Download Capital structure and volatility of risk

Capital structure and volatility of risk ∗
Nikolay Halov
UCSD Rady School of Management
[email protected]
Florian Heider
European Central Bank
[email protected]
Kose John
NYU Stern School of Business
[email protected]
Abstract
In this paper we show that the volatility of risk is an important factor in explaining capital
structure choices of firms. This effect is over and above the traditional determinants of capital
structure such as the current level of risk, size, market-to-book ratio, tangibility of assets and
profitability. We show that both (1) the fraction of debt in total new external financing raised by
the firm, and (2) the long term debt as a fraction of the assets of the firm, are decreasing in the
volatility of risk of the firm. Moreover this negative relationship is significantly stronger for
firms that do not have a credit rating. These results are consistent with the theoretical reasons
that we provide to explain the negative relationship between leverage and volatility of risk.
PRELIMINARY AND INCOMPLETE
Current Draft
June, 2009
∗
We thank Jennifer Carpenter, Stephen Figlewski, Allan Timmermann, Dalida Kadyrzhanova and Ross Valkanov
for helpful comments and suggestions. Usual disclaimer applies.
0
Introduction
It has been long recognized that volatility is not constant through time and could evolve
stochastically through time. We also know that the dynamics of the underlying asset values
would be an important factor in the pricing of debt claims of the firm. In this paper we examine
the effect of the volatility of the firm cash flow variance on the leverage choices made by the
firm.
We hypothesize that the firm’s optimal leverage choices would be decreasing in the
volatility of the firm cash flow variance, holding constant other determinants of its leverage such
as its level of cash flow volatility, size, market-to-book ratio, tangibility of assets and
profitability. Our hypothesis regarding the negative relationship between the volatility of the firm
cash flow variance also extends to the leverage composition of any external financing undertaken
by the firm.
There are three arguments that form the basis of our hypothesized relationship.
The first argument follows from a simple adaptation of the static trade-off theory in
which the firm’s volatility is stochastic and the costs of adjusting leverage are large. Compare
two firms with identical average cash flows, one with a known level of standard deviation of
cash flows, say σ, and a second firm whose cash flow standard deviation is stochastic and drawn
from a distribution with mean equal to σ and variance ε. Even though both firms have the same
mean standard deviation of firm cash flows, the second firm would use less leverage optimally
(according to its static trade-off optimization) if the net costs of debt are asymmetric in σ.
1
For example, a bankruptcy cost structure that is convex in the degree of default would
give rise to optimal debt choices that are lower for the firm with stochastic volatility, and
declining in ε (the volatility of volatility). To see this assume that debt related benefits are linear
in the face value of debt, (Corporate tax shield could be argued to be approximately linear).
If the volatility is higher than the expected value σ, say (σ + ε), the incremental expected
bankruptcy costs would be larger than the savings in incremental bankruptcy costs from a
volatility realization (σ – ε). This means that the optimal leverage trade-off for the stochastic
volatility firm will occur at lower values than that for a firm with constant volatility of σ. Its
leverage choices would be correspondingly conservative, i.e., the higher its ε, the lower the
leverage chosen. Firms with asset types (e.g., intangible assets or firm-specific assets) that are
associated with high bankruptcy costs are all the more prone to be conservative in their leverage
choices in response to the volatility of their volatility. The sensitivity of leverage to its volatility
of volatility would be increasing in the extent of intangible/specific assets in the firm’s balance
sheet. Our reasoning here made use of the fact that large costs of adjustment of leverage in
response to changing volatility lead firms to make conservative leverage choices based on the
higher variance of the unconditional distribution for the firm with stochastic volatility. Similar
results obtain even if the adjustment costs are smaller, but asymmetric, i.e., reducing leverage is
more costly than increasing leverage (see for example van Binsbergen et al. (2008), Byoun
(2008) and Flannery and Rangan (2003) for some evidence suggesting that such an asymmetry
may exist).
2
A second reason for conservative leverage choices by firms with high volatility of
volatility may be that corporate insiders may have private information regarding their own
earnings volatility and this is more likely in firms with stochastic volatility. In firms where
volatility is not stochastic the market can learn from history about firm volatility. On the other
hand, in firms with high volatility of volatility, it is harder for the market to learn, and often the
insiders have a better read on its current volatility. In such a setting of asymmetric information
about firm volatility, there is a lemons problem in pricing debt claims and the firms are better off
issuing equity securities. Issuing levered equity (with call option features) can be justified as a
defensive measure or as a signal of low volatility. Here the volatility of volatility may serve as a
proxy for the degree of asymmetric information that exists in the market regarding the variance
of firm cash flows. (Volatility of volatility can serve as a proxy of the range of the support of the
volatility distribution from the perspective of the less informed market). Interestingly, issuing
debt serves as a defensive strategy to solve the lemons problem associated with issuing equity,
when there is asymmetric information about the mean of the cash flows, issuing equity-like
securities may be a solution when the lemons problem arises from asymmetric information about
the volatility of firm cash flows (although not analyzed explicitly, this possibility is in fact
discussed in Myers and Majluf (1984)).
A third reason for conservative leverage choices by firms with high volatility of volatility
may be to pre-commit not to risk-shift (switch into high variance, lower net-present-value
projects) in the future. If the market believes that firms with a high volatility of volatility are also
those with a large menu of risky projects that they can adopt after the external financing is in
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place, it would be important to precommit not to do so by issuing levered equity or convertible
debt to outsiders. As Green (1984) has shown, such mechanisms as a well-designed convertible,
are optimal in that they reassure the market that the firm does not gain by adopting risk-shifting
strategies with such securities outstanding. We argue that the firm would precommit not to riskshift by raising a larger component of their external finance as equity. Again the volatility of
volatility of a firm may be a good proxy for the importance of making such a precommitment
through conservative leverage choices.
We construct two measures of volatility of volatility (VOV). First, we calculate the
volatility of assets in the 12 preceding calendar months and then take the annual standard
deviation of the monthly volatilities. This is our measure of volatility of realized volatility
(VRV). Second we obtain daily series of volatilities implied from option prices for each day in
the previous calendar year. The standard deviation of these IVs provides our second measure
called volatility of implied volatility (VIV). All our results are implemented both of these
measures of volatility of volatility. We rank firms in deciles according to our volatility of
volatility measures (both VRV and VIV) and we find that the firms in the higher deciles issue
monotonically smaller component of debt in their external financing.
In this paper we show that the volatility of risk is an important factor in explaining capital
structure choices of firms over and above the traditional determinants of capital structure such as
the level of risk, size, market-to-book ratio, tangibility of assets and profitability. We show that
the volatility of risk explains 1) the fraction of debt in total new external financing raised by the
firm, 2) the long term debt as a fraction of the assets of the firm.
