect the corresponding payoffs. This is why fear leads to an overall decrease in investor wealth (see columns ( 4) and ( 5)). We summarise our predictions regarding bankruptcy and earnings in Conjecture C.

III.4 Robustness checks for conjectures III.4.1 Conjecture A

We fix η = 100, π = 0.01, µ = 1.0 and vary α and λ to see the robustness of the effect of {ω -, ω + }. In each panel, three combinations of {ω -, ω + } ({1.0, 1.0} (thin solid lines), {1.0, 0.0} (thin dashed lines), and {0.0, 0.0} (thick solid lines)) are considered. The figure shows that the increase in bids as a result of suffering from the tail event is not observed for {ω -, ω + } = {0.0, 0.0} unless α = 1.0. For {ω -, ω + } = {1.0, 0.0}, on the contrary, the increase in bids as a result of suffering from the tail event is observed for most values of α considered except for α ∈ {0.25, 0.5} with ρ i = 0.5. In each panel, three combinations of {ω -, ω + } ({1.0, 1.0} (thin solid lines), {1.0, 0.0} (thin dashed lines), and {0.0, 0.0} (thick solid lines)) are considered. The figure shows that the increase in bids as a result of suffering from the tail event is not observed for {ω -, ω + } = {0.0, 0.0} for the four values of λ considered. However, for {ω -, ω + } = {1.0, 0.0}, for λ ∈ {2.0, 2.5}, the increase in bids as a result of suffering from the tail event is observed both with and without recency bias.

III.4.2 Conjecture B

Here we consider the effect of varying µ in various combinations of parameters. Figure III.4.3 exhibits a negative relationship between ∆b and µ for all four combinations of η and ρ i , regardless of whether investors suffered or not the tail event. Note that ∆b becomes the same for µ = {1, 2, 4} for (η, ρ i ) = (100, 1.0) or for µ = {2, 4} for (η, ρ i ) = (100, 0.5) in panel (a), because investors reduced their bid to zero after observing the tail event, while the pre-tail event bids were similar in all of these cases. Wealth -18×10 -4 * * * -26×10 -4 * * * -22×10 -4 * * * -15×10 -4 * * * -27×10 -4 * * * -21×10 -4 * * * (3×10 -4 ) (4×10 -4 ) (3×10 -4 ) (2×10 -4 ) (3×10 -4 ) (1×10 -4 ) Number of Tail Events -1.571 We note that the p-value for 'Prob > χ 2 ' is not reported in some instances in Stata and we thus show it as missing '-'. This is because we use robust standard errors. Not using robust standard errors, we obtain similar results and the p-value for Prob > χ 2 is less than 0.001. a: We had to conduct a linear panel probability model for regressions (1) to (3) because the probit panel model could not be estimated.

Wealth 21×10 -6 19×10 -6 28×10 -6 -6×10 -6 (46×10 -6 ) (46×10 -6 ) (38×10 -6 ) (39×10 -6 ) Period -18×10 -4 * * * -15×10 -4 * * * -21×10 -4 * * * -13×10 -4 * * * (4×10 -4 ) (4×10 -4 ) (4×10 -4 ) (4×10 -
Wealth -18×10 -6 84×10 -6 20×10 -6 -12×10 -6 15×10 -6 -6×10 -6 (60×10 -6 ) (73×10 -6 ) (46×10 -6 ) (51×10 -6 ) (55×10 -6 ) (39×10 -6 ) Period -10×10 -4 * -23×10 -4 * * * -15×10 -4 * * * -11×10 -4 * * -17×10 -4 * * * -14×10 -4 * * * (6×10 -4 ) (7×10 -4 ) (4×10 -4 ) (5×10 -4 ) (5×10 -4 ) (4×10 -
Wealth -49×10 -6 101×10 -6 34×10 -6 12×10 -8 64×10 -6 33×10 -6 (58×10 -6 ) (85×10 -6 ) (45×10 -6 ) (48×10 -6 ) (72×10 -6 ) (38×10 -6 ) Period -13×10 -4 * * -25×10 -4 *** -20×10 -4 *** -18×10 -4 *** -24×10 -4 *** -21×10 -4 *** (6×10 -4 ) (7×10 -4 ) (4×10 -4 ) (5×10 -4 ) (7×10 -4 ) (4×10 -
Wealth -56×10 -6 -80×10 -6 -74×10 -6 16×10 -6 -54×10 -6 -15×10 -6 (64×10 -6 ) (111×10 -6 ) (62×10 -6 ) (47×10 -6 ) (103×10 -6 ) (51×10 -6 ) Period -11×10 -4 * -14×10 -4 -13×10 -4 ** -17×10 -4 *** -22×10 -4 ** -19×10 -4 *** (6×10 -4 ) (10×10 -4 ) (6×10 -4 ) (5×10 -4 ) (9×10 -4 ) (5×10 -
6×10 -6 -3×10 -6 -94×10 -6 77×10 -6 2×10 -6 (22×10 -6 ) (21×10 -6 ) (15×10 -6 ) (65×10 -6 ) (63×10 -6 ) (49×10 -6 ) Period -23×10-5 -55×10-5** -38×10-5** -10×10 -4 -26×10 -4 *** -18×10 -4 *** (20×10-5) (23×10-5) (15×10-5) (6×10 -4 ) (7×10 -4 ) (5×10 -
Table IV.15: Bids,Tail Losses and Anger (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period. We note that the p-value for 'Prob > χ 2 ' is not reported in some instances in Stata and we thus show it as missing '-'. This is because we use robust standard errors. Not using robust standard errors, we obtain similar results and the p-value for Prob > χ 2 is less than 0.001. a: We had to conduct linear panel probability models because probit panel models could not be estimated.

Table IV.18: Bids,Tail Events and Fear (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period. Wealth -60×10 -6 44×10 -6 10×10 -6 -10×10 -6 (44×10 -6 ) (41×10 -6 ) (41×10 -6 ) (36×10 -6 ) Period -14×10 -4 * * * -12×10 -4 * * * -23×10 -5 -30×10 -5 (4×10 -4 ) (4×10 -4 ) (39×10 -5 ) (34×10 < 0.001 < 0.001 < 0.001 < 0.001 a: In the second wave of data collection, we have not elicited hopeful personality for the sake of reducing the length of the questionnaire, which was conducted online. Our new approach was to elicit the valence of emotions (anger, fear, joy and sadness) in a survey conducted at the end of the experiment. * * * p< 0.01, * * p< 0.05, * p< 0.1 In Online Appendix IV.7, we show that the results in Table A.1 are robust to using an instrumental variable panel regression.

Table IV.20: Arousal and Tail Events (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period. < 0.001 < 0.001 * * * p< 0.01, * * p< 0.05, * p< 0.1 a: In the second wave of data collection, we have not elicited hopeful personality for the sake of reducing the length of the questionnaire, which was conducted online. Our new approach was to elicit the valence of emotions (anger, fear, joy and sadness) in a survey conducted at the end of the experiment.

52

IV.8 For Table A Prob > χ 2 (F) 0.617 < 0.001 Observations 112 167 * * * p< 0.01, * * p< 0.05, * p< 0.1 Baseline decision arousal index is defined as BFA except that it uses recordings for decision arousal instead of feedback arousal. We control for decision arousal because the literature on the 'somatic marker hypothesis' has suggested it affects one's likelihood of going bankrupt in gambling tasks (see [START_REF] Bechara | Deciding advantageously before knowing the advantageous strategy[END_REF][START_REF] Bechara | The somatic marker hypothesis: A neural theory of economic decision[END_REF].

53

IV.9 For Table A.3 Table IV.22: Dynamics of change in bids, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. A change in bids is calculated as the difference in bids between two consecutive periods.

Figure 1 :

 1 Figure 1: Basic Emotions in the Arousal/Valence/Approach Space

Figure 2 :

 2 Figure 2: Dynamics of Bids around the Tail Event for Three Values of ρ for PT Investors with α = 0.75, λ = 2.0 (top) and EUT Investors with α = 0.75 (bottom). Blue: not suffered. Red dashed: suffered.

  Figure A.1: Actual Sequence of Token Draws for all 15 Sessions of Each Wave.

Figure A. 2 :

 2 Figure A.2: Typical Shape of Event-Related Electrodermal Activity[START_REF] Christopoulos | The body and the brain: measuring skin conductance responses to understand the emotional experience[END_REF]

•

  Figure II.1.1: Relationship between the Change in Bids after Observing (But Not Suffering) the Tail-Event (∆b) and the Prior for the Tail-Event (π) for Two Values of Weight for the Prior η = 100 (thin) and 300 (thick) and Two Values of Recency Bias ρ i = 1.0 (solid) and 0.5 (dashed). (a) risk-averse EUT (α = 0.75) and (b) risk-averse PT (α = 0.75, λ = 2.0) (a) EUT (π = 0.01, η = 100) (b) PT (π = 0.01, η = 100) (c) PT (π = 0.01, η = 100)

Figure

  Figure II.1.3: Dynamics of Bids around the (Observed But Not Suffered) Tail Event for Two Values of ρ i (1.0 (solid) and 0.5 (dashed)) with PT Agents with Four Combinations of the Degree of Risk (α ∈ 0.25, 0.75) and Loss Aversion (λ ∈ 1.0, 2.0).

  Figure II.2.1 shows the relationship between ∆b and the prior for the tail event π, in case the tail event was both observed and suffered by risk-averse EUT investors with α = 0.75 (panel (a)) and risk-averse PT investors with α = 0.75, λ = 1.5 (panel (b)).

  Figure II.2.2 shows the relationship between ∆b and the degree of risk aversion α for two values of ρ i (1.0 (solid line) vs. 0.5 (dashed line)) for EUT investors (panel (a)) and PT investors (panel (b)) with two values of λ (1.0 (thin line) and 2.0 (thick line)). Figure II.2.2 shows the relationship between ∆b and the degree of loss aversion, λ, for two values of ρ i (1.0 (solid line) vs. 0.5 (dashed line)) with two values of α (1.0 (thin line) and 0.75 (thick line)) (panel (c)).

  Figure II.2.1: Relationship between the Change in Bids after Observing (and Suffering from) the Tail Event (∆b) and the Prior for the Tail Event (π) for Two Values of Weight for the Prior η = 100 (thin) and 300 (thick) and Two Values of Recency Bias ρ i = 1.0 (solid) and 0.5 (dashed). (a) risk-averse EUT (α = 0.75) and (b) risk-averse PT (α = 0.75, λ = 2.0) (a) EUT (π = 0.01, η = 100) (b) PT (π = 0.01, η = 100) (c) PT (π = 0.01, η = 100)

  Figure III.1.1: Dynamics of Bids around the Tail Event for Three Values of ρ and Four Values of ω i -for PT Investors with α = 0.75, λ = 2.0, ω i + = 0.0. Blue: not suffered. Red dashed: suffered.

Figure

  Figure III.2.1 show that PT investors experiencing fear (µ = 4 and µ = 2) after suffering tail losses are less likely to increase their bids than those experiencing hope (µ = 0.5 and µ = 0.25).

Figure

  FigureIII.4.1 shows the relationship between ∆b and α (with λ = 2.0). Panel (a) shows the result for an agent without recency bias (ρ i = 1.0) and panel (b) shows the result for an agent with recency bias (ρ i = 0.5). In each panel, three combinations of {ω -, ω + } ({1.0, 1.0} (thin solid lines), {1.0, 0.0} (thin dashed lines), and

  Figure III.4.2 shows the relationship between ∆b and λ (with α = 0.75). Panel (a) shows the result for an agent without recency bias (ρ i = 1.0) and panel (b) shows the result for an agent with recency bias (ρ i = 0.5).

  Figure III.4.1: Relationship between (∆b) and α for Three Combinations of {ω -, ω + } ({1.0, 1.0} (thin solid lines), {1.0, 0.0} (thin dashed lines), and {0.0, 0.0} (thick solid lines)). (a) Without Recency Bias (ρ i = 1.0) and (b) With Recency Bias (ρ i = 1.0). λ = 2.0, η = 100, π = 0.01, µ = 1.0 (a) Without recency bias (ρ i = 1.0) (b) With recency bias (ρ i = 0.5)

  FigureIII.4.3: Relationship between (∆b) and µ for Four Combinations of η (100 (thin) vs. 300 (thick)) and ρ i (1.0 (solid) vs. 0.5 (dashed)), for Investors NotSuffering (panel (a)) andSuffering (panel (b)) the Tail Event. λ = 2.0, α = 0.75, ω -= ω + = 1.0, and π = 0.01

Table 1 :

 1 Table 1 summarises the composition of sessions. Composition of Sessions.

		Number of ses-	Number of par-	Composition of	Sequences	of
		sions	ticipants	groups	draws
	Wave 1	15	86	11 groups of 6	1
				4 groups of 5

Table 2 :

 2 Bids and Tail Events. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE	BID
		(1)	(2)
	BDM Thresholds	BDM10-or BDM40+ BDM20-or BDM30+
	Tail Event Dummy	-1.196 *	-0.833 *
		(0.712)	(0.462)
	BDM-a	-0.389 * * *	-0.262 * * *
		(0.082)	(0.058)
	Tail Event × BDM-Dummy	2.797 * *	1.377 *
		(1.187)	(0.706)
	Wealth	-22×10 -4 * * *	-21×10 -4 * * *
		(3×10 -4 )	(1×10 -4 )
	Number of Tail Events	-1.616 * * *	-1.631 * * *
		(0.176)	(0.094)
	Constant	33.346 * * *	33.312 * * *
		(2.894)	(2.772)
	Observations	18,384	37,267
	Number of investors	169	169
	Prob > χ 2	< 0.001	< 0.001
	a: BDM-= BDM10-[BDM20-] in regression (1) [(2)].
	* * * p< 0.01, * * p< 0.05, * p< 0.1
	Individual controls include gender, availability index, loss aversion, risk
	aversion and yellow prior; see the complete regression Table IV.1 in the
	Online Appendix for more details.

