Executive Compensation and Risk Taking in the Property and Liability Insurance Industry

Executive Compensation and Risk Taking in the Property and Liability Insurance Industry Yu Luen Ma 1 and Ping Wang 2 Abstract: Agency theory suggests that granting stock based compensation to executives incentivize risk taking by aligning managerial interests with those of the shareholders. This study examines the relationship between executives stock based compensation and managerial risk taking behavior in the property liability insurance industry. We calculate the sensitivity of the value of executives stock holdings and option holdings to stock price movement and hypothesize that the more sensitive executives pay is to share price movement, the greater the incentive it provides to induce risk taking that may result in equity volatility. Using data from 2006 to 2010, we find that firms whose executive compensation is more sensitive to stock price movement are associated with greater unsystematic risks. Additionally, consistent with risk averse theory, our results show that the positive relationship between stockbased compensation and firm risks is weakened when stock based compensation accounts for a greater percentage of executives total compensation. Our main results remain consistent and robust when we use different model specifications and risk measures. We also find that stock holdings and option holdings create different effects on firm risks when executives receive a significant amount of such compensation. The findings suggest that stock granting and option granting should be treated separately in designing and evaluating the executive compensation package, and more research is in call for finding the optimal weight of each in the package. [Key words: executive compensation; market risk; property liability insurer.] R INTRODUCTION isk taking is a key issue for the insurance industry due to the unique nature of its business, which is to accept and diversify risks transferred from policyholders. In addition to investment risk and policy 1 Professor, Katie School of Insurance and Financial Service, Illinois State University, E mail: yma@ilstu.edu. Tel: 309 438 7081. 2 Associate Professor, School of Risk Management, Insurance and Actuarial Science, St. John s University. E mail: wangp1@stjohns.edu. Tel: 212 277 5195. 187 Journal of Insurance Issues, 2014, 37 (2): 187 207. Copyright 2014 by the Western Risk and Insurance Association. All rights reserved.

188 MA AND WANG specific risks such as property damages, personal injuries, and liability losses, insurance companies are also exposed to risks arising from internal governance, organizational structure, and separation of ownership and management, like any other business. The agency theory describes the problem caused by the separation of ownership and management of business (see, for example, Berle and Means, 1932; Ross, 1973; Jensen and Meckling, 1976; and Fama and Jensen, 1983). According to the theory, the diversified principal (owner) is riskneutral while the agent (executive) is risk averse, and thus the agent may not be willing to take on risks that the owner feels are optimal for the firm. The compensation package can be designed in a way to mitigate the problem of separation of ownership and management. Granting stockbased compensation to executives may alleviate the separation issue by more closely aligning managerial interests with those of the shareholders. As noted by Hambly and Wendelken (2002), stock based remuneration, including stock ownership, stock options, and restricted stocks, now constitutes the most lucrative and fastest growing portion of CEO pay. In this paper we investigate the relationship between executives stock based compensation and managerial risk taking behavior. 3 While the relationship between risk taking and equity based executive compensation would be of interest to stakeholders of publicly traded firms in various industries, the focus of this study is on U.S. insurance companies in an effort to control for regulatory variations across industries. Given the dissimilarity in investment portfolio and market orientation between life insurance and property liability insurance, we limit our study to property liability insurers to further control for differences in risk taking behavior. Our paper contributes to the literature in several important ways. First, compared with previous studies we use a more sophisticated measure for stock based compensation. We calculate the sensitivity of the value of stock and option holdings by executives to stock price movement. 4 Earlier research most often uses either the volume (number of options) or the value of options holding as the measure for stock based compensation (see, for example, Eckles and Halek, 2010; Chen and Ma, 2011; Beatty and Zajac, 1994), which reflects expected value of existing wealth, while our measure captures the volatility of the value of existing wealth. In the decision making process, volatility might be a more appropriate means of measurement than expected value. Second, in our calculation of stock based 3 We refer to stock ownership, stock options, and restricted stocks as stock based compensation. 4 Browne et al. (2009) use a similar measure in an examination of reserve errors of propertyliability insurers.

