Price Bubbles with Discounting: A Web-Based Classroom Experiment

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1 Price Bubbles with Discounting: A Web-Based Classroom Experiment AJ A. Bostian and Charles A. Holt October 15, 2007 Abstract The authors describe a web-based classroom experiment with two assets: cash and a stock that pays a random dividend. The interest rate on cash, coupled with a well-chosen final redemption value for the stock, induces a flat trajectory for the fundamental value of the stock. However, prices typically rise above this value during a session. The bubbles and crashes that occur in this experiment can stimulate a discussion of asset valuation, discounting, and pricing patterns that are determined by expectations and animal spirits. Keywords: asset markets, classroom experiments, discounting, price bubbles, present value JEL codes: A22, C99, G12 AJ A. Bostian (ajbostian@virginia.edu) is a Ph.D. candidate in economics at the University of Virginia, and Charles A. Holt is the A. Willis Robertson Professor of Political Economy at the University of Virginia. This work was funded in part by the National Science Foundation (SBR ). The authors thank Lindsay Osco for helpful suggestions. 1

2 Most financial analysts believe that equity markets exhibit strong growth in the long run, but short-term stock prices display sharp rises and dips that do not seem to be correlated with underlying fundamentals. We describe a web-based classroom asset market that usually generates a significant price increase above fundamental value, followed by a crash. Students begin the experiment with an endowment of cash and shares of a stock. Cash is riskless and earns interest, but shares pay randomly-determined dividends in each period. Shares are bought and sold using limit orders. The uniform market-clearing price is determined by matching ranked buy and sell orders, that is, the price is determined by the intersection of the pseudo-demand (bids arrayed from high to low) and pseudo-supply (asks arrayed from low to high). With an infinite horizon, the present value of the stock can be determined straightforwardly, because it is just a discounted stream of expected dividends. In a classroom experiment with a finite number of periods, the present value is used as a terminal redemption value, or the rate at which shares are exchanged for cash after the final trading period. This method of assigning the redemption value induces a fundamental value that is flat (unchanging) from one period to the next. Of course, shares could trade for less than this value if the market participants are risk averse. But, in fact, share prices typically rise far higher during the middle periods of the experiment, and then crash back near the end. Even students who understand that they can lose money by buying overvalued assets can be quite impressed by the extent to which they lose their unrealized gains. Indeed, one of our students mentioned his performance in this experiment as one of the most valuable lessons learned in our Experimental Economics class, three months after the fact. The exercise is implemented as a web-based program with integrated instructions and data displays, and the results can be used to initiate a discussion of discounting, asset valuation, and other factors that may lead traders to participate in a bubble. The program is appropriate for courses in Finance, Macroeconomics, Money and Banking, or Experimental Economics. Background Smith, Suchanek and Williams (1988) surprised many in the economics profession by reporting research experiments showing price bubbles and sharp crashes in a single-asset market, even though the fundamental value of that asset was very easy to calculate. In their main design, each share paid a random dividend with a positive expected value for 15 periods, after which the share was worthless. Thus, the fundamental value was the expected dividend multiplied by the 2

