Managerial incentives to increase firm volatility
provided by debt, stock, and options
Joshua D. Anderson
jdanders@mit.edu
(617) 253-7974
John E. Core*
jcore@mit.edu
(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 reflect the option value of equity,
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.
This draft: February 2014
_______________
* Corresponding author. We gratefully acknowledge comments from Ana Albuquerque (discussant), Divya
Anantharaman, 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, Tulane
University, the University of Technology Sydney, and Washington University at St. Louis. 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 three shortcomings: (1) it does not reflect the
option value of equity; (2) it does not capture potential risk incentives from managers’ stock and
inside debt (unsecured pensions and deferred compensation); and (3) 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.
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
1
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 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
being strongly positive.
Because vega does not capture these 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 risk: stock
volatility, research and development expense, and leverage. We specify regression models
similar to those in 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.
2
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
scaled equity vega.1
Our new measures require only data from CRSP, Compustat, and Execucomp. The
measures can be computed for virtually all of the sample for which vega can be computed.2 A
program to compute the measures is available on request.
A concern about regressions of incentives on risk-taking is that risk-taking incentives are
endogenous. To explore the robustness of our results, we estimate two-stage least squares (2SLS)
regressions. The inference from the 2SLS regressions is similar: The total sensitivity measure
explains risk choices better than vega. We also follow Hayes et al. and examine changes in
incentives and in risk-taking around the introduction of option expensing in 2005 as a potentially
exogenous event that changed incentives. Our evidence from this analysis also suggests that the
total sensitivity measure explains risk choices better than vega.
Our derivation of the sensitivity of debt, stock, and options also implies that the relative
risk-taking measures (the relative leverage ratio and the relative incentive ratio) used in the
1
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.
2
As described below, to compute the total sensitivity requires data on outstanding employee stock options. This data
is missing from Compustat for about 4% of our main sample. In addition, in a small number of cases, the algorithm
to compute debt values does not converge, which makes it impossible to compute our measure.
3
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 over
2.3 times his equity incentives to increase volatility. By contrast, the corrected measure, which
explicitly takes into account the incentives to increase firm volatility from options, is much
smaller and suggests that CEOs have little alignment with debt holders: the average CEO has
incentives to reduce volatility that are equal to 0.4 times his equity incentives to increase
volatility. Consistent with prior literature, we find that these ratios are negatively associated with
risk choices. However, our scaled total sensitivity measure can be computed for about 70% more
observations and 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
4
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)
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:
5
(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)
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. So long as increases in
volatility do not change the value of the firm, any gains to the options are offset by losses to the
stock. This result for options on stock is similar to the result when stock is an option on the value
of the levered firm.
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 a call option on the assets, but they have
granted options on the equity to employees. They are in a position with respect to the equity
6
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 option on the asset but to lose on
the options on the equity. Since the change in stockholders’ value is a combination of these two
opposing effects, whether stockholders prefer more volatility depends on the number of
employee options outstanding and firm leverage, as we illustrate next.
2.1.1
Estimating 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,
and as noted above, a program to compute the measures is available on request.
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 maturity amount of
the firm’s debt.3
3
Eberhart (2005) converts the firm’s debt into a single zero-coupon bond (as do Bharath and Shumway, 2008;
Campbell et al., 2008; and Hillegeist et al., 2004). In following this method, we abstract away from different types
of debt in the firm’s capital structure and different types of debt in the CEO’s portfolio. Although doing this
involves some measurement error, it affords us a larger sample (in part because we do not require data on individual
debt issues) and allows us to focus on the main effect: equity values increase more after an increase in firm volatility
when the firm has more debt.
7
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
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% increase in the standard deviation of the assets (from 35.00% to 35.35%), at various levels of
leverage. An increase in volatility reduces debt value, and this reduction is greater for greater
leverage. The 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
8
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
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 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). 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 vega with the
total sensitivity in (8), one can see that vega is a subset of total risk-taking incentives. In
9
particular, it does not reflect the option value of equity, 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 (8) and (9) reveals that for vega to be similar to total risk-taking
incentives, the firm must have low or no leverage (so that the volatility increase causes little redistribution 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:
4
(10)
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.
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
4
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:
10
.
“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:5
(11)
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.,
Cassell et al., 2012; Sundaram and Yermack, 2007) uses this measure, and terms it the “relative
leverage ratio,” as it compares the manager’s leverage to the firm’s leverage. To operationalize
the relative leverage ratio when firms have employee options, these researchers make an ad hoc
adjustment by adding the Black-Scholes value of the options to the value of the firm’s stock and
CEO’s stock. 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 Black-Scholes delta. These adjustments for options are not correct because the option
sensitivity to firm volatility is different from option value or delta. Only when the firm has no
employee options are the relative leverage and incentive ratios equal to the relative sensitivity
ratio.
More important, 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
5
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
and re-arranging.
11
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).
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% 1.01
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 in calculating vega 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
12
correlated (0.91) with the 0.01 increase vega used in the prior literature, and all of our inferences
below with the 1% vega are identical to those with the 0.01 increase vega.6
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
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 vega for the example CEO. In contrast to the equity sensitivity and the
total sensitivity which both increase in leverage, vega first increases and then decreases with
leverage in this example. Part of the reason is that vega does not capture the debt and stock
sensitivities. Holding this aside, 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
6
We also compute the change in the CEO’s wealth for a one sample standard deviation increase in firm volatility.
The results, in terms of significance, are very similar to our main results.
13
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.
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
thousand for the low-leverage firms and $57 thousand for the high-leverage firms. The riskincreasing 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 risk-taking 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), we illustrate 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 2.8%), also shows high identification
14
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.
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 beginning only 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
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 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
15
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 13%, and the mean is 18%. 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.7
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
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. Vega is smaller than the total sensitivity, and has strictly
positive values as compared to the total sensitivity which has about 8% negative values.8
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
7
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.
8
As discussed above, 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.
16
will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse.9
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.10 We use
the measure of CEO outside wealth developed by Dittmann and Maug (2007).11,12 The average
scaled total sensitivity is 0.14% of wealth. The value is low because the sensitivities are
calculated with 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 relatively large risk-reducing incentives, a one standard
deviation decrease in firm volatility increases the CEO’s wealth by 2%.
