The methodology matters: What influences market reaction, and post-issue returns in seasoned equity offerings?

Krishnan, C. N. V.; Wu, Minghao Article The methodology matters: What influences market reaction, and post-issue returns in seasoned equity offerings? Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Krishnan, C. N. V.; Wu, Minghao (2022) : The methodology matters: What influences market reaction, and post-issue returns in seasoned equity offerings?, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 10, pp. 1-18, https://doi.org/10.3390/jrfm15100473 This Version is available at: https://hdl.handle.net/10419/274993 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Journal of Risk and Financial Management 15: 473. https://doi.org/10.3390/jrfm 15100473 Academic Editor: Svetlozar (Zari) Rachev Received: 17 September 2022 Accepted: 5 October 2022 Published: 18 October 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article The Methodology Matters: What Influences Market Reaction, and Post-Issue Returns in Seasoned Equity Offerings? C. N. V. Krishnan * and Minghao Wu Weatherhead School of Management, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA *Correspondence: [email protected] Abstract: Using a large database of U.S. seasoned equity offering (SEO) announcements from 2010 to 2015, we examine the effects of several explanatory variables—firm specific, macroeconomic, fixed income, and stock market variables—on the announcement period abnormal stock returns and on the longer-run post-issue abnormal returns. We use five different statistical methods—multivariate linear regression, regression on a reduced model using principal components analysis, year-by-year regression on a reduced model using principal components analysis, random forest regression on the whole sample, and year-by-year random forest regression. In general, across the methods, we find that firm’s profitability in the recent past is an important explanatory factor in both short-term and long-term abnormal stock returns, but several other significant explanatory factors change based on the statistical method used. Therefore, the statistical method used affects the results reported. Keywords: seasoned equity offerings; SEO; announcement period abnormal stock returns; long-run post-issue abnormal returns; principal components analysis; random forest regression; key determinants JEL Classification: G14 1. Introduction In this paper, we examine the determinants of the announcement period abnormal stock returns and post-issue abnormal stock returns in seasoned equity offerings, which include firm specific, macroeconomic, fixed income, and stock market variables. We use several different statistical methods to examine the significant explanatory variables and come to the conclusion that the statistical method used in research can influence the findings. Previous studies have, generally, reported negative short-term or announcement period abnormal stock returns around SEO (Shahid et al. 2010;Masulis and Korwar 1986), presumably because of the negative effects on new equity on stock prices stemming from asymmetric information and dilution. Deshmukh et al. (2017) argues for the presence of informed short selling around SEO announcements. Gerard and Nanda (1993) find that informed traders acting strategically may try to manipulate offering prices by selling shares prior to SEO and profit from lower prices in the offering. Research on post-issue longer-term abnormal stock performance post-issue has found SEOs that are more overvalued prior to the announcement day experience a significantly larger decline over the subsequent five years (Purnanandam and Swaminathan 2006). Spiess and Affleck-Graves (1995) have also shown persistent stock underperformance in the three years post issue, when controlling for variables such as the trading system, firm’s financials, and age. Asad et al. (2020) find that firms that are ex ante overlevered and overvalued were more likely to announce a seasoned equity offering. Perhaps as a result, Botta and Colombo (2019) find that both shareholders and bondholders experience negative returns following SEOs. From the J. Risk Financial Manag. 2022,15, 473. https://doi.org/10.3390/jrfm15100473 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 473 2 of 22 perspective of a firm’s earnings and expenditure management, Xiang (2022) argues that the firms with high R&D spending experience stock overpricing and negative market reaction when they announce SEOs. Prior research has also used several explanatory variables—for example, past growth rate of firms (Purnanandam and Swaminathan 2006), or externalities such as hedge fund variables (Hull et al. 2018). Previous research have usually used linear regression to explain abnormal stock returns (e.g., Deshmukh et al. 2017), or two sample t-tests of difference in mean abnormal returns, or test of differences of median abnormal returns. We use several groups of explanatory variables—firm financial variables, stock market variables, fixed income, and macroeconomic variables—to explain several measures of announcement period and long-run post-SEO abnormal returns, after controlling for time and industry fixed