Table 3 :

 3 Bids, Availability Bias and Tail Events. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE			BID
		(1)	(2)	(3)	(4)	(5)	(6)
		High	Low	All	High	Low	All
	SAMPLE	Avail.	Avail.		Avail.	Avail.
		Bias	Bias		Bias	Bias
	BDM Thresholds		BDM10-or BDM40+			BDM20-or BDM30+
	Tail Event Dummy	-2.054 * *	0.480	0.208	-1.771 * * *	0.607	0.273
		(0.905)	(1.176)	(1.270)	(0.613)	(0.700)	(0.743)
	BDM-	-0.435 * * *	-0.326 * * *	-0.319 * *	-0.311 * * *	-0.193 * *	0.181 * *
		(0.113)	(0.117)	(0.126)	(0.079)	(0.085)	(0.090)
	Tail Event ×	4.579 * *	-0.296	0.253	0.426	2.205 * *	2.034 *
	BDM-Dummy	(1.663)	(1.723)	(1.861)	(0.975)	(1.017)	(1.079)
	High Availability Dummy	-	-	-3.440 *	-	-	-3.168 *
				(1.830)			(1.810)
	Tail Event ×	-	-	-2.039	-	-	-1.794 *
	High Availability Dummy			(1.526)			(0.945)
	BDM-×	-	-	-0.120	-	-	-0.137
	High Availability Dummy			(0.165)			(0.118)
	Tail Event × BDM-×	-	-	4.262 *	-	-	-1.502
	High Availability Dummy			(2.435)			(1.425)

Table 4 :

 4 Bids, Loss Aversion and Tail Events. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE			BID
		(1)	(2)	(3)	(4)	(5)	(6)
	SAMPLE	High	Low	All	High	Low	All
		Loss	Loss		Loss	Loss
		Aversion	Aversion		Aversion	Aversion
	BDM Thresholds		BDM10-or BDM40+			BDM20-or BDM30+
	Tail Event Dummy	-2.378 * *	0.417	0.443	-1.148 *	-0.376	-0.359
		(0.954)	(1.067)	(1.088)	(0.635)	(0.665)	(0.690)
	BDM-	-0.473 * * *	-0.280 * *	-0.279 * *	-0.334 * * *	-0.156 *	-0.170 *
		(0.110)	(0.121)	(0.124)	(0.080)	(0.084)	(0.088)
	Tail Event × BDM-Dummy	3.663 * *	1.726	1.659	2.209 * *	-0.022	-0.170
		(1.508)	(1.971)	(2.016)	(0.940)	(1.070)	(1.115)
	High Loss Aversion Dummy	-	-	-0.557	-	-	-0.289
				(1.791)			(1.763)
	Tail Event ×	-	-	-2.848 * *	-	-	-0.851
	High Loss Aversion Dummy			(1.429)			(0.925)
	BDM-×	-	-	-0.194	-	-	-0.162
	High Loss Aversion Dummy			(0.165)			(0.117)
	Tail Event × BDM-×	-	-	2.133	-	-	2.560 *
	High Loss Aversion Dummy			(2.495)			(1.438)

  * * p< 0.01, * * p< 0.05, * p< 0.1 Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.7 in the Online Appendix for more details.

						* * *	-1.631 * * *
		(0.208)	(0.304)	(0.176)	(0.105)	(0.175)	(0.094)
	Constant	32.476 * * *	24.488 * * *	33.826 * * *	31.930 * * *	24.715 * * *	33.576 * * *
		(2.809)	(4.947)	(3.244)	(2.657)	(4.589)	(3.119)
	Observations	10,354	8,030	18,384	21,103	16,164	37,267
	Number of investors	96	73	169	96	73	169
	Prob > χ 2	< 0.001	< 0.001	< 0.001	< 0.001	< 0.001	< 0.001

*

Table 5 :

 5 Bids, Tail Losses and Emotional Arousal. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE			BID
		(1)	(2)	(3)	(4)	(5)	(6)
	SAMPLE	No	Feedback	All	No	Feedback	All
	(Loss-averse investors)	feedback	arousal		feedback	arousal
		arousal			arousal
	BDM Thresholds		BDM10-or BDM40+			BDM20-or BDM30+
	Tail Event Dummy	-2.900 * *	-1.526	-3.731 * * *	-1.260	-0.404	-1.036
		(1.364)	(1.538)	(1.352)	(0.937)	(0.888)	(0.919)
	BDM-	-0.361 * * *	-0.584 * * *	-0.340 * * *	-0.197 * *	-0.486 * * *	-0.230 * *
		(0.129)	(0.212)	(0.127)	(0.092)	(0.152)	(0.091)
	Tail Event × BDM-Dummy	-3.045	2.481	-1.875	-1.155	2.777 * *	-1.508
		(2.729)	(2.048)	(2.737)	(1.588)	(1.188)	(1.569)
	Feedback Arousal Dummy	-	-	0.219	-	-	-0.076
				(0.192)			(0.144)
	Tail Event ×	-	-	2.547	-	-	-0.177
	Feedback Arousal Dummy			(1.911)			(1.279)
	BDM-×	-	-	-0.613 * *	-	-	-0.478 * *
	Feedback Arousal Dummy			(0.268)			(0.196)
	Tail Event × BDM-×	-	-	6.790 * *	-	-	5.718 * * *
	Feedback Arousal Dummy			(3.338)			(1.989)

  * * p< 0.01, * * p< 0.05, * p< 0.1 Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.10 in the Online Appendix for more details.

						* * *	-1.550 * * *
		(0.239)	(0.512)	(0.212)	(0.128)	(0.293)	(0.107)
	Constant	32.118 * * *	36.499 * * *	32.444 * * *	31.903 * * *	33.300 * * *	31.99 * * *
		(2.912)	(3.586)	(2.819)	(2.7)	(3.033)	(2.662)
	Observations	7,967	2,263	10,230	16,344	4,518	20,862
	Number of investors	95	95	95	95	95	95
	Prob > χ 2	< 0.001	< 0.001	< 0.001	< 0.001	< 0.001	< 0.001

*

Table 6 :

 6 Bids, Tail Losses and Anger. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE

  Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.13 in the Online Appendix for more details.

							4 )
	Number of Tail Events	-2.300***	-1.194***	-1.585***	-2.048***	-1.254***	-1.549***
		(0.395)	(0.226)	(0.212)	(0.192)	(0.119)	(0.107)
	Constant	31.308***	35.222***	34.308***	31.912***	34.016***	34.148***
		(3.093)	(4.741)	(3.042)	(2.615)	(4.570)	(2.891)
	Observations	4,885	5,345	10,230	10,115	10,747	20,862
	Number of investors	45	50	95	45	50	95
	Prob > χ 2	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001

* * * p< 0.01, * * p< 0.05, * p< 0.1

Table 7 :

 7 Bids and Fear. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE

  Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.16 in the Online Appendix for more details.

							4 )
	Number of Tail Events	-1.540***	-1.799***	-1.653***	-1.470***	-1.874***	-1.652***
		(0.248)	(0.258)	(0.179)	(0.130)	(0.140)	(0.095)
	Constant	38.415***	33.614***	33.496***	38.619***	32.936***	33.257***
		(3.987)	(2.703)	(3.107)	(3.898)	(2.429)	(2.980)
	Observations	10,305	7,844	18,149	20,692	16,106	36,798
	Number of investors	94	73	167	94	73	167
	Prob > χ 2	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001

* * * p< 0.01, * * p< 0.05, * p< 0.1

Table 8 :

 8 Model fitting exercise. Number (%) of participants for which a given model is the best fit according to the Akaike Information Criterion.

	#	Model

Table A .

 A 1: Arousal and Tail Events. Panel probit regressions with random effects and robust standard errors clustered at the individual levels in parentheses and session fixed effects included.

	VARIABLE	FEEDBACK AROUSAL DUMMY	DECISION AROUSAL DUMMY
		(1)	(2)	(3)	(4)
	BDM Thresholds	BDM10-or BDM40+	BDM20-or BDM30+	BDM10-or BDM40+	BDM20-or BDM30+
	Tail Event Dummy	1.172 * * *	1.199 * * *	-0.092	-0.093
		(0.158)	(0.107)	(0.212)	(0.114)
	Tail Event × BDM-Dummy	0.508 *	0.134	0.056	-0.159
		(0.291)	(0.169)	(0.349)	(0.181)
	BDM-Dummy	0.105 * * *	0.059 * * *	-0.026	-0.021
		(0.022)	(0.016)	(0.022)	(0.016)
	Fear Dummy a	0.034	0.024	-0.040	-0.016
		(0.074)	(0.073)	(0.066)	(0.063)
	Anger Dummy	0.055	0.059	-0.041	-0.057
		(0.065)	(0.063)	(0.057)	(0.052)

  * * p< 0.01, * * p< 0.05, * p< 0.1 Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.19 in the Online Appendix for more details. In Online Appendix IV.7, we show that the results in TableA.1 are robust to using an instrumental variable panel regression.

*

Table A .

 A 2: Bankruptcy, Earnings and Baseline Arousal. (1) Probit regressions, (2) Tobit (with a lower bound at zero) with robust standard errors clustered at the individual levels in parentheses.

	VARIABLE	BANKRUPTCY DUMMY	EARNINGS
		(1)	(2)
	Baseline feedback arousal index (BFA) (std)	-0.204	-245.183
		(0.203)	(260.180)
	BFA × Anger Dummy	0.010	280.660
		(0.279)	(330.071)
	BFA × Fear Dummy	-0.292	166.195
		(0.296)	(321.369)
	Anger Dummy	-0.184	-244.922
		(0.321)	(329.916)
	Fear Dummy	-0.344	-117.301
		(0.305)	(319.811)
	BFA × Anger × Number of Tail Events	-	-78.825
			(147.586)
	BFA × Fear × Number of Tail Events	-	62.442
			(141.085)
	BFA × Number of Tail Events	-	85.125
			(134.989)
	Anger × Number of Tail Events	-	175.942
			(161.950)
	Fear × Number of Tail Events	-	27.806
			(157.474)
	Number of Tail Events	-0.177	-611.674***
		(0.161)	(117.031)
	Constant	-0.329	3,379.458***
		(0.555)	(250.239)
	Prob > χ 2 (F)	0.617	< 0.001
	Observations	112	167
	* * * p< 0.01, * * p< 0.05,

* p< 0.1

Table A . 3 :

 A3 Dynamics of Change in Bids. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. A change in bids is calculated as the difference in bids between two consecutive periods. * * p< 0.01, * * p< 0.05, * p< 0.1 Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.22 in the Online Appendix for more details.

	VARIABLE	CHANGE IN BID
		(1)	(2)
	CHANGE IN BID in t-1	-	-0.280***
			(0.004)
	Tail Event Dummy in t-1	0.016	-0.007
		(0.375)	(0.369)
	Tail Event Dummy in t-2	0.432	0.444
		(0.410)	(0.382)
	Tail Event Dummy in t-3	0.013	0.141
		(0.416)	(0.383)
	Tail Event Dummy in t-4	-0.598	-0.619
		(0.410)	(0.382)
	Tail Event Dummy in t-5	-0.065	-0.187
		(0.379)	(0.373)
	BDM10-in t-1	-0.401***	-0.402***
		(0.080)	(0.079)
	BDM10-in t-2	0.063	-0.052
		(0.086)	(0.081)
	BDM10-in t-3	0.036	0.061
		(0.088)	(0.081)
	BDM10-in t-4	0.091	0.097
		(0.087)	(0.081)
	BDM10-in t-5	-0.117	-0.087
		(0.080)	(0.079)
	Tail Event × BDM10-Dummy in t-1	3.003**	2.977**
		(1.193)	(1.174)
	Tail Event × BDM10-Dummy in t-2	0.297	1.198
		(1.299)	(1.208)
	Tail Event × BDM10-Dummy in t-3	0.301	0.292
		(1.315)	(1.210)
	Tail Event × BDM10-Dummy in t-4	1.191	1.455
		(1.299)	(1.208)
	Tail Event × BDM10-Dummy in t-5	-2.945**	-3.002**
		(1.194)	(1.175)
	Wealth	-34×10 -6	-42×10 -6
		(39×10 -6 )	(44×10 -6 )
	Number of Tail Events	-0.034	-0.045
		(0.026)	(0.030)
	Constant	0.173	0.208
		(0.171)	(0.194)
	Observations	47,024	47,024
	Number of investors	169	169
	Prob > χ 2	0.329	< 0.001

*

Table A .

