Event Study Template (Abnormal Returns, CAR)

Event Study: [Event type and sample, for example earnings announcements of listed toolmakers]

Write-up template for a short-window event study that measures how security prices react to an event: earnings announcements, mergers and acquisitions, dividend changes, rating changes, regulatory decisions or index inclusions. It covers the event definition, date verification, sample selection and confounding-event screen, estimation and event windows, the normal return model, abnormal and cumulative abnormal returns, parametric and non-parametric tests, cross-sectional analysis, robustness and the data and code record. The method follows the established event-study literature (Fama, Fisher, Jensen and Roll 1969; Brown and Warner 1985; MacKinlay 1997); the formulas are standard statistics written in our own notation. Replace every [bracketed] value and every row marked Example. This is a document format, not investment, financial or legal advice; the example firm "Halvard Tools" and all numbers are fictional.

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Contents

1. Event definition and hypotheses
2. Event dates and sources
3. Sample selection and confounding events
4. Estimation and event windows
5. Normal return model
6. Abnormal and cumulative abnormal returns
7. Test statistics
8. Results
9. Cross-sectional analysis
10. Robustness
11. Limitations and deviations
12. Data and code
13. Glossary and references
14. Standard and licence note

1. Event definition and hypotheses

1.1 Event definition

[Define the event, the information it conveys and the first moment the market could know it. Example: The event is the first public release of a firm's quarterly earnings, defined as the earliest timestamp of the earnings press release or regulatory filing, whichever comes first.]

1.2 Research question and hypotheses

1.3 Information leakage and anticipation

[State whether the event could be anticipated or leaked (scheduled earnings dates, merger rumours, regulatory consultation papers). This drives the choice of a pre-event window in section 4.]

2. Event dates and sources

2.1 Date verification

2.2 Date rules

• Use exchange trading calendars, not calendar days.
• Record the time zone of every timestamp and of the exchange.
• When the database date and the primary source disagree, use the primary source and log the correction.
• When an event falls on a non-trading day, day 0 is the next trading day.

Review the date file before you compute any return. Draw a random sample of at least 20 events and check each one by hand against the primary source; if more than one or two dates are wrong, check the whole file. Database announcement dates are often the date the record was entered, which can lag the true release by a day or more, and a one-day error moves the reaction out of a short window. For events released during trading hours, decide whether day 0 is the release day (daily data) or whether you need intraday data to separate the reaction from other news that day. Keep the hand-checked dates in a versioned file and cite it in section 12.

3. Sample selection and confounding events

3.1 Selection steps

3.2 Confounding-event screen

[List the news types you screened for (other earnings, dividends, mergers, management changes, rating changes, litigation) and the sources searched (newswire, filings database). State the screen window, usually the event window plus a margin of one or two days.]

3.3 Event clustering

[State whether events cluster in calendar time (many firms on the same date, or one regulatory event affecting a whole industry). Clustering makes abnormal returns cross-correlated and invalidates simple tests; see section 7.3.]

4. Estimation and event windows

Check each length: from minus 250 to minus 31 inclusive is 220 days; from minus 10 to minus 2 inclusive is 9 days; from plus 2 to plus 20 inclusive is 19 days.

5. Normal return model

5.1 Model choice

Selected model: [Example: market model with the value-weighted exchange index as the market proxy].

5.2 Market model

For security $i$ on day $t$ in the estimation window:

Estimate $\hat{\alpha}_i$, $\hat{\beta}_i$ and $\hat{\sigma}_{\varepsilon_i}$ by ordinary least squares on the estimation window. Record the market proxy, whether returns include dividends, and how missing days were treated.

6. Abnormal and cumulative abnormal returns

6.1 Definitions

6.2 Worked example: one event

Event EV-001, Halvard Tools, market model from section 5.2 ($\hat{\alpha} = 0.02\%$, $\hat{\beta} = 1.20$):

The CAR is 0.20% + 2.28% + 1.24% = 3.72%.

A simple test for this one event treats the daily abnormal returns as independent with the estimation-window residual standard deviation. The standard deviation of a three-day CAR is then $1.60\% \times \sqrt{3} = 2.77\%$, and the t-statistic is $3.72 / 2.77 = 1.34$. This ignores the small extra variance from estimating $\hat{\alpha}$ and $\hat{\beta}$; with 218 estimation days the adjustment is negligible, but state it in your write-up. One event rarely gives a significant result on its own; the power of an event study comes from aggregating across events.

6.3 Average abnormal returns by day

Plot the mean CAR from the start of the pre-event window to the end of the post-event window, with a confidence band, as Figure 1.

7. Test statistics

7.1 Cross-sectional t-test

Uses the dispersion of CARs across events, so it is robust to event-induced variance but assumes events are independent:

where $s_{CAR}$ is the cross-sectional standard deviation of the individual CARs.

