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

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

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

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

Emperor Has No Clothes Speculative Bubbles

Speculative Bubbles

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

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

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

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

Newspaper Beauty Contest Which Face is the prettiest? Speculative Bubbles

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

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

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

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

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

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

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

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

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

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

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

Finite Maturity Securities Speculative Bubbles

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

Indefinite Maturity Securities Speculative Bubbles

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

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

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

Speculative Bubbles

Speculative Bubbles

Trading Screen Speculative Bubbles

Speculative Bubbles

Speculative Bubbles

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

Speculative Bubbles

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

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

Speculative Bubbles

Speculative Bubbles

Speculative Bubbles

Speculative Bubbles

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

Speculative Bubbles

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

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

Speculative Bubbles

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

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

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

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

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

Speculative Bubbles

Speculative Bubbles

Speculative Bubbles

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

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

Speculative Bubbles

Levels of Analysis Speculative Bubbles

Thank You The paper, and slides will be available next week at http://www.som.yale.edu/faculty/sunder/research.html or email to shyam.sunder@yale.edu Speculative Bubbles

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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