Relative Performance Evaluation in Executive Compensation Contracts
J. Carr Bettisa
Arizona State University, Incentive Lab
John Bizjakb
Texas Christian University
Jeffrey Colesc
Arizona State University
Brian Youngd
Mississippi State University
First Attempt: April 28, 2012
This Draft: January 30, 2014
Preliminary and Incomplete
Please do not quote without permission.
a
W.P. Carey School of Business, Arizona State University, Tempe, AZ, 85287, USA; [email protected]
Neeley School of Business, Texas Christian University, Fort Worth, TX, 76129, USA; [email protected]
c
W.P. Carey School of Business, Arizona State University, Tempe, AZ, 85287, USA; [email protected]
d
Mississippi State University, Mississippi State, MS 39762, USA; [email protected]
b
The authors are grateful to Incentive Lab, a Scottsdale, Arizona compensation data and science firm, for generously
providing the data. The analysis and conclusions in this paper are those of the authors and have been formulated
independently of the views of Incentive Lab. For financial support, Bizjak thanks TCU, Coles is grateful to ASU, and
Young thanks MSU. The authors thank seminar participants at the University of Utah for helpful comments.
Relative Performance Evaluation in Executive Compensation Contracts
Abstract
Using data that includes specific contractual details of Relative Performance Evaluation
(RPE) contracts granted to executives for 1,833 firms for the period 1998 to 2012, we develop new
methods to characterize RPE awards and measure their value and incentive properties. The
frequency in the use of these awards has grown over time with 37% of the firms in our sample
granting an RPE award in 2012. When RPE awards are used they are typically granted to the five
named executive officers and they represent about 32% of total recipient compensation. Stock is
most frequently the instrument conveyed, followed by cash, and options are almost never granted.
RPE awards are more likely to be used at firms with diversified business lines, less concentrated
industries, greater exposure to systematic risk, larger size, lower M/B, higher dividend yield, fewer
insiders on the board, greater institutional ownership, and that engage a compensation consultant.
The typical award is a rank-order tournament based on three year stock returns compared
to a select group of 13 peers (median) and is paid out with stock. Payout functions typically include
regions of concavity, convexity, explicit inelasticity, and implicit inelasticity. The median firm
achieves a threshold for at least some payout of stock or cash about 70% of the time and target
payout about 50% of the time. In general, RPE grant value differs significantly from the fair
market value reported by firms. We find that RPE awards convey to executives the incentive to
increase shareholder wealth. RPE awards of stock contingent on either stock or accounting
performance and RPE awards of cash contingent on accounting performance convey the incentive
to increase firm risk, while RPE cash awards do not. These incentives can be significant in
comparison to those conveyed by APE grants with similar attributes.
I. Introduction
In the context of the standard agency problem (Holmstrom, 1979; Shavell, 1979), the
intuition for using relative performance evaluation (RPE) in the structure of incentive
compensation is compelling. When agents face common shocks then their compensation should
depend not only on the agent’s own performance but also on the performance of the others
(Holmstrom, 1982). For example, if firms face a common exogenous random shock, because of
macroeconomic movements or shifts in industry conditions, for instance, then an optimal
compensation contract for a CEO or other top executive would be contingent on performance of
the firm relative to other firms. RPE is consistent with removing forces that the CEO can’t control,
thereby increasing the principal’s power of inference from observables about unobservable
managerial actions. Insulating the executive from such risk permits better risk sharing and more
powerful incentive alignment than would be possible otherwise.
Further impetus for using RPE in executive pay arises from shareholders, institutional
investors, and the media. A common shared criticism of stock and option grants is that corporate
executives can and frequently do benefit from broad stock market gains for which the executives
are not responsible (e.g., see the analysis in Garvey and Milbourn, 2006). On the other side, one
suspects that executives themselves resist the notion that their equity-based awards should be
structured so as to expose award value to broad downward movements in the stock market. Such
“pay for luck, whether it is good or bad, can be diminished or perhaps eliminated by paying
executives based on own-firm performance relative to performance of other firms.
RPE could be implemented by various contracts, including indexed options or formulaic
payouts based on return compared to a broad index of performance, industry performance, or
1
performance of a peer group.
Likewise, Lazear and Rosen (1981) suggest that in some
circumstances a rank-order tournament among competitors is optimal. Without knowing what
specific forms might characterize contracts, researchers have searched for implicit evidence of
RPE. The general approach has been to regress CEO pay against the firm’s return and some
benchmark performance measure, such as industry or market return. A positive coefficient on firm
return and a negative coefficient on the benchmark return would be evidence in favor of RPE. As
Albuquerque (2009, Table 1) indicates, however, numerous attempts to detect RPE have been
largely unsuccessful.
Among others, Antle and Smith (1986), Barro and Barro (1990),
Janakiraman et al (1992), Jensen and Murphy (1990), Aggarwal and Samwick (1999a, b),
Himmelberg and Hubbard (2000), Garvey and Milbourn (2003, 2006), and Rajgopal et al. (2006)
find little support for the existence of RPE. Gibbons and Murphy (1990) find some evidence of
RPE, but the mechanism appears to be through board discretion over salary and bonus rather than
a formulaic contract specifying payout of cash, stock, or options.
