Event Studies

Event Studies

Event studies are generally employed by financial economists to specify and test interesting economic hypotheses. Systematically nonzero abnormal security returns that persist after a particular type of corporate event are inconsistent with market efficiency. Common examples include earnings, share buybacks, mergers, and capital issuances.

Abnormal Returns and Unconditional Expected Returns

If the earnings disclosures have information content, higher than expected earnings should be associated with increases in the value of the equity and lower than expected earnings with decreases. Specifically, the abnormal return, eit, is the difference between the observed return and the predicted return: eit =Rit-Kit. Equivalently, eit is the difference between the return conditional on the event and the expected return unconditional on the event. A model of normal returns (i.e., expected returns unconditional on the event but conditional on other information) must be specified before an abnormal return can be defined. A variety of expected return models (e.g., market model, constant expected returns model, capital asset pricing model) have been used in event studies. The cumulative average residual method (CAR) uses as the abnormal performance measure the sum of each month’s average abnormal performance. Instead, the buy-and-hold method (BHAR) first compounds each security’s abnormal returns and then uses the mean compounded abnormal return as the performance measure. Specifically, the Standardized Unexpected Earnings (SUE) in a given quarter is equal to X – E(X) divided by σ, the standard deviation of earnings surprises over the last eight quarters. Instead, the Earnings Announcement Return (EAR) is the difference between the compounded return of a stock and the compounded return of its benchmark over a three-day window centered on the announcement date.

Theoretical Considerations

According to Kothari and Warner, event studies literature focus on the mean of the distribution of abnormal returns because the specific null hypothesis to be tested is whether the mean abnormal return at time t is equal to zero. Indeed, the aim is to understand whether the event is, on average, associated with a change in security holder wealth and if one is testing economic models and alternative hypotheses that predict the sign of the average effect. It is also of interest to examine whether mean abnormal returns for periods around the event are equal to zero. First, if the event is partially anticipated, some of the abnormal return behavior related to the event should show up in the pre-event period. Second, in testing market efficiency, the speed of adjustment to the information revealed at the time of the event is an empirical question. Both CAR and buy-and-hold methods test the null hypothesis that mean abnormal performance is equal to zero. Note that event study tests are well-specified only to the extent that the assumptions underlying their estimation are correct. This poses a significant challenge because event study tests are joint tests of whether abnormal returns are zero and of whether the assumed model of expected returns (i.e. the CAPM, market model, etc.) is correct.

An implementation in Python

Aflac Incorporated (AFL), provides voluntary supplemental health and life insurance products including products designed to protect individuals from depletion of assets comprising accident, cancer, critical illness/care, hospital indemnity, fixed-benefit dental, and vision care plans; and loss-of-income products, such as life and short-term disability plans in the United States. In Japan, the firm sells product including cancer plans, general medical indemnity plans, medical/sickness riders, care plans, living benefit life plans, ordinary life insurance plans, and annuities in Japan.

The notebook shows the last earnings dates with analysts’ estimation and actual values and plots abnormal and cumulative abnormal returns for such dates. Finally, volatility is estimated.

The same study is performed on another security showing a different behavior before the announcement date. Note that a Pre-Announcement Strategy can be implemented trading 2-8 days in advance of the announcement. General Motors Company (GM) designs, builds, and sells cars, trucks, crossovers, and automobile parts worldwide. Further, the company provides automotive financing services. General Motors Company was founded in 1908 and is headquartered in Detroit, Michigan.


Event studies are sensitive to sample size and firm characteristics. Daily (and sometimes intraday) data allow for more precise measurement of abnormal returns and announcement effects. For instance, the event will be the earnings announcement and the event window will include the one day of the announcement. However, the period of interest is often expanded to multiple days, including at least the day of the announcement and the day after the announcement to capture the price effects of announcements occurring after the stock market closes on the announcement day. Therefore, in an event study using daily data and the market model, the market model parameters could be estimated over the 120 days prior to the event. However, the event period itself is not included in the estimation period to prevent the event from influencing the normal performance model parameter estimates. The absence of any overlap and the maintained distributional assumptions imply that the abnormal returns and the cumulative abnormal returns will be independent across securities. However, event-time clustering renders the independence assumption for the abnormal returns in the cross-section incorrect. This would bias the estimated standard deviation estimate downward and the test statistic upward. To address the bias, the significance of the event-period average abnormal return can be gauged using the variability of the time series of event portfolio returns in the period preceding or after the event date.


