Marie-Hélène Broihanne

Efficiency of Betting Markets and Rationality of Players: Evidence from the French 6/49 Lotto

Abstract We analyse the existence of preferred numbers on the French Lotto market and prove that this market is not strongly efficient in the sense of Thaler & Ziemba (1988). The preference for low numbers is investigated by means of stochastic dominance tests. The specific features of the French Lotto game allow us to build a simple estimate of the probability distribution of numbers actually played. The results are compared with the (highly time-consuming) maximum likelihood estimator used by Farrell et al. (2000). It is shown that the two methods give very close results. Our conclusions stress the perspectives of this study in various domains.

The Ability of Children to Delay Gratification in an Exchange Task.

The ability to wait for a reward is a necessary capacity for economic transactions. This study is an age-related investigation of childrens ability to delay gratification in an exchange task requiring them to wait for a significant reward. We gave 252 children aged 2-4 a small piece of cookie, then offered them an opportunity to wait for a predetermined delay period before exchanging it for a larger one. In a first experiment, the children had to exchange the initial food item for rewards two, four or eight times larger. Results showed that children aged 3-4 years old sustained longer time lags for larger rewards than for smaller rewards. This effect was not found in 2-year-old subjects. In a second experiment, a reward 40 times larger than the initial piece was offered to determine the maximum waiting time that children could sustain. All age groups increased their performances. Older children were more successful at waiting, but some children as young as 2 years old were able to tolerate delays of up to 16 min. Older children who chose to give up waiting earlier than their known capacity demonstrated anticipation skills which had not been seen in younger children, showing that they had anticipated an increase in the time lag, and that they had considered both time and reward value when making their decision. Despite the age effect, we did not establish any limits for delaying gratification in children. This study may have educational implications for dealing with behavioral misconduct, which is known to be related to impulsivity control in young children.

Decision-making under risk of loss in children

In human adults, judgment errors are known to often lead to irrational decision-making in risky contexts. While these errors can affect the accuracy of profit evaluation, they may have once enhanced survival in dangerous contexts following a “better be safe than sorry” rule of thumb. Such a rule can be critical for children, and it could develop early on. Here, we investigated the rationality of choices and the possible occurrence of judgment errors in children aged 3 to 9 years when exposed to a risky trade. Children were allocated with a piece of cookie that they could either keep or risk in exchange of the content of one cup among 6, visible in front of them. In the cups, cookies could be of larger, equal or smaller sizes than the initial allocation. Chances of losing or winning were manipulated by presenting different combinations of cookie sizes in the cups (for example 3 large, 2 equal and 1 small cookie). We investigated the rationality of childrens response using the theoretical models of Expected Utility Theory (EUT) and Cumulative Prospect Theory. Children aged 3 to 4 years old were unable to discriminate the profitability of exchanging in the different combinations. From 5 years, children were better at maximizing their benefit in each combination, their decisions were negatively induced by the probability of losing, and they exhibited a framing effect, a judgment error found in adults. Confronting data to the EUT indicated that children aged over 5 were risk-seekers but also revealed inconsistencies in their choices. According to a complementary model, the Cumulative Prospect Theory (CPT), they exhibited loss aversion, a pattern also found in adults. These findings confirm that adult-like judgment errors occur in children, which suggests that they possess a survival value.

Diversification, Gambling and Market Forces

Though simple and appealing, mean-variance portfolio choice theory does not describe actual diversification choices by investors, especially their propensity to gamble and the solvency constraints they face. Using 8 million trades realized by 90,000 individual investors, we show that diversification choices are in fact strongly driven by the skewness of returns, especially in bull markets, but also by the amount to be invested in risky assets. Increasing this amount by 10 % leads to increase by 3.8 % the number of stocks in investors’ portfolios, controlling for portfolio skewness. An important contribution of this paper is to show that the strength of the relationship between diversification and the skewness of returns is shaped by market forces. A strong negative relationship exists in bull markets but disappears in bear markets, a result not found in the literature. Our results survive several robustness checks, including controlling for individual heterogeneity and time-variability of stock price co-movements.In this paper, we first prove analytically that the skewness of returns of portfolios built with Arrow-Debreu securities decreases with diversification. Through simulations, we also show that this result remains true in a financial market with a finite number of states of nature. We then analyze the behavior of over 85,000 individual investors at a large brokerage house. Though the main determinant of underdiversification is the portfolio value we find that the skewness of returns remains significant in explaining diversification after controlling for this value. Moreover, we show that the decrease in skewness induced by diversification is essentially driven by the share of total variance of stock returns due to common factors. These findings extend those of Mitton and Vorkink (2007) and explain the variability over time of the relationship between skewness and diversification.

Appetite for Information in Mandatory Profiling of Individual Investors

Financial knowledge and the investment in information of retail investors have been under scrutiny on the side of regulators and of academics. Actually, increasing financial literacy of individuals is one of the promising avenues in order to increase financial markets participation. In this paper, we use a natural field experiment offered by MiFID questionnaires to analyze the relationships between personal traits and trading behavior of retail investors who ask for supplementary information. Under a random matching procedure that controls for various survey answers, we analyze the trading characteristics of investors only differing from others on the side of their information appetite. We find that the investors who voluntary ask for more financial information, revealing de facto a particular personality trait, tend to behave more consistently with the Traditional Finance theory. Actually, they trade on a larger stock universe, execute less day-trades and are better diversified. They finally earn higher returns.

Children Base Their Investment on Calculated Pay-Off

To investigate the rise of economic abilities during development we studied children aged between 3 and 10 in an exchange situation requiring them to calculate their investment based on different offers. One experimenter gave back a reward twice the amount given by the children, and a second always gave back the same quantity regardless of the amount received. To maximize pay-offs children had to invest a maximal amount with the first, and a minimal amount with the second. About one third of the 5-year-olds and most 7- and 10-year-olds were able to adjust their investment according to the partner, while all 3-year-olds failed. Such performances should be related to the rise of cognitive and social skills after 4 years.