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A Meta-Analysis in Finance A META-ANALYSIS IN FINANCE CHANG-SOO KIM Department of Finance and Business Economics, University of Washington, Seattle, WA, USA Department of Business Administration, Yonsei University Yonseidae-gil 1, Heungup-myon, Wonju, Gangwon-do 26493, South Korea E-mail: [email protected] Abstract- A tremendous amount of academic papers have been published in finance over the past several decades. Important topics include internal capital market, corporate social responsibility, socially responsible investment, mergers and acquisitions, and so forth. Many researchers have attempted to figure out whether variables pertaining to these subjects have a positive relationship with corporate financial performance. However, it is not easy to synthesize empirical results of extant research, since papers are so different in terms of methodology used, research period, measurement of key variables, data set, etc. A meta-analysis is an excellent tool to aggregate a variety of heterogeneous results and comprehend the overall picture scientifically. This method is far better than a synthesis paper produced by a single person due to the problem of researcher bias. It is also better than a voting method since it takes care of the size and variance of impacts. This paper investigates the possibility of using meta-analysis in finance area and discusses issues regarding statistical test, bias correction, small sample problems, data collection, and so on. In addition to the discussion of the meta-analysis per se, we also provide an example of meta-analysis applied in one of finance areas, socially responsible investments. Keywords- Meta-analysis, effect size, fixed-effect model, random-effect model, socially responsible investments I. INTRODUCTION help managers build up their reputation at the expense of firm resources, SRI will generate a lower return A meta-analysis is an excellent tool to aggregate a than equivalent conventional investments. Portfolio variety of heterogeneous results and comprehend the theory also predicts a negative influence of SRI. overall picture scientifically. This method is far better Since SRI screening imposes constraints in the than a synthesis paper produced by a single person process of portfolio formation, the efficient frontier of due to the problem of researcher bias. It is also better SRI is inferior to that of conventional investments than a voting method since it takes care of the size that have no restrictions at all (Markowitz, 1952; and variance of impacts. We apply a meta-analysis to Girard et al., 2007). However, if diversification costs one of most interesting areas in finance, socially from SRI are not big and the increase in corporate responsible investments (SRI) to figure out whether performance from improved reputation and SRI performs better than conventional investments. governance caused by SRI activities is large, then There have been attempts to synthesize the existing SRI will generate positive impact on average (Boutin- literature, but they had many flaws which can be Dufresne and Savaria, 2004). improved (Orlitzky et al. 2003, Margolis et al. 2007, and Rathner 2013). Since existing papers are very Since theory indicates effects in both directions, the heterogeneous in terms of methodology and empirical impact of SRI has to be delineated by empirical results, scientific evidence needs to be provided by investigation. For this we attempt to synthesize employing a sound and comprehensive statistical existing literature by adopting a meta-analysis, which method. Since meta-analysis on SRI is quite rare, this is an excellent tool to aggregate many different research will contribute to understanding overall papers and results. Meta-analysis follows these steps: performance of SRI. In addition, since we plan to 1) identifying research questions, 2) collecting data, address many research issues in performing meta- 3) evaluating data, 4) analyzing and interpreting data, analysis, this paper can contribute to understanding and 5) reporting. and improving methodology, too. 1. Identifying Research Questions II. METHODOLOGY To achieve the goal of figuring out the impact of SRI on financial performance, we will calculate the We begin our research by investigating theoretical weighted average ESs for both a SRI group (SRI arguments related to the effect of SRI, since it will mutual funds, SRI indices, and SRI portfolios) and a enrich interpretation of empirical results. SRI effects non-SRI group (conventional funds, indices and have both positive and negative dimensions portfolios). Since ESs can vary systematically with (Hamilton et al., 1993). A positive theory argues that dimensions of SRI such as location of markets, SRI can serve as a channel for expressing social financial performance measures, investment horizons, responsibility values, so it will produce a positive SRI thematic approaches, types of researcher, impact on investment performance. A negative theory publishing status, and data comparison method, we emphasizes agency problems. Since CSR activities Proceedings of 62nd ISERD International