effects, and offer size. Using a comprehensive sample of 2139 SEO announcements between 2010 and 2015, we first examine sample descriptive statistics and abnormal returns over different periods, and over and above different benchmarks. The results are consistent with the previous papers in the terms of announcement period abnormal returns around SEO announcements and post-issue longer-term abnormal returns, particularly longer-run post-issue underperformance. We propose the following hypothesis in the null form, to be tested in this paper: The significant variables that explain announcement period abnormal returns and longerrun post-issue abnormal returns depend on the statistical method used. To test this hypothesis, we compare and contrast results using several different methods including panel regression, regression using principal components, random forest regression, and year-by-year regression. Across all the methods we use, we find that there are factors such as firm profitability of the immediate past, as measured, for example, by the return on assets, that significantly affect abnormal returns, but different statistical methods also yield different significant explanatory variables for short-term and longer-term returns. In conclusion, this research shows that results presented in empirical studies can depend on the statistical method used. The next section describes our data and the variables we used. Section 3reports the descriptive statistics. Section 4reports on the analyses and the results, while Section 5 concludes. 2. Data and Variables 2.1. Data Our initial data sample consisted of 3755 seasoned equity offering (SEO) announcements over a 5-year period from 2010 to 2015 collected from Refinitiv’s Securities Data Company’s (SDC) Platinum Global Public Issues database. For each firm making the SEO announcement, we used firm data (taken from the COMPUSTAT database), stock returns and market return data (taken from the Center for Research in Security Prices—CRSP database), and economy-wide and fixed income data (taken from the Federal Reserve database, FRED). After excluding observations for which we could not find all the available data, our final sample contained 2138 SEO announcements. We normalized all explanatory variables by using their z-scores. Following Altman (2018), the original value, x, was converted as xa=x−x σx where xa is the transformed variable that would be used in regressions, x is the mean value, and σxis the standard deviation. J. Risk Financial Manag. 2022,15, 473 3 of 22 2.2. Variables We calculated announcement periods’ abnormal returns in several different ways based on various benchmark returns. We used S&P 500 index returns, equal-weighted index, or the value-weighted index published by the Center for Research in Security Prices (CRSP) as alternative benchmarks to calculate the abnormal returns. As suggested by Aggarwal and Rivoli (1990) and Durukan (2002), we defined short-term abnormal returns as each stock’s 3-day, 7-day, or 21-day cumulative abnormal return (CAR) around the SEO announcement over and above equity beta times the corresponding benchmark return. The beta, β , was estimated by monthly returns in the pre-announcement period over the 3 years prior to the SEO announcement. For long-term abnormal returns, we followed Barber and Lyon (1997) to compute long-term CAR. The cumulative abnormal return (CAR) was calculated as CARi=Rf irm −β∗Rbenchmark We subtracted equity beta ( β ) times the monthly returns of a benchmark from the monthly returns of the firm, and took the sum. We calculated CAR for SEO firms over 6 months and 12 months, post-issue. For examining the various factors that could be related with the announcement period and post-announcement abnormal returns, we divided them into three different groups. These are: the firm variables (Group A), economy-wide and fixed income variables (Group B), and market variables (Group C). For the firm variables, following Nassar (2016), we computed financial ratios that included the return on asset (ROA), the return on equity (ROE), as at one, two, and four quarters before the SEO announcement, as proxies of the firm’s financial performances. Following Mohanram (2003), we calculated the book-tomarket ratio (BTM) as a measure of the growth options of the firm. Following Erawati and Widayanto (2016), we computed the operating income to total asset (OI/A) ratio as a proxy of firm’s operating profits. For the group of economic and fixed income indices, following Daniell et al. (2010), we used the gross domestic product (GDP) index, consumer price index (CPI), and the GDP growth for the year before the SEO announcement as proxies of economic trend. Following Angbazo (1997), we used the shortand long-term rate of US government treasury as proxies for cost of funds. For the group of stock market variables, we calculated the stock index return in 3 months, 6 months, and 12 months before the SEO announcement. We standardized all our variables using “z” scores by subtracting the mean of a variable and dividing the result with the standard deviation, to convert all data to the same scale. We also used the following control variables in our analyses. Following Islam et al. (2010), we used year and industry dummy variables, as the trends in the levels of underpricing and overpricing for SEOs could depend on time and industry. We also controlled for offer size, on which the underpricing may depend (see Corwin 2003); and underpricing and overpricing of an issue can affect announcement period returns and longer-term returns. 