The Leverage-Profitability Puzzle Re-examined Alan Douglas, University of Waterloo Tu Nguyen, University of Waterloo Abstract:

The Leverage-Profitability Puzzle Re-examined Alan Douglas, University of Waterloo Tu Nguyen, University of Waterloo Abstract: We present new insight into the Leverage-Profitability puzzle showing that it reflects relatively low debtadjustment costs that facilitate a residual debt financing (RDF) strategy for a range of operations. RDF generates a negative correlation in the numerators of the leverage and profitability ratios, in contrast to the mechanical correlation in the denominators generated by an adjustment-cost avoidance strategy. We show that the puzzle is stronger within the safe range of Altman Z-scores and disappears when the firm enters a grey zone between safety and distress, where traditional trade-offs are more likely to outweigh residual financing concerns. The puzzle also reflects interactions between RDF and other sources/uses of funds, including the use of RDF to support dividend smoothing. JEL classification codes: G32, G35. Keywords: Capital Structure Determinants, Trade-off Theory, Residual Debt Financing, Credit Facilities, Dividend Smoothing.

The Leverage-Profitability Puzzle Re-examined One of the leading and most intuitive theories of capital structure predicts that firms trade off the costs and benefits of debt. While the data supports many predictions consistent with the theory (leverage is positively related to firm size and asset tangibility, negatively related to growth opportunities), it does not support the predicted relation between leverage and profitability. Since more profitable firms face higher taxes and lower bankruptcy costs, the theory predicts a positive leverageprofitability (LP) relation. Empirically, however, the relationship is strongly negative. The "LP puzzle" has received considerable attention in the literature. A leading explanation focuses on capital structure adjustment costs (Frank and Goyal 2009, 2015). Fixed adjustment costs imply it can be optimal to remain `passive' and simply retain profits rather than adjust leverage to target; this retention increases equity value and thus lowers the leverage ratio mechanically (Welch 2004). When leverage deviates sufficiently from target, firms become active i.e., they bear the fixed cost and adjust leverage to its target. Since the target is positively related to profitability, the fixed adjustment cost explanation implies a negative LP relation when firms as passive and a LP positive relation when they are active. On average, therefore, we could observe a negative LP relation. Unfortunately, the LP relation remains negative even when firms are active. Fixed adjustment costs, therefore, cannot fully resolve the puzzle. Frank and Goyal (2015) argue that variable adjustment costs are needed. With variable costs firms adjust only part way toward target. As a result, only part of the negative mechanical correlation is offset and we can observe a negative LP relation even when firms are active. Consistent with combined adjustment costs, Frank and Goyal demonstrate that the LP relation is less negative when debt levels change by a greater amount, and that changes in debt are positively related to changes in profit. While Frank and Goyal (2015) provide valuable insight, a number of findings suggest that the puzzle runs deeper. In particular, Denis and McKeon (2012) and Welch (2012) find that leverage is frequently adjusted away from target in a manner that is heavily influenced by operating needs. DeAngelo, Goncalves and Stulz (2018) show that many firms allow leverage to vary within a strikingly wide range (from near zero to over fifty percent), at times with little variation in traditional costs and benefits of debt. Such behaviour is unlikely to be explained by adjustment costs alone. Similarly, it seems unlikely 1

that the mechanical effect would dominate the adjustment effect so pervasively across numerous stratifications of the data (e.g., subsamples based on firm size, leverage, magnitude of debt changes, deviations from target, etc.). In this paper we propose an alternative perspective based on a combination of low debt adjustment costs and a range of acceptable leverage values, and demonstrate that this perspective can significantly improve our understanding of the puzzle. Within the acceptable range deviations from target are of second-order importance and firms focus on funding uncertain operations without concern for the leverage ratio. Since debt is a more efficient shock-absorber when debt adjustment costs are lower, this perspective leads to the prediction that the LP puzzle weakens with debt adjustment costs. This potentially counter-intuitive prediction reflects that lower debt adjustment costs make it more efficient for debt levels to vary with funding needs that are inversely related to profits. More formally, we develop our hypotheses based on two main assumptions. First, we posit a substantial range of operations where managers are unconcerned with leverage. This assumption is supported by three lines of research: (i) survey results: 71% of the CFOs in Graham and Harvey (2001) say that they target a zone or range leverage values, (ii) empirical evidence: Leary and Roberts (2005), DeAngelo and Roll (2015) and DeAngelo, Gonçalves and Stulz (2018) show that firms exhibit a surprisingly wide range of leverage values, and Denis and McKeon (2012) show that firms rely significantly on debt financing even after increasing leverage by at least ten percent to a level at least ten percent above standard target estimates, and (iii) theoretical analysis: Miller (1977), DeAngelo and Masulis (1980), DeAngelo, DeAngelo and Whited (2011) and Bolton, Chen and Wang (2016) show how personal taxes, alternative tax shields, flexibility and liquidity considerations can offset the corporate tax advantage of leverage; Dybvig and Zender (1980), DeMarzo and Sannikov (2006), DeMarzo and Fishman (2007) and Thakor (2011) and Douglas (2018) show that agency and information costs can also be controlled over a wide range of operations. Second, we assume that firms can reduce debt adjustment costs within a range by using credit lines and other debt facilities. Creditors will supply these facilities if they too perceive that agency, information, and bankruptcy concerns are of second-order importance within a range. This assumption is supported by the notably large credit facilities observed in practice averaging, for example, 16% of assets in Sufi (2009) and 24% of assets in Campello et al (2010). In comparison, total debt averages 20% 2

