1. Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets
Shin’ichi Hirota and Shyam Sunder
Osaka University (ISER) Workshop, March 6, 2002
Speculative Bubbles

2. The Purpose of Our Study
Explore why the price bubble occurs in stock markets
What investors believe about others’ beliefs
Experimental study
Speculative Bubbles

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

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

5. Which face they will choose as the prettiest?
Speculative Bubbles

6. Which face they will believe that they will choose as the prettiest?
Speculative Bubbles

7. Newspaper Beauty Contests
I believe that
A is the prettiest.
others choose B
others believe that
B is the prettiest
others choose B …
So, I choose B
Speculative Bubbles

8. Stock Markets So, I consider XB I believe that others believe that
F (fundamental value) = XA
others consider XB
others believe that
F (fundamental value) = XB
others consider XB …
So, I consider XB
Stock price = XB even if
every investor believes F = XA
Speculative Bubbles

9. Plausible Story?? Well-known to practitioners and economists
True in real world?
証券レディ (フィナンシャル・プランナー)
「みんなそう思ってますよ」
Central role of beliefs about others, and about others’ beliefs
Emperor’s Clothes, 日本の大学？
Speculative Bubbles

10. Common Knowledge
When XA = XB the value of the stock is common knowledge.
In a great deal of modeling, common knowledge is routinely assumed
What happens when it breaks down?
When our higher order beliefs differ from first order belief, do they converge? (Aumann (1976)).
Speculative Bubbles

11. Speculative Bubbles

12. Irrational Exuberance
Less-than-rational behavior
People do not know fundamentals (XA)
People trade without considering fundamentals
Bubble occurs due to investors’ error and emotional behavior (psychology)
Drawbacks
definition of bubbles, inconsistent exploration, useful exploration ? “Jack got lost because he is foolish”
Speculative Bubbles

13. Beauty Contest Bubble “Rational behavior”
Investor need not be irrational in decisions or beliefs, and need not believe the others to be irrational.
Bubbles generated by gap between the first and second (higher) order beliefs.
Do not depend on investor heterogeneity
Speculative Bubbles

14. How to verify?
In the field it is difficult enough to know the first order investor beliefs (fundamental value), and their diversity
Second and higher order beliefs are also unobservable and 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

15. Experimental Design
Double auction market for multiple units of a single security 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

16. 2 Types of Keynes’ Bubble
Type I
A gap between 1st and higher order beliefs
Absence of common knowledge about dividends
Type II
Self-floating
Is this same as ‘rational bubble’??
Blanchard & Watson (1982), Tirole (1982)(1985)
Occurs in infinite maturity securities
Speculative Bubbles

17. F=S sessions FS sessions
Dividend Value = Dividend Range
Common Knowledge
F=S
No Type I bubble
Dividend Value  Dividend Range
Absence of Common Knowledge
F<S
Type I bubble may be observed
Speculative Bubbles

18. Finite Maturity Securities Sessions
15 periods.
Single liquidating dividend is paid at the end of Period 15
By design, second order beliefs have the chance of being higher than the first order beliefs
Type I bubbles may be observed.
Bubbles continue until period T-1 and crash crash in the last period
Speculative Bubbles

19. Indefinite Maturity Securities Sessions
Investors do not know ex ante how many periods they will have.
Dividend is paid at the end of Period 30, but session is likely to end before Period 30.
Terminal payoff by endogenous prediction game
Type II bubble may be observed. The price is totally dependent on market expectations
Speculative Bubbles

20. Trading Screen
Speculative Bubbles

21. Speculative Bubbles Table 2: Experimental Design 09/21/01 1 Type I
M/D/Y
Session
Final
Payoff on
Stock
Type of Bubble Predicted to Observe
Dividends on cards given to investors
Range of
Dividend Announced
Number of
Subjects (Investors)
$/point
Conv. Rate
Actual # of
Periods
Announced # of Periods
Q&A/
V&C
09/21/01 1
Predicted
Value
Type I
Type II
40 for 2,
75 for 3
[10, 300] 7
(5)
0.025 12
≤ 30
No/ No
09/29/01 2
70 for 3, 130 for 3
[70, 130] 8
(6)
0.015 15
09/30/01 3
Dividend
80 for 3, 150 for 3
[40, 300]
11/16/01 4
120 for 2,
205 for 3
[ ]
0.01
Yes/
Speculative Bubbles

22. Speculative Bubbles 12/01/01 5* Type I 105 for 2, 175 for 3 [55-350] 7
M/D/Y
Session
Final
Payoff on
Stock
Type of Bubble Predicted to Observe
Dividends on cards given to investors
Range of
Dividend Announced
Number of
Subjects
$/point
Conv. Rate
Actual # of
Periods
Announced # of Periods
Q&A/
V&C
12/01/01 5*
Dividend
Type I
105 for 2,
175 for 3
[55-350] 7
(5)
0.012 15
Yes/ No
02/15/02 6
150 for 5
[40, 300]
0.015
Yes
02/22/02
105 for 3, 8
(6)
03/01/02
Predicted
Value
Type II
40 for 2,
75 for 3
[10, 300] 5
(4)
[Points/
Average]
 $25 17
≤ 30
* One predictor violated instructions
Speculative Bubbles

23. Tentative Results Type I bubble ?? Type II bubble Keynes is right?!
Bubble occurred in 1 of 4 sessions
Type II bubble
Bubble occurred in all of 3 sessions
Keynes is right?!
Bubble did not occur in Session 4.
Market expectations tend to follow the market price.
Speculative Bubbles

24. Discussion
Significant part of market returns realized as capital gains, not dividends
Valuation models should incorporate second order beliefs
Link between uncertainty and bubbles
Link between low dividend securities (larger duration) and bubbles
Difference between stock and debt
Exchange rate bubbles
French and Roll: Market trading itself creates volatility (possibly through formation of second order beliefs?)
Speculative Bubbles