stock return volatility and capital structure decisions
TRANSCRIPT
Electronic copy available at: http://ssrn.com/abstract=2346642
Stock Return Volatility and Capital Structure Decisions∗
Hui Chen† Hao Wang‡ Hao Zhou§
January 5, 2014
Abstract
Stock return volatility significantly predicts active leverage adjustment, consistent
with the trade-off theory. Firms respond asymmetrically to rising volatility instead
of falling volatility, more with debt reduction than equity issuance. The forecasting
power of stock return volatility mostly resides on surprise (idiosyncratic) volatility, as
a proxy for uncertainty; while the forecasting power of expected (systematic) volatility
is largely subsumed by those of firm fundamentals and market information. Falling
earning growth appears to be the channel through which increasing volatility predicts
leverage reduction and investment contraction.
JEL Classification: G32, G17.
Keywords: Stock Return Volatility, Leverage Ratio, Surprise Shocks, Idiosyncratic
Volatility, Uncertainty.
∗Preliminary and incomplete. Please do not distribute without the authors’ consent. Wewould like to thank Redouane Elkamhi, Yangru Wu, seminar participants at the Toronto-McGill Risk Man-agement Conference, the National University of Singapore RMI Conference, the Five Star Conference annualmeetings for helpful discussions. Hao Wang acknowledges funding support from the National Natural ScienceFoundation of China (Grant No. 71272023).†MIT and NBER, Sloan School of Management, 77 Massachusetts Avenue, E62-637, Cambridge, MA
02139, USA; e-mail: [email protected]; tel: 1 617-324-3896.‡Tsinghua University, School of Economics and Management, 318 Weilun Building, Beijing 100084, China;
e-mail: [email protected]; tel: 86 10-62797482.§Tsinghua University, PBC School of Finance, 43 Chengfu Road, Haidian District, Beijing 100083, China;
e-mail: [email protected]; tel: +86 10-62790655.
Electronic copy available at: http://ssrn.com/abstract=2346642
Stock Return Volatility and Capital Structure Decisions
Abstract
Stock return volatility significantly predicts active leverage adjustment, consistent with
the trade-off theory. Firms respond asymmetrically to rising volatility instead of falling
volatility, more with debt reduction than equity issuance. The forecasting power of stock
return volatility mostly resides on surprise (idiosyncratic) volatility, as a proxy for uncer-
tainty; while the forecasting power of expected (systematic) volatility is largely subsumed by
those of firm fundamentals and market information. Falling earning growth appears to be
the channel through which increasing volatility predicts leverage reduction and investment
contraction.
JEL Classification: G32, G17.
Keywords: Stock Return Volatility, Leverage Ratio, Surprise Shocks, Idiosyncratic Volatil-
ity, Uncertainty.
Electronic copy available at: http://ssrn.com/abstract=2346642
1 Introduction
One of the striking yet puzzling features of corporate capital structure decisions is that firms
appear to do little to counteract the changes in market leverage induced by equity price
fluctuations (Welch, 2004). On one common explanation of such a lack of response is costly
adjustment, and several papers have empirically estimated the speed of adjustment towards
the target leverage ratio.1 However, Cochrane (2010) argues that perhaps there is no need
for adjustment as to equity value fluctuations anyway, if such fluctuations are due to discount
rate news rather than cash flow news. Yet, volatility or uncertainty shock not only affects
pricing kernel but also affects earning growth.
In this paper, we try to directly identify the information embedded in stock return volatil-
ity that causes firms’ active adjustments of their capital structure, while purging out passive
leverage changes due to accumulated retained earnings (for book leverage) or mechanical
capital gain (for market leverage). If firms are completely passive as to equity return or
volatility information, there should be no active adjustment in leverage. By focusing on the
volatility of returns, we introduce econometric tools for stochastic volatility and volatility
forecasting into the tests of capital structure decisions. We address the following questions:
(1) Whether and to what extent are leverage adjustments predicted by the volatility of stock
returns? (2) Which information component in volatility contributes to such a predictability?
(3) What are the economic driving forces behind such a predictability?
We show that firms with high return volatility in current year will reduce their leverage
ratios in the subsequent year. The trade-off theory (Modigliani and Miller, 1958; Scott,
1976) predicts that firms with high volatility face higher probability of financial distress,
hence, they should use less debt. In this case, what matters for predicting leverage changes
should be primarily the changes in volatility, not necessarily the level of volatility. Firms
will adjust their leverage downward (upward) when volatility has risen (fallen). Hence,
1See, for example, Leary and Roberts (2005) and Flannery and Rangan (2006). There is large variationin the estimates for the speed of adjustment in the literature (Iliev and Welch, 2010).
1
we construct two measures of volatility shocks: (1) changes in expected volatility and (2)
volatility surprise, which is the difference between realized and expected volatilities. We find
that both types of volatility shocks are negatively related to future leverage changes, but
more so for volatility surprises. The surprise component in volatility shock appears to play a
leading role in determining the effect of uncertainty on capital structure, while the expected
volatility change is mostly subsumed by firm fundamental and macroeconomic information.
This finding echoes Abel and Eberly (1994) in that uncertainty is less influential when it is
largely predictable.
The predictability of stock return volatility for active leverage adjustments is unbalanced,
asymmetric, and short-run. Although firms adjust simultaneously debt downward and equity
upward when the total volatility risk is high, they tend to respond more significantly to
surprise volatility shocks with debt reduction rather than equity issuance. The volatility
effect is asymmetric, i.e., active adjustment in leverage is much stronger in response to
positive (rising) volatility shocks than to negative (falling) ones. The impact of surprise
shocks on capital structure is mainly short-term within one year, consistent with the notion of
uncertainty shock (Bloom, 2009). The predictive power is stronger for firms with lower rating,
smaller size, and lower profitability, but nonmonotonic with respect to external financing
need. Our result quantifies the the trade-off theory prediction in answering the question to
what extent firms reduce leverage to counter-balance the rising likelihood of default due to
higher volatility risk.
In explaining volatility’s significant predictive power for leverage adjustment, we find that
stock return volatility contains unique information about future earnings growth, beyond
that contained in firm fundamental and macroeconomic variables. In particular, firms with
high stock return volatility tend to have a decline in earnings growth in the future. Firms
adjust investment and leverage downward simultaneously with earnings reduction, which are
all predicted by rising volatility of stock returns. The surprise component of stock return
volatility is largely the driving force behind the volatility effect on corporate policies. Our
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findings not only are consistent with the trade-off theory (Modigliani and Miller, 1958) and
the uncertainty shock effect (Bloom, 2009), but also identify an active channel of financing
through stock return volatility to affect investment decision and firm fundamentals.
To the best of our knowledge, this paper is the first comprehensive examination on capital
structure decisions from the perspective of stock return volatility risk. Empirical evidence
indicates that firms change their capital structures over time (Fama and French, 2002; Baker
and Wurgler, 2002; Leary and Roberts, 2005). The survey results reported by Graham and
Harvey (2001) confirm that corporate managers consider distress risk in their financing de-
cisions. Traditional capital structure determinants do not perform well or consistently in
explaining the with-in firm leverage change over time (Graham and Leary, 2011). Early
research focuses on capital structure and earnings volatility, but reaches conflicting conclu-
sions (Harris and Raviv, 1991).2 One caveat of using accounting-based volatility measures
is that they must rely on low frequency data over long history, which may not represents
the current firm and market situations accurately. In comparison, stock return volatility not
only contains rich and timely current information, but also reflects firm’s future fundamental
in a forward-looking manner.
Our work is closely related a few recent papers on leverage, volatility, and investment.
Welch (2004) investigates the interaction between capital structure and stock return, while
controlling for the negative relationship between implied leverage ratio and stock return
volatility. Nikolay et al. (2010) find that Black-Scholes formula implied volatility marginally
explains change in debt level conditional on firm experiencing internal financial deficit. In
contrast, we focus on examining volatility of observed stock returns and active changes in
leverage in a more general setting. Bloom et al. (2007) show that uncertainty, measured
by stock return volatility, reduces the sensitivity of investment to demand shocks; while
2For example, Titman and Wessels (1988) find that earnings volatility does not appear to be related tothe various measures of leverage, whereas Bradley et al. (1984) and Friend and Lang (1988) find leveragenegatively correlated with earnings volatility. Kim and Sorensen (1986) find that EBIT variations arepositively correlated with debt ratios.
3
Bloom (2009) shows that rising aggregate uncertainty, measured by stock index volatility,
discourages investment and hiring. We further show that at individual firm level, rising stock
return volatility or uncertainty shock predicts reduction in earning growth. Importantly,
we demonstrate that the effects of uncertainty on corporate decisions are mostly driven
by the surprise component in volatility shocks, not by the expected component. Panousi
and Papanikolaou (2012) find that idiosyncratic stock return volatility negatively affects
investment at individual firm level, attributing the cause to managerial risk aversion. We
uncover that surprise (idiosyncratic) volatility shocks significantly affect capital structure,
likely through the channel of expected earnings growth.
The rest of the paper is organized as follows: Section 2 describes the empirical method-
ology, data, and summary statistics. Section 3 analyzes the relationships between leverage
adjustment and volatility shocks, controlling for their interactions with various firm funda-
mentals. Section 4 examines the driving force behind the volatility’s predictability power for
leverage adjustment. Section 5 concludes.
