Conservatism

Conservatism

Conservatism (Edwards, 1968) is the systematic tendency to update beliefs too slowly in the face of new information. In the Rabin (1998) parametric template
$\frac{\pi (A\mid S)}{\pi (B\mid S)}={\left(\frac{p(S\mid A)}{p(S\mid B)}\right)}^c{\left(\frac{p(A)}{p(B)}\right)}^d,$
conservatism is the case $c<1$ — the investor places less than full Bayesian weight on the likelihood ratio of the new signal $S$. Bayes’ rule corresponds to $c=d=1$; the conservative agent puts less weight on $S$ and therefore moves her posterior less than she should.

In behavioral asset pricing, conservatism is the leading microfoundation for under-reaction to news. An investor who absorbs each earnings announcement only partially leaves predictable drift on the table, which the next investor exploits — but slowly, because she too is conservative. The result is gradual price adjustment over weeks or months instead of an instantaneous jump. Conservatism is the cognitive content of Regime $1$ in the Barberis-Shleifer-Vishny (1998) model, where the representative investor over-weights the hypothesis that earnings are mean-reverting and therefore under-reacts to single shocks. Together with representativeness (the over-reaction half), it produces the joint pattern of $1$–$12$ month momentum and $13$–$36$ month reversal that any complete behavioral model must explain.

Intuition

Bayes’ rule says that to update a prior belief about which of two states is true, you multiply the prior odds by the likelihood ratio of the new signal. Conservatism is what happens when a person multiplies by a power of the likelihood ratio less than one — taking, say, the square root or cube root of the Bayesian update. The direction of belief change is correct, but the magnitude is dampened. A signal that should move the posterior from $0.5$ to $0.8$ instead moves it to $0.65$.

Conservatism shows up in the laboratory whenever subjects are asked to update beliefs about an urn’s composition after drawing a small sample, in field data on professional analysts who revise earnings forecasts too little after each quarterly announcement, and in the post-earnings-announcement drift that has been one of the most replicated anomalies in asset pricing for forty years. The drift is exactly what conservative under-updating predicts: news arrives, prices move part of the way, and the residual information gets incorporated only over the following weeks as further evidence accumulates.

Properties

(Parametric Form) Conservatism is $c<1$ in the Rabin template.

In the Rabin (1998) deviation from Bayes’ rule, $c$ governs the weight on the new signal’s likelihood ratio. Bayes is $c=1$. Conservatism is $c<1$, with empirically estimated values typically between $0.4$ and $0.8$ depending on the experimental setting. The parameter $d$ on the prior is left at $1$, meaning the conservative investor still uses the prior correctly — she just under-weights new evidence relative to it.

(Mechanism for Under-Reaction) Slow updating produces gradual price drift.

If every investor in the market is conservative to the same degree, no single trader has the incentive to push prices to fundamentals immediately — each one, looking at the same news, computes a posterior that is too close to her prior and therefore submits orders that move price only partially. The residual information is incorporated as further evidence accumulates and as conservative investors gradually absorb the implications. This is the mechanism behind post-earnings-announcement drift, the underperformance of issuing firms, and the slow incorporation of analyst forecast revisions.

(Joint with Representativeness in BSV) Conservatism alone cannot generate reversal.

A model with only conservatism produces continuation but no overshoot — prices drift toward fundamentals and stop. To generate the long-run reversal observed in the data (De Bondt & Thaler, 1985), a second mechanism is required. BSV pair conservatism with representativeness: after a long string of same-direction news, the conservative regime loses weight in the agent’s mind and the trending regime takes over, producing over-reaction. Continuation and reversal therefore emerge from a single agent who oscillates between two biases, not from one bias acting alone.

(Empirical Estimate) Edwards (1968) and follow-ups estimate $c\approx 0.4$ in the laboratory.

Edwards’ original “book bag” experiments asked subjects to draw chips from one of two urns and report posterior odds. Subjects’ updates were systematically less aggressive than Bayes’ rule, with implied $c$ values around $0.4$–$0.5$. Subsequent replications across decades and across populations have confirmed the pattern, though the exact magnitude depends on the cognitive load of the task and the salience of the prior.

(Tension with Base-Rate Neglect) The two biases pull in opposite directions.

Conservatism says investors under-weight the new signal ($c<1$). Base-rate neglect says investors under-weight the prior ($d<1$). Both have empirical support. The reconciliation, due to Griffin & Tversky (1992), is that conservatism dominates when the signal is weak but its underlying generating process is well understood (book-bag-and-chip experiments), while base-rate neglect dominates when the signal feels diagnostic but the underlying base rate is abstract (the Linda problem, the engineer-vs-lawyer problem). The two biases are not mutually exclusive — they operate in different parts of the information environment.

Examples

Post-earnings-announcement drift

A firm announces quarterly earnings of $$1.20$ per share against a consensus estimate of $$1.00$. The Bayesian benchmark would have analysts revise their estimate of the firm’s earnings power immediately and fully, with prices jumping to the new fundamental value at announcement. Empirically, the price jumps about $60\%$ of the way on announcement day and then drifts the remaining $40\%$ over the following $60$ trading days. Conservative under-updating predicts exactly this pattern: each investor processes the announcement with $c<1$, so the initial price move is partial, and the residual information leaks into prices as further evidence accumulates and as more conservative investors gradually adjust.

Edwards' book-bag experiment

Two book bags each contain $100$ poker chips. Bag $A$ has $70$ red and $30$ blue. Bag $B$ has $30$ red and $70$ blue. A bag is chosen at random and the subject draws $12$ chips with replacement, observing $8$ red and $4$ blue. The Bayesian posterior probability that the bag is $A$ is approximately $0.97$. Subjects in Edwards’ experiments report posteriors averaging around $0.75$. The implied $c$ in the Rabin template is roughly $0.5$ — the subjects update in the right direction but at half the speed Bayes’ rule prescribes.

See Also

• 8.6. Belief-Based Biases — parent hub.
• 8.6.5. Representativeness Heuristic — sibling: the bias that pairs with conservatism in BSV to generate over-reaction.
• 8.6.3. Base-Rate Neglect — sibling: the parametric mirror image of conservatism ($d<1$ instead of $c<1$).
• 8.9.1. Barberis-Shleifer-Vishny Model — the asset-pricing model where conservatism is Regime $1$.
• 8.8. Momentum — the empirical pattern that conservative under-reaction helps explain.