of assets in Sufi s sample, so that credit facilities average approximately 80% of total debt, slightly larger than the 63% reported by DeMarzo and Sannikov (2006) for the from 1995-2004 period. The combined assumptions (low debt adjustment costs within an acceptable leverage range) generate a setting in which firms can efficiently use residual debt financing (RDF) to absorb uncertainty in funding requirements. This RDF perspective can significantly enhance our understanding of the LP puzzle. The negative leverage-profitability relation generated by RDF is distinct from that generated by traditional adjustment cost theories. In particular it is driven by the numerators of the leverage and profitability ratios, in contrast to the mechanical correlation generated by an adjustment cost avoidance strategy. A RDF strategy can also explain the frequent debt adjustments observed empirically, including frequent adjustments away from estimated targets. The data provide strong support for our RDF hypotheses. First, the puzzle strengthens -- i.e., the profitability coefficient in standard leverage regressions becomes more negative -- when firms face lower debt adjustment costs. We employ three debt adjustment cost proxies identified in the literature: access to a line of credit, a credit rating, and firm size (Leary and Roberts 2005, Faulkender and Petersen 2006, Leary 2009, Acharya et al. 2014). We also show that the puzzle coefficient strengthens significantly with the amount of undrawn credit available, another proxy for the ability to adjust debt cheaply. Next we show that the puzzle strengthens with the likelihood that leverage remains within an acceptable range. We use three proxies for this likelihood: the safe range of Altman Z-scores identified in the literature (Altman et al. 2016), relatively small changes in debt, and relatively wide debt ranges exhibited by firms. A particularly interestingly result is that the puzzle disappears (the profitability coefficient becomes positive) when Z-values enter the grey zone identified in the literature. Firms in the grey zone are approaching financial distress but have not lost control of their capital structure. As such, they are more likely to focus on traditional trade-offs than RDF and thus more likely to adjust leverage downward if profitability declines, exacerbating their concern with distress. We broaden our investigation to allow for interactions between the LP puzzle and corporate payout policy. Lambrecht and Myers (2012, 2017) and DeAngelo and Roll (2015) argue that leverage and payout patterns cannot be examined properly in isolation. A traditional view of payout policy is that managers take positive NPV investments and return any excess (residual) cash flow to shareholders (Farre-Mensa, Michaely and Schmalz 2015). A competing view is that managers smooth payouts toward a target level. 3

As DeAngelo and Roll (2015) point out, it not possible to simultaneously pursue target payout levels and target leverage ratios: the corporate budget constraint implies that "something must give" (note that our RDF hypothesis predicts that the target leverage ratio gives within an acceptable range). In general both views have merit, especially considering that dividend and repurchase components of payout policy can differ in flexibility and commitment, and thus their costs of adjustment. Consistent with the interactions between payout policy and RDF, we find that the LP puzzle strengthens when firms exhibit a smoother payout policy. We further examine interactions through the budget constraint following Denis and McKeon's (2012) analysis of financial surpluses and deficits. We find that the puzzle strengthens with proportion of financial surpluses used to reduce debt, and the proportion of debt used to fund financial deficits. In contrast, the puzzle weakens with the proportion of surpluses used to repurchase shares and is unrelated to the proportion of deficits financed by new equity issues (possibly because the size of equity issues is dominated by factors other than the current deficit). The last section of our paper brings us full circle, employing firm-level regressions to first distinguish between firms that exhibit a negative versus positive LP relation (puzzle versus no-puzzle firms) and then comparing the extent to which they differ regarding our proxies for the likelihood of RDF. Consistent with RDF being a strong determinant of the puzzle, we find that the firms exhibiting a negative LP relation are more likely to have a credit rating and employ substantial lines of credit, exhibit greater stability in their payout policy, and are more likely to be in the safe Altman Z range. 1. Data Description and Summary Statistics The sample includes firm observations from the Compustat and Capital IQ databases from 1996 to 2015. We exclude financial firms (SIC 6000-6999), utilities (SIC 4900-4999), and firms that are missing the standard leverage regression variables (leverage, profit, assets, tangibility, and market to book). We exclude observations where market leverage exceeds 95%, and winsorize all other variables at the 1% level. The final sample consists of 94,882 firm-year observations. The summary statistics reported in Table 1 are similar to other studies (Frank and Goyal 2009, 2015). The average book value of debt, equity and assets are $0.7 billion, $1.0 billion and $2.7 billion, 4

