Managerial incentives to increase firm volatility provided by debt, stock, and options. Joshua D. Anderson

Transcription

1 Managerial incentives to increase firm volatility provided by debt, stock, and options Joshua D. Anderson (617) John E. Core* (617) Abstract We use option pricing theory to derive and to calculate an overall measure of risk-taking incentives using managers debt, stock, and option sensitivities to firm volatility. We compare this measure to option vega and relative measures used by the prior literature. Vega does not capture risk incentives from managers ownership of stock and debt, and does not reflect the fact that employee options are warrants. The relative measures do not correctly incorporate the sensitivity of option value to firm volatility. We find that the new measure is more highly associated with risk choices than vega and the relative measures. First draft: October 19, 2011 This draft: March 25, 2013 * Corresponding author. We gratefully acknowledge comments from Ana Albuquerque (discussant), Wayne Guay, Mitchell Petersen, Eric So, Daniel Taylor, Anand Venkateswaran, and seminar participants at Columbia University, MIT Sloan, Northeastern University and the financial support of the MIT Sloan School of Management. We thank Ingolf Dittmann for his estimates of CEO non-firm wealth.

2 1. Introduction A large literature uses the sensitivity of stock options to an increase in stock volatility ( vega ) to study whether options provide managers incentives to increase risk (e.g., Guay, 1999; Core and Guay, 2002; Coles et al., 2006; Hayes et al., 2012). Studies on early samples show a strong positive association between vega and risk-taking (Guay, 1999; Coles et al., 2006), whereas studies on later samples show mixed results (e.g., Hayes et al., 2012). We re-examine vega and show that it has two shortcomings: (1) it does not capture potential risk incentives from managers ownership of stock and of debt (unsecured pensions and deferred compensation), and (2) it does not reflect the fact that employee options are warrants. Limited liability implies that firm 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, 1973, 1974). When a firm has options, this increase in equity value is shared between the stock and options. This implies an option sensitivity to volatility that is larger than vega. Because options are warrants, an increase in volatility that increases the value of an option comes in part from a reduction in the value of stock. If the firm has no debt, all of the increase in option value from an increase in volatility comes from a decrease in stock value. This implies a stock sensitivity to volatility that goes from being negative to positive as leverage increases. These interrelations at the firm level imply that a manager s attitude toward an increase in firm volatility will be affected by the relative magnitudes of the firm s debt, stock, and option sensitivities to firm volatility and by the relative magnitudes of the managers holdings of debt, stock, and options. To estimate the sensitivities of the firm s debt, stock, and options to firm volatility, we value total firm equity (stock and stock options) as an option on the value of firm assets (e.g., 1

3 Eberhart, 2005; Campbell et al., 2008; Bharath and Shumway, 2008). This option pricing model gives an estimate of the decrease in debt value for a given increase in firm volatility. Since total firm value has no sensitivity to volatility, a decrease in debt value implies an equal increase in equity value. This 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. Our primary sample contains 6,020 Execucomp CEO-years from 2006 to The typical firm in this sample has low leverage. It is intuitive therefore that the typical firm has a very low debt sensitivity to firm volatility, and therefore low equity sensitivity to firm volatility. As the firms leverage increases, however, the debt sensitivity to firm volatility becomes much more negative, while the option sensitivity remains fairly constant. The stock sensitivity to firm volatility is negative for low values of leverage (where the dilution effect of warrants dominates), but becomes strongly positive for high levels of leverage (where the option value of equity dominates). We calculate a total sensitivity measure that sums the sensitivities of the CEO s debt, stock, and options to firm volatility. The average CEO in our sample owns roughly 2% of the debt, 2% of the stock, and 16% of the options. Accordingly, in terms of incentives to increase volatility, the typical CEO has small negative incentives from debt, small or negative incentives from stock, and large positive incentives from options. Further, 92% of our CEOs have total incentives from debt, stock, and options to increase risk, and these incentives can be substantial. A one standard deviation increase in firm volatility increases the average CEO s wealth by $3 million, or 7% of total wealth. As leverage increases, the average CEO s debt sensitivity to firm volatility decreases, but the average CEO s equity sensitivity (the sum of stock and option 2

