Risk attitudes in large stake gambles: evidence from a game show (original) (raw)

2008, Applied Economics

https://doi.org/10.1080/00036840701235704

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Abstract

the Mexican version of Deal or No Deal. We consider both dynamic agents who fully backward induct and myopic agents that only look forward one period. Further, we vary the level of forecasting sophistication by the agents. We find substantial evidence of risk aversion, the degree of which is more modest than what is typically reported in the literature.

Risk Aversion when Gains are Likely and Unlikely: Evidence from a Natural Experiment with Large Stakes

Theory and Decision, 2008

In the television show Deal or No Deal a contestant is endowed with a sealed box, which potentially contains a large monetary prize. In the course of the show the contestant learns more information about the distribution of possible monetary prizes inside her box. Consider two groups of contestants, who learned that the chances of their boxes containing a large prize are 20% and 80% correspondingly. Contestants in both groups receive qualitatively similar price offers for selling the content of their boxes. If contestants are less risk averse when facing unlikely gains, the price offer is likely to be more frequently rejected in the first group than in the second group. However, the fraction of rejections is virtually identical across two groups. Thus, contestants appear to have identical risk attitudes over (large) gains of low and high probability.

Empirical investigation of some properties of the perceived riskiness of gambles

Organizational Behavior and Human Decision Processes, 1986

Empirical tests of some properties of the perceived riskiness of gambles are reported. In experiments conducted with U.S. and German subjects, we observed a remarkable consistency in risk judgments. Four possible measures of risk, derived by R. Duncan Lute, were examined. We found that risk decreases as a constant amount is added to all outcomes of a gamble. ?ivo of Lute's measures require that risk not change with the addition of a constant, and thus these measures are not appropriate for describing perceived risk. We also found that Lute's logarithmic measure is not empirically valid. Lute's fourth measure (the expectation of the absolute value of the outcomes raised to a parameter 0) seems to have more promise than his other three measures. These results provide some necessary conditions that a new theory or extension of Lute's measures must satisfy. 0 1986 Academic Press, Inc. We thank the referees for their suggestions and Joao Becker for his assistance in carrying out statistical tests.

Are more risk averse agents more optimistic? Insights from a rational expectations model

Economics Letters, 2008

We analyse the link between optimism and risk aversion in a model with endogeneous beliefs formation. We consider a model of partially revealing, competitive rational expectations equilibrium with diverse information, in which the distribution of risk aversion across individuals is unknown. We show that when a high individual level of risk-aversion is taken as a signal for a high average level of risk aversion, more risk averse agents are more optimistic. Such a positive correlation is important for the analysis of collective decision making as shown by Jouini and Napp (2007).

Risk aversion in prediction markets: A framed-field experiment

Journal of Business Research, 2016

To make better decisions today, companies and other economic agents are interested in getting accurate predictions of future events. Prediction markets can, at least potentially, give those accurate forecasts for the probability of the event by aggregating information from traders. However, formal studies highlight that the risk attitudes of market participants may bias the market equilibrium prices, and consequently make the prediction unreliable. This research examines the effect of participants' risk attitudes on prediction market prices, through a framed field experiment on the two semifinals at the 2015 NCAA Men's Division Basketball Tournament. The results of the experiment show a significant price difference between the risk-averse group and the less risk-averse group. The large price discrepancy between markets with participants with varying risk aversion suggests that risk aversion deserves a critical consideration in future prediction-market research and implementation.

Decision making and risk aversion in the Cash Cab

Journal of Economic Behavior & Organization, 2012

We use the Emmy Award-winning game show Cash Cab to study decision-making in a risky framework. This is a unique environment because, unlike other studies on risk-aversion, players participate individually or in teams varying in number from two to five. This creates a natural laboratory to measure performance and risk aversion conditional upon the size of the team as well as the characteristics of the team members. Our results are striking. Teams are much more likely to complete overall tasks successfully. There are noted differences conditional on gender makeup of the groups. Most importantly, risk aversion estimates indicate that when participants are part of a group, they focus on the overall size of the dollar amounts that are "at risk", rather than their "slice of the pie". The implications of our results span a number of areas where groups are part of the financial decision-making process, including investment analysis and portfolio management, corporate governance, and corporate finance. 1 The authors would like to thank Tom Cohen of Lion Television and Christine Murphy for her assistance with data entry. All remaining errors are our own. We would also like to thank Peng Peng for his research assistance.

