Price of Regulations: Regulatory Costs and the Cross-section of Stock Returns

Abstract

Regulations introduce significant fixed costs and add to operating leverage. Fixed regulatory costs that contribute to operating leverage should generate a risk premium. To explore whether such a premium exists, we introduce a measure of “regulatory operating leverage” that reflects the importance of fixed regulatory costs in a firm’s cost structure. Regulatory operating leverage predicts stock returns in the cross-section, and a zero-cost high-low regulatory operating leverage strategy generates positive and significant risk-adjusted return. Finally, the impact of regulatory operating leverage on returns is due to the (systematic) risk contribution of fixed regulatory costs.

Benefits and costs of regulations have been widely discussed. Regulations enhance market safety and stability, and increasing levels of regulations can prevent the concentration of market power. Regulations also aim to protect consumers, even if it means lower profits for businesses. On the other hand, regulations can reduce overall social welfare. Opponents of regulations argue that free markets, dominated by rational actors, efficiently allocate resources and competition protects consumers. They believe that even if a company gains monopolistic power due to limited government interference, the market will eventually correct the issue.

Hahn and Hird (1991) are some of the first economists to analyze the costs and benefits of federal regulations. As many economists and policy makers attempt to quantify regulations with the number of pages in Federal Register, Goff (1996) introduces a measure of total regulation through factor analyses and finds a causal effect of regulation on economic activity. Subsequently, Nicoletti and Scarpetta (2003), Djankov et al. (2002), Bandiera et al. (2000), and Dawson and Seater (2013) estimate the effects of regulations on macroeconomic measures like real aggregate output, total factor productivity, capital, and labor. Additionally, Coffey, McLaughlin, and Peretto (2016) show that federal regulations have increased over the years, and if the level of regulations would had remained constant since 1980, the U.S. economy would have been 25% larger in 2012. Similarly, Crain and Crain (2014) estimated the total cost of U.S. federal regulations to be around $2 trillion in 2012.

In the context of asset pricing, despite a growing interest in the cross-sectional pricing of governmental policies and policy uncertainty (Pastor and Veronesi 2012, 2013, 2020; Kelly, Pastor and Veronesi 2016), no prior study has documented the relationship between regulations and subsequent stock returns.¹ This paper aims to fill that gap by (a) offering a firm-level measure of regulatory operating leverage that captures a firm’s exposure to fixed regulatory costs, (b) documenting that regulatory operating leverage predicts stock returns, and (c) providing a rational risk-based explanation for this prediction: regulatory operating leverage contributes to risk.

Bradford (2004) and Crain and Crain (2014) document that most of regulatory costs, including capital expenditures, information costs, reporting, and recordkeeping, are fixed. Smaller firms often struggle with regulatory compliance because of limited resources, making regulatory costs more burdensome for them. Additionally, regulatory costs are distributed unevenly across industries.² The size- and industry-dependent regulatory burden differences imply that the significant cross-sectional regulatory cost spreads might be an important factor in firms’ risk exposure, which in turn affects their risk premiums. Building on this idea, this paper focuses on the cross-sectional pricing of firm-level regulatory fixed costs and contributes to the literature on regulatory framework and operating leverage.

Lev’s (1974) seminal article is the first to mention that operating leverage can trigger systematic risk and, therefore, expected stock returns. Carlson, Fisher, and Giammarino (2004), Zhang (2005), and Cooper (2006) show that operating leverage is critical to the models that generate value premium, and value stocks generate higher returns due to systematic risk. Novy-Marx (2011) documents that interindustry differences in book-to-market are mainly driven by differences in operating leverage. In addition, operating margin differences within industry might give rise to book-to-market differences.^3,4

The rationale behind the association between operating leverage and systematic risk is as follows. If a firm’s costs are mostly fixed as opposed to variable, then it loses operating flexibility. During economic expansions, such a firm’s revenues increase at a faster rate than its costs. As a result, it generates larger profits in comparison to a firm whose costs are mostly variable. Similarly, during recessions, a firm with high operating leverage experiences larger losses. Therefore, prospects of a firm with high operating leverage are more dependent on business cycles, and such a firm is more exposed to systematic risk. As a result, investors demand extra compensation in the form of higher expected returns to hold stocks with high operating leverage. This suggests that regulatory fixed costs, which contribute to operating leverage, should generate a risk premium. To explore whether such a risk premium exists, this paper introduces a measure of regulatory operating leverage (ROL) that captures the importance of regulatory fixed costs in a firm’s cost structure and examines its cross-sectional pricing implications.

To generate a measure of regulatory operating leverage, the study utilizes the “RegData 4.0” database, which quantifies the incidence of regulatory restriction words imposed on industries based on a text analysis of federal regulatory code. Then, we estimate firm-specific time-series regressions of SG&A expenses on regulatory restrictions and sales, and introduce the ratio of fixed costs attributable to regulatory restrictions in the regression over the SG&A expenses as “regulatory operating leverage.” ROL is a firm-specific measure that varies over time.

Common operating leverage measures imply profitability and growth prospects. As the long run trend of the U.S. economy has been positive, firms with a high operating leverage ratio tend to generate larger profits compared to those with a low fixed cost ratio (Chen, Harford, and Kamara 2019). Differing from common operating leverage measures, regulatory operating leverage (fixed costs) does not contribute to firms’ profitability. Regulatory costs are considerably recurrent expenses that appear in firms’ cost structure regularly, constraining their cost structure and decreasing profitability.⁵

Building on the fixed cost channel, this study investigates the cross-sectional predictive power of federal-level regulations on the future stock returns. More specifically, we sort individual stocks into quintile portfolios based on their regulatory operating leverage measure during the previous quarter and examine the monthly returns on the resultant portfolios from April 1991 to December 2021. Stocks in the highest regulatory operating leverage quintile generate 6.48% (5.88%) more equal (value)-weighted annualized returns compared to the stocks in the lowest regulatory operating leverage quintile. After controlling for the well-known market, size, book-to-market, momentum, liquidity, investment, and profitability factors of Fama and French (1993, 2015), Carhart (1997), Pastor and Stambaugh (2003), and Hou, Xue, and Zhang (2015), we find that the difference between the returns on the portfolios with the highest and the lowest regulatory operating leverage remains significantly positive.

To ensure that the observed return differences are driven by regulatory operating leverage rather than other firm-specific characteristics and risk factors, we perform bivariate portfolio sort analyses and firm-level cross-sectional Fama-Macbeth (1973) regressions. We control for market beta, size and book-to-market (Fama and French 1992, 1993), intermediate-term-momentum (Jegadeesh and Titman 1993), short-term-reversal (Jegadeesh 1990), illiquidity (Amihud 2002), idiosyncratic volatility (Ang et al. 2006), maximum of daily returns (Bali, Cakici, and Whitelaw 2011), asset growth and return on equity (profitability) (Fama and French 2015; Hou, Xue, and Zhang 2015), and operating margin. After controlling for this large set of stock return predictors, we find the positive relation between the regulatory operating leverage and future returns remains economically and statistically significant.⁶

Value premium is driven by cross-industry operating leverage differences and intraindustry operating margin spreads. First, capital-intensive industries tend to carry a higher level of asset heaviness. As a result, firms within capital intensive industries tend to have higher book-to-market ratios because of their asset heaviness. Second, firms within the same industry with different levels of operating margin are exposed to industry-specific shocks in different degrees. A firm with a lower operating margin is more exposed to shocks; as a result, it would have a lower market value and higher book-to-market ratio in comparison to firms with higher operating margin within the same industry. Additionally, firms’ hiring decisions and fixed labor expenses play important roles in firms’ capital structure and operating leverage, and they are priced in the cross-section of stock returns (Rosett 2001; Danthine and Donaldson 2002; Donangelo et al. 2019). To ensure that our results are not driven by cross-sectional differences in operating margin, operating leverage, and labor expenses, we construct additional bivariate portfolio sorts. The results suggest that the cross-sectional relation between regulatory operating leverage and subsequent stock returns are robust to such controls. Additionally, we find a stronger relation between regulatory operating leverage and future stock returns within stock subgroups with low operating margin, high operating leverage, and high labor expenses.

We provide a risk-based explanation for the observed cross-sectional relation between regulatory operating leverage and stock returns. More specifically, we conduct Fama-Macbeth (1973) regressions of cash flow volatility (four-quarter forward volatility of EBITDA scaled by assets) on regulatory operating leverage and find the relation between the two to be strongly statistically significant.⁷ Regression results document that regulatory operating leverage triggers future cash flow volatility both during recessionary and nonrecessionary periods. Furthermore, the positive association between regulatory operating leverage and cash flow volatility is stronger during recessions.⁸ This finding supports the idea that systematic risk implications of regulatory operating leverage contributes to the positive relation between regulatory operating leverage and stock returns. Additionally, we find that the relation between regulatory operating leverage and cash flow volatility is stronger during decreasing CFNAI (Chicago Fed National Activity Index) and decreasing industrial production periods. This suggests that economic activity and industrial production growth are important macroeconomic state variables on the systematic risk exposure of stocks with high regulatory operating leverage. In addition, we find the relation between regulatory operating leverage and cash flow volatility to be more pronounced among small-cap and mid-cap firms since they lack economies of scale.