EXECUTIVE COMPENSATION AND RISK TAKING 189 compensation, we consider total shares and stock options held, rather than granted. Annual granting of stock and stock option reflects current compensation while shares and stock options held reflect a person s total wealth. A person s risk management or investment decision is likely to be based on total wealth rather than current compensation. Third, we use the volatility of stock price as the measure for firm risk because payoff of stockbased compensation is directly linked to share values. Previous researchers have commonly examined a variety of risks that are accounting based, including credit risk, market risk, liquidity risk, and leverage ratios (see, for example, Rogers, 2002; Cummins et al., 2001; John and John, 1993; Mehran, 1992 and 1995; Berger et al., 1997). Each of these measures captures one aspect of a business s operation risks without regard to other risks. We believe stock price movement is a better measurement as it is reflective of the entirety of various firm risks. Last, we investigate the potential nonlinear relationship between executive compensation and firm risks. Previous studies have reported differing results on stock based compensation and managerial risk taking behavior. Given the diverse theories and findings, we consider the possibilities that the incentive created by stock based compensation may vary at different levels of stock or option holdings. Our analysis allows us to examine the various incentive effects created by stockbased compensation simultaneously. Using data from 2006 to 2010, we find that firms whose executive compensation is more sensitive to stock price movement experience greater risks, mainly driven by unsystematic risks. Additionally, our results confirm the risk aversion effect when stock based compensation is sufficiently high. Our main results remain consistent and robust when we use different model specifications and different ways of measuring risks. We also find that stock effects on firm risks are slightly different from option effects. This paper is organized as follows. We first review the literature that investigates the relationship between stock based executive compensation and risk taking behavior. Research methodology and data are then discussed, followed by empirical results. We conclude with a summary of the results. STOCK BASED COMPENSATION AND RISK TAKING BEHAVIOR Stock based compensation has gained its popularity in large U.S. firms within the past twenty years. As of the mid 1990s, one third of total U.S. chief executive officers compensation was in the form of stock option awards, up from one fifth during 1980s (Hall and Liebman, 1998). 5 As documented in

190 MA AND WANG the agency theory literature, shareholders have stronger incentives to take risks than do managers (see, for example, Jensen and Meckling, 1976). Firms can overcome managerial risk aversion by paying executives stock based compensation. Given that the value of stock options is positively connected with the variance of underlying stock, granting option based compensation to executives will incentivize managers to engage in higher levels of risks. Many public firms and shareholders consider stock options as one of the best compensation devices to incentivize managerial behavior, as it aligns executives interests with those of shareholders. The existing empirical analysis has found that granting stock ownership and stock options to executives is related to managerial risk taking behavior. The findings, however, are mixed. The majority of the literature tends to document a positive relationship between the usage of incentive compensation and firm risks (e.g., Agrawal and Mandelker, 1987; DeFusco et al., 1990; Tufano, 1996; Mehran, 1992 and 1995; Berger et al., 1997; Rogers, 2002; Denis et al., 1997; Chen and Ma, 2011; Guay, 1999; Low, 2009). In contrast, several studies find managerial equity based compensation to bear a negative relationship with firm risks (e.g. Beatty and Zajac, 1994; Yermack, 1995; Bloom and Milkovich, 1998; Geczy et al., 1997; Smith and Stulz, 1985; Gay and Nam, 1998; and Knopf et al., 2002). Bryan et al. (2000) suggest that stock options can be used to reduce, rather than induce, firms risk taking behavior because executives personal portfolios become less diversified when stock based compensation increases. Ross (2004) shows that incentive compensation schemes can make executives either more or less risk averse. He gives the necessary and sufficient conditions under which incentive schedules make agents more or less risk averse. Panageas and Westerfield (2009) also show that the risk seeking incentives of optionlike contracts rely on a combination of finite horizons and convex compensation schemes, rather than on convexity alone. Yet there are some studies reporting no significant relationship between incentive compensation and risk measures (e.g. Mehran, 1995; Houston and James, 1995; and Hentschel and Kothari, 2001), possibly due to the trade offs between the positive and negative risk taking incentives. While the relationship between stock based compensation and firm risks have been extensively studied, only limited research has been done on the insurance industry. The risk pooling and risk sharing nature of insurance business makes the industry unique among other industries. It 5 Granting common stocks and restricted stocks increases the employer s compensation expense, while granting stock options usually does not affect a firm s reported earning as almost all options are granted at the money. This might be one of the reasons why employers may prefer granting stock options as a form of executive compensation.

EXECUTIVE COMPENSATION AND RISK TAKING 191 is heavily regulated by state regulators in the United States. Empirical studies that examine the insurance industry benefit from the removal of inter industry differences, and can focus on key issues being examined. Downs and Sommer (1999) examine the relationship between insider ownership and risk taking in the insurance industry and find that managers may have a greater inclination for risk taking when their stakes in the firm increase from low levels. Barrese et al. (2007) study the concentration in insurance companies ownership of the United States and how it relates to insurer performance. Browne et al. (2009) find that property liability insurers whose executives holding of stock options is more sensitive to stock price have either lower over reserve error or higher under reserve error, implying greater risks. Eckles and Halek (2010) find that managers holding restricted stock tend to under reserve during the current year while no relationship is found between the award of stock options and restricted stocks and reserve errors. More recently, Cheng et al. (2011) study the relationship between institutional ownership stability and a variety of accounting based and market based risk measures. Using data from the life and health insurance industry, they fail to find a relationship between managerial ownership and risk taking. In this paper, we extend previous studies and examine whether the risk taking decisions of property liability insurers are associated with stock based compensation of executive officers. DATA AND MODEL SPECIFICATION The literature generally agrees that stock based executive compensation is related to managerial decision making, even though the findings are inconsistent. When a large portion of an executive s income is closely tied to the performance of the firm s stock price, the executive may have stronger incentive to strive for higher stock price, which aligns with shareholders interest. We calculate three types of firm risk: total risk, systematic risk, and unsystematic risk. Total risk is defined as the standard deviation of monthly return on a firm s publicly traded stocks. 6 We also decompose total risk into systematic risk and unsystematic risk using two different models. In one factor models, systematic risk is the standard deviation of predicted return obtained by regressing the individual firm s return on market return. In two factor models, systematic risk is obtained from 6 As an alternative, we also used the volatility of an insurer s monthly (or daily) stock price as a measure of insurer risk. We calculate coefficient of variation of an insurer s stock price by dividing the standard deviation of each insurer s monthly (or daily) stock price by its average monthly stock price. The results are consistent with the ones reported here.