Are More Risk-Averse Agents More Optimistic? Insights from a Simple Rational Expectations Equilibrium Model

Social Science Research Network, 2006

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Risk aversion in economic transactions

Europhysics Letters (EPL), 2002

PACS. 02.50.Le -Decision theory and game theory PACS. 05.45.-a -Nonlinear dynamics and nonlinear dynamical systems PACS. 05.90.+m -Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems Abstract Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of "expected utility theory" which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude under risky choices; this index q is in fact the entropic one which plays a central role in nonextensive statistical mechanics. Different long term patterns of average asset redistribution are observed according to the distribution of parameter q (chosen once for ever for each operator) and the rules (e.g., the probabilities involved in the gamble and the indebtedness restrictions) governing the values that are exchanged in the transactions. Analytical and numerical results are discussed in terms of how the sensitivity to risk affects the dynamics of economic transactions.

Rationality on the rise: Why relative risk aversion increases with stake size

Journal of Risk and Uncertainty, 2010

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that, contrary to gains, no coherent change in relative risk aversion is observed for losses. The increase in relative risk aversion over gains cannot be captured by the curvature of the utility function. It is driven predominantly by a change in probability weighting of a majority group of individuals who exhibit more rational probability weighting at high stakes. These results not only challenge expected utility theory, but also prospect theory.

Risk Preferences at Different Time Periods: An Experimental Investigation

I ntertemporal decision making under risk involves two dimensions: time preferences and risk preferences. This paper focuses on the impact of time on risk preferences, independent of the intertemporal trade-off of outcomes, i.e., time preferences. It reports the results of an experimental study that examines how delayed resolution and payment of risky options influence individual choice. We used a simple experimental design based on the comparison of two-outcome monetary lotteries with the same delay. Raw data clearly reveal that subjects become more risk tolerant for delayed lotteries. Assuming a prospect theory-like model under risk, we analyze the impact of time on utility and decision weights, independent of time preferences. We show that the subjective treatment of outcomes (i.e., utility) is not significantly affected by time. In fact, the impact of time is completely absorbed by the probability weighting function. The effect of time on risk preferences was found to generate probabilistic optimism resulting in a higher risk tolerance for delayed lotteries.

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Forecasting risk attitudes: An experimental study using actual and forecast gamble choices

Journal of Economic Behavior & Organization, 2008

We develop and evaluate a simple gamble-choice task to measure attitudes toward risk, and apply this measure to examine differences in risk attitudes of male and female university students. In addition, we examine stereotyping by asking whether a person's sex is read as a signal of risk preference. Subjects choose which of five 50/50 gambles they wish to play. The gambles include one sure thing; the remaining four increase (linearly) in expected payoff and risk. Each subject also is asked to guess which of the five gambles each of the other subjects chose, and is paid for correct guesses. The experiment is conducted under three different frames: an abstract frame where the two highest-payoff gambles carry the possibility of losses, an abstract frame with no losses, and an investment frame that mirrors the payoff structure of the former. We find that women are significantly more risk averse than men in all three settings, and predictions of both women and men tend to confirm this difference. While average guesses reflect the average difference in choices, only 27 percent of guesses are accurate, which is slightly higher than chance.

Risk Attitudes Toward Small and Large Bets in the Presence of Background Risk

Review of Finance, 2011

If an individual with expected utility and a reasonable level of wealth rejects a small actuarially favorable gamble, it implies a very high degree of risk aversion. It also predicts (counterfactually) the rejection of more sizable and very attractive bets. If additional background uncertainty affects wealth, this result also applies to non-expected utilities. The authors describe a set of reasonable conditions under which an individual may reject the small bet but accept the large bet, even in the presence of background uncertainty. The two critical assumptions that the authors use are rank-dependent utility and a discrete distribution for background risk. Plausible calibrations can reconcile large/small bet risk attitudes and the empirical evidence on limited stock market participation in the presence of labor income risk. JEL Classification: G10 * We are grateful for detailed comments from Thierry Foucault (the editor) and an anonymous referee. We also thank Nick Barberis for comments on some results obtained at the early stage of this project.