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
9
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. 10
We value the options as warrants following Schulz and Trautmann (1994). This is consistent with how we
calculate the sensitivities of the CEOs’ portfolios.
11
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.
12
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. 17
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.
3.5
Correlations – CEO incentive measures
Panel B 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
(12)
The form of the regression is similar to those in Guay (1999), Coles et al. (2006) and Hayes et al.
(2012).
18
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. 330) 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 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). To ease comparisons, we use this delta in all of our
regressions.13
Finally, 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 Volatility) measured using daily
stock volatility over year t+1, (2) R&D Expense measured as the ratio of R&D expense to total
assets, and (3) Book Leverage measured as the book value of long-term debt to the book value of
assets.14 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
13
Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest
that delta as calculated in the prior literature can also be noisy. We calculate a dilution-adjusted delta by estimating
the increase in the value of the CEO’s stock and option portfolio when the firm’s equity value increases by 1%. If
we instead use this dilution-adjusted delta in our tests, the results using this delta are very similar to those presented
below.
14
We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility
below.
19
risk. We measure all control variables at t and all risk choice variables at t+1. By doing this, we
attempt to mitigate potential endogeneity.
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 our regressions include year and 2-digit SIC industry fixed effects.
In the regression with ln(Stock Volatility), we also control for risk from past R&D
Expense, 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.
Following Hayes et al. (2012), we use nominal values that are not adjusted for inflation
and estimate our regressions using OLS. If we follow Coles et al. (2006) and adjust for inflation,
our inference is the same. Coles et al. also present the results of instrumental variables
regressions. We report our main results using ordinary least squares. In section 4.5.1 below, we
examine the sensitivity of our results using two-stage least-squares (2SLS), and find similar
inference.
4.1.2
Scaled incentive measures
Prior literature identifies CEO wealth as an important determinant of a CEO’s attitude
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
20
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
(13)
To enable comparison across the models, we include the same control variables in (13) as in (12)
above.
4.2
Association of level and scaled incentive measures with firm risk choices
In Table 4, we present our main results. Panel A contains estimation results for the
unscaled incentive variables (Eq. (12)), and Panel B contains estimation results for the scaled
incentive variables (Eq. (13)). Each panel contains three columns for vega (scaled vega) and
three columns for total sensitivity (scaled total sensitivity). Each set of columns shows regression
results for ln(Stock Volatility), R&D Expense, and Book Leverage.
Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)
in Column (1) of Panel A and for leverage in Column (3). These results are inconsistent with
findings in Coles at al. (2006) for 1992-2001.15 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. In column (2), however, vega has the expected positive and significant relation with R&D
Expense.
To ease interpretation of our variables, we standardize each dependent and independent
variable (by subtracting its mean and dividing by its standard deviation) so that that the variables
have a mean of zero and standard deviation of one. This transformation does not affect the t 15
In Section 4.4 below, we examine 1994-2005 data. During this time period that is more comparable to Coles et al.
(2006), we find a positive association between vega and ln(Stock Volatility).
21
statistic, but helps with interpretation. For example, the 0.151 coefficient on vega in Column (2)
indicates that a one standard deviation increase in vega is associated with a 0.151 standard
deviation increase in R&D Expense.
At the bottom of the panel, the average coefficient on vega (0.008) is not significantly
greater than zero, suggesting that overall vega is not significantly associated with these three risk
choices. In contrast, the total sensitivity is positive in all three specifications and significant in
the models for R&D Expense and Book Leverage.16 The average coefficient on total sensitivity
(0.077) is significantly greater than zero, and is significantly greater than the average coefficient
on vega. This result suggests that for this sample total sensitivity better explains risk choices than
vega.
As noted above, scaling the level of incentives by total wealth can provide a better crosssectional measure of CEOs’ incentives. In Panel B, the scaled vega is positive in all three
specifications and significant in the models for R&D Expense and Book Leverage. The sum of
the three coefficients on scaled vega is significantly greater than zero. The scaled total sensitivity
is both positively and significantly related to all three risk variables. The average coefficient on
both scaled vega and scaled sensitivity are significantly greater than zero, suggesting that both
variables explain risk choices. However, the average coefficient on scaled sensitivity (0.231) is
16
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).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.
22
significantly greater than the average coefficient on scaled vega (0.131), suggesting that scaled
sensitivity explains risk choices better.
Overall, the results in Table 4, suggest that the total sensitivity explains firms’ risk
choices better than vega.
In Columns (1) and (2) of Table 5, we show robustness to using asset volatility as the
dependent variable instead of stock volatility. For parsimony and because our main interest is
risk-taking incentives, in the remainder of the paper, we tabulate only the risk-taking incentive
variables. Panel A shows that vega and total sensitivity are significantly related to asset volatility.
While the coefficient on total sensitivity is 19% larger than that on vega, the difference is not
significant. In Panel B, both scaled incentive variables are significantly related to asset volatility.
Scaled total sensitivity has a 14% larger effect on asset volatility than scaled vega, but this
difference is not significant.
In the remaining columns, we decompose stock volatility into its systematic and
idiosyncratic components by regressing daily returns on the Fama and French (1993) factors.
Columns (3) through (6) of Table 5 show the regressions using the components of stock
volatility as the dependent variables. In Panel A, vega has a significantly negative relation with
both systematic and idiosyncratic volatility. Total sensitivity has a positive, but insignificant
relation with both components. In Panel B, scaled vega has an insignificant positive relation with
both systematic and idiosyncratic volatility. In contrast, scaled total sensitivity has a significant
positive relation with both systematic and idiosyncratic volatility. Scaled total sensitivity has a
significantly larger association with both components of volatility than does scaled vega.
4.3
Association of relative ratios with firm risk choices
23
The preceding section compares the total sensitivity to vega. In this section and in Table
6, we compare the scaled total sensitivity to the relative leverage ratio. 17 The regression
specifications are identical to Table 4. These specifications are similar to, but not identical to,
those of Cassell et al. (2012).18
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 6 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
the ratio at the 90th percentile.19 We present results for the subsample where the relative leverage
ratio is defined in Panel A.