4 sensitivities) to volatility increases more because the stock sensitivity changes from being negative to strongly positive. The total sensitivity increases as leverage increases, but the vega roughly remains constant with leverage. The vega and total sensitivity have a Pearson correlation of Because vega ignores debt and stock sensitivities, it can be a noisy and biased measure of risk-taking incentives. If the total sensitivity better reflects CEO incentives, we expect it to exhibit a higher association with CEO s risk-taking choices. To test this conjecture, we examine the association between the measures and three proxies for future firm risk: stock volatility, research and development expense, and leverage. We follow similar specifications in Coles et al. (2006) and Hayes et al. (2012). In general our results suggest that the total sensitivity is more highly associated with risk-taking. Measuring incentives with total sensitivity, we find the expected positive associations, though they are not always significant. Unexpectedly, we find that vega has a negative and significant coefficient in some regressions for our sample as compared to positive and significant coefficients for the sample in Coles et al. We examine modified specifications in which we scale the the CEO s risk-taking incentives with a proxy for the CEO s total wealth. We also scale CEO s incentive to increase stock price ( delta ) and with a proxy for the CEO s total wealth. Theory suggests that higher risk-taking incentives relative to wealth lead to higher risk-taking, and that higher delta relative to wealth leads to lower risk-taking. Prior research (e.g., Coles et al., 2006) controls for wealth effects by using tenure and compensation as proxies for CEO wealth. We find that the scaled measures explain firm risk better than the unscaled measures, and that the scaled total sensitivity explains firm risk better than the scaled vega. 3

5 The total sensitivity measure requires data on CEOs inside debt, which data became available only in To avoid this limitation, we also examine the equity sensitivity, which is equal to the total sensitivity minus the debt sensitivity. Empirically, the sample CEOs have little incentives from their inside debt, so their equity sensitivity is almost perfectly correlated with their total sensitivity. We compute the equity sensitivity from and compare it with vega. In this sample, we also find that equity sensitivity explains risk-taking better than vega, and that the scaled equity sensitivity is superior to the unscaled measures. A concern about our results is reverse causality (that is, when risk is expected to be high, firm use high risk-taking incentives). To explore the robustness of our results, we follow Hayes et al. (2012) and use the introduction of option expensing (SFAS 123R) as an exogenous change to incentives. Consistent with Hayes et al., we find no significant association between the change in vega and changes in firm risk for our sample. However, the change in scaled equity sensitivity is significantly positively associated with both the change in stock volatility and the change in leverage. To the extent that scaled equity sensitivity is a superior measure than vega, our results suggest that it may be premature to conclude that CEOs risk-taking incentives are not causally related to their risk-taking choices. Our analysis of the interrelation between the sensitivity of debt, stock, and options also implies that the relative risk-taking measures used in the recent literature (e.g., Cassell et al., 2012; Sundaram and Yermack, 2007; Wei and Yermack, 2011) are noisy and can be biased. Although the calculations are slightly different, these measures do not correctly incorporate the sensitivity of option value to firm volatility. We calculate a measure that attempts to correctly weight the manager s debt, stock, and option sensitivities. The prior measures suggest that CEOs on average tend to have a fairly large identification with debt holders: the average CEO has debt 4

6 incentives to reduce volatility that are three times his equity incentives to increase volatility. By contrast, the corrected measure, which explicitly takes into account volatility incentives from options, is an order of magnitude smaller, suggesting that CEOs have little identification with debt holders: the average CEO has incentives to reduce volatility that are equal to 0.3 times his equity incentives to increase volatility. 1 Despite these problems, these ratios provide reasonable explanatory power for risk choices. However, our scaled total sensitivity measure is generally more highly associated with risk-taking choices than the relative ratios. We contribute to the literature in several ways. We provide 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 option vega and relative measures used by the prior literature. Vega does not capture risk incentives from managers ownership of stock and debt, and does not reflect the fact that employee options are warrants. The relative measures do not correctly incorporate the sensitivity of option value to firm volatility. We find that the new measure is more highly associated with risk choices than vega and the relative measures. Finally, our measure offers a potential resolution to the unexpected result in Hayes et al. (2012) that changes in risk-taking incentives do not seem to be related to changes in risk-taking. The remainder of the paper proceeds as follows. In the next section, we first define the sensitivity of firm debt, stock, and options to firm volatility, and then define the corresponding measures of manager s sensitivities to volatility. In the third section, we describe how we select a 1 While the relative measures can address the question of whether a given CEO has more incentives to reduce risk than to increase risk, they do not necessarily order risk-taking incentives across CEOs. For example, suppose that two CEOs each have relative incentives of 0.9, and are otherwise identical but one CEO has risk-reducing incentives of -$900 and has risk-increasing incentives of $1,000, while the other CEO 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, even though the second CEO benefits more from increasing risk. 5

