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Price Bubbles sans Dividend Anchors:

Evidence from Laboratory Stock Markets

Shinichi Hirota (Waseda University)

and

Shyam Sunder (Yale University)Odette School of Business, University of Windsor

February 1, 2008February 1, 2008

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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/hirotasunderpublished.pdf

Please send your comments to

shyam.sunder@yale.edu