Cumulative Abnormal Return (CAR): Formula, Event Windows, and How to Use It

Cumulative abnormal return (CAR) measures how much a stock moved above or below expectations around a specific event. Earnings releases, mergers, regulatory rulings, ESG disclosures: each one leaves a footprint in the data. CAR is how researchers and investors measure that footprint precisely.

This guide covers the formula, how to pick an event window, which benchmark model to use, and when to switch to a different method entirely.

What is Cumulative Abnormal Return?

Cumulative abnormal return (CAR) is a financial metric used to assess the performance of a stock or portfolio relative to its expectations. 

Abnormal return is a term used to describe the difference between the expected return on an investment and the actual return.

An abnormal return can either be positive or negative, depending on whether or not the actual return was higher or lower than expected.

The Cumulative Abnormal Return is simply the total of all of these abnormal returns. This is considered over a specific period of time in order to assess an investment’s performance in the context of broader factors like market conditions.

How are cumulative abnormal returns calculated?

An investment’s cumulative abnormal return can be calculated simply by figuring out all of the abnormal returns over a period of time, and then adding them together.

The formula for a single-day abnormal return is:

AR = Actual Return – Expected Return

A positive AR means the stock did better than the model predicted. A negative AR means it underperformed. CAR is the sum of all daily ARs across your chosen event window:

CAR(t1, t2) = AR(t1) + AR(t1+1) + … + AR(t2)

For example: a stock earns +3% on day -1, +5% on day 0, and -1% on day +1 around an earnings announcement. The expected return from your benchmark model is +1% each day. The daily ARs are +2%, +4%, and -2%. The CAR over the [-1, +1] window is +4%. That 4% represents the market’s reaction to the announcement above and beyond normal market movement.

How to Choose Your Event Window

The event window is the range of trading days around your event date (day 0) over which you sum abnormal returns. Your choice directly changes your CAR result.

Short windows like [-1, +1] or [-3, +3] capture the immediate market reaction. They are less likely to be contaminated by unrelated news. Most M&A and earnings-announcement studies use these.

Longer windows like [-10, +10] or [-20, +20] can capture anticipatory effects, where prices start moving before the event is publicly announced. Recent empirical work on product introductions and M&A finds that pre-event price drift often dominates the post-announcement move, making a symmetric short window miss most of the signal.

A practical starting point for most studies:

👉 Quick takeaway: Shorter windows give cleaner attribution but miss pre-event leakage. Longer windows capture drift from rumor and anticipation but introduce more noise from unrelated market events. Match the window to the expected information environment around your event.

Run at least two window lengths and compare. If your CAR changes dramatically between [-1, +1] and [-5, +5], that tells you something important about when the information reached the market.

Which Benchmark Model Should You Use?

Your CAR result is only as reliable as your expected-return model. Four models are in common use, and they do not always agree.

Market-adjusted model subtracts the market return from the stock return. Simple and fast, but it ignores a stock’s systematic risk.

CAPM (single-factor) adjusts for beta. Better than the raw market model, but it misses the size and value effects that explain a large share of cross-sectional return variation.

Fama-French three-factor model adds size (SMB) and value (HML) factors. Standard in academic work since the 1990s and still widely used.

Fama-French five-factor model adds profitability (RMW) and investment (CMA). Recommended for studies involving firms with unusual profitability or capital structures.

👉 Quick takeaway: The market-adjusted model is the fastest to implement but the least precise. CAPM adds beta and works for most corporate event studies. The Fama-French models add factors progressively and are the standard for academic research requiring cross-sectional robustness.

Using a simpler model than your data warrants inflates or deflates your CAR estimate. That is not a minor issue. It changes your conclusions.

Statistical Testing: Which Test to Use and When

A CAR of +4% means nothing without a significance test. Two broad families of tests apply.

Parametric tests (t-tests) assume abnormal returns are normally distributed. They work well with large, non-overlapping samples. The standard cross-sectional t-test divides the average CAR by its cross-sectional standard deviation across firms.

Nonparametric tests (rank tests, sign tests) make no distributional assumption. They are more reliable when your sample is small, your events cluster in calendar time, or returns are fat-tailed. Current methodological guidance recommends nonparametric tests as a robustness check in nearly all event studies, not just edge cases.

Two specific problems to watch for:

1. Event clustering: if your events all fall in the same calendar period (e.g., all firms announcing during a market crisis), returns are correlated across firms. A standard t-test will overstate significance. Use a cross-sectional test or a portfolio-based approach.
2. Overlapping estimation and event windows: if your estimation window overlaps with a prior event, your expected-return parameters are contaminated. Keep estimation windows clean and at least 120 trading days long.

Running only a t-test and calling it done is no longer considered sufficient in published event-study work.

When CAR Is the Wrong Tool: Long-Horizon Studies

CAR works well for short windows around discrete events. Extend the window past 12 months and the method starts to break down.

Two problems compound over long horizons. First, abnormal returns accumulate in a way that distorts the distribution, making standard tests unreliable. Second, benchmark drift means the expected-return model becomes a worse fit the further you get from your estimation window.