4
The organization of the paper is as follows. Section 1 develops our empirical strategy.
Section 2 describes the sample and presents some descriptive statistics. Section 3 contains the
main empirical results. Possible alternative explanations are analyzed in section 4. Section 5
provides a discussion on factors that affect volatility of volatility and its effect on capital
structure. Section 6 concludes.
1. Empirical strategy
Our empirical strategy builds upon the tests of the standard pecking order by ShyamSunder and Myers (1999) and Frank and Goyal (2003) and the vast empirical literature testing
trade-off models of capital structure (see among others Rajan and Zingales (1995)).
Focusing on cash-flows
Shyam-Sunder and Myers (1999) propose a test of the original pecking order based on
how firms finance their need for external capital. The starting point is the following accounting
identity of cash flows:
DEF = I + DIV + ∆W-C = ∆D + ∆E
(1)
A firm’s financing deficit DEF, i.e. the difference between uses of funds (dividends DIV,
investment I and changes in net working capital ∆W) and internal sources of funds (the internal
cash-flow C), must be balanced by external sources of funds, i.e. either the issuance of debt ∆D
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or equity ∆E (we follow the definitions of Frank and Goyal (2003); see also Helwege and Liang
(1996), Shyam-Sunder and Myers (1999), and Chang and Dasgupta (2003)).
Shyam-Sunder and Myers (1999) and Frank and Goyal (2003) are interested in the
proportion of debt relative to equity that is issued to finance the deficit. They want to test
whether the standard pecking order holds in which debt dominates equity, i.e. DEF = ∆D, and
therefore run the following pooled panel regression:
∆D
it
= a + bDEF + ε
it
(2)
Debt dominates equity issuance fully if b is large as b, roughly speaking, represents the average
proportion of debt in total external financing. Moreover, a close to zero indicates that there are
no other factors unrelated to the financing needs of a company that drive debt issuance.
We employ (2) conditionally by ranking firms into deciles, n =1, 2…10, according to
measures of volatility of volatility (we discuss these measures in the next section), and then run
regression (2) separately in each decile n:
∆D = a + b D DEF + ε
it
n
n
it
(3)
We expect the estimated coefficients on the financing deficit to be ranked monotonically:
)
)
)
b D > b D > ... > b D . Firms in higher volatility of volatility deciles issue more equity and less
1
2
10
debt to finance their deficit.
In addition to (3), we also test the extent to which equity is issued to finance the deficit in
each decile n:
6
∆E
it
= a + b E DEF + ε
n
n
it
(4)
Since (1) is an accounting identity, checking that the estimated coefficients on the deficit from
)
)
(3) and (4) add up to one in each decile, b D + b E = 1 for all n, is a useful test of the accuracy of
n
n
our cash-flow data.
Measures of the level of recent asset volatility
We construct two measures of asset volatility. The first one consists of unlevering the
volatility of equity. Unlevering is needed since the volatility of equity mechanically increases
with leverage ceteris paribus. We compute the standard deviation of the daily return on the
market value of a firm. The market value of assets is defined as in Fama and French (2002) (see
also the Appendix).1 If there are less than 90 days of stock price data, the firm/year observation
is deleted from the sample.
The second measure recognizes that equity is a call option on the value of firm assets
with the exercise price being the value of the debt (Merton (1974)). From Ito’s lemma, we have
σ
where σ
E
E
=σ
V ∂E
t
t
V E ∂V
t
t
(5)
is the instantaneous variance of the rate of return on equity (the standard deviation of
daily stock returns from CRSP), σ
V
is the instantaneous variance of the rate of return on the
1
We also try the definition of Baker and Wurgler (2001), which excludes convertible debt, and also try using just
total liabilities. The results are not affected.
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firm (to be solved for), Vt is the market value of the firm and Et is the market value of equity
(both calculated as above).2 The derivative of the market value of equity with respect to the
market value of the firm in the Merton model is:
1


ln (V /B ) + (r + σ 2 )T 

t t
f 2 V
t =Φ


∂V
σV T


t


∂E
(6)
where Φ is the cumulative distribution function of the standardized normal distribution )(0,1), T
is the time to maturity of the debt (we try both 10 and 20 years) and rf is the risk free rate (from
Kenneth French’s website).
The Spearman rank correlation between the two measures of asset risk in our sample is
0.95. The rank correlation is the appropriate measure since we use asset risk only to rank firms
into deciles. Given that both measures give virtually identical rankings, we continue using the
simpler first measure (see also Welch (2004); and Jones et al. (1984) for a comparison of these
two measures of asset volatility).
To ensure that there is no contemporaneous interplay between the issue decision and
asset volatility, we use last year’s asset volatility. Using longer lags would weaken the link
between the role of risk in the adverse selection problem and the current capital structure
decision.3
2
An advantage of the Merton method is that we can use the CRSP return series that is adjusted for stock splits and
dividends.
3
There is an issue concerning the overlap or gap between the calendar year used for stock price data and the fiscal
year used for financial data. This overlap or gap exists for 48% of all firms. We check the robustness of our results
by using only firms whose fiscal year is the calendar year. The results are unchanged.
8
Measures of the volatility of volatility (VOV): VRV and VIV
We construct two proxies for the volatility of volatility of each firm. One is based on
expectations of outsiders about the future volatility of the firm as shown in the prices of the stock
options of the firm and the second is based on the recent variation of realized asset volatility of
the firm.
For our first proxy we calculate the variation in firm specific implied volatility form
option prices (VIV). We use end-of-day option prices, option open interest and implied volatility
estimates from the Ivy DB database provided by OptionMetrics. The sample is from January
1996 to December 2001. To filter out misrecorded data and very illiquid contracts, we exclude
days/contracts that have zero open interest or have a bid-ask spread larger than 50% of the option
price at midpoint. To alleviate potential endogeneity problems we use data from the previous
calendar year. The sample includes at-the-money call options with maturity closest to but higher
than 182 days. Ideally, we would use longer maturity contracts, e.g. LEAPS, to include the
whole year during which we study the financing decision and get closer to longer investment
horizon of outsiders but these contracts are quite illiquid so that our sample would be
considerably reduced. Our raw option data sample has 13,418,700 day-firm implied volatility
estimates. Following Welch (2004) we unlever these equity volatility estimates by scaling by
Et/(Et+Dt), where Et is the market value of firms equity as of the end of the fiscal year and Dt is
the book value of debt. We then calculated the standard deviation of these implied asset
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volatilities for each firm over the previous calendar year. If there are less than 90 trading days the
firm-year is excluded from the sample.
