Continued from page 1.
Brenner et al. (2000) gather repricing data from 1992-1995 for 134 companies and 333 affected executives. They find evidence that firms reprice executive options after poor firm-specific performance. They also show that repricing may be a function of compensation committee conflicts.
Carter and Lynch (2001) compare a cross-section of 263 firms that repriced stock options in 1998 to a control sample of firms that did not reprice executive stock options, despite options being out of the money. They find that firms reprice in response to poor firm-specific performance, but find no evidence that industry performance causes repricing. They also find no evidence that repricing is related to agency problems.
Chidambaran and Prabhala (2003) analyze 213 firm-repricing events from the Execucomp database for 1992-1997. They find that repricing firms have relatively high CEO turnover rates and smaller boards. Additionally, CEOs are often not the beneficiaries of repricings because they have larger share holdings and fewer options. Overall, these authors conclude that repricing does not reflect entrenched management or weak governance.
Both Carter and Lynch (2001) and Chidambaran and Prabhala (2003) find repricing happens most often in high-technology industries. Their findings suggest that repricing serves as a retention tool in competitive labor markets.
None of the empirical papers cited above address the incentive effects associated with repricing. Acharya et al. (2000) argue that the optimality of providing an agent with a "repriceable" option occurs because the benefits from providing the agent with the "right" incentive after stock price declines are greater than the costs associated with the negative incentives provided at the time of the initial option grant.
Johnson and Tian (2000) analyze the initial incentive effects of a repriceable option grant. They illustrate that repriceable options offer lower (relative to Black-Scholes) incentives to increase the stock price, especially as the price falls below the exercise price. They also find that the incentives to increase volatility are greater (relative to Black-Scholes) for executives who hold repriceable options.
The principal contribution of this study is that it provides an examination of the effect of executive risk-taking incentives on the repricing decision. By using variables that proxy for "poorly aligned" incentives, I hypothesize that such incentives are positively associated with repricing.
II. Casino Industry, 1993-1998
The investment, operating, and financing environment of gaming firms between 1993 and 1998 could best be described as "turbulent." The period was characterized by significant revenue growth amid heavy capital spending, declining profitability, and the increased use of debt financing.
Casino gaming industry revenues grew substantially from $7.56 billion in 1989 to $26.29 billion in 1998 (see Rohs and Blaydes, 1999), a 14.8% compound annual growth rate. Native American and riverboat gaming markets generated most of this growth. Nevada, the state synonymous with gambling, saw its share of gaming revenues decline from 62.9% in 1989 to 30.7% in 1998, while riverboat and Native American markets contributed 27.7% and 26.2%, respectively, in 1998 (Rohs and Blaydes, 1999).
The growth in industry revenues during this time frame occurred because of high levels of investment by casino gaming firms. Table I illustrates mean and median values of capital expenditures (net of depreciation) as a percentage of sales between 1993 and 1998 across the gaming firms in the sample. Through 1997, the casino gaming industry spent heavily on capital assets. As a point of comparison, the median level of net capital expenditures for the S&P 1500 during 1993-1998 ranged from 1.1% to 1.3%.
Furthermore, the nature of the investment spending is fairly homogeneous across gaming firms. My examination of 10-K filings by sample firms shows that gaming firms invest in new casino development projects; renovate existing casino properties; add room capacity; maintain casinos and hotels; and acquire existing casinos, other gaming companies, and land. The largest portion of capital expenditures goes toward casino development and renovations. The most visible investment spending goes into developing new casino projects. Some Las Vegas Strip developments, such as Bellagio (owned by Mirage), Venetian (owned by MGM Grand), and Mandalay Bay, have all required well in excess of $1 billion of capital to build (Rohs and Blaydes, 1999).
Such a homogeneous investment opportunity set might be unlikely to increase a firm's risk. Nevertheless, at least two feasible investment opportunities could add to a casino's risk profile. First, managers of publicly held casino firms increasingly acquired other casino operations (both public and private) in response to the increasingly competitive environment. For example, MGM Grand acquired Mirage during 2000 in a deal that essentially quadrupled its asset base. Large acquisitions might generate increased uncertainty among investors about the ability of the merged firm to achieve the sorts of benefits sought from the acquisition (i.e., cost savings, revenue gains, other synergies, etc.).
Second, if a casino firm's expertise and income is heavily skewed toward gaming rather than hotel operations, investment in a new hotel may pose relatively more risks than would investment in additional gaming facilities. For example, according to Prudential Equity Group Research Quarterly Take (2003), 76% of Harrah's revenue is derived from its casino gaming operations, but only 19% of its revenues is attributable to rooms, and food and beverage. The same report suggests that Harrah's largest competitors, MGM Mirage and Mandalay Resort Group, strike a more even balance between earnings from casino operations relative to hotel earnings.
The heavy investments made by casino gaming firms coincided with declining profitability. Table I also shows that in 1993, although the typical gaming firm profitability is similar to that of the S&P 1500 (if not greater), accounting returns declined significantly in subsequent years. Means and medians of return on invested capital of gaming firms declined well below those of S&P 1500 firms.
