Confidential, authorship-first academic support

Event Study Analysis: Abnormal Returns, CAR, BHAR and Significance Tests

An event study measures how security prices respond to new information — an acquisition, earnings surprise, rating change or policy announcement. We help you define events cleanly, pick an expected-return model, compute abnormal returns and test them with statistics that fit your sample.

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  • Explained so you can defend it yourself
  • Confidential, and you remain the author

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Overview

The short-horizon event study is one of the most widely used designs in finance and accounting research. Its logic is simple — compare actual returns around an event with what would have been expected without it — but details decide whether results are credible: accurate event dates, a clean estimation window, the right benchmark model, and a test statistic that copes with event-induced volatility and events clustered on the same dates.

We work through each design choice with you and record it: the event definition and data source, the estimation and event windows, the expected-return model (market model, market-adjusted, Fama–French or Carhart factor models), and the aggregation into cumulative abnormal returns (CAR) or buy-and-hold abnormal returns (BHAR) for longer horizons. We then run a set of parametric and non-parametric tests and cross-sectional regressions explaining which firms reacted more.

You receive the full workflow as code, with tables of average abnormal returns by day, CARs over each window, test statistics and figures, plus explanations for your methods and results chapters.

Who it’s for and the problems it solves

This is for you if you are…

  • Master's and doctoral students in finance and accounting
  • Researchers studying market reactions to M&A, earnings, dividends, ESG news, regulation or political events
  • Authors revising papers after comments on test statistics, confounding events or benchmark models
  • Researchers extending event studies to non-US or emerging markets with thin trading

Common problems we help with

  • You are unsure how long the estimation and event windows should be
  • Many of your events happen on the same day, such as a regulatory announcement
  • Returns in your market are thinly traded, with many zero-return days
  • Your CAR is significant with a t-test but not with a rank test
  • A reviewer asked for BHAR or a calendar-time portfolio approach for long-run returns

What’s included — and what isn’t

Included

  • Event definition, date verification and handling of confounding events
  • Choice of estimation window, gap and event windows, with sensitivity checks
  • Expected-return models: market model, market-adjusted, mean-adjusted, Fama–French three- and five-factor, Carhart four-factor
  • Daily abnormal returns (AR), average abnormal returns (AAR) and cumulative abnormal returns (CAR/CAAR)
  • Buy-and-hold abnormal returns (BHAR) and calendar-time portfolio regressions for long-horizon questions
  • Parametric tests: cross-sectional t, Patell Z, BMP standardized cross-sectional test and adjusted versions for cross-correlation
  • Non-parametric tests: sign and generalized sign tests, Corrado rank test and generalized rank tests
  • Cross-sectional regressions of CARs on firm or deal characteristics with robust standard errors
  • Adjustments for thin trading, such as Scholes–Williams or Dimson betas, where needed
  • Code in Stata, R, Python or Excel-based templates, and figures of CAAR paths

Not included

  • Investment recommendations or trading signals from the results
  • Selecting windows or tests after seeing which ones are significant, without disclosure
  • Accessing subscription databases on your behalf that you are not licensed to use
  • Writing your thesis or paper for you

What you receive

Design specification
Event definition, sample filters, windows, benchmark model and test statistics, agreed before running the study.
Abnormal return tables
AAR by day and CAAR for each event window with several test statistics side by side, and the number of events.
Figures
CAAR plots with confidence bands, and distributions of CARs across events.
Cross-sectional analysis
Regressions explaining variation in CARs with firm, deal or event characteristics.
Reproducible workflow
Code that takes raw price and index data to final tables, with comments and a data dictionary.

How it works

  1. Define the events

    We confirm how events are identified, how dates are verified (announcement versus effective date) and how confounded events are screened.

  2. Set the design

    We agree windows, the benchmark model and the set of test statistics.

  3. Prepare returns

    Prices, indices and factors are aligned to trading calendars, and missing or stale prices are handled.

  4. Estimate and test

    We compute abnormal returns, aggregate them and run tests and cross-sectional regressions.

  5. Report and explain

    Tables, figures and code are delivered with a walkthrough session.

Models and test statistics

Market model
Regresses the stock's return on the market index over the estimation window; abnormal returns are deviations from predicted returns during the event window.
Factor models
Fama–French or Carhart factors adjust for size, value, profitability, investment or momentum exposures, important for longer windows and specific samples.
CAR vs BHAR
CARs sum daily abnormal returns and suit short windows; BHARs compound returns and better reflect investor experience over months, but have skewness and benchmark issues.
Patell and BMP tests
Standardize abnormal returns by estimation-window variance; BMP also accounts for event-induced increases in variance.
Adjusted tests for clustering
Kolari–Pynnönen adjustments correct Patell and BMP statistics for cross-sectional correlation when events share dates.
Rank and sign tests
Corrado rank and generalized sign tests are robust to non-normal returns; generalized rank tests also handle event-induced volatility.

