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Inicio Journal of Innovation & Knowledge A replication of Bowman's paradox across 28 countries
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Vol. 3. Issue 3.
Pages 128-142 (September - December 2018)
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Vol. 3. Issue 3.
Pages 128-142 (September - December 2018)
Empirical paper
DOI: 10.1016/j.jik.2016.12.006
Open Access
A replication of Bowman's paradox across 28 countries
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Pankaj C. Patela,
Corresponding author
pankaj.patel@villanova.edu

Corresponding author.
, Mingxiang Lib, Haemin Dennis Parkc
a Villanova University, Management and Operations, Villanova School of Business, 800 Lancaster Ave., Villanvoa, PA 19401, United States
b Florida Atlantic University, College of Business, Department of Management, 777 Glades Road, Boca Raton, FL 33431, United States
c Department of Management, LeBow College of Business, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104-2875, United States
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Tables (8)
Table 1. Basis of replication.
Table 2. Empirically observed cross-sectional risk–return relationship for non-US sample.
Table 3. Correction for spuriousness (Henkel, 2009) – Empirically observed cross-sectional risk–return relationship for non-US sample.
Table 4. Empirically observed longitudinala risk–return relationship for non-US sample.
Table 5. Empirically observed cross-sectional risk–return relationship for the US sample.
Table 6. Correction for spuriousness (Henkel, 2009) – Empirically observed cross-sectional risk–return relationship for the US sample.
Table 7. Empirically observed longitudinala risk–return relationship for US sample.
Table A.1. Distribution of firms across countries and industries.
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Abstract

This study assessed the generalizability of Bowman's paradox across 12,235 firms from 28 countries. Cross-sectional and longitudinal relationships between risk and return provided broad support for the presence of Bowman's paradox in diverse country settings (Asia, Europe, and South Africa), except India, Japan, and South Korea, where the relationship was positive. This replication confirms that Bowman's paradox generally holds across diverse institutional and cultural settings and supports prior studies on Bowman's paradox based on US samples.

Keywords:
Bowman's paradox
International business
Risk
Return
Skewness
JEL classification:
G3
Full Text
Introduction

Risk is generally expected to be positively associated with returns. However, Bowman (1980) observed an interesting phenomenon in a sample of 387 firms from 11 industries (from 1955 to 1973) and in a sample of 1572 firms from 85 industries (from 1968 to 1976). He found a negative correlation between accounting risk and return at the industry level. This phenomenon has since been referred to as Bowman's risk paradox, or the negative correlation between accounting based performance and the variance of accounting-based performance.

Bowman's paradox is considered a phenomenon and not a theoretical framework because it is counterintuitive to the generally accepted logic in financial economics – higher risk must accompany higher returns. Since Bowman's initial findings in 1980, strategy literature has addressed Bowman's paradox in a series of studies (Andersen & Bettis, 2015; Andersen, Denrell, & Bettis, 2007; Núñez Nickel & Rodriguez, 2002). Broadly, explanations for Bowman's paradox have focused on prospect theory or behavioral theory of the firm, statistical artifacts, and good management conduct (Andersen & Bettis, 2014, page 63). Drawing on prospect theory (Kahneman & Tversky, 1979), researchers have argued that low performing firms had a negative risk–return relationship and high performing firms had a positive risk–return relationship (Fiegenbaum & Thomas, 1988). Others have found a curvilinear relation between risk and return (Chang & Thomas, 1989). Relatedly, drawing on behavioral theory of the firm (Bromiley, 1991a), researchers have found that, when performance is below (above) aspiration levels, managers take more (less) risks, resulting in a negative (positive) cross-sectional relationship between risk and return (Bromiley, 1991b; Miller & Leiblein, 1996; Palmer & Wiseman, 1999). Others have proposed that the negative relationship is more likely among firms with high levels of unrelated diversification (Bettis & Hall, 1982; Chang & Thomas, 1989; Kim, Hwang, & Burgers, 1993), among firms with high market power who have lower variation in sales (Cool, Dierickx, and Jemison, 1989; Woo, 1987), or among firms with high risk in the previous period (Miller & Leiblein, 1996). Furthermore, as firms get closer to bankruptcy, the relationship between risk and return becomes increasingly negative (Miller & Bromiley, 1990).

Interest in Bowman's paradox has continued in recent years. Although studies have traditionally used ROA as a measure of return, For instance, Brick, Palmon, and Venezia (2015) conclude that “positive relationship between mean ROE and its standard deviation is far more likely than a negative one” (page 99). In another study, Brick, Palmon, and Venezia (2012) conclude that the risk–return relationship is positive or non-significant after adjustments to beginning of year, instead of end of year, for equity and reported net income of accruals. To resolve Bowman's paradox using computational simulations, Andersen and Bettis, 2014 find that “both imperfect learning and a mindless random walk can lead to the inverse longitudinal risk–return relationships observed empirically” (page 1135), and others support for a U-shaped relationship (Pan & Zhou, 2015). Recent theoretical focus include behavioral theory of the firm (Xiaodong, Fan, & Zhang, 2014), managerial myopia (Holder, Petkevich, & Moore, 2016), and adaptive systems (Song, An, Yang, & Huang, 2012). Bowman's paradox was recently used as a backdrop to understand variations in risk preferences among female executives (Perryman, Fernando, & Tripathy, 2016).

In addition to theoretical explanations, others have pointed to potential statistical issues such as the use of accounting-based performance data (Marsh & Swanson, 1984), lack of lags (Miller & Leiblein, 1996), outliers and spurious correlation, and non-normal distribution of performance at the industry level (Henkel, 2009). A review of studies on Bowman's risk paradox also reveals that virtually all studies have drawn on US based samples, using Compustat, Fortune 500 firms, Value line, Census of Manufacturing, Arbitron, and PIMS [except for Jegers (1991) who drew on a sample of 3250 Belgian firms] (Andersen & Bettis, 2015; Núñez Nickel & Rodriguez, 2002).

The above discussion suggests that despite focus on mostly US based samples and correcting for statistical artifacts, Bowman's paradox continues to be supported in studies over the years. However, to extend the validity of this phenomenon, whether the relationship can be replicated in a cross-country context is essential to further build this framework.

The strategic management literature increasingly seeks to improve generalizability of management phenomena and scholars have called for a greater need for replication in different contexts (Harzing & Harzing, 2016; Hubbard, Vetter, & Little, 1998). Testing Bowman's risk paradox in a cross-country context is theoretically important and practically relevant as risk preferences, the mainstay of prospect theory and behavioral theory of the firm, are known to be culture specific or influenced by institutional factors (Rieger, Wang, & Hens, 2014). As risk–return relationship is influenced by cross-country differences, Bowman's risk paradox could vary across countries. Indeed, if Bowman's paradox were inconsistent across different countries, future research could further explore boundary conditions based on variations in cultural and institutional factors. In contrast, if the relationship were less variable across countries, firm- or industry-specific effects would be stronger in driving the relationship, and culture and institutional factors would be less influential. The proposed framework could help practitioners further understand the drivers of risk–return relationship.

This study assesses the generalizability of Bowman's risk paradox through a replication across 28 countries. It attempts to increase generalizability of the past findings by: (a) replicating past findings for US firms using a different time period (1998–2012); (b) generalizing Bowman's paradox by drawing on a sample 12,235 firms from 28 countries (excluding the US) from 1998 to 2012; (c) assessing robustness of findings by using proposed corrections of statistical artifacts by using lags, and splitting firms above and below median industry performance; and (d) correcting for potential spuriousness due to right skewness in performance of firms in the industry as recommended by Henkel (2009). Overall, our study contributes to the literature at the intersection between strategy and international business management by replicating the generalizability of Bowman's paradox in different countries around the world.

Background on Bowman's risk paradox

Investors require higher returns for undertaking higher levels of risk. Unlike investors who can generally mitigate financial risk through diversification, firm managers must manage multiple forms of business risks that cannot be diversified easily. Considering a broader set of risks, Miller and Bromiley (1990) propose three types of risks – income stream risk, stock returns risk, and strategic risk. Although the three forms of risks are interrelated, managers are concerned about long-term strategic risk and variations in income over time. As investors can diversify stock return risk, stock return risk may not fully capture the total risk faced by the firm. Due to variegated notions of both income and strategic risks, literature on Bowman's paradox has proposed a variety of accounting-based measures of performance and alternate specifications of variation in accounting-based measures of performance. Studies have found broad support for a negative relationship between cross-sectional accounting performance and variance of performance (Andersen & Bettis, 2015; Núñez Nickel & Rodriguez, 2002).

