Overconfidence and Trading Volume

Overconfidence and Trading Volume

Overconfidence is the cognitive microfoundation that the Miller and Harrison-Kreps bubble models leave open. Both models assume that investors disagree but not why. Scheinkman & Xiong (2003) supply the answer: investors are overconfident in their own private signals and underweight the signals of others. Two traders observing the same public information form different posteriors because each one trusts her own interpretation more than is rationally justified. Overconfidence solves a problem that pure information asymmetry cannot: by the No-Trade Theorem (Milgrom & Stokey, 1982), rational investors with common priors and different private information cannot generate trading volume in equilibrium, because each investor infers the others’ signals from their willingness to trade and updates accordingly. Overconfidence breaks this by ensuring that no trader fully updates from the others’ actions — each one keeps trusting her own signal too much, and trade happens.

The Scheinkman-Xiong (2003) model. Two groups of risk-neutral investors observe two public signals about an asset’s fundamental. Each group overweights its own signal relative to the other group’s, even though both are observing the same data. The asymmetric weighting causes the groups’ posterior beliefs to diverge over time as new information arrives, with the identity of the more-optimistic group flipping back and forth. Combined with short-sale constraints, this generates a Harrison-Kreps-style speculative equilibrium in which the asset is repeatedly resold from one group to the other, the price exceeds every group’s buy-and-hold valuation, and trading volume is high. Overconfidence is therefore the cognitive engine that powers the rotating-optimism assumption of Harrison-Kreps.

Empirical hook. Two complementary findings link overconfidence to trading volume. First, Grinblatt & Keloharju (2009) use Finnish data to show that individuals whose self-reported confidence exceeds their actual aptitude-test performance trade more frequently. Second, Barber & Odean (2001) use a large U.S. brokerage dataset to show that men trade $45\%$ more than women and earn $1.4$ percentage points lower annual returns — interpreted as a consequence of men being on average more overconfident than women. The cognitive bias produces measurable, costly trading behavior in real markets.

Intuition

A central puzzle in finance is that observed trading volume is enormous — the average S&P $500$ stock turns over its entire market cap roughly once a year — while standard rational models predict almost no trade. The Milgrom-Stokey No-Trade Theorem makes the puzzle precise: if all investors are rational, share a common prior, and differ only in private information, then any proposed trade reveals so much about the proposer’s information that the counterparty refuses. Each rational investor reasons “if you want to sell to me, you must know something bad, so I won’t buy.” By backward induction, no trade happens. Real markets violate this prediction by orders of magnitude.

Overconfidence breaks the no-trade logic in a simple way: an overconfident investor does not fully update from the counterparty’s willingness to trade. She thinks her own signal is more reliable than it is, so when someone offers to sell to her, she discounts the inference “they must know something bad” because she trusts her own positive signal more. Both sides of the trade behave this way, and trade happens. Overconfidence is the cheapest departure from rationality that delivers trading volume — it requires no asymmetry of information, no irrational exuberance, just a uniform tendency for everyone to overweight their own analysis. This is why overconfidence has become the default cognitive ingredient in behavioral models of bubbles and trading.

Properties

(Definition) Overconfidence is overweighting your own signal relative to others’.

In a Bayesian framework, an overconfident agent computes posteriors with too-tight precision on her own signal and too-loose precision on others’ signals. If the true precision of her own signal is $\tau$ but she perceives it as $\alpha \tau$ with $\alpha >1$, her posterior is shifted toward her own observation and away from the public consensus. Two overconfident agents observing the same data therefore form different posteriors, with the gap proportional to $\alpha -1$. This is not the same as the representativeness heuristic or extrapolation — those are biases about how to read data; overconfidence is a bias about whose data to trust.

(No-Trade Theorem) Rational common-prior investors cannot generate trading volume.

Milgrom & Stokey (1982) prove that if all investors share a common prior and update rationally on private information, then no Pareto-improving trade exists. The intuition: any trade requires someone to be willing to sell and someone to buy at the same price. But the offer to sell reveals information to the buyer, who updates her posterior unfavorably and refuses. By iteration, no trade is sustainable. The theorem explains why models of “informed vs. uninformed traders” need an exogenous source of liquidity demand (noise traders, liquidity shocks, hedging needs) — without one, the rational mechanism produces zero volume. Overconfidence offers a different escape: by preventing full Bayesian updating, it leaves residual disagreement that supports trade.

(Three Sources of Disagreement) Different priors, different information, or departures from rationality.

If two rational investors with the same prior observe the same information, they reach the same posterior. Disagreement therefore requires at least one of: (i) different priors (people start with different beliefs about the world), (ii) different information (people observe different signals), or (iii) departures from rationality (people process the same information differently). The no-trade theorem rules out (ii) alone as a source of trading volume. Overconfidence is the leading example of (iii). Most behavioral models of trade combine (ii) and (iii): traders have private signals and are overconfident about how to interpret them.

