risk changes and the dynamic trade-off theory of capital structure · 2015. 1. 21. · martin j....
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Risk changes and the dynamic trade-off theory of capital structure*
Martin J. Dierker Korea Advanced Institute of Science and Technology (KAIST)
Jun-Koo Kang Nanyang Technological University of Singapore
Inmoo Lee Korea Advanced Institute of Science and Technology (KAIST) &
University of Texas at Austin [email protected]
Sung Won Seo
Dongguk University [email protected]
January 2015
Abstract
We provide new insight into the relevance of the dynamic trade-off theory of capital structure by examining firms’ external capital raising activity following risk changes. Consistent with the prediction of the dynamic trade-off theory but inconsistent with the pecking order theory and the market timing explanation, we find that firms issue equity (debt) following risk increases (decreases). The results hold when we use subsamples of firms with investment-grade credit ratings or those without financial constraints in the analysis and are robust to a variety of risk measures: stock return volatility, default probability, implied asset volatility, and adjusted Ohlson (1980) scores.
* We thank Tim Loughran and Sheridan Titman for useful comments. All errors are our own.
Risk changes and the dynamic trade-off theory of capital structure
Abstract We provide new insight into the relevance of the dynamic trade-off theory of capital structure by examining firms’ external capital raising activity following risk changes. Consistent with the prediction of the dynamic trade-off theory but inconsistent with the pecking order theory and the market timing explanation, we find that firms issue equity (debt) following risk increases (decreases). The results hold when we use subsamples of firms with investment-grade credit ratings or those without financial constraints in the analysis and are robust to a variety of risk measures: stock return volatility, default probability, implied asset volatility, and adjusted Ohlson (1980) scores.
1. Introduction
What drives a firm’s capital structure decisions is one of the most controversial issues in corporate
finance. Although several explanations have been proposed for a firm’s capital structure choice, such as
those based on the trade-off between the tax benefits of debt and the expected costs of bankruptcy (Kraus
and Litzenberger (1973); Miller (1977)), adverse selection costs (Myers and Majluf (1984)), and market
timing (Baker and Wurgler (2002)), the empirical evidence on the relevance of each explanation is still
largely debatable.
In response to this debate, particularly that on the relevance of the static trade-off theory (Myers
(1993); Andrade and Kaplan (1998); Graham (2000); Hovakimian, Kayhan, and Titman (2012)), 1
academics have turned to dynamic versions of the trade-off theory. Fischer, Heinkel, and Zechner (1989),
for instance, show that in the presence of recapitalization costs, a firm’s debt ratio can vary over time
because any leverage ratios within a set of boundaries are optimal. Therefore, according to their argument,
firms with similar characteristics can have different leverage ratios at any point in time. However, to the
extent that these firms have similar recapitalization criteria, it is also possible that their capital structures
exhibit similar intertemporal behavior. Consequently, the dynamic trade-off theory proposed by Fischer,
Heinkel, and Zechner (1989) suggests that firms take recapitalization actions only when the benefits from
recapitalization outweigh the costs.
As emphasized by several studies, the presence of adjustment costs has important effects on testing a
dynamic trade-off theory of capital structure. For instance, consider a sample of firms that have received a
(persistent) positive shock to profitability and experienced an increase in the market value of their assets,
as in Strebulaev (2007). In the absence of adjustment costs, the trade-off theory suggests that these firms
increase their leverage ratios to take advantage of tax shields of debt, resulting in a positive relation
1 Myers (1993) and Graham (2000) point out that a negative correlation between the profitability and leverage ratios is the most critical evidence against the static trade-off theory, while Andrade and Kaplan (1998) argue that, from an ex-ante perspective, expected financial distress costs are likely to be small in comparison to the tax benefits of debt. Hovakimian, Kayhan, and Titman (2012) find that firms’ choice of leverage leads to default probabilities that are inconsistent with the static trade-off theory.
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between profitability and leverage. However, taking into account the adjustment costs, some firms may
find it optimal to remain inactive in the external financial markets since raising capital may sometimes be
too costly for them, resulting in a leverage ratio that deviates from what it would be in the absence of
adjustment costs. Hennessy and Whited (2005) and Strebulaev (2007) focus on this important aspect of a
dynamic trade-off model (i.e., the existence of issue (adjustment) costs) to explain the observed negative
relation between market leverage ratios and profitability, an approach that can also help overcome other
empirical challenges inherent in tests of the static model.
However, other studies present evidence challenging the results of this approach. Welch (2004), for
example, argues that stock returns, not target leverage, drive capital structures and shows that market
leverage varies with fluctuations in stock prices. In addition, while Leary and Roberts (2005) find
evidence on the importance of adjustment costs, they conclude that further work is needed to distinguish
between the predictions of the dynamic trade-off theory and those of a pecking order theory modified for
bankruptcy risk.2
While the dynamic trade-off theory has the potential to explain the existing evidence better than the
static trade-off theory, there are considerable challenges in testing the former theory since its empirical
tests can be conducted only after making assumptions regarding parameters in the model. For example, in
estimating model parameters, Strebulaev (2007) assumes that the present values of net payouts and book
assets are scaled to have identical values for all sample firms on the date of external financing, thereby
ignoring any potential differences in parameter values across different size groups.
This paper attempts to overcome this challenge and test the relative importance of the dynamic
trade-off capital structure theory compared with other capital structure theories by examining one of the
key features of the trade-off theory, namely, the effects of risk changes on a firm’s optimal capital
2 Even when bankruptcy costs are introduced into the pecking order theory, firms may still prefer to issue debt rather than equity since debt is likely to be associated with fewer adverse selection problems. As shown in Lemmon and Zender (2010), firms may prefer to issue debt rather than equity unless increases in risk significantly constrain their ability to borrow.
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structure. Previous studies show that a firm’s risk changes over time and that this fluctuation in risk
significantly affects its expected returns, i.e., the cost of capital (Campbell el al (2001); Ang et al. (2006);
Adrian and Rosenberg (2008)). In addition, Leland (1994) theoretically shows that increases in risk
reduce debt capacity, while Chen (2010) points out that the presence of countercyclical variation in risk
premiums, default probabilities, and default losses increases the present value of expected default losses,
leading to lower optimal leverage ratios. In spite of the evidence on the change in firm risk over time and
the strong theoretical link between risk changes and capital structure, empirical evidence on such a link is
scarce.3 Moreover, previous studies that examine the association between the risk level and capital
structure do not provide conclusive evidence.4
We test the effects of risk changes on a firm’s capital structure decision by examining its choice of
external financing method following risk changes. This approach has several advantages. First, it allows
us to test the relevance of each competing capital structure theory without measuring adjustment costs
since we focus on the group of firms that have already raised or reduced external capital and thus realized
the adjustment costs. Second, our approach does not require estimating a target leverage ratio, which is
hard to define and to be measured (e.g., Chen and Zhao (2007); Chang and Dasgupta (2009)). Instead of
estimating target leverage ratios, our approach simply utilizes the fact that, holding everything else
constant, an increase (decrease) in risk tends to lower (raise) the target leverage ratio. Thus, according to
the dynamic trade-off theory, when a firm decides to raise or reduce external capital after experiencing
risk changes, it is likely to choose a financing method that moves it towards its new lower or higher target
leverage ratio. Although previous studies also examine a firm’s capital structure decision around its
external capital raising period (e.g., Hovakimian, Hovakimian, and Tehranian (2004); Danis, Rattl, and
3 Gormley, Matsa, and Milbourn (2012) show that leverage is related to the change in firm risk for a small set of firms: they find that firms with a well-designed compensation structure reduce their leverage conditional on an exogenous increase in litigation risk. Numerous studies also show that leverage decreases with asset volatility or return volatility (e.g., Harris and Raviv (1991); Ju, Parrino, Poteshman, and Weisbach (2005)). However, these studies do not explicitly examine how firms respond to changes in risk. 4 For example, Harris and Raviv (1991) show that out of five studies that document the negative association between return volatility and leverage ratios, two present a weak or statistically insignificant association.
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Whited (2013); Korteweg and Strebulaev (2013)),5 our approach differs from these studies in that we
focus on the choice of a firm’s external financing methods following a change in risk.
In the dynamic trade-off theory, a firm’s capital structure decision in response to a change in risk
depends on its risk level as well as the (hard to observe) adjustment costs associated with external
financing. For example, the firm may choose to remain inactive in external capital markets if adjustment
costs are higher than the benefits obtained from adjusting its capital structure. On the other hand, if the
benefits from raising external capital after risk changes are greater than the adjustment costs, possibly due
to the emergence of good investment opportunities or the arrival of the optimal time to exercise its real
option caused by risk changes, we expect the firm to raise a type of external capital that allows it to move
closer to its optimal leverage (see Leary and Roberts (2005) and Strebulaev (2007) for further discussion).
Alternatively, when a firm’s investment opportunities disappear and it consequently seeks to reduce
capital, it should respond to changes in risk level by reducing a particular type of external capital.6 Thus,
all else being equal, as far as an increase (decrease) in risk tends to lower (raise) the target leverage ratio,
the dynamic trade-off theory predicts that a firm experiencing an increase (decrease) in risk is more likely
to issue equity (debt) or buyback debt (equity), suggesting that risk increases (decreases) are associated
with leverage-decreasing (increasing) activities.7
5 For example, Hovakimian, Hovakimian, and Tehranian (2004) focus on the period during which firms issue both debt and equity. Danis, Rattl, and Whited (2013) pay close attention to the case when firms simultaneously issue a large amount of debt and pay out a large amount of internal capital through cash dividends or share repurchases, whereas Korteweg and Strebulaev (2013) examine cases of refinancing in which firms’ net debt (equity) issuance is greater than 5% of the book value of assets. 6 Strebulaev (2007) emphasizes that since firms adjust their capital structures infrequently due to high adjustment costs, the results from standard cross-sectional capital structure tests could lead to a misleading conclusion, and he shows that leverage is likely to be at the optimum level only at the time of readjustment. Previous studies focus mainly on adjustment costs associated with raising external capital. However, since forgoing the opportunity to invest in good projects that unexpectedly arrive after the reduction of capital can be considered a part of the adjustment costs associated with reducing external capital, the adjustment costs associated with activities that reduce external capital can be also significant. 7 As the risk increases (decreases), the discount rate (i.e., the cost of debt) tends to increase (decrease). Thus, if a firm has issued long-term debt at a fixed interest rate, the present value of its tax shields is likely to decrease (increase). This decrease (increase) in the present value of tax shields will further lower (raise) the target leverage ratio compared with the case in which the present value of tax shields does not change, and therefore the trade-off theory predicts that a firm decreases (increases) its leverage ratio either by issuing equity (debt) or by repurchasing
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Other capital structure theories, by contrast, suggest that firms choose a different type of financing
method when they experience risk changes. The pecking order theory, for example, predicts that to the
extent that an increase in risk does not significantly reduce a firm’s ability to borrow, such a firm will
choose debt as the source of its external capital. Similarly, the market timing theory predicts that, all else
being equal, a firm experiencing an increase in risk will prefer debt over equity because, as we show later,
the market valuation of its equity decreases following the increase in risk.8 When a firm experiences a
decrease in risk, however, the pecking order theory predicts that the firm will issue debt while the market
timing theory predicts that it will choose equity.
Similarly, if a firm decides to reduce (i.e., buy back) external capital following risk changes, the
dynamic trade-off theory and the other two alternative capital structure theories predict that firms will
choose different buyback actions. The dynamic trade-off theory, for example, predicts that following risk
increases (decreases), firms will reduce debt (equity), but the market timing theory predicts the opposite.
On the other hand, the pecking order theory predicts that firms reduce debt in response to both risk
increases and risk decreases.9
debt (equity), as its risk increases (decreases). 8 For example, consider a firm that has recently experienced a large fall in stock price as in Welch (2004), while the amount of debt, asset volatility, and book value remain constant. This firm’s equity is now less valuable than before and thus its financial distress risk increases since it is much closer to default in the sense of Merton (1974). However, since its valuation has gone down significantly, the firm has few incentives to issue equity. Thus, the market timing argument suggests that a firm experiencing a risk increase is more likely to issue debt. Alternatively, as a firm’s risk level increases, its value is likely to decrease due to an increase in the cost of capital, holding everything else constant. Thus, according to the market timing theory, firms prefer to issue debt over equity when they experience a risk increase. 9 Both the pecking order theory and the market timing theory are silent about firms’ external capital-reducing activities in responses to risk changes. However, the pecking order theory, which is based on the argument that firms try to minimize adverse selection costs, implicitly suggests that firms always prefer to buy back debt to preserve future debt capacity, while the market timing theory, which is based on security misvaluation, suggests that firms buy back a security that is undervalued (or relatively less overvalued). Since equity prices tend to go up (down) following risk decreases (increases), holding everything else constant, if managers believe that a firm’s equity is more likely to be overvalued (undervalued) following price increases (decreases), the market timing theory predicts that firms will reduce equity capital following risk increases but reduce debt following risk decreases. One caveat is that due to asymmetric information, it is possible that firms may issue overvalued equity or buy back undervalued stocks under the pecking order theory if the benefits obtained from exploiting misvaluation are greater than the adverse selection costs, leading to the predictions similar to those of the market timing theory. Under this explanation, the pecking order theory predicts a negative relation between risk changes and leverage-increasing external financing activities, which is opposite to the prediction made under the dynamic trade-off theory.
