What do we really know about corporate hedging? A meta-analytical study

Geyer-Klingeberg, Jerome; Hang, Markus; Rathgeber, Andreas W.; Stöckl, Stefan; Walter, Matthias Article What do we really know about corporate hedging? A metaanalytical study Business Research Provided in Cooperation with: VHB - Verband der Hochschullehrer für Betriebswirtschaft, German Academic Association of Business Research Suggested Citation: Geyer-Klingeberg, Jerome; Hang, Markus; Rathgeber, Andreas W.; Stöckl, Stefan; Walter, Matthias (2018) : What do we really know about corporate hedging? A meta-analytical study, Business Research, ISSN 2198-2627, Springer, Heidelberg, Vol. 11, Iss. 1, pp. 1-31, https://doi.org/10.1007/s40685-017-0052-0 This Version is available at: https://hdl.handle.net/10419/177276 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ REVIEW What do we really know about corporate hedging? A meta-analytical study Jerome Geyer-Klingeberg 1 •Markus Hang 1 • Andreas W. Rathgeber 1 •Stefan Sto ¨ckl 2 • Matthias Walter 3 Received: 30 October 2016 / Accepted: 22 July 2017 / Published online: 9 August 2017 The Author(s) 2017. This article is an open access publication Abstract This paper employs meta-analysis to aggregate and systematically analyze the mixed empirical evidence on the determinants of corporate hedging reported in 132 previously published studies covering data from more than 73,000 firms. Among the fourteen proxy variables analyzed by multivariate meta-analysis, three variables emerge as reliable explanatory factors for corporate hedging decisions supporting the bankruptcy and financial distress hypothesis: dividend yield (positive sign), liquidity (negative sign), and firm size (positive sign). Moreover, for tax-loss carry forwards (positive sign) and research and development (positive sign), our findings indicate a weak impact on corporate hedging behavior reflecting tax reasons, the coordination Electronic supplementary material The online version of this article (doi:10.1007/s40685-017-00520) contains supplementary material, which is available to authorized users. &Stefan Sto ¨ckl [email protected] Jerome Geyer-Klingeberg [email protected] Markus Hang [email protected]augsburg.de Andreas W. Rathgeber [email protected]ni-augsburg.de Matthias Walter [email protected] 1 Institute of Materials Resource Management, Faculty of Mathematics and Natural Sciences, University of Augsburg, Universita ¨tsstrasse 2, 86135 Augsburg, Germany 2 Department of Finance, Audit, Accounting and Control, ICN Business School Nancy-Metz (Grande e ´cole), CEREFIGE-European Centre for Research in Financial Economics and Business Management, 3 place Edouard Branly, 57070 Metz, France 3 FIM Research Center, University of Augsburg, Universita ¨tsstrasse 12, 86159 Augsburg, Germany 123 Business Research (2018) 11:1–31 https://doi.org/10.1007/s40685-017-0052-0 between financing and investment, and agency conflicts between shareholders and debtholders. Regarding the asymmetric information and agency conflicts of equity hypothesis, we find no explanatory power. The further analysis of heterogeneity via meta-regression reveals several factors that determine the mixed empirical evidence reported in previous studies. First, the results indicate that studies analyzing firms from North America report, on average, a lower impact of leverage on the corporate hedging decision. Moreover, studies examining more recent data samples tend to find a weaker relation between tangible assets and hedging, R&D and hedging, respectively. Overall, our results encourage scientific research to put more emphasis on finer-grained examinations of hedging variations and to discover rationales of corporate hedging extending classical financial theories. Keywords Corporate hedging Corporate risk management Derivatives  Meta-analysis 1 Introduction The motivation for non-financial firms to engage in corporate hedging is one of the most intensively discussed topics in corporate finance research. Neoclassical finance theory claims that under the conditions of a perfect capital market, hedging on the firm level does not create additional value, since shareholders can perfectly hedge their position (Modigliani and Miller 1958). However, more recent financial theory suggests that when financial markets are not frictionless, there are several ways through which corporate hedging can increase firm value in the sense of the maximization of shareholder value (Bessembinder 1991; DeMarzo and Duffie 1991; Froot et al. 1993; Smith and Stulz 1985). In this manner, hundreds of primary studies have empirically investigated the theoretical explanations for corporate hedging. However, despite or perhaps exactly because of the vast amount of studies, the empirical literature presents rather mixed evidence for the drivers of corporate hedging (Aretz and Bartram 2010; Bartram et al. 2009; Fauver and Naranjo 2010;Judge2007). Two previous studies present quantitative summaries of the existing empirical findings for the hedging determinants (Aretz et al. 2007; Arnold et al. 2014). Aretz and Bartram (2010) conduct a broad literature review and apply vote counting to compare the number of statistically significant and insignificant results from the univariate/multivariate analysis sections reported in 31 primary studies. Their findings show weak evidence for the coordination of financing and investment policy hypothesis as well as the tax hypothesis. Although these results exhibit a detailed summary of the distribution and the extent of disagreement within the outcomes of prior research, vote counting approaches have been strongly criticized as ‘fatally flawed’ (Borenstein et al. 2009: 252; Stanley and Doucouliagos 2012:2).This assessment arises from the fact that vote counts collapse the observed estimates into a few categories based on their statistical significance, do not present an economic magnitude for the aggregated effects, and ignore differences of sample sizes and precision of the findings reported in the primary studies (see, among others, Borenstein et al. 2009; Hedges and Olkin 1985; Stanley and Doucouliagos 2012). 