This measure has several advantages. It is a forward looking measure; it does not suffer
from problems common to accounting variables and it represent all information available to
outside investors that concerns the volatility of the firm. It does however reduce our sample
significantly as cross sectional option pricing data is available only from 1996 to 2001.
Second we look at the volatility of realized asset volatility (VRV). In particular we
calculate the equity volatility of the firm in each month of the previous calendar year, unlever it
to account for the capital structure of the firm in that year by scaling by Et/(Et+Dt), where Et is
the market value of firms equity as of the end of the fiscal year and Dt is the book value of debt,
and use the standard deviation of the monthly volatility estimates as another proxy for volatility
of volatility that we argue is positively related to asymmetric information about risk.
Controlling for other determinants of debt issuance
The empirical methodology employed in (1)-(4) using cash-flow data and examines the
extent of debt issuance. Alternatively, one can examine the level of debt using balance and
income sheet data. This second approach is found mostly in cross -sectional empirical research
on capital structure that is usually rooted in the trade-off theory. The basic trade-off theory states
that the level of leverage is determined by trading off the tax benefit of debt against the cost of
financial distress (see for example the account given by Myers (1984)). Hence, firms with a high
present value of tax benefits and/or a low present value of distress costs should have higher
10
levels of debt (see also the classification in the survey by Harris and Raviv (1991)). Rajan and
Zingales (1995) narrow the list of conventional determinants down to four main variables:
profits, size, tangibility of assets and the market-to-book ratio.
More tangible assets support debt because it means that firms can collateralize the debt
which reduces bankruptcy costs. The market-to-book ratio is usually seen as a proxy for growth
opportunities that should be negatively related to leverage. The argument is that leverage exposes
firms to the “debt overhang” problem (Myers 1977). A recent alternative explanation for a
negative relationship is market timing. Firms with a high market-to-book ratio are overvalued
and hence issue equity to take advantage of it (Baker and Wurgler (2001)). Sales are usually
positively associated with leverage. There is no clear theoretical foundation but one normally
argues that larger firms have a higher reputation or are safer so they can borrow more. Profits
show up regularly as a negative determinant of leverage. Traditionally this has been seen as the
strongest empirical challenge for conventional trade-off models of leverage. They predict that
more profitable firms should issue more debt since more profitable firms have a smaller risk of
bankruptcy and have more taxable income to shield (see Titman and Wessels (1988) and Fama
and French (2002)).
We follow Faulkender and Petersen (2004) among others and add interaction terms of the
financing deficit with the conventional determinants to (3). This allows a nesting of the
conventional determinants of leverage from the trade-off theory within a framework to examine
debt issuance. The set of decile regressions (3) then becomes (where LoV is the level of risk):
11
∆D = a + b DEF + bVoV DEF *VoV
+ b LoV DEF * LoV
+ bTA)G DEF * TA)G
it
n n
it n
it
it − 1 n
it
it − 1 n
it
it
+ b MTB DEF * MTB + b PROF DEF * PROF + b LOGSALES DEF * LOGSALES
n
it
it n
it
it n
it
it
+ CO)TROLS + ε
(7)
We expect a negative sign on the coefficient of interaction term of financing deficit with our
volatility of volatility (VOV) measures once we add the conventional determinants of leverage.
Following the vast empirical literature we also model empirically the level of leverage as
measured by the long term debt of the firm scaled by its total book assets. In particular we run
the following specification:
D = a + bVoV VoV
+ b LoV LoV
+ bTA)GTA)G
+ b MTB MTB
it − 1 n
it − 1
it
n n
it − 1 n
it − 1 n
PROF
LOGSALES
+b
PROF
+b
LOGSALES
+ CO)TROLS + ε
n
it − 1 n
it − 1
(8)
2. Data
Sample construction
We study a large, unbalanced panel of all firms from the merged CRSP-Compustat
(CCM) database from 1971 to 2001. Our sample only starts in 1971 since we require cash flow
data. We make the following standard adjustments. We exclude financial firms (SIC codes 60006999), regulated utilities (SIC codes 4900-4999), and firms involved in major mergers and
acquisitions (Compustat footnote code AB). Furthermore, we exclude firm/year observations that
report cash flows data using format code (item 318) 4 or 6 (both undefined by Compustat) and 5
(for the Canadian file) or if the format code is missing.
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To be able to link Compustat reliably to CRSP data we use only records with link type
‘LC', 'LN', 'LO', 'LS', 'LU' or ’LX’. A small number of CRSP securities that link into more than
one Compustat firm have also been deleted.
In order to remove outliers and misrecorded data, we remove observations for certain
variables that have missing values or are in the extreme 0.5 % left or right tail of the distribution
(see the Appendix for the list of variables that have been treated this way). To ensure that the
sample does not contain equity issues due to IPOs, we exclude observations for the year in which
a firm’s stock price becomes first available in the CRSP database. The maximum number of
observations in our sample then is 103,351 firm-years.
Descriptive statistics
Table 1 shows balance sheets, cash flows and other descriptive statistics at the beginning
and at the end of our sample period, 1971 and 2001, as well as for two intermediate dates, 1980
and 1990.
Panel A presents average balance sheets and panel B shows the average of the cash flows
in the accounting identity (1). The central observation is that equity plays an important role in
financing the deficit. It contradicts the argument that most external financing uses debt (see also
Frank and Goyal (2003)).4
Note also the difference between the mean and the median of net debt and equity issues.
The median is zero for both. A typical firm appears to stay out of the market for external finance
4
The table confirms that dividends are a disappearing use of corporate cash flows (see Fama and French (2001) and
also Baker and Wurgler (2003)). A comparison of the average and the median dividend indicates that typical firms
stop paying dividends and that those who continue paying them, nevertheless reduce the amount paid.
13
most of the time, but if it does seek external finance, the magnitude of the market intervention is
large relative to firm size.
Table 2, Panel A.1 gives the summary statics for the level of volatility (risk) and for the
volatility of realized volatility (VRV). Panel A.2 shows that there is positive and moderate
correlation between the level of risk and VRV. Riskier firms also tend to experience more
changes in risk. Panels B.1 and B.2 show summary statistics for the volatility of implied
volatility (VIV).