Finally, we investigate the robustness of the findings. We propose two alternative regulatory operating leverage measures based on our primary measure. Additionally, we estimate regulatory operating leverage from quarterly regressions of SG&A expenses on regulatory restrictions and sales using a 60-quarter fixed window estimation. The results consistently support the cross-sectional relationship between regulatory operating leverage and future stock returns. In other words, the cross-sectional predictive power of regulatory operating leverage over subsequent stock returns is robust to alternative specifications and estimation methods.

1. Data and Variables

1.1 The Code of Federal Regulations and RegData

In this study, we utilize several data sets. To examine the cross-sectional predictive power of regulatory operating leverage, which represents the significance of regulatory fixed costs in a firm’s cost structure, we first need to quantify the regulations specific to each firm. To achieve this, we rely on a database called “RegData 4.0.,” developed by the Mercatus Research Center of George Mason University (Al-Ubaydli and McLaughlin 2017). This database quantifies regulatory exposure of two-, three-, and four-digit-level NAICS industries from 1970 to 2020 in the Code of Federal Regulations (CFR).

The CFR, published annually since 1969, contains all regulations issued at the federal level. It consists of 50 titles that represent various regulatory areas at the federal level, such as agriculture, commerce, environment, health, and transportation. Each title is further divided into chapters, parts, sections, and subsections. “RegData 4.0” employs a two-stage methodology involving text analysis and machine learning algorithms to create an industry-level data set. First, it counts regulatory restriction words in the CFR parts, such as “shall”, “must”, “may not”, “prohibited”, and “required”. Second, a machine learning algorithm assigns a relevance score (ranging from 0 to 1) between the CFR parts and NAICS-level industries. These relevance scores quantify the relationship between each CFR title and the NAICS-level industries and scores reflect the extent to which the regulations in a CFR title are applicable or relevant to a specific industry. The scores are determined through a combination of expert judgment, textual analysis, and statistical techniques. The aim is to assess the degree of regulatory burden or exposure faced by different industries due to the regulations contained within a CFR title. Once the relevance scores are calculated for each CFR title and NAICS-level industry pairing, they can be aggregated to construct industry-level regulatory exposure. Aggregation involves summing up the relevance scores across the CFR titles that are applicable to a specific industry. This provides a cumulative measure of the regulatory impact on that industry, taking into account the relevance of multiple CFR titles. As a result, by aggregating all regulatory restriction words coming from different titles, an industry-specific regulatory restriction data set is constructed.⁹

Figure 1 plots the total number of regulatory restriction words (in thousands) in the CFR from 1990 to 2020 with gray-shaded areas indicating recessionary periods in the United States determined by the National Bureau of Economic Research (NBER). The total number of regulatory restrictions increased from 786,512 in 1990 to 1,082,486 in 2020. Although a slight decrease occurred between 1995 and 1996, the overall trend shows an upward trajectory. Moreover, the figure suggests that the growth of regulatory restrictions is not dependent on business cycles, as there is no observable change in their growth during recessionary and nonrecessionary periods.

Throughout the study, we focus on regulatory exposure of three-digit-level NAICS industries. To analyze interindustry differences in regulatory burden more comprehensively, Table 1 presents the 50 broad titles of the CFR and the NAICS-3-level industries most exposed to each title based on the relevance scores assigned by “RegData 4.0.” To compute the industry-specific regulatory relevance, we compute the time-series averages of the yearly industry-specific regulatory restriction exposure to the CFR titles. To illustrate, “agriculture” (title 7) related regulations are updated every January. The food manufacturing industry is the industry most exposed to agricultural regulations, and the textile product mills industry is the one least exposed to federal-level agricultural regulations. “Transportation” (title 49) regulations are updated every October. As expected, transportation equipment manufacturing is the industry that is the most exposed to transportation-related regulations.

Additionally, Table A1 of the Internet Appendix provides information on the number of firms and selected moments of restriction count (mean, minimum, maximum) for each two-digit NAICS industry. The sample comprises 2,565 firms per year on average. The manufacturing industry represents half of the sample. Arts, entertainment, and the recreation industry; wholesale trade, retail trade are among the least regulated industries. Some of the highly regulated industries are educational services, administrative and support and waste management and remediation services. Subsectors such as waste collection, waste treatment, and disposal and waste management services increase regulatory exposure of administrative and support and waste management industry. The health care and social assistance industry has experienced increasing regulatory restrictions since 2010, partly because of the Patient Protection and Affordable Care Act (Obamacare).

1.2 Financial and accounting variables

We employ industry-level regulatory restriction data provided by “RegData 4.0” and take various business sectors that each firm operates in into consideration. Specifically, since firms often operate in multiple sectors, they are subject to different regulations specific to each sector. To create firm-level regulatory restriction data, we calculate the average restrictions weighted by sales for the various segments in which each firm operates. To accomplish this, we retrieve the primary three-digit NAICS code and segment sales data from the historical segments data of the CRSP/Compustat merged database.¹⁰

To create a firm-specific quarterly-varying “regulatory operating leverage” measure, we estimate firm-specific time-series regressions of quarterly selling, general, and administrative expenses (XSAQ) on firm-specific regulatory restrictions and quarterly sales (SALEQ).¹¹ Quarterly selling, general, and administrative expenses (XSAQ), quarterly sales (SALEQ), quarterly cost of goods sold (COGSQ), quarterly total assets (ATQ), quarterly operating income after depreciation (OIADPQ), long-term debt (DLTT), debt in current liabilities (DLC), and annual total assets (AT) are from CRSP/Compustat merged database.

The stock sample includes all common stocks traded on the New York Stock Exchange (NYSE), American Stock Exchange (Amex), and Nasdaq exchanges from March 1991 to December 2021. The daily and monthly returns and the volume data are from the Center for Research in Security Prices (CRSP). We require at least 15 available daily observations for each stock-month observation. Stocks under $1 are excluded to ensure that our results are not driven by micro-cap/illiquid firms

Following Fama and French (1992), we estimate the market beta of individual stocks using monthly returns over the prior 60 months if available. Market capitalization (SIZE) is calculated as the stock’s number of shares outstanding multiplied by its price per share. The book value of a firm is calculated as the sum of the book value of stockholders’ equity (SEQ), deferred taxes (TXDB), and investment tax credit (ITCB) minus the book value of the preferred stock (PSTKRV, or PSTKL, or PSTK depending on availability). BM is the natural logarithm of the ratio of the book value of a firm to its market capitalization.

Following Jegadeesh and Titman (1993), intermediate-term momentum (MOM) is the cumulative return of a stock over the 11-month period before the portfolio formation month. Following Jegadeesh (1990), short-term reversal (REV) is the excess return generated over the portfolio formation month. We use the illiquidity (ILLIQ) measure proposed by Amihud (2002). Daily illiquidity is quantified as the ratio of daily absolute stock return scaled by its daily dollar trading volume. A stock’s monthly illiquidity measure is computed as the average of its daily illiquidity within a month. Amihud illiquidity measure is scaled by $106$⁠.

Following Ang et al. (2006), we calculate idiosyncratic volatility (IVOL) as the monthly standard deviation of the daily residuals from a regression of daily excess stock returns on daily excess market returns, small-minus-big size factor, and high-minus-low book-to-market factor. Introduced by Bali, Cakici, and Whitelaw (2011), we use the average of the five highest maximum daily returns within a month (MAX) as a proxy for demand for lottery-type stocks.

Hou, Xue, and Zhang (2015) Q-factor model adds return on equity as a proxy for profitability and annual growth of assets to measure investment. Following their methodology, we quantify the annual growth of total assets (I/A) by the change in the book value of assets (Compustat item AT) divided by lagged AT. To measure quarterly operating profitability (ROE), we divide income before extraordinary items (item IBQ) by one-quarter-lagged book equity.

The monthly excess market returns (MKT) and the small-minus-big size (SMB), high-minus-low book-to-market (HML), up-minus-down momentum (UMD), robust-minus-weak profitability (RMW), and conservative-minus-aggressive investment (CMA) factors of Fama and French (1993; 2015), Carhart (1997), and Fama-French-48 industry classifications are from Kenneth French’s data library. The liquidity factor (LIQ) is from Lubos Pastor’s data library. The Hou, Xu, and Zhang (HXZ) empirical Q-factor model factors (market, size, investment, and profitability factors) are supported by Lu Zhang upon our request. Stambaugh and Yuan (2017) mispricing factors (MGMT and PERF) are obtained from Robert Stambaugh’s website. Daniel, Hirshleifer, and Sun (2020) short- and long-horizon behavioral factors (PEAD and FIN) are obtained from Kent Daniel’s website. Quarterly institutional stock holdings data are from Thompson-Reuters’ Institutional Holdings (13F) database. We obtain analyst coverage data from summary files of I/B/E/S.

