Non-Standard beliefs II

Two consequences of the law of small numbers

1) Gambler's fallacy (known process: expect reversal). 2) Overinference (unknown process: draw too strong a conclusion from a few observations).

Gambler's fallacy - definition

Believing that after a streak of one outcome, the opposite becomes more likely, because a small sample 'should' look balanced.

Gambler's fallacy - urn illustration

Urn: 5 Up, 5 Down, drawn with replacement. True P(Up after Up, Up) = 0.5. Fallacy treats draws as without replacement: 3/8 = 0.375.

Terrell (1994) - New Jersey pick-three

Players avoid recently winning numbers. Prizes are shared, so recent winners pay out more if they win again. Gambler's fallacy lowers expected payoffs.

Gambler's fallacy and momentum

Investors expect recent price rises to reverse, so underreact to good news. Prices adjust slowly, creating momentum (short-term continuation of returns).

Overinference - definition

Placing too much weight on a few observations, forming overly strong beliefs about the underlying process. Expects streaks to continue (like the hot hand).

Overinference - fund illustration

Fund well managed (70% Up) or poor (30% Up), prior 0.5. After Up, Up, Up: Bayesian says about 93% well managed. Law-of-small-numbers believer says about 97%: overinfers skill.

Benartzi (2001)

Employees put far more of their retirement contributions into employer stock at the best-performing firms than the worst, though past performance did not predict future returns. Overinference.

De Bondt and Thaler (1985)

Past loser stocks outperformed past winners over the next three years. Investors overreact to past performance, then prices reverse.

Overinference and price reversals - steps

Strong returns, overweight past performance, excess optimism pushes price above fundamental value, then beliefs correct and price falls back.

Gambler's fallacy vs overinference

Gambler's fallacy: expects reversal, underreaction and momentum. Overinference: expects continuation, overreaction and reversal.

Overconfidence - definition

Systematic errors in beliefs about one's own knowledge, performance or relative standing.

Overestimation

Thinking your own performance is better than it is.

Overplacement

Thinking your performance relative to others is better than it is.

Overprecision

Being too sure your beliefs or estimates are correct.

DellaVigna and Malmendier (2006) - gym

People buy gym memberships expecting to go often but attend far less, so pay more per visit than pay-as-you-go. Overconfidence about future self-control (naivety).

Burks et al. (2013) - social signalling

Some apparent overconfidence is about social image: claiming to be better to impress others, not genuinely believing it.

Camerer and Lovallo (1999) - question

Why do so many firms enter markets with high failure rates? Tests whether overconfidence about relative skill causes excess entry.

Camerer and Lovallo (1999) - design

Subjects decide simultaneously whether to enter a market with capacity c. Entrant payoffs depend on rank: random ranking vs skill-based ranking (trivia or logic scores).

Camerer and Lovallo (1999) - results

Much more entry and losses when rank depended on skill: industry profits mostly positive under random ranking but negative on average under skill ranking.

Camerer and Lovallo (1999) - why it is overconfidence

Subjects correctly forecast how many others would enter and expected entrants on average to lose, yet entered anyway, believing they personally would rank high.

Camerer and Lovallo (1999) - self-selection

Volunteers for a skill-based competition showed even more excess entry: self-selection magnifies overconfidence.