192 MA AND WANG regressing the individual firm s return on both market return and the interest rate. 7,8 Unsystematic risk is the standard deviation of the regression residuals. Specifically, we estimate the following regressions for each stock: One factor model: r j,t+k = β 0 +β 1 m t+k + ε j,t+k. (1) Two factor model: r j,t+k = β 0 +β 1 m t+k + β 2 i t+k +ε j,t+k., (2) where r j,t+k, m t+k, and i t+k denote the monthly return of j th individual stock and the market portfolio and interest rate during the k th month of the t th year. Then, for a particular j and t, total risk for the j th individual stock during the t th year is the standard deviation of r j,t+k, systematic risk for the j th individual stock during the t th year is the standard deviation of rˆj, t+ k during year t, and unsystematic risk for the j th individual stock during the t th year is the standard deviation of e j,t+k during year t where rˆj, t+ k and e j,t+k denote the predicted return and residual. Our main focus is the relationship between the sensitivity of the executives portfolio of stock and options to stock price and the insurer s risk taking behavior. Stock based compensation includes stock options and shares. Stock options are valued using the Black Scholes model, modified to account for dividend payouts: Option value = Se dt Z Xe rt Z T, (3) where: Z = Tr d 2 + + ----- T ln S X 2 Φ = cumulative distribution function of standard normal distribution; S = price of the underlying stock; X = exercise price of the option; σ = expected stock return volatility over the life of the option; r = natural logarithm of risk free interest rate; T = time to maturity of the option in years; d = natural logarithm of expected dividend yield over the life of the option. Our key variable of interest is the sensitivity of executives stock option and stock holdings to stock price. Sensitivity of options and stocks is ; 7 Market return is monthly return on a value weighted market portfolio, defined and calculated by CRSP. 8 We use short term (i.e., three month bill) yield as our measure for interest rate in two factor models. We also tried an alternative measure by using long term yield (i.e., 10 year bond), and the results are materially identical to the ones reported here.

EXECUTIVE COMPENSATION AND RISK TAKING 193 defined as the combined change in the value of common stocks, restricted stocks, and stock options held by executives for a dollar change in the price of a share of the stock. We scale the sensitivity variable by executives total compensation during the current year, an approach similar to Bergstresser and Philippon (2006). Total compensation is the sum of salary, bonus, stock, and option awards, other incentive plan, and changes in pension. We hypothesize that when executives stock based compensation is more sensitive to changes in stock price, the firm has a higher incentive to take on more risky projects. The sensitivities of stocks and restricted stocks to share price are linear in the underlying stock price in the sense that every dollar change in stock price results in a one dollar change in the value of each share of stock and restricted stock holdings. According to the Black Scholes formula, the value of a stock option is also positively related to the current market price of the underlying stock. The sensitivity of stock options to the stock price is computed using the Black Scholes model with the same data inputs as those used for option valuation and is thus defined as: option value price = e dt Z. We expect firms whose executives share and option values are more sensitive to stock price movement to take on more risks that result in greater equity volatility. 9 Our first hypothesis is that executives share and option holdings induce greater risk taking. The incentive effect, however, may be weakened when executives receive a significant portion of compensation in the form of company stock and options. While these executives may benefit from stock appreciation, they may find that a significant amount of their wealth is invested in the company, along with their human capital. Concentration of wealth and human capital is not in their best interest. When executives human capital becomes highly correlated with their investment in company stocks, they may become risk averse. Thus, we expect the risk taking incentive induced by stock based compensation to be a decreasing function of the level of stock based compensation. 10 This leads to our second hypothesis, that the risk taking incentive induced by share and option holdings will be less significant when executives hold more stock based compensation. To test our hypotheses, we estimate the following model: 9 We consider total shares and options held by executives, instead of current year grants, as one year compensation may not be sufficient to provide value increasing incentives desired by shareholders. 10 We also estimate alternative models by including only salary in the cash compensation variable. Empirical findings from the alternative models are consistent with the results presented here.

