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Neuro-finance and stock trading
Experiment tests
A preliminary research proposal Paul Farah

Introduction ............................................................................................................................................ 3 Procedures and methodology .................................................................................................................. 4 Experiments ............................................................................................................................................ 5 References .............................................................................................................................................. 7

Introduction The ability to attribute mental states, including beliefs, desires, intentions, and emotions to others is a crucial social ability. Known as Theory of Mind (ToM), it is the capacity to use a working model that attributes internal mental states to others in order to manage interpersonal relations, regulate one’s own behavior, and predict the behavior of others (Premack and Woodruff (1978)). It is the ability to think about what another person is thinking about, even if the latter makes no sense in one’s own mind; and it is the ability to think about what another person thinks about you; etc. (Hampton, Bossaerts and ] O'Doherty (2007)). A variety of behavioral tests have been developed to measure ToM abilities (Baron-Cohen, Jolliffe, Mortimore and Robertson (1997)), and more recently imaging studies have identified the neural substrates of ToM (Baron-Cohen, Ring, Wheelwright and Bullmore (1999), Fletcher, Hae, Frith, Baker, Dolan, Frackowiak and Frith (1995), Gallagher, Happé, Brunswick, Fletcher, Frith and Frith (2000), Goel, Grafman, Sadato and Hallet (1995)). While ToM is generally regarded to have evolved under the adaptive pressures of direct human social interaction, more recent technological advances have made it possible for humans to build complex systems that represent the interactions of large numbers of human agents. A paradigmatic example of such multi-agent systems is financial markets, in which trading activity is a complex function of many interacting agents. A fundamental property of this trading activity is that it reveals information regarding the collective opinions of investors about the future prospects of assets. The widespread belief that it is possible to “beat the market” depends on opportunities to rapidly infer exploitable information from market activity before that information is fully available to other investors, making trader success dependent on rapid learning from market activity. The prospects of success is complicated by the fact that once a trader begins to act on the basis of such information, their trading activity will signal this information to other investors. Thus, when new information enters the market, trading activity rapidly disseminates that information to other investors. Once disseminated, the price of an asset will reflect all available information regarding its value and there is no longer an opportunity to profit on the basis of superior information. This phenomenon is a key element of the Efficient Markets Hypothesis, the proposition that markets are informational efficient and thus prices correctly reflect all the information available (Fama (1998)). Here, we investigate the alternative hypothesis that humans use ToM to predict the behavior of financial markets, even though markets do not literally have a mind of their own. To date, it is not known whether humans solve complex problems in multi-agent systems by using ToM heuristically although two considerations suggest such use is plausible. First, it appears that the human brain implements strategies and mechanisms that are specialized for social exchange (Premack and Woodruff (1978), Adolphs (2003)), and there is evidence that human performance can be improved when an abstract logic problem is translated into an equivalent one involving social exchange (Cosmides (1989)). Second, there is substantial evidence that human problem-solving in complex domains often involves approximate solutions that utilize heuristics rather than exact solutions, due to such factors as processing limitations or tradeoffs between accuracy and processing time. It may therefore be a useful and cognitively efficient

procedure for humans to understand large-scale multi-agent systems by using ToM as a heuristic strategy even when ToM does not literally apply.

Procedures and methodology To examine how traders can infer other traders’ knowledge from market activity, we created a novel “neurofinance” approach that involved three steps. The first step is to generated trading data with an experimental market that allowed us to control the dissemination of information. This step made use of the fact that experimental finance has made significant progress in understanding how markets function by studying markets in the laboratory whose parameters are under strict control. By controlling the distribution of information across traders, it has been shown that markets can disseminate information from those who know (insiders) to those who do not in the absence of verbal communication and even if exchange is entirely anonymous (Plott and Sunder (1988)). Using this approach, we will be able to construct markets that differed only by the absence (control sessions) or presence (test sessions) of insiders and thus in the saliency of the information traded through market activity. An “insider” merely refers to a trader who has information that is not publicly available and of course does not connote illegal insider trading. In the second step, we will replayed the trading activity obtained in the previous step to a separate group of subjects while recording brain activity with functional magnetic resonance imaging (fMRI). Our goal in this step is to determine whether the resulting pattern of brain activation provided evidence for the mathematical hypothesis or for the ToM hypothesis. To do so, we will construct two types of predictors to identify loci of significant brain activation for the test sessions relative to the control sessions: block predictors, i.e., dummy variables that identified the type of session, and parametric predictors, which changed as a function of transaction price level as well as the type of session. As the parametric predictors quantified the information transmitted through market activity, the only dimension along which test and control sessions varied, these predictors allowed us to test our hypothesis that brain activation in ToM-related structures would correlate with changes in the information transmitted through market activity. Importantly, given our design and the contrast between test and control sessions, we will avoid confounding factors such as expected reward, risk, conflict, decisionmaking, the amount of human interaction, visual activations, and motor actions. In the third step, we will investigat whether mathematical or ToM abilities are better predictors of trader success by conducting a series of behavioral experiments: a financial market prediction (FMP) task, two ToM tasks, and a test of mathematical ability (M). The FMP task consist of predicting transaction price changes in our experimental markets with insiders. We will use two standard ToM tasks. The first one, known as the “eye test,” determines whether a subject can correctly infer intention and belief solely by looking at the expression in an

