Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota

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


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


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?


Stories of Common Knowledge Assumption

• In a great deal of business modeling, common knowledge is routinely assumed

• What happens when it breaks down?


Emperor Has No Clothes



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


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


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


Stock Market

• Stock Market is like a newspaper beauty contest

• John Maynard Keynes, (1936)


Newspaper Beauty Contest

Which Face is 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?










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)


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


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


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


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?


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?


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


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


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


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


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)


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


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)


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


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:


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)


Trading Screen

Figure 1


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


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


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


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


Tentative Conjectures

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


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


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)


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.


Cell D (session 4)

• Exogenous termination, no gap

• No bubble

• Fundamental price and allocations


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.


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


Results A: Gap, Endogenous Termination


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


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


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.”


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


Thank You

• The paper will be available on

• http://www.som.yale.edu/faculty/sunder/research

• My email is [email protected]

http://www.som.yale.edu/faculty/sunder/research

http://www.som.yale.edu/faculty/sunder/research





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


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


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


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…


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]


The purpose of our study

• Explore why the price bubble occurs in stock markets

• Investor’s belief on other’s belief

• Stock market experiments


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


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

–


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.


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


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


Bubbles

• Price Fundamental Value– Price

• Second-order-belief

– Fundamental Value• First-order-belief

• Second-order-belief First-order-belief


Keynes

• Newspaper beauty contests– Well-known and popular story– True in real world?

• How to verify? – Fundamental value is unobservable– Gap is unobservable


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!


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


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

•


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.


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


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


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.

Documents

Speculative Bubbles1 Keynes’ Beauty Contest: Speculative Price Bubbles in the Absence of Common Knowledge in Experimental Stock Markets Shin’ichi Hirota