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In sum, by examining the differences in the relation between risk changes and future external
financing activities, we can investigate which capital structure theory out of the three alternatives is the
most relevant in explaining firms’ capital structure decisions following risk changes.
Table 1 summarizes the preferred type of security that a firm issues (or buybacks) as its risk changes
under each of three competing capital structure theories. The dynamic trade-off theory predicts a negative
relation between risk changes and future leverage-increasing external financing activities, while the
pecking order theory and the market timing explanation predict either an ambiguous or the opposite
relation between them.
To perform our analysis, we use both market- and accounting-based risk measures.10 We use stock
return volatility, default probability, and implied asset volatility estimates as market-based measures of
firm risk. The default probability risk measure captures the likelihood of a firm’s financial distress and the
implied asset volatility measure captures the unobservable volatility of its underlying assets, which affects
its optimal capital structure. Both the default probability and the implied asset volatility measures are
estimated using the Merton (1974) model. In addition, despite the limitations of accounting-based
measures documented by Hillegeist et al. (2004), we use an adjusted Ohlson’s (1980) O-score (Franzen,
Rodgers, and Simin (2007)) as an alternative measure of risk. For each of these risk measures, we
investigate how changes in a firm’s risk are associated with its future external financing activities and
leverage changes.
Using a sample of firms listed on NYSE, Amex, or Nasdaq from 1972 to 2011, we find that firms are
more likely to issue equity (debt) when they raise external capital following risk increases (decreases).
Similarly, firms are more likely to buy back debt (equity) when they reduce external capital following risk
increases (decreases). These results are consistent with the predictions of the dynamic trade-off theory but
10 Since financial markets incorporate a firm’s relevant information in a timely manner (Roll (1984)), market-based measures of firm risk are likely to reflect a firm’s financial condition more fully and accurately than accounting-based measures of firm risk (e.g., Hillegeist et al. (2004)). We therefore focus on market-based measures as our key variables of interest.
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inconsistent with those of the pecking order theory and the market timing theory. In terms of economic
significance, a one standard deviation increase in annual changes in equity volatility (19%) leads to an
increase in firms’ net equity issue (or a decrease in firms’ net debt issue) of 0.55% of their total assets in
the following year, which in turn leads to a decrease in market leverage of 1.18%. These results are more
pronounced when we extend the observation window from one to three years after the increase in risk and
are also robust to a variety of alternative risk and sample specifications and endogeneity controls. The
results also do not change when we use book instead of market leverage ratios.
We also find that our results do not change when we limit our attention to the subsamples of firms
with investment-grade credit ratings or those facing fewer financial constraints. The pecking order theory
suggests that these firms particularly prefer to issue debt over equity because they have a greater ability to
issue debt due to their easy access to debt markets. Therefore, these results further support the dynamic
trade-off theory but dispute the pecking order theory.11
Moreover, we find that an increase in firm risk is indeed associated with a fall in a firm’s valuation
as measured by the market-to-book ratio. This result, together with a significantly negative relation
between risk changes and leverage-increasing external financing activities, further suggests that the
dynamic trade-off theory explains a firm’s capital structure decision better than the market timing theory.
In short, our results are most consistent with the implications of the dynamic trade-off theory and are
in contrast with the results of recent studies that document evidence against the trade-off theory of capital
structure. For example, Hovakimian, Kayhan, and Titman (2012) find that firms with a higher likelihood
of substantial losses in bankruptcy tend to choose capital structures that have greater exposure to
bankruptcy risk, which cannot be easily reconciled with the (static) trade-off theory.
Our study contributes to the ongoing debate about firms’ capital structure decisions in several ways.
First, focusing on the relation between risk changes and external financing decisions, we propose a simple,
11 Using Canadian data, Dong et al. (2012) show that firms time their equity issuance when they are not financially constrained. They further show that firms follow the pecking order only when their shares are not overvalued.
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clear way to test the implications of the dynamic trade-off theory that allows us to minimize the problems
caused by the potential mismeasurement of adjustment costs and target leverage ratios. Our approach is
different from those used in previous studies that examine a firm’s capital structure decisions during its
external capital raising period. Built on the argument that the dynamic trade-off theory predicts a different
relation between risk changes and a firm’s external financing decision compared with those predicted by
alternative capital structure theories, we test the relevance of the competing capital structure theories with
less ambiguity by focusing on a firm’s external capital raising/reducing activities following risk changes.
Second, our study emphasizes the importance of the changes in, not the levels of, risk in capital
structure decisions. In spite of the strong theoretical link between risk changes and capital structure and
the empirical evidence on the time variation of risk, previous studies on capital structure focus mainly on
the relation between leverage and the level of risk. We provide new insights on the importance of various
capital structure theories by directing attention to the relation between risk changes and capital structure
decisions.
Third, our findings add to the literature on capital structure that emphasizes firms’ dynamic financing
choice problems in which the tax benefits of debt and expected bankruptcy costs play an important role.
While some recent studies show that the (static) trade-off theory does not have any significant power in
explaining the cross-sectional variation of firms’ capital structure choices (e.g., Hovakimian, Kayhan, and
Titman (2012)), our study provides evidence that the time-series variation of observed firms’ financing
choices is consistent with the dynamic trade-off theory. This evidence complements the findings of
previous studies on the dynamic trade-off theory, which use other alternative approaches, such as the
structural estimation approach of Hennessy and Whited (2005) and the simulation approach of Strebulaev
(2007), to explain persistent cross-sectional patterns in firms’ capital structures.
The paper proceeds as follows. In Section 2, we describe our key risk measures of interest and
outline the empirical methodology. Section 3 presents our main empirical results and Section 4
summarizes our findings and provides concluding remarks.
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2. Data and Methodology
2.1. Data
Our sample consists of all NYSE, Amex, or Nasdaq firms available on both CRSP and Compustat
between 1971 and 2011. As in Vassalou and Xing (2004), we start our sample period in 1971 because
there is insufficient debt-related financial data prior to 1971 in Compustat. All the variables used in the
paper are measured at fiscal year-ends. To focus on firms with meaningful data, we exclude firms with a
negative book equity value, a market-to-book asset ratio above 10, or total assets below US$ 10 million.
We also exclude utility (SIC 6000-6999) and financial (SIC 4900-4949) firms since their capital structure
decisions are subject to regulatory constraints. In addition, as in Kayhan and Titman (2007), we exclude
firms with book leverage ratios above 100%. Finally, to mitigate potential problems caused by extreme
outliers, we winsorize all variables at the 1st and 99th percentiles in each year, as in Leary and Roberts
(2005) and Kale and Shahrur (2007). Since our analyses require the measurement of changes in risk, we
further delete the first year of our sample period. Our final sample consists of 82,723 firm-year
observations over the period 1972-2011.
2.2. Risk Measures
To test the importance of firms’ risk changes in their capital structure decisions, we use various risk
measures. Roll (1984) argues that financial markets tend to incorporate information about firms in a
timely and forward-looking manner, suggesting that market-based risk measures are good measures of
firm risk and thus accurately measure time-series fluctuations in risk. Confirming this argument,
Hillegeist et al. (2004) show that as predictors of financial distress, market-based risk measures, such as
those obtained by fitting the Merton (1974) model, significantly outperform accounting-based risk
measures. Therefore, we focus on the following three market-based risk measures as our key measures of
firm risk: stock return volatility and default risk and implied asset volatility estimated on the basis of the
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Merton (1974) model. We also use a risk measure based on financial statements, namely, a version of
Ohlson’s (1980) adjusted O-score as in Franzen, Rodgers, and Simin (2007), as an alternative measure of
firm risk.
First, the volatility of stock returns reflects uncertainty in the market value of a firm’s equity.
Although the volatility of a firm’s total assets may provide a better measure of its risk, we focus on equity
volatility in measuring firm risk due to the illiquidity of debt markets.12 To measure stock return volatility,
EquityVol, we calculate the standard deviation of 52 weekly stock returns in each fiscal year and multiply
it by the square root of 52 to annualize it.
Second, default risk, which is closely related to financial distress costs, is measured based on the
Merton (1974) model. We measure Merton’s (1974) default risk, Merton, in a similar way to Vassalou and
Xing (2004).
Third, implied asset volatility serves as an important measure of firm risk since it captures the
uncertainty in asset values, not equity values, which ultimately matter in avoiding financial distress. We
define implied asset volatility, AssetVol, as the annualized standard deviations of daily changes in asset
values calculated in the process of estimating Merton’s default probabilities in each year (i.e., estimated
𝜎𝜎𝐴𝐴). To annualize the standard deviation of daily changes in asset values, we multiply it by the square root
of 252, the approximate number of trading days per year.
Finally, we use the adjusted O-scores (1980), O-Score, as our measure of accounting-based risk. This
measure is estimated following Franzen, Rodgers, and Simin (2007), who propose the adjustment method
for net income, total assets, and total liabilities to avoid misclassifying financially healthy R&D-intensive
firms as financially distressed firms and to treat R&D in a more conservative way. A detailed description
12 Due to the residual nature of equity claims, the use of equity volatility may entail a potential endogeneity problem when studying market leverage since an increase in equity risk reflected in the cost of equity is likely to decrease the market value of equity more than the value of debt, thereby resulting in an increase in the leverage ratio. However, it is important to note that this effect goes in the opposite direction compared with the effect predicted in the dynamic trade-off theory (i.e., firms issue more equity when risk increases). Thus, all else being equal, this endogeneity problem should make it harder for us to support the dynamic trade-off theory. It should be also noted that we present results based on the book value of leverage, which is not affected by this potential endogeneity problem.
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on how Merton, AssetVol, and O-score are measured is provided in Appendix B.
2.3. Leverage Ratio, External Financing Activity, and Other Measures
Leverage is measured by both book and market leverage ratios. The book (market) leverage ratio is
defined as the book value of debt divided by the book (market) value of total assets. The market value of
total assets is computed as total assets (AT) minus the book value of equity plus the market value of equity,
and the book value of debt is computed as total assets minus the book value of equity. As in Kayhan and
Titman (2007), the book value of equity is estimated as total assets minus the sum of total liabilities (LT)
and the liquidation value of preferred stock (PSTKL) plus deferred taxes, investment credit (TXDITC),
and convertible debt (DCVT). When PSTKL is not available, the redemption value (PSTKRV), or the
carrying value (PSTK) if PSTKRV is not available, is used.13 The market value of equity is measured at
the fiscal year-end.
To measure external financing activity following risk changes, we create a variable, leverage-
increasing external financing activities, LIEFA [t+1], which is measured as the ratio of the difference
between net long-term debt issue and net equity issue in year t+1 to lagged total assets.14 The difference
between net debt issue and net equity issue is calculated as long-term debt issuance (DLTIS) minus long-
term debt reduction (DLTR) minus sale of common and preferred stocks (SSTK) plus purchase of
common and preferred stocks (PRSTKC). LIEFA [t+2] and LIEFA [t+3] are calculated by summing
LIEFAs over two and three years starting from year t+1, respectively.15
13 Annual Industrial Compustat data variable names are in parentheses. 14 Specifically, LIEFA is defined as the difference in external financing activities that increase a leverage ratio (i.e., issue of new debt and repurchase of equity) and those that reduce a leverage ratio (i.e., reduction of debt and issue of new equity). Whether a positive value of LIEFA indeed leads to an increase in leverage depends on both the original level of leverage and other factors such as retained earnings, deprecation (book leverage), or stock returns (market leverage). For example, suppose that a firm with a debt-to-equity ratio of 10% raises 2% of existing equity value (E) through equity issuance and 1% of existing equity value through debt issuance. After issuance, this firm’s debt-to-equity ratio will increase from 10% to 10.78% (= (0.1× E + 0.01×E) / (E +0.02×E) = 0.11/1.02), but it will have a negative LIEFA. 15 As an alternative way to measure leverage-increasing external financing activity over multiple years, we define LIEFA [t+2] (LIEFA [t+3]) as the ratio of the difference between net long-term debt issue and net equity issue during
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Although, as discussed above, there is a debate on the existence and measurement of target leverage
ratios, we control for these ratios in our analysis to facilitate comparison with previous studies (e.g.,
Hovakimian, Opler, and Titman (2001)). We estimate target leverage ratios (Tlev) using a similar method
to that in Kayhan and Titman (2007), which is described in Appendix C, and measure market (book)
leverage deficit, LdefM(B)t, as the difference between the target market (book) leverage ratio and the
actual market (book) leverage ratio, TlevM(B)t – LevM(B)t. If a firm pursues a target leverage ratio, we
expect that the firm’s financing and capital structure decisions depend on how far it is away from its target
(i.e., the leverage deficit).16
Similar to Frank and Goyal (2003), to measure the amount of external financing, we define a firm’s
financial deficit, FD, as the ratio of the sum of net equity and long-term debt issues to total assets at the
beginning of the year (i.e., [sale of common and preferred stock (SSTK) – purchase of common and
preferred stock (PRSTKC) + long-term debt issuance (DLTIS) – long-term debt reduction (DLTR)]
divided by AT in year -1).17
As shown in previous studies (e.g., Loughran and Ritter (1995)), a firm’s financing decision may
depend on its market valuation, which also affects its capital structure. To measure the market valuation
of the firm, we estimate the market-to-book total assets ratio, MB. Given that changes in firm valuation
and stock performance can also affect firms’ external financing decisions, we control for changes in MB
(MB Change) and one-year stock return (r) during the fiscal year in the regressions.