To provide a theoretical lens to explain the negative association between risk and return, scholars have drawn on prospect theory (Fiegenbaum & Thomas, 1988; Kahneman & Tversky, 1979) and behavioral theory of the firm (Bromiley, 1991b). Through the lens of behavioral theory of the firm, managers undertake more risk when performance is below aspiration, and they take low risk when performance is above aspirations. Due to contemporaneous association between risk-taking and low performance, contemporaneous relationship could be negative; as lower performance and higher risk are observed in cross-sectional accounting data, or lagging effects of risk and performance would continue in the short-term in longitudinal accounting data. Through the lens of prospect theory (Kahneman & Tversky, 1979), studies have argued that managers in low performing firms face negatively framed prospects and are thus more likely to undertake high risk. In contrast, managers in high performing firms face positively framed prospects and take low risk, resulting in negative correlation between high performance and low risk. Thus, prospect theory and behavioral theory of the firm provide possible explanations for the negative relationship between risk and return. Comeig, Holt, and Jaramillo-Gutiérrez (2015) further elucidate the joint mechanisms of prospect theory and behavioral theory of the firm in the context of Bowman's risk paradox by identifying reference points (of relative performance) and probability weights (of payoffs from risk). That is, when performance is below aspirations, decisions are framed negatively and managers undertake more risk. In evaluating such risky actions, managers underweigh downside of lower payoffs from increased risk. Similarly, when performance is above aspirations, managers undertake lower risk and assign low probability to higher payoff and thereby avoid risky actions.1

In addition, studies have shown that the negative relationship is also driven by adaptation capabilities, nature of diversification, distance from bankruptcy, and market power. Firms with high adaptation capabilities realize higher returns despite taking lower risks (Andersen et al., 2007). Adaptation capabilities allow firms to meet challenges of the changing environment, thus lowering variance in performance. Firms with high levels of unrelated diversification have lower variation in returns, and thus have negative correlation between variance in performance and mean performance (Chang & Thomas, 1989). As higher market power is negatively related to variance in performance, the negative risk–return relationship is likely to be higher in such firms. Finally, firms closer to bankruptcy could also have a negative risk–return relationship.

In addition to the theoretical explanations, several studies attribute the negative relationship to statistical artifacts. First, prior studies have often measured risk contemporaneously with returns. As mean return and variance in return are derived from the same underlying distribution of returns, the negative correlation may not be based on a theoretically meaningful relationship but on statistical artifacts resulting from model specification. However, Bowman's risk paradox is robust under lagged models (Andersen & Bettis, 2015) or under alternate measures of risk (based on survey questionnaire or managerial risk aversion coefficient obtained from utility function) or prospective and non-accounting measure of ex-ante level of risk – variability in stock analyst forecasts (for a review refer to Núñez Nickel & Rodriguez, 2002).

Second, others indicate that managers take multifaceted and multi-contextual view of risk. Managers focus more on downside risk than on upside risk and therefore their assessment of risk must be distinct from the theoretically espoused understanding of risk. However, studies using alternate measures of risk have found support for Bowman's paradox (Núñez Nickel & Rodriguez, 2002).

Third, and more importantly, critics have highlighted the endogenous relationship between return and variance in returns, non-normality in distribution of returns (Marsh & Swanson, 1984), and choice of aggregation periods (Ruefli & Wiggins, 1994; Ruefli, 1990, 1991). While studies have relied on shorter time periods to lower effects of non-stationarity in returns, estimates from such specifications are sensitive to outliers.

Finally, focusing on different time periods to understand the risk–return relationship could also bias the findings (Bromiley, 1991a). Furthermore, due to different strategic and competitive goals over the life-cycle of a firm, and changing industry characteristics over time could influence risk–return relationship. Therefore, relying on longitudinal samples or lowering survivor bias could help provide more robust inferences. As an example of where longitudinal data with industry controls could offer different inferences, Henkel (2009) shows that the negative correlation could be an artifact of right skewness in distribution of return among firms in the industry, and proposed a methodology to correct for such spuriousness.

Overall, past research has proposed different theoretical rationales for explaining the negative correlations, or has suggested that negative correlation could be an artifact of sampling criteria or statistical artifacts in measurement and analyses.

The need for replication

We undertake the replication with multiple objectives in mind. First, most studies on Bowman's risk paradox have drawn on US firms. We do not know whether Bowman's paradox is generalizable across different countries. It is possible that different country – and country×industry-specific unobserved heterogeneity could show a positive, negative, or non-significant association. Therefore, the primary aim of this study is to replicate Bowman's paradox in firms across 28 countries (excluding US firms).

Second, past studies have found different relationships based on different specifications of time periods used to analyze the data. To address this issue, we also conduct a split sample analysis by including different periods for generalizing cross-sectional (1998–2002; 2003–2007; 2008–2012) and lagged relationship (1998–2007; 2007–2012).

A criticism of studies on Bowman's risk paradox is the contemporaneous measurement of risk. Based on Andersen and Bettis (2015), we also test for longitudinal relationship between risk and return. Moreover, as most US based studies of Bowman's paradox have relied on samples of US firms from 1970s to mid-1990s, we also replicate these findings using US firms from a more recent time period – from 1998 to 2012.

Third, to assess generalizability of prospect theory or behavioral theory of the firm explanations, following Andersen et al. (2007), we test for differences in correlation for firms with performance below and above median industry performance.

Fourth, in response to Henkel (2009) call for correction for potential spuriousness in risk–return correlation driven by skewness in performance of firms in the industry, we include correction for spuriousness.

Table 1 provides a summary of theoretical and empirical issues incorporated from past work into this replication study.

Table 1.

Basis of replication.

Issue  Criticisms  Addressed in current replication 
Past studies have almost exclusively relied on US firms  Limited generalizability of Bowman's paradox across countries  • Compustat Global data representing 12,235 firms from 28 countries from years 1998 to 2012
• Replication of US firms using a different time period – 1998–2012 
Risk and return measured cross-sectionally  Lagged values could affect direction of risk–return relationships  The relationship is tested using lags in a longitudinal setting (Anderson and Bettis, 2014). 
Prospect theory and Behavioral theory explanations  Based on (Anderson et al., 2007), median split of the sample helps control for it.  Robustness of relationship is tested using full-, below-, and above-median effects. 
Time periods affect risk–return relationship  Past work found different relationships when using different time periods  Robustness of relationship is tested using:
• three-time periods for contemporaneous outcomes: 1998–2002; 2003–2007; 2008–2012 and
• two-time periods for longitudinal outcomes: from 1998 to 2007 and from 2003 to 2012 
Correction for spurious effects (Henkel, 2009Due to skewness in performance, risk–return correlations could be spurious in cross-section.  Included Henkel's (2009) spuriousness correction approach. 
Sample description

To replicate the testing of Bowman risk paradox in non-US sample, we obtained data from Global COMPUSTAT, which provides data items similar to the North American COMPUSTAT. In their review of the literature, Núñez Nickel and Rodriguez (2002) identify ROA and ROE as widely used outcome measures (as reviewed in Table 2 of their article). However, as equity levels are subject to different regulations in different countries and firms use different policies to value equity, we use ROA that is subject to lesser biases on differences in equity valuation practices in cross-country settings. Following previous studies (Andersen et al., 2007; Fiegenbaum & Thomas, 1988; Henkel, 2009; Núñez Nickel & Rodriguez, 2002), we used return on asset (ROA) as the measure for firm performance and to ensure reliability of aggregated correlations we only included industries with more than 25 firms in the sample.

Table 2.

Empirically observed cross-sectional risk–return relationship for non-US sample.

