Relative Versus Absolute Performance Evaluation and CEO Decision-Making

Abstract We provide new evidence on how performance-based compensation plans affect CEO decision-making, especially risk-taking. Our main finding is that relative performance evaluation (RPE) plans provide incentives for CEOs to make decisions that generate more idiosyncratic performance outcomes; absolute performance evaluation (APE) plans do not. After switches from APE to RPE, the correlation between firm stock return and industry index return falls and firm idiosyncratic risk increases. Further, switches to RPE are followed by larger deviations in financial, investment, and operating policies from industry norms (i.e., more idiosyncratic strategies). All results are opposite for switches to APE.


I. Introduction
Studies of the relation between CEO incentives and decision-making often examine whether equity-based incentives, specifically stock and stock options, provide risk-taking incentives. Such studies typically examine the relation between measures of firm-level risk, including firm policy variables and stock return risk, and CEO risk-taking incentives as captured by CEO vega, the sensitivity of CEO wealth to changes in equity risk. To date, much of the work in this area focuses on time-vesting grants of stock and options (see Coles, Daniel, and Naveen (2006), Hayes, Lemmon, and Qiu (2012), and Shue and Townsend (2017), among many We thank John Graham, Lok-Si Ieong, Swaminathan Kalpathy (discussant), Yen-Jung Lee (discussant), and Yan Luo (discussant) for helpful comments. We also thank participants at the 2017 Annual Meeting of the Financial Management Association International and 2018 International Conference of Taiwan Finance Association and seminar participants at The Ohio State University, National Taiwan University, Yuan Ze University, and Chung Yuan Christian University. We offer special thanks to Jeffrey Coles (the referee) and Paul Malatesta (the editor) for their insightful comments. Wruck is grateful for research support from the Dice Center for Financial Economics at The Ohio State University Fisher College of Business. Wu is grateful for research support from the Center for Research in Econometric Theory and Applications (grant no. 108L900201) and from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan. Wu also acknowledges financial support from the Ministry of Science and Technology in Taiwan (MOST 107-2410-H-002-057-MY2).
with switches from APE to RPE (RPE to APE) is reflected in alternative measures of firm-specific risk. We find that it is; switches to RPE (APE) are followed by an increase (decrease) in the vulnerability of the firm's stock to extreme negative stock price movements and higher (lower) credit risk.
The rest of this article is organized as follows: In Section II, we develop our hypotheses and briefly describe our primary contribution. Section III presents data and descriptive analyses. Section IV presents our idiosyncratic risk results, robustness checks, and analyses to address endogeneity concerns. Section V presents the analysis of firm-level policies and other analyses. Section VI concludes.

II. Hypothesis Development and Our Contribution
A. Hypothesis Development As stated above, our primary hypothesis is that all else constant, switches from APE to RPE plans create incentives for the CEO to adopt differentiating strategies that make her firm less similar to its peers. This implies that RPE plans provide incentives to increase firm-specific risk and to select more idiosyncratic firm-level policies. Put differently, RPE provides CEOs with a disincentive to herd, or follow the crowd, with respect to firm policies. Switches from RPE to APE plans create the opposite incentives. Thus, following a switch from APE to RPE, we predict that a firm's performance will be less correlated with the performance of its industry peers and, relatedly, its idiosyncratic risk will increase. 1 For switches from RPE to APE, predictions are the opposite.
There are at least two potential mechanisms through which RPE plans provide stronger idiosyncratic risk-taking incentives relative to APE. First, by setting performance targets on a relative basis, RPE plans create external (or inter-firm) tournament incentives. This provides incentives for the CEO to make firm-level policy decisions with more idiosyncratic performance outcomes. In this way, the CEO increases the likelihood of outperforming the RPE performance benchmark by distinguishing her firm from the competition. If her policies deliver positive results, her compensation is higher (e.g., Knoeber and Thurman (1994), Brown, Harlow, and Starks (1996), Kempf and Ruenzi (2008), and Coles, Li, and Wang (2018)).
The tournament-style incentives provided by RPE are analogous to the incentives provided by indexed stock options (options whose exercise price is tied to a market or industry index). This is because, like indexed options, payouts under RPE plans depend on the firm's performance relative to a benchmark. The value of 1 A simple example helps illustrate the differences in incentives under RPE versus APE. Suppose there are two projects with equal expected net present values except for the correlation between their performance and industry peer performance. A CEO compensated under APE will be indifferent between the two. If, however, the Board of Directors switches that CEO to an RPE plan, because the RPE payoff depends on her firm's performance relative to performance of peer firms in the horse race, she will be motivated to differentiate her firm's performance from peers and prefer the project with lower correlation. As a result of this change in incentives, over time the firm's performance will become less correlated with the performance of its peers and its idiosyncratic component of total firm risk may increase. If the same CEO is switched back to an APE plan, she will again become indifferent and the firm's performance will drift back, becoming more correlated with the performance of its peers. standard, nonindexed, stock options depends on total risk and thus creates incentives to increase total risk. In contrast, Johnson and Tian (2000), (2004), and Duan and Wei (2005) show that the value of indexed stock options depends only on idiosyncratic risk; indexed options are in the money only if the stock price outperforms the relevant index. Thus, a CEO compensated under RPE has incentives to make decisions that differentiate her firm's performance from that of its peers in the horse race.
Second, the convexity of the grant date (ex ante) p-v schedule and/or the convexity of the schedule of ex post realized payouts could result in amplified risk-taking incentives for RPE plans relative to APE plans. 2 To understand how this might be possible, it is important to first understand how the p-v grant schedules of performance-based compensation plans are structured. Most commonly, performance-based compensation plans reward the CEO with award "units" comprised of stock, stock options, cash, or a combination among these. These units are called back-end units. Under a typical p-v grant schedule, the CEO does not receive any back-end units until a minimum performance threshold is met, at which point the p-v schedule jumps to some positive number of units. There is also typically a performance ceiling beyond which no additional units are awarded. Between the performance threshold and the performance ceiling is the incentive zone.
For performance in the incentive zone, the number of back-end units to be granted typically increases with the performance metric. For many plans, the p-v schedule is convex in the incentive zone (see examples 2 and 3 in Supplementary Material Appendix B), potentially increasing risk-taking incentives. However, it is not uncommon for the p-v schedule to be concave in the incentive zone (see Bettis et al. (2018), Figure 1a), potentially reducing risk-taking incentives. Bettis et al. (2018) measure the grant date (ex ante) discounted expected value of the ex post realized payout associated with APE plans (which they term "economic value"). For plans using accounting-based performance metrics, they estimate both a marginal and an aggregate "accounting vega." Marginal (aggregate) accounting vega is the change in economic value for a 0.01 change in the accounting metric's volatility (in both stock return volatility and the accounting metric's volatility). Based on their findings, they argue that convexity in an APE plan's p-v grant schedule can amplify risk-taking incentives by way of both the standard measure of CEO vega and their new vega measures.
Our data show that the vast majority of RPE plans use stock performance metrics, while the vast majority of APE plans use accounting-based performance metrics. Holden and Kim (2017) show that because each of a wide variety of accounting performance metrics has its own stochastic process, not to mention the joint stochastic processes between stock return and each accounting metric, the accuracy of marginal and aggregate accounting vegas depends on the assumed underlying stochastic process. While some studies report a positive relationship between accounting metrics and stock return, others report a negative or no relationship at all (Riffe andThompson (1998), Bushman, Lerman, andZhang (2016)).
Thus, even if the p-v schedule for an APE plan provides risk-taking incentives, those incentives may pertain primarily to the variability of the relevant accounting metric. They do not necessarily translate into greater stock return variability or greater firm-specific risk. Thus, we test whether convexity in the p-v schedule amplifies risk-taking incentives more for RPE plans than for APE plans.
Further, our data show that the vast majority of RPE plans use stock in back-end units, while the vast majority of APE plans use cash. If the use of stock in back-end units enhances the risk-taking incentives reflected in a plan's p-v schedule, p-v convexity could again amplify risk-taking incentives more for RPE than for APE plans. When the back-end payout is cash, as it is in most APE plans, the ex post realized award schedule will look exactly like the ex ante p-v grant schedule. However, if the back-end payout is stock and the performance metric is stock performance, which is the case for many RPE plans, then both the number of back-end units paid out and the value of those units increase with stock price. Thus, the ex post schedule of the value of the stock award will generally be convex, or more specifically quadratic, in stock price in the incentive zone.
It is important to note that the alternative to our primary hypothesis is meaningful (see, e.g., Ozdenoren and Yuan (2017), Albuquerque, Cabral, and Guedes (2019)). Using RPE with a market or industry index as the performance benchmark allows shareholders to insulate a risk-averse CEO from poor performance due to systematic risk. However, the CEO remains exposed to idiosyncratic risk. Shielding a risk-averse CEO from systematic risk while exposing her to idiosyncratic risk could provide her with incentives to take on systematic risk and eschew idiosyncratic risk. Consequently, it is not necessarily the case that RPE plans provide incentives to increase firm-specific risk; it will depend on whether the tournament-style incentives of RPE generate an expected payout that is high enough to overcome risk-aversion.