In Panel A, the relative leverage ratio is negatively related to all three risk choices. This
expected negative relation is consistent with CEOs talking less risk when they are more
identified with debt holders. The relation, however, is significant only for Book Leverage. In
contrast, the scaled total sensitivity is positively and significantly related to all three risk choices
in this subsample. Because the relative leverage ratio has a negative predicted sign and total
sensitivity has a positive predicted sign, we take absolute values to compare the coefficient
magnitudes. The average coefficient on scaled sensitivity (0.244) is significantly greater than the
absolute value of the average coefficient on the relative leverage ratio (0.045), suggesting that
scaled sensitivity explains risk choices better.
17
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.
18
An important difference is in the control for delta. We include delta scaled by wealth in our regressions as a proxy
for risk aversion due to concentration in firm stock, 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, and the variable is generally not significant.
19
If instead we winsorize the relative leverage ratio at the 99th percentile, it is not significant in any specification.
24
As another way of addressing the problem of extreme values in the relative leverage ratio,
Cassell et al. (2012) take 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 CEOyears.
We present results for the subsample where ln(Relative Leverage) is defined in Panel B.
Unlike the relative leverage ratio, the logarithm of the relative leverage ratio has the expected
negative and significant relation with all three risk choices. The scaled total sensitivity is also
positively and significantly related to each of the risk choices. The average coefficient on scaled
sensitivity (0.209) is significantly greater than the absolute value of the average coefficient on
the logarithm of the relative leverage ratio (0.155), suggesting that scaled sensitivity explains
risk choices better.
Overall, the results in Table 6 indicate that the scaled total sensitivity measure better
explains risk-taking choices than the relative leverage ratio and its logarithm. In addition, the
total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its
natural logarithm, and can be used to study incentives in a broader sample of firms.
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 of unusual shocks to returns and to return volatility, which may have
affected both incentives and risk-taking.
25
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
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 7, we repeat our analysis in Table 4 for this earlier period using the equity
sensitivity in place of total sensitivity. Panel A compares the results using vega and equity
sensitivity for our three risk choices. Vega has the expected positive relation with ln(Stock
Volatility) in this earlier sample, unlike in our main sample, though the relation is insignificant.
As in Table 4, vega has a significantly positive association with R&D Expense and a
significantly negative association with Book Leverage.20 At the bottom of the panel, we find that
the average coefficient on vega (0.018) is not significantly greater than zero, suggesting that
overall vega is not significantly associated with the three risk choices. In contrast, the total
20
The book leverage regressions include controls based on Hayes et al. (2012), and the results therefore are not
directly comparable to the Coles et al. (2006) findings. 26
sensitivity is positive and significant in all three specifications (Columns 4 to 6). The average
coefficient on total sensitivity (0.095) is significantly greater than zero. Finally, the average
coefficient on total sensitivity is significantly greater than the average coefficient on vega,
suggesting that total sensitivity better explains risk choices than vega.
In Panel B, the scaled vega has significantly positive associations with ln(Stock Volatility)
and R&D Expense. However, scaled vega has an insignificant, negative association with Book
Leverage. The sum of the three coefficients on scaled vega, however, is significantly greater than
zero. The scaled equity sensitivity is both positively and significantly related to all three risk
variables. As in Table 4, Panel B, the average coefficient on both scaled vega and scaled equity
sensitivity are significantly greater than zero, suggesting that both variables explain risk choices.
However, the average coefficient on scaled sensitivity (0.181) is significantly greater than the
average coefficient on scaled vega (0.072), suggesting that scaled sensitivity explains risk
choices better.
The results in Table 7 suggest that our inferences from our later sample also hold in the
earlier period 1994-2005.
4.5
Robustness tests
4.5.1
Endogeneity
Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives
at t. These models are well-specified under the assumption that incentives are predetermined or
exogenous, that is, incentives at time t are uncorrelated with the regression errors for time t+1
risk choices. To assess the sensitivity of our results to this assumption, we re-estimate our
models using two-stage least squares.
27
In the first stage, we model the incentive variables (vega, delta, and total sensitivity) and
the incentive variables scaled by wealth. We model each incentive variable as a linear
combination of (1) second-stage control variables that explain risk choices and (2) instruments
that explain incentives but not risk choices. We use the following instruments employed by
Armstrong and Vashishtha (2012) and Cassell et al. (2013): cash and short-term investments as a
percentage of total assets, current year return on assets, current and prior year stock returns, CEO
age, and the personal income tax rate of the state in which the firm has its headquarters. In our
models for R&D Expense and Book Leverage, we use current year volatility as an additional
instrument (Coles et al., 2006). In addition to these instruments, we include an indicator for
whether CEO’s salary exceeds $1 million. CEOs with salaries over $1 million are more likely to
defer compensation to increase the tax deductibility of this compensation to the firm. Finally, in
our models for the level of vega, total sensitivity, and delta, we include the CEO’s total wealth.
(This variable is a control variable in our scaled models, so it cannot be used as an instrument for
the scaled incentive variables.) As discussed above, we expect CEOs with higher outside wealth
to have more incentives.
Panel A of Table 8 shows first-stage results for a two-stage least squares model for
ln(Stock Volatility) from 2006 to 2010. The number of observations in this specification (5,916)
is slightly lower than for the corresponding specification in Table 4 due to missing values of the
instruments. In Panel A, we show the controls first followed by the instruments. The partial Fstatistics at the bottom of the panel indicate that the instruments provide a significant amount of
incremental explanatory power. In untabulated analysis, we compute Hansen’s (1982) J-statistic
for overidentification for each of our models. The J-statistic provides a test of model
specification by testing whether the instruments are uncorrelated with the estimated error terms.
28
None of the J-statistics are significantly different from zero, which suggests that the exclusion
restrictions hold for our instruments and that our models are not mispecified.
To conserve space, we do not present first-stage results for our models for R&D and
leverage. The results are very similar in that the instruments add a significant amount of
incremental explanatory power, and none of the J-statistics are significantly different from zero.
Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using
the unscaled incentive variables. These are analogous to the OLS regression results in Table 4,
Panel A. In the regression for ln(Stock Volatility), vega is positive (unlike Table 4), but
insignificant. As in Table 4, vega has a significant positive association with R&D Expense and a
significant negative association with Book Leverage.21 In contrast to Table 4, total sensitivity has
a significant positive association with ln(Stock Volatility). Total sensitivity also has significant
positive associations with R&D Expense and Book Leverage. The average 2SLS coefficient on
total sensitivity is significantly larger than that on vega.
In Panel C, the 2SLS estimates for scaled vega produce different inference than the OLS
estimates in Table 4, Panel B. Scaled vega remains positive and significant in Column (2), but
changes sign in Columns (1) and (3), and becomes significantly negative in Column (3). The
average 2SLS coefficient on scaled vega is still significantly positive, however. Scaled total
sensitivity remains positive in all three regressions, but is only marginally significant in the
models for ln(Stock Volatility) (t-statistic = 1.80) and for Book Leverage (t-statistic = 1.66). The
average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled
vega.
21
As in Table 4, the variables are standardized, so that, for example, the 1.006 coefficient on vega in Column (2)
indicates that a one standard deviation increase in instrumented vega is associated with a 1.006 standard deviation
increase in R&D Expense.
29
A concern with 2SLS is that if instruments are weak, confidence intervals can be too
small, leading to false rejections (Stock and Yogo, 2005). To ensure that our inference is robust,
we also compute Anderson-Rubin (AR, 1949) 95% confidence intervals (untabulated).22 These
intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen,
2008). If the confidence interval contains only positive (negative) values, the coefficient is
significantly greater (less) than a zero, and we indicate this in bold print in Panels B and C. In
Panel B, this analysis confirms that vega has a significant positive association with R&D
Expense, and that total sensitivity has a positive and significant associations with ln(Stock
Volatility), R&D Expense, and Book Leverage. In Panel C, the analysis confirms that vega has a
significant positive association with R&D Expense, and total sensitivity has a positive and
significant association with R&D Expense. This more conservative procedure does not find a
significant association between vega and Book Leverage, scaled vega and Book Leverage, and
between scaled total sensitivity and ln(Stock Volatility) and Book Leverage. Unfortunately, we
could not compute Anderson-Rubin confidence intervals for the average coefficients or their
differences.
In untabulated results, we find that the 2SLS results for the 1994-2005 sample produce
similar inference to that in Table 6. Equity sensitivity explains risk choices better than vega.
Overall, our results using two-stage least squares to address endogeneity are consistent with our
earlier conclusions from Table 4: total sensitivity explains risk choices better than vega. We note
that while the 2SLS results mitigate concerns about endogeneity, we cannot completely eliminate
endogeneity as a potential confounding factor.
4.5.2
Changes in vega, changes in equity sensitivity and changes in firm risk choices
22
We compute the intervals using Stata code “weakiv” developed by Finlay, Magnusson, and Schaffer (2013).
30
A second way of addressing the concern about incentives being endogenous is to identify
an exogenous 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.
We follow Hayes et al. (2012) and estimate Eqs. (12) and (13) using changes in the mean
value of the variables from 2002 to 2004 and 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 9 shows the results of these regressions. Similar to Hayes et al. (2012), we find that
the change in vega is negatively, but not significantly, related to the change in our three risk
choices (Panel A). The change in equity sensitivity is also negative and insignificant using the
change in stock volatility, is positive but insignificant using R&D, and positive and significant
using leverage. The average coefficient on the change in vega (-0.020) is insignificantly negative.
The average coefficient on the change in equity sensitivity (0.041) is significantly positive. The
difference between the average coefficients is significant.
When we examine instead the scaled measures in Panel B, the change in scaled vega is
again is not significantly related to any of the risk choices. In contrast, the change in scaled
equity sensitivity is significantly positively related to the change in stock volatility in Column (4)
and leverage in Column (6). The average coefficient on the change in scaled vega is positive
(0.014), but insignificant. The average coefficient on the change in scaled equity sensitivity
31
(0.105) is an order of magnitude larger and highly significant. The difference between the
average coefficients is again significant. Scaled equity sensitivity explains the change in risk
choices around the introduction of option expensing under SFAS 123R better than scaled vega
does.
4.5.3
Convexity in long-term incentive awards
Another concern with our analysis is that firms may have responded to stock option
expensing by replacing the convexity in options with the convexity in long-term incentive
awards (Hayes et al., 2012). These plans are more heavily used since the change in stock option
expensing in 2005, so this concern is greatest in our 2006-2010 sample period. As discussed in
Hayes et al., typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO
that varies from a threshold number to a target number to a maximum number as a function of
firm performance. When the number of shares vested in these plans is explicitly or implicitly
based on stock price performance, variation in the number of shares vested as a function of the
share price can create incentives to increase volatility (Bettis et al., 2013).
To estimate the risk-taking incentives provided by LTIAs, we follow the procedure
described in Hayes et al. (2012, p. 186) and in the related internet appendix (Hayes et al., 2011).
The procedure assumes that the grant vests in three years, and that the degree of vesting is a
function of stock price performance during those three years. 23 This procedure allows us to
estimate the value, vega, and delta for each grant.
We find that 36% of our sample CEO received LTIA grants from 2006-2010. Following
the Hayes et al. procedure, we compute the convexity of these LTIA grants. We find the mean
23
Most LTIAs make vesting contingent on accounting numbers such as earnings and sales. To value the grants,
procedures in Hayes et al. (2012) and Bettis et al. (2013) assume a mapping from accounting numbers into stock
returns.
32
convexity to be $3.92 thousand, which is consistent with, though slightly larger than, the mean of
$1.56 thousand computed by Hayes et al. for the 2002-2008 period.