This environment of heavy investment and declining returns forced many gaming firms to increase their debt loads substantially (see Table I). In 1993, the median gaming firm was capitalized with 53.3% debt. By 1998, the median had increased to 70%. The heavy debt loads of casino firms typically underlie long-term assets. Net property, plant, and equipment accounted for over 70% of total assets during all years of the sample period.
This combination of operating and financial factors negatively affected gaming firm equity values (see Table I). Asset market-to-book ratios declined during 1993-1998, reflecting some combination of expectations of continued weakness in operating performance and greater risk. The median market-to-book ratio of gaming firms was 2.33 in 1993, and gaming firm assets were typically valued more highly than those of S&P 1500 firms. By 1998, the market had taken a decidedly more pessimistic view of gaming firms as the median market-to-book ratio had fallen to 1.11.
Given the industry's poor performance, CEO turnover occurred relatively frequently. Eleven CEO changes took place during 1994-1998 among the 35 casino firms. This rate is high compared to the various rates cited in Chidambaran and Prabhala (2003). These authors show a 25.82% turnover rate among repricing firms in the years of and after repricing. However, only three turnover events happened among the 18 repricing firms in the casino sample. Rather than being evidence of CEO entrenchment, closer examination of the proxy statements shows that repricing occurred after the CEO change. In general, CEOs in the casino sample did not have long tenures at the top. The average CEO in the sample was in the position for an average (median) of 5.3 (3.5) years. CEOs who had options repriced had less tenure, with an average (median) of 4.6 (2) years. (4)
Senior executives of gaming firms had reason to be concerned about the condition of the industry and their companies. Most of these executives held substantial equity stakes in their employers, and most of the wealth was in the form of options. For example, based on year-end stock prices, 60.8% (72.6%) of the average (median) executive's value of company equity was in the form of options. Furthermore, the value of options was substantial relative to cash compensation. The average (median) value of option holdings at fiscal year-ends relative to cash compensation was 452.8% (171%) across all executives in the gaming industry sample. Option compensation was even more important for repriced executives. The mean (median) of option values relative to cash compensation was 578% (307%) for the group of repriced executive-year observations.
Meanwhile, casino CEOs owned significant percentages of stock. The average (median) CEO held 15% (8%) of the firm's outstanding shares during the study period. As a point of comparison, the mean percentage share holdings of CEOs listed in Execucomp for 1998 was 3.3%.
III. Managerial Incentives from Stock Options and Repricing
Here, I define the managerial risk-taking incentive measures and discuss how reductions in the stock price and subsequent repricing affect incentives.
A. Incentive Effects of Executive Stock Options
Although managers do gain incentives from owning both company stock and options, one clear difference between stock and options is that option grants can encourage managers to take risky, positive NPV investments (Guay, 1999), but executives who hold an excess of company stock may become overly risk-averse (Smith and Stulz, 1985).
I follow Guay (1999) by measuring the incentive provided by options to increase risk with the partial derivative of the Black and Scholes (1973) value with respect to volatility of the underlying stock, multiplied by 1%. Throughout the rest of the article, I refer to this value as "vega."
[differential]Value/[differential][sigma] * 0.01 = 0.01 * [exp {-dT}N'(Z)S[square root of T]] (1)
where,
z = 1n[(S/X)] + T [(r - d + [[sigma].sup.2]/2])]/[sigma][square root of T]
N(.) = Normal cumulative probability distribution function
S = Price of the firm's stock
[delta] = Dividend yield
X = Exercise price of the option
r = Risk-free rate
[sigma] = Standard deviation of stock returns
T = Remaining years to maturity of option
Vega represents the executive's incentive (in dollars) to take actions that increase the volatility by one percentage point.
I also use Guay's (1999) definition of "delta." Delta measures the dollar change in option value for a 1% change in the price of the underlying stock.
[differential]Value/[differential]S * S/100 = exp{-dT}N(z) * S/100 (2)
where N(*) = Cumulative probability function for the normal distribution.
Essentially, this value represents the executive's incentive (in dollars) to take actions that will increase stock price by 1%.
Figure 2 illustrates the effects of stock price changes on delta and vega values using a simple example (although these effects are broadly applicable). Figure 2 illustrates the magnitudes of delta and vega for a hypothetical option over a range of stock prices. I assume that the option has an exercise price of $20 with seven years until expiration. I assume that the underlying stock pays no dividends and has annual volatility of 40%. I assume that the risk-free rate is 5%.
[FIGURE 2 OMITTED]
I denote the delta and vega values for an at-the-money option at the points D1 and V1, respectively. A decline in stock price to $12 per share causes a decline in both delta and vega to the points denoted by D2 and V2, respectively. However, while the reduction in vega is minimal, delta declines significantly.
