Long-Run Event Study
The initial return-based event studies as put forward by Fama, Fisher, Jensen, and Roll in 1969 capture the short-term effects of events on stock prices. For longer-term effects, related methods have been developed that capture if events have a persistent impact on stock prices over periods of time (e.g., several months or years). These methods thus measure more effect persistence than the size of the short-term effect. Areas of application vary and include stock performances following M&A transactions or public offerings of equity.
There are two related approaches for such analyses: (1) The buy-and-hold abnormal return approach, and (2) the calendar-time portfolio method, also referred to as Jensen’s alpha approach. Both approaches involve the construction of stock portfolios.
(1) Buy-and-hold abnormal return approach (BHAR)
Buy-and-hold is an investment strategy where an investor buys stocks and holds them for a long time. The BHAR grounds on this strategy and calculates abnormal returns by deducting the normal buy-and-hold return from the realized buy-and-hold return. The main difference between BHAR and a regular abnormal return calculation is the time period over which the returns are measured - for BHAR typically several months or years vs. days in regular abnormal return calculations. Another difference lies in the way that expected returns are calculated. In a BHAR calculation, expected returns are typically based on the average returns of the security or index over a longer time period, such as the past year or several years, in contrast to the daily consideration of regular abnormal return calculations.
(2) Calendar-time portfolio approach (CTIME)/Jensen's alpha approach
The CTIME approach calculates the abnormal return of a portfolio consisting of all firms that experienced the event of interest. The abnormal return is defined as the excess return that cannot be explained by expected return models, such as the CAPM or other factor models. The CTIME approach is also named “alpha approach” since "alpha", both in a statistical and an investment theory sense, closely relates to the excess return concept of the CTIME approach. Statistically, alpha refers to the intercept in a time-series regression on actual returns that statistically tests whether these models do explain the actual returns. If they do not explain the actual returns sufficiently, an intercept significantly different from zero results that represents the abnormal returns occured at the event date. Within the context of investments, this alpha reflects the risk-adjusted return measure that expresses the so-called active return on an investment, the return that would be attributable to the investment manager. In event studies, the event substitutes the "investment manager" in being responsible for the abnormal returns. The CTIME approach thus reflects an investor's actual investment experience in the respective stock portfolio. While the method has typically been applied in investment and behavioral and corporate finance research, it got adopted also by other domains, such as marketing (e.g., Moorman et al., 2012).