Do Firms Adjust Capital Structures to Manage Risk? *
Martin J. Dierker
Korea Advanced Institute of Science and Technology (KAIST)
[email protected]
Jun-Koo Kang
Nanyang Technological University of Singapore
[email protected]
Inmoo Lee
Korea Advanced Institute of Science and Technology (KAIST)
[email protected]
Sung Won Seo
Korea Advanced Institute of Science and Technology (KAIST)
[email protected]
October 2013
Abstract
We provide a new insight on how changes in risk affect a firm’s capital structure decisions. Using an
approach that alleviates potential problems caused by high capital structure adjustment costs, we test
whether firms that experience a substantial increase in risk choose an external financing method that is
consistent with the implications of dynamic trade-off theories of capital structure. We find that these firms
indeed choose a financing method that lowers their leverage ratios. This finding is particularly
pronounced for firms with a high level of risk or firms that raise a large amount of external capital, and is
robust to a variety of risk measures such as stock return volatility, default probability and implied asset
volatility based on the Merton (1974) model, and an adjusted Ohlson (1980) score.
*
We thank Tim Loughran, Sheridan Titman, and the participants at the 2012 Allied Korean Finance Associations
Meetings and KAIST for useful comments. All errors are our own.
Do Firms Adjust Capital Structures to Manage Risk?
Abstract
We provide a new insight on how changes in risk affect a firm’s capital structure decisions. Using an
approach that alleviates potential problems caused by high capital structure adjustment costs, we test
whether firms that experience a substantial increase in risk choose an external financing method that is
consistent with the implications of dynamic trade-off theories of capital structure. We find that these firms
indeed choose a financing method that lowers their leverage ratios. This finding is particularly
pronounced for firms with a high level of risk or firms that raise a large amount of external capital, and is
robust to a variety of risk measures such as stock return volatility, default probability and implied asset
volatility based on the Merton (1974) model, and an adjusted Ohlson (1980) score.
1
1. Introduction
The determinants of firms’ capital structure decisions are among the most controversial issues in the
corporate finance literature. According to the static trade-off theory of capital structure, firms choose
optimal leverage by weighing the costs and benefits of debt (e.g., tax advantages of debt versus costs of
financial distress (Kraus and Litzenberger (1973)). Over the past decade or so, however, several studies
have highlighted the possibility that firms’ capital structure decisions are significantly affected by their
historical financing characteristics. For example, Baker and Wurgler (2002) argue that firms try to time
the market by issuing equity when their market value is high and show that firms’ capital structure is
related to their historical market value of equity. This result suggests that capital structure is the
cumulative outcome of past attempts to time the equity market, which runs counter to the static trade-off
theory of capital structure. Other studies, however, show that market timing does not have a long-run
effect on firms' leverage and thus firms still pursue target leverage ratios (Kayhan and Titman (2007)).1
In yet other related studies, Kisgen (2006) and Hovakimian, Kayhan, and Titman (2009) show that credit
rating targets affect capital structure decisions and Welch (2004), Leary and Roberts (2005), and
Hovakimian, Kayhan and Titman (2012) document the importance of adjustment costs that may occur
when firms rebalance their capital structure.
In this paper we revisit the impact of firms’ historical financing characteristics on their capital
structure decisions by investigating whether they adjust their external financing decisions in response to
changes in their underlying risk (“risk timing”) and whether this risk timing behavior significantly affects
their capital structure. 2 Both market and risk timing explanations contend that the current capital
1
Previous papers also show evidence against the market timing explanation of capital structure decisions. For
example, Alti (2006) finds that firms that went public during hot markets when valuation is high increase their
leverage ratios more than firms that went public during cold markets, suggesting that market timing does not have a
long-lasting impact on capital structure of initial public offering firms. Liu (2009) also presents evidence that
historical market-to-book ratio has a significant impact on leverage not because of market timing but because it
measures firms’ growth options.
2
We define risk timing as a firm’s optimal response to changes in risk under the trade-off theory of capital structure.
2
structure is the the cumulative outcome of past external financing decisions. However, while the market
timing explanation posits that managers time equity issuance to take advantage of favorable market
conditions, the risk timing explanation postulates that they time equity issuance to manage risk. Given
that the cost of capital structure adjustment is high, if managers decide to raise external capital, consistent
with the implication of a dynamic trade-off theory with adjustment costs (e.g., Fischer, Heinkel and
Zechner (1989), Leary and Roberts (2005), Strebulaev (2007)), 3 they may choose a source of external
financing that allows the firm to optimally adjust its financial leverage and maintain desirable levels of
risk. Therefore, according to the risk timing explanation, a firm’s capital structure is the cumulative
outcome of past attempts to time external financing to manage risk. 4
To illustrate the importance of risk timing in firms’ capital structure decisions, consider the following
statement by Michael Kelly, CFO of Piedmont Pharmaceuticals: “In response to the collapse of Lehman
Brothers and the housing market, risk management has risen to the top of the list for CFOs. […] leverage
has gotten a significant rethink. […] now they [CFOs] are reducing the debt on their balance sheets”. 5
Similarly, Doherty (2000) argues that “management of the capital structure of the firm and risk
Unlike the market timing theory of capital structure, our risk timing argument on a firm’s capital structure decision
does not require information asymmetry or the presence of irrational investor.
3
For example, Fischer, Heinkel, and Zechner (1989) show that in the presence of recapitalization costs, a firm’s
debt ratio can vary over time because any leverage ratios within a set of boundaries are optimal. Therefore, firms
with similar characteristics can have different leverage ratios at any point in time. However, since these firms are
likely to have similar recapitalization criteria, their capital structures may exhibit similar intertemporal behavior.
Their theory suggests that firms take recapitalization actions only when the benefits from recapitalization outweigh
the costs.
4
We focus on risk as an important factor that affects firms’ capital structure since previous studies show that a
firm’s market-based risk, such as stock return volatility, changes significantly over time (Campbell, Lettau, Malkiel,
and Xu (2001)) and is closely related to the firm’s expected returns, thereby affecting the firm’s cost of capital (e.g.,
Ang, Hodrick, Xing, and Zhang (2006), Adrian and Rosenberg (2008)). Corporate managers therefore have strong
incentives to pay close attention to their firms’ risk and act before the risk reaches an alarming level, suggesting that
risk timing should play an important role in firms’ capital structure decisions. Throughout the paper, our focus is on
firms’ ex-ante incentives to manage risk in order to keep expected bankruptcy costs under control, as the trade-off
theory of capital structure suggests. It is possible, however, that some firms experience a substantial increase in risk,
and thus have an incentive to engage in asset substitution (Jensen and Meckling (1976)) and actively seek more risk.
However, it is important to note that asset substitution usually refers to firms’ choice of operational risk and not
leverage, since lenders are unlikely to allow such firms to increase leverage even further.
“The
evolving
role
of
the
CFO”,
2011,
Parker
http://www.parkerlynch.com/Documents/downloads/PL-wp-cfo.pdf.
5
3
and
Lynch,
retrieved
from
management are inseparable” (Ch. 13) and dedicates several chapters of his book to analyzing this link,
advocating that firms adjust their capital structure ex-post after certain risky events and set up leverage to
be ex-ante conditional on other risky events, for instance, by using reverse convertible debt. 6 Further
reflecting the importance of risk in firm policies, the risk management literature also recognizes the close
link between hedging and capital structure policies (Froot and Stein (1998)).
In addition, the trade-off theory of capital structure and other optimal capital structure theories show
that the optimal leverage ratio is negatively related to risk. For example, Leland (1994) shows that the
optimal leverage ratio decreases as risk increases. In a more recent paper, Chen (2010) incorporates
business cycle variation in default risk, the cost of default, volatility, and the risk premium into a capital
structure model and finds that risk is negatively related to leverage ratios.
In spite of the strong theoretical link between risk changes and capital structure, empirical evidence
on such a link is scarce. 7 Moreover, previous studies that examine the association between risk levels and
capital structure do not provide conclusive results. 8 In this paper we examine the direct link between risk
changes and capital structure by testing how risk timing behavior affects firms’ capital structure. Focusing
on risk timing behavior allows us to examine how firms’ capital structure decisions are affected by their
external financing decisions from a perspective that is similar to their market timing behavior but with
different implications. First, when firms have high equity valuation ratios, market participants and
managers are likely to be optimistic about firms’ future prospects, thus lowering their perceived risk
levels. As documented in previous studies on market timing, firms tend to issue equity and lower their
6
For example, see the report by the Squam Lake Working Group on Financial Regulation, which is available at
http://www.squamlakegroup.org/.
7
Gormley, Matsa, and Milbourn (2012) show that leverage is related to the change in firm risk for a small set of
firms: firms with a well-designed compensation structure reduce leverage conditional on an exogenous increase in
litigation risk. Previous 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 the changes in risk.
8
For example, Harris and Raviv (1991) show that out of five studies that document the negative association
between return volatility and leverage ratios, two present weak or statistically insignificant associations.
4
debt ratios when their valuation ratios (market-to-book) are high (Baker and Wurgler (2002)). In contrast,
as firms’ risk levels increase, their valuation ratios tend to decrease, which reduces market participants’
optimism about firms’ prospects. According to the market timing argument, the reduced optimism should
provide the firms with fewer incentives to issue equity. The risk timing argument, on the other hand,
suggests that firms issue equity to manage their cumulative underlying risk even when their valuation
ratios are low. Therefore, it is an empirical question whether managers time equity issuance to take
advantage of favorable market conditions or to manage risk, and if firms engage in both timing behaviors,
which behavior dominates.
Second, while the market timing theory of capital structure challenges the trade-off theory, the risk
timing argument is consistent with it. Since changes in risk are likely to affect firms’ optimal level of debt
by changing their expected bankruptcy costs, as long as the present value of tax shields remains constant
when risk changes, the risk timing argument and the trade-off theory predict the same managerial decision
regarding capital structure changes. 9 However, while target debt ratios are difficult to observe and
estimate (Chen and Zhao (2007), Chang and Dasgupta (2009)), risks are relatively easy to measure and
quantify, and hence investigating firms’ risk timing behavior is an alternative way to examine firms’
optimal capital structure without facing the difficulty related to observing and measuring target debt
ratios. 10 Moreover, by examining the capital structure decisions of firms that have a tendency to raise
external capital in response to increases in risk (i.e., firms with a high correlation between their risk and
financial deficit), we can test the implications of the trade-off theory without worrying about capital
9
In reality, as risk increases, the discount rate (i.e., the cost of debt) tends to increase. If the firm issues long-term
debt at a fixed interest rate, the present value of tax shields is likely to decrease. This decrease in the present value of
tax shields will further lower the target leverage ratio compared to the case in which the present value of tax shields
does not change, and therefore both the risk timing argument and the trade-off theory predict that firms decrease
their leverage ratio by issuing equity as their risk increases.
10
Recent studies take an alternative approach to examine optimal capital structure. For example, Hovakimian,
Kayhan, and Titman (2012) examine whether firms that are likely to have the largest tax benefits of financial
leverage and the lowest financial distress costs choose capital structures that result in the highest probability of
bankruptcy. They find results that are inconsistent with the static trade-off theory.
5
structure adjustment costs as emphasized in Welch (2004), Leary and Roberts (2005), and Hovakimian,
Kayhan, and Titman (2012). Since firms typically adjust their capital structures when raising external
capital, examining their external financing choices in response to changes in risk allows us to directly test
whether managers make their capital structure decisions in line with the trade-off theory of capital
structure. Similar approaches are used in Hovakimian, Hovakimian, and Tehranian (2004), Danis, Rattl,
and Whited (2013), and Korteweg and Strebulaev (2013). 11 Under the dynamic trade-off theory with
adjustment costs, we expect firms that raise external capital to choose an external financing method that is
consistent with their optimal capital structure. This implication of the trade-off theory is consistent with
the prediction of the risk timing argument of capital structure.
To conduct our analysis, we employ both market- and accounting-based risk measures. 12 We use as
market-based measures of firm risk stock return volatility, default probability, and implied asset volatility
based on the Merton (1974) model. Implied asset volatility measures the unobservable volatility of a
firm’s underlying assets that affects its optimal capital structure, while default risk captures the likelihood
of the firm’s financial distress. Despite the limitations of accounting-based measures documented by
Hillegeist, Keating, Cram, and Lundstedt (2004), we also use an adjusted Ohlson’s (1980) O-score
(adjusted as in Franzen, Rodgers, and Simin (2007)) as an alternative measure of risk.
For each of the above risk measures, we construct corresponding risk timing variables by associating
the risk measures with the firm’s financial deficit (i.e., external financing needs), similar to the approach
used by Kayhan and Titman (2007) in their test of the market timing theory of capital structure. When a
11
Specifically, Hovakimian, Hovakimian and Tehranian (2004) focus on the periods when firms issue both debt and
equity. Similarly, Danis, Rattl, and Whited (2013) pay a close attention to the time 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 refinancing times when firms’ net debt (equity) issuance is
greater than 5% of the book value of assets.
12
Since financial markets incorporate information in a timely manner (Roll (1984)), market-based measures of firm
risk are likely to reflect its financial condition more fully and accurately than accounting measures of firm risk (e.g.,
Hillegeist, Keating, Cram, and Lundstedt (2004)). We therefore focus on market-based measures of firm risk as our
key variables of interests.
6
firm engages in risk timing by adjusting its external financing decisions in response to changes in its
underlying risk, it will issue more equity when risk increases, thus decreasing its leverage ratio. Thus,
firms that are more likely to raise external capital in response to increases in risk tend to have lower
leverage ratios when they follow risk timing behavior. We therefore use the correlation between risk and
financial deficit as our key measure of risk timing and examine whether this risk timing variable is
negatively correlated with changes in leverage ratios. 13 For robustness checks, we also investigate
whether a firm is more likely to engage in leverage-decreasing external financing activities as it
experiences an increase in risk.
Using a sample of firms listed on NYSE, Amex, or Nasdaq from 1975 to 2011, we find that firms