respectively. Average market value of equity is 2.75 times that of book. Medians are considerably smaller than means. A significant fraction of firms have zero debt observations (the 10 th percentile is 0) and zero payout observations (the 50 th percentile is 0 for both dividends and repurchases). Average and median profitability (ratio of operating income before depreciation to assets) are 5 and 10 percent, respectively, but the sample also includes a large number of unprofitable firms (the 10th percentile is -.18). The market-to-book ratio (M/B), defined as the ratio of the market value of assets to book assets, averages at about 1.9. Tangibility, defined as the ratio of net property, plant and equipment to assets, averages at about 30%. Our firms have a credit line approximately 48% of the time, and a credit rating about 24% of the time. The credit facilities are quite large: on average, drawn credit and undrawn credit available are 10.5 and 11.8 percent of assets, respectively. The average Altman Z-score (discussed below) is 4.6. About half of the firms are in the safe Z- score category (Z > 2.99), 30% are in the distressed category and the remaining 20% are in a grey zone between safe and distressed (Z < 1.81). 2. The LP Puzzle and Residual Debt Financing A distinguishing feature of our residual debt financing hypothesis is the prediction that debt levels adjust frequently, with deliberate movements away from standard estimates of target leverage. This is consistent with the debt adjustment patterns generally observed in the data, as illustrated in the histograms of debt presented in Figure 1. Figure 1 here: Distribution of Debt Changes Panel A of Figure 1illustrates that the distribution of changes in debt is fairly continuous, including frequent changes close to zero that appear inconsistent with large fixed adjustment costs. The second and third histograms show that the changes are largely unrelated to whether firms are above or below their estimated target (estimated following Frank and Goyal 2015) -- i.e., firms frequently adjust debt levels away from target levels, which again is inconsistent with an adjustment cost avoidance strategy. Panel B of Figure 1 presents similar histograms, but with all zero debt observations omitted. 5

The omitted zeros greatly reduce the number of zero changes, illustrating that the quasi-mode at zero in Panel A largely reflects firms that have no debt. In sum, there is no apparent mode indicative of the desire to avoid fixed adjustment costs, and adjustments are frequently away from estimated target. 1 The patterns in Figure 1 reflect flexible debt levels that may be adjusted according to funding needs in a manner that affects the LP puzzle. In the remainder of this section we examine this possibility more formally, focusing on the conditions under which residual debt financing is more likely to be part of an optimal financial strategy. 2.1 The LP Puzzle and the Cost of Residual Debt Financing In this section we examine our hypothesis that the LP puzzle reflects the use of residual debt financing (RDF) to absorb uncertainty in profits, focusing on debt adjustment costs. Lower debt adjustment costs increase the efficiency of RDF leading to a stronger negative relation between leverage and profitability (a more negative profitability coefficient in standard leverage regressions). We examine this hypothesis using three proxies for lower debt level adjustment costs: access to a substantial line of credit (Acharya et al. 2015), an established credit rating (Leary and Roberts 2005), and firm size (Faulkender and Petersen 2006, Leary 2009). T2 ABOUT HERE: The LP Puzzle and Debt Flexibility Table 2 presents the results. The dependent variable in each regression (column) is market leverage. The independent variables include the standard variables in the literature (profitability, firm size, industry leverage, market-to-book and tangibility; Lemmon, Roberts and Zender 2008, Frank and Goyal 2009, 2015), and our proxies for debt adjustment costs which are interacted with the profitability variable to determine the effects on the puzzle (profitability) coefficient. We present regressions that include year and firm fixed effects. 2 1 Welch (2012) presents a similar looking histogram for changes in leverage (debt/capital) caused by managerial issuing and repurchasing activity (his Figure 3), and concludes that there is little evidence that fixed adjustment costs drive leverage patterns. 2 With the exception of one of our Z-score regression results (particularly the regression for distressed firms below), all of our results hold using market or book leverage as the dependent variable. All of our results also hold with regressions that include industry fixed effects in lieu of firm fixed effects. 6

The first regression (Column 1) confirms the familiar results from the literature the coefficients on the firm size, tangibility, and industry leverage are positive, while the coefficients on market-to-book and profitability are negative (all are highly significant). The negative profitability coefficient defines the LP puzzle, as it counters the intuition that firms with greater profitability have higher marginal benefits and lower marginal costs of leverage, and thus choose to be more levered. The remaining regressions in Table 2 focus on interactions between profitability and our proxies for lower debt-adjustment costs, and thus lower-cost residual debt financing. Regression (2) interacts profitability with a dummy variable that equals one if the firm has access to a credit facility (line of credit), showing that such access makes the profitability coefficient more negative (more puzzling). In Column (3) we replace the dummy with a continuous variable for the amount of undrawn credit, showing that the profitability coefficient continuously declines with the amount of unused credit available to the firm. Column (4) illustrates that the puzzle is stronger in firms that have an established credit rating, which we proxy with a dummy variable that equals one if the firm has a rating (Leary and Roberts 2005). Column (5) replaces the rating dummy with a finer variable that distinguishes twenty three distinct rating categories (detailed in the appendix), and shows that the profitability coefficient again declines for higher rated firms. Column (6) illustrates that the puzzle is stronger for bigger firms, employing a big firm dummy in place of the continuous size variable. This allows us to capture the relation between firm size and adjustment costs (Faulkender and Petersen 2006, Leary 2009) without the mechanical correlation in the denominator of profitability. Columns (7) and (8) show that the cost proxies remain significant (and material) when included simultaneously. In sum, the results in Table 2 support the hypothesis that RDF increases with lower debt adjustment costs in a manner that significantly exacerbates the puzzle. 2.2 The LP Puzzle and RDF within an Acceptable Range. We now examine our hypothesis that RDF is more likely to be efficient, and thus more likely to feed the LP puzzle, for a range of operations particularly a range managers are more focused on absorbing operational uncertainties than on the traditional costs of debt (e.g., financial distress). Recent studies show that leverage fluctuates significantly within a range, exhibiting little concern for distress 7