3. Descriptive Statistics The three panels of Figure 1show the year-by-year time-series plots of the average announcement period abnormal returns around the announcement: 1 day before to 1 day after, 3 days before to 3 days after, and 10 days before to 10 days after. Plots in green, red, and blue show the abnormal return over and above the S&P 500 index, CRSP value-weighted index, and CRSP equal-weighted index, respectively. The plots show that the abnormal return is volatile year to year, but generally negative for 3-day and 7-day abnormal returns and generally positive for the 21-day returns (also see Henry and Koski 2010). Hibbert et al. (2020) suggest that differences in beliefs in the market are a determinant of the volatility of short-term announcement period returns around SEO, which is what we also noticed. However, in line with Malladi and Fabozzi (2017), the equally weighted CRSP-adjusted abnormal returns were less volatile than the other abnormal returns. On average, the 3-day and 7-day abnormal returns, except in 2010 for the 3-day abnormal return, were negative, while the 21-day abnormal returns were all positive except 2010. The positive returns were J. Risk Financial Manag. 2022,15, 473 4 of 22 more in 2015. Our data indicate that the 21-day abnormal return was 0.14% higher than the 3-day abnormal return and 0.85% higher than the 7-day abnormal return, on average, of three different benchmarks. This result may imply a short selling around the time of the announcement and there is an overreaction immediately at the announcement. This figure shows the time series plots of annual average announcement period abnormal returns around SEO announcements: from − 1 to +1 day, from − 3 to +3 days, and from − 10 to +10 days around the announcement date (date 0). These announcement period abnormal returns are over and above beta times the S&P index return (the green plot), the value-weighted CRSP market return (the red plot), or equal-weighted CRSP market return (the blue plot). The time period is SEO announcements made from 2010 to 2015. J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 4 of 24 CRSP-adjusted abnormal returns were less volatile than the other abnormal returns. On average, the 3-day and 7-day abnormal returns, except in 2010 for the 3-day abnormal return, were negative, while the 21-day abnormal returns were all positive except 2010. The positive returns were more in 2015. Our data indicate that the 21-day abnormal return was 0.14% higher than the 3-day abnormal return and 0.85% higher than the 7-day abnormal return, on average, of three different benchmarks. This result may imply a short selling around the time of the announcement and there is an overreaction immediately at the announcement. (A) (B) Figure 1. Cont. J. Risk Financial Manag. 2022,15, 473 5 of 22 J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 5 of 24 (C) Figure 1. Announcement period abnormal return. Panel A: Average -1 to +1 Day Abnormal Return by Year. Panel B: Average -3 to +3 Day Abnormal Return by Year. Panel C: Average -10 to +10 Day Abnormal Return by Year. This figure shows the time series plots of annual average announcement period abnormal returns around SEO announcements: from −1 to +1 day, from −3 to +3 days, and from −10 to +10 days around the announcement date (date 0). These announcement period abnormal returns are over and above beta times the S&P index return (the green plot), the value-weighted CRSP market return (the red plot), or equal-weighted CRSP market return (the blue plot). The time period is SEO announcements made from 2010 to 2015. The two panels in Figure 2 show the year-by-year time series plots of long-term abnormal returns that generated 6 months and 12 months after the issue. Post-issue longer run returns are mostly negative, in line with Spiess and Affleck-Graves (1995), who argue that this may be because managers take advantage of overvaluation in markets. On average, the 12-month abnormal return is −4.71%, 2.37% lower than the 6-month abnormal return, depending on the benchmark, in line with Carlson et al. (2006), who point out that there is post-issuance underperformance of SEO stocks using options framework. Figure 1. Announcement period abnormal return. Panel A : Average − 1 to +1 Day Abnormal Return by Year. Panel B : Average − 3 to +3 Day Abnormal Return by Year. Panel C : Average − 10 to +10 Day Abnormal Return by Year. The two panels in Figure 2show the year-by-year time series plots of long-term abnormal returns that generated 6 months and 12 months after the issue. Post-issue longer run returns are mostly negative, in line with Spiess and Affleck-Graves (1995), who argue that this may be because managers take advantage of overvaluation in markets. On average, the 12-month abnormal return is −4.71%, 2.37% lower than the 6-month abnormal return, depending on the benchmark, in