with a high correlation between risk and financial deficit significantly lower their leverage ratios: a one
standard deviation increase in risk timing estimated using stock return volatility is associated with a
reduction in the market leverage ratio of 0.43 percentage points. In comparison, the corresponding
decrease associated with the market timing variable is only 0.17 percentage points. Thus, the economic
effect of risk timing on a firm’s capital structure decision is more than twice as large as that of market
timing. We also find that, consistent with our risk timing argument, the risk timing effects are especially
pronounced for firms that raise substantial amounts of external capital and those that have high risk. In
addition, we find that firms that experience an increase in risk in recent years are more likely to issue
equity. 14
13
Our approach focuses on the financing choice made by managers when firms raise (or reduce) external capital but
ignores other leverage-changing financing activities that do not result in any net increases or decreases in external
capital (e.g., repurchasing shares with borrowed money). To examine whether our results are robust when
considering these leverage-changing financing activities, in Section 4, we classify firms’ external financing activities
into leverage-increasing (debt issues and equity repurchases) and leverage-decreasing (debt reductions and equity
issues) activities and find that firms that experience an increase in risk engage in significantly more leverage
decreasing financing activities.
14
Although we find that firms make their external financing decisions in response to changes in both market
valuation and perceived risk, and these financing decisions significantly affect their capital structures, the
implications of these behaviors to investors are not the same. For example, when firms issue equity in response to an
increase in market valuation, this financing decision benefits their existing shareholders but hurts uninformed
outside investors who purchase overvalued stocks. However, when firms respond to changes in risk by moving
7
Our study contributes to the ongoing debate about firms’ capital structure decisions in several ways.
First, our study is the first to examine the impact of cumulative past changes in firms’ underlying risk and
financing decisions on capital structure. Although Kisgen (2006) and Hovakimian, Kayhan, and Titman
(2009) examine whether credit rating targets affect capital structure decisions, 15 to the best of our
knowledge, no prior study investigates whether firms engage in risk timing by optimally choosing
external financing methods in response to past changes in their underlying risk and whether such risk
timing behavior affects their capital structure. We find evidence of economically significant risk timing
behavior even after controlling for several factors that affect firms’ capital structure decisions such as
long-term target leverage ratios and target credit ratings.
Second, our study complements previous literature on the trade-off theory of capital structure by
documenting that firms respond to changes in their underlying risk in a way that is consistent with the
trade-off theory (i.e., they consider costs of financial distress in determining their optimal capital
structure). Given that there is some disagreement regarding the existence of target leverage ratios (Chang
and Dasgupta (2009)), examining risk timing behavior instead of target leverage ratios allows us to avoid
problems arising from mismeasurement of unobservable target leverage ratios in testing predictions of the
trade-off theory of capital structure. In addition, by focusing on firms with a high correlation between
toward optimal levels of leverage, this financing decision is beneficial to various investors including existing
shareholders, new shareholders, and creditors.
15
While a firm’s credit rating can be considered an important risk measure, our study differs from prior studies that
examine the effects of credit rating targets on capital structure at least in two important respects. First, while prior
studies examine how credit ratings or rating targets affect firms’ capital structure decisions, our study focuses on
whether firms that tend to raise more external capital in response to increases in risk choose a financing method that
lowers their leverage ratios (i.e., risk timing behavior). Second, unlike previous studies that use credit ratings as the
sole measure of risk, we employ various measures of firm risk. Results using credit ratings as a sole measure of risk
may be subject to alternative explanations because credit ratings can be viewed as a summary statistic that captures
various elements of a firm’s capital structure such as its debt ratio, the maturity and priority structure of its debt, and
the volatility of its cash flows (Hovakimian, Kayhan, and Titman (2009)). In addition, credit ratings may not fully
reflect firm risk in a timely manner and thus there may be a gap between rating agencies’ assessments of a firm’s
credit risk and the firm’s true underlying risk (e.g., Altman and Rijken (2004)). Altman and Rijken (2004) also point
out that rating agencies focus on long-term default probabilities and put less weight on short-term risk. In our tests,
we examine the effect of firms’ risk timing behavior on their capital structure decisions after controlling for target
credit ratings. Thus, our tests allow us to examine whether firms’ capital structure decisions depend on changes in
risk beyond the risk captured by changes in credit ratings.
8
their risk and financial deficit (i.e., firms with a high value of risk timing variables), we can test
implications of the trade-off theory without facing problems caused by high adjustment costs. This
approach allows us to examine optimal leverage at times when firms change their leverage and therefore
is likely to capture managers’ intention regarding how they manage their capital structures more clearly.
Similarly, Strebulaev (2007) argues that since firms adjust their capital structures infrequently due to high
adjustment costs, the results of standard cross-sectional capital structure tests could lead to a misleading
conclusion, and shows that leverage is likely to be at the optimum level only at the time of readjustment.
Our findings show that firms’ risk timing can explain the residual fluctuation in their capital structure
even after taking into account the drift towards their long-term targets and other determinants of capital
structure. This result contrasts with that of Hovakimian, Kayhan, and Titman (2012) who find that firms
with higher bankruptcy costs tend to choose capital structures with greater exposure to bankruptcy risk,
which cannot be easily reconciled with a (static) trade-off theory.
The paper proceeds as follows. In Section 2, we describe our key risk measures of interest and
outline the empirical methodology for testing firms’ risk timing behavior. Section 3 presents our main
empirical results and Section 4 shows the results from an alternative test of risk timing behavior. Section
5 summarizes the results and provides concluding remarks.
2. Data and Methodology
2.1. Data
Our sample consists of all NYSE, Amex, or Nasdaq firms available on both CRSP and Compustat
between 1971 and 2011. As in Vassalou and Xing (2004), we start our sample period in 1971 because of
insufficient debt-related financial data prior to 1971 in Compustat. All 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 4900-4999) firms since their capital structure
9
decisions are subject to regulatory constraints. In addition, as in Kayhan and Titman (2007), we exclude
firms with book leverage ratios above 100%. Finally, to mitigate potential problems caused by extreme
outliers, we winsorize all variables at the 1st and 99th percentiles as in Leary and Roberts (2005) and Kale
and Shahrur (2007). Since our risk timing measures discussed in Section 2.4 below require five years of
data, we further delete the first four years of our sample period (i.e., 7,909 firm-year observations from
1971 to 1974) when constructing our risk timing measures. Our final sample consists of 43,620 firm-year
observations over the period, 1975-2011. 16
2.2. Leverage Ratio, External Financing, Valuation, and Control Variables
Leverage is measured by both book and market leverage ratios. The book (market) leverage ratio is
defined as the book value of debt divided by the book (market) value of total assets. The market value of
total assets is computed as total assets (AT) minus the book value of equity plus the market value of equity,
and the book value of debt is computed as total assets minus the book value of equity. As in Kayhan and
Titman (2007), the book value of equity is estimated as total assets minus the sum of total liabilities (LT)
and the liquidation value of preferred stock (PSTKL) plus deferred taxes, investment credit (TXDITC),
and convertible debt (DCVT). When PSTKL is not available, the redemption value (PSTKRV), or carrying
value (PSTK) if PSTKRV is not available, is used. 17 The market value of equity is measured at the fiscal
year-end.
Although there is a debate about the existence and measurement of target leverage ratios as discussed
above, we control for these ratios in our analysis to facilitate comparison with previous studies using them
(e.g., Hovakimian, Opler, and Titman (2001)). We estimate target leverage ratios (Tlev) using a similar
method as in Kayhan and Titman (2007). The detailed description on the estimation method and the
16
Among firms that meet our screening requirements, 141 stay in our sample for 35 or more years over our sample
period (1975 to 2011) and 1,828 (2,329, 798, and 345) stay in our sample for 1-5 (6-15, 16-25, and 26-34) years.
17
Annual Industrial Compustat data variable names are in parentheses.
10
results of target leverage regressions are provided in Appendix B.
As target leverage ratios change, firms are likely to adjust their capital structure. We measure the
change in target market (book) leverage ratios, dTlevM(B)[0,4]t, as the difference in target market (book)
leverage ratios over the past five years, TlevM(B)t – TlevM(B)t-4. In addition, we measure market (book)
leverage deficit, LdefM(B)[0,4]t, as the difference between the target market (book) leverage ratio and the
actual market (book) leverage ratio five years back, TlevM(B)t-4 – LevM(B)t-4. If a firm pursues a target
leverage ratio, we would expect speed with which the firm adjusts its capital structure towards its target to
depend on how far it is away from its target (i.e., the leverage deficit).
Similar to Frank and Goyal (2003), to measure the amount of external financing, we define a firm’s
financial deficit over the past five years, FD[0,4], as the ratio of the sum of net equity and long-term debt
issues over the past five-year period to total assets in year -4 (i.e., [sale of common and preferred stock
(SSTK) – purchase of common and preferred stock (PRSTKC) + long-term debt issuance (DLTIS) – longterm debt reduction (DLTR)] over the past five years divided by AT in year -4). 18 In addition, we define a
dummy variable, FDd, to represent firms with positive FD values.
As shown in previous studies (e.g., Loughran and Ritter (1995)), firms’ financing decisions may
depend on the market value of their stock, which also affects their capital structure. To measure the
market valuation of the firm, we estimate MB of total assets as described above.
Graham and Harvey (2001) and Hovakimian, Kayhan, and Titman (2009) show that managers pay
close attention to their firm’s target credit rating. This finding suggests that any gap between target and
actual credit ratings is likely to induce managers to adjust their firm’s capital structure in an effort to
maintain the firm’s target credit rating. To control for the effect of a firm’s target credit rating on its
capital structure, we estimate a firm’s target credit rating, TRating, by calculating the fitted value from an
ordered probit regression estimated in each year as in Hovakimian, Kayhan, and Titman (2009). The
18
Given high transaction costs, firms are more likely to adjust their capital structure when they have to rely on
external financing.
11
details of this regression model and the results from the ordered probit regression used to estimate target
credit rating in 2011 are available in Appendix C. We define credit rating deficit (CD) as the difference
between TRating and the actual credit rating. Finally, since credit ratings are only available for a subset of
sample firms, 19 we use a dummy variable, CRdummy, to indicate whether the firm has credit rating
information available.
2.3. Risk Measures
To test for the effect of firms’ risk timing behavior on their capital structure adjustments, we use
various risk measures. Our main criterion in choosing measures of risk is that they accurately measure
time-series fluctuations in risk and thus allow us to investigate whether changes in firms’ true risk affect
their capital structure. 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. Hillegeist, Keating, Cram, and Lundstedt (2004) also find that, as predictors of
financial distress, market-based risk measures, such as those obtained by fitting a Merton (1974) model,
significantly outperform accounting-based risk measures. Accordingly, we use the following three
market-based risk measures as our key measures of firm risk: stock return volatility, Merton’s (1974)
default risk, and implied asset volatility estimated based on the Merton (1974) model. However, for
robustness purposes we also use a risk measure based on financial statements, namely, a version of
Ohlson’s (1980) adjusted O-score as in Franzen, Rodgers, and Simin (2007) (O-Score), as an alternative
measure of firm risk.
The volatility of stock returns reflects uncertainty in the market value of a firm’s equity. While the
volatility of the firm’s total assets may provide a better measure of its risk, we use only equity volatility in
19
Credit rating information is available for about 14% of firms over the full sample period and 20% of firms over
the 1985 to 2011 subperiod.
12
measuring firm risk due to illiquidity of debt markets. 20 Default risk, which is closely related to financial
distress costs, is measured based on the Merton (1974) model. Finally, implied asset volatility serves as an
important measure of firm risk since it captures the uncertainty in asset values, not equity values, which
ultimately matter in avoiding financial distress.
To measure stock return volatility over the past five years, EquityVol[0,4], we first calculate the
standard deviation of 52 weekly stock returns each year and multiply it by the square root of 52 to
annualize it. We then calculate the average of these annualized standard deviations over the past five years.
Merton’s (1974) default risk is measured in a similar way as in Vassalou and Xing (2004). We use
the average of the past five years’ default probabilities, Merton[0,4], estimated following the Merton
(1974) approach, as a measure of default risk. A detailed description of the measurement of default risk is
provided in Appendix D.
Implied asset volatility, AssetVol[0,4], is estimated using the approach to measure default risk
described in Appendix D. Specifically, we use the average of the past five years’ annualized standard
deviations of daily changes in asset values calculated in the process of estimating Merton’s default
probabilities in each year (i.e., estimated 𝜎𝜎𝐴𝐴 ) as a measure of the riskiness of a firm’s total assets. 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 average of the past five years’ adjusted O-scores (1980) ending in year -1, OScore [0,4], as our measure of accounting-based risk. This measure is estimated based on Franzen,
Rodgers, and Simin (2007), who propose the adjustment method for net income, total assets, and total
20
Due to the residual nature of equity claims, the use of equity volatility may entail a potential endogeneity problem
since an increase in equity risk reflected in the cost of equity is likely to decrease the market value of equity more
than the value of debt, thereby resulting in an increase in the leverage ratio. However, it is important to note that this
effect goes in the opposite direction compared to the effect under our risk timing argument, which predicts that firms
issue more equity when risk increases. Thus, all else being equal, this endogeneity problem should make it harder
for us to detect risk timing in the data. In additional tests, we also present results based on the book value of leverage,
which is not affected by this potential endogeneity problem.
13
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 of our measurement of O-score is
provided in Appendix D.
2.4. Risk and Market Timing Measures
To capture market timing behavior, Kayhan and Titman (2007) construct yearly and long-term market
timing variables that are closely related to the measure used in Baker and Wurgler (2002). The yearly
market timing (YT) measure is defined as the covariance between the market-to-book asset ratio (MB) and
financial deficit (FD) over the past five years and the long-term market timing (LT) measure is the
average MB over the past five years multiplied by the average FD over the past five years. To be
consistent with these market timing measures, we estimate YT and LT using the following two equations,
respectively: 21

