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Price Bubbles and Common Knowledge:
Evidence from Laboratory Stock Markets
Shinichi Hirota (Waseda University)
and
Shyam Sunder (Yale University)Southwestern Jiatong University, Chengdu, China
July 16, 2007
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Purpose Explore
Why Bubbles Occur in Stock Markets.
Focus on Effect of the Investors’ Time Horizon
Conduct Laboratory Experiments.
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Main Result from the Lab
Bubbles Arise
if investors have short-term horizons and difficulty in backward induction.
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Previous Research on Bubbles
(A) Rational Bubbles Blanchard and Watson (1982), Tirole (1985) Infinite Maturity
(B) Irrational Bubbles Shiller (2000), Behavioral Finance Emotion, Psychological Factors
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Our Paper
Provides a different view.
includes (A) as a special case.
suggests when (B) is likely to occur.
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Why Experiments?
Do “Mickey Mouse” markets help us understand real stock markets?
Advantages of Experiments
1) Control Environments
Powerful tests of hypotheses
2) Avoid Joint-Hypothesis Problem
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Fundamental Value vs. Price for a simple, single dividend security
Fundamental value:
Long-term Investor’s Valuation:
(1)
(2)
Short-term Investor’s Valuation:
)( mtttt DEVP
)( mttt DEF
)( ktttt PEVP (3)
Pt is not necessarily equal to Ft
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Textbooks: Pt = Ft
Rational Expectation of P t+k
Homogeneous Investors
The Law of Iterated Expectations By recursive process, Pt = Ft is derived
by the backward induction.
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Difficulty of Backward Induction Backward Induction may fail.
Infinite maturity (rational bubbles) Blanchard and Watson (1982), Tirole (1985)
Infinite number of trading opportunities Allen and Gorton (1993)
Heterogeneous Information Froot, Scharfsten, and Stein (1992), Allen, Morris, and Shin
(2002)
Rationality is not common knowledge Delong et al. (1990a)(1990b), Dow and Gorton (1994)
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Price Bubble sans Dividend Anchors
There are cases where short-term investors have difficulty in backward induction.
Stock prices (Pt ) form bubbles ( Ft )
No longer anchored by future dividends
)( ktttt PEVP
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Our Experimental Study
What happens when short-term investors have difficulty in the backward induction?
Two kinds of the lab markets (1) Long-term Horizon Session (2) Short-term Horizon Session
Bubbles are more likely to arise in (2)?
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Long-term Horizon Session
Single terminal dividend at the end of period 15.
An investor’s time horizon is equal to the security’s maturity.
Prediction: Pt = D
Period 1 Period 15
D(Trade)
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Short-term Horizon Session
Single terminal dividend at the end of period 30.
The session will “likely” be terminated earlier.
If terminated earlier, the stock is liquidated at the following period predicted price.
An investor’s time horizon is shorter than the maturity and it is difficult to backward induct.
Prediction: Pt D
Period 1 Period x Period 30
DEx (Px+1)(Trade)
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Subjects Assigned One of Two Roles
Investors: Each endowed with 10 shares, 10,000 points in
“cash” (US$ paid depending on earned points).
Predictors: Write down the next period price predictions (US$ paid depending on the prediction accuracy)
Terminal value in short-horizon sessions Price prediction data
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Trading Screen
Figure 1
Caplab system installed into Yale SOM lab room
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Conducted Experiments
Yale university, Sep. 2001 – Jul. 2002
Subjects: undergraduate students
5 long-horizon sessions 6 short-horizon sessions We present results from ALL experiments we
conducted, including our errors
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Long-Horizon Sessions
Sessions 3, 4, 5, 6, 7
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Result 1
In the long-horizon sessions, security prices converge to the fundamental values.
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Figure 3: Stock Prices and Efficiency of Allocations for Session 3 (Exogenous Terminal Payoff Session)
Figure 3: Stock Prices and Efficiency of Allocations for Session 3 (Exogenous Terminal Payoff Session)
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Figure 4: Stock Prices and Efficiency of Allocations for Session 4(Exogenous Terminal Payoff Session)
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Figure 5: Stock Prices and Efficiency of Allocations for Session 5(Exogenous Terminal Payoff Session)
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Figure 6: Stock Prices for Session 6 (Exogenous Terminal Payoff Session)
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Figure 7: Stock Prices and Efficiency of Allocations for Session 7(Exogenous Terminal Payoff Session)
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Discussion (long-horizon sessions)
Long-horizon Investors play a crucial role in assuring efficient pricing. Their arbitrage brings prices to the
fundamentals. Speculative trades do not seem to
destabilize prices. 39.0% of transactions were speculative
trades.
