Risk Changes and External Financing Activities: Tests of the ......other capital structure theories...
Transcript of Risk Changes and External Financing Activities: Tests of the ......other capital structure theories...
Risk Changes and External Financing Activities: Tests of 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)
Sung Won Seo Ajou University
February 2017
* Phone numbers are +82-2-958-3415 (Dierker), +65-6790-5662 (Kang), +82-2-958-3441 (Lee), and +82-31-219-3688 (Seo). We are grateful for valuable comments from Tim Loughran, Sheridan Titman, and seminar participants at KAIST, the 2012 Allied Korean Finance Association Meetings, and the 2013 Annual Conference on Asia-Pacific Financial Markets. We also thank Byoung Hyun Jeon for his excellent research assistance. All errors are our own.
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Risk Changes and External Financing Activities: Tests of 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 financing activities 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 for subsamples of financially unconstrained firms and are robust to a variety of risk measures including stock return volatility, default probability, implied asset volatility, and adjusted Ohlson (1980) scores. Keywords: Capital structure theory, Dynamic trade-off, Pecking-order, Market timing, Risk change, External financing activities JEL Classification: G32, G33, G35
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I. Introduction
There has been much debate about the relative importance and relevance of various capital
structure theories such as theories 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)). In particular, in
response to the debate on the relevance of the static trade-off theory,1 academics have turned to
dynamic versions of the trade-off theory. Fischer, Heinkel, and Zechner (1989), for instance,
show that when capital structure adjustments are costly, firms take recapitalization actions only
when the benefits of recapitalization outweigh its costs.2 As emphasized by several studies, such
adjustment costs are nontrivial and can impose a serious challenge in testing the dynamic trade-
off theory of capital structure due to numerous assumptions required in the measurement of
adjustment costs.3
In this study, we evaluate the importance of the dynamic trade-off theory relative to two
other capital structure theories (pecking order and market timing theories) by examining firms’
external financing decisions following changes in one of the key determinants of the trade-off
theory, risk. In spite of strong evidence on significant changes in firm risk over time (e.g.,
1 For example, Myers (1993) and Graham (2000) point out that a negative correlation between 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. 2 In the absence of adjustment costs, the trade-off theory suggests a positive relation between profitability and leverage ratios, as profitable firms are more likely to utilize bigger debt tax shields. However, firms facing high adjustment costs may find it optimal to remain inactive in the external financial market. Hennessy and Whited (2005) and Strebulaev (2007) demonstrate that adjustment costs in a dynamic trade-off theory can explain the observed negative relation between market leverage ratios and profitability and other empirical challenges. Welch (2004), however, argues that stock returns, not target leverage, drive capital structures. Leary and Roberts (2005) find evidence on the importance of adjustment costs but 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. 3 For example, while Strebulaev (2007) calibrates a multitude of parameters to generate meaningful cross-sectional variation, he still assumes that certain parameters are equal for all firms. As an example, he assumes that the present values of net payouts and book assets are scaled to an identical value for all firms at the initial date.
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Campbell et al. (2001), Ang et al. (2006), Adrian and Rosenberg (2008)) and the theoretical link
between risk changes and capital structure, empirical evidence on the effects of risk changes on a
firm’s capital structure decision is scarce.4 We fill this gap in the literature by using a firm’s
external financing activities as a setting for our study.
Focusing on external financing activities has several advantages. First, as we discuss later, it
allows us to test the importance and relevance of the three capital structure theories we consider
in our study because they yield quite different predictions about the optimal financing method
when firms enter external capital markets following risk changes. Second, it allows us to
examine the dynamic trade-off theory of capital structure without measuring adjustment costs
since firms that engage in external financing activities have already incurred adjustment costs.
This avoidance of adjustment cost measurement greatly reduces the challenge in testing the
dynamic trade-off theory of capital structure that previous studies have faced. Third, unlike many
prior studies that examine leverage decisions over time, our approach does not require the
estimation of a target leverage ratio, which is hard to define and difficult to measure. Instead of
estimating target leverage ratios, our approach utilizes the fact that, according to the dynamic
trade-off theory, an increase (decrease) in firm risk lowers (raises) its target leverage ratio,
holding everything else constant. Thus, if the firm decides to enter external capital markets to
raise capital after experiencing risk changes, it is likely to choose a financing method that moves
it towards a lower (higher) target leverage ratio.5 In performing our tests, we address potential
4 Leland (1994) theoretically shows that increases in risk reduce debt capacity, while Chen (2010) points out that countercyclical variation in risk premiums, default probabilities, and default losses increases the present value of expected default losses, leading to lower optimal leverage ratios. Gormley, Matsa, and Milbourn (2012) empirically show that leverage is related to the change in firm litigation risk for a small set of firms. Numerous studies also show that leverage decreases with asset 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 and change their capital structures accordingly. 5 Interestingly, many previous studies that estimate target ratios do not explicitly model risk as an explanatory
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problems arising from persistent unobservable factors such as indirect bankruptcy costs by
including firm fixed effects.