 t −4

 ∑ FDs × MBs
YT[0,4]i,t =  s = t
− FD × MB 
5






t −4
LT[0,4]i,t =
σ FD × σ MB = Correl(FD, MB)
,
(1)
t −4
∑ FD ∑ MB
s
s =t
5
×
s =t
5
s
= FD × MB
The key intuition behind these timing measures is that if managers issue more equity and lower
leverage ratios when the market is more optimistic about their firm’s prospects, we should observe greater
covariance between FD and MB, and a negative relation between YT and leverage ratios. We also expect
LT to have a negative correlation with leverage ratios if managers who believe that the cost of equity is
21
Different from Kayhan and Titman (2007) who use the covariance in measuring market timing variables to
emphasize the link between their measures and the measure used by Baker and Wurgler (2002), we use the
correlation to incorporate the differences in the levels of standard deviations of market-to-book ratio and external
financing measures. Similarly, we use the correlation, instead of covariance, in defining our risk timing measures
discussed below.
14
negatively related to MB issue more equity when MB is high.
Our risk timing measure is developed following a similar logic. If firms issue more equity to lower
risk when risk is high, we expect to observe a high correlation between risk measures and financial deficit,
and a negative correlation between the risk timing measure and changes in leverage ratios. Thus, for each
of our risk variables described above, we calculate a yearly risk timing measure as follows: 22