2 Business Research (2018) 11:1–31 123 To overcome the shortcomings of vote counting, Arnold et al. (2014) calculate weighted averages for a set of 15 different hedging determinants across a sample of 37 primary studies. Contradicting Aretz and Bartram (2010), their main result is that financial distress costs induce firms to hedge. In addition, they find weak evidence that the underinvestment problem and the dependence on costly external financing influence corporate hedging behavior. However, their univariate meta-analysis approach bears an essential caveat, since the computation of mean values across primary studies does not account for interactions between the examined proxy variables. Riley (2009) shows that ignoring these dependencies in a meta-analysis can lead to a heavily biased estimation of the aggregated results. Furthermore, independent testing of correlated effects increases the chance of finding spuriously significant results (Bender et al. 2008). Beyond the threat of biased estimates caused by the assumption of uncorrelated proxy variables, none of the mentioned reviews explores the sources of heterogeneity among the primary studies’ results. Hence, explanations for the mixed empirical evidence are still missing. Table 1 illustrates the contribution of this study to the existing literature and especially the two previous reviews on the determinants of corporate hedging. First, the field of corporate hedging is characterized by its multivariate interrelations. For example, in the case of existing corporate taxes, a combination of several influencing factors determines firm value creation through corporate hedging, such as volatility of pre-tax income, convexity of the tax function, and the amount of tax payments. For this reason, we employ the first multivariate metaanalysis in corporate finance research. This approach simultaneously integrates reported results for the fourteen most frequently analyzed hedging determinants based on manually collected data from a sample of 132 primary studies. The data availability from a sufficiently large number of studies allows to apply this multivariate approach, which requires reported estimates for the bivariate relations among all proxy variables. The number of articles included in this study is about three times larger than the samples analyzed by Aretz and Bartram (2010) or Arnold et al. (2014). In this way, we aim to comply with the requirement of any metaanalysis to examine the population of studies available in order to avoid systematic biases due to misspecification and publication selection while incorporating the multidimensional nature of empirical research findings (Stanley and Doucouliagos 2012). Moreover, this comprehensive data set increases the number of observations from different data sources and time periods, which reduces the impact of sampling errors within individual primary studies. In a second type of analysis, we employ meta-regression to explain the heterogeneity among the reported effect estimates by exploring the impact of regional differences, study quality, and observation period on the reported results. Finally, we consider the presence of a potential data mining bias, publication selection bias, and misspecification bias. These aspects have not been investigated in the other reviews on corporate hedging so far. In summary, our multivariate estimates of the aggregated primary studies’ results provide evidence for the bankruptcy and financial distress hypothesis. In this respect, we obtain statistically significant results (at least at a significance level of 5%) for the following proxy variables: dividend yield (positive sign), liquidity (negative sign), and firm size (positive sign). In addition, we find weak explanatory Business Research (2018) 11:1–31 3 123 Table 1 Summary of existing quantitative reviews This study Aretz and Bartram (2010) Arnold et al. (2014) Data No. of studies 132 29 37 No. of observations 700 a 200/267 b 211 Literature search process is reported Yes No Yes Inclusion criteria are reported Yes No Yes Publication date of sample studies 1993–2015 1983–2009 1993–2011 Inclusion of unpublished studies Yes Yes Yes Methodology Aim of the review Calculation of mean effect sizes considering the interdependencies among the proxy variables; Analysis of heterogeneity Overview of reported sign and statistical significance Calculation of mean effect sizes Applied method Multivariate meta-analysis following Becker (1992); metaregression for analysis of heterogeneity following Stanley and Doucouliagos (2012) Vote counting Univariate meta-analysis following Hedges and Olkin (1985) Effect sizes Zero-order correlations between proxies and hedging variable Dummy variables for significant results from univariate and multivariate analyses reported in primary studies Standardized mean differences calculated from the univariate analyses reported in primary studies Analyzing and explaining differences in study characteristics (heterogeneity) Yes Only separate results for FX and IR hedgers No Accounting for publication selection bias Yes No Only graphical analysis Accounting for data mining bias Yes No No This table provides an overview of the existing review articles in the corporate hedging literature and compares these reviews with the study at hand. a This number includes only the observations for the correlations between the proxy variables and the binary hedging variable. For a better comparison of the studies, the correlations measuring the interrelations among the proxies are not considered. b The number on the left-hand side refers to the observations from univariate primary studies’ results and the number of the right-hand side refers to multivariate results. 4 Business Research (2018) 11:1–31 123 power for the tax-loss carry forwards variable and the research and development (R&D) proxy (each at a significance level of 10%). This indicates weak support for the corporate tax hypothesis and agency costs of debt argument. Furthermore, we cannot find consistent evidence for the hypothesis that hedging alleviates asymmetric information and agency conflicts between managers and shareholders. Overall, these results differ from Aretz and Bartram (2010) and Arnold et al. (2014), since the former also find evidence for the asymmetric information hypothesis and both reviews identify some support for hedging to be driven by the motivation of firms to avoid agency conflicts of debt. The further analyses reveal that our main findings are robust against data mining bias and publication selection bias. Solely the results for interest coverage ratio, capital expenditure, and R&D seem to be slightly distorted towards reporting stronger and statistically significant results. Moreover, the impact of financial distress costs measured by the corporate leverage ratio are found to be less pronounced for US firms. Finally, the relation between tangible assets and corporate hedging, as well as R&D expenses and hedging decreases over time. The remainder of the paper is structured as follows. Section 2provides an overview of the four basic hypotheses of firm value creation by corporate hedging. Section 3serves as a short introduction to the methodology of multivariate metaanalysis. Section 4presents the search for literature, the data preparation, and descriptive statistics. Section 5reports our empirical findings, which are discussed in the subsequent Sect. 6. Section 7concludes. 