Event studies: how to measure and test price reactions to events
An event study measures how strongly share prices react to an event: quarterly results, a takeover, a dividend cut or inclusion in an index. It compares the actual return with the return that would have been expected without the event, and tests whether the difference across many cases is more than chance. Here you will find the complete procedure, with the estimation and event windows, the market model, abnormal and cumulative abnormal returns, the usual tests and a fully worked example.
The idea: price reaction against a normal return
In an informationally efficient market, the effect of news shows up quickly in the price. But if you want to measure the price reaction, you have to strip out what would have happened anyway. On a day when the whole market falls by 2%, a loss of 1% is good news. The difference between the actual and the normal return is called the abnormal return. The basic approach was set out by Fama et al. (1969) using stock splits and by Ball and Brown (1968) using annual earnings; MacKinlay (1997) gives an overview of today's procedure. A first simple example appears in the article on insider trading, and an application in the article on the index effect.
Timeline: estimation window and event window
Time is counted relative to the event day τ = 0. In the estimation window before the event, the model for the normal return is estimated; in the event window, the abnormal return is measured. There is often a gap between the two so that rumors or leaked information do not distort the estimate. A post-event window after the event window shows whether the reaction continues or reverses.
| Window | Typical choice with daily data | Purpose |
|---|---|---|
| Estimation window | about 120 to 250 trading days, ending a few days before the event | estimate α, β and the dispersion of the residuals |
| Event window | one to a few days around τ = 0, e.g. (−1, +1) or (−5, +5) | measure abnormal returns; absorb uncertainty about the exact timing |
| Post-event window | a few weeks to months | check for continuation or reversal |
An example of the set-up: in their simulations, Brown and Warner (1985) estimated the model over 239 days (τ = −244 to −6) and measured in an event window from −5 to +5. The longer the estimation window, the more precise the parameters, as long as the stock's risk does not change over that period.
Models for the normal return
mean-adjusted: E[R_it] = R̄_i
market-adjusted: E[R_it] = R_mt
market model: R_it = α_i + β_i × R_mt + ε_it
abnormal return: AR_iτ = R_iτ − (α̂_i + β̂_i × R_mτ)- R_it, R_mt
- return of stock i and of the market index on day t
- α̂_i, β̂_i
- estimated in the estimation window by ordinary least squares regression
- ε_it
- residual with dispersion σ_i; it determines how much chance there is in an abnormal return
The market model is the standard: it removes the common market movement and so reduces the dispersion of the abnormal returns, which gives the tests more power. Multi-factor models such as the Fama-French model usually add little over short windows, but a great deal over long horizons. According to Brown and Warner (1980), simple methods perform hardly worse than elaborate ones, and with daily data the market model is well specified (Brown and Warner 1985).
Worked example: one event step by step
So that everything can be checked by hand, the estimation window here is only ten days long; in practice you would use many times that. Daily returns in % (illustrative figures):
The estimation error is added because α̂ and β̂ are themselves uncertain. For a single day, following MacKinlay (1997):
Var(AR_iτ) = σ_i² × (1 + 1/L₁ + (R_mτ − R̄_m)² / Σ(R_mt − R̄_m)²)
Var(CAR_i) = σ_i² × 1ᵀ (I + X* (XᵀX)⁻¹ X*ᵀ) 1- L₁
- length of the estimation window
- X, X*
- constant and market return in the estimation and event window respectively
- 1
- vector of ones over the days of the event window
With 250 estimation days the addition is small; with ten days, as here, it raises the standard deviation of the CAR from 1.76% to 2.01%.
Many events: averaging and testing
Across N events, the abnormal returns are averaged for each event day (AAR) and summed over the window to give the cumulative abnormal return CAAR. There are several ways to test it:
cross-sectional t-test: t = CAAR / (s(CAR_i) / √N)
Patell: SCAR_i = CAR_i / σ(CAR_i), Z = Σ SCAR_i / √(N × (L₁ − 2) / (L₁ − 4))
BMP: t = mean SCAR / (s(SCAR_i) / √N)- s(·)
- standard deviation across events
- σ(CAR_i)
- standard deviation of the CAR from the estimation window of event i
- SCAR_i
- standardized CAR: events involving calm stocks count for more
The test of Patell (1976) standardizes each CAR by its own dispersion from the estimation window, so that volatile stocks receive less weight. The test of Boehmer et al. (1991) (BMP) standardizes in the same way but estimates the dispersion of the standardized values cross-sectionally, and so remains valid when the event itself increases volatility. The rank test of Corrado (1989) replaces the abnormal returns with their ranks over the entire period and therefore does not require a normal distribution; the sign test only counts how many reactions were positive.