The incentive measures are also dependent on volatility and the remaining option life. In unreported analyses, I find that vega exhibits an inverse U shape relative to volatility. The peak of the function occurs at low volatility levels (compared to those observed in the study's sample) for options that are not deep out of the money, so risk-taking incentives typically decline with volatility. For options deep out of the money, the risk-taking incentives increase in volatility over reasonable volatility ranges. When options are not deep out of the money, delta displays the opposite relation to volatility with less sensitivity (i.e., a shallow U shape). For options deep out of the money, delta is an increasing function of volatility.
Vega displays an inverse U shape as the time to option expiration increases. Nevertheless, the peak of the function is typically at or beyond ten years until expiration, so I can characterize vega as an increasing, concave function of time for typical executive stock options. Delta shows positive sensitivity to time until expiration as options are deeper out of the money. This sensitivity becomes relatively small as the ratio of stock price to exercise price increases.
B. Repricing and Managerial Incentives from Options
Since repricing an option lowers the exercise price, it is useful to understand the effect of changing exercise price on delta and vega values. Figure 3 shows delta and vega values for the hypothetical option if the stock price is set to $12. The points D2 and V2 represent the delta and vega values for the option with an exercise price of $20 (i.e., these points are the same values as D2 and V2 from Figure 2). Lowering the exercise price to $12 causes delta to increase to the value denoted by D3. Repricing will always increase the value of delta per option by increasing the value of Z in Equation (2).
[FIGURE 3 OMITTED]
On the other hand, the effect on vega of decreases in the option's exercise price is negative as long as the following condition holds prior to repricing:
1n[(S/X)] > -T(r - d + [[[sigma].sup.2]/2]]) (3)
Equation (3) states that the ratio of stock price to exercise price must not be so low that the numerator of Z in Equation (1) is negative prior to repricing. For example, lowering the exercise price will not guarantee a lower vega if the exercise price on the hypothetical option from Figure 3 is well above $30. However, I note that lowering the exercise price down to $12 lowers vega from all values illustrated in Figure 3. In the example, repricing causes a decline in vega from V2 to V3 for the hypothetical option. Overall, the act of repricing increases delta and decreases vega per option, thus realigning incentives towards a greater emphasis on value maximization and away from greater risk-taking.
IV. Sample
To identify the sample of casino firms, I conduct searches in Lexis-Nexis and Compustat for firms with three-digit SIC codes of 799. This SIC code includes companies from a broad range of industries, such as ski areas, health clubs, and golf facilities, which 799 categorizes as "Miscellaneous Amusement." I review the business descriptions in 10-K filings to identify those firms that operate primarily in the casino gaming business.
I drop firms that lack adequate disclosure on their option holdings in proxy statements or 10-K filings and/or those that lack market value data in CRSP, because I am unable to calculate the managerial incentive variables. This process yields a sample of 35 casino firms that were in operation for two or more years during 1993-1998.
Table II shows summary statistics across executives' option holdings from proxy data for the 35 casino firms in my sample. The average (median) number of options held by named executives is 368,800 (105,000). Out of 555 executive-years, 479 hold options, and of those, 397 observations include out-of-the money options. The mean (median) number of out-of-the-money options is 174,915 (50,000). The underwater options are, on average, well out of the money. The mean (median) percentage that underwater options are below the exercise price is 30.05% (28.73%).
A. Repricing Events
To identify repricing events, I review proxy statements (or 10-Ks if I cannot find a proxy statement) from the SEC EDGAR database for each of the firms. From this sample, I identify 19 repricing firms, 27 repricing events, and 88 affected individuals. I summarize these data in the Appendix.
The repricing event date refers to the effective date of the repricing. This date is not publicly known until the release of the proxy statement. The distribution of repricing events is almost uniformly distributed across 1995-1998, with only one repricing occurring in 1994. While most firms repriced only once during the study period, six firms repriced twice, and one firm repriced three times (twice in 1995). Three firms repriced during early December 1998 after the FASB's announcement of a new regulation affecting accounting for repriced options, but before the December 15, 1998 effective date. Unlike Chen (2004), I find no evidence that any of the nonreprieing firms explicitly restrict repricing of options. From the 125 firm-year observations I gather for my analysis, 27 repricings occur for a 21.6% reprice rate.
One notable feature of the data is that CEOs are rarely included in the repricing of options. Only ten of the 27 repricings include options held by CEOs. This rate of approximately 37% is even lower than that found in Chidambaran and Prabhala (2003).
Repricing occasionally serves as a form of severance for outgoing executives. Seven repriced managers were no longer employed by the firm as of the date the firm prepared the proxy statement. In one instance, a firm reported a repricing as only applying to the three company directors who held options.
Table III shows summary statistics of the distribution of repricing events over all affected executive options. The columns labeled "number of original options" show the number of options held before repricing. The mean (median) number of options per affected executive is 201,615 (60,000). Across the 27 firm-repricing events, the mean (median) number of options is 657,117 (243,333).
