# 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**, e_{it}, is the difference between the observed return and the predicted return: e_{it} =R_{it}-K_{it}. Equivalently, e_{it} 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.