194 MA AND WANG 2 y it, = 1 k it, + 2 k it, + x it, + i + t + it, (4) where i represents insurer i, and t represents year t. The dependent variable y it, represents various types of risk measures, including total risk, systematic risk, and unsystematic risk. k i,t is the main variable of interest, which measures the sensitivity of executives stock and option holdings to share price movement. We also include the squared term of k i,t to capture the potential risk aversion effect at higher level of stock based compensation. x i,t is a matrix of firm specific control variables, μ i is company specific effects, t is time specific intercepts, and ε i,t is the random error term of the model. Year dummy variables are included in the models to capture the variation in market climate from year to year. Firm specific control variables included in the model that are hypothesized to affect a firm s risktaking generally follow previous literature (see, for example, Cole et al., 2011). Such variables include firm size, book of business mix, product line and geographic diversification, distribution system, solvency rating, reinsurance usage, and board composition. The main parameter of interest is 1. If greater stock and option holdings induce greater risk taking, we expect 1 to bear a positive sign. We also expect 2, the coefficient associated with the squared term of k i,t, to carry a negative sign if the incentive effects induced by holding stocks and options are weakened at a high level of stock based compensation. We estimate the models using White s (1980) consistent covariance matrix estimation to adjust for heteroscedasticity. To account for serial correlation in stock price volatility, we assume the covariance structure in the models follows a first order autoregressive process AR (1). Our data are collected from various sources. Most accounting data for insurers are obtained from the SNL database. Supplementary data, such as the distribution system and rating information, are obtained from publications of the A.M. Best Company. Executive compensation data and board composition information are collected from annual reports insurers filed with the Securities and Exchange Commission (SEC). To calculate option values, we need data on stock price, expected stock return volatility, expected dividend yield, and interest rate. Stock price information as well as other required inputs to calculate stock option values and market risk measures are derived from the CRSP database. Risk free interest rates are derived from Treasury bill yields corresponding to the time to maturity of the stock options being valued. Our data cover the time period 2006 2010 as detailed stock option data are available only since 2006. We collected data of 77 firms that have executive compensation and stock return data available for at least one year in the observation period. Among those firms,

EXECUTIVE COMPENSATION AND RISK TAKING 195 58 of them also have complete data for other control variables. Our final sample includes a total of 247 observations. 11 EMPIRICAL RESULTS Table 1 reports the definitions of the variables, and the descriptive statistics are presented in Table 2. Our data show that the sensitivity of stock based compensation to a one dollar increase in stock price ranges from 0.4 percent to 9.85 times, with an average of 43.2%, of executives annual total compensation. The distribution of the variable suggests that there are some executives who possess significant values of company stocks and options. Additionally, on average 75.6 percent of board members are non officers in our sample. Table 3 reports our model results based on equation (4). The results are reported separately for total risk, systematic risk, and unsystematic risks. All models include firm specific intercepts as well as year dummy variables. There are a total of five models corresponding to different risk measures. All of our models are robust where standard errors are heteroscedasticity and autocorrelation consistent. As expected, the coefficient of the sensitivity of stock based compensation variable is positively related to total risk, which suggests that firms with greater stock based compensation experience greater volatility in stock prices. Specifically, responding to a one dollar change in stock price, if the weight of executives stock based compensation to total annual compensation increases by one percentage point (say, from 43.2% to 44.2%), the standard deviation in monthly return of the insurer s stock (total risk) will increase by 0.918 of one percent (from 0.109 to 0.118 if the effects of the squared term of sensitivity are not accounted for). The squared term of the sensitivity measure is negative and statistically significant, suggesting that the risk taking behavior induced by stock based compensation reduces at higher level of stocks and options holding. Using the previous illustration, the total risk will increase from 0.109 to 0.115 when the effects of both the first order and second order terms of sensitivity measure are accounted for. In all models, stock based compensation is not found to be associated with systematic risk, consistent with the notion that systematic risk is coherent in the market and beyond the control or effects of any individual player. On the other hand, we found a non linear relationship between the 11 The maximum possible number of firm year observations is 385, of which 66 do not have executive compensation or stock return data; 37 do not provide CEO tenure or age information, and other 35 are missing data on some control variables.

196 MA AND WANG Table 1. Variable Definitions Variable Definitions Total risk One-factor systematic risk One-factor unsystematic risk Two-factor systematic risk Two-factor unsystematic risk Stock and option holdings Standard deviation of monthly return on a firm s publicly traded stocks. Standard deviation of predicted return obtained by regressing individual firm s return on market return. Standard deviation of the regression residuals by regressing individual firm s return on market return. Standard deviation of predicted return obtained by regressing individual firm s return on market return and interest rate. Standard deviation of the regression residuals by regressing individual firm s return on market return and interest rate. Sensitivity of stock option and shares held by executives to $1 increase in stock price, scaled by executives total compensation. Recorded as percentage. % Commercial lines Percentage of premiums written in commercial lines. Size Geographic HI Natural log of total assets. Herfindahl index based on premiums written across states. Product HI % Independent board members Good rating Independent agency Herfindahl index based on premiums written on product lines. Percentage of board directors that are not affiliated. Dummy variable that takes the value 1 if received rating of A or above from A.M. Best. Dummy variable that takes the value 1 if using independent agency system. % Reinsurance ceded Reinsurance premiums ceded divided by the sum of direct premiums written and the percentage of reinsurance premiums assumed. sensitivity of stock based compensation and unsystematic risk. The stockbased compensation variable is found to be positively significant in both one factor and two factor models, which suggests that stock based compensation is associated with greater variability in a firm s return after controlling for market volatility. Our results indicate that stock based compensation may actually provide incentives for firms to take on more risks that could possibly be diversified. This finding is consistent with Harrington (1983) and Cummins and Harrington (1998), who found a relationship between nonsystematic risks and stock returns. Similar to the

