Belief-Based Biases

Belief-based biases are systematic deviations from Bayes’ rule. They are the second of the two pillars of investor psychology in behavioral finance — the first being preference-based deviations from expected utility. Where prospect theory keeps beliefs Bayesian and changes the utility function, belief-based models keep utility standard and change how investors form expectations from data.

A useful parametric template (Rabin, 1998) writes the deviation from Bayes’ rule as
$\frac{\pi (A\mid S)}{\pi (B\mid S)}={\left(\frac{p(S\mid A)}{p(S\mid B)}\right)}^c{\left(\frac{p(A)}{p(B)}\right)}^d,$
where $c$ governs the weight on the new signal’s likelihood ratio and $d$ governs the weight on the prior odds. Bayes’ rule is the special case $c=d=1$. The four corners of this family are documented behavioral biases:

• Conservatism — $c<1$, under-weight new evidence.
• Overreaction — $c>1$, over-weight new evidence (especially after streaks).
• Base-rate neglect — $d<1$, under-weight the prior.
• Confirmation bias — $d>1$, over-weight the prior (asymmetric updating against disconfirming signals).

Beyond the parametric template, three further biases sit at the cognitive level. Representativeness is the cognitive root of base-rate neglect and of post-streak overreaction; it produces the gambler’s fallacy, hot-hand bias, and belief in the law of small numbers. Extrapolative beliefs (Greenwood-Shleifer 2014; Barberis-Greenwood-Jin-Shleifer 2015, formalized as the X-CAPM) are the modern unifying framework — investors form expectations as a recency-weighted average of past returns or past fundamentals, generating excess volatility, predictability, momentum, and long-run reversal in a single mechanism. Experience effects (Malmendier-Nagel 2011, 2016) add cross-sectional heterogeneity by limiting each investor’s data to her own lifetime. Anchoring (Tversky-Kahneman 1974) is a distinct adjustment-process bias — estimates are pulled toward an arbitrary starting value and the adjustment away from it is systematically insufficient.

How to use this hub. Reach for conservatism and representativeness when reasoning about under- and over-reaction models of momentum (BSV uses both as building blocks). Reach for base-rate neglect and representativeness when explaining the gambler’s fallacy or hot-hand bias. Reach for extrapolative beliefs when the application is the aggregate stock market, bubbles, or any setting where investor survey data is the empirical hook. Reach for experience effects when the cross-section of investors (young vs. old, depression babies vs. boomers) is the empirical hook.

Intuition

Standard finance assumes investors are Bayesian: they start with a prior, observe data, and update by the rules of probability. Belief-based behavioral finance documents and models the systematic ways real investors fail to do this. The deviations are not random noise — they show up in laboratory experiments, in field data on professional analysts, in survey expectations of households, and in the price patterns of major asset classes.

Two generations of models build on these biases. The first generation (1990s) focused on discrete cognitive biases — conservatism and representativeness in BSV (1998), slow information diffusion in Hong-Stein (1999) — and used them to jointly explain momentum and long-run reversal. The second generation (2010s onward) replaced the discrete-bias menu with a unified extrapolation mechanism: investors form beliefs as a recency-weighted average of recent observations, regardless of whether those observations are returns, earnings growth, or macroeconomic shocks during their lifetime. The same single parameter generates excess volatility, predictability, bubbles, and the cross-section of stock returns at once.

Children

• 8.6.1. Conservatism — investors under-weight new signals relative to the Bayesian benchmark ($c<1$). The cognitive root of under-reaction.
• 8.6.2. Overreaction — investors over-weight new signals relative to the Bayesian benchmark ($c>1$). The cognitive root of long-run reversal and BSV’s Regime $2$.
• 8.6.3. Base-Rate Neglect — investors under-weight the prior relative to the Bayesian benchmark ($d<1$). The parametric expression of representativeness.
• 8.6.4. Confirmation Bias — investors over-weight the prior relative to the Bayesian benchmark ($d>1$). Generates belief polarization and asymmetric absorption of disconfirming evidence.
• 8.6.5. Representativeness Heuristic — investors judge probabilities by resemblance to a stereotype rather than by base rates. Generates the law of small numbers, gambler’s fallacy, hot-hand bias, and the cognitive root of over-extrapolation.
• 8.6.6. Anchoring — estimates are pulled toward an arbitrary starting anchor, and the adjustment away from it is insufficient. Distinct from conservatism in that the “prior” is not a legitimate belief but an accidental salient value. Tversky-Kahneman (1974).
• 8.6.7. Extrapolative Beliefs — investors form expectations as a recency-weighted average of past returns or past fundamentals. The unifying second-generation framework. Includes return extrapolation, earnings extrapolation, and the X-CAPM of Barberis, Greenwood, Jin & Shleifer (2015).
• 8.6.8. Experience Effects — investors form expectations from data observed during their own lifetime, with more weight on recent observations. Generates cross-sectional heterogeneity in beliefs by age cohort.

See Also

• 8.5. Prospect Theory — sibling pillar: preference-based deviations from expected utility.
• 8.9. Reaction Models — first-generation belief-based asset-pricing models that BSV built on conservatism and representativeness.
• 8.8. Momentum — the empirical pattern that motivates both first- and second-generation belief-based models.
• 8.7. Bubbles — heterogeneous-belief and overconfidence models of bubbles use a related strand of belief biases.
• 8.1. Principles of Behavioral Finance — places belief biases inside the broader behavioral framework.
• 8. Behavioral Finance — top-level hub.