The Behavioral Biases of Individuals: formula sheet

Key formulas

Traditional finance decision rule

Rational investors maximize expected utility: E(U) = Σ p × U(outcome)

Expected utility is the traditional way to model a rational, risk-averse investor who uses final wealth and processes information correctly. It is not the only tool: mean-variance analysis is also used for portfolios.

Bounded rationality / satisficing

Satisficing = choose a good-enough option, not the optimal one

Comes from limited information, time and processing ability.

Prospect theory (behavioral)

Value depends on gains and losses relative to a reference point, not on final wealth

Losses weigh more than equal gains; this is loss aversion.

Efficient market vs behavioral view

Traditional: prices reflect available information. Behavioral: price can differ from value because of biases

Mispricing may persist, but anomalies can also have non-behavioral explanations.

Conservatism bias

Old belief kept; new information under-weighted

Slow updating. Often described as under-reaction to new information.

Confirmation bias

Seek supporting evidence; discount contradicting evidence

Selective search and weighing of evidence that agrees with your view.

Representativeness bias

Classify by resemblance; ignore base rates and sample size

Two forms: base-rate neglect and sample-size neglect.

Illusion of control bias

Overestimate ability to influence outcomes

Shown by believing your own actions steer results, such as frequent trading.

Hindsight bias

Past outcomes seen as more predictable than they were

You remember the past as more foreseeable than it was.

Mitigation rule

Cognitive errors: correct with information, education and process

Emotional biases are harder to fix; you often adapt to them instead.

Anchoring and adjustment

Estimate = initial anchor + insufficient adjustment

The investor starts from a reference such as a past price, a purchase price or a prior forecast and does not move far enough from it.

Mental accounting

Money is treated as non-fungible: separate accounts, separate rules

The investor ignores correlations across accounts, so the overall portfolio may be inefficient. A layered, pyramid-like portfolio of separate goals is a typical result.

Framing

Same facts, different presentation → different decision

The same outcome described as a gain or as a loss can lead to different decisions. For example, a treatment described as having a 90% survival rate is often preferred to the same treatment described as having a 10% mortality rate.

Availability

Perceived probability ∝ ease of recall

Vivid, recent or personally experienced events are judged more likely than the data supports.

Classification rule

Information processing biases = cognitive errors (not emotional biases)

Cognitive errors are generally more correctable through education and better information.

Loss aversion

Pain from a loss > pleasure from an equal-sized gain

Prospect theory idea. Leads to the disposition effect: sell winners too early, hold losers too long.

Disposition effect

Sell winners early + hold losers too long

A result of loss aversion. Can create unplanned risk and poor tax outcomes.

Prediction overconfidence

Confidence ranges too narrow

Overestimating the precision of your own forecasts and knowledge.

Certainty overconfidence

Stated probability of being right > actual probability

Too much certainty that your view is correct.

Consequences of overconfidence

Excess trading + under-diversification + underestimated risk

Excess trading raises costs and typically lowers net returns.

Treatment of emotional biases (such as loss aversion)

Moderate or adapt, not correct

Emotional biases are harder to fix than cognitive errors. Adapt the plan to the bias where needed.

Treatment of overconfidence (a cognitive error)

Reduce with feedback + training + better information, supported by rules and diversification

Cognitive errors can generally be corrected. Forecast records, a written policy and diversification rules also help.

Emotional vs cognitive

Emotional bias: feelings and impulses → adapt to it. Cognitive error: faulty reasoning → moderate or correct it

This is the standard CFA split. It is a tendency, so do not call it a law.

Self-control bias

Immediate gratification > long-term goals → undersaving, possibly excess risk-taking later

Key sign: not saving enough for retirement.

Status quo bias

Prefers to keep things unchanged → inertia, no rebalancing

Key sign: leaves the portfolio or allocation alone.

Endowment bias

Values an owned asset above its market value → reluctance to sell

Key sign: holds an inherited or employer stock for sentimental reasons.

Regret aversion bias

Fear of a bad outcome and the regret that follows → avoids acting

Key sign: avoids decisions, or follows the crowd for comfort.

Moderate vs adapt rule

Cognitive error → moderate (reduce the bias); Emotional bias → adapt (accept the bias and plan around it)

This is the default answer. It is a practical guideline, not an absolute law, so read the question for any contrary facts.

