Event Study

A financial event study compares observed returns around news with a model-based benchmark to measure abnormal returns, subject to timing and inference limits.

An event study, in financial markets, compares a security’s observed returns around a defined event with the returns estimated by a normal-return model. The difference is an abnormal return. It helps researchers examine market reactions to news, but does not automatically prove that the event caused the entire difference.

This article covers short-horizon return event studies, such as an analysis around an earnings release or merger announcement. The broader term also appears in research using other outcomes and statistical designs.

Key Takeaways

  • Abnormal return is relative to a specified model, not simply a rise or fall in the share price.
  • The announcement timestamp, return interval, estimation sample, and event window must be defined.
  • Cumulative abnormal return adds abnormal returns over the window; it is not the stock’s compounded holding-period return.
  • A large or statistically significant result does not, by itself, establish causation or a repeatable trading opportunity.

Define the Event and the Return Window

The event date identifies the news being studied. The event window includes the return intervals being examined, while the estimation window supplies observations used to fit the normal-return model. Separating these windows helps avoid fitting that model to the very reaction being measured. MacKinlay’s Event Studies in Economics and Finance describes this framework.

Suppose a fictional company releases results after the exchange closes on Tuesday. With close-to-close daily returns, label Wednesday’s trading session day 0: its return interval includes the first opportunity for the announcement to affect the next closing price. Check holidays, time zones, and the actual release time rather than assigning dates mechanically.

One illustrative design is:

SegmentTrading days relative to day 0Purpose
Estimation window-130 through -11Fit the normal-return model using 120 observations
Gap-10 through -2Leave 9 observations between model fitting and the event window
Event window-1 through +1Examine 3 daily returns around the announcement

These lengths are assumptions for this example, not a universal standard. A wider window may capture anticipation or delayed reaction, but also admits more unrelated news. A narrow window can miss a response that began before the selected timestamp.

Estimate Normal and Abnormal Returns

A simple market model estimates the relationship between the stock’s returns and a chosen market benchmark:

$$ \widehat{R}_{i,t}=\widehat{\alpha}_i+\widehat{\beta}_i R_{m,t} $$

Here, the estimated normal return uses an intercept, alpha, plus the stock’s estimated market sensitivity, beta, multiplied by the market return for the same interval. The coefficients are fitted in the estimation window; the market return is observed during the event window.

Abnormal return is the difference between the observed stock return and this fitted normal return:

$$ AR_{i,t}=R_{i,t}-\widehat{R}_{i,t} $$

Wharton’s WRDS event-study implementation illustrates this calculation and alternative benchmark models. The simple market model shown here uses returns directly; it is not automatically a CAPM regression of excess returns.

Worked Example: Three Days Around an Announcement

Assume the fictional company’s pre-event estimates are daily alpha of 0.05% and beta of 1.20. These are supplied example inputs, not estimates from a real dataset. Use arithmetic daily total returns with consistent currency, dividend, and split treatment for both stock and benchmark.

DayMarket returnStock returnEstimated normal returnAbnormal return
-1+0.50%+0.40%+0.65%-0.25%
0-1.00%+2.00%-1.15%+3.15%
+1+0.25%-0.10%+0.35%-0.45%

On day 0, the model gives 0.05% plus 1.20 times -1.00%, or -1.15%. The stock actually returns +2.00%, so it exceeds the modeled normal return by 3.15 percentage points.

The positive abnormal return is therefore not just the stock’s 2% gain. It also reflects the fact that the benchmark-based model estimated a negative return that day.

Cumulative Abnormal Return Is Additive

Cumulative abnormal return, or CAR, sums the abnormal returns in the chosen window:

$$ CAR_{i,[-1,+1]}=\sum_{t=-1}^{+1}AR_{i,t} =-0.25\%+3.15\%-0.45\%=2.45\% $$

The example’s three-day CAR is +2.45%. It summarizes deviations from the model, not the actual return earned by holding the stock.

Using the stock-return column, its compounded three-day total return is:

$$ (1.004\times1.02\times0.999)-1=0.02305592\approx2.31\% $$

The two numbers answer different questions. Compounding the daily abnormal returns would not turn them into an actual buy-and-hold stock return either.

What the Result Does and Does Not Establish

Direction: The positive CAR means the stock outperformed this model across the specified three days.

Statistical uncertainty: The table alone cannot establish significance. An analysis needs an appropriate estimate of sampling variability, including uncertainty in the fitted benchmark. No estimation residuals or standard errors are supplied here, so there is no basis for reporting a t-statistic or p-value.

Economic importance: Whether the estimated difference matters depends on the question and its uncertainty. A detectable return difference is not necessarily large enough to cover trading costs.

Causation: Other information released in the same window can contribute to the measured return. A significant result does not identify the announcement as its sole cause.

The American Statistical Association’s statement on p-values explains why significance is not a measure of effect size or the probability that a hypothesis is true. Report the estimate and its uncertainty, not only whether a threshold was crossed.

Risks and Limitations

  • Overlapping news: An earnings release accompanied by a dividend change measures the market response around a package of information unless the design can distinguish the announcements.
  • Anticipated information: A well-telegraphed announcement may produce little new reaction. A small CAR does not show that the underlying business development is unimportant.
  • Unstable benchmark exposure: If the event changes the company’s market sensitivity, a pre-event beta may no longer describe its normal returns. Federal Reserve researchers examine this problem in Level Shifts in Beta, Spurious Abnormal Returns and the TARP Announcement.
  • Data and timing errors: Unadjusted stock splits, stale prices, or mismatched market closing times can create misleading differences.
  • Selective reporting: Trying many windows or models and reporting only a favorable result makes the evidence look stronger than a fully disclosed analysis would.

For a study of many firms, explain how events are pooled and how dependence between observations is handled. Firms responding to the same policy announcement are not necessarily independent observations.

This explanation is educational, not personalized investment advice. Observing a reaction after publication does not mean a reader could have traded before it occurred or can profit from the next announcement.

  • Stock Analysis: The broader evaluation of shares using business information, valuation, and market data.
  • Regression Analysis: Estimates relationships such as the market model used to construct normal returns.
  • Beta: Measures sensitivity to a selected market benchmark and can change across periods.
  • Market Efficiency: Concerns how prices incorporate information; event studies can investigate the timing of adjustment.
  • Total Return: Includes price changes and distributions, distinct from a model-relative abnormal return.

Knowledge Check

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FAQs

Can a falling stock have a positive abnormal return?

Yes. If a stock returns -1% while its modeled normal return is -2%, its abnormal return is +1%. It performed better than the model implied, but a shareholder still experienced a negative stock return over that interval.

Does an event study require intraday data?

No. Daily returns can be used when they fit the research question and event timing. Intraday data can narrow the interval around an announcement, but also require reliable timestamps and attention to trading conditions. Higher frequency does not automatically make a study causal or more reliable.
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