3. Main empirical result
The central results of the paper relate the capital structure of a firm to the volatility of
volatility (realized or implied). We find that in the lowest decile based on VRV a one standard
deviation change in the financing deficit from the mean produces 0.871 standard deviations
change in the net debt issued. In the highest decile based on VRV, one standard deviation change
of the financing deficit from its mean produces 0.153 standard deviations change in the net debt
issues. At an intuitive level the debt component in the external financing raised is roughly 87%
in the lowest decile of VRV and it is roughly 15 % in the highest decile. Using VIV measure the
ratio of the debt component in external financing goes from 85.7% in the lowest decile to 17.7%
in the highest decile. Therefore volatility of volatility is an important determinant of the debtequity mix of new external financing. Table 3 and 4 report results from specification (3) using
VIV and VRV.
14
Alternatively, looking at leverage as measured by the proportion of long term debt in
total assets we find that the leverage ratio is 31.7% in the lowest decile of VRV (31.7% when
using VIV), monotonically decreases as VOV increases, reaching a value of 9.5% (10.4 using
VIV) in the highest decile of VRV. Based on these univariate results VOV seems to be an
important determinant of leverage ratio.
To examine further the determinants of leverage, we use a multivariate regression that
included VOV as well as the traditional determinants such as size tangibility market-to-bookratio and profitability. In this regression we want to ensure that VOV is not proxing for the role
of asset volatility in determining the leverage ratio. Therefore we include level of asset volatility
as an additional control variable. In the following discussion we examine the role of these
variables in determining as before the debt component of external financing as well as leverage.
Based on the multivariate regression we find that the relation between the debt
component in external financing and VOV (both VRV and VIV measures) is negative and
significant. This relation holds even after we introduce the level of asset volatility as an
additional control variable. We find that the debt component in external financing is negatively
related to both the VOV and the level of asset volatility. In fact the VOV continues to be at least
as significant the level of asset volatility. Even when introduce as control variables the usual
capital structure determinants, the significance of VOV continues to hold. These results suggest
that VOV is an important determinant of capital structure in addition to the previously known
determinants of capital structure. Results from empirical model (8) are in Table 5 and 6.
15
Next we explore how this negative relation between volatility of volatility and debt as a
proportion of external financing varies with the existence of a credit rating.
4. Reasons why the cost of debt financing to the firms is increasing in the
volatility of risk of its assets. (Motivation and hypotheses)
In this section, we explore the theoretical reasons why (1) the optimal leverage choice of
firms should be negatively related to its volatility of volatility (in addition to its current level of
volatility, and (2) the optimal debt component in any new external financing undertaken would
be negatively related to its volatility of volatility (in addition to its current level of volatility).We
provide three different frameworks in which such a relationship may obtain. The first framework
is that of symmetric information static trade-off reasoning that is augmented to allow for
stochastic volatility and some nonlinear cost of bankruptcy or adjustment costs of changing
leverage. The second framework is that of asymmetric information in which the corporate
insiders are better informed about the volatility of the firm compared to the market and they face
a lemons cost of issuing debt securities. A third framework is that of private action regarding
risk-choices in which issuing debt securities would give rise to severe risk-shifting incentives for
firms with high volatility of volatility. All of the three frameworks yield the results (1) and (2)
mentioned above.
First take the case of a firm with stochastic volatility, where the volatility is drawn from a
distribution with mean σ and variance ε. (Volatility is the standard deviation of the cash flow
realizations of the firm). Compare it to a firm of constant volatility σ. Also assume that the costs
of changing leverage are very high. If the net debt related costs are convex in σ, it can be shown
16
that the firm with stochastic volatility would make optimal choices of leverage that are lower
than that of the firm with constant volatility, and the leverage would be decreasing in ε. For
example, if the costs of reducing long term debt are higher than taking on additional debt, a
stochastic volatility firm would take on lower levels of debt defensively given the asymmetric
structure of adjustment costs. (see for example van Binsbergen et al. (2008), Byoun (2008) and
Flannery and Rangan (2003) for some evidence suggesting that such an asymmetry may exist).
A bankruptcy cost structure that are convex in the degree of default would also give rise
to optimal debt choices that are lower for the firm with stochastic volatility, and declining in ε
(the volatility of volatility). To see this assume that debt related benefits are linear in the face
value of debt, (Corporate tax shield could be argued to be approximately linear).
If the volatility is higher than the expected value σ, say (σ + ε), the incremental expected
bankruptcy costs would be larger than the savings in incremental bankruptcy costs from a
volatility realization (σ – ε). This means that the optimal leverage trade-off for the stochastic
volatility firm will occur at lower values than that for a firm with constant volatility of σ.5
Moreover, the optimal leverage of such a firm would be declining in its volatility of volatility, ε.
Another framework in which the volatility of volatility may affect the optimal leverage
choices (and that of optimal debt component in external financing) is one in which the corporate
insiders have private information about the current volatility of the firm. The informational
5
More generally it is true that if volatility of volatility contributes to the deadweight cost born by the firm, the tradeoff
with debt related benefits is going to yield an optimum that can be mapped back to a simpler model where the volatility of the
cash flows is a higher number. However in general this inverse mapping may be complex.
17
advantage of the insiders may be larger with a higher ε. A firm with private information about
risk suffers a lemons problem in issuing debt securities. For such a firm, issuing levered equity or
convertible securities with embedded options may be an optimal strategy either to get around the
lemons costs or the right security to issue in the signaling equilibrium. The cost of placing equity
securities with outsiders is lower for a firm whose true volatility is lower. In the separating
equilibrium, the gains from tilting towards equity would be increasing in the degree of
asymmetric information, proxied here by ε, the volatility of volatility. ε can be thought of as the
range of the support of the private information attribute σ in the market.
A third frameworks in which firms with high volatility of volatility tilt away from high
leverage would be one of moral hazard in which leverage induces risk-shifting incentives. If
firms with stochastic volatility are plausibly less able to contractually precommit to specific
levels of volatility, debt holders would anticipate higher levels of risk-shifting from these firms
and incorporate that in the pricing of debt securities issued by these firms. These firms therefore
would optimally go for lower leverage or issue equity or convertible debt (with embedded
options). As Green (1984) showed, precommitting not to risk-shift through well-designed optionembedded securities would be optimal for these firms. Again, higher the ε, the volatility of
volatility of a firm, higher the importance of making such a precommitment through conservative
leverage choices.
5. Discussion
5.1. Factors that ameliorate or accentuate the effect of volatility of volatility
18
Depending on which one of the explanations drive our empirical results, the effect of
volatility of risk on capital structure may be weakened or strengthened by certain firm
characteristics. If volatility of risk captures the asymmetry of information about risk between
corporate insiders and creditors, it is possible that the following factors ameliorate the effects of
volatility of volatility. As the creditor becomes more and more familiar with the operations of the
borrowing firm it is possible that the volatility of volatility becomes less important. Some
examples would be 1) the availability of a credit rating for the firm, 2) The number of analysts
following the firm 3) the age of the firm 4) Longer banking relationship the borrower and the
creditor.
