‘In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer. The initial value, or starting point, may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, adjustments are typically insufficient (Slovic & Lichtenstein, 1971). That is, different starting points yield different estimates, which are biased toward the initial values. We call this phenomenon anchoring."

Tversky and Kahneman (1974)

‘Overconfidence and anchoring definitely appear to be part of the explanation underlying post-earnings-announcement drift."

Shefrin (2000)

Anchoring is a cognitive heuristic in which decisions are made based on an initial 'anchor.'

[KaST82] ‘In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer. The initial value, or starting point, may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, adjustments are typically insufficient (Slovic & Lichtenstein, 1971). That is, different starting points yield different estimates, which are based toward the initial values. We call this phenomenon anchoring."

stability of market

Anchoring - reflects the degree to which the initial judgment about an event or situation prohibits one from deviating from that position regardless of new Information to the contrary

‘In the absence of any solid information, past prices are likely to act as anchors for today's prices.’

‘The stock market has a tendency to under-react to fundamental information -- be it dividend omission, initiation or an earnings report.’

Montier (2002)

Anchoring

Underreact

Bubbles and crashes

Sudden acceleration in the market deterioration

"Psychologists have documented that when people make quantitative estimates, their estimates may be heavily influenced by previous values of the item. For example, it is not an accident that a used car salesman always starts negotiating with a high price and then works down. The salesman is trying to get the consumer anchored on the high price so that when he offers a lower price, the consumer will estimate that the lower price represents a good value. Anchoring can cause investors to underreact to new information."

"It is important to note that different heuristics (anchoring and overconfidence) cause underreaction and the conditions under which investors are vulnerable to these heuristics are different from the conditions that cause investors to be vulnerable to overreaction."

"If the analysts are overconfident and also anchored to their most recent estimate, they may be reluctant to give as much weight as they should to the information in the current earnings announcement and not raise their estimate."

"Again, it is important to note that analysts are unlikely to be vulnerable to the heuristics biases associated with anchoring and overconfidence, except under unusual conditions."

Thus, the keys to exploiting the true source of the earnings surprise alpha are determining under what conditions analysts are likely to be overconfident and anchored, and whether the earnings change associated with the surprise is permanent in nature.

"Underreaction is likely due to biases associated with the overconfidence and anchoring heuristics and may be the source of the alpha for most momentum and earnings surprise strategies."

Fuller (2000)

"The results suggest that people use the stage-by-stage probability as an anchor, and adjust
insufficiently."

"The evidence indicates that when estimating the compound probability of success (px), subjects
use the stage-by-stage probability of success (p) as an anchor. Apparently, subjects ‘start’ with
p, anchor to that, and either do not adjust at all, or adjust insufficiently to changes in the
parameters. In total, 40 out of the 106 estimations were p=px. Moreover, if we look at a comparison of the distance (px - mean)/(p - mean) , as done in table 6, we see that the mean
of estimates was at least 2.5 times closer to p than to px for all but the n=4 case in experiment
2.
The consequence of changing the starting amount was tested in experiment 1, where it was
shown that there is some adjustment, always in the correct direction, but the adjustment is
insufficient. In experiment 2 we changed the size of the interval, and found no sign of
adjustment. Experiment 3 shows that estimations are not sensitive to changes in the stage-bystage
probability.

This is not the first attempt to look at estimations of compound probabilities. Bar-Hillel (1973)
investigated the hypothesis that the subjective probability of compound events are systematically
biased in the direction of their components, resulting in over-estimation of the likelihoods of
conjunctive events and under-estimation of the likelihood of disjunctive events. e.g. a probability
of a conjunctive event may be the probability of winning 5 times in a row, and the probability
of disjunctive event is the stage by stage probability. Bar-Hillel concluded that “… The
probability of the individual stage in a chain of events thus appear to have greater influence on
the evaluation of the whole chain’s probability than the number of stages in question.” (p.405).
This is similar to our result in the sense that people anchor to the probability of the individual
stage, and fail to fully appreciate the affect of enlarging the number of stages. However, this
work focuses on the probability of a certain path, and not on the probability of outcomes. Note
also that increasing the number of stages has an opposite affect than in our story, i.e. it reduces
the compound probability.

Other studies that reports under-estimation in multi-stage problems are Wagenaar and Sagaria
(1975), and Wagenaar and Timmers (1979). These studies consider a different type of problem,
namely estimations of exponential growth. They show that exponential growth is considerably
under-estimated; people tend to extrapolate exponentially, that is with a constant multiplier for
successive steps, but with an exponent that is too small."

Gneezy (1995)

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