 A 4: Bids, Tail Losses and Anger-based PT. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	VARIABLE			BID
		(1)	(2)	(3)	(4)	(5)	(6)
	SAMPLE	Anger-	Anger-	All	Anger-	anger-	All
		based PT=1	based PT=0	based PT=1	based PT=0
	BDM Thresholds	BDM10-or BDM40+			BDM20-or BDM30+
	Tail Event Dummy	-4.036**	-2.252	-2.284*	-0.314	-1.296	-1.352
		(1.763)	(1.425)	(1.349)	(1.206)	(1.934)	(0.894)
	BDM-	-0.276*	-0.444***	-0.447***	-0.393***	-0.151*	-0.148*
		(0.149)	(0.118)	(0.112)	(0.110)	(0.083)	(0.079)
	Tail Event × BDM-Dummy	0.956	-2.796	-2.614	-1.711	-0.937	-0.844
		(3.303)	(2.845)	(2.691)	(1.865)	(1.564)	(1.494)
	Feedback Arousal Dummy	0.176	-0.239	-0.243	0.003	-0.237*	-0.250**
		(0.219)	(0.175)	(0.166)	(0.170)	(0.129)	(0.124)
	Tail Event × Feedback	-0.572	3.199*	3.220*	-3.282**	1.457	1.488
	Arousal Dummy	(2.506)	(1.791)	(1.697)	(1.650)	(1.167)	(1.117)
	BDM-× Feedback	-0.568*	0.227	0.229	-0.170	-0.177	-0.176
	Arousal Dummy	(0.308)	(0.244)	(0.231)	(0.230)	(0.175)	(0.168)
	Tail Event × BDM-× Feedback	4.872	6.152*	6.032*	9.301***	2.145	2.114
	Arousal Dummy	(4.292)	(3.320)	(3.142)	(2.489)	(1.879)	(1.796)
	Anger-based PT Dummy	-	-	2.148*	-	-	2.410**
				(1.101)			(1.081)
	Tail Event × Anger-based	-	-	-1.663	-	-	1.198
	PT Dummy			(2.475)			(1.635)
	BDM-× Anger-based PT Dummy	-	-	0.162	-	-	-0.255
				(0.209)			(0.148)
	Tail Event × BDM-× Anger-based	-	-	3.394	-	-	-1.032
	PT Dummy			(4.733)			(2.600)
	Feedback Arousal × Anger-based	-	-	0.416	-	-	0.259
	PT Dummy			(0.308)			(0.230)
	BDM-× Feedback Arousal ×	-	-	-3.583	-	-	-4.731**
	Anger-based PT Dummy			(3.419)	-	-	(2.187)
	Tail Event × Feedback Arousal	-	-	-0.789*	-	-	0.014
	× Anger-based PT Dummy			(0.432)			(0.311)
	Tail Event × BDM-× Feedback Arousal	-	-	-1.379	-	-	7.218**
	× Anger-based PT Dummy			(5.969)

  * * p< 0.01, * * p< 0.05, * p< 0.1 Individual controls include gender, availability index, loss aversion, risk aversion and yellow prior; see the complete regression TableIV.23 in the Online Appendix for more details.

							4 )
	Number of Tail Events	-1.965***	-1.582***	-1.653***	-2.069***	-1.553***	-1.654***
		(0.387)	(0.203)	(0.179)	(0.207)	(0.107)	(0.095)
	Constant	42.372***	29.714***	32.406***	42.163***	29.896***	32.373***
		(4.143)	(3.128)	(2.895)	(3.898)	(2.965)	(2.860)
	Observations	5,213	12,936	18,149	10,513	26,285	36,798
	Number of investors	48	119	167	48	119	167
	Prob > χ 2	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001

*

  You are looking at six rings, all of which are of poor quality. How likely do you think it is that these rings were produced by the machine on the left (L) (select your answer below)? (correct answer: You observe six rings, three of which are of good quality and three of poor quality. How likely do you think it is that these rings were produced by the machine on the left (L) (select your answer

	Question 3. 100%)
	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%
	Question 4. below)? (correct answer: 70%)
	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%
	This test was incentivised: participants received 0.5 euros for each correct answer. The average earning is 0.41
	euro (minimum earning: 0 euro; maximum earning: 2 euros).
			Table I.1: Distribution of Bayesian updating scores
				Bayesian updating scores % of participants
					0			44.19
					1			33.72
					2			19.77
					3			1.16
					4			1.16
					Mean			0.81
				Standard deviation		0.87
	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%
	Question 2. You are looking at a poor quality ring. How likely do you think it is that this ring was
	produced by the machine on the left (L) (select your answer below)? (correct answer: 70%)
	100%	90%	80%	70%	60%	50%	40%	30%	20%	10%	0%

Table I .

 I 3: Descriptive Statistics and Cronbach-α for the Personality Traits

	Personality trait	α	Mean	Standard devia-	Median
				tion
	HONESTY-HUMILITY	0.79	33.55	7.34	33
	(wave 1)
	EMOTIONALITY	wave 1: 0.80	32.22	7.18	33
	(2 waves)	wave 2: 0.63	31.58	4.57	31
		waves 1 & 2:	31.93	6.06	32
		0.68
	EXTRAVERSION	0.79	35.68	6.06	36
	(wave 1)
	AGREEABLENESS	0.73	30.87	6.03	31
	(wave 1)
	CONSCIENTIOUSNESS	0.81	36.28	6.40	36
	(wave 1)
	OPENNESS TO EXPERIENCE	0.67	36.14	5.62	36
	(wave 1)
	Fear	wave 1: 0.59	8.80	2.72	8
	(2 waves)	wave 2: 0.55	8.04	1.70	8
		waves 1 & 2 0.27	8.43	2.31	8
	Liveliness (hopefulness)	0.68	7.53	1.60	8
	(wave 1)
	Anger	wave 1: 0.86	5.15	2.33	5
	(2 waves)	wave 2: 0.52	5.64	1.78	6
		waves 1 & 2:	5.40	2.08	5
		0.65
	HONESTY-HUMILITY score is defined as the sum of answers to questions: 6, 30R, 54, 12R, 36, 60R, 18, 42R, 24R, 48R, where R stands for reversed item
	(which is scored as: 6-personality test score); EMOTIONALITY score is defined as the sum of answers to questions: 5, 29, 53R, 11, 35R, 17, 41R, 23, 47,
	59R; EXTRAVERSION score as the sum of answers to questions: 4, 28R, 52R, 10R, 34, 58, 16, 40, 22, 46R; AGREEABLENESS score as the sum of answers
	to questions: 3, 27, 9R, 33, 51, 15R, 39, 57R, 21R, 45; CONSCIENTIOUSNESS as the sum of answers to questions: 2, 26R, 8, 32R, 14R, 38, 50, 20R, 44R,
	56R; OPENNESS TO EXPERIENCE as the sum of answers to questions: 1R, 25, 7, 31R, 13, 37, 49R, 19R, 43, 55R; fear as the sum of answers to questions:
	5, 29, 53R; liveliness as the sum of answers to: 22, 46R, and anger as the sum of answers to questions: 21, 45R.

Table I

 I

	Estimation of yellow to-	[0,1(	[1,2(	[2,3(	[3,10(	≥ 10	Mean	Standard
	ken (%)							deviation
	% of participants wave 1	36.90	17.86	11.90	8.33	25	6.06	9.41
	% of participants wave 2	25.71	17.14	17.14	11.43	28.57	5.67	9.07
	% of participants waves 1	31.82	17.53	14.29	9.74	26.62	5.87	9.25
	& 2

.6: Distribution of Estimations for the Yellow Token

  Are there more words where the letter L appears in fourth or first position?

	What is your estimate of the ratio of words where the letter L appears in fourth position to words
	where the letter L appears in first position? [true ratio: 2.37]
	3 Are there more words where the letter P appears in second or fifth position?
	What is your estimate of the ratio of words where the letter P appears second to words where the
	letter P appears fifth? [true ratio: 0.84]
	Table I.8: Distribution of Availability Scores
	Availability heuristic scores	0	1	2	3	4	5	Mean Std. Dev.
	% of participants wave 1	5.8 25.6 32.6 29.1 6.0 0.0	2.1	1.0
	% of participants wave 2	5.9 27.1 40.0 16.5 9.4 1.2	2.0	1.1
	% of participants waves 1 & 2 5.8 26.3 36.3 22.8 8.2 0.6	2.0	1.0

4 Are there more words where the letter N appears first or fifth?

What is your estimate of the ratio of words where the letter N appears first compared to words where the letter N appears fifth:

[true ratio: 0.18] 5 Are there more words where the letter D appears last or sixth?

What is your estimate of the ratio of words where the letter D appears last compared to words where the letter D appears sixth:

[true ratio: 0.07]

This test was not incentivised and yielded no earnings.

  This test was not incentivised and yielded no earnings. Table I.10: Distribution of Scores in the Availability Heuristic 2 Test

	COOPER, Anne EDWARDS, Susan WOOD, Coco CHANNEL, Emma HILL, Ellen MOORE, Dylan MILLER,
	Michael JACKSON, Peter HALL, Alice WARD, Patricia GREEN.
	Were the following names on the list? You will have 4 seconds to answer for each name. Please click OK
	to view the list of names.
	Harry ROBINSON, Marie CURIE, Jack BROWN, Holly WILKINSON, Edit PIAF, Charles HUNT, Coco
	CHANNEL, Brandon HUGHES, Elvis PRESLEY, Albert EINSTEIN, Justin TAYLOR, Pablo PICASSO, Nelson
	MANDELA, Nancy PALMER, Vincent VAN GOGH, Emily ROBERTS, Bill GATES, Christopher LLOYD,
	Britney SPEARS, Dennis ELLISON.
	Availability heuristic	<0.3	[0.3,0.4(	[0.4,0.5(	[0.5,0.6(	[0.6,0.7(	>0.7	Mean	Std. Dev.
	scores
	% of participants	0.0	1.2		24.4	62.8	11.6	0.0	0.52	0.05
	wave 1
	% of participants	0;0	0.0		14.5	68.7	16.9	0.0	0.53	0.05
	wave 2
	% of participants	0.0	0;6		19.5	65.7	12.2	0.0	0.53	0.06
	waves 1 & 2
							50]	Mean	Standard de-
									viation
	% of participants	0	1.16	22.09	67.44	9.30	33.14	5.21

  You will earn 50 cents for each correct answer. 1) You have entered a price of 23 at which you are ready to buy the lottery. The computer randomly chose between 1 and 50 the number 15. What is your payout if the orange token (which pays 30 cents) was selected? 7 cents; 15 cents (correct answer); 0 cent; 30 cents 2) You have entered a price of 30 at which you are ready to buy the lottery. The computer randomly chose between 1 and 50 the number 45. What is your payout if the blue token (which pays 10 cents) was selected? 15 cents; 0 cents (correct answer); 35 cents; 40 cents3) If you have not entered a price at which you are willing to buy the lottery: The default bid is 0 and you buy the lottery; Your default bid is 50 and you do not buy the lottery (correct answer)

	Emotion	Anger	Fear	Joy	Sadness
	Situation of investors
	Suffered tail losses	4-Very much	1-Not at all	1-Not at all	2-A little
	Experience a tail event
	but did not suffer losses	1-Not at all	1-Not at all	4-Very much	1-Not at all
	I.6 Post-experimental understanding questionnaire
	Here is a post-experimental understanding questionnaire.
	On average, participants answered correctly in 92.5 of the cases.

Table III . 1 :

 III1 Relationship between Average Bids, Likelihood of Bankruptcy and Final Earnings with Anger andFear. Result of OLS regressions.

	VARIABLES		AVERAGE BIDS	BANKRUPTCY		FINAL EARNINGS
		(1)	(2)	(3)	(4)	(5)
		# of Tail	# of Tail	# of Tail	# of Tail	# of Tail
		Events <2	Events ≥2	Events ≥2	Events <2	Events ≥2
	ω -(Anger)	0.802***	0.681***	0.0091***	-5.287	-48.674***
		(0.087)	(0.071)	(0.0006)	(6.447)	(4.266)
	µ (Fear)	-0.073***	-0.459***	-0.0009***	-5.668***	-18.250***
		(0.026)	(0.021)	(0.0002)	(1.930)	(1.277)
	Constant	21.20	21.36	0.080	3249.3	2081.85
		(0.069)	(0.057)	(0.0005)	(5.125)	(3.391)
	No. Obs	28,800	43,200	43,200	28,800	43,200
	*** p<0.01, ** p<0.05, * p<0.1.

  Table IV.1: Bids and Tail Events, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. * * p< 0.01, * * p< 0.05, * p< 0.1 Table IV.2: Increase and Decrease in Bids, and Tail Events. Probit panel regressions with random effects and robust standard errors (reported in parentheses), session fixed effects included.