5.2. Factors that affect volatility of volatility
Income smoothing by managers can possibly affect volatility of volatility.
What are some of the ways that managers volatility of volatility. For example if managers
pursue different degrees of income smoothing they might increase the volatility of volatility of
reported income even though the volatility of volatility of the underlying operations of the firm
may not have changed. Another example is pursuing different risk management policies. Here
the volatility of volatility of overall profits might increase even though the volatility of volatility
of the operating profits may be smaller. One scenario consistent with such changes in income
smoothing or risk management procedures could come from a turnover of CEOs/CFOs.
A more fundamental reason for changing volatility may be changes in the product line,
changes in the technology of operations, changes in the degree of competitiveness in the
19
industry. Empirically it is possible that changes in the degree of concentration in the industry
would be related to volatility of volatility.
Consider a firm whose volatility currently is low and its volatility of volatility is also low. The
firm is switching its operations into an activity with higher volatility as well as volatility of
volatility. Doing aggressive income smoothing may enable the firm to maintain a low volatility
of volatility for an additional time period.
However, it is possible that volatility of volatility is more difficult to manipulate than
simple cash flows or level of volatility. The objective of this paper will be 1) to provide
examples of changes in volatility and 2) possibly to argue that volatility of volatility is probably
less directly subject to manipulation by mangers than level of volatility.
Volatility of risk could lead to higher bankruptcy cost, especially for long term debt issues.
6. Conclusion
In addition to volatility of the assets (risk), the variability of risk is an important
determinant of capital structure. In this paper we show that the volatility of risk is an important
factor in explaining capital structure choices of firms over and above the traditional determinants
of capital structure such as the level of risk, size, market-to-book ratio, tangibility of assets and
profitability. We show that the volatility of risk explains 1) the fraction of debt in total new
external financing raised by the firm, 2) the long term debt as a fraction of the assets of the firm.
20
Table 1: Balance sheets, cash flows and other descriptive statistics over time
The table reports average balance sheets for the sample. Financial firms, utilities and companies that could not be
matched properly with CRSP are excluded. Unless labeled as median, each item in Panel A and Panel B is
calculated as a percentage of the book value of total assets and then averaged across all firms of our sample in that
year. Definitions of variables follow Frank and Goyal (2003) and Fama and French (2002). See text and Appendix 2
for details.
Year
Number of observations
Panel A: Balance sheet items
Assets:
+Cash (#162)
+Short term investments (#193)
+Receivables-total (#2)
+Inventories (#3)
+Current assets-other (#68)
+Current assets-total (#4)
+Net property plant and equipment (#8)
+Investments and advances - equity
method (#31)
+Investments and advances - other (#32)
+Intangibles (#33)
+Assets - other (#69)
=Total assets (#6)
Liabilities
+Debt in current liabilities (#34)
+Account payable (#70)
+Income taxes payable (#71)
+Current liabilities - other (#72)
=Current liabilities - total (#5)
+Long-term debt - total (#9)
+Liabilities - other (#75)
+Deferred taxes and ITC (#35)
+Minority interest (#38)
=Liabilities - total (#181)
+Preferred stock - carrying value (#130)
+Common equity - total (#60)
=Stockholders'
equity
total
(#216)=(#130)+(#60)
=Total liabilities and stockholders'
equity
Panel B: Corporate cash flows
+Cash Dividends (#127)
+Change in net working capital
-Internal cash flow
+Investments
=Financial deficit (Mean)
Financial deficit (Median)
Net debt issues (#111-#114) Mean
1971
1518
1980
2925
1990
3481
2001
3810
0.040
0.035
0.194
0.247
0.014
0.539
0.356
0.030
0.045
0.217
0.245
0.020
0.575
0.349
0.085
0.031
0.205
0.186
0.029
0.544
0.320
0.127
0.056
0.154
0.126
0.037
0.501
0.276
0.020
0.025
0.036
0.024
1.000
0.014
0.026
0.020
0.023
1.000
0.010
0.025
0.049
0.054
1.000
0.010
0.020
0.128
0.064
1.000
0.068
0.090
0.020
0.061
0.239
0.199
0.012
0.020
0.005
0.476
0.011
0.513
0.066
0.114
0.018
0.087
0.286
0.200
0.015
0.026
0.003
0.529
0.009
0.461
0.094
0.111
0.008
0.097
0.312
0.192
0.034
0.020
0.006
0.564
0.015
0.422
0.063
0.086
0.006
0.118
0.274
0.184
0.045
0.016
0.005
0.524
0.021
0.456
0.524
0.471
0.437
0.476
1.000
1.000
1.000
1.000
0.018
0.022
0.099
0.082
0.023
0.001
0.012
0.015
0.024
0.106
0.102
0.034
0.003
0.017
0.009
-0.011
0.044
0.071
0.025
-0.001
0.004
0.005
-0.022
0.000
0.058
0.041
0.002
0.001
21
Net debt issues (Median)
Net equity issues (#108-#115) (Mean)
Net equity issues (Median)
Panel C: Other descriptive statistics
Age (years since first appearance
CRSP)
Market value of assets (in millions
dollars)
Book value of assets (#6) (in millions
dollars)
Tangibility (#8/#6)
Log sales (log(#12))
Market-to-book ratio
Profitability=Operating income(#13)
Assets(/#6)
0.000
0.011
0.000
0.000
0.017
0.000
-0.001
0.021
0.000
0.000
0.040
0.001
7
11
12
13
503.233
464.232
966.102
2943.950
436.892
0.356
4.73
1.52
514.434
0.349
4.74
1.40
858.079
0.320
4.45
1.54
1550.136
0.276
5.25
1.90
0.128
0.144
0.065
0.014
in
of
of
/
22
Table 2: Measures of volatility and volatility of volatility
This table reports descriptive statistics and correlation matrix of the alternative measures of risk and volatility of
risk. The monthly standard deviation of asset volatility is the standard deviation of the 12 monthly asset volatility
estimates from the previous calendar year. All correlation coefficients are significant at the 1% level.
