What is the cumulative abnormal return (CAR)?

The cumulative abnormal return (CAR) is the sum of all abnormal returns over a specified event window. An abnormal return for any period equals the actual stock return minus the expected (normal) return. CAR is widely used in academic finance and event studies to measure how a specific event — like an earnings announcement, merger, or regulatory change — affected a stock's price beyond what the market would have predicted.

How is abnormal return (AR) calculated?

Abnormal Return (AR) for a period t = Actual Return(t) − Expected Return(t). The expected return is typically estimated using a benchmark model such as the Market Model (alpha + beta × market return), the Capital Asset Pricing Model (CAPM), or a simple mean return from a pre-event estimation window. The choice of expected-return model matters — different models can produce different ARs for the same event.

What time window should I use for an event study?

The event window typically includes the event date (Day 0) and several days before and after, commonly [−2, +2] or [−5, +5] trading days. A wider window captures information leakage before the event and the market's full reaction after. The estimation window (used to calibrate the expected-return model) is usually 100–250 trading days ending 30–60 days before the event to avoid contamination.

What does a negative CAR indicate?

A negative CAR indicates the stock underperformed its expected return over the event window — the event was associated with negative news or market surprise. For example, a CAR of −4.5% around a product recall announcement suggests the market interpreted the event as destroying approximately 4.5% of firm value beyond normal market movements. Whether this is statistically significant depends on the variance of ARs across the event window.

How do I test if a CAR is statistically significant?

To test significance, compute the standardized CAR (SCAR) by dividing CAR by its standard error, which is estimated from the variance of ARs in the estimation window scaled by the window length. Under the null hypothesis of no abnormal return, SCAR follows an approximately normal distribution. A |t-statistic| > 1.96 indicates significance at the 5% level. For small samples, non-parametric tests like the Wilcoxon signed-rank test or rank test are also commonly used.

What is the Market Model for estimating expected returns?

The Market Model is the most common expected-return model in event studies: Expected Return(i,t) = α_i + β_i × R_m,t, where α_i and β_i are firm-specific parameters estimated from a pre-event regression of the stock return on the market return, and R_m,t is the market return on day t. The parameters are estimated over a 120–250 day window before the event window begins. The Market Model removes systematic (market-wide) risk, making the ARs reflect firm-specific price movements.

Can I use CAR for portfolios of stocks (not just one stock)?

Yes — when studying a group of firms experiencing the same event type (e.g., all earnings surprises in a quarter), researchers compute the average CAR (ACAR) across all firms. This cross-sectional averaging reduces idiosyncratic noise and improves statistical power. The ACAR and its significance test follow the same logic as single-firm CAR but uses the cross-sectional standard deviation of CARs for the t-test.

Cumulative Abnormal Return Calculator

Calculates abnormal returns and cumulative abnormal return (CAR) per period for finance event studies.

How to Use This CAR Calculator

This cumulative abnormal return calculator computes AR and CAR for any event window — enter the actual stock return and expected return for each period in your event window. The calculator computes the abnormal return (AR) for each period and the cumulative abnormal return (CAR) across all periods. The default data shows a 5-day window (Day −2 through Day +2) centered on an event date.

You can add or remove periods using the + Add Period button. Expected returns are typically estimated using the Market Model or CAPM from a pre-event estimation window. Enter returns as percentages (e.g., −2.1 for −2.1%).

What Is Cumulative Abnormal Return?

Cumulative Abnormal Return (CAR) is the sum of all abnormal returns over an event window. An abnormal return (AR)measures how much a stock's actual return deviates from its expected return on a given day. CAR aggregates these deviations to capture the total price impact of an event — such as an earnings release, M&A announcement, dividend change, or regulatory decision.

For example, if a company announces a surprise earnings beat on Day 0, the CAR over Days [−2, +2] measures the cumulative price reaction starting from any pre-announcement leakage through the full post-announcement drift.

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CAR Formula and Calculation

The calculation proceeds in two steps:

Abnormal Return per period: AR(t) = R(i,t) − E[R(i,t)], where R(i,t) is the actual return of stock i on day t and E[R(i,t)] is the expected return estimated from a model.
Cumulative Abnormal Return: CAR(t₁, t₂) = Σ AR(t) from t = t₁ to t₂.

A positive CAR indicates the stock outperformed expectations over the event window; a negative CAR indicates underperformance. The economic interpretation is that the event contributed positively or negatively to firm value beyond market-wide movements.

Expected Return Models

Choosing the right expected-return model is critical to a valid event study. The most common models are:

Market Model: E[R] = α + β × R_m, where α and β are estimated from a pre-event regression. This is the standard in published academic research.
Constant Mean Return: E[R] = mean return from the estimation window. Simple but ignores systematic risk.
CAPM: E[R] = R_f + β × (R_m − R_f). Uses the risk-free rate and market risk premium. More theoretically motivated but similar results to the Market Model in practice.
Fama-French 3- or 5-Factor Model: Adds size (SMB), value (HML), and other factors. Used when beta alone may miss systematic risk exposures.

Event Window and Estimation Window

An event study has two distinct time windows:

Estimation window: The period before the event used to estimate model parameters (α, β). Typically 120–250 trading days, ending 10–60 days before the event to avoid contamination.
Event window: The period around the event date (Day 0) over which ARs and CAR are computed. Commonly [−2, +2], [−5, +5], or [−10, +10] trading days.

The gap between the estimation window and event window (the clean period) ensures that event-related price movements do not bias the expected-return model.

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Interpreting CAR Results

Interpreting CAR requires both economic and statistical assessment:

Sign and magnitude:A CAR of +5% over a [−2, +2] window suggests the event created roughly 5% in excess returns relative to the benchmark. Compare this to the event's nature — an acquisition announcement might show a large positive CAR for the target but a small negative CAR for the acquirer (bidder's curse).
Statistical significance: Use a t-test or standardized CAR test to determine if the CAR is significantly different from zero. See the financial modeling resources section for further reading.
Pre-event drift: A rising CAR in the days before Day 0 may indicate information leakage or insider trading.

Applications of CAR in Finance

CAR is used across a wide range of research and practitioner contexts. Academic finance uses event studies to test market efficiency — if markets are semi-strong efficient, all public information should be reflected in prices immediately, leaving no sustained CAR after an announcement. M&A research uses CAR to compare bidder vs. target wealth effects. Regulatory studies use CAR to evaluate how policy changes affect firm value. Corporate governance researchers use CAR around CEO appointments, dividend announcements, and stock buyback programs. See the dividend calculator to model dividend income expectations that can inform your expected return estimates.

Limitations of CAR Analysis

CAR assumes the expected-return model is correctly specified and that the event is cleanly identified with a precise date. Confounding events (other news on the same day), thin trading, market microstructure effects, and model misspecification can all distort CAR estimates. Cross-sectional variation in beta, firm size, and industry can also affect results. For robust inference, researchers often use portfolio approaches, bootstrapped confidence intervals, or non-parametric tests alongside the standard CAR framework.

Financial Disclaimer

This calculator is for educational and research purposes only. It is not investment advice. CAR calculations depend on the accuracy of your expected-return model and input data. Consult a qualified financial professional before making investment decisions based on event study results.