Experiential Learning of The Efficient Market Hypothesis: Two Trading Games

Transcription

1 Experiential Learning of The Efficient Market Hypothesis: Two Trading Games Andreas Park Assistant Professor University of Toronto Department of Economics 150 St. George Street Toronto, ON, M5S 3G7, Canada Phone: Fax:

2 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 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 takes about 30 minutes, including classroom discussions, and 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 1

3 One of the hallmarks of finance theory is that financial markets are informationally efficient, that is, that asset prices correctly reflect market participants information. Yet this notion is difficult to convey in the classroom: to many students it seems rather miraculous that prices should aggregate information. In this article I propose two classroom games that help students get a feel for the process of information aggregation. Both games have a common theme: students are presented an item that represents the fundamental value of a company s share. Its value is represented by a glass jar of nickels or small, identically sized glass objects and it is thus tangible, yet uncertain. With some effort and patience, students can count the objects and thus get a good estimate of the asset s true value. Students record their first estimate before trading starts so that in the aftermath they can determine if indeed prices reveal the average opinion. Asking them to also record their estimate after trading has concluded allows them to document whether there is learning from prices. Students opinions about the share s value will differ, but if prices aggregate information correctly, then, loosely, the market price that equilibrates demand and supply should reveal the average opinion. When there are also sufficiently many opinions, this average should be close to the true value of the underlying asset. And indeed I usually observe both outcomes. The first game represents an idealized Walrasian market in which students submit demand-supply-schedules for an asset. Demands and supplies are aggregated centrally and a market clearing price is determined in the spirit of a Walrasian auction (henceforth: the Walrasian game). The second game mimics the dynamic trading environment of most 2

4 traditional stock exchanges. Students trade assets face-to-face and all transactions are publicly listed (henceforth: the face-to-face trading game). The details are outlined below. For the Walrasian game I observed that the market price is close to and usually slightly below the average opinion. 1 Moreover, provided that there are sufficiently many students present, prices also reflect the true value. There are several possible explanations for why the price is slightly below the average opinion, for instance, people may be avoiding the winner s curse, there may be too much noise in the small sample, or people may be simply risk averse. The classroom discussion will help students get an intuitive grasp of these concepts. Aggregate demand and supplies are usually monotonic, and it never fails to impress students how smoothly the market aggregates their different opinions. With face-to-face trading, prices typically fluctuate widely in the first few minutes. The simplest explanation for this fluctuation is that the first few trades are arranged oneon-one without public guidance as to what the correct price might be. Eventually, prices settle on a tentative upward trajectory. If the group is not too large and trading is transparent, then after about two-thirds of the trading time, activity comes to a stop for several minutes. Towards the end trading activity resumes and often prices fall a little. This is consistent with learning: early trades are only observed with a lag, whereas later trades are more transparent because there are fewer transactions. There are two types of buyers: those with high valuations and those who speculate on rising prices. Together these two types create a tentative upward trajectory of prices. As prices rise, it becomes harder to find someone with a high enough valuation to sell shares to. Eventually, as the market closing time approaches, speculators try to unload their positions, causing price 3

5 drops. After the game, the spread of opinions tightens, which illustrates learning from prices. There are three simple messages that students can derive from playing these games: (1) the wisdom of masses holds, that is, the average prior opinion is close to the truth, (2) markets and prices aggregate opinions, and (3) people often act according to the efficient market hypothesis even if they have not yet been taught the concept. Although these learning objectives obtain independently of the trading mechanism, the trading outcomes differ in the two games, illustrating the importance of the organization of financial market trading. In a nutshell, in the Walrasian game prices are generally closer to the true value and the average opinion than in the face-to-face trading game. There are several possible reasons for the differences. For instance, there may be behavioral biases such as the unwillingness to realize losses. Another explanation is that endowments may be too limited and short selling is not allowed. The latter hinders the revelation of low valuations compared to the Walrasian game, which implicity allows short-selling and where endowments play no role. The Walrasian game is thus the cleanest way to show how well prices aggregate the average opinion. The face-to-face trading game, on the other hand, can illustrate the relevance of limited endowments or short-selling constraints. The latter game also provides an intuitive background for discussions of no-trading results, which state that two parties cannot agree to be both benefiting from a trade. Moreover, it also illustrates other trading motives such as the greater-fool-fallacy that is based on the idea that while one may be a fool to buy, one expects to find an even greater fool who one can sell to at a higher price. 4