Although previous studies also examine a firm’s capital structure decision around its
external capital raising period,6 our approach differs from these studies in that we focus on the
choice of a firm’s external financing method following a change in risk. Under the dynamic
trade-off theory, a firm’s capital structure decision in response to a change in risk depends not
only on its risk level, but also on the (hard to observe) costs of raising external capital. When risk
changes, the firm is likely to raise external capital to move toward its optimal leverage as far as
the benefits from such a capital-raising activity is sufficiently greater than its costs.7 If an
increase (decrease) in risk lowers (raises) the target leverage ratio and a firm decides to enter
external capital markets to raise additional external capital, the dynamic trade-off theory predicts
that the firm is more likely to issue equity (debt) or buy back debt (equity) following an increase
(decrease) in risk. Therefore, risk increases (decreases) are expected to be associated with
leverage-decreasing (increasing) activities.8
In contrast, the capital structure explanations by Myers and Majluf (1984) and Baker and
Wurgler (2002) do not assign an equally important and explicit role to firm risk. For example, variable. It is also important to note that, as shown by Chen and Zhao (2007) and Chang and Dasgupta (2009), the results in prior studies that firms pursue a target leverage ratio do not necessarily imply evidence in favor of the dynamic trade-off theory. Although the estimation of target leverage ratios is not required in our analysis, we nevertheless include estimated target leverage ratios as a control in the regressions to make our results comparable to those in prior studies. 6 For example, Hovakimian, Hovakimian, and Tehranian (2004) focus on the period during which firms issue both debt and equity. Danis, Rattl, and Whited (2014) 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. 7 Costly adjustment of its capital structure represents a real option to a firm, and the value and optimal exercise timing of this option also depend on the firm’s risk level. Only if the benefits from raising (reducing) external capital are sufficiently large, the firm is expected to raise (retire) a type of external capital that allows it to move closer to its optimal leverage. 8 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, such adjustment costs can also be significant.
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under the pecking order theory, a firm’s preference for debt over equity does not depend on its
risk level as far as the risk level does not affect the degree of the firm’s information asymmetry.
An increase in risk, however, may restrict the firm’s ability to raise debt. However, at least for a
subsample of firms that are financially unconstrained (and thus are unlikely to exhaust their debt
capacity when risk increases), the pecking order theory predicts that these firms will choose debt
as the source of their external capital whenever they raise external capital regardless of the
direction of risk changes.
The market timing argument of Baker and Wurgler (2002), which suggests that firms are
more likely to issue equity at times when their valuation (measured by the market-to-book ratio)
is high, also does not explicitly model firm risk and the complex interplay between dynamically
changing risk levels and market misvaluation. However, their argument implicitly suggests that
as a firm’s risk increases, its equity value tends to decrease,9 for example, due to an increase in
the cost of equity capital, and therefore, it is less likely to issue equity following an increase in its
risk.10
The above three capital structure theories also have different predictions for firms’ external
capital reducing activities (i.e., buyback decisions) following risk changes. While the dynamic
trade-off theory predicts that, following risk increases (decreases), firms will buy back debt
(equity), the market timing theory predicts the opposite. Although Baker and Wurgler (2002) are
not explicit about how firms buy back external capital in responses to risk changes, according to
their key argument that equity misvaluation drives firms’ financing decisions, firms are expected
9 We empirically support this prediction later in our analysis. 10 One may argue that the change in risk affects only a firm’s fundamental equity value but not its misvaluation (i.e., difference between observed and fundamental values) and thus does not influence the firm’s incentives to take advantage of misvaluation. However, given managers’ general view that misvaluation is correlated with past stock return performance (Graham and Harvey (2001)), significant changes in prices following risk changes are likely to affect misvaluation (or at least managers’ perception of misvaluation of firms’ shares) and therefore, our prediction above is likely to hold.
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to buy back securities that are undervalued (or relatively less overvalued). As we show later, the
market-to-book ratio tends to decrease (increase) following risk increases (decreases), all else
being equal. If managers believe that a firm’s equity is more likely to be undervalued
(overvalued) following an increase (decrease) in the market-to-book ratio, the market timing
theory predicts that firms repurchase equity following risk increases but retire debt following risk
decreases.
On the other hand, the pecking order theory predicts that firms reduce debt in response to
both increases and decreases in risk. Under the pecking order theory, as Shyam-Sunder and
Myers (1999) argue, firms with financing surpluses prefer debt retirements over stock
repurchases when they use their surpluses to buy back securities, possibly to preserve their debt
capacity or to avoid the payment of high equity prices when they repurchase shares under
asymmetric information. Thus, the pecking order theory suggests that, irrespective of the
direction of risk changes and whether firms are financially constrained or not, firms prefer to
retire debt when they have to reduce external capital.11
In sum, the different predictions for the relation between risk changes and future external
financing activities discussed above allow us to evaluate the importance of the dynamic trade-off
theory of capital structure relative to other competing capital structure theories. Table 1
summarizes the preferred type of security that a firm issues (or buys back) as its risk changes
under each of the three competing capital structure theories.12 To provide supporting evidence
on the effect of risk changes on capital structure under the dynamic trade-off theory, we perform
11 One caveat is that, due to asymmetric information, it is possible that firms issue overvalued equity or buy back undervalued equity if the benefits obtained from exploiting misvaluation are greater than the adverse selection costs. This possibility predicts that firms repurchase equity following risk increases but retire debt following risk decreases, the predictions similar to those of the market timing theory. 12 Risk changes are likely to affect the width of the target range of leverage under the dynamic trade-off theory but we do not explicitly address this issue since our approach focuses on external financing activities that occur after considering adjustment costs and changes in the target ranges of leverage.