The hot hand belief and the gambler’s fallacy in investment decisions under risk

Theory and Decision, 2010

We conduct experiments to analyze investment behavior in decisions under risk. Subjects can bet on the outcomes of a series of coin tosses themselves, rely on randomized 'experts', or choose a risk-free alternative. We observe that subjects who rely on the randomized experts pick those who were successful in the past, showing behavior consistent with the hot hand belief. Obviously the term 'expert' suffices to attract some subjects. For those who decide on their own, we find behavior consistent with the gambler's fallacy, as the frequency of betting on heads (tails) decreases after streaks of heads (tails).

Hindsight bias and individual risk attitude within the context of experimental asset markets

The Journal of …, 2002

This paper investigates (i) the robustness of hindsight bias in experimental as-set markets, (ii) the time invariance of the different experimental risk elicitationmethods of certainty equivalents and binary lottery choices, and (iii) their corre-spondence. The results of our within-subjects approach with 133 traders do notsupport the conjecture that hindsight bias is a general phenomenon. Furthermore,our findings challenge the presumption of time-stable risk preferences and of pro-cedural invariance with respect to different experimental risk elicitation methods.

Rational Expectations at the Racetrack : Testing Expected Utility Using Prediction Market Prices

Empirical studies have cast doubt on one of the bedrocks of applied economic modeling -the expected utility hypothesis. Economists have documented pricing anomalies, like the long-shot bias in prediction markets (low probability events are priced too high), that are inconsistent with representative agent models. In this paper, we show that the inconsistency is due to the representative agent assumption, and not to the expected utility hypothesis. When agents differ in their information sets and risk preferences, we show that trader heterogeneity can easily explain the observed pattern of price variation across betting and prediction markets. In particular, the long shot bias is found to be due to a group of traders, whom we dub the "risk-averting grandmas", who make up about 40 percent of the trading group and bet on the top favorite in a race in exchange for a premium. We show also that the expected utility hypothesis outperforms the main "behavioral" alternatives, rank dependent expected utility, and cumulative prospect theory.

Hindsight Bias, Risk Perception, and Investment Performance

Management Science, 2009

Once they have observed information, hindsight-biased agents fail to remember how ignorant they were initially; “they knew it all along.” We formulate a theoretical model of this bias, providing a foundation for empirical measures and implying that hindsight-biased agents learning about volatility will underestimate it. In an experiment involving 66 students from Mannheim University, we find that hindsight bias reduces volatility estimates. In another experiment, involving 85 investment bankers in London and Frankfurt, we find that more biased agents have lower performance. These findings are robust to differences in location, information, overconfidence, and experience.

Do bettors prefer long shots because they are risk-lovers, or are they just overconfident?

Insurance: Mathematics and Economics, 1996

This study examines whether bettors' risk preferences or overconfidence in choosing winners better explains their well documented preference for low-probability wagers. Although previous studies using racetrack data often suggest that risk-loving behavior explains long-shot preference, such data cannot distinguish between the alternative explanations. We use football betting data to make the comparison and find that overconfidence more closely fits the data. This result complements evidence of overconfidence from behavioral studies as well as stock-market models of overconfident noise traders.

