Categorical Thinking and Comovement

Categorical Thinking and Comovement

Categorical thinking is the cognitive observation that humans organize the world into broad categories — “small-cap stocks,” “value stocks,” “tech stocks,” “emerging markets” — and form beliefs at the category level rather than at the level of individual securities. Barberis and Shleifer ($2003$) take this premise as the foundation for a behavioral theory of comovement: when investors put assets into a category and update their beliefs about the whole category in response to news about any one member, the assets in the category should move together more than their fundamentals warrant.

The two-asset Barberis-Shleifer model. A continuum of investors choose between two risky assets and a riskless asset. Some investors are fundamental and price each asset according to its own dividend stream; the rest are style switchers who allocate between two pre-defined style categories (say, small-cap and large-cap) based on relative past performance. When the style switchers move funds into small-caps, every small-cap stock receives extra demand simultaneously, generating excess comovement among small-caps that has no fundamental driver. The model produces three sharp predictions:

• Excess comovement within a category beyond what cash-flow fundamentals justify.
• Reduced comovement across categories beyond what fundamentals justify.
• Comovement that changes when an asset’s category membership changes, even with fundamentals held fixed.

The Barberis-Shleifer-Wurgler ($2005$) test on S&P $500$ inclusions. The cleanest empirical test of the third prediction. When a stock is added to the S&P $500$ index, its fundamentals do not change, but its category membership does — it becomes “an S&P $500$ stock.” If categorical thinking matters, the stock’s beta with the S&P $500$ index should rise after inclusion (and its beta with non-S&P $500$ stocks should fall). This is exactly what Barberis-Shleifer-Wurgler ($2005$) find. The added stocks’ betas with the index rise by $0.1$–$0.2$ over the months following inclusion, with no comparable change in the firm’s underlying business.

Empirical anomalies the model addresses. Categorical thinking provides a unified behavioral explanation for several long-standing comovement puzzles:

• Twin shares (Royal Dutch / Shell, Unilever NV / PLC): Dual-listed claims to the same cash-flow stream that fail to comove perfectly, deviating by $10$–$20\%$ from theoretical parity for years.
• Closed-end funds: CEFs comove with one another more than their underlying assets do; closed-end country funds comove with the country where the fund is traded as much as with the country where its assets are held.
• Value and small stocks: Strong common factors that exceed what common factors in earnings would imply (Fama-French $1995$).
• Commodities: Pindyck-Rotemberg ($1990$) document strong comovement among commodities with unrelated fundamentals.

Relation to representativeness. Categorical thinking shares cognitive roots with the representativeness heuristic — both involve judging members of a category by category-level attributes — but operates at a different level. Representativeness is about probability judgment (how likely is this member to have property $X$?); categorical thinking is about belief formation (what do I expect about this member’s return?). The two are complementary; representativeness is one cognitive root of category-level belief formation.

Intuition

The world contains thousands of public stocks, each with its own quarterly cash flows, capital structure, and idiosyncratic risk profile. A fully rational investor would form beliefs about each one separately, drawing on the unique features of every firm. The cognitive cost of doing this is enormous, so investors economize by collapsing the universe into a manageable set of categories. “Tech stocks.” “Banks.” “Emerging markets.” Once a stock is filed under a category label, the investor’s belief about it moves whenever the category-level belief moves, regardless of whether the stock’s own fundamentals have changed.

The mechanism is simple but powerful. Imagine an investor who categorizes stocks as either “growth” or “value” and adjusts her allocation between the two categories based on relative past performance — a “style switcher.” When growth has outperformed for a year, she shifts funds from value to growth. Her shift bids up every growth stock simultaneously and depresses every value stock simultaneously. The result is that growth stocks comove together (they all received the same demand shock) and value stocks comove together (they all received the same negative demand shock), even when the individual stocks have nothing in common at the cash-flow level.

The S&P $500$ inclusion test is the cleanest demonstration. A stock added to the index is, on day $t-1$, a regular non-index stock; on day $t$, it is an S&P $500$ stock. Its underlying business is identical. But its category has changed, and the investors who allocate at the category level (index funds, S&P $500$ ETFs, asset allocators thinking in terms of “S&P $500$ exposure”) now treat it differently. Its returns become more correlated with the rest of the index and less correlated with non-index stocks. There is no fundamental story for this; the only thing that changed is the label.

Properties

(Excess Within-Category Comovement) Stocks within a category move together beyond fundamentals.

The headline prediction of the Barberis-Shleifer model: stocks sharing a salient category label exhibit return correlations exceeding what could be justified by the comovement of their cash flows or by exposure to common risk factors. Tested in many settings — small-caps move together more than their earnings do (Fama-French $1995$), commodities move together more than their underlying supply-demand fundamentals warrant (Pindyck-Rotemberg $1990$), closed-end funds move together more than their portfolios do (Lee-Shleifer-Thaler $1991$).

(Reduced Across-Category Comovement) Stocks in different categories comove less than fundamentals warrant.

The mirror prediction. If category-switching investors move from one style to another, they bid up one category while bidding down the other, generating negative comovement at the category level beyond fundamentals. Empirical tests are harder because the prediction requires identifying a counterfactual fundamental comovement, but the dual-listed company anomaly (Royal Dutch / Shell trading apart despite claims to the same dividend stream) illustrates the point: when investors categorize Royal Dutch as a “European stock” and Shell as a “U.K. stock,” cross-category demand shocks pull them apart even though their fundamental should be perfectly identical.

