Shin’ichi Hirota and Shyam Sunder University of Iowa Workshop, Dec 7, 2001

1. Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota and Shyam Sunder University of Iowa Workshop, Dec 7, 2001 Speculative Bubbles

2. Valuation of Securities • Value = net present value of future cash flows • Future is uncertain, value depends on investor beliefs about the future cash flows • How far into the future? • From now to liquidation of the the security • From now to investment horizon (sale) • Sale price depends on beliefs of other investors about the cash flows after the sale • Return to formalization later Speculative Bubbles

3. Simple Example • Investor A believes the net present value of cash flows from now on to be $100 (=fundamental value) • Investor should buy below $100 and sell above • What if A also believes that tomorrow, others will believe the net present value to be $150 • Considering second order beliefs, it may not necessarily be best for A to sell at $110. A may be better off buying at that price, with the expectation of being able to sell at a higher price • What is the best thing to do for an investor whose first and second order beliefs are not identical? Speculative Bubbles

4. Stories of Common Knowledge Assumption • In a great deal of business modeling, common knowledge is routinely assumed • What happens when it breaks down? Speculative Bubbles

5. Emperor Has No Clothes Speculative Bubbles

6. Speculative Bubbles

7. Emperor’s Clothes • The scoundrels made people believe that the clothes will be invisible only to the incompetent and the stupid • People thought that others believed it • Nobody wants to be seen as stupid or incompetent by others, lose his/her job • Visibility of clothes was private, it was easy to fake seeing the clothes Speculative Bubbles

8. Emperor’s Clothes (Contd.) • Scenario 1: Everyone was privately convinced of their incompetence, and cheered to deny it publicly • Scenario 2: People did not believe they were incompetent just because they could see the naked emperor, but believed that others so believed, and cheered to avoid being seen as stupid Speculative Bubbles

9. What about the Child? • The child did not know the link between visibility and competence • Child was innocent, and said what he saw • People know children to be innocent • People knew that people knew this Speculative Bubbles

10. Stock Market • Stock Market is like a newspaper beauty contest • John Maynard Keynes, (1936) Speculative Bubbles

11. Newspaper Beauty Contest Which Face is the prettiest? Speculative Bubbles

12. Which face will they judge to be the prettiest? Speculative Bubbles

13. Which face will they judge to be the prettiest? Speculative Bubbles

14. LIFO Inventory Accounting • If your inventory prices rise, and end-of-year inventory volume is stable or rising • You can delay paying taxes (higher net present value of cash flows) • But have to report lower income also • Many firms don’t adopt LIFO • Apprehension about stock market reaction (no empirical support) Speculative Bubbles

15. Agency Problem • Agency problem: how to induce managers to maximize shareholder value (e.g., choose LIFO) • Solution: Link managerial compensation to shareholder value • Problem 2: Value manipulation • Solution: Use market, not accounting, measures of value Speculative Bubbles

16. Value Maximizing Manager in an Efficient Market • LIFO can increase NPV of cash flow • But manager maximizes stock price • What does manager believe about how stock prices are determined? • Suppose manager believes that stock prices depend on income, not cash • Then manager is rationally led to reject LIFO even if it saves cash for the firm Speculative Bubbles

17. Beliefs About Others’ Beliefs • Common elements to the three stories about the emperor‘s clothes, stock market and LIFO • Central role of what we believe about others, and about their beliefs Speculative Bubbles

18. Closing the Gap in Beliefs • Is it possible for our first and higher order beliefs to differ? • When they do differ, what does it take to get them to converge? Aumann (1976). • Do they actually converge? Why or why not? • When the beliefs of all around you are wrong, does it pay to hold on to the right beliefs? Fight them or join them? • Prior experimental results • What are the consequences for theories of bubbles? Speculative Bubbles

19. Bubbles in Economic History • “Self-evident” bubbles: Galbraith, Kindleberger • Econometric studies of long term recorded data: stock prices move sufficiently closely with dividend over the long run to reject bubbles • Contemporary investors knew more than what the econometricians have in their data • What changes in fundamentals can justify the 90 percent price drop during the Great Crash? Speculative Bubbles

20. Beliefs and Observation • Theories of valuation are a function of beliefs • In the field it is difficult enough to know the first order investor beliefs, and their diversity • Second and higher order beliefs are practically out of reach • In lab we might have a better, though still limited, chance to know beliefs, perhaps even open a gap between the first and higher order beliefs and observe their consequences under controlled conditions Speculative Bubbles