3 number of remaining periods, or a decreasing linear function in time. 1 3 This design was implemented for classroom use in a computerized design by Williams and Walker (1993) and in a hand-run design by Bell (1993). The latter also included an informative discussion of the features of the experiment that are relevant for finance classes. The Bell (1993) experiment was conducted over several weeks of the semester, presumably so that market-clearing prices could be calculated between classes. The Williams and Walker (1993) experiment also involved several weeks of trading, presumably because a lab of sufficient size was not available. (The exercise was conducted with several hundred students in an introductory economics class.) We note that the Smith, Suchanek and Williams (1988) design can be implemented in our web-based program by specifying a $0 redemption value and a zero percent interest rate. The default settings for our two-asset, flat-fundamental-value design also address two limitations noted by Bell (1993): the absence of interest compounding (our interest increases the value dividends paid today) and the absence of a risk-return tradeoff (our cash is a riskless second asset that permits positive earnings without holding stock). In addition, the web-based program can be run quickly, allowing students to absorb the main lessons of the experiment before reading the relevant material. A follow-up series of research experiments by King et al. (1993) showed that the bubbleand-crash pattern in a declining-value setup is robust to the incorporation of many institutional features of financial markets, such as short-selling, margin-buying, transactions costs, and the presence of professional traders. In fact, repetition of the experiment and not the ability to easily exploit arbitrage opportunities seemed to be the most reliable way to reduce the bubble. Van Boening, Williams and LaMaster (1993) showed a similar result regarding repetition and also noted that bubbles form when either the call market or the double auction is used to sell the asset. Lei, Noussair and Plott (2001) presented research experiments to argue that bubbles arise primarily from the irrationality of individuals, and not from errors in their perception or a lack of common knowledge. Caginalp, Porter and Smith (2001) showed that a bubble is more easily formed when participants are cash-rich and dividends are paid frequently. Bostian, Goeree and Holt (2006) reported a series of research experiments using the design described in this article and found that a high-cash treatment (with high interest rates and high dividends) produced stronger bubbles. Although most designs have used a declining fundamental value, it is possible to induce other fundamental dynamics. By using an expected dividend of $0, Noussair, Robin and 1 The authors also ran several sessions with a final-period redemption value that was related to previous random realizations of dividend payments.

4 Ruffieux (2001) constructed a market with a flat fundamental value at $0. The observation of bubbles in this environment demonstrated that the bubble-and-crash pattern is not an artifact of the declining-value design. Hommes et al. (2005) utilized a two-asset design similar to the one presented in this article to study belief formation in experimental asset markets. They focused primarily on constructing models of expectations formation in the absence of bubbles, and so the design included a rational, computerized trader with sizable market power whose specific purpose was to retard bubble formation. Ball and Holt (1998) described a classroom design that generates a flat fundamental value by combining random destruction of shares each period with positive dividend payments. The probability of destruction essentially plays the role of a discount rate, diminishing the expected value of future dividends. Bubbles were observed in about half of the sessions conducted. Like the Bell (1993) design, the Ball and Holt (1998) setup does not require computers, but generating randomness by throwing dice or similar means takes time, thins out trading volume, and is more difficult to relate to present-value or other fundamental calculations. The advantage of the web-based setup we describe here is that it is faster and easier to run, with fully integrated instructions and graphics to motivate subsequent discussion. The price bubbles generated by the web-based version are also somewhat stronger and more reliable, in part because a computerized experiment permits the completion of more periods, which tends to amplify the price deviations from fundamental value. Finally, it is possible to run this experiment outside of class, which can involve more students and save class time. Procedures The limit order market experiment we used can be found at the Veconlab website in the Macro/Finance category. 2 A guide to setting up a session can be found in the Appendix. With 10 trading periods, a session lasts about 30 to 45 minutes. The only technological requirement is that participants use computers with Internet access. No special software is needed because all interaction occurs via a standard web browser. The experiment can also be run after hours with students logging in from remote locations, a practice that conserves class time and eliminates the need for a computer lab. The default settings involve an initial endowment of $50 in cash and 6 asset shares for each trader, and a market duration of 20 trading periods. (Each period will probably last about 2 minutes, and so it may be necessary to decrease the number of periods to save time for 2 The Veconlab menu of experiments can be found at 4