2 Empirical Design
The innovation of our approach is to introduce new explanatory variables for capital structure
changes, based on the stochastic volatility model of Engle (1982) and Bollerslev (1986). Our
empirical methodology follows Welch (2004, 2011) to focus on the “active” adjustments of
firms’ leverage decisions. The statistical properties of key variables are also discussed.
2.1 Stochastic Volatility
The trade-off theory (Modigliani and Miller, 1958; Scott, 1976) predicts that firms with
high volatility face higher probability of financial distress. Hence, they should use less debt.
What matters for changes in leverage should be changes in expected volatility, not the level
of volatility. Firms will adjust their leverage downward (upward) when they expect that
volatility has risen (fallen). To investigate the information sources of stock return volatility
4
affecting capital structure decisions, we apply econometric tools for stochastic volatility to
construct change in expected volatility, ∆V olExpdt , and surprise volatility shock, V olSurpriset .
In doing so, we first estimate expected volatility using the ARMA(1,1) model:
V oli,t = θ0,i + θ1,iV oli,t−1 + θ2,iεi,t−1 + εi,t. (1)
The change in expect volatility for firm i at time t is computed as ∆V olExpdi,t = V̂ oli,t−V̂ oli,t−1,
and surprise volatility shock for firm i at time t is computed as V olSurprisei,t = V oli,t − V̂ oli,t.
We use ARMA(1,1) model of realized volatility similar to GARCH(1,1) model of Bollerslev
(1986), but with an explicit observable proxy for latent surprise volatility as in Andersen
et al. (2001).
To connect with existing literature, we also decompose total volatility into systematic
and idiosyncratic volatilities, by estimating daily idiosyncratic returns using the residuals
from the Fama and French (1993) three-factor model,
ri,t − rft = βMi (rMt − r
ft ) + βSMB
i rSMBt + βHML
i rHMLt + ξi,t, (2)
where rMt , rft , rSMBt , and rHML
t represent market return, risk-free rate, and the returns for size
and book-to-market ratio portfolios, respectively.3 We compute annual systematic volatility
V olSysi,t as the standard deviation of the estimated systematic returns, r̂Sysi,t = β̂Mi (rMt − r
ft ) +
β̂SMBi rSMB
t + β̂HMLi rHML
t + rft , and annual idiosyncratic volatility V olIdioi,t as the standard
deviation of the idiosyncratic returns, r̂Idioi,t = ri,t − r̂Sysi,t .
When estimating expected and surprise components of systematic and idiosyncratic
3For robustness check, we also apply the CAPM model to estimate systematic returns. The regressionresults with the systematic and idiosyncratic volatilities estimated from the CAPM model are very similarto those estimated from the Fama-French model. For simplicity, we report the results associated with theFama-French model only.
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volatilities, we apply the same ARMA(1,1) model with lags of each type of volatilities:
V olSysi,t = θSys0,i + θSys1,i V olSysi,t−1 + θSys2,i εi,t−1 + θSys3,i V ol
Idioi,t−1 + εi,t,
V olIdioi,t = θIdio0,i + θIdio1,i V olIdioi,t−1 + θIdio2,i εi,t−1 + θIdio3,i V ol
Sysi,t−1 + εi,t.
The change in expected systematic/idiosyncratic volatilities and their surprise shocks are
then computed in the same way as for total volatilities.
2.2 Empirical Methodology
We examine the predictability of stock return volatility for active leverage adjustment, in the
presence of traditional capital structure determinants suggested by theories and empirical
evidence. Book debt ratio at time t is defined as
BDRt ≡Dt
Dt + EBookt
(3)
where D represents total liabilities on balance sheet and EBook represents book equity. We
compute the active adjustment in book debt ratio at time t as
dbcat ≡Dt
Dt + (EBookt −∆REt)
− Dt−1
Dt−1 + EBookt−1
(4)
where ∆REt represents change in accumulative retained earnings on balance sheet between
time t and t − 1, ∆REt = REt − REt−1. We follow Welch (2004, 2011) to use ADRt to
represent actual (market) debt ratio at time t,
ADRt ≡Dt
Dt + EMktt
(5)
where EMkt represents the market value of equity. Since market leverage changes when
equity price fluctuates, it is important to purge out such mechanical effect to examine the
impact of stock return volatility on future capital structure adjustment. A latent implied
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debt (leverage) ratio is defined as
IDRt ≡Dt−1
Dt−1 + EMktt−1 . (1 + xt−1,t)
, (6)
where xt−1,t is the capital gain of equity over time t − 1 to t. The actual and implied debt
ratios formulated above allow us to define total capital structure change at time t, dctt, as
dctt ≡ ADRt − ADRt−1 =Dt
Dt + EMktt
− Dt−1
Dt−1 + EMktt−1
, (7)
which can be decomposed into two parts: dctt = dcat + dcpt, where dcat denotes active
leverage change due to net debt/equity issuance,
dcat ≡ ADRt − IDRt =Dt
EMktt +Dt
− Dt−1
Dt−1 + EMktt−1 . (1 + xt−1,t)
, (8)
and dcpt denotes passive leverage change due to equity return,
dcpt ≡ IDRt − ADRt−1 =Dt−1
Dt−1 + EMktt−1 . (1 + xt−1,t)
− Dt−1
Dt−1 + EMktt−1
. (9)
Previous research documents that firm capital structure is influenced by a set of fun-
damental and macroeconomic factors.4 Besides lagged book/market debt ratios for firm i,
BDRi,t−1 and ADRi,t−1, we consider the following variables in our analysis. (1) ri,t represents
firm i’s stock return between time t−1 and t. Welch (2004) shows that market debt ratio may
change passively with stock price fluctuation, which does not reflect directly active financing
decisions. (2) The natural logarithm of sales normalized by the consumer price index (CPI),
denoted by SALEi,t, as a proxy for firm size. Titman and Wessels (1988) and Baker and
Wurgler (2002) find a positive relationship between debt ratio and firm size. (3) Tangibility,
denoted by TANGi,t, is computed as gross properties, plant and equipment (PPE) divided
by total assets. A firm with higher proportion of tangible assets should have higher asset
4Harris and Raviv (1991), Rajan and Zingales (1995), Frank and Goyal (2003), and Graham and Leary(2011) present reviews of the capital structure literature.
7
recovery in bankruptcy and, hence, lower debt financing costs, which in turn encourages debt
financing. (4) Market-to-book ratio, denoted by MBi,t, as a proxy for growth. (5) Return
on assets, denoted by ROAi,t, is a proxy for profitability. Both market-to-book ratio and
return on assets are found to be negatively related to leverage. It is computed using earnings
before interest and tax (EBIT) divided by total assets. (6) corporate tax rate is denoted
by TAXi,t. The trade-off theory suggests that debt ratio should be positively related to tax
rate as firms could enjoy greater tax savings through debt financing. (7) Cash ratio, denoted
by CASHi,t, is computed as cash on balance sheet divided by interest expenses. It measures
short-term solvency and is expected to be positively correlated with leverage. (8) Dividend
yield, denoted by DYi,t, is computed as common equity dividend divided by the market value
of common equity. Cooper and Lambertides (2011) report a positive relationship between
change in dividend payout and subsequent change in leverage ratio. (9) Financial deficit
normalized by sales, denoted by DEFi,t, as a measure of the degree of external financing
need.5
We include three variables to measure market condition and macroeconomic environment:
S&P value-weighted return and volatility, denoted by SPRt and SPVt, respectively, and
industrial production index growth, IPGt, between time t− 1 and t. Further, we include an
industry dummy, INDi,t to control for the industry effect. For the panel regressions, we apply
the robust standard error method proposed in Petersen (2009) to control simultaneously for
the firm and time clustering effects.
5Following the literature, we compute
DEFi,t =Cash Outflowi,t − Internally Generated Cashflowi,t
Salesi,t
=(INVi,t + ∆WCi,t)− (NIi,t −DVDi,t + DEPi,t + DTi,t)
Salesi,t,
where INVi,t represents investment in capital assets (PPEi,t−PPEi,t−1+ investment in intangible assets).∆WCi,t represents change in working capital between time t− 1 and t, where working capital is defined ascurrent assets excluding cash minus current liabilities. NIi,t denotes net income. DVDi,t denotes dividend.DEPi,t and DTi,t are the non-cash expenses—depreciation and amortization and deferred tax, respectively.
8
The discussion above leads to the following regression equation
LEVi,t+1, = α + β1V OLi,t + β2ri,t + β3BDR/ADRi,t + β4SALEi,t
+β5TANGi,t + β6MBi,t + β7ROAi,t + β8TAXi,t (10)
+β9CASHi,t + β10DYi,t + β11DEFi,t + β12SPRt
+β13SPVt + β14INDt + β15IPGt + εi,t,
where LEVi,t+1 represents various capital structure measures at time t+1. Those of primary
interest are active book and market debt ratio changes, dbcai,t+1 and dcai,t+1, among which
dbcai,t+1 is the principle measure. We use book or market debt ratio, BDRi,t+1 or ADRi,t+1,
total debt ratio change, dcti,t+1, and capital gain-induced debt ratio change, dcpi,t+1, in
some regressions for comparison and illustration. V OLi,t represents stock return volatil-
ity or expected volatility & surprise volatility shocks—the primary explanatory variables
under investigation. They include stock return volatility, V oli,t, estimated using daily eq-
uity returns in a 365-calendar-day window before time t, systematic volatility, V olSysi,t , and
idiosyncratic volatility, V olIdioi,t .
