Basics of Behavioural Finance: formula sheet

Key formulas

Traditional finance assumption

Investors are rational + markets are efficient

Rational means using all information correctly to maximise wealth for the risk taken.

Behavioural finance assumption

Investors are "normal" (bounded rational) + psychology affects decisions and prices

Errors can be systematic and predictable, not just random.

Two broad groups of behavioural errors

Cognitive errors (thinking/information processing) and emotional biases (feelings, impulse)

Cognitive errors can often be reduced by better information or training. Emotional biases are harder to correct, so advisers often adapt the advice to them.

Expected utility

EU = Σ [pᵢ × U(xᵢ)]

pᵢ is the probability of outcome i and U(xᵢ) is the utility of that outcome. A rational investor picks the highest EU.

Risk-averse utility

U′(W) > 0 and U″(W) < 0

More wealth is preferred, but each extra rupee adds less utility. This is diminishing marginal utility.

Weak-form EMH

Price reflects past prices and volume

Technical analysis fails to give consistent excess returns.

Semi-strong EMH

Price reflects all public information

Fundamental analysis on public data fails. Insiders may still gain.

Strong-form EMH

Price reflects all public and private information

Even insider information gives no excess return.

Nesting of forms

Strong ⊃ Semi-strong ⊃ Weak

If a stronger form holds, all weaker forms hold. If the weak form fails, the stronger ones fail.

Reference point

Outcome is judged as: Gain or Loss = Final outcome − Reference point

The reference point is often the purchase price or current wealth, not final total wealth.

Shape of value function

Gains: concave (risk averse) | Losses: convex (risk seeking) | Loss side is steeper

S-shaped curve passing through the reference point. The steeper loss side is loss aversion.

Loss aversion

Pain of a loss of ₹X > Pleasure of a gain of ₹X

Often described as about twice as strong, but this is an approximate research finding.

Disposition effect

Sell winners early + hold losers too long

Result of risk aversion in gains and risk seeking in losses.

Cognitive vs emotional

Cognitive = faulty reasoning (correctable by information); Emotional = feelings or impulse (hard to correct)

Exams often ask which type an adviser should try to correct and which to accommodate.

Belief perseverance group

Cognitive dissonance, Conservatism, Confirmation, Representativeness, Illusion of control, Hindsight

Common core of this group is clinging to existing beliefs.

Information-processing group

Anchoring and adjustment, Mental accounting, Framing, Availability

Common core is faulty handling or weighting of data.

Overconfidence effects

Overconfidence → excess trading + under-diversification + underestimated risk

Typical consequence statements in options. Overconfidence is generally treated as an emotional bias.

Cognitive vs emotional bias

Cognitive = faulty reasoning or information handling; Emotional = feeling or impulse driven

Cognitive biases are easier to reduce with information. Emotional biases are often only accommodated.

Loss aversion

Pain from a loss > pleasure from an equal gain

A common consequence is the disposition effect: holding losers too long and selling winners too early. The pain comes from the loss itself.

Endowment effect

Value placed on an asset when owned > value placed on it when not owned

Ownership alone raises the value. The reason is not performance.

Status quo bias

Preference to do nothing and keep the existing portfolio

Linked to inertia and avoiding the effort or discomfort of change.

Regret aversion

Avoid decisions that may lead to regret

Can mean staying out of markets after a loss or following the herd.

Mental accounting (cognitive bias)

Money is split into mental accounts and treated as not interchangeable

This is an information-processing and framing error, not an emotional bias. It ignores that all money is fungible, so the total portfolio view is lost.

Self-control bias

Present consumption preferred over future needs

Leads to under-saving. As a consequence, the client may later take excess risk to make up the shortfall.

Heuristic

Heuristic = mental shortcut → fast decision → possible systematic bias

Heuristics are not always wrong. The exam tests the error they can cause.

Fungibility of money

₹1 from any source = ₹1 from any other source

Mental accounting violates this principle in traditional finance.

Framing effect

Same facts + different presentation → different choice

Decisions change with wording (gain frame vs loss frame) even though the outcome is unchanged.

Key heuristics to match

Representativeness = resemblance; Availability = ease of recall; Anchoring = reference point; Familiarity = known is safe

Match the scenario cue to the heuristic name.

Herding

Decision = copy the crowd, not own analysis

Driven by assuming others are better informed and by fear of regret. It is a group behaviour, not an individual bias like overconfidence.