	VARIABLE BDM Thresholds Tail Event Dummy BDM-a Tail Event × BDM-Dummy Wealth Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 a: BDM-= BDM10-[BDM20-] in regression (1) [(2)]. BID (1) BDM10-or BDM40+ BDM20-or BDM30+ (2) -1.196 * -0.833 * (0.712) (0.462) -0.389 * * * -0.262 * * * (0.082) (0.058) 2.797 * * 1.377 * (1.187) (0.706) -22×10 -4 * * * -21×10 -4 * * * (3×10 -4 ) (1×10 -4 ) -1.616 * * * -1.631 * * * (0.176) (0.094) -2.523 * * -2.350 * * (1.077) (1.059) 0.620 0.602 (0.690) (0.681) -0.762 -0.706 (0.543) (0.536) -1.015 * -1.014 * (0.528) (0.520) 0.688 0.636 (0.521) (0.513) 33.346 * * * 33.312 * * * (2.894) (2.772) 18,384 37,267 169 169 < 0.001 < 0.001 BID (1) (2) (3) (4) UP DOWN UP DOWN BDM Thresholds BDM10-or BDM40+ BDM20-or BDM30+ Tail Event Dummy -0.049 -0.359 -0.061 0.016 (0.203) (0.256) (0.143) (0.145) BDM--0.108*** --0.091 -(0.026) (0.018) Tail Event Dummy × BDM-0.785*** -0.338 -(0.300) (0.210) BDM+ --0.121*** --0.094*** (0.027) (0.021) Tail Event Dummy × BDM+ -0.559** -0.337* VARIABLE (0.273) (0.175)

*

  * * p< 0.01, * * p< 0.05, * p< 0.1Table IV.3: Bids and Tail Events (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period.TableIV.4: Bids, Availability Bias and Tail Events, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. * * p< 0.01, * * p< 0.05, * p< 0.1 TableIV.5: Decrease in Bids, Availability Bias and Tail Events. Probit panel regressions with random effects and robust standard errors (reported in parentheses), session fixed effects included.

	IV.2 For Table 3
	4 ) 0.041 (0.027) -0.240** (0.100) 0.106 (0.081) 0.082 (0.055) -0.179*** (0.048) 0.091* (0.054) -0.510 (0.332) 37,267 169 <0.001 (5) Low Avail. Bias BDM20-or BDM30+ -0.282*** 0.053** (0.027) (0.103) 0.113 (0.088) 0.058 (0.056) -0.198*** (0.050) 0.097* (0.056) -0.514* (0.278) 37,267 169 <0.001 BID -0.636 (0.738) 2.692*** (0.291) 1.705* (1.026) 15×10 -6 720×10 -6 -0.020*** (0.006) -0.511 (0.435) -2.352** (1.146) 0.486 (0.579) -0.750 (0.519) -0.841 (0.588) 0.592 (0.500) 26.544*** (3.984) 47,531 169 < 0.001 *** p < 0.01, ** p < 0.05, * p < 0.1 Number of Tail Events 0.034 0.061* (0.033) (0.032) Individual controls Male -0.282*** -0.196* (0.103) (0.103) Availability Index (std) 0.137 0.084 (0.083) (0.081) Loss Aversion (std) 0.051 0.086 (0.055) (0.053) Risk Aversion (std) -0.177*** -0.195*** (0.047) (0.050) Prior Yellow (std) 0.102* 0.101* (0.056) (0.054) Constant -0.601** -0.607 (0.269) (0.404) Observations 18,384 18,384 Number of investors 169 169 Prob > χ 2 <0.001 <0.001 VARIABLE Tail Event Dummy Buy Dummy Tail Event × Buy Dummy Wealth Period Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 BID (1) (2) (3) (4) High Low All High Avail. Avail. Avail. Bias Bias Bias BDM Thresholds VARIABLE SAMPLE BDM10-or BDM40+ Tail Event Dummy -2.054 * * 0.480 0.208 -1.771 * * * 0.607 (0.905) (1.176) (1.270) (0.613) (0.700) BDM--0.436 * * * -0.326 * * * -0.319 * * -0.311 * * * -0.193 * * (0.113) (0.117) (0.126) (0.079) (0.085) Tail Event × 4.579 -0.296 0.253 0.426 2.205 * * BDM-Dummy (1.663) (1.723) (1.861) (0.975) (1.017) High Availability Dummy ---3.440 * --(1.830) Tail Event × ---2.039 --High Availability Dummy (1.526) BDM-× ---0.120 --High Availability Dummy (0.165) Tail Event × BDM-× --4.262 * --High Availability Dummy (2.435) Wealth -21×10 -4 * * * -25×10 -4 * * * -22×10 -4 * * * -19×10 -4 * * * -25×10 -4 * * * -21×10 -4 * * * (6) All 0.273 (0.743) 0.181 * * (0.090) 2.034 * (1.079) -3.168 * (1.810) -1.794 * (0.945) -0.137 (0.118) -1.502 (1.425) (4×10 -4 ) (4×10 -4 ) (3×10 -4 ) (2×10 -4 ) (2×10 -4 ) (1×10 -4 ) Number of Tail Events -2.027 * * * -1.045 * * * -1.620 * * * -2.139 * * * -0.923 * * * -1.631 * * * (0.244) (0.246) (0.176) (0.132) (0.126) (0.094) Individual controls Male -1.949 -3.443 * * -2.407 * * -2.035 -2.985 * -2.238 * * (1.419) (1.685) (1.068) (1.399) (1.645) (1.052) Availability Index (std) 3.110 * * 1.565 1.974 * * 2.998 * * 1.211 1.863 * (1.475) (1.393) (0.984) (1.459) (1.373) (0.974) Loss Aversion (std) -0.546 -1.631 * -0.734 -0.579 -1.565 * -0.679 (0.725) (0.865) (0.538) (0.718) (0.855) (0.532) Risk Aversion (std) -0.328 -3.952 * * * -1.115 * * -0.284 -4.011 * * * -1.108 * * (0.637) (0.867) (0.526) (0.629) (0.845) (0.518) Prior Yellow (std) 2.300 * * * -0.606 * * * 0.689 2.407 * * * -0.782 0.637 (0.782) (0.654) (0.515) (0.770) (0.645) (0.509) Constant 28.025 * * * 38.074 * * * 34.522 * * * 28.378 * * * 37.824 * * * 34.370 * * * (5.926) (3.013) (2.937) (5.776) (2.789) (2.818) Observations 10,656 7,728 18,384 21,629 15,638 37,267 Number of investors 98 71 169 98 71 169 Prob > χ 2 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 (2) (3) (4) (5) (6) VARIABLE DOWN BDM Thresholds BDM10-or BDM40+ BDM20-or BDM30+ SAMPLE High avail. Low avail. All High avail. Low avail. All bias bias bias bias Tail Event Dummy 0.259 0.065 0.062 0.388*** 0.288 0.297 (0.222) (0.274) (0.272) (0.132) (0.201) (0.198) BDM-0.130*** 0.107*** 0.102*** 0.092*** 0.098*** 0.095*** (0.038) (0.038) (0.038) (0.027) (0.033) (0.033) Tail Event Dummy × BDM--0.533 -0.547 -0.552 -0.153 -0.597** -0.586** (0.361) (0.407) (0.406) (0.226) (0.281) (0.278) High Availability Dummy --0.288 --0.190 (0.179) (0.177) Tail Event × --0.213 --0.089 High Availability Dummy (0.353) (0.237) BDM-× --0.032 ---0.001 High Availability Dummy (0.053) (0.042) Tail Event × BDM-× --0.009 --0.424 (1) High Availability Dummy (0.546) (0.360)

* *

  TableIV.6: Bids, Availability Bias and Tail Events (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period.TableIV.7: Bids, Loss Aversion and Tail Events, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included.

	IV.3 For Table 4
	VARIABLE							BID
				(1)		(2)		(3)	(4)	(5)	(6)
	SAMPLE			High		Low		All	High	Low	All
				Loss		Loss			Loss	Loss
	VARIABLE BDM Thresholds Tail Event Dummy		Aversion -2.378 * * (0.954)	Aversion BDM10-or BDM40+ 0.417 (1.067)	(1) High avail. 0.443 bias (1.088)	Aversion BID (2) BDM20-or BDM30+ Aversion (3) Low avail. -1.148 * -0.376 All bias (0.635) (0.665)	-0.359 (0.690)
	BDM-	Tail Event Dummy		-0.473 * * * (0.110)	-0.280 * * (0.121)		-1.271 (0.873) -0.279 * * (0.124)	0.283 (1.273) -0.334 * * * (0.080)	0.587 -0.156 * (1.232) (0.084)	-0.170 * (0.088)
	Buy Dummy Tail Event × BDM-Dummy		3.663 * * (1.508)		1.726 (1.971)		3.074*** (0.434) 1.659 (2.016)	2.073*** (0.327) 2.209 * * (0.940)	2.208*** -0.022 (0.348) (1.070)	-0.170 (1.115)
	Tail Event × Buy Dummy High Loss Aversion Dummy -		-		1.097 (1.426) -0.557 (1.791)	2.434 (1.498) -	1.645 -(1.521)	-0.289 (1.763)
	High Availability Bias Dummy -High Loss Aversion Dummy Tail Event ×	-		--2.848 * * (1.429)	-	-	-3.100** -(1.568)	-0.851 * * (0.925)
	Tail Event × High Availability Bias Dummy --High Loss Aversion Dummy BDM-×		--0.194 (0.165)	-	-	-2.116 -(1.482)	-0.162 (0.117)
	Buy × High Availability Bias Dummy Tail Event × BDM-× -High Loss Aversion Dummy	-		-2.133 (2.495)	-	-	0.803 -(0.580)	2.560 * (1.438)
		Tail Event × Buy × High Availability Bias Dummy		-	-	0.107
									(2.072)	4 )
	Number of Tail Events Wealth		0.049 (0.046)	0.072* (0.044)		0.061* 13×10 -4 (0.032) (9×10 -4 )	0.059 -20×10 -4 ** (0.037) (10×10 -4 )	0.015 68×10 -6 (0.036) (712×10 -6 )	0.041 (0.027)
	Individual controls Male Period	-0.284** (0.137)	-0.0001 (0.182)		-0.208** -0.031*** (0.103) (0.008)	-0.311** -39×10 -4 (0.139) (84×10 -4 )	-0.052 -0.020*** (0.171) (0.006)	-0.247** (0.101)
	Availability Index (std) Number of Tail Events -0.091	-0.011		-0.034 -0.172	-0.015 -0.927	0.056 -0.540	0.032
				(0.143)	(0.147)		(0.113) (0.553)	(0.144) (0.622)	(0.142) (0.433)	(0.113)
		Individual controls
	Loss Aversion (std) Male		0.083	0.112		0.083 -1.933	0.091 -3.520*	0.069 -2.273*	0.080
				(0.076)	(0.104)		(0.053) (1.409)	(0.083) (2.100)	(0.101) (1.161)	(0.055)
	Risk Aversion (std) Availability Index (std) -0.219***	-0.107	-0.186*** 2.590**	-0.196*** 1.255	-0.118 1.553*	-0.174***
				(0.062)	(0.088)		(0.050) (1.292)	(0.062) (1.467)	(0.087) (0.817)	(0.050)
	Prior Yellow (std) Loss Aversion (std)		0.074	0.175**		0.101* -0.458	0.078 -1.599*	0.152** -0.732	0.091*
				(0.092)	(0.072)		(0.055) (0.666)	(0.095) (0.907)	(0.068) (0.530)	(0.055)
	Constant	Risk Aversion (std)		-0.041	-1.174**		-0.829** -0.422	-0.073 -3.242***	-0.837** -0.932	-0.671**
				(0.225)	(0.499)		(0.406) (0.753)	(0.192) (0.961)	(0.383) (0.579)	(0.338)
	Observations Prior Yellow (std) Number of investors		10,656 98	7,728 71		18,384 2.233*** 169 (0.769)	21,629 -0.705 98 (0.797)	15,638 0.588 71 (0.501)	37,267 169
	Prob > χ 2 *** p < 0.01, ** p < 0.05, * p < 0.1 Constant	< 0.001	< 0.001		< 0.001 18.052*** (2.726)	< 0.001 35.773*** (4.433)	< 0.001 27.925*** (3.996)	< 0.001
		Observations						27,608	19,923	47,531
		Number of investors					98	71	169
		Prob > χ 2						< 0.001	< 0.001	< 0.001
		* * * p< 0.01, * * p< 0.05, * p< 0.1

  * * p< 0.01, * * p< 0.05, * p< 0.1 Table IV.8: Increase in Bids, Loss Aversion and Tail Events. Probit panel regressions with random effects and robust standard errors (reported in parentheses), session fixed effects included.