Industries (grouped by SIC)  SIC range  1998–20022003–20072008–2012
    Correlation coefficientCorrelation coefficientCorrelation coefficient
    Sample size  Full sample  Above media  Below median  Sample size  Full sample  Above media  Below median  Sample size  Full sample  Above media  Below median 
Metal mining  0100–1220  536  −0.725  0.324  −0.755  480  −0.780  0.350  −0.864  400  −0.761  0.356  −0.832 
Energy extraction  1311–1389  171  −0.777  0.294  −0.880  142  −0.758  0.187  −0.884  122  −0.691  0.215  −0.846 
Operative builders  1531–1731  361  −0.530  0.679  −0.898  314  −0.205  0.143  −0.604  265  −0.184  0.225  −0.560 
Food products  2000–2111  840  −0.139  0.328  −0.624  723  −0.259  0.407  −0.783  651  −0.466  0.354  −0.865 
Textile industry  2200–2273  342  −0.435  0.388  −0.869  304  −0.263  0.324  −0.633  286  −0.531  0.334  −0.804 
Apparel industry  2300–2390  196  −0.214  0.064  −0.540  168  −0.464  0.198  −0.731  139  −0.526  0.142  −0.776 
Lumber & wood products  2400–2452  121  −0.539  0.752  −0.813  100  −0.558  0.154  −0.782  85  −0.840  0.410  −0.914 
Household & office furniture  2510–2590  67  −0.246  −0.037  −0.540  59  −0.840  0.062  −0.964  48  −0.523  −0.150  −0.762 
Paper milling & products  2600–2673  293  −0.483  0.334  −0.835  256  −0.701  0.180  −0.797  231  −0.870  0.286  −0.971 
Newspaper & book publication  2711–2790  143  −0.768  0.089  −0.852  120  −0.672  0.162  −0.763  105  −0.149  0.250  −0.573 
Chemical & pharmaceutical products  2800–2891  1083  −0.713  0.307  −0.772  964  −0.717  0.245  −0.795  882  −0.685  0.324  −0.781 
Petroleum refining  2911–2990  105  −0.480  0.376  −0.877  94  −0.826  −0.064  −0.931  85  −0.806  0.031  −0.929 
Rubber & plastic products  3011–3089  273  −0.606  0.129  −0.780  238  −0.362  0.330  −0.704  225  −0.414  0.388  −0.618 
Stell works & metals  3300–3390  521  −0.381  0.314  −0.800  466  −0.202  0.475  −0.780  429  −0.798  0.326  −0.933 
Fabricated metal products  3400–3490  275  −0.414  0.427  −0.858  239  −0.485  0.058  −0.716  210  −0.718  0.382  −0.933 
Industrial machinery  3510–3569  547  −0.548  0.396  −0.844  463  −0.682  0.281  −0.889  414  −0.679  0.225  −0.857 
Computer & office equipment  3570–3590  246  −0.656  0.278  −0.752  214  −0.853  0.143  −0.913  185  −0.705  0.092  −0.729 
Electrical equipment & electronics  3600–3695  855  −0.707  0.126  −0.774  766  −0.793  0.347  −0.855  685  −0.782  0.284  −0.849 
Vehicles & transportation equipment  3700–3790  431  −0.692  0.177  −0.787  382  −0.624  0.240  −0.719  360  −0.636  0.205  −0.748 
Industrial instruments & equipment  3812–3873  306  −0.684  0.221  −0.718  257  −0.816  0.267  −0.847  219  −0.804  0.259  −0.826 
Toys, games, sporting goods, etc.  3910–3990  133  −0.408  0.526  −0.853  115  −0.152  0.483  −0.602  102  −0.258  0.116  −0.565 
Line-haul operations & trucking  4011–4213  356  −0.296  0.231  −0.605  311  −0.096  0.426  −0.507  275  −0.331  0.226  −0.681 
Air transportation  4512–4522  237  −0.786  0.493  −0.862  207  −0.675  0.420  −0.842  184  −0.556  0.096  −0.719 
Communication & broadcasting  4812–4899  309  −0.778  0.096  −0.844  252  −0.618  0.442  −0.824  208  −0.763  0.322  −0.892 
Electric services  4911  194  −0.169  0.437  −0.615  166  −0.051  0.653  −0.495  153  0.380  0.759  −0.615 
Gas transmission & distribution  4922–4991  198  −0.699  0.543  −0.885  175  −0.774  0.339  −0.930  166  −0.818  0.373  −0.910 
Miscellaneous wholesaling  5000–5190  745  −0.515  0.463  −0.825  636  −0.749  0.443  −0.901  561  −0.724  0.153  −0.829 
Department & variety stores  5311–5399  148  0.116  0.290  −0.141  120  −0.150  0.101  −0.611  107  −0.155  0.307  −0.664 
Grocery & convenience stores  5411–5412  114  −0.410  −0.030  −0.573  86  −0.370  −0.002  −0.653  72  0.341  0.348  0.038 
Apparel & clothing stores  5600–5661  134  −0.471  0.142  −0.866  106  −0.105  0.121  −0.772  88  −0.459  0.094  −0.925 
Restaurants & eating places  5810–5812  113  0.162  0.416  −0.489  80  −0.218  0.282  −0.794  66  −0.051  0.322  −0.478 
Miscellaneous shopping stores  5912–5990  152  −0.884  0.326  −0.929  128  −0.239  0.020  −0.775  104  −0.713  0.007  −0.931 
Banking and real estate  6159–6799  63  −0.677  0.570  −0.860                 
Hotels & motels  7011  178  −0.357  0.233  −0.750  146  −0.596  0.325  −0.943  134  −0.207  0.204  −0.607 
Advertising & other services  7200–7363  179  −0.471  0.579  −0.787  150  −0.405  0.270  −0.818  113  −0.651  0.249  −0.861 
Programming & software services  7370–7389  1005  −0.714  0.223  −0.765  812  −0.703  0.262  −0.753  617  −0.718  0.420  −0.824 
Motion pictures & theaters  7812–7841  94  −0.678  0.066  −0.908  84  −0.319  0.432  −0.612  58  −0.859  0.326  −0.895 
Amusement & recreation services  7900–7997  144  −0.719  0.222  −0.918  108  −0.482  0.363  −0.825  89  −0.376  0.264  −0.485 
Medical & nursing services  8000–8093  75  −0.873  0.115  −0.924  62  −0.055  0.390  −0.658  53  −0.123  0.249  −0.194 
Engineering & management services  8700–8744  215  −0.703  0.232  −0.810  178  −0.494  0.365  −0.709  154  −0.584  −0.106  −0.584 
Corporate conglomerates  9995–9997  170  −0.879  0.363  −0.971  159  −0.772  0.584  −0.826  145  −0.856  0.381  −0.871 
Mean      −0.535  0.305  −0.774    −0.497  0.280  −0.770    −0.526  0.251  −0.740 

We focused on a 15-year period from 1998 to 2012. This allows us to calculate three concurrent risk–return relationship (consecutive 5-year periods: 1998–2002; 2003–2007; 2008–2012) and two sets of longitudinal risk–return relationship (the first ten year period from 1998 to 2007 and the second ten year period from 2003 to 2012). The final sample from COMPUSTAT Global data consisted of 12,235 firms from 28 countries from years 1998 to 2012. We list country-industry distribution of firms in Table A.1 in Appendix.

Analyses

We first computed concurrent risk–return correlation using the correlation between ROA and standard deviation of ROA. Table 2 summarizes results for concurrent risk–return relationship for the three time periods.

Table 3 summarizes results for concurrent risk–return relationship with Henkel's (2009) spuriousness corrections for the three time periods. It is clear from the tables that the negative risk–return correlation broadly exist in countries other than the US. Related to Table 2, for years between 1998 and 2002, only two out of 41 industries had a positive risk–return correlation. For years between 2003 and 2007, no industry had a positive relation between risk and return. For years between 2008 and 2012, only two industries have positive risk and return relationship. These statistics strongly suggest that negative risk–return relationship is independent of country differences. In addition, we also found that average risk–return relationships are very stable for these three 5-year periods (average correlations for these three periods are −0.535, −0.497, and −0.526 for 1998–2002; 2003–2007; 2008–2012, respectively). Similar patterns are observed with Henkel's (2009) correction in Table 3.

Table 3.

Correction for spuriousness (Henkel, 2009) – Empirically observed cross-sectional risk–return relationship for non-US sample.

