Cognitive errors: belief perseverance and information processing

Why do beliefs persist?

Belief perseverance biases come from the mental discomfort of meeting information that conflicts with what we already believe. That discomfort is called cognitive dissonance . To resolve it, people ignore, modify or explain away the conflicting information, using statistical, processing or memory errors to do so. Five biases fall in this group.

Belief perseverancecognitive dissonance: conflicting information is uncomfortable

• Conservatism Memorize slow to update; underreacts to news
• Confirmation Memorize seeks and notices only agreeing evidence
• Representativeness Memorize classifies by resemblance to a familiar type
  • Base-rate neglect ignores how common the event is
  • Sample-size neglect treats a small sample as typical
• Illusion of control Memorize believes they can influence outcomes
• Hindsight Memorize past events seem to have been predictable

Bias	Tell-tale	Investor consequence	Fix
Conservatism	slow to update a forecast after new information	underreacts to news	weigh new information properly; ask what it really changes
Confirmation	seeks only evidence that agrees	ignores warnings; concentrated positions	actively look for the opposite case
Representativeness	judges by resemblance; ignores base rate or small sample	“good company means good stock”; chasing last year’s top fund	check base rates; use more data
Illusion of control	believes they can influence outcomes	trades too much; under-diversifies	remember investing is probabilistic; seek contrary views
Hindsight	“I knew it all along”	overestimates ability to predict	write decisions and reasons down at the time

Conservatism. Conservatism bias is maintaining a prior view by inadequately incorporating new, conflicting information. In Bayesian terms, the person overweights the prior probability and underweights the new evidence. It is worst for information that is technical or statistical, because processing it costs effort. The fix is to ask, each time: “How does this information change my forecast?”

Confirmation. Confirmation bias is looking for, and noticing, what supports an existing belief while ignoring or undervaluing what contradicts it. A client who researches a holding and reads only the bullish articles is a typical case. The consequences are one-sided analysis, screens that overlook contrary data, and concentrated, under-diversified positions. Seek out the opposite case, and corroborate a decision with a second source.

Representativeness. Representativeness bias is sorting new information into a familiar category because it looks like that category, even when the resemblance is misleading. It has two forms. Base-rate neglect lets specific information about a case override how common the event is in its wider group. Sample-size neglect treats a small sample as if it described the whole population. The fix is to compare the group the investment looks like with the group it most often turns out to belong to, then gather base-rate data or a wider sample before deciding.

Illusion of control. Illusion of control bias is believing that you can control or influence outcomes when you cannot. It leads to inadequate diversification (a big stake in your own employer), too much trading, and forecasts and models that are overly detailed in the belief that detail controls uncertainty. The fix is to accept that investing is a probabilistic activity and to seek contrary viewpoints.

Hindsight. Hindsight bias is believing that past events were predictable and reasonable to expect. People also remember their own predictions as more accurate than they were. It breeds overconfidence and unfair assessment of managers, who are judged on what happened instead of on what could be known at the time. The fix is to record decisions and their reasons in writing when they are made.

How does base-rate neglect work with numbers?

Use it

Base-rate neglect is a Bayes error. A signal, such as a screen flag, has a hit rate and a false-positive rate. The probability that a flagged case really has the event also depends on how rare the event is, and that is the base rate.

$$P(E \mid F) = \frac{P(E)\,P(F \mid E)}{P(E)\,P(F \mid E) + [1 - P(E)]\,P(F \mid \text{not } E)}$$

Here $P(E)$ is the base rate, $P(F \mid E)$ is the hit rate and $P(F \mid \text{not } E)$ is the false-positive rate.

Exam tip Counting 1,000 companies is faster than the formula on a tight clock. Flagged and real, divided by all flagged.

How do information-processing biases differ?

Information-processing biases are not about clinging to a belief. They are about using facts and numbers illogically. There are four.

Information processingfacts and numbers used illogically

• Anchoring and adjustment Memorize starts from an initial number and adjusts too little
• Mental accounting Memorize treats money differently by bucket or source
• Framing Memorize the answer depends on how the question is posed
  • Narrow framing looks at one or two points, loses the big picture
• Availability Memorize likelihood judged by how easily examples come to mind
  • Retrievability the first idea to come to mind wins
  • Categorization familiar search sets bias the estimate
  • Narrow range of experience one country, one sector, one product
  • Resonance close to my own situation

Bias	Tell-tale	Investor consequence	Fix
Anchoring and adjustment	sticks to an initial number (the purchase price, last year’s forecast) and adjusts too little	holds until “back to what I paid”	ask whether you would buy it today at today’s price
Mental accounting	treats money differently by bucket or source	a “safe” pot and a “fun” pot; correlations between pots ignored	combine all assets and look at the whole portfolio
Framing	the answer depends on how the question is posed	risk-tolerance answers swing with wording	restate neutrally; ignore gains and losses so far
Availability	judges likelihood by how easily examples come to mind	buys what is in the news; narrow opportunity set	written policy, disciplined research, long-term data

Anchoring and adjustment. Anchoring and adjustment bias is relying on an initial piece of information, an anchor, and adjusting from it too little. A retailer’s same-store sales forecast nudged down 2% from this year’s figure after a key supplier has failed is anchored on this year’s number; the estimate should be rebuilt from the new conditions. A price paid is irrelevant to the market’s view of the future, yet investors anchor on it.

Mental accounting. Mental accounting bias is dividing money into mental accounts that influence decisions, even though money is fungible. Consequences: missing the chance to reduce risk by combining assets with low correlations, treating income and capital gains as different things (chasing income and risking principal), and “playing with house money”. A good detection exercise is to list all holdings together, with the account names removed, and look at the combined allocation.

Framing. Framing bias means answering a question differently depending on how it is posed. “Seven in ten new restaurants survive their first year” and “three in ten new restaurants close within a year” say the same thing, yet they draw different answers. With a gain frame people become more risk-averse, and with a loss frame more risk-seeking. Narrow framing is a special case: attending to one or two points, such as a single product launch, and losing the big picture of industry, financial results and valuation.

Availability. Availability bias is estimating the probability or importance of something by how easily it comes to mind. It can restrict the investment opportunity set, lead to choosing funds by advertising or news coverage, and cause a failure to diversify. The four sources in the tree are worth knowing by name.

Match each short vignette to its bias. The second tab runs the base-rate example with sliders, so you can see the posterior fall when the base rate falls.

Go deeper Conservatism or anchoring?

Both underreact, and the curriculum notes that anchoring and adjustment is closely related to conservatism. For the exam, use the clue. Conservatism is about beliefs and probabilities: the person does not revise a view enough when evidence arrives. Anchoring is about a number, such as a price paid or last year’s figure, from which the estimate is adjusted too little.

Go deeper Why framing matters for risk questionnaires

If a client sees returns first and risk second, or sees a 95% return range instead of a standard deviation, the chosen portfolio can change even though nothing about the portfolios has changed. An adviser who relies on one questionnaire may misidentify the client’s risk tolerance. Asking the same question in more than one form is a simple safeguard.

Go deeper When mental accounting helps

Separate buckets can help a saver stay disciplined: a pot labeled “house deposit” is harder to raid. The problem arises in portfolio construction, where treating the buckets as independent hides their correlation and the total risk. The cure is to keep the budgeting benefit and still view the whole portfolio.