	* * * (0.208) -2.569 * (1.502) 0.065 (0.809) -1.846 * (1.064) -1.682 * * (0.726) 1.278 * (0.672) 32.476 * * * (2.809) 10,354 96 < 0.001 BDM10-or BDM40+ -1.698 * * * (0.304) -3.915 * * * (1.308) 2.263 * * (1.036) 0.424 (1.293) 0.892 (0.639) 2.219 * * * (0.748) 24.488 * * * (4.947) 8,030 73 < 0.001 (2) High loss. Low loss aversion aversion -0.221 0.205 (0.257) (0.344) -0.103*** -0.115*** (0.033) (0.041) 1.002*** 0.465 (0.353) (0.572) -------- (1) Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 VARIABLE BDM Thresholds SAMPLE Tail Event Dummy BDM-Tail Event Dummy × BDM-High Loss Aversion Dummy Tail Event × High Loss Aversion Dummy BDM-× High Loss Aversion Dummy Tail Event × BDM-× High Loss Aversion Dummy	-1.619 * * * (0.176) -2.558 * * (1.081) 0.585 (0.696) -0.517 (0.859) -1.034 * (0.530) 0.706 (0.523) 33.826 * * * (3.244) 18,384 169 < 0.001 (3) All 0.193 (0.205) 0.049 (0.049) 0.756 (0.461) -0.056 (0.185) 0.110 (0.276) -0.103 (0.064) -1.057* (0.634)	UP	-1.540 * * * (0.105) -2.458 (1.498) -0.001 (0.811) -1.892 * (1.065) -1.746 * * (0.725) 1.267 * (0.670) 31.930 * * * (2.657) 21,103 96 < 0.001 (4) High loss aversion -0.315 (0.208) -0.088*** (0.022) 0.747*** (0.250) ----	-1.742 * * * (0.175) -3.800 * * * (1.266) 2.370 * * (1.008) 0.537 (1.258) 0.873 (0.620) 2.090 * * * (0.726) 24.715 * * * (4.589) 16,164 73 < 0.001 (5) BDM20-or BDM30+ -1.631 * * * (0.094) -2.370 * * (1.063) 0.583 (0.687) -0.570 (0.848) -1.024 * (0.522) 0.647 (0.516) 33.576 * * * (3.119) 37,267 169 < 0.001 (6) Low loss All aversion 0.224 0.063 (0.202) (0.161) -0.094*** -0.001 (0.031) (0.027) -0.261 0.157 (0.394) (0.270) --0.069 (0.186) --0.054 (0.232) --0.017 (0.034) 0.105 (0.370)

*

  TableIV.9: Bids, LossAversion and Tail Events (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period. Table IV.10: Bids, Tail Losses and Emotional Arousal, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. * * p< 0.01, * * p< 0.05, * p< 0.1 Table IV.11: Increase in bids, Tail Losses and Emotional Arousal. Probit panel regressions with random effects and robust standard errors (reported in parentheses), session fixed effects included.

	IV.4 For Table 5
	4 ) 0.055** (0.027) -0.286*** (0.104) 0.109 (0.088) 0.086 (0.086) -0.200*** (0.050) 0.099* (0.056) -0.507* (0.305) 37,267 169 < 0.001 (6) All -1.036 (0.919) -0.230 * * (0.091) -1.508 (1.569) -0.076 (-0.144) -0.177 (1.279) -0.478 * * (0.196) 5.718 * * * (1.989) -15×10 -4 * * * BDM20-or BDM30+ 0.079** (0.040) -0.220 (0.190) 0.180 (0.143) -0.088 (0.202) -0.245*** (0.069) 0.090 (0.119) -0.218 (0.272) 16,164 73 < 0.001 (3) Low loss 0.032 (0.038) -0.203 (0.131) 0.061 (0.091) 0.250*** (0.081) -0.223*** (0.064) 0.054 (0.066) -0.536** (0.272) 21,103 96 < 0.001 BID (2) All aversion 0.020 -0.104 (1.065) (1.065) 3.292*** 3.496*** (0.524) (0.532) -0.520 -0.479 (1.616) (1.583) -0.368 (1.639) --0.940 (1.443) --1.458** (0.625) -3.641* (2.059) -6×10 -4 14×10 -6 (10×10 -4 ) (712×10 -6 ) -0.020** -0.020*** (0.009) (0.006) -0.631 -0.509 (0.562) (0.431) -3.296** -2.379** (1.318) (1.170) 2.042* 0.466 (1.118) (0.577) 0.122 -0.653 (0.987) (0.766) 0.810 0.857 (0.558) (0.590) 2.085*** 0.607 (0.696) (0.508) 20.629*** 26.413*** (2.418) (4.280) 20,546 47,531 73 169 < 0.001 < 0.001 (4) (5) No Feedback feedback arousal arousal -1.260 -0.404 (0.937) (0.888) -0.197 * * -0.486 * * * (0.092) (0.152) -1.155 2.777 * * (1.588) (1.188) ---------15×10 -4 * * * BID High loss 0.043 (0.032) -0.287*** (0.104) 0.132 (0.084) 0.078 (0.084) -0.179*** (0.048) 0.104* (0.056) -0.642** (0.294) 18,384 169 < 0.001 (1) aversion -0.966 (1.017) 1.661*** (0.259) 2.853** (1.333) ----51×10 -5 (7×10 -5 ) -0.021*** (0.007) -0.324 (0.494) -2.694 (1.852) -0.048 (0.765) -1.845* (1.017) -1.472* (0.830) 1.134 (0.753) 25.701*** (4.128) 26,985 96 < 0.001 (3) All -3.731 * * * (1.352) -0.340 * * * (0.127) -1.875 (2.737) 0.219 (-0.192) 2.547 (1.911) -0.613 * * (0.268) 6.790 * * (3.338) -18×10 -4 * * * Tail Event × Buy × High Loss Aversion Dummy Number of Tail Events -0.014 0.086* (0.046) (0.048) Individual controls Male -0.237* -0.197 (0.130) (0.181) Availability Index (std) 0.094 0.175 (0.086) (0.136) Loss Aversion (std) 0.257*** -0.085 (0.080) (0.192) Risk Aversion (std) -0.210*** -0.195*** (0.061) (0.067) Prior Yellow (std) 0.063 0.093 (0.068) (0.109) Constant -0.485* -0.237 (0.271) (0.259) Observations 10,354 8,030 Number of investors 96 73 Prob > χ 2 < 0.001 < 0.001 *** p < 0.01, ** p < 0.05, * p < 0.1 VARIABLE Tail Event Dummy Buy Dummy Tail Event × Buy Dummy High Loss Aversion Dummy Tail Event × High Loss Aversion Dummy Buy × High Loss Aversion Dummy Wealth Period Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 * * * p< 0.01, * * p< 0.05, * p< 0.1 VARIABLE (1) (2) SAMPLE No Feedback (Loss-averse investors) feedback arousal arousal BDM Thresholds BDM10-or BDM40+ Tail Event Dummy -2.900 * * -1.526 (1.364) (1.538) BDM--0.361 * * * -0.584 * * * (0.129) (0.212) Tail Event × BDM-Dummy -3.045 2.481 (2.729) (2.048) Feedback Arousal Dummy --Tail Event × --Feedback Arousal Dummy BDM-× --Feedback Arousal Dummy Tail Event × BDM-× --Feedback Arousal Dummy Wealth -17×10 -4 * * * -26×10 -4 * * * -19×10 -4 * * * (4×10 -4 ) (8×10 -4 ) (3×10 -4 ) (2×10 -4 ) (5×10 -4 ) (2×10 -4 ) Number of Tail Events -1.646 * * * -1.434 * * * -1.588 * * * -1.601 * * * -1.320 * * * -1.550 * * * (0.239) (0.512) (0.212) (0.128) (0.293) (0.107) Individual controls Male -2.770 * -2.005 -2.425 -2.589 * -1.474 -2.300 (1.536) (1.528) (1.514) (1.518) (1.544) (1.507) Availability Index (std) -0.076 0.030 0.021 -0.149 -0.015 -0.050 (0.822) (0.812) (0.813) (0.818) (0.828) (0.813) Loss Aversion (std) -1.862 * -2.882 * * * -1.914 * -1.949 * -2.298 * * -1.960 * (1.081) (1.062) (1.069) (1.076) (1.082) (1.069) Risk Aversion (std) -1.804 * * -0.932 -1.779 * * -1.824 * * -1.716 * * -1.844 * * (0.744) (0.750) (0.735) (0.737) (0.750) (0.733) Prior Yellow (std) 1.196 * 0.879 1.215 * 1.211 * 0.977 1.202 * (0.685) (0.700) (0.677) (0.679) (0.7) (0.674) Constant 32.118 * * * 36.499 * * * 32.444 * * * 31.903 * * * 33.300 * * * 31.992 * * * (2.912) (3.586) (2.819) (2.700) (3.033) (2.662) Observations 7,967 2,263 10,230 16,344 4,518 20,862 Number of investors 95 95 95 95 95 95 Prob > χ 2 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 (2) (3) (4) (5) (6) VARIABLE UP BDM Thresholds BDM10-or BDM40+ BDM20-or BDM30+ SAMPLE No feedback Feedback All No feedback Feedback All arousal arousal arousal arousal Tail Event Dummy -0.340 -0.123 -0.337 -0.517* -0.111 -0.526* (0.374) (0.351) (0.369) (0.282) (0.284) (0.275) BDM--0.062 -0.258*** -0.055 -0.076*** -0.144*** -0.070*** (0.039) (0.062) (0.039) (0.025) (0.044) (0.025) Tail Event × BDM-Dummy 0.147 1.250** 0.187 0.453 0.822** 0.453 (0.767) (0.521) (0.745) (0.489) (0.334) (0.482) Feedback Arousal Dummy 0.077 -0.008 (0.049) (0.039) Tail Event × 0.165 0.374 Feedback Arousal Dummy (0.523) (0.392) BDM-× Feedback Arousal Dummy -0.180** -0.066 (0.075) (0.050) Tail Event × BDM-× 1.088 0.397 (1) Feedback Arousal Dummy (0.948) (0.624)

*

  * * p< 0.01, * * p< 0.05, * p< 0.1Table IV.12: Bids, Tail Losses and Emotional Arousal (IV regression). IV panel regressions with instrumental variable for the 'Buy Dummy' that takes value one if an investor bought the asset in the previous period. We use random effects and robust standard errors (reported in parentheses), session fixed effects included. The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period.TableIV.13: Bids, Tail Losses and Anger, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. * * p< 0.01, * * p< 0.05, * p< 0.1 TableIV.14: Increase in Bids, Tail Losses and Anger. Linear (Probit) panel regressions with random effects and robust standard errors (reported in parentheses) in regressions (1) to (3) ((4) to (6)), session fixed effects included. a