7 sample of CEOs from 2006 to 2010, and compare various measures of incentives. In the fourth section, we examine the determinants of the incentive measures. In the fifth section, we compare regressions using the measures to explain various firm outcomes and provide robustness tests. In the sixth 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 O. For simplicity in our notation, we assume for the moment that all options have the same exercise price and time to maturity and that each option is worth O. 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. Changes in firm volatility do not change the value of the firm, so: 0 (3) 6

8 Therefore, any loss in debt value due to volatility increases is offset by an equal gain in equity value: (4) More volatile returns increase the value of equity holders call option, which reduces the value of debt. The interests of debt and equity conflict. Equity prefers higher firm volatility, which raises the value of its call; debt prefers lower firm volatility, which increases the value of its short call. Now consider a firm with no debt financed with stock and employee stock options. Employee stock options are warrants because exercising the options results in the firm issuing new shares of stock and receiving the strike price. From above: (5) Analogous to (4), an increase in firm volatility has the following effect on the stock price and the option price: (6) Equation (6) shows that the price of a share of stock in a firm with only stock and employee stock options decreases when firm volatility increases (Galai and Schneller, 1978). The share price decreases because the increased volatility makes it more likely that the option will be in the money and that the current value of a share outstanding will be diluted. This result for options on stock is similar to the result when stock is an option on the value of the levered firm. Increases in volatility do not change the value of the firm: Therefore, any gains to the options are offset by losses to the stock. Now we combine the results for debt and options. An increase in firm volatility affects debt, stock, and option value according to the following relation: 7

9 (7) In firms with both debt and options, shareholders have purchased a call on the assets, and they have sold a call on the equity to employees. They are in a position with respect to the equity similar to the position of the debt holders with respect to the assets. When the firm is levered, increasing firm volatility causes shareholders to gain from the call on the asset but to lose on the call on the equity. Since the change in stockholders value is a combination of these two opposing effects, whether stockholders prefer more volatility depends on the number of options outstanding and firm leverage, as we illustrate next Estimation of firm sensitivities To estimate the sensitivities described above, we calculate the value of debt and options using standard pricing models. We then increase firm volatility by 1%, hold firm value fixed, and recalculate the values of debt, stock, and options. We estimate the sensitivities to a one percent change in firm volatility as the difference between these values. Appendix A describes the details. We first price employee options as warrants using the Black-Scholes model, as modified to account for dividend payouts by Merton (1973), and modified to reflect warrant pricing by Schulz and Trautmann (1994). Calculating option value this way gives a value for total firm equity. Second, we model firm equity as an option on the levered firm following Merton (1974) using the Black-Scholes formula. This model allows us to calculate total firm value and firm volatility following the approach of Eberhart (2005). With these values in hand, we calculate the value of the debt as a put on the firm s assets with strike price equal to the face value of debt. To calculate the sensitivities, we increase firm volatility by 1%, which implies a 1% increase in stock volatility. We use this new firm volatility to determine a new debt value. The sensitivity of the debt to a change in firm volatility is the difference between this value and the 8

10 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 Example of firm sensitivities In Panel A of Table 1, we show an example firm with $2.5 billion market value assets and firm volatility of 35%. We use values that are approximately the mean values of our sample described below. Options are 7% of shares outstanding, and have a price-to-strike ratio of The options and the debt have a maturity of four years. Leverage is the face value of debt divided by the sum of the book value of debt and market value of equity. To calculate the values and sensitivities, we assume a risk-free rate of 2.25%, that the interest rate on debt is equal to the risk-free rate, and that the firm pays no dividends. The first set of rows shows the change in the value of firm debt, stock, and options for a 1% change in the standard deviation of the assets at various levels of leverage. An increase in volatility reduces debt value, and this reduction is greater for greater leverage. This reduction in debt value is shared between the stock and options. Options always benefit from increases in volatility. When leverage is low, the sensitivity of debt to firm volatility is very low. Since there is little debt to transfer value from, option holders gain at the expense of stockholders when volatility increases. As leverage increases, the sensitivity of debt to firm volatility increases. As this happens, the stock sensitivity becomes positive as the stock offsets losses to options with gains against the debt. 9