EXECUTIVE COMPENSATION AND RISK TAKING 197 Table 2. Descriptive Statistics of Variables Variable Mean Std. Dev. Minimum Maximum Total risk 0.109 0.098 0.024 0.731 One factor systematic risk 0.048 0.043 0.002 0.221 One factor unsystematic risk 0.092 0.087 0.020 0.701 Two factor systematic risk 0.048 0.044 0.003 0.225 Two factor unsystematic risk 0.092 0.088 0.020 0.701 Stock and option holdings 0.432 0.966 0.004 9.582 % Commercial lines 0.725 0.342 0.000 1.000 Size 15.028 1.635 10.617 18.695 Geographic diversification 0.157 0.190 0.035 1.000 Product diversification 0.467 0.317 0.126 1.000 % Independent board 0.756 0.142 0.300 1.000 members Good rating 0.625 0.485 0.000 1.000 Independent agency 0.444 0.498 0.000 1.000 % Reinsurance ceded 0.437 0.237 0.000 1.000 findings for total risk, the coefficients of the squared terms of stock based compensation are also found to be negatively significant for unsystematic risk. Taken together, our results suggest that greater stock and option holdings do indeed provide incentives for executives to take on more unsystematic risks. However, the tendency to take on more risks is diminishing when executives wealth is heavily weighted by the holding of their company s stocks and options. Our findings are consistent with the risk aversion theory that suggests executives may become risk averse when their personal portfolios are less diversified (e.g., Knopf et al., 2002). We believe the non linear relationship found in our analyses also provides an explanation to the insignificant relationship between stock based compensation and firm risk found in some of the previous research. With regard to the relationship between control variables and risk measures, diversification strategies are found to be associated with firm risks. Both geographic and product Herfindahl indexes are found to be positively associated with unsystematic risk. Our results suggest that firms that are diversified either geographically or through product lines

198 MA AND WANG Table 3. Fixed Effects Results for the Effect of Stock Based Compensation on Firm Risks Total risk One-factor risk Systematic risk Unsystematic risk Two-factor risk Systematic risk Unsystematic risk Stock and option holdings Stock and option holdings-squared 0.918*** (0.337) 0.364*** (0.133) % Commercial lines 0.725 (0.528) Size 0.099 (0.273) Geographic HI 0.694*** (0.199) Product HI 1.075* (0.649) % Independent board members 0.252 (0.553) 0.003 (0.004) 0.002 0.016 (0.013) (0.003) 0.955*** (0.248) 0.351*** (0.099) 0.181 (0.522) 0.157 (0.245) 0.715*** (0.184) 1.287** (0.602) 0.370 (0.506) 0.023 (0.024) 0.009 (0.010) 0.026 (0.021) 0.014 (0.025) 0.024* (0.014) 0.028 (0.033) 0.016 (0.019) 0.951*** (0.243) 0.348*** (0.097) 0.139 (0.246) 0.703*** (0.180) 1.372** (0.622) 0.347 (0.503) 0.041 (0.116) Good rating 0.051 (0.124) Independent agency 0.091 (0.088) % Reinsurance ceded 0.335 (0.218) Constant 4.057 (4.162) 0.002 0.003 (0.004) 2.901*** (0.035) 0.040 (0.115) 0.054 (0.101) 0.266 (0.188) 6.014 (3.883) 0.006 (0.007) 0.003 (0.006) 0.014 (0.020) 3.037 (0.369) 0.050 (0.100) 0.264 (0.187) 5.834 (3.904) 0.951*** (0.243) Firm dummies Yes Yes Yes Yes Yes Year dummies Yes Yes Yes Yes Yes 2 Res Log Likelihood 227.8 928.1 208.1 655.0 208.2 Notes: Standard errors are heteroscedasticity and autocorrelation consistent, and are shown in parentheses below coefficients. Company-specific intercepts and year dummy variables are included in the models, but are not reported here. Natural log transformation was taken on all compensation variables, as well as geographic diversification, due to right-skewed distributions. * significance at 10% level; ** significance at 5% level; *** significance at 1% level. experience smaller risk, in particular unsystematic risk. Geographic diversification is also found to share a positive relationship with two factor systematic risk, but statistically significant only at 10% level.

