For the purpose of direct comparison of the laboratory and field studies, we provide results from the laboratory and contrast them with the findings from the field study presented in [
17]. Each comparison comes with a discussion about the similarities and differences between the two experimental settings. Please note that, while we expected differences between the laboratory and field settings, we did not have clear expectations on the nature of these differences because our investigation provides the first such direct comparison for a study with a large number of participants and of traded securities. We further summarise this analysis in
Section 6. Data from the field and the laboratory experiments are published on the Open Science Framework at
https://osf.io/6jm9p/.
5.1. Comparison and Quantification Criteria for Assessing Similarities and Differences between Experimental Environments
We test for the existence of the same stylised facts in the laboratory and in the field experimental settings. Also, we investigate the differences in the processes and dynamics of how these stylised facts appear in the laboratory and in the field. Due to the fact that the two experiments differed in duration and number of participants, hypothesis testing using neither the frequentist nor Bayesian approach is conceptually feasible to investigate similarities and differences between the laboratory and field environments. Hence, we use Jensen-Shannon divergence (cf. JSD) to measure information similarity between two distributions, such as price and belief distributions in the laboratory and in the field settings. JSD is a symmetric and bounded metric of the difference between the mixture entropy and the entropy of the mixture of distributions [
53]. Therefore, JSD of the price distribution in the market reflects the entropy of the market. For two probability distributions
P and
Q, Jensen-Shannon divergence equals:
and
is the Shannon Entropy of a probability distribution
X with density
for assets
, denoted as:
Another way to describe disorganisation of the market is to measure its mi-pricing. To quantify market mispricing, we use the Relative Deviation (cf. RD) [
54], which in the experimental asset markets is used as a “bubble measure”. RD measures raw price deviations from the rational market price. RD indicates whether a market was over or under-valued such that
implies no mispricing and the larger the deviation from 0, the larger the mispricing is. To analyse the pricing rationality of the market, we calculated three market indices: index 1—sum of security prices in the market, index 2—sum of highest bid offers and index 3—sum of lowest ask offers. Due to the fact that the dividend pays 100 units of currency, index 1 should not exceed the value of 100 and for the market to be rationally priced, index 1 should equal to 100. If index 2 exceeds 100, or index 3 is lower than 100, there would be a straightforward arbitrage opportunity against positive and negative bubble on the market respectively. Therefore, for
N periods
p, we calculate RD of index
i (
) according to the formula:
5.2. Trading Activity
We observe an increase of participants’ activity from the first to the third round. The total number of orders increased from 676 in Round 1, through 844 to 922 in the final trading round. The average trading volume of each security is 6, 9.8, and 12.7 shares for round 1–3 respectively, which are 91%, 81%, 69% lower than the field experiment. As shown in
Figure 2, the number of transactions in the laboratory increased within the first 1–5 min (5 min equals half of the trading time), when it reached the peak and then fluctuated at around 30 transactions per minute. This indicates that participants learned the task and started to react quicker in later rounds. This pattern of trading activity in the laboratory is in contrast to the trading activity in the field experiment, where the number of orders in each round decreased across rounds and the activity within each trading round had a clear cyclical pattern, with the daily peaks of activity in the morning and in the evening and the weekly peaks of activity just after the market opened and just before it closed (similarly to real financial markets). We do not observe such patterns in the laboratory.
On average, each student submitted 18.8, 23.4 and 25.6 orders in rounds 1–3. This indicates very high activity during the short trading periods lasting 10 min, compared to the classroom setting with the average number of orders per students within the 6-day period would equal 34.1, 26.5 and 19.7. We surmise that this increase in activity in the laboratory was related to learning and improving at the task. In contrast, the decreasing activity in the field could have resulted from the lack of interest in the task or improvement of trading strategies such that one would become more efficient with fewer trades. To correctly disentangle these effects, we conducted a follow-up experiment in Fall 2016 described in [
17], where we found no difference in trading activity of experienced student traders during trading rounds lasting six days and two hours.
Figure 3 shows the trading volume of each security in the laboratory and in the field experiment. Similarly to the classroom setting, the prices in the laboratory market were strongly correlated with the trading volume (
and
,
for Rounds 1–3). While, in both settings, the security listed as the first one (i.e., left-most) has a relatively high volume, in the laboratory the volume of that security was higher relative to the volume of other securities. This is especially pronounced in Round 1, where the first security on the list (i.e., Security 1) was traded twice as much as the next most traded security. In addition, in all three rounds, securities with larger numbers (on the right tail of the probability distribution) exhibit little or no activity. This is due to the limited time of laboratory trading rounds that restricted exploration and exploitation of all available securities. Additionally, in
Appendix B, we provide a summary of the self-reported measures describing trading activity and strategies.