2.3 Summary Statistics
We collect data on firm financial information, stock returns and macroeconomic variables
from several sources. The annual financial information used to compute debt ratios and
the control variables is obtained from COMPUSTAT. To avoid selection bias, we include all
available U.S. firms from the database’s starting year of 1950 up to 2010. The daily stock
returns of all U.S. firms available in CRSP between the database’s starting year of 1948 and
2010 are downloaded. Our study requires an unbroken time series of debt ratios for each firm.
Hence, we only keep firms that have financial information that enables us to compute at least
four consecutive years’ debt ratios. There are 78,003 firm-year observations when debt ratios
and stock return volatilities are merged together. After removing the financial and utility
9
firms, we have 61,925 observations from 4,413 firms in a period between June 1959 and May
2010. The daily S&P value-weighted index returns are obtained from CRSP as well. The
Fama-French three factors and monthly industrial production index are downloaded from
WRDS and the Federal Reserve Bank at St. Louis website, respectively.
Descriptive statistics of the key variables—median across the sample firms—are reported
in Table 1. The average book and market debt ratios, BDR and ADR, are 50.99% and
37.54%, respectively. They are highly persistent with AR(1)’s of 0.99 and 0.98, respectively.
The active change in book debt ratio has a mean of 1.11% and a standard deviation of
6.21%, and the counterparts of market debt ratio are 1.33% and 4.86%, respectively. The
AR(1)’s of the active book and market debt ratio changes are 0.08 and 0.10, respectively,
suggesting that they are much more suitable variables to study capital structure decisions.
The AR(1) of the total debt ratio change, dct, is -0.06, consistent with the notion that debt
ratios are mean-reverting (Fama and French, 2002; Baker and Wurgler, 2002; Leary and
Roberts, 2005).
The volatility of stock returns has a mean of 44.40% and a standard deviation of 14.63%.
It is highly persistent with an AR(1) of 0.97. The average change in expected volatility and
volatility surprise are slightly negative of -0.09% and -0.10%, respectively. The change in
expected volatility is negatively autocorrelated with an AR(1) of -0.24, while the volatility
surprise is positively autocorrelated with an AR(1) of 0.30. The average systematic and
idiosyncratic volatilities are 13.19% and 41.24%, respectively. The average annual stock
return is 17.00% with a standard deviation of 46.37% and AR(1) of 0.12. For simplicity, we
omit the discussion of other control variables, given that they are similar to those reported
in existing literature.
Table 2 reports the univariate correlations between the key variables—median across the
sample firms with at least 10 consecutive observations. The subsequent active book debt ra-
tio change, dbcat+1, is negatively correlated with stock return volatility, change in expected
volatility and volatility surprise. The correlations are -0.14, -0.03 and -0.12, respectively.
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The active market debt ratio change, dcat+1, displays very similar levels of correlation as
well. The correlation between contemporaneous dbcat+1 and dcat+1 is 0.92, suggesting that
examining the active book or market debt ratio changes is likely to produce similar results. In
contrast, the correlation between book debt ratio, BDRt+1, and market debt ratio, ADRt+1,
is only 0.69. The correlations between active change in book (market) leverage and con-
temporaneous changes in earnings growth and change in capital expenditure are 0.11 (0.12)
and 0.25 (0.27), respectively, suggesting that capital structure decisions may respond to cash
flow information, and that firms’ need of debt may change with investment policy.
Figure 1 illustrates the median active book (market) debt ratio changes with respect to
expected volatility shock and volatility surprise shock over the sample period. The active
book and market debt ratio change closely resemble each other. They tend to move in the
opposite direction as the expected/surprise volatility shocks do, especially around the NBER
recession. Book debt ratios, however, behave differently over time.
The volatility measures are positively correlated with each other. In particular, the
correlation between volatility and volatility surprise (idiosyncratic volatility) is 0.85 (0.98).
The correlation between volatility surprise and idiosyncratic volatility is 0.79, suggesting
that firms are likely to experience greater surprise idiosyncratic shocks where volatility risk
level is high. The stock return is negatively correlated with volatility with a correlation of
-0.13. The correlations between the stock return and subsequent active book and market
debt ratio changes are 0.07 and 0.09, respectively. The industrial production index growth
is negatively correlated with stock return volatility, expected and surprise volatility shocks
with correlations of -0.31, -0.11, and -0.33, respectively. The industrial production index
growth is positively correlated with future capital structure adjustment, change in earnings,
and change in investment. The correlations are 0.15, 0.15, 0.13, and 0.18, respectively.
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3 Empirical Result
We show that stock return volatility and volatility shocks negatively and significantly predict
subsequent active debt ratio adjustment. The level of idiosyncratic volatility and surprise
volatility shock have phenomenally strong predictive power. Firms rely more on debt reduc-
tion than equity issuance in response to volatility shocks, much stronger to rising volatility
shocks than to negative ones. The predictive power of volatility shocks is short-term within
one year, and more evident for firms with lower credit rating, lower profitability, and smaller
size, but nonlinear with respect to external financing need. Our findings are consistent
with the trade-off theory (Modigliani and Miller, 1958) and uncertainty shock effect (Bloom,
2009). We further quantify the the trade-off theory prediction in answering the questions to
what extent firms reduce leverage ratios conditional on rising return volatilities and through
which informational channel volatility risk impacts capital structure decisions. We show that
surprise volatility shocks mostly drive the uncertainty effect on capital structure decisions.
3.1 Benchmark Regressions
Table 3 first compares the regression of active book debt ratio adjustment at time t + 1 on
volatility and stock return. Column (1) shows that in a univariate regression, subsequent
adjustment in book leverage is negatively and significantly correlated to stock return volatil-
ity. The coefficient of -7.069 implies that on average, one standard deviation increase in
stock return volatility (14.63%) will lead a firm to lower its book debt ratio by 1.03%. The
t-statistic is -23.35 and the R2 is 6.20%, suggesting that the influence of volatility risk on
capital structure decisions is not only economically significant, but also statistically signif-
icant. This evidence confirms the finding in Leary and Roberts (2005) that firms adjust
capital structures over time. It quantifies the the trade-off theory prediction in answering
the question to what extent firms reduce leverage to counter-balance the rising likelihood
of default due to increased volatility risk (Black and Scholes, 1973; Merton, 1974). Column
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(2) shows that stock return positively affects subsequent leverage adjustment as well, with
a marginally significant t-statistics of 1.98. Firms tend to use more debt when their stocks
perform well. The coefficient of 0.492 suggests that one standard deviation increase in stock
return (46.37%) helps to elevate book debt ratio by 0.23%. The R2 is 0.10%, much lower
than 6.20% for volatility. The result does not contradict the prediction of the market timing
theory that debt ratio should be negatively related to stock performance, since positive stock
return does not necessarily mean equity being overvalued (Baker and Wurgler, 2002).
We then regress change in book debt ratio on volatility, stock return, and lagged book
debt ratio, and report the result in Column (3) of Table 3. The correlation between volatility
and subsequent debt ratio adjustment remains strong. The coefficient of volatility is -7.426
with a t-statistic of -26.69. The stock return volatility contains additional information beyond
stock returns and leverage itself in predicting future leverage adjustment. The forecasting
power of volatility is in the same order of the lag leverage—(i) the R2 increases from 6.20%
in Column (1) to 13.80% in Column (3); (ii) one standard deviation increase in volatility
and book debt ratio (14.63% and 10.07%) causes 1.09% and 1.16% upward adjustment
in debt ratio, respectively. The result reported in Column (4) confirms that the effect of
volatility risk on capital structure adjustment is robust in the presence of the market- and
firm-level leverage determinants. The negative coefficient of stock return volatility remains
statistically significant at the 1% level. In comparison, the coefficient of stock return switches
sign from positive to be negative. Stock return has a positive correlation (0.27) with return
on assets, and ROA seems to dominate stock return for explaining leverage adjustment.6
The S&P500 index volatility is not statistically significant. Industrial production index
significantly predicts positive debt ratio change, suggesting that leverage is procyclical (Chen,
2010). Column (5) shows that the stock return volatility is negatively and significantly
correlated with future book debt ratio.7
6Unreported, we regress active change in book leverage, dbcat+1, on stock return and ROA at time t, andfind that the coefficient sign of stock return is driven to be negative, suggesting that fundamental profitabilityinformation subsumes that embedded in stock returns.
7We split our sample into early and late samples, and conduct sub-sample regressions. We find that
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For completeness, we also report regressions results on market debt ratio adjustment
in Table 4. Column (1) shows that, in a univariate regression, the stock return volatility
negatively and significantly affects the subsequent active change in market debt ratio. The
coefficient is -3.023 and the t-statistic is -17.17, implying that on average one standard
deviation increase in volatility will decrease market debt ratio by 0.44%. The adjusted R2
is 2.3%, which is much higher than R2 for stock return,0.8%, as reported in Column (2).