Misspecification of the regression model is an obvious potential explanation for the paucity
of supporting evidence. For example, it is likely that firms face varying economic circumstances,
so that it is appropriate for some firms to use RPE while other firms should not and do not. Even
among firms that do use RPE, the functional dependence of CEO compensation on firm
performance is unlikely to be the same as specified by the regression models. Furthermore, a
regression model must specify the elements of pay covered by RPE (e.g., cash bonuses versus
stock or options), the timing of pay, any performance measure(s) (e.g., accounting versus market
performance) and measurement period(s), and the component contributors to the performance
benchmark (such as the industry or members of a peer group), and control variables. Finally,
2
endogeneity concerns arise when performance affects pay and causation likely runs in the other
direction as well. While some studies attempt to address misspecification,1 for RPE Lewellen
(2013, p. 1) asserts that “thirty years of empirical research has found little evidence consistent with
the agency hypothesis.”
Perhaps a more promising line of attack would pursue explicit evidence from surveys or
financial disclosures. Based on data from a 1997 Towers Perrin survey of 177 large U.S. firms,
Murphy (1999) reports claimed RPE usage by 51 of those firms in the annual cash bonus plan.
These data are quite limited but serve as early evidence of RPE usage. Carter et al (2009) examine
the 2002 financial reports for UK firms in the FTSE 350 index and find 129 of 252 firms report
usage of RPE as a component of total compensation. Gong et al (2011) examine the proxy
statements of the firms in the S&P 1500 for the year 2006, just following the implementation by
the SEC of enhanced compensation disclosure requirements, and find 361 of 1,419 firms report
using RPE in compensating executives and that implicit tests fail to detect RPE in the 2006 data.
These three papers combined provide some initial indication that at least some firms use RPE
contracts. Nonetheless, due in part to data limitations, these studies rely on small samples, provide
little detail on the specific characteristics of grants to executives, and provide no evidence on usage
patterns through time.
From Incentive Lab we obtain hand-collected data from proxy statements for 1,833 large
US firms on all long-term grants of stock, options, and cash to named executive officers (NEOs)
1
Albuquerque (2009) and Lewellen (2013) attack misspecification of the peer group. Antle and Smith (1986) in
part address the notion that perhaps only some firms use RPE.
3
over the period 1998-2012.2 The data facilitate a comprehensive characterization of the incidence
and form of both performance-vesting (p-v) and traditional time-vesting (t-v) provisions in large
US listed companies.
As Figure 1 indicates, traditional time-vested grants, which are not
contingent on a performance metric, are being displaced by awards that use a p-v provision that
specifies the size of the award contingent on some measure of firm performance. Approximately
86 percent of large US companies use a p-v provision in one or more awards to one or more NEOs
during 2012. While Bettis, Bizjak, Coles, and Kalpathy (2013) use these data to focus on p-v
awards that use absolute performance evaluation (APE), we focus attention on RPE. Of the firms
using conditional p-v awards in 2012, almost half specify that performance be measured relative
to performance of other firms.
RPE has been and continues to be a common feature of executive compensation contracts.
Beginning with about 13 percent usage in 1998, RPE is present over the entire 1998-2012 period.
In 2012 three in eight large U.S. companies will have issued an RPE grant to one or more NEOs.
Conditional on any RPE usage in 2012, on average 4.6 of the (five) NEOs receive an RPE award,
and RPE represents about 32 percent of total compensation among those recipients, based on the
grant date value reported in firm financial disclosures. The first contribution of this study is to
document frequent, longstanding usage of RPE in compensation contracts of corporate executives.
Second, the propensity to use RPE increases when the industry is less concentrated, firm
exposure to systematic risk is greater, and when the firm is larger and has lower M/B, higher
2
Incentive Lab initiated the data collection project in 2002. Because of the wide span of data items collected, wide
variation in how firms report compensation data, and extensive efforts for quality control, the Incentive Lab data have
become publicly available only in 2013. Both the data collection time interval and dataset contain 2006, the data year
used in Gong, Li, and Shin (2011),
4
dividend yield, fewer insiders on the board, greater institutional ownership, and the firm uses a
compensation consultant. Consistent with the theoretical predictions from the agency model, RPE
usage is less likely when aggressive price or quantity competition is destructive and more likely
when the stock return of the firm is a noisier signal of managerial actions, the firm is more exposed
to systemic (common) shocks, and the firm operates across diverse business segments.
Third, when disclosure is sufficiently comprehensive, careful examination of the proxy
statements allows us to characterize fully the RPE award as a function of performance. We find
that 79% to 89% of the time that a firm makes a RPE grant the firm uses a rank-order tournament.
