Shinichi Hirota and Shyam Sunder Yale University April 16, 2003

Shinichi Hirota and Shyam Sunder Yale University April 16, 2003
Stock Markets as a ‘Beauty Contest’: Investor Beliefs and Price Bubbles sans Dividend Anchors Shinichi Hirota and Shyam Sunder Yale University April 16, 2003 2019/9/13 Stock Markets as a 'Beauty Contest'

Stock Markets as a 'Beauty Contest'
Bubble Stories Shiller (2000) Irrational exuberance Blanchard and Watson (1982), Tirole (1985) Rational discount rate bubbles with infinite horizon (no collapse story) 2019/9/13 Stock Markets as a 'Beauty Contest'

The Present Study Explores an alternative story What happens if investors cannot arrive at stock prices through backward induction from their beliefs about the future dividends? Conduct a controlled experiment with and without the possibility of backward induction Report the data and conjectures on another source of price bubbles 2019/9/13 Stock Markets as a 'Beauty Contest'

Short-Term Investor Standard textbook treatment: If the security matures at t+m, fundamental value is defined as: Equating price to fundamental value needs assumptions 2019/9/13 Stock Markets as a 'Beauty Contest'

Representative Investor Model
All investors within and across generations homogenous Assumption R1: Investors form rational expectations, i.e., they use all available information to form their expectations, and know that the price equation (1) holds every period. By RE, investor knows at t that equation (1) applies at t+1 also, and forms his expectation of the price at t+1 2019/9/13 Stock Markets as a 'Beauty Contest'

Using homogeneity of agents, and the law of iterated expectations Through repeated substitution, terminal price remains: 2019/9/13 Stock Markets as a 'Beauty Contest'

Assuming finite maturity eliminates the terminal price and equate current price to the fundamental value: Assumption R2: The security matures in finite time (t+m); after paying dividend Dt+m, the security is worthless. With assumptions R1 and R2, current price equals Ft , derived from a finite sequence of rational expectations and corresponding backward inductions anchored in future dividends 2019/9/13 Stock Markets as a 'Beauty Contest'

If R1 does not hold beyond some period t+k, we cannot substitute expectations of dividends beyond that time for Pt+k and current price would not be equal to the fundamental value If R2 does not hold, the price equation includes an undetermined terminal price which cannot be eliminated from the price equation Price indeterminacy gives rise to the “rational bubbles” (Blanchard and Watson 1982, Tirole 1985): price bubble must grow at the discount rate, even if it is indeterminate 2019/9/13 Stock Markets as a 'Beauty Contest'

Heterogeneous Investor Model
Without representative investors, expectations of the future generations of investors cannot be substituted by the expectations of their predecessors in (4), leaving higher order expectations in the equation. Assumption H1: Investors can form higher order expectations. 2019/9/13 Stock Markets as a 'Beauty Contest'

To substitute for these higher order expectations, we use a common knowledge assumption about rational expectations, and formation of higher order expectations. Assumption H2: Assumption R1 (that investors can form rational expectations) is common knowledge. Assumption H3: Assumption H1(that investors can form higher order expectations) is common knowledge Through successive substitutions,. 2019/9/13 Stock Markets as a 'Beauty Contest'

Note that R2 is not sufficient in heterogeneous investor environment. We use a common knowledge assumption about maturity of the security Assumption H4: Assumption R2 (that the security matures at time (t+m)) is common knowledge among all investors. This assumption allows us to replace the higher order expectation of the terminal price by the higher order expectation of the terminal dividend: This price is not necessarily equal to the fundamental value (based only on the first order expectations); the two backward inductions can be different 2019/9/13 Stock Markets as a 'Beauty Contest'

Is Price Equal to the Fundamental Value?
Even with these strong assumptions, the price need not be equal to the fundamental value Besides, there is the problem of whether the aggregate behavior of the market corresponds to the predictions made on the basis of such strong assumptions about rationality, higher order beliefs, common knowledge, and backward induction through multiple layers of such expectations Securities with longer maturity and duration, high growth, greater uncertainty and asymmetric information about dividends should be more susceptible to bubbles Investors and market behavior under such conditions: an empirical issue, we address experimentally 2019/9/13 Stock Markets as a 'Beauty Contest'

Keynes: Stock Market as a Newspaper Beauty Contest
Stock price is determined not by investor’s own beliefs, but by their beliefs about others’ beliefs, … He should pick the face that others think that others think that others think that others think that … What is the anchor for the reader’s choice? 2019/9/13 Stock Markets as a 'Beauty Contest'