The multivariate regression result reported in Column (3) confirms such strong impact of
stock return volatility on capital structure decisions in the presence of the other leverage
determinants, in particular, the lag market debt ratio.
We also analyze whether stock return volatility affects market debt ratio, total debt ratio
change, and capital gain-induced debt ratio change, respectively. As reported in Column
(4) and Column (5) of Table 4, stock return volatility is negatively correlated to market
debt ratio and total debt ratio, but only significant at the 5% level. The relationships
between volatility risk and the level of leverage ratio and total change in capital structure
are less significant than that associated with the active leverage adjustments. The result
reported in Column (6) offers a potential explanation—stock return volatility is insignificant
in predicting debt ratio change that is mechanically induced by capital gain. These results
underscore the argument of Welch (2004, 2011) that it is desirable to focus on examining
active debt ratio adjustments in order to draw meaningful implications on how firm capital
structure decisions respond to various information shocks.
3.2 Volatility Shocks and Asymmetric Response
What are the sources behind the strong predictability of stock return volatility for capital
structure change? We first decompose volatility information by constructing two different
shocks—the expected shock, ∆V olExpdt and surprise shock, V olSurpriset , as specified in Section
the results are sensitive to how to split samples. However, the predictability of stock return volatility onsubsequent leverage adjustment is strong and robust after the 1970s. This may be due to few observationsand unreliable data quality in early years.
14
2.1. The evidence shows that the predictability of expected volatility change is largely
subsumed by the firm fundamental and market information, while surprise volatility shock
remains a significant predictor of leverage change. Further corroborating this finding, we
also decompose both volatility shocks into positive and negative components. We find that
expected volatility change has no predictive power in the presence of firm fundamental and
market information, while positive surprise shock—rising volatility uncertainty—contains
significant and nonredundant predictability for the active leverage adjustments.
Panel A in Table 5 shows how the expected and surprise volatility shocks affect subse-
quent debt ratio adjustment. Column (1) shows that active book leverage change dbcat+1
is negatively and significantly correlated to ∆V olExpdt . The coefficient is -4.199 and statisti-
cally significant at the 1% level. Column (2) shows that surprise volatility shock negatively
affects subsequent debt ratio adjustment. The coefficient is -4.336. The t-statistic and R2
are -7.73 and 1.00%, respectively. Column (3) indicates that firms decrease debt ratio when
stock return volatility is expected to increase. One standard deviation (8.38%) change in
the expected volatility results in a 0.57% reduction in the book debt ratio. The results are
not only consistent with the dynamic trade-off theory prediction (Strebulaev, 2007; Bhamra
et al., 2010), but also offer quantitative implications on how change in expected/surprise
change in volatility affects leverage adjustment.
Column (4), (5) and (6) show that the negative impacts of expected and surprise volatil-
ity shocks on leverage adjustment are robust after including the control variables in the
regressions. ∆V olExpdt becomes insignificant when putting together with V olSurpriset in a
multivariate regression, as reported in Column (7). Surprise shocks matters more than ex-
pected shocks in determining debt ratio. The finding echoes Abel and Eberly (1994) in that
uncertainty is less influential when it is more predictable. Such significant predictability
cannot be reduced in the presence of expected volatility level, as shown in Column (8). We
find that both expected and surprise volatility shocks negatively affect debt ratio, but the
results are much stronger and more robust for surprise shocks.
15
Figure 2 plots the results of applying the Fama-McBeth method to regress the active book
(market) debt ratio change, dbcat+1 on the expected (surprise) volatility shock, ∆V olExpdt
(V olSurpriset ), by year. During most of our sample period, surprise/expected volatility shocks
negatively and significantly affect subsequent active leverage adjustments. The impacts
appear to be weak before year 1970. This phenomenon could be caused by fewer observations
and poor data quality in early years. It could also be due to the learning effect that firms
become more sensitive to volatility risk in financing over time.
In Panel B of Table 5, we divide our sample by positive and negative ∆V olExpdt and
V olSurpriset , respectively. The univariate regression results reported in Column (1) and (3)
indicate that the positive expected shocks significantly decrease the debt ratios, while the
negative shocks significantly increase them. However, once we control for firm characteristics
and market conditions, the effects of the positive and negative expected shocks become
insignificant with t-statistics of -1.52 and 0.41, respectively. For surprise shock, the univariate
regression results reported in Column (5) and (7) show that the positive surprise shocks
significantly decrease the subsequent debt ratios, while the negative shocks significantly
increase them. The active leverage chance is asymmetric: the coefficient and R2 for positive
volatility shocks are -10.18 and 3.90%, respectively; while the coefficient and R2 for negative
volatility shocks are 7.15 and 1.00%, respectively. More importantly, Column (6) and (8)
confirm that in the multivariate regression, the positive surprise shocks have coefficient and
t-statistics of -1.42 (large) and -2.42 (significant), while the negative surprise shocks have
coefficient and t-statistics 0.33 (small) and -0.47 (insignificant). Therefore, only positive
volatility shocks—rising volatility uncertainty—possess nonredundant information for active
leverage reduction.
3.3 Systematic Volatility versus Idiosyncratic Volatility
We further decompose volatility and volatility shocks into systematic and idiosyncratic parts
to analyze the impacts of different volatility information contents on leverage adjustment.
16
Column (1) of Table 6 shows that in a univariate regression, both systematic and idiosyncratic
volatilities negatively and significantly predict debt ratio adjustment. However, Column
(2) shows that idiosyncratic expected volatility shock negatively affects debt ratio change,
while systematic expected volatility is not significant. The idiosyncratic expected shocks
are statistically significant at the 1% level. The same pattern is also found for the surprise
shocks, as shown in Column (3), idiosyncratic surprise volatility shock negatively affects debt
ratio change, while systematic surprise volatility shock is not significant. The multivariate
regression results reported in Column (4), (5), and (6) are qualitatively the same, except that
∆V olIdio Exptt becomes not significant. We find that only ∆V olIdio Surprise
t remains significant
when all types of shocks are jointly considered in the presence of the control variables, as
shown in Column (7). In short, the negative impact of stock return volatility on active
leverage change is mainly through the idiosyncratic-surprise volatility channel, not through
the expected or systematic volatility channel.
3.4 Debt Adjustment and Equity Adjustment
To address the question how firms adjust capital structure in response to volatility shocks,
we compute financing-resulted percentage changes in debt and equity between time t and
t + 1, and regress them on stock return volatility and volatility shocks. The results are
reported in Table 7. Column (1) and (5) show that stock return volatility affects negatively
debt change but positively equity change. Both are statistically significant at the 1% level.
The multivariate regression results reported in Column (3) and (7) confirm such effects. We
find that surprise volatility shocks affect debt change negatively and equity change positively,
while the expected volatility shocks do not have significant impacts. Column (2) and (6)
report that the surprise shocks’ impacts are statistically significant at the 1% and 10%
level for the debt and equity changes, respectively. The surprise shocks’ negative impact on
the debt change remains significant in the presence of the control variables, but becomes
insignificant on the equity change, as reported in Column (4) and (8) . It seems that when
17
surprise volatility shocks hit home, firms tend to actively reduce outstanding debt rather than
issuing new equity. Equity issuance and repurchase are more driven by firm fundamentals
than by surprise volatiity shocks.
3.5 Temporal Effect of Volatility Shocks
We examine the temporal effect of volatility risk on leverage adjustment, by including the
lagged observations of stock return volatility, V ol, change in expected volatility, ∆V olExpd,
volatility surprise, V olSurprise between time t−5 and t in univariate and multivariate regres-
sions, respectively. The multivariate regressions contain firm and market control variables
observed at time t. The results are reported in Table 8. Column (1) shows that the coeffi-
cient of V olt is -6.12, and the t-statistic is -8.07. The further lags of V ol are not statistically
significant. The multivariate regression result reported in Column (2) shows that V olt re-
mains significant in the presence of the other lagged volatility observations, among which
V olt−1 and V olt−2 remain insignificant. The results suggest that volatility’s predictability
on leverage adjustment is short-term, consistent with the notion that uncertainty shock is
short-lived (Bloom, 2009). Column (3) shows that the coefficients of all lagged observations
of ∆V olExpd are negative and statistically significant at least at the 5% level. As shown in
Column (4), V olExpdt remains significant at the 1% level and V olExpd
t−1 is significant at the
10% level in the presence of the control variables. The results suggest that expected volatil-
ity shocks tend to have long-term impacts due to its persistence, but to some extent the
impacts of further lags are subsumed by more recent firm fundamental and business cycle
information. Column (5) and (6) indicate that V olSurpriset is the only surprise shock that is
consistently significant at the 1% level in both the univariate and multivariate regressions,
suggesting that the impact of the surprise shock is unequivocally short-term.
18
3.6 Interactions with Firm Characteristics
To understand the economic meaning of volatility’s predictability for leverage change, we
analyze how the relationship between leverage adjustment and stock return volatility in-
teracts with some key firm characteristics including credit quality, size, profitability, and
external financial need. The predictive power of volatility shocks for leverage adjustment is
stronger for firms with lower rating, smaller size, and lower profitability, but nonmonotonic
with respect to external financing need.
