Liquidity, Leverage Deviation, Target Change and the Speed of Leverage Adjustment

Transcription

1 Liquidity, Leverage Deviation, Target Change and the Speed of Leverage Adjustment 1. Introduction The capital structure decision, which relates to how firms are financed, is one of the most debated topics by modern finance scholars and practitioners around the world. The traditional trade-off theory of capital structure argues that a firm s value can be maximized by targeting a leverage ratio that minimizes its cost of capital (Fischer, Heinkel, & Zechner, 1989; Flannery & Rangan, 2006; Harris & Raviv, 1991; Hovakimian & Li, 2011). Dynamic trade-off models predict that a firm has an incentive to adjust its actual debt/equity ratio towards its optimal (target) ratio. However, the speed of adjustment (SOA) is likely to be modified if the firm faces significant adjustment costs. Myers (1984) points out that where the costs of leverage adjustment are high, one might expect to see firm s deviating from their target debt-equity ratios by large amounts for extended periods. Hence, it is important to pay attention to, and explain, cross-sectional differences in the dynamics of corporate capital structure decisions, rather than just concentrating on refining static trade-off theories (Graham and Leary, 2011). As a consequence, a new strand of the literature has developed that studies the sources of leverage adjustment costs and/or firm characteristics that may affect the SOA. Although researchers have widely discussed the determinants of leverage SOA, e.g., equity mispricing (Warr, Elliott, Koëter-Kant, & Öztekin, 2012), corporate governance (Chang, Chou, & Huang, 2014; Liao, Mukherjee, & Wang, 2015), firm s crash risk (An, Li, & Yu, 2015), sensitive of cost of equity on leverage deviation (Zhou, Tan, Faff, & Zhu, 2016), debt covenants (Devos, Rahman, & Tsang, 2017), macroeconomic factors (Cook & Tang, 2010), institutional determinants (Öztekin & Flannery, 2012), and business cycles (Halling, Yu, & Zechner, 2016), some important possible contributing factors have been neglected. Specifically, a growing body of literature has highlighted the important role of liquidity in reducing transaction costs (Amihud & Mendelson, 1986; Berkman & Nguyen, 2010; Butler, Grullon, & Weston, 2005; Dang, Moshirian, Wee, & Zhang, 2015; Fernandes & Ferreira, 2008; Levine & Schmukler, 2006; Lipson & Mortal, 2009; Stoll & Whaley, 1983). This suggests that the liquidity of a firm s stocks will influence not only its cost of capital but also influence its SOA. Further, besides the adjustment cost, leverage SOA also depends on the incentive of firms to access the market capital for other reasons. For instance, 1

2 if firms can observe their target leverage, but their actual leverage ratios deviate too far from the targets, or these targets change very frequently, firms may find it expensive (or impossible) to adjust to their target. Prior studies (Faulkender, Flannery, Hankins, & Smith, 2012; Kayhan & Titman, 2007; Welch, 2004) suggest that deviation between observed and desired leverage, and change in target leverage ratios may affect decisions by management relating to capital structure. This raises the possibility that any relationship between a firm s liquidity and its SOA will be influenced by the extent of its deviation from its target ratio and the variability of this ratio. In this study, we investigate the relationship between a firm s stock liquidity and its SOA and how this might be modified by the extent of its deviation from its target leverage ratio and the variability of that ratio. More specifically, we examine the following four important questions: 1. Does stock liquidity affect a firm s speed of leverage adjustment? 2. Does leverage deviation influence a firm s leverage SOA? 3. Does target change influence a firm s leverage SOA? 4. Does leverage deviation and target change impact on the association between stock liquidity and leverage SOA? Our findings show that liquidity positively affects SOA, suggesting that firms with higher stock liquidity exhibit a higher speed of adjusting their capital structure to its target level. We also find a positive relationship between leverage deviation and SOA, indicating that firms which deviate further from their target leverage will converge back more quickly. Moreover, target change has a negative impact on SOA, implying that firms with high volatility in target leverage have a slower speed of adjustment. In a closer analysis, we observe an interactive relationship among stock liquidity, leverage deviation, target change, and SOA: the results show that the significant positive relationship between stock liquidity and SOA is less pronounced for firms with high leverage deviation and/or high target change. The findings of our study contribute to several strands of corporate finance. First, while prior studies have pointed out the essential role of stock liquidity in financial decisions making and well documented the relation between stock liquidity and leverage,(e.g., Lipson and Mortal (2009)), there has been no prior research that examines the relationship between stock liquidity and leverage SOA. Our study also fills a knowledge gap by being the first to 2