5.3. Market Prices and Participants’ Beliefs
Figure 4 shows that the price distribution emerged in the first 30% of the total trading time, compared to the 6% of the available trading time in the field experiment. However, in absolute terms, the price emergence in the laboratory was very quick as it took only 3 min, likely forced by the fact that all participants had a strictly designated limited trading time.
Further, in Round 1, only Security 1 had a price in the first minute of the trading round. In addition, the securities that were priced early during the trading were much more expensive than the securities for which the price is established later in the trading round. The prices of these first securities diminished after minute 3 of the trading. We did not observe a similar pattern in the field experiment. In the laboratory experiment, 23, 17 and 10 (40%, 31% and 20% of available securities) securities remained without price in Rounds 1–3, in comparison to none in the field experiment. The fact that fewer securities remained without price across rounds shows that participants learned to explore all available securities and traded them.
Based on the median split of the final price at the end of a trading round, we distinguish between the “expensive” (i.e., good and possibly paying out the dividend) and “cheap” (i.e., bad and possibly not paying out the dividend) securities. Once the prices of the securities were established, the “expensive” securities remained expensive and the “cheap” securities remained cheap till the end of each trading round, which replicates the effect observed in the field experiment. This conclusion is confirmed by the JSD measuring divergences between the distributions of two consecutive minutes (see
Table 1) ranging between 0 and 1, such that values close to 0 indicate almost identical distributions and values close to 1 indicate substantially different distributions. Thus, the JSD also confirms that the price emerges quickly, as the JSD falls below 0.1 after 5, 4, and 3 min for rounds 1–3 respectively.
Table 2 demonstrates the entropy values of the pre- and post-trading belief distributions and of the market distributions in the laboratory and in the field settings, as well as the JSD between the laboratory and the field. According to the table, the entropy of market price distribution in the laboratory is always larger than those in the field, while the entropy of belief distributions is always smaller than those in the field setting. This implies that the market distributions in the laboratory are less concentrated than the those in the field experiment. According to the JSD between the distributions of the laboratory, belief distributions in the laboratory are similar to those in the field (i.e.,
), showing that traders in the laboratory and in the field experiments have similar beliefs about the final results. However, the JSD between the market distributions in the laboratory and the field experiments are much larger, providing another evidence that the traders’ beliefs have not yet been fully reflected in the laboratory market distributions, possibly due to the much shorter trading time than in the field.
This price emergence resulted from the aggregated initial beliefs of the market participants. According to
Figure 5, the average pre- and post-trading beliefs were very strongly aligned with the price distribution in each week. The post-trading distribution was more strongly correlated with the price distribution than the pre-trading belief (Pearson correlations of the price with the post-trading belief:
; Pearson correlations of the price with the pre-trading belief:
,
for all correlations), while the beliefs were more correlated with each other than with the price (
,
for all correlations). This replicates the corresponding finding from the field experiment. As outlined in Equation (
4), for each round, we implemented a regression analysis demonstrating that the difference between the post-trading belief and the market can be predicted by the difference between the pre-trading belief and the market:
In all three rounds ( equalled 0.70, 0.84, 0.80 in Rounds 1–3) was significant at and the percentage of explained variance was medium and high (: 0.57, 0.38, 0.64). The dependent and independent variables in this regression are expressed as differences between beliefs and the marked distributions to avoid the multicollinearity problem.
Further, the peaks of the distribution for each week were always the lowest for the price distribution, second highest for the pre-trading belief and the highest for the post-trading distribution. This is in contrast to the field experiment, where the peak of the price distribution was always higher than the peaks of the belief distributions. This means that, in the laboratory, the beliefs of the market players were directed towards particular securities more than the market (showing a coordinated opinion of the players), while it is the opposite in the field experiment.
Figure 6 shows that the beliefs of individual participants were convergent on which of the securities would pay out a dividend. The securities that were assigned with more weight are close to the realised securities. Overall, the beliefs in Round 1 were more dispersed than beliefs in Rounds 2–3 and most of the belief were assigned close to the executed securities. This finding is consistent for the two experimental settings.