11 The second set of rows show the sensitivity of the debt, stock, and options as a percentage of the market value of each security. As leverage increases, the market value of the debt increases because more debt is outstanding. However, the increase in the sensitivity of the debt increases faster than the value of the debt, as shown in Column (2). The percentage stock sensitivity in Column (3) and the percentage option sensitivity in Column (4) both increase as leverage increases. 2.2 Managers incentives from the sensitivity of firm capital structure to firm volatility 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: where (8) is the manager s average per option sensitivity to firm volatility, computed to reflect that employee options are warrants. (At this point, we begin to use the notation W to indicate that the option is valued as a warrant, in contrast to the notation O to indicate that the option is valued using Black-Scholes.) Vega incentives to stock volatility Prior literature uses the option vega, the sensitivity of managers option holdings to a change in stock volatility, as a proxy for incentives to increase volatility (Guay, 1999; Core and Guay, 2002; Coles et al., 2006; Hayes et al., 2012). The vega is the change in the Black-Scholes option value for a change in stock volatility: 10

12 (9) Comparing the vega with the total sensitivity in (8), one can see that the vega is a subset of total risk-taking incentives, and in particular 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 the vega to be similar to total risk-taking incentives, the firm must have low or no leverage (so that the volatility increase causes little re-distribution from debt value to equity value) and the firm must have low amounts of options (so that the volatility increase causes little re-distribution from stock value to option value) Relative incentives to increase volatility Jensen and Meckling (1976) suggest a scaled measure of incentives: the ratio of riskreducing incentives to risk-increasing incentives. The ratio of risk-reducing to risk-taking incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option incentives: (10a) From Panel A of Table 1 above, the sensitivity of price to volatility can be negative when the firm has options but little leverage. In this case the ratio of risk-reducing to risk-taking incentives is: (10b) We term this ratio the relative sensitivity ratio. As in Jensen and Meckling, the ratio is informative about whether the manager has net incentives to increase or decrease firm risk. It can be useful to know whether risk-reducing incentives are greater than risk-increasing incentives (that is, whether Eq. (8) is negative or positive, or equivalently whether the ratio in Eq. (10) is 11

13 greater or less than one). If the ratio in Eq. (10) is less than one, then the manager has more risktaking 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 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 relative sensitivity ratio (10) becomes: (11) The first equality follows from (4):, and the sensitivity of total debt value to volatility divides off. The second equality follows from the definition of β and α as the manager s fractional holdings of debt and stock. An advantage of this ratio is that, if in fact the firm has no employee options, one does not have to estimate the sensitivity of debt to volatility to compute the ratio. Much prior literature (e.g., Anantharaman et al., 2011; Cassell et al., 2012; Sundaram and Yermack, 2007; Tung and Wang, 2011; Wang et al., 2010, 2011) uses this measure, and terms it the relative leverage ratio, as it compares the manager s leverage to the firm s leverage. Since most firms have options in their capital structure, to operationalize the relative leverage ratio, researchers make an ad hoc adjustment by adding the Black-Scholes value of the options to the value of the firm s stock and CEO s stock: (12) 12

14 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 : (13) These adjustments for options are not correct because the correct relative sensitivity measure shown in (10) uses the option sensitivity to firm volatility, which is quite different than the option value or the option delta. Only when the firm has no employee options are the relative leverage and incentive ratios equal to the relative sensitivity ratio. However, it is important to note that scaling away the levels information contained in (8) can lead to incorrect inference, even when calculated correctly. For example, imagine two CEOs who both have $1 million total wealth and both have a relative sensitivity ratio of 0.9. Although they are otherwise identical, CEO A has risk-reducing incentives of -$900 and has riskincreasing 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) 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 13

15 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. Prior literature (e.g., Guay, 1999) calculates vega using a 0.01 increase in stock volatility. The disadvantage of using a 0.01 increase in stock volatility for our calculations is that it implies an increase in firm volatility that grows smaller than 0.01 as firm leverage increases. Throughout this paper we report results using a 1% increase in firm volatility, which is equivalent to a 1% increase in stock volatility. So that the measures are directly comparable, we therefore use 1% increase in stock volatility to compute vega. The 1% vega is very highly correlated (0.93) with the 0.01 increase vega used in the prior literature, and our results with the 1% vega are very similar to results with the 0.01 increase vega 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. We assume that the value of the CEO s wealth outside the firm is 50% of the value of the CEO s debt, stock, and options. Wealth for the example CEO declines slightly with leverage. The CEO owns a slightly smaller percentage of debt than of equity, and as leverage increases his debt value increases less than his equity value decreases. The first set of rows shows 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 14