2. Fixed Regulatory Costs: Regulatory Operating Leverage

Companies face fixed costs and variable costs, with Selling, General, and Administrative expenses (SG&A) being a quarterly reported cost structure. A significant portion of SG&A expenses is due to advertising expenses, bad debt expenses, commissions, directors’ fees and remuneration, distribution expenses, engineering expenses, freight-out expenses, indirect costs, lease expenses, marketing expenses, pension, retirement, profit sharing, provision of bonus and stock options, employee insurance, and other employee benefit expenses, research and development expense, software and strike expenses. While Chen, Harford, and Kamara (2019) introduce SG&A expenses scaled by total assets (AT) as a measure of operating leverage (a proxy for fixed costs within total costs), they show that, on average, firms adjust their COGS (Cost of Goods Sold) by 0.86% and their SG&A expenses by 0.41% in response to a 1% decrease in sales revenue. This implies that SG&A expenses contain both fixed and variable cost components.

Firm-specific sales accounts for the variable cost component of SG&A expenses. While $βsale* SALE$ captures the variable part of SG&A expenses, the objective is to disentangle fixed regulatory costs.¹² Most of the regulatory compliance costs, expenses, such as bookkeeping, recording, and reporting, are recurrent. Hence, they appear in the firms’ cost structure every time period.¹³ As a result, this paper takes the levels of SG&A expenses and sales into account rather than the changes or logarithms.¹⁴  $βREG$ captures the sensitivity of SG&A expenses to the regulatory restrictions while accounting for sales. The term $βREG* log(REG)$ represents the fixed regulatory cost component of SG&A expenses. The natural logarithm of regulatory restrictions is used to account for regulatory changes. For instance, if two firms with different levels of regulatory restriction exposure experience a new regulatory reform, the new regulatory restriction will affect the firms’ cost structures at distinct degrees.

Table 2 presents the regression results in which the dependent variable is the firm-specific quarterly-varying selling, general, and administrative expenses. The first column reports the bivariate regression results. As expected, sales positively and significantly explains the variation in SG&A expenses. The second row of the table reports the economic and statistical significance of the natural logarithm of regulatory restriction count. The results show that the regulations significantly increase SG&A expenses, with a slope coefficient for restrictions yielding a t-statistic of 6.74 according to the first column.

The remaining regression specifications account for NAICS-2-level industry and year fixed effects. The last column presents the full regression specification results. When we simultaneously control for the industry and year fixed effects, the natural logarithm of regulatory restrictions continues to significantly explain the variation in SG&A expenses. In other words, even after accounting for the variable component of SG&A expenses, and industry and year fixed effects, there is a positive and significant relationship between regulatory restrictions and SG&A expenses.

2.1 Stationarity

As a firm grows, it is expected that its costs and sales will increase. Additionally, Figure 1 documents a significant rise in regulations over the years. This raises concerns about stationarity issues. When the dependent variable and independent variables in a regression model exhibit trends or are nonstationary, it can lead to a spurious relationship and a misleadingly high correlation between them. To investigate this, we first test whether the dependent variable (SG&A expenses) and the independent variables (log(REG) and SALE) are stationary. Initially, we employ a Fisher unit root test on each variable separately and find that all three variables are nonstationary in their levels. Next, we test whether their first differences are stationary. As SG&A expenses and SALE vary quarterly and log(REG) varies yearly, we allow four quarterly lags for SG&A expenses and SALE and one lag for log(REG) to maintain consistency. The unit root tests confirm that the first differences of all variables are stationary. This suggests that the dependent and independent variables are integrated of order 1, denoted as I(1). Finally, we examine whether the variables are cointegrated or if the regression model is spurious. In our context, as all variables (dependent and independent) are I(1), if the error term is stationary, we can conclude that the dependent and independent variables are cointegrated.

Panel cointegration tests can be categorized into two groups: tests that examine the hypothesis of no cointegration and tests that assess the null hypothesis of integration. Kao (1999) investigates the residual-based tests for cointegration regression in panel data and examines the asymptotic null distribution of residual-based cointegration tests. More specifically, he investigates Dickey-Fuller (DF) tests and an augmented Dickey-Fuller (ADF) test to test the null of no cointegration. Adding to classical DF test, Kao (1999) discusses four additional modified DF tests: modified Dickey–Fuller, augmented Dickey–Fuller, unadjusted modified Dickey–Fuller, and unadjusted Dickey–Fuller statistics. The null hypothesis of these tests is $H0$⁠: $ρ$ = 1, indicating no cointegration, while the alternative hypothesis is $Ha$⁠: $ρ <$1.

Table A2 of the Internet Appendix displays the test statistics and corresponding p-values for each test (Stata code: xtcointtest kao SGA log(REG) SALE). The results demonstrate that all four test statistics reject the null hypothesis of no cointegration. This provides evidence of cointegration among the variables in our model, indicating the presence of a long-term relationship between them.

2.2 Firm-level regulatory operating leverage

Figure 2 plots the regulatory operating leverage of a median ROL firm from 1991 to 2021. To do so, we compute the cross-sectional median of ROL across all the firms in the sample. The time-series average of the median ROL is 0.48. Although ROL exhibits significant volatility, no evident trend is observed between 1991 and 2021. The figure reveals an increasing trend in ROL during periods of economic recession. For instance, the regulatory operating measure slightly increased around 2001, while a substantial surge in ROL is observed during the 2008–2009 period. This suggests that during economic downturns, firms are unable to reduce their regulatory fixed costs, resulting in a higher proportion of their SG&A expenses being attributed to regulations. Similarly, ROL follows an upward trajectory during the COVID-19 pandemic crisis and the subsequent period. One plausible explanation is that although firms were able to cut some costs during this period, they still had to comply with the regulations to which they were exposed. Consequently, regulations constituted a larger share of the overall cost burden for firms throughout 2020.

2.3 Industry-level regulatory exposure

Table 3 presents additional findings regarding the differences in regulatory burden across industries and the average fixed regulatory costs faced by each industry. The table is organized by sorting all industries at the NAICS-3 level in descending order of their regulatory restriction count burdens, with each industry’s NAICS-3-level code shown in parentheses.

The second column provides the average industry-specific regulatory restriction count, which represents the time-series average of the exposure to regulatory restriction words. According to this measure, the chemical industry (NAICS-3 code: 325) is identified as the industry most exposed to regulatory restriction words, with an average exposure of 64,575 words. Following this, the petroleum and coal products manufacturing industry (NAICS-3 code: 324), educational services (NAICS-3 code: 611), waste management and remediation services (NAICS-3 code: 562), air transportation (NAICS-3 code: 481), and credit intermediation and related activities (NAICS-3 code: 522) are among the highly regulated industries. Conversely, the industries with the lowest exposure to regulatory restriction words are data processing hosting and related services (NAICS-3 code: 518), real estate (NAICS-3 code: 531), and amusement gambling and recreation industries (NAICS-3 code: 713).

The third column presents the time-series average of the cross-sectional median of regulatory operating leverage (ROL) for each NAICS-3-level industry. Examining the median ROL values, we find that the industries with the highest median fixed regulatory cost burdens include electrical equipment, appliance, and component manufacturing; primary metal manufacturing; crop production; computer and electronic product manufacturing; merchant wholesalers nondurable goods; chemical manufacturing; and machinery manufacturing. In contrast, waste management and remediation services, ambulatory health care services, and animal production and aquaculture exhibit the lowest fixed regulatory cost burdens.

Furthermore, upon comparing the second and third columns, we observe that having an extreme exposure (highest or lowest) to regulatory restriction words does not necessarily imply carrying an extreme regulatory fixed cost burden for the relevant industries. While the amusement, gambling, and recreation industry has one of the lowest exposures to regulatory restriction words, its median ROL of 0.519 exceeds the cross-industry average. Similarly, although animal production and aquaculture industry faces high exposure to regulatory restriction words, its median regulatory operating leverage is significantly lower than the sample average.

While real estate and amusement, gambling, and recreation industries are among the lowest with the lowest regulatory restriction exposures, their median regulatory operating leverage exposures are not. Additional potential reasons for them not carrying high regulatory exposures are (a) The real estate industry, while subject to regulations, primarily deals with property transactions, rentals, and management. The regulatory requirements are often related to property zoning, land use, and building codes. These regulations tend to remain relatively stable over time and do not necessarily scale linearly with the size of the real estate holdings. Therefore, as real estate firms expand, the incremental regulatory costs may not increase significantly, leading to a lower regulatory operating leverage measure, (b) while the gambling and casino sectors do face stringent regulations, the regulatory costs are typically associated with obtaining and maintaining licenses, ensuring fair gaming practices, and addressing issues related to addiction and responsible gaming. Once a casino or amusement facility is established, the regulatory costs may not grow at the same rate as the revenue, especially if the casino already complies with all necessary regulations. This can lead to a relatively lower regulatory operating leverage measure, (c) many firms within these sectors are often large and operate at scale. Larger companies may have the resources and expertise to navigate complex regulatory frameworks more efficiently. They can spread the cost of compliance over a larger revenue base, making the regulatory burden less significant in proportion to their size, (d) The regulatory environment can vary significantly by location and jurisdiction. Some states or regions may have more permissive regulatory frameworks, allowing businesses in these industries to operate with relatively lower regulatory costs, (e) certain industries, including real estate and gambling, may have a strong lobbying presence and political influence, which can shape regulatory conditions in their favor. This influence can lead to regulations that are perceived as more business-friendly.

