1.7 Event Studies

Basic Prerequisites: Econometrics & Time Series (return aggregation, market-model regression, OLS, serial correlation) and Statistics & Inference (hypothesis testing, the t-statistic, the CLT). (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

An event study measures the stock-price impact of a specific corporate event - an earnings announcement, a merger, an index inclusion, a regulatory change - by asking one clean question: how much of the return around the event is not explained by the normal (expected) return the stock would have had anyway? That residual is the abnormal return, and its cross-sectional average directly measures the (unanticipated) wealth effect of the event on shareholders.

The idea traces to Fama, Fisher, Jensen & Roll (1969) on stock splits and was hardened into the modern toolkit by Brown & Warner (1980, 1985) - who established, via large-scale simulation, that short-horizon event-study tests are well-specified and powerful - and surveyed authoritatively by MacKinlay (1997) and Kothari & Warner (2007). The framework is the empirical workhorse of market-efficiency testing: systematically nonzero abnormal returns that persist after an event are inconsistent with efficiency and imply a profitable (pre-cost) trading rule.

This folder is the topic-hub for event studies in Kwant-Atlas. It (a) gives the fast formula lookup below - job #1 of a hub - and (b) routes to six sub-pages walking from raw intuition through the methodology, abnormal returns & CAR, statistical testing, failure modes, and advanced extensions (information content, PEAD).

The one-sentence essence. “An event study isolates the impact of an event by subtracting the expected return from the observed return to get the abnormal return, averaging it across firms to cancel noise, and cumulating it over the event window to get the CAR - then testing whether that CAR is statistically distinguishable from zero under a model of expected returns.”

2. Mathematical Ground Truth & Derivations

Quick-Reference Lookup (job #1). All formulas below are transcribed from the verified corpus papers - Kothari & Warner (2007), Econometrics of Event Studies (Handbook of Corporate Finance, Ch. 1; verified refs/52) and Brown & Warner (1985), Using Daily Stock Returns: The Case of Event Studies (JFE; verified refs/50) - and cross-checked against MacKinlay (1997; refs/51). Numbers in the check column were re-executed and reproduced exactly from the working Python in §3 and the sub-pages.

Notation. $R_{it}$ observed return of security $i$ at event-relative time $t$; $R_{mt}$ market/index return; ${\hat{\alpha }}_i,{\hat{\beta }}_i$ OLS market-model estimates from the estimation window; $A{R}_{it}$ abnormal return; $A{R}_t$ cross-sectional mean abnormal return at $t$; $N$ number of sample firms; $L$ event-window length in periods.

Critical caveat (Kothari–Warner). Event-study tests are joint tests of market efficiency and of the expected-return model. A rejection says either abnormal returns are nonzero or the benchmark model is wrong. Short-horizon windows (a few days) make this ambiguity small - daily expected returns are ~0.05%, so even a 50% beta-misestimation barely moves a short-window AR - but long-horizon windows (≥1 year) are dominated by the joint-test problem and have low power.

3. Computational Implementation - the formula engine

Standard library only. The working examples in the sub-pages reproduce every verified number above. The core idea in one block - estimate the market model out-of-sample, compute the event-day abnormal return, and test it:

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the full analysis lives in 05 · Failure Modes. In one line each:

1. Event-window contamination - any other value-relevant news in the window gets attributed to the event of interest, biasing the abnormal return.
2. Non-synchronous trading - OLS market-model $\beta$ is biased/inconsistent with daily data (thin stocks), mis-sizing expected returns.
3. Cross-sectional correlation / event-date clustering - inflates the test statistic by $\sqrt{1+(N-1)\rho }$ (KW eq. 10); the t-stat can be overstated by ~1.7× at $\rho =.02$.
4. Event-period variance increase - volatility rises around events (Beaver 1968); estimation-window SEs understate it, so tests over-reject the null.
5. Long-horizon low power & the joint-test problem - risk-adjustment error compounds; long-window CARs/BHARs are “treacherous” (Lyon, Barber & Tsai 1999).

5. References

• Fama, Fisher, Jensen & Roll (1969), The Adjustment of Stock Prices to New Information, IER 10(1)
• Brown & Warner (1980), Measuring Security Price Performance, JFE 8(3). Verified refs/49
• Brown & Warner (1985), Using Daily Stock Returns: The Case of Event Studies, JFE 14(1). Verified refs/50
• MacKinlay, A. Craig (1997), Event Studies in Economics and Finance, J. Economic Literature 35(1). Verified refs/51
• Kothari, S.P. & Warner, J.B. (2007), Econometrics of Event Studies, Handbook of Corporate Finance
• Campbell, Lo & MacKinlay (1997), The Econometrics of Financial Markets

6. Connected Graph Bridges

• Foundational base: Econometrics & Time Series (market-model regression, stationarity) · Statistics & Inference (t-tests, CLT) · Probability & Measure Theory
• Sibling topics (this pillar): Fundamental Multi-Factor Models (the expected-return model feeding abnormal returns) · Momentum (PEAD’s drift is a return-continuation cousin) · Backtesting Hygiene (multiple-testing & deflated significance)
• Efficiency & pricing: ES) (event-induced volatility) · Time Series (return aggregation)
• Sub-pages (in-folder): 01 From Zero · 02 Event-Study Methodology · 03 Abnormal Returns & CAR · 04 Statistical Testing · 05 Failure Modes & Practice · 06 Advanced Extensions

Beginner: start at 01 · Practitioner: start at 05