3 examine the joint association between stock liquidity, leverage deviation, target change and leverage SOA. Specifically, we document robust evidence that shows the positive relation between stock liquidity and leverage SOA is stronger and significant for firms with lower leverage deviation and/or target change. Next, the association between leverage deviation and leverage SOA that is still debatable in the literature is also confirmed in our study. The effect of target variability on leverage SOA is also first investigated in this paper. The paper proceeds as follow. In section 2, we explore the relevant literature and develop the hypotheses. Section 3 describes the data and constructs the variables we use in the study. Section 4 explains the empirical methods. Section 5 discusses the results. Section 6 concludes the study. 2. Literature review and hypotheses development Our hypotheses are developed based on the literature of dynamic leverage adjustment. This strand focuses on the adjustment of firm s leverage ratio toward their target levels, and specifically, the determinants of leverage SOA. Based on the pivotal work of Modigliani and Miller (1958), a strand of studies has focused on the trade-off theory a predominant view of capital structure (Fischer et al., 1989; Goldstein, Ju, & Leland, 2001; Strebulaev, 2007). This body of research has investigated several essential questions: Do firms have target leverage ratios? Which factors may prevent firms from converging to those targets? And how quickly do they adjust to those targets? These studies have concluded that firms have a time-varying target leverage that optimally balances various costs (e.g., agency costs due to the conflict between debtholder and stockholder, bankruptcy costs or financial distress costs) and benefits (e.g., tax saving, mitigate agency costs due to conflict between stock holder and manage) of debt. Existing studies also support this view and document that firms have target leverage and attempt to adjust toward those target (Byoun, 2008; Flannery & Rangan, 2006; Huang & Ritter, 2009). The literature on capital structure further evidences that the speed at which firms converge to their targets vary with each firm facing different adjustment costs (transaction costs). In particular, Leary and Roberts (2005) show that the cost of adjustment significantly affects a firm s behavior with respect to leverage rebalancing. Furthermore, Strebulaev (2007) and Goldstein et al. (2001) find that firms with lower transaction costs converge their 3

4 leverage more frequently. This has motivated a line of research into what are the sources of these adjustment costs and how they can explain cross-sectional variation in the SOA. Drobetz and Wanzenried (2006) argue that faster-growing firms and those that diverge further away from their optimal leverage will adjust their capital structure position more quickly. Warr et al. (2012) find that equity mispricing affects a firm s SOA, the extent to which depending on whether the firm is under- or over-levered. Chang et al. (2014) and Liao et al. (2015) provide evidence on an association between corporate governance and dynamic capital structure, suggesting that forms with strong corporate governance face lower costs of adjustment and so will adjust more quickly towards their target. An et al. (2015) show that a firm s crash-risk exposure has a significantly negative impact on leverage SOA, and this impact is attenuated by a transparent information environment. Most recently, Zhou et al. (2016) and Devos et al. (2017) examine the relationship between the cost of equity and debt covenants, respectively, on leverage SOA. The effects of macroeconomic conditions, business cycles and institutional factors on the SOA has also been investigated (Cook & Tang, 2010; Drobetz & Wanzenried, 2006; Öztekin & Flannery, 2012). In brief, though this strand of research has investigated several significant determinants of leverage SOA, it remains silent on whether stock liquidity and volatility in target leverage can affect the speed of leverage adjustment, which is the focus of our study. There has been a stream of literature that documents the role of stock liquidity on firm s capital structure decisions. Stoll and Whaley (1983) first note that transaction costs need to be taken into account when evaluating equity investments and argue that they may explain the higher required rates of return on small stocks that are illiquid. Amihud and Mendelson (1986) propose a formal model in which required rates of return for equity investment rise because of transaction costs, such as tax. Concentrating on issuance costs, Butler et al. (2005) note that investment banks apply lower fees for more liquid firms. These issuance costs must be acknowledged when raising equity through external financing and are an implicit cost of external equity. Brennan and Subrahmanyam (1996) and Brennan, Chordia, and Subrahmanyam (1998) are other important empirical studies that propose a negative relationship between liquidity and cost of capital. This body of study suggests that stocks with higher liquidity have lowers cost of equity that might have implications for leverage SOA. Öztekin and Flannery (2012) investigate the link between capital structure s SOA and security trading cost. Particularly, the study indicates that higher trading costs are associated 4

5 with significantly lower estimated adjustment speeds. Zhou et al. (2016) also suggest the indirect link between cost of equity and leverage SOA. They show that firms with a cost of equity that is more sensitive to the leverage deviation, display faster speeds of adjustment toward target leverage. In our tests, we examine whether greater equity liquidity, which reduces the transaction cost, leads to relatively higher adjustment speed to target capital structure. An alternative explanation of the relationship between liquidity and speed of capital structure s adjustment can be drawn from the pecking order theory introduced by Myers and Majluf (1984). It is argued that the adverse selection problems will be lower for firms with higher liquidity. Consequently, those firms face lower transaction costs and this will translate to a faster speed of adjustment. Based on the previous discussion, we propose the following research questions: Research Question 1 (RQ1): What impact does equity liquidity have on leverage SOA? The extent of the deviation between the actual leverage ratio and the target ratio will predict whether a firm finances its capital gap by raising equity or debt (Hovakimian, Opler, and Titman (2001). If the fixed cost associated with the adjustment (e.g., investment bank fees, legal fees) are substantial, a firm with a sub-optimal capital structure will adjust its leverage ratio only if it is sufficiently far away from those targets (Banerjee, Heshmati, & Wihlborg, 1999). As a consequence, the association between leverage deviation and SOA could be positive (Drobetz & Wanzenried, 2006; Flannery & Rangan, 2006). On the other hand, if the fixed costs of changing capital structure are prohibitively expensive, instead of accessing capital markets, firms may well change their dividend policy in order internal funds to adjust towards its target leverage ratio. It implies that the higher the magnitude of the absolute distance between observed and target leverage ratios, the higher the costs of leverage adjustment are accumulative. Consequently, if firm s leverage is changed internally by changing dividend policy rather than externally by accessing the capital market due to high adjustment costs, leverage deviation should affect negatively the SOA. Hence there is a conflict as to the impact of leverage deviation on the SOA which we will try and resolve in this paper. 5