5 discussion.) The default settings also include an interest rate of 10 percent and dividends of either $1.00 or $0.40 per share in each period, paid with equal probability. The expected dividend in each period is thus $0.70. If this dividend were paid in perpetuity, the expected present value in each period would be determined by dividing by the interest rate to obtain $0.70 / 0.1 = $7 (i.e., by applying the geometric-series formula). As explained below, this flat fundamental value can be translated to a finite horizon by setting the final redemption value for each share to $7. In other words, the redemption value is set equal to the present value of all future payments that would have been received after the final round, had the experiment continued indefinitely. Classroom Discussion In our experience, this experiment always generates a bubble with a subsequent return to fundamental value by the last period. The most common pattern is a gradual increase followed by a very sharp crash in last rounds, although we have also observed roller-coaster double bubbles in longer experiments. The pricing graph shown in Figure 1 (taken directly from the Veconlab website) comes from an in-class session using the default settings described previously. The dark dots show transactions, all of which occur at the same market-clearing price. The transaction volume is indicated by the horizontal distance between periods; if no transactions occur during a round (i.e., if all ask prices are higher than all bid prices), there is no such interval. The lighter dots above and below the market-clearing price indicate the bid and ask prices for the accepted orders. In this session, prices initially rose steadily on strong volume, and this sharp rise was then followed by a decline over several periods. The market failed to agree on a price during a few of the later periods, but the price eventually fell to almost exactly the redemption value by the end of the session. [Figure 1 about here] Different parameterizations can help students to understand how the market ingredients can affect prices. Bostian, Goeree and Holt (2006) illustrated the role of wealth in fueling a bubble in the following manner: if both the expected dividend and the interest rate are doubled, the fundamental value is unaltered (according to the present-value formula, the fundamental value is 2($0.70) / 2(0.1) = $7). One might expect that because the fundamental value is the same, the price dynamics should also be the same. Figure 2 presents the results of a research 5

6 session using this high-cash design. The bubbles are typically much stronger with the additional wealth, the peaks being two to three times higher than in the standard parameterization. (Note that the price axis has been scaled to six times the fundamental value, rather than twice the fundamental value as in Figure 1.) Comparing the two results highlights the role of excess cash in bubble formation, as proposed by Caginalp, Porter and Smith (2001). [Figure 2 about here] Figure 3 shows results of another market conducted in the final 40 minutes of an Experimental Economics class, with students who had already participated in numerous other computerized experiments. There were 24 students working in pairs from 12 lab computers, and it was known that one team would be selected at random ex post to be paid a very low fraction of earnings, with the fraction being announced ex post as well. A number of students had a finance concentration in their economics major, and several even had hand-held calculators with bondpricing functions. In this session, prices started above the fundamental value and fell to $8 in rounds 4-7. This was late in the semester, and so the instructor s admonishments about not talking during the experiment had little effect, and one person announced publicly and with confidence, The fundamental value is $7. When the price then proceeded to rise to $9 in the period 9, another called out incredulously, Who paid $9?! The price continued to rise before crashing in period 14, and there was no trade in many of the periods following the crash. In our experience, it is likely that a class will be composed of both fundamental traders who utilize the present value and irrational traders who either do not know the present value or choose not to use it. The formation of bubbles in this setting is similar to a simulation result by Steiglitz and Shapiro (1998) in which bubbles form even if the market is only partly composed of irrational trend traders. If there is some process that leads prices to increase, this model predicts that the trend traders can bid the price up amongst themselves by buying from the fundamental traders, until the former run out of money. The experimental outcome certainly complements this intuition. [Figure 3 about here] Considering this anecdote and comparing Figures 1 and 3, one might conjecture that allowing students to discuss fundamentals during the session generates price paths that are more muted. Discussion is a nonprice source of data that permits students to refine their beliefs; with small numbers of students, open discussion by a handful of students may contribute greatly to 6