Under this schema performance is measured for the target firm and a group of peers for a defined
period of time. After the performance period ends, the granting firm is ranked by performance
among the peer firms. The percentile rank is then mapped grant schedule to the payout of shares,
options, or cash to the executive. Figure 2, Panel A depicts a roughly-representative p-v RPE
percentile stock grant to the CEO of Allete, Inc. The number of shares to be conveyed to the CEO,
specified as a percentage of a target number of shares, depends on the ranking of Allete total stock
return (TSR) over a three-year performance period relative to TSR of 16 peer firms. This
tournament in TSR yields a lumpy grant schedule as a function of finishing position (Panel A).
Recasting the number of shares granted based on Allete TSR as the domain, the grant schedule
resembles a saw blade, with the location of steps depending on the ex post realization of
performance for the 16 peers. Panels B and C depict the schedule for two possible realizations of
performance of the 16 peers.
The other primary form of RPE grant schedule specifies the number of units of the backend instrument conveyed as a piecewise-linear, mostly-continuous function of firm performance
5
net of a benchmark. Panel A of Figure 3 depicts a grant schedule, with cash as the back-end
instrument, for the CEO of American Express in 2008, that depends on three-year annualized TSR
of the company net of a benchmark of TSR for the S&P 500.
While p-v RPE grant schedules vary widely in structure, some rough general statements
are possible. Stock is the most common back-end instrument, cash is second in frequency, and
RPE grants of options are rare. The most common performance measure is stock return, though
some grants use accounting or other metrics. Most grants use a single performance metric, though
others use two or more. The most common measurement period for performance is three years.
Often awards are described by a target number of back-end units and then the grant schedule is
defined by percent of target. Both percentile (saw-blade) and “smooth” (or benchmark-adjusted)
grants can have a jump in payout at a threshold, an increasing number of shares granted as
performance or percentile increases over an incentive zone (which often contains a point
designated as target), and a ceiling on units granted. Our data indicate that, when the grant
schedule contains such milestones (threshold, target, ceiling), the corresponding performance
requirements pose meaningful hurdles. Finally, many grant schedules have convexity in the
incentive zone and at threshold, concavity at the ceiling and threshold, discernible performance
sensitivity in the incentive zone around target, and no additional performance sensitivity (beyond
the value of the shares or options) below threshold and above the maximum. On the other hand,
some grant schedules display significant concavity around target in the incentive zone.
Finally, we develop and implement new methods to measure the value and incentive
properties of p-v RPE grants. Even relatively basic RPE grant schedules, such as the Allete and
American Express examples, can be complex or “messy,” as are the implied mappings from firm
6
and peer (and benchmark) performance to value of the grant at the end of the performance period.
For this reason, and because the grant is contingent on one or more accounting or other non-price
measure, the underlying arguments for using risk-neutral valuation methods often are not
applicable. Simulations based on our risk-adjusted approach suggest that the economic value of
the typical RPE award departs significantly from the value reported in the firm’s financial
disclosure. This departure has broad implications. All parties to the formation of pay in practice,
including shareholders, institutional investors, and regulators, and perhaps even the media, have a
fundamental need for the facts. Moreover, solving the measurement problem is a necessary
condition for assessing whether the level and incentive properties of executive pay are appropriate,
vary in the cross-section according to hypothesized economic factors, or affect firm value and risk.
For a given grant the typical measure of executive incentive alignment, delta, compares the
value of the grant before and after perturbation of stock price upward. The typical measure of the
incentive to take risk, known as vega, gauges convexity though a comparison of grant value after
and before a change in volatility of stock return. For a p-v APE grant based on stock performance,
these measures are intuitive and not too difficult to apply (see Bettis, Bizjak, Coles, and Kalpathy,
2010, 2013). For a p-v grant based fully or in part on accounting performance or for a p-v RPE
grant contingent on peer or benchmark performance, some adjustments to delta and vega are
required. Because accounting performance and peer performance often are correlated with stock
returns, we develop new measures of delta and vega that aggregate the direct, traditional effects
on executive incentives that come through stock performance and stock return volatility and the
indirect effects that arise through accounting and peer-firm performance and volatility. We find
that p-v RPE grants convey significant managerial incentives. Our analysis indicates that RPE
7
provisions shape the incentives of executives to advance shareholder interests and take risk, effects
that are likely to imply substantial consequences for firm performance, risk, investment policy,
and financial policy.
The remainder of this paper is as follows. Section II describes the data. Section III
provides descriptive statistics for RPE usage, hypotheses for RPE usage, tests regarding the
determinants of usage, and descriptive statistics for the role of RPE in overall compensation.
Section IV presents statistics on contractual details. Section V develops a new framework for
characterizing RPE grants and measuring their value. Section VI develops new measures of the
incentive properties of RPE awards. Section VII empirically implements these new methods to
analyze award outcomes and measure grant date expected value and incentives conveyed by RPE
contracts. Section VIII concludes.
