Download Managerial incentives to increase firm volatility provided by debt

Managerial incentives to increase firm volatility
provided by debt, stock, and options
Joshua D. Anderson
[email protected]
(617) 253-7974
John E. Core*
[email protected]
(617) 715-4819
Abstract
We measure a manager’s risk-taking incentives as the total sensitivity of the manager’s debt,
stock, and option holdings to firm volatility. We compare this measure to the option vega and to
relative measures used by the prior literature. Vega does not capture risk incentives from
managers’ stock and debt holdings, and does not reflect the fact that employee options are
warrants. The relative measures do not incorporate the sensitivity of options to volatility. The
new measure explains risk choices better than vega and the relative measures. Our measure
should be useful for future research on managers’ risk choices.
First draft: October 2011
This draft: May 30, 2013
_______________
* Corresponding author. We gratefully acknowledge comments from Ana Albuquerque (discussant), Wayne Guay,
Mitchell Petersen, Eric So, Daniel Taylor, Anand Venkateswaran, Jerry Zimmerman, and seminar participants at the
American Accounting Association 2012 Annual Meeting, Columbia University, MIT Sloan School of Management,
Northeastern University, Pennsylvania State University, Temple University, and the University of Technology
Sydney. We thank Ingolf Dittmann for his estimates of CEO non-firm wealth. We appreciate the financial support of
the MIT Sloan School of Management.
1.
Introduction
A large literature uses the sensitivity of stock options to an increase in stock volatility
(“vega”) to study whether managers’ equity portfolios provide incentives to increase risk.
Studies on early samples show a strong positive association between vega and risk-taking (Guay,
1999; Coles et al., 2006), whereas studies on later samples show mixed results (e.g., Hayes et al.,
2012). We re-examine vega and show that it has two shortcomings: (1) it does not capture
potential risk incentives from managers’ stock and inside debt (unsecured pensions and deferred
compensation), and (2) it does not reflect the fact that employee options are warrants. We derive
and calculate an overall measure of a manager’s risk-taking incentives using the total sensitivity
of the manager’s debt, stock, and option holdings to firm volatility.
Limited liability implies that equity is an option on firm value with a strike price equal to
the face value of debt. Consequently, an increase in firm volatility increases equity value by
reducing debt value (Black and Scholes 1973; Merton, 1974). When a firm has options, this
increase in equity value is shared between the stock and options. This implies that the option
sensitivity to volatility is larger than vega. Because options are warrants, an increase in volatility
that increases option value comes in part from a decrease in stock value. If the firm has no debt,
all of the increase in option value comes from a decrease in stock value. This implies a stock
sensitivity to volatility that goes from being negative to positive as leverage increases. A
manager’s attitude toward risk will be affected by the sensitivities of the managers’ holdings of
debt, stock, and options to firm volatility.
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To estimate these sensitivities, we follow Merton (1974) and value total firm equity
(stock and stock options) as an option on the value of firm assets. The model gives an estimate of
the decrease in debt value for an increase in firm volatility. This decrease in debt value implies
an equal increase in equity value. In turn, the increase in equity value is shared between the stock
and stock options. We estimate the CEO’s sensitivities by applying the CEO’s ownership of debt,
stock, and options to the firm’s sensitivities.
We estimate these sensitivities for a sample of 5,967 Execucomp CEO-years from 2006
to 2010. The typical CEO in our sample owns roughly 2% of the debt, 2% of the stock, and 16%
of the options. In terms of incentives to increase volatility, this CEO has small negative
incentives from debt, small positive incentives from stock, and large positive incentives from
options. A one standard deviation increase in firm volatility increases the average CEO’s wealth
by $3 million, or 7% of total wealth.
The total sensitivity increases as leverage increases, but the vega roughly remains
constant with leverage. As leverage increases, the debt sensitivity becomes more negative
(making the CEO averse to risk increases), but the equity sensitivity (the sum of stock and option
sensitivities) increases more rapidly. This occurs because the stock sensitivity changes from
being negative to strongly positive.
Because vega ignores the debt and stock sensitivities, it can be a noisy and biased
measure of risk-taking incentives. If the total sensitivity better reflects CEO incentives, we
expect it to be more highly associated with CEOs’ risk-taking choices. To test this conjecture, we
examine the association between the total sensitivity and vega and three proxies for future firm
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risk: stock volatility, research and development expense, and leverage. We specify regression
models following Coles et al. (2006) and Hayes et al. (2012). Our results suggest that the total
sensitivity is more highly associated with risk-taking than is vega.
Theory suggests that incentives relative to wealth determine risk-taking. For this reason,
we examine modified specifications in which we scale the CEO’s risk-taking incentives with a
proxy for the CEO’s total wealth. We also scale the CEO’s incentives to increase stock price
(“delta”) by total wealth. Prior research (e.g., Coles et al., 2006) controls for wealth effects by
using tenure and cash compensation as proxies for CEO wealth. We find that the scaled measures
explain firm risk better than the unscaled measures, and that the scaled total sensitivity explains
firm risk better than the scaled vega.
The total sensitivity measure requires data on CEOs’ inside debt, which data became
available only in 2006. To avoid this limitation, we also examine the equity sensitivity, which is
equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus
the debt sensitivity). The equity sensitivity is very highly correlated with the total sensitivity
because the debt sensitivity is small and has low variance. We compute the equity sensitivity
from 1994-2005 and compare it with vega. In this sample, we also find that equity sensitivity
explains risk-taking better than vega, and that the scaled equity sensitivity is superior to the
unscaled measures.1
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Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important
incentives. Guay (1999) also examines the stock sensitivity, but finds that it does not have a large effect on
incentives. Potential reasons for the difference in our findings include: (1) we value options as warrants, (2) we use a
different asset volatility calculation, and (3) we use a different sample.
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A concern about regressions of incentives on risk-taking is reverse causality (that is,
when risk is expected to be high, firms use high risk-taking incentives). To explore the
robustness of our results, we follow Hayes et al. (2012) and use the introduction of option
expensing in 2005 as an exogenous change to incentives. Consistent with Hayes et al., we find
no significant association between changes in vega and changes in firm risk for our sample.
However, the change in scaled equity sensitivity is significantly positively associated with both
the change in stock volatility and the change in leverage. We find no association, however, with
the change in R&D expense.
Our derivation of the sensitivity of debt, stock, and options also implies that the relative
risk-taking measures used in the recent literature (e.g., Cassell et al., 2012; Sundaram and
Yermack, 2007; Wei and Yermack, 2011) are noisy and can be biased. These measures do not
correctly incorporate the sensitivity of option value to firm volatility. We calculate a measure
that correctly weights the manager’s debt, stock, and option sensitivities. The prior measures
suggest that CEOs on average are highly aligned with debt holders: the average CEO has debt
incentives to reduce volatility that are three times his or her equity incentives to increase
volatility. By contrast, the corrected measure, which explicitly takes into account the incentives
to increase firm volatility from options, is an order of magnitude smaller, suggesting that CEOs
have little alignment with debt holders: the average CEO has incentives to reduce volatility that
are equal to 0.4 times his or her equity incentives to increase volatility. Consistent with prior
literature, we find that these ratios are negatively associated with risk choices. However, our
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scaled total sensitivity measure is more highly associated with risk-taking choices than the
relative ratios.
We contribute to the literature in several ways. We calculate a measure of risk-taking
incentives that includes the sensitivity of managers’ debt and stock holdings. In addition, our
measure better calculates the sensitivity of the manager’s stock options to firm volatility. We
compare this measure to vega and to the relative measures used by the prior literature. We find
that the new measure is more highly associated with risk choices than vega and the relative
measures. Our measure should be useful for future research on managers’ risk choices.
The remainder of the paper proceeds as follows. In the next section, we define the
sensitivity of firm debt, stock, and options to firm volatility. We then define the corresponding
measures of the sensitivity of the CEO’s portfolio to firm volatility. In the third section, we
describe how we select a sample of CEOs, and compare various measures of incentives. In the
fourth section, we compare regressions using the measures to explain various firm outcomes and
provide robustness tests. In the fifth section, we conclude.
2.
Definition of incentive measures
In this section we first show how firm debt, equity, and option values change with
changes in firm volatility, and then we relate these changes to measures of managerial incentives.
2.1
Sensitivity of firm capital structure to firm volatility
In general, firms are financed with debt, equity, and employee options:
(1)
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Debt is the market value of the debt, Stock is the market value of stock, and Options is the
market value of options. It is convenient to express stock and option values in per share amounts,
and we assume the firm has n shares of stock outstanding with stock price P. The firm has qn
stock options outstanding with option price W. For simplicity in our notation, we assume for the
moment that all options have the same exercise price and time to maturity so that each option is
worth W.
To begin, suppose that there are no stock options outstanding, so that (1) becomes:
(2)
Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a
strike price equal to the face value of debt. Under the assumption that changes in firm volatility
do not change the value of the firm:
0
(3)
Therefore, any loss in debt value due to volatility increases is offset by an equal gain in equity
value:
(4)
More volatile returns increase the value of equity holders’ call option, which reduces the value of
debt. The interests of debt and equity conflict. Equity prefers higher firm volatility, which raises
the value of its call; debt prefers lower firm volatility, which increases the value of its short call.
Now consider a firm with no debt financed with stock and employee stock options:
(5)
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Employee stock options are warrants (W) because exercising the options results in the firm
issuing new shares of stock and receiving the strike price. Analogous to (4), an increase in firm
volatility has the following effect on the stock price and the option price:
(6)
Equation (6) shows that the price of a share of stock in a firm with only stock and employee
stock options decreases when firm volatility increases (Galai and Schneller, 1978). The share
price decreases because the increased volatility makes it more likely that the option will be in the
money and that the current value of a share outstanding will be diluted. This result for options on
stock is similar to the result when stock is an option on the value of the levered firm. Increases in
volatility do not change the value of the firm: Therefore, any gains to the options are offset by
losses to the stock.
Now we combine the results for debt and options. An increase in firm volatility affects
debt, stock, and option value according to the following relation:
(7)
In firms with both debt and options, shareholders have purchased a call on the assets, and they
have “sold” a call on the equity to employees. They are in a position with respect to the equity
similar to the position of the debt holders with respect to the assets. When the firm is levered,
increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the
call on the equity. Since the change in stockholders’ value is a combination of these two
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opposing effects, whether stockholders prefer more volatility depends on the number of options
outstanding and firm leverage, as we illustrate next.
2.1.1 Estimation of firm sensitivities
To estimate the sensitivities described above, we calculate the value of debt and options
using standard pricing models. We then increase firm volatility by 1%, hold firm value fixed, and
recalculate the values of debt, stock, and options. We estimate the sensitivities to a one percent
change in firm volatility as the difference between these values. Appendix A describes the details.