Panel A. 1971-2001
A1. Descriptive statistics
Variable
Std. dev. of monthly asset volatility
Level of asset volatility
Number of
observations
101291
103210
Mean
0.007
0.022
Std. Dev. Of
Monthly Asset
Vol
1.000
0.246
Level of Asset
Vol
0.246
1.000
Number of
observations
5758
5787
5777
Mean
0.009
0.028
0.045
Std Dev
0.007
0.021
0.042
Std. Dev. Of
Monthly Asset
Vol
1.000
0.593
0.423
Level of Asset
Vol
0.593
1.000
0.504
Std Dev of
Implied Vol
0.423
0.504
1.000
Std Dev
0.009
0.043
A2. Correlation matrix
Std. dev. of monthly asset volatility
Level of asset volatility
Panel B. Option data, 1996-2001
B1. Descriptive statistics
Variable
Std. dev. of monthly asset volatility
Level of Asset Volatility
Std dev of implied volatility
B2. Correlation matrix
Std. dev. of monthly asset volatility
Level of asset volatility
Std. dev of implied volatility
23
0.828
579
0.857
0.016
0.541
0.759
Adjusted R squared
Number of
observations
Financial deficit
0.117
579
0.143
0.016
0.299
578
0.269
0.017
0.463
579
0.461
0.021
3
-0.014
0.002
579
0.539
0.021
3
0.014
0.002
578
0.731
0.017
Panel B: Dependent variable - net equity issued
Decile
1 (Low)
2
Intercept
-0.010
-0.014
0.002
0.002
Adjusted R squared
Number of
observations
Financial deficit
Panel A: Dependent variable - )et debt issued
Decile
1 (Low)
2
Intercept
0.010
0.014
0.002
0.002
0.325
578
0.312
0.019
4
-0.008
0.002
0.702
578
0.688
0.019
4
0.008
0.002
24
0.482
575
0.471
0.020
5
-0.007
0.003
0.538
575
0.528
0.020
5
0.007
0.003
0.400
579
0.425
0.022
6
-0.001
0.003
0.548
579
0.574
0.022
6
0.001
0.003
0.585
578
0.605
0.021
7
0.002
0.003
0.376
578
0.395
0.021
7
-0.002
0.003
0.631
579
0.644
0.021
8
0.002
0.004
0.342
579
0.355
0.021
8
-0.002
0.004
0.185
574
0.177
0.016
0.752
578
0.735
0.018
0.831
574
0.823
0.016
9 10 (High)
0.003
0.007
0.004
0.004
0.281
578
0.265
0.018
9 10 (High)
-0.003
-0.007
0.004
0.004
, ∆Eit = a + bnE DEFit + ε it . Ranking based on the daily standard deviation of the implied volatility of the long term stock options of the
firm during the previous calendar year. Firms with rank 10 have highest standard deviation. Standard errors are reported below the coefficients, in
italics. All coefficients on financial deficit are significant at the 1 % level.
∆Dit = a + bnD DEFit + ε it
Pooled panel OLS regressions of net debt issues ∆D and net equity issues ∆E on the financing deficit DEF are estimated for each decile n=1,…10:
Table 3: Financing the deficit across deciles of volatility of volatility (implied volatility)
Figure 1: Financing the deficit across deciles of volatility of volatility (implied volatility)
Pooled panel OLS regressions of net debt issues ∆D and net equity issues ∆E on the financing deficit DEF are
estimated for each decile n=1,…10: ∆Dit = a + bnD DEFit + ε it , ∆Eit = a + bnE DEFit + ε it . Ranking based on the daily
standard deviation of the implied volatility of the long term stock options of the firm during the previous calendar
year. The figure plots coefficients on financial deficit and adjusted R-squared for each decile.
Net equity issued: coefficient on financing deficit
Net equity issued: adjusted R-squared
Net debt issued: coefficient on financing deficit
Net debt issued: adjusted R-squared
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
Std. Dev. of Implied Volatility
25
0.876
Adjusted R squared
0.825
10125
0.825
0.004
10141
0.131
Adjusted R squared
0.126
0.003
Number of
observations
Financial deficit
10131
0.177
0.174
0.183
0.004
3
0.000
0.000
0.809
10132
0.814
0.004
3
0.000
0.000
10124
0.174
0.004
Panel B: Dependent variable - net equity issued
Decile
1 (Low)
2
Intercept
0.000
-0.002
0.000
0.000
10142
0.871
0.003
Number of
observations
Financial deficit
Panel A: Dependent variable - net debt issued
Decile
1 (Low)
2
Intercept
-0.001
0.002
0.000
0.000
E
0.241
10128
0.247
0.004
4
0.000
0.001
0.744
10129
0.751
0.004
4
0.000
0.001
26
0.313
10120
0.332
0.005
5
0.003
0.001
0.649
10122
0.668
0.005
5
-0.003
0.001
0.444
10134
0.467
0.005
6
0.004
0.001
0.508
10134
0.532
0.005
6
-0.004
0.001
0.599
10128
0.615
0.005
7
0.006
0.001
0.369
10130
0.385
0.005
7
-0.006
0.001
0.686
10130
0.709
0.005
8
0.007
0.001
0.269
10130
0.290
0.005
8
-0.007
0.001
0.139
10113
0.153
0.004
0.771
10124
0.782
0.004
0.833
10112
0.847
0.004
9 10 (High)
0.009
0.014
0.001
0.001
0.206
10126
0.217
0.004
9 10 (High)
-0.009
-0.014
0.001
0.001
, ∆Eit = a + bn DEFit + ε it . Ranking based on the annual standard deviation of the monthly standard deviations of the stock returns
during the 12 months of the previous calendar year. Firms with rank 10 have highest standard deviation. Standard errors are reported below the
coefficients, in italics. All coefficients on financial deficit are significant at the 1 % level.
∆Dit = a + bnD DEFit + ε it
Pooled panel OLS regressions of net debt issues ∆D and net equity issues ∆E on the financing deficit DEF are estimated for each decile n=1,…10:
Table 4: Financing the deficit across deciles of volatility of volatility (realized monthly volatility)
Figure 2: Financing the deficit across deciles of volatility of volatility (realized monthly volatility)
Pooled panel OLS regressions of net debt issues ∆D and net equity issues ∆E on the financing deficit DEF are
estimated for each decile n=1,…10: ∆Dit = a + bnD DEFit + ε it , ∆Eit = a + bnE DEFit + ε it . Ranking based on the annual
standard deviation of the monthly standard deviations of the stock returns during the 12 months of the previous
calendar year. The figure plots coefficients on financial deficit and adjusted R-squared for each decile.
Net equity issued: coefficient on financing deficit
Net equity issued: adjusted R - squared
Net debt issued: coefficient on financing deficit
Net debt issued: adjusted R-squared
1.000
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
1 (Low)
2
3
4
5
6
7
Std. Dev. of Monthly Volatility
27
8
9
10(High)
Table 5: Relation between net debt issued and standard deviation of monthly realized volatility
The table reports estimates from pooled panel regressions of net debt issued on financing deficit, the standard
deviation of monthly realized asset volatility, level of realized asset volatility and conventional leverage variables.