(Category Reassignment Changes Comovement) Recategorizing an asset changes its return correlations.

The sharpest, most testable prediction: hold an asset’s fundamentals fixed and change only its category label. If category-level investing matters, comovement should rebalance. Barberis-Shleifer-Wurgler ($2005$) implement this test using S&P $500$ inclusion events — the asset’s business is unchanged but its index membership shifts — and find significant beta shifts in the predicted direction over the year following inclusion. The same logic has been applied to Russell $2000$ reconstitutions, MSCI emerging-markets index changes, and the introduction of new exchange-traded funds.

(Mechanism — Style Switching) Within-category demand shocks affect all members.

The microfoundation in the Barberis-Shleifer model is style switching. A fraction of investors allocate between style categories based on relative past category performance. Their allocation decisions affect aggregate demand for each member of the category proportionally, transmitting category-level demand shocks into individual-stock returns. The category-level demand is, by construction, common to all members, generating the within-category comovement. The model shows the magnitude of excess comovement scales with the share of style switchers and the cross-sectional correlation of their style demand.

(S&P $500$ Inclusion Test) Beta with the index rises after inclusion; beta with non-index stocks falls.

Barberis, Shleifer, and Wurgler ($2005$) examine $455$ stocks added to the S&P $500$ between $1976$ and $2000$. After inclusion, the average added stock’s beta with the index rises from approximately $0.7$ to $0.8$–$0.9$ over the following year, while its beta with the non-S&P stock universe falls correspondingly. The fundamentals of the added firms do not change in any systematic way at inclusion (the index committee weights several criteria but does not require any business-line change). The result is a clean demonstration that category membership itself — independent of fundamentals — affects return comovement.

(Limits) Categorical thinking does not predict which categories will be salient.

The model takes the existing set of categories as given. It does not explain why investors categorize stocks as “value vs. growth” rather than, say, “high-employment vs. low-employment” or “Pacific-Coast vs. Atlantic-Coast.” The salient categories are partly determined by financial-market practice (analyst coverage by industry, fund classification by style box) and partly by media-framing conventions. A complete theory of comovement would endogenize the choice of categories; the Barberis-Shleifer model takes them as primitives and shows the consequences.

Examples

S&P $500$ inclusion of Tesla in December $2020$

Tesla was added to the S&P $500$ on December $21$, $2020$. Its underlying business was unchanged at the moment of inclusion — the same automobile-and-energy-storage firm with the same revenue trajectory. But its category membership shifted: now an “S&P $500$ stock,” held by every S&P $500$ index fund and tracked by every S&P $500$ ETF. Following the Barberis-Shleifer-Wurgler logic, Tesla’s beta with the S&P $500$ should have risen after inclusion. Empirically, Tesla’s $60$-day rolling beta with the index rose from approximately $1.6$ in the months before inclusion to approximately $2.0$ in the months after, with no corresponding change in the firm’s reported fundamentals. The shift is consistent with categorical thinking: index-focused investors bought Tesla in lockstep with their index allocation decisions, generating fresh comovement.

Twin-share comovement failure: Royal Dutch / Shell

Royal Dutch Petroleum and Shell Transport were two separate publicly-traded companies that together owned the Royal Dutch / Shell oil-and-gas business in fixed proportions ($60\%$ Royal Dutch, $40\%$ Shell, by long-standing agreement). Their cash-flow claims should have traded at exactly the $60$/$40$ ratio. In practice, the two stocks’ market values deviated from this ratio by up to $35\%$ for extended periods, with Royal Dutch trading at a premium when European equity sentiment was strong and at a discount when U.K. equity sentiment was strong (Froot and Dabora, $1999$). The deviation persists for years and resists arbitrage. Categorical thinking explains it: investors categorize Royal Dutch as a “European” stock and Shell as a “U.K.” stock, and category-level sentiment shocks move them apart. The fundamental claim — both equities own the same underlying business — is overridden by the category labels.

Closed-end country funds (Lee-Shleifer-Thaler $1991$, Bodurtha-Kim-Lee $1995$)

Closed-end country funds — say, the Mexico Fund traded on the NYSE — hold portfolios of Mexican equities but trade in the U.S. as a single security. Their returns can be decomposed into (i) returns on the underlying Mexican portfolio (the asset country) and (ii) returns on the U.S. market (the trading country). A pure rational benchmark says the fund’s return should track only (i). Empirically, the fund returns correlate strongly with both (i) and (ii) — the U.S. market component carries roughly equal weight to the Mexican market component in driving fund returns. Categorical thinking explains the result: U.S. retail investors who trade the Mexico Fund categorize it as “an emerging-market fund” or “a stock trading on the U.S. market” depending on context, and their demand shocks transmit U.S. sentiment into the fund’s price.

See Also

• 8.11. Bounded Rationality — parent hub.
• 8.6.5. Representativeness Heuristic — the cognitive root of category-level belief formation.
• 8.4. Noise — the broader limits-to-arbitrage framework that explains why the categorical-thinking mispricings persist.
• 8.11.1. Limited Attention and PEAD — sibling: information-processing limit operating at a different stage.
• 8.3. Challenges to Rational Pricing — places excess comovement among the broader set of efficient-markets puzzles.
• 8.6.7. Extrapolative Beliefs — modern alternative theory that also generates within-category comovement at shorter horizons.