 t −4

 ∑ FDs × Risk s
YT( Risk )[0,4]i,t =  s = t
− FD × Risk 
5






σ FD × σ Risk = Correl(FD, Risk ) ,
(2)
In Appendix A, we discuss all variables used in estimating equation (2) and their definitions in detail. One
potential problem of our risk timing measure is that it may not adequately capture a firm’s risk timing
behavior if the firm responds to an increase in risk by engaging in external financing activities in years
following the risk increase. To address this concern, in Section 4, we present an alternative approach to
measure the effects of the changes in firm risk on capital structure decisions.
2.5. Regression Specification
To test whether changes in leverage ratios over a five-year period are related to the risk timing
measures developed in the previous subsection, we run the following panel regression model, which
controls for various factors that affect a firm’s capital structure:
22
In untabulated tests, similar to the long-term market timing measure used in Kayhan and Titman (2007), we
define a long-term risk timing variable as average FD multiplied by average risk over the past five-year period,
include it in the regression analyses, and find qualitatively similar results as those reported in the paper. Unlike
yearly risk timing measures whose correlation with FDs is low, long-term risk timing measures are highly correlated
with FDs. Thus, to disentangle the effect of risk timing on leverage from the effect of financial deficits and to
minimize multicollinearity problems, we focus on only yearly risk timing variables in our analyses. However, to
make our study comparable to Kayhan and Titman (2007), we include the long-term market timing variable in the
regression analyses.
15
Levi ,t − Levi ,t −4= β 0 + β1YT [0,4]i ,t + β 2YT [0,4]i ,t × DummyVari ,t + β 3 LT [0,4]i ,t
+ β 4 Risk[0,4]i ,t + β 5YT ( Risk )[0,4]i ,t + β 6YT ( Risk )[0,4]i ,t × DummyVari ,t
+ β 7 × DummyVari ,t + β 8 MB[0,4]i ,t + β 9 FD[0,4]i ,t + β10 FDd [0,4]i ,t + β11CDi ,t −4 ,
(3)
+ β12 dTRating[0,4]i ,t + β13 r[0,4]i ,t + β14 EBITD[0,4]i ,t + β15 LdefM ( B)[0,4]i ,t
+ β16 dTlevM ( B)[0,4]i ,t + β17YearDi ,t + β18 FirmDi ,t + ε t
where r[0,4]t refers to buy-and-hold stock returns over the past five fiscal years and EBITD[0,4]t is the
sum of earnings before interest, tax, and depreciation (OIBDP) over the previous five years divided by
total assets in year -4. DummyVar is a placeholder that represents one of three indicators that allow us to
investigate firms’ risk timing behavior in more depth (but is absent when we report our results for the
entire sample). These three indicators are: 1) High Fiscal Deficitt (High FDt), which takes the value of
one if a firm’s financial deficit during the past five years is within the top 50% (or 25%) of all firms
available in fiscal year t with a positive financial deficit over the same period, and zero otherwise, 2) High
Risk Levelt, which takes the value of one if a firm’s average risk over the past five years is within the top
50% of all firms available in fiscal year t, and zero otherwise, and 3) High Risk Changet, which takes the
value of one if a firm’s increase in risk over the past five years is within the top 50% among firms
available in fiscal year t with an increase in risk over the same period, and zero otherwise. In untabulated
tests, we also experiment with 25% as a cutoff point in defining High Risk Level and High Risk Change
and find that our results do not change. All other variables are defined as described above.
To address potential problems that arise from using overlapping periods in the regression analyses,
we use a bootstrapping method in estimating the statistical significance of the coefficients as described in
Kayhan and Titman (2007). In addition, we use pooled ordinary least squares (OLS) regressions with firm
and year dummy variables to deal with unobservable firm and time fixed effects. However, as shown in
Petersen (2009), including firm dummy variables is effective only if firm fixed effects are permanent.
Therefore, as an additional cautionary treatment, we use firm-clustered standard errors in calculating tstatistics as suggested by Petersen (2009).
16
As indicated earlier, our approach to testing firms’ capital structure decisions allows us to largely
avoid problems caused by adjustment costs and the estimation of target debt ratios. In the next section, we
present results for tests of these predictions of firms’ risk timing behavior.
3. Empirical Results
3.1. Summary Statistics
Table 1 shows summary statistics for our sample firms. The mean market (book) leverage over the
past five years is 39.7% (44.7%) while the mean change in market (book) leverage over the past five
years is 1.3% (1.7%). The mean market (book) leverage deficit (LdefM(B)[0,4]) is 2.6% (2.4%). Thus, our
sample firms’ market (book) leverage ratios are on average 2-3% lower than their target leverage ratios
four years prior to the measuring year. We also find the average change in target market (book) leverage
over the past five years is 0.4% (1.1%), suggesting that during our sample period, target leverage ratios
changed only slightly over a five-year interval.
The average (median) cumulative financial deficit, FD[0,4], is 14.4% (3.7%), indicating that the total
amount of external financing over the past five years is around 15% (4%) of total assets in year -4. The
average (median) yearly market timing, YT[0,4], is 0.06 (0.07), which implies that a firm’s financial
deficit and market-to-book ratio are not highly correlated. The average (median) long-term market timing,
LT[0,4], is 4.5 (0.9).
The results on the annual risk timing variables show that their average and median values are close to
zero except for the risk timing measures based on Merton’s default risk and O-score. These results
suggest that the magnitude of the correlations between financial deficit and risk vary across the risk
measures used in the analysis. Low correlations between financial deficit and risk are not necessarily
inconsistent with risk timing given high transaction costs as shown in earlier studies (e.g., Welch (2004)).
Summary statistics for our various risk measures are presented in the bottom rows of Table 1.
17
3.2. Correlation Analysis
In Table 2, we report the correlations among changes in leverage, risk, and the risk timing variables
used in our analyses. We find that the correlations between changes in leverage and the yearly market
timing variables are negative (-0.01 and -0.04 for changes in market and book leverage, respectively) but
significant only for changes in book leverage. The correlations between changes in leverage and longterm market timing are positive and significant (0.09 and 0.05 for changes in market and book leverage,
respectively). In addition, we find that the risk timing variables are significantly negatively correlated
with changes in leverage, even though their correlations are not large.
We also find that our risk timing measures are significantly positively correlated with each other
although the magnitude of the correlation coefficients varies across the pairs of risk timing measures used
in the analysis. There are also significant positive correlations among our risk measures. However, the
correlations between our risk measures are typically lower than one, suggesting that they capture different
aspects of firm risk. All three market-based risk measures are only weakly correlated with the O-score, an
accounting-based risk measure, perhaps due to the latter’s lack of timely updates.
Cumulative financial deficit, FD[0,4], is significantly positively correlated with changes in market
and book leverage, suggesting that external capital is more likely to be raised by issuing debt than by
issuing equity. This result is consistent with the prediction of the pecking order theory and the findings in
previous studies (e.g., Leary and Roberts (2010)). We also find a very high and significant correlation of
0.93 between FD[0,4] and long-term market timing, LT[0,4]. Thus, to disentangle the effect of market
timing from the effect of financial deficits, it is important to consider the short-term yearly market timing
variable, YT[0,4], whose correlation with the financial deficit variable is only 0.06. 23 FD[0,4] is
significantly positively correlated with YT(EquityVol)[0,4] and YT(AssetVol)[0,4] while it is significantly
negatively correlated with Merton default risk, YT(Merton)[0,4], and O-score, YT(O-score)[0,4], albeit the
23
For alternative arguments in favor of short-term market timing, see Kayhan and Titman (2007).
18
magnitudes of these correlations are low. The average market-to-book asset ratio, MB[0,4], is significantly
negatively correlated with changes in market and book leverage, which is consistent with the market
timing theory of capital structure.
In untabulated tests, we check the correlations between our risk (risk timing) measures and other firm
characteristics reported in Table 1 and find that none of the correlations is high enough to cause
multicollinearity problems in our subsequent empirical analyses.
3.3. Main Findings: Regression of Changes in Leverage on Market and Risk Timing Variables
In this subsection we present the results from panel regressions of changes in market (book) leverage
on market and risk timing variables. In all tables below, we report the significance of the coefficient
estimates in two ways, one based on the bootstrapping method (denoted by asterisks) and the other based
on clustered standard errors at the firm level (t-statistics in parentheses).
Table 3 presents our main regression results. The first five regressions use the change in market
leverage as the dependent variable and the next five regressions use the change in book leverage as the
dependent variable. In columns (1) and (6), we replicate the results of previous studies on market timing
(Baker and Wurgler (2002), Kayhan and Titman (2007)) and credit rating targets (Graham and Harvey
(2001), Hovakimian, Kayhan, and Titman (2009)). We confirm the significance of market timing and
credit rating targets in explaining firms’ capital structure decisions. The significant negative coefficient
estimate of -0.41 on the yearly market timing variable in column (1) suggests that a one-standard
deviation increase in the value of a yearly market timing variable (0.42) leads to a 0.17 percentage point
decrease in the market leverage ratio over the five-year period. 24 The significantly negative coefficient
estimates on the change in target credit rating, dTRating, in both columns (1) and (6) suggest the presence
of credit rating targets.
24
Recall that we focus on yearly market timing since long-term market timing suffers from having a very high
correlation with cumulative financial deficit in excess of 0.9 (see Table 2). See also Kayhan and Titman (2007).
19
In columns (2) and (7) of Table 3, we add average equity volatility over the past five years,
EquityVol[0,4], and yearly equity volatility risk timing, YT(EquityVol)[0,4], as additional explanatory
variables. We find that the coefficient estimates on EquityVol[0,4] are significantly positive at the 1%
level while those on YT(EquityVol)[0,4] are significantly negative at the 1% level. These results hold for
tests using the bootstrapping method described in Kayhan and Titman (2007) as well as tests using
clustered standard errors at the firm level.
The positive coefficient estimates on EquityVol[0,4] indicate that firms that experience an increase in
risk over the past five years tend to also experience an increase in leverage. By itself, this result does not
necessarily contradict the trade-off theory - even though the level of risk increases, a firm would still like
to increase its leverage if its previous leverage is below the optimal level. 25 Indeed, we find significant
positive coefficient estimates on both leverage deficits and change in target leverage ratios, suggesting
that firms increase their leverage when their target leverage ratios are above actual leverage ratios or their
target leverage ratios increase during the past five years. These results are consistent with the trade-off
theory.
The significant negative coefficient estimates on YT(EquityVol)[0,4] are consistent with risk timing
behavior in firms’ capital structure decisions. A firm actively engaging in risk timing will tend to issue
more equity when its risk increases and therefore has a high correlation between financial deficit and risk,
which in turn suggests a significant negative relation between changes in leverage and the risk timing
variables. 26 The effect of risk timing on firms’ capital structure is also economically significant. The
coefficient estimate on YT(EquityVol)[0,4] is -1.04 in column (2). This magnitude suggests that a onestandard deviation increase in YT(EquityVol)[0,4] (0.41) is associated with a 0.43 percentage point
25
Alternatively, it is possible that, almost by definition, firms that increase their leverage ratios will have riskier
equity. This effect might cause the regression coefficient to be positive.
26
However, if the pecking order preference dominates any concerns over increased risk, even the firm with a high
correlation between financial deficit and risk may end up issuing more debt, rather than equity, resulting in a
positive relation between the changes in leverage and the risk timing variables.
20
decrease in the market leverage ratio. Thus, the economic effect of risk timing on a firm’s market leverage
is more than twice as large as that of market timing (0.17 as reported above). 27
The remaining columns in Table 3 present the results using alternative measures of risk and risk
timing variables. Columns (3) and (8) use implied asset volatility as the risk measure, columns (4) and (9)
use Merton’s (1974) default risk, and columns (5) and (10) use an adjusted O-score. We find that the
results echo those in (2) and (7). In particular, the coefficient estimates on the risk timing variables are all
negative and significant. Although the economic significance of risk timing effects in columns (3), (4),
and (5) is smaller than that of equity volatility timing in column (2), it still exceeds that of market timing
in columns (3), (4), and (5). 28 These results are consistent with managers engaging in risk timing.
We also find that as in columns (2) and (7), an increase in the underlying risk measure is typically
associated with significantly positive changes in market and book leverage. A noteworthy exception to
these results is asset volatility, which is significantly negatively related to changes in market and book
leverage (columns (3) and (8)).
As discussed earlier, changes in risk will affect target leverage ratios and thus, risk timing, if it exists,
is consistent with capital structure adjustments toward target leverage ratios. Tests of the existence of risk
timing behavior after controlling for variables related to target leverage ratios can therefore be considered
a simple and straightforward way to examine the trade-off theory of capital structure, which thus far has
27
Kayhan and Titman (2007) show that the economic effect of long-term market timing on the leverage ratio is
much larger than that of yearly market timing. To examine the economic effect of long-term risk timing on the
leverage ratio, we define a long-term risk timing measure as average FD multiplied by average risk over the prior 5year period and find that its economic impact is greater than that of the yearly risk timing measure, albeit its
economic impact is less than that of the long-term market timing measure. For example, using Equity Vol, we find
that a one-standard deviation increase in the long-term risk timing variable leads to a 0.66% decrease in the market
leverage ratio while the corresponding increase in the long-term market timing variable is associated with a 3.76%
decrease in the market leverage ratio. Thus, while risk timing may not be the most important factor in explaining
variation in capital structure, it is still important in that it is a new way of testing and providing evidence regarding
the trade-off theory of capital structure that emphasizes a strong link between risk and leverage as pointed out by
previous theoretical papers (e.g., Leland (1994) and Chen (2010)).
28
When YT(AssetVol)[0,4] increases by one standard deviation (0.41), the market leverage ratio decreases by 0.19
percentage points [=0.41×(-0.46)]. Similarly, one-standard deviation increases in YT(Merton)[0,4] and YT(OScore)[0,4] correspond to market leverage ratios that are lower by 0.27, and 0.33 percentage points, respectively.
21
mainly been examined based on hard-to-identify target debt ratios. Of course, the significant explanatory
power of risk timing variables beyond that of target leverage ratios may also suggest the existence of
critical factors not captured by target leverage ratios.
Overall, the results in Table 3 suggest that the effects of market timing and risk timing on firms’
capital structure decisions are both statistically and economically significant. While Hovakimian, Kayhan,
and Titman (2012) use an innovative approach to test the direct implication of the static trade-off theory
and document several results that are not consistent with its predictions, our approach provides the results
that are consistent with its predictions. Our results are also consistent with Huang and Ritter (2009) who
argue that both the market timing model and the static trade-off model are important determinants of
capital structure.
3.4. Further Analysis and Robustness Checks
In this subsection, we check the robustness of our results by performing several additional tests. First,
we examine whether our results in the previous section are more pronounced for firms that raise a large
amount of external capital. Since the main implication of the risk timing hypothesis is that firms choose
an external financing method to maintain acceptable levels of risk, if risk timing indeed exists, we expect
our results to be more evident for firms that actually raise a large amount of external capital. Second, we
reestimate the previous regressions using a residual approach to measuring risk and risk timing variables.
Third, we examine whether our results are more pronounced for firms that have a high level of risk, or
firms that experience large changes in risk.
3.4.1. Effect of Financial Deficit
As Leary and Roberts (2005) point out, adjustment costs prevent firms from continuously
rebalancing their capital structure, and therefore a natural time for firms to rebalance their capital
structure is when they are in need of external capital (Frank and Goyal (2003)). If our risk timing
22
hypothesis holds, we expect that firms that raise a large amount of external capital adjust their leverage
ratios more aggressively in response to the change in underlying risk.
To test this prediction, we reestimate the Table 3 regressions by including an indicator, High
Financial Deficit (High FD), and its interaction with risk and market timing variables. In columns (1) to
(4), High FDt is set to one if a firm’s financial deficit during the past five years is within the top 50% of
all firms available in fiscal year t with a positive financial deficit over the same period, and zero otherwise.
In columns (5) to (8), we use the top 25% instead of the top 50%.
The results are reported in Table 4. We find that the coefficient estimates on the interaction terms
between High FD and the risk timing variables are all negative and significant. We also find that the
coefficient estimates on risk timing, YT(risk measure), are negative and significant in all columns except
for columns (2), (4) and (6) in which these estimates are negative but insignificant. Thus, the risk timing
results hold for both high and low financial deficit firms but the effects are stronger for firms with a high
financial deficit than those with a low financial deficit, consistent with our prediction above.
Overall, the results in this subsection suggest that when firms raise a large amount of external capital,
their financing decisions are consistent with the risk timing explanation (i.e., lower leverage in response
to increases in risk). Firms with a small financial deficit, on the other hand, adjust their leverage less,
possibly because the desire for risk timing is counterbalanced by significant transaction costs. These
results are consistent with the important role of adjustment costs in explaining firms’ capital structure as
emphasized in previous studies (e.g., Leary and Roberts (2005)).
3.4.2. Residual Approach
One concern with our results in previous sections is that they may be driven by spurious correlations
between risk timing variables and other well-known determinants of optimal capital structure (e.g.,
Kayhan and Titman (2007)) discussed above. To address this concern, we first regress risk variables on
several determinants of optimal capital structure as follows:
23
Riski ,t= α + β1 FDi ,t + β 2 FDd i ,t + β 3CDi ,t −1 + β 4 EBITDi ,t + β 5 dTRating i ,t
+ β 6 ri ,t + β 7 LdefM ( B) i ,t + β 8 dTlevM ( B) i ,t + β 9YearDi ,t + β10 FirmDi ,t + ε t ,
(4)
where Risk is one of four risk variables used in Table 3 (equity volatility (EquityVol), implied asset
volatility (AssetVol.), Merton default risk (Merton), and adjusted O-score (O-Score)); FD is financial
deficit; FDd is a dummy variable that takes the value of one if FD is positive, and zero otherwise; CD is
credit rating deficit; EBITD is profitability; dTRating is the change in target credit rating; r is the one-year
buy-and-hold stock return; LdefM(B) is the market (book) leverage deficit; dTlevM(B) is the change in
target market (book) leverage; YearD is a year dummy variable; and FirmD is a firm dummy variable. See
Appendix A and our discussion above for precise definitions of each variable.
We next use the residual from this regression as our new risk variable and construct a new risk
timing variable (“Residual Risk Timing”). Using Residual Risk Timing in the regressions allows us to
mitigate concerns that our previous risk timing variables simply capture other determinants of firms’
capital structure.
Table 5 reports the regression results using the change in market (book) leverage as the dependent
variable and residual risk timing variables as our key independent variables of interest. We find that our
main results change little except for columns (4) and (8), where a residual O-Score timing variable is used
as an independent variable: coefficient estimates on the residual EquityVol, Asset Vol., and Merton risk
timing variables are negative and significant with magnitudes very similar to those of the corresponding
variables in Table 3. However, although the coefficient estimates on the residual O-Score risk timing
measure are still negative, they lose their significance, possibly because, unlike market-based risk
measures, O-Score as an accounting-based risk measure does not fully capture timely and forwardlooking information about firms’ prospects (Hillegeist, Keating, Cram, and Lundstedt (2004)).
24
Overall, the results in Table 5 show that our risk timing results are not merely driven by a high
correlation of our risk timing measures with other factors known to affect firms’ capital structure
decisions, but rather reflect the effect that risk timing has on firms’ capital structure. 29
3.4.3. Subsample Analysis
Our risk timing hypothesis posits that firms that raise external capital at a time of increasing risk will
issue more equity in order to maintain an acceptable level of risk. This hypothesis therefore predicts that
firms more concerned about risk will be more active in issuing equity to reduce their leverage ratios.
In general, firms are more likely to be concerned about managing their risk if their level of risk is
high in comparison to other firms, or if they have recently experienced a significant increase in risk. For
example, if firms are already quite risky and on the verge of entering financial distress, they may need to
more aggressively respond to increases in risk than safer but otherwise identical firms. However, it is
possible that firms maintain a risk level, regardless of whether it is high or low, that reflects their optimal
capital structure. In this case, using risk levels to capture firms’ incentive to engage in risk timing may not
be appropriate. Instead, changes in risk may serve as a better measure of firms’ incentive to engage in risk
timing since firms that experience unusually large increases in risk may have strong incentives to manage
their financial distress risk. A significant increase in risk, even when it does not have any material effect
on the likelihood of bankruptcy (e.g., for high quality firms), can induce managers to engage in risk
timing and reduce leverage since large increases in risk are likely to increase the probability of a rating
downgrade and in turn the cost of capital.