2 Determinants of corporate hedging By incorporating capital market imperfections, scholars have developed several hypotheses explaining why hedging at the firm level adds value to shareholders (e.g., Bessembinder 1991; DeMarzo and Duffie 1991; Froot et al. 1993; Smith and Stulz 1985). These theories especially gain in importance due to the increasing volatility in financial markets, in particular foreign exchange rates, interest rates, and commodity prices, which drive a firm’s market value to the extent to which it depends on the development of these risk factors (Rawls and Smithson 1990). Following previous literature (e.g., Aretz and Bartram 2010; Arnold et al. 2014; Guay and Kothari 2003;Ku ¨rsten 2006), the theoretical hypotheses can be subsumed under the maximization of shareholder value. Within the shareholder value maximization theory, we review four hypotheses that explain how corporate hedging increases firm value by (1) reducing the corporate tax burden, (2) lowering bankruptcy and financial distress costs, (3) mitigating asymmetric information and agency conflicts of equity, as well as (4) improving the coordination of financing and investment policy and alleviating agency conflicts of debt. As most of the theoretical arguments are not directly observable, academics make use of proxy variables to test whether firms with properties according to the hedging hypotheses are more likely to hedge. Table 2sums up our analyzed proxy variables for each of the hypotheses together with the hypothetical signs and variable Business Research (2018) 11:1–31 5 123 definitions. As these variables are the standard proxies examined in the majority of the hedging literature, we do not further discuss them. Excellent discussions of the proxy variables are provided, among others, by Bartram et al. (2009), Ge ´czy et al. (1997), or Haushalter (2000). 2.1 Corporate taxes Mayers and Smith (1982) as well as Smith and Stulz (1985) show that, if a firm faces a convex tax function (i.e., taxes increase overproportionally with taxable income), corporate hedging can increase post-tax firm value by reducing the volatility of pre-tax income. This is due to Jensen’s inequality as less volatile cash Table 2 Summary of proxy variables for the determinants of corporate hedging Variable Hyp. sign Description Corporate taxes (H1) Tax-loss carry forwards ?Dummy variable that takes a value of ‘1’ if the firm has tax-loss carry forwards available and ‘0’ otherwise Bankruptcy and financial distress costs (H2) Dividend yield ? Dividend per share (scaled) Interest coverage ratio -(Logarithm of) Earnings before interest and taxes 7interest expenses Leverage ratio ?Book value of long-term or total debt (scaled) Liquidity -Current assets or cash and cash equivalents (scaled) Profitability -(Logarithm of) Sales or return on assets or EBIT (scaled) Firm size ?(Logarithm of) Book value of total assets or market value of the firm Tangible assets -Tangible assets (scaled) Asymmetric information and agency conflicts of equity (H3) Institutional investors -Percentage or number of shares held by institutional investors Option ownership ? (Logarithm of) Number, percentage or market value of options held by managers or directors Share ownership ?(Logarithm of) Number, percentage, or market value of shares held by managers or directors Coordination of financing and investment policy and agency conflicts of debt (H4) Capex ?Capital expenditures (scaled) R&D expenses ?Research and development expenses (scaled) Tobin’s Q ?(Logarithm of) Market value of firm 7book value of total assets This table sums up the proxy variables reviewed in the paper at hand, including their hypothetical sign for the impact on the corporate hedging decision, as well as the corresponding variable definition. The hypothesized sign describes the theoretical relationship between the proxy and the incentive for corporate hedging. Our variable definitions arise from an aggregation of the variables in the reviewed studies and are similar to those of Aretz and Bartram (2010). The descriptions are generalizations of the studyspecific variable definitions. 6 Business Research (2018) 11:1–31 123 flows lead to a lower expected tax liability. Thus, we receive the following hypothesis H1, which we test by tax-loss carry forwards as proxy variable: H1: Firms use corporate hedging as an instrument to profit from tax advantages. 2.2 Bankruptcy and financial distress costs Volatile future cash flows and a high leverage may induce situations in which a firm’s liquidity is insufficient to fully meet its contractually fixed payment obligations (Rawls and Smithson 1990). This increases the risk of bankruptcy and the firm might encounter direct and indirect costs of financial distress (Jensen and Meckling 1976). Since corporate hedging lowers cash flow volatility and therefore also the default probability, it reduces expected costs of financial distress and adds value to the firm (Brown and Toft 2002; Hahnenstein and Ro ¨der 2003; Smith and Stulz 1985; Stulz 1996). Thus, we receive the following hypothesis H2, which we test by dividend yield, interest coverage ratio, leverage ratio, liquidity, profitability, firm size, and tangible assets as proxy variables: H2: Firms use corporate hedging as an instrument to reduce the risk of bankruptcy and financial distress costs. 2.3 Asymmetric information and agency conflicts of equity 1 DeMarzo and Duffie (1991,1995) show that information asymmetries can arise from a manager’s proprietary information on the firm’s dividend stream. Due to preferred managerial access to corporate information, shareholders cannot fully replicate the firm’s hedging decision. Accordingly, under information asymmetry firms can hedge more effectively than its shareholders. Such informational asymmetries may result from high expenses for disseminating necessary information to the shareholders, whereby the costs increase with firm complexity (Dolde and Mishra 2007), or from protecting information transmission to competitors (Marshall and Weetman 2007). By reducing the variability of the corporate cash flow and thus lowering the noise in the firm’s dividend stream, hedging can be used as an instrument to overcome informational asymmetries between shareholders and managers. Hence, we receive the following hypothesis H3, which we test by institutional investors, option ownership, and share ownership as proxy variables: H3: Firms use corporate hedging to reduce information asymmetry and to mitigate agency conflicts of equity. 