Experimental Study Many empirical studies on the existence of stock market bubbles Diverse findings Fundamental values unknown in the field Difficult to examine the mechanisms of bubble formation in the field (observe actions, not strategies) Experimental research can focus on the mechanism Can choose fundamental values to compare with data Does the stock market bubble occur when the future price expectations are not anchored by dividends? 2019/9/13 Stock Markets as a 'Beauty Contest'

One Main Lab Treatment (discuss others, time permitting)
Terminal value exogenously or endogenously specified Exogenously specified terminal value: Investors are informed of the dividend. Dividend is paid at the end of Period 15. With the exogenously specified terminal value, the price should be equal to this dividend. 2019/9/13 Stock Markets as a 'Beauty Contest'

Main Treatment: Exogenous Terminal Payoff
Period 1 Period 15 15-period security, termination date is common knowledge Single terminal dividend (may vary across traders) A separate set of subjects record their price predictions at the beginning of each period, their mean is announced at the end of each period 2019/9/13 Stock Markets as a 'Beauty Contest'

Main Treatment: Endogenous Terminal Payoff
Period 1 Period 15-17 Period 30 30-Period Security with a terminal dividend to be paid at the end of period 30 The security will be terminated earlier than 30 at a time written in the sealed envelope (in fact terminated at periods) Liquidation at average of the prices predicted by the predictors for the period following termination 2019/9/13 Stock Markets as a 'Beauty Contest'

Laboratory Stock Markets
Double auction market for a single security that pays a single liquidating dividend 15-17 trading periods (3 minutes each) Each investor endowed with 10 shares, 10,000 points in “cash” Predictors write down their price predictions before trading starts each period (know the rules, no endowments, no ability to trade, can watch trading, know the range of terminal dividends) 2019/9/13 Stock Markets as a 'Beauty Contest'

Trading Screen 2019/9/13 Stock Markets as a 'Beauty Contest'

Main Treatment: Terminal Payoff
Main Treatment: Terminal Payoff Robustness Variations Endogenous Exogenous Subsidiary Treatment 1: Potential inequality of the first and higher order beliefs about dividends Potential for a gap between first and higher order beliefs Sessions 1, 8 Sessions 3, 5, 6, and 7 Equality between first and higher order beliefs Sessions 2, 9, 10, and 11 Session 4 Subsidiary Treatment 2: Heterogeneity of pre-written dividends Non-identical pre-written dividends Sessions 1, 2, 8, and 9 Sessions 3, 4, 5, and 7 Identical pre-written dividends Sessions 10 and 11 Session 6 Subsidiary Treatment 3: Common Knowledge of pre-written dividends Dividends common knowledge Dividends not common knowledge Sessions 3, 4, 5, 6, and 7 Subsidiary Treatment 4: Verification of proper understanding of the instructions No questionnaire, answer, verification and correction Sessions 1, and 2 Sessions 3, 4 and 5 Questionnaire, answer, verification and correction Sessions 8, 9, 10, 11 Sessions 6 and 7 Subsidiary Treatment 5: Subjects paid by absolute or relative performance Payoff based on absolute performance Sessions 1 and 2 Sessions 3, 4, 5, 6 and 7 Payoff based on relative performance 2019/9/13 Stock Markets as a 'Beauty Contest'

Conducted Experiments
5 sessions for the exogenous terminal values (Session 3, 4, 5, 6, 7) 6 sessions for the endogenous terminal values (Session 1, 2, 8, 9, 10, 11) Yale university, undergraduate students Money is paid depending on each subject’s earned points (absolute, RPE in sessions 8-11). Yale School of Management, B-74 Room September 21, 2001 – July 12,2002 2019/9/13 Stock Markets as a 'Beauty Contest'

Exogenously-Specified Terminal Value Sessions
(Variations: dividend heterogeneity, common knowledge of dividends, gap in first and higher order beliefs, understanding of instructions, relative/absolute payments) 2019/9/13 Stock Markets as a 'Beauty Contest'

Will Show All Data In a couple of sessions we made experimental errors We refined the instructions on the basis of observations in the earlier sessions Subjects occasionally make decisions which they sometimes inform us were made in error e.g., bidding 2000 when they intended to bid 200 Forgot that there was a terminal dividend It is better to see all the data, and not just the “cleaned up” data 2019/9/13 Stock Markets as a 'Beauty Contest'

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) 2019/9/13 Stock Markets as a 'Beauty Contest'

(Exogenous Terminal Payoff Session) 2019/9/13 Stock Markets as a 'Beauty Contest'

Figure 6: Stock Prices for Session 6

Endogenously- Specified Terminal Value Sessions
(Variations: dividend heterogeneity, common knowledge of dividends, gap in first and higher order beliefs, understanding of instructions, RPE) 2019/9/13 Stock Markets as a 'Beauty Contest'