The columns labeled "number of options repriced" in Table III show the number of options retained after repricing. For approximately two-thirds of the repriced executives and firms, the number of options held is unchanged after the repricing. In the remaining cases, executives lose some options in exchange for the repricing. This exchange results in a lower distribution of options repriced.
The column labeled "ratio of exercise prices" in Table III shows the ratio of the new exercise price to the old exercise price. (5) The mean (median) ratio of the exercise price after repricing relative to the exercise price before repricing is 60.23% (62.28%). Given that most option grants (including repricings) set the exercise price approximately equal to current market price, the mean and median figures suggest that on average, repricing occurs when there has been a roughly 40% decline in price since the original grant date. This result is consistent with the findings in prior repricing literature.
B. Measurement of Managerial Incentives
To analyze managerial risk-taking incentives from company stock and option holdings as a possible factor in explaining repricing decisions, and to obtain estimates of Equations (1) and (2) for each named executive among the 35 sample gaming firms, I gather data from the following sources.
From proxy statements (or 10-K filings) available on the SEC EDGAR website, I obtain the terms of the prior year's option grants, option holdings and the intrinsic values of these holdings, stock holdings, and salary and bonus data. From the oldest proxy statement available for each firm, I use the Core and Guay (2002) methodology to estimate the exercise price and time until maturity for option holdings as of the beginning of the sample period. I consider new option grants as separate entities for which I can directly observe the terms of option grants. As I examine subsequent proxy statements, I build each executive's option portfolio using the method described in Guay (1999).
I gather daily stock prices from CRSP for each sample firm. The standard deviation I use for each firm-year is the annualized standard deviation measured during the year. For repriced firms and executives, the stock price I use in the incentive calculations is the closing price on the day before the repricing date. For non-repriced firms and executives, I use the minimum closing price that occurred during the fiscal year. Essentially, I construct the variables at a point in time when repricing would be most likely (with perfect hindsight) for the non-repriced observations. This assumption might bias the results against finding any evidence that repricing is related to high risk-taking incentives.
I measure vega for a firm-year (or executive-year) as the sum across all option tranches of the product of number of options in each tranche and the vega per option in each tranche. Because Guay (1999) finds that stock holdings provide practically zero risk-taking incentives, I assume no addition to vega from stock holdings. I measure delta in the same way for firm and executive observations, with the exception that I add the number of shares multiplied by 1% to the total option delta. The resulting sample consists of 125 firm-year observations and 545 executive-year observations.
Table IV, Panel A, shows the distributions of delta and vega across all executive-year observations and across the 387 observations with out-of-the-money options. Panel A also shows the distributions of vega and delta across all sample firm-years and the 113 observations in which options are out of the money.
In the analysis that follows, I measure risk-taking incentives using two definitions. First, to measure risk-taking incentives relative to value-increasing incentives, I follow Rogers (2002) by using the ratio of vega-to-delta. The strength of this measure is that it measures risk-taking incentives as a proportion of incentives to increase value. As this ratio increases, managers may face increasing incentives to pay more attention to whether an action will increase risk. Nevertheless, the vega-to-delta ratio suffers from a potential weakness. If both vega and delta are relatively small dollar values, then this ratio may not provide an accurate picture of management's incentives.
I note that an implicit assumption underlying the vega-to-delta ratio is that increasing both stock price by 1% and volatility by 1% are equally costly activities to the firm's executives. If I assume efficient markets, then managers should only have the power to increase the stock price by committing capital to positive NPV projects. However, positive NPV projects are not ubiquitous, and in fact such investments may be difficult to identify (see Chapter 11 of Brealey and Myers, 2000). On the other hand, it should be much easier to identify projects that increase risk regardless of the consequences to value. This asymmetry implies that the relative level of vega-to-delta might be underestimated in the comparisons.
In my second measure, I divide vega by the sum of salary plus bonus. Graham and Rogers (2002) use this metric to measure risk-taking incentives. Guay (1999) poses cash compensation as a measure of executives' outside wealth. In essence, this choice of scaling provides a variable that gives a clearer value of the economic magnitude of a manager's risk-taking incentives relative to outside wealth than does the vega-to-delta ratio.
Panel B of Table IV shows the values of vega-to-delta and vega as a percentage of salary plus bonus for all executive-year observations, and also the underwater option observations. Panel B also illustrates the same variables for the firm-year observations.
Several points are worth noting in Table IV, Panel B. First, for the executive-year observations, the distributions of both risk-taking incentive measures are higher when I limit the sample to include only those executives with underwater options. This result occurs because of the elimination of zero-vega observations (i.e., no option holdings) and of observations with lower vega-to-delta (i.e., in-the-money options). This increased distribution implies a larger effect from the elimination of executives holding few or no options (i.e., low vega) relative to the elimination of executives holding in-the-money options (i.e., high vega).
