What is an event study?
An event study is an empirical method used in finance and economics to measure how a specific, identifiable occurrence (the “event”) affects the value of a security, a firm, an industry, or the market. The basic idea: if markets are (at least partially) informationally efficient, the release of new information should be incorporated into prices quickly. By comparing observed returns around the event to the returns that would be “expected” if the event had not happened, an event study isolates the event’s impact.
Key takeaways
– Event studies quantify the abnormal return (actual minus expected return) associated with a discrete event (earnings announcement, merger news, regulatory change, bankruptcy filing, dividend change, etc.).
– The standard workflow: define the event and sample → choose estimation and event windows → estimate expected returns → compute abnormal returns and aggregate them → test statistical significance.
– Common expected-return models: constant mean, market model (single-factor), CAPM or multifactor models (e.g., Fama–French). Choice affects power and bias.
– Primary statistics: Abnormal Return (AR), Cumulative Abnormal Return (CAR), Average Abnormal Return (AAR) and Cumulative/Average CAR/CAAR across firms.
– Practical issues: confounding events, cross-sectional dependence, thin trading, event-timing uncertainty, multiple testing and clustering must be addressed.
When to use an event study
– To test if a news item or policy causes a statistically significant change in value.
– To examine market reaction speed and magnitude for mergers, earnings surprises, regulatory announcements, litigation outcomes, stock splits, dividend changes, macro shocks, etc.
– For regulatory impact analysis (interrupted time series / difference-in-differences variants), insurance/life tables and duration analysis applications (event-history analysis).
Core assumptions
– The market reasonably impounds available information into prices.
– Expected-return model used for “normal” returns is appropriate and stable over the estimation window.
– No systematic confounding events coincide with the event window, or such confounds are controlled for.
Step‑by‑step methodology (practical workflow)
1) Define the event precisely and assemble the sample
– Determine event date(s). For firm announcements, use announcement timestamp (date/time).
– Choose sample firms theoretically affected by the event and any control group if needed. Exclude firms with overlapping/confounding events where possible.
2) Choose timing windows
– Estimation window: period used to estimate parameters of the expected-return model (commonly -250 to -31 trading days relative to event day 0).
– Event window: period to measure abnormal returns (a few days around event, e.g., [-1,+1] for intraday/short-run effects or wider to capture slow adjustments).
– Avoid overlap between estimation and event windows.
3) Compute returns and prepare data
– Use returns (p_t / p_{t-1} – 1) or log returns. Use consistent frequency (daily, intraday, monthly).
– Clean data: adjust prices for splits/dividends, handle missing days, align trading calendars.
4) Select and estimate an expected‑return model on the estimation window
Common choices:
– Constant mean model: E[R_it] = μ_i (simple but ignores market movements).
– Market model: R_it = α_i + β_i R_mt + ε_it (most common; estimate α, β by OLS using estimation window; R_mt is market return).
– CAPM: R_it − R_f,t = α_i + β_i (R_m,t − R_f,t) + ε_it (adds risk‑free rate).
– Multifactor models (Fama–French, Carhart, etc.) for better control of systematic risk.
Estimate model parameters for each firm (or portfolio) using the estimation window.
5) Calculate abnormal returns (AR)
– For firm i on day t: AR_it = R_it − E[R_it], where E[R_it] is predicted return from chosen model.
– For cross-sectional averages: AAR_t = (1/N) Σ_i AR_it.
6) Aggregate abnormal returns across time and/or firms
– Cumulative Abnormal Return for firm i over event window [T1, T2]: CAR_i(T1,T2) = Σ_{t=T1}^{T2} AR_it.
– Cumulative Average Abnormal Return across firms (CAAR) = (1/N) Σ_i CAR_i(T1,T2). CAAR is often the main statistic for testing.
7) Statistical inference
– Compute standard errors and t-statistics for ARs, AARs, CARs and CAARs.
– If returns and residuals are approximately iid: t = CAAR / SE(CAAR). But iid rarely holds; adjust for cross-sectional correlation and heteroskedasticity (see practical issues).
– Use non-parametric tests (rank tests, sign tests) or bootstrap/permutation tests when distributional assumptions are dubious.
– When analyzing many firms and dates, apply multiple-testing corrections or cluster robust standard errors.
8) Robustness checks and extensions
– Try alternative estimation windows, event windows and expected-return models.
– Exclude or control for confounding announcements.