II. Data
We obtain from Incentive Lab detailed data from proxy statements (DEF 14A) on the
various aspects of long- and short-term stock, option, and cash awards to named executive officers
(NEOs) over the period 1998-2012. The sample of firms is based on the largest 750 firms,
measured by market capitalization, in each of those years. The set of 750 largest firms changes
from year to year. Back- and forward-filling yields 1,833 firms during the period between 1998
and 2012, though data will not be available for some firms in a given year for the usual reasons
(e.g., merger, not listed). In each year, the sample fully contains the S&P 500 and encompasses
about 80% of the S&P 400 (mid-cap) and 5% of the S&P 600 (small-cap). We have 19,435 firmyears in sample. In 3,620 of those firm-years the company made one or more awards using RPE
8
to one or more NEOs. The vehicle for RPE always is a performance-vesting provision. Some pv provisions do not use RPE so we also record the presence and characteristics of p-v awards that
use absolute performance evaluation (APE).
Several items are noteworthy. Since multiple individuals can receive an award, there can
be many firm-year-person observations per firm-year. Some individuals receive at the same time
multiple RPE and APE awards. In some cases the grant “components” are side-by-side and do not
explicitly interact (though value can be correlated). In other cases one grant is contingent on
another. Thus, there can be multiple firm-year-person-component observations per firm-yearperson. As a further complication, each component may have its own performance period and
payout table in the DEF 14A. Herein, each table specifies the level of reporting. For some analysis
it is appropriate to roll data up to the firm-year level.
At the award level the data contain recipient name and title, award date, target payout
amount, ex-post vesting conditions, the number of components, and type of each component
(relative or absolute). The interaction between components, if any, also can be available. At the
component level the data contain the performance measure (i.e. stock returns or accounting data),
the specific details on construction of the performance measure, and the characteristics of the
performance benchmark(s) (including peer firms or performance index). For each associated
performance period and payout table (typically just one), the data contain the method of
comparison of performance measures, the range of dates of the performance period, and the details
of the grant function. More recent data contain the name of the compensation consultant used we have these data for 3,711 firm-years from 2006 to 2011. We supplement our data from CRSP
9
and Compustat. We obtain board data from Risk Metrics. Data on institutional ownership come
from 13F filings made available by Thomson Reuters.
III. RPE Usage and Role in Overall Compensation
An advantage of the data used in this study is that it is the only longitudinal data set for
RPE awards to executives. In this section we present statistics on the role of RPE in compensation
and test for factors associated with RPE usage, first-time adoption, and discontinuation.
III.A. RPE Usage
Panel A of Table 1 reports grant patterns through time to named executive officers (NEOs).
Firms using long-term (performance period exceeds one year) RPE awards constitute 18.6% of the
firm-years in our total sample, with firm-year usage rising through time to 37% of all firms in
2012. Including only long-term awards, in 2012 69.9% of the firms in our sample grant stock,
options, or cash with a p-v provision that extends beyond one year.3 Of these, roughly half use an
absolute p-v provision, while the other half (34.4% of firms in 2012) employ long-term RPE in the
grant schedule.4 Three in eight large U.S. firms issue one or more short- and/or long-term RPE
awards in 2012. RPE usage is consistent after adoption, with the median firm using an RPE award
in 87.5% of the years subsequent to initial adoption. Even though reporting prior to the 2006
enhancement in standards is likely to be incomplete, Panel A reports direct evidence of RPE usage
for large U.S. firms over the full sample period. When used, RPE awards constitute a significant
3
This is consistent with the data in BBCK (2013), which indicate that over the past 15 years performance vesting is
displacing time vesting in stock and option grants.
4
Compare the RPE usage figures in Table 1 to 25%, 29%, 51%, and 28% for Gong et al (2011), Murphy (1999),
Carter et al (2009), and Bannister and Newman (2003) respectively – from small samples that cover one year only.
10
portion of compensation. Based on reported fair market value at the date of grant (or the grantdate value of the target award when FMV is not available), RPE awards represent approximately
32% of overall compensation from 2006 to 2012. The reported proportion of value from RPE is
even higher in earlier periods.
Panel B shows that, conditional on an RPE award, by 2012 the back-end instrument has
shifted primarily to stock (82.4% of grants), with options rarely used (1.9%), and cash used with
intermediate frequency (27.5%). Panel C describes who receives RPE awards. If the firm uses
RPE, CEOs are included 91% to 96% of the time and on average 4.5 of the top five executives
receive an RPE award. In contrast, non-employee directors rarely receive RPE grants.
III.B. Determinants of Usage
We now explore firm and industry characteristics that are associated with RPE usage. We
generate several hypotheses and apply standard statistical tests. Nonetheless, without stronger
identification strategies we are unwilling to make strong claims about causation. We view the
results in this section as largely descriptive.
The Informativeness Principle (Holmstrom, 1982) states that an optimal contract should
depend on any variable that is additionally informative about the agent’s actions. A corollary is
that RPE, based on one or more variables that reflect common shocks, should be a component of
the optimal contract. Restated in the negative, if there is no common shock to remove from
performance, so there is little association between industry, peer-firm, or systematic returns and
own-firm performance, then RPE as a contractual feature adds little value. Other circumstances
as well likely reduce the desirability of an RPE contract. First, Lazear and Rosen (1981) point out
that RPE can be destructive in concentrated industries where cooperation among firms, in terms
11
of price or quantity decisions, for example, may prove beneficial to all. Second, it is likely to be
more difficult for firms operating across multiple segments to assemble a set of peers that reflect
similar business lines and remove common shocks. Third, a manager with a lower skill level or
lesser desire (higher cost) to work may prefer to be paid based on a noisier signal of output.