In addition, since large firms are more likely to be diversified and have better access to capital
markets, size can affect firms’ financing decisions and therefore we include the natural logarithm of total
assets (AT), LTA, to control for size effect. According to the dynamic trade-off theory, a firm’s profitability
the year t+1-year t+2 (t+3) period to total assets in year t. In unreported results, we find that the qualitative results based on this alternative measure are similar to those reported in the paper. 16 We calculate both market and book leverage deficits and use them in the regression analyses. However, since the results using these two leverage deficit measures are qualitatively similar, we report only the results based on book leverage deficits in the paper. 17 We focus on external financing activity since, given high transaction costs, firms are more likely to adjust their capital structure when they have to raise external capital.
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can be an important determinant of its capital structure since profitable firms are more likely to be able to
take advantage of debt tax shields. The pecking order theory also suggests that profitable firms are less
likely to depend on external financing. Therefore, we control for profitability, EBITD, defined as earnings
before interest, tax, and depreciation (OIBDP) over total assets at the beginning of the fiscal year in the
regressions.
Graham and Harvey (2001) and Hovakimian, Kayhan, and Titman (2009) show that firms pay close
attention to their target credit ratings. This finding suggests that any gap between target and actual credit
ratings is likely to induce firms to adjust their capital structure in an effort to maintain their credit ratings
at target levels. To control for the effect of a firm’s target credit rating on its capital structure, we estimate
a firm’s target credit rating, TRating, by calculating the fitted value from an ordered probit regression
estimated in each year as in Hovakimian, Kayhan, and Titman (2009). The details of this regression
model and the results from the ordered probit regression used to estimate target credit rating in 2011 are
presented in Appendix D. We define credit rating deficit (CRdef) as the difference between TRating and
the actual credit rating and include it in the analyses. Since there are many firms that do not have
available credit rating information, we include a dummy variable, CRdummy, to indicate those firms with
available credit rating information.
2.4. Regression Specification
To test whether firms engage in leverage-increasing external financing activities following changes in
risk, we run the following panel ordinary least squares (OLS) regression model, which controls for
various factors that affect a firm’s capital structure decision:
titititi
titititi
tititititististi
FirmD YearDLdefB EBITDr CRdummyCRdef FD
MBMBLTARiskRisk =LevorLIEFA
,,13,12,11
,10,98,7,6
1,5,4,31,2,10,, )(
εββββββββ
ββββββ
++++
+++++
+∆+++∆+∆ −−++
, (1)
13
where YearD and FirmD indicate dummy variables for year and firm, respectively. All other variables are
defined in previous sections and are also summarized in Appendix A.
Controlling for firm fixed effects mitigate the endogeneity concern that our results are driven by
omitted unobservable firm characteristics. However, as shown in Petersen (2009), including firm dummy
variables is effective only if firm fixed effects are permanent. Therefore, as an additional cautionary
treatment, we use firm-clustered standard errors in calculating t-statistics, as suggested by Petersen (2009).
3. Empirical Results
3.1. Summary Statistics
Table 2 shows the summary statistics for our sample firms. The average total assets and market
capitalization are $2.07 billion and $2.04 billion (adjusted to 2011 purchasing power using the Consumer
Price Index), respectively. The average annual stock returns and the profitability (EBITD) are 18.2% and
14.5%, respectively. The mean market (book) leverage is 38.2% (44.2%) while the mean annual change in
market (book) leverage is 0.8% (0.7%), indicating that during our sample period, on average, firms have
slightly increased their leverage ratios. The mean book leverage deficit (LdefB) is 1.4%, suggesting that
our sample firms’ book leverage ratios are on average about 1% lower than their target leverage ratios.
The average LIEFA[t+1] is 0.54% while the median LIEFA[t+1] is -0.22%. These results suggest that
on average, firms issued more debt than equity during our sample period, albeit the median suggests the
opposite. The average (median) financial deficit, FD, is 4.4% (0.0%), indicating that the average (median)
annual total amount of external financing is around 4% (0%) of total assets at the beginning of each year.
Since the sum of FD and LIEFA[t+1] represents twice the amount of net long-term debt issuance, on
14
average, firms raised about 2.5% (≈ (4.4% + 0.54%)/2) of total assets through net long-term debt issuance
per year.18
The average (median) annual equity volatility, implied annual asset volatility, default risk, and
adjusted-Ohlson’s score are, respectively, 53% (46%), 50% (41%), 2.7% (0.0%), and -1.6 (-1.6). The
average (median) annual changes in market-based risk measures vary from -0.56% (-0.74%) to 0.19%
(0.00%) and the annual average (median) change in Ohlson’s score is 0.02 (-0.01).
3.2. Correlation and Univariate Analyses
In Table 3, we report the correlations among changes in leverage, external financing activity, the level
of risk, and the change in risk used in our analyses. We find that risk change variables are significantly
negatively correlated with changes in market leverage and LIEFA in the following year, even though the
magnitudes of their correlation coefficients are not high. The correlations between risk changes and book
leverage changes in the following year and their significance vary across risk measures.
We also find that our risk change variables are significantly positively correlated with each other,
although the magnitude of the correlation coefficients varies across the pairs of risk change measures.
There are also significant positive correlations among levels of our risk measures. It is noteworthy that the
correlations between our risk measures are typically lower than one, suggesting that consistent with our
previous discussion, they capture different aspects of firm risk. All three market-based risk measures are
only weakly, albeit significantly, correlated with the O-score, an accounting-based risk measure, perhaps
due to the latter’s lack of timely updates.
Financial deficit, FD, is significantly positively correlated with changes in market and book leverage
ratios in the following year, suggesting that after raising external capital, leverage ratios tend to increase
in the following year. However, it is negatively correlated with LIEFA in the following year. We do not
18 This number is a rough estimation because FD is measured as the sum of net equity and net debt issuances in year t whereas LIEFA[t+1] is measured as the difference between net debt and net equity issuances in year t+1.
15
find any consistently strong correlation between FD and risk change (or risk level) variables. MB and
stock returns are significantly positively correlated with changes in market leverage in the following year,
but they are significantly negatively correlated with changes in book leverage and LIEFA in the following
year. Finally, MB and stock returns are significantly negatively correlated with risk change variables,
consistent with the conjecture that holding everything else constant, stock prices decrease as risk
increases. In untabulated tests, we check the correlations between risk change (level) measures and other
firm characteristics reported in Table 3 and find that none of the correlations is high enough to cause
multicollinearity problems in our subsequent empirical analyses.
In Table 4, we report univariate results for changes in MB, LIEFA, and leverage ratios for each group
formed on the basis of firms’ annual risk changes. In each year, firms in the top 20%, the middle 60%, and
the bottom 20% of each risk change measure are classified as “High risk change,” “Middle risk change,”
and “Low risk change” firms, respectively.
The number of observations in each category is shown in the first row, and the average change in
risk is shown in the second row. As expected, changes in the risk of “High risk change” firms are
significantly greater than those of “Low risk change” firms, as shown in the last column. Consistent with
the results in Table 3, MB decreases significantly more for “High risk change” firms than for “Low risk
change” firms, indicating that, on average, increases in risk lower firm valuation.
The next three (last three) rows show the average LIEFA and changes in leverage ratios for each
group during the one-year (three-year) period following risk changes. As shown in the last four columns,
where the differences of the averages between “High risk change” and “Low risk change” groups are
presented, we find that relative to firms experiencing a low change in equity volatility (our main risk
measure), firms experiencing a high change in equity volatility are significantly less likely to engage in
external financing activities that increase their leverage. These results hold both for the subsequent year
(t+1) as well as over the following three years (t+3). As a result, the average change in market leverage
for “High risk change” firms over the subsequent one-year (three-year) period is 1.19 (2.58) percentage
16
points lower than the average change made by “Low risk change” firms. This difference is significant at
the 1% level. The same pattern is observed when we replace equity volatility with the estimated
likelihood of default. With respect to the other risk measures, although we find that the effect has
consistently the same sign, it is not always statistically significant. Overall, the results in Table 4 suggest
that “High risk change” firms engage in less leverage-increasing external financing activities than “Low
risk change” firms, consistent with the prediction of the dynamic trade-off theory.
Figure 1 graphically presents the average LIEFA and changes in leverage ratios during one- and
three-year periods following risk changes across risk change deciles using four different risk measures.
Although we do not observe monotonic patterns in LIEFA and changes in leverage ratios across risk
change deciles, the highest risk change decile group generally shows lower LIEFAs and lower changes in
leverage ratios over the three-year period compared with other decile groups. These results suggest that
firms experiencing a significant increase in risk (i.e., top 10%) are substantially more active in choosing
external financing activities that are aimed at decreasing leverage ratios and that, on average, they
succeed in considerably reducing their market leverage ratios. The results also indicate that this process
tends to take a long time (i.e., three years rather than one year), consistent with the slow adjustment of
debt ratios toward target ratios as documented by Leary and Roberts (2005). In the next subsection we
examine whether a firm’s risk changes are associated with its LIEFA after controlling for factors known to
affect capital structure decisions.
3.3. Regression of LIEFA and Changes in Leverage on Risk Change Variables
Table 5 presents the results from panel regressions of LIEFA and changes in market (book) leverage
in the following year on changes in risk. The dependent variables are as follows: LIEFA in columns (1)
through (4), changes in book leverage ratios in columns (5) through (8), and changes in market leverage
ratios in columns (9) through (12). T-statistics based on clustered standard errors at the firm level are
reported in parentheses. In general, consistent with the predictions of the dynamic trade-off theory, we
17
observe significantly negative associations between risk changes and both LIEFA and changes in leverage
ratios in the following year. The results in column (1) suggest that a one standard deviation increase in
annual changes in equity volatility (19%) leads to a decrease in LIEFA of 0.55% (= 0.19 × -0.029) in the
following year, which is close to the average absolute value of LIEFA for the full sample (0.54%). Such
an increase in risk reduces book leverage by 0.21% (= 0.19 × -0.011, see column (5)) and market
leverage by 1.18% (= 0.19 × -0.062, see column (9)) on average, both of which are significant at the 1%
level.
Managers may be concerned not only about large increases in risk but also about high risk levels.
Supporting this view, we find that the risk level at the beginning of the year is significantly negatively
related to LIEFA and changes in leverage in the following year. The results in columns (1), (5), and (9)
indicate that a one standard deviation increase in the level of equity volatility (29%) leads a firm to
decrease LIEFA by 0.81% (= 0.29 × -0.028) and market [book] leverage by 1.77% (= 0.29 × -0.061)
[0.41% (= 0. 29 × -0.014)] in the subsequent year.
Columns (2) to (4), (6) to (8), and (10) to (12) provide the results for the alternative risk measures
we consider. Overall, the results confirm our intuition that pronounced increases in risk as well as high
risk levels lead firms to adopt external financing choices that serve to decrease leverage and that these
choices indeed result in lower leverage ratios.
Turning to the control variables, consistent with previous studies, we find that issue activity and
leverage changes are only weakly correlated and often go in opposite directions (Welch (2011)). In
addition, we find that, as pointed out by Chen and Zhao (2007) and Chang and Dasgupta (2009), changes
in the leverage ratios of firms with high or low leverage ratios do not match with their financing choices
unless they take extreme financing choices: for example, a firm with 10% leverage needs to issue at least
nine times more equity than debt in order to reduce its leverage ratio.