line with Carlson et al. (2006), who point out that there is post-issuance underperformance of SEO stocks using options framework. This figure shows the time series plots of annual average long-term post-SEO abnormal returns: the cumulative abnormal return (CAR) 6 months and 12 months post-SEO over and above value-weighted CRSP market return (the red plot), or equal-weighted CRSP market return (the blue plot). The time period is SEO announcements made from 2010 to 2015. For the whole sample, the year-by-year SEO descriptive statistics a shown in Table 1. Table 1. Descriptive statistics of SEOs by year. This take shows the year-by-year descriptive statistics of our final sample of Seasoned Equity Offering announcements made from 2010 to 2015. Year Number of SEOs Average Proceeds (USD Million) Average Time between Announcement and Issue (Days) Percentage Bank SEOs Average Equity Beta 2010 164 335.4 467.5 44.5% 1.3 2011 393 170.9 318.2 33.8% 1.4 2012 407 289.9 266.8 39.8% 1.3 2013 455 190.2 189.2 33.2% 1.2 2014 406 200.2 129.9 26.8% 0.7 2015 232 256.7 36.3 19.4% 1.4 Overall 2139 270.7 311.9 36.6% 1.3 J. Risk Financial Manag. 2022,15, 473 6 of 22 J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 6 of 24 (A) (B) Figure 2. Longer Term Post-Issue Abnormal Return. Panel A: Average 6-month post-issue Cumulative Abnormal Return by Year. Panel B: Average 12-month post-issue Cumulative Abnormal Return by Year. This figure shows the time series plots of annual average long-term post-SEO abnormal returns: the cumulative abnormal return (CAR) 6 months and 12 months post-SEO over and above value-weighted CRSP market return (the red plot), or equal-weighted CRSP market return (the blue plot). The time period is SEO announcements made from 2010 to 2015. For the whole sample, the year-by-year SEO descriptive statistics a shown in Table 1. Figure 2. Longer Term Post-Issue Abnormal Return. Panel A : Average 6-month post-issue Cumulative Abnormal Return by Year. Panel B : Average 12-month post-issue Cumulative Abnormal Return by Year. The number of announcements and the average proceeds have remained more or less steady, around the average, over the years, but the average time between announcement and the issue and the proportion of SEOs announced by banks, as they seemed to have shored up their capital adequacy over time, have decreased. The SEOs are announced, on average, by firms that are slightly riskier (in terms of the equity beta) firm than the market. The year-by-year abnormal stock returns are shown in Table 2: short-term abnormal return in Panel A, and long-term post-issue abnormal returns in Panel B. J. Risk Financial Manag. 2022,15, 473 7 of 22 Table 2. SEO returns by year. Panel A reports the average percentage announcement period abnormal returns, computed in different ways over different periods around the SEO announcement date, while Panel B reports the average longer-run post-issue abnormal returns, computed in different ways over different periods after the SEO issue date. All variables are defined in the Appendix A. Panel A Year SP AR3 SP AR7 SP AR 21 VW AR3 VW AR7 VW AR 21 EW AR3 EW AR7 EW AR 21 2010 1.05 −0.22 0.07 0.99 −0.33 0.20 0.83 −0.45 −0.53 2011 −0.56 −0.72 0.92 −0.52 −0.71 0.93 −0.23 −0.34 1.44 2012 −0.45 −0.23 0.28 −0.46 −0.33 0.09 −0.54 −0.33 −0.05 2013 −0.68 −0.81 1.35 −0.66 −0.79 1.25 −0.64 −0.80 0.97 2014 −0.84 −1.28 0.52 −0.83 −1.21 0.73 −0.79 −0.81 1.71 2015 −0.39 −0.65 3.06 −0.43 −0.75 2.85 −0.48 −0.72 3.05 Overall −0.24 −0.57 0.48 −0.26 −0.63 0.32 −0.28 −0.73 −0.18 Panel B Year SP CAR6 SP CAR12 VW CAR6 VW CAR12 EW CAR6 EW CAR12 2010 −6.75 −4.14 −7.09 −5.17 −4.07 −2.32 2011 −1.49 −5.39 −1.85 −6.58 −0.07 −4.59 2012 −2.97 −3.44 −4.09 −5.37 −4.13 −5.51 2013 −2.37 −7.01 −3.14 −7.67 −2.86 −3.71 2014 1.57 −1.01 1.48 −0.19 2.74 4.57 2015 0.10 −3.19 1.02 −2.75 6.48 2.66 Overall −2.97 −5.35 −3.21 −6.02 −0.83 −2.75 Short selling around the SEO announcement may provide an opportunity to profit from share price manipulation (Deshmukh et al. 2017), which may explain the pattern in Panel A that shows reversal as we move from 7 days around the announcement date (generally negative) to 21 days around the announcement date (generally positive). For long-term post-issue abnormal returns, shown in Panel B, the average overall abnormal return is negative for all the benchmarks and becomes more negative, on average, as we examine longer-run returns. This is in line with previous studies that have documented negative long-term abnormal stock returns following SEO issues (Eberhart and Siddique 2002;Lizi´nska 2018). However, the long-term abnormal stock returns were higher in the later years of our sample—2014 and 2015—and some even turned positive. 