Endogenous Terminal Payoff Session) 2019/9/13 Stock Markets as a 'Beauty Contest'

(Endogenous Terminal Payoff Session) 2019/9/13 Stock Markets as a 'Beauty Contest'

Figure 14: Dispersion of Investor Profits
2019/9/13 Stock Markets as a 'Beauty Contest'

Inferences 1. When it is possible/easy for the investors to backward induct the value of the security, the security prices converge to the equilibrium level derived from the fundamental values of individual investors. 2019/9/13 Stock Markets as a 'Beauty Contest'

Inferences 2. When it is impossible/difficult for investors to backward induct the value of the security, a) Prices may deviate from the fundamental values to form bubbles, and b) Prices are indeterminate (free-floating) 2019/9/13 Stock Markets as a 'Beauty Contest'

Formation of Price Expectations
If the expectation of future price cannot be formed on the basis of the investors’ own knowledge of dividends, how do they form these expectations? In the absence of anchors that might be provided by common knowledge of dividends and of expectation formation process, backward induction becomes difficult, perhaps impossible. How do investors value securities when backward induction is not possible Soccer: goalkeeper versus striker 2019/9/13 Stock Markets as a 'Beauty Contest'

When You Can’t Do Backward Induction
Try forward induction Keynes (1936, 148) “It would be foolish, in forming our expectations, to attach great weight to matters which are very uncertain. … For this reason, the facts of the existing situation enter, in a sense disproportionally, into formation of our long-term expectations” Is he hinting at technical analysis? We examined the price prediction data 2019/9/13 Stock Markets as a 'Beauty Contest'

Analysis of Predictions
Backward induction: Fundamental Model, 0 <   1: Forward induction: First order adaptive model, 0 <   1: Forward induction: Trend model,   0 : 2019/9/13 Stock Markets as a 'Beauty Contest'

Backward vs.Forward Induction with Exogenous Payoff Data
Fundamental versus first order adaptive model: Adjusted. R2 =0.76, N=102, a1 = 1 and 0 < a2 <1, the data support the fundamental over the adaptive model Fundamental versus Trend Model: Adjusted R2 =0.36, N=102; b1 = 0 and 0 < b2 <1, the data support the fundamental model over the trend model 2019/9/13 Stock Markets as a 'Beauty Contest'

Backward vs.Forward Induction with Endogenous Payoff Data
Fundamental versus first order adaptive model: Adjusted R2 =0.66, N=166; a1=1 and a2<0, neither the fundamental nor the adaptive model fits the data well Fundamental versus Trend Model: Adjusted R2 =0.43, N=166; b1  0 and b2 = 0, the data support the trend model over the fundamental model 2019/9/13 Stock Markets as a 'Beauty Contest'

Inferences 3. When it is difficult for investors to backward induct the value of the security, price expectations are consistent with forward induction; when backward induction is easy to do, price expectations are consistent with backward induction. 2019/9/13 Stock Markets as a 'Beauty Contest'

Inferences 4. Allocative efficiency is high when backward induction is easy to do, and unpredictable when backward induction is difficult. 5. The cross-sectional dispersion of investor wealth increases with the size of bubbles. 2019/9/13 Stock Markets as a 'Beauty Contest'

Concluding Remarks Difficulty or impossibility of backward induction from an anchor tends to give rise to price bubbles Stock prices become indeterminate. When securities mature within the investment horizon of investors, we do not see bubbles Without bubbles, allocative efficiency is high and wealth dispersion is low; with bubbles, it becomes unpredictable 2019/9/13 Stock Markets as a 'Beauty Contest'

Concluding Remarks Bubbles more likely to occur in markets for securities with long maturity and duration It has long been known that securities with high-growth and new technologies, and short-horizon investors are more susceptible to price bubbles (their dividend anchors are difficult to pin down) Free floating prices supported purely by higher order expectations Distributional effects of bubbles and public policy 2019/9/13 Stock Markets as a 'Beauty Contest'

Concluding Remarks Conjecture: Investors resort to forward induction from whatever data they can use when the door to backward induction is blocked History and financial reports as a source for forward induction 2019/9/13 Stock Markets as a 'Beauty Contest'

Thank You Paper and the presentation will be available at Please send comments to 2019/9/13 Stock Markets as a 'Beauty Contest'

2019/9/13 Stock Markets as a 'Beauty Contest'

Shinichi Hirota and Shyam Sunder Yale University April 16, 2003

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Shinichi Hirota and Shyam Sunder Yale University April 16, 2003

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