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a simulation based on Strebulaev (2007). The result in Figure 1 shows a negative relation
between risk changes and the optimal leverage.13
Changes in other determinants of capital structure could also be very useful to understand a
firm’s optimal capital structure decisions. We focus on risk changes since, as discussed above,
risk changes play a different role in a firm’s choice of external financing methods under the three
different capital structure theories. 14 In contrast, these predictions are unclear for other
determinants of capital structure such as asset tangibility.15
To perform our analysis, we use both market- and accounting-based risk measures. We use
stock return volatility, default probability, and implied asset volatility estimates as market-based
measures of firm risk. 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.16 We find that all these risk measures are highly persistent
during our sample period. Since a firm would not necessarily need to react to risk changes if they
were transitory, this result provides another rationale for why risk changes should be an
important consideration in the test of capital structure theories.17
13 Appendix A describes the details on the procedures used to obtain simulation results in Figure 1. 14 Another reason for focusing on risk changes is that, unlike risk levels, they have been largely neglected in the literature. Moreover, unlike some other determinants that are important in the trade-off theory, such as bankruptcy costs, market-based measures of firm risk have the advantage of being observable at high frequency and displaying pronounced variation over time. 15 For example, increases in asset tangibility predict increases in leverage under the trade-off and pecking order theories due to increased debt capacity, while the market timing theory does not provide a clear prediction except that the market timing behavior is less likely to be observed since valuation becomes easier. 16 To the extent that these risk measures are affected by changes in leverage, contemporary changes in risk may be related to leverage changes. However, this is not a major concern in our paper since we examine external financing activities following risk changes instead of examining the contemporaneous relation between external financing activities and risk changes. 17 Results are unreported for brevity but available upon request.
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Using a sample of firms listed on NYSE, Amex, or Nasdaq from 1972 to 2011, we find a
significantly positive relation between risk changes and leverage increasing external financing
activities. Specifically, 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 reduce
external capital by buying back debt (equity) following risk increases (decreases). These results
are consistent with the predictions of the dynamic trade-off theory but 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%. Given that the
mean market leverage for the full sample is 38.8%, this effect is economically large and
significant. 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 using a variety of alternative
risk measures and controlling for endogeneity bias.
We also find that our results do not change when we limit our attention to subsamples of
firms facing fewer financial constraints, as measured by the Whited and Wu (2006) index of
constraints and the size-age (SA) index proposed by Hadlock and Pierce (2010). The pecking
order theory suggests that these firms particularly prefer to issue debt over equity because they
are likely to have easier access to debt markets due to their large debt capacity even after risk
increases. Therefore, these results further support the dynamic trade-off theory but dispute the
pecking order theory.18
18 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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Moreover, we find that an increase in firm risk is associated with a fall in a firm’s valuation
as measured by the market-to-book ratio. Thus, according to the market timing theory, firms are
less likely to issue equity following risk increases since they may perceive their equity not being
overvalued. This result, together with evidence that firms are more likely to choose equity
financing following risk increases, further suggests that the dynamic trade-off theory explains a
firm’s capital structure decision following risk changes better than the market timing theory. In
sum, our results are most consistent with the implications of the dynamic trade-off theory but
inconsistent with the results of recent studies that document evidence against the trade-off theory
of capital structure.19
Our study contributes to the ongoing debate about firms’ capital structure decisions in
several ways. First, we propose a simple, clear way to test the relevance of the dynamic trade-off
theory relative to the pecking order theory and the market timing explanation. Unlike previous
studies that examine a firm’s capital structure decisions during its external capital raising period,
we focus on the relation between risk changes and external financing decisions, which allows us
to minimize the concern about mismeasuring adjustment costs and target leverage ratios.
Second, our study emphasizes the importance of changes in, not levels of, risk in capital
structure decisions. In spite of a strong theoretical link between risk changes and capital structure
and empirical evidence on time variation in risk, previous studies on capital structure focus
mainly on the relation between leverage and the level of risk.
Third, our findings add to the literature on a firm’s dynamic capital structure choice in
which the tax benefits of debt and expected bankruptcy costs play an important role. While some
19 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.
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recent studies show that the (static) trade-off theory does not have significant power in
explaining the cross-sectional variation of firms’ capital structure choices (e.g., Hovakimian,
Kayhan, and Titman (2012)), our study shows that the time-series variation of observed firms’
financing choices is consistent with the dynamic trade-off theory. This result complements the
findings of previous studies on the dynamic trade-off theory, which use other approaches (e.g.,
structural estimation in Hennessy and Whited (2005), simulation in Strebulaev (2007)) to explain
persistent cross-sectional patterns in firms’ capital structures.
The paper proceeds as follows. In Section II, we describe our key risk measures and control
variables and outline the methodology. Section III presents our main empirical results. In Section
IV we further examine the relevance of each capital structure theory by performing additional
tests. Section V summarizes and concludes.
II. Data and Methodology
A. 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 are 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,
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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.
B. 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 capture 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, default
risk, and implied asset volatility. The latter two are estimated on the basis of the Merton (1974)
model.20 We also use a risk measure based on financial statements, namely, a version of
Ohlson’s (1980) adjusted O-score (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.
20 In a dynamic capital structure trade-off theory, the underlying source of risk comes typically from the volatility of a firm’s assets, such as the volatility of its unlevered asset value (Fischer, Heinkel, and Zechner (1989)), or the volatility of cash flow generated from its assets (Goldstein, Ju, Leland (2001), Stebulaev (2007)). Although equity volatility and the probability of bankruptcy typically play a less prominent role in developing dynamic capital structure models, we still use them in our analyses since they are easy to measure and, in reality, can play an important role in a firm’s capital structure decision. For example, managers may pay a significant attention to the probability of bankruptcy when making borrowing decisions since a high level of the probability of bankruptcy jeopardizes their job security and related other benefits.