Accordingly, firms with a governance structure that imposes low monitoring would be less likely
to use RPE. Finally, it is likely that RPE contracts are sufficiently complex that the advice of a
compensation consultant is required. It is also possible that the compensation consultants justify
their fees by introducing innovative and complex compensation contracts, so that the use of RPE
is driven by the presence of a compensation consultant. Regardless of the direction of causation,
in the data we observe many similarities in RPE contractual structures and wording that lead us to
believe the compensation consultant is central in the adoption and form of these awards. We
propose the following hypotheses:
H1a
The propensity to use RPE increases as firm return is associated more strongly
with systematic return.
H1b
The propensity to use RPE increases with lower industry concentration.
H1c
The propensity to use RPE increases in firm focus.
H1d
H1e
The propensity to use RPE increases with governance structures that imply
stronger monitoring (a smaller board, fewer insiders on the board, and higher
institutional ownership).
The propensity to use RPE increases if the firm utilizes a compensation
consultant.
To test these hypotheses, we estimate the following logistic regression for RPE versus no
RPE and, conditional on the presence of a p-v provision, for p-v RPE versus p-v APE.
12
logit[Pr(𝑅𝑃𝐸 = 1)]
= 𝛽0 + 𝛽1 𝑆𝐸𝐺_𝐻𝐸𝑅𝐹 + 𝛽2 𝐼𝑁𝐷_𝐻𝐸𝑅𝐹 + 𝛽3 𝑀𝐾𝑇_𝑅𝐼𝑆𝐾
+ 𝛽4 𝐿𝑁_𝐴𝑆𝑆𝐸𝑇𝑆 + 𝛽5 𝑀/𝐵 + 𝛽6 𝑅𝑂𝐴 + 𝛽7 𝐼𝑁𝐷𝐴𝐷𝐽_𝑅𝑂𝐴 + 𝛽8 𝑅𝐸𝑇
(1)
+ 𝛽9 𝐼𝑁𝐷𝐴𝐷𝐽_𝑅𝐸𝑇 + 𝛽10 𝑅𝐸𝑇_𝑉𝑂𝐿 + 𝛽11 𝐶𝐹_𝑉𝑂𝐿 + 𝛽12 𝑆𝐴𝐿𝐸𝑆_𝐺𝑅
+ 𝛽13 𝐼𝑁𝑉 + 𝛽14 𝐷𝐼𝑉_𝑌𝐼𝐸𝐿𝐷 + 𝛽15 𝑃𝐶𝑇_𝐼𝑁𝑆𝐼𝐷𝐸
+ 𝛽16 𝐵𝑂𝐴𝑅𝐷_𝑆𝐼𝑍𝐸 + 𝛽17 𝐼𝑁𝑆𝑇𝑂𝑊𝑁 + 𝛽18 𝐶𝑂𝑁𝑆𝑈𝐿𝑇 + 𝑒̃
All variables are defined in Appendix A. We lag all dependent variables by one year.
MKT_RISK is constructed per Gong et al (2011). This variable describes the portion of firm
returns that can be explained by market returns. Since higher values of this variable mean
systematic risk has a greater effect on the firm’s stock returns, a positive coefficient for this
variable supports Hypothesis H1a.
IND_HERF measures industry concentration using the
Herfindahl Index. The maximum value of one signifies a pure monopoly while a lower value
approaching zero signifies perfect competition. A negative coefficient provides support for H1b.
SEG_HERF serves as a proxy for the ability to define a peer group that has similar expected
returns. The maximum value of one means the firm’s sales are fully concentrated in one industry
and a value approaching the minimum of zero is firm diversified into many lines of business. A
positive coefficient supports H1c.
PCT_INSIDE and BOARD_SIZE proxy for strength of
governance.5 Larger values for each conventionally are viewed as signifying weaker governance,
so a negative coefficient supports H1d. INSTOWN proxies for the level of monitoring of the board
by large shareholders, so a positive coefficient supports H1d.
5
CONSULT is a dichotomous
While this broad generalization is often accepted by researchers, Coles et al (2008) demonstrate that some firms have
characteristics that require larger board size and a less independent board.
13
variable equal to one if the firm uses a compensation consultant. A positive coefficient supports
Hypothesis 1e. All other variables serve as controls.
Panel A of Table 2 presents our results. In models (1) and (2), the dependent variable takes
the value of 1 if a firm made an RPE award to one or more NEOs in that year, and 0 otherwise (no
p-v or p-v APE). Model (2) differs from model (1) only by inclusion of a variable indicating use
of a compensation consultant.