B. Our Primary Contribution
There is an ongoing debate as to whether the structure of CEO compensation contracts affects managerial risk-taking incentives. For example, Hayes et al. (2012) examine time-based vesting option grants around the 2005 adoption of FAS 123R and find that the decline in option usage is unrelated to changes in firm risk. However, their approach overlooks the fact that there was, at the same time, a dramatic shift away from the use of time-based vesting option grants to performance-based vesting compensation plans (e.g., Li and Wang (2016), Bettis et al. (2018)). We weigh in on this debate by providing evidence on the risk-taking incentives generated by performance-based compensation plans. More specifically, this article contributes to the contract design literature and managerial risk-taking literature by showing that the tournament-style incentives induced by RPE contracts motivate idiosyncratic risk-taking. Park and Vrettos (2015) is perhaps the most relevant prior study. Based on a single year of hand-collected data, they examine the interaction between the risk-taking incentives provided by CEO stock options (standard CEO vega) and the use (or not) of RPE plans. They find that the use of RPE plans dampens the incentives provided by CEO options to take on systematic risk (Armstrong and Vashishtha (2012)) and enhances option-based incentives to take on idiosyncratic risk.
Our study uses 17 years of compensation plan data (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) from the Institutional Shareholder Services (ISS) Incentive Lab database, in addition to data from other sources. Our findings differ from Park and Vrettos (2015) in many important respects. First, they find no evidence that the use of an RPE plan, in and of itself, is related to risk-taking incentives. In contrast, we show that after firms switch from APE to RPE (RPE to APE) they have relatively higher (lower) idiosyncratic risk. Further, Park and Vrettos (2015) do not provide evidence on how the use of RPE versus APE affects CEO decision-making. We show that firms switching from APE to RPE (RPE to APE) adopt financial, investment, and acquisition policies that are more (less) idiosyncratic and dissimilar (similar) to those of their industry peers. Further, our more extensive data allow us to examine whether and how other features of performance-based compensation plans, such as p-v grant schedule convexity and form of back-end payout, affect idiosyncratic risk-taking. Finally, our battery of robustness tests and additional analyses enable us to draw causal inferences. In summary, our study not only extends and complements prior work in the contract design and managerial risk-taking literature, but provides new findings and insights using far more extensive data.

A. Sample Selection
Detailed data on performance-based CEO compensation plans are obtained from Institutional Shareholder Services' (ISS) Incentive Lab Database. 3 Additional data on CEO compensation, CEO characteristics, corporate governance, and other firm and industry characteristics are obtained from ExecuComp, Equilar Consultants, Risk Metrics, and Compustat, respectively. Components of firm risk are estimated using data from the Center for Research in Security Prices (CRSP) and the 48 industry portfolio data from the Kenneth R. French data library. For firmyears with missing CEO characteristic data in the above databases, data are handcollected from SEC filings. Financial firms (SIC codes between 6000 and 6999) and utilities (SIC codes between 4900 and 4999) are excluded from the sample. The sample period is 1998 to 2014 (17 years). We eliminate firm-years in which only time-based vesting plans (i.e., nonperformance-vesting plans) are used. This sharpens our tests by allowing us to concentrate on the type of performance evaluation used 3 The ISS database contains compensation data from proxy statements (DEF 14A) for named executive officers of large publicly traded companies in the USA. For each year from 1998 through 2014, public firms are ranked based on average market capitalization for each day in the month of November. For the top 750 firms in each year, executive compensation data are collected from proxy statements. S&P 500 firms are always included in the database regardless of whether or not they rank in the top 750. If a "new" firm appears in the top 750 for a specific year, its information is backfilled to 1998 (or the firm's IPO date) and the database continues to track the company even if it falls out of the top 750. If a firm is acquired, goes private or goes out of business, its historical data continues to be carried in the database. In total, the database has over 2,000 unique companies, of which about 1,200 were active as of 2014.
(RPE vs. APE). 4 Detailed definitions of all variables used in this study can be found in Supplementary Material Appendix A. Table 1 summarizes the characteristics of our sample of CEO performancebased compensation plans. ISS Incentive Lab database provides a variable (PERFORMANCE_TYPE in ISS) that classifies a firm's use of performance-based compensation as APE only, RPE only, or a mixture of both APE and RPE plans in the same year. We define an RPE year as a firm-year in which at least one of its CEO's compensation plans relies on performance benchmarks set relative to a specified group of peer firms or a published index. We define an APE year as a firm-year in which its CEO's compensation plan relies exclusively on performance targets defined in absolute terms. As discussed in more detail below, the characteristics of our sample of performance-based compensation plans are similar to prior studies.