6 Although prices usually converge to the true underlying value, one must be careful when setting up the game. It matters how many shares are available for trading: the more shares there are, the less trading activity is observed. Even if prices ultimately do not reflect the true value, the classroom discussion helps students greatly to understand how prices aggregate information and why market frictions may impede this mechanism. The ultimate goal of the games is for students to get a feel for trading and the informational role of prices, and to establish credibility for the idea that financial market prices aggregate information. In contrast to most games that are used in the financial markets experimental literature (discussed in the next section), the games proposed here do not require students to compute the value of a stock with a mathematical model. The simple setup and its easy implementation make it more likely that the learning objectives are achieved. The game is suitable for most standard undergraduate finance courses, and may be useful in graduate financial economics courses or speciality courses on financial market microstructure. 2 In the next section I review the literature on market-efficiency games and their adaptations to the classroom. I then explain the setups of my two trading games, outline some common findings of the games and provide guidelines for the classroom discussion. The appendices contain the games instructions. LITERATURE ON FINANCIAL MARKET (CLASSROOM) GAMES The games that I propose are a blend of classroom market games in the tradition of Smith (1962) and winner s curse games as described, among others, in Thaler (1988). In contrast to all other games in the literature that mimic financial market trading, students are not expected to compute the value of a financial asset. This simplifies the 5

7 implementation of the games in the classroom greatly and avoids distorted outcomes caused by the students limited mathematical capabilities. Several financial market game authors studied the emergence of bubbles in market experiments, starting with Smith, Suchanek, and Williams (1988), and, more recently, Lei, Noussair, and Plott (2001) and Haruvy and Noussair (2006). The frameworks employed in these articles are very similar, and Ball and Holt (1998) provided an adaptation of these setups for a classroom environment. In all these games, there is an underlying fundamental value that is constant (or decreasing) over time. 3 All information is public, and students can effectively compute the (risk-neutral) fundamental value by backward induction. In these games one frequently observes large positive deviations from this value, and this is usually interpreted as the emergence of a bubble. In a second strand of literature Plott and Sunder (1988) and Forsythe and Lundholm (1990) examined how information is aggregated through prices. In these games people receive private signals, and the pooled information reveals the true value of the underlying asset. These studies usually find that the existence of informational efficiency crucially depends on the market structure. All of these experiments require that participants understand a problem on a relatively high level of abstraction. At the very least, participants have to compute a (discounted) sum of expected future payments and understand backward induction. It cannot be overemphasized that problems and settings that seem simple to academic economists may be hard for our student audience. 4 Information aggregation is also taught in the context of auctions. Bazerman and Samuelson (1983) were the first to auction glasses of pennies, nickels, or paper clips. 5 6

8 The penny-auction is usually designed to illustrate the winner s curse, and so when setting up the game, one tries to ensure that winner s-curse-type overbidding occurs. A first step towards this goal is making it difficult to estimate the true value. For instance, in Bazerman and Samuelson (1983) the value of the object is $8, but the average opinion is only about $5. The purpose of the games that I propose is different: people are supposed to be able to estimate the value correctly (and they do on average), and prices are meant to reveal information (which they do). The first definition of the efficient markets by Fama (1965) is still the one found in most textbooks, yet it gives very little guidance as to exactly how information aggregation is achieved, and under which conditions we would accept or reject that a price or market is informationally efficient. The seminal micro foundation of the efficient market hypothesis (EMH) was provided by Grossman (1976, 1977) and Grossman and Stiglitz (1976, 1980) and the games proposed here are best described as an experimental implementation of Grossman s work. However, for teaching purposes, especially on the undergraduate level, Grossman s models are usually considered to be too advanced. Moreover, the underlying theoretical models are very specific, usually combining constant absolute risk aversion (CARA) utility functions with normally distributed asset returns. This specific structure makes an experimental implementation difficult. The games that I outline here can thus be seen as filling a gap, allowing instructors to discuss the information aggregation role of prices as well as, tentatively, allowing a simple illustration of Grossman s results. 7

