Limited Attention and PEAD

Limited Attention and PEAD

Limited attention is the bounded-rationality hypothesis that investors process only a subset of public news on any given day. Its canonical empirical signature is post-earnings-announcement drift (PEAD): stocks that report large positive earnings surprises continue to deliver positive abnormal returns for $60$–$90$ days after the announcement, and stocks with large negative surprises continue to deliver negative abnormal returns. The drift is one of the most robust violations of the efficient-markets benchmark: it appears in U.S. data from the $1960$s onward, in international markets, and across most developed-market sub-samples.

Standardized unexpected earnings (SUE). Drift is conventionally measured by sorting stocks into deciles on
${\text{SUE}}_{i,t}=\frac{e_{i,t}-{\mathbb{E}}_t[e_{i,t}]}{\sigma (e_{i,t})},$
where $e_{i,t}$ is reported earnings, ${\mathbb{E}}_t[e_{i,t}]$ is the analyst consensus or a time-series forecast, and $\sigma (e_{i,t})$ is the historical volatility of earnings forecast errors. The top-minus-bottom decile of SUE earns roughly $7$–$10\%$ in cumulative abnormal returns over the $60$ trading days after the announcement.

Three diagnostic tests. A limited-attention explanation predicts that PEAD should be stronger exactly when investor attention is scarcer:

• Hirshleifer-Lim-Teoh (2009): PEAD is stronger for firms whose earnings are announced on a day when many other firms also announce.
• DellaVigna-Pollet (2009): PEAD is stronger for firms that announce on Friday afternoon, when traders pay less attention.
• Hou-Peng-Xiong (2008): PEAD is stronger for low-volume stocks, which receive less analyst and media coverage.

The three tests share a common identification strategy: hold the size of the earnings surprise constant and vary the amount of attention the announcement is likely to receive. Each test confirms that drift increases when attention is scarce.

Related under-reactions to non-earnings news. Limited attention also explains slow incorporation of news about other firms into a focal firm’s price. Cohen-Frazzini ($2008$) document a customer-supplier under-reaction: a positive shock to a customer firm predicts higher returns at the supplier firm over the following month. DellaVigna-Pollet ($2008$) document under-reaction to demographic shifts: firms whose products are age-sensitive (toy makers, golf equipment, beer) underperform when investors fail to anticipate the future demand implied by current demographic shifts.

Relation to belief-based under-reaction. Limited attention is one of two leading explanations for under-reaction. The other is conservatism — a Bayesian-updating bias that leaves the right amount of new evidence on the table even when the investor is paying full attention. The two stories share predictions but differ on the inattention margin: only limited attention predicts that PEAD should increase when the announcement is competing with other news, made on a Friday, or about a low-volume stock.

Intuition

The classic efficient-markets prediction is that good news is incorporated into prices instantaneously. Once a firm announces a large positive earnings surprise, the price should jump to its new fundamental value within minutes and then drift no further than the risk premium would imply. The drift puzzle is that prices do not fully adjust at announcement. The full adjustment takes weeks or months, and the speed of adjustment varies systematically across firms and announcements in a way that maps onto how much investor attention each announcement receives.

The intuition behind limited attention is mechanical. A typical institutional trader watches dozens of stocks and many news feeds simultaneously. On a day when several large firms report at the same time, each individual report receives less attention from the marginal trader, and the price reaction at the announcement is therefore smaller than it would be on a quiet day. The information is still public — anyone could read the $10$-Q — but the price incorporates it slowly because traders process it slowly. Over the following weeks, more attention is paid, the surprise is gradually absorbed, and the price drifts to the level a fully-attentive market would have set on day zero.

The asymmetry between attention-scarce and attention-abundant settings is what discriminates the limited-attention story from rational alternatives. A purely rational benchmark cannot explain why two announcements with the same surprise size produce different drift just because one was made on a Friday afternoon. A model with risk-based explanations of drift would have to argue that Friday-announcement firms are systematically riskier, which seems implausible.

Properties

(Decile Sort Magnitude) Top-minus-bottom SUE decile earns $7$–$10\%$ over $60$ trading days.

PEAD is conventionally documented by sorting all stocks into deciles on standardized unexpected earnings ($\text{SUE}$) on the announcement day, forming a long-short portfolio that buys the top decile and sells the bottom decile, and tracking its cumulative abnormal return over the next $60$ trading days. The portfolio earns roughly $7$–$10\%$ — far larger than transaction costs and far larger than the immediate announcement-day return, which is itself only $2$–$4\%$. The drift is the post-announcement portion, and it is the part that the rational benchmark cannot account for. The portfolio’s Sharpe ratio is comparable to or higher than that of momentum or value, making PEAD one of the most profitable cross-sectional anomalies on record.

(Hirshleifer-Lim-Teoh 2009) PEAD is stronger when many firms announce the same day.

Hirshleifer, Lim, and Teoh ($2009$) sort earnings announcements by the number of other earnings announcements occurring on the same trading day. They find that drift is roughly twice as large for announcements made on “high-distraction” days (top quintile of competing announcements) as for announcements made on “low-distraction” days (bottom quintile). The size of the earnings surprise itself is held constant by the decile sort, so the result cannot be explained by differential surprise magnitude. The effect survives controls for size, book-to-market, and industry. Identification rests on the natural-experiment interpretation: a firm cannot easily choose to schedule its announcement on a busy or quiet day relative to the entire universe of other firms.

