D. To Fly to Quality or Disinvest? The Dilemma of Political Violence and Investor
D.4. Methodology
Event studies are now common in academic research, particularly within financial literature at the firm or even stock level. James Dolley (1933) is widely credited for conducting the first event study in an academic setting, in his paper which considered the impact of stock splits on equity prices, largely finding a common upward effect. However, the aim of Dolley’s paper was to outline the corporate procedures involved in stock splits rather than develop an event study methodology, meaning that the methodology he used was very straightforward, simply comparing the changes in price per share with the ratio of each stock split before and after the event.
Event study methodology then evolved somewhat. Ball and Brown (1968) and Fama et al. (1969) effectively provided the procedure that is the academic standard today, in their respective studies of how stock prices are affected by the release of accounting reports and by stock splits that have been adjusted for increased dividend pay-out ratios. Since then, most refinements have been introduced to deal with study-specific challenges; such as including controls for common market trends when studying firm-level impacts (Ashley 1962), as well as the development of robustness tests such non-parametric techniques (Brown and Warner, 1980). Additionally, Brown and Warner (1980, 1985) studied the differences in event study characteristics under monthly and daily periodicities while Fama and French (1993, 2015) introduced their three and then five-factor asset pricing models, adjusting for certain risk factors and thereby developing more sophisticated baselines which can be used as fairer comparisons for post-event outcomes.
The basic setup is as follows: first, an estimation window is established, from which the processes that we are interested in can be observed under ordinary conditions. The period immediately preceding the event is used, since it provides the most recent information without being biased by the event itself. This paper uses the 24 months prior to, and not including, the
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event as the estimation window. Although Brown and Warner (1980) use a 38-month window, in this paper, excluding events with ‘endogenous estimation windows’ reduces sample sizes significantly. Endogenous estimation windows are defined as estimation windows that contain at least part of the event window for a previous event, thereby invalidating the assumption that they represent returns under normal circumstances, which can be used as baselines from which to estimate abnormal returns during the subsequent event window. Therefore, the 24-month estimation window, here, is a compromise between sample size and the stability of the pre-event benchmarks. However, a sensitivity analysis described in the appendix shows that estimation windows of up to 48 months yield highly consistent results.
Next, the event window is determined, the period beginning with the event and either lasting the duration that the effect of the event is expected to continue to have an impact, or else a specific duration dictated by the study. The response functions from figure D.3., discussed below, guided decision-making here, indicating that an event window of 12 months is appropriate for this study. Again, a sensitivity analysis is conducted and comparable results are found for event windows as small as 3 months, although a more detailed analysis is left to a later discussion.
The setup can be summarised by figure D.1., below, where 𝑡1 is the event itself, 𝑡0 to 𝑡1 is the estimation window, 𝑡1 to 𝑡2 is the event window, and the periods before 𝑡0 and after 𝑡2 are not considered.
Figure D.1. Timing of an Event
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Once the estimation and event windows have been set, baseline returns are calculated over the estimation window and used as counterfactuals with which to calculate ‘abnormal’
returns in the event window. Many methods of estimating ‘normal’ returns exist, although the
‘constant mean return model’ from equation 3 is used here.
𝑅𝑖𝑡 = 𝜇𝑖 + 𝑢𝑖𝑡 (3)
Where 𝑅𝑖𝑡 are the actual returns in the event window, 𝜇𝑖 refers to the mean return over the estimation window and 𝑢𝑖𝑡 is an error term. Despite its simplicity, the constant mean return model typically provides similar outcomes to those from more sophisticated models (Brown and Warner 1980, 1985). This is potentially because future returns are inherently difficult to predict, in accordance with the efficient market hypothesis.
As a robustness test, a ‘market return model’ is also used; the main results of which are reported in tables D.4. to D.6. This model controls for common market trends.
𝑅𝑖𝑡 = 𝛼𝑖+ 𝛽𝑖𝑅𝑚𝑡+ 𝜀𝑖𝑡 (4) Where 𝑅𝑚𝑡 is the market return and 𝛼𝑖 is the constant mean return after controlling for the market return.
Since this study is conducted at an international level, the market return is defined as a global median return. The median is used here rather than the mean, because a global market is potentially susceptible to many unknowns, as well as outliers and measurement error, which could produce improbable results if economic or financial crises took place elsewhere, for example. However, there is a precedent for using world markets, set by authors such as Solnik (1974), Harvey (1991), Grauer et al. (1976) and Du and Hu (2015). Nevertheless, in order to make it a more suitable baseline, the market return is separated into three groups based on income categories (United Nations 2014). Although increasingly sophisticated baselines could be calculated using factor models (Fama and French 1993, 2015), the benefits of doing so are
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limited at best, and imprecisely estimated factors could even bias the results (MacKinlay 1997).
Therefore, only the constant mean return and market models are used in this study.
After estimating these ‘normal’ return series for the event window, abnormal returns are simply calculated by subtracting the expected normal return from the actual, realised return.
𝐴𝑅 𝑖𝜏= 𝑅𝑖𝜏− 𝐸(𝑅𝑖𝜏) (5)
Where 𝐴𝑅𝑖𝑡 are the estimated abnormal returns, 𝑅𝑖𝑡 are the actual returns and 𝐸(𝑅𝑖𝑡) are the expected ‘normal returns’. Note that 𝜏 differs from t; t refers to the date whereas 𝜏 refers to the number of periods (months) from the event.
Next, the abnormal returns are summed together to form cumulative abnormal returns, the total effect of the event on the returns over the event window.
𝐶𝐴𝑅𝑖𝑇 = ∑ 𝐴𝑅𝑖𝜏
𝑡2
𝑡=𝑡1
(6)
Where T refers to the duration of the event window.
Finally, the impact of the events is tested for significance. Each individual event can be tested by using a t-test.
Alternatively, to test for the significance of all events simultaneously and, therefore, to estimate the impact of assassinations on each of the series of interest, the cumulative abnormal returns are simply regressed on a constant.
𝐶𝐴𝑅𝑖𝑇 = 𝜑𝑖𝑇+ 𝑣𝑖𝑇 (8)
Where 𝜑𝑖𝑇 is a constant term and 𝑣𝑖𝑇 is a stochastic error term.
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As a gauge of robustness, regressions following equation 8 are run with robust standard errors, bootstrapped standard errors (with 50 replications) and quantile regression.