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Although the volatility of a firm’s total assets may provide a better measure of its risk on
theoretical grounds, we focus on equity volatility in measuring firm risk due to the illiquidity of
debt markets. 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. Due to the residual nature of equity claims, the use of equity volatility may entail a
potential endogeneity problem when studying firms’ capital structure using 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 a contemporaneous increase in
the leverage ratio. However, this is not a major concern in our paper since we examine external
financing activities following risk changes instead of the contemporaneous relation between
external financing activities and risk changes. Furthermore, it should be noted that this effect
goes in the opposite direction compared with the effect predicted by the dynamic trade-off theory
(i.e., firms reduce leverage when risk increases). Thus, all else being equal, this endogeneity
problem should make it harder for us to support the dynamic trade-off theory. Finally, we also
present results based on the book value of leverage, which is not affected by this potential
endogeneity problem.
Second, default risk, which is effectively a measure of the probability that a firm will enter
into costly financial distress, is measured based on the Merton (1974) model. We measure it,
Merton, in a similar way as in Vassalou and Xing (2004).
Third, implied asset volatility captures the uncertainty in asset values, not equity values,
which ultimately matter in avoiding financial distress. Another important reason to use asset
volatility as one of our risk measures is the fundamental role it plays in dynamic trade-off models.
We compute implied asset volatility, AssetVol, as the annualized standard deviations of daily
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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-score (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 on how Merton, AssetVol, and O-score are
measured is provided in Appendix C.
C. Dependent Variables
To examine the effects of risk changes on firms’ capital structure decisions, we use three
measures as dependent variables: leverage-increasing external financing activities (LIEFA [t+1]),
book leverage ratio, and market leverage ratio. As discussed above, the dynamic trade-off theory
predicts that firms adjusting external capital following a risk increase (decrease) are likely to
choose a financing method that helps decrease (increase) their leverage ratio. To capture this
external financial activity, we create a variable, leverage-increasing external financing activities,
LIEFA [t+1], as one of our key dependent variables of interest. LIEFA [t+1] is computed as the
scaled sum of external financing activities that increase a leverage ratio (i.e., issue of new debt
and repurchase of equity) minus those that reduce a leverage ratio (i.e., reduction of debt and
issue of new equity).21 The reason for using LIEFA [t+1] is as follows. If two otherwise similar
21 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
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firms differ in their adjustment costs and investment opportunities, it is possible that one firm
prefers to respond to a risk increase by issuing equity, while the other firm finds it more cost-
effective to buy back debt in order to reduce its leverage. LIEFA allows us to verify whether
firms respond to changes in risk in a manner consistent with the dynamic trade-off theory, as
both of the aforementioned firms will have negative LIEFA.
Specifically, LIEFA 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. 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.22
As alternative dependent variables, we use the book (market) leverage ratio, measured as the
ratio of the book value of debt to 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,
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. This is one of several reasons why the relation between external financing decisions and leverage changes is known to be complex (Welch (2011)). Therefore, we also use changes in market and book leverage ratios as alternative dependent variables in our analyses to check whether the choice of external financing method is in line with the direction of changes in leverage ratios. 22 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 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.
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the redemption value (PSTKRV), or the carrying value (PSTK) if PSTKRV is not available, is
used.23 The market value of equity is measured at the fiscal year-end.
D. Regression Specification and Control Variables
To test whether firms engage in leverage-increasing external financing activities following
changes in risk, we run the following ordinary least squares (OLS) panel regression model that
controls for various factors that affect a firm’s capital structure decision:
titititi
titititi
tititititististi
FirmD YearDLdefB CRdummyCRdef FDEBITDLTA
r MBMBRiskRisk =LevorLIEFA
,,13,12,11
10,9,8,7,6
,51,4,31,2,10,, )(
εβββ
βββββ
ββββββ
++++
+++++
++∆++∆+∆ −−++
, (1)
Our main independent variables of interest in Eq. (1) are the change in risk, ∆𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡, and
lagged risk level, 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡−1. The other variables are well known to explain firms’ capital
structure and external financing choices and are included as controls. 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 (or
changes in investment opportunities) can also affect firms’ external financing decisions and
changes in leverage, we also control for changes in MB, MB Change (Baker and Wurgler
(2002)).24
23 Annual Industrial Compustat data variable names are in parentheses. 24 In Eq. (1), for risk and MB, we use both their changes and lagged values. However, for LTA, FD, r and EBITD, we use only their values in year t and do not include their changes in the regression. We include changes in MB since they are related to changes in both firm valuation (market timing theory) and investment opportunities (pecking order and dynamic trade-off theories) and thus are relevant to all three capital structure theories considered in the
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Welch (2004) demonstrates that past stock returns are a driver of market leverage, which in
turn may also affect financing decisions in subsequent periods. Thus, we include one-year stock
return (r) during the fiscal year in our regression.
Size can affect firms’ financing decisions in several ways. For example, large firms are more
likely to be mature and diversified, and have better access to capital markets. They are also less
subject to information asymmetry, which, according to the pecking order theory, may help reduce
the extent of price drops if the firm issues equity. Finally, large firms’ information is easily
available to outside investors and they are subject to fewer trading frictions, which is likely to
reduce the likelihood of stock price misvaluation in the stock market, affecting the potential for
market timing. Thus, to control for these effects, we include the natural logarithm of total assets
(AT), LTA, in the regressions.
According to the dynamic trade-off theory, a firm’s profitability can be an important
determinant of its capital structure since profitable firms can take advantage of larger debt tax
shields. Profitability is also important under the pecking order theory, which 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.
How leverage changes over time and what types of capital firms choose also depend on the
total amount of external financing raised. To measure the latter, similar to Frank and Goyal
(2003), 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
paper. However, in unreported tests, we repeat our analyses using both levels of and changes in LTA, FD, r, EBITD, risk and MB in the regressions and find qualitatively similar results as those reported in the paper.
16
(DLTIS) – long-term debt reduction (DLTR)] divided by AT in year t-1).
