Event Study Analysis: CLM Chapter 4

Definition:
An event study attempts to measure the valuation effects of a corporate event, such as a merger or earnings announcement, by examining the response of the stockprice around the announcement of the event.
One underlying assumption is that the market processes information about the event in an efficient and unbiased manner (more on this later).

Event Study Analysis
The steps for an event study are as follows:
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Event Definition
Selection Criteria
Normal and Abnormal Return Measurement
Estimation Procedure
Testing Procedure
Empirical Results
Interpretation

Event Study Analysis
The time line for a typical event study is shown below in event time:

T0

T1

0

T2

T3

The interval T0-T1is the estimation period
The interval T1-T2 is the event window
Time 0 is the event date in calendar time
The interval T2-T3 is the post-event window
There is often a gap between the estimation and event periods Models for measuring normal performance
In an event study we wish to calculate the abnormal performance associated with an event. To do so, we need a model for normal returns.
– For example: Suppose a firm announces earnings and the stock price rises by 3%, but the market also went up 2% that day. How much of the 3% rise should be attributed to the announcement of earnings. • Fortunately, over short event windows (one or two days) the choice of normal return models usually has little effect on the results Statistical or economic models for normal returns? Statistical models of returns are derived purely from statistical assumptions about the behavior of returns
Economic models apply restrictions to a statistical model that result from assumptions about investor behavior motivated by theory (i.e., CAPM)
– If the restrictions are true, we can calculate more precise measures of abnormal returns.

Statistical models of returns
Assume that returns on stocks are jointly multivariate normal and are distributed iid through time.
A1: Let Rt be an (Nx1) vector of asset returns for calendar time period t. Rt is independently multivariate normally distributed with mean : and covariance matrix S for all t.
– This assumption is sufficient for constant mean return and market model return models to be correctly specified.

Constant mean return model
For each asset i, the constant mean return model assumes that asset returns are given by:
Rit = µ i + ξ it , where
E[ξ it ] = 0 and Var[ξ it ] = σ ξ2i
Brown and Warner (1980, 1985) find that the simple mean returns model often yields results similar to those of more sophisticated models because the variance of abnormal returns is not reduced much by choosing a more sophisticated model

Market model (the most popular in practice)
For each asset i, the market model assumes that asset returns are given by:
Rit = α i + β i Rmt + ε it , where
E[ε it ] = 0 and Var[ε it ] = σ ε2i
In this model Rmt is the return on the market portfolio, and the model’s linear specification follows from the assumed join normality of returns.
– In applications, a broad-based stock index, such as the S&P 500 or the CRSP equal- or value-weighted indices are used as the market portfolio Market model
Note that when $i = 0, the market model collapses to the constant mean return model
The market model represents a potential improvement over the constant mean return model by removing the portion of the return that is related to the return on the market portfolio The benefit of using the market model will depend on the
R2 of the regression
– The higher the R2, the greater is the reduction in the variance of abnormal returns, which increases the power to detect abnormal performance Estimating the market model
First, index the returns for all securities in event time, then use data from the estimation window (T0+1 to T1) to estimate the parameters of the market