29
We also use a three-stage least squares (3SLS) method to deal with the endogeneity of our risk timing variables,
where risk and risk timing variables are treated as endogenous variables. We use industry mean risk and industry
mean risk timing variables as instrument variables for risk and risk timing variables, respectively. In untabulated
tests, we find that the results are qualitatively similar and risk timing variables are significantly negatively related to
the changes in leverage ratios.
25
To investigate whether firms’ incentives to engage in risk timing are greater when they have higher
risk or when they experience a significant increase in risk, we include the dummy variables High Risk
Level and High Risk Change, and interact them with risk and market timing variables. This approach
allows us to examine whether risk timing, if it exists, is driven primarily by riskier firms or firms that
have observed a recent increase in risk, or by safe firms that adjust their leverage to a higher optimal level
in response to decreases in risk. For example, it may be relatively easy for less risky firms to borrow
funds to increase their leverage to an optimal level. In contrast, risky firms may find it more difficult to
issue equity in order to reduce risk to an acceptable level.
Table 6 presents the effects of High Risk Level and High Risk Change on market leverage. We use the
sample median to define High Risk Level and High Risk Change. The unreported results using book
leverage and those using the 25% cutoff value to define High Risk Level and High Risk Change are
qualitatively similar. Columns (1) to (4) present results using High Risk Level and columns (5) to (8)
report results using High Risk Change. With respect to equity volatility (EquityVol), the results in column
(1) indicate that the coefficient estimates on both risk timing and its interaction with High Risk Level are
negative and significant. These results suggest that both low and high risk firms engage in risk timing but
high risk firms tend to more aggressively adjust their capital structure in response to changes in risk. The
coefficient estimates for firms with high risk (sum of the coefficient estimates on risk timing and its
interaction with High Risk Level) are more than twice as large as those for firms with low risk (coefficient
estimate on risk timing).
With respect to the other risk measures, we again find that firms’ risk timing incentives are generally
stronger when they have a high level of risk. When firms have a low level of risk, however, their
incentives to engage in risk timing are statistically insignificant (t-statistics for the coefficient estimates
26
on risk timing lie between -0.67 and -1.51), indicating that only firms with high levels of risk actively
engage in risk timing. 30
Overall, these results suggest that compared to firms with a low level of risk, firms with high risk are
more active in lowering their leverage by engaging in risk timing. These results are consistent with the
view that although risker firms may find it difficult to raise external capital, they have more urgent needs
to do so to manage their risk.
In columns (5) through (8), we replace High Risk Level with High Risk Change. Consistent with the
results in column (1), when we use equity volatility (EquityVol) as a measure of risk, the coefficient
estimates on both risk timing and its interaction with High Risk Change are negative and significant.
However, in other regressions that use default risk (Merton), implied asset volatility (Asset Vol.), and
adjusted O-score (O-Score), the coefficient estimates on the risk timing variables are negative and
significant but the coefficient estimates on the interactions between the risk timing variables and High
Risk Change are insignificant. Thus, the risk timing incentives of firms that experience high increases in
default risk, asset volatility, or accounting-based risk are statistically indistinguishable from those of firms
that do not experience such increases. Overall, the results suggest that firms engage in risk timing
regardless of whether they experience high or low changes in firm risk. The results also suggest that our
risk timing results obtained in Table 3 are not driven by firms with lower risk increasing their leverage.
4. Alternative Approach to Test the Risk Timing Hypothesis
Thus far, our approach to test the risk timing hypothesis closely follows that of Kayhan and Titman
(2007) who examine the market timing theory of capital structure. In equation (3), we examine whether
firms that engage in external financing activities after an increase in risk tend to choose a source of
financing that lowers their leverage ratio. A potential concern about this approach is that firms that
30
Note that in regression (2), the sum of the coefficient estimates on risk timing and its interaction with High Risk is
statistically significant at the 10% level.
27
experience an increase in risk may engage in external financing activities a few years later after the
increase in risk, not during the year of risk increase. 31 In this case, we will observe a low correlation
between risk and financial deficit even though the firm’s choice of financing is still driven by risk
consideration.
To alleviate this concern, we classify firms’ external financing activities into leverage-increasing
(debt issues, equity repurchases) and leverage-decreasing (debt reductions, equity issues) activities. We
then examine whether the difference between leverage-increasing and leverage-decreasing external
financing activities, scaled by total assets, is related to our risk variables. Specifically, we define LDEFA
[t+s], the magnitude of leverage decreasing external financing activities, as net equity issue minus net
debt issue, divided by lagged total assets, over fiscal years from t+1 to t+s (s ≥ 1). The difference between
net equity issue and net debt issue is calculated as follows: sale of common and preferred stocks (SSTK)
minus purchase of common and preferred stocks (PRSTKC) minus long-term debt issuance (DLTIS) plus
long-term debt reduction (DLTR). We then run the following regression to investigate whether, all else
being equal, firms with a higher level of risk, or those that recently experience an increase in risk, engage
in more external financing activities that decrease their leverage ratios than otherwise identical firms with
a lower level of risk or those without experiencing an increase in risk:
LDEFA[t + s ]i ,t = β 0 + β1Riski ,t −1 + β 2 ∆Riski ,t + β 3 MBi ,t −1 + β 4 ∆MBi ,t + β 5 FDi ,t
+ β 6 FDDi ,t + β 7CDi ,t + β8 dTRating i ,t + β 9 ri ,t
(5)
+ β10 EBITDi ,t + β11LdefBi ,t + β12 dTlevBi ,t + β13YearDi ,t + β14 FirmDi ,t + ε i ,t
The key difference between this equation and equation (3) is that independent variables are
measured over one year, instead of over past five years. Equation (5) also includes ∆Riskt, which is the
31
For instance, if timing of a firm’s investment is determined by the presence of real options, then the firm that
experiences an increase in risk may want to delay the adoption and funding of an available project until a later date
when uncertainty is reduced. Leary and Roberts (2005) report that when a firm experiences a shock to equity prices,
the median time until it rebalances its capital structure is five to six calendar quarters.
28
change in risk during year t, respectively. We also replace the long-term and yearly market timing variable
with the lagged market to book ratio and the change in market to book ratio, respectively.
Table 7 presents the results. The first four regressions examine a firm’s external financing activities
in year t+1. Overall, we find that risk is an important factor for a firm’s choice of the source of external
financing. For example, the results in column (1) show that firms with higher equity volatility engage in
significantly more leverage decreasing financing activities than otherwise identical firms with lower
equity volatility. Similarly, firms that experience an increase in equity volatility in the previous year
engage in significantly more leverage decreasing financing activities than other firms. These results
suggest that firms that have high levels of risk or those that experience increases in risk choose a source
of external financing that reduces leverage and risk. These results are consistent with the risk timing
hypothesis. The coefficient estimates on lagged equity volatility and the change in equity volatility are
0.021 and 0.028, respectively, suggesting that a one standard deviation increase in lagged equity volatility
(30.96%) is associated with an increase in a firm’s leverage decreasing financing activity in year t+1 by
0.65% (0.021×30.96%) of its total assets. Likewise, a one standard deviation increase in the change in
equity volatility (20.50%) is associated with an increase in a firm’s leverage decreasing financing activity
in year t+1 by 0.57% (0.028×20.50%) of its total assets.
We find similar results for Merton and O-score (columns (3) and (4)). However, the level of and
change in risk measured using AssetVol are not significant in explaining a firm’s external financing
activities.
In columns (5) through (8), we examine a firm’s external financing activities over the years t+1 and
t+2. The results echo those of the previous four regressions. Besides supporting the risk timing hypothesis,
these results are also consistent with the presence of long term effects of risk on a firm’s future choice of
financing sources. We also find that while changes in the market to book ratio are always significantly
positively related to leverage-decreasing financing activities, lagged market to book ratio is insignificant
29
in columns (1) through (4), and negatively related to leverage-decreasing financing activities in columns
(5) through (8). In untabulated tests, we also examine a firm’s external financing activities in year t+3 and
obtain similar results. 32
5. Summary and Conclusion
Previous studies document important findings on how firms determine their capital structure. Yet we
remain far from a comprehensive unified theory of capital structure that is consistently supported by
existing evidence. In this paper, we focus on one of the most basic factors that influence firms’ capital
structure decisions, namely, risk. Since firm risk varies considerably over time, we exploit this variation
and examine whether changes in risk and firms’ external financing decisions in response to these changes
significantly affect their capital structure. We use various risk measures to construct risk timing variables,
including stock return volatility, default risk and implied asset volatility, which are estimated based on the
Merton (1974) model, and an adjusted O-score.
We find clear evidence that firms adjust their leverage ratios in response to changes in risk,
suggesting that managers make external financing decisions in response to both changes in market
valuation and perceived risk. This risk timing result is robust to controlling for other well-known
determinants of capital structure.
Overall, our results show that risk considerations can explain fluctuations in capital structure even
after controlling for the drift towards long-term targets and other determinants of capital structure such as
market timing. In addition, the results suggest that firms’ capital structure decisions are the cumulative
outcome of past attempts to adjust external financing decisions in response to changes in risk as well as
32
As discussed earlier, previous studies show non-persistence effects of market timing on the leverage ratios. For
example, Kayhan and Titman (2007) show that in the long-run, the market timing effect on the leverage ratios is
reversed. We do not explicitly address the issue regarding persistency effects of risk timing on the leverage ratios
since the risk timing explanation is consistent with the trade-off theory and therefore, we do not expect these effects
to be changed over time. In unreported tests, we confirm this expectation for book leverage changes.
30
market valuation.
Thus, our paper, together with those on the market timing theory of capital structure, provides new
insights on how managers’ reactions to various shocks affect firms’ capital structure. However, unlike
market timing results that challenge the trade-off theory, our risk timing results are generally consistent
with this theory. To the extent that firms’ risk and external financing activities vary over time, by
exploiting such variations in risk and external financing activities, our study provides valuable new
insights about how firms determine their capital structure in response to changes in risk. However, it
should be noted that our study does not provide detailed analyses on the determinants of a firm’s external
financing decisions induced by significant changes in risk. An in-depth analysis of this issue will help us
better understand a firm’s dynamic capital structure decisions and thus represents a valuable area for
future research.
31
Appendix A. Variable Definitions
This appendix shows detailed descriptions of the construction of all the variables used in the tables.
Variable
Leverage measures
Market leverage (LevM)
Book leverage (LevB)
Definitions
Market leverage ratio is the 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 ratio is the book value of debt divided by total assets. The book
value of debt is defined as above.
Change in target leverage
(dTlevM(or B)[0,4])
Change in target market (book) debt ratio (Tlev) over the past five years
(dTlev[0,4]t= Tlevt – Tlevt-4), where the target ratio is calculated using a Tobit
regression as described in Appendix B.
Leverage deficit
Difference between the target market (book) leverage, Tlev, and the actual
(LdefM(or B)[0,4])
market (book) leverage ratio, Lev, in year -4 (Ldef[0,4]t=Tlevt-4 –Levt-4).
External financing and valuation measures
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)).
Cumulative financial deficit
(FD[0,4])
Cumulative financial deficit over the past five years as a percentage of total
assets at the beginning of the five-year period.
Cumulative financial deficit
dummy (FDd[0,4])
Dummy variable indicating firms with positive financial deficits during the past
five years (i.e., takes the value of one if FD[0,4] > 0 and zero otherwise).
Average market-to-book asset
ratio (MB[0,4])
Average of market-to-book asset ratios (MB) over the past five years, where 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).
Net equity issue minus net debt issue, divided by lagged total assets, over fiscal
years from t+1 to t+s (s ≥ 1). The difference between net equity issue and net
debt issue is calculated as follows: sale of common and preferred stocks (SSTK)
– purchase of common and preferred stocks (PRSTKC) – long-term debt
issuance (DLTIS) + long-term debt reduction (DLTR).
Leverage decreasing external
financing activity (LDEFA
[t+s])
Risk measures
Average equity volatility
(EquityVol[0,4])
Average Merton asset volatility
(AssetVol[0,4])
Average Merton’s default risk
Average of five annualized standard deviations of 52 weekly stock returns in
each fiscal year over the past five years. Firms with less than 12 weeks of stock
return data during a fiscal year are excluded from the sample for the
corresponding year.
Average of five annualized standard deviations of daily changes in asset values
calculated in the process of estimating the Merton (1974)’s default probabilities
in each year during the past five years.
Average of five default probabilities based on the Merton (1974)’s model and
32
(Merton [0,4])
estimated by the methodology described in Vassalou and Xing (2004) in each
year over the past five years.
Average Ohlson’s score (OAverage of five Franzen, Rodgers, and Simin (2007)’s adjusted Ohlson scores
Score [0,4])
calculated in each year over the five-year period ending in year -1.
Market and risk timing variables
Yearly market timing (YT[0,4])
Correlation between financial deficit (FD) and market-to-book asset ratio (MB)
over the past five years.
����������������������������
Long-term market timing
Fınancıal
defıcıt (𝐹𝐹𝐹𝐹) × �����������������������������������������
Market-to-book asset ratıo(𝑀𝑀𝑀𝑀), where the averages
(LT[0,4])
are calculated over the past five years.
Correlation between financial deficit (FD) and equity volatility (EquityVol) over
Yearly equity volatility risk
the past five years. In each year, annual equity volatility is estimated by
timing (YT(EquityVol)[0,4])
annualizing the standard deviation of 52 weekly stock returns during the past
five years.
Yearly Merton asset volatility
Correlation between financial deficit (FD) and Merton (1974) asset volatilities
timing (YT(AssetVol[0,4])
(Merton asset volatilities) over the past five years.
Correlation between financial deficit (FD) and Merton’s (1974) default risk
Yearly Merton’s default risk
(Merton) over the past five years.
timing (YT(Merton)[0,4])
Yearly Ohlson score risk timing Correlation between financial deficit (FD) and Ohlson score over the past five(YT(O-Score)[0,4])
year period ending in year -1.
Other control variables used in the main regressions
Buy-and-hold stock returns over the past five years.
Cumulative stock returns
(r[0,4])
Credit rating deficit (CDt-4)
Difference between the target credit rating and the actual credit rating in year -4,
where the target credit rating is estimated using an ordered probit model as
described in Appendix C. For those without credit rating information or with the
negative value of credit rating deficits, the value is set to zero. Higher scores are
assigned to higher credit ratings (the highest score is 19).
Change in target credit rating
Change in target credit rating (TRating) over the past five years (dTRating[0,4]t
= TRatingt – TRatingt-4), where the target rating is calculated using an ordered
(dTRating [0,4])
probit regression as described in Appendix C.
Profitability (EBITD[0,4])
Sum of earnings before interest, tax, and depreciation (OIBDP) over the
previous five years / total assets in year -4 (AT).
Other control variables used in the target leverage ratio and/or target credit rating regressions
Profitability (EBITD)
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)
Asset tangibility (PPE)
Operating risk (OCF Risk)
Natural log of (Sales (SALE)).
Property, Plant, and Equipment (PPENT) divided by total assets (AT).
Annualized standard deviations of past 20 quarterly operating cash flows as a
percentage of total assets (quarterly ATQ) at the beginning of the quarter over
the past five years where operating cash flows are defined as quarterly net
profit(quarterly NIQ) plus interest expenses (quarterly XINTQ), depreciation
and amortization (quarterly DPQ) ) and income taxes (quarterly TXTQ).
Average of credit ratings over the four-year period ending in year -1.
Historical credit rating (HCR)
33
Appendix B. Target Leverage
1. Target leverage ratios
Target leverage ratios (Tlev) are measured using a similar method as in Kayhan and Titman (2007).
Specifically, as shown in equation (A1) below, for each firm we run a Tobit regression of the market
(book) leverage ratio, LevM(B), on lagged market to book total assets (MB), asset tangibility (PPE),
profitability (EBITD), R&D expenses (RD), an R&D dummy (RDd), selling expenses (SE), sales (Size),
and year and industry dummies. The coefficient estimates from this regression are used to calculate fitted
values of market (book) leverage ratios, which are used as the estimates of target market (book) leverage
ratios, TlevM(B). More specifically, we estimate:
LevM(B)i ,t= α + β1MBi ,t −1 + β 2 PPEi ,t −1 + β 3 EBITDi ,t −1 + β 4 RDi ,t −1 + β 5 RDd i ,t −1
+ β 6 SEi ,t −1 + β 7 Sizei ,t −1 + β 8YearDi ,t −1 + β 9 IndustryDi ,t −1 + ε i ,t
,
(A1)
where MB is calculated by dividing the market value of total assets by the book value of total assets (AT),
with the market value of total assets given as described above. PPE, which is used to control for asset
tangibility, is constructed by dividing net property, plants, and equipment (PPENT) by AT. As a measure
of profitability, EBITD, we use earnings before interest, taxes, and depreciation (OIBDP) divided by AT,
while our measure of growth potential or investment opportunities, RD, is computed as the ratio of R&D
expenses (XRD) to sales (SALE). Since many firms do not report small R&D expenses, missing R&D
values are set to zero. To check for potential problems with this treatment, following prior capital
structure literature we use a dummy variable to indicate missing R&D values (RDd). Selling expenses (SE)
is selling, general, and administrative expenses (XSGA) divided by AT. To capture firm size, we use the
natural log of SALE. Finally, we use industry (based on thirty industry classification definitions available
on Ken French’s website) 33 and year dummy variables to control for industry effects and any time-related
co-variation in target leverage ratios, respectively. 34
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
33
The results are robust to alternative definitions of industry dummy variables based on five-, ten-, or twelveindustry classification.
34
Note that the number of observations used in these regressions is greater than those used in other analyses
because we do not require firms to have five years of data to be included in the analysis.
34
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 4900-4999) companies since their capital structure decisions are
under regulatory constraints. Firms with book leverage ratios above 100% are also excluded from the
sample. A market leverage ratio is the book value of debt divided by the market value of total assets. A
book leverage ratio is the book value of debt divided by total assets. The market value of total assets is
defined as total assets minus the book value of equity plus the market value of equity. The book value of
debt is defined as total assets minus the book value of equity that is estimated as total assets minus the
sum of total liabilities and the liquidation (redemption or carrying, whichever is first available) value of
preferred stock plus deferred taxes, investment credit, and convertible debt. The variables used in the
regressions are defined in Appendix A.
Market Leverage
Variable
Coefficient
S.E
t-value
Book Leverage
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 (EBITD 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
35
Appendix C. 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):
CreditRating i,t= α + β1 MBi,t + β 2 PPEi,t + β 3 RDi,t + β 4 RDd i,t + β 5 SEi,t + β 6 EBITDi,t
+ β 7 Sizei,t + β 8OCF Risk i,t + β 9 HCRi,t + ε t
,
(A2)
where CreditRating is a numerical credit rating value based on the S&P long-term issuer rating
(SPLTCRM) available from Compustat 35 and MB, PPE, RD, RDd, SE, EBITD, and SIZE are defined as in
Appendix B. OCF Risk, operating risk, is measured as the annualized standard deviation of 20 recent
quarterly operating cash flows 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 36
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 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 4900-4999) companies since
their capital structure decisions are under regulatory constraints. Firms with book leverage ratios above
100% are also excluded from the sample. Only the results for 2011 are reported in this appendix but
results for other years are available upon request. The dependent variable is a numerical credit rating
value based on the S&P long-term issuer rating available from Compustat (SPLTCRM). The numerical
credit rating takes the value of 1 for the lowest rating (CCC-) and 19 for the highest rating (AAA). All
variables are measured at the fiscal year end. The variables used in the regressions are defined in
Appendix A.
35
The lowest rating (CCC-) is set to 1 and the highest rating (AAA) is set to 19.
Because of the additional data requirements used in the analysis, the number of observations (692) used in
estimating the regression is smaller than the number of firms with a credit rating in 2011 (825).
36
36
Variables
Coefficient
S.E
t-value
Pr > |t|
Intercept
-5.21**
0.63
-8.23
0.00
Market to book ratio (MB)
0.46**
0.10
4.68
0.00
Asset tangibility (PPE )
-0.25
0.26
-0.96
0.34
R&D (RD)
0.44
1.21
0.36
0.72
R&D dummy (RDd)
0.31**
0.12
2.64
0.01
Selling expense (SE)
-0.61
0.50
-1.21
0.23
Profitability (EBITD)
3.87**
0.88
4.4
0.00
Firm size (Size)
0.15**
0.04
3.46
0.00
-0.29
1.06
-0.27
0.79
1.19**
0.04
28.05
0.00
Operating risk (OCF Risk)
Historical credit rating (HCR)
Log likelihood
-812.1274
Number of observations
692
37
Appendix D. Measuring Risk
This appendix describes three risk measures, Merton, AssetVol, and O-Score, used in the regression
analysis.
1. Default Risk and Implied Asset Volatility
The probability of default is estimated by the following equation: 37
 ln (V A,t / X t ) + ( µ − 0.5 × σ A2 )T 
 ,
Mertont = N  −