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. As a credit rating is also closely related to firm risk,
we need to control for it in our regression. 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 the target credit rating in 2011 are presented
in Appendix D.25 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.
Although our approach does not require us to measure target leverage ratios in testing the
dynamic trade-off theory of capital structure and, 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 E. We measure book leverage deficit, LdefBt, as the difference
between the target book leverage ratio and the actual book leverage ratio, TlevBt – LevBt. If a
firm pursues a target leverage ratio, we expect that the firm’s financing and capital structure
25 Results for other years are available upon request.
17
decisions depend on how far it is away from its target (i.e., the leverage deficit).26 A non-zero
leverage deficit at time t can arise because the firm may have deviated from its target capital
structure in the past or because the target leverage ratio has shifted over the last year. Thus,
lagged leverage deficit and changes in target leverage that are used in the previous studies are
subsumed in a single variable here for the sake of simplicity.
Despite the importance of risk as a determinant of the optimal target leverage ratio in the
dynamic trade-off theory, previous studies have often not explicitly included firm risk in their
estimation of target leverage ratios. The focus of our study is not to propose a marginal
improvement in estimating target leverage ratios, but to test if firms rationally respond to
changes in risk levels in a way which is consistent with the dynamic trade-off theory. Thus, we
follow the method used in previous studies and do not include risk in estimating target leverage
ratios to make the comparison with these studies easier.
It should be also noted that some of our independent variables such as EBITD and MB are
also used as inputs to calculate other control variables. For instance, EBITD is included in the
calculation of FD and LdefB, and MB is included in LdefB. This inclusion is consistent with the
literature (e.g., Kayhan and Titman (2007)) and ensures that our results are not driven by a
simple correlation between risk changes and other variables that are known to be important
determinants of capital structure decisions.
Finally, we control for year and firm fixed effects by using year and firm dummy variables,
YearD and FirmD, respectively. Controlling for firm fixed effects mitigates the endogeneity
concern that our results are driven by omitted unobservable firm characteristics. However, as
26 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.
18
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). All other variables are defined
in previous sections and are also summarized in Appendix B.
III. Empirical Results
A. 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
38.8% (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 average, firms raised about 2.5% (≈ (4.4% +
0.54%)/2) of total assets through net long-term debt issuance per year.27
27 This number is a rough estimation because FD is measured as the sum of net equity and net debt issuances in year
19
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).
B. 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 magnitudes of the correlation coefficients vary across the pairs of risk change
measures. There are also significant positive correlations among the 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
t whereas LIEFA[t+1] is measured as the difference between net debt and net equity issuances in year t+1.
20
tend to increase in the following year. However, it is negatively correlated with LIEFA in the
following year. We do not 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
21
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 (2.46) percentage 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.
C. 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 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,
22
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.28
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
(FD) 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
necessarily match with their 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.
28 Interestingly, the coefficients on lagged risk levels in columns (1), (2) and (9) are very similar to those on risk changes. There is no theoretical reason for this to be the case, and indeed, unreported results show that this is no longer true when we analyze LIEFA or leverage changes over two- and three-year windows following a risk change.
23
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 could lead to differences in results between the studies. For example,
consistent with Hovakiminan, Opler and Titman (2001), we find that although 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
24
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.29
Due to adjustment costs, firms may not adjust their capital structure immediately after risk
changes. As documented in Leary and Roberts (2005), it can take more than a year before firms
adjust their capital structures. 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
29 In untabulated tests, we repeat the regression analyses of LIEFA[t+1] reported in Table 5 after decomposing LIEFA into two parts, Net Debt Issues[t+1] and Net Equity Issues[t+1] to examine which component drives the results. We find that the results are mostly driven by Net Debt Issues[t+1]. For Net Debt Issues[t+1], the coefficients on the change in risk are significantly negative except for AssetVol, while for Net Equity Issues[t+1] × -1, the corresponding coefficients are significantly negative only when O-Score is used as a risk measure.
25
across four risk measures as we extend the time horizon to measure the external financing and
leverage changing activities.
In particular, with respect to AssetVol, the main underlying risk measure of Fischer, Heinkel,
and Zechner (1989), we find that consistent with the dynamic trade-off theory of capital structure,
its increase leads firms to significantly reduce their book (column (6)) and market leverage
(column (10)) in subsequent years. Interestingly, however, these reductions do not appear to be
driven by external financing choices (column (2)).
D. Robustness Tests
In this subsection we examine whether our results are robust to controlling for potential
endogeneity problems not captured by firm fixed effects. 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-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
26
indicator; and FirmD is a firm indicator. See Appendix B 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.30
The results are presented in Table 7. In the first three rows, we report the results for the one-
year period following risk changes and in the next three rows, 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.31
IV. 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
over equity and therefore would issue debt even after risk increases unless such increases in risk
significantly constrain their ability to borrow. However, when firms are financially constrained, 30 The common approach to address the endogeneity problems is to have either an exogenous event that exogenously changes firm risk but that does not affect firm leverage in any other way, or an instrumental variable (IV) that is related to the change in firm risk but unrelated to firm leverage. However, such an event or an IV that is related to risk changes but truly exogenous to firm leverage is hard to come by in our analysis. Nevertheless, we reestimate the regressions using a two-stage least squares regression in which we use the industry median risk change and the industry lagged risk level as the IVs for risk change and lagged risk level, respectively. Industry is defined based on the two-digit SIC codes. We find that the results for three-year horizons are qualitatively similar to those reported in Table 5 except for changes in book leverages. We admit the possibility that these IVs may not satisfy the exclusion condition of the IVs. 31 In untabulated tests, as an alternative way to control for time-invariant omitted firm characteristics, we use the first-difference method by replacing all dependent and explanatory variables with those measured using the change, and reestimate all regressions reported in Table 5. We find that the qualitative results do not change.
