The impact of near-miss events on betting behavior: An examination of casino rapid roulette play

We examine how almost winning in roulette affects subsequent betting behavior. Our main finding is heterogeneity in gambler behavior with some gamblers less likely to bet on numbers that were near misses on the prior spin and other gamblers more likely to bet on near miss numbers. Using a unique data set from the game rapid roulette, we model the likelihood of a gambler betting on a near miss number while controlling for the favorite number bias and the likelihood of a number being a near miss. We also find no evidence that near misses in roulette leads to gamblers extending the time spent gambling or to the placing of more bets

The impact of near-miss events on betting behavior: An examination of casino rapid roulette play

We examine how almost winning in roulette affects subsequent betting behavior. Our main finding is heterogeneity in gambler behavior with some gamblers less likely to bet on numbers that were near misses on the prior spin and other gamblers more likely to bet on near miss numbers. Using a unique data set from the game rapid roulette, we model the likelihood of a gambler betting on a near miss number while controlling for the favorite number bias and the likelihood of a number being a near miss. We also find no evidence that near misses in roulette leads to gamblers extending the time spent gambling or to the placing of more bets

Fear in Asset Allocation During and After Stock Market Crashes An Experiment in Behavioral Finance

Abstract We test for the presence of fear in an experiment in which subjects make portfolio allocation decisions with market returns from the Great Crash of 1929. Half the subjects make allocation decisions prior to the market crash while the other half make allocation decisions at the start of the crash. The results show that subjects who start the experiment with declining stock returns allocate 8% less to stocks than subjects who start the experiment with increasing stock returns. Risk aversion, hedging and reactive loss aversion are all present in subjects' behavior, but cannot explain a significant fraction of the variance in stock allocations during and after crashes. It is also found that fear during and after crashes is associated with the behavior of male participants. Fear in Asset Allocation During and After Stock Market Crashes An Experiment in Behavioral Finance "Now a practical theory of the future based on these three principles 1 has certain marked characteristics. In particular, being based on so flimsy a foundation, it is subject to sudden and violent changes. ) Knowing that our own individual judgment is worthless, we endeavor to fall back on the judgment of the rest of the world which is perhaps better informed. That is, we endeavor to conform with the behavior of the majority or the average. The psychology of a society of individuals each of whom is endeavoring to copy the others leads to what we may strictly term a conventional judgment. 50 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) Introduction In this paper we consider the impacts of asset crashes on the rationality of the individual investor. A recent Money magazine column opened with the question "What would it take to diminish the terrifying memories of the worst financial crisis since the Depression? Well, a massive bull market could do the trick" (Bigda & Wang, 2011). Our experimental evidence suggests that while a massive bull market cannot hurt, it is not likely to completely erase the memory of the crash. As Keynes noted in 1937, the gap between rationality and fear may be as slim as water on a flat rock. If investors fall prey to fear during stock market crashes, the question addressed in this paper is what effect this has on subsequent investment behavior. This paper examines the asset allocation behavior of investors under extreme conditions. In an asset allocation experiment, subjects were exposed to the equity return stream of one of the most volatile periods in stock market history, the period surrounding the stock market collapse of 1929, often refereed to as Black Tuesday. The results from this experiment show that risk-taking behavior is influenced by age and gender, the history of the prior returns, and the magnitude of asset declines. But the primary finding from the experiment is that even after controlling for several rational factors that impact subject asset allocation decisions there is a leftover amount of stock selling, which we attribute to fear, which causes diminished risk taking behavior. This result is consistent with the findings of Malmendier and Nagel (2001), who suggest that the market returns investors experience early in their life have a long term impact on future allocations to risky assets. The asset allocation experiment and results are summarized next. Subjects made asset allocation decisions for 20 years and had a choice of one risky asset and one riskless asset. The experimental design is a 2x2 between subject design. One factor varied the return stream on the equity investment; one group of subjects (the UP group) began investing in a strong bull market where the returns on the risky asset were significantly positive in Years 1-4. The other group (the DOWN group) began investing in a steep bear market where the returns on the risky asset were significantly negative in Years 1-4. The initial equity returns for the UP group came from the time period from 1925-1928 and the returns for the DOWN group began with the equity returns from [1929][1930][1931][1932]. Both groups then received the same equity returns from [1933][1934][1935][1936][1937][1938][1939][1940][1941][1942][1943][1944]. The second experimental factor varied whether subjects received a happy or sad face (the FACE group) to highlight the prior year's return or simple received quantitative feedback data (the NO FACE group). Summarizing some important regression results from the experiment's data, we find that a variable derived from the Consumption Capital Asset Pricing (C-CAPM) model is among the most influential factors in predicting the allocation to the risky investment. After controlling for this rational explanation of investment behavior, the results show that subjects in the DOWN group allocate about 7.5% less to the risky asset, and each year of age adds about 0.2% to holdings of the risky asset. Additionally, after controlling for age, gender and the C-CAPM variable, subjects were also sensitive to losses incurred in prior periods, reducing their stock holdings by 2 to 3 percentage points after three periods of cumulative losses and by as much as 7-8 percentage points following a single period of losses. Finally, our analysis highlights the importance of the year 1931. The return on the Dow Jones Industrial Average was -53% in 1931, making it the worst performing year of the Dow in history. Following this year (1933) in the experiment, and after controlling for all of the prior factors just identified, male subjects 51 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) allocate about 17% less to the risky asset in the next year (1934) of the experiment. We interpret this statistically significant and quantitatively large finding as evidence of the existence fear in these subjects' allocation decisions. The remainder of this paper is organized as follows: Section 2 reviews the literature which motivated this study. Section 3 presents the data and methodology. Section 4 discusses our results. Section 5 summarizes the major findings and concludes the paper. 2. Relevant literature and motivation for the study Modern Portfolio Theory (MPT) is an optimal model of how investors should make investment decisions. If investors are only concerned with the mean and variance of their portfolio returns over a single period, MPT 2 shows how investors can maximize expected utility by splitting their asset allocation between the riskless asset and the risky market portfolio. One of the underlying assumptions in the model is that investors can and should behave perfectly rational in making investment decisions (see The long history of market booms and busts calls into question the perfect rationality of investors and markets. 52 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) markets have gone up and investing more conservatively after markets have gone down (see i.e. DeBondt & Thaler (1985), The idea that greed and fear are periodic components of financial markets is in the background of Minsky's financial instability hypothesis (Minsky, 1992). The financial instability hypothesis is a theory of endogenous changes in risk preferences over the financial cycle, as they reflect on corporate debt structure and its impact on economic activity. Minsky suggests that like many actors in a capitalist economy bankers behave entrepreneurially and seek out market innovations. Bankers and other financial market participants are profit-driven and subject to forces of greed and fear. A long period of prosperity eventually erases memories of panics and crashes, attenuating fear and leading to increasingly risky decisions. Minsky proposes that this fear attenuation progressively tilts the debt-income relations of economic units from hedge to speculative finance at first, and then from speculative to Ponzi finance, the most fragile debt-income structure. When Ponzi finance prevails, the economy becomes unstable and asset values eventually collapse. The crash acts by attenuating greed, and for as long as the memories about the crash remain fresh, debt structures are of the hedge type, the most prudent, since behavior is dominated by fear. What this paper tests for is the presence of fear during and after a crash in asset prices. To examine how subjects react to market crashes in an experimental setting we begin by specifying how they should behave assuming they invest rationally. To do this, we use the C-CAPM as the model of how subject should behave. The C-CAPM encompasses the standard CAPM, and describes how risk-averse agents make rational asset allocations (see Breeden Experimental Design and Procedures An experiment was designed in which the subjects experienced the returns from the period surrounding the Crash of 1929. Subjects made repeated asset allocation decisions 53 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) choosing between a risk free asset and a risky asset. The risk free asset had constant return of 4% while the risky asset returns were those of the Dow Jones Industrial Average (DJIA). The subjects were divided into two groups. One group experienced returns from 1925-1944 the other from 1929-1948. Returns over that period are shown in the figure below. [Insert Figure I Here] One of the behaviors examined in the paper is how the initial asset returns affect subsequent subject behavior. One group experiences mostly positive returns for the first four periods while the second group experiences four periods of large negative returns. As seen in [Insert Table I Here] The basic task for subjects in the experiment was to allocate an endowment of money across a riskless (Cash) and risky (Stock) investment options. Subjects made these allocation decisions using a spreadsheet interface which is shown in [Insert Table II Here] Subjects