Table 9 reports the results of the univariate regressions of active book debt ratio change,
dbcat+1 on V olt, ∆V olExpdt , and V olSurpriset by credit rating, firm assets and ROA, respec-
tively. Panel A reports the regression results by firm rating groups: AAA-A, BBB, and
BB & Below. The evidence suggests that a firm will be more sensitive to volatility risk
for financial decision as default risk increases. As shown in Column (1), (3), and (5), the
coefficients (t-statistics) are -2.30 (-1.66), -4.30 (-3.28), and -5.83 (-7.57), respectively. The
R2’s increase monotonically from 0.2% to 0.9% then to 2.7%. Further, surprise volatility
shocks negatively affects the debt ratio changes for all rating groups, when controlling for
the effects of expected volatility changes. The impacts are significant at the 1% for BBB
and BB & Below, but not significant for AAA-A, suggesting that the high investment grade
firms’ financial decisions are not very sensitive to volatility shocks.The BBB group has the
highest coefficient of -6.29 and R2 of 1.3%. The BBB firms are the most sensitive to sur-
prise volatility shocks and, hence, adjust capital structure accordingly. Since those firms
have the greatest concerns over being downgraded from the investment grades to speculative
grades. This result lends further support to the trade-off theory—firms more sensitive to
credit screening adjust their leverage downward more actively when volatility surprise shock
has risen.
Column (1), (3), and (5) in Panel B show that stock return volatility negatively predicts
subsequent leverage adjustment, statistically significant at the 1% level for all three size
groups. The coefficients (R2’s) are -6.94 (5.1%), -6.76 (3.8%), and -6.12 (3.2%), respectively.
19
The results imply that small firms are slightly more sensitive to volatility risk in adjusting
capital structure. As shown in Column (2), (4), and (6), the regressions of surprise volatility
shocks do not show remarkable difference between different groups. This result indicates size
effect of the influence of total volatility risk on capital structure decisions.
Panel C reports the regression results by ROA. The negative impact of stock return
volatility on subsequent debt ratio adjustment is statistically significant at the 1% level for
all three groups. The R2’s are 4.2%, 1.1%, and 1.5%, respectively, as shown in Column
(1), (3), and (5). Low (negative) profitability firms are more sensitive to volatility risk for
their capital structure adjustments. This pattern is confirmed by the regression results with
volatility shocks. Column (2), (4), and (6) show that the R2’s decrease from 0.7% to 0.6%
then to 0.5% as firm profitability increases. Firms with higher profitability should be able
to issue or rollover debt more easily.
We examine how firm external financing need affects the predictability of stock return
volatility on subsequent leverage adjustment, by dividing our sample by internal financial
deficit into quantiles, and by internal financial surplus versus deficit. Panel A and B of Table
10 reports the univariate and multivariate regression results, respectively.
Columns (1)-(4) in Panel A show that stock return volatility significantly predicts sub-
sequent leverage adjustment in all quantiles. The R2’s are 5.4%, 4.1%, 2.9%, and 8.0% as
firms’ external financing need grows. The results suggest that volatility risk matters more
for financial decisions when firms are either in very urgent external need or not in external
financing need at all. As reported in the lower section of Panel A, surprise shock negatively
predicts leverage adjustment, statistically significant at the 1% level for all quantiles. The
R2’s are 1.8%, 1.4%, 0.6%, and 0.8%, respectively, as the internal deficit grows. (The R2’s
reported in Column (5) and (6) do not show consistent patterns.)
The multivariate regression results in Panel B confirm the significant predictive power of
stock return volatility and shocks. Comparing the R2’s of both the volatility and volatility
shocks in Columns (1)-(4), we find the R2 in Column (4) are remarkably higher than those
20
in Columns (1)-(3), around 30% versus 10-12%. It is evident that firms with urgent external
financing are the most responsive to the fundamental and market information in adjusting
leverage. The R2’s reported in Column (5) and (6) confirm such a pattern, around 25%
versus 12%. Combining the results in Panel A and Panel B suggests the following: volatility
shocks have greater impacts for firms without urgent external financing needs, while the
fundamentals have greater impacts for firms needing external financing.
4 Future Earnings and Investment
Finally, we relate stock return volatility to future earnings growth and investment policy,
in order to identify the economic channels through which stock return volatility weighs into
the corporate decision-making. We first investigate whether stock return volatility is able to
predict future earnings growth, defined as
debitt+1 ≡EBITt+1 − EBITt
EBITt, (11)
where EBIT denotes earnings before interest and tax. We carry out regressions with debitt+1
as the dependent variable on stock return volatility and volatility shocks, together with the
control variables specified in Equation (10). We also ran regressions of earnings growth on
the contemporaneous active debt ratio change to examine their relationship.
Column (1) of Table 11 shows that stock return volatility negatively and significantly
predicts future earnings growth. The coefficient is -0.239, implying that one standard devi-
ation rise in stock return volatility (14.63%) predicts a future earnings drop of 3.50%. The
result reported in Column (2) indicates a significant and positive simultaneous correlation
between earnings change and active debt ratio change. Column (3) shows that expected and
surprise volatility shocks predict subsequent earnings growth in the opposite directions—
the coefficients (t-statistics) of ∆V olExpdt and V olSurpriset are 0.158 (2.70) and -0.277 (-4.22),
respectively, with surprise volatility shock more significant than expected volatility change.
21
One standard deviation change in expected shock (8.22%) predicts an earnings increase of
1.30%, whereas one standard deviation change in surprise shock (14.65%) predicts an earn-
ings reduction of 4.06%. Column (4) shows that the predictive power of both systematic
and idiosyncratic volatilities on future earnings growth is significant. The coefficients (t-
statistics) of V olSyst and V olIdiot are -0.329 (-2.10) and -0.234 (-11.05), respectively, with
idiosyncratic volatility much more significant than systematic volatility.
The multivariate regressions yield consistent results, except that the predictive powers
of systematic and expected volatility shocks become insignificant or marginally significant—
their predictive powers appear to be subsumed by that of the S&P 500 return volatility.
Firms’ surprise volatility and idiosyncratic volatility shocks carry strong predictive informa-
tion beyond that embedded in the fundamental and market control variables. Overall, high
level of stock return volatility and surprise/idiosyncratic volatility shocks signal low future
cash flow growth, which in turn may affect firms’ active financing decisions.
Bloom (2009) shows that rising aggregate uncertainty, measured by stock index return
volatility, negatively affects corporate investment and hiring. Panousi and Papanikolaou
(2012) find that idiosyncratic stock volatility negatively affects investment at the firm level.
We analyze the predictability of stock return volatility and volatility shocks on subsequent
investment adjustments, as an economic channel through which stock return volatility affects
future capital structure decisions. We measure change in future investment using change in
capital expenditure at time t + 1 normalized by net property, plant and equipment at time
t:
dcet+1 ≡CEt+1 − CEt
NetPPEt
, (12)
where CE denotes capital expenditure and NetPPE denotes net property, plant and equip-
ment. Following the literature, we delete the observations with the absolute value of CEt+1-
to-NetPPEt ratio over one. We regress dcet+1 on stock return volatility and volatility shocks,
together with the control variables specified in Equation (10). We examine the correlation
between contemporaneous leverage adjustment and investment adjustment as well.
22
Table 12 reports the results. Column (1) and (5) show that stock return volatility nega-
tively and significantly predicts subsequent change in investment in the absence (presence)
of the control variables. The impact is phenomenal. The multivariate regression coefficient
is -0.934, implying that one standard deviation rise in the stock return volatility (14.63%)
leads to a 13.66% reduction in capital expenditure. Column (2) shows that the simultane-
ous changes in investment and active debt ratio are positively and significantly correlated.
The coefficient (t-statistic) of dbcat+1 is 0.188 (8.72). The R2 is 1.1%. Column (3) shows
that the surprise volatility shock significantly affects investment change—the coefficient and
t-statistic of V olSurpriset are -4.01 and -4.22, respectively, while expected volatility changes
is insignificant. Column (4) shows that the predictive power of idiosyncratic volatility on
investment change is negative and highly significant, while that of systematic volatility is
only marginally significant.
The evidence indicates that rising stock return volatility, the second moment shock in
Bloom (2009), predicts reduction in future cash flow, the first moment shock. Firms reduce
simultaneously investment and leverage with falling earnings, which are all predicted by
rising stock return volatility. In particular, the surprise component and/or the idiosyncratic
component of volatility shocks constitute the most significant driving forces behind the effects
of economic uncertainty on corporate investment and financing decisions.
5 Conclusions
The Graham and Harvey (2001) survey shows that distress risk is carefully considered in
capital structure decisions. Hence, stock return volatility that reflects distress risk should
naturally affect leverage adjustment. Unfortunately, little attention has been given to exam-
ine the information contents of stock return volatility in affecting capital structure decisions,
although asset volatility and leverage ratio are the fundamental state variables in credit risk
modeling (Black and Scholes, 1973; Merton, 1974) .
