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![Page 1: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/1.jpg)
Speculative Bubbles 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
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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
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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?
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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?
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Speculative Bubbles 5
Emperor Has No Clothes
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Speculative Bubbles 6
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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
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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
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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
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Speculative Bubbles 10
Stock Market
• Stock Market is like a newspaper beauty contest
• John Maynard Keynes, (1936)
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Speculative Bubbles 11
Newspaper Beauty Contest
Which Face is the prettiest?
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Speculative Bubbles 12
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
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Speculative Bubbles 13
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which face will they judge to be the prettiest?
![Page 14: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/14.jpg)
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)
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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
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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
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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
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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?
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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?
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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
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Speculative Bubbles 21
Models of Bubbles
• Tirole (1082, 1985): bubbles grow at discount rate, no prediction about levels
• First order beliefs Dti ≠ Dt
ij (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
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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
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Speculative Bubbles 23
Finite Maturity Securities
1 1 2( , ,..., , ( ), ( ),..., ( ))i i i i i i i it t t t T t t TV f D D D E P E P E P
(2) (2) (2) (3) (3) (3) ( ) ( ) ( 1)1 1 2 1 2 1( , ,..., , , ,..., , , ,..., ,..., , ,..., )T t T t T t
t t t t T t t T t t T T T TP G D D D D D D D D D D D D
1( , ,..., )t t t t TP G D D D
tt tB P P
(2)
1
( )
(1 )T T
t T t
D DB
r
![Page 24: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/24.jpg)
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)
![Page 25: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/25.jpg)
Speculative Bubbles 25
Indefinite Maturity Securities
1 1 2 1( , ,..., , ( ), ( ),..., ( ), ( ))i i i i i i i i it t t t T t t T TV f D D D E P E P E P E P
(2) (2) (2) (3) (3) (3) ( ) ( ) ( 1)1 1 2 1 2 1
(2) (3) ( 1)1 1 1 1
( , ,..., , , ,..., , , ,..., ,..., , ,...,
( ), ( ), ( ),..., ( ))
T t T t T tt t t t T t t T t t T T T T
T tT T T T
P G D D D D D D D D D D D D
E P E P E P E P
1 1 2( , ,..., , , ,..., ,.........)t t t t T T T T mP H D D D D D D
tt tB P P
11
1
( )(1 )
(1 )
T sT s
st T t
DE P
rB
r
![Page 26: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/26.jpg)
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)
![Page 27: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/27.jpg)
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
![Page 28: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/28.jpg)
Speculative Bubbles 28
Experimental Design
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:
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Speculative Bubbles 29
Experimental Parameters
Treatment
Session Final
Payoff on Stock
Dividends on cards given to investors
Range of Dividend
Announced
Initial Shares
per subject
Initial Cash
Number
of
Subjects
Number
of
Investors
Number
of
Predictors
Predictor
Fixed
Number*
(N)
$/point
Conv.
Rate
Actual Number
of Periods
Announced No.
of Periods
Cell A
1 Predicted Value
40 for 2, 75 for 3
[10, 300]
10 10,00
0 7 5 2 150 0.025 12
? 30
Cell B 2 Predicted Value
70 for 3, 130 for
3
[70, 130]
10 10,00
0 8 6 2 100 0.015 15
? 30
Cell C 3 Dividend
80 for 3, 150 for
3
[40, 300]
10 10,00
0 7 6 1 100 0.015 15
15
Cell D 4 Dividend
150 for 2,
205 for 3
[150-205]
10 10,00
0 7 5 2 150 0.01 15
15
*Predictor compensation = (N - absolute price prediction error)
![Page 30: Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota.](https://reader036.fdocuments.us/reader036/viewer/2022062714/56649d485503460f94a22d83/html5/thumbnails/30.jpg)
Speculative Bubbles 30
Trading Screen
Figure 1
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Speculative Bubbles 31
Figure 1 Time Series of Stock Prices (Market 1 Session 1)
0
50
100
150
200
250
300
350
400
Period
Transaction Price Fundamental Price Maximum Possible Dividend Average Predicted Price
1 2 3 4 5 6 7 8 9 10 11 12
86 84 83 83 82 82 83 82 83 83 83Average Price
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Speculative Bubbles 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
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Speculative Bubbles 33
Figure 2: Time Series of Stock Prices (Market 1 Session 2)
0
200
400
600
800
1000
1200
Period
Transaction Price Fundamental Price Average Predicted Price
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
17 24 154 781 970 845 879 989 963 1974* 909 903 941 903 897Average Price
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Speculative Bubbles 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
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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.
