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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:

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Presentation Transcript
  • 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 knowledge

Complete rationality

Rational structural uncertainty

Behavioral theories

Evolution of the competing theories


With all relevant structural knowledge

Rational expectations world


Rational expectations Rationality all structural knowledge

cognitive biases
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

  • 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. 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


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


which is equivalent to



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)


DON’T know

Crucial differences between the irrational investors and the rational investors
1.4 Rational investors with structural uncertainty

Using Bayesian change-point analysis (Smith, 1975),


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. 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

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
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.
  • 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…