4. Methods and Results 4.1. Methods To examine the determinants of the announcement period abnormal returns and post-issue longer term returns, the patterns of which were documented above, we use several methods. Indeed, the objective of the paper is to show that the results could change depending on the method used. In Method 1, we start with a panel regression using our full sample, with the various abnormal returns as the dependent variables and the groups of explanatory variables as the independent variables, controlling for year and industry fixed effects and offer size. We document the significant explanatory variable(s), at the 1% level, for each announcement period and longer-term abnormal return. This is the normal “kitchen-sink” panel regression approach. In Method 2, to reduce the number of explanatory variables, we perform principal component analysis on each factor group (on the standardized “z” variables) and determine the principal component(s) that explain at least 80% of each factor group. The original independent variables of each factor group that have at least 75% correlation with each of the important principal components identified above are now the reduced number of independent variables in the panel regressions to explain each abnormal return, after J. Risk Financial Manag. 2022,15, 473 8 of 22 controlling for year and industry fixed effects and offer size. In this method, we are more careful in selecting the explanatory variables. Method 3’s approach to identify the key determinants of abnormal returns is a yearby-year one. We perform principal component analysis on each factor group each year and determine the principal component(s) that explain at least 80% of each factor group each year. The original independent variables of each factor group that have at least 75% correlation with each of the important principal components identified above are now the reduced number of independent variables each year (could be different) in year-by-year regressions to explain each abnormal return. This method allows the determinants of the shortand longer-term returns to vary by year, which would not have been feasible using all explanatory variables because of their number. In Method 4, we use a random forest regression method to check the key determinants of SEO abnormal returns. As Biau and Scornet (2016) suggests, when we have a dataset with a large number of variables, a random forest algorithm can be a successful classification and regression method. In other classification processes, as used in the methods 2 and 3, or in machine learning, the predictor variables space is required to be substantially reduced, which can lead to missing some insight of a complex dataset. As Uddin et al. (2022); Liu et al. (2015); and Zou et al. (2015) show, the random forest regression method is widely used in the finance industry, for example in fraud detection, credit analysis, prices, etc., when we have high-dimensional data. Following Liu et al. (2012), the random forest regression can be summarized as follows. Random forest regression is a method of machine learning that involves planting trees randomly and then using reliable predictors by taking an average of trees. Following Archer and Kimes (2008) and Biau and Scornet (2016), the random forest classifier generates the effectiveness of each variable in each group, and can identify the important predictor(s) among all the candidate predictors. A random forest classifier does not require reduction in the predictor space prior to classification, as in Methods 2 and 3. In Method 5, we conduct the random forest regression year-by-year. In our approach, we used 40% (see Hastie et al. 2009) of the sample in each regression for training and the remainder for testing. For evaluating the performance of predictor(s), following Chai and Draxler (2014), the root mean squared error (RMSE) that measures the error between the statistical result and real data is an appropriate measure of the method’s performance. Using n samples of errors calculated as ( ei ,i= 1, 2, . . . ,n), the RMSE is calculated for the data set as: RMSE =s1 n n ∑ i=1 e2 i A large RMSE indicates that the method is inaccurate. In Figure 3, we can see differences in the values of RMSE between short-term abnormal returns and long-term post-issue abnormal returns. Panel A reports the RMSE value for full-sample regression, and Panel B the RMSE for the year-by-year regression. We see only small differences between the method’s performance for abnormal returns over the same period but using different benchmarks, but the accuracy is better for the short-term (announcement period) abnormal returns (also see Mitchell and Stafford 2000). Figure 3reports RMSE values generally under 0.2 for short-term abnormal returns and under 0.55 for long-term abnormal returns. This indicates an efficient method, and the variables are interpretable explanatory variables for the dependent variables. J. Risk Financial Manag. 