Buy-and-Hold Abnormal Return

The first approach to be described is the BHAR. It is described as the “average multiyear return from a strategy of investing in all firms that complete an event and selling at the end of a pre-specified holding period versus a comparable strategy using otherwise similar non-event firms” (Mitchell & Stafford, 2000; page 296). The approach is said to be capable of depicting discrete investor behavior (Ang &

Zhang, 2015; Loughran & Ritter, 2000). Hence, the calculation will rely on a comparison of the return development of the event companies and the matched counterparts. The BHAR approach considers company returns which occurred at a certain time after an actual SEO announcement, and therefore collects returns from different points in time, which is illustrated below.

Figure 7: Event-time buy-and-hold abnormal return calculation

The BHAR for company i is calculated in the following way:

𝐵𝐻𝐴𝑅_{𝑖;(𝑡,𝑇)}= ∏^𝑇_𝑡=1(1 + 𝑟_𝑖;𝑡) − ∏^𝑇_𝑡=1(1 + 𝑟_{𝑚𝑖;𝑡}) (20) where 𝑟_𝑖;𝑡 is the monthly return of our event company in month t, and 𝑟_{𝑚𝑖;𝑡} is the monthly return of a matched benchmark investment, which displays similarities to the respective event company.

If a company is delisted over the examined three year period, the return of the matched investment benchmark is adopted for the delisted company, and hence a BHAR of 0 from the month following the delisting is assumed and the BHAR prior to the delisting is stated after 3 years.

The equally-weighted average for the BHAR over all companies is the aggregated BHARs for all companies over the specified period divided by the number of companies N:

𝐴𝐵𝐻𝐴𝑅_𝑡,𝑇 = ¹

𝑁∑^𝑁_𝑖=1𝐵𝐻𝐴𝑅_{𝑖;(𝑡,𝑇)} (21)

and for the value-weighted approach it is as follows, given the sum of 𝑤_𝑖 is 1:

𝐴𝐵𝐻𝐴𝑅_𝑡,𝑇 = ∑^𝑁_𝑖=1𝑤_𝑖 ∗ 𝐵𝐻𝐴𝑅_{𝑖;(𝑡,𝑇)} (22) Matching procedure

In order to calculate the BHAR of each event company, the respective companies have to be matched to a corresponding fit. The assumption is that these matched benchmarks simulate returns of the event firms, should the event have never occurred. The first decision to make is if the match should rely on a reference portfolio or a single firm.

Figure 8: Benchmark options for the BHAR approach

Many scholars agree that the benchmark choice is crucial as long-term abnormal returns feature an ample sensitivity to this benchmark (Barber & Lyon, 1997; Ikenberry, Lakonishok & Vermaelen, 1995;

Kothari & Warner, 1997; Lyon, Barber & Tsai, 1999). We will use the single firm benchmark approach as it appears to be the most commonly used approach in our reference studies (e.g. Eckbo et al., 2000;

Jeanneret, 2005; Loughran & Ritter, 1995). Furthermore, Barber & Lyon (1997) stress that matching with a single firm will mitigate the so-called new issue, rebalancing and skewness bias in contrast to a reference portfolio match. The new-issue bias occurs since it is assumed that firms constituting the reference portfolio typically include newly traded firms compared to event companies that are traded for a long time already. The rebalancing bias is also characteristicly for a portfolio match since the reference portfolio returns are typically calculated using periodic rebalancing, while event firm returns are calculated without rebalancing. Lastly, the skewness bias refers to the characteristic that long-run

Buy-and-Hold Approach Benchmark

Reference Portfolio Benchmark Single Firm Benchmark

abnormal returns tend to be positively skewed. This bias is further mitigated with an increasing sample size (Kothari & Warner, 2007).

Furthermore, the matching company has to be chosen given certain characteristics that are shared with the event company and which also affect a company’s performance. As displayed in chapter 2

“Literature Review”, the commonly used matching criteria are size, book-to-market, industry, momentum and combinations thereof. For this thesis, we rely on the size criteria in terms of the individual market capitalization as sole matching characteristic. Our choice of utilizing only size as matching criterion is based on the several aspects. For instance, Spiess & Affleck-Graves (1995) demonstrate that the introduction of industry as a further matching criterion does not led to significantly different results over a size only match. Loughran & Ritter (1995) evince further reasons to not include industry as a matching criterion, for instance the low number of publicly traded companies within each industry will lead to the same company being matched more frequently. Lastly, the time at hand and scope of the thesis has also led us to follow the example of Loughran & Ritter (1995) in solely relying on size.