costs until the higher end of the range is reached (Leary and Roberts 2005, Denis and McKeon 2012, DeAngelo and Roll 2015, DeAngelo, Goncalves and Stulz 2016). We employ three measures to test our hypothesis linking the puzzle to RDF within an acceptable range. Our first measure is the Z-score from Altman s widely used bankruptcy prediction model. We focus on the three categories established in the literature (Altman et al. 2016). Firms with the highest Z- scores(z > 2.99) are safe and have little concern with the traditional costs of distress; we hypothesize that these firms focus on funding operations and are more likely to absorb uncertainty in profit realizations with RDF. Thus, we predict that the safe group exhibits the greatest LP puzzle. Firms with intermediate Z-scores (1.81 < Z 2.99) fall into a grey zone they have significant leverage concerns but not to the point of financial distress. As such, these firms are more likely to heed the traditional costs of debt, and in particular are more likely to adjust leverage downward if profitability declines (exacerbating their concern with distress). Thus we predict that the puzzle is weaker for firms in the grey zone. Firms with the lowest Z-scores (Z 1.81) are considered seriously distressed, with a high likelihood of bankruptcy in the coming years. These firms may have lost some degree of control over their capital structure choices and exhibit leverage patterns driven by factors that dominate RDF and traditional trade-offs, making it more difficult to predict the relative effects of RDF versus traditional factors. Our second and third measures are designed to identify debt changes that are more likely to remain within the firm s acceptable range. ΔD measures the relative magnitude of debt changes (computed as the absolute value of the percentage change in debt), capturing the likelihood that leverage remains within the acceptable range after the change in the firm s debt level. Smaller percentage changes are more likely remain within the range and therefore more likely to reflect RDF, so we predict that the puzzle weakens (the profitability coefficient increases) with ΔD. Our third measure is the range of leverage values exhibited by the firm during the last ten years (computed as the variance of market leverage using the last ten annual observations). This measure is firm-specific capturing the width of the firm s range. As the width increases so does the likelihood that a given debt change remains within the acceptable range, so we predict that the puzzle weakens with the leverage volatility measure. T3: The LP Puzzle and Proxies for an Acceptable Range 8

Our regression results are presented in Table 3. Regressions (1) and (2) show that the LP puzzle is significantly stronger (the interaction of the safe dummy reduces the profitability coefficient) for Altman Z-scores in the safe range (Z > 2.99). The positive profitability coefficient is particularly interesting as it implies that the puzzle disappears for the base case in these regressions. Since the base case is the grey zone the positive coefficient is consistent with our prediction that traditional trade-offs are most relevant for this Z-score category, and in fact the data suggest that traditional trade-offs dominate in this zone. Regression (1) differs from (2) in that it includes distressed firms (Z 1.81). Distressed firms also generate a positive profitability coefficient meaning that the puzzle also disappears in the distressed zone. Following our discussion above there is a strong possibility that the leverage choices of distressed firms are heavily influenced by other (omitted) variables, so we do not focus on this result. In fact it is noteworthy that this is our one result that does not carry over to a book leverage regression (i.e., the profitability coefficient for distressed firms is negative when the dependent variable is book leverage). Regressions (3)-(5) provide additional support for the hypothesis that the LP puzzle reflects a range of RDF, using alternative proxies for the likelihood of remaining within an acceptable range. Column (3) shows that the puzzle weakens for larger debt changes ΔD, which are less likely to stay within the range. This is consistent with Frank and Goyal s (2015) finding that the profitability coefficient is less negative for firms that issue debt in excess of five percent of asset value. Smaller changes are considered passive in Frank and Goyal, who do not consider the effects of a residual debt financing strategy. Column (4) shows that the profitability coefficient is more negative for firms that exhibit a wider range of leverage values (greater variance in observed leverage), so that a given change in debt is more likely to remain within an acceptable range and thus reflect RDF. Columns (5) and (6) show that the range proxies remain significant when included together. The results in this section support the idea of RDF within a range and its effects on the LP puzzle. In the next sections we extend our analysis to include additional components of the firm s budget constraint that are also likely to affect the relation between RDF and the puzzle. 3. The LP puzzle and Payout Policy 9