B. Summary Statistics
Supplementary Material Appendix B presents three examples of the ways in which RPE performance benchmarks are set. Example 1 is Campbell Soup Company's RPE plan for the 2007-2009 performance period. Under this plan, the company's total stock return (TSR) is ranked relative to the TSR of 10 peer firms. The performance target is a rank of fifth or sixth out of 11 firms (the 10 peer firms plus Campbell Soup Company). The ex ante payout function is a step function that specifies the CEO's payout as a percentage of the number of target shares. For example, if the firm ranks first then the CEO receives 200% of the target shares and if it ranks tenth or eleventh then the CEO receives no shares.
Example 2 is Dow Inc.'s RPE plan for the 2006-2008 performance period. Under this plan, the company's TSR is assessed relative to the average TSR for 14 peer firms. If performance is more than 5% below the peer average (performance threshold), the CEO receives no shares. For performance ranging from 5% below the peer average to the peer average (performance target), the CEO receives between 35% and 100% of target shares on a linear schedule. For performance ranging from the peer average to 5% above the peer average (performance ceiling), the CEO receives between 100% and 200% of target shares on a linear schedule. For performance greater than 5% above the peer average, no additional shares are awarded. Note that the p-v grant schedule is piecewise-linear and the ex ante payout function is convex in TSR relative to peer average in the incentive zone.
Example 3 is International Flavors & Fragrances Inc.'s (IFF's) RPE plan for the 2007-2009 performance period. Under this plan, the company's TSR is assessed as a percentile of the S&P 500. If performance is below the 40th percentile of the S&P 500 (performance threshold), the CEO receives no shares. For performance ranging from the 40th to the 55th percentile of the S&P 500 (performance target), the CEO receives between 25% and 100% of target shares on a linear schedule. For performance ranging from the 55th percentile to the 75th percentile of the S&P 500 (performance ceiling), the CEO receives between 100% and 200% of target shares on a linear schedule. Table 1 presents information on how our sample of 18,251 firmyears is divided between RPE and APE firm-years. RPE is used in approximately 26% of firm-years (4,761 firm-years for 904 unique firms) and APE is used in approximately 74% of firm-years (13,490 firm-years for 1,730 unique firms). 5 Firms sometimes award multiple grants to CEOs in a given firm-year, so we also present information at the grant level where the split between RPE and APE is 23%  Table 1 summarizes the type of performance metrics used. Stock performance metrics are used in 66.0% of RPE firm-years, but in only 1.1% of APE firm-years. In contrast, accounting performance metrics are used in only 20.2% of RPE firm-years, but in 40.6% of APE firm-years. Therefore, switches in performance-based compensation plans are often associated with a change in % of plans that do not disclose target that state reason is due to confidentiality 1.02% 1.81% † The fraction of total CEO compensation that RPE (APE) represents for RPE (APE)-granting firms based on reported fair market value (FMV) at the date of RPE (APE) grant or the grant-date value of the target award when FMV is not available. † † Stock price metrics include stock return or stock price level. Accounting metrics include earnings, growth in earnings, EPS, growth in EPS, ROA, ROI, ROS, sales, sales growth, operating income, growth in operating income, operating margin, EBITDA, EBITDA growth, EBITDA margin, EBIT, EBIT growth, EBIT margin, EBT, EBT growth, EBT margin, cash flow, cash flow per share, cash flow growth, economic value added (EVA), EVA growth, EVA per share, etc. Other performance metrics include measures such as productivity, ethics, customer satisfaction (loyalty), employee work safety (health, safety, and environmental performance), success in damage prevention, etc. Supplementary Material Appendix B provides examples of plans that use other performance metrics.
† † † Stock awards include restricted stock, restricted stock units, phantom stock, phantom stock units, and common stock equivalents. Option awards include stock options, stock appreciation rights, and other instruments with option-like features. Cash is defined as an annual or long-term payout in cash. Long-term cash is primarily the payout of long-term cash performance units. † † † † Payout is based on grant date fair value. For a restricted stock (option) award, grant date fair value is the stock price per unit (Black-Scholes option value per unit) on the grant date times the threshold, target, and maximum units of that back-end instrument. For a cash award, firms report the actual cash value at threshold, target, and maximum. Actual less threshold and Actual less target performance in the grant year are standardized by total assets when the plan performance metric is dollar earnings or sales measure, or by actual stock price when the plan performance metric is the stock price. For other performance metrics, such as EPS, ROA, ROE and growth rates, differences are unstandardized.
performance metrics. Performance metrics that are neither stock price-nor accounting-based are less commonly used (4.9% of APE firm-years and 0.8% of RPE firm-years). Supplementary Material Appendix B, example 4, provides examples of plans that use such performance metrics. Panel C of Table 1 presents the type of back-end instruments paid out. Among RPE plans, 62.8% use stock or options as the back-end instrument: 61.5% grant only stock, 0.8% grant only options, and 0.5% grant both stock and options. In contrast, 63.6% of APE plans use cash as the back-end instrument: 56.4% grant only annual cash awards, 3.5% grant only long-term cash awards, and 3.7% grant both annual and long-term cash awards. Therefore, switches in performance-based compensation plans often lead to a significant change in the type of back-end instrument. In addition, it is worth noting that as only 0.8% of the CEO RPE plans use options as the back-end instrument, our findings regarding the risk-taking incentive properties of CEO RPE plans are not driven by the risk-taking incentives of granted options.
Panel D of Table 1 summarizes details of the grant date (ex ante) p-v schedules. For plans using cash as the back-end instrument, the value of the threshold, target, and maximum awards is expressed in terms of actual value at grant date. For plans using stock or options as the back-end instrument, the value of the threshold, target, and maximum awards is expressed in terms of grant date fair value. Relative to target payout, on average (or at the median), threshold payout is set slightly higher for RPE than for APE plans. Maximum payout is set similarly for the two types of plans. Following Bennett, Bettis, Gopalan, and Milbourn (2017), we define payoutperformance convexity as a binary variable that equals 1 if the slope to the left of the target performance scaled by the slope to the right of the target performance is less than 1, and zero otherwise.
Our data show a little over 40% of RPE and almost 50% of APE plans have convex payout-performance functions, suggesting that neither type of plan consistently provides risk-taking incentives through convexity in its p-v grant schedule. For CEO RPE plans, target (threshold) performance is 3.11 percentile points higher (23 percentile points lower) on average than the actual performance in the grant year and is set at the 55th (30th) percentile of peer performance. For CEO APE plans, target (threshold) performance, standardized as appropriate, is 0.053 higher (0.035 lower) on average than the actual performance in the grant year. 6 Detailed information on the characteristics of performance peers and performance benchmarks for CEO RPE plans can be found in Supplementary Material Appendix C. In summary, the structure of performance-based compensation contracts differs between RPE and APE plans and across firms using the same type of plan. Therefore, it is important to control for the contractual features of performancebased compensation plans in order to examine whether the incentives induced by RPE versus APE differ with respect to idiosyncratic risk-taking.
However, before moving to our main analyses, we verify empirically that each plan type influences CEO compensation in a way that is consistent with evidence supporting the use of weak-form RPE. More specifically, weak-form tests of RPE regress total CEO compensation (or changes in the log of total compensation) on own firm stock return and peer firm stock return, along with various control variables. If firms use RPE, the coefficient on peer firm return will be significantly negative, reflecting the fact that RPE nets out peer firm performance in assessing CEO performance (see, e.g., Garvey and Milbourn (2006), Albuquerque (2009), Gong et al. (2011), and Jayaraman, Milbourn, Peters, and Seo (2020)). We run similar analyses and find evidence of weak-form RPE use only by sample firms that actually use RPE performance plans. Details of this analysis are presented in Supplementary Material Appendix D.