were recruited through an advertisement in the campus mail sent to all University of Nevada, Reno staff employees, approximately 1,400 employees. The flyer stated that a subject could earn between $5.00 and$50.00 depending upon performance for participation in a one hour experiment on investment decision making. Fifty nine subjects signed up to participate in the experiment. The experiment was conducted in a computer lab in the College of Business at the University of Nevada, Reno. Upon sitting down, each subject received a copy of the human subject consent form and condition instructions. The experiment began with the reading aloud of the consent form and instructions. After consent was obtained, each subject received a $5.00 show-up fee. Since the recruitment flyer stated that subjects would receive a minimum compensation of$5.00, the show-up fee was given to fulfill this promise. Subjects were then 54 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) told that any further compensation in the experiment was contingent on their performance in an asset allocation task. After all the instructions were read and questions answered, the subjects then made two practice decisions for which they were not paid. After their practice decisions, the subjects had a final opportunity to ask any remaining questions. Each subject then proceeded at his or her own pace in making their asset allocation decisions for each of the 20 years. Most subjects took 25 to 45 minutes to make all of their decisions. After all the decisions were completed, each subject filled out a short questionnaire and a receipt documenting their earnings. Each subject then walked to the back of the room where they were paid individually and anonymously in cash for their performance, thanked, and dismissed from the laboratory. The subject pool was 41% male and 59% female. The average age of participants was 40, with 19% in the 18-25 age bracket, 37% in the 25-39 age bracket, 31% in the 40-59 age bracket and 14% were 60 or older. Each subject was asked to self report on how much experience he or she had with investment decisions similar to those in the experiment. On a 1-7 scale (1= none at all, 7 =a great deal) the average response to this investment experience question was 3.2, with 36% answering 1 or 2, 58% answering 3, 4 or 5, and 7% answering 6 or 7. Discussion of Results Condition Effects The design of the experiment is a 2x2 (Up/Down x Face/No Face) between subjects design. To test for condition effects, a repeated measures ANOVA is conducted using the Proc Mixed procedure in SAS. Two dependent measures are used: 1) the percentage asset allocation to the stock investment (PS); and 2) the change in the percentage asset allocation to the stock investment from the prior period (ChS). The independent variables include the condition variables UP (Up/Down) and FACE (Face/No Face), the repeated measure variable YEAR, and the interaction effects (UP*FACE, UP*YEAR, FACE*YEAR, UP*FACE*YEAR). For both dependent variables there are significant effects for YEAR (p<0.01) and the UP*YEAR (p<0.01) interaction effect; the FACE variable shows no significance in either model and will be dropped from future analyses. The average change in the allocation to S (defined as the allocation to S in time period t minus the allocation to S in time period t-1) across the twenty years is almost identical in the Up 55 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) and Down conditions at 0.2% and -0.2% respectively. But the overall average change in the allocation to S does not show the significant change on a year by year basis. In the Up condition, the least squares means test show that there is significant difference in the allocation to S in years 10 (11.3%, p<0.01), 14 (-16.4%, p<0.01), 15 (16.9%, p<0.01), and year 16 (8.2%, p<0.05). In the Down condition, there is significant difference in the allocation to S in years 3 (-11.5%, p<0.01), 6 (13.9%, p<0.01), 10 (-10.3%, p<0.05), 11 (14.3%, p<0.01) and year 20 (9.0%, p<0.05). The pattern in the change in the allocation to S is quite consistent and it appears as if subjects are predominantly responding in manner consistent with beliefs of positive autocorrelation in market returns. As shown in This positive autocorrelation pattern is consistent across the Up and Down conditions as seen in [Insert figure IV here] Figure IV overlaps the level of S and the change in S allocations in the Up and Down conditions and matches up the years in which the S returns were the same. After matching the years in which subjects in the Up and Down conditions received the same returns on S, a differences in least squares means test reveal no statistical significant difference in any year on either the level of S or the change in S. The Identification of Fear in Stock Allocations Our strategy to identify the presence of fear in stock allocations relies on three key elements, which involve exploiting the experimental design, separating rational and emotional responses (i.e., separating risk aversion and loss aversion from fear), and separating fear from anxiety, a confounding emotion. The experimental design was such that, by construction, the only difference between the Up & Down groups is one of timing in the return streams to which they were exposed. Recall that the subjects in the Down group started the experiment with precipitous falls in stock prices that mimic the falls that actually took place during the Great Depression whereas the subjects in the Up group only saw those falls in later years and started the experiment observing solid gains in stock returns. Therefore, since the stream of returns only