σ
T
A


(A3)
where 𝑉𝑉𝐴𝐴,𝑡𝑡 is the value of total assets at time t and 𝑋𝑋𝑡𝑡 is the book value of debt defined as the sum of
long-term debt due in one year and 0.5 × long-term debt at time t. 𝜇𝜇 is the instantaneous growth rate of
𝑉𝑉𝐴𝐴 , and 𝜎𝜎𝐴𝐴 is the instantaneous standard deviation of 𝑉𝑉𝐴𝐴 . The time to maturity, T, is assumed to be one
year as in Vassalou and Xing (2004). Since we cannot observe the market value of total assets, estimation
of these parameter values is not straightforward. Thus, at the end of each year, we estimate σA using the
following iterative procedure.
First, we estimate the volatility of equity return, σE, using the daily stock returns over the past 12
months. This estimated σE is used as an initial estimate of σA. As Merton (1974) shows, the value of equity,
VE, can be represented as a call option written on the assets of a firm. Since the market value of equity, VE,
is observed from the stock market, using the Black-Scholes model together with the estimated 𝜎𝜎𝐴𝐴 and
other parameters, the implied value of total assets, 𝑉𝑉𝐴𝐴 , can be estimated by identifying the 𝑉𝑉𝐴𝐴 that makes
the value of the call option equal to the market capitalization of the firm. We can estimate 𝑉𝑉𝐴𝐴 for each
trading day during the past 12 months. Based on these daily estimates of 𝑉𝑉𝐴𝐴 , we can calculate 𝜎𝜎𝐴𝐴 , which
will be used in the next iteration. This newly estimated 𝜎𝜎𝐴𝐴 replaces the initial σA estimate and we repeat
the above procedure. We repeat the iterations until the estimated 𝜎𝜎𝐴𝐴 converges to the σA used at the
beginning of the iteration, with the difference becoming less than 0.01%. If convergence does not occur
after 1,000 iterations, we drop the observation from the sample.
Using the estimated set of 𝑉𝑉𝐴𝐴 s in the final iteration, we estimate the instantaneous growth rate, 𝜇𝜇, by
calculating the average change in ln (𝑉𝑉𝐴𝐴 ). Using these estimated parameter values, we next calculate the
default probability as specified in equation (A3). The average of the past five years’ default probabilities
37
As discussed in Vassalou and Xing (2004), equation (A3) 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.
38
(Merton[0,4]) is used as our measure of default risk. Simultaneously, we also determine the implied asset
volatility, AssetVol[0,4], as the average of the past five years’ estimated asset volatilities, 𝜎𝜎𝐴𝐴2 .
2. Adjusted Ohlson (1980) Score
Adjusted Ohlson (1980) scores are estimated based on Franzen, Rodgers, and Simin (2007) as
specified in equation (A4):
 A _ TLi ,t
O − Scorei ,t= − 1.32 − 0.407 × ln ( A _ TAi ,t ) + 6.03 × 
 A _ TAi ,t
 CL
+ 0.076 ×  i ,t
 CAi ,t

 WCi ,t
 − 1.43 × 

 A _ TA
i ,t



 A _ NI i ,t
 − 1.72 × Dummy1i ,t − 2.37 × 

 A _ TA
i ,t


 FFOi ,t
− 1.83 × 
 A _ TAi ,t








 A _ NI i ,t − A _ NI i ,t −1

 + 0.285 × Dummy 2 i ,t − 0.521 × 

 A _ NI i ,t + A _ NI i ,t −1


(A4)