Columns 4 and 5 present information on the median selling, general, and administrative (SG&A) expenses and the total SG&A expenses (in millions) for each industry in 2021. As this study measures the regulatory operating leverage (ROL) as the proportion of fixed costs attributed to federal-level regulations relative to a firm’s SG&A expenses, multiplying the ROL (third column) by the median SG&A (fourth column) can be interpreted as the fixed regulatory burden of a typical firm. Similarly, multiplying the ROL by the sum of SG&A expenses (fifth column) can be viewed as the industry-level fixed regulatory burden as of 2021. Based on this analysis, firms in industries, such as petroleum and coal products manufacturing, paper manufacturing, air transportation, beverage and tobacco product manufacturing, food and beverage stores, educational services, animal production and aquaculture, and transportation equipment manufacturing, are likely to have a high regulatory operating leverage, indicating a significant portion of fixed regulatory costs within their SG&A expenses. Moreover, chemical manufacturing, credit intermediation and related activities, petroleum and coal products manufacturing, transportation equipment manufacturing, beverage and tobacco product manufacturing, insurance carriers and related activities, telecommunications, and air transportation are the industries with the highest fixed regulatory cost burden.

2.4 Major regulations and regulatory operating leverage

If Regulatory Operating Leverage (ROL) truly reflects a firm’s regulatory cost burden, it would be expected that the ROL responds significantly to expensive regulatory reforms. To investigate this, we analyze the time-series changes in ROL for for firms following major regulations that impose substantial regulatory costs specific to their industry.

The Office of Management and Budget (OMB) provides annual reports to Congress on the benefits and costs of federal regulations. These reports include estimates of the benefits and costs of major final rules. We select major regulatory reforms from these reports, categorized by relevant departments, such as Agriculture, Energy, Health and Human Services, Homeland Security, Housing and Urban Development, and Justice, Labor, and Transportation. Detailed cost and benefit analyses of these regulations, including dollar amounts and sources, have been available since 1999. While we consider major regulations from various departments based on the reports, our focus is solely on the most expensive regulations.¹⁸ Additionally, we include two regulatory reforms in our analysis: the Patient Protection and Affordable Care Act (Obamacare) and the Dodd-Frank Wall Street Reform and Consumer Protection Act. Panel A of Table 4 provides information on these major regulatory reforms and their introduction dates.

To demonstrate the changes in the ROL measure around the introduction of major regulations, panel B of Table 4 presents regression results of yearly changes in ROL using year dummies. We group firms belonging to industries most affected by the regulations and calculate yearly ROL changes around the regulatory reforms. Then, we regress these yearly ROL changes on year dummies, considering the 3 years before the announcement of the regulatory change and the 2 years after the announcement. We exclude the dummy variable for 3 years before the announcement to avoid multicollinearity issues. For instance, as the Dodd-Frank Wall Street Reform and Consumer Protection Act was announced in July 2010, we use the yearly ROL changes from 2007 to 2012 to capture the changes. Therefore, when calculating ROL changes around this regulation, we compare the ROL in the first quarter of 2011 with that of the first quarter of 2010, the second quarter of 2011 with the second quarter of 2010, and so on. The regressions include fixed effects for the year and four-digit SIC industry.

The regression results indicate a significant increase in ROL from one year before the regulatory reform to the reform year, as well as from the reform year to the following year. The increase in regulatory fixed cost burden from one year before the reform to the reform year is expected. Additionally, legislators allow for implementation delays in enforcing regulations in some cases. As a result, regulatory costs may be reflected in cost structures with a delay. The event study regression results suggest that the change in the ROL measure is significantly positive only around the time of the major regulation, but not elsewhere.¹⁹

3. Empirical Results

So far, the fixed cost component of regulations and a measure of regulatory operating leverage, which reflects the importance of regulatory fixed costs in a firm’s cost structure, are introduced. According to the well-established operating leverage hypothesis, firms with a high fixed cost ratio (operating leverage) are associated with low operating flexibility, and they are more exposed to business cycle risks. Therefore, a firm with higher operating leverage is more dependent on business cycles, making it more vulnerable to systematic risk. This suggests that fixed regulatory costs, which contribute to operating leverage, should generate a risk premium. To explore whether such a risk premium exists, we investigate the cross-sectional relation between regulatory operating leverage (ROL) and subsequent stock returns using univariate portfolio-level analyses, bivariate portfolio-level analyses, and firm-level cross-sectional regressions.

3.1 Univariate portfolio-level analyses

Table 5 presents univariate (panel A) and industry-controlled (panel B) equal- and value-weighted average excess monthly returns and risk-adjusted returns generated using three different factor models: (a) $αFF5$ is the intercept from the regression of the excess portfolio returns on a constant, and Fama and French (1992, 1993, 2015) market, size, book-to-market, investment, and profitability factors; (b) $αFFCPS$ the alpha relative to Fama and French (1992, 1993, 2015) market, size, book-to-market, investment, and profitability factors, Carhart’s (1997) momentum factor, and Pastor and Stambaugh (2003) liquidity factor; and (c) $αQ$ is the alpha relative to Hou, Xue, and Zhang (2015) market, size, investment, and profitability factors.²⁰ Quintile portfolios are formed by sorting stocks based on their regulatory operating leverage (ROL) over the past quarter. Quintile portfolio 1 (5) consists of stocks with the lowest (highest) ROL. The last row presents the differences in excess returns and alphas between the extreme quintile portfolios. The results span the period from April 1991 to December 2021.

Panel A of Table 5 presents the univariate portfolio sort results. The highest ROL quintile generates the highest excess and risk-adjusted returns within both equal-weighted and value-weighted portfolios. Moving from the lowest to the highest ROL quintile, the equal (value)-weighted average monthly excess return increases from 75 (68) to 130 (117) basis points per month. A zero-cost high-low equal (value)-weighted strategy generates 54 (49) basis points return per month with a t-statistic of 6.30 (3.28). When we multiply by 12, the high-low equal (value)-weighted strategy generates a 6.48% (5.88%) annualized return.

The differences in returns between equal-weighted and value-weighted strategies can be considered as an indicator of economies of scale. Regulations significantly contribute to the cost rigidity of firms, particularly smaller ones. Larger firms have the advantage of spreading their fixed costs over a larger output, resulting in lower costs per unit of output. This implies that economies of scale reduce exposure to fixed (regulatory) costs. Since larger firms have larger weights in value-weighted strategies compared to equal-weighted strategies, moving from equal-weighted ROL to value-weighted ROL sorts, the return spread between the extreme ROL quintile portfolios decreases.

In addition to the raw returns, Table 5 presents the magnitude and statistical significance of various risk-adjusted returns. Equal (value)-weighted $αFF5$ increases from −14 (−15) to 41 (25) basis per month, moving from the lowest to the highest ROL quintile portfolio. In addition, a zero-cost high-low equal (value)-weighted ROL strategy produces 50 (35) basis points $αFFCPS$ per month with a t-statistic of 5.80 (2.49). Similarly, a zero-cost equal (value)-weighted high-low ROL strategy produces 47 (35) basis points $αQ$ per month with a t-statistic of 5.34 (2.35). The results show that the positive relationship between ROL and future stock returns cannot be captured by common risk factor models.²¹

Next, we investigate the source of the significant alpha spreads between the extreme ROL quintiles. For this, we focus on the economic and statistical significance of the risk-adjusted returns generated by quintile 1 and quintile 5. As reported, while quintile 1 produces insignificant alphas, quintile 5 generates positive and significant risk-adjusted returns. The highest ROL quintile portfolio earns 41 (25) basis points equal (value)-weighted $αFF5$ per month with a t-statistic of 3.53 (2.34). Similarly, the highest ROL quintile portfolio produces positive and significant $αFFCPS$ and $αQ$⁠. Hence, the significantly positive alpha difference between extreme ROL stocks is due to the outperformance by high ROL stocks. In other words, investors demand a compensation in the form of higher expected returns to hold stocks with high ROL.²²

Throughout the study, we exclude stocks with a price lower than $1 to eliminate the effect of micro-cap/illiquid firms. Fama and French (2008) document that the returns on equal-weighted hedge portfolios can be dominated by tiny stocks, which are defined as stocks with market capitalization below the 20th NYSE percentile. After eliminating stocks with market capitalization below the 20th NYSE percentile, a zero-cost high-low ROL equal (value)-weighted strategy generates 42 (50) basis points excess return per month with a Newey-West-adjusted t-statistic of 4.55 (3.33) and 46 (42) basis points monthly $αFF5$ with a t-statistic of 5.58 (3.22).^23,24

Novy-Marx (2011) introduces (COGS+SG&A)/AT as a proxy for operating leverage and shows that cross-industry book-to-market differences are driven by asset heaviness (operating leverage) differences between industries. Hence, operating leverage is critical to models that generate the value premium. To investigate whether interindustry ROL differences drive significantly positive alpha spread between the extreme ROL portfolios, panel B of Table 5 constructs NAICS-2-level industry controlled ROL-sorted quintile portfolios. Industry controlled high-low equal-weighted ROL strategy generates 68 (71) basis points subsequent excess return (⁠$αFF5$⁠) with a t-statistic of 8.83 (9.51), while the industry controlled value-weighted raw return (⁠$αFF5$⁠) spread between extreme ROL portfolios is 59 (64) basis points per month with a t-statistic of 3.90 (4.68). Additionally, the alternative equal- and value-weighted risk-adjusted return spreads are positive and significant. This provides evidence to the idea that the significant return differences between extreme ROL portfolios is not driven by cross-industry differences in ROL and the positive cross-sectional predictive power of ROL over future stock returns is robust to industry controls.