6 Research Question 2 (RQ2): What impact does leverage deviation have on leverage SOA? If adjustments costs were zero, then one might expect an almost instantaneous adjustment to the target leverage ratio. However, the existence of adjustment costs is an important factor to explain why firms pursue a more gradual adjustment towards their target leverage ratio. Since the ideal target ratio will itself change overtime driven by changes in the characteristics of the firm, the presence of fixed cost indicates that the firms might not quickly converge back to their targets when these target levels change very frequently with large magnitude. In this case, the adjustment costs are likely to be higher than the benefit derived from rebalancing. This potential volatility in the target leverage ratio, further, dissuades management from implementing a quick adjustment to the current target ratio as they will have less incentive to do so given their uncertainty as to what will be the target ratio in the future. Consequently, the greater the change in target, the lower the incentive to adjust and the lower the speed at which a firm converges. We propose the following research question: Research Question 3 (RQ3): What is the impact of absolute change in the target leverage ratio on the SOA? Thought both CAPM and Modigliani and Miller (1958) theory specify a positive equity return-leverage association, the empirical results are mixed (e.g., Fama and French (1992) and George and Hwang (2010) suggest a negative relation while Dhaliwal, Heitzman, and Zhen Li (2006) and Ippolito, Steri, and Tebaldi (2012) suggest a positive relation). One important reason for the mixed results is that previous empirical studies that explore leverage ratios disregard the role of target leverage in raising extensive heterogeneity. Indeed, two firms with the same leverage level but different target leverage will have different risk profiles, then different cost of equity and require different equity risk premium (Ippolito et al., 2012). In a dynamic framework with market frictions, firms are rational to maintain a reasonable proximity to their targets, and may change their target levels overtime, rather than persistently strive for a single target leverage ratio. As such, we expect to observe cross-sectional deviation of leverage from their targets as well as change in target levels regarding to different costs of equity. Zhou et al. (2016) suggest a positive relationship between leverage deviation and firm s cost of equity. They show that as a firm financial leverage deviates further from the 6

7 target leverage, the higher (lower) is the cost of equity when the firm s leverage is above (below) target leverage. By affecting the cost of equity, then affecting the equity liquidity, it is possible that firm s with different leverage deviation from their targets or different changing in targets may have different equity liquidity-leverage SOA relation. Building on the above discussion, we investigate whether higher leverage deviation and/or a higher target change mitigate the relationship between liquidity and SOA: Research Question 4 (RQ4): What is the effects of leverage deviation and target change on the relationship between equity liquidity and SOA? 3. Data and variable definitions 3.1. Data We retrieve annual firm-level and industry-level accounting data from the Worldscope via the Datastream database. To estimate liquidity measures, we collect daily data (e.g., share price, stock return and trading volume) from this database. Our sample consists of UK firms for whom we collected data over the period of 21 years from 1996 to We apply the following filters to our sample. Only firms with common securities are retained and those with special features such as warrants, trusts, funds, and non-equity stocks are excluded. We also eliminate financial and utility corporations since these corporations are subjects to special regulations on financing policies. Following conventional practices (Halling et al., 2016), we drop firm-year observations that have a zero book value for total assets, zero market capitalization, negative cash, negative long-term and/or negative short-term debt. We remove very small firms that have average book values of total assets less than 10 million US dollars to avoid outliers. We further drop observations with negative net sales and net leverage ratio of less than We do allow firms, at some point in time, to be cash savers, i.e., carrying a negative net leverage ratio, rather than borrowers. However, we remove firm-year observations with net leverage ratio less than -1 because such firms hold a very large amount of cash relative to their other types of assets and, hence, are unlikely to be regular industrial firms. In addition, we remove firm-years with book leverage ratios or market leverage ratios greater than one. After imposing all these filters, our final sample consists of 20,090 firm-year observations. We winsorized both the dependent and independent variables at the 1 st and 99 th percentiles to mitigate the potential impact of extreme values. 1 Net leverage ratio refers to the ratio of total debt less cash plus short-term investments to market (book) value of total assets. 7

8 3.2. Variable construction [Insert Table 1 here] Leverage measurements Based on existing studies (An et al., 2015; Chang et al., 2014; Flannery & Rangan, 2006; Öztekin & Flannery, 2012), we measure our dependent variable, leverage, using both the book ratio (BLEV) and the market ratio (MLEV). Specifically, our book leverage ratio is: BLEV i,t = D i,t TA i,t (1) where D i,t is book value of firm i s interest-bearing debt (sum of short-term and longterm book value of interest-bearing debt) at time t, TA i,t denotes book value of firm i s assets at time t. We use the following market leverage ratio: MLEV i,t = D i,t D i,t + S i,t P i,t (2) where D i,t is book value of firm i s interest-bearing debt (sum of short-term and longterm book value of interest-bearing debt) at time t, S i,t P i,t denotes the product of the number of common shares outstanding and the stock price per share at time t, which equals the market value of firm i s equity at time t Equity liquidity In this study, we use four proxies for equity liquidity: Amihud illiquidity (Amihud, 2002), zero proportion (Lesmond, Ogden, & Trzcinka, 1999), daily percentage quoted spread (Chung & Zhang, 2014; Fong, Holden, & Trzcinka, 2017), and turnover (Berkman & Nguyen, 2010; Lipson & Mortal, 2009). In the main analysis, we use Amihud illiquidity score that is the most popular measure of liquidity (Lipson & Mortal, 2009; Nadarajah, Ali, Liu, & Haung, 2016). We also test the robustness of our findings using the other three alternative measures. Note that while turnover is measure of liquidity, the two others measure provide an inverse measure of liquidity, or illiquidity. Specifically, the Amihud (2002) illiquidity measure defined is the average ratio of the daily absolute stock return divided by the dollar value of volume: LIQ i,t,d = R i,t,d DVOL i,t,d (3) 8