A second point is that the distribution of vega-to-delta for firm-year observations is considerably lower than that for executive-year observations. For example, the mean vega-to-delta across 113 firm-years with underwater options is only 25.02%, compared to the corresponding average value of 63.05% for executive-year observations. This difference occurs because the firm-year observations are weighted averages across the executives in the firm. In the sample, CEOs tend to have much greater share holdings relative to option holdings. If CEO vegas and deltas are large relative to those of the executive group, then the firm-level vega-to-delta ratios are more influenced by the low CEO vega-to-delta.
Finally, the economic magnitude of vega retains similar average values for the firm-year observations compared to executive-year values. The mean vega as a percentage of salary plus bonus is 3.82% for the 113 firm-year underwater observations. This result is very close to the 3.94% average value for executive-year observations.
Given that managerial incentive measures are not independent because of the panel nature of the data, traditional univariate comparisons are not statistically valid. Nevertheless, I examine the distributions of the risk-taking incentive measures between observations for which options are repriced and those for which options are not repriced. I present these results in Table IV, Panel C.
The table shows only those observations for which options are underwater. This exclusion does not remove any observations for which options are repriced at the executive or firm level.
The vega-to-delta ratios appear to be slightly greater for repriced observations at both the firm and executive level.6 For example, the median vega-to-delta in the executive-year sample is 68.5% for repriced observations compared to 60.6% for nonrepriced observations. A comparison of the other risk-taking incentive measure suggests that repriced observations possess greater risk-taking incentives as well. Vega scaled by salary plus bonus is 4% at the median, for repriced executives compared to a median of 1.6% for nonrepriced executives. Across firm-years in which repricing of options occurs, the median vega as a percentage of salary plus bonus is 3.1%, compared to 1.5% for firm-years in which repricing does not occur.
C. Effect of Repricing on Managerial Incentives of Options
In Section III, I illustrated the effects of repricing on a hypothetical option. Now I briefly show that the sample firms repricing options achieve similar effects.
Table V presents the dollar change in vega and delta incentives, as well as the value change associated with repricing. I obtain the data from all repriced executives and their associated firms, regardless of whether they are ultimately in the sample I use in the regression analysis (i.e., I use all 88 repriced executive observations in this examination).
The primary effect of repricing is the lowering of risk-taking incentives, rather than increasing value-increasing incentives. At the firm level, the average vega decline from repricing is $22,882. The average delta decline is $297. (I note that delta can decline after repricing if the number of options is reduced sufficiently. Table III illustrates that some repricing actions reduce the number of options.). Given the values of vega and delta presented in Table IV, the vega changes appear economically significant, but the delta changes do not.
The act of repricing is often criticized because it serves as extra compensation to executives occurring after a period when shareholders have fared poorly. The average value change of firms' executive stock options is $345,755 around repricing. To provide some perspective on this value, the mean prerepricing value of repriced options is about $4.6 million. Thus, although repricing transfers some value from current shareholders to executives, the dollar value is not a highly significant percentage of option value.
V. Do Risk-taking Incentives Affect the Repricing Decision?
In this section, I structure multivariate probit regressions to examine whether risk-taking incentives are positively associated with repricing, after controlling for other possible influences. I conduct separate analyses using both firm-year and executive-year observations. The firm-level analysis allows for more direct comparison to the results of other firm-level repricing studies. The results of executive-level regressions are useful in that firms often do not reprice all executives (even when all hold underwater options).
In the subsequent regression analyses, I include only observations with underwater options. Given that I do not observe repricing in any of the excluded observations (at the firm or executive level) and that the excluded values have mostly low risk-taking incentive measures, including these observations would bias the results in the predicted direction. In untabulated analysis, when I include all observations, I find similar relations between the risk-taking incentive measures and repricing.
A. Control Variables
Stock Price Performance: The most prominent result from prior research is that repricing is undertaken after negative stock price performance. This relation is especially significant, given that negative stock price performance causes the ratio of vega to delta to increase for outstanding executive options. I control for such performance by including the percentage stock price change during the full year prior to repricing (for repriced firms) or the percentage stock price change during the reference year (for nonrepriced firms).
Out-of-the-Money Options: Carter and Lynch (2001) find that the extent to which repriced options are underwater is positively related to repricing in their sample. As in their paper, I calculate the weighted average exercise price of out-of-the-money options for each executive. The variable is then measured as by Carter and Lynch: (weighted average exercise price minus stock price) divided by weighted average exercise price. I also include a variable that controls for the percentage of underwater options (relative to total options).
Cash Compensation: Executives who receive greater cash compensation may be less affected by the decline in value of their equity-based holdings. Thus, firms may be less likely to reprice options in such cases. To control for this, I include the natural logarithm of sum of salary plus bonus.
Corporate Governance: Working under the assumption that repricing may be a function of weak governance and/or entrenched management, most empirical studies of repricing examine the link between corporate governance and repricing. I include the three following variables to control for governance-related rationales: an indicator variable for firms in which the CEO is also the chairman of the board, the percentage of inside directors, and the number of institutional blockholders of each firm's stock.
