Accounting, Common Knowledge and the Dynamics of Stock Markets Shyam Sunder, Yale University Mini-conference on Overcoming Financialization and Its Crisis: Ideas from and Suggestions for Accounting, Economics and Law 21 st 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

Common Knowledge Sunder, Shyam. "Knowing What Others Know: Common Knowledge, Accounting, and Capital Markets." Accounting Horizons 16, no. 4 (December 2002):

Emperor Has No Clothes

Stock Market Stock Market is like a newspaper beauty contest John Maynard Keynes, (1936)

Newspaper Beauty Contest Which Face is 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

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):

Textbooks: P t = F t Rational Expectation of P t+k Homogeneous Investors The Law of Iterated Expectations By recursive process, P t = F t 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: P t = D Period 1Period 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 xPeriod 30 DE x (P x+1 ) (Trade)

Result 1 In the long-horizon sessions, security prices converge to the fundamental values.

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.

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)

Figure 12: Stock Prices for Session 10 (Endogenous Terminal Payoff Session)

Figure 13: Stock Prices for Session 11 (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 Theory of Accounting and Control. Cengage Publishing.

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

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 search.html or to