We first price employee options as warrants using the Black-Scholes model, as modified
to account for dividend payouts by Merton (1973), and modified to reflect warrant pricing by
Schulz and Trautmann (1994). Calculating option value this way gives a value for total firm
equity. Second, we model firm equity as an option on the levered firm following Merton (1974)
using the Black-Scholes formula. This model allows us to calculate total firm value and firm
volatility following the approach of Eberhart (2005). With these values in hand, we calculate the
value of the debt as a put on the firm’s assets with strike price equal to the face value of debt.
To calculate the sensitivities, we increase firm volatility by 1%, which implies a 1%
increase in stock volatility. We use this new firm volatility to determine a new debt value. The
sensitivity of the debt to a change in firm volatility is the difference between this value and the
value at the lower firm volatility. From (7), equity increases by the magnitude of the decrease in
the debt value. Finally, we use the higher equity value and higher stock volatility to compute a
new value for stock and stock options following Schulz and Trautmann (1994). The difference
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between these stock and option values and those calculated in the first step is the sensitivity to
firm volatility for the stock and options.
2.1.2 Example of firm sensitivities
To give intuition for the foregoing relations, in Panel A of Table 1, we show the
sensitivities for an example firm. We use values that are approximately the median values of our
sample described below. The market value of assets is $2.5 billion and firm volatility is 35%.
Options are 7% of shares outstanding, and have a price-to-strike ratio of 1.35. The options and
the debt have a maturity of four years. Leverage is the face value of debt divided by the sum of
the book value of debt and market value of equity. To calculate the values and sensitivities, we
assume a risk-free rate of 2.25%, that the interest rate on debt is equal to the risk-free rate, and
that the firm pays no dividends.
The first set of rows shows the change in the value of firm debt, stock, and options for a
1% change in the standard deviation of the assets at various levels of leverage. An increase in
volatility reduces debt value, and this reduction is greater for greater leverage. This reduction in
debt value is shared between the stock and options. Options always benefit from increases in
volatility. When leverage is low, the sensitivity of debt to firm volatility is very low. Since there
is little debt to transfer value from, option holders gain at the expense of stockholders when
volatility increases. As leverage increases, the sensitivity of debt to firm volatility decreases. As
this happens, the stock sensitivity becomes positive as the stock offsets losses to options with
gains against the debt.
2.2
Managers’ incentives from the sensitivity of firm capital structure to firm volatility
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2.2.1
Total incentives to increase firm volatility
We now use the above results to derive measures of managerial incentives. A manager’s
(risk-neutral) incentives to increase volatility from a given security are equal to the security’s
sensitivity to firm volatility multiplied by the fraction owned by the manager. If the manager
owns α of the outstanding stock, β of the outstanding debt, and
options, the manager’s total
incentives to increase firm volatility are:
(8)
where
is the manager’s average per option sensitivity to firm volatility, computed to reflect
that employee options are warrants.
2.2.2
Vega incentives to increase stock volatility
Prior literature uses the vega, the sensitivity of managers’ option holdings to a change in
stock volatility, as a proxy for incentives to increase volatility (Guay, 1999; Core and Guay,
2002; Coles et al., 2006; Hayes et al., 2012). The vega is the change in the Black-Scholes option
value for a change in stock volatility:
(9)
(Here, we use the notation O to indicate that the option is valued using Black-Scholes, in contrast
to the notation W to indicate that the option is valued as a warrant.) Comparing the vega with the
total sensitivity in
(8), one can see that the vega is a subset of total risk-taking incentives. In
particular, it does not include incentives from debt and stock and does not account for the fact
that employee stock options are warrants. Inspection of the difference between
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(8)
and
(9)
reveals that for the vega to be similar to total risk-taking incentives, the firm must have low or no
leverage (so that the volatility increase causes little re-distribution from debt value to equity
value) and the firm must have low amounts of options (so that the volatility increase causes little
re-distribution from stock value to option value).
2.2.3
Relative incentives to increase volatility
Jensen and Meckling (1976) suggest a scaled measure of incentives: the ratio of risk-
reducing incentives to risk-increasing incentives. The ratio of risk-reducing to risk-increasing
incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option
incentives:
(10a)
From Panel A of Table 1, the sensitivity of stock to volatility can be negative when the firm has
options but little leverage. In this case the ratio of risk-reducing to risk-increasing incentives is:
(10b)
We term this ratio the “relative sensitivity ratio.” As in Jensen and Meckling, the ratio is
informative about whether the manager has net incentives to increase or decrease firm risk. It can
be useful to know whether risk-reducing incentives are greater than risk-increasing incentives
(that is, whether Eq. (8) is negative or positive, or equivalently whether the ratio in Eq. (10) is
greater or less than one). If the ratio in Eq. (10) is less than one, then the manager has more riskincreasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one.
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When the manager’s portfolio of debt, stock, and options mirrors the firm’s capital structure, the
ratio in (10) is one. Jensen and Meckling (1976) posit that a manager with such a portfolio
“would have no incentives whatsoever to reallocate wealth” between capital providers (p. 352)
by increasing the risk of the underlying assets.
If the firm has no employee options, the stock sensitivity is always positive and the
relative sensitivity ratio (10) becomes:
(11)
The first expression follows from (4):
, and the sensitivity of total debt value to
volatility divides off. The second equality follows from the definition of β and α as the
manager’s fractional holdings of debt and stock. An advantage of this ratio is that, if in fact the
firm has no employee options, one does not have to estimate the sensitivity of debt to volatility to
compute the ratio. Much prior literature (e.g., Anantharaman et al., 2011; Cassell et al., 2012;
Sundaram and Yermack, 2007; Tung and Wang, 2011; Wang et al., 2010, 2011) uses this
measure, and terms it the “relative leverage ratio,” as it compares the manager’s leverage to the
firm’s leverage. Since most firms have options in their capital structure, to operationalize the
relative leverage ratio, researchers make an ad hoc adjustment by adding the Black-Scholes value
of the options (O for the firm and
for the CEO) to the value of the firm’s stock and CEO’s
stock:
(12)
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Alternatively, Wei and Yermack (2011) make a different ad hoc adjustment for options by
converting the options into equivalent units of stock by multiplying the options by their BlackScholes delta
forthe irmand
fortheCEO :
(13)
That these adjustments for options are not correct may be seen by comparing the measures to the
correct relative sensitivity measure shown in (10), which uses the option sensitivity to firm
volatility. Equations (12) and (13), which instead use the option value and delta implicitly
assume that options are less sensitive to firm volatility then stock or debt. Only when the firm
has no employee options are the relative leverage and incentive ratios equal to the relative
sensitivity ratio.
However, it is important to note that scaling away the levels information contained in
(8) can lead to incorrect inference, even when calculated correctly. For example, imagine
two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 0.9.
Although they are otherwise identical, CEO A has risk-reducing incentives of -$900 and has
risk-increasing incentives of $1,000, while CEO B has risk-reducing incentives of -$90,000 and
has risk-increasing incentives of $100,000. The relative measure (0.9) scales away the
sensitivities and suggests that both CEOs make the same risk choices. However, CEO B is much
more likely to take risks: his wealth increases by $10,000 (1% of wealth) for each 1% increase in
firm volatility, while CEO A’s increases by only $100 (0.01% of wealth).
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2.2.4 Empirical estimation of CEO sensitivities
We calculate CEO sensitivities as weighted functions of the firm sensitivities. The CEO’s
debt and stock sensitivities are the CEO’s percentage ownership of debt and stock multiplied by
the firm sensitivities. We calculate the average strike price and maturity of the manager’s options
following Core and Guay (2002). We calculate the value of the CEO’s options following Schulz
and Trautmann (1994). Appendix A.5 provides details and notes the necessary Execucomp,
Compustat, and CRSP variable names.
Calculating the sensitivities requires a normalization for the partial derivatives.
Throughout this paper we report results using a 1% increase in firm volatility, which is
equivalent to a 1% increase in stock volatility. In other words, to calculate a sensitivity, we first
calculate a value using current volatility, then increase volatility by 1% and re-calculate the value.
The sensitivity is the difference in these values. Prior literature (e.g., Guay, 1999) calculates vega
using a 0.01 increase in stock volatility. The disadvantage of using a 0.01 increase in stock
volatility for our calculations is that it implies an increase in firm volatility that grows smaller
than 0.01 as firm leverage increases. So that the measures are directly comparable, we therefore
use a 1% increase in stock volatility to compute vega. The 1% vega is highly correlated (0.91)
with the 0.01 increase vega used in the prior literature, and all of our inferences in Tables 4, 6, 7,
and 8 below with the 1% vega are identical to those with the 0.01 increase vega.
2.2.5 Example of CEO sensitivities
In Panel B of Table 1, we illustrate how incentives to take risk vary with firm leverage
for an example CEO (of the example firm introduced above). The example CEO owns 2% of the
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firm’s debt, 2% of the firm’s stock, and 16% of the firm’s options. These percentages are similar
to the averages for our main sample described below.
Columns (2) to (4) show the sensitivities of the CEO’s debt, stock, and options to a 1%
change in firm volatility for various levels of leverage. As with the firm sensitivities, the
example CEO’s debt sensitivity decreases monotonically with leverage, while the sensitivities of
stock and options increase monotonically with leverage. Column (5) shows that the total equity
sensitivity, which is the sum of the stock and option sensitivities, increases sharply as the stock
sensitivity goes from being negative to positive. Column (6) shows the total sensitivity, which is
the sum of the debt, stock, and option sensitivities. These total risk-taking incentives increase
monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase
in the equity sensitivity.
Column (7) shows the vega for the example CEO. In contrast to the equity sensitivity and
the total sensitivity which both increase in leverage, the vega first increases and then decreases
with leverage in this example. Part of the reason is that the vega does not capture the debt and
stock sensitivities. Holding this aside, the vega does not measure well the sensitivity of the
option to firm volatility. It captures the fact that the option price is sensitive to stock volatility,
but it misses the fact that equity value benefits from decreases in debt value. As leverage
increases, the sensitivity of stock price to firm volatility increases dramatically (as shown by the
increasingly negative debt sensitivity), but this effect is omitted from the vega calculations.
Consequently, the vega is likely to be a good approximation of the CEO’s incentives to increase
risk when leverage is very low, but the approximation is much noisier as leverage increases.