It should be also noted that the dependent variables used in our study (i.e., changes in future leverage)
are different from those in most previous studies (i.e., levels of current or future leverage ratios), and this 18
could lead to differences in results between the studies. For example, consistent with Hovakiminan, Opler
and Titman (2001), although we find that profitability is negatively associated with changes in book
leverage, it is positively associated with LIEFA. We also find that the change in the market to book ratio is
positively associated with changes in market leverage but negatively associated with LIEFA. In addition,
the coefficients on size are significantly negative for changes in book leverage but significantly positive
for both LIEFA and changes in market leverage. Although the coefficients on the control variables do not
always have consistent signs in explaining changes in book leverage, changes in market leverage, and
LIEFA, we find consistent results across different dependent variables: The coefficients on risk changes
are significantly negative for LIEFA and leverage changes, indicating that firms experiencing risk
increases tend to engage in fewer leverage-increasing financing activities in the following year.
In Table 6, we examine whether the relation between risk changes and leverage changes are
consistent across positive and negative risk changes. We replace the risk change variables used in Table 5
with the maximum (minimum) of risk change and zero for positive (negative) risk changes (i.e., positive
risk changes = max (risk change, 0) and negative risk changes = min (risk change, 0)). We use this
approach since firms with positive and negative risk changes may face different levels of difficulty in
raising capital; for example, while firms that experience a decrease in risk may find it relatively easy to
increase leverage by buying back shares or issuing debt, firms that experience an increase in risk may face
greater challenges in reducing leverage by issuing equity or buying back debt. However, the results in
Table 6 show that our key findings are generally consistent across positive vs. negative risk changes. With
respect to our main risk measure, EquityVol, columns (1), (5) and (9) document nearly identical regression
coefficients for positive and negative risk changes. The same pattern generally holds with respect to other
risk measures except that the result for negative risk changes based on O-score is the opposite of the
previous results for book leverage changes. Overall, these results rule out our concern that the results in
Table 5 are driven by an inherent asymmetry in firms’ ability to respond to positive vs. negative changes
in risk.
19
Due to adjustment costs, firms may not adjust their capital structure immediately after risk changes,
and thus it can take more than a year before they adjust their capital structures, as documented in Leary
and Roberts (2005). To address this issue, in Table 6, we also examine the relation between risk changes
in year t and external financing activities over year t+1 to year t+2 (t+3). Our results are indeed
consistent with the argument that the speed of firms’ capital structure adjustment is slow. We find that the
association between risk changes and future external financing (leverage decisions) becomes more
pronounced and consistent across alternative risk measures over longer horizons. To facilitate comparison
with our results in Table 5, consider a firm experiencing a one standard deviation increase in the change
of equity volatility: Over the next three years, this firm decreases LIEFA by 0.86% (= 0.19 × - 0.045). At
the same time, its book and market leverage ratios decrease by 0.63% (= 0.19 × - 0.033) and 2.01% (=
0.19 × - 0.106), respectively. Adjusted R-squared also increases and the results become more consistent
across four risk measures as we extend the time horizon to measure the external financing and leverage
changing activities.
3.4. Robustness Checks
In this subsection we examine whether our results are robust to controlling for potential endogeneity
problems using a residual risk measurement approach and the two-stage least squares (2SLS) method.
One concern with our results in the previous section is that the results may be driven by spurious
correlations between risk variables and other well-known determinants of optimal capital structure
discussed above. To address this concern, we first regress the risk variables on several determinants of
capital structure as follows:
titititititi
titititititi
FirmD YearDLdefB EBITDr CRdummyCRdef FDMBMBLTA =Risk
,,11,10,9,8,7
6,5,41,3,2,10,
εββββββββββββ
++++++
++++∆++ − , (2)
where Risk is one of four risk variables used in Table 4 (equity volatility (EquityVol), implied asset
volatility (AssetVol), Merton default risk (Merton), and adjusted O-score (O-Score)); MB is the market-to-
20
book asset ratio; FD is financial deficit; CRdef is credit rating deficit; CRdummy is an indicator for those
firms with available credit rating information; r is the one-year buy-and-hold stock return; EBITD is
profitability; LdefB is the book leverage deficit; YearD is a year indicator; and FirmD is a firm indicator.
See Appendix A and our discussion above for precise definitions of each variable.
We then use the residuals from the above panel regressions as the measures of firms’ residual risk
levels. Residual risk changes are subsequently measured as the changes in the residuals over two
consecutive years. This approach allows us to mitigate the concern that our previous risk variables simply
capture other determinants of firms’ capital structure.
The results are presented in Table 7. In the first row of Panel A, we report the results for the one-year
period following risk changes and in the first row of Panel B, we report the results for the three-year
period following risk changes. We find that the results are similar to those presented in Tables 5 and 6.
Thus, our results in the previous sections are unlikely to be driven by close correlations between our risk
measures and other control variables.
As an alternative way to address the endogeneity concern, we use a 2SLS method where we use the
industry median lagged risk level and risk change as the instrumental variables for lagged risk level and
risk change variables, respectively. In unreported tests, we verify that these instrument variables are
significantly positively related to firms’ lagged risk level and risk change variables, respectively, thus
satisfying the relevance requirement of instrumental variables. To the extent that individual firms’ capital
structure decisions are not directly influenced by the median risk lever or risk change in the industry, the
instrumental variables are also likely to satisfy the exclusion requirement.
When we use a one-year horizon (Panel A), although the results for LIEFA[t+1] are consistent with
those in the OLS regressions, the results for leverage changes in which risk is measured by implied asset
volatilities are inconsistent with those estimated from the OLS regressions (columns (6) and (10)).
However, when we extend the horizon to three years (Panel B), the results become more in line with
previous results even though we do not find any significant results for book leverage changes. Overall, the
21
results from the 2SLS regressions indicate that the negative association between risk change and LIEFA
remains significant, albeit the results become weakened for changes in leverages.
4. Pecking Order or Market Timing?
While the results thus far are generally consistent with the dynamic trade-off theory, in this section,
we further examine the relevance of the pecking order theory and the market timing theory in explaining
our results. According to the pecking order theory, firms prefer to issue debt rather than equity and
therefore would issue debt even after risk increases unless such increases in risk significantly constrain
their ability to borrow. Therefore, under the pecking order theory, we would expect financially
unconstrained firms to be more likely to engage in LIEFA after risk increases. To test this prediction, we
use a subset of sample firms that are not likely to be financially constrained. We use two measures to
identify firms that are less likely to be financially constrained, credit ratings and Hadlock and Pierce’s
(2010) financial constraints measures.19 In Table 8, we repeat our previous analyses using only firms with
investment-grade credit ratings (i.e., BBB- or higher) and those with below the median value of financial
constraints measured using the Hadlock and Pierce (2010) method.
The results show that the effects of a change in equity volatility on LIEFA and changes in market
leverage in the following year (Panel A) are consistent with those reported in Table 5. However, due to
increased standard errors, the effect on book leverage is no longer statistically significant. Admittedly, the
results are less clear for the other three risk measures. However, as in Table 6, we observe a much
stronger effect (both in terms of economic magnitude and statistical significance) when we extend the
observation window for the dependent variables from one to three years (Panel B), but the results are
again not robust across all risk measures.
19 Hadlock and Pierce (2010) use a size and age index (SA index) to measure financial constraints, which is calculated as -0.737 × size + 0.043 × size2 – 0.040 × age, where size is the log of inflation-adjusted book assets (capped at $4.5 billion) and age is the number of years (capped at thirty-seven years) the firm has been on Compustat.
22
Although the results using a subsample of financially less constrained firms are similar to those using
a subsample of firms with investment-grade credit ratings, they show stronger significance of the risk
change variables.
In summary, while the subsample analysis does not allow us to claim universal statistical
significance and some of the results regarding changes in book leverage are ambiguous, the results in
Table 8 appear more consistent with the predictions of the dynamic trade-off theory than the pecking
order theory. In particular, our results for LIEFA presented in columns (1) – (4) show that less financially
constrained firms tend to be less likely to make leverage-increasing security choices following risk
increases, which appears hard to reconcile with the pecking order theory.
Next, to further test the relevance of the market timing theory in explaining firms’ capital structure
decisions, we examine whether a firm’s market valuation (MB ratio) is indeed affected by its risk changes.
The evidence presented thus far is inconsistent with the market timing explanation as far as MBs decrease
as risk increases. Although the correlation results presented in Table 3 confirm this view, we conduct a
formal test to see whether MB actually increases as risk increases after controlling for several variables
that affect firm valuation.
The results are reported in Table 9. We regress the change in MB on several variables including i)
risk change (Risk Change), ii) risk level at the beginning of the year (Risklag), iii) MB at the beginning of
the year (MBlag), iv) size (LTA), v) profitability (EBITD), and vi) year and firm fixed effects. The results
show that risk changes are indeed significantly negatively related to contemporaneous changes in MB,
supporting the conjecture that risk increases lead to decreases in MBs. Therefore, our main results
showing that firms tend to engage less LIEFA following risk increases are inconsistent with the market
timing explanation.
Finally, we check whether the relations between risk changes and future LIEFA and between risk
changes and changes in leverage ratios differ between positive and negative FD groups (i.e., firms that
raise external capital and those that reduce external capital) and between risk increase and risk decrease
23
groups. As summarized in Table 1, the three capital structure theories we consider predict that firms
choose different types of securities to achieve their external financing goals depending on their need to
raise or reduce external capital following risk changes. The results are reported in Table 10. We find that
consistent with the dynamic trade-off theory, in the majority of categories, the significant coefficients are
negative.20
In sum, the results in Tables 8, 9, and 10 indicate that our main results of significant negative
relations between risk changes and LIEFA and between risk changes and changes in leverage ratios are
most consistent with the dynamic trade-off theory of capital structure rather than the two alternative
theories of capital structure.
5. Summary and Conclusion
Although there has been much debate over the importance of various capital structure theories in
explaining firms’ actual capital structure decisions, the evidence in the literature is not conclusive. In this
paper we focus on one of the most important factors that affect firms’ capital structure decisions, namely
risk, and examine how firms determine their capital structure in response to changes in risk. More
specifically, we use various measures of risk, including stock return volatility, default risk, implied asset
volatility, and an adjusted O-score, and study which theory of capital structure out of three alternatives
best explains firms’ external financing decisions in response to risk changes.
To the extent that firm risk fluctuates over time and risk affects optimal leverage ratios, focusing on
the relation between risk changes and future external financing activities allows us to obtain new insights
into the importance of various capital structure theories. Our approach also allows us to test the relevance
of capital structure theories without measuring adjustment costs since we focus on the group of firms that
20 However, there are a few cases where the results are more consistent with alternative theories. For example, the only significantly positive coefficient on the risk change variables in the regression of LIEFA [t+3] is found for firms with a negative FD in column (2), where risk is measured by implied asset volatilities. This result is more consistent with the market timing explanation.
24
have already undertaken external capital raising activities. In addition, our approach does not require
estimating a target leverage ratio since it utilizes the fact that, holding everything else constant, an
increase (decrease) in risk tends to lower (raise) the target leverage ratio.
Consistent with the prediction of the dynamic trade-off theory of capital structure, we find that firms
tend to issue equity (debt) following risk increases (decreases). These findings are robust to using a
variety of risk measures. Our results also hold when we limit our attention to the subsample of firms with
investment-grade credit ratings or the subsample of firms with fewer financial constraints in the analysis
for which the pecking order theory is more likely to be applied. Moreover, we find that an increase in a
firm’s risk is associated with a fall in its equity valuation as measured by the market-to-book ratio,
indicating that risk increases reduce the likelihood of the firm’s overvaluation. This result further suggests
that the dynamic trade-off theory explains a firm’s capital structure decisions in response to changing risk
levels better than the market timing theory. Finally, we examine whether our results hold regardless of
firms’ needs to raise or reduce external capital and the direction of changes in risk and find that the
relation between risk change and future financing activities is most consistent with the dynamic trade-off
theory.
Overall, our study shows that the dynamic trade-off theory best explains the evolution of capital
structures over time in relation to changes in risk, thus highlighting the importance of this theory in
explaining firms’ external financing and capital structure decisions over time.
25
Appendix A. Variable Definitions This appendix shows detailed descriptions of the construction of all the variables used in the tables.
Variable Definitions External financing and leverage measures
Leverage-increasing external financing activity (LIEFA [t+s])
Net debt issue minus net equity issue, divided by lagged total assets, over fiscal years from t+1 to t+s (s ≥ 1). The difference between net debt issue and net equity issue is calculated as: long-term debt issuance (DLTIS) - long-term debt reduction (DLTR) - sale of common and preferred stocks (SSTK) + purchase of common and preferred stocks (PRSTKC). LIEFA [t+2] and LIEFA [t+3] are calculated as the sum of LIEFAs over two and three years starting from year t+1, respectively.
Financial deficit (FD)
Annual financial deficit over total assets at the beginning of the fiscal year, where financial deficit is defined as: sale of common and preferred stocks (SSTK) – purchase of common and preferred stocks (PRSTKC) + long-term debt issuance (DLTIS) – long-term debt reduction (DLTR).
