We base our tests on a sample of U.S. firms over the period 2004 to 2009. Our sample begins in 2004 because this is the first year employee stock option data are available on
Compustat for a broad set of firms. We obtain stock prices and returns from CRSP and analyst forecasts from I/B/E/S. We calculate implied equity volatility using data from Optionmetrics and the approach in Bartov, Mohanram, and Nissim (2007). We estimate equations (1), (2), and (3) using the pooled cross-sectional sample and base reported t-statistics on standard errors clustered by firm and year to mitigate intertemporal and cross-sectional correlation of residuals (Gow, Ormazabal, and Taylor 2010). We estimate several versions of the equations using different combinations of the explanatory variables. We do so in part because data availability reduces the number of observations for some variables.
Table 1, Panel A, presents descriptive statistics for each variable we use in our analyses.
Regarding our measures of common equity risk and expected return, Panel A reveals that realized equity volatility, EQUITYVOL, averages 49%, and implied volatility, IMPLIEDVOL, averages 46%. Panel A also reveals that the mean of expected equity cost of capital, ECC, is 13%. Panel A reveals that the mean of OPTIONS is 0.09, which indicates that the average ratio of options outstanding to the total of common equity shares and option outstanding is 9%. This
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is slightly larger than the 6.4% reported by Core and Guay (2001) over an earlier sample period and is consistent with the use of options increasing over time.28
Regarding the control variables, Panel A reveals that the mean of LEVERAGE is 16%, which is consistent with the findings of Barth, Hodder, and Stubben (2008).29 The means of earnings, EARN, and change in earnings, CHANGE_EARN, are negative, but the medians are not. The mean (median) of EARN is –4% (3%) and of CHANGE_EARN is –1% (0%). The left skewness of earnings is consistent with prior research (e.g., Ball, Sadka, and Sadka 2009).
Panel B of Table 1 presents the Pearson correlations between the variables. Most of the correlations are as expected. For example, the correlation between EQUITYVOL and
IMPLIEDVOL is large and positive (Pearson Corr. = 0.59; Spearman Corr. = 0.68). In addition, consistent with theory, both measures of risk are positively correlated with CREDITRISK and GROWTH (Pearson Corr. = 0.39 and 0.50 for CREDITRISK; 0.18 and 0.23 for GROWTH), and negatively correlated with SIZE (Corr. = –0.40 and –0.57), EARN (Corr. = –0.44 and –0.44), and CHANGE_EARN (Corr. = –0.13 and –0.08), consistent with the findings of Hanlon, Rajgopal, and Shevlin (2004). Also as expected, PROPENSITY is positively correlated with EQUITYVOL and IMPLIEDVOL (Corr. = 0.16 and 0.17). Although the univariate correlations generally are supportive of our predictions, we base our inferences on the multivariate relations specified by equations (1), (2), and (3).
Findings: Employee stock options and equity risk
Table 2, Panel A, presents summary statistics from estimating four versions of equation (1). Consistent with our prediction, the coefficient on OPTIONS is significantly negative in all
28 Core and Guay (2001) reports options divided by common shares. For ease of comparison, we convert the ratio in Core and Guay (2001) to the ratio we use.
29 Barth, Hodder and Stubben (2008) measures leverage as the ratio of debt to the book value of total assets. Our inferences are invariant to using this alternative measure of leverage.
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specifications, with t-statistics of –3.73, –3.77, –3.14, and –3.89. That is, the extent to which a firm has outstanding employee stock options is significantly negatively associated with equity risk, as measured by realized equity volatility. Panel A also reveals that leverage is significantly positively associated with equity volatility in all specifications (t = 4.85, 5.84, 4.21, and 5.05).
Finding a significant positive association between leverage and common equity volatility coupled with finding a significant negative association between employee stock options and common equity volatility indicates that employee stock options de-lever common equity, as predicted.
Regarding the other control variables, Panel A reveals, as expected, that CREDITRISK is positively associated with common equity risk in all versions, although the association is not significant in the version that includes GROWTH (t = 2.87, 0.98, 3.20, and 2.82). Also as expected, SIZE is significantly negatively associated with common equity volatility (t = –5.03, – 5.40, –5.68, and –4.94). In all specifications, earnings, EARN, is significantly negatively associated with common equity volatility, consistent with the findings of Hanlon, Rajgopal, and Shevlin (2004) (t = –11.22, –8.63, –11.25, and –12.45). The coefficient on change in earnings, CHANGE_EARN, is only marginally significant in two of the specifications (t = 1.65, –0.95, 1.64, and 0.82). The sign of the coefficient on CHANGE_EARN is sensitive to the inclusion of GROWTH, which suggests that CHANGE_EARN also is a proxy for growth. Consistent with growth reflecting greater risk, GROWTH is significantly positively associated with common equity volatility (t = 7.84). The coefficient on future risk taking, represented by CHANGE_RD,
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is also significantly positive (t = 3.02). Panel A also reveals that PROPENSITY is negatively associated with equity volatility, incremental to the other variables (t = –2.12).30, 31
Table 2, Panel B, presents summary statistics from estimating equation (1) with implied volatility, IMPLIEDVOL, as the measure of common equity risk. Panel B reveals inferences identical to those revealed by Panel A with respect to the relation between common equity risk and employee stock options. In particular, the coefficient on OPTIONS is significantly negative in all four specifications of equation (1), with t-statistics ranging from –3.96 to –5.04.