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A test of the rational expectations hypothesis using data from a natural experiment

Applied Economics, 2011

Data on contestants' choices in Italian Game Show Affari Tuoi are analysed in a way that separates the effect of risk attitude from that of beliefs concerning the amount of money that will be offered to contestants in future rounds. The importance of belief-formation is confirmed by the estimation of a mixture model which establishes that the vast majority of contestants are forward-looking as opposed to myopic. The most important issue addressed in the paper is what belief function is actually being used by contestants. This function is estimated in an unconstrained way as a component of the choice model, which is estimated using maximum simulated likelihood. Separate identification of the belief function and preferences is possible by virtue of the fact that at a certain stage of the game, beliefs are not relevant, and risk attitude is the sole determinant of choice. The rational expectations hypothesis is tested by comparing the estimated belief function with the "true" offer function which is estimated using data on offers actually made to contestants. We find that there is a significant difference between these two functions, and hence we reject the rational expectations hypothesis. However, when a simpler "rule-of-thumb" structure is assumed for the belief function, we find a correspondence to the function obtained from data on actual offers. Our overall conclusion is that contestants are rational to the extent that they make use of all available relevant information, but are not fully rational because they are not processing the information in an optimal way. The importance of allowing the choice data to convey the belief function without prejudice is emphasised. JEL Codes: C15; C23; C25; D81.

Risk-Taking Behavior: An Experimental Analysis of Individuals and Dyads

Southern Economic Journal

The decision to undertake risk is often made by pairs (dyads), while much of the economics literature on risk taking focuses on the individual. We report the results of controlled laboratory experiments that compare behavior between individuals and pairs. Using the Holt and Laury (2002) procedure and a within-subjects design, we find that pair choices are largely consistent with subjects bargaining over the outcome rather than the pairs taking a more extreme stance than the individual members. Further, gender and age but not personality seem to influence relative bargaining weight. We also find that individuals are more willing to take risks after making decisions as part of a pair than beforehand. Both the personality of one's partner and nontask social interaction influence subsequent individual risk-taking behavior.

Who Really Wants to Be a Millionaire? Estimates of Risk Aversion from Gameshow Data

Journal of Applied Econometrics, 2013

There is a considerable variation in estimates of the degree of risk aversion in the literature. This paper analyses the behaviour of contestants in one of the most popular TV gameshows ever to estimate a CRRA model of behaviour. This gameshow has a number of features that makes it well suited for our analysis: the format is extremely straightforward, it involves no strategic decision-making, we have a large number of observations, and the prizes are cash and paid immediately, and cover a large range -up to £1 million. Our data sources have the virtue that we are able to check the representativeness of the gameshow participants. While the game requires skill, which complicates our analysis, the structure of the game is very simple so that complex probability calculations are not required of participants.

Do measures of risk attitude in the laboratory predict behavior under risk in and outside of the laboratory?

Journal of Risk and Uncertainty

We consider the external validity of laboratory measures of risk attitude. Based on a large-scale experiment using a representative panel of the Dutch population, we test if these measures can explain two different types of behavior: (i) behavior in laboratory risky financial decisions, and (ii) behavior in naturally-occurring field behavior under risk (financial, health and employment decisions). We find that measures of risk attitude are related to behavior in laboratory financial decisions and the most complex measures are outperformed by simpler measures. However, measures of risk attitude are not related to risk-taking in the field, calling into question the methods currently used for the purpose of measuring actual risk preferences. We conclude that while the external validity of measures of risk attitude holds in closely related frameworks, this validity is compromised in more remote settings.

Risk Preferences and Risk Perceptions among Smallholder Maize Farmers in Tanzania: Evidence from a Framed Field Experiment

Theoretical Economics Letters, 2023

The information on risk preferences and risk perceptions among maize farmers in maize highly growing highlands is limited. Similarly, relationships between socio-demographic factors and risk preferences are not clearly explored. A risk game with pay-offs and a hypothetical scenario in a survey questionnaire were performed to assess the risk preferences of maize farmers in maize-growing regions of the Southern and Northern highlands of Tanzania. Risk ranking was executed during focus group discussions and revealed that risk perceptions of maize farmers varied across gender and location. Cross-sectional data on farmers' and farms' characteristics including risk scenarios from an Agronomic Panel Survey (APS) of the 2016/2017 growing season was collected from 560 Household Heads (HHs), randomly selected within a spatial sampling frame. The study recommends the inclusion of risk preferences and risk perceptions status of farmers in policy-making and the introduction of new agricultural technologies in order to foster a high adoption rate and advancement of agricultural development.