9 where R iyd is the return on stock i on day d year t and DVOL itd is the respective daily volume in dollars. This ratio reflects the daily price change related to one dollar of trading volume, or the daily price impact of the order flow. In this study, we use the annual average of this daily liquidity measure for each stock i: D i,t R i,t,d LIQ i,t = 1/D i,t (4) DVOL i,t,d 1 where D i,t is the number of days for which volume of stock i in year t is positive: The other three measures of liquidity that we employ are: 1. Following Lesmond et al. (1999) and Goyenko, Holden, and Trzcinka (2009), we define zero-return proportion (PropZero) as a proxy for liquidity, that is the proportion of trading days in the year that had zero price change (zero return) from the previous day, for firm i in year t. There are two important arguments to support this measure. First, illiquid stocks have higher probability to have zero-volume days and hence, zero-return days. Second, stocks with lower liquidity or higher transaction costs are more difficult to overcome to acquire private information. Therefore, even on positive volume days, they are more likely to have noinformation-revelation and thus, zero-return days. 2. Following Chung and Zhang (2014) and Fong et al. (2017), we also define the daily closing percent quoted spread (Spread i,t ) as a proxy for liquidity, i.e., daily closing bid-ask spread divided by the midpoint spread averaged over the number of positive volume days. They show that the simple daily bid-ask spread measure provides a good approximation of and is highly correlated with the bid-ask spread from intraday data. Note that this is also an inverse measure of liquidity (essentially measure of trading costs or illiquidity). The annual average of this daily liquidity proxy for each stock i is measured as follow: Spread i,t = 1/D i,t D i,t 1 Closing Ask i,t,d Closing Bid i,t,d (Closing Ask i,t,d + Closing Bid i,t,d )/2 (5) Where Closing Ask i,t,d is the closing ask price of stock i on day d year t, Closing Bid i,t,d is the closing bid price of stock i on day d year t, and D i,t is the number of days for which volume of stock i in year t is positive. 9

10 3. Turnover (Turnover i,t ), which has been used as a general measure of liquidity in a large number of previous studies (e.g., Datar, Naik, and Radcliffe (1998), Berkman and Nguyen (2010)), is defined as the number of shares traded on a day, divided by the total number of shares outstanding. The turnover for each stock, for each year is calculated as the average turnover across all trading days in that year. Using turnover rate as a measure of liquidity has a strong theoretical support. Amihud and Mendelson (1986) prove that in equilibrium, liquidity is correlated with trading frequency. Therefore, turnover rate is an approximate indirect measure of liquidity. Specifically, the higher the turnover is the higher liquid the stock is Target leverage What determines optimal capital structure? Current literature models each firm s target debt ratio in a specific country or institutional framework as a function of time-varying firm s characteristics and industrial elements (Frank & Goyal, 2009). Following Flannery and Rangan (2006), Öztekin and Flannery (2012), and An et al. (2015), we regress the observed leverage ratio (LEV) on a set of leverage determinants, estimating the optimal for both book leverage ratio (BLEV) and market leverage ratio (MLEV). Using this regression, we model for the possibility that target leverage might differ across firms or over time: LEV i,t+1 = α i + βx i,t + μ i+1, LEV {BLEV, MLEV} (6) where each firm is indexed by i and time by t. X i,t is a vector of firm and industry variables related to the costs and benefits of operating with various leverage ratios including firm size (Size i,t ), which is the natural logarithm of book value of total assets; tangibility (Tang i,t ), which is net property, plant and equipment dividend by book value of assets; growth opportunity (MTB i,t ), which is ratio of book value of assets less book value of equity plus market value of equity to book value of assets; profitability (Prof i,t ), which is earning before interests, taxes, depreciation and amortization divided by book value of assets; depreciation (Dep i,t ), which is depreciation and amortization divided by book value of assets; research and development (RD i,t ), which is research and development expenses divided by book value of assets; research and development dummy (RDDum i,t ), which is dummy variable that equals to one if research and development expenses are not reported and zero otherwise and industry median of leverage (IndMed), which is the median leverage ratio of an industry to which a firm belongs. Under the trade-off hypothesis, β 0, and the variation in LEV i,t+1 is nontrivial. We 10

11 also note that by modeling optimal capital structure in period t+1 as a function of determinants observed in period t, then any endogeneity concerns are somewhat mitigated. regression (6): leverage ratio: Target leverage ratio of each firm is measured as the fitted value obtained from LEV i,t+1 = βx i,t (7) Leverage deviation Leverage deviation is measured as the absolute difference between target and observed Lev_Dev i,t = LEV i,t LEV i,t (8) Where LEV i,t is the fitted value from the regression of firm s leverage ratio of firm i on the capital structure determinants at time t and LEV i,t is the observed leverage ratio of firm i at time t Target change Based on Kayhan and Titman (2007), the change in target leverage ratio is measured as: Target i,t = LEV i,t LEV i,t 1 (9) Where LEV i,t and LEV i,t 1 is the fitted value from the regression of firm s leverage ratio of firm i on the capital structure determinants as of time t and t-1, respectively. 4. Empirical methods The trade-off leverage behavior of firms should be estimated by a regression specification that allows each firm s optimal capital structure to vary over time and accept that the deviation from the optimal capital structure is not fully, but partially offset. Both requirements are satisfied with the standard partial adjustment model. There are two methods to estimate this model suggested by prior research. The first method is used by Hovakimian et al. (2001), Fama and French (2002), Hovakimian and Li (2011), An et al. (2015) who all estimate the two-step model. Specifically, in the first stage de3scribed above, observed capital structure will be regressed on a set of capital structure determinants. The fitted value from the regression will be used as a proxy for the unobservable optimal capital structure. In the second stage, a partial adjustment model will be estimated based on the optimal capital structure obtained in the first step in order to calculate a measure of the leverage s SOA. The one-step approach is used by Flannery and Rangan (2006) that estimates a reduced-form model to obtain an estimate of the SOA directly. The detail on the one-step and two-step approaches will be provided below. 11