EXECUTIVE COMPENSATION AND RISK TAKING 199 ROBUSTNESS CHECKS While previous studies have shown that stock based compensation may increase or decrease a firm s risk taking, one may argue that firm risks also impact executives compensation contracts, thereby raising concerns for a possible endogeneity issue. To address the potential estimation bias created by an endogenous relationship, we also use the simultaneous equation system with a two stage least squares (2SLS) regression process. In the first stage, the stock based compensation variable is first estimated using all exogenous variables included in equation (4), in addition to the number of years the CEO has been with the company as well as the average age of the CEO and CFO. 12 The predicted vector from the first stage regression then replaces the endogenous stock and option holdings variable in equation (4). The results from the 2SLS method are reported in Table 4. As can be seen, the signs of the main variables remain the same when significant and there is no material difference in the findings between the fixed effects models and the 2SLS models. It appears that controlling for potential endogeneity does not change the conclusion presented in the results section. We also re examine the relationship between stock based compensation and firm risks by separating the effect of stock from that of stock option. Owning company stocks and owning stock options may be associated with different incentives, as the sensitivities of common stocks and restricted stocks to share price are linear in underlying stock price, while it is not the case for the sensitivity of stock options. Table 5 reports the relationship between stock based compensation and total risks where stock effects and stock option effects are tested and reported separately. Tables 6 and 7 present the model results between these incentive compensation and systematic risks and unsystematic risks, respectively. For each measure of risks, we estimate both a linear model and a model that includes a squared term of the compensation variable to see if both stock and stock options share non linear relationships with firm risks. Our findings in Table 5 show that both stock and stock options share a non linear relationship with total risks. However, they are related to total risks in different ways. In the model that examines effects of stock holdings, the coefficient for the stock variable is positively significant while the squared term of the same variable is negatively significant, which suggests that stock ownership induces greater risk taking but the marginal incentive effect decreases 12 We have tried a couple of variations of the age variable, including the average age of named executive officers or the CEO alone, and the results have been substantially the same.

200 MA AND WANG Table 4. Simultaneous Equation Results for the Effect of Stock Based Compensation on Firm Risks using Two Stage Least Squares (2SLS) Total risk One-factor risk Systematic risk Unsystematic risk Two-factor risk Systematic risk Unsystematic risk Stock and option holdings Stock and option holdings-squared 3.091** (1.580) 1.236* (0.653) % Commercial lines 1.477 (0.956) Size 0.224 (0.462) Geographic HI 0.651*** (0.245) Product HI 2.234* (1.215) % Independent board members 0.160 (0.729) Good rating 0.148 (0.225) Independent agency 0.051 (0.148) % Reinsurance ceded 0.177 (0.360) Constant 1.374 (6.850) 0.028 (0.222) 0.015 (0.092) 0.025 (0.135) 0.070 (0.065) 0.016 (0.034) 0.062 (0.171) 0.036 (0.103) 0.019 (0.032) 0.006 (0.021) 0.007 (0.051) 5.242*** (0.964) 2.908** (1.459) 1.130* (0.603) 0.782 (0.883) 0.220 (0.427) 0.681*** (0.226) 2.106** (1.122) 0.182 (0.673) 0.140 (0.208) 0.055 (0.136) 0.023 (0.333) 0.873 (6.324) 0.083 (0.105) 0.037 (0.043) 0.049 (0.063) 0.019 (0.031) 0.007 (0.016) 0.035 (0.080) 0.049 (0.048) 0.007 (0.015) 0.006 (0.010) 0.017 (0.024) 4.448*** (0.453) 2.862*** (1.452) 1.112* (0.600) 0.775 (0.878) 0.220 (0.425) 0.668*** (0.225) 2.137* (1.116) 0.170 (0.670) 0.137 (0.207) 0.049 (0.136) 0.017 (0.331) 0.848 (6.294) Firm dummies Yes Yes Yes Yes Yes Year dummies Yes Yes Yes Yes Yes Wald X 2 8240.27 739657 10623.26 3350000 10717.30 Notes: Standard errors are heteroscedasticity and autocorrelation consistent, and are shown in parentheses below coefficients. Company-specific intercepts and year dummy variables are included in the models, but are not reported here. Natural log transformation was taken on all compensation variables, as well as geographic diversification, due to right-skewed distributions. * significance at 10% level; ** significance at 5% level; *** significance at 1% level. with increase in the level of stock ownership. The findings for stock effects are consistent with the main results reported in Tables 3 and 4. The stock option ownership, however, shows a different effect. The coefficient for the squared term of the stock option variable is positively significant, which

