Competing Theories of Financial Anomalies Alon Brav & J. B. Heaton

Outline  Background and definitions  Objectives  Main body:  Models  Explaining financial anomalies  Learning and arbitrage  Conclusion

Financial Anomalies: patterns of price behavior inconsistent with the predictions of traditional efficient markets, rational expectations asset pricing theory, such as overreaction, underreaction, calendar effect, puzzle of close-end mutual fund and etc.

EMH & rational expectations asset pricing theory Complete knowledgeComplete rationality Behavioral theories Rational structural uncertainty Evolution of the competing theories

Rational expectations Rationality all structural knowledge Rational expectations world With all relevant structural knowledge Rationality

Cognitive Biases  Representativeness heuristic: a phenomenon where subjects expect key population parameters to be “represented” in any recent sequence of general data. Thereby, recent evidence is overweighted while base rates (prior beliefs and/or other data) and older evidence are ignored.  Conservatism: a documented deviation from Bayesian judgment where base rates receive excessive weight and new data are underweighted.  Opposite in some sense: Representativeness heuristic Conservatism

Objectives  To demonstrate how financial anomalies arise in Behavioral and Rational theories, and why these two theories are difficult to distinguish  To explore the implications of each theory for long-term disappearance of financial anomalies

1. Models 1.1 The assets and the representative investors: --a one-period risky asset -- ’s payoff at the end of period t Representative investor: risk neutral and values at its expected payoff, called the valuation-relevant parameter Key structural feature of the economy—stability of : Stable, if Unstable, if it varies through time, with the location of change point

1.2 Irrational investors subject to the representativeness heuristic (1) where is the mean of the most recent n/2 payoffs, Beh denotes “behavioral” RH denotes the “representativeness heuristic”  Assume the investor subject to the RH ignores prior beliefs completely and uses only recent half payoffs to estimate

1.3 Irrational investors subject to conservatism Risk-neutral Bayesian investor’s estimator (2) which is equivalent to (3) (4) where, which implies subscript C denotes “conservatism”  Equation (3) is the benchmark rational expectations estimator

Crucial differences between the irrational investors and the rational investors Irrational investors Rational investors Estimating methods NOT/Biased Bayesian methods Fully Bayesian methods Key structural features (stability of and if not stable, the location of change point) KnowDON’T know

1.4 Rational investors with structural uncertainty Using Bayesian change-point analysis (Smith, 1975), (8) where is a posterior distribution for or, conditioned on the change having occurred at a given change point, r.  Equation(8) nests equation(3) as a special case, when

2. Explaining Financial Anomalies 2.1 Overreaction and underreaction  Overreaction: The predictability of good(bad) future returns from bad(good) past performance  Underreaction: The predictability of good(bad) future returns from good(bad) past performance 2.2 Overreaction and underreaction in the behavioral and rational models

Figure 1. Overreaction

Figure 2. Underreaction

2.3 Distinguishing the theories Reasons for difficulty in distinguishing the theories arise from:  Some parameterization of behavioral models may force the Beh and SU curves much closer(e.g. to adjust C in conservatism)  The different environments in which overreaction and underreaction arise fit well with their respective reasons in the two theories.  The mathematical similarity is the driving force behind the difficulty

3. Learning and Arbitrage  Two means by which an anomaly might disappear: Learning, which is expected to be effective in both cases Arbitrage, which is expected to be effective in the behavioral case  If RSU causes the anomalies, then their disappearance depends on the ability of rational investors to better understand the structural feature.  If irrationality causes the anomalies, their disappearance may still hinges on rational learning, i.e. on the ability of rational arbitrageurs and their investors to reject competing rational explanations for observed price patterns.  If “limit of arbitrage” is caused by RSU, the role of rational learning will be more important than arbitrage itself.

Conclusion  What has been done by this article: explored and highlighted the explanatory approaches of behavioral and rational theories and the need to more carefully distinguish them  What needs greater and further study: connections between the competing theories  What has not been explored: normative differences that exist in the competing theories(more details next)

 In a normative sense, anomalous prices are “wrong”, implying the possibility of social gains if correctable.  Question: whether financial anomalies justify government intervention in capital markets, and if so, what kind of intervention?  The goals of intervention are likely to be quite different depending on which theory of financial anomalies dominates public debates: Rational theory improve information disclosure by firms Behavioral theory restrictions on investment choice  However, the lawmakers and regulators are likely to face the same problems as mentioned before in distinguishing them so that it is difficult for even a rational regulator to determine the reasons behind anomalies…

Thank you!