In model (1), the coefficient for MKT_RISK supports the hypotheses (H1a) that firms are
more likely to use RPE if the firm has greater exposure to systematic risk. The negative coefficient
on IND_HERF suggests that a less competitive product market leads to a lower likelihood of RPE
usage, which is consistent with H1b and similar in direction to the results in Gong et al. (2011) in
the 2006 cross section. The estimated coefficient, however, is statistically insignificant. Our
approach differs from that in Gong et al. (2011) insofar as we measure industry concentration using
the three-digit SIC and cluster our errors at the firm level. Clustering errors reduces the t-statistic
from -3.32 to -1.90. The coefficient on SEG_HERF is inconsistent with H1c. Firms operating
across more business lines are more likely to use RPE. This result warrants further investigation
to identify, for example, the characteristics of peers specified by conglomerate firms.
Of the governance variables, only the positive coefficient on PCT_INSIDE supports the
hypotheses (H1d) that “better” governance increases the propensity to use RPE. In contrast, the
estimated coefficients on BOARD_SIZE, INSTOWN, and DUALITY are insignificant in both
specifications.
Model (2) differs from model (1) by inclusion of the consultant dummy, CONSULT, and
by the lack of data on compensation consultants prior to 2006. The estimated coefficient on
14
CONSULT is positive and highly significant, which is consistent with the hypothesis (H1e) that
the presence of compensation consultant is associated with an increased propensity to use RPE.
The empirical support for the effect of common risk and managerial ownership, however, is
diminished. In both models, RPE firms tend to be larger and have higher sales growth and dividend
yield. Though we use different models, data, explanatory variables, and controls than Gong, Li,
and Shin (2011), our results are roughly supportive of their estimates, which are based only on
2006 data.
Models (3) and (4) repeat the analysis for the subsample of firms that use p-v RPE or no
p-v RPE (meaning APE) in a given year. Because we exclude firms in years that the firm makes
no p-v award, as compared to models (1) and (2) the samples are smaller and the results
(potentially) differ. Indeed, the signs of the coefficients are similar to those in models (1) and (2),
though statistical significance in some cases is lessened.
RPE usage is persistent once adopted, so it is possible that using our panel data essentially
duplicates the same cross-section. Moreover, we have an interest in identifying the reasons for
switching from RPE to APE or the reverse. Models (5) and (6) perform logit analysis of adoption
of RPE and elimination of RPE, respectively. Exposure to common shocks is a primary factor
positively associated with adoption of RPE (model (5)) and negatively related to dropping RPE
(model (6)).
Panel B provide results for the propensity to use a stock performance metric (MEASRET
= 1, 0 otherwise), stock (versus cash or options) as the back-end instrument (STOCKPAY = 1, 0
otherwise), or both (STOCKRET = MEASRET x STOCKPAY). Higher exposure to systematic
risk reduces the likelihood that the RPE grant uses a performance metric based on stock price
15
(model (8)) and increases the probability that stock is the back-end instrument (model (7)). Higher
stock return volatility reduces both, while use of a compensation consultant increases both.
IV. RPE Contractual Details
This study provides explicit evidence of frequent and persistent usage of RPE in
compensation contracts for executives. Based on output of the Incentive Lab data project, we now
describe in detail the characteristics of observed RPE contracts.
Performance-vesting awards can consist of a single relative or absolute award. Other
awards have multiple components. In our sample, 45.8% of RPE awards consist of a single relative
component.
Of awards with multiple components, 25% of the awards have interacting
components.6 For example, one award in our sample to the CEO of Macy’s consists of an initial
hurdle of $8 billion in EBITDA. If that hurdle were to be surmounted, the CEO would receive
company shares in three components, with 50% of the award continuously contingent on EBITDA
scaled by sales, 30% contingent on ROIC, and 20% contingent on TSR relative to a peer group.
A common element in RPE design is selection of a peer group. As shown in Table 3, the
proportion of RPE awards based on selection of individual firms to comprise a peer group varies
from 62% to 76% across years. Otherwise, 16% to 30% of the time the firm uses the constituents
of an industry-specific index as the definition of the peer group, and 12% to 21% use the
constituents of a broad index, such as the S&P 500. Once again, the percentages add to more than
100% because of simultaneous usage by a firm in a grant.
6
Various types of interactions include the achievement of one award to trigger the use of another award, the
substitution of one award if the other isn’t met, and modification of the payout plan contingent on performance with
the other award.
16
An RPE award measures a signal that proxies for the executive’s actions. Panel A of Table
4 reports that 70% to 83% of RPE awards use a performance metric based on stock price, while
28% to 39% specify an accounting metric. Some awards use both, so the figures in a given year
sum to more than 100%. These proportions are very different for absolute p-v awards. Per BBCK
(2013), as of 2012 approximately 75% of conditional p-v APE grants use an accounting
performance metric, while 48% use a stock performance metric. Panel B describes the accounting
metric that is measured when the conditional p-v RPE grant is based on accounting performance.
The two largest categories in our sample are Earnings Growth (38% to 60%, depending on year)
and Return on X (35% to 71%, across years), where X could stand for Equity, Assets, or Invested
Capital, to name a few.