	IV.5 For Table 6
	Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 VARIABLE SAMPLE Tail Event Dummy Buy Tail Event × Buy Dummy -0.019 (0.049) -0.246* (0.139) 0.098 (0.090) 0.271*** (0.082) -0.201*** (0.065) 0.065 (0.070) -0.541 (0.344) 7,967 95 < 0.001 Feedback Arousal Dummy Tail Event × Feedback Arousal Dummy -0.029 (0.081) -0.314** (0.144) 0.074 (0.083) 0.207** (0.094) -0.182*** (0.054) 0.149** (0.067) -0.304 (0.403) 2,263 95 < 0.001 Buy × Feedback Arousal Dummy Tail Event × Buy × Feedback Arousal Dummy Wealth Period Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 * * * p< 0.01, * * p< 0.05, * p< 0.1 VARIABLE (1) (2) SAMPLE Anger-Not anger-(Loss-averse investors) prone prone BDM Thresholds BDM10-or BDM40+ No feedback -0.004 (0.046) -0.453* (0.271) 10,460 97 < 0.001 (1) arousal -1.001 (1.688) 1.477*** (0.248) 2.725 (2.346) 45×10 -5 (70×10 -5 ) -0.019*** (0.007) -0.351 (0.468) -2.689 (1.952) -0.109 (0.795) -1.797* (1.044) -1.667* (0.857) 1.188 (0.766) 25.658*** (4.077) 20,919 95 < 0.001 (3) All Tail Event Dummy -6.032** -2.469 -2.689 (2.527) (1.507) (1.672) BDM--0.320 -0.361** -0.347* (0.200) (0.161) (0.178) Tail Event × BDM-Dummy -5.260 0.716 0.544 (4.814) (3.166) (3.515) Feedback Arousal Dummy 0.058 0.359 0.357 (0.317) (0.233) (0.259) Tail Event × Feedback 5.385 0.862 0.871 Arousal Dummy (3.527) (2.146) (2.385) BDM-× Feedback Arousal -0.504 -0.688 -0.692* Dummy (0.447) (0.323) (0.359) Tail Event × BDM-× Feedback 7.866 5.675 5.792 Arousal Dummy (5.914) (3.846) (4.272) Anger Dummy ---2.442 (1.565) Tail Event × Anger Dummy ---2.950 (2.827) BDM-× Anger Dummy --0.014 (0.254) Tail Event × BDM-× Anger Dummy ---5.520 (5.603) Feedback Arousal × Anger Dummy ---0.302 (0.387) BDM-× Feedback Arousal --0.180 × Anger Dummy (0.542) Tail Event × Feedback Arousal --4.609 × Anger Dummy (3.991) Tail Event × BDM-× Feedback --1.799 Arousal × Anger Dummy (6.860) Wealth -12×10 -4 ** -21×10 -4 *** -18×10 -4 *** (6×10 -4 ) (4×10 -4 ) (3×10 -4 ) Number of Tail Events -2.300*** -1.194*** -1.585*** (0.395) (0.226) (0.212) Individual controls Male -6.106** -2.223 -3.469** (2.535) (2.544) (1.633) Availability Index (std) 1.372 -0.549 0.193 (0.942) (1.426) (0.813) Loss Aversion (std) 0.967 -2.555 -2.118** (1.740) (1.644) (1.067) Risk Aversion (std) -3.324*** -3.401*** -2.034*** (1.155) (1.183) (0.746) Prior Yellow (std) 2.161*** 0.933 1.377** (0.677) (1.756) (0.679) Constant 31.308*** 35.222*** 34.308*** (3.093) (4.741) (3.042) Observations 4,885 5,345 10,230 Number of investors 45 50 95 Prob > χ 2 <0.001 <0.001 <0.001 (1) (2) (3) BDM Thresholds BDM10-or BDM40+ SAMPLE Anger-Not anger-All prone prone Tail Event Dummy -0.104 -0.068 -0.074 (0.107) (0.113) (0.112) BDM--0.033** -0.001 -0.001 (0.014) (0.017) (0.017) Tail Event × BDM-Dummy -0.111 0.140 0.140 (0.131) (0.282) (0.281) Feedback Arousal Dummy 0.010 0.038* 0.038* (0.020) (0.019) (0.019) Tail Event × Feedback Arousal Dummy -0.100 0.068 0.066 (0.202) (0.186) (0.184) BDM-× Feedback Arousal Dummy -0.045 -0.052* -0.053* (0.027) (0.029) (0.029) Tail Event × BDM-× 0.852*** 0.085 0.095 Feedback Arousal Dummy (0.242) (0.395) (0.392) Anger Dummy -0.027 (0.030) Tail Event × Anger Dummy -0.024 (0.153) BDM-× Anger Dummy -0.031 (0.022) Tail Event × BDM-× Anger Dummy -0.254 (0.308) Feedback Arousal × Anger Dummy -0.029 (0.027) BDM-× Feedback Arousal × -0.167 Anger Dummy (0.272) Tail Event × Feedback Arousal × 0.008 Anger Dummy (0.040) Tail Event × BDM-× 0.756* Feedback Arousal × Anger Dummy (0.458) VARIABLE Wealth -12×10 -6	4 ) 0.038 (0.039) -0.494* (0.257) 21,321 97 < 0.001 (6) All -1.829 (1.295) -0.306** (0.127) 2.484 (2.255) 0.008 (0.197) 1.297 (1.777) -0.488* (0.268) -0.271 (2.773) -2.830* (1.557) 1.603 (1.835) 0.157 (0.181) -7.691** (3.137) -0.185 (0.288) 0.036 (0.394) -3.069 (2.560) 12.742*** (4.009) -15×10 -4 *** BDM20-or BDM30+ 0.050 (0.074) -0.223 (0.141) 0.076 (0.091) 0.185* (0.098) -0.203*** (0.062) 0.114 (0.071) -0.343 (0.345) 4,518 95 < 0.001 (3) All -1.113 (1.688) 1.853*** (0.283) 3.025 (2.351) -0.008 (0.228) 0.152 (2.047) -0.111 (0.281) -0.067 (2.893) 53×10 -5 (79×10 -5 ) -0.021*** (0.007) -0.384 (0.521) -2.607 (1.847) -0.101 (0.759) -1.914* (1.015) -1.507* (0.830) 1.053 (0.743) 25.702*** (4.227) 26,687 95 < 0.001 (5) Not anger-prone -1.655 (1.165) -0.313*** (0.115) 2.546 (2.030) 0.011 (0.177) 1.263 (1.598) -0.487** (0.241) -0.281 (2.495) ---------13×10 -4 *** 0.024 (0.040) -0.233 (0.141) 0.062 (0.096) 0.268*** (0.084) -0.211*** (0.069) 0.067 (0.070) -0.643* (0.368) 16,344 95 < 0.001 BID (2) Feedback arousal -0.331 (1.175) 1.160*** (0.310) 2.591 (1.620) 12×10 -4 (8×10 -4 ) -0.029*** (0.008) 0.317 (0.547) -1.774 (1.991) 0.189 (0.821) -2.229** (1.061) -1.596* (0.907) 0.905 (0.867) 25.778*** (4.264) 5,768 95 < 0.001 BID (4) Anger-prone -0.485 (1.431) -0.145 (0.142) -5.308** (2.397) -0.176 (0.231) -1.753 (2.024) -0.456 (0.317) 12.477*** (3.178) ---------17×10 -4 *** (3×10 -4 ) (2×10 -4 ) (2×10 -4 ) -2.048*** -1.254*** -1.549*** (0.192) (0.119) (0.107) -6.676*** -2.000 -3.465** (2.497) (2.508) (1.624) 1.332 -0.683 0.140 (0.941) (1.409) (0.811) 1.311 -2.838* -2.192** (1.757) (1.620) (1.066) -3.680*** -3.371*** -2.128*** (1.164) (1.166) (0.742) 2.159*** 1.367 1.381** (0.681) (1.718) (0.675) 31.912*** 34.016*** 34.148*** (2.615) (4.570) (2.891) 10,115 10,747 20,862 45 50 95 <0.001 <0.001 <0.001 UP (4) (5) (6) BDM20-or BDM30+ Anger-Not anger-All prone prone -0.398 -0.691* -0.701* (0.377) (0.416) (0.412) -0.072** -0.078** -0.080** (0.035) (0.036) (0.036) 0.118 0.813 0.848 (0.692) (0.673) (0.670) -0.022 0.015 0.018 (0.054) (0.056) (0.056) -0.566 0.998* 0.987* (0.681) (0.550) (0.546) -0.107 -0.027 -0.029 (0.074) (0.071) (0.070) 1.948** -0.668 -0.670 (0.946) (0.899) (0.893) -0.141 (0.128) 0.334 (0.555) 0.011 (0.050) -0.773 (0.963) -0.039 (0.078) -0.082 (0.871) -1.579* (0.102) 2.625** (1.297)
	44

* *

  TableIV.16: Bids and Fear, Individual Controls. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. * * p< 0.01, * * p< 0.05, * p< 0.1 TableIV.17: Decrease in Bids and Fear. Linear panel regressions with random effects and robust standard errors (reported in parentheses), session fixed effects included. a * * p< 0.01, * * p< 0.05, * p< 0.1

	IV.6 For Table 7
	VARIABLE SAMPLE Tail Event Dummy Buy Dummy Tail Event × Buy Dummy Feedback Arousal Dummy Tail Event × Feedback Arousal Dummy Buy Dummy × Feedback Arousal Dummy Tail Event × Buy Dummy × Feedback Arousal Dummy Anger Dummy Tail Event × Anger Dummy Buy Dummy × Anger Dummy Tail Event × Buy Dummy × Anger Dummy Feedback Arousal × Anger Dummy Buy Dummy × Feedback Arousal × Anger Dummy Tail Event × Feedback Arousal × Anger Dummy Tail Event × Buy Dummy × Feedback Arousal × Anger Dummy Wealth Period Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 * * * p< 0.01, * * p< 0.05, * p< 0.1 VARIABLE (1) (2) (3) SAMPLE Not fearful Fearful All (Loss-averse investors) BDM Thresholds BDM10-or BDM40+ Tail Event Dummy -3.925** -1.279 -3.996*** (1.516) (1.707) (1.495) BDM--0.374*** -0.451*** -0.373*** (0.127) (0.141) (0.125) Tail Event × BDM-Dummy 2.453 -4.949* 2.387 (3.418) (2.955) (3.374) Feedback Arousal Dummy -0.344* 0.188 -0.345* (0.188) (0.209) (0.186) Tail Event × Feedback 5.462*** -0.448 5.477 Arousal Dummy (2.030) (2.123) (2.006) BDM-× Feedback -0.269 0.394 -0.269 Arousal Dummy (0.262) (0.292) (0.259) Tail Event × BDM-× -3.369 13.428*** -3.285 Feedback Arousal Dummy (4.006) (3.570) (3.958) Fear Dummy -0.227 (1.163) Tail Event × Fear 2.804 Dummy (2.281) BDM-× Fear -0.078 Dummy (0.190) Tail Event × BDM-× -7.314 Fear Dummy (4.504) Feedback Arousal × 0.537* Fear Dummy (0.282) Tail Event × Feedback -5.931** Arousal × Fear Dummy (2.942) BDM-× Feedback Arousal 0.661* × Fear Dummy (0.393) Tail Event × BDM-× Feedback 16.651*** Arousal × Fear Dummy (5.362) Wealth -23×10 -4 *** -21×10 -4 *** -22×10 -4 *** 29×10 -4 *** (1) Anger-prone -0.848 (3.015) 2.489*** (0.446) -0.843 (3.573) 0.407 (0.410) -1.338 (4.011) 0.211 (0.506) 6.438 (5.102) (10×10 -4 ) -0.036*** (0.010) -0.032 (0.784) -5.347* (3.059) 1.369 (0.878) 0.839 (1.565) -3.189** (1.527) 2.065*** (0.798) 18.654*** (3.383) 12,879 45 < 0.001 BID (4) Not fearful Not anger-BID (2) prone -1.721 (1.627) 2.296*** (0.445) 7.001** (3.021) -0.112 (0.380) 1.161 (1.855) -0.545 (0.392) -5.217 (3.380) -18×10 -4 (13×10 -4 ) -0.003 (0.011) -1.303 (0.812) -2.270 (3.073) -0.681 (1.157) -2.580 (1.934) -2.786** (1.389) -0.127 (2.976) 34.003*** (7.752) 13,808 50 < 0.001 Fearful 1.963*** (3) All -1.087 (1.500) (0.392) 5.368* (2.894) -0.121 (0.311) 1.096 (1.737) -0.434 (0.347) -4.882 (3.271) -2.528 (1.579) -0.030 (3.311) -0.110 (0.595) -5.041 (4.720) 0.193 (0.451) 0.727 (0.587) -2.572 (4.308) 11.645* (6.090) 51×10-5 (80×10-5) -0.020*** (0.007) -0.410 (0.529) -3.622* (2.010) 0.078 (0.754) -2.110** (0.990) -1.747** (0.856) 1.217 (0.741) 27.661*** (4.728) 26,687 95 < 0.001 (5) BDM20-or BDM30+ -3.494*** 1.926* -3.593*** (6) All (1.037) (1.081) (1.020) -0.194** -0.253** -0.190** (0.090) (0.100) (0.088) 1.492 -4.219** 1.356 (1.786) (1.676) (1.757) -0.198 -0.136 -0.199 (0.141) (0.154) (0.139) 3.276** -3.170** 3.284** (1.297) (1.417) (1.277) -0.355* 0.047 -0.356* (0.192) (0.208) (0.189) -0.974 9.358*** -0.967 (2.147) (2.127) (2.114) 0.125 (1.143) 5.631*** (1.500) -0.068 (0.135) -5.441** (2.449) 0.064 (0.210) -6.441*** (1.929) 0.403* (0.285) 10.316*** (3.029) -24×10 -4 *** -18×10 -4 *** -21×10 -4 *** (4×10 -4 ) (4×10 -4 ) (3×10 -4 ) (2×10 -4 ) (2×10 -4 ) (1×10 -4 ) Number of Tail Events -1.540*** -1.799*** -1.653*** -1.470*** -1.874*** -1.652*** (0.248) (0.258) (0.179) (0.130) (0.140) (0.095) Individual controls Male -2.121 -2.879* -2.752** -1.834 -2.672* -2.550** (1.466) (1.556) (1.084) (1.441) (1.515) (1.065) Availability Index (std) 1.590* 0.472 0.514 1.590* 0.354 0.496 (0.893) (0.922) (0.688) (0.886) (0.899) (0.678) Loss Aversion (std) -1.270* -1.523* -0.753 -1.239* -1.244 -0.693 (0.694) (0.857) (0.540) (0.688) (0.837) (0.533) Risk Aversion (std) -0.594 -0.679 -1.049** -0.577 -0.749 -1.057** (0.704) (0.805) (0.528) (0.695) (0.784) (0.519) Prior Yellow (std) -0.214 0.493 0.763 -0.331 0.409 0.692 (0.684) (0.629) (0.524) (0.680) (0.613) (0.517) Constant 38.415*** 33.614*** 33.496*** 38.619*** 32.936*** 33.257*** (3.987) (2.703) (3.107) (3.898) (2.429) (2.980) Observations 10,305 7,844 18,149 20,692 16,106 36,798 Number of investors 94 73 167 94 73 167 Prob > χ 2 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 DOWN (1) (2) (3) (4) (5) (6) BDM Thresholds BDM10-or BDM40+ BDM20-or BDM30+ SAMPLE Not fearful Fearful All Not fearful Fearful All Tail Event Dummy 0.003 0.104 0.003 0.193** 0.053 0.190** (0.112) (0.123) (0.112) (0.090) (0.086) (0.090) BDM-0.027** 0.033** 0.027** 0.027*** 0.027*** 0.027*** (0.012) (0.014) (0.012) (0.009) (0.009) (0.009) Tail Event × BDM-Dummy 0.387** 0.051 0.388** 0.037 -0.106 0.046 (0.192) (0.170) (0.193) (0.181) (0.107) (0.181) Feedback Arousal Dummy 0.024* -0.007 0.024* 0.031*** 0.018 0.031*** (0.014) (0.017) (0.014) (0.011) (0.012) (0.011) Tail Event × 0.065 -0.051 0.066 -0.165 0.076 -0.163 Feedback Arousal Dummy (0.156) (0.158) (0.156) (0.110) (0.112) (0.110) BDM+ × Feedback Arousal Dummy 0.034* 0.003 0.034* 0.011 -0.007 0.011 (0.019) (0.022) (0.019) (0.014) (0.014) (0.014) Tail Event × BDM-× -0.595** -0.457** -0.591** -0.111 -0.098 -0.111 Feedback Arousal Dummy (0.258) (0.198) (0.258) (0.202) (0.157) (0.202) Fear Dummy -0.013 -0.008 (0.030) (0.027) Tail Event × Fear Dummy 0.101 -0.131 (0.165) (0.124) BDM-× Fear Dummy 0.006 0.001 (0.018) (0.013) Tail Event × BDM-× Fear Dummy -0.339 -0.166 (0.258) (0.209) Feedback Arousal × Fear Dummy -0.030 -0.012 (0.022) (0.016) BDM-× Feedback Arousal × -0.032 -0.019 Fear Dummy (0.029) (0.020) Tail Event × Feedback Arousal × -0.118 0.235 Fear Dummy (0.221) (0.157) Tail Event × BDM-× 0.132 0.016 Feedback Arousal ×Fear Dummy (0.326) (0.256) Wealth 18×10 -6 -8×10 -6 7×10 -6 26×10 -6 * 29×10 -6 ** 5×10-7 (21×10 -6 ) (15×10 -6 ) (13×10 -6 ) (15×10 -6 ) (14×10 -6 ) (108×10-7) Period -42×10-5** -39×10-5** -40×10-5*** -46×10-5*** -23×10-5 -34×10-5*** (18×10-5) (15×10-5) (12×10-5) (14×10-5) (14×10-5) (10×10-5) Number of Tail Events 0.017 0.014 0.015* 0.018 0.001 0.009 (0.015) (0.010) (0.009) (0.011) (0.009) (0.007) Individual controls Male 0.012 -0.048 -0.047* 0.006 -0.067** -0.054** (0.031) (0.034) (0.025) (0.029) (0.032) (0.023) Availability Index (std) 0.032 0.004 0.027 0.037 0.019 0.033* (0.027) (0.025) (0.020) (0.026) (0.025) (0.019) Loss Aversion (std) 0.032* 0.034* 0.019 0.029* 0.028 0.018 (0.016) (0.019) (0.012) (0.016) (0.019) (0.012) Risk Aversion (std) -0.032 -0.071 -0.053*** -0.027 -0.061*** -0.046*** (0.019) (0.019) (0.013) (0.018) (0.018) (0.012) Prior Yellow (std) 0.040** 0.029** 0.025** 0.041** 0.028* 0.025** (0.018) (0.015) (0.012) (0.019) (0.014) (0.012) Constant 0.418*** 0.326*** 0.302*** 0.437*** 0.389*** 0.313*** (0.056) (0.088) (0.085) (0.049) (0.081) (0.079) Observations 10,305 7,844 18,149 20,692 16,106 36,798 Number of investors 94 73 167 94 73 167 Prob > χ 2 --< 0.001 --< 0.001 VARIABLE
	47