5.4. Mispricing and Market Rationality
Figure 7 shows the evolution of the three indices across 10 min of each trading round. First, the market was overpriced in all three experimental rounds, which is confirmed by the RD presented in
Table 3. The negative RD of index 2 in all three rounds are due to the fact that many securities remained without price, where the number of priceless securities was larger in the laboratory than in the field. This could potentially be explained by the much snorter trading time in the laboratory. The bubble levels in the laboratory and the field experiments are similar. However, this overpricing was not as pronounced as in the field experiment. In Round 1, index 1 exceeded 100 only after 4 min of trading (i.e., 40% of the trading time) and stayed at the level of about 150. In Rounds 2 and 3, index 1 exceeded 100 after about 2 min. In the laboratory setting, we did not observe decrease of this mispricing across rounds. As the average bid prices were smaller than 100 almost all the time, there were no obvious arbitrage opportunities in the laboratory setting
on average. However, given that the prices were at times very large for some securities, in the self-reported questionnaire, seven participants reported that they applied an arbitrage strategy, selling the securities with high prices. In the field experiment, we observed one strong arbitrage opportunity in Round 1 and one in Round 4, in the sense that the best bid price became transiently larger than the best ask price. The development of all three indices is very similar in all three trading rounds.
Second, the over-pricing was particularly well characterised by the time intervals during which index 2 becomes larger than 100: in Round 1 briefly at the end of the sixth minute and during the eight and ninth minutes, in Round 2 during the second, third and fourth minutes, and in Round 3 from the second to the fifth minute. The fact that the best bid was larger than 100 means that any transaction had to be concluded at a price that would result in an aggregate price significantly above 100, in clear violation of the rationality and fair value argument.
In the field experiment, the overpricing was the highest during the first half of the day when the market opened (i.e., 5% of the trading time) and it decreased towards the end of each trading round. In addition, the mispricing diminished across rounds. We attribute these differences to the time constraint and late formation of the price distribution in the laboratory.
5.5. Trading Performance and the Illusion of Control
In the final questionnaire that followed the trading task, 18 participants (50%) responded that they realised that the market index should equal 100. Three of the seven persons that reported implementing arbitrage strategy were in the top quartile, two were in the second best quartile and only the remaining two did not receive any bonus, but were in the third quartile. This supports the observation that there were some arbitrage opportunities only based on recognising that the market (and a number of securities) were overpriced.
In the post-trading questionnaire, one participant reported to have had a few years of experience in trading, two people reported having 3–6 months experience (an equivalent of an internship) with trading, while others had no experience. The person with a few years of experience was fifth on the final rank.
In contrast to the field setting, we found no correlation between the number of submitted orders and participants’ earnings. There was only one person (an outlier), who not only submitted substantially more orders () than other participants (Range: 16–119, ), but also, this person had a substantially higher total earnings () than the rest of the participants (Range: 2471–1041, ). Therefore, this participant had rank 1. This suggests that the laboratory setup promotes more of a gambling atmosphere with insufficient time to ponder and evaluate the options as well as keep or recover a cool trading mind.
Further, for each participant, we calculated the primary illusion of control [
52], which relates to the belief that one has a control over the outcome of the stochastic process, the secondary illusion of control, which defines that a person aligns themselves with having extraordinary skills such as “feeling lucky moments”. For each participant, we computed the average of responses from the questions corresponding to each subscale (primary and secondary), where each question was measured on the scale 1–10. The total score of the illusion of control is the average from all questions in the survey. Overall, all participants had a low primary (
, Range: 0.5–5.67) and secondary (
, Range: 0–5.33) illusion of control, as well as the total score (
, Range: 0.8–4.8) of the illusion of control. The last question of the illusion of control questionnaire asks on a scale 1–10 whether “It was all chance”. Six people replied 1 on this question meaning that they believed that their performance was completely attributed to their actions. Only three people responded 10 (maximum value) indicating that they believed that they had no influence on their performance. The distribution of responses was slightly positively skewed, with the median of 4 and mean equal
.
We found a moderate correlation between the final earnings at the end of the three trading rounds and the total illusion of control (). This correlation was driven by the strong correlation between the secondary illusion of control and the final earnings (), while there was no correlation of the final earnings and the primary illusion of control. Given the fact that the survey of the illusion of control was preceded by the trading task and that the participants generally had no trading experience, we interpret that those participants, who received better scores in the trading task, attributed their success to their skills such as “feeling the market”. This relation was also reflected in the negative correlation between the final rank and the total illusion of control (), the negative correlation between the final rank and the secondary illusion of control () and no correlation between the final rank and the primary illusion of control. There was no correlation between the trading volume or number of orders and any measure of the illusion of control, which means that the illusion of performing well was attributed only to the final results of the trading.
Ref. [
52] found that higher illusion of control was correlated with people’s prior beliefs about the outcome of a gambling task that their participants performed. In our experiment, we find that participants in the laboratory condensed their beliefs to fewer securities than the participants in the field experiment. The distribution of the prior beliefs had a larger peak and thinner tails than in the field. We surmise that the laboratory participants formed more extreme beliefs while being less confident about these beliefs and their actions.