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The final Columns (8) to (10) illustrate the various relative incentive measures. The
relative sensitivity measure in Column (8) is calculated following Eq. (10) as the negative of the
sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is
negative (as for the three lower leverage values) and as the negative of debt sensitivity divided
by the sum of the stock and option sensitivity otherwise. Thus, risk-reducing incentives are -$6
for the low-leverage firms and -$57 for the high-leverage firms. The risk-increasing incentives
are $46 for the low-leverage firms and $115 for the high-leverage firms. Accordingly, as
leverage increases, the relative sensitivity measure increases from 0.13 (= 6/46) to 0.50 (=
57/115), indicating that the CEO is more identified with debt holders (has fewer relative risktaking incentives). This inference that risk-taking incentives decline is the opposite of the
increase in risk-taking incentives shown in Column (6) for the total sensitivity and total
sensitivity as a percentage of total wealth. This example illustrates the point above that scaling
away the levels information contained in Eq.
(8) can lead to incorrect inference even
when the relative ratio is calculated correctly.
In columns (9) and (10) of the final rows, we illustrate how the relative leverage and
relative incentive ratios for our example CEO. The relative leverage ratio is computed by
dividing the CEO’s percentage debt ownership (2%) by the CEO’s ownership of total stock and
option value (roughly 2.4%). Because these value ratios do not change much with leverage, the
relative leverage ratio stays about 0.8, suggesting that the CEO is highly identified with debt
holders. The relative incentive ratio, which is similarly computed by dividing the CEO’s
percentage debt ownership (2%) by the CEO’s ownership of total stock and option delta (roughly
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2.8%), also shows high identification with debt holders and little change with leverage. Again,
this is inconsistent with the substantial increase in risk-taking incentives illustrated in Column (6)
for the total sensitivity. As noted above, these ratios only measure relative incentives correctly
when the firm has little or no options, and even a correctly calculated relative risk-taking ratio
can lead to incorrect inference. The incentive ratios are not informative about the magnitude of
the sensitivity of the manager’s wealth to an increase in firm volatility.
3.
Sample and Variable Construction
3.1
Sample Selection
We use two samples of Execucomp CEO data. Our main sample contains Execucomp
CEOs from 2006 to 2010, and our secondary sample, described in more detail in Section 4.4
below, contains Execucomp CEOs from 1994 to 2005.
The total incentive measures described above require information on CEO inside debt
(pensions and deferred compensation) and on firm options outstanding. Execucomp provides
information on inside debt only beginning in 2006 (when the SEC began to require detailed
disclosures). Our main sample therefore begins in 2006. The sample ends in 2010 because our
tests require one-year ahead data that is only available through 2011. Following Coles et al.
(2006) and Hayes et al. (2012), we remove financial firms (firms with SIC codes between 6000
and 6999) and utility firms (firms with SIC codes between 4900 and 4999). We identify an
executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in
office at the end of the year. If the firm has more than one CEO during the year, we choose the
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individual with the higher total pay. We merge the Execucomp data with data from Compustat
and CRSP. The resulting sample contains 5,967 CEO-year observations that have complete data.
3.2
Descriptive statistics – firm size, volatility, and leverage
Table 2, Panel A shows descriptive statistics for volatility, the market value of firm debt,
stock, and options, and leverage for the firms in our sample. We describe in Appendix A.3 how
we estimate firm market values following Eberhart (2005). To mitigate the effect of outliers, we
winsorize all variables each year at the 1st and 99th percentiles. Because our sample consists of
S&P 1500 firms, the firms are large and have moderate volatility. Most firms in the sample have
low leverage. The median value of leverage is 14%, and the mean is 19%. These low amounts of
leverage suggest low agency costs of asset substitution for most sample firms (Jensen and
Meckling, 1976).
3.3
Descriptive statistics – CEO incentive measures
Table 3, Panel A shows full sample descriptive statistics for the CEO incentive measures.
We detail in Appendix A how we calculate these sensitivities. As with the firm variables
described above, we winsorize all incentive variables each year at the 1st and 99th percentiles.2
The average CEO in our sample has some incentives from debt to decrease risk, but the
amount of these incentives is low. This is consistent with low leverage in the typical sample firm.
Nearly half of the CEOs have no debt incentives. The magnitude of the incentives from stock to
increase firm risk is also small for most managers, but there is substantial variation in these
2
Consequently, the averages in the table do not add, i.e., the average total sensitivity is not equal the sum of the
average debt sensitivity and average equity sensitivity.
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incentives, with a standard deviation of approximately $47 thousand as compared to $16
thousand for debt incentives. The average sensitivity of the CEO’s options to firm volatility is
much larger. The mean value of the total (debt, stock, and option) sensitivity is $65 thousand,
which indicates that a 1% increase in firm volatility provides the average CEO in our sample
with $65 thousand in additional wealth. The vega is smaller than the total sensitivity, and has
strictly positive values as compared to the total sensitivity which has about 8% negative values.3
While the level measures of the CEO’s incentives are useful, they are difficult to interpret
in cross-sectional comparisons of CEOs who have different amounts of wealth. Wealthier CEOs
will respond less to the same incentives if wealthier CEOs are less risk-averse.4 In this case, a
direct way to generate a measure of the strength of incentives across CEOs is to scale the level of
incentives by the CEO’s wealth. We estimate CEO total wealth as the sum of the value of the
CEO’s debt, stock, and option portfolio and wealth outside the firm.5 We use the measure of
CEO outside wealth developed by Dittmann and Maug (2007). 6 , 7 The average scaled total
sensitivity is 0.14% of wealth. The value is low because the sensitivities are calculated with
3
This vega is calculated for a 1% increase in stock volatility rather than the 0.01 increase used in prior literature to
make it comparable to the total sensitivity.
4
It is frequently assumed in the literature (e.g., Hall and Murphy, 2002; Lewellen, 2006; Conyon et al., 2011) that
CEOs have decreasing absolute risk aversion. 5
We value the options as warrants following Schulz and Trautmann (1994). This is consistent with how we
calculate the sensitivities of the CEOs’ portfolios.
6
To develop the proxy, Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth,
and then accumulates outside wealth from cash compensation and selling shares. Dittmann and Maug assume that
the CEO does not consume any of his outside wealth. The only reduction in outside wealth comes from using cash to
exercise his stock options and paying U.S. federal taxes. Dittmann and Maug claim that their proxy is the best
available given that managers’ preferences for saving and consumption are unobservable. We follow Dittmann and
Maug (2007) and set negative estimates of outside wealth to missing.
7
The wealth proxy is missing for approximately 13% of CEOs. For those CEOs, we impute outside wealth using a
model that predicts outside wealth as a function of CEO and firm characteristics. If we instead discard observations
with missing wealth, our inference below is the same. 19
respect to a 1% increase in firm volatility. If the average CEO increases firm volatility by one
standard deviation (19.9%), that CEO’s wealth increases by 7%. While some CEOs have net
incentives to decrease risk, these incentives are small. For the CEO at the first percentile of the
distribution who has large risk-reducing incentives, a one standard deviation decrease in firm
volatility increases the CEO’s wealth by 2%.
We present sample descriptive statistics sorted by leverage in Table 3, Panel B. We rank
the sample by leverage and divide it into five groups of 1,193 firm-years. The first set of rows
shows the sensitivity of the value of CEO’s debt, stock, and options for a 1% increase in firm
volatility at various levels of leverage.
The second set of rows show the mean sensitivity of the CEO’s debt, stock, and options
as a percentage of the CEO’s wealth. Since CEO wealth varies greatly, the percentage values are
more interpretable, and we concentrate our discussion on the values in these rows. Column (2)
shows that as leverage increases the mean of the CEOs’ debt sensitivity to firm volatility
decreases. Intuitively, the sensitivity of the firm’s debt decreases in leverage, so the sensitivity of
the CEO’s inside debt also decreases, holding percentage ownership constant. The mean stock
and option sensitivities in Columns (3) and (4) both increase with leverage. While the CEO’s
stock sensitivity is negative for low levels of leverage, the mean incentives from stock are very
small as a fraction of wealth. When leverage is high, the magnitude of the stock sensitivity is
much larger. CEOs’ option sensitivity also increases with leverage. Given the large increase in
equity sensitivity shown in Column (5), the CEOs’ total sensitivity to firm volatility in Column
(6) increases across leverage bins. By contrast, the vega in Column (7) has no relation with
20
leverage. The vega excludes one of the two channels that affect option sensitivity to firm
volatility: the stock-sensitivity channel. When leverage is high, the stock price responds strongly
to increases in firm volatility, changing the value of the stock options. Since the vega excludes
this channel, it is biased downwards when leverage is high.
3.4
Descriptive statistics – CEO relative incentive measures
Panel A shows that the mean (median) relative leverage ratio is 3.09 (0.18), and the mean
(median) relative incentive ratio is 2.31 (0.15). These values are similar to those in Cassell et al.
(2012), who also use an Execucomp sample. These ratios are skewed, and are approximately one
at the third quartile, suggesting that 25% of our sample CEOs have incentives to decrease risk.
This fraction is much larger than the 8% of CEOs with net incentives to reduce risk based on the
total sensitivity measure, and suggests a bias in the relative leverage and incentive measures. By
contrast, the mean (median) relative sensitivity ratio is 0.42 (0.03), suggesting low incentives to
decrease risk.
Panel B shows that the relative ratios (Columns (8) through (10) in the second set of rows)
all decrease in leverage, consistent with the increase in the total sensitivity in Column (6). The
mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins. This is
consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase
risk. For the 40% of firms with the lowest leverage, the relative leverage and incentive ratios are
much greater than one. These measures suggest that low leverage firms choose to strongly
identify their CEOs with their debt holders. However, these are the firms that have few agency
problems from debt, so there is little need to provide strong identification with debt holders. This
21
puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOs’
options to firm volatility.
3.5
Correlations – CEO incentive measures
Panel C of Table 3 shows Pearson correlations between the incentive measures. Focusing
first on the levels, the total sensitivity and vega are highly correlated (0.69). The total sensitivity
is almost perfectly correlated with the equity sensitivity (0.99). Since CEOs’ inside debt
sensitivity to firm volatility has a low variance, including debt sensitivity does not provide much
incremental information about CEOs’ incentives. The scaled total sensitivity and scaled vega are
also highly correlated (0.79), and the scaled total sensitivity is almost perfectly correlated with
the scaled equity sensitivity (0.98). The relative leverage and relative incentive ratios are almost
perfectly correlated (0.99). Because the correlation is so high, we do not include the relative
incentive ratio in our subsequent analyses.
4.
Associations of incentive measures with firm risk choices
4.1
Research Design
4.1.1
Unscaled incentive measures
We examine how the CEO’s incentives at time t are related to firm risk choices at time
t+1 using regressions of the following form:
Firm Risk Choice
Risk-taking Incentives
Delta
∑
Control
(14)
The form of the regression is similar to those in Guay (1999), Coles et al. (2006) and Hayes et al.
(2012).
22
Guay (1999, p. 46) shows that manager’s incentives to increase risk are positively related
to the sensitivity of wealth to volatility, but negatively related to the increase in the manager’s
risk premium that occurs when firm risk increases. Prior researchers examining vega (e.g.