,
where TA, TL, WC, CL, CA, NI, and FFO stand for total assets, total liabilities, working capital, current
liabilities (LCT), current assets (ACO), net income (NI), and funds from operations (FOPT), respectively.
Dummy1 is an indicator that takes the value of one when total liabilities are greater than total assets, and
zero otherwise. Dummy 2 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&Dintensive firms as financially distressed firms and thus to treat R&D in a more conservative way, NI, TA,
and TL should be adjusted as in equation (A5):
A _ NI i ,t= NI i ,t + [ RDi ,t − 0.2 × ( RDi ,t −1 + RDi ,t −2 + RDi ,t −3 + RDi ,t −4 + RDi ,t −5 ] × (1 − tax)
A _ TAi ,t= TAi ,t + ( RDt + 0.8 × RDi ,t −1 + 0.6 × RDi ,t −2 + 0.4 × RDi ,t −3 + 0.2 × RDi ,t −4 )
, (A5)
A _ TLi ,t= TLi ,t + ( RDt + 0.8 × RDi ,t −1 + 0.6 × RDi ,t −2 + 0.4 × RDi ,t −3 + 0.2 × RDi ,t −4 ) × tax
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). We use the average of the past five
years’ adjusted O-scores ending in year -1 (O-score [0,4]) as our adjusted Ohlson (1980) score, where the
higher the adjusted O-score, the higher the firm’s default risk.
39
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42
Table 1
Summary Statistics
The sample includes all NYSE, Amex, and Nasdaq firms from 1975 to 2011, except for firms with a negative book equity value,
a market-to-book asset ratio above 10, or total assets below $10 million, utility (SIC 6000-6999) and financial (SIC 4900-4999)
firms, and firms with book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles and measured at the
fiscal year-end. Variables are defined in Appendix A. The market capitalization and total assets are adjusted for inflation using
US seasonally-adjusted consumer price index –all urban consumers.
Variables
N
Mean
S.D
Median
1%
99%
Average total assets over the past five years (2011
US$ million)
Average market cap. over the past five years (2011
US$ million)
Annual stock returns; %
Cumulative stock returns (x[0,4]): %
Cumulative profitability (EBITD[0,4]): %
43,614
3,047
13,259
349.69
12.05
508,111
43,614
2,953
1,462
271.17
2.61
448,432
43,614
43,614
43,614
17.70
116.60
90.35
54.97
216.43
61.74
9.58
55.33
82.13
-93.02
-97.15
-88.12
615.46
2,042
344.64
Average market leverage over the past five years: %
Change in market leverage over the past five years: %
Market leverage deficit (LdefM[0,4]): %
Change in target market leverage (dTlevM[0,4]): %
Average book leverage over the past five years: %
Change in book leverage over the past five years: %
Book leverage deficit (LdefB[0,4]): %
Change in target book leverage (dTlevB[0,4]): %
43,463
43,614
43,614
43,614
43,463
43,614
43,614
43,614
39.72
1.29
2.61
0.44
44.67
1.72
2.42
1.10
21.10
19.21
16.49
11.34
17.60
15.19
16.47
5.89
38.33
1.00
3.86
-0.48
44.95
1.19
3.19
1.00
0.69
-59.60
-42.39
-40.80
1.70
-49.11
-83.39
-54.94
97.15
70.11
43.56
47.11
96.65
56.57
76.90
71.91
Credit rating deficits (CD)
Change in target credit rating (dTrating)
43,614
43,614
0.03
-0.03
0.18
0.42
0.00
0.00
0.00
-4.00
2.00
3.00
Cumulative financial deficit (FD[0,4]): %
Average market to book ratio over the past five years
(MB[0,4])
43,614
43,614
14.43
1.45
46.51
0.77
3.69
1.22
-102.30
0.26
411.16
8.91
Yearly Market Timing (YT[0,4])
Long-term Market Timing (LT[0,4])
43,614
43,614
0.06
4.49
0.42
17.92
0.07
0.86
-0.77
-76.33
0.78
152.66
Yearly equity volatility risk timing
(YT(EquityVol)[0,4])
Yearly Merton asset volatility risk timing
YT(AssetVol)[0,4])
Yearly Merton’s default risk timing (YT(Merton)[0,4])
Yearly O-score risk timing ( YT(O-Score)[0,4])
43,614
-0.01
0.41
-0.02
-0.77
0.77
42,815
0.03
0.41
0.03
-0.77
0.78
42,815
22,303
-0.08
-0.03
0.38
0.42
-0.11
-0.05
-0.79
-0.78
0.79
0.78
Average equity volatility over past five years
(EquityVol[0,4]): %
Average Merton asset volatility (AssetVol [0,4]): %
Average Merton’s default risk (Merton[0,4]): %
Average Ohlson’ score (O-score [0,4] )
43,614
43.67
16.90
40.21
16.12
129.69
42,815
42,815
22,303
44.33
2.28
-0.12
21.66
6.06
2.23
38.90
0.00
-0.44
13.53
0.00
-4.64
141.15
51.02
19.27
43
Table 2
Correlations of Market and Risk Timing Measures
The sample includes all NYSE, Amex, and Nasdaq firms from 1975 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 4900-4999) firms, and firms with book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles and measured
at the fiscal year-end. Book leverage is the book value of debt divided by total assets and market leverage is the book value of debt divided by the market value of total assets. The book value
of debt is defined as total assets minus the book value of equity, which is estimated as total assets minus the sum of total liabilities and the liquidation value (redemption or carrying value,
whichever is available first) of preferred stock plus deferred taxes, investment credits, and convertible debt. The market value of total assets is defined as total assets minus the book value of
equity plus the market value of equity. Other variables are defined in Appendix A. P-values are in parentheses.
dLevM
Market leverage change (dLevM[0,4]) (%)
YT
LT
YT
(Equity
Vol.)
YT
(Asset
Vol.)
YT
YT
Equity
(Merton) (O-score) Vol.
Asset
Vol.
Merton O-score
FD
MB
1.00
0.66
(0.00)
-0.01
Yearly market timing (YT[0,4])
(0.14)
0.09
Long-term market Timing (LT[0,4])
(0.00)
-0.02
Yearly equity vol. risk timing (YT(EquityVol)[0,4])
(0.00)
-0.02
Yearly asset vol. risk timing (YT(AssetVol)[0,4])
(0.00)
-0.02
Yearly default risk timing (YT(Merton)[0,4])
(0.00)
-0.02
Yearly O-score risk timing ( YT(O-score)[0,4])
(0.00)
0.06
Average equity vol. over past five years (EquityVol[0,4])
(0.00)
0.06
Asset Merton asset volatility (AssetVol [0,4] )
(0.00)
0.07
Average Merton’s default risk (Merton[0,4] )
(0.00)
-0.05
Average Ohlson’ score (O-score [0,4] )
(0.00)
0.14
Cumulative financial deficit (FD[0,4])
(0.00)
-0.07
Average market-to-book ratio (MB[0,4])
(0.00)
Book leverage change (dLevB[0,4]) (%)
dLevB
1.00
-0.04
(0.00)
0.05
(0.00)
-0.02
(0.00)
-0.04
(0.00)
-0.03
(0.00)
-0.02
(0.00)
0.01
(0.01)
0.02
(0.00)
0.06
(0.00)
-0.01
(0.01)
0.12
(0.00)
-0.06
(0.00)
1.00
0.05
(0.00)
-0.06
(0.00)
-0.04
(0.00)
-0.21
(0.00)
-0.02
(0.00)
0.10
(0.00)
0.09
(0.00)
0.01
(0.31)
0.00
(0.74)
0.06
(0.00)
-0.01
(0.00)
1.00
0.01
(0.04)
0.03
(0.00)
-0.04
(0.00)
-0.07
(0.00)
0.17
(0.00)
0.13
(0.00)
-0.01
(0.01)
0.11
(0.00)
0.93
(0.00)
0.10
(0.00)
1.00
0.54
(0.00)
0.34
(0.00)
0.12
(0.00)
-0.03
(0.00)
0.00
(0.61)
-0.05
(0.00)
-0.02
(0.00)
0.01
(0.15)
0.04
(0.00)
44
1.00
0.52
(0.00)
0.04
(0.00)
0.02
(0.00)
-0.01
(0.31)
-0.02
(0.00)
0.02
(0.00)
0.03
(0.00)
(0.00
(0.63)
1.00
0.15
(0.00)
-0.05
(0.00)
-0.04
(0.00)
-0.02
(0.00)
-0.03
(0.00)
-0.05
(0.00)
0.05
(0.00)
1.00
-0.02
(0.00)
0.01
(0.11)
-0.03
(0.00)
-0.05
(0.00)
-0.07
(0.00)
0.10
(0.00)
1.00
0.64
(0.00)
0.35
(0.00)
0.19
(0.00)
0.14
(0.00)
0.00
(0.63)
1.00
0.27
(0.00)
0.01
(0.15)
0.09
(0.00)
0.09
(0.00)
1.00
0.18
(0.00)
0.00
(0.67)
-0.17
(0.00)
1.00
0.11
(0.00)
-0.29
(0.00)
1.00
0.05
(0.00)
1.00
Table 3
Panel Regressions of Changes in Leverage on Market and Risk Timing Measures
This table reports the results of panel regressions of changes in book and market leverage on market and risk timing measures as well as other control variables. The sample includes all
NYSE, Amex, and Nasdaq firms from 1975 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 4900-4999) firms, and firms with book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles 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 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, 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. Other variables are defined in Appendix A. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% significance levels,
respectively, using a bootstrapping method. T-statistics based on clustered errors (firm) are reported in parentheses.
Market Leverage
Dependent Variable
Yearly market timing (YT[0,4])
Long-term market timing (LT[0,4])
No Risk
Timing
(1)
-0.41**
(-2.11)
-0.19***
(-10.67)
Risk measure
Yearly risk timing (YT(risk measure)[0,4])
Average market to book ratio (MB[0,4])
Cumulative financial deficit (FD[0,4])
Cumulative financial deficit dummy (FDd[0,4])
Credit rating deficits (CDt-4)
Changes in target credit rating (dTRating)
Cumulative stock returns (x[0,4])
Profitability (EBITD[0,4])
Market (book) leverage deficit (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝐵𝐵)[0,4])
Change in target market (book) leverage (dTlevM(B)[0,4])
-1.39***
(-4.32)
0.13***
(17.32)
2.60***
(12.73)
-0.82**
(-2.08)
-1.86***
(-8.52)
-2.85***
(-40.12)
-0.48
(-1.48)
0.72***
(73.11)
0.57***
Equity
Vol.
(2)
-0.52***
(-2.67)
-0.20***
(-11.11)
0.11***
(7.75)
-1.04***
(-5.20)
-1.48***
(-4.58)
0.13***
(17.52)
2.58***
(12.70)
-0.77**
(-1.97)
-1.69***
(-7.90)
-2.85***
(-40.53)
-0.10
(-0.32)
0.74***
(75.28)
0.58***
Book Leverage
Asset Vol.
(3)
Merton
(4)
O-Score
(5)
-0.41**
(-2.09)
-0.19***
(-10.72)
-0.03***
(-4.00)
-0.46**
(-2.25)
-1.31***
(-4.12)
0.13***
(17.49)
2.58***
(12.53)
-0.81**
(-2.05)
-1.87***
(-8.59)
-2.86***
(-39.95)
-0.50
(-1.54)
0.72***
(73.08)
0.57***
-0.56***
(-2.86)
-0.19***
(-11.22)
0.41***
(12.38)
-0.71***
(-3.52)
-1.16***
(-3.66)
0.13***
(17.98)
2.60***
(12.81)
-0.55
(-1.41)
-1.73***
(-8.10)
-2.79***
(-39.21)
-0.16
(-0.51)
0.74***
(75.57)
0.58***
-0.30
(-1.19)
-0.22***
(-7.98)
0.99***
(6.77)
-0.77***
(-2.97)
-1.81***
(-4.07)
0.14***
(12.37)
2.30***
(8.49)
-0.86**
(-2.15)
-1.46***
(-5.81)
-3.04***
(-26.91)
0.40
(0.82)
0.78***
(59.10)
0.57***
45
No Risk
Timing
(6)
-1.65***
(-7.85)
-0.27***
(-13.02)
0.98***
(2.74)
0.14***
(17.03)
2.42***
(11.13)
0.25
(0.63)
-1.54***
(-6.45)
-0.13***
(-2.72)
-4.16***
(-11.31)
0.77***
(69.72)
0.55***
Equity
Vol.
(7)
-1.75***
(-8.35)
-0.28***
(-13.60)
0.14***
(9.71)
-0.80***
(-3.76)
0.91**
(2.54)
0.14***
(17.29)
2.41***
(11.13)
0.32
(0.82)
-1.30***
(-5.48)
-0.18***
(-3.64)
-3.58***
(-9.84)
0.78***
(71.26)
0.57***
Asset Vol.
(8)
Merton
(9)
O-Score
(10)
-1.64***
(-7.72)
-0.26***
(-12.77)
-0.02**
(-2.45)
-0.64***
(-2.96)
1.04***
(2.87)
0.14***
(16.85)
2.34***
(10.72)
0.28
(0.73)
-1.57***
(-6.63)
-0.14***
(-2.72)
-4.12***
(-11.14)
0.76***
(69.28)
0.55***
-1.76***
(-8.21)
-0.27***
(-13.07)
0.38***
(10.69)
-0.62***
(-2.89)
1.22***
(3.42)
0.14***
(17.12)
2.38***
(11.02)
0.51
(1.34)
-1.43***
(-6.16)
-0.10**
(-2.07)
-3.75***
(-10.32)
0.78***
(69.65)
0.56***
-1.61***
(-5.88)
-0.27***
(-7.91)
1.74***
(9.01)
-0.48*
(-1.70)
1.52***
(3.20)
0.14***
(11.08)
2.13***
(7.48)
0.08
(0.20)
-1.20***
(-4.55)
-0.28***
(-3.50)
-3.98***
(-7.41)
0.87***
(58.27)
0.57***
(49.26)
1.85***
(3.22)
Yes
(50.20)
-3.97***
(-4.29)
Yes
(48.99)
3.52***
(4.78)
Yes
(50.36)
-0.78
(-1.32)
Yes
(34.60)
-2.72***
(-3.44)
Yes
(27.47)
-1.79***
(-3.00)
Yes
(28.50)
-9.40***
(-9.86)
Yes
(26.86)
-0.63
(-0.81)
Yes
(27.92)
-4.12***
(-6.74)
Yes
(19.50)
-7.18***
(-8.57)
Yes
Adjusted R-square
0.682
0.684
0.682
0.688
0.688
0.468
0.475
0.468
0.477
0.505
Number of observations
43,614
43,614
42,815
42,815
22,303
43,614
43,614
42,815
42,815
22,303
Intercept
Year & firm dummies
46
Table 4
Panel Regressions of Changes in Market Leverage on Market &
Risk Timing Measures with a High Financial Deficit Dummy
This table reports the results of panel regressions of changes in market leverage on market and risk timing measures, a dummy variable indicating firms with a high financial deficit, and
other control variables. The sample includes all NYSE, Amex, and Nasdaq firms from 1975 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 4900-4999) firms, and firms with book leverage above 100%. All variables are winsorized at the 1st and
99th percentiles 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 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, 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. High FD is an indicator that takes the value of one if a firm’s financial deficit during the past five years is within
the top 50% (or 25%) of all firms available in a fiscal year with positive financial deficits during the same period and zero otherwise. Other variables are defined in Appendix A. ***, **, and
* indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% significance levels, respectively, using a bootstrapping method. T-statistics based on clustered
errors (firm) are reported in parentheses.
Dependent Variable
Yearly market timing (YT[0,4])
Yearly market timing × High FD (YT[0,4] × High FD)
Long-term market timing (LT[0,4])
Risk measure
Yearly risk timing (YT(risk measure)[0,4])
YT(risk measure)[0,4] × High FD
Average market to book ratio (MB[0,4])
High Financial Deficit Dummy (High FD)
Cumulative financial deficit (FD[0,4])
Cumulative financial deficit dummy (FDd[0,4])
Credit rating deficits (CDt-4)
Changes in target credit rating (dTRating)
Market Leverage & Top 50% High Financial Deficits
Equity Vol.
Asset Vol.
Merton
O-Score
(1)
(2)
(3)
(4)
0.03
0.12
0.02
0.29
(0.12)
(0.57)
(0.10)
(1.10)
-2.11***
-2.04***
-2.32***
-2.72***
(-5.10)
(-4.89)
(-5.53)
(-4.38)
-0.19***
-0.18***
-0.19***
-0.22***
(-10.69)
(-10.37)
(-10.85)
(-7.91)
0.11***
-0.04***
0.41***
0.99***
(7.80)
(-4.06)
(12.40)
(6.84)
-0.71***
-0.14
-0.43*
-0.43
(-3.29)
(-0.65)
(-1.91)
(-1.54)
-1.29***
-1.28***
-1.14***
-1.48**
(-3.12)
(-2.99)
(-2.62)
(-2.40)
-1.54***
-1.37***
-1.21***
-1.82***
(-4.73)
(-4.28)
(-3.80)
(-4.10)
1.77***
1.84***
1.67***
1.30***
(7.50)
(7.73)
(7.08)
(3.69)
0.12***
0.12***
0.12***
0.13***
(15.79)
(15.86)
(16.28)
(11.53)
2.30***
2.29***
2.33***
2.14***
(11.46)
(11.30)
(11.63)
(8.04)
-0.75*
-0.81**
-0.53
-0.79**
(-1.90)
(-2.03)
(-1.36)
(-1.97)
-1.70***
-1.88***
-1.74***
-1.47***
47
Market Leverage & Top 25% High Financial Deficits
Equity Vol.
Asset Vol.
Merton
O-Score
(5)
(6)
(7)
(8)
-0.13
-0.04
-0.16
0.12
(-0.64)
(-0.22)
(-0.82)
(0.49)
-3.18***
-2.96***
-3.39***
-4.90***
(-5.26)
(-4.84)
(-5.58)
(-4.97)
-0.20***
-0.19***
-0.20***
-0.23***
(-11.02)
(-10.74)
(-11.20)
(-8.03)
0.11***
-0.03***
0.41***
1.00***
(7.85)
(-4.00)
(12.39)
(6.84)
-0.79***
-0.25
-0.56***
-0.53**
(-3.90)
(-1.19)
(-2.71)
(-2.01)
-1.84***
-1.65***
-1.28**
-2.64***
(-3.32)
(-2.79)
(-2.11)
(-2.83)
-1.48***
-1.31***
-1.15***
-1.75***
(-4.58)
(-4.11)
(-3.65)
(-3.96)
1.02***
1.03***
0.81**
0.44
(3.19)
(3.19)
(2.49)
(0.87)