Firm Size: Among prior empirical research of repricing in cross-sectional samples a common finding is that smaller firms are more likely to reprice. Additionally, firm size may play a role in equity ownership and option compensation, thus affecting the incentive variables. I include the natural logarithm of net sales as a measure of firm size in the regression analysis.
Operating Performance: Chance et al. (2000) document a significant decline in operating performance leading up to and including the year of repricing. I include return on assets as a control.
Other Financial Policies: Investment and financing policies impact the risk level of the firm, thus affecting the firm's decisions on equity-based compensation (see Guay, 1999). To control for leverage, I include the lagged ratio of debt to assets. As controls for investment opportunities, I include the ratio of capital expenditures-to-sales and the lagged market-to-book of assets.
Time Effects: I include indicator variables for each year 1995 through 1998 to control for any time effects apparent in repricing decisions.
B. The Firm-Repricing Decision
I test probit regression models to explain repricing at the firm level. I label a firm as a repricer for a given year if the firm discloses any repricing action during the reference year, and use an indicator variable that takes the value of one for such firms. I include only firms with underwater options in the regression analysis. The regressions include 112 observations with 24 repricing events.
Table VI illustrates the results of the probit regressions on firm-repricing events. I adjust the standard errors in the probit regressions to account for clustering on company observations (and executive observations on the tests shown in Table VII). (7)
Model 1 of Table VI incorporates the vega-to-delta ratio as the measure of managerial risk-taking incentives. The vega-to-delta ratio shows a statistically strong (at a 5% significance level) positive relation with repricing. This result suggests that the relative risk-taking incentive of senior management, aggregated across managers, is a factor in explaining the corporate decision to reprice options of managers.
The economic magnitude of managerial risk-taking incentives also appears to be effective in explaining repricing at the firm level. Models 2 and 3 of Table VI use vega as a percentage of salary plus bonus as the proxy for risk-taking incentives. In these two models vega and delta are correlated at approximately 47%. Model 3 shows that the positive relation between vega and repricing is not driven by collinearity of vega and delta.
Overall, the combination of results from Table VI suggests that firms in which managers face high risk-taking incentives are more likely to reprice. This relation is also robust to several alternate definitions of risk-taking incentives.
C. The Executive-Repricing Decision
Because firm-repricing decisions often do not affect all option-holding executive officers, executive incentives may explain the decision to reprice options for some, but not all, managers. Here, I analyze the sample of casino executives. I add an indicator variable to control for whether the executive is CEO. As in the firm-level regressions, I include only those executives with underwater options. The dependent variable is an indicator equal to one if the executive has options repriced during the year, and zero otherwise.
Table VII shows the results of the probit regressions conducted at the executive level. In contrast to the results of the firm-level regressions, the vega-to-delta ratio shows little statistical power in explaining whether an executive holding underwater options gets them repriced. On the other hand, Model 2 illustrates a very strong and significant (0.1% significance) relation between executive repricing and vega as a percentage of salary plus bonus.
Overall, the results suggest that the economic magnitude of risk-taking incentives is more important than relative incentives in the executive repricing decision. A possible explanation for the difference in results between the firm and executive regressions is that at the firm level, relative risk-taking incentives are a major concern because of the potential for the group of senior executives to engage in risky and suboptimal investment and financial policies. If relative risk-taking incentives are high across all executives, then economic magnitude of these incentives may also be high. On the other hand, when deciding whom to reprice, the overriding concern is not the individual's relative risk-taking incentives, but the economic magnitude of risk-taking incentives, because the two may not be correlated.
An examination of the correlations between the two risk-taking incentive variables is consistent with this interpretation. At the firm level, the correlation between vega-to-delta and vega as a percentage of salary plus bonus is 0.47 (statistically significant at 1%). For the executive-year observations, the correlation between these two variables is only 0.08.
D. Other Results
Although the focus of this article is on the role of risk-taking incentives in explaining repricing, several other results from Tables VI and VII are worth noting. The results suggest that firm performance, the proportions of options that are out of the money, financial structure, governance, and size factors are helpful in explaining repricing.
Repricing is negatively related to one-year stock price changes and to the lagged market-to-book ratio. Both results imply that option repricing follows weak market performance. Return on assets (ROA) shows a positive relation with repricing. Although it may seem counterintuitive, I note that ROA is measured as of the year-end during which repricing occurs. Thus, by improving executive incentives, repricing may be associated with higher accounting returns.
The proportion of options that are out of the money is negatively related to the incidence of repricing. This result suggests that repricing serves an incremental role in improving option incentives, rather than being a "house-cleaning" of out-of-the-money options.
Lagged leverage is negatively associated with repricing, although this result is not statistically strong in the firm-year regressions. One interpretation of this result is that firms with low financial risk are more likely to reprice. This interpretation would seem to be inconsistent with risk-taking incentives being a causal factor in the repricing decision. Nevertheless, a more likely explanation is that gaming firms with lower leverage are better able to issue debt and use debt proceeds to fund risky investments. Thus, repricing might reduce managerial incentives to take such actions.