12 4.1. Two-step model to estimate SOA In the first step, target leverage is measured as the fitted value from the regression of firm s leverage ratio as in the section In the second step, we measure how rapidly the firm converges to its optimal capital structure from their current positions. We estimate the standard partial adjustment model of capital structure: LEV i,t+1 LEV i,t = α 0 + j (LEV i,t+1 LEV i,t ) + ω i,t+1 (10) where j is a measure of aggregate SOA of firm leverage in a specific country that diverges away from the target of next period. The gap between target and real leverage ratios should decrease over time, provided j is greater than zero. Further, due to the presence of adjustment cost, firms do not fully adjust their leverage level, resulting in j being smaller than one One-step model to estimate SOA Following Flannery and Rangan (2006), and Halling et al. (2016), the one-step approach of partial adjustment model are extracted by substituting target leverage from Eq. (9) into Eq. (10) and rearranging yielding the following specification: LEV i,t+1 = α 0 + (1 j )LEV i,t + j βx i,t + ω i,t+1 (11) Estimating Eq. (11) also allow us estimating the leverage SOA as well as the coefficients of control variables in a single step. Meanwhile a great amount of deviation in firm s leverage is explained by unobservable and time-invariant firm-specific elements (Lemmon, Roberts, & Zender, 2008), we control for firm fixed-effect (μ i ) during model estimation. By doing that, we also lessen another source of endogeneity owing to corporation firm heterogeneity. To answer our research questions, we follow the one-step method (Flannery & Rangan, 2006; Halling et al., 2016), which gives us the estimates of leverage SOA in a single stage. As target leverage is unobservable and generated rather than known, and the whole set of its determinants is not identified and/or observed, they are measured with errors. This lead to errors of the SOA estimates in the two-step regression (Pagan, 1984). Using one-step regression helps to eliminate this matter Effect of liquidity, leverage deviation and target change on SOA 12

13 We investigate four main issues, stock liquidity, leverage deviation, target change, and SOA. The first research question (RQ1) relates to the relationship between the SOA and liquidity. We model this economic relation as follows: i,t = 0 + β 1 LIQ i,t (12) Where LIQ i,t is proxied by Amihud illiquidity measure. β 1 is the coefficient on the liquidity variable. Since we hypothesize that liquidity have a positive impact on the SOA, we expect the coefficient on the illiquidity measure, β 1, to be negative. Next, substituting equation (12) into equation (11), we obtain the following model: LEV i,t+1 = α 0 + (1 ( 0 + β 1 LIQ i,t ))LEV i,t + j βx i,t + ω i,t+1 (13) Which we can further simplify to yield: LEV i,t+1 = α 0 + β 1 (LIQ i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (14) Where the coefficient β 1 = β 1. An essential advantage of Eq. (14) is that we can define the average SOA, 0, and the effects of liquidity on the SOA, β 1, in one step. The impact of liquidity on the SOA is captured by the coefficients of the interaction terms of illiquidity measure and leverage, (LIQ i,t LEV i,t ), with the same magnitude but opposite sign. We note that equation (14) does not include the liquidity variable, LIQ i,t, but only their interaction term with leverage. The reason is, as mentioned above, we follow the convention in the capital structure literature and model target leverage in equation (8) as a function of its most relevant firm- and industry-specific determinants, which do not include the liquidity measure (An, Li, & Yu, 2016; Devos et al., 2017; Öztekin & Flannery, 2012; Zhou et al., 2016). Similarly, we employ the following panel data model to examine the impact of leverage deviation and change in target leverage (RQ2 and RQ3), respectively, on the leverage SOA 2 : 2 We model the economic relations between leverage SOA and leverage deviation and target change, respectively, as follows: i,t = 0 + θ 1 LevDev i,t i,t = 0 + γ 1 ΔTarget i,t Where LevDev i,t is the measure of leverage deviation from target and ΔTarget i,t is the measure of change in target. θ 1 is the coefficient on the leverage deviation variable and γ 1 is the coefficient on the target change variable. Next, substituting the two above equations into equation (11), we obtain the following model: LEV i,t+1 = α 0 + (1 ( 0 + θ 1 LevDev i,t ))LEV i,t + j βx i,t + ω i,t+1 13

