Reaction Models
Reaction models are the belief-based behavioral asset-pricing models designed to explain — jointly — two empirical patterns that any complete theory of momentum must produce simultaneously: short-run continuation (– month momentum and post-earnings drift) and long-run reversal (– year De Bondt-Thaler mean-reversion and the value premium). Two generations share this goal. The first generation (late 1990s) assembles the patterns from discrete cognitive biases — conservatism, representativeness, slow information diffusion. The second generation (2010s) derives them from a single extrapolation parameter in a full equilibrium model of the aggregate market.
Three leading models define the family:
- Barberis, Shleifer & Vishny (1998) — a single representative investor whose beliefs oscillate between a mean-reverting regime (capturing conservatism bias) and a trending regime (capturing representativeness). When earnings shocks first arrive, the conservative regime dominates and the investor under-reacts; after a long string of same-direction shocks, the trending regime dominates and the investor over-reacts. Continuation followed by reversal emerges from a single agent confused about which earnings process is generating the data.
- Hong & Stein (1999) — two boundedly-rational agent types interacting in the same market. Newswatchers trade on private fundamental information that diffuses slowly across the population, generating gradual under-reaction. Momentum traders condition only on past prices and chase trends with simple univariate strategies. Adding momentum traders mitigates under-reaction but creates eventual over-reaction, because their trades are partially misread as fundamental news by future generations. Continuation and reversal emerge from the interaction between heterogeneous agents.
- Barberis, Greenwood, Jin & Shleifer (2015) — a continuous-time equilibrium model of the aggregate stock market with a fraction of extrapolators (who forecast next-period returns as a recency-weighted average of past returns) and a fraction of rational traders with finite risk tolerance. A single extrapolation parameter simultaneously generates excess volatility, price-dividend-ratio predictability, aggregate bubbles, and time-series momentum-then-reversal — unifying anomalies the first-generation models needed separate stories for.
Decision rule. Use BSV when the question is about a single representative investor’s psychology and the target involves cross-sectional cognitive biases — conservatism and representativeness map directly onto its two regimes. Use Hong-Stein when the question is about heterogeneous-agent interaction, gradual information diffusion, or when the empirical evidence involves cross-sectional variation in information environments (analyst coverage, firm size, trading volume). Use X-CAPM when the target is the aggregate stock market and the empirical hook is survey-expectation data or the joint fit to excess volatility, predictability, and bubbles — X-CAPM is silent on the cross-section. The three are complementary rather than rival.
Both models share three substantive commitments: (i) arbitrage by fully rational types is limited; (ii) the goal is to explain deviations from efficiency, not to prove markets are inefficient from scratch; (iii) success requires not just fitting momentum and reversal but generating additional testable predictions that can be falsified out of sample. Critics of behavioral finance argue that any single anomaly can be retrofitted with a story; both BSV and Hong-Stein answer this by predicting cross-sectional variation in momentum strength that subsequent empirical work has confirmed.
Intuition
The puzzle is sharp: the same cross-section produces both short-run continuation and long-run reversal. A pure under-reaction story explains the drift but predicts monotonic convergence with no overshoot. A pure over-reaction story explains the reversal but predicts immediate overshoot with no drift window. A credible behavioral model has to produce both halves with one mechanism and one parameter set.
BSV and Hong-Stein are the first-generation answers, and they take opposite modeling routes. BSV puts a single investor in front of a random walk and gives her two competing mental models — a mean-reverting regime and a trending regime — that she switches between as evidence accumulates. Continuation and reversal both fall out of the trajectory of her posterior. Hong-Stein keeps each agent rational but limits what they pay attention to: newswatchers see fundamentals and ignore prices, momentum traders see prices and ignore fundamentals. Continuation comes from gradual diffusion of news across newswatchers; reversal comes from momentum traders piling in late and being unable to tell whether the recent drift is news or earlier momentum-trader flow.
X-CAPM, the second-generation answer, collapses both routes into one mechanism. Instead of assembling continuation and reversal from separate biases or separate agent types, it posits a single extrapolation parameter for one agent type and lets limited rational arbitrage keep the system from exploding. The same parameter that amplifies dividend shocks on impact also produces the slow mean-reversion that follows, so excess volatility, predictability, bubbles, and time-series momentum-then-reversal all come from the same place. The tradeoff is scope: X-CAPM targets the aggregate market only and says nothing about the cross-section that BSV and Hong-Stein were built to explain.
Comparison
| Dimension | BSV (1998) | Hong-Stein (1999) | X-CAPM (2015) |
|---|---|---|---|
| Generation | First | First | Second |
| Modeling philosophy | Single representative investor with biased beliefs | Two heterogeneous agent types interacting | Two investor types in continuous-time equilibrium |
| Source of continuation | Conservatism: under-weights single news shocks | Slow diffusion of private info across newswatchers | Extrapolators chase past price changes |
| Source of reversal | Representativeness: over-extrapolates streaks | Momentum traders chase prices and overshoot | Rational-trader pull + sentiment decay |
| Information structure | Public earnings observed by everyone | Private fundamental info diffuses gradually | Public dividend diffusion (Brownian) |
| Role of arbitrage | Implicitly limited; not formalized | Implicitly limited; not formalized | Formalized via finite CARA risk tolerance |
| Empirical target | Cross-section of stocks | Cross-section of stocks | Aggregate stock market only |
| Distinctive prediction | Reaction to streaks single shocks | Momentum stronger in low-analyst-coverage stocks | Survey expectations positively correlated with past returns, negatively with future returns |
| Empirical confirmation | Bloomfield & Hales (2001); Poteshman (2001) | Hong, Lim & Stein (2000); Lee & Swaminathan (2000) | Greenwood & Shleifer (2014) surveys |
| Unification | Separate biases for each anomaly | Separate mechanisms for each anomaly | One parameter generates all aggregate-market anomalies |
When to Use Which
Reach for BSV when the empirical hook is time-series — how an investor’s beliefs evolve as evidence streams in — or experimental evidence on how subjects react to streaks vs. single shocks (Bloomfield & Hales, ). Reach for Hong-Stein when the hook is cross-sectional — momentum stronger in low-analyst-coverage stocks (Hong, Lim & Stein, ) or correlated with trading volume (Lee & Swaminathan, ). Reach for X-CAPM when the target is the aggregate market — excess volatility, predictability, aggregate bubbles, or survey-expectation data (Greenwood & Shleifer, ). The three are complementary: most modern syntheses combine extrapolative beliefs (X-CAPM-flavored) with heterogeneous-agent dynamics (Hong-Stein-flavored).
See Also
- 8.9.1. Barberis-Shleifer-Vishny Model — child: representative-investor regime-switching model.
- 8.9.2. Hong-Stein Model — child: heterogeneous-agent newswatcher / momentum-trader model.
- 8.9.3. X-CAPM — child: continuous-time equilibrium model with extrapolators and rational traders.
- 8.6.7. Extrapolative Beliefs — the belief primitive X-CAPM formalizes in equilibrium.
- 8.8. Momentum — the empirical pattern these models exist to explain.
- 8.8.1. Cross-Sectional Momentum — the headline anomaly both models target.
- 8.8.3. Momentum Crashes — failure mode that neither model explicitly predicts.
- 8.6.1. Conservatism — the cognitive bias underlying BSV’s mean-reverting regime.
- 8.6.5. Representativeness Heuristic — the cognitive bias underlying BSV’s trending regime.
- 8.3. Challenges to Rational Pricing — efficient-markets framework these models depart from.
- 8. Behavioral Finance — top-level hub.