16 stock and options increase monotonically with leverage. Column (5) shows the total equity sensitivity, which is the sum of the stock and option sensitivities, increases sharply as the stock sensitivity goes from being negative to positive. Column (6) shows the total sensitivity, which is the sum of the debt, stock and option sensitivities. These total risk-taking incentives increase monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase in the equity sensitivity. Column (7) shows the vega for the example CEO. In contrast to the equity sensitivity and the total sensitivity which both increase in leverage, the vega first increases and then decreases with leverage in this example. Part of the reason is that the vega does not capture the debt and stock sensitivity. Holding this aside, the vega does not measure well the sensitivity of the option to firm volatility. It captures the fact that the option price is sensitive to stock volatility, but it misses the fact that equity value benefits from decreases in debt value. As leverage increases, the sensitivity of equity value to firm volatility increases dramatically (as shown by the increasingly negative debt sensitivity), but this effect is omitted from the vega calculations. Consequently, the vega is likely to be a good approximation of the CEO s incentives to increase risk when leverage is very low, but the approximation is much noisier as leverage increases. While the level measures of the CEO s incentives are useful, they essentially assume the same amount of CEO wealth across comparisons. If, as is frequently assumed in the literature (e.g., Hall and Murphy, 2002; Lewellen, 2006; Conyon et al., 2011), CEOs have decreasing absolute risk aversion, CEOs with different levels of wealth will value incentives with the same payoffs differently. Similarly, the same level of incentives will motivate a less wealthy CEO much more than a wealthier CEO. 15

17 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. The second set of rows show scaled incentive measures. Columns (2) through (7) show the sensitivities in the corresponding columns above as percentages of total wealth. These scaled measures show similar, but muted, relations with leverage as do the level measures. The percentages shown by the scaled measures appear small, but recall that the underlying sensitivities are for a 1% change in volatility. If the example CEO of the lowest leverage firm could increase firm volatility by (our sample standard deviation), the CEO s total wealth would increase by 2.3%. The final Columns (8) to (10) illustrate the various relative incentive measures. The relative sensitivity measure in Column (8) is calculated following Eq. (10) as the negative of the sum of debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is negative (as for the three lower leverage values) and as the negative of debt sensitivity divided by the sum of the stock and option sensitivity otherwise. The risk-reducing incentives decrease from -6 to -55 as leverage increases, while the risk-increasing incentives increase more slowly from 46 to 112. Accordingly, as leverage increases, the relative sensitivity measure increases from 0.13 (= 6/46) to 0.49 (= 46/112), 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) of the final rows, we illustrate how the relative leverage and relative incentive ratios for our example CEO. The relative leverage ratio is computed by 16

18 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 incentive ratio stays about 0.8, suggesting that the CEO is highly identified with debt holders. The relative incentive ratio, which has 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 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 and total sensitivity as a percentage of total wealth. Again, as noted above, these ratios only measure relative incentives correctly when the firm has little or no options, and even a correctly calculated relative-risking ratio can lead to incorrect inference. The incentive ratios are not informative about the magnitude of the sensitivity of the manager s wealth to an increase in firm volatility. 3. Sample and Variable Construction 3.1 Sample Selection We use two samples of Execucomp CEO data. Our main sample contains Execucomp CEOs from 2006 to 2010, and our secondary sample, described in more detail in Section 5.4 below contains Execucomp CEOs from 1992 to The total incentive measures described above require information on CEO inside debt (pensions and deferred compensation) and on firm options outstanding. Execucomp provides information on inside debt only beginning in 2006 (when the SEC began to require detailed disclosures). Our main sample therefore begins in The sample ends in 2010 because our tests require one-year ahead data that is only available through Following Coles et al. 17