14 LEV i,t+1 = α 0 + θ 1 (LevDev i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (15) LEV i,t+1 = α 0 + γ 1 (ΔTarget i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (16) The impact of leverage deviation and change in target leverage, respectively, on the SOA are captured by the coefficients of the interaction terms of leverage deviation and leverage, (LevDev i,t LEV i,t ) and the interaction terms of change in target leverage and leverage, (ΔTarget i,t LEV i,t ) with the same magnitudes but opposite signs. Specifically, if the coefficient θ 1 (γ 1 ) is positive, there is a negative relationship between leverage deviation (change in target leverage) and the SOA and vice versa. We investigate the effect of all liquidity, leverage deviation and change in target leverage on the leverage SOA (RQ1, RQ2 and RQ3) by formulating the following regression: LEV i,t+1 = α 0 + β 1 (LIQ i,t LEV i,t ) + θ 1 (LevDev i,t LEV i,t ) + γ 1 (ΔTarget i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (17) In this model, we incorporate stock liquidity, leverage deviation, and target change as independent variables on the leverage SOA specification Effect of liquidity on SOA: conditional on leverage deviation and target change Our fourth research question (RQ4) relates to the impact of leverage deviation and target change on the relationship between equity liquidity and SOA. To examine this issue we include the interaction term between stock liquidity and leverage deviation, and between stock liquidity and target change, respectively into the SOA regression (Eq. (12)): i,t = 0 + β 1 LIQ i,t + β 2 LIQ i,t LevDev i,t (18) i,t = 0 + β 1 LIQ i,t + β 3 LIQ i,t ΔTarget i,t (19) i,t = 0 + β 1 LIQ i,t + β 2 LIQ i,t LevDev i,t + β 3 LIQ i,t ΔTarget i,t (20) By substituting Eq. (18) (20) into Eq. (11) and further simplification, we obtain: LEV i,t+1 = α 0 + (1 ( 0 + γ 1 ΔTarget i,t ))LEV i,t + j βx i,t + ω i,t+1 Which we can further simplify to yield equation (15) and equation (16). 14

15 LEV i,t+1 = α 0 + β 1 (LIQ i,t LEV i,t ) + β 2 (LIQ i,t LevDev i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (21) LEV i,t+1 = α 0 + β 1 (LIQ i,t LEV i,t ) + β 3 (LIQ i,t ΔTarget i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (22) LEV i,t+1 = α 0 + β 1 (LIQ i,t LEV i,t ) + β 2 (LIQ i,t LevDev i,t LEV i,t ) + β 3 (LIQ i,t ΔTarget i,t LEV i,t ) + (1 0 )LEV i,t + j βx i,t + ω i,t+1 (23) As we propose that leverage deviation and target change increase the cost of equity (Zhou et al., 2016), this would suggest a positive relation between stock liquidity and leverage SOA is less pronounced for firms with high leverage deviation and/or high level of target change. Hence we might expect a positive signs on interaction term LIQ*LEV and negative signs on the interactions terms LIQ*LevDev*LEV and LIQ*ΔTarget*LEV. We use leverage deviation and target change as dummy variables by assigning 1 for high leverage deviation (high target change), and 0 for low leverage deviation (low target change) based on the median value. Specifically, if values of leverage deviation (target change) are higher than the median, the represent high leverage deviation (target change); otherwise low leverage deviation (target change) Econometric method Since the original partial adjustment model, Eq. (11), and our main regression models, Eq. (12) (23), are dynamic panel data models, using traditional pooled OLS or FE estimators would lead to biased and inconsistent estimates (Baltagi, 2008). OLS tends to overestimate the coefficient of the dynamic term, (1 j ), hence, underestimating the SOA, j. Although the FE estimator eliminates the firm fixed effect, it still produces biased estimates due to a correlation between the transformed error term and the dynamic term. Particularly, FE underestimates the coefficient of the dynamic term, thus, overestimating the SOA (Nickell, 1981). The bias tends to be serious if the sample has a relatively small number of time period (Flannery & Hankins, 2013). Hence, the use of OLS in this study would have implications for the inferences that we could draw from the findings. 15

16 Given the above limitations of the OLS and FE estimators and dynamic essence of our panel models, we follow recent research and use Blundell and Bond (1998) s two-step system GMM (Flannery & Hankins, 2013; Zhou et al., 2016). In applying the two-step system GMM, we estimate our model using appropriate instruments for the dynamic term(s) (e.g., leverage ratios, interaction terms between leverage ratios and main variables), that is, lagged values of dynamic term(s). 5. Empirical results 5.1. Descriptive statistics Table 2 presents the summary statistics for the entire sample including descriptive statistics (Panel A) and correlation coefficients of determinants of target leverage and the leverage SOA, respectively (Panel B and C). The average firm in the sample has a book leverage ratio of and a market leverage of There is a large cross-sectional difference in the leverage ratio with the first quartiles of book leverage and market leverage being and and the third quartiles being and , respectively. In term of the liquidity measure, the means of Amihud, zero-return days proportion, turnover and daily quoted spread are , 0.413, and 0.053, respectively. Mean of book leverage deviation is lower than mean of market leverage deviation, i.e., compared to On average, changes in target market leverage is also higher than changes in target book leverage, and 0.003, respectively. The average firm in our sample has an asset tangibility-total asset ratio of 27.4%, a market-to-book ratio of 2.53, a profitability-total asset ratio of 6.5%, a depreciation-total asset ratio of 4.6% and a R&D-total asset ratio of 2.2%. Panel B and C reports the correlations between the determinants of the target leverage ratio and the SOA, respectively. We see in both instances that these correlations are low suggesting that there little concern with multicollinearity. [Insert Table 2 here] In order to illustrate the consistency of our target leverage regressions with the existing literature, we present the coefficient estimates in Panel A of Table 3 where we use a panel regression with both firm and year fixed effects. The standard errors are corrected for both heteroscedasticity and clustering (Zhou et al., 2016). The estimates are very consistent with those found in previous studies (An et al., 2015; Flannery & Rangan, 2006; Öztekin & Flannery, 2012; Zhou et al., 2016). Specifically, the greater use of debt in the target capital structure increases 16

