Notes / Behavioral Finance

Behavioral Finance

Behavioral finance is the study of everything that departs from the classic model of frictionless markets with prices set entirely by rational agents. These are my working notes on the ideas, biases, and equations from the class.

Market efficiency

The Efficient Market Hypothesis (EMH) holds that all information is reflected in stock prices, so there's no point gathering information to try to beat the market. Behavioral finance mostly agrees there's "no free lunch," but disagrees that price always equals fundamental value. EMH itself comes in three nested forms:

The three forms of market efficiency, nested Strong form contains semi-strong form, which contains weak form, showing each level includes the information of the one before it. Strong form all information, incl. private Semi-strong form all public information Weak form past prices only

Each form of efficiency assumes prices reflect everything the form before it does, plus more.

Weak form efficiency

Prices contain all information contained in past prices.

Semi-strong form efficiency

Prices reflect all public information — information that is free and everyone can see.

Strong form efficiency

Prices reflect all information, including private information — information that is costly to gather, seen only by certain traders.

Paradoxes & theorems

Two results that shape how far "efficient markets" can really go.

Grossman–Stiglitz paradox

It's impossible for markets to be completely efficient unless information is free. If information is costly, investors only gather it when the benefit outweighs the cost — so markets are only partially efficient. If your cost of information is lower than everyone else's, you can beat the market (which also implies there are losers).

Milgrom & Stokey (no trade theorem)

If the only motive for trade were using private information, all trade would break down. If everyone is rational and everyone shares the same prior beliefs, no trade occurs — because nobody would be willing to take the other side.

Biases & fallacies

Systematic ways real investors depart from the fully rational agent.

Overconfidence

Leads to excessive trading. Breaks down into three flavors:

  • Overplacement — thinking you're better than the group than you are
  • Overestimation — more certain of your own skill than you should be
  • Overprecision — more precise in your estimates than you should be

Biased self-attribution

People believe they're skilled, and will dismiss or downweight evidence that contradicts that belief.

Home bias

Insufficient international diversification.

Familiarity bias

Investors tend to buy stock in companies they're familiar with.

Favorite (longshot) bias

Bets on favorites have higher average returns than bets on longshots — longshots get over-bet and favorites get under-bet, a violation of weak-form EMH.

Gambler's fallacy

Expecting reversals — that a streak is "due" to end.

Hot hand fallacy

Expecting a streak to continue.

Prospect theory

A set of behaviors that comes from a value function that gives greater weight to avoiding losses than to acquiring equivalent gains — roughly, losses hurt about twice as much as similarly-sized gains feel good.

The prospect theory value function An S-shaped curve through the origin: concave and shallow for gains on the right, convex and steep for losses on the left, showing losses are felt roughly twice as strongly as equivalent gains. Gains Losses Value felt gains: concave, diminishing sensitivity losses: convex, and steeper

The curve is steeper on the loss side than the gain side — the shape behind loss aversion.

Documented effects

Empirical patterns in returns and behavior, several of which sit uneasily with a purely efficient market.

Disposition effect

Investors tend to sell winners and hold losers — about a 6.8% difference in the rate at which gains vs. losses get sold.

Framing effects

Seemingly irrelevant details in how a question is framed change the decisions people make.

Relative age effects

Those relatively older within a class or cohort tend to have better outcomes.

Portfolio ordering (rank effect)

Extreme positions in a portfolio get disproportionate attention.

January / weekend / holiday effects

Stocks tend to do better in January (concentrated in small stocks), better on Fridays than Mondays, and better right before holidays.

Momentum

Abnormal returns are positively correlated over 3–12 month horizons.

Long-run reversal

Negative autocorrelation in abnormal returns over 3–5 year horizons.

Size & B/M effects

Low market-cap firms, and firms with a high book-to-market ratio, both tend to have higher returns.

Key concepts & definitions

Heuristics

Algorithms the brain uses to process information quickly, sometimes at the cost of accuracy.

Representativeness heuristic

Using "what fits" the story rather than correctly applying probability — leads people to underweight mundane information and overreact to dramatic news.

Anchoring

Subconsciously using a reference point (an anchor) to form predictions under uncertainty.

Conservatism (belief perseverance)

Ignoring evidence inconsistent with your existing worldview — a driver of confirmation bias.

Conformity

A strong tendency to go along with the group even when it doesn't seem to make sense individually.

Ambiguity aversion

Disliking situations where the probability distribution of outcomes itself is uncertain.

Cognitive dissonance

The mental discomfort of holding two conflicting beliefs, values, or attitudes at once.

Mental accounting

People sort financial decisions into separate, non-fungible mental "accounts" and track gains/losses per account rather than total wealth.

Post-earnings announcement drift (PEAD)

Prices move on the day of an earnings announcement, then keep drifting in the same direction for a while after.

Arithmetic of active management

Taken as a whole, active management can't outperform the market once trading and information costs are counted.

Tactical asset allocation (TAA)

Shifting between asset classes over time in response to perceived changes in the risk/return tradeoff.

Portfolio types

Unit cost: weights sum to 1. Zero cost / self-financing: weights sum to 0. Leveraged: weights exceed 100% on both sides.

Key equations

The formulas that come up most often in this material.

Single-period return

Return equals the dividend received plus the price change, scaled by the starting price.

Price as discounted future dividends

The fundamental-value view of price: today's price is the expected value of all future dividends, discounted back to the present.

CAPM

Cross-sectional differences in returns are explained entirely by a single market factor. Under CAPM, the tangency portfolio equals the market portfolio.

Sharpe ratio

Excess return per unit of risk. The mean-variance-efficient (MVE) portfolio is the one with the highest Sharpe ratio.

R-squared

Share of variance in returns explained by the model.

Proportion of gains / losses sold

Used to measure the disposition effect directly: PGR is typically found to be higher than PLR.

Other facts & observations

Sophisticated managers are less prone to certain biases, but not immune to them.

People trade so much largely because they disagree — driven by differing beliefs, not just differing information.

Trading volume and volatility are positively correlated.

Biases only move prices when they're systematic — i.e. when many investors are biased in the same direction.

Men trade more than women on average (linked to overconfidence), and consequently tend to lose more.

If expected returns are constant, differences in actual returns are unpredictable.

Lottery-style bets on unpopular numbers tend to have higher returns.

Possible causes of mispricing: investor irrationality, incomplete markets, or prohibitive institutional structure.

A t-statistic above 2 is generally considered statistically significant (p < 0.05).

The tangency portfolio has an alpha (intercept) of zero — and is also the highest-Sharpe-ratio portfolio.

Quotes worth remembering

The market can stay irrational longer than you can stay solvent.— Keynes
In every poker game, there is a fool who is being exploited by the other players. If you don't know who the fool is, he is probably you.— old saying (also attributed to Buffett)
If the structure of the world is common knowledge, rational agents cannot agree to disagree.— unknown
It is not best that we should all think alike; it is differences of opinion that make horse races.— Twain
It is too dangerous and crazy to short. You could have shorted the market in March of 1929 and lost everything.— Soros