Bubbles

A bubble is an episode in which an asset’s price becomes significantly overvalued relative to a reasonable estimate of its fundamental value, sustains the overvaluation for a meaningful period, and typically ends in a sharp collapse. Empirically, bubble episodes share four markers: high trading volume, extrapolative survey expectations, sophisticated investors riding rather than correcting the bubble, and good fundamental news near the start of the run-up.

Two theoretical traditions account for bubbles:

• Rational bubbles exploit the multiplicity of solutions to the asset-pricing Euler equation. A bubble component $B_t$ satisfying ${\mathbb{E}}_t[B_{t+1}]=(1+r)B_t$ can be added to the fundamental price without violating any rationality condition. But rational bubbles cannot start, cannot be negative, cannot exist on finite-horizon assets, and cannot survive in dynamically efficient economies — so they fail to match the empirical patterns. See 8.7.1. Rational Bubbles.
• Behavioral bubbles combine two ingredients: belief disagreement (so prices are not pinned down by a single rational consensus) and limits to arbitrage (so the disagreement cannot be neutralized by smart money). The leading limit to arbitrage in this literature is the short-sale constraint. Three nested models build on this template:
  1. Miller (1977) — static. Heterogeneity plus short-sale constraints push the price above fundamentals to the optimist’s valuation.
  2. Harrison-Kreps (1978) — dynamic extension of Miller. Rotating optimism creates a resale option, and the price exceeds every current investor’s buy-and-hold value.
  3. Scheinkman-Xiong (2003) — cognitive microfoundation. Overconfidence about one’s own private signal generates the rotating disagreement Harrison-Kreps assumes, and resolves the No-Trade Theorem (Milgrom-Stokey, 1982) that would otherwise rule out the trading volume bubbles produce.

Decision rule. Reach for Rational Bubbles only as a benchmark — the framework matters historically but does not match the data. For overpricing without volume, use Miller. For overpricing with high turnover, use Harrison-Kreps. For a cognitive microfoundation explaining where the disagreement and volume come from, use Scheinkman-Xiong overconfidence. The three behavioral models nest each other: each one adds one ingredient and explains one more empirical fact.

Intuition

The rational story explains overvaluation only as a self-financing mathematical curiosity that the data do not support. The behavioral story replaces it with a single recipe — disagreement plus short-sale constraints — and then adds layers. Static disagreement gives overvaluation. Dynamic rotating disagreement gives overvaluation and volume and a resale option. Overconfidence gives all three plus a cognitive reason why the disagreement keeps arising. Each step in the sequence resolves one criticism of the previous step.

Two ingredients stay constant across all three behavioral models. First, short-sale constraints are not optional — without them, pessimists short the asset until the price falls back to consensus, killing the overvaluation in every model. Bubble episodes empirically concentrate in asset classes where shorting is hardest: IPO-locked tech stocks, hard-to-borrow small caps, illiquid real estate, cryptocurrencies before futures markets. Second, the cross-section of disagreement is the testable handle. Diether-Malloy-Scherbina (2003) verify that stocks investors disagree most about (measured by analyst-forecast dispersion) underperform subsequently — exactly Miller’s prediction.

Children

• 8.7.1. Rational Bubbles — the rational benchmark: self-financing bubble components allowed by the Euler equation but ruled out empirically by impossibility theorems.
• 8.7.2. Heterogeneous Beliefs and Overvaluation — Miller (1977): disagreement plus short-sale constraints produces static overvaluation.
• 8.7.3. Speculative Bubbles — Harrison-Kreps (1978): the dynamic extension where rotating optimism creates a resale option and high trading volume.
• 8.7.4. Overconfidence and Trading Volume — Scheinkman-Xiong (2003): the cognitive microfoundation, plus the No-Trade Theorem that motivates why overconfidence is needed.

See Also

• 8.3. Challenges to Rational Pricing — the empirical anomalies (excess volatility, return predictability) that bubble models address.
• 8.6. Belief-Based Biases — the broader hub of cognitive biases that distort investor beliefs.
• 8.6.7. Extrapolative Beliefs — an alternative microfoundation for bubbles via recency-weighted expectations rather than overconfidence.
• 8.8. Momentum — the cross-sectional return pattern that bubble dynamics also generate.
• 8. Behavioral Finance — top-level course hub.