1. Shin’ichi Hirota and Shyam Sunder
Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets
Shin’ichi Hirota and Shyam Sunder
University of Houston Workshop, March 22, 2002
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. Experimental Design and Hypothesized Bubble Types
Maturity of the Stock
(Payoff)
Indefinite
(Payoff = Predicted Price)
Definite
(Payoff = Dividend)
Presence of A Gap Between the First and Second Order Beliefs About the Fundamentals
Yes (FS)
Cell C: Type I
(Sessions 3,5*,6**,7**)
No (F=S)
Cell B: Type II
(Session 2)
Cell D: No Bubble
(Session 4*)
Cell A:Type I, II (Sessions 1,8**)
* Questionnaire and Answers
** Questionnaire, Answer, Verification, and Correction
Speculative Bubbles

29. Speculative Bubbles

30. Speculative Bubbles

31. Trading Screen
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32. Speculative Bubbles

33. Speculative Bubbles

34. Cell A (Session 1 and 8**) Endogenous ending, gap in beliefs
Small bubble in 1, huge bubble in 8**
Session 1 is highly stable, 8** is not
No crash
High correspondence between actual and predicted prices
Efficient security transfer in 1 (late in the session)
Reverse security transfer in 8**, terminal dividends played no role in driving trading
Speculative Bubbles

35. Speculative Bubbles

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

37. Tentative Conjectures
Conjecture 1: In absence of exogenously specified terminal dividend, price bubbles can form, and persist through the end of a session.
Conjecture 2: If the terminal dividends are unlikely to be effective, their role in driving trading may diminish, even disappear
Speculative Bubbles

38. Speculative Bubbles

39. Speculative Bubbles

40. Speculative Bubbles

41. Speculative Bubbles

42. Cell C (Session 3, 5*, 6**, 7**) Exegenous termination, gap
Large bubble, prices above upper limit of second order beliefs in Session 3
Bubble burst earlier than last period
Error by one trader (forgot terminal dividend)
No bubbles in Session 5*,6**, 7** with improved instructions
High allocative efficiency without bubbles
Speculative Bubbles

43. Speculative Bubbles

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

45. 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

46. Speculative Bubbles

47. 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

48. 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

49. 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

50. 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

51. Thank You The paper will be available on
My is
Speculative Bubbles

52. Speculative Bubbles

53. Speculative Bubbles

54. Speculative Bubbles

55. Financial Analysis, Trading Volume and Bubbles
Mostly fundamental analysis, assumes common knowledge
Assumption relaxed by convenience
Models of price bubbles based on relaxing the common knowledge assumption
Trading volume models based on diverse beliefs
Speculative Bubbles

56. Models of Weakening Common Knowledge Assumption
Efficient markets may fail to discipline managers (Amershi and Sunder)
Alternatives to fundamental valuation model, even technical models
Models of corporate disclosure (unraveling does not work in practice)
Understanding results of ultimatum games
Speculative Bubbles

57. Speculative Bubbles

58. Levels of Analysis
Speculative Bubbles

59. Thank You The paper, and slides will be available next week at
or to
Speculative Bubbles

60. The purpose of our study
Explore why the price bubble occurs in stock markets
Investor’s belief on other’s belief
Stock market experiments
Speculative Bubbles

61. Stock market bubble in the real world
Internet Bubble
e.g. Yahoo
10$ now, $250 in the peak
Japan late 80’s
e.g. Nikkei 225 Average
10,000 yen now, 40, 000 yen in the peak
Must be bubbles
Why bubbles occur
Speculative Bubbles

62. Investor should expect ...
Infinitely lived investor
Discounted value of future dividends
Finite horizon investor
Resale price
Others’ valuation
Others’ expectation for the future
Future dividends
Future price
Speculative Bubbles

63. If he believes that …
Others will believe high future dividends or high future price,
What should he do?
Even if he does not believe high future dividends or high future price.
Speculative Bubbles

64. If every investor believes that
Others will believe high future dividends or high future price,
What will happen?
Even if every investor himself does not believe high future dividends or high future price
Speculative Bubbles

65. Stock prices are determined by
not investors’ own beliefs (first-order-beliefs)
but investors’ beliefs on others’ beliefs (second-order-beliefs)
Any Price can be observed depending on second-order-beliefs
Speculative Bubbles

66. Bubbles Price  Fundamental Value
Second-order-belief
Fundamental Value
First-order-belief
Second-order-belief  First-order-belief
Speculative Bubbles

67. Keynes Newspaper beauty contests How to verify?
Well-known and popular story
True in real world?
How to verify?
Fundamental value is unobservable
Gap is unobservable
Speculative Bubbles

68. Experimental Study Laboratory Experimental Results
Fundamental value is observable
Create the gap between FOB and SOB
See the effect of the gap on the stock price
Experimental Results
Bubbles occurred due to the gap
Keynes is right!
Speculative Bubbles

69. Experimental Markets Stock market in the laboratory
Trade a single stock
15 (12) periods of 3 minutes each
Stocks has a life during the experiment
Speculative Bubbles

70. How to create the gap between FOB and SOB
Each investor knows dividends (FOB)
But… SOB may be different from FOB
[Market 1]
Dividends may not be received in the investment life.
Dividends are paid only if the session lasts for 30 periods
The subjects can easily guess that the session ends earlier
The stock at the last period is evaluated at the predicted price of the next period
They have to expect what the market expects the price
Speculative Bubbles

71. How to create the gap between FOB and SOB (continued)
[Market 2]
15 periods. Dividends are paid at the end of Period 15.
Each knows his dividend, but does not know others’ dividends
Investors draws the dividend card
Private information
The dividend range is informed to everyone
Investors have to guess others’ dividends, i.e., others’ valuation of the stock.
Speculative Bubbles

72. Investrors and Predictors
Investors
10 stocks, 10,000 cash
trade stocks using caplabTM system
receive money depending on profits
Predictors
predict the next period’s price
receive money depending on the accuracy
Speculative Bubbles

73. Conducted Experiments what, who, where, when
2 sessions for Market 1 (Session 1, 2)
1 session for Market 2 (Session 3)
Yale university, undergraduate students
Yale School of Management, B-74 Room
September 21, 29, 30, 2001
Speculative Bubbles

74. Conclusion (from preliminary experimental results)
The investors’ beliefs on other’s belief (SOB) significantly affect the stock prices.
The gap between FOB and SOB seems to create bubbles in stock markets.
Speculative Bubbles