Example: With N = 120 events, mean CAR(-1, +1) of 1.15% and a cross-sectional standard deviation of 4.20%, the standard error is $4.20\% / \sqrt{120} = 0.383\%$ and $t = 1.15 / 0.383 = 3.00$.

7.2 Choosing among tests

7.3 Clustering and dependence

[If many events share a date, form an equal-weighted portfolio of the affected firms and treat it as one event, or use a test that adjusts for cross-correlation. State which you used and why.]

Practical review points for the test section: report the test statistics you chose before seeing the results, not the most favourable ones; show the number of events behind every statistic, since events can drop out of some windows; and check that the parametric and non-parametric tests agree in sign. When they disagree, the mean is usually driven by a few large abnormal returns, and the reader needs to see them. With daily data and fewer than about 30 events, rely more on the rank and sign tests than on the t-tests, whose normal approximation is then weak. When events cluster on a few dates, say how many distinct calendar dates the sample covers; 120 events on 15 dates carry far less independent information than 120 events on 120 dates.

8. Results

8.1 Main window results

8.2 Economic magnitude

[Convert the mean CAR into a market value change for a typical firm: pre-event market capitalisation multiplied by the CAR. Example: for a firm worth EUR 2.0 billion, a 1.15% CAR is a gain of about EUR 23 million.]

8.3 Interpretation

[Relate the results to each hypothesis in section 1.2: supported, not supported, or inconclusive. Discuss the pre-event window for leakage and the post-event window for drift.]

Common errors in interpreting results: reading a positive mean CAR as support for a directional hypothesis when the sample mixes good and bad news (split by the sign of the surprise first); treating a significant pre-event CAR as leakage without checking for a confounding event; and reading post-event drift as inefficiency when the normal return model may simply be wrong over a longer window. For drift, show that the result survives a multi-factor model (ER-002) before drawing conclusions, and state the economic magnitude in money terms as in 8.2.

9. Cross-sectional analysis

EH-002 is a test of $\gamma_3 > 0$: a given surprise moves the price more when few analysts cover the firm. Without the interaction term the regression cannot test EH-002, because the main effect $\gamma_2$ only shifts the mean CAR of low-coverage firms whatever the sign of their surprise.

Use heteroskedasticity-robust standard errors and cluster by calendar date or industry when events cluster.

10. Robustness

11. Limitations and deviations

11.1 Limitations

[Discuss date uncertainty, thin trading, overlapping events, the market proxy, survivorship in the sample, and whether the event was partly anticipated so that the measured reaction understates the full effect.]

11.2 Deviation log

12. Data and code

Use the Replication Package README (academic/replication-package-readme) for the deposit and the Reproducibility Checklist (science/reproducibility-checklist) for a final self-check.

13. Glossary and references

13.1 Glossary

13.2 References

• Fama, Eugene F., Lawrence Fisher, Michael C. Jensen and Richard Roll (1969). The adjustment of stock prices to new information. International Economic Review 10(1).
• Patell, James M. (1976). Corporate forecasts of earnings per share and stock price behavior: empirical tests. Journal of Accounting Research 14(2).
• Brown, Stephen J. and Jerold B. Warner (1985). Using daily stock returns: the case of event studies. Journal of Financial Economics 14(1).
• Corrado, Charles J. (1989). A nonparametric test for abnormal security price performance in event studies. Journal of Financial Economics 23(2).
• Boehmer, Ekkehart, Jim Musumeci and Annette B. Poulsen (1991). Event study methodology under conditions of event-induced variance. Journal of Financial Economics 30(2).
• Scholes, Myron and Joseph Williams (1977). Estimating betas from nonsynchronous data. Journal of Financial Economics 5(3).
• Dimson, Elroy (1979). Risk measurement when shares are subject to infrequent trading. Journal of Financial Economics 7(2).
• Cowan, Arnold R. (1992). Nonparametric event study tests. Review of Quantitative Finance and Accounting 2(4).
• MacKinlay, A. Craig (1997). Event studies in economics and finance. Journal of Economic Literature 35(1), 13-39.
• Kolari, James W. and Seppo Pynnonen (2010). Event study testing with cross-sectional correlation of abnormal returns. Review of Financial Studies 23(11).

Related templates: Empirical Finance Paper (academic/empirical-finance-paper), Pre-Analysis Plan (academic/pre-analysis-plan) to fix the design in advance, Equity Research Report (finance/equity-research-report) for practitioner analysis of a single firm, and Finance Formula Sheet (finance/formula-sheet).

14. Standard and licence note

Based on the established academic event-study methodology described in the method papers listed in section 13.2. The formulas are standard statistics written in our own notation; no text, tables or examples were taken from those papers. Check the original papers and current methodological literature for test details before relying on them. All text and the fictional examples (Halvard Tools and the 120-event sample) are original, and example numbers are illustrative. Template licence: MIT.