* *

  * * p< 0.01, * * p< 0.05, * p< 0.1 50 IV.7 For Table A.1 Table IV.19: Arousal and Tail Events, Individual Controls. Panel probit regressions with random effects and robust standard errors clustered at the individual levels in parentheses and session fixed effects included.

	VARIABLE SAMPLE Tail Event Dummy Buy Dummy Tail Event × Buy Dummy Feedback Arousal Dummy Tail Event × Feedback Arousal Dummy Buy × Feedback Arousal Dummy Tail Event × Buy × Feedback Arousal Dummy Fear Dummy Tail Event × Fear Dummy Buy × Fear Dummy Tail Event × Buy × Fear Dummy Feedback Arousal × Fear Dummy Buy × Feedback Arousal × Fear Dummy Tail Event × Feedback Arousal × Fear Dummy Tail Event × Buy × Feedback Arousal × Fear Dummy Wealth Period Number of Tail Events Individual control Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 FEEDBACK AROUSAL DUMMY Not fearful (1) -3.074** (1.262) 2.524*** (0.404) 2.676 (2.776) -0.248 (0.216) 3.078 (1.930) 0.426 (0.518) -1.891 (3.135) -51×10-5 (99×10-5) -0.017* (0.009) -0.545 (0.591) -1.782 (1.406) 1.356* (0.722) -1.080* (0.641) -0.494 (0.916) -0.040 (0.681) 34.241*** (6.380) 26,418 94 < 0.001 (1) (2) BDM Thresholds BDM10-or BDM40+ BDM20-or BDM30+ BDM10-or BDM40+ BID (2) Fearful 0.261 -2.881** (3) All (2.315) (1.246) 2.191*** 2.489*** (0.321) (0.398) 0.553 2.339 (2.585) (2.694) -0.156 -0.346* (0.237) (0.202) -0.176 2.843 (2.522) (1.914) 0.381 0.511 (0.340) (0.542) 1.871 -1.744 (3.186) (3.123) -0.317 (1.220) 3.341 (2.601) 0.250 (0.558) -1.755 (3.739) 0.227 (0.337) -0.195 (0.657) -3.375 (3.154) 3.862 (4.472) 13×10-5 16×10 -6 (93×10-5) (726×10 -6 ) -0.021*** -0.020*** (0.008) (0.006) -0.630 -0.547* (0.582) (0.438) -2.645 -2.565** (2.174) (1.155) 0.352 0.397 (1.014) (0.570) -1.272 -0.736 (1.068) (0.518) -0.673 -0.880 (1.019) (0.595) 0.295 0.667 (0.754) (0.498) 27.072*** 26.953*** (4.176) (4.201) 20,517 46,935 73 167 < 0.001 < 0.001 DECISION AROUSAL DUMMY (3) (4) BDM20-or BDM30+ Tail Event Dummy 1.172 * * * 1.199 * * * -0.092 -0.093 (0.158) (0.107) (0.212) (0.114) Tail Event × BDM-Dummy 0.508 * 0.134 0.056 -0.159 (0.291) (0.169) (0.349) (0.181) BDM-Dummy 0.105 * * * 0.059 * * * -0.026 -0.021 (0.022) (0.016) (0.022) (0.016) Fear Dummy a 0.034 0.024 -0.040 -0.016 (0.074) (0.073) (0.066) (0.063) Anger Dummy 0.055 0.059 -0.041 -0.057 VARIABLE (0.065) (0.063) (0.057) (0.052)

*

  .2 Table IV.21: Bankruptcy, Earnings and Baseline Arousal, Individual Controls. (1) Probit regressions, (2) Tobit (with a lower bound at zero) with robust standard errors clustered at the individual levels in parentheses.

	VARIABLE	BANKRUPTCY DUMMY	EARNINGS
		(1)	(2)
	Baseline feedback arousal index (BFA) (std)	-0.204	-245.183
		(0.203)	(260.180)
	BFA × Anger Dummy	0.010	280.660
		(0.279)	(330.071)
	BFA × Fear Dummy	-0.292	166.195
		(0.296)	(321.369)
	Anger Dummy	-0.184	-244.922
		(0.321)	(329.916)
	Fear Dummy	-0.344	-117.301
		(0.305)	(319.811)
	BFA × Anger × Number of Tail Events	-	-78.825
			(147.586)
	BFA × Fear × Number of Tail Events	-	62.442
			(141.085)
	BFA × Number of Tail Events	-	85.125
			(134.989)
	Anger × Number of Tail Events	-	175.942
			(161.950)
	Fear × Number of Tail Events	-	27.806
			(157.474)
	Number of Tail Events	-0.177	-611.674***
		(0.161)	(117.031)
	Male	0.228	-9.203
		(0.319)	(213.140)
	Availability index (std)	-0.140	8.583
		(0.162)	(90.491)
	Loss aversion (std)	0.124	-81.786
		(0.149)	(91.521)
	Risk aversion (std)	-0.130	33.292
		(0.177)	(102.325)
	Prior Yellow (std)	0.105	11.091
		(0.148)	(100.123)
	Baseline decision arousal index (std)	0.043	-100.908
		(0.135)	(93.325)
	Constant	-0.329	3,379.458***
		(0.555)	(250.239)

  * * p< 0.01, * * p< 0.05, * p< 0.1 54 IV.10 For Table A.4 Table IV.23: Bids, Tail Losses and Anger-based PT. Linear panel regressions with random effects and robust standard errors with an AR(1) error term in parentheses, session fixed effects included. * * p< 0.01, * * p< 0.05, * p< 0.1

	VARIABLE			CHANGE IN BID
				(1)	(2)
	CHANGE IN BID in t-1 Tail Event Dummy in t-1 Tail Event Dummy in t-2 Tail Event Dummy in t-3 Tail Event Dummy in t-4 Tail Event Dummy in t-5 BDM10-in t-1 BDM10-in t-2 BDM10-in t-3 BDM10-in t-4 BDM10-in t-5 Tail Event × BDM10-Dummy in t-1 Tail Event × BDM10-Dummy in t-2 Tail Event × BDM10-Dummy in t-3 Tail Event × BDM10-Dummy in t-4 Tail Event × BDM10-Dummy in t-5 Wealth Number of Tail Events Individual controls Male Availability Index (std) Loss Aversion (std) Risk Aversion (std) Prior Yellow (std) Constant Observations Number of investors Prob > χ 2 (1) (2) Anger-Anger-based PT=1 based PT=0 BDM10-or BDM40+ -34×10 -6 *** -0.016 (0.375) 0.433 (0.410) 0.013 (0.416) -0.598 (0.410) -0.065 (0.379) -0.401*** (0.080) 0.063 (0.086) 0.036 (0.088) 0.091 (0.087) -0.117 (0.080) 3.003** (1.192) 0.297 (1.298) 0.301 (1.315) 1.191 (1.299) -2.945** (1.194) (39×10 -6 ) -0.034 (0.026) 0.004 (0.049) -0.004 (0.031) 0.002 (0.024) 0.0001 (0.024) -0.003 (0.024) 0.173 (0.171) 47,024 169 0.329 (3) All -4.036** -2.252 -2.284* (1.763) (1.425) (1.349) -0.276* -0.444*** -0.447*** (0.149) (0.118) (0.112) 0.956 -2.796 -2.614 (3.303) (2.845) (2.691) 0.176 -0.239 -0.243 (0.219) (0.175) (0.166) -0.572 3.199* 3.220* (2.506) (1.791) (1.697) -0.568* 0.227 0.229 (0.308) (0.244) (0.231) 4.872 6.152* 6.032* (4.292) (3.320) (3.142) --2.148* (1.101) ---1.663 (2.475) --0.162 (0.209) --3.394 (4.733) --0.416 (0.308) ---0.789* (0.432) ---3.583 (3.419) Tail Event × BDM-× Feedback Arousal SAMPLE BDM Thresholds Tail Event Dummy BDM-Tail Event × BDM-Dummy Feedback Arousal Dummy Tail Event × Feedback Arousal Dummy BDM-× Feedback Arousal Dummy Tail Event × BDM-× Feedback Arousal Dummy Anger-based PT Dummy Tail Event × Anger-based PT Dummy BDM-× Anger-based PT Dummy Tail Event × BDM-× Anger-based PT Dummy Feedback Arousal × Anger-based PT Dummy BDM-× Feedback Arousal × Anger-based PT Dummy 5 Tail Event × Feedback Arousal × Anger-based PT Dummy ---1.379 × Anger-based PT Dummy (5.969) Wealth -28×10 -4 *** -19×10 -4 *** -22×10 -4 *** BID -34×10 -6 *** -0.280*** (0.004) -0.007 (0.369) 0.444 (0.382) 0.141 (0.383) -0.619 (0.382) -0.187 (0.373) -0.402*** (0.079) -0.052 (0.081) 0.061 (0.081) 0.097 (0.081) -0.087 (0.079) 2.977** (1.173) 1.198 (1.208) 0.292 (1.210) 1.455 (1.208) -3.002** (1.175) (39×10 -6 ) -0.034 (0.026) 0.006 (0.056) -0.004 (0.035) 0.003 (0.028) -0.001 (0.027) -0.005 (0.027) 0.208 (0.194) 47,024 169 < 0.001 (4) Anger-based PT=1 -0.314 (1.206) -0.393*** (0.110) -1.711 (1.865) 0.003 (0.170) -3.282** (1.650) -0.170 (0.230) 9.301*** (2.489) ----------26×10 -4 *** BDM20-or BDM30+ (5) anger-based PT=0 -1.296 (1.934) -0.151* (0.083) -0.937 (1.564) -0.237* (0.129) 1.457 (1.167) -0.177 (0.175) 2.145 (1.879) ----------19×10 -4 *** -21×10 -4 *** (6) All -1.352 (0.894) -0.148* (0.079) -0.844 (1.494) -0.250** (0.124) 1.488 (1.117) -0.176 (0.168) 2.114 (1.796) 2.410** (1.081) 1.198 (1.635) -0.255* (0.148) -1.032 (2.600) 0.259 (0.230) 0.014 (0.312) -4.731** (2.187) 7.218** (3.364) (5×10 -4 ) (3×10 -4 ) (3×10 -4 ) (3×10 -4 ) (2×10 -4 ) (1×10 -4 ) Number of Tail Events -1.196*** -1.582*** -1.653*** -2.069*** -1.553*** -1.654*** (0.387) (0.203) (0.179) (0.207) (0.107) (0.095) Individual controls Male -13.953*** -0.196 -2.753** -13.544*** -0.055 -2.567** (3.048) (1.164) (1.072) (3.055) (1.138) (1.052) Availability Index (std) -1.998 1.246 0.332 2.026 1.130 0.300 (1.490) (0.773) (0.686) (1.489) (0.762) (0.676) Loss Aversion (std) -4.837*** -0.121 -0.745 -4.814*** -0.036 -0.692 (1.303) (0.562) (0.534) (1.293) (0.555) (0.527) Risk Aversion (std) 1.385 -1.381** -1.086** 1.566 -1.422*** -1.087** (1.019) (0.539) (0.523) (1.012) (0.530) (0.513) Prior Yellow (std) 2.369* 0.704 0.879* 2.487* 0.603 0.830 (1.334) (0.568) (0.519) (1.325) (0.559) (0.510) Constant 42.372*** 29.714*** 32.406*** 42.163*** 29.896*** 32.373*** VARIABLE (4.143) (3.128) (2.895) (3.898) (2.965) (2.764)
	Observations	5,213	12,936	18,149	10,513	26,285	36,798
	Number of investors	48	119	167	48	119	167
	Prob > χ 2	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001

* *

For the remainder of the paper, we simply refer to negative tail events as tail events.