7 belief formation and the overall market outcome. The instructor may want to consider whether to strictly enforce silence during the session to preclude this information. It is also possible that bubbles will be more muted when students have advanced economics or finance backgrounds, because they would probably understand (at least intuitively) elements of asset pricing. However, the one constant we have observed in this design is that bubbles occur with solid regularity. Even with doctoral-level students, classroom sessions yield bubbles that are at least 50 percent higher than the fundamental value. The post-experiment discussion often begins with a review of who earned the most and what trading strategies were followed. At some point, the instructor should direct the discussion towards the question of asset valuation. In any given economics class, there are usually significant numbers of students who intend to become financial analysts, and they will be genuinely interested in how to price these shares based on fundamentals. Some students might already know that the value should be $7 in all rounds, especially after observing that price in the final round. Sometimes, we ask students before trading begins to write down the price at which they think a share will trade in the first round, and the ex post discussion can begin with a comparison of actual prices with their expectations. 3 The initial assessments are often too high. For example, when the default setup was described in a presentation at a conference involving credit-union CEOs, one economist predicted an initial price of $35 for a 40-round experiment, and nobody in the audience objected. This answer was justified by simply summing the expected dividends for all 40 rounds and adding on the $7 redemption value. However, this price is grossly inflated: because a second asset is available, all dividend payments must be discounted. That is, it is the relative return, not the absolute return, that is relevant when pricing an asset. The instructor should review the concept of present value in the context of the experimental dollar amounts. For example, $7 in cash at present becomes $7.70 one period later, so a promised income of $7 at the start of the next period is worth less than $7 at present. The instructor should lead students to the single-period discount of $7 / 1.1 = $6.36, because investing $6.36 at 10 percent interest at present will yield $7 one period hence. Another approach to valuation is to make a simple backwards-induction argument starting from the final period. If a share trades for price P in the final round, then the return is the $0.70 dividend plus the $7 redemption value, minus P. A good leading question for students is, If a person starts the final period with $7 in cash and buys a share that pays a $0.70 dividend, 3 This pretest has an important instructional value, because research on the efficacy of teaching with laboratory experiments in the physical sciences indicates that students will frequently rationalize an unexpected result as being what they thought would happen. Forcing students to write down a prediction ex ante causes them to realize that the mispricing really was unanticipated, which induces them to pay more attention to the ensuing discussion. 7

8 what is the final earnings position after redeeming the share? A series of follow-up questions can compare this return to the cash return. For example, What is the rate of return for someone who begins with $P and buys a share when P < $7? This should lead students to realize that such an investment yields more than a 10 percent return. Discuss similarly the case of P > $7. This argument should firmly establish that the share should be valued at $7 in the final period. Then, the logic can be repeated from the perspective of the second-to-last period, assuming that a share is valued at the fundamental price of $7 in the final period. Students should notice that the argument for the second-to-last period is identical to that of the final period. This process establishes a share value of $7 for all rounds. Yet another explanation of the share price can be developed by assuming a flat price trajectory and calculating the price that yields this trajectory. In equilibrium, the price P must make a trader indifferent between holding cash and shares. A person who has $P in cash at the start of a period could either buy a single share or just hold the cash. This person would have (1.1)$P from holding cash for one period, and the person would have $ $P from buying a share and reselling it at the start of the next period. Equating these expressions yields 0.1P = $0.70, or P = $7. The computation of the fundamental price is probably not too difficult an exercise for most students concentrating in economics. The main question of interest in a classroom discussion is why this price is not attained. Many students will say that they expected prices to keep rising, some may admit that they did not think that the shares were actually overvalued, and others will say that they planned to sell them in time. There are also usually a few students who follow a contrarian strategy, that is, converting to cash early while the price is still rising. A discussion of these two strategies could be best directed in the context of the efficient-markets versus behavioral theories of finance. Efficient-markets theory suggests that individual variations in beliefs do not affect aggregate prices, and that prices almost always reflect fundamentals. A person with non-fundamental beliefs will earn less wealth in the long run, and so this person must either correct the belief or stand to lose significant wealth. This is true in some sense in our experiment, for those who bought during the height of the bubble are typically those who have the worst overall earnings once the price crashes. But even though the efficient-markets theory might describe the terminal outcome accurately (i.e., when the fundamental price becomes just the redemption value), it is an inaccurate description of trading behavior during most rounds of the experiment. Students simply do not appear to be concerned about fundamentals during these periods. 8