19 (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, and the resulting sample contains 6,020 CEO-year observations that have complete data. 3.2 Descriptive statistics firm size, volatility, and leverage Table 2, Panel A shows descriptive statistics for volatility, the market value of firm debt, stock, and options, and leverage for the firms in our sample. We describe in Appendix A.3 how we estimate firm market values following Eberhart (2005). To mitigate the effect of outliers, we winsorize all variables each year at the 1 st and 99 th percentiles. Since our sample consists of S&P 1500 firms, the firms are large, with mean (median) market value of assets of $9.0 ($2.0) billion dollars. The mean (median) value of common stock is $7.1 ($1.5) billion, and the mean (median) value of debt is $1.5 ($0.3) billion. Employee stock options are a much smaller part of the capital structure with a mean (median) value of options is $118 ($29) million. A majority of firms in our sample have low leverage. The median value is 14%, although the mean in our sample is 19%. These low amounts of leverage suggest low agency costs of asset substitution for most sample firms (Jensen and Meckling, 1976). Table 2, Panel B presents sample descriptive statistics sorted by leverage in the same format as Table 1, Panel A. We rank the sample by leverage and divide it into five groups of 1,204 firm-years. Similar to Table 1, Panel A, the first set of rows shows the sensitivity of the value of firm debt, stock, and options for a 1% increase in firm volatility at various levels of 18

20 leverage. We describe in Section above and detail in Appendix A.4 how we calculate these sensitivities. The second set of rows show the sensitivity of the debt, stock, and options as a percentage of the market value of each security. Since firm size varies greatly, the percentage values are most interpretable, and we concentrate our discussion on the values in the second set of rows. Column (2) shows that as leverage increases the mean sensitivity of firm debt to firm volatility decreases. Intuitively, if the debt holders will be repaid with a very high probability, the value of their claims changes little with increases in firm volatility. The mean stock and option sensitivities in Columns (3) and (4) both increase with leverage. It is noteworthy that the stock sensitivity is negative for low levels of leverage (as increases in volatility benefit options at the expense of stock), but becomes positive for higher levels of leverage (as increases in volatility benefit both stock and options at the expense of debt). 3.3 Descriptive statistics CEO incentive measures Table 3, Panel A shows full sample descriptive statistics for the incentive measures. As discussed above in Section 2.2.4, 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.4 and A.5 provide details and notes the necessary Execucomp, Compustat and CRSP variable names. We begin by looking at the incentives provided by the CEOs debt, stock, and options. 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. In fact, 19

21 a CEO with large debt incentives (at the first quartile of the distribution) gains only $2,490 in additional wealth for a 1% decrease in firm volatility. Over half the CEOs have no debt incentives. The magnitude of the incentives from stock to increase firm risk is also small on average. However, there is substantial variation in the stock incentives, with a standard deviation of approximately $47 thousand as compared to $19 thousand for debt incentives. The average sensitivity of the CEO s options to firm volatility is an order of magnitude 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. As with the firm variables described above, we winsorize all incentive variables each year at the 1 st and 99 th percentiles. 2 The vega, calculated for a 1% increase in stock volatility rather than the 0.01 increase used in prior literature, is smaller than the total sensitivity, and has strictly positive values as compared to the total sensitivity which has about 8% negative values. To provide another comparison that abstracts away from size differences, we scale the sensitivities by CEO total wealth. We estimate CEO total wealth as the sum of the value of the CEO s debt, stock, and option portfolio and non-firm outside wealth as measured by Dittmann and Maug (2007). 3 The distributions of the scaled incentive measures are similar to those of the level measures. The average scaled total sensitivity is 0.14% of wealth. The value is low because 2 Consequently, the averages in the table do not add, i.e., the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity. 3 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., selling shares, and exercising options. 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. Dittmann and Maug provide the measure on their website. For those CEOs missing the measure, we impute the fraction of equity wealth to total wealth using a generalized linear model. We use the same explanatory variables in this model as in the model for incentive determinants described in 4.1 below. 20