2.4 Coordination of financing and investment policy and agency conflicts of debt High leverage and a low present value of the firm may give rise to the following agency conflicts of debt, because under these conditions managers may have 1 The agency conflicts of equity hypothesis can also be derived from the maximization of manager’s private utility theory. However, we follow Aretz and Bartram (2010), Arnold et al. (2014) and Guay and Kothari (2003), and classify this hypothesis under the shareholder value maximization theory. Business Research (2018) 11:1–31 7 123 incentives to transfer wealth from bondholders to shareholders. First, managers may forego positive net present value projects if the expected project gains are required to satisfy fixed payment obligations to the bondholders (Myers 1977). Corporate hedging can relieve this problem, as a reduction of cash flow variability increases the probability that shareholders are residual owners after reimbursing the bondholders. Moreover, when external financing is more costly than internal financing (Myers and Majluf 1984), firms may forgo profitable investments due to a lack of internal funds. Froot et al. (1993) show that under this condition, corporate hedging may be used as instrument to coordinate the availability of internal funds. Secondly, managers acting in the best interest of shareholders may give rise to asset substitution by replacing low-risk assets with high-risk investments (Smith and Warner 1979). This is because shareholders’ equity positions are a call option on the company’s assets, and high variance projects enlarge option value (Mason and Merton 1985). However, for fixed payment receivers this exchange of assets raises additional risk. Hence, bondholders anticipating the opportunistic behavior of management claim higher returns or protective bond covenants, due to increasing risk and higher agency costs (Jensen and Meckling 1976). Corporate hedging adds value to the firm by lowering the project’s risk and accordingly diminishing agency costs which arise from the managerial incentive of asset substitution. Campbell and Kracaw (1990) additionally contribute that also credible commitments to hedge (for example, obligated hedging of interest rate risks via debt covenants) reduce agency costs of debt by lowering the incentive to asset substitution. Thus, we receive the following hypothesis H4, which we test by capital expenditures, R&D expenses, and Tobin’s Q as proxy variables: H4: Firms use corporate hedging as an instrument to coordinate investment and financing policies and to mitigate agency conflicts of debt. 3 Methodology of multivariate meta-analysis The objective of this multivariate meta-analysis is to comprehensively test the hedging determinants on an aggregated empirical level across a broad set of primary studies. In detail, we investigate the relationship between fourteen proxy variables and the corporate hedging behavior, which is modeled as a dummy variable that is equal to one for hedgers and zero otherwise. 2 As effect size measure for this relationship we use the Pearson correlation coefficient between each proxy variable j(j¼1;...;pÞand the hedging variable reported in study i(i¼1;...;k). 2 In contrast, other studies (e.g., Belghitar et al. 2013; Graham and Rogers 2002; Knopf et al. 2002) propose a continuous hedging variable to measure the extent of hedging (e.g., the gross notional derivative value or the fair value of derivative contracts). However, studies using a hedging dummy variable routinely report the descriptive statistics for hedgers and non-hedgers or a mean difference test between both groups, consequently providing us with sufficient information to extract correlations. In contrast, studies examining a continuous hedging variable do usually not present this information. Moreover, the number of studies using a dummy instead of a continuous hedging variable is much higher, and therefore a meta-analysis based on these studies yields more reliable results. 8 Business Research (2018) 11:1–31 123 hedging dummy variable. Further, we describe the findings from the analysis of heterogeneity. Therein, we test for the impact of study quality, time effects, and regional differences. Moreover, we explicitly analyze potential biases through data mining or publication selection at the end of this section. 5.1 Multivariate meta-analysis For the correct specification of the multivariate model, one main aspect of metaanalysis is the detection and consideration of between-study variation. As the effect sizes are collected from studies examining data from different countries and time periods, it would be problematic to assume that there is one single underlying population effect across all studies in our sample (Borenstein et al. 2009; Card 2012; Lipsey and Wilson 2001). In the case of heterogeneity, the effect size variation is not only driven by sampling error but also by variation between studies. For example, country-specific regulation or firm characteristics influence the true effect size, although the initial decision to hedge is the same. The Cochran’s Q-test is a commonly applied test for heterogeneity in meta-analysis that measures the excess variation beyond sampling error. The Q-test results in a test statistic of 41,056, 17 which obviously leads to a rejection of the null hypothesis of homogenous effect sizes at all common significance levels. We consider this aspect of heterogeneous effect sizes by applying random effects estimation, which explicitly accounts for the between-study variation. The estimates of the linear model estimated by multivariate meta-analysis are displayed in Table 4. 18 Regarding the corporate tax hypothesis (H1), the results reveal weak empirical evidence. The aggregated effect for tax-loss carry forwards is 0.0711 and slightly significant at the 10% level (p-value is 0.0956). The positive sign of the estimate indicates that hedging companies can better time the use of taxloss carry forwards, which results from the reduction in cash flow volatility hedging. This leads to an increase in the present value of tax preference items (Ge ´czy et al. 1997). The proxy variables used to test the bankruptcy and financial distress costs hypothesis (H2) show high significance levels for the influence of dividend yield (b¼0:0741;p¼0:0202), liquidity (b¼0:0893;p¼0:0108), and firm size (b¼0:2148;p¼0:0002). The estimate for firm size is the dominating effect in terms of statistical and economic significance. The positive sign of the size effect provides evidence that economies of scale are highly relevant for hedging firms. The finding that more liquid firms tend to hedge less is in line with theoretical predictions that financial liquidity enables greater flexibility in meeting financial requirements, which helps to mitigate financial distress costs. Consequentially, cash management can help to build a financial buffer acting as a substitute for hedging (Ge ´czy et al. 1997). Moreover, the results show that corporate dividend policy 17 The test statistic is approximately Chi-squared distributed with 1,522 degrees of freedom. 