Industries (grouped by SIC)  SIC range  1998–20022003–20072008–2012
    Correlation coefficientCorrelation coefficientCorrelation coefficient
    Sample size  Full sample  Corrected coef  Spurious effect  % of inflation  Sample size  Full sample  Corrected coef  Spurious effect  % of inflation  Sample size  Full sample  Corrected coef  Spurious effect  % of inflation 
Metal mining  0100–1220  536  −0.725  −0.625  −0.100  13.84%  480  −0.780  −0.210  −0.570  73.12%  400  −0.761  −0.637  −0.124  16.33% 
Energy extraction  1311–1389  171  −0.777  −0.660  −0.117  15.06%  142  −0.758  0.071  −0.829  109.43%  122  −0.691  −0.610  −0.081  11.66% 
Operative builders  1531–1731  361  −0.530  −0.479  −0.051  9.58%  314  −0.205  −0.020  −0.185  90.10%  265  −0.184  −0.224  0.041  −22.27% 
Food products  2000–2111  840  −0.139  −0.162  0.024  −17.04%  723  −0.259  −0.368  0.109  −42.10%  651  −0.466  −0.217  −0.249  53.42% 
Textile industry  2200–2273  342  −0.435  −0.681  0.245  −56.34%  304  −0.263  −0.284  0.021  −7.87%  286  −0.531  −0.266  −0.264  49.82% 
Apparel industry  2300–2390  196  −0.214  −0.160  −0.054  25.23%  168  −0.464  −0.120  −0.344  74.14%  139  −0.526  −0.142  −0.384  73.05% 
Lumber & wood products  2400–2452  121  −0.539  −0.720  0.181  −33.53%  100  -0.558  −0.418  −0.140  25.16%  85  −0.840  −0.294  −0.545  64.95% 
Household & office furniture  2510–2590  67  −0.246  −0.341  0.096  −38.84%  59  −0.840  −0.796  −0.044  5.28%  48  −0.523  −0.553  0.030  −5.77% 
Paper milling & products  2600–2673  293  −0.483  −0.251  −0.232  48.06%  256  −0.701  −0.488  −0.213  30.33%  231  −0.870  0.053  −0.923  106.12% 
Newspaper & book publication  2711–2790  143  −0.768  −0.643  −0.125  16.34%  120  −0.672  −0.570  −0.102  15.13%  105  −0.149  0.083  −0.233  155.76% 
Chemical & pharmaceutical products  2800–2891  1083  −0.713  0.037  −0.750  105.18%  964  −0.717  −0.534  −0.184  25.59%  882  −0.685  −0.401  −0.284  41.51% 
Petroleum refining  2911–2990  105  −0.480  −0.503  0.023  −4.84%  94  −0.826  −0.720  −0.107  12.90%  85  −0.806  −0.840  0.034  −4.16% 
Rubber & plastic products  3011–3089  273  −0.606  −0.524  −0.082  13.49%  238  −0.362  −0.351  −0.011  3.14%  225  −0.414  −0.516  0.103  −24.88% 
Stell works & metals  3300–3390  521  −0.381  −0.318  −0.063  16.47%  466  −0.202  −0.299  0.098  −48.49%  429  −0.798  −0.575  −0.223  27.93% 
Fabricated metal products  3400–3490  275  −0.414  −0.249  −0.165  39.82%  239  −0.485  −0.505  0.021  −4.24%  210  −0.718  −0.415  −0.302  42.15% 
Industrial machinery  3510–3569  547  −0.548  −0.397  −0.151  27.63%  463  −0.682  −0.457  −0.225  32.99%  414  −0.679  −0.598  −0.081  11.95% 
Computer & office equipment  3570–3590  246  −0.656  −0.549  −0.107  16.29%  214  −0.853  −0.681  −0.172  20.19%  185  −0.705  −0.225  −0.480  68.03% 
Electrical equipment & electronics  3600–3695  855  −0.707  −0.611  −0.096  13.55%  766  −0.793  −0.118  −0.675  85.12%  685  −0.782  0.414  −1.196  152.96% 
Vehicles & transportation equipment  3700–3790  431  −0.692  −0.565  −0.127  18.35%  382  −0.624  −0.724  0.100  −16.00%  360  −0.636  −0.400  −0.237  37.20% 
Industrial instruments & equipment  3812–3873  306  −0.684  −0.586  −0.098  14.32%  257  −0.816  −0.633  −0.184  22.52%  219  −0.804  −0.754  −0.050  6.27% 
Toys, games, sporting goods, etc.  3910–3990  133  −0.408  −0.313  −0.095  23.22%  115  −0.152  0.155  −0.307  201.95%  102  −0.258  −0.420  0.162  −62.78% 
Line-haul operations & trucking  4011–4213  356  −0.296  −0.466  0.170  −57.44%  311  −0.096  −0.253  0.156  −161.76%  275  −0.331  −0.169  −0.163  49.11% 
Air transportation  4512–4522  237  −0.786  −0.599  −0.187  23.82%  207  −0.675  0.012  −0.687  101.82%  184  −0.556  −0.446  −0.109  19.69% 
Communication & broadcasting  4812–4899  309  −0.778  −0.407  −0.371  47.70%  252  −0.618  −0.282  −0.335  54.28%  208  −0.763  −0.325  −0.438  57.42% 
Electric services  4911  194  −0.169  −0.218  0.050  −29.43%  166  −0.051  0.079  −0.130  255.46%  153  0.380  0.386  −0.006  −1.66% 
Gas transmission & distribution  4922–4991  198  −0.699  −0.472  −0.228  32.55%  175  −0.774  0.176  −0.950  122.68%  166  −0.818  0.841  −1.659  202.83% 
Miscellaneous wholesaling  5000–5190  745  −0.515  −0.557  0.042  −8.12%  636  −0.749  −0.563  −0.185  24.76%  561  −0.724  −0.646  −0.078  10.73% 
Department & variety stores  5311–5399  148  0.116  0.077  0.039  33.80%  120  −0.150  −0.061  −0.089  59.16%  107  −0.155  −0.130  −0.025  16.03% 
Grocery & convenience stores  5411–5412  114  −0.410  −0.135  −0.275  67.10%  86  −0.370  −0.034  −0.336  90.77%  72  0.341  0.265  0.076  22.27% 
Apparel & clothing stores  5600–5661  134  −0.471  −0.413  −0.058  12.40%  106  −0.105  0.006  −0.111  105.74%  88  −0.459  −0.510  0.050  −10.96% 
Restaurants & eating places  5810–5812  113  0.162  0.191  −0.029  −18.20%  80  −0.218  −0.425  0.206  −94.54%  66  −0.051  0.133  −0.183  362.72% 
Miscellaneous shopping stores  5912–5990  152  −0.884  −0.810  −0.074  8.41%  128  −0.239  0.034  −0.273  114.15%  104  −0.713  −0.824  0.111  −15.60% 
Banking and real estate  6159–6799  63  −0.677  −0.362  −0.315  46.50%                     
Hotels & motels  7011  178  −0.357  −0.389  0.032  −8.98%  146  −0.596  0.185  −0.781  131.00%  134  −0.207  −0.143  −0.063  30.71% 
Advertising & other services  7200–7363  179  −0.471  −0.214  −0.257  54.59%  150  −0.405  −0.171  −0.234  57.68%  113  −0.651  0.120  −0.771  118.41% 
Programming & software services  7370–7389  1005  −0.714  0.076  −0.790  110.58%  812  −0.703  −0.558  −0.145  20.65%  617  −0.718  −0.011  −0.707  98.44% 
Motion pictures & theaters  7812–7841  94  −0.678  −0.585  −0.093  13.71%  84  −0.319  0.163  −0.481  151.00%  58  −0.859  −0.867  0.008  −0.93% 
Amusement & recreation services  7900–7997  144  −0.719  −0.340  −0.379  52.67%  108  −0.482  0.029  −0.511  106.08%  89  −0.376  −0.108  −0.268  71.34% 
Medical & nursing services  8000–8093  75  −0.873  0.671  −1.544  176.84%  62  −0.055  −0.138  0.083  −151.16%  53  −0.123  −0.136  0.013  −10.65% 
Engineering & management services  8700–8744  215  −0.703  −0.552  −0.151  21.43%  178  −0.494  −0.185  −0.310  62.62%  154  −0.584  −0.169  −0.415  71.08% 
Corporate conglomerates  9995–9997  170  −0.879  −0.207  −0.672  76.50%  159  −0.772  0.712  −1.484  192.24%  145  −0.856  −0.382  −0.474  55.38% 

To assess support for prospect theory or behavioral theory of firm explanations, we split the sample using the median performance of the industry following Andersen et al. (2007) approach. In years between 1998 and 2002, only two industries had a negative risk and return relationship among firms with performance above industry median. Therefore, for firms with performance above industry median the contemporaneous risk–return relationship is mainly positive. In contrast, risk and return relationship is broadly negative for firms performing below the industry median. Similar pattern carries on to the samples in years between 2003 and 2007 and years between 2008 and 2012. As such, we conclude that across 28 countries, firms performing below industry median generally have a negative correlation between risk and return, whereas firms performing above industry median generally have a positive correlation between risk and return.

The contemporaneous correlation between risk and return has been criticized by prior studies (e.g. Andersen & Bettis, 2015). Empirical evidence has shown that correlation between average performance and standard deviation of subsequent period tends to be less negative than the cross-sectional risk–return relationship (Miller & Chen, 2004). To replicate these results, we used longitudinal risk–return correlation suggested by Andersen and Bettis (2015). Their computation of longitudinal risk–return relationship is calculated as the correlation between the average ROA over the first five period and the standard deviation of ROA over the next five year period. As such, our first set of risk–return relationship was calculated as correlation between the mean ROA over year 1998–2002 and the standard deviation of ROA over years 2003–2007. Our second set of risk–return relationship was computed as the correlation between the mean ROA over year 2003–2007 and the standard deviation of ROA over years 2008–2012. Table 4 summarizes our findings.