For studies covering 12 to 60 months after an event, practitioners use two alternatives:

• Buy-and-Hold Abnormal Return (BHAR) compounds actual and expected returns separately, then takes the difference. It more accurately reflects the experience of an investor who bought on the event date and held.
• Calendar-time portfolio method forms a portfolio of event firms each month and measures the portfolio’s alpha against a factor model. It handles cross-sectional correlation better than BHAR.

Neither method is perfect. BHAR is sensitive to the benchmark chosen. The calendar-time approach can lose power when the number of event firms varies widely month to month. For studies beyond 36 months, both methods should be reported alongside each other.

Robustness Checks: How to Stress-Test Your CAR Results

A single CAR estimate from one window and one model is not a finding. It is a starting point. Peer reviewers and serious practitioners expect at least three types of robustness checks.

1. Alternative event windows. Report CAR for at least two window lengths. If the result holds for [-1, +1] and [-3, +3] but disappears at [-5, +5], that is a meaningful finding about timing, not evidence of noise.
2. Placebo or pseudo-event tests. Assign fake event dates (randomly or from a prior period) and run the same analysis. If your method produces significant CAR around fake events, something is wrong with your specification.
3. Alternative benchmark models. Run the analysis with both a market-adjusted model and a multi-factor model. Disagreement between the two tells you the result is model-sensitive and should be reported with caution.

Recent work in emerging markets and cross-market settings adds a fourth check: STL (Seasonal-Trend decomposition using Loess) decomposition, which separates trend and seasonal components from the event-driven signal. A 2026 study on UAE financial markets found that STL-based robustness checks confirmed conventional CAR findings, strengthening confidence in the results.

CAR in ESG and Alternative-Data Research

Event studies originally focused on corporate announcements like earnings and M&A deals. The methodology has expanded significantly.

ESG disclosures are now a major application. A 2026 bibliometric study found that ESG signals and investor sentiment correlate with CAR and CAAR patterns across sectors, and that ESG-related event studies are one of the fastest-growing areas of the event-study literature. The energy sector shows particularly large CAR responses to ESG announcements, with results varying by firm size and disclosure quality.

A second emerging application is text-based CAR prediction. Researchers now use natural language processing to extract signals from earnings call transcripts, regulatory filings, and news articles, then feed those signals into CAR estimation models. A 2025 study demonstrated that text embeddings of timely disclosures improve CAR prediction accuracy in event studies, suggesting that qualitative information moves prices in ways that traditional factor models miss.

For practitioners, this means two things. First, if your event involves an ESG disclosure or a regulatory announcement, standard benchmark models may underperform. Second, sentiment and text data are increasingly available as covariates that can sharpen your CAR estimate.

What is Cumulative Abnormal Return Used For?

Cumulative abnormal return is used to assess the impact of external forces on an investment, judge its performance, and monitor risk.

For instance, an investor could use CAR following an earnings release to assess whether the market’s reaction was in line with expectations or if there were significant deviations. This could indicate market inefficiencies, which could then be explored.

This concept is widely used in hypothesis testing, valuation analysis, and to better understand market anomalies.

CAR also helps in assessing whether stock prices fully reflect all available information, or if there are inefficiencies in the market that can be exploited for abnormal profits.

CAR is used across four main contexts in finance:

1. Event studies: measuring whether an event (earnings release, merger announcement, regulatory change) moved a stock price beyond normal market expectations.
2. Market efficiency research: testing whether prices fully reflect available information, or whether systematic patterns exist that could be exploited.
3. Investment strategy evaluation: comparing the risk-adjusted performance of a portfolio against a benchmark over a defined period.
4. Risk management: identifying which types of events produce the largest abnormal return swings for a given firm or sector, then sizing positions accordingly.

Frequently Asked Questions

What is the difference between AR, AAR, CAR, and CAAR?

Abnormal Return (AR) is the single-day excess return for one firm. Average Abnormal Return (AAR) is the mean AR across all firms on a given day. Cumulative Abnormal Return (CAR) sums the ARs for one firm across multiple days. Cumulative Average Abnormal Return (CAAR) sums the AARs across both firms and days. CAAR is what most academic papers report when studying a sample of firms around a common event type.

What event window is most common in published research?

Short windows of [-1, +1] and [-3, +3] dominate earnings and M&A studies. Longer windows of [-10, +10] or beyond are used when pre-event price drift is expected. Run more than one window and report all of them.

What is the difference between CAR and BHAR?

CAR adds abnormal returns day by day. BHAR (Buy-and-Hold Abnormal Return) compounds them, which better reflects what a real investor earns over time. For windows longer than 12 months, BHAR is generally preferred over CAR because compounding distortions accumulate in simple sums.

How do overlapping events affect CAR?

If two events affect the same firm within your event window, or if many firms in your sample experience events in the same calendar period, returns are correlated across observations. A standard t-test will overstate statistical significance. Use cross-sectional tests or nonparametric methods in these cases.

Can CAR be negative and still be a valid result?

Yes. A negative CAR simply means the stock underperformed its benchmark over the event window. Negative CAR around a bad-news announcement (a dividend cut, a regulatory penalty, a failed merger) is an expected and informative finding.

Is CAR used outside of equity markets?

Mostly in equities, but the framework extends to any asset with a return series and a benchmark. Recent work applies CAR to bond markets, cryptocurrency events, and cross-market macro shocks in emerging economies.