18 The corresponding random effects mean correlation matrix calculated by Eq. (1) (which serves as input for the linear model) can be found in Online Appendix E. Business Research (2018) 11:1–31 15 123 influences corporate hedging behavior. The positive aggregated effect for dividend yield can be explained by the fact that higher dividend payments lower the availability of internal funds required for payments to fixed claimholders, which leads to raising expected costs of financial distress (Nance et al. 1993). In addition, Kalay (1982) argues that higher dividend payouts introduce underinvestment problems and associated costs occurring from agency conflicts between shareholders and bondholders. Therefore, firms offering higher dividend payments to their shareholders have more incentives to engage in hedging to avoid distress costs and underinvestment problems. The findings for liquidity and dividend yield also pronounce the important interactions between hedging and other corporate financial decisions, namely cash management and dividend policy. Regarding the coordination of financing and investment policy and agency conflicts of debt hypothesis (H4), the results show ambiguous empirical evidence. The estimated mean effects reveal a positive relation between R&D expenses and corporate hedging, which confirms the hypothesized direction (b¼0:0910;p¼0:0541). As R&D expenses measure the availability of growth options in a firm’s investment opportunity set, firms with greater R&D expenses can benefit more from the risk reduction of corporate hedging through lower risk of underinvestment problems and associated agency costs (Choi et al. 2013). In addition, neither capital expenditures for property, plant and investment, nor Tobin’s Q show significant results at any conventional levels. 5.2 Further analyses To verify the robustness of our multivariate results, we perform two groups of additional tests: (1) investigation of data mining bias, (2) analysis of publication bias and exploration of heterogeneity. 5.2.1 Data mining bias First, we account for the fact that primary studies use different definitions for the examined proxy variables. Due to the large amount of emerging primary studies, this effect is even amplified. By using the testing methodology developed by Harvey et al. (2016), we consider the so-called data mining bias. In this manner, we account for the fact that various alternative variable definitions are used for the proxy variables. This large variety of definitions might by reasoned by an opportunistic behavior of researchers to favor certain findings. The corresponding results of the test are displayed in Table 5. As an assumption for this test, we suppose that authors select the variable definitions of the proxies to reach significant results. This means, the larger the variety of different variable definitions for the same proxy variable, the higher the risk of biased primary studies’ results driven by data-mining activities. To control for an overestimation of the multivariate effects arising from data-mining, we have to accommodate the test statistics of our results. Therefore, we calculate an adjusted 5% significance level for each proxy variable to get a more conservative limit. In the case of a high number of different variable definitions in relation to the number of 16 Business Research (2018) 11:1–31 123 effect size observations, the probability level is diminished in order to provide a more conservative significance level. For example, the significance level for dividend yield decreases from 5 to 2.17%. In some cases, the variable definitions are quite consistent across the sample of effect sizes, which leads to an increasing probability level (larger than 5%). For a conservative estimation, we leave these probability levels at 5% instead of increasing them as, for example, in the case of tax-loss carry forwards. As a result from this robustness test, it appears that our strongly significant findings are not affected by data mining bias as these estimates are still significant even when applying the more conservative, adjusted significance levels. For example, in the case of dividend yield, the 5% significance level is adjusted to 2.17%, due to 7 different variable definitions used in 41 studies. However, the estimated p-value for dividend yield (p¼0:0202) is still significant at the adjusted significance level. The same conclusions hold for liquidity and firm size. Table 4 Statistical results from multivariate meta-analysis Proxy variable Hyp. sign No. of firms bSE(b)p-value Corporate taxes (H1) Tax-loss carry forwards ?12,529 0.0711 0.0427 0.0956* Bankruptcy and financial distress costs (H2) Dividend yield ? 17,038 0.0741 0.0319 0.0202** Interest coverage ratio -16,187 -0.0127 0.0404 0.7530 Leverage ratio ?51,866 0.0302 0.0269 0.2607 Liquidity -33,767 -0.0893 0.0350 0.0108** Profitability -33,308 0.0751 0.0604 0.2135 Firm size ?52,667 0.2148 0.0574 0.0002*** Tangible assets -11,938 0.0715 0.0611 0.2425 Asymmetric information and agency conflicts of equity (H3) Institutional investors -18,040 0.0869 0.0559 0.1203 Option ownership ? 13,026 -0.0279 0.0442 0.5275 Share ownership ?13,643 -0.0421 0.0335 0.2091 Coordination of financing and investment policy and agency conflicts of debt (H4) Capex ?25,482 -0.0263 0.0262 0.3169 R&D expenses ?28,770 0.0910 0.0472 0.0541* Tobin’s Q ?38,937 0.0433 0.0327 0.1856 This table shows the results for the proxy variables used to test the corporate hedging hypotheses in a multivariate meta-analysis. Names of the proxy variables are listed in the first column, and the second column shows the specific hypothesized sign; the third column shows the number of firm observations summed up from the primary studies testing the respective proxy variable. Next, the results from multivariate meta-analysis are presented. Using the standardized regression slopes bfrom the multivariate linear model and their standard deviations SE(b) for each proxy variable, we calculate the z-statistic and the corresponding p-value to test the null hypotheses of bi¼0: *, ** and *** indicate the rejection of the null hypotheses at the 10, 5, and 1% probability levels. Business Research (2018) 11:1–31 17 123 Table 5 Results of the robustness test for data mining bias Proxy variable Number of different variable operationalizations in the primary studies a Hyp. sign Multivariate results Multivariate results based on adjusted 5% significance levels Emp. sign p-value Adjusted 5% significance levels a(PF) =0.05 b p-value Corporate taxes (H1) Tax-loss carry forwards 1 definition in 18 studies ?? 0.0956* 0.0500 0.0956 Bankruptcy and financial distress costs (H2) Dividend yield 7 definitions in 41 studies ? ?0.0202** 0.0217 0.0202** Interest coverage ratio 5 definitions in 30 studies -- 0.7530 0.0361 0.7530 Leverage ratio 9 definitions in 108 studies ?? 0.2607 0.0401 0.2607 Liquidity 6 definitions in 72 studies -- 0.0108** 0.0500 0.0108** Profitability 8 definitions in 68 studies -? 0.2135 0.0387 0.2135 Firm size 7 definitions in 115 studies ?? 0.0002*** 0.0500 0.0002** Tangible assets 3 definitions in 11 studies -? 0.2425 0.0302 0.2425 Asymmetric information and agency conflicts of equity (H3) Institutional investors 5 definitions in 22 studies -? 0.1203 0.0242 0.1203 Option ownership 7 definitions in 19 studies ? -0.5275 0.0087 0.5275 Share ownership 6 definitions in 44 studies ?- 0.2091 0.0352 0.2091 Coordination of financing and investment policy and agency conflicts of debt (H4) Capex 5 definitions in 35 studies ?- 0.3169 0.0420 0.3169 R&D expenses 3 definitions in 37 studies ?? 0.0541* 0.0500 0.0541 18 Business Research (2018) 11:1–31 123 Table 5 continued Proxy variable Number of different variable operationalizations in the primary studies a Hyp. sign Multivariate results Multivariate results based on adjusted 5% significance levels Emp. sign p-value Adjusted 5% significance levels a(PF) =0.05 b p-value Tobin’s Q 3 definitions in 79 studies ?? 