27
they may have difficulty in accessing debt markets after risk increases. Therefore, focusing only
on the subsample of financially unconstrained firms instead of the full sample allows us to
unambiguously test the importance of the pecking order theory relative to the dynamic trade-off
theory (which predicts the issuance of equity following risk increases). We use the Whited and
Wu index of constraints (Whited and Wu (2006)) and the size-age (SA) index proposed by
Hadlock and Pierce (2010) to identify firms that are less likely to be financially constrained.32
Table 8 reports the results using firms with below-median values of financial constraints as
measured by these methods. Panel A shows the effect of changes in risk on LIEFA and changes in
market (book) leverage in the following year. The results are similar to those reported in Table 5.
When we extend the observation window for the dependent variables from one to three years
(Panel B), we again observe similar results.33
In summary, the results in Table 8 are qualitatively similar to those using the full sample,
which is 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 is 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 32 Following Whited and Wu (2006) and Hennessy and Whited (2007), the Whited and Wu index is constructed as – 0.091 × cash flow over total assets – 0.062 × indicator set to one if the firm pays cash dividends, and zero otherwise + 0.021 × long term debt over total assets – 0.044 × logarithm of total assets + 0.102 × average industry sales growth, estimated separately for each three-digit SIC industry and each year – 0.035 × firm sales growth, with all variables defined as in Whited and Wu (2006). Hadlock and Pierce (2010) use a size and age 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. 33 These results are consistent with those of Fama and French (2005). They find that most firms issue or retire equity each year and that typical equity issuers are healthy firms not under financial difficulties, contradicting with the pecking order theory. They conclude that equity issuing decisions of more than half of their sample firms violate the pecking order.
28
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 examine 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 divide the firms into four subgroups according to whether they have positive or
negative FD in year t+1 (i.e., whether they raise or reduce external capital) and whether they
experience an increase or a decrease in risk and examine whether the relations between risk
changes and future LIEFA (changes in leverage ratios) differ across these subgroups by
estimating the regression separately for them. 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, the coefficient estimates on risk change variables that are significant
have a negative sign in the majority of subgroups.34 Moreover, we find the negative coefficient
34 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
29
on risk changes not only for capital raising (positive FD) subsamples but also for capital
reducing (negative FD) subsamples where we expect the negative coefficient only under the
dynamic trade-off theory even among financially constrained firms. This negative coefficient
suggests that firms tend to decrease their book and market leverage ratios when they experience
an increase in risk, which is consistent with the dynamic trade-off theory.
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.
V. 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 among the dynamic trade-off theory, the pecking order theory, and the
market timing theory explains firms’ external financing decisions best 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 these capital structure theories. Our approach also
with the market timing explanation.
30
allows us to test the relevance of capital structure theories without measuring adjustment costs
since we focus on the group of firms that have already undertaken external financing 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, our
simulation results show that the optimal leverage is negatively related to risk changes. More
importantly, we find that firms prefer to issue equity (debt) over debt (equity) 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 a subsample of firms facing few
financial constraints for which the pecking order theory is more likely to be applicable. In
addition, 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, when we repeat our regression analyses separately for subsamples classified
according to whether firms raise or reduce external capital and whether they experience an
increase or a decrease in risk, we find that the coefficient estimates on risk change variables are
significantly negative in the majority of subsamples. These results further support 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 its importance in
explaining firms’ external financing and capital structure decisions over time.
31
Appendix A. Numerical Example of the Relation between Optimal Leverage and Risk
Changes
In Figure 1, to better understand the relation between the optimal leverage ratio and risk
changes in a dynamic trade-off theory setting, we present simulation results based on Strebulaev
(2007). This appendix describes the details on the procedures used to obtain these simulation
results. Specifically, in Table I of his paper, Strebulaev (2007) states that the optimal market
leverage ratio (ML) decreases as the volatility of firm’s cash flow (σ) increases, but does not
provide any details on the magnitudes of the impacts of risk changes on optimal leverage ratios.
Using the mean parameter values reported in Table II of Strebulaev (2007), we examine how
much a firm’s optimal market leverage ratio changes as the volatility of its cash flow changes
around the sample mean (i.e., 25.5%).
Similar to Goldstein, Leland and Ju (2001), Strebulaev (2007) assumes that firms will retire
their outstanding debt at par and sell a new, larger debt if their values increase, thus reaching an
upper refinancing boundary (U). However, if firms perform poorly and reach a liquidity barrier
(L), they will sell a fraction (1 – k) of assets to resolve financial distress. Following asset sales,
these poorly performing firms may recover and reach an upper refinancing boundary (LU) or
they may need to inject new equity capital. Equity holders will optimally default if the firm’s
condition continues to worsen and reaches a default barrier (B). Figure 1 of Strebulaev (2007)
summarizes possible paths of firm values under these scenarios. At each refinancing point, the
amount of debt outstanding and consequently net payout increase by either γU or γLU, depending
on whether the liquidity barrier has not (γU) or has been hit (γLU) before reaching the refinancing
point. Under these assumptions, Strebulaev (2007) shows that it is sufficient to examine a firm’s
32
capital structure decision by focusing on the dynamic optimal capital structure problem over a
single refinancing cycle (i.e., a period from one debt issue until the upper refinancing barrier,
either U or LU, is hit and the refinancing decision is made). This simplification is possible
because a single refinancing cycle is representative of all subsequent cycles in the sense that in a
subsequent refinancing cycle, the firm can be considered as a larger copy of itself (i.e. at each
refinancing point, the values of equity and debt as well as net payouts all increase by the same,
constant rate, either γU or γLU, depending on whether the liquidity barrier has been hit before
reaching the refinancing point). Thus, once the optimal values of debt and equity during a single
refinancing cycle are identified at the beginning of its cycle, we can directly calculate the firm’s
optimal market leverage ratio at the refinancing point as the ratio of the value of debt divided by
the combined values of debt and equity.