We extend our analysis to incorporate interactions between leverage and payout policies following the arguments by Lambrecht and Myers (2012, 2017) and DeAngelo and Roll 2015) that the corporate budget constraint implies that leverage and payout patterns must be examined in tandem. A conventional view of payout policy asserts that managers pursue all positive NPV investment opportunities and return any excess (residual) cash to shareholders (Farre-Mensa, Michaely and Schmalz 2015). This view is related to our RDF hypothesis because the budget constraint implies that simultaneous residual debt and residual payout policies are infeasible. The components of payout policy specifically dividends and repurchases differ significantly with respect to their commitment and flexibility features. Accordingly, we develop their predicted effects on the LP puzzle separately. In practice managers tend not to follow a residual dividend policy. They are strongly averse to cutting dividends and will even pass up positive NPV investments before doing so (Graham and Harvey survey 2001, Daniel, Denis, and Naveen 2011). An aversion to cuts also generates a reluctance to increase dividends so that, altogether, managers typically prefer smooth dividend payments. We hypothesize that managers employ residual debt financing to help facilitate dividend smoothing, effectively assuming that debt adjustments are less costly than cutting back investment. More precisely we predict that firms employ RDF in a manner that strengthens the LP puzzle when they pursue smoother dividends. Our tests below employ four proxies for dividend smoothness. The first two are developed in detail in Leary and Michaely (2011) and Larkin, Leary and Michaely (2017), namely (i) the speed of dividend adjustment (SOA) inspired by Lintner (1956), and (ii) the volatility of dividends relative to that of earnings (Relative volatility). Our third measure focuses directly on stickiness of dividends (the number of quarters that dividend per share (DPS) is held constant during the last three years). The fourth measures the volatility of dividends scaled by assets (Dividend volatility), which is computed using annual observations over the last ten years and directly comparable with our repurchase volatility measure below. 3 Managers view share repurchases as more flexible than dividends, and in some instances may prefer repurchases to debt adjustments (e.g., when managers believe their shares are under-valued or 3 Our results are similar when we (i) count annual DPS sticks during the last five or ten year period, and (ii) compute volatility using quarterly observations. 10

prefer a higher leverage value). As a result, we hypothesize that residual share repurchases offset the degree of residual debt financing, weakening the LP puzzle. We test this prediction using the variation in repurchase amounts ( Repurchase volatility ) as a proxy for the extent to which firms employ a residual repurchase policy. Table 4: The LP Puzzle and payout policy The tests are presented in Table 4. Regressions (1)-(4) interact the profitability coefficient with our four measures of dividend smoothing, respectively. Note that higher values of SOA, relative volatility and dividend volatility imply less smoothing, while a greater number of zero-dps-changes implies more smoothing. In each regression, therefore, the puzzle strengthens with the degree of smoothing. Regressions (5)-(10) include the repurchase component of payout policy. Similar to our dividend volatility measure, we compute the variance of the dollar amounts repurchased over the last ten years (again scaled by assets), and use the variance to measure the degree to which repurchases are used as a flexible method to disburse residual (excess) cash. Column (5) shows that the LP puzzle weakens with the variance of repurchase activity, consistent with our prediction. Columns (6)-(9) show that the repurchase and dividend predictions are supported when included simultaneously. Finally, Column (10) shows that the puzzle weakens with the variance of total (dividend plus repurchase) payout. The link between RDF and payout policy in the budget constraint is also related to the analysis of financial surpluses and deficits in Denis and McKeon (2012). We examine this relation next. 4. The LP puzzle and RDF of financial deficits and surpluses We extend our analysis to incorporate financial surpluses and deficits following Denis and McKeon (2012) who focus on firms that increase their leverage by at least ten percent to a level at least ten percent above estimated target. Denis and McKeon find that firms rely significantly on debt financing even when above their estimated leverage target (consistent with histograms in Figure 1), suggesting that the range where leverage concerns are second order is quite wide. Following Denis and McKeon (2012) equation (13), we a define financial surplus as 11

FS i t = OCF i t DIV i,t 1 I i t [ΔWC ΔCash], where OCF is operating cash flow, DIV i,t 1 is the dividend payout from the prior year, I is net investment, ΔWC is the change in working capital, and ΔCash is the change in cash and short-term investments. Note that this definition treats last period s dividend as committed (an implicit dividend stickiness assumption), and it backs out change in cash from the change in working capital. Financial surpluses are then decomposed into four uses: debt reduction, share repurchase, increased dividends and cash retentions. Our analysis focuses on RDF and the therefore the proportion of surpluses used for debt reduction. Analogously, financial deficits (defined as negative surpluses) are funded through four sources (debt issuance, equity issuance, reduced dividends, reduced cash balances) and we focus on the proportion of deficits funded by debt. Specifically, firms relying more heavily on RDF are likely to finance a greater proportion of deficits with debt, and use a greater proportion of surpluses to reduce debt. Thus, we hypothesize that the LP puzzle strengthens (profitability coefficient decreases) with these proportions. The analysis is presented in Table 5. Table 5 here. Regression (1) interacts profitability with a dummy variable that equals one if firms exhibit some degree of RDF i.e., if the firm either (i) uses part of their financial surplus to decrease debt, or (ii) finances some of their deficit with debt. Consistent with RDF strengthening the LP puzzle the profitability coefficient is more negative when the dummy equals one. Regressions (2) and (3) replace the dummy variable with a continuous variable representing the degree of residual debt financing, measured by the percentage of deficits financed with debt and the percentage of surpluses used to pay down debt, respectively. Column (2) illustrates that the LP puzzle strengthens (the profitability coefficient is more negative) with the percentage of surpluses used to reduce debt; Column (3) illustrates that the puzzle strengthens with the RDF exhibited by deficit firms. Regressions (4) and (5) focus on adjustments in the firm s equity capital. By definition firms rely less on RDF during periods of equity adjustment, and similar to our arguments above we predict that equity adjustments are associated with a weaker LP puzzle. Column (4) illustrates that the puzzle weakens with the proportion of surpluses used to repurchase shares, supporting our prediction for the case of financial surpluses. In Regression (5), however, the proportion of deficits financed by equity 12