0.1856 0.0500 0.1856 This table shows the results of the data mining test. The second column contains the number of different variable operationalizations that we aggregated in our proxy variable definitions. The following column includes their hypothetical sign for the impact on the corporate hedging decision. Beside, the results (empirical signs and p-values) revealed from multivariate meta-analysis are presented, followed by the results using adjusted p-values to test the presence of data mining bias. a If one study uses several variations for a specific proxy variable, we considered only the definition with the least deviation related to the other studies testing the same proxy variable. A spot check revealed that the underlying sample covers most variations in the proxy-specific definitions b To account for the usage of different variable definitions and the possible data mining bias, we adjusted the p-values similar to Harvey et al. (2016). Therefore, we used the Bonferroni correction, respectively its exact version (the Sidak correction), both adjusting for the fact that the probability of a type I error in a multiple test differs from the error probability in a single test. However, in this connection we had to account for two issues (for details, see for example Abdi 2007). First, there are ns number of studies applying the same variable definition. This effect leads to a change in the probability of the type I error in ns trials. Second, there are the number of variable definitions nv leading to an increase in the probability of a type I error. Altogether, this results in a probability a(PF) of making as least one type I error, which depends on the probability of making a type I error a(PT), when only dealing with a specific test. Consequently, the adjusted probabilities can be expressed as follows: aPTðÞ¼11aPFðÞðÞ ns nv . In the case that ns =nv, there is no probability adjustment, because both effects equalize. In the other case (ns \nv), following Harvey et al. (2016), different studies applying different definitions lead to similar results. Hence, the probability of making a type 1 error in the first study depends on the probability in the second study. We model this dependence structure by applying a binary variable (0 =reject the null hypothesis; 1 =accept the null hypothesis). Due to the fact that we use a binary variable, the correlation coefficient can be easily calculated and comprises the complete dependence structure of the variables [in our case, arefers to a(PF)] Korr ¼1ajoint 1aðÞ 2 1aðÞ1aðÞ 2: Inverting the equation, the correlation structure can be fixed and the joint probability of making a type I error can be calculated as follows ajoint ¼1Korr 1 aðÞ1aðÞ 2  þ 1aðÞ 2: After applying the calculation of the probability for a quasi-independent event asing ¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1ajoint p, the formula changes to aPTðÞ¼11asing  ns nv : A look at the different studies shows a high dependency between the p-values of different studies having the same variable definition. Hence, we decided to use a high correlation Korr =0.8 in order to adjust for the correlation effect. Only those values were depicted, for which a(PT) \0.05 *, ** and *** indicate the rejection of the null hypotheses at the 10, 5, and 1% probability levels. Business Research (2018) 11:1–31 19 123 5.2.2 Publication bias and analysis of heterogeneity In this section, we test the heterogeneity of our dataset using a similar approach as presented by Carney et al. (2011). Consequently, we analyze and control for systematic differences in the reported effect sizes via multiple meta-regression analysis following recent publications in economics and finance (among others, Carney et al. 2011; Feld et al. 2013; Hang et al. 2017; Havranek and Irsova 2011). This step should serve as a verification that the aggregation of reported results in the multivariate meta-analysis is appropriate. Analogous to the work of Carney et al. (2011), this procedure especially allows us to examine the impact of overlapping firms and time periods in our sample. As dependent variable in the meta-regression, we investigate the effect size estimates measuring the direct effect of the proxy variable on the hedging dummy variable. For each effect size, we consider the impact of study quality, observation period, regional effects, and publication bias as explanatory variables in a regression model. In this regard, the number of citations is calculated as the logarithm of [(Google Scholar citations)/(age of the study) ?1]. 19 The number of citations is chosen as a criteria for study quality, as it considers study-specific quality characteristics and is available for all studies including unpublished papers. Second, to consider potential temporal variations due to regulatory changes or the development of financial markets, the mean observation year of each primary study sample is integrated in the analysis. Third, as a remarkable part of literature examines hedging data from US firms, we include a dummy variable that indicates whether a study uses data from North America (=1 for North America studies, zero otherwise). Finally, we investigate the existence of a potential publication selection bias in the reported results. Publication selection arises when researchers favor results based on their statistical significance or because they are consistent with the majority of literature (Card and Krueger 1995). This biasing effect may distort statistical inferences and especially averaged effects from meta-analysis. As commonly included in meta-regression analysis research, our model consequently contains the standard deviation of the effect sizes (m) as explanatory variable (Doucouliagos and Laroche 2009; Stanley 2004). A significant regression coefficient for the effect size’s standard error would imply that positive (negative) outcomes are more frequently reported than negative (positive) ones, due to a subjective selection of results (Stanley and Doucouliagos 2012). This test procedure follows the idea of the Egger’s test (Egger et al. 1997). Overall, the general metaregression model can be formularized as zij ¼b0þb1mþb2Citations þb3North America þb4Mean year þeij ð3Þ with the error term following a normal distribution with an expected value of zero and a variance set to the variance of the effect sizes according to 19 The number of citations was collected on January 13, 2017. 20 Business Research (2018) 11:1–31 123 eij Nð0;m2 ijÞ:ð4Þ The estimated regression coefficients b1;...;4measure the explanatory power of the independent variables for the variation of the z-transformed correlation coefficients. Thus, they indicate whether a certain variable systematically influences the reported results. For example, a significant positive effect for b3could be interpreted as finding that studies with US data, on average, report larger effects for a certain hedging determinant than non-US studies. Table 6reports the results for the meta-regression model including the four explanatory variables. The results show that the explanatory variables do not reveal a significant pattern across the various determinants of corporate hedging. 