Insights

CAR (Cumulative Abnormal Return): Definition

Alphanume Team · February 24, 2026

Glossary entry with computation and use.

Cumulative abnormal return (CAR) is the sum of daily abnormal returns over an event window. It is the standard summary statistic for event studies. Computing it correctly requires three components: defining the event window, computing daily abnormal returns within the window, and aggregating them. Each component has methodology choices that affect the resulting statistic.

The formula

For a security i over event window [t1, t2]:

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

Where AR(i, t) is the daily abnormal return computed per the chosen benchmark model. See abnormal return definition.

The worked example

Consider a 5-day event window (t1=0, t2=4) for a security with the following daily abnormal returns:

Day	AR (%)
0 (event day)	-3.0
1	-0.5
2	-0.8
3	0.3
4	-0.6

CAR(0, 4) = -3.0% + -0.5% + -0.8% + 0.3% + -0.6% = -4.6%

The security underperformed its benchmark by 4.6% over the 5-day window.

Window selection

Standard windows:

(-1, +1): immediate event reaction.
(0, +1): event day and next day.
(+1, +20): short-horizon drift.
(+1, +60): medium-horizon drift.
(+1, +252): annual-horizon drift.
(-5, +5): bracketing the event for leakage analysis.

Standard practice: report CARs at multiple windows so the time profile of the response is visible.

CAR vs BHAR

For long windows, buy-and-hold abnormal return (BHAR) is often preferred:

BHAR(i, t1, t2) = ∏(1+R(i,t)) − ∏(1+E[R(i,t)])

BHAR compounds rather than sums, which is more faithful to actual investor experience over multi-month windows. For short windows (under 30 days), CAR and BHAR produce similar results. For windows over 60 days, divergence becomes meaningful.

Cross-sectional aggregation

For a sample of N events:

Mean CAR = (1/N) × Σ CAR(i, t1, t2)

Standard cross-sectional inference:

Cross-sectional standard deviation.
T-statistic = Mean CAR / (Standard error of CAR).
Significance test against null of zero mean.

What CAR tells you

Did the event produce a statistically significant return effect?
What is the average magnitude of that effect?
How does it vary across event windows (event-day vs drift period)?
How does it vary across subsamples (size, sector, structure)?

What CAR doesn't tell you

Whether the effect is tradeable (gross of transaction costs and borrow).
The distribution beyond the mean (median, tails).
Causation (correlation with event doesn't prove event causes return).
Time-stability of the effect (mean estimate could mask period-by-period variation).

Reporting practices

Good practice:

Report mean and median.
Report cross-sectional standard deviation or IQR.
Report multiple windows.
Report subsample analysis.
Show time-path plot (cumulative average AR over event time).

The time-path plot is often more informative than any single window CAR — it reveals the shape of the response and helps identify when the effect concentrates.

Common errors

Confusing CAR with raw return. CAR is benchmark-adjusted. Raw return is not. They can have different signs.
Using mean as representative of any single event. Cross-sectional variance is large; the mean characterizes the population, not the individual.
Ignoring heavy tails. Event-window returns often have heavy tails; standard t-tests can produce misleading inference.
Selecting windows after the fact. Testing many windows and reporting the significant ones is p-hacking.

For dilution-event research specifically

Standard reporting:

(0, +1): captures immediate market reaction to offering announcement.
(+1, +20): captures short-horizon drift.
(+1, +60): captures the standard drift window.
(+1, +120): captures longer-horizon effects.

Subsample analysis by offering structure, size, and issuer characteristics adds substantial information.