Table 4.

Empirically observed longitudinala risk–return relationship for non-US sample.

Industries (grouped by SIC)  SIC range  1998–20072003–2012
    Correlation coefficientCorrelation coefficient
    Sample size  Full sample  Above media  Below median  Sample size  Full sample  Above media  Below median 
Metal mining  0100–1220  480  −0.380  0.144  −0.268  397  −0.336  0.138  −0.244 
Energy extraction  1311–1389  142  −0.448  −0.114  −0.368  122  −0.414  0.260  −0.359 
Operative builders  1531–1731  314  −0.119  0.055  −0.235  263  −0.117  0.044  −0.459 
Food products  2000–2111  723  −0.262  0.136  −0.467  643  −0.228  0.300  −0.527 
Textile industry  2200–2273  304  −0.275  0.109  −0.415  275  −0.016  −0.035  −0.009 
Apparel industry  2300–2390  168  −0.092  −0.077  −0.168  138  −0.161  −0.062  −0.193 
Lumber & wood products  2400–2452  100  −0.516  0.435  −0.727  85  −0.361  −0.075  −0.558 
Household & office furniture  2510–2590  59  −0.397  0.112  −0.593  48  −0.272  0.155  −0.665 
Paper milling & products  2600–2673  256  −0.280  0.109  −0.314  229  −0.664  0.105  −0.724 
Newspaper & book publication  2711–2790  120  −0.404  0.265  −0.513  104  −0.539  0.247  −0.734 
Chemical & pharmaceutical products  2800–2891  964  −0.591  0.114  −0.631  872  −0.413  0.169  −0.421 
Petroleum refining  2911–2990  94  −0.526  0.151  −0.611  84  −0.235  0.085  −0.223 
Rubber & plastic products  3011–3089  238  −0.231  0.256  −0.320  219  −0.340  0.104  −0.506 
Stell works & metals  3300–3390  466  −0.026  0.427  −0.291  426  −0.277  0.182  −0.541 
Fabricated metal products  3400–3490  239  −0.266  0.037  −0.461  207  −0.415  0.063  −0.655 
Industrial machinery  3510–3569  463  −0.438  0.084  −0.714  412  −0.557  0.189  −0.728 
Computer & office equipment  3570–3590  214  −0.553  0.187  −0.573  185  −0.467  0.088  −0.482 
Electrical equipment & electronics  3600–3695  766  −0.416  −0.031  −0.438  680  −0.438  0.053  −0.489 
Vehicles & transportation equipment  3700–3790  382  −0.389  0.242  −0.421  357  −0.544  0.156  −0.709 
Industrial instruments & equipment  3812–3873  257  −0.518  0.117  −0.489  219  −0.551  0.090  −0.547 
Toys, games, sporting goods, etc.  3910–3990  115  −0.056  0.278  −0.320  102  −0.044  0.268  −0.187 
Line-haul operations & trucking  4011–4213  311  0.011  0.152  −0.271  273  0.073  0.497  −0.255 
Air transportation  4512–4522  207  −0.546  0.248  −0.691  181  −0.672  −0.067  −0.807 
Communication & broadcasting  4812–4899  252  −0.283  0.006  −0.247  207  −0.375  0.566  −0.498 
Electric services  4911  166  −0.179  0.164  −0.212  151  0.189  0.530  −0.306 
Gas transmission & distribution  4922–4991  175  −0.431  0.634  −0.504  164  −0.431  0.282  −0.465 
Miscellaneous wholesaling  5000–5190  636  −0.303  0.054  −0.382  555  −0.475  0.095  −0.512 
Department & variety stores  5311–5399  120  −0.067  0.028  −0.301  105  −0.105  0.249  −0.289 
Grocery & convenience stores  5411–5412  86  −0.044  0.138  −0.104  72  0.063  −0.088  −0.219 
Apparel & clothing stores  5600–5661  106  −0.142  0.282  −0.502  87  −0.063  0.198  −0.088 
Restaurants & eating places  5810–5812  80  −0.243  0.343  −0.539  63  −0.025  0.351  −0.273 
Miscellaneous shopping stores  5912–5990  128  −0.432  0.431  −0.448  103  −0.195  0.315  −0.522 
Banking and real estate  6159–6799  21  −0.584  0.827  −0.759  −0.482  0.909  −0.878 
Hotels & motels  7011  146  0.014  0.052  −0.206  133  −0.545  0.376  −0.909 
Advertising & other services  7200–7363  150  −0.110  0.607  −0.448  111  −0.512  0.367  −0.909 
Programming & software services  7370–7389  812  −0.380  0.013  −0.320  612  −0.389  0.159  −0.447 
Motion pictures & theaters  7812–7841  84  −0.069  0.321  −0.236  58  −0.263  0.213  −0.113 
Amusement & recreation services  7900–7997  108  −0.503  0.202  −0.567  89  −0.317  0.103  −0.473 
Medical & nursing services  8000–8093  62  −0.383  0.046  −0.652  53  −0.290  0.544  −0.404 
Engineering & management services  8700–8744  178  −0.545  −0.028  −0.598  152  −0.233  0.143  −0.289 
Corporate conglomerates  9995–9997  159  −0.594  0.266  −0.636  144  −0.728  0.288  −0.752 
Mean      −0.317  0.191  −0.438    −0.321  0.209  −0.472 
a

Average ROA over the first five period and the standard deviation of ROA over the next five year period.

We continue to find negative risk and return relationship. For instance, in the first ten year period (1998–2007), only two industries show weak positive risk and return relationship (r<0.015). Over the next ten-year period (2003–2012), three industries show positive risk and return relationship. Again, such relationship is relatively stable (average correlations are −0.317 and −0.321 for the two periods). As expected, the average correlations are weaker than the cross-sectional correlations. Of these, electric services (SIC=4911) in 2003–2012 shows moderate positive relationship (r=0.189). Similarly, when we only considered firms with performance above median, we did detect most industries experience positive risk and return relationship for both periods. Again, when we exclusively focused on firm performance below median, we did find broad support for positive risk and return correlations. Overall, both cross-sectional and longitudinal calculations provide strong support for the existence of inverse risk and return relationship across 28 countries. Fig. 1 presents the cross-sectional (Table 2), and longitudinal (Table 4) relationship between performance and variance in performance and the risk–return relationship for firms with performance above or below industry median (Table 4).

Fig. 1.

Bowman paradox – global firms.

(0.79MB).
Robustness check with the US sample

Our replication using Global COMPUSTAT provides results consistent with previous studies (e.g. Andersen & Bettis, 2015; Andersen et al., 2007). However, one might question whether our results will hold in the US sample for period that we used. Hence, we replicated our study using US COMPUSTAT for years between 1998 and 2012. We replicated Tables 2 and 4 in Tables 5 and 7, respectively, for the US sample between 1998 and 2012. The US sample shows a similar pattern.

Table 5.

Empirically observed cross-sectional risk–return relationship for the US sample.