Market leverage (LevM)
Book value of debt divided by the market value of total assets. The market value of total assets is defined as total assets (AT) minus the book value of equity plus the market value of equity. The book value of debt is defined as: total assets minus the book value of equity (= total assets (AT) – total liabilities (LT) – liquidation value of preferred stock (PSTKL) or PSTKRV or PSTK if not available) + deferred taxes and investment credit (TXDITC) + convertible debt (DCVT)). The market value of equity is measured at the fiscal year-end.
Book leverage (LevB)
Book value of debt divided by total assets. The book value of debt is defined as above.
Leverage deficit (LdefB)
Difference between the target book leverage, TlevB, and the actual book leverage ratio, LevB (LdefBt=TlevBt –LevBt), where the target ratio is calculated using a Tobit regression as described in Appendix C.
Risk measures Equity volatility (EquityVol) Annualized standard deviations of 52 weekly stock returns in each fiscal year.
Firms with less than 12 weeks of stock return data during a fiscal year are excluded from the sample for the corresponding year.
Implied asset volatility (AssetVol)
Annualized standard deviations of daily changes in asset values calculated in the process of estimating the Merton (1974) default probabilities in each year.
Merton’s default risk (Merton)
Default probabilities on the basis of the Merton (1974) model. It is estimated by the methodology described in Vassalou and Xing (2004) in each fiscal year.
Ohlson’s score (O-Score)
Franzen, Rodgers, and Simin (2007)’s adjusted Ohlson scores calculated in each year.
Other control variables used in the main regressions Market-to-book asset ratio (MB)
Market-to-book asset ratio (MB) is defined as: total assets (AT) - book value of equity (= total assets (AT) – total liabilities (LT) – liquidation value of preferred stock (PSTKL) or PSTKRV or PSTK if not available) + deferred taxes and investment credit (TXDITC) + convertible debt (DCVT)) + market value of equity (CSHO × PRCC_F) / total assets (AT).
26
Stock returns (r) Buy-and-hold stock returns during a fiscal year. Credit rating deficit (CRdef)
Difference between the target credit rating and the actual credit rating, where the target credit rating is estimated using an ordered probit model as described in Appendix D. For those without credit rating information, the value is set to zero. Higher scores are assigned to higher credit ratings (the highest score is 19).
Credit rating dummy (CRdummy)
Dummy that is set to one when the credit rating information is available, and zero otherwise.
Profitability (EBITD)
Earnings before interest, tax, and depreciation (OIBDP) / total assets in year -1 (AT).
Other control variables used in the target leverage ratio and/or target credit rating regressions
Profitability (PROFIT) Earnings before interest, tax, and depreciation (OIBDP) over total assets (AT). R&D (RD)
Research and development expenditure (XRD) divided by sales (SALE). It is set to zero when missing.
R&D dummy (RDd)
Research and development dummy that is set to one when the R&D value (XRD) is missing.
Selling expense (SE)
Selling, general, and administration expenses (XSGA) divided by sales (SALE).
Firm size (Size)
Natural log of sales (SALE).
Asset tangibility (PPE)
Property, Plant, and Equipment (PPENT) divided by total assets (AT).
Operating risk (OCF Risk)
Annualized standard deviations of past 20 quarterly operating income before depreciation (OIBDPQ) as a percentage of total assets (quarterly ATQ) at the beginning of the quarter over the past five years.
Historical credit rating (HCR)
Average of credit ratings over the four-year period ending in year -1.
27
Appendix B. Measuring Risk This appendix describes three risk measures, Merton, AssetVol, and O-Score, used in the regression
analysis.
1. Default Risk (Merton) and Implied Asset Volatility (AssetVol)
The probability of default is estimated by the following equation:21
×−+−=
TTXV
NMertonA
AttAt σ
σµ )5.0()/(ln 2, , (A1)
where 𝑉𝑉𝐴𝐴,𝑡𝑡 is the value of total assets at time t and 𝑋𝑋𝑡𝑡 is the book value of debt defined as the sum of
long-term debt due in one year and 0.5 × long-term debt at time t. 𝜇𝜇 is the instantaneous growth rate of
𝑉𝑉𝐴𝐴, and 𝜎𝜎𝐴𝐴 is the instantaneous standard deviation of 𝑉𝑉𝐴𝐴. The time to maturity, T, is assumed to be one
year as in Vassalou and Xing (2004). Since we cannot observe the market value of total assets, estimation
of these parameter values is not straightforward. Thus, at the end of each year, we estimate σA using the
following iterative procedure.
First, we estimate the volatility of equity return, σE, using the daily stock returns over the past 12
months. This estimated σE is used as an initial estimate of σA. As Merton (1974) shows, the value of equity,
VE, can be represented as a call option written on the assets of a firm. Since the market value of equity, VE,
is observed from the stock market, using the Black-Scholes model together with the estimated 𝜎𝜎𝐴𝐴 and
other parameters, the implied value of total assets, 𝑉𝑉𝐴𝐴, can be estimated by identifying the 𝑉𝑉𝐴𝐴 that makes
the value of the call option equal to the market capitalization of the firm. We can estimate 𝑉𝑉𝐴𝐴 for each
trading day during the past 12 months. Based on these daily estimates of 𝑉𝑉𝐴𝐴, we can calculate 𝜎𝜎𝐴𝐴, which
will be used in the next iteration. This newly estimated 𝜎𝜎𝐴𝐴 replaces the initial σA estimate and we repeat
the above procedure. We repeat the iterations until the estimated 𝜎𝜎𝐴𝐴 converges to the σA used at the
beginning of the iteration, with the difference becoming less than 0.01%. If convergence does not occur
after 1,000 iterations, we drop the observation from the sample.
Using the estimated set of 𝑉𝑉𝐴𝐴s in the final iteration, we estimate the instantaneous growth rate, 𝜇𝜇, by
calculating the average change in ln (𝑉𝑉𝐴𝐴). Using these estimated parameter values, we next calculate the
default probability as specified in equation (A1). Simultaneously, we also determine the implied asset
volatility, AssetVol, as the volatility of estimated 𝑉𝑉𝐴𝐴s.
21 As discussed in Vassalou and Xing (2004), equation (A1) may not measure default probability in the strict sense because it does not correspond to the true probability of default in large samples, albeit it is a measure of the theoretical probability of default under the Merton (1974) model.
28
2. Adjusted Ohlson (1980) Score
Adjusted Ohlson (1980) scores are estimated based on Franzen, Rodgers, and Simin (2007) as
specified in equation (A2):
+−
×−×+
×−
×−×−
×+
×−
×+×−−−
−
−
1,,
1,,,
,
,
,
,,
,
,
,
,
,
,,,
____
521.02285.0_
83.1
__
37.2172.1076.0
_43.1
__
03.6)_(ln407.032.1
titi
tititi
ti
ti
ti
titi
ti
ti
ti
ti
ti
tititi
NIANIANIANIA
Dummy TLA
FFO
TAANIA
Dummy CACL
TAAWC
TAATLA
TAA=ScoreO
, (A2)
where TA, TL, WC, CL, CA, NI, and FFO stand for total assets, total liabilities, working capital, current
liabilities (LCT), current assets (ACO), net income (NI), and funds from operations (FOPT), respectively.
Dummy1 is an indicator that takes the value of one when total liabilities are greater than total assets, and
zero otherwise. Dummy2 is an indicator that takes the value of one when NIt < 0 for the last two years,
and zero otherwise.
Franzen, Rodgers, and Simin (2007) argue that to avoid misclassifying financially healthy R&D-
intensive firms as financially distressed firms, NI, TA, and TL should be adjusted as in equation (A3):
taxRDRDRDRDRDTL=TLARDRDRDRDRDTA=TAA
taxRDRDRDRDRDRDNI=NIA
titititittiti
titititittiti
titititititititi
××+×+×+×++
×+×+×+×++
−×++++×−+
−−−−
−−−−
−−−−−
)2.04.06.08.0(_)2.04.06.08.0(_
)1(](2.0[_
4,3,2,1,,,
4,3,2,1,,,
5,4,3,2,1,,,,
, (A3)
where RDt represents R&D expenditures and tax is the tax rate. The tax rates that are applied are 46%
(1980-1986), 40% (1987), 34% (1988-1992), and 35% (1993-2005). Our adjusted Ohlson (1980) scores
(O-score) are the adjusted O-scores estimated on the basis of equation (A2), where the higher the adjusted
O-score is, the higher the firm’s default risk is.
29
Appendix C. Target Leverage
1. Target leverage ratios
Target leverage ratios (Tlev) are measured using a similar method as in Kayhan and Titman (2007).
Specifically, as shown in equation (A4) below, for each firm we run a Tobit regression of the market
(book) leverage ratio, LevM(B), on lagged market to book total assets (MB), asset tangibility (PPE),
profitability (PROFIT), R&D expenses (RD), an R&D dummy (RDd), selling expenses (SE), sales (Size),
and year and industry dummies. The coefficient estimates from this regression are used to calculate fitted
values of market (book) leverage ratios, which are used as the estimates of target market (book) leverage
ratios, TlevM(B). More specifically, we estimate:
tititititi
titititititi
IndustryDYearDSizeSERDdRDPROFITPPEMB α=LevM(B)
,1,91,81,71,6
1,51,41,31,21,1,
εβββββββββ
+++++
+++++
−−−−
−−−−− , (A4)
where MB is calculated by dividing the market value of total assets by the book value of total assets (AT),
with the market value of total assets given as described above. PPE, which is used to control for asset
tangibility, is constructed by dividing net property, plants, and equipment (PPENT) by AT. As a measure
of profitability, PROFIT, we use earnings before interest, taxes, and depreciation (OIBDP) divided by AT,
while our measure of growth potential or investment opportunities, RD, is computed as the ratio of R&D
expenses (XRD) to sales (SALE). Since many firms do not report small R&D expenses, missing R&D
values are set to zero. To check for potential problems with this treatment, following prior capital
structure literature we use a dummy variable to indicate missing R&D values (RDd). Selling expenses (SE)
is selling, general, and administrative expenses (XSGA) divided by AT. To capture firm size, we use the
natural log of SALE (Size). Finally, we use industry (based on thirty industry classification definitions
available on Ken French’s website)22 and year dummy variables to control for industry effects and any
time-related co-variation in target leverage ratios, respectively.23
2. Tobit regression results
The results below show those from a Tobit regression of market (book) leverage ratio on various
firm characteristic variables. All variables are measured at the fiscal year end. The sample includes all
22 The results are robust to alternative definitions of industry dummy variables based on five-, ten-, or twelve-industry classification. 23 Note that the number of observations used in these regressions is greater than those used in other analyses due to fewer data requirements.
30
NYSE, Amex, and Nasdaq firms from 1971 to 2011 except for the firms with a negative book equity
value, a market-to-book asset ratio above 10, or total assets below $10 million. We also exclude utility
(SIC 6000-6999) and financial (SIC 4900-4949) companies since their capital structure decisions are
under regulatory constraints. Firms with book leverage ratios above 100% are also excluded from the
sample. A market leverage ratio is the book value of debt divided by the market value of total assets. A
book leverage ratio is the book value of debt divided by total assets. The market value of total assets is
defined as total assets minus the book value of equity plus the market value of equity. The book value of
debt is defined as total assets minus the book value of equity that is estimated as total assets minus the
sum of total liabilities and the liquidation (redemption or carrying, whichever is first available) value of
preferred stock plus deferred taxes, investment credit, and convertible debt. The variables used in the
regressions are defined in Appendix A. Market Leverage Book Leverage
Variable Coefficient S.E t-value Pr > |t| Coefficient S.E t-value Pr > |t|
Market to book ratio (MBt-1) -7.20*** 0.05 -133.62 0.00 -1.56*** 0.05 -28.93 0.00
Asset tangibility (PPE t-1) 0.06*** 0.00 17.78 0.00 0.05*** 0.00 17.19 0.00
Profitability (PROFIT t-1) -0.54*** 0.01 -104.49 0.00 -0.44*** 0.01 -85.02 0.00
Selling expense (SE t-1) -0.17*** 0.00 -44.96 0.00 -0.10*** 0.00 -25.75 0.00
R&D (RD t-1) -0.17*** 0.01 -22.80 0.00 -0.21*** 0.01 -27.63 0.00
R&D dummy (RDd t-1) 2.58*** 0.13 20.20 0.00 2.16*** 0.13 16.90 0.00
Firm size (Size t-1) 1.24*** 0.03 37.71 0.00 2.49*** 0.03 75.64 0.00
Intercept 60.71*** 0.36 167.34 0.00 39.90*** 0.36 109.73 0.00
Year and industry dummies Yes Yes
Log likelihood -528,695 -529,029
Number of observations 121,955 121,955
31
Appendix D. Target Credit Rating 1. Target credit rating
Target credit ratings are estimated using the following ordered probit regression in each year, as in
Hovakimian, Kayhan, and Titman (2009):
ttitititi
tititititititi
IndustryDHCRRiskOCFSizePROFITSERDdRDPPEMB α=ngCreditRati
εββββββββββ
+++++
++++++
,10,9,8,7
,6,5,4,3,2,1, , (A5)
where CreditRating is a numerical credit rating value based on the S&P long-term issuer rating
(SPLTCRM) available from Compustat24 and MB, PPE, RD, RDd, SE, PROFIT, SIZE and IndustryD are
defined as in Appendix A. OCF Risk, operating risk, is measured as the annualized standard deviation of
20 recent quarterly operating incomes before depreciation divided by total assets over the past five years.