Governance variables largely do not exhibit relations with repricing in this sample. One exception is the percentage of inside directors. This variable is positively related to repricing in models using the vega-to-delta ratio. If having more inside directors is indicative of weak corporate governance in a firm, then the result is consistent with the commonly held ideas that repricing indicates weak governance. Nevertheless, the relation is not particularly robust in my sample.
Firm size shows a positive relation with repricing, especially in the executive-year sample. Although this result is contrary to those found in some prior repricing studies, the relation may support the incentive argument: relative to their smaller industry rivals, larger firms in this industry are likely in more favorable positions to generate the capital to fund large, risky investments. Repricing may serve to temper such risky empire-building incentives.
E. Robustness Checks
To check the robustness of the findings reported in Tables VI and VII, I extend the definition of risk-taking incentives to include unscaled vega (e.g., Coles, Daniel, and Naveen, 2003), logarithm of vega (e.g., Knopf et al., 2002), vega divided by value of stock and option holdings, and vega divided by the firm's market value of equity. Regardless of the definition I use, my firm-level observations indicate that risk-taking incentives are positively and significantly associated with repricing.
However, the relation between the alternative risk-taking incentive metrics and repricing is not as strong in the executive sample. Unscaled vega shows a positive and significant association with repricing. The other three risk-taking incentive variables show positive but statistically insignificant relations with repricing.
In early December 1998, the FASB announced that it intended to release an exposure draft detailing a change in accounting for repriced options, and that the effective date of the change would be December 15, 1998. Carter and Lynch (2003) find that firms responded to this announcement by accelerating their repricing decisions. Three of my sample firms repriced during the window between the announcement date and December 15. The positive association between risk-taking incentives and repricing are not affected by deleting these three firm and corresponding executive observations from the analyses.
In my executive-level analysis I utilize standard errors corrected for clustering of individual executives in the sample. However, an alternative specification is to correct standard errors for clustering of firms. This alteration in the model framework does not alter the general findings of the paper. Another alternative is to use a random effects probit model to incorporate the correlations across observations within the same firms. Using this model, both vega-to-delta and vega-to-compensation ratios show positive and statistically significant relations with repricing.
VI. Conclusion
Although executive stock option repricing imposes additional costs upon shareholders, in this paper I argue that there may be a positive side to this compensation policy. Declines in stock price may cause scenarios in which option-holding managers have incentives to increase risk, but do so at the possible expense of value maximization. Repricing offers a mechanism that might alleviate such incentives. I show that on average, executives whose options are repriced have greater incentives to increase risk than do managers who are not repriced.
Since this research has begun, FASB has imposed an additional regulation on firms that reprice options. According to FASB Interpretation 44, if their stock price rises after repricing, then firms that choose to reprice employee and/or executive stock options must expense the difference between the old and new exercise prices multiplied by the number of options affected. Because the cost of granting fixed exercise price options has not been expensed on corporate income statements, this action may be perceived as a punitive measure imposed by FASB, thus raising the perceived cost of repricing (e.g., Murphy, 2002).
While the topic of how to properly account for granted stock options is currently being resolved by FASB, the different accounting treatment historically accorded to repriced options might have reflected unfair policy if repricing serves as an effective mechanism to realign managerial incentives. (8)