issuance does not significantly affect the puzzle, possibly reflecting that size of equity issues is dominated by factors other than the current deficit. 4 Finally, Columns (6) and (7) illustrate that these results are robust when debt and equity percentages are included simultaneously. 4 Consistent with equity issuance reducing the degree of RDF, in unreported regressions we find that the puzzle is weaker for firms that issue equity, and moreso for active issuers defined as firms that issue more than 3% of their equity (McKeon 2016 shows that equity issuance between 0 and 3% typically reflects the exercise of employee options, considered passive equity issuance). 13

5. The LP Puzzle and Firm-Specific Regressions Our final section takes a somewhat different approach: we focus on firm-specific (longitudinal) leverage regressions following DeAngelo, Goncalves and Stulz (2016) who argue that pooled regressions can mask important variation within firms. We run the standard leverage regression (Column (1), Table 2) for each firm during the sample period which we extend backward to 1960 to increase the power of the firm-specific regressions. Based on the resulting profitability coefficients, we sort firms into two groups: a group of firms with negative and significant coefficients (the puzzle group), and a group with positive and significant coefficients (the no puzzle group). We then compare the characteristics of each group, focusing on the extent to which they differ with respect to our proxies for the likelihood of RDF in Tables 2 and 3. Table 6 presents the results. The values reported are computed by first averaging the variable for each firm across years, and then computing the average (median) across firms within the group. Note that the values for line of credit (LOC) and credit rating reflect data availability: the Capital IQ credit line data is available only from 1996-2015, and the Compustat credit rating data is available only from 1978-2015. 5 Table 6: here The first five rows report the average (median) values of the variables in the standard regression for each group (ML, Profitability, Market-to-Book, Tangibility and Assets). Rows 5-12 report values for our RDF proxies, which are our variables of interest (note that Assets is both a standard variable and one of our proxies for debt adjustment costs in Table 2). We test for differences in the means/medians across groups in the last two columns of each row. We do not expect significant differences in the standard variables across the puzzle and no-puzzle 5 We obtain similar results if we restrict our sample period to 1978-2015 or 1996-2015, but in the latter case the small number of observations (twenty) in the longitudinal regressions reduces the number of significant profitability coefficients, and the difference in credit ratings between the two groups is not statistically significant. 14

groups (again with the exception of Assets). The tests indicate that only profitability is significantly different across the groups, possibly reflecting a positive effect of RDF on profitability. Of greater interest is that the groups differ significantly with respect to our RDF proxies from Tables 2 and 3. Puzzle firms are larger, more likely to have a line of credit and/or a credit rating, and more likely to be in the safe Z-score range; they also exhibit smaller changes in debt levels and greater variation in leverage over time. Thus, the firm-specific regression results re-enforce our previous findings that RDF is a significant component of corporate financial policy and is a significant contributor to the LP puzzle. 6. Conclusion Our paper provides new insight into the renowned LP puzzle. We present convincing evidence that the puzzle reflects more than capital structure adjustment costs. Indeed, a financial strategy based on relatively low debt adjustment costs appears to be an important contributor. Lower debt adjustment costs make debt an efficient shock absorber for a substantial range of operations. Firms employing such a residual debt financing (RDF) strategy will exhibit debt levels that vary inversely with profits, and thus a negative LP relation that is generated by the numerators of the leverage and profitability ratios. We show that the negative coefficient on profitability in the standard leverage regression (the puzzle coefficient) strengthens with proxies for lower debt adjustment costs (substantial lines of credit, credit ratings and firm size) and with proxies for leverage changes that are more likely to remain within an acceptable range (higher Altman Z scores, smaller changes in debt levels, and a wider range of exhibited leverage values). We find that the puzzle disappears when the firm goes beyond its acceptable range so that the traditional costs of debt (e.g., financial distress, incentive conflicts) are likely to dominate the benefits of RDF. We identify this zone using the Altman Z-score categories defined in the literature: a safe zone where Z is greater than 2.89, a grey zone where Z is less than 2.89 but greater than 1.81, and a distress zone where Z is less than 1.81 (DeAngelo and Roll 2015, Altman et al. 2016). While the puzzle coefficient is negative in the safe zone (consistent with residual financing concerns dominating traditional trade- 15

offs), it turns positive in the grey zone where traditional concerns such as financial distress are likely to dominate. We also find that the LP puzzle reflects payout policy in a manner related to residual financing, particularly the substitutability between residual debt adjustments and residual payouts to equity. We find that the puzzle is stronger when there is less variation in dividend and repurchase payments, consistent with firms using debt adjustments to support smoother dividends and/or fewer share repurchases. Finally, we show that the puzzle is stronger when firms fund a greater proportion of financial deficits with debt, or use their financial surplus to pay down debt; these findings are again consistent with RDF influencing the LP puzzle. We also show find re-enforcing support for our RDF hypotheses using a longitudinal regression analysis. 16