9 THE SETUP OF THE TRADING GAMES I ran the games with several groups of undergraduate students: about 2/3 were third or fourth year students in economics or commerce, who had one term training in basic finance; the remaining third were second year students of commerce and economics with two years of standard training in economics (but no training in finance). I also ran the games with a class of Financial Economics graduate students, who usually proceed to become analysts or traders in major Canadian financial institutions. The group sizes varied between 13 and 36 people; larger classes were split in half. One needs about two instructors per 20 students to organize trading efficiently. Each game requires four steps: first, explaining the rules, second, playing the game, third, analyzing and summarizing the information collected during the game and Insert Figure 1 here. fourth, discussing the outcomes in class. Ideally one would perform Steps 1 and 2 in the last 20 minutes of the class or tutorial/discussion section that precedes the lecture where the efficient markets are to be taught, so that one can analyze the data between classes (Step 3) and then discuss the outcomes in the following lecture (Step 4). 6 Common Setup for Both Games The asset. The security is represented by a glass filled with a number of identical objects. The objects and the jars should be chosen in such a manner that it is possible to get a good estimate of the number of objects. I find that small glasses (spice jars) filled with 8

10 $2-$3 worth of U.S. or Canadian 5 cent coins or glass-pebbles worth 5 cents each work well. Photos of sample shares are in Figure 1. Note that a bank-roll of nickels is worth $2. The number of jars. I suggest using one jar per three participants. Market activity and the number of shares are negatively related. If there are too few jars, on the other hand, then the game no longer resembles a market but becomes an auction. Ex ante information extraction. Before trading starts, participants are allowed to examine the jar for a limited amount of time. The time constraint ensures some residual uncertainty, leading to differences in perception. One usually observes that some, though not all, participants try to count the number of coins (some will be taking notes). Assessing the average opinion. Each student will be assigned a trader ID. Before the start of trading/the submission of orders, participants are asked to record their initial assessment of the value of the asset. This information is to be collected right away. In the face-to-face setting students will be asked for their valuation again after the games concludes. If they see their original opinion they may feel inclined to give the same number to be consistent. Suitable class size. The Walrasian game can be played with classes of arbitrary size. Face to face trading requires a manageable group size of about people. If the group is too large, trade reporting becomes logistically challenging. 7 Timing relative to the teaching of informationally efficient markets. I suggest letting students play the game prior to the lecture on informationally efficient markets. This ensures that students approach the games with an open mind instead of wondering what is required of them given the material that was just covered in class. One can then combine 9

11 the formal introduction of informational efficiency with the discussion of the game(s) (see Section 5). Organization of Trading In addition to standard finance classes, I use both games in a course on financial market microstructure to illustrate the institutional differences in market trading arrangements. These two games allow an illustration of two major mechanisms: continuous trading as practiced on most stock exchanges during the day and simultaneous order submission as practiced during the opening sessions of exchanges. 8 Organization of the demand-supply-schedule trading process. Each student receives a sheet of paper with the printout of a table. The first column of this table lists prices (in cents), and in the second and third column students are to enter the number of units they would buy and sell if the price in the first column were the equilibrium price. The maximum quantity that students can buy or sell at any price is restricted (for instance, 10 units) and there is a fixed number x of assets in supply. The instructions (see Appendix A) state that all individual participants demands and supplies will be added up for each price. The price at which the aggregate demand minus supply is closest to x is the market price. Students are also informed how their payoffs are computed. These payoffs depend on the price that they pay and the true value of the asset, and are computed as (quantity demanded at the market price quantity supplied at the market price) (true value market price). 10

12 Students record the number of units that they wish to buy or sell in the table that is given to them, their orders are collected, entered in a spread sheet and the market clearing price is computed. Organization of the face-to-face trading process. The face-to-face trading occurs in a simple, lightly regulated double auction market, in structure akin to floor-based open outcry markets (for instance, the New York Board of Trade). 9 Deals are arranged face-toface, trading tickets are filled out, and prices plus transactions are reported. A fixed number of shares is distributed at random to students. Students are told that those who receive a share have to pay the instructor the true value of the stock after trading concludes and that those who own the stock after trading concludes will be paid the true value by the instructor. 10 Therefore there is a firm terminal value and full information revelation after trading concludes. All other payments are self-explanatory buy-sell transactions. Students are asked to leave their seats to roam the classroom in search of trading partners. The trading process itself is unregulated. For instance, they can negotiate with several people at a time or they can auction their share. Once an agreement is reached, both trading parties record their transactions on trading tickets, and the seller reports the trade to the central trading desk. Transaction prices are then centrally listed on the blackboard. Instructions are in Appendix B. The trading session lasts for roughly 8-12minutes, depending on the class size. The rule of thumb is that the larger the class size, the longer the trading time should be. With groups of students 7 to 8 minutes are sufficient. Although it may be beneficial to have students trade for longer (so that there is more time for price adjustment and 11