EXECUTIVE COMPENSATION AND RISK TAKING 201 Table 5. Effect of Incentive Compensation on Total Risks: Stock Effects and Stock Option Effects Stock Effects Stock Option Effects (1) (2) (3) (4) Incentive Compensation Incentive Compensationsquared 0.158 (0.129) % Commercial lines 0.647 (0.551) Size 0.159 (0.276) Geographic HI 0.765*** (0.201) Product HI 1.095 (0.695) % Independent board members 0.411 (0.552) 1.031*** (0.374) 0.425*** (0.151) 0.704 (0.489) 0.091 (0.265) 0.689 (0.197) 1.026 (0.668) 0.200 (0.557) 0.677 (0.570) 0.603 (0.642) 0.144 (0.291) 0.756*** (0.204) 1.133* (0.673) 0.336 (0.549) 2.583 (1.655) 10.222*** (4.047) 0.864 (0.762) 0.111 (0.291) 0.722*** (0.205) 1.418** (0.660) 0.359 (0.530) Good rating 0.040 (0.129) Independent agency 0.087 (0.089) % Reinsurance ceded 0.405 (0.272) Constant 5.025 (4.232) 0.066 (0.124) 0.096 (0.088) 0.338 (0.211) 3.886 (4.035) 0.032 (0.133) 0.089 (0.090) 0.383 (0.263) 4.810 (4.422) 0.012 (0.141) 0.114 (0.091) 0.427 (0.256) 4.430* (4.419) Firm dummies Yes Yes Yes Yes Year dummies Yes Yes Yes Yes 2 Res Log Likelihood 231.3 226.4 228.4 218.8 Notes: Standard errors are heteroscedasticity and autocorrelation consistent, and are shown in parentheses below coefficients. Company-specific intercepts and year dummy variables are included in the models, but are not reported here. Natural log transformation was taken on all compensation variables, as well as geographic diversification, due to right-skewed distributions. * significance at 10% level; ** significance at 5% level; *** significance at 1% level. suggests that the incentive effect created by stock option ownership grows exponentially. The potential gain from stock options promotes greater risktaking to a greater extent when the intensity of executive compensation on stock options increases. The different signs of the squared terms of stocks

202 MA AND WANG Table 6. Effect of Incentive Compensation on Systematic Risks: Stock Effects and Stock Option Effects Stock effects One-factor risk Stock option effects Stock effects Two-factor risk Stock option effects (1) (2) (3) (4) (5) (6) (7) (8) Incentive compensation Incentive compensation squared % Commercial lines 0.014 (0.009) Size Geographic HI Product HI 0.015 (0.014) % Independent board members Good rating Independent agency % Reinsurance ceded Constant 2.891*** (0.029) 0.002 (0.003) 0.014 (0.009) 0.015 (0.014) (0.003) 0.002 2.896*** (0.033) 0.014 (0.009) 0.016* (0.010) 0.002 0.020 (0.013) 0.002 0.002 2.903*** (0.035) 0.030 (0.032) 0.053 (0.084) 0.014 (0.010) 0.002 0.019 (0.013) 0.002 0.002 2.897*** (0.034) 0.007 (0.008) 0.030 (0.021) 0.011 (0.023) 0.022* (0.013) 0.031 (0.034) 0.021 (0.021) 0.005 (0.006) 0.003 (0.006) 0.012 (0.019) 0.027 (0.028) 0.011 (0.011) 2.988*** (0.332) 0.026 (0.022) 0.015 (0.026) 0.024* (0.015) 0.032 (0.036) 0.015 (0.019) 0.006 (0.007) 0.003 (0.006) 0.015 (0.020) 3.054*** (0.380) 0.005 (0.014) 0.032 (0.022) 0.010 (0.022) 0.021* (0.013) 0.028 (0.032) 0.017 (0.018) 0.005 (0.006) 0.003 (0.006) 0.011 (0.019) 0.002 (0.051) 0.023 (0.134) 2.977*** (0.322) 0.031 (0.023) 0.010 (0.022) 0.022* (0.013) 0.027 (0.034) 0.017 (0.018) 0.005 (0.006) 0.003 (0.006) 0.011 (0.019) 2.981*** (0.319) Firm dummies Yes Yes Yes Yes Yes Yes Yes Yes Year dummies Yes Yes Yes Yes Yes Yes Yes Yes 2 Res Log Likelihood 938.2 927.4 944.2 937.1 661.6 655.3 664.3 664.0 Notes: Standard errors are heteroscedasticity and autocorrelation consistent, and are shown in parentheses. Company-specific intercepts and year dummy variables are included in the models, but are not reported here. Natural log transformation was taken on all compensation variables, as well as geographic diversification, due to right-skewed distributions. * significance at 10% level; ** significance at 5% level; *** significance at 1% level. and that of stock options may be due to the different characteristics of the return of these two investment instruments. The potentially unlimited upside return and zero downside return of stock options may inflate executives tolerance to risk, thus encouraging them to take on more risky