20 For the standard deviation as a test for publication bias, we observe significant values for interest coverage ratio with a coefficient of 1.8619, for capital expenditure with a coefficient of -1.1952, and for R&D with a coefficient of 1.7484, all significant at 5%. This finding allows us to conclude that the reported effect sizes tend to be biased in the way that authors favor to report positive effects for interest coverage ratio and R&D, and to report negative effects for Capex. Nevertheless, our main conclusions for tax-loss carry forwards, dividend yield, liquidity, and size are not distorted by selective reporting. Moreover, we find no explanatory power for the number of study citations. This indicates that study quality captured by the number of citations has no systematic impact on the reported results. Furthermore, for the North America dummy, the results reveal a significant effect for leverage at the 5% level (bLeverage 3=-0.1375). This means that the relation between capital structure and corporate hedging is diminished in North America studies compared to studies examining firm data from the rest of the world, where the effect tends to be more in line with the hypothesized positive sign. Additionally, we reveal significant temporal differences at the 5% level for tangible assets with a coefficient of -0.0679 and R&D with a coefficient of -0.0112. According to the empirical signs derived from multivariate analysis, the impact of tangible assets on the decision to hedge becomes less apparent over time. Furthermore, studies covering more recent data tend to report lower effect sizes for R&D expenses. 6 Discussion In this section, we first compare our main results with the ten leading primary studies included in our sample. 21 These studies are Allayannis and Weston (2001), Campello et al. (2011), Choi et al. (2015), Donohoe (2015), Ge ´czy et al. (1997), Jin and Jorion (2006), Nance et al. (1993), Pe ´rez-Gonza ´lez and Yun (2013), Pincus and Rajgopal (2002), Tufano (1996), which can be seen as representatives of 20 In addition to a mixed effects multilevel model as displayed in Table 6, we also applied a simple ordinary least squares model as shown in Online Appendix F. Overall, both models show quite similar results. 21 For the selection of studies we used the VHB-JOURQUAL3 and incorporate studies, which are classified as A?. Business Research (2018) 11:1–31 21 123 Table 6 Results of the robustness test for systematic differences in the heterogeneity of effect sizes Hypothesis Taxes (H1) Bankruptcy and financial distress costs (H2) Dep. variable/ effect size Tax-loss carryforwards Dividend yield Interest coverage ratio Leverage ratio Liquidity Profitability Firm size Tangible assets Hyp. sign ??– ?––?– This study ?*?** – ?–** ??*** ? Intercept 0.0120 (0.08) 0.2117 (1.64) –0.1355 (–0.91) 0.2319** (2.57) –0.1147 (–0.78) 0.1593 (1.04) 0.3181* (1.86) 0.6392*** (2.60) m1.0863 (1.06) –1.1137 (–1.37) 1.8619** (2.01) –0.4779 (–0.92) –0.5823 (–0.95) 0.3538 (0.49) –0.1855 (–0.26) 2.4189 (1.64) Citations 0.0056 (0.15) 0.0082 (0.22) –0.0224 (–0.51) –0.0052 (–0.19) 0.0194 (0.46) 0.0386 (0.91) 0.0074 (0.17) –0.0300 (–0.57) North America –0.0505 (–0.71) –0.0917 (–1.04) 0.0194 (0.24) –0.1375** (–2.33) 0.0639 (0.42) –0.1522 (–0.74) –0.0886 (–0.43) –0.0844 (–0.41) Mean year 0.0002 (0.03) 0.0041 (0.44) 0.0014 (0.13) –0.0096 (–1.57) –0.0002 (–0.01) –0.0010 (–0.12) 0.0008 (0.07) –0.0679*** (–3.74) Observations 18 41 30 108 72 68 115 11 Hypothesis Asymmetric information and agency conflicts of equity (H3) Coordination of financing and investment policy and agency conflicts of debt (H4) Dep. variable/ effect size Institutional investors Option ownership Share ownership Capex R&D expenses Tobin’s Q Hyp. sign – ? ?? ? ? This study ?––– ?*? Intercept 0.3565* (1.94) –0.0415 (–0.35) –0.0907 (–0.79) 0.1022 (1.14) –0.0517 (–0.54) 0.0288 (0.32) m–1.1190 (–1.19) 0.7877* (1.70) 0.9188 (1.36) –1.1952** (–2.26) 1.7484** (1.97) 0.0077 (0.01) Citations –0.0543 (–1.22) 0.0427* (1.70) 0.0340 (0.90) –0.0153 (–0.63) 0.0171 (0.70) 0.0101 (0.37) North America 0.0369 (0.29) –0.0313 (–0.38) –0.0839 (–1.07) 0.0271 (0.53) 0.0775 (1.36) 0.0407 (0.74) Mean year –0.0167 (–1.09) –0.0086 (–0.87) –0.0118 (–1.39) –0.0036 (–0.71) –0.0112** (–2.02) –0.0039 (–0.68) 22 Business Research (2018) 11:1–31 123 Table 6 continued Hypothesis Asymmetric information and agency conflicts of equity (H3) Coordination of financing and investment policy and agency conflicts of debt (H4) Dep. variable/ effect size Institutional investors Option ownership Share ownership Capex R&D expenses Tobin’s Q Observations 22 19 44 35 37 80 This table presents the results of the meta-regression analysis. This approach allows the inspection of systematic variation in the effect sizes. As dependent variable, we use the ztransformed effect sizes measuring the direct influences of each proxy variable on the hedging dummy variable. As independent variables, we use explanatory variables representing study quality, observation period, regional effects, and publication bias. In this regard, the number of citations is calculated as the logarithm of [(Google Scholar citations)/(age of the study) ?1]. The number of citations was collected on January 13, 2017. The number of citations is preferred, as it considers study-specific quality characteristics and it is available for each study, including unpublished works. As a remarkable part of literature examines hedging data from US firms, we include a dummy variable that indicates whether a study uses US data (=1 for US studies, 0 otherwise). To consider potential temporal variation due to regulatory changes or the development of financial markets, the mean observation year of a sample is integrated in the analysis. Finally, we investigate the existence of a potential publication selection bias in the reported results. As commonly included in metaregression analysis research, our model contains the standard deviation of the effect size (m) as explanatory variable. The estimated regression model in general terms corresponds to zij ¼b0þb1mij þb2Citationsiþb3North Americaiþb4Mean yearij þeij;eij Nð0;m2 ijÞ: We estimate this model by a multilevel mixed-effects regression with country and time level effects. This estimation procedure controls for data dependencies between firm observations from the same country and the same decade. The table shows the regression coefficients, with the corresponding t-statistics reported in brackets below. *, ** and *** indicate the rejection of the null hypotheses at the 10, 5, and 1% probability levels. Business Research (2018) 11:1–31 23 123 the empirical literature in this field of research. The studies cover firm