The portfolio values are of direct interest for our study. Under the assumption that the
grants vest in three years, the portfolio of LTIA incentives is the sum of the incentives from this
year’s grant and from the grants in the two previous two years. For example, for a CEO in 2006,
we compute LTIA convexity as the sum of grants from 2004, 2005, and 2006. We re-compute
the incentives of earlier years’ grants to reflect their shorter time to maturity and changes in
prices and volatility. For the 45% of CEOs who have current or past LTIA grants, we compute
portfolio convexity of $5.77 thousand.24 When averaged with CEOs without LTIAs, the average
portfolio LTIA convexity, computed as the change in LTIA value for a 1% change in volatility,
is $2.52 thousand, approximately 6% of the sample mean vega shown in Table 4. (We are unable
to calculate the LTIA value for 18 CEO-years in our sample). Similarly, we compute portfolio
LTIA sensitivity, which incorporates increases in equity value due to reductions in debt value, to
be $3.35 thousand or approximately 5% of the sample mean sensitivity shown in Table 4.25
In Table 10, we show regression results for our main sample in which the incentive
variables include LTIA convexity. Adding the LTIA incentives does not affect our inference.
However, we caveat that our estimates are noisy because data on LTIA plans is not welldisclosed.26
24
Note that the portfolio, which may contain as many as three grants, has average convexity of $5.77 thousand,
which is only about 47% greater than grant convexity of $3.92 thousand. This occurs because (1) some CEOs do not
receive grants each year, and (2) as with a standard option, the convexity of an LTIA grant falls as it goes farther in
the money. 25
Similar to our main sample computations above, we compute LTIA sensitivity to incorporate increases in equity
value due to reductions in debt value. Because the total number of shares awarded to all employees under LTIA
plans is not disclosed, however, we do not adjust for the potential dilution from these plans. 26
Like Hayes et al. (2011, 2012), we base our estimates on LTIA data from Execucomp. More detailed data on
LTIAs is available from IncentiveLab, but this data set covers only about 60% of the Execucomp sample, and
concentrates on larger firms.
33
4.5.4 Other robustness tests
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
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, total risk-reducing incentives should include future cash pay as well as pensions and
deferred compensation.27 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 are small in comparison to risk-increasing incentives, our inferences remain
unchanged.
Second, 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. 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
27
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
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, 6, and 7. Our inference is the
same after attempting to mitigate measurement error in this way.
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, 6, and 7 are unchanged.
5.
Conclusion
We measure the total sensitivity of managers’ debt, stock, and option holdings to changes
in firm volatility. Our measure incorporates the option value of equity, 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. We also calculate an equity
35
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.
36
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 ln(1+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 one plus the yield of the risk-free interest rate for a four-year maturity
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.
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:
37
∗
´
´
(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 /
/
, adjusted
F = the future value of the firm’s debt including interest, i.e., (dlc + dltt)
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).
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
1.01. This also implies a 1% increase in firm
We increase stock volatility by 1%:
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 ´
.
38
The new equity value is the old equity value plus the change in debt value
∗
( ∗´
´). Substituting this equity value and into (A2) and (A3), we calculate a
´
. The option sensitivity is difference between the
new P and ∗ . The stock sensitivity is
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.
´
(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).
39
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 .
´
(A11)
Using the derivative of the Black-Scholes-Merton equation (A10), the sensitivity of an option to
a change in the price is:
(A12)
The sensitivity of the CEO’s stock and option portfolio to a 1% increase in stock price (the
“delta”) is:
∗ 0.01 ∗
∗
∗ 0.01 ∗
(A13)
A.5.3 Relative sensitivity ratio
If the sensitivity of stock price to volatility is positive, the ratio is:
(A14a)
If the sensitivity of stock price to volatility is negative, the ratio is:
(A14b)
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.
(A15)
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.
40
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.
(A16)
Where:
= sum of the delta of the CEO’s stock holding and the Black-Scholes delta of the
CEO’s option portfolio as in (A13), calculated following Core and Guay (2002)
= sum of the number of shares outstanding and the delta of the options calculated
according to (A13) above using the firm parameters from Appendix A.3
41
Appendix B: Measurement of Other Variables
The measurement of other variables, with the exception of Total Wealth and State Income Tax Rate, 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.
Dependent Variables
ln(Stock Volatility)
R&D Expense
Book Leverage
ln(Asset Volatility)
ln(Systematic Volatility)
ln(Idiosyncratic Volatility)
The natural logarithm of the variance of daily stock returns over
fiscal year t+1
The ratio of the maximum of zero and R&D expense (xrd) to total
assets (at) for fiscal year t+1
The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal
year t+1
The natural logarithm of , the variance of firm value, calculated
using Eq. (A5) in fiscal year t+1
The natural logarithm of the variance of systematic daily stock
returns over fiscal year t+1. Systematic returns estimated using
the Fama and French (1993) three factor model over the
previous 36 months
The natural logarithm of the variance of residual daily returns over
fiscal year t+1. Systematic returns estimated using the Fama
and French (1993) three factor model over the previous 36
months
Control Variables
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
CAPEX
Surplus Cash
ln(Sales Growth)
Return
ROA
PPE
Modified Z-Score
Rating
The tenure of the CEO through year t
The sum of salary (salary) and bonus compensation (bonus)
The natural logarithm of total revenue (revt)
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 capital expenditures (capx) less sales of property,
plant, and equipment (sppe) to total assets (at)
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 natural logarithm of the quantity total revenue in year t (revtt)
divided by sales in year t-1 (revtt-1)
The stock return over the fiscal year
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
42
Total Wealth
The sum of non-firm wealth calculated according to Dittman and
Maug
(2007)
(non_firm_wealth
available
from
http://people.few.eur.nl/dittmann/data.htm and set to missing
when negative), stock holdings (shrown_excl_opts * prcc_f),
and CEO options valued as warrants following Eq. (A9) in
A.5.1 above, and inside debt (pension_value_tot plus
defer_balance_tot) beginning in 2006
Instruments
Cash Ratio
State Income Tax Rate
CEO Age
High Salary
ln(Monthly Stock
Volatility)
The ratio of cash and short-term investments (che) to total assets
(at)
The maximum state tax rate on individual income calculated using
the TAXSIM model (Feenberg and Coutts, 1993) and obtained
from http://www.nber.org/~taxsim/state-rates. Set to zero for
firms outside the United States.