21. Models of Bubbles • Tirole (1082, 1985): bubbles grow at discount rate, no prediction about levels • First order beliefs Dti ≠ Dtij (second order beliefs) • Investor need not be irrational in decisions or beliefs, and need not believe the others to be irrational. • Aumann: common knowledge priors imply common knowledge posteriors Speculative Bubbles

22. Professional Security Analysis • Multi-billion dollar information intermediary industry in U.S. alone • Typical report has current market price compared to what the analyst predicts the future price to be, and what the analyst believes the firm to be worth • If investor beliefs were common knowledge, there will be no rationale for such beliefs • Bubbles generated by gap between the first and second order beliefs do not depend on investor heterogeneity Speculative Bubbles

23. Finite Maturity Securities Speculative Bubbles

24. Finite Maturity Securities • Cells C and D (sessions 3 and 4) • All dividends except terminal dividends are zero • Equilibrium price is constant through the 15 sessions • By design, second order beliefs have the chance of being higher than the first order beliefs • Expect to observe bubbles as late as period T-1 in Cell C • Expect the bubble to crash in the last period (Figure B) Speculative Bubbles

25. Indefinite Maturity Securities Speculative Bubbles

26. Indefinite Maturity Securities • Cells A and B • All dividend except liquidation dividend are zero • Session does, and is expected to end before liquidation • Terminal payoff by endogenous prediction game (see Figure A for price path) Speculative Bubbles

27. Experimental Design • Double auction market for multiple units of a single security that pays single liquidating dividend • Multiple trading periods (3 minutes each) • Each investor endowed with 10 shares, 10,000 points in “cash” • Liquidation by dividend or predicted price • Predictors knew the rules, no endowments, no ability to trade, could watch trading, knew the range of terminal dividends Speculative Bubbles

28. Final Payoff Predicted Price Dividend Gap between first and second order beliefs Yes Cell A: Session 1 Cell C: Session 3 No Cell B: Session 2 Cell D: Experimental Design Speculative Bubbles

29. Experimental Parameters Speculative Bubbles

30. Trading Screen Speculative Bubbles

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32. Cell A (Session 1) • Endogenous, gap • Small bubble (10 percent) • Highly stable • No crash • High correspondence between actual and predicted prices • Efficient security transfer late but not early Speculative Bubbles

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34. Cell B (Session 2) • Endogenous, no gap • Huge bubble, well above second order belief limits • Highly stable • Did not crash • Allocations suggest that terminal dividends ceased to play any important role in driving trading, largely driven by prediction Speculative Bubbles

35. Tentative Conjectures • Conjecture 1: In absence of exogenously specified terminal dividend, price bubbles can form, and persist through the end of a session. Speculative Bubbles

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37. Cell C (Session 3) • Exegenous termination, gap • Large bubble, prices above upper limit of second order beliefs • Bubble burst earlier than last period • Error by one trader (forgot terminal dividend) Speculative Bubbles

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39. Cell D (session 4) • Exogenous termination, no gap • No bubble • Fundamental price and allocations Speculative Bubbles

40. Tentative Conjectures • Conjecture 2: Even with exogenous terminal dividend and known horizon, bubbles can form when there is a gap between first and second order beliefs. • Conjecture 3: In the presence of exogenously specified terminal dividend, end-of-the-session prices converge to the equilibrium level determined by such dividends. Speculative Bubbles

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42. Results A: Gap, Endogenous Termination Speculative Bubbles

43. Discussion • Shiller: prices too volatile • French and Roll: Market trading itself creates volatility (possibly through formation of second order beliefs?) • Significant part of market returns realized as capital gains, not dividends • Valuation models should incorporate second order beliefs Speculative Bubbles

44. Discussion • Stock prices can stabilize far from fundamental price levels • Price predictions can simply reinforce deviations from fundamentals • In a market dominated by “capital gains” traders, price can be decoupled from fundamentals • Consistent with gap between first and higher order beliefs generating price bubbles Speculative Bubbles

45. Bubbles and Rationality • Lei, Noussair and Plott: observe bubbles in absence of speculative trading • Lack of understanding by subjects of the market structure, task, opportunities • Lack of correspondence between the intended and subjective experimental environment • Difficult to determine the correspondence • Is lack of understanding “irrational?’ • Need get inside “irrationality.” Speculative Bubbles

46. Candidates to be Examines • Gap between intended and subjective experimental environment • We tried this in a fifth session; observed many errors in spite of better instructions • Link between uncertainty and bubbles • Link between low dividend securities (larger duration) and bubbles Speculative Bubbles

47. Thank You • The paper will be available on • http://www.som.yale.edu/faculty/sunder/research • My email is shyam.sunder@yale.edu Speculative Bubbles

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