The t-test and the BMP test use 5 degrees of freedom (critical value 2.57), Patell uses the normal distribution, and the sign test the binomial distribution (two-sided). The chart, with illustrative figures for good and bad news, shows how such averages build up over time.
Illustrative figures, schematic: information leaks out before the event, the price adjusts on the event day and the day after, and the CAAR then stays almost unchanged. This is what a quick reaction in an efficient market looks like.
Advanced: event-induced variance and cross-sectional correlation
Two assumptions of the simple tests are often violated. First, an event frequently increases volatility. In the simulations of Brown and Warner (1985), with the variance doubled on the event day, the usual tests rejected in about 12.0% of cases even though there was no effect. That is almost three times as often as the 4.4% without the increase in variance. This is exactly what the BMP test is designed for. Second, events often fall on the same days, such as an industry's quarterly results or the changes from an index review. The abnormal returns are then correlated across the cross-section, and even a small correlation leads to far too many rejections (Kolari and Pynnönen 2010). The authors correct the BMP test using the mean correlation r̄:
t_KP = t_BMP × √((1 − r̄) / (1 + (N − 1) × r̄))- r̄
- mean correlation of the abnormal returns between events
- N
- number of events
Long horizons: BHAR and calendar-time portfolios
Over months and years, the sum of abnormal returns is misleading because it ignores compounding. The usual measure is then the buy-and-hold abnormal return (BHAR): the compounded return of the stock minus the compounded return of a benchmark portfolio.
BHAR_i = Π (1 + R_it) − Π (1 + R_bt)- R_bt
- return of the benchmark portfolio, e.g. firms of similar size and similar book-to-market ratio
Barber and Lyon (1997) show that tests over one to five years against a market index are misspecified; control firms of similar size and similar book-to-market ratio largely fix this. Lyon et al. (1999) recommend BHAR with carefully constructed benchmark portfolios and a skewness-adjusted t-test or, alternatively, calendar-time portfolios: each month, all stocks with an event in the preceding years are combined into a portfolio, and its return is regressed on factors; the alpha is the abnormal return. Their conclusion: in random samples both approaches work, in non-random samples often not. Mitchell and Stafford (2000) found hardly any reliable long-term excess returns for takeovers, seasoned equity offerings and share buybacks once cross-sectional dependence was taken into account.
What the research shows
Event studies are among the most important tools of empirical finance. Fama et al. (1969) showed that prices adjust quickly to the information around stock splits, and Ball and Brown (1968) that much of the information in annual earnings is already in the price before publication. Patell (1976) examined 336 voluntarily published earnings forecasts from 1963 to 1967 and found clear price adjustments; his standardized test is still widely used today. Brown and Warner (1985) tested the methods on 250 samples of 50 stocks each: the market model detected an abnormal return of 1% on the event day in 80.4% of cases. With short windows and no clustered event dates, the standard methods are therefore reliable; the difficulties come from increases in variance, cross-sectional correlation and long horizons (Boehmer et al. 1991; Kolari and Pynnönen 2010; Barber and Lyon 1997).
Limitations and common mistakes
- Wrong event day: does the day of the announcement count, or the first trading day after it? News released after the market close only has an effect the next day. A window of (−1, +1) absorbs this kind of uncertainty.
- Contaminated estimation windows: if another event falls within the estimation window, β and σ are biased.
- Clustered event dates: quarterly results or index reviews on the same day create cross-sectional correlation; without a correction, effects look more certain than they are.
- Selection of events: events with a large reaction are more likely to make it into databases and the news. If you test many subgroups, you will find some that are significant by chance (multiple testing).
- Long horizons: small errors in the model of the normal return add up over years. Here the results are particularly sensitive to the benchmark and the test statistic.
- Replicability: an abnormal return from the event day onwards could only be earned by someone who knew in advance. For investors, what counts is the reaction from the moment they know the news, after costs.
