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2023 | OriginalPaper | Chapter

11. Event Studies

Authors : James W. Kolari, Seppo Pynnönen

Published in: Investment Valuation and Asset Pricing

Publisher: Springer International Publishing

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Abstract

One of the most common applications of asset pricing models is event studies. Today, event studies not only provide evidence on the question of market efficiency but how investors perceive different kinds of information that will impact stock prices. Asset pricing models are used to measure abnormal returns not explained by systematic risk factors. A large body of literature has evolved to investigate the abnormal returns of stocks in response to important news events, including both firm-level announcements and macroeconomic announcements. Short-run and long-run event study tests provide insights into abnormal stock returns as well as market efficiency in terms of how fast markets react to new market information.

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previous chapter A Special Case of the Zero-Beta CAPM: The ZCAPM
Appendix
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Footnotes
1
See, for example, Dolley (1933), Myers and Baker (1948), Baker (1956, 1957, 1958), Ashley (1962), Ball and Brown (1968), and many others.
 
2
For example, see studies by Sunder (1973, 1975), Aharony and Swary (1980), Binder (1985), and others.
 
3
For example, see studies by Schwert (1981a, b), Schipper and Thompson (1983), Brockett et al. (1999), Sharpe (2001), Knif et al. (2008), and others.
 
4
See also Campbell et al. (1997) and Binder (1998).
 
5
Here the conditioning information set \(X_t = R_{mt}\), and the conditional expectation itself is simplified to the linear model \(E(R_{it}| R_{mt}) = \alpha _i + \beta _i R_{mt}\), where the coefficients are assumed to be time independent.
 
6
In statistical testing, Type I error means falsely rejecting the null hypothesis when it is true (false alarm), and Type II error means accepting the null hypothesis when it is not true (missed alarm). The probability of Type I errors is set by the researcher. Typical values are 5% or 1%. The Type II error probability depends on the Type I error probability, sample size, distribution of the sample statistic, and the extent to which the true parameter value deviates from the null hypothesis value. Statistical power is measured by \(1 - \text {Type-II-probability}\), or the probability of detecting a false null hypothesis (correct alarm). It is important to use statistical tests that have maximum power in event studies.
 
7
The respective standard errors in Eqs. (11.7) and (11.9) are defined as:
$$\begin{aligned} \mathrm {s.e}({\overline{ AR }_0}) = \sqrt{\frac{1}{n(n - 1)} \sum _{i = 1}^n\left( AR _{i0} - \overline{ AR }_0\right) ^2} \qquad {(11.11)} \end{aligned}$$
and
$$\begin{aligned} \mathrm {s.e}({\overline{ CAR }_{\tau _1, \tau _2}}) = \sqrt{\frac{1}{n(n-1)} \sum _{i = 1}^n\left( CAR _i(\tau _1, \tau _2) - \overline{ CAR }_{\tau _1, \tau _2}\right) ^2}. \qquad {(11.12)} \end{aligned}$$
 
8
The standard error used in the CAR t-statistic (11.9) is an example of clustering robust standard errors (with respect to serial correlation), where the event windows over which individual CARs are aggregated from the clusters. See Cameron et al. (2011), Dutta et al. (2018), and Kolari et al. (2018) for further information.
 
9
With the market model \(R_{it} = \alpha _i + \beta R_{mt} + e_{it}\), \(d_{it}\) in Eq. (11.14) becomes:
$$\begin{aligned} d_{it} = \frac{1}{T} + \frac{(R_{mt} - \bar{R}_m)^2}{\sum _{s = 1}^{T}(R_{ms} - \bar{R}_m)^2} \end{aligned}$$
and \(d_{i\tau }\) in Eq. (11.16)
$$\begin{aligned} d_{i\tau } = \tau ^2\left( \frac{1}{T} + \frac{(\bar{R}_{m\tau } - \bar{R}_m)^2}{\sum _{s = 1}^{T}(R_{ms} - \bar{R}_m)^2}\right) , \end{aligned}$$
where T is the estimation window length, \(\bar{R}_m\) is the average market return in the estimation window, and \(\bar{R}_{m\tau }\) is the average market return in the window over which CAR is computed. Because calendar times of the event are assumed not overlapping, estimation and event windows are unique for each stock i, such that we use the subscript i in \(d_{it}\) and \(d_{i\tau }\).
In general, for a factor model with p factors, the correction terms are \(d_{it} = x_t' (X'X)^{-1}x_t\) and \(d_{i\tau } = \tau ^2\bar{x}_\tau ' (X'X)^{-1}\bar{x}_{\tau }\), where \(x_t = (1, F_{1t}, \ldots , F_{pt})'\) includes event time t returns, \(\bar{x}_{\tau } = (1, \bar{F}_{1\tau }, \ldots , \bar{F}_{p\tau })'\) includes factor averages over the CAR-window of length \(\tau\), and \((X'X)^{-1}\) is the inverse of the \((p+1)\times (p+1)\) matrix of estimation window cross-products of the constant term and factor returns.
 
10
See Campbell et al. (1997, Chapter 4) for an excellent discussion and further details.
 
11
Approaches for taking into account cross-sectional correlation with clustering robust estimation methods as well as estimating the average cross-sectional correlation explicitly in the partial clustering case are discussed in Kolari et al. (2018).
 
14
This standard error is computed as:
$$\begin{aligned} \mathrm {s.e}(\overline{ BHAR }) = \sqrt{\frac{1}{n(n-1)}\sum _{i = 1}^n( BHAR _{iT} - \overline{ BHAR })^2}. \qquad {(11.25)} \end{aligned}$$
Assuming the independence of \(BHAR _{iT}\)s, the asymptotic null distribution of \(t_{ BHAR }\) is standard normal.
 
15
We should note that, because the number of stocks in each month can vary from 1 to n (the total number of stocks), weighted least squares are recommended in the regression estimation.
 
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Metadata
Title
Event Studies
Authors
James W. Kolari
Seppo Pynnönen
Copyright Year
2023
Book
Investment Valuation and Asset Pricing

Print ISBN: 978-3-031-16783-6

Electronic ISBN: 978-3-031-16784-3

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-3-031-16784-3_11