IV. Does the Use of RPE Versus APE Influence Firm-Level
Idiosyncratic Risk?

A. Baseline Difference-In-Differences Models
We use a difference-in-differences (DID) research design in our main analysis, which is summarized in the diagram below: DID models of potential switches from APE to RPE are based on an initial sample comprised of all APE firm-years. A firm-year is classified as an APE firmyear if the CEO's performance-based compensation plans in that year rely exclusively on a target or targets defined in absolute terms (8,451 firm-years). For potential switches from RPE to APE, our initial sample is comprised of all RPE firm-years. A firm-year is classified as an RPE firm-year if at least one of the CEO's performance-based compensation plans in that year relies on performance benchmarks set relative to a specified group of firms or a published index (3,885 firmyears). 7 Thus, in the pre-treatment period (TIME = 0, YEAR = t-1) all firms have Potential Switches from APE t-1 to RPE t

Sample of 8,451 APE firm -years for year t-1
Pre-Treatment (t-1) Time = 0 the same performance-based compensation plan classification. We then observe whether or not each firm switches in the following year (TIME = 1, YEAR = t).

Control Firms
Firms that do not switch form the control group (SWITCH = 0 for both the pre-and post-treatment year). Firms that switch form the treated group (SWITCH = 1 for both the pre-and post-treatment year). 8 The diagram above provides descriptive statistics regarding the frequency of switches from APE to RPE and vice versa for our sample. As it shows, switches between plan types are not uncommon; 734 (8.7%) of APE firms in year t À 1 switch to RPE in year t, while 400 (10.3%) of RPE firms in year t À 1 switch to APE in year t. Panel A of Table 2 presents results from our baseline DID models. The dependent variables are three different measures of idiosyncratic risk: i) the correlation of firm returns with industry index returns (IND_INDEX_CORRELATION), ii) idiosyncratic stock return risk (IDIOSYNCRATIC_RISK), and iii) idiosyncratic stock return risk as a proportion of TSR risk (IDIOSYNCRATIC/TOTAL_RISK). They are computed using daily data and are measured in year t þ 1 (the year following a firm's decision to switch from APE to RPE or to continue with APE and vice versa). IDIOSYNCRATIC_RISK is the square root of the residual variance from a regression of the firm's daily stock return on the return to the CRSP value-weighted daily market index and the return to its Fama-French (1997) valueweighted daily industry index. TOTAL_RETURN_RISK is the standard deviation of the firm's daily stock return. The model estimated is: Year and firm fixed effects þ ε i,tþ1 : All specifications include firm and year fixed effects, which subsume the standalone effects of the TIME and SWITCH indicator variables (Bakke, Mahmudi, Fernando, and Salas (2016)). 9 The main coefficient of interest is β 1 , the coefficient for the DID interaction variable; if it is significant, then it shows that after controlling for firm and year fixed effects, performance-based compensation plan status in year t has a significant effect on the relevant measure of idiosyncratic risk in year t þ 1.
Results from baseline models are consistent with our predictions that switching from APE to RPE creates incentives to increase idiosyncratic risk and reduce the correlation between a firm's performance and the performance of its industry peers. IND_INDEX_CORRELATION is lower for firms switching to RPE (model 1, coefficient of À0.0402) relative to APE firms that do not switch and higher for firms switching to APE (model 2, coefficient of 0.0284) relative to RPE firms that do not switch. For firms switching to RPE (APE), subsequent IDIOSYNCRATIC_RISK is relatively higher (lower), as reflected in positive (negative) coefficient on the DID interaction term of 0.0398 (À0.0200) in model 3 (model 4). Models 5 and 6 show that IDIOSYNCRATIC/TOTAL_RISK is significantly higher for firms switching to RPE and lower for firms switching to APE, respectively. DID interaction term coefficients are statistically significantly different from each other across corresponding regression models (i.e., β 1 in models 1 versus 2, 3 versus 4, and 5 versus 6). 10 Further, switches between types of performance-based compensation plans lead to economically significant changes in the dependent variables. Following a switch to RPE (APE), IND_INDEX_CORRELATION is lower (higher) by 8.0% (5.1%), IDIOSYNCRATIC_RISK increases (decreases) by 34.8% (19.8%), and IDIOSYNCRATIC/TOTAL_RISK is higher (lower) by 11.7% (4.5%), relative to the pre-switch mean. 11 The significance of our DID results suggests that switches in a CEO's performance plan type over a single year are sufficient to alter risk-taking incentives in a meaningful way. On closer inspection, however, the fact that the duration of APE plans is typically 1 year (see Table 1), suggests that firms switching to RPE are not generally subject to conflicting incentives from overlapping plans. The duration of RPE plans is typically 3 years, suggesting that firms switching to APE are more subject to conflicting incentives from overlapping plans, but this works against us finding significant results. Although the statistical and economic significances are weaker following a switch from RPE to APE, the results remain significant and are robust to alternative tests performed below.