opponent’s eyes (Baron-Cohen, Jolliffe, Mortimore and Robertson (1997)). The second test, inspired by Heider and Simmel (1944), concerns prediction of movement of geometric objects which normal subjects tend to personify (i.e., they imagine that the movement reflects social interaction). The mathematical test will consist of questions typically asked during finance job interviews (Crack (2004)). We predict that performance in the FMP and ToM tasks would be significantly correlated, while performance in the FMP and M tasks would not. Under the alternative hypothesis, only the M task will be correlated with FMP performance. Finally, we will ask subjects to report in a written questionnaire the strategy they used when predicting the price changes during the FMP task and the movement of objects in the Heider test. This will allow us to ascertain to what extent subjects explicitly personified the situation to help them in the prediction.

Experiments Step 1: Trading Data Collection Experiment thirty subjects will participate in a parameter-controlled market experiment that used an anonymous, electronic exchange platform. The following situation will be replicated several times; each replication will be referred to as a session. Subjects will be endowed with notes, cash, and two risky securities, all of which expired at the end of a session. The two risky securities (“stocks”) paid complementary dividends between 0 and 50¢: if the first security, called stock X, paid x cents, then the second security, called stock Z, would pay 50-x cents. The notes always paid 50¢. Allocation of the securities and cash will vary across subjects, but the total supplies of the risky securities will be equal; hence, there will be no aggregate risk, and, theoretically as well as based on observations in prior experiments (Bossaerts, Plott and Zame (2007)), prices should converge to levels that equal expected payoffs; that is, risk neutral pricing should arise. Subjects could trade their holdings for cash in an anonymous, continuous openbook exchange system. Subjects will be not allowed to trade security Z, however. Consequently, risk averse subjects that hold more of X than of Z would want to sell at riskneutral prices; the presence of an equal number of subjects with more of Z than of X allowed markets to clear, in principle. In most of the sessions, to be referred to as test sessions, a number of subjects (the “insiders”) will be given an estimate of the dividend in the form of a (common) signal within $0.10 of the actual dividend. All subjects were informed when there were insiders; only the insiders will know how many insiders there were. Subjects will be paid in cash according to their performance and made $55 on average. Step 2: fRMI Experiment Thirty new subjects will be shown a replay of the 13 previously recorded market sessions in random order while being scanned with fMRI. These subjects will play the role of outsiders who did not trade. Subjects will be given the instructions of the markets experiment, so that they

are equally informed as the outsiders in that experiment. Subjects first chose whether they would bet on stock X or Z, after being told whether there were insiders in the upcoming session or not. Subsequently, the order flow and transaction history of stock X will be replayed in a visually intuitive way (see Figure 2 and Video 1). During replay, subjects will be asked to push a button each time they saw a trade, indicated by a 500ms (millisecond) change in color of the circle corresponding to the best bid or ask. Step 3: Behavioral Experiment Thirty new subjects will be given a series of four tasks that were administered in random order. The first task will be a Financial Market Prediction (FMP) task in which the trading activity are replayed to the subjects at original speed and paused every 5 seconds. During half of the pauses, we will ask subjects to predict whether the next trade was going to occur at a higher, lower, or identical price as the previous trade that had happened. For the other half of the pauses, we will remind subjects of their predictions and informed them of their success. The second task is a ToM task based on eye gaze (Baron-Cohen, Jolliffe, Mortimore and Robertson (1997)). The third task is a ToM task based on displays of moving geometric shapes (Heider and Simmel (1944)). As with the FMP task, we will pause the movie every five seconds and asked subjects to predict whether two of the shapes would get closer, farther, or stay at the same distance. For the other half of the pauses, we will report the outcomes and the subjects’ predictions.


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