Conference, Boston, USA, 14th-15th January 2017, ISBN: 978-93-86291-88-2 28 A Meta-Analysis in Finance will perform various subgroup analyses and meta- 3. Evaluating Data regression using many moderator variables. In the stage of data evaluation, we establish the criteria for inclusion in the analysis and code data for 2. Collecting Data computer-assisted analysis. To be included in the Data collection is very important for the success of final analysis, a study has to satisfy various screening meta-analysis. First, all relevant documents will be criteria. First of all, the study has to have necessary extensively collected to avoid the possibility that final quantitative information to calculate ESs, so all results are driven by the data collected. For this, we qualitative studies will be excluded. Second, studies will search all databases that are considered to without information on control groups will be contain documents about SRI performance such as excluded, since it is impossible to evaluate whether Scopus, ABI Inform/Global, EBSCO, JSTOR, SRI performance is better or not without information Econlit, Science Direct, Wiley-Blackwell, Web of on comparison groups. Third, event studies will be Science and SSRN for full-text articles. We will also excluded since the focus of this paper is on the long- include web search engines such as Google Scholar term performance, not the immediate reaction to SRI and Google Books. When searching, we are going to announcements. Fourth, an overrepresentation bias use a list of phrases that are formed by combining will be controlled for. It is possible that there are basic keywords like ‘SRI’, ‘ethics’, ‘responsible’, multiple studies on the same subject by the same ‘social’, ‘financial’, ‘funds’, and ‘performance’. We author in different forms like dissertation, working will carefully design the combination of keywords to paper, and published article. If all of these studies are reduce redundancies by considering necessary and included, the study will be over-weighted. In this sufficient conditions. case, only the version that has the necessary information and is most reliable will be included. In addition, we will search academic journals that are related to SRI and perform manual searches of the When applying deletion criteria, we use upper level reference lists of selected papers. The list of journals criteria first and then use lower level criteria. We includes Academy of Management Journal, American clearly indicate the number of articles and documents Economic Review, Journal of Finance, Review of that are deleted and the number of documents Financial Studies, Journal of Corporate Finance, included in the final meta-analysis by reporting a Journal of Banking and Finance, Financial Analysts flow chart of deleting process. Journal, Journal of Financial and Quantitative Analysis, Journal of Portfolio Management, Journal This stage is very important since it can have a of Financial Economics, Journal of Business Ethics significant impact on the final results, so we proceed and Corporate Governance. very carefully during the deleting process. After we decide on papers to be included in this analysis, data When collecting documents and data, we will try to entry into a computer is performed. Since there is avoid typical biases that may have a significant always a chance of making errors, two people impact on the results of meta-analysis. First, a independently enter data and the resulting files are publication bias that is caused by collecting only compared to confirm the accuracy of input data. published articles and documents will be taken into account. In general, published materials are better in 4. Analyzing and Interpreting Data quality and more reliable, but it is also true that only In the stage of data analysis and interpretation we papers with a high statistical significance tend to be have to calculate the effect size (ES) of individual published. On the other hands, many good papers studies. For this we use Cohen's (1969) d which is with meaningful empirical contents are rejected from similar to Hedges’ (1981) g that is calculated as academic journals due to a lower statistical follows: significance. To avoid publication bias, we include all articles and documents regardless of publication status and test whether meta-analysis results are systematically different by the status of publication. where is the average performance of SRI A bias caused by an inconsistent use of terms will (conventional) group and σ is the pooled within- also be considered. For example, experiment, group standard deviation which can be computed randomized trial, and RCT have the same meaning using the following formula: but they are used more frequently in one area but not in other areas. In this case, if only one term is used, a significant amount of information can be lost. We make a table of core keywords that summarize all of the variety of SRI related words with the same Here, NT(NC) is the sample size of SRI meaning and check the number of articles and (conventional) group and VT(VC) is the variance of documents to avoid this bias.
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