Armstrong et al., 2013, p. 7) argue that “vega provides managers with an unambiguous incentive
to adopt risky projects,” and that this relation should manifest empirically so long as the
regression adequately controls for differences in the risk premiums. Delta (incentives to increase
stock price) is an important determinant of the manager’s risk premium. When a manager’s
wealth is more concentrated in firm stock, he or she is less diversified, and requires a greater risk
premium when firm risk increases. We control for the delta of the CEO’s equity portfolio
measured following Core and Guay (2002). We also control for cash compensation and CEO
tenure, which prior literature (Guay, 1999; Coles et al. 2006) uses as proxies for the CEO’s
outside wealth and risk aversion.
We use three proxies for firm risk choices: (1) ln(Stock Volatilityt+1) measured using
daily stock volatility over year t+1, (2) R&D Expenset+1 measured as the ratio of R&D expense
to total assets, and (3) Book Leveraget+1 measured as the book value of long-term debt to the
book value of assets. Like the prior literature, we consider ln(Stock Volatility) to be a summary
measure of the outcome of firm risk choices, R&D Expense to be a major input to increased risk
through investment risk, and Book Leverage to be a major input to increased risk through capital
structure risk. We measure all control variables at t and all risk choice variables at t+1. By doing
this, we hope to mitigate concerns about reverse causality.
23
Other control variables in these regressions follow Coles et al. (2006) and Hayes et al.
(2012). We control for firm size using ln(Sales), and for growth opportunities using Market-toBook. All regressions include year and 2-digit SIC industry fixed effects.
In the regression with ln(Stock Volatilityt+1), we also control for risk from past R&D
Expense and CAPEX and Book Leverage. In the regression with R&D Expense, we also control
for ln(Sales Growth) and Surplus Cash. In the regression with Book Leverage as the dependent
variable, we control for ROA, and follow Hayes et al. (2012) by controlling for PPE, the quartile
rank of a modified version of the Altman (1968) Z-score, and whether the firm has a long-term
issuer credit rating.
4.1.2
Scaled incentive measures
Prior literature identifies CEO wealth as an important determinant of CEO’s attitudes
toward risk. As noted above, the larger delta is relative to wealth, the greater the risk premium
the CEO demands. Likewise, the larger risk-taking incentives are relative to wealth, the more a
given risk increase will change the CEO’s wealth, and the greater the CEO’s motivation to
increase risk. To capture these effects more directly, we scale risk-taking incentives and delta by
wealth and control for wealth in the following alternative specification:
Firm Risk Choice
Risk-taking Incentives/wealth
Delta/wealth +
wealth +
Control
(15)
24
To enable comparison across the models, we include the same control variables in (15) as in (14)
above.
4.2
Association of level and scaled incentive measures with firm risk choices
Table 4, Panel A contains the Stock Volatility regressions. Vega in Column (1) has an
unexpected significant negative coefficient. This result is inconsistent with findings in Coles at al.
(2006) for 1992-2001. When we examine data from 1994-2005 in Section 4.4 below, however,
we find a positive coefficient on vega. This finding and findings in Hayes et al. (2012) are
consistent with changes in the cross-sectional relation between vega and risk-taking over time.
The coefficient on total sensitivity in Column (2) is positive but not significant. As noted above,
scaling the level of incentives by total wealth can provide a better cross-sectional measure of
CEOs’ incentives. The coefficients on both the scaled vega in Column (3) and the total
sensitivity in Column (4) are both positive, and the coefficient on scaled total sensitivity is
significant.
To evaluate the nonnested hypothesis that the scaled total sensitivity in Column (4) better
explains stock volatility than the scaled vega in Column (3), we test whether the adjusted R2 is
significantly greater using a Vuong test. This test compares the explanatory power of the
regressions (Vuong, 1989).8 We cluster the standard errors by firm and year (Barth, Gow, and
Taylor, 2012). This test (labeled Col. 3 = Col. 4 at the bottom of Panel A) rejects the scaled vega
8
The J-test is another widely-used test of nonnested hypotheses. In contrast to the J-test, the Vuong test is preferable
because it compares the specifications directly without embedding one model in the other (Greene, 2008, p. 139).
25
in favor of the scaled total sensitivity (p-value < 0.01). A similar test (labeled Col. 2 = Col. 4)
rejects the level of total sensitivity in favor of the scaled total sensitivity (p-value < 0.01).
In contrast, in Panel B all four measures have positive and significant relations with R&D
Expense, consistent with the prediction that greater risk-taking incentives lead to more R&D. In
this instance, vega has significantly higher explanatory power than the total sensitivity (p-values
< 0.01). Again, the scaled measures do a better job of explaining R&D Expense than the level
measures (p-values < 0.02).
In Panel C, vega is unexpectedly negatively related to Book Leverage. The total
sensitivity, however, is positively related to leverage. We note that the total sensitivity is a noisy
measure of incentives to increase leverage. An increase in leverage does not affect asset
volatility, but does increase stock volatility. The total sensitivity therefore is only correlated with
a leverage increase through components sensitive to stock volatility (options and the warrant
effect of options on stock), but not through components sensitive to asset volatility (debt and the
debt effect on equity).9 The scaled measures are both positively and significantly associated with
leverage. Consistent with Panel A, using the scaled total sensitivity rather than the scaled vega
improves the explanatory power (p-value < 0.01).
9
Similar to Lewellen (2006), we also calculate a direct measure of the sensitivity of the manager’s portfolio to a
leverage increase. To do this, we assume that leverage increases because 1% of the asset value is used to repurchase
equity. The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from
the repurchase. The CEO does not sell stock or options. The sensitivity of the manager’s portfolio to the increase in
leverage has a 0.67 correlation with the total sensitivity. The sensitivity to increases in leverage has a significantly
higher association with book leverage than the total sensitivity. However, there is not a significant difference in the
association when both measures are scaled by wealth.
26
Based on Table 4, the total sensitivity scaled by wealth is positively related to each of the
risk variables. The specification that includes scaled total sensitivity also provides the most
explanatory power for most of the firm risk variables. In summary, scaling the incentive
variables and including wealth significantly improves the specification, and using the scaled total
sensitivity rather than the scaled vega improves the explanatory power further.
4.3
Association of relative ratios with firm risk choices
The preceding section compares the total sensitivity to vega. In this section, we compare
the scaled total sensitivity to the relative leverage ratio. 10 The regression specifications are
identical to Table 4. These specifications are similar to, but not identical to, those of Cassell et al.
(2012).11 Because our main interest is the incentive variables, the only controls we tabulate are
wealth and delta scaled by wealth.
The relative leverage ratio has two shortcomings as a regressor. First, it is not defined for
firms with no debt or for CEOs with no equity incentives, so our largest sample in Table 5 is
4,994 firm-years as opposed to 5,967 in Table 4. Second, as noted above and in Cassell et al.
(2012), when the CEOs’ inside debt is large relative to firm debt, the ratio takes on very large
values. As one way of addressing this problem, we trim extremely large values by winsorizing
10
Again, because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio, results
with the relative incentive ratio are virtually identical, and therefore we do not tabulate those results.
11
An important difference is in the control for delta. We include delta scaled by wealth in our regressions as a proxy
for risk aversion, and find it to be highly negatively associated with risk-taking as predicted. Cassell et al. (2012)
include delta as part of a composite variable that combines delta, vega, and the CEO’s debt equity ratio. They find
inconsistent signs and little significance with the variable.
27
the ratio at the 90th percentile.12 We present results for the subsample where the relative leverage
ratio is defined in Columns (1) and (2) of each panel. As another way of addressing this problem,
Cassell et al. (2012) use the natural logarithm of the ratio; this solution (which eliminates CEOs
with no inside debt) results in a further reduction in sample size to a maximum of 3,329. We
present results for the subsample where ln(Relative Leverage) is defined in Columns (3) and (4)
of each panel. Note that the total sensitivity measure is defined more often than the relative
leverage ratio or its natural logarithm. The total sensitivity measure could be used to study
manager’s incentives in a broader sample of firms than the relative ratios.
In Panel A, the relative leverage ratio is negatively related to stock volatility, which is
consistent with CEOs talking less risk when they are more identified with debt holders, but the
relation is not significant. Scaled total sensitivity is significantly related to stock volatility in this
subsample. In addition, this regression has a higher adjusted R2 (p-value: 0.01). In this subsample,
both the logarithm of the relative leverage ratio and the scaled total sensitivity are significantly
related to stock volatility. However, in the restricted subsample, the explanatory power of the
logarithm of the relative leverage ratio and the scaled total sensitivity are not significantly
different.
In Panel B when R&D expense is the dependent variable, the relative leverage ratio is
again insignificant in Column (1), while the scaled total sensitivity is significantly related to
R&D expense in the larger subsample in Column (2). In addition, this regression has a higher
12
If instead we winsorize the relative leverage ratio at the 99th percentile, it is not significant in any specification.
28
adjusted R2 (p-value: 0.02). In the smaller subsample, the coefficient of the logarithm of the
relative leverage ratio has the expected negative sign, but the adjusted R2 is significantly lower
than that of the model using the scaled total sensitivity (p-value: 0.02).
All of the incentive measures are significantly related to leverage in the expected
direction (Panel C). In the larger subsample, the scaled sensitivity measure has significantly
higher explanatory power than the relative leverage ratio. In the smaller subsample, the
specification using the natural logarithm of the relative leverage ratio has an insignificantly
higher adjusted R2 than that using the scaled total sensitivity.
Overall, the results in Table 5 indicate that the scaled total sensitivity measure better
explains risk-taking choices than the relative leverage ratio. However, there is only weak
evidence that the scaled total sensitivity measure better explains risk-taking than the logarithm of
the relative leverage ratio for the smaller subsample where the latter is defined.
4.4
Association of vega and equity sensitivity with firm risk choices – 1994-2005
On the whole, Tables 4 and 5 suggest that the total sensitivity measure better explains
future firm risk choices than either vega or the relative leverage ratio. Our inference, however, is
limited by the fact that we can only compute the total sensitivity measure beginning in 2006
when data on inside debt become available. In addition, our 2006-2010 sample period contains
the financial crisis, a time unusual of shocks to returns and to return volatility, which may have
affected both incentives and risk-taking.
In this section, we attempt to mitigate these concerns by creating a sample with a longer
time-series from 1994 to 2005 that is more comparable to the samples in Coles et al. (2006) and
29
Hayes et al. (2012). To create this larger sample, we drop the requirement that data be available
on inside debt. Recall from Table 3 that most CEOs have very low incentives from inside debt,
and that the equity sensitivity and total sensitivity are highly correlated (0.99). Consequently, we
compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as
the total sensitivity minus the debt sensitivity).
