1.7.6 Advanced Extensions

Basic Prerequisites: 04 · Statistical Testing and 05 · Failure Modes.

1. Intuition & Practical Objective

Event studies are not only used to detect an effect - they are used to measure the information content of an announcement and to discriminate among economic hypotheses. This page is the launchpad for those uses, plus the single most-studied event anomaly: post-earnings-announcement drift (PEAD).

Three advanced uses:

Information content (Ball & Brown 1968; Beaver 1968): regress/rank the size of the abnormal return against the size of the surprise (e.g. standardized unexpected earnings, SUE). A bigger surprise → bigger abnormal return measures how informative the announcement is.
Cross-sectional tests (Kothari–Warner §3.7): regress abnormal returns on firm characteristics (size, analysts following, book-to-market) to test why the event effect varies across firms - relevant even when the mean event effect is zero.
Post-announcement drift (PEAD): after an earnings surprise, abnormal returns continue drifting in the direction of the surprise for weeks - a systematic market underreaction inconsistent with semi-strong efficiency. Ball & Brown (1968) first documented it; Bernard & Thomas (1989) quantified it.

The methodological lesson (Kothari–Warner §4): for long-horizon event studies like PEAD, the two workhorse measures are the BHAR (matched-firm buy-and-hold) and the Jensen-alpha / calendar-time portfolio (regress event-firm portfolio returns on the Fama–French–Carhart factors and read off the intercept). These differ in power and misspecification, and neither is a clean winner.

2. Mathematical Ground Truth & Derivations

Standardized unexpected earnings (SUE). The earnings surprise scaled by its standard deviation - the cross-sectional regressor for information-content tests:

S U E_{i t} = \frac{A EP S _{i t} - E [ A EP S _{i t} ]}{σ ( Δ A EP S _{i} )},

where $A EPS$ is the change in earnings per share and the expectation is from a model (e.g. seasonal random walk: expected $Δ$ EPS = last year’s $Δ$ EPS). Positive SUE = good news.

Cross-sectional regression (information content). For a sample of $N$ event firms,

A R_{i} = a + b S U E_{i} + u_{i},

with $b > 0$ if the surprise is priced - a direct measure of the information content of the announcement. This is the classic Sefcik–Thompson (1986) / Kothari–Warner §3.7 cross-sectional test.

Post-announcement drift (PEAD). If the market underreacts, the event-window abnormal return captures only part of the information; the rest arrives as drift in the direction of $S U E$ :

A R_{i, t} = f (S U E_{i}) + ε_{i, t}, t > 0,

with $\partial A R_{t} / \partial S U E > 0$ persisting for weeks after the announcement. Under efficiency, $E [A R_{i, t}] = 0$ for all $t > 0$ ; PEAD is the empirical violation.

Long-horizon measures (Kothari–Warner eq. 7–8):

BHAR (matched-firm): $B H A R_{i} = \prod (1 + R_{i}) - \prod (1 + R_{B})$ .
Jensen alpha / calendar-time portfolio: form a portfolio each calendar month of all firms that had the event within the prior $T$ months, then regress

R_{pt} - R_{f t} = a_{p} + b_{p} (R_{m t} - R_{f t}) + s_{p} SM B_{t} + h_{p} H M L_{t} + m_{p} U M D_{t} + e_{pt},

and read $a_{p}$ (average monthly abnormal performance) off the intercept. This is the Fama–French–Carhart four-factor event test (Kothari–Warner §4.3.2).

3. Computational Implementation - measuring PEAD

Stdlib only. Sixty firms announce earnings at day 0 with a SUE. The market underreacts: the day-0 price reaction captures ~50% of the surprise, and the remainder drifts for the following ~60 days in the direction of the surprise. The code sorts firms into big-positive-SUE and big-negative-SUE buckets and measures the drift spread.

Reading the output. Good-news firms keep drifting up (+2.90% over 60 days post-announcement) and bad-news firms keep drifting down (−5.98%) - the drift spread is a large +8.87%. This is PEAD, the empirical underreaction that motivated Ball & Brown (1968) and Bernard & Thomas (1989), and it is precisely the persistent post-event abnormal return that Kothari–Warner §3.2.2 flags as inconsistent with semi-strong market efficiency.

4. Failure Modes & First-Principles Breakdowns

PEAD is a long-horizon event study - trust it with caution. Measuring 60-day drift inherits every long-horizon failure: risk-adjustment error, cross-correlation of overlapping windows, right-skewed BHARs, and low power. A “drift” can be spurious if the expected-return model is wrong (joint-test problem, Kothari–Warner §4).
Cross-correlation across the drift window. All firms’ post-announcement windows overlap, so their 60-day returns are cross-correlated; ignoring this inflates the drift’s significance by up to ~1.7× (see 04).
Partial anticipation / endogenous timing. If the market anticipated the earnings surprise, part of the effect is already priced pre-announcement, biasing the measured information content. Event timing is endogenous (management chooses when/what to announce) - standard cross-sectional coefficients can be biased (Eckbo, Maksimovic & Williams 1990).
The drift’s economic interpretation is contested. Whether the “abnormal” drift is mispricing (behavioral) or compensation/measurement error is unresolved (Fama 1998; Kothari–Warner §4.1). Do not read a measured drift as proof of inefficiency without addressing the benchmark model.
Factor-model choice drives long-horizon answers. BHAR matched on size/book-to-market vs calendar-time four-factor alpha give different magnitudes; neither is immune to misspecification (Kothari–Warner §4.3, §4.4.3).

5. References

Ball, Ray & Brown, Philip (1968), An Empirical Evaluation of Accounting Income Numbers, J. Accounting Research 6(2), 159–178
Beaver (1968), The Information Content of Annual Earnings Announcements, J. Accounting Research 6(Supplement), 67–92
Bernard & Thomas (1989), Post-Earnings-Announcement Drift: Delayed Price Response or Risk Premium?, J. Accounting Research 27
Kothari & Warner (2007), Econometrics of Event Studies, Handbook of Corporate Finance
Fama (1998), Market Efficiency, Long-Term Returns, and Behavioral Finance, J. Financial Economics 49(3)
Sefcik & Thompson (1986)

6. Connected Graph Bridges

Back: 05 · Failure Modes · Index Hub
Sibling: Cross-Sectional Momentum (PEAD’s drift is a return-continuation cousin) · Fundamental Multi-Factor Models (the Fama–French–Carhart benchmark)
Practice: Backtesting Hygiene (is the measured drift just data-snooping?) · ES) (event-induced volatility)
Base: Statistics & Inference · Econometrics & Time Series

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