HCR, historical credit rating, is measured as the average credit rating over the past four-year period
ending in year -1.
2. Results from the Ordered Probit regression used to estimate target credit rating in 2011
The results from an ordered probit regression of numerical credit rating values on various firm
characteristics to estimate target credit ratings are reported below. As in Hovakimian, Kayhan, and
Titman (2009), the target credit ratings are calculated using annual cross-sectional regressions to prevent
a look-ahead bias. The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for
the firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below
$10 million. We also exclude utility (SIC 6000-6999) and financial (SIC 4900-4949) companies since
their capital structure decisions are under regulatory constraints. Firms with book leverage ratios above
100% are also excluded from the sample. Only the results for 2011 are reported in this appendix but
results for other years are available upon request. The dependent variable is a numerical credit rating
value based on the S&P long-term issuer rating available from Compustat (SPLTCRM). All variables are
measured at the fiscal year end. The variables used in the regressions are defined in Appendix A.
Variables Coefficient S.E t-value Pr > |t|
Intercept -6.57*** 0.80 -8.17 0.000
Market to book ratio (MB) 0.25*** 0.09 2.79 0.005
24 The lowest rating (CCC-) is set to 1 and the highest rating (AAA) is set to 19. 32
Asset tangibility (PPE ) -0.21 0.26 -0.80 0.423
R&D (RD) 1.73 1.21 1.43 0.153
R&D dummy (RDd) 0.19 0.11 1.64 0.102
Selling expense (SE) -0.33 0.48 -0.70 0.486
Profitability (PROFIT) 3.92*** 0.87 4.52 0.000
Firm size (Size) 0.14*** 0.04 3.24 0.001
Operating risk (OCF Risk) -1.06 0.67 -1.57 0.116
Historical credit rating (HCR) 1.84*** 0.06 30.48 0.000
Industry dummy Yes Yes Yes Yes
Log likelihood -663.42
Number of observations 780
33
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37
Table 1 Predictions of Relation between Risk Change and Future Leverage-Increasing External
Financing Activity under Three Different Capital Structure Theories
This table presents predictions of the relation between risk changes and leverage-increasing external financing activities under the dynamic trade-off, pecking order, and market timing theories. The external financing activities are divided into two groups according to firms’ financial deficit (FD): positive FD and negative FD. Positive FD refers to the case when firms raise external capital, and negative FD refers to the case when firms reduce external capital. Columns (1) and (2) show the type of securities that firms are likely to choose to raise and reduce external capital when their risk increases and decreases, respectively, under each capital structure theory. For the pecking order theory, the predictions in parentheses are made under the presumption that due to asymmetric information, firms may issue overvalued equity or repurchase undervalued equity if the benefits obtained from exploiting misvaluation caused by risk changes are greater than the adverse selection costs.
External financing activities
Capital Structure Theories
Risk increase
(1)
Risk decrease
(2)
Relation between risk change and leverage-increasing activities
(3)
Positive FD
(Raise
external capital)
Dynamic trade-off Equity Debt -
Pecking order Debt Debt (or Equity) ? (or +)
Market timing Debt Equity +
Negative FD
(Reduce
external capital)
Dynamic trade-off Debt Equity -
Pecking order Debt (or Equity) Debt ? (or +)
Market timing Equity Debt +
38
Table 2 Summary Statistics
The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. Variables are defined in Appendix A. The market capitalization and total assets are in 2011 $US, adjusted for inflation using US seasonally-adjusted consumer price index – all urban consumers.
Variables Sample
size Mean S.D. Median 1% 99%
Total assets : $ million 82,723 2,071.3 6,918.4 245.4 10.7 101,212.7 Market cap.: $ million 82,723 2,038.9 7,863.0 175.8 2.2 134,954.4 Annual stock returns: % 82,723 18.20 64.04 7.63 -92.92 664.10 Profitability (EBITD): % 82,723 14.47 13.33 14.39 -68.11 60.10 Market leverage: % 82,723 38.82 23.43 36.38 1.56 95.11 Change in market leverage(dLevM[t+1]): % 81,763 0.84 11.32 0.35 -45.05 54.07 Book leverage: % 82,723 44.17 19.63 44.18 4.38 93.99 Change in book leverage(dLevB[t+1]): % 81,794 0.74 8.75 0.09 -33.03 42.55 Book leverage deficit (LdefB): % 82,723 1.39 17.25 2.33 -45.89 41.16 Leverage-increasing external financing activities (LIEFA[t+1]): % 82,723 0.54 14.36 -0.22 -110.00 91.85 Financial deficit (FD): % 82,723 4.40 18.14 0.00 -30.35 200.56 Market to book ratio (MB) 82,723 1.52 1.00 1.20 0.40 7.90 Credit rating deficits (CRdef) 82,723 -0.001 0.204 0.000 -2.000 1.000 Credit rating dummy (CRdummy) 82,723 0.154 0.361 0.000 0.000 1.000 Equity volatility (EquityVol): % 82,723 52.84 28.68 45.87 11.10 229.06 Merton asset volatility (AssetVol): % 82,486 49.52 29.88 41.23 9.68 199.53 Merton’s default risk (Merton): % 82,486 2.70 9.42 0.00 0.00 83.98 Ohlson’ score (O-score) 58,897 -1.617 2.023 -1.613 -8.181 4.594 Annual change in equity volatility (∆EquityVol): % 82,723 -0.10 19.00 -0.74 -103.50 111.63 Annual change in Merton asset volatility (∆AssetVol): % 81,661 -0.56 23.80 -0.69 -108.77 109.95 Annual change in Merton’s default risk (∆Merton): % 81,661 0.19 8.23 0.00 -56.89 70.15 Annual change in Ohlson’ score (∆O-score) 54,292 0.024 1.324 -0.010 -5.835 7.160
39
Table 3 Correlations among Risk Changes, Risk Levels, and Leverage-Related Variables
The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. Book leverage is the book value of debt divided by total assets, and market leverage is the book value of debt divided by the market value of total assets. The book value of debt is defined as total assets minus the book value of equity, which is estimated as total assets minus the sum of total liabilities and the liquidation value (redemption or carrying value, whichever is available first) of preferred stock plus deferred taxes, investment credits, and convertible debt. The market value of total assets is defined as total assets minus the book value of equity plus the market value of equity. Other variables are defined in Appendix A. P-values are in parentheses.
dLevM [t+1]
dLevB [t+1]
LIEFA [t+1]
∆Equity Vol
∆Asset Vol
∆Merton
∆O- Score
Equity Vol
Asset Vol Merton O-score FD MB r
Market leverage change in year t+1 (dLevM[t+1]) (%) 1.00 Book leverage change in year t+1 (dLevB[t+1]) (%) 0.59 1.00
(0.00)
Leverage-increasing activity in year t+1 (LIEFA[t+1]) (%) 0.30 0.39 1.00
(0.00) (0.00)
Change in equity volatility (∆ EquityVol) -0.08 -0.01 -0.04 1.00
(0.00) (0.02) (0.00)
Change in asset volatility (∆AssetVol) -0.03 0.00 -0.01 0.51 1.00
(0.00) (0.21) (0.02) (0.00)
Change in default risk (∆Merton) -0.04 0.01 -0.02 0.34 0.43 1.00
(0.00) (0.00) (0.00) (0.00) (0.00)
Change in O-score (∆O-score) -0.01 0.03 -0.02 0.11 0.02 0.07 1.00 (0.01) (0.00) (0.00) (0.00) (0.00) (0.00)
Equity volatility (EquityVol) -0.08 0.00 -0.15 0.36 0.20 0.15 0.00 1.00 (0.00) (0.68) (0.00) (0.00) (0.00) (0.00) (0.82)
Asset volatility (AssetVol) 0.00 0.03 -0.10 0.17 0.39 0.19 0.00 0.71 1.00 (0.50) (0.00) (0.00) (0.00) (0.00) (0.00) (0.57) (0.00)
Merton’s default risk (Merton) -0.12 -0.02 -0.06 0.20 0.22 0.52 0.01 0.41 0.31 1.00 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.03) (0.00) (0.00)
Ohlson’ score (O-score) -0.11 -0.07 -0.15 0.11 0.04 0.07 0.34 0.33 0.07 0.24 1.00 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Financial deficit (FD) 0.11 0.04 -0.06 -0.01 0.01 -0.01 0.08 0.07 0.11 -0.05 0.12 1.00 (0.00) (0.00) (0.00) (0.13) (0.00) (0.11) (0.00) (0.00) (0.00) (0.00) (0.00)
Market-to-book ratio (MB) 0.14 -0.02 -0.05 -0.07 -0.03 -0.04 -0.09 -0.02 0.08 -0.14 -0.31 0.17 1.00 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Stock return (r) 0.07 -0.08 -0.02 -0.19 -0.06 -0.22 -0.30 -0.02 0.00 -0.09 -0.14 0.10 0.30 1.00 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.19) (0.00) (0.00) (0.00) (0.00)
40
Table 4 Univariate Tests
The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; financial (SIC 6000-6999) and utility (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. Book leverage is the book value of debt divided by total assets, and market leverage is the book value of debt divided by the market value of total assets. The book value of debt is defined as total assets minus the book value of equity, which is estimated as total assets minus the sum of total liabilities and the liquidation value (redemption or carrying value, whichever is available first) of preferred stock plus deferred taxes, investment credits, and convertible debt. The market value of total assets is defined as total assets minus the book value of equity plus the market value of equity. Leverage-increasing external financing activity (LIEFA) is measured as the ratio of the difference between annual net debt issuance and annual net equity issuance (long-term debt issuance (DLTIS) - long-term debt reduction (DLTR) - sale of common and preferred stocks (SSTK) + purchase of common and preferred stocks (PRSTKC)) to total assets at the beginning of the fiscal year. Other variables are defined in Appendix A. In each fiscal year, sample firms are divided into three groups according to the annual change in each risk variable. Firms in top 20% and bottom 20% are classified as “High risk change” and “Low risk change” firms, respectively. LIEFA[t+3], Change in Book Lev[t+3], and Change in Market Lev[t+3] are calculated by summing up the annual values over three years from year t+1 to year t+3. In the High-Low column, ***, **, and * indicate that the difference of each variable between High and Low risk change firms is significantly different from zero at the 1%, 5%, and 10% levels, respectively.
Change in Risk Low Mid High High - Low
Equity Vol
Asset Vol Merton O-Score Equity
Vol Asset Vol Merton O-Score Equity
Vol Asset Vol Merton O-Score Equity
Vol Asset Vol Merton O-Score
# of observations 16,558 16,348 16,586 10,872 49,636 48,996 48,960 32,576 16,529 16,317 16,115 10,844 Change in Risk[t] -21.26 -28.45 -6.19 -1.71 -0.54 -0.67 0.01 0.01 22.39 27.74 7.32 1.82 43.66*** 56.19*** 13.50*** 3.53*** Change in MB[t] -0.03 -0.05 0.04 0.06 -0.05 -0.05 -0.09 -0.03 -0.19 -0.18 -0.14 -0.16 -0.16*** -0.13*** -0.18*** -0.22***
LIEFA[t+1] 0.10 -0.04 -0.22 0.19 1.17 0.97 1.31 1.65 -0.94 -0.15 -0.99 -0.40 -1.04*** -0.11 -0.77*** -0.59*** Change in Book Lev[t+1] 0.72 0.83 0.07 0.19 0.73 0.67 0.98 0.59 0.78 0.83 0.66 0.82 0.06 0.00 0.59*** 0.63***
Change in Market Lev [t+1] 1.31 1.10 0.14 0.56 0.92 0.72 1.45 0.54 0.13 0.81 -0.43 0.35 -1.19*** -0.29** -0.58*** -0.21 LIEFA[t+3] 0.41 0.15 0.16 2.50 3.56 3.17 3.79 4.92 -1.75 -0.08 -2.29 -1.04 -2.16*** -0.23 -2.45*** -3.54***
Change in Book Lev[t+3] 1.17 1.24 -0.26 1.14 1.57 1.37 2.24 1.31 0.55 1.14 -0.19 0.43 -0.62*** -0.10 0.06 -0.71*** Change in Market Lev [t+3] 1.62 1.35 -0.70 1.31 1.37 0.94 2.74 0.81 -0.84 0.66 -3.19 -1.43 -2.46*** -0.68*** -2.49*** -2.73***
41
Table 5 Panel Regressions of LIEFA and Leverage Changes in Year t+1 on Changes in Risk
This table reports the results of panel regressions of leverage-increasing external financing activities (LIEFA) and changes in book and market leverage ratios in year t+1 on the changes in risk (Risk Change) during year t, the level of risk at the beginning of year t (Risklag), and other control variables. The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. LIEFA is measured as the ratio of the difference between annual net debt issuance and annual net equity issuance (long-term debt issuance (DLTIS) - long-term debt reduction (DLTR) - sale of common and preferred stocks (SSTK) + purchase of common and preferred stocks (PRSTKC)) to total assets at the beginning of the fiscal year. We estimate Risk Change using four different risk measures: EquityVol, AssetVol, Merton, and O-Score. Other variables are defined in Appendix A. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% levels, respectively. T-statistics based on clustered standard errors at the firm level are reported in parentheses.