In this paper we identify information content in stock return volatility that causes firms’
23
active adjustments of their capital structure. We aim at active leverage adjustment that
directly reflects capital structure decisions. By focusing on the volatility of stock returns,
we introduce econometric tools for stochastic volatility and volatility forecasting into tests
of capital structure models. In particular, we decompose the information of return volatility
into expected and surprise shocks. The predictability of stock return volatility for active
leverage adjustment is both economically and statistically significant, stronger for idiosyn-
cratic volatility and surprise volatility shock. The evidence suggests that surprise volatility
shock is a more precise measure of uncertainty shock than total return volatility.
The predictive power of stock return volatility is short-term and asymmetric. The active
adjustment in leverage is much stronger in response to a positive (rising) shock in volatility
than to a negative (falling) one, and the response is more through debt reduction than equity
issuance. In explaining its predictive power, we find stock return volatility contains unique
information about future profitability. In particular, firms with rising volatility tend to have
a decline in earnings growth in the future. Firms adjust simultaneously investment and
leverage downward as earnings growth falls. Our findings are consistent with the trade-off
theory (Modigliani and Miller, 1958) and uncertainty shock effect (Bloom, 2009). Moreover,
our result quantifies the the trade-off theory prediction in answering the question as to what
extent firms reduce leverage to counter-balance the rising likelihood of default due to higher
volatility risk. We identify an active volatility channel of financing that affects investment
and firm fundamentals.
24
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26
Table 1 Summary StatisticsThis table presents the notations and descriptive statistics of the key variables in the paper. The
statistics are computed as the median of the statistics of the sample firms.
Variable Notation Mean Std. Dev. Skewness Kurtosis AR(1)
Active Change in Book Leverage (%) dbcat+1 1.11 6.21 0.15 3.45 0.08Book Debt Ratio (%) BDRt 50.99 10.07 0.21 2.27 0.99Active Change in Mkt. Leverage (%) dcat+1 1.33 4.86 0.36 3.54 0.10Total Change in Mkt. Leverage (%) dctt+1 0.23 9.79 0.14 2.92 -0.06Return-induced Chg. in Mkt. Lev. (%) dcpt+1 -1.01 8.15 0.18 2.99 0.00Actual Market Debt Ratio (%) ADRt 37.54 12.72 0.33 2.39 0.98Implied Market Debt Ratio (%) IDRt 35.94 13.08 0.34 2.40 0.98
Stock Return Volatility (%) V olt 44.40 14.63 0.77 2.80 0.97
Change in Expd. Volatility (%) ∆V olExpdt -0.09 8.22 -0.02 3.00 -0.24
Volatility Surprise (%) V olSurpriset -0.10 14.65 0.62 2.99 0.30
Systematic Volatility (%) V olSyst 13.19 5.85 1.45 4.55 1.03
Idiosyncratic Volatility (%) V olIdiot 41.24 13.05 0.69 2.68 0.97
Stock Return (%) rt 17.00 46.37 0.72 3.12 0.12Sales (million) Salest 540.97 269.11 0.41 2.12 1.06Assets (million) Assetst 537.11 261.13 0.45 2.14 1.05Tangibility TANGt 0.55 0.11 0.11 2.18 0.99M/B Ratio MBt 2.13 1.06 0.71 2.93 0.91ROA (%) ROAt 9.33 5.31 -0.07 2.52 0.92Effective Tax Rate TAXt 0.33 0.18 -0.46 4.84 0.81Cash/Interest Expenses CASHt 8.17 8.07 1.52 4.21 0.76Dividend Yield (%) DY t 1.34 1.13 1.27 3.70 0.87Financial Deficit/Sales (%) DEF t 0.14 12.71 0.39 3.81 0.08Change in EBIT (%) debitt+1 8.14 69.68 0.16 3.05 0.15Change in Capitall Expenditure (%) dcet+1 1.08 6.54 0.40 3.49 -0.04
S&P Return (%) SPRt 10.43 19.04 -0.55 2.59 0.38S&P Return Volatility (%) SPV t 15.99 6.73 1.29 4.24 1.01Industrial Production Growth (%) IPGt 2.06 4.66 -1.10 4.50 0.41
27
Table
2C
orr
ela
tions
Th
ista
ble
rep
orts
the
un
ivar
iate
corr
elat
ion
sb
etw
een
the
key
vari
able
s.T
he
corr
elat
ion
sar
eco
mp
ute
das
the
med
ian
of
the
corr
elati
on
s
ofth
esa
mp
lefi
rms.
Ser
ial
#1
23
45
67
89
1011
12
13
14
15
16
17
18
dbcat+
11
1.00
BDR
t2
-0.3
61.
00dca
t+1
30.
92-0
.32
1.00
dct
t+1
40.
52-0
.22
0.57
1.00
dcp
t+1
50.
05-0
.07
0.03
0.86
1.00
ADR
t6
-0.3
00.
69-0
.29
-0.3
7-0
.28
1.00
IDR
t7
-0.2
50.
57-0
.26
-0.3
6-0
.28
0.94
1.00
Vol
t8
-0.1
40.
19-0
.13
-0.1
5-0
.09
0.25
0.28
1.00
∆Vol
Expd
t9
-0.0
30.
05-0
.04
-0.0
5-0
.03
0.07
0.08
0.27
1.00
Vol
Surprise
t10
-0.1
20.
13-0
.11
-0.1
1-0
.07
0.21
0.21
0.85
0.55
1.00
Vol
Sys
t11
-0.1
00.
07-0
.11
-0.0
9-0
.05
0.12
0.13
0.51
0.14
0.48
1.0
0
Vol
Idio
t12
-0.1
10.
20-0
.11
-0.1
5-0
.11
0.27
0.27
0.98
0.26
0.79
0.3
61.0
0r t
130.
07-0
.06
0.09
0.07
0.03
-0.3
4-0
.32
-0.1
3-0
.03
-0.1
8-0
.21
-0.0
61.0
0debitt+
114
0.11
0.01
0.12
-0.1
5-0
.27
-0.0
3-0
.05
-0.0
6-0
.05
-0.0
8-0
.10
-0.0
40.1
91.0
0dce
t+1
150.
25-0
.14
0.27
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71.0
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120.
140.
10-0
.19
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.33
-0.0
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.28
-0.5
7-0
.20
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70.1
10.0
91.0
0SPV
t17
-0.1
20.
11-0
.12
-0.1
1-0
.06
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0.55
0.16
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60.3
6-0
.24
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0IPG
t18
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-0.0
50.
150.
170.
11-0
.19
-0.2
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.31
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.33
-0.5
1-0
.17
0.2
00.1
30.1
80.4
6-0
.49
1.0
0
28
Table 3 Book Leverage Ratio Adjustment and Stock Return VolatilityThis table reports the regression results of book leverage ratio adjustment and stock return volatil-
ity. dbcat+1 represents active book debt ratio change due to net debt/equity issuance between
time t and t+ 1. BDRt+1 represents book debt ratio. Volatility, V olt is the realized volatility
estimated using past one year daily equity returns. Two-dimensional (firm and time) clustered
standard errors in the regressions are adjusted as in Petersen (2009). The numbers in the brackets
are t-statistics.
(1) (2) (3) (4) (5)dbcat+1 dbcat+1 dbcat+1 dbcat+1 BDRt+1
V olt -7.069 -7.426 -1.843 -2.116(-23.35) (-26.08) (-6.13) (-4.30)
Stock Return 0.492 0.372 -0.368 -0.460(1.98) (2.78) (-4.14) (-4.63)
BDR -0.115 -0.122 0.824(-28.69) (-22.42) (102.09)
Log Sales 0.423 0.564(10.66) (11.45)
Tangibility 0.250 0.177(1.33) (0.77)
MB Ratio -0.0685 0.0126(-2.44) (0.35)
ROA 14.610 14.560(19.86) (13.12)
Tax Rate 0.364 0.405(2.05) (1.84)
Cash Ratio -0.000 -0.000(-1.62) (-3.69)
Dividend Yield -9.092 -17.290(-2.14) (-2.55)
Financial Deficit 0.0723 -0.009(1.19) (-0.12)
S&P Return 1.540 1.860(3.58) (3.54)
S&P Volatility 1.256 1.447(0.85) (0.89)
Industry -0.0451 -0.060(-6.68) (-7.95)
IP Growth 0.147 0.142(7.52) (6.43)
Adj. R-sq 0.062 0.001 0.138 0.221 0.796
29
Table 4 Market Leverage Ratio Adjustment and Stock Return VolatilityThis table reports the regression results of market leverage ratio adjustment on stock return volatil-
ity. dcat+1 represents active market debt ratio change due to net debt/equity issuance between
time t and t+ 1. ADRt+1 represents actual market debt ratio. dctt+1 denotes total debt ratio
change between time t and t+ 1. dcpt+1 represents passive debt ratio change due to stock return
between time t and t+ 1. Volatility, V olt is the realized volatility estimated using past one year
daily equity returns. Two-dimensional (firm and time) clustered standard errors in the regressions
are adjusted as in Petersen (2009). The numbers in the brackets are t-statistics.