B. Controlling for Contractual Features of Performance-Based Compensation Plans
Contractual features of CEO performance-based compensation plans, other than the use of relative versus absolute performance targets, can affect CEO risktaking incentives. Thus, it is important to control for these features to ensure that they do not drive our findings. Results from DID models that include controls for such contractual features are presented in Panel B of Table 2. It is worth noting that because DID estimation includes firm-year observations for both pre-and post-treatment years, these contractual variables capture the features of both prior 10 This study's sample period is from 1998 to 2014. However, prior to 2006, many of the details of CEO performance-based compensation plans were not required to be disclosed in SEC filings. Thus, for the pre-2006 period, the identification of APE and RPE is based on voluntary disclosures, which could be subject to self-selection biases. To address the potential impact of such misclassification, we split the sample observations into pre-and post-disclosure periods (1998-2005 and 2007-2014, respectively). The frequency of switches from APE to RPE is somewhat higher at 9.6%, while the frequency of switches from RPE to APE is somewhat lower at 8.8% following the SEC's 2006 mandatory executive compensation disclosure rules. Robustness tests (untabulated) show that our main results hold for both subperiods.
Specific features controlled for are the convexity of the grant date (ex ante) payout-performance schedule around target performance (PLAN_CONVEXITY_ INDICATOR), the natural log of the number of months between start and end of a plan's performance measurement period (ln(PLAN_DURATION)), form of payout using an indicator variable that equals 1 for stock or options as the back-end instrument, and zero for cash as the back-end instrument (STOCK_AWARD_ INDICATOR), and type of performance metric using an indicator variable that equals 1 for stock performance metrics, and zero otherwise (STOCK_METRIC_ INDICATOR). 12 As Panel B of Table 2 shows, even after controlling for these plan features, the sign, magnitude, and statistical significance of the DID interaction variable coefficients (β 1 ) are similar to those in Panel A. Differences between β 1 coefficients across corresponding models remain significant as well. Therefore, while some of the plan feature variables are statistically significant, they do not drive our findings.
The PLAN_CONVEXITY_INDICATOR variable is positively associated with IND_INDEX_CORRELATION and negatively associated with idiosyncratic risk measures across all models. This suggests that the risk-taking incentives provided by plan convexity encourage systematic, rather than idiosyncratic, risktaking. Coefficients for ln(PLAN_DURATION) carry the opposite sign of the DID interaction coefficient. 13 As explained earlier, plans with stock-based payouts should create stronger risk-taking incentives than plans that pay out in cash. Indeed, the STOCK_AWARD_INDICATOR is negatively associated with IND_INDEX_ CORRELATION and positively associated with idiosyncratic risk measures across all six models. Because accounting-based performance metrics are more subject to managerial discretion (Bennett et al. (2017), Gong, Li, and Yin (2019)), they might dampen risk-taking incentives associated with a performance-based compensation plan. Furthermore, as explained earlier, plans using accounting-based performance metrics may create incentives to increase the variability of that metric, but this does not necessarily translate into incentives to increase stock return variability. With the exception of model 4, the coefficient for the STOCK_ METRIC_INDICATOR variable is insignificant.
The difficulty of hitting a plan's performance target might also influence risk-taking incentives. Easy targets provide little incentive. In contrast, the more challenging the performance targets, the stronger are the incentives to "swing for 12 Including plan feature variables reduces the number of observations from 15,392 to 11,047 firmyears (28% reduction) for potential switches from APE to RPE and from 7,304 to 5,632 firm-years (23% reduction) for potential switches from RPE to APE. 13 The literature is ambiguous regarding the effect of plan duration on risk-taking. Some studies argue that CEOs take less risk the more frequently their performance is evaluated (e.g., Thaler, Tversky, Kahneman, and Schwartz (1997)), this suggests that plans with longer duration will be associated with more risk-taking. In contrast, other studies argue that CEOs take more risk when their performance is evaluated more frequently (e.g., Eriksen and Kvaløy (2014)), this suggests that plans with shorter duration will be associated with more risk-taking. In addition, Gopalan, Milbourn, Song, and Thakor (2014) find that riskier firms offer shorter CEO pay duration contracts. the fences" and adopt riskier strategies. 14 Panel C of Table 2 adds a TARGET> ACTUAL_INDICATOR variable, which equals 1 if firm performance in year t (t À 1) is below the plan's performance target for the new (prior) grant. 15 The TARGET>ACTUAL_INDICATOR is negatively associated with IND_INDEX_ CORRELATION and positively associated with idiosyncratic risk measures for all six models, suggesting a potential asymmetry in risk-taking at different levels of actual relative to target performance. This finding also suggests that if a firm's actual performance is above its performance target, the CEO may engage in strategic mimicry or herding behavior. 16 Because the inclusion of this variable results in a substantial loss of observations, we do not include it in subsequent analyses. We also include the interaction of STOCK_AWARD_INDICATOR variable with STOCK_METRIC_INDICATOR variable to control for the possibility that the payoff function is more convex when both features are at play. The sign and significance of this interaction variable are similar to those for the STOCK_ AWARD_INDICATOR variable.

C. Models With Additional Control Variables
Firm fixed effects control only for time-invariant firm characteristics. Thus, in our next set of models, we include variables that control for time-varying elements of CEO compensation, CEO and firm characteristics, and CEO turnover events. While there is no consensus regarding the ideal control variables to include in our regressions, we survey the literature for commonly used control variables and include them in our models. Panel D of Table 2  To address concerns that some elements of a CEO's compensation package have payoff profiles that could affect risk-taking incentives, we include ln(1 þ PRIOR_CEO_VEGA), ln(1 þ PRIOR_CEO_DELTA), 17 and the ratio of the CEO's 14 Cabral (2003) formalizes the intuition that laggards have little to lose and deliberately adopt riskier strategies when they are behind in the tournament (e.g., they have incentives to pursue a "Hail Mary" strategy). Knoeber and Thurman (1994) and Brown et al. (1996) show empirically that those who are unlikely to win a tournament adopt riskier strategies. In contrast, Brown (2011) provides evidence that when golfers are confronted with a superstar competitor (e.g., Tiger Woods), they do not adopt riskier strategies. 15 Genakos and Pagliero (2012) show an inverted-U relationship between risk-taking and rank. Indeed, laggards tend to take greater risks than leader. However, catching up with the leaders becomes progressively more unlikely as one moves down in ranking and may reduce risk-taking when one is far from the competitors. This finding motivates our use of the TARGET>ACTUAL_INDICATOR rather than the actual difference between a plan's performance target and the performance measure in the grant year. 16 We are grateful to Professor John Graham for pointing out the relevance of the herding literature as it pertains to the impact of the difficulty of hitting a plan's performance target on idiosyncratic risk-taking behavior (e.g., Graham (1999)). 17 Following Appendix A of Hayes et al. (2012), we measure the risk-neutral (Black-Scholes) CEO vega using ExecuComp data on option exercise price and option terms, the annual standard deviation of a firm's stock return based on returns from the preceding 36 months and annual dividend yield averaged salary to total compensation (CEO_SALARY_COMP). 18 Consistent with prior research (e.g., Armstrong and Vashishtha (2012)), ln(1 þ PRIOR_CEO_VEGA) is significantly negatively associated with IDIOSYNCRATIC_RISK for switches in both directions (models 3 and 4). ln(1 þ PRIOR_CEO_DELTA) is significantly negatively associated with IND_INDEX_CORRELATION and positively associated with both idiosyncratic risk measures. CEO_SALARY_COMP is significantly positively associated with IND_INDEX_CORRELATION, and negatively associated with both idiosyncratic risk measures for switches in both directions.
To address a potential concern that CEO turnover or CEO risk-taking characteristics drive our findings, we include ln(1 þ CEO_TENURE), and indicator variables for whether or not the CEO joined the firm no more than 2 years earlier (NEW_AND_OUTSIDE_CEO), has an explicit employment contract (CEO_ EMPL_CONTRACT), is a founder of the firm (FOUNDER), or chairs the firm's board of directors (CEO_DUALITY). The only variable that is consistently significant is the CEO_EMPL_CONTRACT indicator, which is positively associated with IND_INDEX_CORRELATION and negatively associated with both idiosyncratic risk measures across models. This finding is consistent with Gillan, Hartzell, and Parrino (2009) who find that by providing CEOs with guaranteed compensation and job security, explicit employment agreements dampen risk-taking incentives. To further rule out the possibility that CEO turnover or CEO risk-taking characteristics drive our findings, we rerun all Table 2 models with year and CEO-firm fixed effects, which control for endogenous CEO-firm matching and time-invariant characteristics of CEOs and firms. Our (untabulated) findings remain unchanged. To summarize, even after including additional controls, the sign, magnitude, and significance of DID interaction variable coefficients (β 1 ) remain similar to those in Panel A. Further, DID interaction coefficients remain statistically significantly different across corresponding regression models. Thus, our results are robust to these controls.
Models are also estimated under alternative DID research designs that require 2 or 3 consecutive years of APE or RPE use prior to potential switches. These research designs impose substantial data restrictions and result in a much smaller number of observations for estimation. Even so, results (untabulated) are similar to Table 2 findings. 19 Finally, models are estimated for first-time RPE and APE adoptions. First-time adoptions could provide a stronger "treatment" effect because over the same period. To make sure that it is not the use of options as a back-end instrument in prior p-v plans (in place in YEAR t À 1, TIME = 0) or in new p-v plans (in place in YEAR t, TIME = 1) that drives the significance of CEO vega, we calculate ln(1 þ PRIOR_CEO_VEGA) based on the CEO's total portfolio of option grants prior to YEAR t À 1 (YEAR t) for the pre-switching (post-switching) period. Similarly, we calculate ln(1 þ PRIOR_CEO_DELTA) based on a CEO's total portfolio of granted shares and options prior to YEAR t À 1 (YEAR t) for pre-switching (post-switching) period. 18 We focus on the salary component of cash compensation and exclude cash bonus because the typical CEO cash bonus contract has option-like features (Shaw and Zhang (2010)). 19 These multi-year window research designs have disadvantages and advantages. Because the median RPE award vesting period is 3 years, the effect of a new RPE grant on managerial behavior is more difficult to isolate from the effect of an RPE award that was granted (e.g., 2 years ago). On the positive side, based on 2 (3) years of data, it is easier to visually inspect whether pre-treatment trends satisfy the parallel trends assumption, which is a key identifying assumption underlying the DID estimation technique. they are not contaminated by prior, possibly overlapping performance-based compensation plans of the same type (Bettis, Bizjak, Coles, and Young (2014)). Results presented in Supplementary Material Appendix E are also consistent with Table 2 findings.