13 learning), the time pressure is important to ensure that speculators feel the need to unload their positions. A word about payments. It may be controversial to ask students for payments in a classroom environment; in my sessions no money changed hands. Despite this, students usually take this exercise very seriously and treat their trading as if it were for real money they cherish gains and loathe losses. After all, there is pride involved when making a good transaction or when beating their classmates. As a control I also ran the games twice during paid experimental sessions and found no difference in behavior. For a more detailed discussion on how to properly motivate students to take classroom games seriously see Marks, Lehr, and Brastow (2006) (their footnote 12). COMMON OUTCOMES Common outcomes of the Walrasian game. Figure 2 displays an example of the aggregate demand and supply schedules from the Walrasian game trading session. The column chart is the transaction volume that could be realized for the given prices. The increasing curve is the aggregate supply as a function of the price, the decreasing curve is the aggregate demand. The underlying true value was $2.35, the average opinion was $2.41, the median opinion was $2.25, the market price would be between $2.20 and $2.30. Allocational efficiency was at 82 percent. An aside: Stock exchanges often describe their opening procedure as a process that tries to determine the price that maximizes volume. The graph illustrates this notion because volume is indeed maximal around the transaction price. 12

14 In general, most students submit monotonic demand and supply schedules, with demands that decline with prices, and supplies that increase. There are always some who submit erratic schedules, but the effect of such orders on the equilibrium price is typically negligible. Prices can also deviate from the average opinion because of some residual noise that cannot be eliminated in a small sample. Insert Figure 2 here. That prices are slightly below the average opinion is consistent with two theoretical concepts. First, there may be a small degree of risk aversion. Second, if the price were set at the average opinion, then on average people should be indifferent between buying and selling. This is, however, not market-clearing because there is also a fixed supply of x shares. Therefore, if the average person would obtain a share at his/her own assessment then s/he would be a victim of the winner s curse. By the same token, if prices are above the average opinion, then this may indicate that students were subject to the winner s curse. In three out of seven sessions, the price was below or just marginally above the average opinion. In four sessions, the price was not below the average opinion; notably this occurred for the groups that had no training in finance. These groups also paid on average more than (a) their assessment, (b) the average opinion and (c) the k-th highest opinion, where k is the number of issued shares. Although the students in these sessions violated the theoretical prediction, there is a point to be made that at least on average students acted rationally, that is, on average they 13

15 submitted demand-supply schedules that avoided the winner s curse. To see this I computed the students virtual gains: this number is obtained by multiplying each student s net demand with the difference of their prior valuation and the market price. For instance, if a student has valuation 310 and would buy 5 shares at price p = 300, then his or her virtual profit is 5 ( ) = 50. Table 1 summarizes the above observations. As can be seen in column labelled average virtual profits, the average virtual profit was positive. Also, the column labelled number virtual losses indicates the number of people who made virtual losses. Overall, less than 42 percent of students made virtual losses; with finance-trained students this number is, somewhat comfortingly, even smaller. Finally, one can ask if those with the highest valuations also ended up buying the shares; I dub this the allocation efficiency of the trading process. As can be see from Table 1, allocation efficiency is highest for the finance-trained groups (82-92 percent). Insert Table 1 here. Common Outcomes with face-to-face trading. Figure 3 plots the price development for an example of a face-to-face trading session. The figure plots trading prices against the time when the transaction occurred in a face to face example. The data is from one of the control sessions where people were paid; these were the only sessions presented here for which I had recorded the times of trades. There were 13 people in the session, the true value was $2.85, and there were 4 assets that could be traded. The average opinion was $3.23, the median $2.90, the 4-th highest opinion was $3.00; allocation efficiency at the end was 75 percent. Prices rise along a linear trend. 14