Regarding the control variables, Panel B reveals that, as expected, SIZE and EARN are consistently negatively associated with implied volatility, with t-statistics ranging from –6.63 to –9.62. LEVERAGE is significant in three of the specifications (t = 2.01, 3.60, 1.53, and 2.03).
However, the coefficients on CREDITRISK are not significantly different from zero; the t-statistics are all less than or equal to 1.00 in absolute value. Also as expected, the coefficient on GROWTH is significantly positive (t = 7.58) and those on CHANGE_EARN are significantly positive, except when GROWTH is included in the equation (t =2.17, 0.39, 2.02, and 2.15). The other control variables are not significantly associated with implied volatility.32, 33
Relation across option attributes
30 Table 1, Panel B, reveals that PROPENSITY is positively correlated with EQUITYVOL (Corr. = 0.16) and with OPTIONS (Corr. = 0.52). This suggests that the association between PROPENSITY and EQUITYVOL is subsumed by other explanatory variables.
31 Because firm size is a determinant of the calculated PROPENSITY and the two variables are highly correlated (Corr. = –0.55), we also estimated a version of equation (1) with PROPENSITY that excludes SIZE. Our inferences are insensitive to this exclusion.
32 We include GROWTH, PROPENSITY, and CHANGE_RD in separate regressions to preserve the sample size.
However, inferences are unchanged if all three are included in equation (1) jointly. Specifically, OPTIONS is significantly negatively related to both EQUITYVOL (t = –3.20) and IMPLIEDVOL (t = –3.16) incremental to the full set of control variables.
33 We also estimated a version of Equation (1) without PROPENSITY on the subsample of firms with PROPENSITY available. When EQUITYVOL (IMPLIEDVOL) is the dependent variable, the coefficient on OPTIONS is
significantly negative and similar in magnitude to that estimated on the full sample—the coefficient and t-statistic are –0.347 and –3.73 (–0.466 and –4.96). Thus, the smaller coefficient on OPTIONS when PROPENSITY is included in Equation (1) results from including PROPENSITY in the equation rather than sample composition.
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The potential for managers to increase the certainty of option payouts by reducing the strike price of the options, and the long term of employee stock options relative to other warrants are two characteristics that distinguish employee stock options from other warrants and that potentially invalidate the theoretical models upon which we base our predictions. Specifically, the role of OPTIONS in a firm’s capital structure should be more similar to liabilities and less similar to equity when 1) the options pose greater risk to the common equity holders because the option strike price is lowered, thereby making option payouts more certain, or 2) the options have longer terms to maturity and therefore have less of a de-levering effect on common equity.34 Thus, to provide additional support for our primary findings and inferences, we investigate whether the relation between RISK and OPTIONS varies predictably with these attributes of the employee stock options.
To examine the effects of increased certainty of option payouts associated with expected strike price reductions, we examine the association between option repricing and the relation between RISK and OPTIONS. Repricing is resetting the strike price on a stock option contract, typically after the stock price declines. We collect repricing data from ExecuComp, and we set an indicator variable, REPRICE, equal to one in the year a firm reprices options for at least one executive, and zero otherwise.35 Because we expect that the relation between employee stock options and common equity risk is less negative when firms have a tendency to reprice options, we predict a positive coefficient on the interaction of REPRICE and OPTIONS.
Warrant value is most sensitive to asset value changes for near-maturity, in-the-money warrants; therefore, warrant volatility increases as time to maturity decreases. Because asset
34 Schultz and Trautmann (1994) simulates and plots (in its Figure 1) equity volatility as a function of time to maturity and price. Equity volatility is at a minimum when the options are at the money and near expiration.
35 This analysis is based on firms covered by ExecuComp, i.e., current and former members of the S&P 1500 plus some requests by clients of S&P.
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volatility is a weighted average of warrant volatility and common equity volatility, for any given level of asset volatility, common equity volatility decreases as warrant volatility increases. This implies that common equity volatility should decrease as the time to maturity of employee stock options decreases. To examine the effects of longer option terms on the relation between RISK and OPTIONS, we set an indicator variable, AVG_TERM, equal to one if the average remaining term of options outstanding is above the pooled sample median, and zero otherwise. We estimate the average remaining term for outstanding options using each firm’s disclosed expected life of newly granted options. Following Landsman et al. (2006), we assume that the average remaining term for all options outstanding equals one-half of the expected life of newly granted options. Because options with longer terms to maturity have less effect on the risk of and expected return on common equity, we predict a positive coefficient on the interaction of AVG_TERM and OPTIONS.