17 with firm size, tangibility, depreciation and industry median leverage, and decreases with the market-to-book ratio and profitability. We also report in Panel B of Table 3, summary statistics for estimated average target leverage across the from 1996 to 2016 in Panel B of Table 3 for both the book leverage and market leverage ratios. Over the sample period, the median target leverage is 0.17 for book leverage and 0.19 market leverage and the mean annual cross-sectional target leverage fluctuates between and for book leverage, and between and for market leverage. Consistent with existing literature (Frank & Goyal, 2009), the median of both book and market leverage are both below target leverage. [Insert Table 3 here] 5.2. Equity liquidity, leverage deviation, target change and SOA We present the baseline regression results (equation 14-17), which determine the stock liquidity-soa relationship (RQ1), leverage deviation SOA relationship (RQ2) and target change SOA relationship (RQ3) in Table 4. All of these regressions are estimated using the two-step GMM method. The results are presented separately for book leverage (BLEV) and market leverage (MLEV), as indicated by column headings. Our independent variable of interest are the interaction terms between these two measure of leverage (LEV) and stock liquidity (Columns 1-2), leverage deviation (Columns 3-4), target change (Columns 5-6), and all three variables of interest (Columns 7-8). [Insert Table 4 here] The regression results of equation (14) are shown in Table 4 (Columns 1-2). The coefficient on the interaction term between liquidity (LIQ) and leverage is positive and highly significant at 5% for book leverage regression and 1% for market leverage regression. Thus, there is a negative relationship between the Amihud illiquidity measure. However, as a low Amihud score is indicative of high liquidity (Amihud & Mendelson, 1986; Lipson & Mortal, 2009), our findings indicate a positive relation between stock liquidity and the leverage SOA. It suggests that high (low) liquid firms have high (low) speeds of leverage adjustment toward their targets, implying that firms with high liquidity have not only low net cost of equity but also lower adverse selection problems, hence, lower transaction costs and lower overall adjustment costs that results in high speed of leverage adjustment. Columns 3-4 of Table 4 report the results of equation (15) for leverage deviation-the SOA relation for book leverage (BLEV) and market leverage (MLEV), respectively. The 17

18 interaction term between leverage deviation and leverage ratio is negatively and significantly related to book and market leverage at the 5% and 10% level, respectively. The results suggest that leverage deviation has a positive impact on the leverage SOA, which is consistent with the findings of prior empirical studies of the Swiss and U.S. markets (Drobetz & Wanzenried, 2006; Zhou et al., 2016). This finding suggests that the costs of adjustment are significant causing firms to only adjust their actual capital structure when they are sufficiently far away from their targets. Columns 5-6 of Table 4 present the regression results of equation (16) for the impact of change in the target leverage on the SOA for both the book and market leverage ratio (BLEV and MLEV, respectively). Importantly, we find that the coefficients on the interaction terms between target change and leverage ratios are positively and highly significant at the 1% level, regardless of whether book leverage or market leverage are exploited. These results answer our research question 3 (RQ3) that is higher volatility of target leverage ratios decrease the incentive of managers to change their capital structure and converge back to their targets. Hence, firms with higher target volatility adjust slower towards their target leverage. While columns 1-6 report on the impact of stock liquidity, leverage deviation, and target change on the leverage SOA, respectively, columns 7-8 examines the joint impact of these three variables with the SOA. The signs of the coefficients are consistent with those found previously with liquidity and leverage variation having a positive impact on SOA and target change having a negative impact. The main result that liquidity speeds up the SOA remains significant for both book value and market value leverage but there is some diminution in the significant of the other two variables with leverage deviation variables now only being significant for book-value leverage while the target change variable is only significant in the case of market-value leverage The coefficients of lagged leverage (LEV) (1 0 ) are positive and highly significant at the 1% level across models, with magnitude ranging between (column 2) and (column 4). This result implies that the based SOA ( 0 ), which do not taken into account the effect of the liquidity is about 26% (book leverage regression) and 44% (market leverage regression). Meanwhile, the based SOA ( 0 ) which do not taken into account the impact of leverage deviation or target change vary between 11% and 17%. When we do not consider all liquidity, leverage deviation and target change, the based SOA ( 0 ) range from 11% (for book leverage model) to 12% (for market leverage model). These results are not only consistent with 18