9 Specific contributions to this debate can be highlighted during the discussion. On the efficient-markets side, one can present the conclusions of Hall (2001), who provided econometric evidence that stock price fluctuations are actually best described by present-value discounting behavior. Hall (2001) found that any apparent inconsistencies with rational pricing can be attributed to unobserved fluctuations in the value of firms intangible assets. This explanation does not apply to our classroom asset market because there is no such unobservable component to the fundamentals. On the behavioral side, the noise trader results of Schleifer and Summers (1990) can be given, in which uninformed agents trading on noise (nonfundamentals) are intentionally manipulated by the informed, rational agents in order to pump the price further before the foreseen crash. This idea is supported by the Brunnermaier and Nagel (2004) analysis of hedge-fund trading behavior during the dot-com bubble of the 1990s. Hedge funds, which are likely to have good estimates of fundamental values, were overweighted with technology stocks during the runup but sold these positions off prior to the crash. Other behavioral issues in asset pricing that might be briefly touched upon are the roles of momentum, overconfidence, and overreaction. The middle-of-the-road assessment of Barsky and De Long (1993) can provide a good counterbalance to the debate. They found that price fluctuations can indeed be attributed largely to long-run dividend movements, but that this fundamental does not explain all price movements. Finally, one can ask students about historical examples of price bubbles. Expect a discussion of the dot-com bust or housing prices. A particularly interesting anecdote of the psychology behind a bubble is found in Charles Mackay s (1841) account of the Dutch tulipmania in the 17th century: Nobles, citizens, farmers, mechanics, seamen, footmen, maid-servants, even chimneysweeps and old clotheswomen, dabbled in tulips. Foreigners became smitten with the same frenzy, and money poured into Holland from all directions. At last, however, the more prudent began to see that this folly could not last forever. Rich people no longer bought the flowers to keep them in their gardens, but to sell them again at cent per cent profit. It was seen that somebody must lose fearfully in the end. As this conviction spread, prices fell, and never rose again. Confidence was destroyed, and a universal panic seized upon the dealers. 9

10 Tulipmania is a widely-cited example of irrational pricing behavior, but there is even a debate over this event that may be interesting to students. Garber (1990) argued that the inflated prices actually reflected fundamentals. For example, some high prices were attributable to the exceptional rarity of the tulip variety a single bulb. These high prices could therefore drop only after the tulip had been propagated extensively, removing the supply-side constraint. Directly comparing the tulipmania prices to the settled prices some years later is legitimate only if the fundamentals were similar in each period, but this may not have been the case if supply increased substantially. The argument highlights the fact that identifying the makeup of fundamentals is itself a difficult problem, and so the rationality of the price may depend on one s perception of the fundamentals. These observations highlight the usefulness of classroom experiments in which the key economic variables are controlled to provide unambiguous fundamental values. Appendix: Setup Guide To begin, the instructor must visit the Veconlab admin page at and obtain a username by following the Get Started link. 4 A username, for example, abc, is associated with one or more session names that correspond to particular experiments, for example, abc1, abc2, etc. The next step is to return to the admin page and follow the Finance/Macro link to the Limit Order Market link, which provides a short introduction and a sample data display such as those shown in Figures 1-3. The instructor will be prompted to enter the username and password chosen in the first step. The next pages allow the instructor to customize the treatment, (e.g., by specifying the numbers of participants and trading periods). The number of participants should not exceed the number of computers available. (Because it is desirable to have two or three students at each computer to stimulate discussion, having more students than computers should not be a discouragement.) Default values that correspond to the design presented in this article are provided for all of the other parameters. Sessions can be configured quickly, and so there is usually no need to set one up in advance. However, if the instructor does configure a session in advance, the instructor can then log on later by following the View Results link to watch decisions as they are made. First-time users may also find it useful to test the setup by logging in some simulated students and running a few trading periods by oneself. 4 See Holt (2007) for a discussion of other experiments that can be run with this software. 10