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Table 1: Data description The sample includes firm observations available in Compustat and Capital IQ databases from 1996 to 2015. We exclude financial firms (SIC 6000-6999) and utilities (SIC 4900-4999). All variables are defined in the Appendix. Variable N Mean Standard Deviation 10th Percentile 50th P Percentile 90th Percentile Assets ($ million) 94882 2752 8602 25 252 5428 Book equity ($ million) 94882 1042 3245 9 116 2009 Market equity ($ million) 94882 2886 9361 17 248 5515 Debt ($ million) 94882 730 2309 0 28 1546 ML 94882 0.223 0.242 0 0.142 0.607 BL 94882 0.318 0.341 0 0.252 0.724 MB 94882 1.894 1.425 0.839 1.433 3.474 Tangibility 94882 0.298 0.260 0.035 0.212 0.728 Profit 94882 0.052 0.205-0.174 0.100 0.224 Line of credit (0,1) 94882 0.477 0.499 0 0 1 Positive undrawn line of credit 13075 0.118 0.107 0.015 0.090 0.254 Positive drawn line of credit 24991 0.105 0.113 0.006 0.067 0.258 With a credit rating (0,1) 94882 0.236 0.425 0.000 0.000 1.000 Altman s Z-score 91790 4.609 8.324-0.269 2.982 10.060 Altman s Distressed zone (0,1) 91790 0.300 0.458 0 0 1 Altman s Grey zone (0,1) 91790 0.202 0.401 0 0 1 Altman s Safe zone (0,1) 91790 0.499 0.500 0 0 1 Equity repurchase 94882 0.014 0.037 0 0 0.043 Dividend 94597 0.009 0.022 0 0 0.028 19

Figure 1: Distribution of Debt Changes Histograms of changes in debt scaled by assets. Panel A includes the whole sample, while Panel B excludes firm-year observations with zero debt. Target leverage estimates follow Frank and Goyal (2015), which are estimated as the predicted values from Regression 1 of Table 2. Panel A: Including zero debt 16000 Frequency of Δ debt / AT 14000 12000 10000 8000 6000 4000 2000 0 6000 5000 4000 3000 2000 1000 0 Frequency of Δ debt / AT (above estimated leverage target) 14000 Frequency of Δ debt / AT (below estimated leverage target) 12000 10000 8000 6000 4000 2000 0 20

Panel B: Excluding zero debt observations 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Frequency of Δ debt / AT 6000 5000 4000 3000 2000 1000 0 Frequency of Δ debt / AT (above target) 6000 5000 4000 3000 2000 1000 0 Frequency of Δ debt / AT (below target) 21

Table 2: The LP Puzzle and Debt Flexibility This table presents the results of an OLS regression where the dependent variable is market leverage. All variables are defined in Appendix. The t-values are reported in parentheses. *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. Dep. Var.: ML (1) (2) (3) (4) (5) (6) (7) (8) Intercept 0.0061 0.0102 0.0069 0.0593-0.6879 0.2639 0.2766-0.0900 (0.05) (0.08) (0.05) (0.45) (-8.17) *** (1.95) * (2.07) ** (-1.06) Profitability -0.1518-0.1061-0.1447-0.1295-0.3027-0.0829-0.0742-0.2550 (-34.88) *** (-22.10) *** (-32.88) *** (-28.91) *** (-7.05) *** (-17.78) *** (-15.89) *** (-4.13) *** Profitability x With line of credit (0,1) -0.1607 (-22.60) *** With line of credit (0,1) 0.0332 (18.96) *** Profitability x -0.8418-0.7583-0.5050 Undrawn line of credit (-11.02) *** (-9.92) *** (-2.77) *** Undrawn line of 0.0228 0.0055 0.0068 credit (1.60) (0.39) (0.20) Profitability x With -0.2260-0.1554 a credit rating (0,1) (-15.43) *** (-9.56) *** 0.1035 0.1126 (33.52) *** (35.58) *** With a credit rating (0,1) Profitability x Credit rating -0.0129-0.0153 (-4.54) *** (-4.95) *** Credit rating -0.0305-0.0240 (-42.65) *** (-33.96) *** Profitability x Big firm (0,1) -0.2147-0.1608-0.1440 (-22.88) *** (-15.62) *** (-4.10) *** Big firm (0,1) 0.0689 0.0558 0.0494 (30.23) *** (24.10) *** (4.75) *** Assets (log) 0.0453 0.0449 0.0452 0.0379 0.0684 (49.52) *** (49.10) *** (49.36) *** (40.51) *** (32.47) *** Industry median ML 0.3327 0.3300 0.3330 0.3242 0.2863 0.3259 0.3207 0.2862 (44.07) *** (43.89) *** (44.02) *** (43.18) *** (24.48) *** (42.78) *** (42.36) *** (23.74) *** MB -0.0136-0.0132-0.0134-0.0136-0.0098-0.0167-0.0160-0.0147 (-32.75) *** (-31.89) *** (-32.26) *** (-32.94) *** (-12.79) *** (-40.37) *** (-39.18) *** (-19.06) *** Tangibility 0.1769 0.1744 0.1759 0.1801 0.1176 0.1812 0.1811 0.0885 (31.94) *** (31.61) *** (31.71) *** (32.72) *** (9.19) *** (32.39) *** (32.61) *** (6.74) *** N 94,882 94,882 94,322 94,882 22,396 94,882 94,322 22,234 Year FE Yes Yes Yes Yes Yes Yes Yes Yes Firm FE Yes Yes Yes Yes Yes Yes Yes Yes Adj R-sq 0.7363 0.7385 0.7365 0.7399 0.7830 0.7319 0.7370 0.7716 22