LIEFA[t+1] Change in Book Leverage[t+1] Change in Market Leverage[t+1]
EquityVol (1)
AssetVol (2)
Merton (3)
O-Score (4)
EquityVol (5)
AssetVol (6)
Merton (7)
O-Score (8)
EquityVol (9)
AssetVol (10)
Merton (11)
O-Score (12)
Change in risk measure (Risk Change) -0.029*** 0.003 -0.058*** -0.871*** -0.011*** -0.007*** -0.000 0.018 -0.062*** -0.011*** -0.115*** -0.087 (-7.37) (1.16) (-7.47) (-9.39) (-4.38) (-3.74) (-0.04) (0.30) (-19.46) (-5.09) (-15.35) (-1.23)
Level of risk at the beginning of the fiscal year (Risklag)
-0.028*** 0.004 -0.071*** -1.555*** -0.014*** -0.009*** -0.002 -0.340*** -0.061*** -0.008*** -0.154*** -0.691*** (-6.60) (1.35) (-6.92) (-13.77) (-5.20) (-4.18) (-0.30) (-4.67) (-18.55) (-3.37) (-17.62) (-8.72)
Log (Total assets) (LTA) 0.645*** 0.821*** 0.781*** -0.248 -0.611*** -0.590*** -0.547*** -0.667*** 1.035*** 1.354*** 1.353*** 1.073*** (4.12) (5.22) (4.99) (-1.34) (-6.24) (-6.11) (-5.70) (-5.34) (9.90) (12.88) (13.10) (7.73)
Change in market to book ratio (MB Change)
-1.032*** -0.935*** -0.962*** -0.459** -0.144* -0.133 -0.120 -0.054 1.499*** 1.651*** 1.615*** 1.539*** (-6.26) (-5.61) (-5.75) (-2.11) (-1.76) (-1.61) (-1.46) (-0.50) (15.88) (17.45) (17.36) (11.02)
Market to book ratio at the beginning of the fiscal year (MBlag)
-0.354** -0.301** -0.335** 0.019 0.116* 0.130* 0.130* 0.187** 2.164*** 2.253*** 2.176*** 2.224*** (-2.49) (-2.10) (-2.34) (0.10) (1.65) (1.83) (1.83) (1.98) (25.20) (25.71) (25.28) (18.04)
Financial deficit (FD) -0.019*** -0.019*** -0.020*** -0.038*** 0.023*** 0.024*** 0.023*** 0.018*** 0.031*** 0.032*** 0.028*** 0.030*** (-3.76) (-3.58) (-3.88) (-5.47) (9.39) (9.44) (9.19) (5.46) (10.52) (10.85) (9.31) (7.23)
Credit rating deficit (CRdef) 0.648*** 0.704*** 0.622*** 0.600*** -0.283** -0.281** -0.277** -0.103 0.394** 0.524*** 0.368** 0.547*** (3.26) (3.53) (3.11) (2.82) (-2.07) (-2.04) (-2.01) (-0.68) (2.35) (3.12) (2.19) (2.95)
Credit rating dummy (CRdummy) -1.608*** -1.560*** -1.563*** -0.394 1.200*** 1.191*** 1.194*** 1.108*** 0.413** 0.402** 0.409** 0.485** (-5.64) (-5.39) (-5.43) (-1.29) (6.48) (6.40) (6.40) (5.24) (2.18) (2.10) (2.15) (2.13)
Stock returns (r) -0.361** -0.481*** -0.481*** -0.331* -0.970*** -1.022*** -1.035*** -0.830*** 1.402*** 1.201*** 1.200*** 1.673*** (-2.57) (-3.43) (-3.36) (-1.91) (-11.98) (-12.63) (-12.65) (-8.08) (14.00) (12.18) (12.19) (12.31)
Profitability (EBITD) 0.108*** 0.116*** 0.112*** 0.012 -0.047*** -0.043*** -0.042*** -0.070*** -0.008 0.010* 0.004 -0.027*** (12.82) (13.76) (13.38) (0.89) (-9.69) (-8.78) (-8.68) (-8.81) (-1.42) (1.88) (0.76) (-3.01)
Book leverage deficit (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿) 0.190*** 0.195*** 0.190*** 0.106*** 0.280*** 0.283*** 0.283*** 0.258*** 0.208*** 0.219*** 0.207*** 0.187*** (29.62) (30.27) (29.32) (10.32) (65.32) (66.14) (65.52) (37.99) (47.74) (50.42) (47.07) (25.44)
Intercept -3.249*** -5.997*** -5.297*** -1.319 5.098*** 4.570*** 3.889*** 3.652*** 4.936*** 0.292 0.442 -1.528* (-3.54) (-6.73) (-6.12) (-1.24) (8.67) (8.15) (7.23) (5.14) (7.21) (0.43) (0.68) (-1.75)
Year & firm dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Adjusted R2 0.0542 0.0531 0.0541 0.0654 0.151 0.151 0.151 0.150 0.236 0.227 0.233 0.237 # of obs. 82,723 81,661 81,661 54,292 81,794 80,748 80,748 53,646 81,763 80,720 80,720 53,631
42
Table 6 Coefficients on Risk Change Variables from the Panel Regressions of Future Leverage-Increasing External Financing
Activities (LIEFA) and Change in Leverage Ratios following Changes in Risk during Year t This table reports the coefficient estimates of risk changes from the panel regressions of leverage-increasing external financing activities (LIEFA) and changes in book and market leverage ratios on the change in risk (Risk Change) during year t, the level of risk at the beginning of year t (Risklag), and other control variables. The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. LIEFA is measured as the ratio of the difference between annual net debt issuance and annual net equity issuance (long-term debt issuance (DLTIS) - long-term debt reduction (DLTR) - sale of common and preferred stocks (SSTK) + purchase of common and preferred stocks (PRSTKC)) to total assets at the beginning of the fiscal year. Other variables are defined in Appendix A. In the “Positive (Negative) risk change” row, risk change is defined as the maximum (minimum) of risk change and zero (i.e., positive risk changes = max (risk change, 0) and negative risk changes = min (risk change, 0)). In the last two rows, In the last two rows, LIEFA, Change in Book Leverage, and Change in Market Leverage are calculated by summing up the annual values over two and three years starting from year t+1, respectively. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% levels, respectively. T-statistics based on clustered standard errors at the firm level are reported in parentheses.
LIEFA[t+s] Change in Book Leverage[t+s] Change in Market Leverage[t+s]
EquityVol (1)
AssetVol (2)
Merton (3)
O-Score (4)
EquityVol (5)
AssetVol (6)
Merton (7)
O-Score (8)
EquityVol (9)
AssetVol (10)
Merton (11)
O-Score (12)
Positive risk change and s = 1
Coefficient -0.030*** 0.001 -0.065*** -0.366*** -0.010*** -0.004** 0.003 -0.107* -0.072*** -0.013*** -0.119*** -0.130** (-5.90) (0.23) (-8.39) (-3.34) (-3.18) (-2.16) (0.58) (-1.94) (-16.63) (-5.27) (-15.40) (-2.25)
Adjusted R2 0.054 0.053 0.054 0.063 0.151 0.151 0.151 0.150 0.235 0.227 0.233 0.237 # of obs. 82,723 81,661 81,661 54,292 81,794 80,748 80,748 53,646 81,763 80,720 80,720 53,631
Negative risk change and s = 1
Coefficient -0.030*** 0.004 -0.016 -0.525*** -0.010** -0.009*** 0.000 0.190** -0.060*** -0.009*** -0.053*** 0.030 (-4.44) (0.93) (-1.22) (-3.85) (-2.34) (-3.60) (0.03) (2.37) (-11.80) (-2.87) (-4.35) (0.35)
Adjusted R2 0.054 0.053 0.053 0.064 0.151 0.151 0.151 0.150 0.232 0.227 0.230 0.237 # of obs. 82,723 81,839 81,839 54,292 81,794 80,921 80,921 53,646 81,763 80,892 80,892 53,631
All risk changes and s = 2
Coefficient -0.045*** 0.004 -0.087*** -1.694*** -0.025*** -0.012*** -0.022*** -0.095 -0.088*** -0.015*** -0.182*** -0.429*** (-6.77) (0.99) (-6.48) (-9.89) (-6.94) (-4.82) (-3.00) (-1.07) (-20.15) (-5.09) (-18.09) (-4.20)
Adjusted R2 0.0803 0.0790 0.0802 0.104 0.246 0.245 0.245 0.245 0.300 0.290 0.299 0.300 # of obs. 70,933 70,012 70,012 46,882 72,760 71,811 71,811 47,999 72,695 71,749 71,749 47,969
All risk changes and s = 3
Coefficient -0.045*** 0.007 -0.104*** -2.164*** -0.033*** -0.012*** -0.037*** -0.034 -0.106*** -0.012*** -0.219*** -0.445*** (-4.89) (1.23) (-5.78) (-8.60) (-7.93) (-4.33) (-4.28) (-0.31) (-19.95) (-3.45) (-18.20) (-3.51)
Adjusted R2 0.0952 0.0943 0.0952 0.122 0.307 0.306 0.306 0.303 0.319 0.308 0.320 0.315 # of obs. 60,884 60,087 60,087 40,490 64,657 63,801 63,801 42,851 64,565 63,718 63,718 42,811
43
Table 7 Tests of Endogeneity: Coefficients on Risk Change Variables
This table reports the coefficient estimates of risk changes from the tests that control for the endogeneity of risk variables. In the “Residual” rows, the residuals from the panel regressions of risk variables on several determinants of capital structure (equation (2) in the text) are used as the measures of firms’ risk. Risk changes are measured as the changes in the residuals. In the “2SLS” rows, two-stage least square methods are used to control for the endogeneity of risk change and lagged risk levels where the industry median risk change and lagged risk level are used as the instrument variables for risk change and lagged risk levels, respectively. Industry is defined based on the two-digit SIC codes. The dependent variables are leverage-increasing external financing activities (LIEFA) and changes in book and market leverage ratios. The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. The variables are defined in Appendix A. LIEFA[t+3], Change in Book Leverage[t+3], and Change in Market Leverage[t+3] are calculated by summing up the annual values over three years from year t+1 to year t+3. In the “Residual” rows, t-statistics based on clustered standard errors at the firm level are reported in parentheses. In the “2SLS” rows, p-values for the endogeneity test are those from the Hausman Chi-Square test for endogeneity. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% levels, respectively.