11 Students begin the experiment by visiting the login page at and entering the session name used by the instructor when setting up the experiment. (If this exercise is to be run after class, the students will need to know the precise login time, the session name, and the commencement time for the first trading period.) They should look for messages at the top of their screens about starting and stopping times during the experiment. Students will first be taken to the instruction pages for the experiment, which are automatically configured to match the design parameters. Then, in each trading period, they enter and confirm limit orders (bids and asks), which are transmitted to the Veconlab server. A limit order to buy consists of a number of shares and a maximum purchase price, and a limit order to sell consists of a number of shares and a minimum sale price. When the market is cleared (either automatically after receiving orders from all participants, or manually when the instructor presses the Terminate Round button), the individual results and earnings for that trading period are calculated and relayed back to the students. The market-wide results and earnings are displayed on the instructor s results page, along with graphs that can be used to guide subsequent class discussions. The process of logging in students and reading instructions takes about 15 minutes, and each trading period can be limited to 2 minutes. The instructor should be strict and press the Terminate Round button on the results page when the time is up. Total earnings are calculated and displayed for participants upon completion of the final round. Because of this, it would be a mistake to set the experiment for more rounds than time permits. Fortunately, we have seen strong bubbles with as few as 15 rounds, so the exercise can be useful even under short horizons. There is no need to pay students because they tend to be competitive in market experiments, although it is customary in our classes to randomly pick one person (or team) ex post and pay some small fraction of that person s (or team s) earnings. The earnings for this experiment can be quite large with many periods or high returns, so the instructor should examine the final earnings before committing to a fraction. The final step is to save the data by saving the results page as an.htm (HTML) file. Similarly, the pricing graph can be saved by right clicking on it and saving it as a.png (Portable Network Graphics) file. Of course, the instructor can always use the View Results link at any time to examine the data from a previously run session, as long as the same session name has not been subsequently used for a different experiment. 11

12 References Barsky, R. B., and B. De Long Why does the stock market fluctuate? Quarterly Journal of Economics. 108 (2): Ball, S. B., and C. A. Holt Classroom games: Speculation and bubbles in an asset market. Journal of Economic Perspectives 12 (1): Bell, C. R A noncomputerized version of the Williams and Walker stock market experiment in a finance course. Journal of Economic Education 24 (4): Bostian, A. A., J. K. Goeree, and C. A. Holt Price bubbles in asset market experiments with a flat fundamental value discussion paper, University of Virginia. Brunnermaier, M. K., and S. Nagel Hedge funds and the technology bubble. Journal of Finance 59 (5): Caginalp, G., D. Porter, and V. Smith Financial bubbles: Excess cash, momentum, and incomplete information. Journal of Psychology and Financial Markets 2 (2): Garber, P. M Famous first bubbles. Journal of Economic Perspectives 4 (2): Hall, R. E Struggling to understand the stock market. American Economic Review 91 (2): Holt, C. A Markets, games, and strategic behavior. Boston: Addison-Wesley. Hommes, C., J. Sonnemans, J. Tunistra, and H. van de Velden Coordination of expectations in asset pricing experiments. Review of Financial Studies 18 (3): King, R. R., V. L. Smith, A. W. Williams, and M. Van Boening The robustness of bubbles and crashes in experimental stock markets. Nonlinear dynamics and evolutionary economics. New York: Oxford University Press. 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): Mackay, C (original printing 1841). Extraordinary popular delusions and the madness of crowds. Hertfordshire, England: Wordsworth Editions Ltd. Noussair, C., S. Robin, and B. Ruffieux Price bubbles in laboratory asset markets with constant fundamental values. Experimental Economics 4 (1): Smith, V. L., G. L. Suchanek, and A. W. Williams Bubbles, crashes, and endogenous expectations in experimental spot asset markets. Econometrica 56 (5): Schleifer A. and L. H. Summers The noise trader approach to finance. Journal of Economic Perspectives 4 (2):

13 Steiglitz, K. and D. Shapiro Simulating the madness of crowds: Price bubbles in an auction-mediated robot market. Computational Economics 12 (1): Van Boening, M. V., A. W. Williams, and S. LaMaster Price bubbles and crashes in experimental call markets. Economics Letters 41 (2): Williams, A. W. and J. M. Walker Computerized laboratory exercises for microeconomics education: Three applications motivated by experimental economics. Journal of Economic Education 24 (4):

14 Figure 1. A classroom session using the standard design. 14

15 Figure 2. A research session illustrating the effect of doubling dividends and interest to generate more wealth. 15

16 Figure 3. A classroom session using the standard design, with some student discussion during the session. 16