Table 3: The LP Puzzle and the Acceptable Debt Range This table presents OLS regression results with market leverage as the dependent variable. The samples in regressions (2) and (6) exclude observations in the distressed z-score zone. All variables are defined in Appendix. The t-values are reported in parentheses. *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. Dep. Var.: ML (1) (2) (3) (4) (5) (6) Intercept 0.0342 0.1119-0.0086-0.3185-0.2552-0.0372 (0.30) (1.87) * (-0.06) (-2.57) ** (-2.32) ** (-0.61) Profitability 0.0239 0.1321-0.2178-0.1076 0.0422 0.1216 Profitability x Distressed zone (0,1) (2.72) *** (17.00) *** (-34.71) *** (-13.89) *** (2.51) ** (6.55) *** 0.0660 0.0718 (7.21) *** (4.76) *** Profitability x Safe zone (0,1) -0.2020-0.2352-0.2032-0.2182 (-22.01) *** (-30.19) *** (-13.08) *** (-15.29) *** Distressed zone (0,1) 0.1313 0.1341 (81.13) *** (55.37) *** Safe zone (0,1) -0.0945-0.1108-0.0963-0.1041 (-61.57) *** (-87.51) *** (-39.70) *** (-48.09) *** Profitability x Absolute 0.0324 0.0252 0.0588 Δ debt (9.47) *** (4.52) *** (6.87) *** Absolute Δ debt 0.0015-0.0036-0.0073 (1.97) ** (-3.23) *** (-4.72) *** Profitability x ML variance -0.7905-0.8366-1.0469 (-14.81) *** (-13.03) *** (-10.76) *** ML variance 0.3402 0.2471 0.2160 (23.78) *** (16.42) *** (10.74) *** Assets (log) 0.0351 0.0250 0.0476 0.0525 0.0397 0.0334 (44.07) *** (31.08) *** (43.23) *** (41.74) *** (29.69) *** (22.80) *** Industry median ML 0.2243 0.1514 0.3280 0.3022 0.1927 0.1291 (33.55) *** (24.27) *** (39.32) *** (33.51) *** (21.64) *** (14.82) *** MB -0.0034-0.0037-0.0223-0.0143-0.0107-0.0104 (-9.57) *** (-11.65) *** (-38.28) *** (-24.00) *** (-13.67) *** (-13.24) *** Tangibility 0.1103 0.0430 0.1811 0.1729 0.1139 0.0650 (22.80) *** (8.56) *** (26.55) *** (22.74) *** (14.21) *** (7.17) *** N 90,927 64,286 77,941 59,170 46,640 31,984 Year FE Yes Yes Yes Yes Yes Yes Firm FE Yes Yes Yes Yes Yes Yes Adj R-sq 0.7932 0.8131 0.7228 0.7713 0.8064 0.8100 23

Table 4: The LP puzzle and payout policy This table presents the results of an OLS regression where the dependent variable is market leverage. Sample sizes in each regressions are different due to availability of key control variables. All variables are defined in Appendix. The t-values are reported in parentheses. *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. Dep. Var.: ML (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Intercept -0.4122-0.3987-0.3781 0.3335 0.2325-0.2285-0.2153-0.4239-0.3536 0.1828 (-5.50) *** (-5.32) *** (-5.42) *** (3.39) *** (3.07) *** (-3.77) *** (-3.56) *** (-6.13) *** (-6.08) *** (2.38) ** Profitability -0.35055-0.34926 0.09983-0.30293-0.18402-0.40330-0.37713 0.0127-0.30681-0.2441 (-15.16) *** (-15.16) *** (1.89) * (-17.66) *** (-13.79) *** (-11.26) *** (-10.61) *** (0.16) (-11.77) *** (-20.14) *** Profitability x SOA 0.1133 0.1756 (2.50) ** (3.06) *** SOA -0.0402-0.0487 (-4.74) *** (-4.33) *** Profitability x Relative 0.0262 0.0160 volatility (2.77) *** (1.15) Relative volatility -0.0073-0.0064 (-4.18) *** (-2.44) ** Profitability x Dividend -0.0347-0.0282 stickiness (-6.02) *** (-3.21) *** Dividend stickiness 0.0120 0.0129 (10.91) *** (7.71) *** Profitability x Dividend 2.6023 3.0317 volatility (7.48) *** (5.35) *** Dividend volatility -0.0626-0.2051 (-0.73) (-1.51) Profitability x Equity 0.5251 2.6683 2.6950 2.3465 1.3544 Repurchase volatility (2.96) *** (5.34) *** (5.42) *** (5.70) *** (3.87) *** Equity Repurchase 0.0957-0.0775-0.0904-0.1682 0.0496 volatility (2.12) ** (-0.66) (-0.77) (-1.63) (0.57) 24