data for the time period from 1993 to 2015. Furthermore, we compare the results with the existing (univariate) reviews by Aretz and Bartram (2010) and Arnold et al. (2014). The univariate results reported in these studies are contrasted with the findings of our multivariate meta-analysis as outlined in Table 7. For the corporate tax hypothesis (H1), we are generally in line with existing literature. All studies in our comparison testing this variable do not find a strongly significant effect. The bankruptcy and financial distress costs hypothesis (H2) represents the most frequently confirmed hedging hypothesis. For dividend yield, our finding of a positive effect is also confirmed by two of five primary studies as well as by Arnold et al. (2014). For leverage, five of ten primary studies and the two reviews state a significantly positive effect. In this case, our estimates contradict with the majority of studies. These deviations might be driven by a notable endogeneity between capital structure and the decision to hedge, as corporate hedging might also be seen as the starting point of the capital structure decision (Bartram et al. 2009; Lin and Smith 2007; Lin et al. 2008). For liquidity, we reveal a negative association with the decision to hedge, which is only in line with the findings reported in Pincus and Rajgopal (2002) and the two previous reviews. The other studies do not find a significant effect for this hedging determinant. For the asymmetric information and agency conflicts of equity hypothesis (H3) the picture is the same as for the coordination of financing and investment policy and agency conflicts of debt hypothesis (H4). For both theories, existing studies partially proclaim strong evidence, which is not confirmed by our multivariate results. Deviations of our results exist in terms of institutional investors and R&D expenses. In both cases, four studies confirm a significantly positive association with the hedging dummy variable, which might be specifically driven by spurious effects in the correlational data we collected as effect sizes. A further aspect that becomes apparent from Table 7is that the choice of the investigated hedging determinants differs across primary studies. This might drive the deviating results through misspecification bias. Kirkham et al. (2012) find out in their simulation study that the multivariate approach as applied in this paper is a method to lower the effect of the publication bias and misspecification bias on the aggregated effect sizes. Frosi et al. (2014) come to a similar conclusion and state that this is especially true in the case of missing outcomes in the primary studies, which underlines the validity of our multivariate results and supports the approach to be used in further applications. Both references clearly point out the added value of the ‘borrowing of strength’-mechanism to the summary effect sizes in the multivariate meta-analysis, which means that ‘one can learn about unreported outcomes through the reported results for other correlated outcomes’ (Frosi et al. 2014: 2). 24 Business Research (2018) 11:1–31 123 Mason, Scott P., and Robert C. Merton. 1985. The Role of Contingent Claims Analysis in Corporate Finance. In Recent Advances in Corporate Finance, eds. Edward I. Altman, and Marti G. Subrahmanyam, 7–54. Homewood: Irwin. Mayers, David, and Clifford W. Smith. 1982. On the corporate demand for insurance. The Journal of Business 55 (2): 281–296. doi:10.1086/296165. Modigliani, Franco, and Merton H. Miller. 1958. The cost of capital, corporation finance and the theory of investment. The American Economic Review 48 (3): 261–297. Myers, Stewart C. 1977. Determinants of corporate borrowing. Journal of Financial Economics 5 (2): 147–175. doi:10.1016/0304-405X(77)90015-0. Myers, Stewart C., and Nicholas S. Majluf. 1984. Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics 13 (2): 187–221. doi:10.1016/0304-405X(84)90023-0. Nance, Deana R., Clifford W. Smith Jr., and Charles W. Smithson. 1993. On the determinants of corporate hedging. The Journal of Finance 48 (1): 267–284. doi:10.1111/j.1540-6261.1993.tb04709.x. Nguyen, Hoa, and Robert Faff. 2002. On the determinants of derivative usage by Australian companies. Australian Journal of Management 27 (1): 1–24. doi:10.1177/031289620202700101. Nguyen, Hoa, and Robert Faff. 2006. Foreign debt and financial hedging: evidence from Australia. International Review of Economics and Finance 15 (2): 184–201. Nguyen, Hoa, and Robert Faff. 2007. Are Financial Derivatives Really Value Enhancing? Australian Evidence. Deakin University School Working Paper in Accounting/Finance Series 2007. Nguyen, Hoa, and Robert Faff. 2010. Are firms hedging or speculating? the relationship between financial and firm risk. Applied Financial Economics 20 (10): 827–843. Olkin, Ingram, and Minoru Siotani. 1976. Asymptotic Distribution of Functions of a Correlation Matrix. In Essays in Probability and Statistics: A Volume in Honor of Professor Junjiro Ogawa, eds. Sadao Ikeda, and Junjiro Ogawa, 235-251. Tokyo: Shinko Tsusho. Pe ´rez-Gonza ´lez, Francisco, and Hayong Yun. 2013. Risk management and firm value: evidence from whether derivatives. The Journal of Finance 68 (5): 2143–2176. Pincus, Morton, and Shivaram Rajgopal. 2002. The interaction between accrual management and hedging: evidence from oil and gas firms. The Accounting Review 77 (1): 127–160. Raudenbush, Stephen W. 1988. Estimating change in dispersion. Journal of Educational and Behavioral Statistics 13 (2): 148–171. doi:10.3102/10769986013002148. Rawls, S.Waite, and Charles W. Smithson. 1990. Strategic risk management. Journal of Applied Corporate Finance 2 (4): 6–18. Riley, Richard D. 2009. Multivariate meta-analysis: the effect of ignoring within-study correlation. Journal of Royal Statistical Society 172 (4): 789–811. Smith, Clifford W., and Jerold B. Warner. 1979. On Financial Contracting: An Analysis of Bond Convenants. Journal of Financial Economics 7 (2): 117–161. Smith, Clifford W., and Rene ´M. Stulz. 1985. The determinants of firms’ hedging policies. Journal of Financial and Quantitative Analysis 20 (4): 391–405. doi:10.2307/2330757. Stanley, Tom D. 2004. Does unemployment hysteresis falsify the natural rate hypothesis? a metaregression analysis. Journal of Economic Surveys. doi:10.1111/j.0950-0804.2004.00231.x. Stanley, Tom D., and Hristos Doucouliagos. 2012. Meta-regression analysis in economics and business. Abingdon: Routledge. Stulz, Rene ´M. 1996. Rethinking risk management. Journal of Applied Corporate Finance 9 (3): 8–25. doi:10.1111/j.1745-6622.1996.tb00295.x. Tufano, Peter. 1996. Who manages risk? an empirical examination of risk management practices in the gold mining industry. The Journal of Finance 51 (4): 1097–1137. doi:10.1111/j1540-6261.1996. tb04064.x. Whiston, Susan C., and Peiwei Li. 2011. Meta-analysis: a systematic method for synthesizing counseling research. Journal of Counseling and Development 89 (3): 273–281. Business Research (2018) 11:1–31 31 123