19 the dynamic trade-off strand of capital structure (Fischer et al., 1989; Goldstein et al., 2001; Strebulaev, 2007) but also the earlier empirical studies (Öztekin & Flannery, 2012). As regards to the effects of the control variables on leverage, most of the results are in line with theoretical expectations and empirical evidences in the literature (An et al., 2015; Öztekin & Flannery, 2012). Particularly, large firm with high tangibility assets or high marketto-book ratios use more leverage. Meanwhile, depreciation ratio and R&D expenditure have negative association with leverage ratio. The impact of profitability is mixed Effect of liquidity on SOA: Alternative measures of liquidity In this section, we examine the robustness on the stock liquidity leverage SOA relation using alternative measure of stock liquidity including zero return proportion (PropZero), turnover (Turnover) and daily closing percent quoted spread (Spread) 3. The regression results are reported in Table 5. [Insert Table 5 here] Columns 1-2, 3-4 and 5-6 report the results for PropZero, Turnover, and Spread, respectively along with control variables that confirm similar results as Table 4 with few exceptions. Specifically, in columns 1-2, the coefficients of interaction term PropZero*LEV is positive and statistically significant at 5% and 10% level in term of book and market leverage regressions, respectively. As PropZero is an illiquidity measure, these results confirm that liquidity has a positive impact on leverage SOA. Next, as a liquidity measure, the negative coefficients of interaction term Turnover*LEV also suggest a positive relationship between liquidity and leverage SOA (columns 3-4). However, while the coefficient of that term is statistically significant at 1% level for book leverage regression, it is insignificant for market leverage model. The results on Spread are similar that indicate a positive liquidity leverage SOA relation (columns 5-6) Effect of liquidity on SOA: conditional on leverage deviation and target change To examine whether the impact that stock liquidity has on the leverage SOA differ between firms with high and low leverage deviation, and firms with high and low level of target change (RQ4), we use the interaction terms between stock liquidity and leverage deviation, and 3 Similar to Amihud illiquidity regression (Eq. 14), the effects of other liquidity measures including proportion of zero-return days, turnover, and spread are represented by following models: LEV i,j,t+1 = α 0 + β 1 LEV i,j,t PropZero i,j,t + (1 0 )LEV i,j,t + β 3 X i,j,t + ω i,j,t+1, LEV i,j,t+1 = α 0 + β 1 LEV i,j,t Turnover i,j,t + (1 0 )LEV i,j,t + β 3 X i,j,t + ω i,j,t+1, LEV i,j,t+1 = α 0 + β 1 LEV i,j,t Spread i,j,t + (1 0 )LEV i,j,t + β 3 X i,j,t + ω i,j,t+1, 19

20 between stock liquidity and target change, respectively. As we hypothesize that leverage deviation and target change increase the cost of equity (Zhou et al., 2016), we expect that the positive relation between stock liquidity and leverage SOA to be impacted by the extent to which a firm s actual leverage ratio differs from its target and by the extent that this target is changing. Applying regression equation (21) (23), we use leverage deviation and target change as dummy variables by assigning 1 for high leverage deviation (high target change), and 0 for low leverage deviation (low target change) based on the median value. Specifically, if values of leverage deviation (target change) are higher than the median, the represent high leverage deviation (target change); otherwise low leverage deviation (target change). [Insert Table 6 here] Columns 1-2 of Table 6 report the regression results of equation (21). The coefficients of the interaction term between liquidity variable (measured by Amihud illiquidity score) and leverage ratios are positively and highly significantly (at 1% level) in both book and market leverage regressions, implying that liquidity has positive impact on leverage SOA for firms that have a low level of leverage deviation. However, the dummy variables term (LIQ i,t LevDev i,t LEV i,t ) is negative and highly significant which results in the coefficient of the relationship between liquidity and SOA being significantly eroded. Although the coefficient is still positive for both measures of leverage, it is now only weakly significant for book value leverage and no longer significant at all for market value leverage. 4 Hence we see that for firms with large leverage deviation, the strong relationship between leverage deviation and the SOA is very much eroded. Columns 3-4 of Table 6 represents the regression results for the impacts of target change on the association between stock liquidity and leverage SOA (equation 22). We continue to find that stock liquidity has positive impact on leverage SOA for low leverage deviation firms, as shown by the positive and significant coefficients on the leverage term. Again, we find that the dummy variables have a negative and significant coefficient consistent with the strength of the relationship being much greater for low leverage deviation than it is for high deviation firms. As with leverage deviation, we find that the impact of liquidity on the SOA is only very weakly significance for high target change firms using book value leverage and not significant at all for market value leverage. 4 This coefficient for the relationship between liquidity and SOA for high deviation firms is ( ) with book vale leverage which is significant at the 10% level using the Wald test. However, the same coefficient for market leverage is which is insignificant. 20

21 We, finally, confirm the impact of leverage deviation and target change on the stock liquidity-leverage SOA association by including both dummy variable terms, LIQ*LEV*LevDev and LIQ*LEV*ΔTarget, in one regressions (equation 23). The results for both book and market leverage specifications are presented in columns 5-6 of Table 6. Consistent with our previous finding, we continue to find a strong positive relationship between liquidity and SOA for firms with both low leverage deviation and target change. We summarise the individual and joint impacts of leverage deviation and target change in Table 7. The strength of this relationship is severely diminished but still remains significant for firms with either high leverage deviation/low target change or low leverage deviation/high target change. The most interesting finding is that for firms with both large leverage deviation and large target change is almost completely dissipated under book leverage and actually turns weakly negative for market leverage.. 6. Conclusion In this study, we investigate how stock liquidity, deviation from target leverage ratio, and change in the target affect the speed that firms converge back to their targets. Based on a sample of 2,000 UK firms over the period from 1996 to 2016, we find a positive association between stock liquidity and leverage SOA, indicating that firms with more equity liquidity adjust more quickly to their targets. This important finding proves to be robust to the use of a range of alternative proxies for equity liquidity. We also find that leverage deviation impacts positively on leverage SOA, suggesting firms, which move far away from their target, have a greater incentive to move back to the target. However, we found a negative relationship between target change and leverage SOA implying that mangers have a lower incentive to move towards their target where there is uncertainty as to what this target will be in the future. On closer analysis, we observe that both leverage deviation and target change have a negative impact on the strength of the relationship between equity liquidity and the SOA: Indeed, for firms with both a large leverage deviation and a large target change, any positive impact that equity liquidity has on their SOA is totally eroded. We contribute to the literature in several ways. First, we are the first to enrich the literature of leverage adjustment by identifying liquidity and target change as new SOA s determinants. Second, we also confirm the relationship between deviation and SOA relationship for which there have been conflicting findings in the prior literature. Third, we provide new empirical evidence of the joint effect of equity liquidity, leverage deviation and target change on 21