16 Although it is not visible from graph, in the last two minutes of trading there almost no activity; only towards the very end did people engage in negotiations again. Generally, in the smaller sized groups (15-20 people), students first negotiate trades bilaterally. After one or two minutes, when the first prices are posted, trading becomes more organized: people often start an open auction by lifting their shares and shouting prices. 11 In the middle of the trading session volume declines, and instead the auctioneers try to sell their assets at very high prices (higher than the last transaction price). Towards the end, transaction activity picks up again, and is often accompanied by a slight downswing in prices (which is observed but not statistically significant). Overall with face-to-face trading, one observes a tentative price increase during the first 2/3 of the session, followed by low activity, followed by a slight downswing in prices. Incidentally, this U-shaped volume pattern is also observed on most stock markets. Students buy for two reasons: first, they think that the security is undervalued. Second, they buy because they speculate that there may be somebody else who has a higher valuation. For a given class size, roughly 2/3 of students are actively transacting. A sizeable number of the non-transacting students try to trade but cannot agree on a price. This is worthy of discussion because people who have a low opinion of the asset cannot easily convey this belief. If short-sales were allowed or if there were larger endowments of assets, then those who believe that the asset is overvalued could potentially bring the price down by selling. Because the shares are allocated randomly and there are fewer shares than students, before trading starts, early sellers are not necessarily those who have a low opinion; 15

17 instead, all participants are in search for the highest opinion. Once they realize that these people are rare, prices slowly fall as speculators unload their positions. Insert Figure 3 here. The number of transactions is negatively related to the number of assets, 12 that is, the more shares there are the lower is the number of transactions. Moreover, there is also a negative correlation between the average trading price (scaled by the true value) and the number of assets, that is, the more shares are available the lower the price. The range of opinions shrinks/tightens from before to after trading and the variance of opinions also shrinks. The average price is above the average opinion by about 11 percent, above the true value by 9 percent, and above the k-th highest opinion by 4.5 percent, where k is the number of issued shares. There is also a substantial amount of speculative trading: on average more than 50 percent of the buyers trade above their valuation, whereas only 25 percent of the sellers transact at prices below their valuation. On average buyers lose in expectation, whereas sellers gain. Allocational efficiency on average is at 64 percent which is lower than in the Walrasian game. All of the above findings are summarized in Table 2. Speculation may account for the (virtual) losses that buyers are willing to incur in the process, but one is left wondering why people hold on to their shares beyond the end of the game when they could have unloaded them earlier. Looking only at the inefficient allocations and excluding a session with poor data recording, 71 percent of the buyers who held on to their shares until the end of trading made an average virtual loss. Half of 16

18 the last owners could have made a profit had they sold at (one of) the last trading prices. This point is worth mentioning to students for it documents the well-known phenomenon that people tend to hang on to their losses. SUGGESTIONS FOR THE CLASSROOM DISCUSSION The classroom discussion following the game is a vital component of the learning exercise and should clarify key concepts. The discussion should center around the question of whether or not prices aggregate information, and the discussion should include the following components. First, students should discuss how they came up with their valuation. This way they learn that there were some people with better and some with worse assessment techniques. Second, the instructor should lead the discussion to let individuals describe how they learned from market behavior. Most likely, those with the most extreme initial valuations revised their opinion after observing trading behavior. Third, informational efficiency of prices can be assessed relative to two numbers: the true value and the average opinion. Usually these two measures are close, the true value can only be revealed if the average opinion is sufficiently close to it. If the two are not close, then prices can still be close to the average opinion and thus aggregate information. Irrespective of whether the true value is revealed, the game will help students understand how actions reveal information and how prices then aggregate information. As stated before, I propose to introduce the standard teaching material on 17

19 efficient markets only after the game has been played. This material can then be intertwined with the discussion of the game outcomes. In what follows I will outline a few core concepts from the theory of informationally efficient markets. The literature on market efficiency originated in Fama (1965). He introduced three notions of efficient markets as follows: first, markets are weak-form efficient if all information from past market trading is reflected by the current price. Next there is the semi-strong form when all publicly available information regarding the prospects of a firm is reflected in the current price. Finally, under the strong-form efficiency, all information relevant to the firm is reflected by the current price, including insider information; Campbell, Lo, and MacKinlay (1997) used the term private information. These three types of market efficiency have their origin in empirical work, and early work lacked a micro foundation. Grossman (1976) filled the gap by developing a framework in which people s private information is incorporated in a rational expectations market clearing price. In the games presented here, arguably, people obtain a private signal from examining the jar of nickels, 13 and thus the games test to what extent prices incorporate information in the sense of Grossman. 14 Because Grossman provided a micro foundation for the EMH, by association the games illustrate the efficient market hypothesis in Fama s sense. To wit, because the private signals are based on public information it is reasonable to assert that the relevant EMH studied here is the semistrong form. The games also help students to get a better understanding of the standard empirical tests of the efficient market hypothesis. One of the implications of the weak-form EMH is that prices are a sub-martingale, or, more loosely, they are a random-walk. Consequently, 18

