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Weekly UpdatesCurrent year's stock return ([R.sub.t]) and an industry variable ([I.sub.t]) are included in the regression to control for their effect on changes in shareholdings. It is quite possible that stock selling is more pronounced in the financial services industry which may have executives who are financially savvy and understand the benefits of portfolio diversification. As a result, there may be an industry-related explanation for stock sales by the executives. The industry variable is coded 1 if the executives belong to financial services firms (SIC Division H: finance, insurance, and real estate), 0 otherwise.
The results in Panel A indicate that the executives sell 364 shares of already owned stock for every 1,000 shares of new stock options that they receive. The [[beta].sub.1] value of -0.364 is significant at the 5 percent level. Overall, there is an evidence that executives adjust their shareholdings but at a lower proportion than the optimal hedge ratio of 60 percent. Of the control variables, the industry variable seems to have a significant influence on stock sales by corporate executives. The [[beta].sub.2] value of 25.153 indicates that executives in the financial services industry seem sell more shares than executives in non-financial sectors.
Panel B of Table 2 presents the findings by the executive's stock ownership in the firm. Ofek and Yermack [2000] argue that portfolio diversification in response to new stock options takes place once the executive reaches a certain ownership level. In other words, executives' willingness to reduce risk through portfolio diversification occurs when their stock ownership in the firm is already high. The authors test this hypothesis by regressing annual changes in shares owned by the executives on two interaction variables ([[beta].sub.1] and [[beta].sub.2]) computed as new stock options times zero-one coded variable based on the sample ownership median of 0.0643 percent. The null hypothesis that/[[beta].sub.i] = 0 (for i = 1, 2) is tested. The regression is of the following form:
[DELTA][S.sub.t] = [[beta].sub.0] + [2.summation over (i-1)] [[beta].sub.i] x [O.sub.it] x [C.sub.t] + [[beta].sub.3] x [R.sub.t] + [[beta].sub.4] x [I.sub.t] (2)
where:
[DELTA][S.sub.t] = change in shares owned by an executive in year t,
[O.sub.1t], = 1 executive ownership is greater than or equal to 0.0643 percent year t, 0 otherwise,
[O.sub.2t] = 1 executive ownership is less than 0.0643 percent year t, 0 otherwise,
[C.sub.t] = new stock options awarded in year t,
[R.sub.t] = current year's (year t) dividend-adjusted stock returns,
[I.sub.t] = 1 if financial services industry, 0 otherwise, and
[beta]s are the parameter estimates.
In regression equation (2), a positive value of coefficient [[beta].sub.1] would indicate an increase in shareholdings for high-ownership executives and a positive value of [[beta].sub.2] would indicates an increase in shareholdings for low-ownership executives. The results of the regression indicate that the high-ownership executives sell 513 ([[beta].sub.1] = -0.513) shares for every 1,000 shares of new stock options and low-ownership executives buy 46 shares for every 1,000 shares of new stock options. These results are consistent with the argument that the need for stock selling in response to stock option awards increases with the executive's ownership level.
In Panel C of Table 2, the results based on gender are presented. The authors hypothesize that the risk-averse female executives will sell more shares in response to new stock options than the male executives. The authors test this hypothesis by regressing annual changes in shares owned by the executives on two interaction variables ([[beta].sub.1] and [[beta].sub.2]) computed as new stock options times zero-one coded variable based on gender. The null hypothesis that/[[beta].sub.i] = 0 (for i = 1, 2) is tested. The regression is given below:
[DELTA][S.sub.t] = [[beta].sub.0] + [2.summation over (i-1)] [[beta].sub.i] x [G.sub.it] x [C.sub.t] + [[beta].sub.3] x [R.sub.t] + [[beta].sub.4] x [I.sub.t] (3)
where:
[DELTA][S.sub.t] = change in shares owned by an executive in year t,
[G.sub.1t] = 1 executive is a male, 0 otherwise,
[G.sub.2t] = 1 executive is a female, 0 otherwise,
[C.sub.t] = new stock options awarded in year t,
[R.sub.t] = current year's (year t) dividend-adjusted stock returns,
[I.sub.t] = 1 if financial services industry, 0 otherwise, and
[beta]s are the parameter estimates.
In regression equation (3), a positive value of coefficient [[beta].sub.1] indicates an increase in shareholdings for male executives and a positive value of [[beta].sub.2] indicates an increase in shareholdings for female executives. The results show that the male executives sell 366 shares ([[beta].sub.1] = -0.366) for every 1,000 shares of new stock options and female executives sell 209 shares for every 1,000 shares of new stock options. Although both groups of executives engage in stock sales, these results are contrary to the authors' prediction that the risk-averse female executives will sell more than the male executives.