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Speculative Bubbles 36
Figure 3: Time Series of Stock Prices (Market 2 Session 1)
0
50
100
150
200
250
300
350
400
Period
Transaction Price Fundamental PriceMaximum Possible Dividend Predicted Price
1 2 3 4 5 6 7 8 10 13 14 15
34 116 272 320 365 360 355 350 250 200 181 37Average Price
9 11 12
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Speculative Bubbles 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)
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Speculative Bubbles 38
Figure 4: Time Series of Stock Prices (Session4)
0
50
100
150
200
250
300
350
400
450
500
Period
Transaction Price Fundamental Price Predicted Price
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
199 519* 139 182 174 202 204 251 206 205 206 207 203 203 252Average Price
* Two transaction in period 2 occurred at 2,155 because the bidder said he inadvertly added 5s to the intended bids of 215.
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Speculative Bubbles 39
Cell D (session 4)
• Exogenous termination, no gap
• No bubble
• Fundamental price and allocations
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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.
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Speculative Bubbles 41
Fi gure 5: Ti mes Seri es of Stock Pri ces (Sessi on 5)
0
50
100
150
200
250
300
350
400
450
Per i od
Tr ansact i on Pr i ce Fundament al Pr i ce Maxi mum Possi bl e Di vi dend Pr edi ct ed Pr i ce
65 120 142 176 181 171 178 179 175 173 175 175 174 175 119
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Aver age Pr i ce
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Speculative Bubbles 42
Results A: Gap, Endogenous Termination
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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
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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
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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.”
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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
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Speculative Bubbles 47
Thank You
• The paper will be available on
• http://www.som.yale.edu/faculty/sunder/research
• My email is [email protected]
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Speculative Bubbles 48
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Speculative Bubbles 49
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Speculative Bubbles 50
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Speculative Bubbles 51
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
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Speculative Bubbles 52
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
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Speculative Bubbles 53
Figure 1: Frequency of acceptance in Slembeck (1999) data(No. of observations at the top of each bar)
0
0.2
0.4
0.6
0.8
1
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
Fraction of Demand by player 1
Frequencyofacceptanceby
player2
5 4 3
7 171
88
33
16 1835
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Speculative Bubbles 54
Levels of Analysis
Level Variable
1 Fundamental value of the firm (FVF)
2 What people believe to be the FVF
3 What people believe about whatpeople believe to be the FVF
4 What people believe about whatpeople believe about what peoplebelieve to be the FVF
5, 6… And so on…
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Speculative Bubbles 55
Thank You
• The paper, and slides will be available next week at
• http://www.som.yale.edu/faculty/sunder/research.html
• or email to [email protected]
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Speculative Bubbles 56
The purpose of our study
• Explore why the price bubble occurs in stock markets
• Investor’s belief on other’s belief
• Stock market experiments
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Speculative Bubbles 57
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
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Speculative Bubbles 58
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
–
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Speculative Bubbles 59
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.
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Speculative Bubbles 60
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
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Speculative Bubbles 61
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
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Speculative Bubbles 62
Bubbles
• Price Fundamental Value– Price
• Second-order-belief
– Fundamental Value• First-order-belief
• Second-order-belief First-order-belief
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Speculative Bubbles 63
Keynes
• Newspaper beauty contests– Well-known and popular story– True in real world?
• How to verify? – Fundamental value is unobservable– Gap is unobservable
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Speculative Bubbles 64
Experimental Study
• Laboratory– 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!
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Speculative Bubbles 65
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
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Speculative Bubbles 66
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
•
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Speculative Bubbles 67
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.
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Speculative Bubbles 68
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
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Speculative Bubbles 69
Conducted Experimentswhat, 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
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Speculative Bubbles 70
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.