20 a so-called technical analysis, which is the extraction of information about the future movement of prices from past prices, should have no merit. The face-to-face setting can actually illustrate why this may or may not be accurate. For instance, it is not true that every trading-action is fully informative, because people speculate so that a buy-trade may originate either from someone who has a favorable opinion or from a speculator. Students understand this idea well, and many apply it. The classroom discussion can then establish that speculative behavior, to some extent, can be understood as trying to exploit alleged short-term inefficiencies, that is, situations in which the price reflects information inaccurately. At the same time, speculators often lose money and although this is not directly caused by the weak-form efficient nature of prices, it illustrates the greater-fool fallacy. It also illustrates that the common initial upward trend is not a useful predictor for future price movements. Next, an implication of the semi-strong form of the EMH is that a fundamental analysis (a careful analysis of the value of the jar) should have no or little merit as prices will incorporate the information that analysts have obtained. When acting on the basis of an accurate analysis, one can avoid making the wrong decision: in the demand-supplyschedule game, most people made virtual profits, that is, given their assessment they took positions that would be profitable from their subjective perspectives. Moreover, people who were more careful in their counting usually did better. In part this thus illustrates what a fundamental analysis is and why it may have merit. At the same time, in the face-to-face trading game, a careful analysis may not pay out: prices are usually high, often exceeding the average opinion. Invariably there will be some students who merely eye-balled the value and thus arrived at a poor quality 19

21 assessment and others, who came up with a careful assessment method that allowed a precise estimate. These latter people are often the ones who believe that trading prices are too high. Yet because endowments are limited and short-selling is not allowed, they cannot utilize their knowledge, and their opinion does not enter prices adequately. This observation can lead to inspiring classroom discussion of real-world institutional and regulatory restrictions: for instance, mutual funds and most pension funds are banned from taking short positions whereas hedge-funds are not. 15 Another issue that merits discussion is that in the face-to-face setting, all profits and losses add to zero. As a consequence, on every trade, one party gains, one loses. Of course, in reality trading can be Pareto-improving because of diversification or tax benefits; the face-to-face trading game can thus inspire a discussion of these trading motives. It should be stressed that the games do not provide a perfect test of the validity of any level of efficient market hypothesis. Indeed, as Forsythe and Lundholm (1990) pointed out, it is generally impossible to devise a test that definitively determines whether or not market efficiency prevails. That being said, it is usually plainly visible in the games that some form of information aggregation occurs; for instance, prices never grossly deviate from the opinions in the room. In summary, for teaching purposes the games provide ample evidence in favor of Grossman s information aggregation models. 20

22 CONCLUSION I presented two simple trading games that allow students to develop an intuitive grasp of how financial market prices aggregate people s opinions. The first game is a setting that is close to an idealized Walrasian market: people submit a demand-supply schedule that lists precisely how much they are willing to buy or sell at each price. The Walrasian market clearing price usually reflects the average opinion and is also often very close to the true value. The second game mimics intra-day trading on financial markets, with all its frantic activity and standard shortcomings. Although prices never grossly deviate from the opinions in the room, they tend to be higher than in the Walrasian game. This allows the instructor to lead students into meaningful, well-founded discussions on, for instance, the impact of short-selling constraints and limited endowments on the inclusion of negative opinions. The major innovation of the games is their simplicity: in contrast to all other financial market trading games in the literature, students do not have to compute a value that is based on a mathematical construction. Instead, students only have to estimate the number of coins in a jar. Thus although I provided a teaching module, there are potential implications for experimental research that may use the games simplicity to check the robustness of existing findings. 21

23 Appendix A INSTRUCTIONS FOR STUDENTS: DEMAND-SUPPLY SCHEDULE You will participate in a simple trading simulation that follows these steps 1. I will show you the asset. Your job is to estimate its true value. 2. You then have to submit your demand-supply schedule. 3. A market price is established (demand=supply). 4. The true cash value of the asset is announced. 5. Trading gains/losses are computed. Profits and losses. To illustrate gains and losses, suppose the market clearing price is 150 whereas the true value is 140. Example 1: You bought 5 assets. Your payoff: 5 ( ) = 50. Example 2: You sold 10 assets. Your payoff: 10 ( ) = 100. Bottom line: If you buy when the market price is above the true value, then you lose money; if you buy when the market price is below the true value, then you win. Likewise, if you sell when the market price is above the true value, then you win and if you sell if the market price is above the true value then you lose. The Asset. You will be trading assets. These assets are jars filled with blue or green pebbles; I will them show to you in a moment. Each pebble is worth 5 cents. You may look at the jar, but you are not allowed to open it. Please note that the jar itself has no value (it is only wrapping) and that all jars are identical and contain the same number of pebbles. 22