Industries (grouped by SIC)  SIC range  1998–20022003–20072008–2012
    Correlation coefficientCorrelation coefficientCorrelation coefficient
    Sample size  Full sample  Above media  Below median  Sample size  Full sample  Above media  Below median  Sample size  Full sample  Above media  Below median 
Metal mining  0100–1220  247  −0.807  0.116  −0.764  192  −0.829  0.356  −0.827  134  −0.779  0.210  −0.748 
Energy extraction  1311–1389  349  −0.833  0.147  −0.811  224  −0.872  0.394  −0.919  163  −0.612  0.284  −0.519 
Operative builders  1531–1731  74  −0.794  0.489  −0.837  52  −0.828  0.112  −0.906  39  −0.726  0.045  −0.532 
Food products  2000–2111  190  −0.647  0.533  −0.676  136  −0.824  0.558  −0.881  103  −0.175  0.604  −0.536 
Textile industry  2200–2273  31  −0.529  0.008  −0.823                 
Apparel industry  2300–2390  68  −0.462  0.185  −0.466  45  −0.608  0.172  −0.581  32  −0.660  0.110  −0.874 
Lumber & wood products  2400–2452  51  −0.891  −0.003  −0.928  34  −0.105  0.886  −0.811  22  −0.856  −0.070  −0.914 
Household & office furniture  2510–2590  40  −0.267  0.426  −0.766  27  −0.279  0.270  −0.094  22  −0.079  0.724  −0.609 
Paper milling & products  2600–2673  73  −0.817  −0.307  −0.813  52  −0.742  0.125  −0.906  34  −0.303  0.201  −0.272 
Newspaper & book publication  2711–2790  95  −0.852  0.548  −0.888  55  −0.948  0.792  −0.968  29  −0.393  0.007  −0.707 
Chemical & pharmaceutical products  2800–2891  704  −0.783  −0.377  −0.644  528  −0.746  −0.271  −0.632  341  −0.727  0.382  −0.646 
Petroleum refining  2911–2990  54  −0.671  −0.147  −0.680  36  −0.856  0.409  −0.958  27  −0.851  -0.214  −0.973 
Rubber & plastic products  3011–3089  90  −0.747  0.027  −0.748  56  −0.895  0.518  −0.914  28  −0.984  0.199  −0.996 
Stell works & metals  3300–3390  115  −0.777  0.233  −0.773  73  −0.465  0.593  −0.625  49  −0.784  0.290  −0.969 
Fabricated metal products  3400–3490  106  −0.942  −0.095  −0.948  67  −0.270  0.178  −0.627  51  −0.799  0.542  −0.978 
Industrial machinery  3510–3569  204  −0.863  −0.006  −0.855  152  −0.828  0.195  −0.840  114  −0.902  −0.011  −0.947 
Computer & office equipment  3570–3590  230  −0.855  −0.182  −0.787  124  −0.674  0.693  −0.689  81  −0.657  0.153  −0.618 
Electrical equipment & electronics  3600–3695  610  −0.771  0.366  −0.768  453  −0.820  0.140  −0.806  319  −0.715  0.272  −0.711 
Vehicles & transportation equipment  3700–3790  165  −0.763  0.077  −0.748  122  −0.878  0.264  −0.898  95  −0.789  0.359  −0.830 
Industrial instruments & equipment  3812–3873  476  −0.748  −0.145  −0.652  345  −0.785  −0.006  −0.734  226  −0.613  0.050  −0.539 
Toys, games, sporting goods, etc.  3910–3990  77  −0.699  0.191  −0.677  41  −0.904  0.572  −0.917  28  −0.909  −0.187  −0.903 
Line-haul operations & trucking  4011–4213  115  −0.921  −0.040  −0.951  82  −0.471  0.317  −0.730  60  −0.565  0.102  −0.818 
Air transportation  4512–4522  87  −0.858  0.245  −0.884  64  −0.924  0.456  −0.968  39  0.008  0.293  −0.422 
Communication & broadcasting  4812–4899  398  −0.852  0.047  −0.841  214  −0.790  0.342  −0.776  143  −0.791  0.491  −0.848 
Electric services  4911  134  −0.909  0.596  −0.967  119  −0.140  0.190  −0.531  105  0.089  0.392  −0.183 
Gas transmission & distribution  4922–4991  225  −0.827  0.433  −0.848  193  −0.833  0.283  −0.832  153  −0.934  0.271  −0.958 
Miscellaneous wholesaling  5000–5190  287  −0.864  0.392  −0.875  180  -0.903  0.240  −0.916  132  −0.632  0.318  −0.813 
Department & variety stores  5311–5399  41  −0.828  0.323  −0.981  30  0.046  0.042  −0.645  24  −0.257  0.581  −0.448 
Grocery & convenience stores  5411–5412  49  −0.028  0.792  −0.635  32  −0.370  0.424  −0.655  25  0.611  0.819  −0.276 
Apparel & clothing stores  5600–5661  97  −0.690  0.244  −0.748  73  −0.509  0.051  −0.806  57  −0.297  −0.074  −0.641 
Restaurants & eating places  5810–5812  116  −0.790  0.014  −0.776  70  −0.851  −0.101  −0.939  41  −0.317  −0.135  −0.670 
Miscellaneous shopping stores  5912–5990  145  −0.884  0.328  −0.885  89  −0.916  0.209  −0.941  48  −0.723  0.270  −0.944 
Banking and real estate  6159–6799  891  −0.484  0.746  −0.784  617  −0.417  0.710  −0.874  455  0.046  0.771  −0.890 
Hotels & motels  7011  40  −0.830  0.892  −0.920                 
Advertising & other services  7200–7363  157  −0.713  0.432  −0.857  96  −0.726  0.162  −0.931  62  −0.903  0.220  −0.986 
Programming & software services  7370–7389  1049  −0.782  −0.357  −0.655  563  −0.736  0.110  −0.687  299  −0.713  0.023  −0.667 
Motion pictures & theaters  7812–7841  53  −0.465  0.735  −0.304  28  −0.920  −0.227  −0.924         
Amusement & recreation services  7900–7997  100  −0.758  0.545  −0.746  57  -0.982  0.312  −0.989  37  −0.963  0.679  −0.988 
Medical & nursing services  8000–8093  121  −0.808  0.271  −0.805  80  −0.890  0.478  −0.920  49  −0.937  0.724  −0.991 
Engineering & management services  8700–8744  170  −0.767  0.257  −0.689  107  −0.860  0.542  −0.855  62  −0.838  0.068  −0.831 
Corporate conglomerates  9995–9997  155  −0.729  −0.541  −0.503  94  −0.751  0.083  −0.751  37  −0.755  −0.544  −0.445 
Mean      −0.739  0.206  −0.773    −0.695  0.297  −0.800    −0.584  0.243  −0.727 

Similar patterns are observed with Henkel's (2009) correction in Table 6. Consistent with past work, we find a negative risk–return relationship and such relationship is more pronounced in samples with relatively lower performance. Furthermore, longitudinal correlations are weaker than cross-sectional correlations. Similar to Fig. 1, for US firms, Fig. 2 presents the cross-sectional (Table 5) and longitudinal (Table 7) relationship between performance and variance in performance and the risk–return relationship for firms with performance above or below industry median (Table 7).

Table 6.

Correction for spuriousness (Henkel, 2009) – Empirically observed cross-sectional risk–return relationship for the US sample.