How Portfolio Lab calculates
Portfolio Lab has no dedicated tool for event studies. You can, however, put the building blocks together: in Settings, set the data frequency to daily, set up the stock in the Backtest as a portfolio with 100%, and choose the market index as the benchmark. With a benchmark, the metrics show beta, alpha and R² from the same regression of excess returns, from six common periods onwards (metrics methodology). If you select only the estimation window as the period in the settings, you get the beta for that window; because the app regresses excess returns over the risk-free rate and annualizes the alpha, the result differs slightly from the market model with raw returns. The CSV export “Period returns” then contains the daily returns of the stock and the benchmark, with which you can calculate AR, CAR and the tests in a spreadsheet. For monthly data and factor models, the Factors tool is suitable, with t-statistics, optionally using Newey-West.
Frequently asked questions
What is an event study?
A method that measures how prices react to an event: the actual return is compared with a normal return that a model provides from the period before the event. The difference (the abnormal return) is averaged across many events and tested.
How do you calculate an abnormal return?
In the market model: actual return minus (α + β × market return), with α and β from a regression in the estimation window. Summed over the event window, this gives the cumulative abnormal return (CAR).
How long should the estimation window be?
With daily data, usually 120 to 250 trading days, with some distance from the event. Shorter windows make α and β less precise and increase the standard deviation of the abnormal returns.
What is the difference between CAR and BHAR?
The CAR sums abnormal returns, while the BHAR compares compounded returns of the stock and a benchmark portfolio. Over days the two are almost the same; over years the BHAR better measures what an investor would actually have achieved by buying and holding.
Which test should you use for an event study?
Often the cross-sectional t-test and the BMP test, which remains valid even when volatility rises on the event day, supplemented by a rank test such as Corrado's. If events fall on the same days, a correction for cross-sectional correlation is needed.
How many events does an event study need?
The smaller the effect and the greater the dispersion, the more. In simulations with samples of 50 stocks, the market model detected an abnormal return of 1% on the event day in about 80% of cases; smaller effects require considerably more cases.
Literature
- Ball, Ray; Brown, Philip (1968): An Empirical Evaluation of Accounting Income Numbers. Journal of Accounting Research 6 (2), pp. 159–178. doi:10.2307/2490232
- Barber, Brad M.; Lyon, John D. (1997): Detecting long-run abnormal stock returns: The empirical power and specification of test statistics. Journal of Financial Economics 43 (3), pp. 341–372. doi:10.1016/S0304-405X(96)00890-2
- Boehmer, Ekkehart; Musumeci, Jim; Poulsen, Annette B. (1991): Event-study methodology under conditions of event-induced variance. Journal of Financial Economics 30 (2), pp. 253–272. doi:10.1016/0304-405X(91)90032-F
- Brown, Stephen J.; Warner, Jerold B. (1980): Measuring security price performance. Journal of Financial Economics 8 (3), pp. 205–258. doi:10.1016/0304-405X(80)90002-1
- Brown, Stephen J.; Warner, Jerold B. (1985): Using daily stock returns: The case of event studies. Journal of Financial Economics 14 (1), pp. 3–31. doi:10.1016/0304-405X(85)90042-X
- Corrado, Charles J. (1989): A nonparametric test for abnormal security-price performance in event studies. Journal of Financial Economics 23 (2), pp. 385–395. doi:10.1016/0304-405X(89)90064-0
- Fama, Eugene F.; Fisher, Lawrence; Jensen, Michael C.; Roll, Richard (1969): The Adjustment of Stock Prices to New Information. International Economic Review 10 (1). doi:10.2307/2525569
- Kolari, James W.; Pynnönen, Seppo (2010): Event Study Testing with Cross-sectional Correlation of Abnormal Returns. Review of Financial Studies 23 (11), pp. 3996–4025. doi:10.1093/rfs/hhq072
- Lyon, John D.; Barber, Brad M.; Tsai, Chih-Ling (1999): Improved Methods for Tests of Long-Run Abnormal Stock Returns. The Journal of Finance 54 (1), pp. 165–201. doi:10.1111/0022-1082.00101
- MacKinlay, A. Craig (1997): Event Studies in Economics and Finance. Journal of Economic Literature 35 (1), pp. 13–39. Source
- Mitchell, Mark L.; Stafford, Erik (2000): Managerial Decisions and Long-Term Stock Price Performance. The Journal of Business 73 (3), pp. 287–329. doi:10.1086/209645
- Patell, James M. (1976): Corporate Forecasts of Earnings Per Share and Stock Price Behavior: Empirical Test. Journal of Accounting Research 14 (2), pp. 246–276. doi:10.2307/2490543
This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.