0.12***
0.13***
0.13***
0.14***
(16.09)
(16.27)
(16.65)
(11.69)
2.62***
2.61***
2.64***
2.35***
(12.82)
(12.60)
(12.91)
(8.58)
-0.78**
-0.83**
-0.56
-0.84**
(-2.00)
(-2.09)
(-1.44)
(-2.11)
-1.70***
-1.88***
-1.74***
-1.49***
Cumulative stock returns (x[0,4])
Profitability (EBITD[0,4])
Market(book) leverage deficit (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝐵𝐵)[0,4])
Change in target market (book) leverage (dTlevM(B)[0,4])
Intercept
Year & firm dummies
Adjusted R-square
Number of observations
(-7.89)
-2.85***
(-40.42)
-0.17
(-0.52)
0.74***
(75.33)
0.58***
(50.09)
-3.59***
(-3.88)
Yes
0.685
43,614
(-8.61)
-2.86***
(-39.79)
-0.57*
(-1.77)
0.72***
(73.17)
0.57***
(48.91)
3.96***
(5.37)
Yes
0.684
42,815
48
(-8.12)
-2.79***
(-39.13)
-0.24
(-0.74)
0.74***
(75.68)
0.58***
(50.21)
-0.35
(-0.58)
Yes
0.690
42,815
(-5.81)
-3.04***
(-26.67)
0.29
(0.59)
0.78***
(58.82)
0.57***
(34.53)
-2.76***
(-3.50)
Yes
0.689
22,303
(-7.94)
-2.84***
(-40.52)
-0.18
(-0.58)
0.74***
(75.37)
0.58***
(50.22)
-3.95***
(-4.27)
Yes
0.685
43,614
(-8.64)
-2.85***
(-39.89)
-0.59*
(-1.81)
0.72***
(73.18)
0.57***
(49.08)
3.60***
(4.90)
Yes
0.683
42,815
(-8.16)
-2.78***
(-39.20)
-0.25
(-0.79)
0.74***
(75.67)
0.58***
(50.34)
-0.68
(-1.15)
Yes
0.689
42,815
(-5.90)
-3.03***
(-26.84)
0.26
(0.53)
0.78***
(59.28)
0.57***
(34.64)
-2.71***
(-3.44)
Yes
0.689
22,303
Table 5
Panel Regressions of Changes in Leverage on Market and Residual Risk Timing Measures
This table reports the results of panel regressions of changes in market and book leverage on the market and residual risk timing measures as well as other control variable. The residuals
from the following regression are used as risk measures:
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑡𝑡 = 𝛼𝛼 + 𝛽𝛽1 𝐹𝐹𝐹𝐹𝑡𝑡 + 𝛽𝛽2 𝐹𝐹𝐹𝐹𝐹𝐹𝑡𝑡 + 𝛽𝛽3 𝐶𝐶𝐶𝐶𝑡𝑡−1 + 𝛽𝛽4 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡 + 𝛽𝛽5 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑡𝑡 + 𝛽𝛽6 𝑟𝑟 + 𝛽𝛽7 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝐵𝐵)𝑡𝑡 + 𝛽𝛽8 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝐵𝐵)𝑡𝑡 + 𝛽𝛽9 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝑡𝑡 + 𝛽𝛽10 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑡𝑡 + 𝜀𝜀𝑡𝑡
The sample includes all NYSE, Amex, and Nasdaq firms from 1975 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 4900-4999) firms, and firms with book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles 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
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, 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. Other variables are defined in Appendix A. ***, **, and * indicate that the coefficients are significantly different from zero at the 1%,
5%, and 10% significance levels, respectively, using a bootstrapping method. T-statistics based on clustered errors (firm) are reported in parentheses.
Market Leverage
Dependent Variable
Yearly market timing (YT[0,4])
Long-term market timing (LT[0,4])
Residual Risk measure
Yearly residual risk timing (YT(risk residual measure)[0,4])
Average market to book ratio (MB[0,4])
Cumulative financial deficit (FD[0,4])
Cumulative financial deficit dummy (FDd[0,4])
Credit rating deficits (CDt-4)
Changes in target credit rating (dTRating)
Cumulative stock returns (x[0,4])
Profitability (EBITD[0,4])
Market(book) leverage deficit (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝐵𝐵)[0,4])
Equity Vol.
(1)
-0.35*
(-1.80)
-0.19***
(-10.50)
-0.01
(-0.63)
-0.51***
(-2.59)
-1.43***
(-4.35)
0.13***
(17.21)
2.59***
(12.70)
-0.89**
(-2.25)
-1.89***
(-8.59)
-2.85***
(-39.87)
-0.46
(-1.42)
0.72***
(72.54)
Asset Vol.
(2)
-0.37*
(-1.85)
-0.19***
(-10.63)
-0.03***
(-3.48)
-0.38*
(-1.87)
-1.35***
(-4.15)
0.13***
(17.34)
2.56***
(12.42)
-0.86**
(-2.16)
-1.88***
(-8.61)
-2.86***
(-39.77)
-0.44
(-1.32)
0.72***
(72.11)
49
Merton
(3)
-0.20
(-0.94)
-0.19***
(-10.63)
2.75
(0.77)
-0.68***
(-3.20)
-1.40***
(-4.25)
0.13***
(17.34)
2.57***
(12.44)
-0.82**
(-2.07)
-1.86***
(-8.48)
-2.87***
(-39.78)
-0.44
(-1.32)
0.72***
(71.71)
Book Leverage
O-Score
(4)
-0.29
(-1.12)
-0.22***
(-7.70)
0.13
(0.87)
-0.11
(-0.40)
-1.87***
(-4.12)
0.14***
(12.46)
2.47***
(9.01)
-0.87**
(-2.17)
-1.57***
(-6.32)
-3.09***
(-26.97)
-0.08
(-0.16)
0.75***
(54.60)
Equity Vol.
(5)
-1.60***
(-7.61)
-0.26***
(-12.76)
-0.02
(-1.23)
-0.50**
(-2.35)
1.02***
(2.81)
0.14***
(16.87)
2.42***
(11.13)
0.16
(0.40)
-1.56***
(-6.54)
-0.13***
(-2.62)
-4.22***
(-11.31)
0.76***
(69.26)
Asset Vol.
(6)
-1.57***
(-7.39)
-0.27***
(-12.58)
-0.02*
(-1.88)
-0.76***
(-3.54)
1.05***
(2.88)
0.14***
(16.67)
2.32***
(10.65)
0.23
(0.58)
-1.58***
(-6.66)
-0.13***
(-2.65)
-4.16***
(-11.07)
0.76***
(68.29)
Merton
(7)
-1.46***
(-6.56)
-0.27***
(-12.55)
-3.64
(-0.94)
-0.51**
(-2.29)
1.03***
(2.81)
0.14***
(16.67)
2.33***
(10.63)
0.24
(0.62)
-1.56***
(-6.53)
-0.14***
(-2.74)
-4.11***
(-10.93)
0.76***
(68.63)
O-Score
(8)
-1.63***
(-5.81)
-0.26***
(-7.64)
0.86***
(4.92)
-0.19
(-0.64)
1.32***
(2.68)
0.14***
(11.06)
2.30***
(7.92)
0.03
(0.09)
-1.37***
(-5.06)
-0.25***
(-3.06)
-4.84***
(-8.71)
0.81***
(52.61)
Change in target market (book) leverage (dTlevM(B)[0,4])
Intercept
Year & firm dummies
Adjusted R-square
Number of observations
0.57***
(48.82)
1.89***
(3.27)
Yes
0.682
43,247
0.57***
(48.51)
1.74***
(3.01)
Yes
0.682
42,460
50
0.57***
(48.46)
1.80***
(3.09)
Yes
0.682
42,460
0.55***
(32.63)
-1.90**
(-2.37)
Yes
0.683
22,154
0.55***
(26.99)
-1.74***
(-2.91)
Yes
0.467
43,247
0.54***
(26.46)
-1.83***
(-3.04)
Yes
0.466
42,460
0.55***
(26.55)
-1.83***
(-3.04)
Yes
0.466
42,460
0.53***
(17.53)
-5.41***
(-6.40)
Yes
0.487
22,154
Table 6
Panel Regressions of Changes in Market Leverage on Market &
Risk Timing Measures with a High Risk (or High Risk Change) Dummy
This table reports the results of panel regressions of changes in market leverage on market and risk timing measures, a dummy variable indicating firms with a high risk level (or a high risk
change), and other control variables. The sample includes all NYSE, Amex, and Nasdaq firms from 1975 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 4900-4999) firms, and firms with book leverage above 100%. All variables are winsorized at the
1st and 99th percentiles 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 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, 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. High Risk Level (Change) is an indicator that takes the value of one if a firm’s average risk (increase in
risk) over the past five years is within the top 50% of all firms available in a fiscal year, and zero otherwise. Other variables are defined in Appendix A. ***, **, and * indicate that the
coefficients are significantly different from zero at the 1%, 5%, and 10% significance levels, respectively, using a bootstrapping method. T-statistics based on clustered errors (firm) are
reported in parentheses.
High Risk Level Dummy
Dependent Variable
Yearly market timing (YT[0,4])
Yearly market timing × High Risk (YT[0,4] × High Risk Level)
Long-term market timing (LT[0,4])
Risk measure
Yearly risk timing (YT(risk measure)[0,4])
YT(risk measure)[0,4] × High Risk Level (or Change)
Average market to book ratio (MB[0,4])
High Risk Level Dummy (High Risk Level)
Cumulative financial deficit (FD[0,4])
Cumulative financial deficit dummy (FDd[0,4])
Credit rating deficits (CDt-4)
Changes in target credit rating (dTRating)
Equity Vol.
(1)
-0.39*
(-1.76)
-0.31
(-0.86)
-0.20***
(-11.07)
0.09***
(5.80)
-0.63***
(-2.91)
-0.92**
(-2.45)
-1.48***
(-4.58)
1.02***
(3.82)
0.13***
(17.43)
2.58***
(12.68)
-0.77**
(-1.99)
-1.67***
Asset Vol.
(2)
0.13
(0.56)
-1.23***
(-3.40)
-0.19***
(-10.76)
-0.04***
(-4.44)
-0.36
(-1.51)
-0.25
(-0.67)
-1.31***
(-4.12)
0.57**
(2.07)
0.13***
(17.50)
2.58***
(12.56)
-0.83**
(-2.09)
-1.87***
51
Merton
(3)
-1.02***
(-4.59)
0.91**
(2.52)
-0.19***
(-11.28)
0.37***
(11.38)
-0.31
(-1.38)
-0.73*
(-1.91)
-0.96***
(-3.10)
2.68***
(11.18)
0.13***
(17.93)
2.58***
(12.72)
-0.53
(-1.37)
-1.58***
High Risk Change Dummy
O-Score
(4)
-0.65**
(-2.08)
0.76
(1.63)
-0.22***
(-7.89)
0.81***
(5.27)
-0.20
(-0.67)
-1.20**
(-2.51)
-1.78***
(-4.02)
1.53***
(3.92)
0.14***
(12.33)
2.28***
(8.42)
-0.86**
(-2.15)
-1.41***
Equity Vol.
(5)
-0.45**
(-2.27)
-0.30
(-0.79)
-0.20***
(-11.35)
0.08***
(5.42)
-0.79***
(-3.93)
-0.86**
(-2.18)
-1.48***
(-4.64)
2.34***
(13.43)
0.13***
(17.77)
2.58***
(12.78)
-0.64
(-1.63)
-1.67***
Asset Vol.
(6)
-0.09
(-0.48)
-1.41***
(-3.73)
-0.19***
(-10.85)
-0.04***
(-4.82)
-0.41*
(-1.96)
-0.24
(-0.63)
-1.34***
(-4.24)
1.11***
(6.38)
0.13***
(17.56)
2.61***
(12.74)
-0.81**
(-2.04)
-1.87***
Merton
(7)
-0.76***
(-3.90)
0.84**
(2.12)
-0.19***
(-11.81)
0.30***
(9.75)
-0.54***
(-2.70)
0.00
(0.01)
-1.02***
(-3.45)
6.04***
(30.73)
0.12***
(17.98)
2.43***
(12.48)
-0.41
(-1.10)
-1.54***
O-Score
(8)
-0.12
(-0.47)
-0.76
(-1.54)
-0.22***
(-7.89)
0.76***
(5.38)
-0.65**
(-2.44)
-0.03
(-0.05)
-1.83***
(-4.20)
3.18***
(13.15)
0.14***
(12.25)
2.27***
(8.56)
-0.72*
(-1.82)
-1.40***
(-7.82)
-2.85***
(-40.55)
-0.11
(-0.35)
0.74***
(75.52)
0.58***
(50.29)
-3.12***
(-3.24)
Yes
(-8.59)
-2.86***
(-39.97)
-0.51
(-1.57)
0.72***
(73.16)
0.57***
(49.02)
3.74***
(5.05)
Yes
(-7.54)
-2.77***
(-39.39)
0.06
(0.20)
0.75***
(77.71)
0.59***
(51.50)
-1.31**
(-2.21)
Yes
(-5.66)
-3.04***
(-26.94)
0.47
(0.97)
0.79***
(59.96)
0.58***
(34.95)
-2.67***
(-3.40)
Yes
(-7.82)
-2.87***
(-40.66)
0.01
(0.03)
0.74***
(75.34)
0.57***
(50.46)
-2.43***
(-2.63)
Yes
(-8.60)
-2.87***
(-40.00)
-0.44
(-1.35)
0.73***
(73.29)
0.57***
(49.04)
3.81***
(5.17)
Yes
(-7.54)
-2.63***
(-38.69)
0.16
(0.54)
0.73***
(78.73)
0.56***
(51.64)
-0.47
(-0.83)
Yes
(-5.72)
-3.08***
(-27.37)
0.69
(1.43)
0.77***
(58.85)
0.55***
(32.96)
-2.84***
(-3.66)
Yes
Adjusted R-square
0.685
0.683
0.691
0.689
0.687
0.683
0.705
0.692
Number of observations
43,614
42,815
42,815
22,303
43,614
42,815
42,815
22,303
Cumulative stock returns (x[0,4])
Profitability (EBITD[0,4])
Market (book) leverage deficit (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝐵𝐵)[0,4])
Change in target market (book) leverage (dTlevM(B)[0,4])
Intercept
Year & firm dummies
52
Table 7
Panel Regressions of Leverage-Decreasing External Financing Activities in Year t+1 (t+2) on Changes in Risk Measures
This table reports the results of panel regressions of leverage-decreasing financing activities in year t+1 (t+2) on the level of and the change in risk measures, the level of
and the change in market to book ratio, and other control variables. The sample includes all NYSE, Amex, and Nasdaq firms from 1975 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 4900-4999) firms, and
firms with book leverage above 100%. All variables are winsorized at the 1st and 99th percentiles and measured at the fiscal year-end. Leverage-decreasing external
financing activity, is measured as the ratio of the difference between annual net equity issuance and annual net debt issuance (sale of common and preferred stocks (SSTK)
– purchase of common and preferred stocks (PRSTKC) – long-term debt issuance (DLTIS) + long-term debt reduction (DLTR)) to total assets at the beginning of the fiscal
year. LDEFA[t+s] is then calculated as the sum of leverage decreasing external financing activity from year t+1 until year t+s. Other variables are defined in Appendix A.
***, **, and * indicate that the coefficients are significantly different from zero at the 1%, 5%, and 10% significance levels, respectively, using a bootstrapping method. Tstatistics based on clustered errors (firm) are reported in parentheses.
Dependent Variable
Change in risk measure (Risk Change)
Level of risk at the beginning of the fiscal year (Risklag)
Change in market to book ratio (MB Change)
Market to book ratio at the beginning of the fiscal year (MBlag)
Financial deficit (FD)
Financial Deficit Dummy (FDD)
Credit rating deficits (CDt-1)
Changes in target credit rating (dTRating)
Cumulative stock returns (r[0,1])
Profitability (EBITD[0,1])
Book leverage deficit (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿[0,1])
Change in target book leverage (dTlevB[0,1])
Intercept
Leverage Decreasing External Financing Activity
LDEFA[t+1]
Equity Vol. Asset Vol.
Merton
O-Score
(1)
(2)
(3)
(4)
0.028***
0.003
0.056***
0.354***
(4.61)
(0.70)
(5.49)
(5.35)
0.021***
-0.002
0.069***
0.133***
(3.70)
(-0.43)
(5.48)
(3.42)
1.731***
1.560***
1.571***
2.404***
(3.99)
(3.58)
(3.60)
(3.16)
-0.049
-0.144
-0.059
-0.124
(-0.21)
(-0.63)
(-0.26)
(-0.34)
0.002
0.005
0.006
0.042**
(0.21)
(0.48)
(0.57)
(2.53)
1.219***
1.180***
1.201***
1.009***
(6.12)
(6.04)
(6.14)
(3.41)
-0.387*
-0.379*
-0.400*
0.082
(-1.72)
(-1.70)
(-1.79)
(0.32)
-1.798***
-1.813***
-1.804***
-1.592***
(-4.92)
(-5.02)
(-5.00)
(-3.77)
-0.261
0.039
0.081
-1.035**
(-0.74)
(0.12)
(0.24)
(-1.98)
-0.137***
-0.145***
-0.144***
-0.096***
(-8.57)
(-9.29)
(-9.15)
(-4.43)
-0.186***
-0.179***
-0.173***
-0.200***
(-15.45)
(-20.58)
(-19.79)
(-15.85)
-0.093***
-0.103***
-0.099***
0.029
(-2.80)
(-3.28)
(-3.14)
(0.54)
1.300*
2.821***
2.170***
2.463***
53
Leverage Decreasing External Financing Activity
LDEFA[t+2]
Equity Vol. Asset Vol.
Merton
O-Score
(5)
(6)
(7)
(8)
0.037***
0.000
0.079***
0.780***
(4.12)
(0.01)
(5.12)
(7.90)
0.024**
-0.003
0.093***
0.261***
(2.52)
(-0.44)
(4.53)
(3.55)
1.712***
1.461***
1.477***
1.288*
(4.13)
(3.70)
(3.73)
(1.87)
-0.954***
-1.094***
-0.988***
-1.653***
(-2.79)
(-3.27)
(-2.94)
(-2.87)
0.023
0.024
0.026
0.096***
(1.34)
(1.46)
(1.54)
(3.85)
2.212***
2.229***
2.257***
1.880***
(7.13)
(7.31)
(7.40)
(3.65)
-0.253
-0.282
-0.308
0.357
(-0.69)
(-0.77)
(-0.84)
(0.86)
-2.106***
-2.174***
-2.177***
-1.895***
(-4.82)
(-5.03)
(-5.04)
(-3.41)
-1.231***
-0.913***
-0.857***
-1.504***
(-3.23)
(-2.80)
(-2.59)
(-2.79)
-0.235***
-0.239***
-0.236***
-0.195***
(-8.79)
(-9.12)
(-9.04)
(-4.98)
-0.305***
-0.298***
-0.290***
-0.342***
(-17.57)
(-20.41)
(-19.67)
(-15.89)
-0.080*
-0.075*
-0.070*
-0.001
(-1.87)
(-1.83)
(-1.72)
(-0.02)
3.559***
5.191***
4.288***
6.794***
Year & firm dummies
(1.95)
Yes
(5.43)
Yes
(4.62)
Yes
(3.75)
Yes
(3.35)
Yes
(5.97)
Yes
(5.62)
Yes
(7.26)
Yes
Adjusted R-square
0.0309
0.0307
0.0315
0.0409
0.0414
0.0410
0.0418
0.0524
Number of observations
84,707
85,827
85,827
43,337
74,745
75,686
75,686
38,030
54