Industries (grouped by SIC)  SIC range  1998–20022003–20072008–2012
    Correlation coefficientCorrelation coefficientCorrelation coefficient
    Sample size  Full sample  Corrected coef  Spurious effect  % of inflation  Sample size  Full sample  Corrected coef  Spurious effect  % of inflation  Sample size  Full sample  Corrected coef  Spurious effect  % of inflation 
Metal mining  0100–1220  247  −0.807  −0.601  −0.207  25.58%  192  −0.829  −0.584  −0.245  29.53%  134  −0.779  −0.647  −0.132  16.89% 
Energy extraction  1311–1389  349  −0.833  −0.274  −0.559  67.10%  224  −0.872  −0.478  −0.394  45.21%  163  −0.612  −0.401  −0.211  34.51% 
Operative builders  1531–1731  74  −0.794  −0.801  0.008  −0.98%  52  −0.828  −0.901  0.072  −8.70%  39  −0.726  −0.481  −0.245  33.73% 
Food products  2000–2111  190  −0.647  −0.127  −0.519  80.30%  136  −0.824  −0.683  −0.141  17.10%  103  −0.175  0.241  −0.415  237.93% 
Textile industry  2200–2273  31  −0.529  −0.496  −0.033  6.28%                     
Apparel industry  2300–2390  68  −0.462  −0.194  −0.268  58.05%  45  −0.608  −0.409  −0.199  32.77%  32  −0.660  −0.012  −0.648  98.23% 
Lumber & wood products  2400–2452  51  −0.891  −0.071  −0.820  92.08%  34  −0.105  0.126  −0.230  220.19%  22  −0.856  −0.090  −0.766  89.43% 
Household & office furniture  2510–2590  40  −0.267  0.300  −0.567  212.58%  27  −0.279  −0.273  −0.006  2.33%  22  −0.079  0.453  −0.532  672.97% 
Paper milling & products  2600–2673  73  −0.817  −0.602  −0.216  26.38%  52  −0.742  −0.087  −0.655  88.30%  34  −0.303  −0.214  −0.090  29.55% 
Newspaper & book publication  2711–2790  95  −0.852  −0.822  −0.030  3.52%  55  −0.948  −0.424  −0.524  55.30%  29  −0.393  −0.458  0.065  −16.49% 
Chemical & pharmaceutical products  2800–2891  704  −0.783  −0.579  −0.204  26.08%  528  −0.746  −0.527  −0.219  29.30%  341  −0.727  −0.557  −0.170  23.35% 
Petroleum refining  2911–2990  54  −0.671  −0.709  0.038  −5.60%  36  −0.856  0.066  −0.922  107.74%  27  −0.851  −0.246  −0.605  71.14% 
Rubber & plastic products  3011–3089  90  −0.747  −0.557  −0.191  25.51%  56  −0.895  −0.803  −0.093  10.36%  28  −0.984  0.626  -1.610  163.62% 
Stell works & metals  3300–3390  115  −0.777  −0.337  −0.440  56.59%  73  −0.465  −0.165  −0.300  64.55%  49  −0.784  −0.054  −0.730  93.10% 
Fabricated metal products  3400–3490  106  −0.942  −0.870  −0.072  7.68%  67  −0.270  0.182  −0.452  167.40%  51  −0.799  −0.100  −0.699  87.45% 
Industrial machinery  3510–3569  204  −0.863  −0.582  −0.280  32.51%  152  −0.828  −0.419  −0.409  49.35%  114  −0.902  −0.108  −0.793  87.97% 
Computer & office equipment  3570–3590  230  −0.855  −0.364  −0.491  57.47%  124  −0.674  0.041  −0.715  106.09%  81  −0.657  −0.350  −0.307  46.78% 
Electrical equipment & electronics  3600–3695  610  −0.771  −0.641  −0.130  16.85%  453  −0.820  −0.712  −0.108  13.16%  319  −0.715  −0.475  −0.239  33.49% 
Vehicles & transportation equipment  3700–3790  165  −0.763  −0.613  −0.150  19.61%  122  −0.878  −0.716  −0.162  18.42%  95  −0.789  0.022  −0.811  102.83% 
Industrial instruments & equipment  3812–3873  476  −0.748  −0.099  −0.649  86.77%  345  −0.785  −0.608  −0.177  22.51%  226  −0.613  0.335  −0.948  154.65% 
Toys, games, sporting goods, etc.  3910–3990  77  −0.699  −0.656  −0.044  6.28%  41  −0.904  −0.143  −0.762  84.23%  28  −0.909  −0.555  −0.354  38.97% 
Line-haul operations & trucking  4011–4213  115  −0.921  −0.797  −0.124  13.45%  82  −0.471  −0.515  0.044  −9.37%  60  −0.565  −0.553  −0.013  2.22% 
Air transportation  4512–4522  87  −0.858  0.251  −1.110  129.28%  64  −0.924  0.042  −0.966  104.51%  39  0.008  −0.023  0.031  399.39% 
Communication & broadcasting  4812–4899  398  −0.852  −0.595  −0.257  30.17%  214  −0.790  −0.510  −0.280  35.42%  143  −0.791  −0.027  −0.764  96.55% 
Electric services  4911  134  −0.909  −0.284  −0.625  68.78%  119  −0.140  −0.062  −0.079  55.99%  105  0.089  0.097  −0.009  −9.89% 
Gas transmission & distribution  4922–4991  225  −0.827  −0.713  −0.114  13.81%  193  −0.833  −0.687  −0.146  17.50%  153  −0.934  −0.408  −0.526  56.28% 
Miscellaneous wholesaling  5000–5190  287  −0.864  −0.688  −0.176  20.35%  180  −0.903  0.168  −1.072  118.65%  132  −0.632  −0.655  0.023  −3.65% 
Department & variety stores  5311–5399  41  −0.828  −0.200  −0.629  75.89%  30  0.046  0.015  0.031  67.55%  24  −0.257  −0.183  −0.074  28.75% 
Grocery & convenience stores  5411–5412  49  −0.028  −0.051  0.023  −81.63%  32  −0.370  −0.442  0.072  −19.41%  25  0.611  0.797  −0.186  −30.39% 
Apparel & clothing stores  5600–5661  97  −0.690  −0.169  −0.521  75.51%  73  −0.509  −0.380  −0.129  25.27%  57  −0.297  −0.349  0.052  −17.62% 
Restaurants & eating places  5810–5812  116  −0.790  −0.801  0.011  −1.39%  70  −0.851  −0.479  −0.372  43.73%  41  −0.317  0.083  −0.400  125.99% 
Miscellaneous shopping stores  5912–5990  145  −0.884  −0.690  −0.195  22.01%  89  −0.916  −0.397  −0.518  56.62%  48  −0.723  0.345  −1.069  147.76% 
Hotels & motels  7011  40  −0.830  0.149  −0.979  118.00%                     
Advertising & other services  7200–7363  157  −0.713  −0.349  −0.364  51.06%  96  −0.726  −0.053  −0.673  92.70%  62  −0.903  0.303  −1.206  133.54% 
Programming & software services  7370–7389  1049  −0.782  −0.292  −0.489  62.60%  563  −0.736  −0.692  −0.044  6.02%  299  −0.713  −0.605  −0.108  15.16% 
Motion pictures & theaters  7812–7841  53  −0.465  −0.628  0.163  −34.96%  28  −0.920  −0.760  −0.160  17.35%           
Amusement & recreation services  7900–7997  100  −0.758  −0.783  0.025  −3.25%  57  −0.982  −0.883  −0.099  10.03%  37  −0.963  0.470  −1.433  148.82% 
Medical & nursing services  8000–8093  121  −0.808  −0.324  −0.484  59.92%  80  −0.890  −0.144  −0.746  83.87%  49  −0.937  −0.321  −0.616  65.76% 
Engineering & management services  8700–8744  170  −0.767  −0.693  −0.074  9.64%  107  −0.860  −0.547  −0.314  36.45%  62  −0.838  −0.661  −0.177  21.17% 
Corporate conglomerates  9995–9997  155  −0.729  −0.564  −0.166  22.71%  94  −0.751  −0.506  −0.245  32.61%  37  −0.755  −0.846  0.091  −12.02% 
Fig. 2.

Replication for US firms.

(0.73MB).
Table 7.

Empirically observed longitudinala risk–return relationship for US sample.

Industries (grouped by SIC)  SIC range  1998–20072003–2012
    Correlation coefficientCorrelation coefficient
    Sample size  Full sample  Above media  Below median  Sample size  Full sample  Above media  Below median 
Metal mining  0100–1220  192  −0.470  −0.113  −0.362  132  −0.354  −0.161  −0.169 
Energy extraction  1311–1389  224  −0.408  −0.143  −0.316  162  −0.393  −0.005  −0.413 
Operative builders  1531–1731  52  −0.399  0.330  −0.470  39  −0.060  −0.201  0.041 
Food products  2000–2111  136  −0.798  0.249  −0.842  103  −0.209  0.366  −0.506 
Apparel industry  2300–2390  45  −0.595  0.013  −0.724  32  −0.120  0.503  0.027 
Lumber & wood products  2400–2452  34  −0.764  0.433  −0.922  25  −0.807  0.103  −0.940 
Household & office furniture  2510–2590  27  0.304  0.275  −0.064  27  0.390  0.740  0.134 
Paper milling & products  2600–2673  52  −0.773  −0.040  −0.779  34  −0.560  −0.352  −0.737 
Newspaper & book publication  2711–2790  55  −0.876  0.785  −0.913  29  −0.551  −0.067  −0.877 
Chemical & pharmaceutical products  2800–2891  528  −0.514  −0.316  −0.313  341  −0.485  −0.241  −0.186 
Petroleum refining  2911–2990  36  −0.724  −0.018  −0.733  27  −0.843  −0.311  −0.969 
Rubber & plastic products  3011–3089  56  −0.436  −0.087  −0.343  28  −0.869  0.334  −0.851 
Stell works & metals  3300–3390  73  −0.492  −0.404  −0.385  48  −0.424  0.588  −0.716 
Fabricated metal products  3400–3490  67  −0.586  −0.204  −0.560  51  −0.176  0.378  −0.150 
Industrial machinery  3510–3569  152  −0.899  −0.120  −0.906  114  −0.895  0.182  −0.935 
Computer & office equipment  3570–3590  124  −0.609  −0.104  −0.450  81  −0.500  −0.105  −0.416 
Electrical equipment & electronics  3600–3695  453  −0.526  −0.016  −0.458  319  −0.611  0.028  −0.585 
Vehicles & transportation equipment  3700–3790  122  −0.728  0.181  −0.728  95  −0.496  0.290  −0.522 
Industrial instruments & equipment  3812–3873  345  −0.630  −0.314  −0.520  226  −0.549  −0.152  −0.448 
Toys, games, sporting goods, etc.  3910–3990  41  −0.311  0.590  −0.212  28  −0.985  −0.157  −0.992 
Line-haul operations & trucking  4011–4213  82  −0.552  0.088  −0.566  60  0.217  0.285  0.130 
Air transportation  4512–4522  64  −0.470  0.207  −0.437  39  0.123  0.683  0.056 
Communication & broadcasting  4812–4899  214  −0.692  0.240  −0.655  143  −0.842  0.582  −0.871 
Electric services  4911  119  −0.225  0.017  −0.175  105  0.048  0.282  −0.219 
Gas transmission & distribution  4922–4991  193  −0.732  0.427  −0.755  153  −0.769  0.368  −0.774 
Miscellaneous wholesaling  5000–5190  180  −0.641  0.053  −0.616  132  −0.649  0.097  −0.679 
Department & variety stores  5311–5399  30  −0.616  0.541  −0.974  24  0.083  −0.185  −0.216 
Grocery & convenience stores  5411–5412  32  0.110  0.297  0.021  25  0.316  0.652  −0.826 
Apparel & clothing stores  5600–5661  73  −0.021  −0.032  −0.170  57  0.012  0.080  −0.391 
Restaurants & eating places  5810–5812  70  −0.753  0.165  −0.908  41  −0.192  0.122  −0.308 
Miscellaneous shopping stores  5912–5990  89  −0.648  −0.089  −0.680  48  −0.139  0.112  0.017 
Banking and real estate  6159–6799  617  −0.313  0.719  −0.544  455  0.232  0.839  −0.491 
Advertising & other services  7200–7363  96  −0.222  0.247  −0.202  62  −0.327  0.327  −0.768 
Programming & software services  7370–7389  563  −0.531  −0.199  −0.399  298  −0.572  −0.067  −0.500 
Motion pictures & theaters  7812–7841  28  −0.405  0.135  −0.169         
Amusement & recreation services  7900–7997  57  −0.581  −0.085  −0.864  35  −0.587  −0.040  −0.450 
Medical & nursing services  8000–8093  80  −0.657  0.327  −0.642  48  −0.595  0.432  −0.753 
Engineering & management services  8700–8744  107  −0.704  0.215  −0.594  62  −0.888  0.243  −0.884 
Corporate conglomerates  9995–9997  94  −0.500  −0.303  −0.321  36  −0.458  −0.440  −0.576 
Mean      −0.523  0.101  −0.529    −0.381  0.161  −0.492 
a