D. Further Robustness Checks
In our DID setting, identification is not perfect as the treatment is not random but is based on a potentially endogenous decision (i.e., switching performancebased compensation plan type). Further, it is possible that omitted variables or hidden factors jointly determine the design of CEO compensation contracts and a firm's industry index correlation and idiosyncratic risk. Still another potential concern is the possibility of reverse causality. For example, a CEO might decide to adjust strategy in YEAR t À 1 and then, in YEAR t, switch to the type of performance plan that will generate the highest pay under the new strategy. 20 In the previous section, we explored the sensitivity of our treatment effect to the inclusion of controls and fixed effects. To further confirm the validity of our main results, we undertake a variety of robustness checks to address these concerns.

Parallel Trends Assumption and Placebo Test
A causal interpretation of our main results requires that the parallel trends assumption underlying DID be satisfied. Evidence of changes in the outcome variables for treated firms, relative to control firms, prior to actual switches in performance-based compensation plan type would cast doubt on the validity of our findings. Specifically, it would imply a violation of the assumption that, in the absence of treatment, treated and control firms will experience ex ante parallel trends in the outcome variables. In Panel A of Table 3, we perform a falsification test in which we falsely assume that switches in the type of performance-based compensation plan occurred 1 year before switching firms actually do so. The coefficient for INTERACTION À1 (TIME À1 Â SWITCH), which equals 1 for firms that will actually switch to a different type of performance-based compensation plan in the following year and zero otherwise, is the estimated placebo treatment effect.
Results show that it is statistically indistinguishable from zero, providing evidence that changes in IND_INDEX_CORRELATION and idiosyncratic risk for treated firms relative to control firms occur after switches in performance plan type, but not before. Overall, this falsification test confirms that, in the absence of treatment, both treated and control firms exhibit similar trends in the outcome variables.

Matched Pair Analysis
We further address the possibility of reverse causality by forming matched pairs of treated and control firms based on logistic models that estimate the propensity to switch from APE to RPE and from RPE to APE (presented in 20 Bhagat, Brickley, and Lease (1985) suggest that compensation contracts may be adopted for signaling reasons (e.g., because insiders are optimistic about the firm's future, rather than to motivate managers). Garvey and Milbourn (2006) suggest that CEOs are more likely to push for the adoption of RPE plans during bad times in order to avoid lower pay, while they are more likely to push to drop RPE plans during good times in order to enjoy pay increases.  Table 3 are Industry index return correlation (IND_INDEX_CORRELATION), IDIOSYNCRATIC_RISK, and IDIOSYNCRATIC/TOTAL_RISK for year t þ 1. Variables are defined in the Appendix. Panel A presents tests of the parallel trends assumption. In Panels B and C, Models (1), (3), and (5) use 605 matched pairs (a total of 1,210 firm-years) that use APE in year t À 1 and either switch to RPE or not in the following year t. Models (2), (4), and (6) use 322 matched pairs (a total of 644 firm-years) that use RPE in year t À 1 and either switch to APE or not in the following year t. Matches are based on Mahalanobis distance covariate matching or nearest neighbor propensity scores matching using models presented in Supplementary Material Appendix F, Table F1. Panel D uses 3,980 matched pairs of RPE and APE firm-years (a total of 7,960 firm-years) and matches are based on Mahalanobis distance covariate matching or nearest-neighbor propensity scores matching using models presented in Supplementary Material Appendix F, Table F2. Controls, firm and year fixed effects, and a constant are included in all models. t-values are based on robust standard errors clustered by firm and by year (2-way) and are reported in parentheses. Chow tests examine whether the coefficients for Interaction in Panel A and Switch Indicator in Panels B and C differ significantly across analogous regression models. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

IND_INDEX_CORRELATIONtþ1
IDIOSYNCRATIC_RISKtþ1  Table F2). It is worth noting that in these models, the coefficients for lagged idiosyncratic risk measures are the opposite of those that would suggest a problem of reverse causality problem. This implies that ex ante differences in idiosyncratic risk measures do not explain our findings. Our matched samples are comprised of firm-year pairs with similar plan choice propensities ex ante, but different plan choices ex post. A total of six matched pair control samples are formed based on Mahalanobis distance covariate matching and nearest-neighbor propensity score matching (Imbens (2000)). Supplementary Material Appendix F, Tables F3 and F4, shows that mean and median values of our matching variables are similar across matched pairs. Importantly, ex ante IND_INDEX_ CORRELATION and IDIOSYNCRATIC_RISK are comparable across matched pairs. Panels B-D of Table 3 present models estimated using our matched pairs. As discussed above, matched pairs have comparable pre-switching characteristics. Thus, we do not include firm-year observations for the pre-switching period and do not use the DID methodology. Accordingly, the DID INTERACTION is replaced with SWITCH_INDICATOR, which equals 1 if the firm changes performance plan type in that year, and zero otherwise, in Panels B and C of Table 3. In Panel D of Table 3, the DID INTERACTION is replaced with RPE_INDICATOR, which equals 1 for RPE firm-years, and 0 for APE firm-years. All models include the same controls used in Panel D of Table 2 and firm and year fixed effects.
Results based on Mahalanobis distance covariate and nearest-neighbor propensity score matched pair analyses show significant differences in all three dependent variables between matched switchers and nonswitchers and between matched RPE and APE plans. The direction of the effect on subsequent idiosyncratic risk is as expected.