Table 2, Panel C, presents the findings. The first four columns present findings from using realized volatility, EQUITYVOL, as the risk measure, and the last four columns present findings using implied volatility, IMPLIEDVOL. Consistent with predictions, the findings in Panel C reveal that the relation between OPTIONS and RISK is significantly less negative for firms that reprice options (t = 2.47 and 2.93 for EQUITYVOL and IMPLIEDVOL). In addition, untabulated findings reveal that the total coefficient on OPTIONS for firms that reprice options, i.e., the sum of the coefficients on OPTIONS and OPTIONS×REPRICE, is significantly positive (t = 1.92 and 2.15 for EQUITYVOL and IMPLIEDVOL). These findings suggest that option repricing changes the characteristics of employee stock options such that the options have characteristics of liabilities.
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Panel C also reveals, as predicted, that the relation between OPTIONS and RISK is muted when the remaining average employee stock option term to maturity is above the sample median.
The positive coefficient on the interaction variable, OPTIONS×AVG_TERM, indicates that the relation is significantly less negative for both risk proxies (t = 2.59 and 2.16 for EQUITYVOL and IMPLIEDVOL). However, untabulated findings reveal that the total coefficient on
OPTIONS for firms with options with longer terms to maturity, i.e., the sum of the coefficients on OPTIONS and OPTIONS×AVG_TERM, is significantly negative for both risk proxies (t = – 2.09 and –4.08 for EQUITYVOL and IMPLIEDVOL). These findings suggest that although employee stock options with longer terms to maturity have characteristics less similar to warrants than shorter-term options, they do not have characteristics of liabilities.
Taken together, the results in Table 2, Panel C, are consistent with the predictions of theory: employee stock options with contractual terms closer to true warrants exhibit stronger negative associations with common equity risk.
Leverage Ratios
Table 2, Panel D, presents summary statistics from estimating four versions of equation (2). As in Table 2, Panel C, the first set of columns presents findings from using realized volatility, EQUITYVOL, as the risk measure, and the second set presents findings using implied volatility, IMPLIEDVOL.
Turning first to the first set of columns in which EQUITYVOL is the risk measure, the first two columns of Panel D, in which LEVERAGE is calculated treating employee stock options as equity, reveal that the coefficient on LEVERAGE is significantly positive, as expected (t = 5.10). The coefficient on LEVERAGE also is significantly positive in the next two columns, where LEVERAGE is calculated treating employee stock options as liabilities (t = 4.31). More
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importantly for our research question, the first set of columns reveal that the coefficient on LEVERAGE is larger when options are treated as equity than when they are treated as liabilities (0.223 vs. 0.196), and an untabulated t-test reveals that this coefficient difference is significant (t
= –7.39). The findings in the second set of columns, relating to IMPLIEDVOL, reveal the same inferences as the first set of columns. In particular, LEVERAGE has a significantly larger coefficient when options treated as equity (0.114 vs. 0.107; untabulated t = –3.43).
The findings in Panel D reveal that treating employee stock options as equity results in a leverage ratio that has a significantly stronger relation with common equity risk than treating the options as liabilities. This indicates that classifying options as liabilities undermines the faithful representation of leverage with respect to common equity risk.
Robustness checks
We conduct tests to check the robustness of our inferences; findings from all tests support the inferences we obtain from the tabulated findings. First, because there are few established models of the determinants of equity volatility, our empirical specification of equation (1) is necessarily ad hoc. Thus, to investigate the robustness of our inferences, we include in equation (1)—with EQUITYVOL and with IMPLIEDVOL as the dependent variable—additional variables shown by prior research to be associated with common equity risk or return. Specifically, we include the equity book-to-market ratio, momentum, analyst forecast dispersion, the inverse of price per share, and firm age as additional explanatory variables. The untabulated findings reveal that although the significance of the association between common equity risk and some of control variables, including CHANGE_EARN, differs when these variables are included in the estimating equation, the association between common equity risk and OPTIONS is consistently significantly negative. Second, because our results could be influenced by the unusually high
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market volatility in 2008, we re-estimate our equations excluding observations from 2008.
Third, as an alternative control for the propensity to issue options, we include option grants in the preceding year. Fourth, we measure OPTIONS as their estimated value, rather than as the
number of options. Fifth, because common equity volatility is serially correlated, we estimate equation (1) including EQUITYVOLt as an explanatory variable when EQUITYVOLt+1 is the dependent variable.
Findings: Employee stock options and expected return on equity
Table 3 presents summary statistics from estimating two versions of equation (3).
Consistent with our findings for common equity risk, statistics in Table 3 from both versions reveal that OPTIONS is negatively associated with the expected equity cost of capital, ECC (t = –3.84 and –5.47). Also consistent with the common equity risk findings, the association between ECC and LEVERAGE is positive (t = 2.40 and 3.25). As expected, SIZE is significantly
negatively associated with ECC (t = –4.94 and –6.55) and BETA is significantly positively associated (t = 3.80 and 2.16). BM and DISPERSION are not significantly associated with ECC (t = –1.26 and –0.43 for BM, and –0.98 for DISPERSION) and, contrary to expectations, MOM is significantly negatively associated (t = –4.47 and –2.30).
V. SENSITIVITY OF CLAIMS VALUES TO CHANGES IN ASSET VALUES