The age of the CEO in year t
An indicator variable set to one when salary is greater than $1
million
The natural logarithm of the variance of monthly stock returns
over the previous 60 months, requiring at least 12 observations
43
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46
Table 1
Panel A: Example firm -- Sensitivity of debt, stock, and options to firm volatility ($ 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 2.25% 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%
47
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. 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.
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
48
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 descriptive statistics
This table provides descriptive statistics on the primary sample of 5,967 firm-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 BlackScholes-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.
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
49
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
50
Panel B: Correlation between Incentive Variables
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
51
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 unscaled (Panel A) and scaled (Panel B) incentive 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: Unscaled Incentive Variables
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
Book Leverage
R&D Expense
CAPEX
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
ln(Stock
Volatility)
(4)
R&D
Expense
(5)
Book
Leverage
(6)
-0.029**
(-2.27)
-0.016
(-1.24)
-0.339***
(-10.00)
-0.130***
(-2.70)
0.112***
(5.82)
0.056***
(2.86)
0.034
(1.55)
-0.057***
(-3.93)
0.035
(1.63)
-0.354***
(-8.13)
0.028
(0.84)
0.038
(1.30)
0.020
(1.08)
0.007
(0.35)
-0.002
(-0.08)
0.112
(1.19)
-0.036***
(-2.78)
-0.029***
(-2.69)
-0.371***
(-11.87)
-0.134***
(-2.65)
0.111***
(4.77)
0.042**
(2.06)
0.035
(1.56)
-0.054***
(-3.82)
0.045**
(2.07)
-0.313***
(-7.64)
0.041
(1.25)
0.017
(0.57)
-0.002
(-0.14)
-0.022
(-1.08)
-0.067***
(-2.58)
0.104
(1.12)
Surplus Cash
-0.084***
(-2.81)
0.266***
(8.20)
0.007
(0.27)
0.000
(0.00)
ln(Sales Growth)
Return
ROA
PPE
Mod. Z-Score
Rating
Delta
Vega
0.004
(0.23)
-0.061**
(-2.04)
0.020
(1.45)
0.151***
(5.95)
0.276***
(8.67)
0.004
(0.13)
-0.006
(-0.13)
0.047
(0.48)
0.055
(1.52)
-0.297***
(-10.81)
0.305***
(12.09)
-0.058**
(-2.53)
-0.067***
(-3.51)
-0.007
(-0.36)
0.017
(1.37)
0.014
(0.60)
5,967
0.462
0.097***
(4.63)
5,585
0.396
0.077***
8.38
Total Sensitivity
Observations
Adj. R-squared
Avg. coefficient
t-statistic
Diff. in avg. coef.
t-statistic
5,967
0.464
-0.106***
(-3.49)
5,585
0.404
0.008
0.82
5,538
0.274
0.069***
8.40
52
0.046
(0.46)
0.059
(1.63)
-0.270***
(-10.06)
0.298***
(12.42)
-0.093***
(-2.85)
0.121***
(4.96)
5,538
0.281
Panel B: Scaled Incentive Variables
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
Book Leverage
R&D Expense
CAPEX
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
ln(Stock
Volatility)
(4)
R&D
Expense
(5)
Book
Leverage
(6)
-0.047**
(-2.37)
-0.029***
(-2.65)
-0.359***
(-12.46)
-0.096**
(-2.03)
0.108***
(5.71)
0.038
(1.54)
0.041*
(1.94)
0.012
(0.88)
0.054***
(2.72)
-0.274***
(-7.18)
0.082***
(2.59)
0.022
(0.78)
0.029
(1.57)
-0.005
(-0.28)
-0.039
(-1.49)
0.121
(1.25)
-0.032
(-1.61)
-0.027***
(-2.68)
-0.347***
(-11.76)
-0.064
(-1.44)
0.049*
(1.93)
0.024
(1.00)
0.043**
(2.05)
-0.015
(-0.97)
0.063***
(2.96)
-0.272***
(-7.03)
0.075**
(2.27)
-0.031
(-0.95)
0.057***
(3.61)
0.004
(0.22)
-0.024
(-1.04)
0.173*
(1.89)
Surplus Cash
-0.116***
(-3.46)
0.262***
(9.24)
0.019
(0.70)
0.022
(0.69)
ln(Sales Growth)
Return
ROA
PPE
Modified Z-Score
Rating
Delta / Total Wealth
Total Wealth
Vega / Total Wealth
-0.184***
(-8.07)
0.024
(1.23)
0.049
(1.59)
-0.118***
(-4.95)
0.078***
(4.16)
0.254***
(7.52)
0.278***
(9.23)
0.009
(0.31)
0.005
(0.15)
0.051
(0.52)
0.065*
(1.73)
-0.284***
(-10.20)
0.306***
(12.61)
-0.062**
(-2.36)
-0.041**
(-2.19)
0.092**
(2.52)
Tot. Sensitivity / Tot. Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
5,967
0.484
5,585
0.424
0.131***
5.95
5,538
0.275
-0.234***
(-12.02)
0.039*
(1.85)
-0.063***
(-2.99)
0.061***
(3.76)
0.061
(0.68)
0.046
(1.33)
-0.226***
(-8.80)
0.264***
(12.72)
-0.173***
(-4.99)
0.003
(0.17)
0.165***
(4.92)
0.177***
(4.70)
0.351***
(7.15)
5,967
0.497
5,585
0.406
0.231***
7.55
5,538
0.343
0.010***
7.37
53
-0.125***
(-3.95)
Table 5
Comparison of the association between vega and total sensitivity and alternative volatility
measures
This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive 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: Unscaled Incentive Variables
ln(Asset Volatility)
(1)
(2)
Vega
0.078**
(2.42)
Total Sensitivity
Observations
Adjusted R-squared
Difference in coefficients
t-statistic
ln(Systematic Volatility)
(3)
(4)
-0.066*
(-1.81)
0.093***
(3.57)
5,967
0.534
5,967
0.536
0.015
1.02
ln(Idiosyncratic Volatility)
(5)
(6)
-0.065**
(-2.48)
0.002
(0.06)
0.013
(0.67)
5,967
5,967
0.448
0.446
0.068***
3.14
5,967
5,967
0.498
0.495
0.078***
6.49
Panel B: Scaled Incentive Variables
ln(Asset Volatility)
(1)
(2)
Vega / Tot. Wealth
0.138***
(2.96)
Total Sens. / Tot. Wealth
Observations
Adjusted R-squared
Difference in coefficients
t-statistic
ln(Systematic Volatility)
(3)
(4)
ln(Idiosyncratic Volatility)
(5)
(6)
0.021
(0.68)
0.048
(1.45)
0.157***
(3.01)
5,967
0.546
5,967
0.549
0.119***
(3.66)
5,967
0.453
0.018
0.79
54
5,967
0.460
0.098***
5.63
0.173***
(4.83)
5,967
0.516
5,967
0.531
0.124***
10.08
Table 6
Comparison of the association between relative leverage and total sensitivity and future
volatility, R&D, and leverage
This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive 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: Relative Incentive Variables
Relative Leverage Ratio
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
-0.010
(-1.23)
-0.011
(-1.23)
-0.114***
(-3.05)
Tot. Sens. / Tot. Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Diff. in absolute value of avg. coef.