3.2 Size-dependent portfolio-level analyses

While some small businesses can be exempted from some regulations, regulations in general introduce fixed costs, such as capital expenditures, information costs, reporting, and compliance costs (Bradford 2004). Consistently, the equal-weighted alpha spread between the extreme ROL quintile portfolios is greater than the value-weighted spread. This suggests that there might be a stronger relationship between ROL and expected stock returns within smaller subsets of stocks, as regulations tend to increase (decrease) cost rigidity (flexibility) among smaller firms.

To investigate whether there is a size-dependent cross-sectional relation between ROL and stock returns, we group stocks into 20-60-20 percentile market capitalization (size) tiers. Then, within each size tier, quintile portfolios are formed by sorting stocks based on their ROL measure from April 1991 to December 2021. Table 6 reports excess returns and five-factor alphas generated by ROL-sorted quintiles. Panel A (B) constructs equal-weighted (value-weighted) portfolios.

There is a positive and significant relation between ROL and subsequent stock returns within all size subsamples. More specifically, within the small market capitalization subsample, equal (value)-weighted high-low ROL strategy generates 73 (83) basis points raw return and 71 (79) basis points risk-adjusted return per month. A zero-cost equal (value)-weighted high-low ROL strategy produces 62 (58) basis points raw return and 64 (63) points risk-adjusted return per month within the mid-cap stock subsample. Finally, while the return differences between the extreme ROL portfolios decrease further moving from the small- and mid-cap stock subsamples to the large-cap subsample, the same strategy continues to generate positive and significant return spreads. More specifically, the five-factor equal (value)-weighted alpha spread between the extreme ROL portfolios is 31 (38) basis points per month with a t-statistic of 3.42 (2.86).

The results are consistent with the economies of scale implications of fixed cost component of regulations. Regulations impose substantial fixed costs, and larger firms can leverage their larger output to benefit from economies of scale, unlike smaller firms. Put differently, smaller firms lack economies of scale. The presence of significant fixed regulatory costs significantly restricts firms’ cost structures and adds to their riskiness. Consequently, risk-averse investors require a premium in the form of higher expected returns when investing in stocks with high ROL, particularly within smaller firm subgroups.

3.3 Average stock characteristics

This subsection examines the average characteristics of stocks with low vs. high ROL based on univariate portfolio-level analyses. Table 7 reports the time-series averages of the median values of firm-specific characteristics and risk factors, such as firm-specific regulatory restriction count, market capitalization, market beta, book-to-market ratio, intermediate-term momentum, illiquidity, idiosyncratic volatility, and operating margin after depreciation.

The first column documents the time-series average of the median values of firm-specific regulatory restriction exposures of ROL-sorted quintile portfolios. It is seen that ROL is not a monotonic transformation of regulatory restriction. Having a closer look, the regulatory restriction counts are the highest for the two highest ROL portfolios and for the lowest ROL portfolio. This shows the difference economic channels captured by the level of regulatory restriction words and the fixed cost component of regulations. Put differently, exposure to many “must”, “shall”, and other regulatory restriction words does not necessarily mean that a firm’s fixed regulatory cost exposure is a higher portion of its costs.

The market capitalization (size) increases from the first to the second ROL quintile. Then, size decreases monotonically from the second to the fifth ROL portfolio. As some small businesses are exempted from regulations and/or as certain regulations allows small firms to prepare for regulatory compliance gradually (staggered adoption) compared to larger firms, some small firms’ regulatory burden might be lower compared to larger ones. Hence, the increase in market capitalization from the first to the second ROL quintile is plausible. On the other hand, most of regulatory compliance costs are fixed and they fall disproportionately on smaller firms. As a result, small firms are significantly constrained by the regulations. This phenomenon explains the decrease in market capitalization from the second to the fifth quintile.

The third column reports the time-series average of median market beta. While the lowest ROL quintile has an average market beta of 0.929, the rest of the quintiles has significantly larger market betas. The third, fourth, and fifth ROL portfolios have a market beta of 1.052, 1.051, and 1.041, respectively. The results are consistent with the operating leverage literature according to which firms with high operating leverage are more dependent on business cycles and, hence, more exposed to systematic risks.

The time-series average of the median book-to-market ratios varies between 0.500 and 0.581. While the intermediate-term-momentum decreases from quintile 1 to 2, the two highest ROL quintiles generate the highest momentum. Similarly, there is no significant variation in Amihud (2002) illiquidity and idiosyncratic volatility from the lowest to the highest ROL portfolio.

Moving from the lowest to the highest ROL quintile portfolio, operating margin after depreciation tends to increase, albeit not monotonically. To examine the relation between operating margin and ROL, we estimate firm-level cross-sectional regressions of operating margin after depreciation on ROL and control variables including natural logarithm of sales, logarithm of market-to-book asset ratio, cash holdings scaled by assets, book leverage, dummy variable of cash dividend payments, cash dividends scaled by assets, and fixed assets scaled by assets. Table A3 of the Internet Appendix documents the regression results. The table suggests a significantly negative relation between regulatory operating leverage and operating margin. In addition, the results indicate a positive relation between operating leverage measures, such as ((COGS+SG&A)/AT) and (SG&A/AT), and operating margin. The long run trend of the U.S. economy gives rise to the positive association between operating leverage and profitability. However, fixed regulatory costs constrain firms’ cost structure in a way that firms cannot cut them. As a result, ROL constrains firms’ operating flexibility and decreases their profitability.²⁵

3.4 Bivariate portfolio-level analyses

The recent literature provides cross-industry and intraindustry explanations to the value premium (Novy-Marx 2011). First, asset-level differences between industries contribute to cross-industry book-to-market spreads. To illustrate, firms in industries such as “utilities” tend to be asset-intensive, whereas firms in industries such as “information technology” are not. This phenomenon leads to firms in capital intensive industries to have higher book-to-market ratios as such firms have high book values compared to their market values. On the other hand, profit margin differences of different firms in the same industry can lead to book-to-market differences. For example, a firm with a 2% operating margin is more exposed to industry-level shocks than a firm with a 10% operating margin. Hence, the firm with a lower operating margin would carry a lower market value and higher book-to-market ratio compared to a firm with a higher operating margin within the same industry. Hence, asset heaviness differences between industries and operating margin differences in the same industry explain a significant portion of the value premium.

Additionally, the literature that provides labor expenses (leverage) based explanations to operating leverage and value premiums (Rosett 2001; Danthine and Donaldson 2002; Donangelo et al. 2019; Favilukis, Lin, and Zhao 2020). More specifically, Rosett (2001) and Danthine and Donaldson (2002) provide evidence to the cost rigidity and operating leverage implications of committed labor expenses. Hence, labor expenses (fixed labor costs) contribute to risk premium. Donangelo et al. (2019) document that firms’ labor costs are significantly inflexible compared to their cash inflows and they are less variable than nonlabor costs.²⁶ Built on this idea, Donangelo et al. (2019) construct a firm-level measure of labor (operating) leverage that quantifies the level of labor expenses scaled by the firm’s value-added and document that labor leverage is positively priced in the cross-section of stock returns. Favilukis, Lin, and Zhao (2020) introduce measures of labor expenses growth and labor share as proxies for labor market frictions. They show that both variables predict credit risk, debt growth, and financial leverage significantly.²⁷

To ensure that the measures described do not fully explain the cross-sectional pricing of regulatory operating leverage, we perform bivariate portfolio sorts and reexamine the return and alpha differences between extreme ROL portfolios. To do so, we use a 5x5 dependent sort based on the control variables: operating margin, opeerating leverage, labor leverage, and labor share growth. To illustrate, first, we control for operating margin by forming quintile portfolios ranked based on the level of operating margin. Then, within each operating margin quintile, we sort stocks into quintile portfolios based on their ROL so that quintile 1 (quintile 5) consists of stocks with the lowest (highest) ROL. For brevity, we do not report returns for all 25 (5x5) portfolios. Instead, Table 8 presents excess returns and alphas averaged across the operating margin quintiles with dispersion in ROL. Naturally, we conduct the same analyses for operating leverage, labor leverage, and labor share growth.²⁸ Panel A (B) reports equal (value)-weighted returns.