(DellaVigna-Pollet 2009) PEAD is stronger for Friday-afternoon announcements.

DellaVigna and Pollet ($2009$) find that the price reaction to Friday-afternoon earnings announcements is roughly $40\%$ smaller than the reaction to Monday-Thursday announcements, while the post-announcement drift is correspondingly larger. The total cumulative response after $60$ days is approximately equal across announcement timings, meaning the same information is eventually incorporated but takes longer for Friday announcements. The Friday-afternoon timing is plausibly exogenous to the size of the earnings surprise itself — managers may strategically schedule bad news for Friday, but the test conditions on the surprise magnitude — so the result identifies an inattention channel.

(Hou-Peng-Xiong 2008) PEAD is stronger for low-volume stocks.

Hou, Peng, and Xiong ($2008$) sort firms by their average trading volume over the months leading up to the announcement. PEAD is several times larger for the lowest-volume quintile than for the highest-volume quintile. Trading volume proxies for analyst coverage, media coverage, and institutional ownership; all three correlate with how much attention the firm receives. The result implies that better-attended firms have their earnings news incorporated faster, exactly as the limited-attention hypothesis predicts.

(Cohen-Frazzini 2008) Investors under-react to customer-link news.

A firm’s major customers are listed in its $10$-K. Cohen and Frazzini ($2008$) show that good news for a customer firm — measured by its own monthly stock return — predicts positive returns at the supplier firm over the following month, with a long-short customer-link strategy delivering roughly $1.5\%$ per month in alpha. Investors are required to read the customer disclosures to make the link, and most retail and many institutional investors do not. The under-reaction is therefore an attention failure rather than an information unavailability problem.

(DellaVigna-Pollet 2008) Investors under-react to demographic news.

DellaVigna and Pollet ($2008$) classify firms by the age of their primary consumers (toys, soft drinks for children; golf equipment, life insurance for older customers). They forecast each firm’s future demand using current population age structure projected forward and compare these forecasts to realized stock returns. Firms whose demographic-implied future demand is high outperform firms whose implied demand is low by a substantial margin. The information needed for the forecast — current age structure plus an aging trajectory — is freely available; the under-reaction is an attention failure on a slow-moving fundamental.

(Identification Strategy) Hold surprise size fixed, vary attention.

The shared empirical recipe of all limited-attention papers is to control for the content of the news (the earnings surprise size, the customer-firm return, the demographic-shift magnitude) and let the attention to the news vary plausibly exogenously across observations. This isolates the inattention margin from confounds like systematic risk or asymmetric information. The robustness of the pattern across very different settings — quarterly earnings, monthly customer returns, decade-long demographic shifts — is what makes the limited-attention pillar a workhorse of the bounded-rationality literature.

Examples

Two earnings announcements, same surprise, different drift

Two firms each announce earnings \0.10$aboveanalystconsensus,withcomparableconsensusstandarddeviations,onthesameTuesday.Firm$A$istheonlymajorannouncementthatday;firm$B$announcesalongside$30$otherlarge-capfirmsreportingthesamemorning.FollowingHirshleifer-Lim-Teoh($2009$),aninvestorwouldpredict(i)firm$A$showsalargerannouncement-dayjumpthanfirm$B$,(ii)firm$B$exhibitssubstantiallymoredriftoverthesubsequent$60$tradingdays,and(iii)the\ast cumulative\ast$60$-day response is similar across the two firms once drift is included. The surprise content is held fixed by construction, so any difference in drift is attributable to attention.

Trading PEAD: a long-short SUE portfolio

A simple implementation: at the end of each calendar quarter, compute ${\text{SUE}}_{i,t}$ for every firm using the most recent quarterly earnings versus the median analyst consensus. Sort firms into deciles. Buy the top decile, sell the bottom decile, hold for $60$ trading days, then rebalance. Historical out-of-sample returns from the early $2000$s onward run roughly $0.6$–$1.0\%$ per month before transaction costs. The strategy is widely cited as evidence that PEAD is real and economically meaningful, but post-publication decay (Chordia, Subrahmanyam, Tong, $2014$) suggests its alpha has compressed as institutional investors have begun to trade it. The compression is itself further evidence for the limited-attention story: as attention to the anomaly grows, the inattention-driven drift shrinks.

Customer-link under-reaction

Suppose a small auto-parts supplier discloses in its $10$-K that one large auto manufacturer accounts for $40\%$ of its revenue. The auto manufacturer reports a strong quarter, with stock up $8\%$ over the announcement month. Cohen-Frazzini ($2008$) predict that the supplier’s stock should also drift up over the following month, by roughly $3\%$ in cumulative abnormal terms — an effect generated by investors’ failure to immediately propagate the customer-firm news to the supplier’s valuation. The under-reaction implies a tradeable signal: long the supplier conditional on a positive return at its disclosed customer.

See Also

• 8.11. Bounded Rationality — parent hub.
• 8.11.2. Attention-Grabbing Stocks and Buy-Sell Asymmetry — sibling: attention as a determinant of buy decisions specifically.
• 8.6.1. Conservatism — alternative cognitive explanation for under-reaction; complements rather than competes with limited attention.
• 8.9.1. Barberis-Shleifer-Vishny Model — first-generation under-reaction model that uses conservatism rather than attention.
• 8.3. Challenges to Rational Pricing — places PEAD inside the broader set of efficient-markets puzzles.
• 8.8. Momentum — closely related cross-sectional anomaly that also reflects slow information incorporation.