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Accounting, Common Knowledge and the Dynamics of Stock
MarketsShyam Sunder, Yale University
Mini-conference on Overcoming Financialization and Its Crisis: Ideas from and Suggestions for Accounting,
Economics and Law21st Annual Conference of the Society of the Advancement of
Socio-economics, Paris, July 16-18, 2009
An Overview• Common knowledge is a basic and oft-used assumption in
analyses of accounting and stock markets• However, absence and not presence of common knowledge is the
norm in the world (Hayek) • Absence of common knowledge undermines the standard present
value models of security valuation• Without common knowledge, markets are susceptible to
speculative indeterminacy• Blocked from a reasonable basis for backward induction, investors
resort to forward induction from history, and use historical data from financial reports
• FASB/IASB attempts to mark-to-market accounting undermine this important use of accounting by investors
• To safeguard from speculative bubbles and financial crises, accounting can serve investors better by providing reliable statistical history, leaving adjustments about the future to non-accountants
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which Face is the prettiest? Which Face is the prettiest? Which Face is the prettiest?
Which face will they judge to be the prettiest?
Which face will they judge to be the prettiest?
Beliefs About Others’ Beliefs
• Common elements to the three stories about the emperor‘s clothes and stock market
• Central role of what we believe about others, and about their beliefs
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
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
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
Keynes on Stock Market
• Price of Microsoft shares is $100
• I expect the price to be $125 six months from now.
• Is it a good buy?
• Rule 1: Yes, if your opportunity cost of capital is less than $25 for six months
Stock Market (Contd.)
• What if I now believe that the stock market’s assessment of the value of Microsoft shares six months from now will be $90?
• Can I change the beliefs of others in the market?
• If not, Rule 2: Sell at $100
• Higher order rules
Should I Pay Attention to Others When I Know I Am Right?
• What if everyone believes them (who are wrong), and not me (who is right)
• Fight them? or
• Join them?
Common Knowledge (Aumann)
• Two people 1 and 2 are said to have common knowledge of an event E if– both know it, – 1 knows that 2 knows it, – 2 knows that 1 knows it, – 1 knows that 2 knows that 1 knows it, – and so on...
Orders of Knowledge
• First order knowledge
• Second order knowledge (about first order knowledge)
• Third order knowledge (about second order knowledge)
• And so on.
Levels of Analysis
Level Variable
1 Fundamental value of the firm (FVF)
2 What people believe to be the FVF
3 What people believe about what people believe to be the FVF
4 What people believe about what people believe about what people believe to be the FVF
5, 6… And so on…
Main Result from the Lab
Bubbles and Price Indeterminacy arise when
• Investors have short-term horizons,• Therefore need to backward induct from higher order
beliefs• But do not have the information to be able to do so• And resort to forward induction• Hirota, Shinici and Shyam Sunder. “Price Bubbles sans Dividend
Anchors: Evidence from Laboratory Stock Markets,” Journal of Economic Dynamics and Control 31, no. 6 (June 2007): 1875-1909.
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
• If investors do not have the knowledge needed to backward induct, this equality will not hold
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: Pt = 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: Pt D
Period 1 Period x Period 30
DEx (Px+1)(Trade)
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 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.
Result 2
• 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)
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.
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.
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
– (ii) higher uncertainty
• Consistent with our lab observations.
• Inputs to expectation formation matter:– Dividend policy matters!
– 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
Theory of Accounting and Control
• Firm as a set of contracts• Agents try to attain their own goals• Agents contribute resources• Agents receive resources in exchange• Accounting as a mechanism to implement
and enforce contracts• Shyam Sunder. 1997. Theory of
Accounting and Control. Cengage Publishing.
Figure 1
Resource Flows in Private-Good Organization
Employees
Shareholders
Creditors
Customers
VendorsGovernment
Managers
Firm as a Set of Contracts
Functions of Accounting
• Measure resource contributions
• Measure out resource entitlements
• Determine contract fulfillment
• Inform and attract potential contract participants
• Common knowledge for conflict abatement and resolution
Shared Facts for Conflict Resolution
• Disputes waste resources• Provision of shared knowledge helps avert
and settle disputes• Unsettled conflicts weaken and wreck
organizations and society• E.g., industrial strikes and lockouts• Careful collection and sharing of data• Shared knowledge, expectations is a large
part of culture and society
Defining Contracts
• Defining executable contracts requires common knowledge
• Otherwise contracts lead to contention or deception
• Less temptation to mislead others when information is common knowledge
• Reduces conflict and concomitant losses
Common Knowledge for Contract Renegotiation
• Most contracts are renegotiated periodically• Intermediate solution between starting a
fresh search and entering long-term or permanent, comprehensive contracts
• Uncertainty, changing environment, and boundedness of human foresight
• Costs of frequent transactions• Learning, increased efficiency, retention
Conflict at Renegotiation
• Contract renewal negotiation can give rise to prolonged conflicts
• Common knowledge as a device to reduce conflict
• Oil well example• Precommitment to reduce information
asymmetries• Making some data available as common
knowledge--public disclosure
Accounting Standards
• Standards as rules of the game
• Must be common knowledge
• Effort expanded on making them CK
• How close do we get to CK
• Penetration into various segments
• Variation across standards
• Link between compliance and CK
• Optimal allocation of resources
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
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
Figure 1: Frequency of acceptance in Slembeck (1999) data(No. of observations at the top of each bar)
0
0.2
0.4
0.6
0.8
1
0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95
Fraction of Demand by player 1
Frequencyofacceptanceby
player2
5 4 3
7 171
88
33
16 1835
To Summarize
• Common knowledge is a basic and oft-used assumption in analyses of accounting and stock markets
• However, absence and not presence of common knowledge is the norm in the world (Hayek)
• Absence of common knowledge undermines the standard present value models of security valuation
• Without common knowledge, markets are susceptible to speculative indeterminacy
• Blocked from a reasonable basis for backward induction, investors resort to forward induction from history, and use historical data from financial reports
• FASB/IASB attempts to mark-to-market accounting undermine this important use of accounting by investors
• To safeguard from speculative bubbles and financial crises, accounting can serve investors better by providing reliable statistical history, leaving adjustments about the future to non-accountants
Thank You
• The paper, and slides will be available next week at
• http://www.som.yale.edu/faculty/sunder/research.html
• or email to [email protected]