Bubble path

Displacement → boom → euphoria → profit-taking → panic

A common stage model. Prices exceed fundamental value at the euphoria stage. Know the order and what investors feel at each stage.

Momentum

Recent winners tend to keep winning in the short to medium term

A tendency, not a guarantee. It often reverses sharply when sentiment turns.

Bubble versus fundamentals

Bubble = market price ≫ fundamental value

The gap is explained by sentiment and herding, not by changes in earnings or cash flows.

Efficient market contrast

EMH: prices reflect information; behavioural view: sentiment can move prices away from value

Anomalies are evidence that raises questions about market efficiency.

Cognitive vs emotional bias

Cognitive bias → generally moderate (educate, give data); Emotional bias → often adapt (adjust the plan)

A guide, not a fixed rule. Cognitive biases are easier to moderate with education and information. Emotional biases come from feelings, so they are harder to change and often need to be adapted to. The choice also depends on how much the bias threatens the client's goals and on the client's wealth.

Risk profile components

Risk profile = risk tolerance (willingness) + risk capacity (ability) + risk required (return needed for goals)

Advisers generally take the more conservative of tolerance and capacity. If the return required for the goals needs more risk than either allows, the goals or the plan must be revisited.

Bias management sequence

Identify → explain → agree rules → document → review

Use this order when a question asks what the adviser should do.

Quick revision

• Traditional finance assumes investors are rational and markets are efficient; behavioural finance studies how real people deviate.
• The Efficient Market Hypothesis has weak, semi-strong and strong forms, based on which information is reflected in prices.
• Prospect theory says people judge outcomes as gains and losses against a reference point, not as final wealth.
• Loss aversion: a loss hurts more than a gain of the same size pleases.
• Cognitive biases come from faulty reasoning or memory; they can often be reduced with information and training.
• Emotional biases come from feelings or impulses; they are harder to correct, so advisers often adapt the plan to them.
• Heuristics are mental shortcuts; they save effort but can produce systematic errors.
• Mental accounting means treating money differently depending on how it is labelled or where it came from.
• Herding is following the crowd; it can feed bubbles on the way up and crashes on the way down.
• Disposition effect: selling winners too early and holding losers too long.
• Always identify the bias from the behaviour in the scenario, not from a word that merely sounds similar.
• An adviser's role is to recognise biases in clients, and in themselves, and build a plan that works despite them.

Common mistakes

• Saying behavioural finance claims all investors are irrational all the time. Fix: Remember it says investors are normal and subject to systematic biases, not always irrational.
• Treating behavioural finance as a branch of accounting or pure statistics. Fix: Link it with psychology and decision making. It explains how people decide, not how books are kept.
• Saying technical analysis works under the semi-strong form. Fix: If past prices are already reflected, which is the weak form, then chart patterns are useless under semi-strong and strong forms too.
• Believing insiders can earn excess returns under the strong form. Fix: The strong form says even private information is already in the price. Insiders gaining means the strong form fails.
• Saying people are risk averse in all situations under prospect theory. Fix: Remember risk aversion applies to gains and risk seeking applies to losses.
• Thinking the value function is a straight line or symmetric. Fix: Picture the S curve: concave above the reference point, convex below, steeper for losses.
• Confusing anchoring with availability. Fix: Anchoring uses a specific reference number. Availability uses how easily an example comes to mind.
• Labelling confirmation bias as conservatism. Fix: Confirmation is about selecting supporting evidence. Conservatism is about updating too slowly.
• Mixing up endowment effect and status quo bias. Fix: Endowment is about valuing an owned asset higher because it is yours. Status quo is about inertia and avoiding change, even without special attachment.
• Calling mental accounting an emotional bias. Fix: Mental accounting is a cognitive bias, an information-processing and framing error. Money is labelled and treated differently by bucket. Do not choose it when a question asks for an emotional bias.

Exam tips

• Expect direct questions on definitions and the contrast between rational and normal investors. Learn the two sets of assumptions word for word.
• Watch for absolute words such as always and never. They usually mark the wrong option.
• Scenario questions often describe behaviour without naming it. Identify the school of thought first, then the bias.
• Wrong answers are penalised by 25% of the marks for the question, and 2-mark caselet questions cost more. Eliminate options before guessing.
• Link each form to its information set first. Most EMH questions can be answered from that alone.
• Watch for words like public, private, historical and insider. They tell you the form.
• Expect questions that ask which statement is true about expected utility theory. Look for rational, risk-averse and final wealth.
• For anomalies, know the names and the direction: January effect, small-firm effect, value effect, momentum.