(1) (2) (3) (4) (5) (6)dcat+1 dcat+1 dcat+1 ADRt+1 dctt+1 dcpt+1
V olt -3.023 -1.779 -2.045 -1.838 0.197(-17.17) (-9.32) (-2.53) (-2.39) (0.24)
Stock Return 0.860 0.285 0.489 0.465 0.161(6.25) (3.65) (1.84) (1.78) (0.74)
ADR -5.121 86.300 -12.370 -6.948(-19.61) (113.95) (-16.82) (-10.08)
Log Sales 0.040 0.304 0.284 0.239(1.46) (3.04) (2.85) (2.46)
Tangibility 0.240 -0.820 -0.812 -1.016(1.99) (-2.90) (-3.18) (-4.29)
MB Ratio -0.055 -0.025 -0.012 0.044(-6.20) (-1.09) (-0.56) (2.29)
ROA 3.294 -3.166 -2.946 -5.802(10.72) (-2.01) (-2.04) (-4.08)
Tax Rate 0.906 0.181 0.176 -0.761(5.62) (0.46) (0.43) (-2.16)
Cash Ratio -0.000 -0.001 -0.001 -0.000(-1.88) (-4.88) (-4.38) (-2.88)
Dividend Yield -2.054 -8.892 -7.636 -5.569(-1.02) (-1.25) (-1.08) (-0.77)
Financial Deficit 0.078 0.070 0.101 0.004(2.24) (1.07) (1.52) (0.07)
S&P Return 0.789 3.785 3.844 3.034(1.74) (1.24) (1.29) (1.06)
S&P Volatility 2.047 -4.894 -4.698 -6.898(1.75) (-0.84) (-0.82) (-1.26)
Industry -0.032 -0.043 -0.038 -0.004(-7.41) (-3.41) (-3.00) (-0.38)
IP Growth 0.112 0.169 0.170 0.060(7.27) (1.41) (1.44) (0.52)
Adj. R-sq 0.023 0.008 0.085 0.738 0.093 0.056
30
Table 5 Capital Structure and Volatility ShocksThis table reports the regression results of active book debt ratio change, dbcat+1, on expected
volatility shocks, ∆V olExpdt , surprise volatility shock, V olSurpriset , and lagged expected volatility,
V olExpdt−1 , in Panel (A). Penal (B) reports the regression results of active book debt ratio change
on positive and negative expected/surprise volatility shocks. Two-dimensional (firm and time)
clustered standard errors in the regressions are adjusted as in Petersen (2009). The numbers in the
brackets are t-statistics.
Panel A: Expected and surprise Volatility Shocks
(1) (2) (3) (4) (5) (6) (7) (8)
dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1
∆V olExpdt -4.199 -0.906 0.318
(-6.91) (-2.28) (0.61)
V olSurpriset -4.336 -1.157 -1.304 -1.794
(-7.73) (-3.45) (-2.98) (-5.31)
V olExpdt−1 -6.877 -1.581 -2.099
(-22.42) (-4.17) (-5.18)
Controls No No No Yes Yes Yes Yes Yes
Adj. R-sq 0.004 0.010 0.046 0.219 0.219 0.220 0.219 0.222
Panel B: Positive and Negative Volatility Shocks
(1) (2) (3) (4) (5) (6) (7) (8)
∆V olExpdt V olSurpriset
> 0 < 0 > 0 < 0
∆V olExpdt -13.76 -1.340 8.140 0.377
(-16.89) (-1.52) (10.25) (0.41)
V olSurpriset -10.18 -1.422 7.151 0.334
(-18.89) (-2.42) (12.96) (0.47)
Controls No Yes No Yes No Yes No Yes
Adj. R-sq 0.031 0.232 0.009 0.204 0.039 0.239 0.010 0.194
31
Table 6 Systematic Volatility and Idiosyncratic VolatilityThis table reports the regression results of active book debt ratio change, dbcat+1, on stock system-
atic volatility, V olSyst , idiosyncratic volatility, V olIdiot , expected systematic/idiosyncratic volatil-
ity shocks, ∆V olSysExpdt /∆V olIdioExpd
t , and surprise systematic/idiosyncratic volatility shock,
V olSysSurpriset /V olIdioSurpriset . Stock systematic volatility is estimated using 250-daily systematic
stock returns computed using the Fama-French 3-factor model. Two-dimensional (firm and time)
clustered standard errors in the regressions are adjusted as in Petersen (2009). The numbers in the
brackets are t-statistics.
(1) (2) (3) (4) (5) (6) (7)
dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1 dbcat+1
V olSyst -5.308 -5.669
(-4.30) (-6.22)
V olIdiot -6.755 -1.692
(-22.52) (-5.36)
∆V olSys Expdt -3.814 0.100 0.856
(-0.97) (0.07) (0.57)
∆V olIdio Expdt -3.475 -0.665 0.672
(-6.25) (-1.61) (1.12)
V olSys Surpriset -3.637 -0.703 -1.056
(-1.35) (-0.39) (-0.52)
V olIdio Surpriset -3.876 -1.042 -1.388
(-9.35) (-3.47) (-3.12)
Controls No No No Yes Yes Yes Yes
Adj. R-sq 0.061 0.003 0.009 0.219 0.215 0.216 0.216
32
Table 7 Debt versus Equity AdjustmentThis table reports the regression results of debt change and equity change between time t and t+ 1
on expected volatility shocks, ∆V olExpdt , surprise volatility shock, V olSurpriset , and lagged expected
volatility, V olExpdt−1 . Debt change is computed as ∆debtt+1 = (Dt+1 − Dt)/Dt. Equity change is
computed as ∆equityt+1 = ((Et+1 − ∆REt) − Et)/Et, where ∆REt is change in accumulative
retained earnings between time t and t + 1. Two-dimensional (firm and time) clustered standard
errors in the regressions are adjusted as in Petersen (2009). The numbers in the brackets are
t-statistics.
(1) (2) (3) (4) (5) (6) (7) (8)
∆debtt+1 ∆equityt+1
V olt -3.566 -2.931 10.440 2.922
(-3.36) (-4.56) (18.82) (6.30)
∆V olExpdt 2.923 0.233 -0.555 -1.863
(1.38) (0.13) (-0.76) (-2.67)
V olSurpriset -12.740 -4.345 1.193 0.238
(-5.04) (-3.59) (1.77) (0.41)
Stock Return 3.535 3.409 2.467 2.600
(8.81) (8.31) (15.47) (16.11)
BDR -0.231 -0.234 0.0385 0.0451
(-21.21) (-21.58) (5.94) (7.02)
Log Sales 0.110 0.283 -0.560 -0.754
(0.99) (2.84) (-9.32) (-12.66)
Tangibility -0.376 -0.294 -0.866 -0.919
(-0.71) (-0.55) (-2.80) (-2.94)
MB Ratio 0.332 0.337 0.737 0.726
(7.16) (7.34) (19.62) (19.20)
ROA 4.018 4.767 -14.680 -15.920
(2.19) (2.63) (-13.87) (-14.72)
Tax Rate 1.874 2.155 -1.199 -1.447
(3.17) (3.65) (-4.78) (-5.85)
Cash Ratio 0.001 0.001 -0.000 -0.000
(2.09) (2.03) (-1.59) (-1.52)
Dividend Yield -36.800 -31.720 -11.720 -14.010
(-3.99) (-3.48) (-2.64) (-3.10)
Financial Deficit 0.760 0.780 0.315 0.271
(4.24) (4.40) (3.28) (2.76)
S&P Return 1.304 1.709 -1.493 -1.580
(0.65) (0.84) (-1.71) (-1.83)
S&P Volatility -5.256 -4.717 -4.589 -0.850
(-0.97) (-0.86) (-1.84) (-0.34)
Industry -0.074 -0.083 0.033 0.042
(-3.63) (-4.03) (2.86) (3.65)
IP Growth 0.524 0.509 -0.0858 -0.0862
(9.05) (8.43) (-2.19) (-2.20)
Adj. R-sq 0.002 0.009 0.086 0.086 0.071 0.000 0.211 0.209
33
Table 8 Lag VolatilitiesThis table reports the regression results of active book debt ratio change, dbcat+1, on stock return
volatility, V ol, expected volatility shocks, ∆V olExpd, and surprise volatility shock, V olSurprise with
lags ranging between time t − 5 to t. Two-dimensional (firm and time) clustered standard errors
in the regressions are simultaneously adjusted as in Petersen (2009). The numbers in the brackets
are t-statistics.
(1) (2) (3) (4) (5) (6)
Time Lag V ol ∆V olExpd V olSurprise
t -6.123 -1.507 -5.129 -1.491 -4.296 -1.288
(-8.07) (-3.62) (-5.76) (-2.67) (-4.67) (-3.15)
t− 1 0.300 0.324 -4.103 -1.092 -0.334 -0.303
(0.44) (0.80) (-6.02) (-1.86) (-0.46) (-0.75)
t− 2 -0.702 -0.448 -2.963 0.0287 -1.490 -0.424
(-1.49) (-0.99) (-4.07) (0.05) (-3.03) (-1.15)
t− 3 0.460 0.982 -2.362 -0.214 -0.0633 0.323
(0.85) (2.02) (-2.32) (-0.31) (-0.11) (0.92)
t− 4 -0.934 -1.193 -2.833 -1.258 -1.098 -0.763
(-1.52) (-2.46) (-2.42) (-2.37) (-1.71) (-1.91)
t− 5 -0.485 0.358 -2.062 -0.875 -0.781 -0.416
(-0.88) (0.74) (-2.73) (-1.73) (-1.40) (-0.92)
Controls No Yes No Yes No Yes
Adj. R-sq 0.063 0.213 0.008 0.207 0.011 0.208
34
Table 9 The Impacts of Rating, Size and ProfitabilityThis table reports the regression results of active book debt ratio change, dbcat+1, on stock return
volatility, V olt, expected volatility shocks, ∆V olExpdt , and surprise volatility shock, V olSurpriset by
S&P credit rating group, asset value group and return on assets (ROA), respectively. Panel A
reports the by rating results. Panel B reports the by asset value results. Panel C reports the by
ROA results. Two-dimensional (firm and time) clustered standard errors in the regressions are
simultaneously adjusted as in Petersen (2009). The numbers in the brackets are t-statistics.