EXECUTIVE COMPENSATION AND RISK TAKING 203 Table 7. Effect of Incentive Compensation on Unsystematic Risks: Stock Effects and Stock Option Effects Stock effects One-factor risk Stock option effects Stock effects Two-factor risk Stock option effects (1) (2) (3) (4) (5) (6) (7) (8) Incentive compensation Incentive compensation squared % Commercial lines 0.217* (0.117) 0.091 (0.550) Size 0.217 (0.245) Geographic HI 0.776*** (0.183) Product HI 1.254** (0.639) % Independent board members 0.487 (0.496) Good rating 0.023 (0.123) Independent agency % Reinsurance ceded 0.053 (0.103) 0.319 (0.231) Constant 6.912* (3.879) 1.040*** (0.282) 0.401*** (0.116) 0.149 (0.481) 0.149 (0.236) 0.711*** (0.182) 1.230** (0.615) 0.311 (0.520) 0.053 (0.114) 0.060 (0.101) 0.267 (0.186) 5.830 (3.776) 0.958* (0.559) 0.036 (0.655) 0.203 (0.264) 0.768*** (0.187) 1.327** (0.632) 0.423 (0.492) 0.022 (0.131) 0.052 (0.103) 0.304 (0.221) 6.577* (4.014) 1.121 (1.608) 6.512* (3.819) 0.199 (0.742) 0.185 (0.261) 0.748*** (0.186) 1.513** (0.657) 0.449 (0.472) 0.012 (0.134) 0.068 (0.106) 0.336 (0.212) 6.745* (3.899) 0.222** (0.117) 0.094 (0.536) 0.199 (0.246) 0.762*** (0.179) 1.339** (0.661) 0.466 (0.493) 0.022 (0.124) 0.050 (0.102) 0.317 (0.230) 5.643 (3.797) 1.038*** (0.276) 0.398*** (0.113) 0.152 (0.469) 0.130 (0.238) 0.698*** (0.179) 1.311** (0.632) 0.289 (0.516) 0.053 (0.115) 0.057 (0.100) 0.265 (0.184) 6.605 (4.125) 0.938* (0.560) 0.037 (0.641) 0.187 (0.266) 0.756*** (0.184) 1.416** (0.658) 0.395 (0.489) 0.022 (0.132) 0.049 (0.102) 0.304 (0.221) 6.411 (4.035) 1.180 (1.617) 6.638* (3.843) 0.206 (0.730) 0.168 (0.262) 0.735*** (0.182) 1.604** (0.684) 0.420 (0.468) 0.012 (0.136) 0.065 (0.105) 0.337 (0.211) Firm dummies Yes Yes Yes Yes Yes Yes Yes Yes Year dummies Yes Yes Yes Yes Yes Yes Yes Yes 2 Res Log Likelihood 212.0 207.1 209.5 202.6 212.0 207.3 209.8 202.7 Notes: Standard errors are heteroscedasticity and autocorrelation consistent, and are shown in parentheses below coefficients. Company-specific intercepts and year dummy variables are included in the models, but are not reported here. Natural log transformation was taken on all compensation variables, as well as geographic diversification, due to right-skewed distributions. * significance at 10% level; ** significance at 5% level; *** significance at 1% level. projects; on the contrary, the potentially unlimited gain and potentially unlimited loss on stocks force executives to think twice before taking more risks. When we break down total risks into systematic risks and unsystem

204 MA AND WANG atic risks and repeat the analysis, as in our main analysis, we find that incentive compensation, whether it is stock holdings or stock options, has no effect on a firm s systematic risks. On the other hand, the results for unsystematic risks are in general consistent with those for total risks. Combined together, our results indicate that the risk aversion theory is supported only by stock holdings, not by stock options. Additionally, stock based executive compensation affects unsystematic risks but not systematic risks. CONCLUSION Stock based compensation may create an incentive for company managers to maximize their own interest in a way that may not always align with that of other company owners. Using data from public propertyliability insurers, this study examines the relationship between executives stock based compensation and volatility in return on firms stocks. We measure three types of risk total risk, systematic risk, and unsystematic risk. We calculate separately the sensitivity of the value of executives stock holdings and option holdings to stock price movement and test for the potential non linear relationship due to the different theoretical hypotheses. Our results show that firms whose stock based executive compensation is more sensitive to the value of their stocks tend to take more unsystematic risks and total risks. However, the relationships are weakened when executives have significant amount of wealth invested in the company. Our results remain robust with different ways of measuring firm risks as well as various model specifications. Additionally, our findings suggest that stock holdings and stock option holdings are related to firm risks in different ways. A decreasing risk taking effect is found only with regard to stock ownership, while option ownership is associated with increasing risk taking. More research, perhaps in broad industries, is called for to further investigate the subtle difference in the effects of stocks and of stock options on a firm s risk taking behavior. Stock based remuneration now constitutes the most lucrative and fastest growing portion of executive pay. The evidence that stock based compensation displays a non linear relationship with managerial risktaking behavior is significant. Identifying an optimal level of risk taking and designing an executive compensation package that motivates the optimal risk level presents a challenge to both academia and boards of directors. It is also important to treat with care the possible different incentive effects of granting stocks and granting stock options to executives. Our findings suggest that regulatory oversight on both stock

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