22 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 a small fraction of the CEOs total wealth. For the CEO with large risk-reducing incentives (at the first percentile of the distribution), a one standard deviation decrease in firm volatility increases the CEO s wealth by 2%. The mean (median) relative leverage ratio is 3.03 (0.18), and the mean (median) relative incentive ratio is 2.29 (0.15). These values are similar to those in Cassell et al. (2012), who also use an Execucomp sample. These ratios are skewed, and are approximately one at the third quartile, suggesting that 25% of our sample CEOs have incentives to decrease risk. This fraction is much larger than the 8% of CEOs with net incentives to reduce risk based on the total sensitivity measure, and highlights the bias in the relative leverage and incentive measures. By contrast, the mean (median) relative sensitivity ratio is 0.32 (0.03), suggesting low incentives to decrease risk. To shed light on the differences between our incentive measures and those used in the prior literature, we present sample descriptive statistics sorted by leverage in Table 3, Panel B. As in Table 2, Panel B, we rank the sample by leverage and divide it into five groups of 1,204 firm-years. Similar to Table 1, Panel B, the first set of rows shows the sensitivity of the value of CEO s debt, stock, and options for a 1% increase in firm volatility at various levels of leverage. The second set of rows show the mean sensitivity of the CEO s debt, stock, and options as a percentage of the CEO s wealth. Since CEO wealth varies greatly, the percentage values are most interpretable, and we concentrate our discussion on the values in these rows. Column (2) shows that as leverage increases the mean of the CEOs debt sensitivity to firm volatility 21

23 decreases. Intuitively, the sensitivity of the firm s debt decreases in leverage, so the sensitivity of the CEO s inside debt also decreases, holding percentage ownership constant. The mean stock and option sensitivities in Columns (3) and (4) both increase with leverage. While the CEO s stock sensitivity is negative for low levels of leverage, the mean incentives from stock are very small as a fraction of wealth. When leverage is high, stock sensitivity is much larger. CEOs option sensitivity has also increases with leverage. Given the large increase is equity sensitivity shown in Column (5), the CEOs total sensitivity to firm volatility in Column (6) increases across leverage bins. By contrast, the vega in Column (7) has no relation with leverage. The vega excludes one of the two channels that affect option sensitivity to firm volatility: the stocksensitivity channel. When leverage is high, the stock price responds strongly to increases in firm volatility, changing the value of the stock options. Since the vega excludes this channel, it is biased downwards when leverage is high. The relative ratios (Columns (8) through (10)) all decrease in leverage, consistent with the increase in the total sensitivity in Column (6). The mean relative sensitivity ratio in Column (8) is below one for all of the leverage bins. This is consistent with the intuition that firms must provide risk-averse CEOs with incentives to increase risk. The relative leverage and incentive ratios are much higher than one for the two lowest leverage firm bins. According to these measures, low leverage firms choose to provide their CEO s with the most identification with debt holders. However, these are the firms that have few agency problems from debt because of their low leverage, so there is little need to provide strong identification with debt holders. This puzzling observation is a result of these ratios incorrectly weighting the sensitivity of the CEOs options to firm volatility. 22

24 Panel C of Table 3 shows correlations between the level sensitivity measures for the full sample. The total sensitivity and vega are highly correlated with each other. The Pearson (Spearman) correlation coefficient is 0.69 (0.83). The fact that the total sensitivity measure can take on negative values because it includes debt and stock sensitivities differentiates this measure from the vega measure. In addition, nearly five percent of the firms in our sample do not provide the CEO with stock options. These firms still provide their CEOs with differing levels of incentives using stock and inside debt even though all of these CEOs have a vega of zero. The total sensitivity is almost perfectly correlated with the equity sensitivity. Since debt sensitivity to firm volatility is low for most firms and CEOs percentage equity holdings are larger than their percentage debt holdings, including debt sensitivity does not provide much incremental information about CEOs incentives. The scaled measures of risk-taking incentives (total sensitivity, vega, and equity sensitivity) show similar correlations as the level measures, though scaled vega is more highly correlated with the scaled sensitivity measures than in levels. The scaled incentive measures exhibit much lower correlations with the relative measures. The relative leverage and incentive ratios, which incorrectly weight the sensitivity of CEOs options to firm volatility, show the lowest correlations with the other incentive measures, which explicitly calculate the sensitivity of stock options to volatility. The relative leverage and relative incentive ratios are almost perfectly correlated with each other. Because the correlation is so high, we do not include the relative incentive ratio in our subsequent analyses below. 4. Determinants of incentives 4.1 Research Design 23