Panel C of Table 4 indicates that the manner in which the conditional RPE grant schedule
compares the performance metric against the peer or industry benchmark(s) comes in two main
forms. 79% to 89% of all RPE awards evaluate firm performance based on a percentile ranking
within the peer group. This mode is consistent with standard tournament theory. The other
significant mode of comparison compares firm performance to a benchmark, such as an industry
index or broader index or to the mean or median of performance of a smaller peer group. Recall
the example of Allete, Inc., which illustrates the former mode of comparison, while the example
from American Express illustrates the latter mode. In both instances, there is a formula or table
that maps a quantitative comparison to an actual payout for the award of stock, options, or cash at
the end of the performance period. We describe these examples in more detail in Section V.
Panel D provides statistics on the length in years of the period over which firm performance
is calculated and compared to peer or benchmark performance. In the latter years of our sample,
17
approximately 80% of firms using RPE have at least one award with a three year performance
period and around 25% have at least one award with a one year performance period. Between 7%
and 16% of RPE awards, depending on year, are broken down into multiple components with
different performance periods. These multiple performance periods may or may not overlap each
other and can also include provisions to roll one performance period into the next if some level of
performance is not achieved.
Long-term performance periods essentially behave the same as vesting periods for stock
and options, requiring the executive to remain with the firm to receive the award. Nonetheless,
8% to 12% of RPE grantors attach additional time-based vesting to the back-end instrument, with
the typical vesting period ranging from 21 to 30 months.
RPE awards typically have a payout table that maps the performance measurement statistic
into a payout. The Grants of Plan Based Awards typically states a target award, often in amount
of cash or number of shares, and the payout table or grant schedule converts relative performance
into a percent of target for the actual payout. The following sections provide detailed examples.
For the remainder of this section and in Table 5, we limit our discussion to the largest class of
awards, those based on percentile rank of firm performance relative to peers. In general, the grant
schedule comes in two forms – either as a single-step function or as a more complex multi-step
function. The former conveys no units of the back-end instrument up to a certain percentile rank
and jumps fully to a target number of units at that percentile. More complex, multi-step schedules
typically have an initial threshold for any units, then an incentive zone over which the number of
shares, options, or cash increases step-wise as each additional peer is passed, and then a ceiling
beyond which increased relative performance earns no more back-end units. The incentive zone
18
often contains a kink point in step size at a target level of relative performance and units. Singlestep function grant schedules account for 11.8% of our sample, and 55.0% of those awards interact
with another PV award component – serving perhaps as a trigger for another function. Multi-step
percentile grant schedules represent 88.2% of our subsample of percentile grants.
Table 5 provides descriptive statistics for various elements of the domain and range of the
grant function. For single-step function grants, the majority pay out for median performance or
above, while other awards require stronger performance. For multi-step awards, the median
payout levels for threshold, target, and maximum performance are 27%, 100%, and 200% of target,
respectively. The median percentile rank required to achieve threshold, target, and maximum
payouts are 30th percentile, 50th percentile, and 80th percentile, respectively.
V. A Framework for Characterizing and Measuring the Value of RPE Grants
V.A. The RPE Grant Schedule
For purposes of describing our methodology for characterizing RPE awards and for
measuring their value and incentive properties, suppose that there are I performance metrics, 𝑋⃑ =
(𝑋1 , 𝑋 2 , … , 𝑋 𝐼 ) and, when there is relative performance evaluation, the performance metrics are
⃑⃑ = (𝑌1 , 𝑌 2 , … , 𝑌𝐽 ). A benchmark for a given
evaluated relative to a vector of J benchmarks, 𝑌
performance metric can be single-valued, such as median performance of a group of peer firms or
an industry or market index defined in terms of the associated performance metric. A benchmark
vector can contain multiple elements for each performance metric. One common case specifies
that the number of shares or options to be granted depends on a performance ranking among a
19
group of peer firms, in which case the benchmarks would comprise the vector of performance
values, one element for each of the members of the peer group.
For concreteness, suppose there are two performance metrics (I = 2), 𝑋1 = 𝐴 and 𝑋 2 = 𝑃,
where 𝑋𝑡1 = 𝐴𝑡 is meant to represent the level of an accounting metric (e.g., EPS, earnings, ROA,
ROE, ROI, etc.) or other performance measure (such as sales, market share, FDA approval, etc.)
and 𝑋𝑡2 = 𝑃𝑡 is a metric based solely on stock price of the firm. Likewise, further suppose that
there is a single benchmark for each performance metric, given by 𝑌𝑡1 = 𝐵𝑡 for accounting
performance and 𝑌𝑡2 = 𝑄𝑡 for stock performance.7 The subscript indicates time t, for t ≥ 0, the
initial grant date (t = 0), and thereafter.
The performance and benchmark vectors have initial values at the grant date, t = 0, denoted
⃑⃑⃑⃑⃑0 = (𝑋01 , 𝑋02 , … , 𝑋0𝐼 ) and ⃑⃑⃑⃑
𝑋
𝑌0 = (𝑌01 , 𝑌02 , … , 𝑌0𝐽 ). For purposes of determining the number of
units of the back-end instrument to be conveyed to the executive, performance is evaluated over
some time horizon, the performance period, from t = 0 to t = τ.