Although calculating the equity sensitivity does not require data on inside debt, it does
require data on firm options outstanding, and this variable was not widely available on
Compustat before 2004. We supplement Compustat data on firm options with data handcollected by Core and Guay (2001), Bergman and Jentner (2007), and Blouin, Core, and Guay
(2010). We are able to calculate the equity sensitivity for 10,048 firms from 1994-2005. The
sample is about 61% of the sample size we would obtain if we used the broader sample from
1992-2005 for which we can calculate the CEO’s vega.
In Table 6, we repeat our analysis in Table 4 for this earlier period using the equity
sensitivity in place of total sensitivity. Column (1) compares the explanatory power of vega to
that our sensitivity measure in Column (2). Vega has a positive sign but is insignificant, while
the equity sensitivity is positive and significant. The equity sensitivity provides a small, but
statistically significant, increase in explanatory power. Similarly, the scaled vega provides less
explanatory power than the scaled equity sensitivity (p-value < 0.01).
When R&D expense is the dependent variable, the results are similar to those in Table 4
for our main sample. While the equity sensitivity and scaled equity sensitivity both have positive
30
and significant coefficients, they explain R&D expense less well than vega and scaled vega.
However, most of these differences are not significant.
As in Table 4, Panel C, vega has a significantly negative relation with book leverage in
this sample. These regressions include controls based on Hayes et al. (2012), and the results
therefore are not directly comparable to the Coles et al. (2006) findings. The adjusted R2 is
higher using equity sensitivity (p-value: 0.02), which has a positive and significant coefficient.
The scaled equity sensitivity has a positive and significant coefficient, and has higher
explanatory power for book leverage than either scaled vega (p-value < 0.01) of the unscaled
equity sensitivity (p-value < 0.01). The results in Table 6 suggest that our inferences from our
later sample hold in the earlier period 1994-2005 as well.
4.5
Changes in vega and equity sensitivity and changes in firm risk choices
A concern about our prior results is that incentives are endogenous and the results may
reflect reverse causality rather than incentives influencing risk choices. Instrumental variables
approaches can mitigate endogeneity concerns, but it is difficult to identify variables that affect
incentives but do not affect policy choices (e.g., Gormley et al., 2013). An alternative is to
identify an environmental change that affects incentives but not risk-taking. Hayes et al. (2012)
use a change in accounting standards, which required firms to recognize compensation expense
for employee stock options beginning in December 2005. Firms responded to this accounting
expense by granting fewer options. Hayes et al. (2012) argue that if the convex payoffs of stock
options cause risk-taking, this reduction in convexity should lead to a decrease in risk-taking.
They do not find evidence that the change in incentives led to a reduction in firm risk-taking.
31
This finding is interesting and could lead to the conclusion that changes in convexity do not lead
to changes in risk-taking. Within the context of our study, however, an alternative explanation is
that vega is a noisy measure of risk-taking incentives, and that changes in vega may not detect a
relation between convexity and risk-taking. We briefly examine this alternative in this section.
We follow Hayes et al. (2012) and estimate Eq. (15) using changes in the mean value of
the variables from 2002 to 2004 and the mean value of the variables from 2005 to 2008. (For
dependent variables, we use changes in the mean value of the variables from 2003 to 2005 and
2006 to 2009.) We use all available firm-years to calculate the mean and require at least one
observation per firm in both the 2002-2004 and 2005-2008 periods.
Table 7 shows the results of these regressions. Similar to Hayes et al. (2012), in Column
(1) we find that the change in vega is negatively, but not significantly, related to the change in
stock volatility (Panel A). The change in equity sensitivity also has a negative and insignificant
coefficient. When we examine instead the scaled measures, the scaled vega is negatively, but not
significantly, related to the change in stock volatility. In contrast, the change in scaled equity
sensitivity in Column (4) is significantly positively related to the change in stock volatility.
None of the incentive measures, however, is associated with the change in R&D expense
in Panel B.
In Panel C, the change in vega is negatively, but not significantly, related to the change in
stock volatility. (Hayes et al. find a significant negative relation.) Both the equity sensitivity and
the scaled equity sensitivity is significantly positively related to the change in book leverage and
have higher explanatory power than the corresponding vega measures (p-values < 0.04). Overall,
32
we find some evidence that changes in the scaled equity sensitivity are related to changes in firm
risk.
4.6
Robustness tests
Our estimate of the total sensitivity to firm volatility depends on our estimate of the debt
sensitivity. As Wei and Yermack discuss (2011, p. 3826-3827), estimating the debt sensitivity
can be difficult in a sample where most firms are not financially distressed, and therefore
estimates of small quantities may contain substantial measurement error. To address this concern,
we attempt to reduce measurement error in the estimates by using the mean estimate for a group
of similar firms. To do this, we note that leverage and stock volatility are the primary observable
determinants of the debt sensitivity. We therefore sort firms each year into ten groups based on
leverage, and then sort each leverage group into ten groups based on stock volatility. For each
leverage-volatility-year group, we calculate the mean sensitivity as a percentage of the book
value of debt. We then calculate the debt sensitivity for each firm-year as the product of the
mean percentage sensitivity of the leverage-volatility-year group multiplied by the total book
value of debt. We use this estimate to generate the sensitivities of the CEO’s debt, stock, and
options. We then re-estimate our results in Tables 4, 5, and 6. Our inferences are the same after
attempting to mitigate measurement error in this way.
We examine incentives from CEOs’ holdings of debt, stock, and options. CEOs’ future
pay can also provide risk incentives, but the direction and magnitude of these incentives are less
clear. On the one hand, future CEO pay is strongly related to current stock returns (Boschen and
Smith, 1995), and CEO career concerns lead to identification with shareholders. On the other
33
hand, future pay, and in particular cash pay, arguably is like inside debt in that it is only valuable
to the CEO when the firm is solvent. Therefore the expected present value of future cash pay can
provide risk-reducing incentives (e.g., John and John, 1993; Cassell et al., 2012). By this
argument, inside debt should include future cash pay as well as pensions and deferred
compensation.13 To evaluate the sensitivity of our results, we estimate the present value of the
CEO’s debt claim from future cash pay as current cash pay multiplied by the expected number of
years before the CEO terminates. Our calculations follow those detailed in Cassell et al. (2012).
We add this estimate of the CEO’s debt claim from future cash pay to inside debt, and
recalculate the relative leverage ratio and the debt sensitivity. Adding future cash pay
approximately doubles the risk-reducing incentives of the average manager. Because riskreducing incentives, however, remain small in comparison to risk-increasing incentives, our
inferences remain unchanged.
Finally, our sensitivity estimates do not include options embedded in convertible
securities. While we can identify the amount of convertibles, the number of shares issuable upon
conversion is typically not available on Compustat. Because the parameters necessary to estimate
the sensitivities are not available, we repeat our tests excluding firms with convertible securities.
To do this, we exclude firms that report convertible debt or preferred stock. In our main
(secondary) sample, 21% (26%) of all firms have convertibles. When we exclude these firms,
our inferences from Tables 4, 5, and 6 are unchanged.
13
Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and
therefore provides less risk-reducing incentives.
34
5.
Conclusion
We measure the total sensitivity of managers’ debt, stock, and option holdings to changes
in firm volatility. Our measure incorporates the incentives from debt and stock and values
options as warrants. We examine the relation between our measure of incentives and firm risk
choices, and compare the results using our measure and those obtained with vega and the relative
leverage ratio used in the prior literature. Our measure explains risk choices better than the
measures used in the prior literature. When we scale the incentive measure by a proxy for total
wealth, we find that using the scaled measure better explains firm risk. We also calculate an
equity sensitivity that ignores debt incentives, and find that it is 99% correlated with the total
sensitivity. While we can only calculate the total sensitivity beginning in 2006, when we
examine the equity sensitivity over an earlier 1994-2005 period, we find consistent results. Our
measure should be useful for future research on managers’ risk choices.
35
Appendix A: Measurement of firm and manager sensitivities
(names in italics are Compustat variable names)
A.1
Value and sensitivities of employee options
We value employee options using the Black-Scholes model modified for warrant pricing by
Galai and Schneller (1978). To value options as warrants W, the firm’s options are priced as a
call on an identical firm with no options:
∗
∗
∗
We simultaneously solve for the price ∗ and volatility
(A3) following Schulz and Trautmann (1994):
∗
1
∗
∗
∗
∗
of the identical firm using (A2) and
∗
∗
∗
(A1)
∗
∗
(A2)
(A3)
Where:
P = stock price
∗
= share price of identical firm with no options outstanding
= stock-return volatility (calculated as monthly volatility for 60 months, with a minimum of
12 months)
=
return
volatility of identical firm with no options outstanding
∗
q = options outstanding / shares outstanding (optosey / csho)
δ = natural logarithm of the dividend yield (dvpsx_f / prcc_f)
= time to maturity of the option
N = cumulative probability function for the normal distribution
∗
ln ∗ /
∗ / ∗
X = exercise price of the option
r = natural logarithm of the risk-free interest rate
The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the
option is just in-the-money and the firm is close to default (Crouhy and Galai, 1994). Since
leverage ratios for our sample are low (see Table 2), bankruptcy probabilities are also low, and
the approximation should be reasonable.
36
A.2
Value of firm equity
We assume the firm’s total equity value E (stock and stock options) is priced as a call on the
firm’s assets:
∗
´
´
(A4)
Where:
∗
∗
´
(A5)
V = firm value
∗
= share price of identical firm with no options outstanding (calculated above)
n = shares outstanding (csho)
∗ = return volatility of identical firm with no options outstanding (calculated above)
. ∗
. ∗
= time to debt maturity,
, following Eberhart (2005)
N = cumulative density function for the normal distribution
´
ln /
/
F = the future value of the firm’s debt including interest, i.e., (dlc + dltt)
, adjusted
following Campbell et al. (2008) for firms with no long-term debt
= the natural logarithm of the interest rate on the firm’s debt, i.e. ln 1
. We
winsorize the interest to have a minimum equal to the risk-free rate, r, and a
maximum equal to 15%.
A.3
Values of firm stock, options and debt
We then estimate the value of the firm’s assets by simultaneously solving (A4) and (A5) for V
and . We calculate the Black-Scholes-Merton value of debt as
1
´
´
(A6)
The market value of stock is the stock price P (prcc_f) times shares outstanding (csho).
To value total options outstanding, we multiply options outstanding (optosey) by the warrant
value W estimated using (A1) above. Because we do not have data on individual option tranches,
we assume that the options are a single grant with weighted-average exercise price (optprcey).
37
We follow prior literature (Cassell et al., 2012; Wei and Yermack, 2011) and assume that the
time to maturity of these options is four years.