Liquidity generally reflects the ability to buy or sell sufficient quantities, quickly, at low trading cost and without impacting the market price too much. In general, post-earnings-announcement drift is prevalent mainly in stocks that are relatively illiquid. Researchers have observed that, over a three day period around the next two earnings announcements, i) the effective bid-ask spread increases, ii) the buy and sell trade sizes increase marginally, and iii) the order imbalance increases. The increase in the effective bid-ask spread suggests that trading costs increase, whereas the moderate increase in trade sizes suggests that mainly uninformed or noise traders are active. In other terms, market makers demand higher expected returns prior to earnings announcements because of increased inventory risks that stem from holding net positions through the release of anticipated earnings news. Thus, portfolio return reversals increase enormously during earnings announcements relative to non-announcement periods, indicating that market makers demand greater compensation for providing liquidity ahead of anticipated information events.


Bartov et al (2000) show that the PEAD drift is lower for companies with higher proportions of institutional investors, who are more sophisticated and less prone to under-reactions. Mikhail et al (2003) provide evidence that the drift is smaller when companies are followed by more experienced analysts. Mendenhall (2003) shows that the drift is stronger for firms subject to higher arbitrage risks. Short-window market reactions to revenue surprises are stronger than those of expense surprises, due to the greater persistence of revenue surprises and the greater heterogeneity of expenses. Thus, when the sales surprise is in the same direction as the earnings surprise, the earnings surprise is more likely to persist in future periods and a greater drift in prices is expected when investors obtain future information confirming the initial earnings. For instance, the proportion of institutional investors can be proxied by aggregating the number of shares held by all managers at the end of quarter t-1. Consistent with Mendenhall (2003), arbitrage risk is estimated as one minus the squared correlation between the monthly return on firm j and the monthly return on the S&P 500 Index, both obtained from CRSP. The correlation is estimated over the 60 months ending one month prior to the calendar quarter-end. The arbitrage risk is the percentage of return variance that cannot be attributed to (or hedged by) fluctuations in the S&P 500 return. The average monthly trading volume has been used by prior studies of the drift as a control in the association between the CAR and SUE. It is expected that a higher trading volume may reduce the costs of arbitrage and are therefore expected to have a negative association with CAR.

Other Events with Informational Content

According to Kummer, the wealth effect of mergers and acquisitions, given a successful takeover, results in large and positive (1.14%) abnormal returns of the targets whereas the abnormal returns of the acquirer are close to zero.

When a corporation announces that it will raise capital in external markets there is, on average, a negative abnormal return (-2.7%). Firms announcing an equity issue show a negative two-day average abnormal return (-3.6%). When a firm decides to use straight debt financing, the average abnormal return is closer to zero (-0.23%).

Companies announcing share repurchase programs are under no obligation to carry them out; in general, past repurchases are considered to assess the firm’s credibility. Note that managers are less likely to launch repurchases unless they believe that the expected performance of the firms stock is better than expected by the market, even after the repurchase program is announced (Yook, 2010). Given a confirmed announcement, the abnormal returns are large and positive (2.15%).

Initial Public Offering (IPO) generated statistically significant abnormal price performances in short-term analyses and longer-term analyses. Specifically, between the offer and initial trading of shares, abnormal performance reaches 11%, whereas the initial trading performance in the first 1-2 days is about 3.44%.


Khotari, S. P. and Warner, J. B. (2006). Econometrics of Event Studies

Mac Kinlay, A. C. (1997). Event Studies in Economic and Finance

Chordia, Goyal, Sadka, Shivakumar (2006). Liquidity and the Post-Earnings-Announcement Drift

So, Wang (N/A). News-driven return reversals: Liquidity provision ahead of earnings announcements

Livnat, J. (2003). Post-Earnings-Announcement Drift: The Role of Revenue Surprises

Smith, Z. (2009). An Empirical Analysis of Initial Public Offering (IPO) Performance

Brandta, M. W., Kishoreb, R., Santa-Clarac P., Venkatachalam, M. (2008). Earnings Announcements are Full of Surprises

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

error: Hey, drop me a line if you want some content!!