25 Prior research focuses on: (1) what determines incentives (i.e., what types of firms use incentives more); and (2) how incentives affect firm risk choices. Coles et al. (2006) and Hayes et al. (2012) examine both of these questions, and we generally follow their research designs. Our regressions for the determinants of incentives take the following form: (14) Our control variables include the CEO s cash compensation, the CEO s age and tenure, which are intended to control for the CEO s outside wealth and risk aversion (Guay, 1999). We control for firm size using the natural logarithm of total sales, ln(sales), and for growth opportunities using Market-to-Book, R&D Expense, and CAPEX. We also control for Book Leverage, the debtto-assets ratio. We include additional variables related to the firm s and CEO s desire to defer compensation. Salary > $1 million indicates whether the CEO s salary is greater than $1 million. Section 162(m) of the Internal Revenue Service code limits the tax deductibility of nonperformance based compensation in excess of $1 million, and many firms require executives to defer compensation above this limit. Ceteris paribus, these firms will show lower cash compensation, higher equity incentives, and higher debt incentives. It will be less advantageous for executives to defer compensation when their current tax rates are lower. We proxy for low executive tax rates with an indicator for whether there is no state income tax on personal income in the state where the firm is headquartered and an indicator for whether the firm s headquarters are outside of the U.S. We also include an indicator for Liquidity Constraint if the firm generates negative cash flow from operations. By offering employees more non-cash compensation, cash-constrained firms can conserve cash. Finally, we include the stock return in years t (Return) and t-1 (Lag 24

26 Return). We also include year effects and fixed effects for industries at the 2-digit SIC level in all of the regressions. Appendix B summarizes how we measure these variables. 4.2 Determinants of incentives Table 4 presents the results of our regressions that examine the determinants of our incentive measures. Column (1) shows that the determinants of vega in our sample are similar to prior research: vega is larger for larger firms, firms with greater growth opportunities, and longer tenured CEOs. The determinants of the total sensitivity to firm volatility in Column (2) are similar with the exception that the total sensitivity is positively related to leverage, while vega is negatively related. The analysis above of Table 1 and Table 3 show that the equity sensitivity increases with leverage while the debt sensitivity decreases, and that the CEO s debt sensitivity is small relative to the equity sensitivity. Accordingly, total sensitivity increases with leverage. This result is consistent with risky firms providing incentives for CEOs to take risk. Vega, by contrast, decreases with leverage. As discussed above, scaling by wealth more directly addresses the fact that the same dollar value of incentives will motivate two CEOs differently if they have different levels of wealth. Columns (3) and (4) show that the determinants of vega and total sensitivity scaled by total wealth are different in several respects from the level measures. Most differences are intuitive: scaling by wealth removes some of the size affect from the levels measures, so the scaled measures show no relation with the size proxies Cash Compensation and ln(sales). CEO Tenure is negatively related to both of the scaled measures. The intuition is that new CEOs face greater risk that they will be a bad fit in their new positions (Gibbons and Murphy, 1992), and so need more risk-taking incentives as insurance against this fit risk. These risk-taking incentives are less important for longer serving CEOs because they have proven their ability to manage the 25

27 firm. The positive relation between tenure and the level of risk-taking incentives can be reconciled by noting that wealth grows faster with tenure (untabulated). One puzzling difference is that the scaled measures are negatively related to Market-to-Book, and one expects a positive relation between growth opportunities and risk-taking incentives per unit of wealth. However, note that the other proxy for growth opportunities, R&D Expense, is positively related to the scaled measures. Finally, we note that the return over the last two years is negatively related to both the level and scaled vega and total sensitivity. This follows from the mechanics of stock options: A positive return increases the price, and as the price increases, the stock and equity options go further in-the-money, and their sensitivities to changes in risk decrease. 4 Although not a focus of our analysis, in Columns (5) and (6) provide an analysis of the determinants of Delta and scaled delta as a comparison with our measures of risk-taking incentives. Consistent with the literature, larger firms and firms with high growth opportunities provide more incentives. Longer-serving CEOs have more incentives in the level, consistent with the idea that more explicit incentives are provided as fit concerns decline. The finding that lower incentives scaled by total wealth decline with tenure and age is puzzling, as here too one expects explicit incentives as fit concerns decline. Finally, we examine the determinants of the relative sensitivity and the relative leverage ratios in columns (7) and (8). 5 Since the ratios have a mass at 0, we estimate Tobit models. As discussed previously, these ratios do not necessarily order CEOs risk preferences as well as the 4 Although it might be desirable for firms to re-set risk-taking incentives following price changes, it is difficult for firms and managers to rebalance risk-taking incentives (Gormley, Matsa, and Milbourn, 2013). 5 As noted above, the relative leverage and incentive ratios are almost perfectly correlated, so we do not include an analysis of the relative incentive ratio. (Results for it are virtually identical to those shown for the relative leverage ratio.) 26