Insights

What Is Cumulative Abnormal Return (CAR)?

Alphanume Team · April 26, 2026

The headline statistic for event studies — what it measures, what it doesn't, and how to interpret it.

Cumulative abnormal return (CAR) is the sum of daily abnormal returns over an event window. It is the standard summary statistic for event studies and the primary output reported in academic and practitioner research on event-driven anomalies. The mechanics are straightforward; the interpretation is more subtle.

The definition

For a security i over an event window from t₁ to t₂:

CAR(i, t₁, t₂) = Σ AR(i, t) for t in [t₁, t₂]

Where AR(i, t) is the daily abnormal return — see how to compute abnormal returns.

For a sample of events, the sample-mean CAR is the average of individual-security CARs.

Event windows

Standard windows for event studies:

(−5, +5): 11-day window centered on the event. Useful for detecting pre-event leakage and immediate post-event reaction.
(0, +1): Event day plus next day. The immediate market reaction.
(+1, +20): Day-after through 20 trading days. Standard short-horizon drift window.
(+1, +60): Day-after through 60 trading days. Medium-horizon drift.
(+1, +252): 12-month post-event window. Long-horizon drift.

Reporting CARs across multiple windows is standard practice — it characterizes the time profile of the response.

CAR vs raw cumulative return

CAR is the abnormal — benchmark-adjusted — measure. Raw cumulative return is total return without adjustment.

A stock that gained 5% over the event window when the market also gained 5% has zero abnormal return; the CAR is roughly zero.
The same stock against a market that declined 5% over the window has 10% abnormal return.
CAR isolates the event-specific component from the broader market movement.

For investment-relevant interpretation, both metrics matter — but CAR is the cleaner measure of whether the event itself drove a return.

CAR vs BHAR

Two ways to aggregate over multiple days:

CAR: Arithmetic sum of daily abnormal returns. Easy to interpret; appropriate for short windows.

BHAR (buy-and-hold abnormal return): Compound the actual returns, compound the benchmark returns, take the difference. More appropriate for long windows.

For windows under 60 days, CAR and BHAR produce similar results. For longer windows, BHAR can differ meaningfully — and is generally preferred as a more faithful representation of investor experience.

What CAR can and can't tell you

CAR can answer:

Did the event produce a statistically significant return effect?
What is the average magnitude of that effect?
How does the effect vary over the event window?
How does the effect vary across subsamples conditioned on event or firm characteristics?

CAR cannot answer:

Whether the effect is tradeable. CARs are gross of transaction costs, borrow costs, and other implementation frictions — see borrow-cost-adjusted return.
Whether the effect is causal. Correlation with the event does not prove the event drove the return.
Distribution properties beyond the mean. The mean CAR may be positive while the median is negative if there are a few large outliers.

Reporting practices

Good practice in reporting CARs:

Report mean and median across the sample. They can differ substantially.
Report cross-sectional standard deviation or interquartile range.
Report at multiple windows.
Report t-statistics or other significance measures.
Show the time path of cumulative average AR (event-time plot) — this often reveals more than a single window CAR.
Report by sub-samples (event type, firm size, etc.) to characterize heterogeneity.

Pitfalls in interpretation

Treating average CAR as representative of any single event. The variance across events is typically large. A 5% mean CAR may have a 25% standard deviation.
Ignoring tail risk. Mean CAR is dominated by extreme observations. Robust statistics (median, winsorized mean) are often more informative.
Inferring causality. An event may correlate with returns without driving them. Confounding variables and selection effects need to be considered.
Mixing parametric inference with non-normal returns. Standard t-tests assume normality. Event-window returns frequently have heavy tails and skewness; non-parametric tests are often more reliable.