Appendix. Repricing Firms, Dates, and Executives
Repricing
Company Date Exec
Ameristar Casinos Inc 14-Dec-98 Sr. VP - Fin
Ameristar Casinos Inc 21-Dec-95 Sr VP -
Finance
Ameristar Casinos Inc 21-Dec-95 Genl Counsel
Argosy Gaming Co 4-Mar-98 Gen Mgr
Boyd Gaming Corp 2-Jun-97 Sr VP - Adm
Boyd Gaming Corp 2-Jun-97 left prior to
repricing
Century Casinos Inc 15-Aug-95 President
Circus Circus 10-Dec-98 CFO - different
Enterprises Inc
Circus Circus 10-Dec-98 Genl Cnsl - different
Enterprises Inc
Circus Circus 10-Dec-98 Controller
Enterprises Inc
Circus Circus 10-Dec-98 former Sr VP 1
Enterprises Inc
Circus Circus 10-Dec-98 former Sr VP 2
Enterprises Inc
Circus Circus 19-Nov-94 CEO, Chm,
Enterprises Inc Pres
Circus Circus 19-Nov-94 COO
Enterprises Inc
Circus Circus 19-Nov-94 Genl Counsel
Enterprises Inc
Circus Circus 19-Nov-94 CFO
Enterprises Inc
Circus Circus 19-Nov-94 Controller
Enterprises Inc
Circus Circus 19-Nov-94 Former VP
Enterprises Inc
Grand Casinos Inc 27-Feb-97 CEO, Chmn
Grand Casinos Inc 27-Feb-97 President
Grand Casinos Inc 27-Feb-97 Exec VP
Harrahs Entertainment Inc 15-Nov-96 CEO, Pres
Harrahs Entertainment Inc 15-Nov-96 Chairman
Harrahs Entertainment Inc 15-Nov-96 Exec VP
Harrahs Entertainment Inc 15-Nov-96 CFO
Harrahs Entertainment Inc 15-Nov-96 Sr VP - HR
Harrahs Entertainment Inc 15-Nov-96 Genl Counsel
Harrahs Entertainment Inc 15-Nov-96 Sr VP - IT
Harrahs Entertainment Inc 15-Nov-96 Sr VP - Mktg
Harrahs Entertainment Inc 15-Jun-95 CEO, Pres
Harrahs Entertainment Inc 15-Jun-95 Chairman
Harrahs Entertainment Inc 15-Jun-95 Exec VP
Harrahs Entertainment Inc 15-Jun-95 Sr VP - HR
Harrahs Entertainment Inc 5-Jan-95 CEO, Pres
Harrahs Entertainment Inc 5-Jan-95 Chairman
Harrahs Entertainment Inc 5-Jan-95 Exec VP
Harrahs Entertainment Inc 5-Jan-95 CFO
Harrahs Entertainment Inc 5-Jan-95 Sr VP - HR
Harrahs Entertainment Inc 5-Jan-95 Genl Counsel
Harrahs Entertainment Inc 5-Jan-95 Sr VP - IT
Harveys Casino Resorts 22-May-97 CEO, Chmn,
Pres
Harveys Casino Resorts 22-May-97 COO
Harveys Casino Resorts 22-May-97 CFO
Harveys Casino Resorts 22-May-97 Sr VP - Bus
Dev
Harveys Casino Resorts 22-May-97 Sr VP
Harveys Casino Resorts 22-May-97 Consultant to
CEO
Hollywood Casino 19-Jun-98 Director 1
Corp
Hollywood Casino 19-Jun-98 Director 2
Corp
Hollywood Casino 19-Jun-98 Director 3
Corp
Hollywood Park Inc 26-Apr-96 CFO
Hollywood Park Inc 26-Apr-96 President
Hollywood Park Inc 26-Apr-96 COO
Hollywood Park Inc 19-May-95 CFO
Hollywood Park Inc 19-May-95 President
MGM Grand Inc 22-Jun-98 Exec VP
MGM Grand Inc 22-Jun-98 Exec VP, CFO
MGM Grand Inc 22-Jun-98 Treasurer
MGM Grand Inc 4-Dec-95 CEO, Chmn
MGM Grand Inc 4-Dec-95 COO, CFO
MGM Grand Inc 4-Dec-95 Vice Chairman
MGM Grand Inc 4-Dec-95 Exec VP
Mirage Resorts Inc 13-Dec-98 CEO, Chmn,
Pres
Mirage Resorts Inc 13-Dec-98 Exec VP - Mktg
Mirage Resorts Inc 13-Dec-98 Genl Counsel
Mirage Resorts Inc 13-Dec-98 CFO
Mirage Resorts Inc 13-Dec-98 Pres - Retail
Div
Players International 19-Sep-96 CEO, Pres
Inc
Players International 19-Sep-96 Genl Counsel
Inc
Players International 19-Sep-96 Retired Genl
Inc Courts
President Casinos Inc 22-Aug-97 COO, Pres
President Casinos Inc 22-Aug-97 Vice Chairman
President Casinos Inc 22-Aug-97 CFO
President Casinos Inc 19-Jun-96 COO
President Casinos Inc 19-Jun-96 CFO
President Casinos Inc 19-Jun-96 Frmer VP - Sales
Rio Hotel & Casino 8-Oct-96 CFO
Inc
Rio Hotel & Casino 8-Oct-96 Genl Counsel
Inc
Sands Regent 12-Dec-97 CFO
Sands Regent 12-Dec-97 Exec VP
Station Casinos Inc 12-Sep-97 VP - Finance
Station Casinos Inc 1-May-95 Exec VP
Station Casinos Inc 1-May-95 CFO
Station Casinos Inc 1-May-95 Genl Counsel
Stratosphere Corp 15-Aug-96 Former
President
Trump Hotel & 18-Nov-98 CEO
Casino Resort
Trump Hotel & 18-Nov-98 Genl Counsel
Casino Resort
Trump Hotel & 18-Nov-98 Exec VP - Corp Fin
Casino Resort
Trump Hotel & 18-Nov-98 Exec VP - Govt
Casino Resort
Table I. Capital Spending, Profitability, Leverage, and Market Value
of Casino Industry Firms (1993 -1998)
Table I shows means and medians of variables representing capital
spending, return on capital, financial leverage, and market valuation.
The casino firms represent data from 35 gaming industry firms. I use
the S&P 1500 sample, which represents historic data from firms in the
S&P 1500 as of May 2004, for comparisons.
Casino Firms: S&P 1500:
Mean Median Mean Median
Capital expenditures - Depreciation
(% of sales):
1993 51.8% 12.8% 4.3% 