Using the mean parameter values (excluding cash flow volatility, σ) specified in Table II of
Strebulaev (2007) together with a chosen cash flow volatility parameter value, σ, and the
linearization assumption of the net payout ratio (Eq. (12) of Strebulaev (2007)) used to determine
the drift rate of payouts, 𝜇𝜇, we discretize and simulate 10,000 sample paths over 500 quarters for
a firm’s net payouts to claimholders including governments (δ: before-tax net cash flows)
according to Eq. (1) of Strebulaev (2007). Based on these simulated net payout paths together
with initial trial values of three of the four control variables (coupon (c) = 2.0582, the proportion
by which the net payout increases between two refinancing points if the refinancing barrier has
not been hit first (γU) = 1.6508, and the proportion by which the net payout increases between
two refinancing points if the liquidity barrier has been hit first (γLU) = 1.6335), we use the
smooth-pasting condition (Eq. (13) of Strebulaev (2007)) to determine the value of the fourth
control variable, the default threshold (δB), and then calculate the market values of equity (ER(δ0))
33
and debt (DR(δ0)) at the beginning of a refinancing cycle as specified in Eqs. (4) and (5) of
Strebulaev (2007), respectively. Next, we calculate the value of debt at time zero (D(δ0)) using
his Eq. (7) and in turn, the ex-ante firm value that shareholders try to maximize at each
refinancing point before debt issuance (F(δ0)) using his Eq. (10). Thus, the value of the
shareholder’s claim after debt issuance (E(δ0)) is determined as F(δ0) – (1-qRC) × D(δ0), where
qRC is the proportional adjustment costs of debt at the refinancing point and it is reflected in the
calculation of F(δ0).
After we estimate initial values of firm, debt and equity, we revise the value of the default
threshold (δB) that satisfies the smooth-pasting condition of Eq. (13) of Strebulaev (2007). Then,
we use standard numerical optimization techniques to search for the values of control variables
that maximize the firm value, F(δ0). We repeat this procedure of updating δB and three control
variables until we cannot make either an improvement in the value of the shareholders’ claim
(F(δ0)) or a change in the values of the control variables, which exceeds preset cutoff points.
Finally, based on firm value maximized, we calculate the optimal market leverage ratio. The
results using this simulation analysis are presented in Figure 1, which shows how the optimal
market leverage changes as the asset (cash flow) volatility changes from 0.055 to 0.455, two
standard deviations below and above the sample mean of 0.255 as reported in Strebulaev (2007).
The figure clearly supports our prediction that the optimal market leverage decreases
monotonically as the asset volatility increases. For example, an optimal market leverage ratio is
64% when the asset volatility is 5.5% but decreases to 55% as the asset volatility increases by a
one-standard deviation (10%) from 5.5% to 15.5%.35
35 In a similar model, Goldstein, Leland, and Ju (2001) show that the optimal leverage ratio drops by 4.36%, from 39.40% to 35.04%, as the asset volatility changes from 23% to 27% as shown in Table 2 of their paper.
34
Appendix B. 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 the beginning of 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 E.
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 as described in Appendix C.
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 as described in Appendix C.
Ohlson’s score (O-Score)
Franzen, Rodgers, and Simin (2007)’s adjusted Ohlson scores calculated in each year as described in Appendix C.
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).
35
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.
36
Appendix C. 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:36
×−+−=
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
36 As discussed in Vassalou and Xing (2004), Eq. (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.
37
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 Eq. (A1). Simultaneously, we also determine
the implied asset volatility, AssetVol, as the volatility of estimated 𝑉𝑉𝐴𝐴s.
2. Adjusted Ohlson (1980) Score
Adjusted Ohlson (1980) scores are estimated based on Franzen, Rodgers, and Simin (2007)
as specified in Eq. (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, while those starting with “A_” are adjusted values as specified below.
Dummy1 is an indicator that takes the value of one when total liabilities are greater than total
38
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 Eq.
(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 Eq. (A2), where the
higher the adjusted O-score is, the higher the firm’s default risk is.
39
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 Compustat37 and MB, PPE, RD, RDd, SE, PROFIT, and SIZE are
defined as in Appendix B. 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
37 The lowest rating (CCC-) is set to 1 and the highest rating (AAA) is set to 19.
40
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 B.
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
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
41
Appendix E. Target Leverage
1. Target leverage ratios
Target leverage ratios (Tlev) are measured using a similar method as in Kayhan and Titman
(2007). Although risk can affect target leverage ratios, we do not include risk measures in
estimating target leverage ratios since we mainly use this variable as a control in our analysis.
Thus, we estimate target leverage ratios the same way as in the previous studies. Specifically, as
shown in Eq. (A4) below, for each firm we run a Tobit regression of the book leverage ratio,
LevB, 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 book
leverage ratios, TlevB. More specifically, we estimate:
tititititi
titititititi
IndustryDYearDSizeSERDdRDPROFITPPEMB α=LevB
,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). 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
42
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) 38 and year dummy
variables to control for industry effects and any time-related co-variation in target leverage ratios,
respectively.39
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 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 B.