2022,15, 473 15 of 22 Table 6. Random forest regression: full sample. (A) YtOI/A 2 ROA 1 SP CAR(−1,+1) −0.007 (−4.40) VW CAR(−1,+1) −0.007 (−4.37) EW CAR(−1,+1) −0.007 (−3.83) 0.005 (2.62) SP CAR(−3,+3) −0.011 (−4.53) 0.012 (4.37) VW CAR(−3,+3) −0.011 (−4.54) 0.012 (4.57) EW CAR(−3,+3) −0.010 (−4.17) 0.013 (4.85) SP CAR(−10,+10) −0.025 (−5.80) 0.028 (5.65) VW CAR(−10,+10) −0.026 (−5.93) 0.031 (6.27) EW CAR(−10,+10) −0.027 (−5.88) 0.042 (8.08) SP CAR 6 months 0.036 (3.06) SP CAR 12 months 0.082 (5.45) VW CAR 6 months 0.038 (3.24) VW CAR 12 months 0.086 (5.68) EW CAR 6 months 0.049 (4.00) EW CAR 12 months 0.104 (6.62) (B) YtROE 4 ROA 1 3MD 6MN OI/A-1 OI/A-4 12MN 5YGR 6MD 6MN SP CAR(−1,+1) 2010(−), 2012(+) 2011(+) 2011(+) 2013(−) 2015(+) 2015(+) VW CAR(−1,+1) 2010(−), 2012(+) 2011(+), 2014(−)2011(+) 2013(−) 2015(+) 2015(+) EW CAR(−1,+1) 2010(−), 2012(+) 2011(+), 2014(−)2013(−) 2015(+) 2015(+) SP CAR(−3,+3) 2010(−) 2010(+) 2015(+) 2015(−) VW CAR(−3,+3) 2010(−) 2015(+) 2015(−) EW CAR(−3,+3) 2010(−) 2015(+) 2015(+) 2015(−) SP CAR(−10,+10) 2010(−)2010(+), 2014(+) VW CAR(−10,+10) 2010(+), 2014(+) EW CAR(−10,+10) 2010(+), 2014(+) 2012(+) SP CAR 6 months 2014(+) SP CAR 12 months 2013(+) 2014(+) 2015(−) 2014(−) 2014(+) VW CAR 6 months 2014(+) 2015(−) VW CAR 12 months 2013(+) 2014(+) 2015(−) 2014(−) EW CAR 6 months 2014(+) 2015(−) EW CAR 12 months 2013(+) 2014(+) 2015(−) 2014(−) 2014(+) Table 6A shows the significant explanatory variables, using random forest regressions with different announcement period abnormal returns and post-issue longer-term abnormal returns as the dependent variables, and the different groups of all explanatory variables, as the independent variables—firm variables (Group A), economic and fixed income variables (Group B), and market variables (Group C), with time and industry fixed effects and offer J. Risk Financial Manag. 2022,15, 473 16 of 22 size. The coefficients and t statistics (in parentheses) of the significant variables (at 1% level) are shown. The regression specification is: AR =α+β1OIA2+β2ROA1+β3BIG +β425YGR +β53MN +β66MN +σ All variables are defined in Appendix A. Table 6B shows the year(s) in which an explanatory variable is significant (at the 1% level), using year-by-year regressions with different announcement period abnormal returns and post-issue longer-term abnormal returns as the dependent variables, and the two most important variables from random forest regression analyses of the different groups of explanatory variables—firm variables (Group A), economic and fixed income variables (Group B), and market variables (Group C)—with time and industry fixed effects and offer size, and which variables appear to be significant in which year. The years in which the variables are significant are shown. The regression specifications are: 2010 : AR =α+β1ROE4+β2ROA1+β3BIG +β425YGR +β512MD +β63MD +σ 2011 : AR =α+β1ROA2+β2ROA1+β3BIG +β425YGR +β512MN +β63MD +σ 2012 : AR =α+β1ROE2+β2ROE4+β3BIG +β45YGR +β56MN +β612MD +σ 2013 : AR =α+β1ROE4+β2OIA1+β3BIG +β45YGR +β53MN +β63MS +σ 2014 : AR =α+β1OIA4+β2ROA1+β3BIG +β45YGR +β512MN +β63MN +σ 2015 : AR =α+β1ROE4+β2ROA4+β325YGR +β45YGR +β56MN +β63MD +β76MD +σ All variables are defined in the Appendix A. Table 7summarizes the results of all the statistical methods. ROA-1, the profitability variable from one quarter before the SEO announcement, affected the announcement period (short-term) abnormal returns most consistently. Husna and Satria (2019), for example, argued that the return on asset significantly reflects on firm value. Chen et al. (2019) argued that investor sentiments, influenced by the most recent earnings disclosed, have a positive impact on short-run abnormal returns. ROA-2 also significantly affected all shortterm abnormal returns in two different methods. The market variables, 12MS and 12MN, significantly affected the 3-day abnormal returns in different ways. On long-term postissue abnormal returns, besides ROA-1, the book-to-market ratios (reflecting the inverse of the growth potential) were significantly associated with all the abnormal returns in 2015. ROA-2 affected the 12 months post-issue abnormal returns negatively in 2015, and ROA-4 was also significantly associated with abnormal returns in the full-sample regression. Table 7shows the method using which a variable is significant (at the 1% level), from different regressions (ASR: full-sample regression; APR: full-sample PC regression; YBY: year-by-year PC regression; RFR: random forest regression; and RFY: random forest yearby-year regression), with different announcement period abnormal returns and post-issue longer-term abnormal returns as the dependent variables, and the different groups of all explanatory variables as the independent variables—firm variables (Group A), economic and fixed income variables (Group B), and market variables (Group C), with time and industry fixed effects and offer size. All variables are defined in Appendix A. 4.3. Robustness Check To check the robustness of our full-sample regression results, we divided the full sample into two parts: 2010–2012 and 2013–2015. Table 8reports the results of the regression and shows consistency between these two samples. The significant explanatory variables in the full sample are also significant in the same direction in the two subsamples. J. Risk Financial Manag. 