Surprise can also be associated with other emotions like anger, fear or hope. When triggered by uncertainty, surprise is also closely associated with stress responses[START_REF] De Berker | Computations of uncertainty mediate acute stress responses in humans[END_REF][START_REF] Peters | Uncertainty and stress: Why it causes diseases and how it is mastered by the brain[END_REF].

Investors experiencing tail events without suffering losses are those who do not buy the asset when a tail event occurs because their stated price is below (or equal to) the random number drawn in the BDM procedure.

An alternative approach to tail events is to consider that even though people learn in a Bayesian way, they misperceive the magnitude of tail events, thus leading to 'outlier blindness'[START_REF] Payzan-Lenestour | Outlier Blindness': Efficient Coding Generates an Inability to Represent Extreme Values[END_REF]. This approach relies on the theory of efficient coding in neuroscience recently introduced to economics[START_REF] Woodford | Prospect theory as efficient perceptual distortion[END_REF][START_REF] Frydman | Efficient coding and risky choice[END_REF] Jin, 2019, Woodford, 2019).

Investors suffering tail losses are those who buy the asset when a tail event occurs because their stated price is strictly above the random BDM number.

Numerous studies in economics and finance have shown that the excess returns of stocks relative to bonds (i.e., the 'equity premium puzzle') could be accounted for by incorporating tail events in the pricing of assets (e.g.,[START_REF] Rietz | The equity risk premium: A solution[END_REF][START_REF] Harvey | Conditional skewness in asset pricing tests[END_REF][START_REF] Barro | Rare disasters and asset markets in the twentieth century[END_REF][START_REF] Barro | Rare disasters, asset prices, and welfare costs[END_REF][START_REF] Bollerslev | Tails, fears, and risk premia[END_REF][START_REF] Gabaix | Variable rare disasters: An exactly solved framework for ten puzzles in macrofinance[END_REF][START_REF] Kelly | Tail risk and asset prices[END_REF][START_REF] Bollerslev | Tail risk premia and return predictability[END_REF][START_REF] Lemperiere | Risk premia: Asymmetric tail risks and excess returns[END_REF]

The other participants knew the picker did not know the instructions for the investment task. An English translation of the instructions for the investment task and for the drawing task is reported in Online Appendix I.3.

This penalty was never implemented. After the picker started his or her task, one of the experimenters installed the physiological tool on the remaining participants (see Section 3.2) who then read the instructions for the investment task. Because the picker started his or her task before the investment task, the potential issue of the picker drawing tokens too slowly never occurred.

This empirical distribution is consistent with random draws because there were exactly two yellow tokens in the bag.

Although some asymmetries in measurements have been observed across hands[START_REF] Picard | Multiple arousal theory and daily-life electrodermal activity asymmetry[END_REF][START_REF] Kasos | Does the electrodermal system "take sides" when it comes to emotions?[END_REF], we do not expect this to be an issue in our design. Indeed, measurements of electrodermal activity on the right and left hands are highly correlated (especially in short lab tasks,[START_REF] Picard | Multiple arousal theory and daily-life electrodermal activity asymmetry[END_REF] so that average estimates, over a large sample (n =

171), are unlikely to be substantially affected. In addition, our statistical analysis does not rely on a precise measurement of the magnitude of emotional arousal but on whether there is an electrodermal reaction to a specific stimulus (the tail event) or not. Finally, asymmetric measurements were mostly observed in social settings, which contrasts with our individual decision-making setup.17 The decision arousal measurement relates to what[START_REF] Bechara | Deciding advantageously before knowing the advantageous strategy[END_REF] refer to as anticipatory arousal.

To maintain focus, we only contemplate basic emotions although the span of emotional reactions is arguably broader[START_REF] Parrott | Emotions in Social Psychology. Key Readings in Social Psychology[END_REF][START_REF] Fox | The Nature of Emotions -Fundamental Questions[END_REF].

We also note that anger personality trait was positively correlated with participants' answers in the post-experiment questionnaire (ρ l = 0.230, p-value = 0.088 for the correlation between the anger trait and participants' self-reported level of anger after incurring tail losses).

The difference in earnings between waves 1 and 2 is explained by the absence of show-up fee for the online step 1 in wave 2 and the difference in the incentivised Blocks conducted in the survey of step 1 (incentivised Blocks 1 and 4 of wave 1 are absent in wave 2, while incentivised Block 13 is only conducted in wave 2) and the additional incentivised comprehension questionnaire in wave 2.

These percentages are based only on periods in which a tail event occurred.

The first availability score is the number of incorrect responses (out of five) on the first availability heuristic test whereas the second availability score is computed as the ratio of correct answers involving a famous name with respect to the total number of correct answers.

The instrument used for 'Buy Dummy' is the random BDM number that was drawn in the corresponding period.

Of the 171 participants, we could not obtain reliable physiological recordings for two because of deficient electrodes.

We note here that as we multiply robustness checks we fall prey to the occurrence of false negatives. If we consider as our main analysis the one using BDM10-and BDM40+ as our bounds for random BDM numbers, then we are conducting 4 robustness checks for each table. That is, for the analysis in Tables5 and 6, we can estimate the probability of obtaining at least one false negative to be greater than one-third.

Cronbach's alpha for wave 1 (wave 2) is 0.59 (0.55).

We selected the 11-item version of the test for its psychometric properties.

We exclude those periods in which participants did not choose their bid within the time limit. This occurred in only 0.4% of the cases.

We thank you for participating in this first session and look forward to seeing you on the SCHEDULED DATE for the second session. We compensate you for your participation. However, you will receive the payoffs related to the tests at the end of the second experimental session. If you do not come to the second session, these payoffs will be permanently lost.

We would like to thank Quentin Thévenet for the design of the computer software and for his assistance during experimental sessions. We also thank Mateus Joffily for his assistance with physiological tools. This research has benefited from the financial support of ( a) the Joint Usage/Research Center, the Institute of Social and Economic Research, Osaka University, (b) Grant-in-aid for Scientific Research Nos. 15H05728, 18K19954 and 20H05631 from the Japan Society for the Promotion of Science, and (c) the French National Research Agency (ANR) under an ORA-Plus project "BEAM" (ANR-15-ORAR-0004), and was performed within the framework of several Programme Investissements d'Avenir under IDEXLYON (ANR-16-IDEX-0005) of Université de Lyon (project INDEPTH), LABEX CORTEX (ANR-11-LABX-0042) of Université de Lyon (ANR-11-IDEX-007) and UCAJEDI (ANR-15-IDEX-01) of Université Côte d'Azur (project UCAinACTION). The design of the experiment reported in this paper has been approved by the IRB of INSERM (#18-493) in May 2018.

The score is computed by summing the evaluations over the 11 statements. This Block is only performed in the first wave of sessions.

Block 10 Availability heuristic 2

Based on Tversky and Kahneman (1974), we administered a second availability heuristic test.

We are going to show you a list of names. Please click OK to view this list. Please pay attention. Mark WRIGHT, Jessica JAMES, Angelina JOLIE, Harry ROBINSON, Steve JOBS, Brandon HUGHES, John CLARKE, Sophie LEWIS, Albert EINSTEIN, Thomas PALMAN, Michelle GARRETT, Joseph SCOTT, Vincent VAN GOGH, Jack BROWN, David CLARKE, Emily ROBERTS, Marie CURIE, Roselyn LACHMAN, Janett SMITH, Julie EVANS, Nelson MANDELA, Oliver JOHNSON, Martin MORTON, Kylie DAVIES, Audrey HEPBURN, Justin TAYLOR, George WILSON, Andrew ROBINSON, Marilyn MONROE, Christine

Online Appendix

The Online Appendix is organised as follows:

I.2 SPECIFIC PROTOCOL FOR STEP 2 (oral instructions)

Once all participants have sat randomly in front of a computer, the experimenter tells them the following.

Welcome. Thank you for participating in this experiment.

Please turn off your phone. You cannot use your phone during this experiment. Paper and pencils are also forbidden. Do not talk to other participants throughout the session.

If at any time during the session you need help, raise your hand and we will immediately come to answer your questions in private. You are 7 people participating in this experiment. Among the 7 participants, one of you was randomly selected to perform a different task from the other 6 participants. This task consists in drawing tokens from the box. This participant will not know the task that the other 6 participants will perform during this experiment. We will now show you the box containing tokens. Look at the box. As you can see, this box contains tokens of 6 different colours.

After the experimenter has shown the box, he tells the participants: We will take a picture that will be reported on your screen to remind you the contents of the box.

The experimenter takes a photograph that is supposed to resemble the one depicted on participants' screens later on.

Once the selected participant goes into the control room, with the box and bag, the experimenter asks him or her: Do you distinguish the 6 colours well?

The selected participant starts the task under the supervision of the experimenter.

For the remaining six participants, the experimenter tells them: This experiment requires the use of a physiological measurement tool. The experimenter will come to each of you to install it on the hand that you don't usually use to write. The experiment will begin when all participants are equipped and we have ensured that the recordings are good.

The experimenter asks participants to rub their hands and installs the physiological tool on the second phalanx of the index and middle fingers of one's participant's hand by applying isotonic gel on the electrodes.

I.3 SPECIFIC INSTRUCTIONS FOR PARTICIPANTS IN STEP 2 (on screen) General presentation at the arrival of the second session

Today is the second experimental session.

I.4 Example of a decision screen

The software in original language is available at: https://bit.ly/2TCY0Av.

To see the task of step 1: In the Config file write session= 1; then launch Myopie.jar, once the first screen appears click on F6 (or Fn F6 from a laptop).

To see the picker's task of step 2: In the Config file write session= 2 and type= 0; then launch Myopie.jar, once the first screen appears click on F6 (or Fn F6 from a laptop).

To see the investor's task of step 2: In the Config file write session= 2 and type= 1; then launch Myopie.jar, once the first screen appears click on F6 (or Fn F6 from a laptop).

I.5 Post-experimental questionnaire about emotions

The order of the two following questions was randomised.

(Q1) When the yellow token was drawn during the experiment and you suffered a loss of 1,000 euro cents, how much did you feel the following emotion? (1-Not at all 2-A little 3-Moderately 4-Very much 5-Very much) (Q2) When the yellow token was drawn during the experiment, but you did not suffer a loss of 1,000 euro cents, how much did you feel the following emotion? (1-Not at all 2-A little 3-Moderately 4-Very much 5-Extremely)

We also randomised the order of presentation of each emotion. We summarise the results below by showing the modal response in each cell.

V Description of the model fitting exercise

We allow noisy bid submission. Namely, in order to fit our model to the data, we assume that investor i submits b in period t according to:

where A std (b, i, t) is the z-score normalised A(b, i, t) (z-score normalization is done across b within each i and t). A(b, i, t) is defined as follows:

Notice that A(b, i, t) is simply the expected "utility" of submitting bid b in period t for investor i. τ i is the noise parameter. If τ i → ∞ then, we are back to the specification of the model in Section 4.1. If τ i → 0, then i submits a bid randomly. We z-score normalised A(b, i, t) to avoid exp(τ i (A(b, i, t))) exploding for some values of τ and α.

In our fitting exercise, we do a grid search to find the set of parameter values that maximise the sum of log-likelihood for each participant i, which can be stated as follows:

where b i t is the bid participant i submitted in period t. 59 We have conducted the following grid search while maintaining the values of η i = 100 and π i = 0.01 for all i in all the models.

for EUT

• α i ∈ [0.2, 2.0], ρ i ∈ [0.0, 1.0], and τ i ∈ [2.0, 20.0] all 2. for PT (with an extension considered in Online Appendix III.1) .1, 2.5], and ρ i ∈ [0.0, 1.0] all with step size 0.2.

• τ i ∈ [2.0, 20.0] with step size of 2.0

• ω -∈ [0.0, 1.0] and ω + ∈ [0.0, 1.0] with step size of 0.2 while assuming ω i -≥ ω i + .

3. A totally random choice, i.e., τ i = 0.

Finally, we use Akaike Information Critrion (AI C = 2k -2ln(L)), where k is the number of parameters in the corresponding model and ln(L) is the sum of the log-likelihood, as the criterion to select among the models discussed in the main text.