Cognitive error categories

Belief perseverance: conservatism, confirmation, representativeness, illusion of control, hindsight. Information processing: anchoring and adjustment, mental accounting, framing, availability

Know which category each bias belongs to.

Emotional biases

Loss aversion, overconfidence, self-control, status quo, endowment, regret aversion

These are the ones the advisor usually adapts to.

Role of the IPS

IPS = objectives (return, risk) + constraints + agreed process, written before stress arrives

It gives a pre-commitment to fall back on when the client wants to act on a bias.

Quick revision

• Traditional finance assumes rational investors who maximize expected utility and update beliefs correctly.
• Behavioral finance studies how real investors actually decide and what that does to prices and portfolios.
• Cognitive errors come from faulty reasoning or memory; they are more easily reduced with information, feedback and advice.
• Emotional biases come from feelings or impulses; they are harder to correct, so advisers often adapt to them.
• Belief perseverance biases are about holding on to existing views and resisting contrary evidence: conservatism, confirmation, representativeness, illusion of control and hindsight.
• Information processing biases are about how data is used or interpreted incorrectly.
• Loss aversion is an emotional bias: losses hurt more than equal gains please, which can lead to holding losers and selling winners early.
• Overconfidence is an emotional bias. It leads to overestimating knowledge and skill, often causing excessive trading and under-diversification, and it is hard to correct, so advisers often adapt to it.
• Status quo bias is a preference to leave things unchanged; endowment bias is valuing something more because you own it.
• Regret aversion means avoiding action to avoid the pain of a bad decision; self-control bias means favoring present spending over saving.
• Always name the bias first, then check its category, then choose the answer.
• The IPS helps reduce bias by setting objectives, constraints and rules in advance.

Common mistakes

• Saying bounded rationality means investors are irrational. Fix: Bounded rationality means rational effort is limited by information, time and ability, so people settle for good-enough choices.
• Treating all anomalies as proof of behavioral bias. Fix: Anomalies may reflect risk, transaction costs, or data mining. Behavioral bias is one possible explanation only.
• Choosing confirmation bias when the investor simply updates too slowly. Fix: Confirmation needs selective searching or discounting of evidence. Plain slow adjustment to new data is conservatism.
• Calling base-rate neglect a form of conservatism. Fix: Base-rate neglect is part of representativeness: the investor judges by resemblance and ignores how common the category is.
• Confusing framing with mental accounting. Fix: Framing is about how a choice is presented, and the decision changes with the wording. Mental accounting is about the investor splitting money into separate buckets with different rules. If the same facts get a different answer because of wording, it is framing.
• Calling any use of a past price anchoring. Fix: Anchoring needs both a reference point and too little movement away from it despite new information. Check that the investor failed to update enough.
• Treating the disposition effect as a separate bias unrelated to loss aversion. Fix: Remember the disposition effect is the trading result of loss aversion: winners sold early, losers held.
• Saying loss aversion means investors avoid all risk. Fix: It is about the asymmetry between losses and gains. It can lead to holding losers, which leaves the portfolio with a risk level that may not match the plan.
• Mixing up endowment and status quo bias. Fix: Endowment is attachment to a specific asset you own, with a higher value placed on it. Status quo is general inertia, even toward a portfolio you chose without attachment.
• Calling self-control bias a cognitive error about returns. Fix: Self-control bias is a lack of discipline. The investor knows the goal but chooses to spend now.

Exam tips

• Expect short conceptual items: you are given a behavior and asked to name the framework or concept.
• Memorize the contrast: final wealth versus gains and losses from a reference point.
• Do not choose options that say anomalies are always caused by bias or that bounded rationality means no rationality.
• Link this topic to market efficiency: if investors are biased but arbitrage is limited, mispricing can last.
• No penalty for wrong answers, so always answer; remove the option that fits traditional finance when the stem describes shortcuts.
• Match the behavior, not the story. Stems use details like sectors and currencies to distract you.
• Know the pairs that look alike: conservatism vs confirmation, and illusion of control vs overconfidence.
• Remember the group label: belief perseverance biases are cognitive errors and are largely correctable.