24 Apart from the jars that are bought and sold by your fellow classmates there is a fixed supply of 8 jars. Before we start trading, we will ask you to assess the value of a share. You will find a form in front of you. Please enter your trader ID (a number I give you), and your assessment. Please also express how confident you are about your own assessment by marking the respective box. Order Submission: attached to these instructions is a yellow sheet of paper that lists prices from For each price, please record how many jars you would buy or sell at this price if this were the market price. (This list is your demand-supply schedule.) Note that the price is only established after all demands and supplies have been collected and aggregated. Rules: At any price, you may buy or sell at most 10 jars. If you do not want to participate, then simply do not submit the yellow sheet. 23

25 Appendix B INSTRUCTIONS FOR STUDENTS: FACE-TO-FACE TRADING You will now participate in a simple face-to-face trading simulation. Before you is a glass filled with nickels (5 cent coins). You may look at the jar, but you are not allowed to open it. The content of these jars represents the fundamental value of one share of company xyz. Please note that the jar itself has no value. All jars are identical and contain the same number of nickels. There are 10 identical jars that can be traded on the market. Just before we start trading I give these jars to some students in the room at random. The value of holding a share is as follows: 1. After the game ends, each initial owner of the jars pays the true value of the jar (i.e., the sum of the nickels). 2. Likewise, those who own the jar at the end of trading will be paid the true value (in return for the content of the jar). Before we start trading, I will ask you to assess the value of a jar. You will find a form in front of you. Please enter your trader ID (the number on the blue or green cover sheet of the handout), and your assessment. The organization of trading is simple: markets will be open for 10minutes. 1 minute before the end I will announce that the market is about to close. All trading must stop after I announce the end of trading. You may record last minute trades, but you cannot negotiate further. 24

26 During these 10 minutes you may buy or sell (if you own it) the jar; you can trade with any person in the room, at any price that you agree upon. You may also abstain from trading. Record keeping. The front of the cover sheet (blue or green) that has been given to you indicates your trader ID, the back is your trading ticket. On it you must record your trades. More specifically, recording works as follows: 1. Both parties record their trades on their trading tickets. 2. On your trading ticket you record Your role (buyer or seller), the ID of the other trader (a number) and the price that you agreed upon. 3. The SELLER reports the trade to the market organizer who will record the IDs of both traders and the transaction price. The market organizer will then publicize the transaction price by writing it on the blackboard. 25

27 1 This result is true for the groups of finance students that I played this game with; 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 computed as follows: At the end of each round, each share pays a $1 dividend. After the dividend, each share is destroyed with probability 1/6, 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. (Comment: $1+$6(5/6)=$6 to clarify) 4 Having run the Ball and Holt 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. 26

28 5 An alternative is Feinstein (2000), who suggested auctioning an envelope that contains either a high 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 efficient market hypothesis. 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 quotedriven, there can be a monopolistic specialist (e.g. 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 heros 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. 27

29 10 In contrast to the auctioning of a jar of pennies, instructors won t 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 Hong, Scheinkman, and 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 of 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 Grossman s (1977) model where people submit complete demand-supply schedules. 28

30 15 Brunnermeier and Nagel (2004) show, however, that hedge-funds strategies are more subtle, even if a fund has determined that a stock is overpriced. 29

31 REFERENCES BALL S. B. AND C. A. HOLT Classroom games: Speculation and bubbles in asset markets. Journal of Economic Perspectives 12 (1): BAZERMAN M. H. AND W. F. SAMUELSON I won the auction but don t want the prize.. The Journal of Conflict Resolution 27 (4): BRUNNERMEIER M. AND S. NAGEL Hedge funds and the technology bubble. Journal of Finance 59 (5): CAMPBELL J. Y. A. W. LO AND A. C. MACKINLAY The econometrics of financial markets. Princeton University Press. FAMA E The behavior of stock market prices. Journal of Business FEINSTEIN S. P Teaching the strong-form efficient market hypothesis and making the case for insider trading A classroom experiment. Journal of Financial Education 26 (2): FORSYTHE R. AND R. LUNDHOLM Information aggregation in an experimental market. Econometrica 58 (2): GROSSMAN S On the efficiency of competitive stock markets where trades have diverse information. The Journal of Finance 31 (2): The existence of futures markets noisy rational expectations and informational externalities. The Review of Economic Studies 44 (3): GROSSMAN S. J. AND J. E. STIGLITZ Information and competitive price systems. American Economic Review 66 (2):