2SLS/IV Model Estimation and Subsample Analyses
Supplementary Material Appendices G and H present the results of two additional robustness checks. In Supplementary Material Appendix G, we treat the potential switches from APE to RPE as endogenous and use the staggered adoption of the Inevitable Disclosure Doctrine (IDD) by U.S. states as a natural experiment that facilitates the staggered adoption of CEO RPE plans both across firms and over time. Results from 2SLS/IV models estimated using matched pairs support our finding that RPE adoption is associated with higher subsequent idiosyncratic risk. In Supplementary Material Appendix H, we examine whether our findings are driven by hidden factors that simultaneously influence both a firm's idiosyncratic risk and the type of performance plan granted to its CEO. To do so, we conduct a subsample analysis that focuses on two plausible hidden factors: i) market or industry downturns and ii) operating inflexibility. We find no evidence that either of these factors drives our findings.

A. Does the Use of RPE Versus APE Influence Corporate Policy Choices?
Our primary finding is that switches from APE to RPE (RPE to APE) are associated with relatively higher (lower) firm-level idiosyncratic risk. In this section, we test whether this higher (lower) idiosyncratic risk is reflected in corporate policy choices. We expect that it will be because corporate policy choices are an important mechanism that drives firm-level idiosyncratic risk.
Specifically, we test whether switches from APE to RPE (RPE to APE) are associated with relatively large (small) deviations in financial and investment policies from industry norms. We also test whether firms switching from APE to RPE (RPE to APE) adopt relatively more (less) idiosyncratic strategies by divesting (adding) lines of business in their primary industry and acquiring (not investing in) targets in lines of business outside their primary industry. Such decisions about corporate strategies would allow CEOs with RPE plans to distinguish their firms from the competition and outperform their peers if their more idiosyncratic strategies turn out well. CEOs with APE plans would not have such incentives.
We measure a focal firm's policy dissimilarity relative to the industry norm as the absolute value of the difference between its corporate policy variable and the median value of that variable among its industry peers. The smaller is this dissimilarity in corporate policy, the more similar the policy of the focal firm is to that which is typical in its industry. Table 4 presents results for DID models for dissimilarities in corporate financial policy (Panel A), dissimilarities in investment policy (Panel B), and dissimilarities in acquisitions and divestitures (Panel C). Explanatory variables include the same controls used in Panel D of Table 2 and firm and year fixed effects. Financial policy variables are CASH_DISSIMILIARITY, LEVERAGE_DISSIMILIARITY, and DEFAULT_DISSIMILARITY, which utilizes the estimated probability of default based on KMV- Merton's (1974) model (Bharath and Shumway (2008)). Investment policy variables are CAPEX_ DISSIMILARITY, R&D_DISSIMILIARITY, and EFD_DISSIMILARITY (external finance dependence), which is based on the fraction of CapEx not financed through internal cash flow (Rajan and Zingales (1998)). For acquisitions and divestitures, we measure the percentage of added business segments that have industry classifications outside the firm's primary industry classification (ADD_SEGMENT_ OUTSIDE (%)), the percentage of divested business segments that have industry classifications outside the firm's primary industry classification (DIVEST_SEGMENT_ OUTSIDE (%)), and the percentage of completed acquisitions that have industry Leverage is excluded as a control variable in (3) and (4)  The characteristics of mergers and acquisitions are added to control variables in models (5) and (6) classifications outside the firm's primary industry classification (ACQUIRE_ TARGET_OUTSIDE (%)).
Panel A of Table 4 shows that for all dissimilarity in financial policy specifications, the DID INTERACTION (TIME Â SWITCH) variable coefficients are positive for firms switching to RPE plans, indicating that after switching to RPE, the focal firm's cash ratio, market leverage, and default risk show larger deviations from industry norms than those of firms that continue to use only APE. The opposite findings hold for firms switching from RPE to APE although the results are not as strong statistically. The DID INTERACTION (TIME Â SWITCH) in Panel B shows that after switching to RPE, a focal firm's CapEx-to-PP&E, R&D-to-assets, and reliance on external financing, are more dissimilar to industry norms than those of nonswitchers. Panel C shows that after switching to RPE, firms adopt more idiosyncratic acquisition strategies; they are more likely to add business segments and acquire targets in industries outside of their primary industry and divest business segments in their primary industry. Again, opposite findings hold for switches in the opposite direction. 21

B. Does the DID Treatment Effect Vary With the Performance-Vesting
Grant Schedule?
In this section, we first examine whether there are differential risk-taking incentives associated with convexity in a p-v grant schedule between RPE and APE plans. As explained earlier, convexity in the p-v grant schedule may provide stronger risk-taking incentives for RPE plans because such plans are based predominately on stock performance metrics and the instrument to be awarded is stock.
Panel A of Table 5 estimates triple difference regressions in which the coefficient of interest is the coefficient on the triple interaction PLAN_CONVEXITY_ INDICATOR Â TIME Â SWITCH (or PLAN_CONVEXITY_INDICATOR Â INTERACTION). The coefficients for the triple interaction are insignificant in five of the six specifications (except model 3), suggesting that differences in idiosyncratic risk between switchers and nonswitchers in the post-period are not due to differences in p-v grant schedule convexity for RPE versus APE plans.
The lack of statistical significance on the triple interaction could be because we use convexity at the grant date (ex ante) rather than convexity in the ex post realized value of the awards. The latter is more convex in stock price for RPE plans as they tend to use stock as a back-end instrument. Thus, a natural extension of our test is to examine if there are differential risk-taking incentives associated with using stock as a back-end instrument between RPE and APE plans. Panel B of Table 5 presents results from triple difference regressions in which the coefficient of interest is the coefficient on the triple interaction STOCK_AWARD_INDICATOR Â TIME Â SWITCH (or STOCK_AWARD_INDICATOR Â INTERACTION). The coefficients for the triple interaction variable are statistically insignificant in five of the six specifications (except model 4), suggesting that differences in idiosyncratic risk between switchers and nonswitchers in the post-period are independent of the stock-based payouts. 22 Convexity in the ex post realized value of the awards is more convex in stock price for RPE plans when both features are at play. Thus, Panel C of Table 5 presents results from triple difference regressions in which the coefficient of interest is the coefficient on STOCK_AWARD_INDICATOR Â STOCK_METRIC_ INDICATOR Â INTERACTION. The coefficient is statistically insignificant in five of the six specifications (except model 6), suggesting that differences in idiosyncratic risk between switchers and nonswitchers in the post-period are independent of the interaction between the use of stock-based performance metrics and stock-based payouts.
In summary, our analyses in Table 5 help shed light on the main underlying mechanism of idiosyncratic risk-taking incentives induced by RPE plans; our analyses suggest that it is not the convexity, the type of back-end instruments, Supplementary Material Appendix I presents triple difference regressions that are estimated in order to examine whether the incentives to increase systematic risk that are provided by CEO vega from option grants during pre-treatment and post-treatment years are dampened following switching to RPE plans (Armstrong and Vashishtha (2012), Park and Vrettos (2015)). As only 0.8% of the CEO RPE plans and 1.1% of the CEO APE plans use options as the back-end instrument, option grants during both the pre-treatment and post-treatment years are primarily associated with time-based vesting plans. Results are somewhat consistent with Park and Vrettos (2015). More specifically, we find that for firms switching to RPE (APE), larger CEO vega during post-treatment period is associated with higher (lower) subsequent measures of idiosyncratic risk. nor the type of performance metrics in RPE contracts, but the tournament-style incentives induced by RPE plans that matter.