LIEFA[t+s] Change in Book Leverage[t+s] Change in Market Leverage[t+s]
EquityVol (1)
AssetVol (2)
Merton (3)
O-Score (4)
EquityVol (5)
AssetVol (6)
Merton (7)
O-Score (8)
EquityVol (9)
AssetVol (10)
Merton (11)
O-Score (12)
Panel A: When s =1
Residual Coefficient -0.030*** 0.003 -0.067*** -0.756*** -0.016*** -0.008*** -0.011* -0.175*** -0.065*** -0.012*** -0.130*** -0.309***
(-7.59) (1.19) (-8.28) (-8.08) (-6.17) (-4.38) (-1.94) (-3.08) (-19.86) (-5.39) (-16.79) (-4.59) Adjusted R2 0.054 0.053 0.054 0.066 0.152 0.151 0.151 0.152 0.228 0.219 0.227 0.232 # of obs. 75,277 74,724 74,724 50,130 74,455 73,913 73,913 49,553 74,430 73,890 73,890 49,539
2 SLS
Coefficient -0.08*** -0.00 -0.16*** -1.55** 0.00 0.02* -0.00 0.25 -0.02 0.04*** -0.02 -0.09 (-4.86) (-0.21) (-2.64) (-2.03) (0.44) (1.74) (-0.02) (0.50) (-1.56) (3.76) (-0.55) (-0.14)
Adjusted R2 0.058 0.059 0.051 0.047 0.076 0.074 0.070 0.066 0.182 0.172 0.178 0.160 # of obs. 82,723 81,661 81,661 54,292 81,794 80,748 80,748 53,646 81,763 80,720 80,720 53,631 Endogeneity test (p-value) 0.000 0.019 0.005 0.137 0.333 0.102 0.056 0.005 0.106 0.000 0.142 0.000
Panel B: When s = 3
Residual Coefficient -0.047*** 0.006 -0.120*** -1.720*** -0.042*** -0.022*** -0.055*** -0.545*** -0.112*** -0.010*** -0.246*** -0.988***
(-5.08) (1.07) (-6.52) (-9.51) (-9.65) (-4.91) (-6.03) (-6.59) (-21.00) (-2.79) (-19.68) (-10.19) Adjusted R2 0.0982 0.0972 0.0985 0.124 0.309 0.307 0.307 0.307 0.313 0.300 0.314 0.313 # of obs. 55,551 55,166 55,166 37,462 58,826 58,409 58,409 39,545 58,747 58,333 58,333 39,507
2 SLS
Coefficient -0.24*** -0.11*** -0.11*** -4.12** -0.02 0.01 -0.03 -0.55 -0.06*** 0.03 -0.13* -2.11** (-6.55) (-3.29) (-3.29) (-2.51) (-0.90) (0.41) (-0.47) (-0.66) (-2.71) (1.29) (-1.69) (-2.09)
Adjusted R2 0.101 0.103 0.100 0.098 0.144 0.143 0.147 0.137 0.207 0.203 0.210 0.182 # of obs. 60,884 60,087 60,087 40,490 64,657 63,801 63,801 42,851 64,565 63,718 63,718 42,811 Endogeneity test (p-value) 0.000 0.000 0.011 0.103 0.002 0.017 0.807 0.570 0.265 0.061 0.737 0.046
44
Table 8 Subsample Analyses of Firms with Investment-Grade Credit Ratings and Firms with Fewer Financial Constrains
This table reports the coefficient estimates of risk changes from the panel regressions of leverage-increasing external financing activities (LIEFA) and changes in book and market leverage ratios on the change in risk measures (Risk Change) during year t, the level of risk at the beginning of year t (Risklag), and other control variables using only firms with investment-grade credit ratings (BBB- or higher) and those with fewer financial constraints (those with below the sample median of financial constraints measured by the method used in Hadlock and Pierce (2010)). The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. LIEFA is measured as the ratio of the difference between annual net debt issuance and annual net equity issuance (long-term debt issuance (DLTIS) - long-term debt reduction (DLTR) - sale of common and preferred stocks (SSTK) + purchase of common and preferred stocks (PRSTKC)) to total assets at the beginning of the fiscal year. Other variables are defined in Appendix A. In Panel B, LIEFA[t+3], Change in Book Leverage[t+3], and Change in Market Leverage[t+3] are calculated by summing up the annual values over three years from year t+1 to year t+3. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% levels, respectively. T-statistics based on clustered standard errors at the firm level are reported in parentheses. Firms with low financial constraints are those firms with financial constraints below the industry median, where financial constraints are measured following Hadlock and Pierce (2010).
LIEFA[t+s] Change in Book Leverage[t+s] Change in Market Leverage[t+s]
EquityVol (1)
AssetVol (2)
Merton (3)
O-Score (4)
EquityVol (5)
AssetVol (6)
Merton (7)
O-Score (8)
EquityVol (9)
AssetVol (10)
Merton (11)
O-Score (12)
Panel A: When s = 1
Investment Grade Firms (BBB- or higher)
Coefficient -0.047** -0.010 0.019 -2.033*** -0.014 0.008 0.037** -0.231 -0.088*** -0.002 0.008 -0.470* (-2.22) (-1.08) (1.02) (-6.63) (-1.14) (1.27) (2.41) (-1.07) (-5.13) (-0.34) (0.36) (-1.90)
Adjusted R2 0.123 0.120 0.120 0.147 0.198 0.199 0.200 0.198 0.261 0.254 0.254 0.257 # of obs. 6,879 6,833 6,833 5,810 6,769 6,724 6,724 5,712 6,766 6,721 6,721 5,711
Firms with Low Financial Constraints
Coefficient -0.052*** -0.000 -0.053*** -0.824*** -0.015*** -0.005** 0.010 0.210** -0.075*** -0.004 -0.083*** -0.100 (-7.62) (-0.06) (-5.03) (-6.19) (-3.38) (-2.00) (1.35) (2.37) (-13.02) (-1.36) (-7.57) (-0.97)
Adjusted R2 0.0678 0.0661 0.0674 0.0816 0.141 0.141 0.141 0.146 0.232 0.221 0.225 0.227 # of obs. 34,140 33,781 33,781 26,766 33,671 33,317 33,317 26,400 33,660 33,306 33,306 26,393
Panel B: When s = 3
Investment Grade Firms (BBB- or higher)
Coefficient -0.107** -0.041** -0.003 -2.914*** -0.065*** -0.007 0.043 0.122 -0.160*** -0.014 0.005 -0.889** (-2.55) (-2.25) (-0.07) (-3.93) (-3.39) (-0.60) (1.64) (0.31) (-6.06) (-1.32) (0.14) (-2.00)
Adjusted R2 0.219 0.219 0.218 0.253 0.366 0.364 0.364 0.363 0.345 0.334 0.333 0.336 # of obs. 5,360 5,326 5,326 4,531 5,538 5,498 5,498 4,651 5,530 5,490 5,490 4,647
Firms with Low Financial Constraints
Coefficient -0.078*** -0.001 -0.124*** -2.384*** -0.041*** -0.010** -0.021 0.335** -0.075*** -0.004 -0.083*** -0.100 (-5.04) (-0.18) (-5.26) (-6.85) (-5.41) (-2.49) (-1.54) (2.12) (-13.02) (-1.36) (-7.57) (-0.97)
Adjusted R2 0.130 0.128 0.130 0.156 0.304 0.303 0.303 0.309 0.232 0.221 0.225 0.227 # of obs. 25,553 25,277 25,277 19,895 27,065 26,765 26,765 21,074 27,036 26,740 26,740 21,055
45
Table 9 Relation between Contemporaneous Changes in Market-to-Book Ratio
and Risk Changes This table reports the results of panel regressions of contemporaneous changes in market-to-book ratio on changes in risk and other control variables. The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. The variables are defined in Appendix A. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% levels, respectively. T-statistics based on clustered standard errors at the firm level are reported in parentheses.
EquityVol (1)
AssetVol (2)
Merton (3)
O-Score (4)
Change in risk measure (Risk Change) -0.002*** -0.001*** -0.003*** -0.018*** (-9.95) (-6.58) (-9.61) (-4.09)
Level of risk at the beginning of the fiscal year (Risklag)
-0.002*** -0.001*** -0.003*** 0.000 (-7.22) (-3.76) (-7.61) (0.05)
Market to book ratio at the beginning of the fiscal year (MBlag)
-0.722*** -0.721*** -0.723*** -0.664*** (-40.62) (-39.76) (-40.01) (-19.87)
Log (Total assets) (LTA) -0.160*** -0.154*** -0.151*** -0.121*** (-17.72) (-17.23) (-17.02) (-12.11)
Profitability (EBITD) 0.020*** 0.020*** 0.020*** 0.019*** (27.16) (27.77) (27.65) (15.58)
Intercept 1.783*** 1.755*** 1.712*** 1.409*** (27.03) (28.65) (28.09) (18.93)
Year & firm dummies Yes Yes Yes Yes Adjusted R-square 0.588 0.585 0.585 0.509
Number of observations 82,723 81,661 81,661 54,292
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Table 10 Coefficients on Risk Changes Estimated from Regressing Leverage-Increasing Financing Activities (LIEFA) and Changes in
Leverage Ratios on Changes in Risk and Other Variables: Subsample Analyses This table reports the coefficient estimates of risk changes from the panel regressions of leverage-increasing external financing activities (LIEFA) and changes in book and market leverage ratios on the changes in risk (Risk Change) during year t, the level of risk at the beginning of year t (Risklag), and other control variables. The regressions are separately estimated according to whether a firm’s FD in year t+1 is positive or negative and whether its risk change is positive or negative. Positive (negative) risk change is defined as the maximum (minimum) of risk change and zero (i.e., positive risk changes = max (risk change, 0) and negative risk changes = min (risk change, 0)). The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. LIEFA is measured as the ratio of the difference between annual net debt issuance and annual net equity issuance (long-term debt issuance (DLTIS) - long-term debt reduction (DLTR) - sale of common and preferred stocks (SSTK) + purchase of common and preferred stocks (PRSTKC)) to total assets at the beginning of the fiscal year. Other variables are defined in Appendix A. In Panel B, LIEFA[t+3], Change in Book Leverage[t+3], and Change in Market Leverage[t+3] are calculated by summing up the annual values over three years from year t+1 to year t+3. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% levels, respectively. T-statistics based on clustered standard errors at the firm level are reported in parentheses.
LIEFA[t+s] Change in Book Leverage[t+s] Change in Market Leverage[t+s]
EquityVol (1)
AssetVol (2)
Merton (3)
O-Score (4)
EquityVol (5)
AssetVol (6)
Merton (7)
O-Score (8)
EquityVol (9)
AssetVol (10)
Merton (11)
O-Score (12)
Panel A: When s = 1
Positive FD[t+1] Positive risk change -0.016 0.006 -0.041** -0.262* -0.003 0.001 -0.009 0.021 -0.068*** -0.007 -0.129*** -0.154
(-1.24) (0.94) (-2.04) (-1.67) (-0.29) (0.26) (-0.71) (0.19) (-7.09) (-1.34) (-8.06) (-1.33)
Negative risk change -0.067*** -0.021** -0.017 -0.725** -0.017* -0.010* -0.022 0.454** -0.052*** -0.006 -0.039 0.139 (-3.39) (-1.97) (-0.47) (-2.09) (-1.70) (-1.76) (-1.18) (2.20) (-4.59) (-0.83) (-1.32) (0.75)
Negative FD[t+1] Positive risk change -0.009** -0.002 -0.018** -0.564*** -0.004 0.001 -0.008 -0.513*** -0.057*** -0.007 -0.112*** -0.526***
(-2.05) (-0.74) (-2.19) (-4.61) (-0.66) (0.41) (-0.95) (-3.96) (-6.43) (-1.53) (-9.23) (-3.26)
Negative risk change -0.005 0.006 0.020 -1.066*** -0.014 -0.018*** 0.016 0.072 -0.035*** -0.010* -0.025 0.108 (-0.72) (1.61) (1.36) (-6.76) (-1.64) (-4.08) (1.03) (0.56) (-3.28) (-1.70) (-1.27) (0.66)
Panel B: When s = 3
Positive FD[t+3] Positive risk change -0.039* 0.003 -0.105*** -0.550 -0.030*** -0.006 -0.043*** -0.044 -0.105*** -0.008 -0.206*** -0.254
(-1.66) (0.24) (-3.03) (-1.41) (-3.68) (-1.43) (-3.08) (-0.39) (-9.33) (-1.44) (-10.87) (-1.27)
Negative risk change -0.057* 0.013 0.029 -2.469*** -0.014 0.001 0.005 -0.114 -0.058*** 0.025*** -0.064** -0.281 (-1.84) (0.56) (0.57) (-4.64) (-1.14) (0.15) (0.24) (-0.56) (-3.72) (2.87) (-2.17) (-1.38)
Negative FD[t+3] Positive risk change -0.006 0.005 -0.043** -2.014*** -0.026** -0.006 -0.029 -0.880*** -0.112*** -0.019** -0.189*** -1.325***
(-0.43) (0.64) (-2.14) (-5.75) (-2.36) (-0.85) (-1.44) (-3.47) (-6.43) (-2.19) (-7.33) (-4.19)
Negative risk change -0.029 0.020** -0.036 -1.926*** -0.023 -0.004 -0.049 -0.216 -0.104*** -0.006 -0.132*** -0.619** (-1.42) (2.08) (-0.88) (-4.17) (-1.45) (-0.51) (-1.39) (-0.82) (-5.08) (-0.62) (-2.60) (-2.03)
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Figure 1. Average Leverage-Increasing Financing Activities (LIEFA) and Changes in Leverage Across Risk Change Deciles. This figure shows the average leverage-increasing external financing activities (LIEFA) and changes in leverage ratios across decile portfolios formed on the basis of changes in firm risk each year. The risk measures used in the analysis are discussed in Appendix A. The sample includes all NYSE, Amex, and Nasdaq firms from 1972 to 2011 except for firms with a negative book equity value, a market-to-book asset ratio above 10, or total assets below $10 million; utility (SIC 6000-6999) and financial (SIC 4900-4949) firms; and firms with a book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles in each year and measured at the fiscal year-end. Change in Book Lev[t+3], and Change in Market Lev[t+3] are calculated by summing up the annual values over three years from year t+1 to year t+3.
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