Finally, in Panel D, results by gender for high- and low-ownership levels are presented. Since diversification-related stock selling occurs at high-ownership level, the authors examine if both male and female executives exhibit similar selling patterns when they are in the high-ownership category. This hypothesis is tested by regressing annual changes in shares owned by the executive on four interaction variables ([[beta].sub.1], [[beta].sub.2], [[beta].sub.3], and [[beta].sub.4]) computed as new stock options times zero-one coded variable based on gender times zero-one coded variable based on median executive share ownership of 0.0643 percent. The null hypothesis that [[beta].sub.i] = 0 (for i = 1, ..., 4) is tested. The regression equation is as follows:
[DELTA][S.sub.t] = [[beta].sub.0] + [[beta].sub.i] x [O.sub.it] x [G.sub.it] x [C.sub.t] + [[beta].sub.5] x [R.sub.t] + [[beta].sub.6] x [I.sub.t] (4)
for [O.sub.it] (i = 1, 2) and [G.sub.it] (i = 1, 2) and [[beta].sub.i] = (i = 1, ..., 4) where:
[DELTA][S.sub.t] = change in shares owned by an executive in year t,
[O.sub.1t] = 1 executive ownership is greater than or equal to 0.0643 percent year t, 0 otherwise,
[O.sub.2t] = 1 executive ownership is less than 0.0643 percent year t, 0 otherwise,
[G.sub.1t], = 1 executive is a male, 0 otherwise,
[G.sub.2t] = 1 executive is a female, 0 otherwise,
[C.sub.t] = new stock options awarded in year t,
[R.sub.t] = current year's (year t) dividend-adjusted stock returns,
[I.sub.t] = I if financial services industry, 0 otherwise, and
[beta]s are the parameter estimates.
In regression equation (4), a positive value of coefficient [[beta].sub.1] indicates an increase in shareholdings for high-ownership male executives, a positive value of [[beta].sub.2] indicates an increase in shareholdings for low-ownership male executives, a positive value of coefficient [[beta].sub.3] indicates an increase in shareholdings for high-ownership female executives, and a positive value of [[beta].sub.4] indicates an increase in shareholdings for low-ownership female executives. The results show that only the high-ownership male executives engage in significant stock selling. The [[beta].sub.1] value of -0.516 indicates 516 shares are being sold by these executives for every 1,000 new stock options.
Overall, the results in Table 2 are not consistent with the predictions that female executives are likely to show risk aversion by selling more of their own shares once stock options are awarded.
The results in Table 2 are based on a substantially bigger sample size for the male executives (N = 67,004) when compared to the much smaller sample size for the female executives (N = 2,763). To circumvent the problem of difference in sample size, the above regressions are run for a smaller subset of the male executives. The smaller sample of male executives is created by randomly selecting 2,763 observations (equal number of observations in the female executive sample) from the full sample of the male executives.
Table 3 reports the findings of the regressions for the sample of female executives and the randomly selected sample of male executives. The results for these smaller sub-samples are similar to those reported in Table 2 although the intensity of stock sales appears to be higher. In Panel A, the [[beta].sub.1] value of -0.779 indicates that the executives sell 779 shares in response to 1,000 new stock options. In Panel B, the [[beta].sub.1] value is -1.072 indicating that the high-ownership executives sell 1,072 shares for every 1,000 stock options they receive. The findings on gender in Panel C show that the male executives sell shares more than the female executives--they sell 867 shares ([[beta].sub.1] = -0.867) for every 1,000 new stock options while the female executives sell 220 shares ([[beta].sub.2] = -0.220) for every 1,000 new stock options. The findings in Panel D show that the high-ownership male executives sell 1,238 shares ([[beta].sub.1] = -1.238) per 1,000 new stock options and the high-ownership female executives sell 247 shares ([[beta].sub.3] = -0.247) per 1,000 new stock options.
Conclusions
Are female executives more risk averse than male executives? In this paper, the authors consider this issue by examining the portfolio adjustment behavior of male and female executives in response to new stock option awards. Selling stocks to reduce the risk of the personal portfolio indicates that the executive is risk averse. The hypothesis is drawn from prior empirical evidence that females take less risk than males in their financial decisions. It is predicted that the risk-averse female executives would sell more shares than their male counterparts. The findings are contrary to this prediction, however. The study finds that the female executives sell fewer shares than the male executives once new stock options are granted. This is true even after controlling for the ownership levels. Hence, female executives do not exhibit higher risk aversion than male executives.
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