Besides the mentioned size criteria, a company has to feature further characteristics to become an event company’s match. Firstly, the matched company is required to not have issued equity itself within 3 years prior and after the announcement date of our event company. This ensures that we actually compare returns of an event and non-event company. Hence, event companies are allowed to be used as matching companies as long as the equity issuance does not take place within the described six year window. Secondly, a company is allowed to be a match for several event companies, if necessary.

Thirdly, the matched company is required to have been traded on a stock exchange within the respective country. Moreover, the matched company should have been traded on said stock exchange for at least the first month following the equity issuance. Lastly, the matching company, while being traded on the respective stock exchange, still has to be located in a similar market than our four markets, which excludes companies from outside the EU zone.

To find the matching firms, all companies that are currently and have ever been traded between 1990 and 2012, on the aforementioned four stock exchanges, are extracted from Datastream. Thus, we are relying with 420 possible matches for Belgium, 1745 for France, 1933 for Germany and 328 for the

Netherlands. The potential country-specific matching companies are ranked by their market capitalization in each calendar month. The firm which has the closest market capitalization at the end of the announcement month, that is also higher than the SEO firm’s market capitalization 5 days prior to the announcement, is chosen as the corresponding match.

Statistical Testing

Statistical testing for the BHAR analysis is in accordance with the explanations given in the statistical testing section of the event study. However, only a modification of the common t-test, the skewness-adjusted t-test (Johnson, 1978), will be applied to test for statistical significance in the long-run. The skewness-adjusted t-test, as the name suggests, was designed to adjust the t-statistic for potentially skewed abnormal performance distributions. The decision to apply only one simple test for the long-run analysis is based upon the findings by Ang & Zhang (2015). In their paper, they identify the importance of understanding the sample rather than of sophisticated statistical tests, given an adequate sample size. Accordingly, we refrain from including any of the more recent test approaches, for instance the advanced bootstrapping method. Besides, these advanced tests rely on random sampling.

Given the randomness of the testing, different researchers will obtain varying results which reversely would lower the reliability and replication of this thesis (Ang & Zhang, 2015; Lyon et al., 1999).

Furthermore, the utilization of the CTP approach should serve as a further robustness check

Johnson (1978) adjusted the common t-test to better fit skewed population resulting in the following:

𝑇 = √𝑁 ∗ (𝑆 +¹₃∗ 𝑦 ∗ 𝑆²+ ¹

6∗𝑁∗ 𝑦) (23)

with

𝑆 = ^{𝐴𝐵𝐻𝐴𝑅𝑡,𝑇}

𝜎(𝐵𝐻𝐴𝑅_{𝑖;(𝑡,𝑇)}) (24)

and the following adjusting terms for the equally- and value-weighted approach respectively 𝑦 =^{∑ (𝐵𝐻𝐴𝑅𝑖,[0;𝑡]−𝐴𝐵𝐻𝐴𝑅𝑖,[0;𝑡])}

𝑁 3 𝑖=1

𝑁∗𝜎(𝐵𝐻𝐴𝑅_[0;𝑡])³ or 𝑦 =^{∑ 𝑤𝑖∗(𝐵𝐻𝐴𝑅𝑖,[0;𝑡]−𝐴𝐵𝐻𝐴𝑅𝑖,[0;𝑡])}

𝑁 3 𝑖=1

𝜎(𝐵𝐻𝐴𝑅_[0;𝑡])³ (25) as well as

𝜎(𝐵𝐻𝐴𝑅) = √ ¹

𝑁−1 ∑^𝑁_𝑖=1(𝐵𝐻𝐴𝑅_{𝑖,[0;𝑡]}− 𝐴𝐵𝐻𝐴𝑅_[0;𝑡])² (26) for the equally-weighted and the following expression for the value-weighted approach.

𝜎(𝐵𝐻𝐴𝑅) = √^{∑ 𝑤𝐼(𝐵𝐻𝐴𝑅𝑖,[0;𝑡]−𝐴𝐵𝐻𝐴𝑅[0;𝑡])}

𝑁 2 𝑖=1

(𝑁−1)∗∑𝑁 𝑤𝑖 𝑖=1 𝑁

(27)

where 𝐴𝐵𝐻𝐴𝑅_𝑡,𝑇 is the average BHAR over a specified time period and 𝐵𝐻𝐴𝑅_{𝑖;𝑡,𝑇} is the buy-and-hold abnormal return over the identical time period for company i and 𝑤_𝑖 are the respective company weights, which add up to 1.