A.4
Sensitivities of firm stock, options and debt to a 1% increase in volatility
We increase stock volatility by 1%:
1.01. This also implies a 1% increase in firm
volatility. We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V
and the new firm volatility, . The sensitivity of debt is then ´
.
The new equity value is the old equity value ( ∗ ) plus the change in debt value (
´). Using
this equity value and , we solve (A2) and (A3) for a new P and ∗ . The stock sensitivity is
´
. The option sensitivity is difference between the option prices calculated in (A1) using
the two sets of equity and ∗ values:
´
.
A.5.1 Sensitivities of CEO stock options, debt, and stock
The CEO’s stock sensitivity is the CEO’s percentage ownership of stock multiplied by the firm’s
stock sensitivity shown in Appendix A.4 above.
´
(A7)
Where:
is the CEO’s ownership of stock shares (shrown_excl_opts) divided by firm shares
outstanding (csho).
Similarly, the CEO’s debt sensitivity is
´
(A8)
Where:
follows Cassell et al. (2012), and is the CEO’s ownership inside debt (pension_value_tot
plus defer_balance_tot) divided by firm debt (dlc plus dltt).
Following Core and Guay (2002), we value the CEO’s option portfolio as one grant of
exercisable options with an assumed maturity of 6 years and as one grant of unexercisable
options with an assumed maturity of 9 years.
The CEO’s option sensitivity is the difference between the values of the CEO’s option portfolio
calculated using these parameters and the equity and ∗ values from above.
38
´
∗
(A9)
A.5.2 Vega and delta
We follow the prior literature and compute vega and delta using the Black-Scholes-Merton
formula to value options:
∗
(A10)
Where:
is the number of options in the CEO’s portfolio.
, X, and
follow the Core and Guay (2002) assumptions about option tranches and
option maturities (in general that unexercisable options have a maturity of 9 years and that
exercisable options have a maturity of 6 years).
To make our calculation of vega comparable to the total sensitivity, we calculate vega as the
difference between the standard Black-Scholes-Merton value in (A10) at and .
Using the derivative of the Black-Scholes-Merton equation (A10), the sensitivity of an option to
a change in the price is:
(A11)
The sensitivity of the CEO’s stock and option portfolio to a 1% increase in stock price (the
“delta”) is:
∗
∗ 0.01 ∗
∗ 0.01 ∗
(A12)
A.5.3 Relative sensitivity ratio
If the sensitivity of stock price to volatility is positive, the ratio is:
(A13a)
If the sensitivity of stock price to volatility is negative, the ratio is:
(A13b)
39
A.5.4 Relative leverage ratio
Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEO’s
percentage debt holdings divided by the CEO’s percentage equity holdings.
(A14)
Where:
= sum of the value of the CEO’s stock holding and the Black-Scholes value
of the CEO’s option portfolio calculated from (A10) following Core and Guay (2002)
= sum of the market value of stock and the Black-Scholes value of options
calculated according to (A10) above using the firm parameters from Appendix A.3.
A.5.5 Relative incentive ratio
Following Wei and Yermack (2011), the relative incentive ratio is the ratio of the CEO’s
percentage debt holdings divided by the CEO’s percentage holdings of delta.
(A15)
Where:
= sum of the delta of the CEO’s stock holding and the Black-Scholes delta of the
CEO’s option portfolio as in (A12), calculated following Core and Guay (2002)
= sum of the number of shares outstanding and the delta of the options calculated
according to (A12) above using the firm parameters from Appendix A.3
40
Appendix B: Measurement of Other Variables
The measurement of other variables, with the exception of No State Tax, is based on compensation data in
Execucomp, financial statement data in Compustat, and stock market data from the Center for Research in Security
Prices (CRSP) database.
ln(Stock Volatility)
R&D Expense
Market-to-Book
Book Leverage
Cash Compensation
ln(Sales)
ln(Sales Growth)
CEO Tenure
CAPEX
Liquidity Constraint
Return
Cash Surplus
ROA
PPE
Modified Z-Score
Rating
The natural logarithm of the variance of daily stock returns over
the fiscal year
The ratio of the maximum of zero and R&D expense (xrd) to total
assets (at)
The ratio of total assets (at) minus common equity (ceq) plus the
market value of equity (prcc_f * csho) to total assets
The ratio of long-term debt (dlc + dltt) to total assets (at)
The sum of salary (salary) and bonus compensation (bonus)
The natural logarithm of total revenue (revt)
The natural logarithm of the quantity total revenue in year t (revtt)
divided by sales in year t-1 (revtt-1)
The tenure of the executive as CEO through year t
The ratio of capital expenditures (capx) less sales of property,
plant, and equipment (sppe) to total assets (at)
An indicator variable set to one if the firm generates negative cash
flow from operations, and zero otherwise
The stock return over the fiscal year
The ratio of net cash flow from operations (oancf) less
depreciation (dpc) plus R&D expense (xrd) to total assets (at).
If depreciation expense is missing (dpc), and if PPE is less than
1% of total assets, we set depreciation expense to zero.
The ratio of operating income before depreciation (oibdp) to total
assets (at)
The ratio of net property, plant, and equipment (ppent) to total
assets (at)
The quartile rank by year of the modified Altman (1968) Z-Score:
3.3 * oiadp / at + 1.2 * (act – lct) / at + sale / at + 1.4 * re / at
An indicator variable set to one when the firm has a long-term
issuer credit rating from S&P
41
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44
Table 1
Panel A: Entire firm -- Sensitivity of debt, stock, and options to firm volatility holding the firm constant ($ Thousands)
The example firm has a $2.5 billion market value of assets and a firm volatility of 35%. Options are 7% of shares outstanding, and have a price-to-strike ratio of
1.4. The options and the debt have a maturity of four years. Leverage is the face value of debt divided by the market value of assets. All values and sensitivities
are calculated using Black-Scholes formulas assuming an interest rate of 2.5% and no dividends. Options are valued as warrants following Schulz and Trautmann
(1994). The debt, stock, and option sensitivity is the dollar change in value for a 1% increase in firm volatility. The equity sensitivity is the total stock and option
sensitivity.
Leverage
(1)
0.01%
4%
14%
25%
50%
Debt
Sensitivity
(2)
$
0
$
0
($ 49)
($ 471)
($2,856)
Stock
Sensitivity
(3)
($ 287)
($ 290)
($ 247)
$ 154
$ 2,441
Option
Sensitivity
(4)
$ 287
$ 290
$ 296
$ 317
$ 415
Equity
Sensitivity
(5)
$
0
$
0
$ 49
$ 471
$ 2,856
Leverage
(1)
0.01%
4%
14%
25%
50%
Debt Sens. /
Debt Value
(2)
0.00%
0.00%
-0.01%
-0.08%
-0.25%
Stock Sens. /
Stock Value
(3)
-0.01%
-0.01%
-0.01%
0.01%
0.19%
Option Sens. /
Option Value
(4)
0.40%
0.42%
0.45%
0.52%
0.84%
Equity Sens. /
Equity Value
(5)
0.00%
0.00%
0.00%
0.03%
0.21%
45
Panel B: CEO
The example CEO owns 2% of the firm’s debt, 2% of the firm’s stock, and 16% of the firm’s options. The CEO’s debt and stock sensitivity is the CEO’s
percentage holding times the firm sensitivity from Panel A. Vega is the sensitivity of the CEO’s option portfolio to a 1% increase in stock volatility. The relative
leverage ratio is the CEO’s percentage debt holdings divided by divided by the CEO’s percentage holdings of equity value. The relative incentive ratio is the
ratio of the CEO’s percentage debt holdings divided by the CEO’s percentage holdings of delta. The relative sensitivity ratio is the ratio the manager’s riskreducing incentives to his risk-taking incentives. See Appendix A for detailed definitions of the incentive variables.
Leverage
Debt
Sensitivity
Stock
Sensitivity
Option
Sensitivity
Equity
Sensitivity
Total
Sensitivity
Vega
(1)
0.01%
4%
14%
25%
50%
(2)
$ 0
$ 0
($ 1)
($ 9)
($57)
(3)
($ 6)
($ 6)
($ 5)
$ 3
$ 49
(4)
$ 46
$ 46
$ 47
$ 51
$ 66
(5)
$ 40
$ 41
$ 42
$ 54
$ 115
(6)
$ 40
$ 41
$ 41
$ 44
$ 58
(7)
$ 49
$ 49
$ 50
$ 50
$ 44
46
Relative
Sensitivity
Ratio
(8)
0.13
0.13
0.13
0.18
0.50
Relative
Leverage
Ratio
(9)
0.83
0.83
0.82
0.82
0.80
Relative
Incentive
Ratio
(10)
0.72
0.73
0.73
0.73
0.72
Table 2
Sample description
This table provides firm descriptive statistics (Panel A), and sample distribution by leverage (Panel B). The primary sample consists of 5,967firm-year
observations from 2006 to 2010, representing 1,574 unique firms. Dollar amounts are in millions of dollars. We estimate the volatility of asset returns following
Eberhart (2005). The market value of debt is calculated as the Black-Scholes-Merton option value of the debt. Employee options are valued as warrants following
Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years.
The market value of assets is the sum of market value of stock, the market value of debt, and the warrant value of employee options. All variables are winsorized
by year at the 1% tails
Panel A: Sample descriptive statistics
Variable
Volatility of Stock Returns
Volatility of Asset Returns
Market Value of Stock
Market Value of Debt
Market Value of Employee Options
Market Value of Assets
Leverage (Book Value of Debt/Market Value of Assets)
$
$
$
$
Mean
0.482
0.395
6,944
1,501
119
8,879
0.179
47
Std. Dev.
0.235
0.199
$ 18,108
$ 3,491
$
287
$ 22,102
0.186
P1
0.163
0.116
$ 50
$ 0
$ 0
$ 72
0.000
Q1
0.318
0.252
$ 568
$ 18
$ 9
$ 738
0.017
Median
0.426
0.355
$ 1,488
$ 259
$
30
$ 2,000
0.133
Q3
0.583
0.485
$ 4,599
$ 1,155
$
95
$ 6,378
0.273
P99
1.330
1.077
$ 117,613
$ 20,703
$ 1,682
$ 145,591
0.807
Table 3
Descriptive statistics for incentive variables ($ Thousands)
The debt, stock, and option sensitivity is the dollar change in value of the CEOs’ holdings for a 1% increase in firm volatility. The equity sensitivity is the sum of
the stock and option sensitivities. The total sensitivity is the sum of the debt, stock, and option sensitivities. Vega is the sensitivity of the CEOs’ option portfolios
to a 1% increase in stock volatility. Total wealth is the sum of the CEOs’ debt, stock, and option holdings and outside wealth from Dittmann and Maug (2007).