t-statistic
4,994
0.496
4,703
0.363
-0.045***
3.44
ln(Stock
Volatility)
(4)
R&D
Expense
(5)
Book
Leverage
(6)
0.200***
(5.02)
0.170***
(4.33)
0.360***
(6.85)
4,994
0.517
4,703
0.383
0.244***
7.17
4,647
0.315
4,647
0.245
0.199***
5.56
Panel B: Log of Relative Incentive Variables
ln(Rel. Lev. Ratio)
ln(Stock
Volatility)
(1)
-0.141***
(-5.08)
R&D
Expense
(2)
-0.033**
(-2.22)
Book
Leverage
(3)
-0.290***
(-9.29)
Tot. Sens. / Tot. Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Diff. in absolute value of avg. coef..
t-statistic
3,329
0.532
3,180
0.403
-0.155***
9.53
ln(Stock
Volatility)
(4)
R&D
Expense
(5)
Book
Leverage
(6)
0.220***
(5.38)
0.091***
(3.52)
0.318***
(9.03)
3,329
0.543
3,180
0.413
0.209***
8.50
3,120
0.400
3,120
0.408
0.055*
1.85
55
Table 7
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 unscaled (Panel A) and scaled (Panel B) incentive 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: Unscaled Incentive Variables
Vega
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
0.035
(1.27)
0.089***
(4.85)
-0.070***
(-3.70)
Equity Sensitivity
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
10,048
0.550
9,548
0.343
0.018
1.44
ln(Stock
Volatility)
(4)
R&D
Expense
(5)
Book
Leverage
(6)
0.058***
(2.69)
0.072***
(6.05)
0.156***
(5.17)
10,048
0.552
9,548
0.342
0.095***
6.63
9,351
0.330
ln(Stock
Volatility)
(4)
R&D
Expense
(5)
Book
Leverage
(6)
0.196***
(13.47)
0.058***
(3.25)
0.288***
(11.04)
10,048
0.594
9,548
0.340
0.181***
14.21
9,351
0.363
9,351
0.317
0.077***
5.39
Panel B: Scaled Incentive Variables
Vega / Tot. Wealth
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
0.103***
(5.51)
0.131***
(6.13)
-0.017
(-0.74)
Equity Sens. / Tot. Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
10,048
0.579
9,548
0.347
0.072***
5.84
9,351
0.315
0.108***
10.56
56
Table 8
Comparison of two-stage least squares estimates of the relation between vega and total
sensitivity and future volatility, R&D, and leverage for 2006 to 2010
This table presents two-stage least squares estimates. First-stage results for the model for ln(Stock Volatility) are
shown in Panel A. Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled
incentive variables in Panel C. Incentive variables, instruments, and controls (untabulated in Panels B and C) are
measured in year t. The risk choices are measured in year t+1. The incentive variables are described in detail in
Appendix A. Other 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: First-stage estimates of incentive variables
Control Variables
CEO Tenure
Cash Compensation
ln(Sales)
Market-to-Book
Book Leverage
R&D Expense
CAPEX
Vega /
Tot. Wealth
(4)
Delta /
Tot. Wealth
(5)
Tot. Sens. /
Tot. Wealth
(6)
0.095***
(4.88)
0.151***
(2.84)
0.208***
(5.60)
-0.018
(-0.81)
0.193***
(7.41)
0.096***
(4.85)
0.028
(1.35)
-0.248***
(-14.85)
0.010
(0.71)
0.048
(1.61)
-0.111***
(-4.00)
0.053***
(2.59)
0.238***
(7.28)
-0.008
(-0.40)
-0.141***
(-5.87)
-0.050**
(-2.36)
0.003
(0.20)
0.099***
(3.57)
0.134***
(3.55)
-0.020
(-1.02)
0.079***
(3.07)
0.010
(0.41)
0.062**
(2.01)
-0.172***
(-10.55)
-0.005
(-0.44)
0.002
(0.09)
-0.145***
(-6.31)
0.374***
(11.15)
0.141***
(4.28)
0.002
(0.11)
-0.121***
(-5.86)
-0.010
(-1.06)
0.017*
(1.86)
0.006
(1.57)
-0.016***
(-2.79)
0.007
(0.86)
-0.025***
(-4.22)
-0.009
(-0.39)
0.904***
(9.36)
0.045**
(2.50)
0.023
(1.32)
0.024
(1.34)
-0.048**
(-2.07)
0.006
(0.38)
-0.023
(-1.53)
0.229***
(3.32)
0.253**
(2.44)
0.070***
(3.19)
-0.063*
(-1.88)
-0.066***
(-2.84)
-0.018
(-0.75)
0.029
(1.46)
-0.070***
(-3.97)
0.107***
(2.58)
-0.036
(-1.58)
0.104
(1.64)
0.030
(1.22)
0.039**
(2.18)
0.004
(0.24)
-0.154***
(-8.63)
-0.086*
(-1.78)
0.053***
(2.98)
-0.025
(-0.68)
-0.034
(-1.15)
-0.056***
(-2.95)
0.007
(0.41)
-0.078***
(-4.63)
-0.003
(-0.07)
5,916
0.866
0.604
24.05
0.004
5,916
0.371
0.0569
4.52
0.081
5,916
0.271
0.0138
11.86
0.015
5,916
0.197
0.0289
11.15
0.017
5,916
0.311
0.00953
11.27
0.017
Vega
(1)
Delta
(2)
Tot. Sens.