(Generates the Volume That Bubbles Need) Overconfidence powers the rotating optimism in Harrison-Kreps.

The Harrison-Kreps model assumes the identity of the optimist rotates over time. Scheinkman-Xiong show this emerges naturally from overconfidence: as new public signals arrive, each group’s posterior moves, and the group whose own private signal happened to align with the new public signal becomes (temporarily) the more optimistic one. The rotation is endogenous rather than assumed. Combined with short-sale constraints, the model produces a speculative bubble with high trading volume — and the volume is predicted by the model, not assumed exogenously, which is the substantive advance over Miller and Harrison-Kreps.

(Grinblatt-Keloharju Empirical Test) Self-rated overconfidence predicts more trading.

Grinblatt & Keloharju (2009) link Finnish brokerage data to military aptitude-test scores and self-confidence questionnaires from psychological evaluations conducted on conscripts. They construct an “overconfidence” measure as self-rated confidence minus a measure of objective aptitude, then test whether high-overconfidence individuals trade more. They do — by a substantial margin — and the relationship survives controls for age, wealth, income, and education. The bias is not a theoretical curiosity but a measurable individual-difference variable that predicts real portfolio behavior.

(Barber-Odean Gender Gap) Men trade more than women and earn lower returns.

Barber & Odean (2001) analyze trades from $35,000$ U.S. brokerage accounts over $1991$–$1997$. Men trade $45\%$ more than women on average, and the additional turnover costs them $1.4$ percentage points per year in net returns relative to women. The interpretation rests on a robust finding from social psychology: men are systematically more overconfident than women in domains they perceive as masculine, including finance. The gap is largest among single men (who lack a counterbalancing partner) and smallest among married women. The result is consistent with overconfidence as a costly bias that translates directly into measurable wealth losses.

Examples

Why men trade more (Barber-Odean 2001)

From $1991$ to $1997$, Barber & Odean tracked all trades in $35,000$ retail brokerage accounts. They found that men’s annual portfolio turnover averaged $77\%$ versus $53\%$ for women — a $45\%$ difference. Both groups earned roughly the same gross returns, but men’s higher trading costs (commissions, bid-ask spreads, market impact) reduced their net returns by $2.65$ percentage points per year versus $1.72$ for women. The $0.94$ percentage-point gap is the cost of overconfidence, paid in foregone wealth. Single men, who lack a partner’s counterweight on financial decisions, fared worst — turning over $85\%$ of their portfolio annually and lagging single women by $1.44$ percentage points. The pattern is what overconfidence theory predicts: groups that overweight their own signals more should trade more and earn lower net returns, exactly because their trades are not actually informed.

The No-Trade Theorem in a simple urn

Two rational investors share a common prior that an urn contains either $7$ red and $3$ blue balls (state $R$) or $3$ red and $7$ blue balls (state $B$), with equal prior probabilities. Each draws one ball privately. Investor $1$ draws red; her posterior $\mathrm{Pr}(R)=0.7$. Investor $2$ draws blue; her posterior $\mathrm{Pr}(R)=0.3$. They each value a security paying \1$ifstate$R$at$$0.70$and$$0.30$respectively.Thereisapparentroomfortrade:investor$1$wouldbuyfrominvestor$2$atanypricebetween$$0.30$and$$0.70$.

But the trade reveals information. If investor $2$ offers to sell at \0.50$,investor$1$caninfer"sh{e}^{\prime }swillingtosell,soherdrawmusthavebeenblue,sothetrueposterioris$0.5$,not$0.7$."Sherefuses.Bysymmetricreasoning,investor$2$refusestosell.Theuniquerationaloutcomeisnotrade.With\ast overconfident\ast investorswhodonotfullyupdatefromeachothe{r}^{\prime }soffers—sayinvestor$1$keepsherposteriorat$0.7$evenafterobservinginvestor$2$‘s willingness to sell — trade happens, because each side keeps trusting her own draw. Volume is the empirical signature of this failure to update.

See Also

• 8.7. Bubbles — parent hub.
• 8.7.3. Speculative Bubbles — the Harrison-Kreps model whose rotating-optimism assumption Scheinkman-Xiong microfound with overconfidence.
• 8.7.2. Heterogeneous Beliefs and Overvaluation — the static Miller model that takes belief disagreement as primitive.
• 8.6. Belief-Based Biases — the broader hub on cognitive biases that distort beliefs.
• 8.4.2. No-Trade Theorem — the Milgrom-Stokey result that overconfidence escapes.
• 8.4.4. The Noise-Trader Risk Model — alternative microfoundation for trading volume via stochastic sentiment shocks.