C. Alternative Measures of Firm-Specific Risk
In this section, we test whether the higher (lower) idiosyncratic risk associated with switches from APE to RPE (RPE to APE) is reflected in alternative measures of firm-specific risk. We also test whether the increase (decrease) in idiosyncratic risk following switches to RPE (to APE) comes about as a result of an increase (decrease) in total risk, a shift between systematic and idiosyncratic risk, or a combination of the two.
Panel A of Table 6 presents DID models with TOTAL_RETURN_RISK, SYSTEMATIC_RISK, NEGATIVE_SKEWNESS, and DOWN_TO_UP_VOL as dependent variables. Explanatory variables include the same controls used in Panel D of Table 2 and firm and year fixed effects. Models 1 through 4 show that observed changes in total risk are mainly the result of changes in idiosyncratic risk. NEGATIVE_SKEWNESS and the DOWN_TO_UP_VOL capture a stock's vulnerability to firm-specific extreme negative price movements. NEGATIVE_ SKEWNESS is À1 multiplied by the skewness of firm-specific weekly returns. The DOWN_TO_UP_VOL is the log of the ratio of the standard deviation of firmspecific weekly returns in down weeks to that in up weeks (Chen, Hong, and Stein (2001), Kim, Li, and Zhang (2011)). Models 5 through 8 show that switches from APE to RPE (RPE to APE) plans are associated with higher (lower) NEGATI-VE_SKEWNESS and DOWN_TO_UP_VOL. 23 Panel B of Table 6 presents DID models using firm-specific measures of the cost of borrowing as dependent variables. More specifically, the dependent variables are: i) JUNK_RATING Indicator, ii) NO_BOND_RATING indicator, iii) ln(BANK_LOAN_SPREAD) defined as the natural logarithm of the average "all in spread" for new bank loans, and iv) ln(BOND_ISSUE_SPREAD) defined as the natural logarithm of the average yield spread at the time of bond issuance. For models using the JUNK_RATING or NO_BOND_RATING indicator as the dependent variable, we run logistic regressions. Results show that switches from APE to RPE (RPE to APE) plans are followed by a higher (lower) likelihood of JUNK_ RATING and of NO_BOND_RATING, and a higher (lower) cost of borrowing. 24 Overall, our results show that switches to RPE are followed by an increase in the vulnerability of the firm's stock to extreme negative stock price movements and higher credit risk. We are not in a position to determine the optimality (or nonoptimality) of RPE contracts and whether these changes are optimal. 25 At a 23 We also run our models using CRASH_RISK as a dependent variable (Hutton, Marcus, and Tehranian (2009)). The definition is provided in the Appendix and results (untabulated) are qualitatively similar to those using other measures of firm-specific stock return risk. 24 Lemmon and Zender (2010) argue that the presence of a rated bond indicates that a firm has access to low-cost borrowing. Our finding that switches to RPE plans are associated with a lower likelihood of having a bond rating the following year (model 3) is consistent with Lemmon and Zender (2010) who show that higher stock return risk is negatively associated with the likelihood of having a bond rating. 25 The literature on the optimality (or nonoptimality) of RPE contracts is mixed (Noe and Rebello (2012), Chaigneau, Edmans, and Gottlieb (2018)). Kale, Reis, and Venkateswaran (2009) find that RPE is associated with improved performance. In contrast, experimental and empirical evidence shows a minimum, however, our findings suggest that credit rating agencies and lenders incorporate CEO risk-taking incentives induced by performance-based compensation plans into their assessment of credit risk (see also, Kuang and Qin (2013)). Panel A of Table 6 presents DID regression results based on alternative measures of firm-specific stock return risk. Dependent variables are TOTAL_RETURN_RISK, SYSTEMATIC_RISK, NEGATIVE_SKEWNESS, and DOWN_TO_UP_VOLATILITY for year t þ 1. Panel B presents DID regression results based on measures of credit risk and the cost of borrowing. Dependent variables are JUNK_RATING, NO_BOND_ RATING, ln(BANK_LOAN_SPREAD), which is the natural logarithm of bank loan spread at loan initiation, and ln(BOND_ISSUE_SPREAD), which is the natural logarithm of bond offering yield spread at bond issuance. Variables are defined in the Appendix. All models include controls, firm and year fixed effects and a constant. t-values are based on robust standard errors clustered by firm and by year (2-way) and are reported in parentheses. Chow tests examine whether the coefficients for INTERACTION (Time period indicator Â Plan switch indicator) differ significantly across analogous regression models. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. higher likelihood of unethical activities, financial misconduct, or sabotage in firms with strong tournament incentives (Harbring and Irlenbusch (2011), Charness, Masclet, and Villeval (2014), and Haß, Müller, and Vergauwe (2015)). From the creditor perspective, Moody's identifies tournament-style incentives as a "red flag" in assessing credit risk (Bertsch, Smith, and Watson (2006)).

VI. Conclusions
Utilizing a DID design, we provide new evidence on how performance-based compensation plans affect CEO corporate policy decision-making and risk-taking. Our main finding is that after a firm makes a switch from an APE to an RPE plan, the firm's industry index return correlation is lower, while both idiosyncratic risk and the idiosyncratic component of total risk are higher relative to firms that continue with an APE plan. Our main finding is consistent with the idea that RPE-driven tournament incentives provide incentives to take on idiosyncratic risk. Our findings are not driven by other performance plan features, CEO or firm characteristics, ex ante differences in industry index return correlation or idiosyncratic risk, or hidden factors. In addition, our results are robust to a battery of analyses designed to address endogeneity concerns.
Consistent with our findings regarding idiosyncratic risk, we find that firms switching to RPE plans subsequently have larger deviations in financial, investment, and acquisition polices from industry norms (i.e., more idiosyncratic strategies). This supports the idea of CEO corporate policy decision-making as a mechanism through which the RPE plans influence the nature of firm's risk. We also find that the higher idiosyncratic risk associated with switches from APE to RPE is reflected in alternative measures of firm-specific risk.
Overall, our findings are consistent with the idea that Boards of Directors find RPE plans feasible when they want to motivate the CEO to undertake more idiosyncratic strategies and distinguish the firm from its competitors. While our study does not address the optimality of RPE contracts, our empirical evidence regarding the effect of CEO RPE plans on risk-taking and firm policies may prove helpful in assessing when RPE incentives create value and when they do not.