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
Purpose Why Bubbles Occur in Stock Markets.
Effect of the Investors’ Time Horizon
Main Result from the Lab
if investors have short-term horizons and difficulty in backward induction.
Previous Research on Bubbles Blanchard and Watson (1982), Tirole (1985) Shiller (2000), Behavioral Finance
Emotion, Psychological Factors
Our Paper Provides a different view. includes (A) as a special case.
suggests when (B) is likely to occur .
Why Experiments? Do “Mickey Mouse” markets help us understand real stock markets? Advantages of Experiments Powerful tests of hypotheses
2) Avoid Joint-Hypothesis Problem
Fundamental Value vs. Price for a simple, single dividend security Fundamental value: Long-term Investor’s Valuation: (1) (2) Short-term Investor’s Valuation: (3) P t is not necessarily equal to F t
Textbooks: P t = F t Rational Expectation of P t + k The Law of Iterated Expectations
By recursive process, P t = F t is derived by the backward induction.
Difficulty of Backward Induction Backward Induction may fail. Infinite maturity (rational bubbles) Blanchard and Watson (1982), Tirole (1985) Infinite number of trading opportunities 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)
Price Bubble sans Dividend Anchors There are cases where short-term investors have difficulty in backward induction. No longer anchored by future dividends
Stock prices ( P t ) form bubbles ( F t )
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)?
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: P t = D Period 1 Period 15 D (Trade)
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: P t D Period 1 Period x Period 30 D E x ( P x+1 ) (Trade)
Subjects Assigned One of Two Roles Each endowed with 10 shares, 10,000 points in “cash” (US$ paid depending on earned points). Write down the next period price predictions (US$ paid depending on the prediction accuracy)
Terminal value in short-horizon sessions
Trading Screen Caplab system installed into Yale SOM lab room
Conducted Experiments Yale university, Sep. 2001 – Jul. 2002 Subjects: undergraduate students
We present results from ALL experiments we conducted, including our errors
Long-Horizon Sessions Sessions 3, 4, 5, 6, 7
In the long-horizon sessions, security prices converge to the fundamental values.
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)
Figure 4: Stock Prices and Efficiency of Allocations for Session 4 (Exogenous Terminal Payoff Session)
Figure 5: Stock Prices and Efficiency of Allocations for Session 5 (Exogenous Terminal Payoff Session)
Figure 6: Stock Prices for Session 6 (Exogenous Terminal Payoff Session)
Figure 7: Stock Prices and Efficiency of Allocations for Session 7 (Exogenous Terminal Payoff Session)
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.
Short-Horizon Sessions Sessions 1, 2, 8, 9, 10, 11
In the short-horizon sessions, the security prices deviate from the fundamental values to form bubbles.
Figure 8: Stock Prices and Efficiency of Allocations for Session 1 (Endogenous Terminal Payoff Session)
Figure 9: Stock Prices and Efficiency of Allocations for Session 2 (Endogenous Terminal Payoff Session)
Figure 10: Stock Prices and Efficiency of Allocations for Session 8 (Endogenous Terminal Payoff Session)
Figure 11: Stock Prices and Efficiency of Allocations for Session 9 (Endogenous Terminal Payoff Session)
Figure 12: Stock Prices for Session 10 (Endogenous Terminal Payoff Session)
Figure 13: Stock Prices for Session 11 (Endogenous Terminal Payoff Session)
Discussion (short-horizon sessions) Price levels and paths are indeterminate. Large Bubble (2, 8, 9, 10) Stable Bubble (1, 11, 2 ?) Growing Bubble (8, 9, 10)
Amplification Mechanism, Positive Feedback
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.
Models of Expectations Backward induction (Fundamental) Model: 0 < 1 : Forward induction (1): Adaptive model, 0 < 1:
Forward induction (2): Trend model, 0 :
Price Expectation Model Estimates: Long-Horizon Sessions Dependent Variable: E t ( P t +1 ) - P t
Price Expectation Model Estimates: Short-Horizon Sessions Dependent Variable: E t ( P t +1 ) - P t
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.
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.
Figure 12: Dispersion of Investor Profits
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.
Implications (1) Bubbles are known to occur more often in markets for securities with (i) longer maturity and duration Consistent with our lab observations. Inputs to expectation formation matter:
Accounting reports matter!
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
Thank You The paper and the presentation available at http://www.som.yale.edu/faculty/Sunder/research
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