Panel A: By Credit Rating
(1) (2) (3) (4) (5) (6)
AAA-A BBB BB & Below
V olt -2.299 -4.296 -5.829
(-1.66) (-3.28) (-7.57)
∆V olExpdt 3.968 3.499 3.143
(1.85) (1.64) (3.08)
V olSurpriset -3.038 -6.292 -4.590
(-1.60) (-3.91) (-7.35)
Adj. R-sq 0.002 0.002 0.009 0.013 0.027 0.009
Panel B: By Assets
(1) (2) (3) (4) (5) (6)
Small Middle Large
V olt -6.939 -6.757 -6.115
(-19.13) (-15.83) (-13.46)
∆V olExpdt -0.566 0.726 3.393
(-0.80) (0.64) (3.29)
V olSurpriset -3.805 -4.425 -6.195
(-6.38) (-3.82) (-4.87)
Adj. R-sq 0.051 0.010 0.038 0.008 0.032 0.015
Panel C: By ROA
(1) (2) (3) (4) (5) (6)
Low Middle High
V olt -6.247 -2.898 -4.519
(-18.24) (-8.75) (-6.81)
∆V olExpdt -0.545 1.571 0.643
(-0.78) (2.07) (0.59)
V olSurpriset -3.156 -3.560 -3.769
(-4.94) (-3.99) (-3.79)
Adj. R-sq 0.042 0.007 0.011 0.006 0.015 0.005
35
Table 10 The Impacts of Internal Financial DeficitThis table reports the regression results of active book debt ratio change, dbcat+1, on stock return
volatility, V olt, expected volatility shocks, ∆V olExpdt , and surprise volatility shock, V olSurpriset by
internal financial deficit quantile, and by negative deficit (surplus) versus positive deficit. Quantile 1
and 4 contain firms of the lowest and highest internal financial gap, respectively. Two-dimensional
(firm and time) clustered standard errors in the regressions are simultaneously adjusted as in
Petersen (2009). The numbers in the brackets are t-statistics.
Panel A: Univariate Regressions
(1) (2) (3) (4) (5) (6)
Quantile 1 Quantile 2 Quantile 3 Quantile 4 DEF t< 0 DEF t> 0(Lowest) (Highest) (Surplus) (Deficit)
V olt -6.482 -5.008 -4.535 -8.928 -5.932 -8.037
(-14.46) (-11.74) (-10.17) (-14.87) (-16.29) (-19.11)
Controls No No No No No No
Adj. R-sq 0.054 0.041 0.029 0.08 0.051 0.076
∆V olExpdt -0.456 1.965 1.906 0.201 0.532 0.744
(-0.37) (1.65) (1.75) (0.22) (0.57) (0.97)
V olSurpriset -5.494 -5.152 -3.828 -4.361 -5.406 -4.260
(-5.48) (-5.95) (-4.46) (-4.94) (-6.76) (-5.01)
Controls No No No No No No
Adj. R-sq 0.018 0.014 0.006 0.008 0.017 0.007
Panel B: Multivariate Regressions
(1) (2) (3) (4) (5) (6)
Quantile 1 Quantile 2 Quantile 3 Quantile 4 DEF t< 0 DEF t> 0(Lowest) (Highest) (Surplus) (Deficit)
V olt -3.399 -2.652 -2.452 -4.956 -3.143 -3.856
(-6.06) (-4.74) (-4.98) (-6.98) (-7.57) (-8.09)
Controls Yes Yes Yes Yes Yes Yes
Adj. R-sq 0.122 0.107 0.11 0.304 0.118 0.245
∆V olExpdt -1.591 1.097 1.640 0.785 -0.499 1.263
(-1.16) (1.01) (1.68) (0.72) (-0.52) (1.91)
V olSurpriset -2.114 -2.818 -1.944 -1.710 -2.422 -1.886
(-1.93) (-3.79) (-2.60) (-2.20) (-3.44) (-3.59)
Controls Yes Yes Yes Yes Yes Yes
Adj. R-sq 0.117 0.103 0.106 0.291 0.114 0.237
36
Table 11 Future Earnings and Stock Return VolatilityThis table reports the regression results of percentage change in earnings, debitt+1, on stock return
volatility, V olt, expected volatility shocks, ∆V olExpdt , and surprise volatility shock, V olSurpriset .
Percentage change in earnings is computed as debitt+1 = (EBITt+1 − EBITt+1)/EBITt, where
EBIT is earnings before interest and tax. Two-dimensional (firm and time) clustered standard
errors in the regressions are simultaneously adjusted as in Petersen (2009). The numbers in the
brackets are t-statistics.
(1) (2) (3) (4) (5) (6) (7) (8)
debitt+1 debitt+1 debitt+1 debitt+1 debitt+1 debitt+1 debitt+1 debitt+1
V olt -0.239 -0.236
(-10.00) (-7.92)
dbcat+1 0.007 0.004
(9.83) (4.87)
∆V olExpdt 0.158 0.11
(2.70) (1.93)
V olSurpriset -0.277 -0.151
(-4.22) (-3.31)
V olSyst -0.329 -0.016
(-2.10) (-0.09)
V olIdiot -0.234 -0.241
(-11.05) (-8.53)
Controls No No No No Yes Yes Yes Yes
Adj. R-sq 0.009 0.006 0.008 0.010 0.041 0.038 0.041 0.041
37
Table 12 Investment and Stock Return VolatilityThis table reports the regression results of change in investment, dcet+1, on stock return volatility,
V olt, expected volatility shocks, ∆V olExpdt , and surprise volatility shock, V olSurpriset . Change in
investment is proxied by change in capital expenditure between time t and t + 1 normalized by
Net PPE at time t: dcet+1=(Capital Expendituret+1−Capital Expendituret)/Net PPEt, where
PPE is property, plant and equipment. Two-dimensional (firm and time) clustered standard errors
in the regressions are simultaneously adjusted as in Petersen (2009). The numbers in the brackets
are t-statistics.
(1) (2) (3) (4) (5) (6) (7) (8)
dcet+1 dcet+1 dcet+1 dcet+1 dcet+1 dcet+1 dcet+1 dcet+1
V olt -2.666 -0.934
(-4.05) (-2.87)
dbcat+1 0.188 0.136
(8.72) (9.44)
∆V olExpdt 0.480 -0.841
(0.55) (-0.84)
V olSurpriset -4.008 -0.352
(-4.42) (-0.60)
V olSyst -5.259 3.600
(-2.02) (2.00)
V olIdiot -2.277 -1.111
(-3.90) (-3.49)
Controls No No No No Yes Yes Yes Yes
Adj. R-sq 0.003 0.011 0.003 0.003 0.053 0.060 0.053 0.053
38
Figure 1 Leverage Changes and Expected/Surprise Volatility ShocksThis figure plots active book (market) debt ratio change, dbca (dca), with respect to expected
volatility shock, ∆V olExpd, and surprise volatility shock, V olSurprise over time. The top graph
plots dbca, dca and ∆V olExpd. The bottom graph plots dbca, dca and and V olSurprise. The gray
areas represent NBER recession time.
−.1
0.1
.2C
hang
e in
Exp
ecte
d Vo
latil
ity
−.1
−.05
0.0
5.1
.15
dbca
& d
ca
1960 1970 1980 1990 2000 2010Time
dca dbca
Change in Expd. Vol.
−.2
0.2
.4Vo
latil
ity S
urpr
ise
−.1
−.05
0.0
5.1
.15
dbca
& d
ca
1960 1970 1980 1990 2000 2010Time
dca dbca
Vol. Surprise
39
Figure 2 Fama McBeth Regressions by YearThis figure plots the results of applying the Fama-McBeth method to regress active book debt ratio
change, dbcat+1, on expected volatility shock, ∆V olExpdt , and surprise volatility shock, V olSurpriset ,
by year. The top and bottom graphs show the univariate regression coefficients and 95% boundaries
of dbcat+1 on ∆V olExpdt and V olSurpriset , respectively. The gray areas represent NBER recession
time.
−40
−20
020
40R
egre
ssio
n C
oeffi
cien
t
1960 1970 1980 1990 2000 2010Time
Coefficient 95% Boundaries
dbca & Change in Expd. Vol.
−40
−20
020
40R
egre
ssio
n C
oeffi
cien
t
1960 1970 1980 1990 2000 2010Time
Coefficient 95% Boundaries
dbca & Vol. Surprise
40