38 The results are robust to alternative definitions of industry dummy variables based on five-, ten-, or twelve-industry classification. 39 Note that the number of observations used in these regressions is greater than those used in other analyses due to fewer data requirements.
43
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
44
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1747-1787. Shyam-Sunder, L., and S. C. Myers, “Testing static tradeoff against pecking order models of capital
structure.” Journal of Financial Economics, 51 (1999), 219-244. Vassalou, M., and Y. H. Xing. “Default risk in equity returns.” Journal of Finance, 59 (2004), 831-868. Welch, I. “Capital structure and stock returns.” Journal of Political Economy, 112 (2004), 106-131. Welch, I. “Two common problems in capital structure research: The financial debt-to-asset ratio and
issuing activity versus leverage changes.” International Review of Finance 11 (2011), 1-17. Whited, T., and G. Wu, “Financial constraints risk.” Review of Financial Studies, 19 (2006), 531-559.
47
Table 1 Predictions of Relation between Risk Change and Future Leverage-Increasing External
Financing Activity under Three Different Capital Structure Theories
This table provides a summary of the predictions of the relation between risk changes and leverage-increasing external financing activities under the dynamic trade-off, pecking order, and market timing theories, as discussed in the text. 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 (or equity for firms that are
financially constrained after risk increases)
Debt (or equity for firms that remain to
be financially constrained even
after risk decreases)
?
Market timing Debt Equity +
Negative FD (Reduce
external capital)
Dynamic trade-off Debt Equity -
Pecking order+ Debt Debt ?
Market timing Equity Debt +
+ The effect of risk changes on equity misvaluation is not considered in this prediction. However, if changes in risk affect the degree of misvaluation and equity overvaluation (undervaluation) is more likely to be present following price increases (decreases), firms are likely to issue (buy back) equity following risk decreases (increases) as far as the benefits from issuing overvalued (buying back undervalued) equity are greater than its negative impacts on adverse selection costs. Thus, consideration of equity misvaluation predicts a positive relation between risk change and leverage-increasing activities for both positive and negative FDs, the same prediction as that under the market timing theory.
48
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 B. 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
49
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 B. 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)
50
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 B. 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***
51
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 B. ***, **, 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)
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)
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)
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)
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)
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)
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 Adjusted R2
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 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
52
Table 6 Coefficients on Risk Change Variables from the Panel Regressions of Future Leverage-Increasing External Financing
Activities (LIEFA) and Changes 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 B. 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, 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 the beginning of 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
53
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. Risk changes are measured as the changes in the residuals. The residuals from the panel regressions of risk variables on several determinants of capital structure (Eq. (2) in the text) are used as the measures of firms’ risk. 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 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. T-statistics based on clustered standard errors at the firm level are reported in parentheses. ***, **, 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)
When s =1 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
When s = 3 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
54
Table 8 Subsample Analyses of Firms Facing Few 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 low financial constraints (below the sample median of financial constraints as measured by the Whited and Wu (2006) index of constraints (WW-index) and the size-age index (HH-index) proposed by 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 B. 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
Firms with Low Financial Constraints (Using WW-Index)
Coefficient -0.046*** 0.001 -0.037*** -0.957*** -0.018*** -0.004* 0.010 -0.019 -0.072*** -0.001 -0.071*** -0.146 (-6.26) (0.18) (-3.65) (-7.08) (-3.86) (-1.95) (1.46) (-0.22) (-12.21) (-0.45) (-6.80) (-1.48)
Adjusted R2 0.0618 0.0596 0.0604 0.0759 0.143 0.143 0.142 0.138 0.244 0.235 0.238 0.238 # of obs. 41,270 40,870 40,870 31,291 40,683 40,289 40,289 30,841 40,669 40,275 40,275 30,834
Firms with Low Financial Constraints (Using HP-Index)
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
Firms with Low Financial Constraints (Using WW-Index)
Coefficient -0.108*** -0.004 -0.107*** -2.386*** -0.040*** -0.009** -0.026** 0.254* -0.134*** -0.002 -0.143*** -0.209 (-6.88) (-0.62) (-4.92) (-7.72) (-5.36) (-2.48) (-2.06) (1.67) (-13.51) (-0.39) (-8.41) (-1.13)
Adjusted R2 0.126 0.122 0.124 0.152 0.292 0.292 0.291 0.286 0.303 0.293 0.298 0.295 # of obs. 31,579 31,279 31,279 24,257 33,282 32,955 32,955 25,487 33,252 32,928 32,928 25,472
Firms with Low Financial Constraints (Using HP-Index)
Coefficient -0.078*** -0.001 -0.124*** -2.384*** -0.041*** -0.010** -0.021 0.335** -0.133*** -0.004 -0.162*** -0.225 (-5.04) (-0.18) (-5.26) (-6.85) (-5.41) (-2.49) (-1.54) (2.12) (-13.45) (-0.81) (-8.80) (-1.18)
Adjusted R2 0.130 0.128 0.130 0.156 0.304 0.303 0.303 0.309 0.323 0.311 0.317 0.316 # 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
55
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 B. ***, **, 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
56
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 on risk changes that are obtained 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. We divide the sample firms into four subgroups according to whether a firm’s financial deficit (FD) in year t+1 is positive or negative and whether its risk change is positive or negative and estimate the regression separately for these subgroups. 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 B. 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)
57
Figure 1. Optimal Market Leverage as a Function of Asset Volatility
This figure plots the optimal market leverage for a given level of cash flow volatility using the dynamic trade-off model of Strebulaev (2007). Parameter values specified in Table II of Strebulaev (2007) are used for simulation. Appendix A describes the procedures used to obtain the results.