Windows and benchmarks

A common design uses an estimation window of roughly 120 to 250 trading days ending some days before the event, so the benchmark is not contaminated by pre-event information leakage. Event windows such as [−1, +1] or [−5, +5] capture the announcement effect; longer windows risk picking up unrelated news. We run the main window you pre-specify and report others as sensitivity checks.

For most short-window studies of large firms, the market model and factor models give similar answers. Differences appear for small firms, long windows and samples concentrated in particular styles, where factor adjustment matters more.

Choosing test statistics that fit your data

The simple cross-sectional t-test ignores the fact that events often increase volatility and that events on the same date produce correlated abnormal returns. Both can lead to over-rejection — finding 'significant' effects too often. We report a small set of tests with different strengths so readers can see whether conclusions are robust.

When all firms share an event date, such as a regulatory announcement, cross-sectional correlation is severe. Adjusted BMP tests, portfolio approaches or regression-based methods with a common event dummy are then more appropriate than standard tests.

  • Event-induced volatility → BMP or generalized rank test
  • Clustered event dates → Kolari–Pynnönen adjusted statistics or portfolio methods
  • Non-normal or thinly traded returns → rank and sign tests, adjusted betas

Interpreting abnormal returns carefully

Event studies measure the market's revaluation around information release, assuming reasonably efficient prices. A significant CAR shows the market reacted; it does not by itself explain why. Confounding news, anticipation before the announcement and small samples all affect interpretation. Long-horizon results are especially sensitive to the benchmark, so we present them with caution and alternative methods.

We also help you connect the economic magnitude of CARs to your hypotheses — for example, converting a percentage reaction into an approximate change in market value — while keeping the analysis squarely in the research domain rather than investment advice.

What the work can look like

Illustrative example — fictional data

Sample excerpt: bidder returns in cross-border acquisitions

A master's student examined acquirer share price reactions to 214 cross-border acquisition announcements in an emerging market, 2015–2024. All numbers are invented for illustration.

Design

Market model estimated over trading days [−260, −11]; event windows [−1, +1] and [−5, +5]. Nineteen events with other material news within two days were excluded.

Results

CAAR[−1, +1] = −0.84%. Cross-sectional t = −2.41; BMP = −2.02; Kolari–Pynnönen adjusted BMP = −1.93; generalized rank Z = −1.88. The negative reaction is modest and borderline across tests, so it is reported as weak evidence.

Cross-sectional regression

Deals paid entirely in cash showed CARs 1.1 points higher than stock-financed deals, 95% CI [0.2, 2.0], controlling for relative deal size and industry.

Illustrative example with invented numbers. Not a real client case and not investment advice.

See more illustrative examples

What you’ll need to provide

  • Your research question and hypotheses about the market reaction
  • The list of events with dates and identifiers, or the criteria to build it
  • Price, index and factor data you are licensed to use, or guidance on public sources
  • Reference studies whose design you want to follow
  • Software preference and any reviewer comments

You don’t need everything ready to ask for a quote — tell us what you have and we’ll say what’s missing.

What affects price and turnaround

Price depends on

  • Number of events and firms, and whether multiple markets are involved
  • Data preparation effort, including aligning trading calendars and handling thin trading
  • Number of windows, models and test statistics
  • Whether long-horizon BHAR or calendar-time analysis is required
  • Cross-sectional regression analysis and robustness checks

Turnaround depends on

  • Availability of verified event dates and licensed price data
  • Size of the event sample and number of markets
  • Scope of sensitivity checks

Every project is quoted individually. How we price our work.

Questions people ask before starting

Which data sources do I need?

Daily prices and a market index at minimum, plus factor returns for multi-factor models. Many universities provide databases for this; public sources exist for some markets and factors. We work only with data you are licensed to use.

Can event studies be done in Excel?

Yes, for small samples and the market model. For larger samples, multiple tests or factor models, Stata, R or Python is more reliable and reproducible. We can provide an Excel version for teaching purposes.

What if my events are all on the same day?

Standard tests will overstate significance. We use adjusted tests, portfolio approaches or regression-based methods designed for clustered events.

Do you give investment advice based on the findings?

No. Event studies here are for academic research and evaluation. We do not provide investment recommendations.

Will you write my results chapter?

No. We deliver tables, figures, code and explanations, and can review your draft for accuracy. The writing is yours.

Design your event study with us

Share your event type, sample and data access. We will propose windows, models and tests, and send a quote.

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