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Short-Horizon Sessions
Sessions 1, 2, 8, 9, 10, 11
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Result 2
In the short-horizon sessions, the security prices deviate from the fundamental values to form bubbles.
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Figure 8: Stock Prices and Efficiency of Allocations for Session 1 (Endogenous Terminal Payoff Session)
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Figure 9: Stock Prices and Efficiency of Allocations for Session 2 (Endogenous Terminal Payoff Session)
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Figure 10: Stock Prices and Efficiency of Allocations for Session 8(Endogenous Terminal Payoff Session)
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Figure 11: Stock Prices and Efficiency of Allocations for Session 9(Endogenous Terminal Payoff Session)
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Figure 12: Stock Prices for Session 10(Endogenous Terminal Payoff Session)
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Figure 13: Stock Prices for Session 11 (Endogenous Terminal Payoff Session)
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Discussion (short-horizon sessions)
Price levels and paths are indeterminate. Level
Small Bubble (Session 1) Large Bubble (2, 8, 9, 10) Negative Bubble (11)
Path Stable Bubble (1, 11, 2 ?)
Rational Bubble Growing Bubble (8, 9, 10)
Amplification Mechanism, Positive Feedback
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Result 3
In the long-horizon sessions, price expectations are consistent with backward induction.
In the short-horizon sessions, price expectations are consistent with forward induction.
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Models of Expectations
1( ) ( )t t t tE P P D P
• Backward induction (Fundamental) Model: 0 < 1:
• Forward induction (1): Adaptive model, 0 < 1:
1 1 1( ) ( ) ( ( ))t t t t t t tE P E P P E P
• Forward induction (2): Trend model, 0 :
1 1( ) ( )t t t t tE P P P P
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Price Expectation Model Estimates:
Long-Horizon Sessions
Model Const. D Pt Et-1 (Pt) Pt Pt Pt-1 2
R N
Fundamental (5)
6.146 (5.603)
0.267 * (0.102)
0.086 100
Adaptive (7)
5.305 (6.523)
0.454 (0.446)
0.046
100
Trend (8)
3.330 (5.713)
0.182 (0.340)
0.001
100
Hybrid (9)
7.553 (6.721)
0.199 ** (0.072)
0.566 (0.297)
0.270 (0.248)
0.097
100
Dependent Variable: Et (Pt+1) - Pt
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Price Expectation Model Estimates: Short-Horizon Sessions
Model Const. D Pt Et-1 (Pt) Pt Pt Pt-1 2
R N
Fundamental (5)
3.543 (4.593)
0.077 (0.042)
0.092 166
Adaptive (7)
19.851 ** (6.869)
0.113 (0.149)
0.010
166
Trend (8)
5.809 (4.411)
0.467 * (0.196)
0.349
166
Hybrid (9)
4.808 (3.244)
0.027 (0.027)
0.543 ** (0.179)
0.829 ** (0.164)
0.506
166
Dependent Variable: Et (Pt+1) - Pt
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Discussion (Price Expectation)
In long-horizon sessions, future price expectations are formed by fundamentals.
Speculation stabilizes prices.
In short-term sessions, future price expectations are formed by their own or actual prices.
Speculation may destabilize prices.
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Results 4 and 5
4. Allocative efficiency is high in the long-horizon sessions, and unpredictable in the short-horizon sessions.
5. The cross-sectional dispersion of investor wealth increases with the size of bubbles.
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Figure 12: Dispersion of Investor Profits
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Conclusion
Investors’ short-term horizons, and the attendant difficulty of the backward induction, tends to give rise to price bubbles. Prices lose dividend anchors and become
indeterminate.
Future price expectations are formed by forward induction.
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Implications (1)
Bubbles are known to occur more often in markets for securities with (i) longer maturity and duration (ii) higher uncertainty
Consistent with our lab observations. Inputs to expectation formation matter:
Dividend policy matters! Accounting reports matter!
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Implications (2)
Ex post, market inefficiency, anomalies, and behavioral phenomena more likely to be observed in markets dominated by short-horizon investors (difficulty of backward induction)
Ex ante, it is difficult to define them, because we do not know the fundamental values
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Thank You The paper and the presentation
available at http://www.som.yale.edu/faculty/Sunder/research
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