2022,15, 473 17 of 22 Table 7. Summary of significant variables. YtBTM2 BTM4 BTM1 ROE4 UNEMP 1YGR OI/A2 CPI OI/A1 ROE1 6MD SP CAR(−1,+1) YBY YBY, RFY YBY YBY, RFR ASR YBY, RFY ASR, YBY RFY VW CAR(−1,+1) YBY YBY, RFY YBY YBY, RFR ASR YBY, RFY ASR, YBY RFY EW CAR(−1,+1) YBY YBY, RFY YBY YBY, RFR ASR YBY, RFY ASR, YBY RFY SP CAR(−3,+3) YBY YBY YBY, RFY YBY YBY RFR YBY ASR RFY VW CAR(−3,+3) YBY YBY YBY, RFY YBY RFR YBY ASR RFY EW CAR(−3,+3) YBY YBY YBY, RFY RFR YBY ASR ASR RFY SP CAR(−10,+10) YBY YBY, RFY YBY RFR YBY ASR ASR VW CAR(−10,+10) YBY YBY YBY YBY RFR YBY ASR ASR EW CAR(−10,+10) YBY YBY YBY YBY RFR YBY ASR ASR, YBY YtOI/A4 ROA2 GDP 12MD 3MD ROA 1 12MS 12MN ROA4 6MN 5YGR SP CAR(−1,+1) ASR, YBY APR, YBY RFY RFY ASR, APR ASR, APR APR RFY VW CAR(−1,+1) ASR, YBY APR, YBY RFY RFY ASR, APR ASR, APR APR RFY EW CAR(−1,+1) ASR, YBY APR, YBY RFR, RFY ASR ASR, APR APR RFY SP CAR(−3,+3) ASR, YBY APR, YBY ASR, APR, RFR ASR, APR RFY VW CAR(−3,+3) ASR, YBY APR, YBY ASR, APR, RFR ASR RFY EW CAR(−3,+3) ASR APR, YBY ASR, APR, RFR ASR RFY RFY SP CAR(−10,+10) APR, YBY ASR, APR, RFR ASR VW CAR(−10,+10) APR, YBY ASR, APR, RFR ASR EW CAR(−10,+10) APR, YBY ASR, APR, RFR RFY YtBTM2 BTM4 BTM1 ROE4 UNEMP 1YGR OI/A2 CPI OI/A1 ROE1 SP CAR 6 months YBY YBY SP CAR 12 months YBY YBY RFY YBY YBY VW CAR 6 months YBY YBY VW CAR 12 months YBY YBY RFY YBY YBY ASR EW CAR 6 months YBY YBY YBY EW CAR 12 months YBY YBY RFY YBY YBY ASR, YBY YtOI/A4 ROA2 GDP 12MD 3MD ROA 1 12MS 12MN ROA4 SP CAR 6 months ASR, RFR SP CAR 12 months YBY APR YBY YBY ASR, APR, RFR APR VW CAR 6 months YBY ASR, APR, RFR VW CAR 12 months YBY APR YBY YBY ASR, APR, RFR APR EW CAR 6 months YBY ASR, APR, RFR EW CAR 12 months YBY YBY YBY YBY ASR, APR, RFR APR J. Risk Financial Manag. 2022,15, 473 18 of 22 Table 8. Robustness check: sub-sample test. 2010–2012 Yt Significant Explanatory Variables (Name and Significance) ROA 1 BTM 1 OI/A 1 OI/A 2 BTM 4 OI/A 4 ROE 2 ROA 2 6MD 12MD 25YGR SP CAR(−1,+1) −0.019 (−3.11) 0.017 (2.77) −0.024 (−4.47) 0.026 (3.09) 0.014 (3.15) VW CAR(−1,+1) −0.019 (−3.06) 0.017 (2.74) −0.024 (−4.46) 0.026 (5.97) 0.015 (3.29) EW CAR(−1,+1) −0.019 (−2.97) 0.016 (2.63) −0.025 (−4.53) 0.025 (5.74) 0.017 (3.58) SP CAR(−3,+3) 0.013 (3.50) VW CAR(−3,+3) 0.012 (3.34) EW CAR(−3,+3) 0.010 (2.94) SP CAR(−10,+10) 0.014 (2.79) 0.016 (2.84) −0.030 (−2.86) −0.239 (−3.03) VW CAR(−10,+10) 0.015 (2.88) 0.015 (2.71) −0.031 (−2.90) −0.226 (−2.87) EW CAR(−10,+10) 0.015 (3.04) 0.014 (2.50) −0.031 ( − 2.91) − 0.243 ( − 3.07) 0.195 (2.98) SP CAR 6 months SP CAR 12 months −0.921 ( − 2.58) VW CAR 6 months VW CAR 12 months EW CAR 6 months EW CAR 12 months 2013–2015 Yt Significant Explanatory Variables (Name and Significance) ROA 1 BTM 1 OI/A 1 BTM 2 ROA 4 5YGR 6MD 6MS SP CAR(−1,+1) 0.029 (2.77) −0.043 (−3.00) VW CAR(−1,+1) 0.012 (2.60) 0.026 (2.55) −0.039 (−2.76) EW CAR(−1,+1) 0.060 (2.64) SP CAR(−3,+3) VW CAR(−3,+3) EW CAR(−3,+3) 0.016 (2.66) SP CAR(−10,+10) 0.061 (5.47) 0.041 (3.45) −0.044 (−3.47) VW CAR(−10,+10) 0.071 (6.26) 0.041 (3.40) −0.034 (−2.69) −0.043 (−3.34) EW CAR(−10,+10) 0.108 (8.63) 0.039 (2.88) −0.055 (−3.89) −0.039 (−2.70) SP CAR 6 months −0.079 (−2.71) SP CAR 12 months −0.089 (−2.70) VW CAR 6 months −0.079 (−2.70) VW CAR 12 months −0.092 (−2.71) EW CAR 6 months EW CAR 12 months Table 8shows the significant explanatory variables (shown in bold), using regressions with different announcement period abnormal returns and post-issue longer-term abnormal returns as the dependent variables, and the different groups of all explanatory variables as the independent variables—firm variables (Group A), economic and fixed income variables (Group B), and market variables (Group C), with time and industry fixed effects and offer size, after dividing the sample into two subsamples—2010–2012 and 2013–2015. The coefficients and t statistics (in parenthesis) are shown. All variables are defined in the Appendix A. 5. Conclusions We examined the main influences of abnormal returns around SEO announcements and in the longer-run post-issue, using several different methodologies. Full-sample panel J. Risk Financial Manag. 2022,15, 473 19 of 22 regression showed that ROA-1, ROE-1, and 12MN were the most significantly associated with announcement period abnormal returns. The full-sample principal components analysis revealed ROA-2 as the most important factor. The full-sample random forest regression showed that the OI/A-2 and ROA-1 were the most important factors. In year-byyear methods, significant variables were different from year to year and there were some consistent variables that were associated with announcement period abnormal returns. In year-by-year regressions on variables most correlated with important PCs, we found that ROE-4 and ROA-2 were consistently influential, while the year-by-year random forest regression showed ROE-4 and ROA-1 were the most significant variables. For the longer-term post-issue abnormal returns, full-sample regression showed ROA1 had significant association, in agreement with the full-sample regression on principal components, and full-sample random forest regression analysis. Year-by-year regression on principal components showed a variety of factors significantly affected longer-run abnormal returns—book-to-market ratios among them. However, in year-by-year random forest regression, ROA-1 was the most consistent variable. Overall, there were some variables such as past firm profitability, for example, the return on assets, that could consistently affect abnormal stock returns at the announcement of SEOs and in the post-issue period, but we found support for our hypothesis that several other significant explanatory variables depended on the statistical method used. This may be especially true when there are a large number of possible explanatory variables. Readers and users of results reported in empirical studies must keep this in mind. There