Average ROA over the first five period and the standard deviation of ROA over the next five year period.

Supplementary analysis

We further checked our analyses for country-specific heterogeneity. Given some countries covered relatively few cases (e.g., 100 cases), we focused on countries with relatively large sample size to calculate longitudinal risk–return relationship. Overall, countries like Australia, England, and most others showed that most industries have negative risk–return relationship. In AppendixFigs. A.1 and A.2, we present country-level results related to for longitudinal risk–return relationships between 1998 and 2007 and between 2003 and 2012. Figs. A.1 and A.2 show that most of correlations are below zero. In certain countries and in certain industries, the correlation is positive. Specifically, India, Japan and Korea have positive risk–return correlation for most of the periods and across industries, but the remaining countries have negative correlation across industries. For example, in Japan 19 out of 37 industries showed positive risk return relationships. Future research might consider the country-specific difference in affecting the risk–return relationship. Overall, Bowman's paradox is broadly supported under different sample and statistical specifications.

Conclusion

The phenomenon of Bowman's risk paradox has for long intrigued strategic management scholars. Bowman's risk paradox refers to the negative relationship between mean and variance in accounting performance. To ascertain the boundary conditions of this phenomenon, predominantly studied in the US context, we replicated Bowman's risk paradox across 12,235 firms from 28 countries in Asia, Europe, and South Africa during the period between 1998 and 2012. We assessed risk–return relationship using contemporaneous (1998–2002; 2003–2007; 2008–2012) and longitudinal (from 1998 to 2007 and from 2003 to 2012) sampling frames. Based on recent work, we also corrected for spuriousness, resulting from right skewness in performance, in risk–return relationship.

In diverse country settings, firms performing below industry median have negative relationship between risk and return, whereas firms performing above industry median have positive relationship between risk and return. These findings are consistent with prospect theory and behavioral theory explanations, and do not support variation in the relationship based on country-related factors, The replication indicates that Bowman's risk paradox phenomenon is broadly supported across a wide range of countries. However, there are some exceptions to the overall results. For instance, many industries in India, Japan, and Korea show positive correlations between risk and return. Future studies could take a closer look at why such differences arise. We hope that our study serves to deepen our understanding in explaining the relationship between accounting based risk and return.

Appendix

Table A.1.

Distribution of firms across countries and industries.

Industries (grouped by SIC)  SIC range  AUS  BMU  BRA  CHE  CHL  CHN  DEU  DNK  ESP  FIN  FRA  GBR  HKG  IDN  IND  ITA  JPN  KOR  MYS  NLD  NOR  PAK  PHL  SGP  SWE  THA  TWN  ZAF  Total 
Metal mining  0100–1220  238  13  43  11  43  14  26  12  26  474 
Energy extraction  1311–1389  57  25  20  149 
Operative builders  1531–1731  11  11  10  12  21  21  125  13  30  318 
Food products  2000–2111  30  15  12  17  51  26  10  37  44  26  97  124  15  52  20  15  11  32  693 
Textile industry  2200–2273  13  35  12  13  113  41  10  18  321 
Apparel industry  2300–2390  11  11  11  15  20  31  13  177 
Lumber & wood products  2400–2452  12  14  31  107 
Household & office furniture  2510–2590  14  11  59 
Paper milling & products  2600–2673  20  10  13  33  38  18  14  254 
Newspaper & book publication  2711–2790  28  22  120 
Chemical & pharmaceutical products  2800–2891  40  15  19  18  191  41  14  29  73  19  192  194  28  19  22  12  12  17  1,001 
Petroleum refining  2911–2990  15  11  10  78 
Rubber & plastic products  3011–3089  20  13  11  11  44  49  21  14  248 
Stell works & metals  3300–3390  10  16  78  13  11  10  13  99  91  14  27  448 
Fabricated metal products  3400–3490  11  11  11  14  20  33  59  17  243 
Industrial machinery  3510–3569  11  26  57  59  13  19  22  40  168  11  16  12  509 
Computer & office equipment  3570–3590  11  25  13  13  17  11  63  20  217 
Electrical equipment & electronics  3600–3695  20  39  13  94  41  30  49  53  10  211  29  32  33  20  41  11  789 
Vehicles & transportation equipment  3700–3790  14  56  18  17  24  53  120  17  23  404 
Industrial instruments & equipment  3812–3873  20  11  13  22  20  39  82  17  270 
Toys, games, sporting goods, etc.  3910–3990  12  11  12  13  38  123 
Line-haul operations & trucking  4011–4213  14  25  10  25  101  16  17  10  328 
Air transportation  4512–4522  13  42  11  10  24  17  11  201 
Communication & broadcasting  4812–4899  22  20  18  15  25  18  10  13  227 
Electric services  4911  29  12  17  32  10  10  163 
Gas transmission & distribution  4922–4991  16  29  15  19  10  11  158 
Miscellaneous wholesaling  5000–5190  27  44  46  19  10  27  52  13  39  253  24  12  36  15  16  676 
Department & variety stores  5311–5399  36  11  30  128 
Grocery & convenience stores  5411–5412  13  44  96 
Apparel & clothing stores  5600–5661  31  22  117 
Restaurants & eating places  5810–5812  33  38  101 
Miscellaneous shopping stores  5912–5990  10  12  24  37  132 
Banking and real estate  6159–6799  20  46 
Hotels & motels  7011  14  11  14  26  15  10  154 
Advertising & other services  7200–7363  17  17  46  43  158 
Programming & software services  7370–7389  76  13  21  113  18  94  196  87  14  109  12  21  20  11  59  19  918 
Motion pictures & theaters  7812–7841  19  12  11  14  88 
Amusement & recreation services  7900–7997  12  43  17  130 
Medical & nursing services  8000–8093  63 
Engineering & management services  8700–8744  14  13  18  52  33  16  13  201 
Corporate conglomerates  9995–9997  31  12  22  19  148 
  Total  764  316  217  171  103  1,056  593  105  97  102  530  1,155  109  171  1,102  140  2,331  202  519  132  117  99  90  256  240  214  135  169  11,235 

Fig. A.1.

Country-level risk–return longitudinal relationship (1998–2007).

(0.19MB).
Fig. A.2.

Country-level risk–return longitudinal relationship (2003–2007).

(0.29MB).
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We thank an anonymous reviewer for this suggestion.

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