differed in their timing, there should be no difference in the allocations of both groups if both groups display full rationality. But, if the Up group holds more stocks after controlling for rational factors affecting the subjects' behavior, then there is evidence that some response beyond purely rational risk-aversion may be at play for the subjects who started the investment experiment under "depression-like conditions" and had no chance to experience the "good times" first. Next, we propose that if fear is present, it should show up during large declines in the stock market. Hence, we first create dummy variables to separate CHANGES in the stock market 56 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) from DECLINES in the stock market with the idea that for fear to matter the DECLINE variables need to be significant, not just changes. We create dummy variables for CHANGES (positive or negative values) in stocks' returns higher than or equal to 15%, 25% and 40% respectively and DECLINE dummy variables for stock market DECLINES (negative values only) higher than or equal to 15%, 25%, and 40% respectively. Since fear is more likely to be present during large declines than during mild declines, in which anxiety is more likely to be the dominant emotion, we expect to find that only DECLINES larger than or equal to 40% are the significant ones, both statistically and quantitatively, when trying to explain portfolio allocations to stocks. To avoid confounding fear with risk aversion, we constructed a variable modeled after C-CAPM which was designed to capture the rational response that risk-averse rational agents would display in the face of rapidly falling stock prices. 4 The C-CAPM variable displays only cross-subjects variation, since there is only one value of the covariance per subject for the whole 20 periods of the experiment. In the C-CAPM, the covariance between the marginal utility of the account balance (which proxies for consumption in our case) and the returns of the risky asset (stocks, in our case) is a core conceptual ingredient. Proceeding in this way we achieve two things. First, we isolate the rational component of the subjects' behavior, and second we avoid confounding fear with risk aversion. Another potential confounding factor when trying to identify fear is loss aversion. In order to control for loss aversion, a set of loss aversion variables was created and used as explanatory variables in the asset allocation regressions. Among those variables, we used the monetary value of losses lagged one period, a dummy variable to identify periods that display losses, and losses as a percent of $5, the initial account balance; this last variable uses the initial amount of money in subjects' accounts as a reference value. Regression Results The presence of fear should be negatively and monotonically related to the changes in stock market returns. However, fear requires significant declines in the market, (as opposed to moderate or small declines) and should operate independently of risk aversion and loss aversion. The following general model is used to explore subject behavior: STOCKS it = 0 + 1 CCAPM i + 2 DECLINE(j) t 3 DOWN i + 4 GENDER i + 5 AGE i + 6 LOSS AVERSION it + 7 NOCHANGE50 i + 8 GENDER i *DECLINE(j) t it (1) The following information was given to subjects regarding the investments and potential return on the assets in the experiment. To explain the Stock investment, subjects were told: U.S. Stocks -This is a portfolio of stocks made up of the largest companies in the United States. This is also called a Large Cap Index. The stocks in this index include a representative sample of the leading companies in leading industries in the U.S. economy. U.S. Stocks -The annualized return on Stocks has averaged 7.7% from 1921-2009. One year during this time period the return on Stocks was as high as 66.7% and another year as low as (negative) -52.7%. The majority of the annual returns on Stocks fell within one standard deviation of the average, or between -12.3% and 27.7%. Subjects were told that Cash was a riskless investment and would always generate an annual return of 4%. 4 The C-CAPM variable is for each subject the covariance between the marginal utility of his/her account balance and the return stream the subject was confronted with. The marginal utility of the account balance was calculated as the inverse of the dollar amount in the subjects' account in each period, since the utility function was assumed to be logarithmic, a function that is both consistent with the risk-aversion assumption of the C-CAPM and standard in empirical applications. For a more detailed explanation of C-CAPM please see 57 Federico L. Guerrero, Gregory R. Stone and James A. Sundali/The Journal of Behavioral Finance & Economics 1 (2012) where, STOCKS i,t is the percentage of stocks that subject i held in period t; DECLINE(j) is a dummy variable that captures the decline of the DJIA (j =15%-24%, 25%-39%, 40% or larger); CCAPM is the covariance between the stream of returns faced by subject i and the marginal utility of consumption (proxied by the inverse of the account balance, under the assumption of logarithmic utility), the key component of C-CAPM model which captures the risk aversion and hedging motives in subjects' behavior (this variable only displays cross-subjects variation, but no time variation, since it is calculated for each subject as the covariance of the inverse of the subject's account balance and stocks' returns over the 20 year period of the experiment); DOWN is the group of subjects which experienced negative stock market returns during the first four periods of their