Pooled OLS standard errors reported under the coefficients in italics.
Intercept
0.000
-0.003
-0.010
0.000
0.000
0.001
Financing deficit(DEF)
DEF*(St. dev. of monthly asset
volatility)
0.522
0.002
0.614
0.002
0.331
0.004
-9.519
0.101
-6.551
0.106
-2.426
0.101
-3.441
0.045
-1.263
0.044
DEF*level of asset volatiltity
DEF*Log(Sales)
0.047
0.001
DEF*Tangibility
0.429
0.006
DEF*Market-to-book ratio
-0.015
0.000
DEF*Profitability
0.071
0.003
St. dev of monthly asset volatility
-0.528
0.027
Level of asset volatility
-0.804
0.027
-0.358
0.027
0.235
0.006
0.106
0.006
Log(Sales)
0.002
0.000
Tangibility
-0.006
0.001
Market-to-book ratio
-0.003
0.000
Profitability
0.02037
0.0013
Adjusted R-squared
0.4294
0.461
0.5788
Number of observations
101283
101283
100676
28
Table 6: Relation between net debt issued and standard deviation of implied volatility
The table reports estimates from pooled panel regressions of net debt issued on financing deficit, the standard
deviation of implied volatility of long term stock options of the firm, level of realized asset volatility and
conventional leverage variables. Pooled OLS standard errors reported under the coefficients in italics.
Intercept
0.011
0.001
0.011
0.002
-0.016
0.006
Financing deficit(DEF)
0.574
0.009
0.707
0.012
0.215
0.028
-2.518
0.099
-1.641
0.110
-0.543
0.111
-4.601
0.270
-1.768
0.285
DEF*(St. dev. of implied volatility)
DEF*Level of asset volatiltity
DEF*Log(Sales)
0.060
0.003
DEF*Tangibility
0.287
0.030
DEF*Market-to-book ratio
-0.001
0.002
DEF*Profitability
0.005
0.014
St.dev of implied volatility
-0.158
0.023
Level of asset volatility
-0.143
0.026
-0.087
0.025
-0.020
0.056
0.012
0.062
Log(Sales)
0.004
0.001
Tangibility
-0.002
0.004
Market-to-book ratio
-0.001
0.000
Profitability
0.020
0.006
Adjusted R-squared
0.456
0.488
0.566
Number of observations
5777
5777
5726
29
0.126
0.004
0.109
Financial deficit
Adjusted R squared
1 (Low)
0.004
0.000
0.849
Adjusted R squared
Decile
Intercept
0.868
0.004
1 (Low)
-0.004
0.000
Financial deficit
Decile
Intercept
E
0.157
0.175
0.004
2
0.001
0.000
0.802
0.822
0.004
2
-0.001
0.000
0.457
0.005
0.326
0.005
0.173
0.192
0.004
0.203
0.235
0.005
30
0.251
0.291
0.005
0.402
0.430
0.005
0.504
0.542
0.005
0.638
0.673
0.005
8
0.003
0.001
0.542
0.570
0.005
Panel B: Dependent variable - )et equity issued
3
4
5
6
7
0.001
0.001
0.003
0.004
0.005
0.000
0.000
0.001
0.001
0.001
0.665
0.708
0.005
0.293
0.728
0.764
0.005
8
-0.003
0.001
0.419
0.787
0.807
0.004
Panel A: Dependent variable - )et debt issued
3
4
5
6
7
-0.001
-0.001
-0.003
-0.004
-0.005
0.000
0.000
0.001
0.001
0.001
0.747
0.770
0.004
9
0.003
0.001
0.209
0.230
0.004
9
-0.002
0.001
0.832
0.853
0.004
10 (High)
0.001
0.001
0.129
0.147
0.004
10 (High)
-0.001
0.001
, ∆Eit = a + bn DEFit + ε it . Ranking based on the daily standard deviation of the return on market value of assets during the previous
calendar year. Firms with rank 10 have highest standard deviation. Standard errors are reported below the coefficients, in italics. All coefficients on
financial deficit are significant at the 1 % level.
∆Dit = a + bnD DEFit + ε it
Pooled panel OLS regressions of net debt issues ∆D and net equity issues ∆E on the financing deficit DEF are estimated for each decile n=1,…10:
Table 7: Financing the deficit across deciles based on the level of asset volatility
0
0.1
0.2
0.3
0.4
1
2
3
4
5
6
7
8
9
10
Asset volatility decile
31
Net equity issued: adj. Rsquared
Net equity issued: coefficient on
financial deficit
Net debt issued: adj. R-squared
0.6
0.5
Net debt issued: coefficient on
financial deficit
0.7
0.8
0.9
1
Pooled panel OLS regressions of net debt issues ∆D and net equity issues ∆E on the financing deficit DEF are estimated for each decile n=1,…10:
∆Dit = a + bnD DEFit + ε it , ∆Eit = a + bnE DEFit + ε it .The figure plots coefficients on financial deficit and adjusted R-squared for each decile.
Figure 3: Financing the deficit across deciles based on the level of asset volatility
0.31654
10143
0.31717
579
VRV
VIV
Ranking variable
1(low
VOV)
0.28507
578
0.26898
10126
2
0.26254
579
0.23777
10132
3
4
0.23835
578
0.21566
10129
Decile
32
0.20408
575
0.19148
10122
5
Table 8: Leverage (long term debt scaled by total assets) by decile of VOV
0.19479
579
0.1682
10136
6
0.1556
578
0.14614
10130
7
0.14931
579
0.12735
10131
8
0.12062
578
0.11269
10127
9
0.10429
574
0.09527
10115
10(High
VOV)
Table 9: Multivariate relation between the level of leverage VOV and control variables
Panel OLS regression, t-stats in parentheses
Variable
VRV
Book
leverage
-3.452
(-50.517)
VIV
Level of vol.
Log(Sales)
Tangibility
Market-toBook
Profitability
Adj. Rsquared
Observations
Book
leverage
-0.237
(-18.576)
0.006
(21.790)
0.242
(96.797)
-0.302
(-4.234)
-2.822
(-17.631)
0.004
(2.242)
0.206
(17.335)
-0.008
(-22.028)
-0.121
(-38.598)
-0.005
(-3.893)
-0.299
(-19.215)
0.155
100682
0.206
5725
33
non rated
rated
firms
2.000
0.816
0.844
1.000
0.857
0.893
0.823
3.000
0.811
0.780
Decile
based on
VRV
4.000
0.744
34
0.741
5.000
0.654
0.756
6.000
0.505
0.743
7.000
0.365
0.667
8.000
0.277
0.600
9.000
0.210
0.609
10.000
0.151
. Ranking based on the annual standard deviation of the monthly standard deviations of the stock returns during the 12 months of the
previous calendar year. Firms with rank 10 have highest standard deviation. Standard errors are reported below the coefficients, in italics. All
coefficients on financial deficit are significant at the 1 % level. The table reports coefficients on the financing deficit (beta).