– Conduct cross-sectional regressions of CAR_i on firm characteristics to explain heterogeneity (e.g., size, leverage, prior returns).
– Use portfolios of similar events to increase power (average across homogeneous events).
Formulas (plain text)
– Market model: R_it = α_i + β_i R_mt + ε_it
– Abnormal return: AR_it = R_it − (α_i + β_i R_mt)
– CAR for firm i over [T1,T2]: CAR_i = sum_{t=T1}^{T2} AR_it
– CAAR = (1/N) sum_{i=1}^N CAR_i
Common practical choices and example timeline
– Estimation window: -250 to -31 days (approximately one trading year, excluding the month before the event).
– Event window: [-1, +1] captures immediate market reaction; extended windows like [-5,+5] or [-20,+20] capture anticipation or delayed effects.
– If event date uncertain, consider longer windows or intra-day data if timestamped announcements are available.
Dealing with practical issues and pitfalls
– Confounding events: Multiple announcements or market-wide shocks can bias ARs. Remove overlapping events or use control groups/difference-in-differences.
– Cross-sectional dependence: When many firms are affected by the same market shock, residuals are correlated. Use cluster-robust SEs, bootstrap, or test statistics that allow correlation (e.g., generalized sign tests).
– Thin trading and nonsynchronous trading: Can bias beta estimates and residuals; use longer estimation windows or adjust for non-synchronous trading.
– Event-timing precision: Intraday timestamps reduce misclassification; daily data can dilute immediate effects.
– Multiple testing: If testing many events or many windows, control the false discovery rate or use Bonferroni/Benjamini-Hochberg corrections.
– Model misspecification: Try alternative expected-return models and check residual diagnostics.
Extensions and related techniques
– Interrupted time series analysis (ITSA): compares pre- and post-event trends in level and slope; useful for policy evaluations and macro events.
– Difference‑in‑differences: compares treated vs. control groups across pre/post periods to control for common trends.
– Duration/event‑history models: when interest is in time until an event (e.g., default, failure), use survival analysis rather than returns-based measures.
– Panel regressions with event indicators: include firm and time fixed effects to control for unobserved heterogeneity.
Practical implementation checklist
– Data: adjusted prices, market index, risk‑free rate (if using CAPM), firm identifiers, and accurate announcement timestamps.
– Software: R (packages: eventstudies, PerformanceAnalytics, fixest, sandwich), Python (pandas, statsmodels; custom functions available), Stata (eventstudy, eventstudy2), SAS/Excel for small samples.
– Steps to run: clean & align data → estimate expected returns → compute ARs → compute CARs/CAARs → run statistical tests → run robustness checks.
Simple numeric example (conceptual)
– Suppose you estimate α_i and β_i for firm i using daily returns from t = -250 to -31. On event day 0, observed R_i0 = 1.5% and market return R_m0 = 0.2%. The market-model expected return E[R_i0] = α_i + β_i * 0.2% = 0.3% (for illustration). AR_i0 = 1.5% − 0.3% = 1.2%. If ARs for days -1, 0, +1 are 0.0%, 1.2%, -0.1% respectively, then CAR_{-1,+1} = 1.1%. Aggregate CAAR across all sample firms and test whether CAAR is statistically different from zero using an appropriate standard error.
Where to read more (key references)
– MacKinlay, A.C. (1997). “Event Studies in Economics and Finance.” Journal of Economic Literature, 35(1): 13–39. (survey paper)
– Campbell, J.Y., Lo, A.W., & MacKinlay, A.C. (1997). The Econometrics of Financial Markets. (textbook with event study material)
– Brown, S.J., & Warner, J.B. (1985, 1980). Foundational papers comparing test procedures for event studies.
– Investopedia: “Event Study” overview (for a practitioner-friendly introduction): https://www.investopedia.com/terms/e/eventstudy.asp
Conclusion
Event studies are a powerful, well-established toolkit for assessing how news and events affect asset values. The method’s rigour depends on careful definition of events, appropriate expected-return models, attention to timing and data quality, and robust inference techniques that address cross-sectional dependence and confounding influences. Running sensitivity analyses and reporting assumptions and limitations are essential for credible results.
If you’d like, I can:
– Draft a reproducible example in R or Python (with code) using a mock dataset or public stock data.
– Help design an event study for a specific event (e.g., merger announcements, earnings surprises) including recommended windows and model choices.