are some limitations to our study. One important limitation is obviously our relatively small size—2010–2015. The data came from Refinitiv’s Securities Data Company’s (SDC) Platinum Global Public Issues database, which has a subscription cost. We used the data we had, which also suited our purpose because we wanted to show that finding the correct significant explanatory variables is an issue that likely gets exacerbated when we have a smaller sample and a large number of candidate explanatory variables. Future studies can test our hypothesis using a longer time series of data, in different contexts (not just seasoned equity offerings), and with additional different methods. Author Contributions: Conceptualization, methodology, and writing—review and editing: C.N.V.K.; Formal analysis, investigation, and writing—original draft preparation: M.W. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Informed Consent Statement: Not applicable. Data Availability Statement: Data taken from CRSP, Compustat, FRED, and Bloomberg. Conflicts of Interest: The authors declare no conflict of interest. J. Risk Financial Manag. 2022,15, 473 20 of 22 Appendix A. Definition of Variables Firm Variables Variable Description Source ROA-1 Return on asset in the quarter ending before the announcement date Wharton Research Data Service (WRDS) ROE-1 Return on equity in the quarter ending before the announcement date Wharton Research Data Service (WRDS) MVE-1 Market value of equity in the quarter ending before the announcement date Wharton Research Data Service (WRDS) BTM-1 Book value to market value in the quarter ending before the announcement date Wharton Research Data Service (WRDS) OI/A-1 Operating income to asset in the quarter ending before the announcement date Wharton Research Data Service (WRDS) ROA-2 Return on asset at the end of 2 quarters before announcement date Wharton Research Data Service (WRDS) ROE-2 Return on equity at the end of 2 quarters before announcement date Wharton Research Data Service (WRDS) MVE-2 Market value of equity at the end of 2 quarters before announcement date Wharton Research Data Service (WRDS) BTM-2 Book value to market value at the end of 2 quarters before announcement date Wharton Research Data Service (WRDS) OI/A-2 Operating income to asset at the end of 2 quarters before announcement date Wharton Research Data Service (WRDS) ROA-4 Return on asset at the end of 4 quarters before announcement date Wharton Research Data Service (WRDS) ROE-4 Return on equity at the end of 4 quarters before announcement date Wharton Research Data Service (WRDS) MVE-4 Market value of equity at the end of 4 quarters before announcement date Wharton Research Data Service (WRDS) BTM-4 Book value to market value at the end of 4 quarters before announcement date Wharton Research Data Service (WRDS) OI/A-4 Operating income to asset at the end of 4 quarters before announcement date Wharton Research Data Service (WRDS) Economy-wide Variables Variable Description CAPE The latest Shilller CAPE Rate disclosed before the announcement date Shiller website GDP The latest US GDP Index disclosed before the announcement date Federal Reserve Economic Data (FRED) CPI The latest US CPI Index disclosed before the announcement date Federal Reserve Economic Data (FRED) UNEMP The latest Unemployment rate disclosed before the announcement date Federal Reserve Economic Data (FRED) GDPG US GDP growth in past 1 year before announcement date Federal Reserve Economic Data (FRED) Fixed Income Variables Variable Description 1MGR US 1-month T-Bill rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) 1YGR US 1-year T-Bill rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) 5YGR US 5-year government bond rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) 10YGR US 10-year government bond rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) 25YGR US 25-month government bond rate closing price on the day before the announcement date U.S. Department of The Treasury TED TED rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) AAA Moody AAA corporate bond rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) BIG Moody below investment grade rate closing price on the day before the announcement date Federal Reserve Economic Data (FRED) Stock Market Variables Variable Description 3MD DJIA Index returns from 3 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 6MD DJIA Index returns from 6 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 12MD DJIA Index returns from 12 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 3MS S&P 500 Index returns from 3 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 6MS S&P 500 Index returns from 6 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 12MS S&P 500 Index returns from 12 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 3MN Nasdaq Index returns from 3 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 6MN Nasdaq Index returns from 6 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data 12MN Nasdaq Index returns from 12 months before the announcement date to 1 day before the announcement date Bloomberg Historical Data References Abdi, Herve, and Lynne J. 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