32 On the impossibility of informationally efficient markets. The American Economic Review 70 (3): HARUVY E. AND C. N. NOUSSAIR The effect of short selling on bubbles and crashes in experimental spot asset markets. Journal of Finance 61 (3): HONG H. J. SCHEINKMAN AND W. XIONG Asset float and speculative bubbles. Journal of Finance 61 (3): LEI V. C. N. NOUSSAIR AND C. R. PLOTT Nonspeculative bubbles in experimental asset markets lack of common knowledge of rationality vs. actual irrationality. Econometrica 69 (4): MARKS M. D. LEHR AND R. BRASTOW Cooperation versus free riding in a threshold public goods classroom experiment. The Journal of Economic Education 37 (2): PLOTT C. R. AND S. SUNDER rational expectiations and the aggregation of diverse information in laboratory security markets. Econometrica 56 (5): SMITH V. L An experimental study of competitive market behavior. The Journal of Political Economy 70 (2): SMITH V. L. G. SUCHANEK AND A. W. WILLIAMS Bubbles, crashes and endogenous expectations in experimental spot asset markets. Econometrica 56: THALER R. H Anomalies the winner s curse. The Journal of Economic Perspectives 2 (1):

33 TABLE 1: Outcomes of the Walrasian Games. True Value Finance trained Average Standard deviation k-th highest Number of traders Price Allocation efficiency Average virtual profits 290 no % no % no % no % yes % yes % yes % Number virtual losses 32

34 TABLE 2: Summary Statistics from Face-to-Face Trading True Value Ø allocation efficiency 29% 85% 67% 75% 50% 43% 80% 82% 75% 60% 65% finance course yes yes yes yes no no no no yes yes number of Assets number of transactions number of people number of active people ø price ø opinion before ø opinion after σ opinion before σ opinion after kth opinion before kth opinion after max ante opinion min ante opinion max post opinion min post opinion buyer ante V p 44(172) -20(82) -45(51) -53(132) -52.5(91) -33(87) -43(64) 5(66) -37(47) -1.9(100) buyer post V p 8(28) -19(56) -39(45) -38(58) 22(180) -8(92) -4(60) 24(72) -17(26) -19(57) seller ante p V -13(53) 23(68) 54(41) 57(91) 49(126) 37(103) 59(71) 4(42) 33(36) -17(127) seller post p V 1(35) 28(52) 50(41) 50(52) -9(153) 26(83) 11(50) -4(67) 23(29) 11(93) ø of ante & post opinion ø price/( ø post & ante) 97% 111% 116% 105% 121% 124% 116% 99% 104% 115% 111% (buyer ante V p)/(ø post & ante) 18% -7% -18% -17% -22% -17% -17% 2% -12% -1% -9% (buyer post V p)/(ø post & ante) 3% -7% -16% -13% 9% -4% -2% 9% -5% -8% -3% (seller ante p V)/(ø post & ante) -5% 8% 22% 19% 20% 19% 24% 2% 10% -7% 11% (seller post p V)/(ø post & ante) 0% 10% 20% 17% -4% 13% 4% -2% 7% 5% 7% buyer neg % ante 33% 69% 67% 56% 59% 53% 67% 35% 73% 61% 57% buyer neg % post 42% 50% 67% 69% 50% 34% 55% 32% 55% 61% 52% seller neg % ante 58% 19% 0% 25% 35% 24% 22% 35% 18% 33% 27% seller neg % post 42% 13% 0% 13% 41% 34% 39% 30% 18% 17% 25% Note: Symbol ø signifies an average and σ a standard deviation. The k in kth highest opinion corresponds to the number of assets available in that setup. neg stands for negative. Buyer ante V-p is the buyer s ex ante valuation minus the price at which s/he traded, averaged over all transactions (similarly for Buyer post and Seller ante/post ) 33