The relative sensitivity ratio is the ratio the manager’s risk-reducing incentives to his risk-taking incentives. The relative leverage ratio is the CEO’s percentage
debt holdings divided by divided by the CEO’s percentage holdings of equity value. The relative incentive ratio is the ratio of the CEO’s percentage debt
holdings divided by the CEO’s percentage holdings of delta. See Appendix A for detailed definitions of the incentive variables. All variables are winsorized by
year at the 1% tails. All dollar values are in thousands of dollars.
Panel A: Full sample
This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample.
Variable
Mean
Debt Sensitivity
($
5.20)
Stock Sensitivity
$ 10.45
Option Sensitivity
$ 57.77
Equity Sensitivity
$ 71.98
Total Sensitivity
$ 65.40
Vega
$ 49.15
Total Wealth
$ 102,027
Equity Sensitivity / Total Wealth
0.15%
Total Sensitivity / Total Wealth
0.14%
Vega / Total Wealth
0.11%
Relative Sensitivity Ratio
0.42
Relative Leverage Ratio
3.09
Relative Incentive Ratio
2.31
Std. Dev.
$ 15.50
$ 46.57
$ 83.02
$ 125.42
$ 115.62
$ 71.01
$ 256,672
0.15%
0.14%
0.10%
1.00
15.73
11.19
P1
Q1 Median
Q3
P99
($ 93.78) ($ 2.00) ($ 0.00) $ 0.00 $
0.00
($ 40.70) ($ 0.49) $ 0.00 $ 4.55 $
290.60
$ 0.00 $ 8.75 $ 27.42 $ 68.74 $
399.07
($ 11.99) $ 10.65 $ 31.84 $ 80.59 $
758.17
($ 32.96) $ 8.78 $ 28.19 $ 74.57 $
675.63
$ 0.00 $ 7.30 $ 22.92 $ 59.39 $
344.45
$ 1,294 $ 13,967 $ 32,806 $ 80,671 $ 1,729,458
0.00%
0.04%
0.12%
0.22%
0.64%
-0.03%
0.03%
0.10%
0.21%
0.63%
0.00%
0.03%
0.08%
0.17%
0.43%
0.00
0.01
0.03
0.19
4.44
0.00
0.00
0.18
1.18
67.99
0.00
0.00
0.15
0.91
48.44
48
Panel B: Descriptive statistics for incentive variables -- sorted by firm leverage
The firms are ranked by leverage and divided into five groups of 1,193 firm-years. Values shown are means within each leverage group.
Debt
Sensitivity
(2)
($ 0)
($ 1)
($ 5)
($ 9)
($11)
Stock
Sensitivity
(3)
($ 4)
($ 2)
$ 4
$ 14
$ 40
Option
Sensitivity
(4)
$ 31
$ 52
$ 65
$ 65
$ 76
Equity
Sensitivity
(5)
$ 28
$ 50
$ 70
$ 86
$ 126
Total
Sensitivity
(6)
$ 27
$ 49
$ 64
$ 75
$ 111
Leverage
Debt Sens. /
Tot. Wealth
Stock Sens. /
Tot. Wealth
Opt. Sens. /
Tot. Wealth
Eq. Sens. /
Tot. Wealth
Tot. Sens. /
Tot. Wealth
Vega /
Tot. Wealth
(1)
0.0%-0.2%
0.2%-8.7%
8.7%-18.6%
18.7%-33.0%
33.0%-87.4%
(2)
0.00%
0.00%
-0.01%
-0.02%
-0.03%
(3)
-0.01%
0.00%
0.01%
0.02%
0.08%
(4)
0.11%
0.10%
0.11%
0.15%
0.20%
(5)
0.10%
0.10%
0.12%
0.17%
0.28%
(6)
0.10%
0.10%
0.11%
0.15%
0.25%
(7)
0.12%
0.10%
0.11%
0.12%
0.11%
Leverage
(1)
0.0%-0.2%
0.2%-8.7%
8.7%-18.6%
18.7%-33.0%
33.0%-87.4%
49
Vega
(7)
$ 34
$ 54
$ 62
$ 53
$ 42
CEO
Wealth
(8)
$ 93,950
$ 133,911
$ 111,195
$ 95,209
$ 75,850
Relative
Sensitivity
Ratio
(8)
0.59
0.38
0.22
0.20
0.18
Relative
Leverage
Ratio
(9)
27.07
4.85
1.50
0.92
0.40
Relative
Incentive
Ratio
(10)
19.95
3.68
1.10
0.69
0.32
Panel C: Correlation between Incentive Measures
This table shows Pearson correlation coefficients for the incentive measures. See Appendix A for detailed definitions of the incentive variables. Coefficients
greater than 0.03 in magnitude are significant at the 0.05 level.
Total
Sens.
Total Sensitivity to Firm Volatility
Vega
Equity Sensitivity to Firm Volatility
Total Wealth
Total Sensitivity / Total Wealth
Vega / Total Wealth
Equity Sensitivity / Total Wealth
Relative Leverage Ratio
Relative Incentive Ratio
Relative Sensitivity Ratio
1.00
0.69
0.99
0.38
0.24
0.10
0.23
-0.04
-0.05
-0.16
Vega
1.00
0.68
0.28
0.15
0.24
0.15
0.00
-0.01
-0.23
Equity
Sens.
Tot.
Wealth
Tot. Sens. /
Tot. Wealth
Vega /
Tot. Wealth
Eq. Sens. /
Tot. Wealth
Rel.
Lev.
Rel.
Incent.
Rel.
Sens.
1.00
0.38
0.22
0.09
0.23
-0.04
-0.05
-0.13
1.00
-0.21
-0.24
-0.23
-0.02
-0.02
0.14
1.00
0.79
0.98
-0.10
-0.11
-0.32
1.00
0.77
-0.04
-0.05
-0.37
1.00
-0.10
-0.11
-0.29
1.00
0.99
0.01
1.00
0.03
1.00
50
Table 4
Comparison of the association between vega and total sensitivity and future volatility, R&D,
and leverage
This table presents OLS regression results using ln(Stock Volatility) (Panel A), R&D Expense (Panel B), and Book
Leverage (Panel C) as the dependent variables. Incentive variables and controls are measured in year t. The
dependent variables are measured in year t+1. The incentive variables are described in detail in Appendix A.
Control and dependent variables are described in Appendix B. All regressions include year and 2-digit SIC industry
fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and
year. ***, **, and * indicate significance at the 1, 5, and 10% levels, respectively.
Panel A: ln(Stock Volatility)
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
Book Leverage
R&D Expense
CAPEX
Delta
(1)
(2)
(3)
(4)
-0.004**
(-2.27)
-0.022
(-1.24)
-0.200***
(-10.00)
-0.116***
(-2.70)
0.584***
(5.82)
0.971***
(2.86)
0.633
(1.55)
0.003
(0.23)
-0.005***
(-2.78)
-0.038***
(-2.69)
-0.218***
(-11.87)
-0.119***
(-2.65)
0.579***
(4.77)
0.718**
(2.06)
0.667
(1.56)
-0.004
(-0.36)
-0.006**
(-2.37)
-0.039***
(-2.65)
-0.211***
(-12.46)
-0.085**
(-2.03)
0.565***
(5.71)
0.653
(1.54)
0.772*
(1.94)
-0.004
(-1.61)
-0.036***
(-2.68)
-0.204***
(-11.76)
-0.057
(-1.44)
0.254*
(1.93)
0.410
(1.00)
0.810**
(2.05)
-56.166***
(-8.07)
0.088
(1.23)
-71.389***
(-12.02)
0.144*
(1.85)
Delta / Tot. Wealth
Total Wealth
Vega
-0.803**
(-2.04)
Total Sensitivity
0.111
(0.60)
Vega / Tot. Wealth
43.514
(1.59)
Tot. Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Tot. Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
108.063***
(4.92)
5,967
0.464
5,967
0.462
Col. 1 = Col. 2
0.002
0.334
5,967
0.484
Col. 1 = Col. 3
0.020
0.000
51
5,967
0.497
Col. 3 = Col. 4
0.013
0.002
Col. 2 = Col. 4
0.035
0.000
Panel B: R&D Expense
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
Book Leverage
Cash Surplus
ln(Sales Growth)
Return
Delta
(1)
(2)
(3)
(4)
-0.001***
(-3.93)
0.003
(1.63)
-0.014***
(-8.13)
0.002
(0.84)
0.014
(1.30)
0.185***
(8.20)
0.002
(0.27)
0.000
(0.00)
0.001
(1.45)
-0.001***
(-3.82)
0.004**
(2.07)
-0.013***
(-7.64)
0.003
(1.25)
0.006
(0.57)
0.192***
(8.67)
0.001
(0.13)
-0.001
(-0.13)
0.001
(1.37)
0.000
(0.88)
0.005***
(2.72)
-0.011***
(-7.18)
0.005***
(2.59)
0.008
(0.78)
0.183***
(9.24)
0.006
(0.70)
0.002
(0.69)
-0.000
(-0.97)
0.006***
(2.96)
-0.011***
(-7.03)
0.005**
(2.27)
-0.011
(-0.95)
0.194***
(9.23)
0.003
(0.31)
0.001
(0.15)
-2.502***
(-4.95)
0.019***
(4.16)
-1.338***
(-2.99)
0.015***
(3.76)
Delta / Tot. Wealth
Total Wealth
Vega
0.135***
(5.95)
Total Sensitivity
0.053***
(4.63)
Vega / Tot. Wealth
15.751***
(7.52)
Tot. Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Tot. Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
7.996***
(4.70)
5,585
0.404
5,585
0.396
Col. 1 = Col. 2
0.008
0.000
5,585
0.424
Col. 1 = Col. 3
-0.020
0.001
52
5,585
0.406
Col. 3 = Col. 4
0.018
0.000
Col. 2 = Col. 4
-0.010
0.021
Panel C: Book Leverage
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
R&D Expense
ROA
PPE
Quartile Mod. Z-score
Rated Debt
Delta
(1)
(2)
(3)
(4)
0.001
(1.08)
0.002
(0.35)
-0.000
(-0.08)
0.023
(1.19)
-0.320***
(-2.81)
0.099
(0.48)
0.053
(1.52)
-0.057***
(-10.81)
0.127***
(12.09)
-0.008**
(-2.53)
-0.000
(-0.14)
-0.007
(-1.08)
-0.009***
(-2.58)
0.021
(1.12)
-0.405***
(-3.49)
0.097
(0.46)
0.057
(1.63)
-0.052***
(-10.06)
0.124***
(12.42)
-0.012***
(-2.85)
0.001
(1.57)
-0.002
(-0.28)
-0.005
(-1.49)
0.025
(1.25)
-0.443***
(-3.46)
0.107
(0.52)
0.062*
(1.73)
-0.055***
(-10.20)
0.127***
(12.61)
0.002***
(3.61)
0.001
(0.22)
-0.003
(-1.04)
0.035*
(1.89)
-0.478***
(-3.95)
0.130
(0.68)
0.044
(1.33)
-0.043***
(-8.80)
0.110***
(12.72)
-4.226**
(-2.36)
-0.033**
(-2.19)
-11.811***
(-4.99)
0.003
(0.17)
Delta / Tot. Wealth
Total Wealth
Vega
-0.194***
(-3.51)
Total Sensitivity
0.221***
(4.96)
Vega / Tot. Wealth
18.359**
(2.52)
Tot. Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Tot. Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
51.544***
(7.15)
5,538
0.274
5,538
0.281
Col. 1 = Col. 2
-0.007
0.193
5,538
0.275
Col. 1 = Col. 3
-0.001
0.764
53
5,538
0.343
Col. 3 = Col. 4
-0.068
0.000
Col. 2 = Col. 4
-0.062
0.000
Table 5
Comparison of the association between relative leverage and total sensitivity and future
volatility, R&D, and leverage
This table presents OLS regression results using ln(Stock Volatility) (Panel A), R&D Expense (Panel B), and Book
Leverage (Panel C) as the dependent variables. Incentive variables and controls (untabulated) are measured in year t.