First two columns of Table 8 reports excess and risk-adjusted returns generated by operating margin controlled ROL-sorted quintile portfolios. When operating margin is the first-stage sorting variable, the equal-weighted excess return and alpha spreads between the extreme ROL quintile portfolios are 58 and 57 basis points per month with Newey-West-adjusted t-statistics of 8.40 and 8.44, respectively. Similarly, a zero-cost operating margin controlled ROL strategy produces a value-weighted excess return of 49 basis points with a t-statistic of 3.30 and five-factor alpha of 41 basis points with a t-statistic of 3.14. The rest of the columns provide similar results. When we control for operating leverage measure of Novy-Marx (2011), the highest ROL quintile generate 66 basis points more equal-weighted alpha compared to the lowest ROL quintile. Similarly, the equal-weighted alpha spread between the extreme ROL quintiles is 62 basis points per month once we neutralize the portfolios to labor (operating) leverage measure of Donangelo et al. (2019). Finally, labor share growth (Favilukis, Lin, and Zhao 2020) controlled equal-weighted alpha difference between quintile 5 and quintile 1 is 68 basis points per month. Similarly, once we control for the first-stage sorting variables, the value-weighted excess return and alpha spreads between the extreme ROL portolios are positive and significant at 5% level.^29,30

This subsection provides evidence to the fact that operating margin and operating leverage, potential drivers of intra- and cross-industry book-to-market differences, cannot capture the positive and significant cross-sectional relation between ROL and subsequent returns. Similarly, labor leverage, a significant contributor to operating leverage, fails to eliminate the predictive power of ROL on future stock returns. Finally, labor share growth controlled ROL-sorted portfiolios continue to generate positive and significant returns. This suggests that the effect of ROL on subsequent returns cannot be subsumed by potential factors that might give rise to operating leverage differences between stocks, which in turn generates significant risk premiums.

Additionally, we divide the sample of stocks into tiers based on the level of first-stage sorting variables and examine the return differences (not reported) between extreme ROL quintiles within each tier. The results show that ROL strategy generates larger return spreads within the subgroups of stocks with lower operating margin, higher operating leverage, higher labor leverage, and higher labor share growth. This provides further evidence to the idea that ROL is more binding for firms that are significantly constrained by their operating margin and their cost structures (i.e., higher labor expenses). As a result, investors demand a higher premium in the form of higher expected returns to invest in stocks with high ROL, particularly those with low operating margin, high operating leverage, high labor leverage, and high labor share.

3.5 Liquidity, institutional holdings, and analysts

It is essential to examine whether the significant cross-sectional pricing of ROL is only prominent among small stocks, illiquid stocks, stocks with low analyst coverage, and stocks with low institutional holdings. If so, the predictive power of ROL on future stock returns could be attributed to mispricing rather than a risk-based explanation. To investigate this, we analyze the association between ROL and future stock returns while accounting for liquidity, institutional holdings, and analyst coverage. Tables 9, 10, and 11 present the results.

Table 9 documents that the significant cross-sectional relation between ROL and subsequent returns is pronounced among all liquidity subgroups. While the value-weighted $αFF5$ spread between the extreme ROL quintile portfolios is 55 basis points per month within the most illiquid stock subsample (LIQ 1), a zero-cost high-low ROL strategy produces 58 (44) basis points alpha within the subgroup of stocks with medium (high) liquidity. Tables 10 and 11 yield similar results.

To measure institutional holdings (INST) of a particular stock, we use the percentage of total shares outstanding owned by institutional investors by the end of the last quarter. There is a significantly positive relationship between ROL and subsequent returns within all stock subgroups with different level of institutional holdings. The results document that the highest ROL portfolio generates both economically and statistically significant subsequent risk-adjusted returns within all institutional holdings tiers. The $αFF5$ difference between the highest and the lowest ROL quintiles is 35 basis points within the highest institutional holdings tier and 31 (78) basis points within the medium (lowest) institutional holdings tier.

Asymmetric (incomplete) information on some stocks might result in arbitrage opportunities. Hence, one might doubt that high ROL stocks generate high subsequent returns because of a lack of information. To test this, we conduct bivariate portfolio-level analyses. We measure analyst coverage (CVRG) as yearly average of the total number of analysts for each stock. Table 11 presents a significant relation between ROL and future stock returns within all analyst coverage subsamples. A zero-cost high-low ROL strategy produces 35 (31) basis points subsequent excess return (⁠$αFFC5$⁠) within the lowest analyst coverage tier. Moving to higher analyst converage subsgroups, we see the excess and risk-adjusted return spreads between the extreme ROL quintiles increase. As an illustration, note that stocks with high ROL generate 50 basis points more excess return and 45 basis points more alpha compared to stocks with low ROL in the medium level of analyst coverage. Similarly, the excess return (alpha) difference between the extreme ROL quintiles is 52 (47) basis points per month with a t-statistic of 2.94 (3.01) within the subsample of stocks high analyst coverage.

3.6 Firm-level cross-sectional regressions

So far, we test the cross-sectional relation between ROL and subsequent stock returns at portfolio-level. We now examine the cross-sectional relation between regulatory operating leverage, regulatory restriction counts, and expected returns at the firm level using Fama-Macbeth (1973) regression methodology. Firm-level cross-sectional regressions have two significant advantages over portfolio sorts. First, portfolio sorts hide a significant amount of information in the cross-section because of stocks accumulating in portfolios. Second, cross-sectional regressions have the advantage of being able to control for several simultaneous effects and factors.

Table 12 reports the time-series averages of the slope coefficients from the regressions of stock returns on regulatory operating leverage (ROL), the natural logarithm of firm-specific regulatory restriction count (REG), market beta (BETA), the natural logarithm of market capitalization (SIZE), the logarithm of book-to-market ratio (B/M), intermediate-term momentum (MOM), short-term reversal (REV), illiquidity (ILLIQ), idiosyncratic volatility (IVOL), asset growth (I/A), return on equity (ROE), maximum of daily returns (MAX), and operating margin after depreciation (OM) from April 1991 to December 2021.³¹

Columns (1) and (2) report slope coefficients of univariate regressions of 1-month-ahead stock returns on regulatory operating leverage and regulatory restrictions. The last two columns document the multivariate regression results in which the independent variables are regulatory operating leverage and the mentioned control variables (column 3) and the natural logarithm of firm-specific restriction count and control variables (column 4).

Consistent with univariate portfolio-level analyses, the first column suggests that the regulatory operating leverage (ROL) measure has a positively significant predicting power on future returns. The average slope from the univariate monthly regressions of 1-month-ahead stock returns on ROL is 0.023 with a Newey-West t-statistic of 4.73. According to the univariate regression of realized returns on the natural logarithm of regulatory restrictions, the coefficient for restriction count is negative albeit insignificant with a t-statistic of −0.96. The first two columns show that the overall effect of regulations on stock returns is distinctly different from the cross-sectional pricing of fixed cost component of regulations.³²

Column 3 reports the multivariate regression results of excess returns on ROL and control variables. According to this specification, the average slope coefficient for ROL is 0.037 (t-stat. =6.04), larger than the univariate regression coefficient. The coefficient for the logarithm of regulatory restrictions is still negative and insignificant after accounting for all firm-specific characteristics and risk factors, which repeatedly documents the different economic channels captured by fixed cost component of regulations and the overall effect of regulations.

To examine the return differences between stocks with the extreme level of ROL, we create quarterly-varying quintile portfolios based on ROL measure and estimate firm-level cross-sectional regressions of excess returns on the dummy variables indicating the ROL quintile that a particular stock belongs to and control variables. According to quintile sort Fama-Macbeth regressions, there is a significant monotonicity from the first to the fifth ROL quintile. More specifically, stocks in the fifth quintile generate 54 basis points return per month more than stocks in the lowest quintile. In other words, after accounting for a number of return predictors, a high-low zero-cost strategy, in which an investor takes a long position at high ROL stocks and a short position at low ROL stocks, generates around 6.5% annualized return.

3.7 Risk contribution of regulatory operating leverage

This section aims to provide further risk-based explanation for the observed positive relation between ROL and subsequent stock returns. Specifically, we examine whether stocks with high ROL generate higher returns compared to stocks with low ROL due to risk exposure.

To investigate this, we conduct firm-level cross-sectional Fama-Macbeth (1973) regressions of firm-level forward-looking cash flow volatility on ROL, along with a set of control variables. We quantify quarterly firm-level cash flows as EBITDA (earnings before interest, tax, depreciation, and amortization) scaled by assets (AT). We define cash flow volatility as firm-level four-quarter forward-looking volatility of EBITDA scaled by assets. Following Dou et al. (2021), we include the natural logarithm of asset value, the natural logarithm of book-to-market ratio, and the natural logarithm of debt-to-equity ratio as control variables. Additionally, we account for the operating leverage measure (SG&A/AT) proposed by Chen, Harford, and Kamara (2019) and operating margin after depreciation.³³  Table 13 presents the regression results.

The first column of Table 13 presents the univariate regressions results of firm-specific four-quarter forward-looking volatility of EBITDA scaled by assets on ROL. The results document that ROL alone positively and significantly predicts the forward-looking cash flow volatility. The second column adds size, book-to-market ratio, and financial leverage to the regression model. According to this specification, the estimated coefficient for ROL is positive and significant with a Newey-West-adjusted t-statistic of 2.40.