Equilibrium Play in Large Group Market Entry Games

Coordination behavior is studied experimentally in a class of noncooperative market entry games featuring symmetric players, complete information, zero entry costs, and several randomly presented values of the market capacity. Once the market capacity becomes publicly known, each player must decide privately whether to enter the market and receive a payoff, which increases linearly in the difference between the market capacity and the number of entrants, or stay out. Payoffs for staying out are either positive, giving rise to the domain of gains, or negative, giving rise to the domain of losses. The major findings are substantial individual differences that do not diminish with practice, aggregate behavior that is organized extremely well in both the domains of gains and losses by the Nash equilibrium solution, and variations in the population action strategies with repeated play of the stage game that are accounted for by a variant of an adaptive learning model due to Roth and Erev (1995).Coordination Behavior, Market Entry Games, Adaptive Learning Models, Games with Multiple Equilibria, Experimental Economics

Booms, Crashes and Early Investment Experiences in a Laboratory Experiment Booms, Crashes and Early Investment Experiences in a Laboratory Experiment

Abstract Standard economic and finance models have for the most part neglected the influence of early life experiences on economic and financial decisions. However, in recent times there has been an interest in researching the importance of early life experiences on portfolio decisions (Bucciol and Miniaci, 2011; Bucciol and Zarri, 2013, for instance). Our research tests the influence of early life experience on portfolio decisions in the laboratory. Our experiment consists of two cohorts playing an investment game in which they allocated a small amount of money between cash and stocks. The "Down" cohort started their investment allocations facing a market downturn, while the "Up" cohort started off the investment game facing returns from a stock market boom. Our main findings are as follows. First, after controlling for the effects of observable characteristics such as age, gender, financial literacy, etc., booms and busts have different effects depending on their timing. In particular, downturns that happen early in life lead subjects to allocate significantly less to ATINER CONFERENCE PAPER SERIES No: BUS2013-0459 7 stocks. Furthermore, this effect is of a permanent nature. Subjects that faced a bust early in life tended to behave more prudently when later confronted with a boom than the subjects who started off the investment game facing a boom, a finding that lends some support to Minsky's hypothesis of endogenous financial cycles. Overall, subjects who started their investment lives facing a stock market downturn held roughly 7% less stocks than subjects that faced a stock market boom at the beginning of their investment lives. A boom early in life is associated with more stock holdings (+ 7.54%; p = 0.005). However, the next time that subjects in the "UP" condition are faced with a boom, there is no significant effect on stock holdings, suggesting that the nature of the early boom experience is neither augmented further by the second boom, nor reduced below its prior level. In other words, the effect of the initial boom is of a permanent nature