The dependent variables are measured in year t+1. The incentive variables are described in detail in Appendix A.
Control and dependent variables are described in Appendix B. All regressions include year and 2-digit SIC industry
fixed effects. The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and
year. ***, **, and * indicate significance at the 1, 5, and 10% levels, respectively.
Panel A: ln(Stock Volatility)
Delta / Tot. Wealth
Total Wealth
Relative Leverage Ratio
(1)
(2)
(3)
(4)
-51.545***
(-6.11)
0.077
(1.00)
-0.001
(-1.23)
-80.856***
(-13.70)
0.192**
(2.15)
-69.900***
(-8.00)
-0.078
(-1.04)
-86.576***
(-11.87)
0.192**
(2.28)
Tot. Sens. / Tot. Wealth
131.029***
(5.02)
ln(Rel. Lev. Ratio)
Observations
Adjusted R-squared
Test: Rel. Lev. Ratio vs. Scaled Tot. Sens
Difference in Adj. R-squared
p value of Vuong test
144.079***
(5.38)
-0.063***
(-5.08)
4,994
0.496
4,994
0.517
Col. 1 = Col. 2
-0.021
0.011
54
3,329
0.532
3,329
0.543
Col. 3 = Col. 4
-0.011
0.194
Panel B: R&D Expense
Delta / Tot. Wealth
Total Wealth
Relative Leverage Ratio
(1)
(2)
(3)
(4)
0.207
(0.59)
0.008**
(2.30)
-0.000
(-1.23)
-1.545***
(-2.70)
0.014***
(3.41)
-0.646*
(-1.70)
-0.001
(-0.26)
-1.270***
(-3.05)
0.005**
(2.21)
Tot. Sens. / Tot. Wealth
7.685***
(4.33)
ln(Rel. Lev. Ratio)
Observations
Adjusted R-squared
Test: Rel. Lev. Ratio vs. Scaled Tot. Sens
Difference in Adj. R-squared
p value of Vuong test
4.094***
(3.52)
-0.001**
(-2.22)
4,703
0.363
4,703
0.383
Col. 1 = Col. 2
-0.020
0.002
3,180
0.403
3,180
0.413
Col. 3 = Col. 4
-0.010
0.018
(1)
(2)
(3)
(4)
-2.216
(-1.42)
-0.053**
(-2.57)
-0.001***
(-3.05)
-13.062***
(-4.38)
0.005
(0.26)
-6.348***
(-5.37)
-0.101***
(-5.01)
-10.069***
(-6.12)
0.003
(0.23)
Panel C: Book Leverage
Delta / Tot. Wealth
Total Wealth
Relative Leverage Ratio
Tot. Sens. / Tot. Wealth
52.866***
(6.85)
ln(Rel. Lev. Ratio)
Observations
Adjusted R-squared
Test: Rel. Lev. Ratio vs. Scaled Tot. Sens.
Difference in Adj. R-squared
p value of Vuong test
46.585***
(9.03)
-0.029***
(-9.29)
4,647
0.245
4,647
0.315
Col. 1 = Col. 2
-0.070
0.000
55
3,120
0.408
3,120
0.400
Col. 3 = Col. 4
0.008
0.558
Table 6
Comparison of the association between vega and equity sensitivity and future volatility,
R&D, and leverage from 1994-2005
This table presents OLS regression results using ln(Stock Volatility) (Panel A), R&D Expense (Panel B), and Book
Leverage (Panel C) as the dependent variables. Incentive variables and controls (untabulated) are measured in year t.
The dependent variables are measured in year t+1. The incentive variables are described in detail in Appendix A.
Control and dependent variables are described in Appendix B. All regressions include year and 2-digit SIC industry
fixed effects. The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and
year. ***, **, and * indicate significance at the 1, 5, and 10% levels, respectively.
Panel A: ln(Stock Volatility)
Delta
(1)
(2)
0.019**
(2.40)
0.013*
(1.73)
Delta / Tot. Wealth
Total Wealth
Vega
(3)
(4)
-70.336***
(-12.41)
0.225***
(3.32)
-74.736***
(-13.18)
0.250***
(3.81)
0.328
(1.28)
Equity Sensitivity
0.300***
(2.69)
Vega / Tot. Wealth
79.536***
(5.51)
Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Equity Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
96.888***
(13.47)
10,048
0.550
10,048
0.552
Col. 1 = Col. 2
0.002
0.065
10,048
0.579
Col. 1 = Col. 3
-0.029
0.000
56
10,048
0.594
Col. 3 = Col. 4
-0.015
0.000
Col. 2 = Col. 4
-0.042
0.000
Panel B: R&D Expense
Delta
(1)
(2)
-0.001**
(-2.21)
-0.001**
(-2.56)
Delta / Tot. Wealth
Total Wealth
Vega
(3)
(4)
-1.672***
(-4.10)
0.004
(0.99)
-0.517
(-1.54)
-0.001
(-0.14)
0.068***
(4.85)
Equity Sensitivity
0.031***
(6.05)
Vega / Tot. Wealth
8.459***
(6.13)
Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Equity Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
2.411***
(3.25)
9,548
0.343
9,548
0.342
Col. 1 = Col. 2
0.001
0.315
9,548
0.347
Col. 1 = Col. 3
-0.004
0.139
9,548
0.340
Col. 3 = Col. 4
0.007
0.002
Col. 2 = Col. 4
0.002
0.236
(3)
(4)
0.349
(0.27)
-0.046***
(-2.95)
-6.083***
(-5.27)
-0.010
(-0.59)
Panel C: Book Leverage
Delta
(1)
(2)
-0.004*
(-1.85)
-0.010***
(-4.68)
Delta / Tot. Wealth
Total Wealth
Vega
-0.131***
(-3.70)
Equity Sensitivity
0.169***
(5.17)
Vega / Tot. Wealth
-2.699
(-0.74)
Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Equity Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
29.172***
(11.04)
9,351
0.317
9,351
0.330
Col. 1 = Col. 2
-0.013
0.012
9,351
0.315
Col. 1 = Col. 3
0.002
0.292
57
9,351
0.363
Col. 3 = Col. 4
-0.048
0.000
Col. 2 = Col. 4
-0.033
0.000
Table 7
Comparison of the association between changes in vega and changes in equity sensitivity
and changes in volatility, R&D, and leverage around the introduction of SFAS 123R
This table presents OLS regression results using the change in ln(Stock Volatility) (Panel A), R&D Expense (Panel
B), and Book Leverage (Panel C) as the dependent variables. Incentive variables and controls (untabulated) are the
difference between the mean from 2005 to 2008 and the mean from 2002 to 2004, following Hayes et al. (2012).
The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005.
The incentive variables are described in detail in Appendix A. Control and dependent variables are described in
Appendix B. The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and
year. ***, **, and * indicate significance at the 1, 5, and 10% levels, respectively.
Panel A: Δ ln(Stock Volatility)
Δ Delta
(1)
(2)
0.034*
(1.81)
0.033*
(1.81)
Δ Delta / Tot. Wealth
Δ Total Wealth
Δ Vega
(3)
(4)
-77.518***
(-8.78)
0.330**
(2.43)
-81.884***
(-9.08)
0.356**
(2.53)
-0.425
(-1.27)
Δ Equity Sensitivity
-0.241
(-1.13)
Δ Vega / Tot. Wealth
21.002
(0.96)
Δ Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Equity Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
33.322*
(1.91)
1,168
0.0587
1,168
0.0587
Col. 1 = Col. 2
0.0000
0.9675
1,168
0.138
Col. 1 = Col. 3
-0.079
0.000
58
1,168
0.140
Col. 3 = Col. 4
-0.002
0.306
Col. 2 = Col. 4
-0.081
0.000
Panel B: Δ R&D Expense
Δ Delta
(1)
(2)
-0.002***
(-2.60)
-0.002***
(-2.72)
Δ Delta / Tot. Wealth
Δ Total Wealth
Δ Vega
(3)
(4)
-0.127
(-0.44)
-0.007**
(-2.22)
-0.049
(-0.18)
-0.008**
(-2.32)
-0.001
(-0.12)
Δ Equity Sensitivity
0.003
(0.67)
Δ Vega / Tot. Wealth
0.234
(0.31)
Δ Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Equity Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
-0.066
(-0.12)
1,131
0.0359
1,131
0.0361
Col. 1 = Col. 2
-0.0002
0.808
1,131
0.0321
Col. 1 = Col. 3
0.0038
0.244
1,131
0.0320
Col. 3 = Col. 4
0.0001
0.918
Col. 2 = Col. 4
0.0041
0.263
(3)
(4)
1.072
(0.62)
-0.051**
(-2.37)
-4.613***
(-2.95)
-0.009
(-0.41)
Panel C: Δ Book Leverage
Δ Delta
(1)
(2)
-0.006**
(-2.18)
-0.010***
(-2.80)
Δ Delta / Tot. Wealth
Δ Total Wealth
Δ Vega
-0.049
(-0.85)
Δ Equity Sensitivity
0.165***
(4.81)
Δ Vega / Tot. Wealth
-1.367
(-0.32)
Δ Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Test: Vega vs. Equity Sens:
Difference in Adj. R-squared
p value of Vuong test
Test: Level vs. Scaled
Difference in Adj. R-squared
p value of Vuong test
18.994***
(6.39)
1,098
0.115
1,098
0.131
Col. 1 = Col. 2
-0.016
0.039
1,098
0.114
Col. 1 = Col. 3
0.001
0.942
59
1,098
0.148
Col. 3 = Col. 4
-0.034
0.003
Col. 2 = Col. 4
-0.017
0.088