The findings in the first two columns demonstrate that firms experience increased cash flow volatility due to regulatory operating leverage. However, it is possible that this positive association is driven by the implications of operating leverage and operating margin related to ROL. In other words, the positive relation between ROL and future cash flows might be captured by the effects of operating leverage and operating margin. To address this, the third column adds the operating leverage measure proposed by Chen, Harford, and Kamara (2019) and operating margin as independent variables, alongside the variables from column 2. The third column reports an estimated coefficient of 0.0012 on ROL with a t-statistic of 4.17. This shows that the significantly positive cross-sectional relation between ROL and forward-looking cash flow volatility is robust to controls for operating leverage and operating margin.

Furthermore, the third column reports the estimated coefficients for operating leverage (OL) and operating margin (OM). Consistent with existing literature on operating leverage literature, the coefficient for the operating leverage (SG&A/AT) is positive and significant. This positive association can be explained by the fact that firms with higher fixed costs, compared to variable costs, have less flexibility in their operations. During economic expansions, these firms experience faster revenue growth compared to their costs, while during recessions, they incur larger losses. Consequently, firms with higher operating leverage are more exposed to systematic risk, leading to greater cash flow volatility. Additionally, there is a significantly negative relation between operating margin and future cash flow volatility. As highlighted by Novy-Marx (2011), firms operating at low margins are more exposed to industry-level shocks compared to firms operating at high margins. Consequently, firms with low margins exhibit greater cash flow volatility compared to firms with high margins.

The fourth column intends to provide detailed explanations for the observed positive relation between ROL and future cash flow volatility. More specifically, we investigate whether ROL triggers future cash flow volatility due to systematic risk, idiosyncratic risk, or both. Then, we provide additional systematic shock explanations for the positive association between ROL and cash flow volatility. To do so, we first estimate cross-sectional regressions of cash flow volatility on ROL and control variables in column 3 for each quarter and obtain slope coefficients for ROL. Then, we estimate time-series regressions of the ROL coefficients for recessionary and nonrecessionary dummy variables, which are defined based on the recessionary periods of NBER (National Bureau of Economic Research). If there is a recessionary month in at least one of the next four quarters, the recessionary dummy variable takes a value of one and otherwise zero. The estimated coefficient for the interaction variable between ROL and recessionary period dummy variable is 0.0019 with a t-statistic of 3.20. On the other hand, the estimated coefficient for the interaction term between ROL and nonrecessionary period dummy variable is 0.0010 with a t-statistic of 4.45. This means that there is a significantly positive relation between ROL and cash flow volatility during recessionary and nonrecessionary periods. The results suggest that ROL significantly contributes to systematic and idiosyncratic risk. Additionally, the economic magnitude of the estimated coefficient for ROL is higher during recessionary periods, almost double of the magnitude during nonrecessionary periods.³⁴ The fourth column also documents the difference in the estimated coefficients for ROL between recessionary and nonrecessionary periods. The coefficient for the difference term is significantly positive with a t-statistic of 1.98.

ROL increases future cash flow volatility, a proxy for risk, during both recessionary and nonrecessionary periods. Furthermore, the positive association between ROL and future cash flow volatility is significantly stronger during recessionary periods. This supports the idea that the impact of ROL on returns is driven by the (systematic) risk contribution of fixed regulatory costs. As regulatory fixed costs have a significant impact on operating leverage, which further triggers firms’ exposure to fluctuations in business cycles, we anticipate that the relation between ROL and cash flow volatility is influenced by the state of the economy. Thus, we examine how macroeconomic state variables contribute to the extent to which ROL affects a firm’s cash flow volatility.

To investigate this, we introduce bivariate interaction terms between ROL and changes in CFNAI (Chicago Fed National Activity Index) as well as the natural logarithm of industrial production. Specifically, we calculate forward-looking four-quarter averages of CFNAI and industrial production index, and compute changes in these variables (to illustrate, the changes in CFNAI is defined as mean(⁠$CFNAIQ+1,Q+4$⁠) − $CFNAIQ$⁠). We then introduce time-series regressions of the ROL coefficients (obtained from the first-stage regression) on changes in CFNAI (⁠$Δ(CFNAI)$⁠) and changes in industrial production index (⁠$Δ(INDP)$⁠). In column 4, we present the estimated coefficients for the interaction terms. The estimated coefficient for the interaction term between ROL and changes in CFNAI (INDP) is −0.0028 (−0.0032) with a t-statistic of −2.24 (−2.22). This suggests that the association between ROL and future cash flow volatility fluctuates depending on the state of the economy (i.e., CFNAI and industrial production). Particularly, there is a stronger relationship between ROL and future cash flow volatility during periods of decreasing economic activity.

The underlying idea is that regulations impose significant fixed costs and add to operating leverage. As regulations significantly contribute to operating leverage, firms with high ROL become more dependent on business cycles. Specifically, firms with high ROL are unable cut their regulation-driven fixed costs as much as firms with low ROL, making them more likely to generate more volatile cash flows, particularly during periods of decreasing economic activity. Consequently, firms with high ROL exhibit greater cash flow volatility compared to firms with low ROL during periods of decreasing economic activity and declining industrial production growth. In other words, CFNAI and industrial production are important macroeconomic state variables on the systematic risk implications of ROL.

Column 5 of Table 13 introduces a new independent variable, the interaction term between ROL and the natural logarithm of asset value (a measure of size). Consistent with the bivariate portfolio analyses (first on market capitalization, then on ROL), there is a size-dependent cross-sectional relation between ROL and future cash flow volatility. In particular, column 5 reports an estimated coefficient of 0.0118 on ROL (t-statistic = 3.26) and a coefficient of −0.0005 on the interaction term between ROL and size (t-statistic = −3.21). These results indicate that the positive association between ROL and future cash flow volatility (risk) triggers moving from large firms to small firms. In other words, the relationship between ROL and cash flow volatility is stronger within smaller stock subgroups. Hence, investors demand extra compensation in the form of higher expected returns to hold smaller stocks with high ROL as they generate more volatile future cash flows.

Specifically, the equal-weighted return spread between the extreme ROL quintiles is 73 (62) basis points per month with a t-statistic of 4.18 (6.00) within small-cap (mid-cap) stock subgroups. In the largest stock subsample, the equal-weighted alpha spread between extreme ROL quintiles decreases to 28 basis points per month with a t-statistic of 2.90. The value-weighted return spreads exhibit a similar pattern when moving from the smallest to the largest stock subsample. In summary, the findings in column 5 are consistent with the previous bivariate portfolio analyses. They suggest that economies of scale decrease the burden of regulatory fixed costs. In other words, large firms are less exposed to the negative implications of ROL. Hence, there is a stronger cross-sectional relation between ROL and future stock returns moving from large to small-cap firms as smaller firms lack economies of scale.

3.8 Regulatory operating leverage and economic mechanism

As the preceding subsections provide evidence of the association between regulatory operating leverage and systematic risk, this subsection investigates the importance of discount rate shocks in the cross-sectional pricing of ROL. To do so, we follow the approach of Dou, Ji, and Wu (2021) and estimate the exposure of ROL-sorted portfolio returns to discount-rate shocks. Specifically, we calculate the sum of ROL-sorted value-weighted portfolio excess returns over the past 36 months (from t-35 to t) and the sum of shocks to the earnings-price ratio over the same period using an AR(1) model. Following Campbell and Shiller (1988, 1998), we employ the cyclically adjusted price-to-earnings ratio as a proxy for discount rates.³⁵ Then, we estimate return loadings on the discount rate shocks for the ROL-sorted portfolios and the return spread between the extreme portfolios. Panel A of Table 14 presents the discount rate exposures. The results show that the exposure to accumulated discount-rate shocks is negative and diminishes across portfolios sorted on ROL. Furthermore, the loading of the extreme ROL spread on the discount rate shocks is significantly negative.³⁶ This contributes to the notion that one reason that ROL is positively priced in the cross-section of stocks returns is the increased exposure to discount rate shocks as the ROL measure increases.

Substantial evidence indicates that costly regulations create barriers to entry, impede market entry, and pose challenges to new entrants attempting to displace market leaders (Djankov et al. 2002; Klapper, Laeven, and Rajan 2006; Suzuki 2013). In essence, the burden of regulatory compliance hardens barriers to entry, resulting in a reduced turnover rate of market leadership. This suggests that reduced entry rates lead to decreased competition and an increase in the monopoly rents enjoyed by incumbents. Dou, Ji, and Wu (2021) develop an asset pricing model and find that discount rates intensify product market competition. Furthermore, industries with a lower rate of leadership turnover are more exposed to fluctuations in discount rate. Consequently, the turnover rate of market leadership (and competition) emerges as an important characteristic in the cross-sectional pricing of ROL, given that exposure to discount-rate fluctuations increase with ROL (panel A of Table 14).

To test this hypothesis, panel B of Table 14 divide our sample based on measures of market turnover rate. Specifically, following the approach of Dou, Ji, and Wu (2022), we introduce a market turnover indicator dummy variable that takes a value of one if (a) the largest firm ranked by sales in the industry (three-digit NAICS industry) in year t + 1 is not among the four largest firms in year t, or (b) any of the second- to fourth-largest firm ranked by sales in the industry in year t + 1 are not among the four largest firms in year t and are large enough that their sales exceed 60% of the sales of the largest firm in year t + 1; otherwise, it takes a value of zero. Panel B divides the sample of firms into two subgroups based on the values of market turnover indicator. The first (last) six columns of panel B report the returns generated by ROL-sorted quintile portfolios within industries with a market indicator of 1 (0). In other words, the first-six columns report the returns in industries characterized by high market turnover, while the remaining columns investigate return differences within industries with low market leader turnover.

