Experiential Learning of the Efficient Market Hypothesis: Two Trading Games

Abstract

In goods markets, an equilibrium price balances demand and supply. In a financial market, an equilibrium price also aggregates people's information to reveal the true value of a financial security. Although the underlying idea of informationally efficient markets is one of the centerpieces of capital market theory, students often have difficulties in grasping and accepting that asset prices fulfill this dual role of information revelation and demand-supply aggregation. The author presents two simple classroom games that illustrate the workings of information transmission and aggregation through prices. The games are easy to comprehend, simple to implement, and short. Each game, including classroom discussions, takes about 30 minutes. By the end, students will have an intuitive feel for informational efficiency.

Keywords:

• efficient capital markets
• information aggregation
• trading

JEL codes:

• A22
• C91
• D82
• G14

Acknowledgments

The author thanks his students at the University of Toronto for their enthusiasm in playing these games and thanks Annie Jekova and Uros Petronijevic for expert research assistance.

Notes

1. This result is true for the groups of finance students that I played this game with; the behavior of groups that were not trained in finance was slightly different.

2. For the latter two, the games are particularly useful in illustrating the different trading mechanisms that are commonly used in capital markets.

3. For instance, in the simple game proposed by Ball and Holt (1998), the fundamental value is $1 + $6 × (5/6) = $6 and is computed as follows: At the end of each round, each share pays a $1 dividend. After the dividend, each share is destroyed with probability one-sixth, the outcome being determined by the roll of a die. At the end of all rounds, after the last roll of the die, the surviving asset pays $6. The fundamental value can then be determined by backward induction. Before the last period, the fundamental value is $1 + (5/6) × $6 = $6. Iterating this argument, the fundamental value is a flat $6 in every period. The other cited papers additionally allow decreasing or stochastic dividends.

4. Having run the Ball and Holt (1998) game in several classes, I have yet to encounter a student who would compute the fundamental value correctly. I find this quite striking (in a sample of about 80). All students in my sample are trained in basic finance, all are able to compute expectations and know backward induction arguments, and most know how to compute fundamental values, at least for this simple form.

5. An alternative is by Steven P. Feinstein (2000), who suggested auctioning an envelope that contains either a high value or a low value, and the class organizer has given students some information about the value. The purpose of his game is to illustrate the strong form of the EMH.

6. Alternatively, a teaching assistant can compute average opinions and Walrasian market prices during the lecture or the games.

7. For instance, the lag between arranging a trade, reporting it, and the price publication becomes too large. Of course large classes can be broken up into subgroups or teams.

8. Market microstructure matters: markets can be centralized (for instance, stock exchanges) or decentralized (such as currency markets). They can be order- or quote-driven. There can be a monopolistic specialist (e.g., formerly the NYSE or Deutsche Börse) or many market makers (NASDAQ). There can be a central, onetime clearing system (as in the opening sessions at TSX, NYSE; or for infrequently traded stocks on Paris Bourse), or trading can occur continuously. The institutional market microstructure differences lead to differences in trading volume, bid-ask-spreads, intra-day trading patterns, and so on.

9. A nice illustration of this trading mechanism can be found in the movie Trading Places: in one of the last scenes, the two heroes engage in floor trading in the trading pit for concentrated frozen orange juice (CFOJ). One should point out to students, however, that the two main characters engage in illegal insider trading.

10. In contrast to the auctioning of a jar of pennies, instructors will not be able to earn their lunch money (see Thaler 1988): they make zero profits.

11. Again this is a noteworthy point in the classroom discussion because it illustrates that people may have a preference for an open process. Of course, it is also possible that students merely copy what they see on television or in the movies.

12. This confirms the recent theoretical result by Harrison Hong, Jose Scheinkman, and Wei Xiong (2006), although the specifications that I looked at always had fewer shares than students. It would probably be interesting to consider the case where all students get share allocations so that the number of shares exceeds the number of students.

13. Although the jar is public information, when examining it with their “information processing technology,” students create a piece of private information. The jar is thus a metaphor for a financial statement. Analysts process the information contained in these statements, and they have different capabilities of processing quantities of information, of seeing linkages between different pieces of information, etc.

14. The trading process in the Walrasian game is actually quite similar to that of Grossman's (1977) model, where people submit complete demand–supply schedules.

15. Markus Brunnermeier and Stefan Nagel (2004) show, however, that hedge funds’ strategies are more subtle, even if a fund has determined that a stock is overpriced.