∆Eit = a + bnE DEFit + ε it
D
Pooled panel OLS regressions of net debt issues ∆D on the financing deficit DEF are estimated for each decile n=1,…10: ∆Dit = a + bn DEFit + ε it ,
Table 10: Financing the deficit across deciles of volatility of volatility (realized monthly volatility): Rated vs non rated firms
Figure 4: Financing the deficit across deciles of volatility of volatility (realized monthly volatility): Rated vs
non rated firms
Pooled panel OLS regressions of net debt issues ∆D on the financing deficit DEF are estimated for each decile
n=1,…10: ∆Dit = a + bn DEFit + ε it , ∆Eit = a + bn DEFit + ε it . Ranking based on the annual standard deviation of the
monthly standard deviations of the stock returns during the 12 months of the previous calendar year. Firms with rank
10 have highest standard deviation. Standard errors are reported below the coefficients, in italics. All coefficients on
financial deficit are significant at the 1 % level. The table reports coefficients on the financing deficit (beta).
D
E
1.000
0.900
0.800
0.700
0.600
Rated
0.500
0.400
0.300
0.200
Non rated
0.100
0.000
1
2
3
4
5
6
7
35
8
9
10
non
rated
rated
0.88835
0.84841
1
0.52488
0.77854
2
0.23361
0.71643
3
0.65183
0.72609
4
36
0.42971
0.71921
5
0.42876
0.75921
6
0.31126
0.63279
7
0.23668
0.86201
8
0.22136
0.50089
9
0.14902
0.61162
10
. Ranking based on the annual standard deviation of the monthly standard deviations of the stock returns during the 12 months of the
previous calendar year. Firms with rank 10 have highest standard deviation. Standard errors are reported below the coefficients, in italics. All
coefficients on financial deficit are significant at the 1 % level. The table reports coefficients on the financing deficit (beta).
∆Eit = a + bnE DEFit + ε it
D
Pooled panel OLS regressions of net debt issues ∆D on the financing deficit DEF are estimated for each decile n=1,…10: ∆Dit = a + bn DEFit + ε it ,
Table 11: Financing the deficit across deciles of volatility of volatility (implied volatility): Rated vs non rated firms
Figure 5: Financing the deficit across deciles of volatility of volatility (implied volatility): Rated vs non rated
firms
Pooled panel OLS regressions of net debt issues ∆D on the financing deficit DEF are estimated for each decile
n=1,…10: ∆Dit = a + bn DEFit + ε it , ∆Eit = a + bn DEFit + ε it . Ranking based on the annual standard deviation of the
monthly standard deviations of the stock returns during the 12 months of the previous calendar year. Firms with rank
10 have highest standard deviation. Standard errors are reported below the coefficients, in italics. All coefficients on
financial deficit are significant at the 1 % level. The table reports coefficients on the financing deficit (beta).
D
E
1
0.9
0.8
0.7
0.6
non rated
0.5
0.4
0.3
0.2
rated
0.1
0
1
2
3
4
5
6
7
37
8
9 10
Appendix
Using a Merton model to compute asset volatility
From Ito’s lemma, we have
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where σ E is the instantaneous variance of the rate of return on equity (the standard deviation of
daily stock returns from CRSP), σ V is the instantaneous variance of the rate of return on the firm
(to be solved for), Vt is the market value of the firm and Et is the market value of equity (both
calculated as described below). The derivative of the market value of equity with respect to the
market value of the firm in the Merton model is:
 ln(Vt / Bt ) + ( rf + 12 σ V2 )T 
∂Et
=Φ

∂Vt
σV T


where Φ is the cumulative distribution function of the standardized normal distribution )(0,1), T
is the time to maturity of the debt (we try both 10 and 20 years) and rf is the risk free rate (from
Kenneth French’s website).
Variable definitions
Investments: For firms reporting under formats 1 to 3, it equals Compustat item #128 + #113 +
#129 + #219 - #107 - #109. For firms reporting under format 7, investments equal #128 + #113 +
#129 - #107 - #109 - #309 - #310.
Change in net working capital: For firms reporting under format 1, it equals Compustat item
#274 - #236 - #301. For firms reporting under format 2and 3, it equals #274 + #236 - #301, and
38
for firms reporting under format 7, it equals - #302 - #303 - #304 - #305 - #307 + #274 - #312 #301.
Internal cash flows: For firms reporting under formats 1 to 3, it equals Compustat item #123 +
#124 + #125 + #126 + #106 + #213 + #217 + #218. For firms reporting under format 7, internal
cash flows equal #123 + #124 + #125 + #126 + #106 + #213 + #217 + #314.
Market value of a firm: Book value of debt = #181 + #10 (or #56 or #130 depending on
availability and in that order) + market value of equity = number of common shares outstanding
times the closing share price (from CRSP)
Variables that are trimmed
In order to remove outliers and misrecorded data, observations that are in the extreme 0.5 % left
or right tail of the distribution or have missing values are removed. This trimming has been
applied to the following variables: current assets (Compustat item #4), current liabilities (#5),
cash dividends (#127), investments (defined above), internal cash flows (defined above), change
in net working capital (defined above), financial deficit, net debt issued (#111-#114), net equity
issued (#108-#115), all as a percentage of total assets, as well as tangibility (#8/#6), market-tobook ratio, profitability (#13/#6), and log(sales) (natural logarithm of #12).
Calculating the variation in firm specific implied volatility from option prices
We use end-of-day option prices, option open interest and implied volatility estimates from the
Ivy DB database provided by OptionMetrics. The sample is from January 1996 to December
2001. To filter out misrecorded data and very illiquid contracts, we exclude days/contracts that
have zero open interest or have a bid-ask spread larger than 50% of the option price at midpoint.
39
The sample includes at-the-money call options with maturity closest to but higher than 182 days.
Ideally, we would use longer maturity contracts, e.g. LEAPS, but these contracts are quite
illiquid so that our sample would be considerably reduced. The sample has 13,418,700 day-firm
implied volatility estimates. We then calculated the standard deviation of the implied volatility
per firm over the previous calendar year. If there are less than 90 trading days the firm-year is
excluded from the sample.
40
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