Panel B documents that the return spread between the extreme ROL quintiles decreases to 29 basis points per month among industries with high market turnover. Similarly, CAPM and five-factor alphas between the highest and lowest ROL portfolios are insignificant within this stock subgroup. In other words, the ROL premium disappears (becomes insignificant) within the subgroup characterized by low leadership turnover. The results provide evidence to the importance of market leadership turnover in the cross-sectional pricing of ROL.

On the other hand, the return and alpha spreads between the extreme ROL quintiles are positive and significant within subgroups of industries with low leadership turnover. Specifically, the excess return spread between the fifth and first quintiles is 71 basis points per month within low turnover. In other words, industries with lower leadership turnover imply that incumbents enjoy longer durations as market leaders and they are likely to face reduced competition and main their positions. This suggests that cash flows of firms (industries) with higher regulatory operating leverage are more susceptible to discount-rate shocks as regulations are likely to introduce significant costs, create barriers to entry, and reduce the turnover rate of market leaders. Consequently, firms (industries) with more costly regulations tend to have higher excess returns and risk-adjusted returns, as market leaders in such industries often secure their positions with longer durations.³⁷

This subsection offers important insights into the literature on regulations, discount rates, and competition. Existing evidence highlights barriers to entry and increased concentration as externalities of regulations, resulting in fewer market entrants and participants, as well as reduced market leadership turnover. This additionally suggests that incumbents in such markets tend to secure their positions with longer durations. Dou, Ji, and Wu (2021) provide evidence of the relationship between market leadership turnover and exposure to discount-rate fluctuations. Specifically, they find that firms’ profit margins in industries with lower turnover rate are highly exposed to discount-rate risk. Additionally, they show that, once they control for leadership turnover spread, the gross-profitability premium becomes insignificant. Building on Dou, Ji, and Wu (2021), Dou, Ji, and Wu (2022) show that the market leadership turnover rate and the cash flow loading on expected growth jointly determine exposure to fluctuations in discount rate and expected growth, where market turnover induces discount-rate risk exposure.

Our paper adds to the literature by showing that regulatory operating leverage contributes to exposure to systematic risks. More specifically, this subsection shows that discount-rate risk affects the risk premium across stocks with varying ROL measures. Given that market leadership turnover is a crucial factor in exposure to discount rate fluctuations, this study provides consistent explanations. As the ROL premium disappears in industries with high market leadership turnover, it remains significant in industries characterized by low leadership turnover. This suggests that firms (industries) with costly regulations generate higher returns in industries where market leaders secure their positions for longer durations. This subsection provides additional evidence that market leadership turnover is an important factor in the cross-sectional pricing of ROL.

3.9 Robustness check: Alternative regulatory operating leverage measures

Table 15 presents the univariate equal-weighted and value-weighted average excess monthly returns and five-factor alphas (⁠$αFF5$⁠) of quintile portfolios that are formed by sorting stocks based on the alternative regulatory operating leverage (ROL) measures, which are estimated by Equations (4) and (5).

The results suggest that the cross-sectional predictive power of ROL on 1-month-ahead returns is robust to alternative ROL specifications. A zero-cost high-low equal (value)-weighted ROL strategy, in which ROL is generated through Equation (4), produces 67 (77) basis points monthly excess return and 73 (85) basis points $αFF5$ per month. Similarly, a zero-cost equal (value)-weighted ROL strategy, where ROL is estimated through Equation (5), generates 65 (52) basis points $αFF5$ per month with a Newey-West-adjusted t-statistic of 7.12 (3.92).

3.10 Robustness check: Rolling window estimation

So far, the cross-sectional relation between ROL and subsequent stock returns is tested where ROL is estimated through firm-specific time-series regressions where a constant regulatory cost beta is estimated for each firm in the sample. As a robustness test, this subsection estimates firm-specific quarterly-varying regulatory operating leverage measure using a 60-quarter fixed window estimation.³⁸ Regulatory operating leverage is defined as fixed regulatory costs that are attributable to regulations over SG&A expenses. Table 16 reports value-weighted excess returns and three sets of alphas (⁠$αFF$⁠, $αFFCPS$⁠, and $αQ$⁠) generated by industry controlled ROL-sorted quintile portfolios.

The first column of Table 16 reports that stocks in the lowest ROL quintile (portfolio 1) have a monthly value-weighted average excess return of 58 basis points. On the other hand, stocks in the highest ROL quintile (portfolio 5) produce 125 basis point value-weighted excess return per month. As a result, the average return difference between the extreme ROL quintiles is 0.67% per month with a Newey-West-adjusted t-statistic of 2.65. When tested against common risk factors, the risk-adjusted return spread between quintile 5 and quintile 1 varies between 42 basis points and 56 basis points per month. More specifically, a zero-cost high-low value-weighted strategy produces 42 basis points $αFF5$⁠, 44 basis points $αFFCPS$⁠, and 56 basis points $αQ$ per month, where the t-statistics vary between 1.95 and 2.47.

4. Conclusion

A significant portion of regulatory compliance costs are fixed, such as information costs, reporting, and recordkeeping, and they are mostly included in the SG&A expenses. Building on this idea, we first show that federal-level regulations indeed impose significant costs on firms’ cost structure. Subsequently, we investigate the impact of regulatory costs in the cross-section of stock returns.

To do so, we introduce a firm-specific quarterly-varying measure, regulatory operating leverage, that captures a firm’s exposure to fixed regulatory costs. We show that regulatory operating leverage predicts returns in the cross-section and that strategies formed by sorting on regulatory operating leverage earn significant excess returns. After controlling for a battery of firm-specific characteristics and risk factors, the relationship between ROL and future stock returns remains economically and statistically significant. Furthermore, the cross-sectional relation between ROL and stock returns is robust to controls for operating margin, operating leverage, labor leverage, and labor share. Additionally, we show that the effect of ROL on future returns is prominent in all liquidity, institutional holdings, and analyst coverage tiers.

To provide further insights into the pricing of regulatory operating leverage and its relation to stock returns, we conduct a regression analysis of cash flow volatility on regulatory operating leverage. The results indicate a statistically significant relation between the two variables, particularly during recessionary periods where the association is even stronger. This finding supports the idea that the impact of ROL on returns is due to the (systematic) risk contribution of fixed regulatory costs. To better understand the systematic shocks that contribute to this relation, we introduce interaction terms between ROL and innovations in macroeconomic state variables, such as the Chicago Fed National Economic Activity Index and industrial production growth. Our findings demonstrate a stronger relationship between ROL and cash flow volatility during periods of decreasing economic activity. Hence, the CFNAI and industrial production are important state variables that contribute to the systematic risk exposure of stocks with high ROL. We additionally find that the relation between ROL and cash flow volatility to be more pronounced among small-cap firms as they lack economies of scale.

Adding to the systematic risk explanations, we provide evidence of the importance of exposure to the discount-rate shocks of ROL-sorted portfolios. Specifically, we find that firms with higher ROL are more exposed to discount-rate shocks. Then, built on the recent literature on discount rates and competition, we provide market turnover based explanations to the observed ROL premium. As discount rate shocks affect market leadership turnover and market concentration, they are likely to play an important role in the cross-sectional pricing of ROL. To test this, we divide our sample into subgroups based on the market leadership turnover indicator. The economic and statistical significance between extreme ROL portfolios diminishes within the subgroup with high market leadership turnover. This contributes to the idea that incumbents in industries with reduced leadership turnover tend to secure their position for longer durations, hence, their cash flows are more exposed to discount rate shocks. As a result, firms (industries) with more costly regulations tend to have higher (risk-adjusted) excess returns, as incumbents in these industries often secure their positions for longer durations. Additionally, the stock characteristics (Table 7) show an increasing pattern in operating margin moving from the lowest to the highest ROL quintile. This might indicate that incumbent firms operating in industries with costly regulations tend to secure their positions for longer durations. As a result, such firms might generate higher profitability and be more exposed to discount rate shocks. Future research on the relation between regulations, competition (barriers to entry), and profitability might provide important insights on the importance of regulatory costs on leadership turnover and gross profitability premiums.

5. Code Availability Statement

The replication code is available in the Harvard Dataverse at https://doi.org/10.7910/DVN/CF7LBA.

We would like to thank Zhiguo He (the editor), two anonymous referees, Yigit Atilgan, Turan Bali, Hamza Demircan, Cem Demiroglu, Umit Gurun, Oguzhan Ozbas, and seminar participants at Bilkent University, Bogazici University, Durham University, Koc University, Koc Finance Day, and Sabanci University for helpful comments and suggestions. This research was supported by a TUBITAK 1001 grant from the The Scientific and Technological Research Council of Turkey [grant number 117K248]. Baris Ince would like to acknowledge the support of Science Foundation Ireland [grant number 16/SPP/3347].

Footnotes

Author notes

Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

References