(3)
0.098***
(3.66)
0.135***
(3.44)
0.422***
(8.55)
0.099***
(4.59)
-0.020
(-1.20)
0.164***
(5.59)
-0.013
(-0.53)
0.005
(0.30)
0.013
(1.24)
0.046**
(2.49)
0.057***
(4.47)
-0.007
(-0.72)
0.006
(0.59)
0.023**
(2.18)
0.040*
(1.91)
-0.028
(-1.10)
-0.023
(-1.44)
-0.030
(-1.32)
0.055***
(3.14)
-0.017
(-1.03)
0.360***
(5.16)
0.095**
(2.20)
5,916
0.386
0.0247
12.16
0.014
Total Wealth
Instruments
Cash Ratio
Returnt
Returnt-1
ROA
State Income Tax Rate
CEO Age
High Salary
Total Wealth
Observations
Adjusted R-squared
Partial R-squared
Partial F-statistic
p-value
57
Table 8, continued
Second-stage estimates
Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in
Panel C. Incentive variables, instruments, and controls (untabulated in Panels B and C) are measured in year t. The
risk choices 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. In Panels B and C, we report coefficient
estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95% confidence intervals.
Panel B: Second-stage estimates using unscaled incentive variables
Vega
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
ln(Stock
Leverage Volatility)
(3)
(4)
0.021
(0.23)
1.007***
(6.27)
-0.196**
(-2.54)
Total Sensitivity
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
5,916
0.462
5,555
0.488
0.277***
4.32
R&D
Expense
(5)
Book
Leverage
(6)
0.419***
(4.05)
1.019***
(4.75)
0.241**
(2.13)
5,916
0.466
5,555
0.465
0.560***
5.14
5,511
0.274
R&D
Expense
(5)
Book
Leverage
(6)
0.280*
(1.80)
0.833***
(5.81)
0.152*
(1.66)
5,916
0.464
5,555
0.472
0.423***
4.75
5,511
0.279
5,511
0.273
0.283***
4.24
Panel C: Second-stage estimates using scaled incentive variables
ln(Stock
Volatility)
(1)
Vega / Total Wealth
-0.087
(-0.64)
R&D
Expense
(2)
Book
ln(Stock
Leverage Volatility)
(3)
(4)
0.876*** -0.346***
(6.16)
(-2.59)
Tot. Sensitivity / Tot. Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
5,916
0.462
5,555
0.506
0.147**
2.26
5,511
0.283
0.274***
3.90
58
Table 9
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 unscaled (Panel A) and scaled (Panel B) incentive
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: Change in unscaled incentive variables
Δ Vega
Δ ln(Stock
Volatility)
(1)
Δ R&D
Expense
(2)
Δ Book
Leverage
(3)
-0.038
(-1.27)
-0.004
(-0.14)
-0.017
(-0.58)
Δ Equity Sensitivity
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
1,168
0.0587
1,131
0.0351
-0.020
-1.19
1,106
0.109
Δ ln(Stock
Volatility)
(4)
Δ R&D
Expense
(5)
Δ Book
Leverage
(6)
-0.036
(-1.13)
0.014
(0.65)
0.145***
(4.95)
1,168
0.0587
1,131
0.0353
0.041**
2.40
1,106
0.128
0.061***
3.95
Panel B: Change in scaled incentive variables
Δ Vega / Total Wealth
Δ ln(Stock
Volatility)
(1)
0.035
(0.96)
Δ R&D
Expense
(2)
0.012
(0.31)
Δ Book
Leverage
(3)
-0.005
(-0.11)
Δ Equity Sens. / Total Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
1,168
0.138
1,131
0.0312
0.014
0.66
1,106
0.109
Δ ln(Stock
Volatility)
(4)
Δ R&D
Expense
(5)
Δ Book
Leverage
(6)
0.074*
(1.91)
-0.005
(-0.13)
0.247***
(6.61)
1,168
0.140
1,131
0.0312
0.105***
5.05
1,106
0.147
0.091***
5.73
59
Table 10
Comparison of the association between vega and equity sensitivity adjusted for long-term
incentive award convexity and future volatility, R&D, and leverage
This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables
adjusted to include the estimated convexity from long-term incentive awards. 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 and adjusted for the convexity of long-term incentive awards. Control and
dependent variables are described in Appendix B. Total wealth is also adjusted by the value of long-term incentive
awards. 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: Unscaled Incentive Variables
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
-0.066**
(-2.05)
0.157***
(6.07)
-0.071***
(-3.74)
Adjusted Vega
Adjusted Total Sensitivity
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
ln(Stock R&D
Book
Volatility) Expense Leverage
(4)
(5)
(6)
0.014 0.101*** 0.124***
(0.58)
(4.73) (5.07)
5,940
0.464
5,560
0.405
0.007
0.71
5,513
0.274
5,940
0.462
5,560
5,513
0.396
0.281
0.080***
9.08
0.073***
8.82
Panel B: Scaled Incentive Variables
Adj. Vega / Adj. Tot. Wealth
ln(Stock
Volatility)
(1)
R&D
Expense
(2)
Book
Leverage
(3)
0.057**
(2.16)
0.249***
(7.72)
0.090**
(2.55)
Adj. Tot. Sens. / Adj. Tot. Wealth
Observations
Adjusted R-squared
Average coefficient
t-statistic
Difference in avg. coef.
t-statistic
ln(Stock R&D
Book
Volatility) Expense Leverage
(4)
(5)
(6)
0.165*** 0.175*** 0.344***
(5.47)
(4.69) (7.22)
5,940
0.491
5,560
0.423
0.132***
6.68
5,513
0.275
0.099***
7.60
60
5,940
0.504
5,560
5,513
0.406
0.343
0.228***
8.30