The means by which RPE impinges on executive wealth is always through a conditional
performance-vesting provision. Let the number of units of the back-end instrument, stock, options
or even cash, that are conveyed to the executive at time τ, the end of the performance period, be
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ). In the two-by-two example, this grant
given by the grant function or grant schedule, 𝑁(𝑋
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) = 𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 )).
schedule is written 𝑁(𝑋
For example, measurement of A versus B and P versus Q can be A – B and P – Q. Obviously, more complex
specifications are accommodated in this framework. While this example and associated notation are meant to focus
on the mix of one accounting metric and one stock-price metric, more generally both A and P can be accounting
performance metrics or both can be stock-price metrics.
7
20
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) =
Grant schedules in practice vary widely in design. In a simple example, for 𝑁(𝑋
𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 )), the schedule could specify a step function, with the number of shares or
options granted equal to zero if one or both of an accounting hurdle, 𝐵𝜏 , and stock price hurdle,
𝑄𝜏 , are not reached, but some N > 0 for any (𝐴𝜏 , 𝑃𝜏 ) with 𝐴𝜏 ≥ 𝐵𝜏 and 𝑃𝜏 ≥ 𝑄𝜏 (performance
surmounts both hurdles). Some schedules specify relative hurdle rates at some threshold, target,
and ceiling, for both 𝐴𝜏 and 𝑃𝜏 , how the number of units conveyed depends on the performance
metrics, and whether and how the hurdles are defined relative to peer, industry, or market
benchmarks (𝐵𝜏 , 𝑄𝜏 ). In many instances the performance comparison is implemented using a
function of stock price or an accounting number. For example, RPE schedules often rely on a
comparison among firms of annualized total stock return (TSR).
Again, measuring performance relative to accounting and/or stock price benchmarks is a
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) represents a performance-vesting provision contingent
form of RPE. The expression 𝑁(𝑋
on performance of ⃑⃑⃑⃑⃑
𝑋𝜏 relative to benchmarks ⃑⃑⃑⃑
𝑌𝜏 .8
V.B. Value of the Back-end Instrument after the Performance Period
Define the value of the stock, options, or cash conveyed at any time t ≥ τ (at or after the
⃑⃑⃑⃑⃑𝑡 ), or 𝑉(𝐴𝑡 , 𝑃𝑡 ) in the illustrative case. Note that the award
end of the performance period) as 𝑉(𝑋
itself could be a number of shares or options that vest fully at time τ. Otherwise, shares or options
could be restricted by a subsequent time-based or p-v schedule, with the relevant performance
period beginning at the end of the first performance period.
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) =
If the grant schedule reflects absolute performance evaluation (APE), rather than RPE, ⃑⃑⃑⃑
𝑌𝜏 is absent and 𝑁(𝑋
⃑⃑⃑⃑⃑𝜏 ).
𝑁(𝑋
8
21
We are particularly interested in t = τ, the point at which the number of units of the backend instrument is known. Setting aside for the moment any question of dilution, if the back-end
⃑⃑⃑⃑⃑𝜏 ) = 𝑉(𝐴𝜏 , 𝑃𝜏 ) = 𝑃𝜏 , the
instrument is shares unrestricted by additional time vesting, then 𝑉(𝑋
stock price per share at τ. If the back-end instrument is options or stock appreciation rights
unrestricted by additional time vesting, and remaining time to maturity is positive, the BlackScholes option value adjusted for dividends may be suitable. We denote the Black-Scholes value
(or simulated value, if that approach is employed) adjusted for dividends of the single call option
as 𝑐(𝑃𝑡 , 𝐾, 𝜎𝑟 , 𝑑(Ŧ𝑡 ), 𝑇 – 𝑡, 𝑟𝑓 ), where Pt is stock price at t ≥ τ, K is exercise price (set at the initial
grant date t = 0), σr is the standard deviation of return on the stock, d(Ŧt) is the schedule of N
remaining (at time t) dividend payments as a proportion of stock price to be paid on dates Ŧt = {t1,
t2, ... ,tN} (with t1 ≥ t and tN ≤ T), remaining time to maturity is T – t, and rf is the risk free rate. In
the data, when cash is the back-end instrument, the value depends on neither Pτ nor Aτ, so
𝑉(𝐴𝜏 , 𝑃𝜏 ) = $1.
V.C. Value of the RPE Grant at the End of the Performance Period (Ex Post)
Ex post value of the conditional p-v grant, at the end of the performance period, is the
product of the number of units earned through the performance-vesting provision and the value at
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 ). In the simple two-metric case with
time t = τ per unit of the back-end instrument, 𝑁(𝑋
no dependence of the back-end instrument on 𝐴𝜏 , ex post value is 𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 ))𝑉(𝑃𝜏 ).
V.D. Two Examples: RPE Grant Function and Ex Post Award Value
V.D.1. Rank Order Tournament Example: Allete, Inc.
In our sample 88% of the RPE firm-years use a rank-order tournament. Under this schema,
the firm grants an RPE award to the executive, whereby performance is measured for the target
22
firm and a group of peers for a defined period of time. After the measurement period ends, the
target firm is pooled with the peers and they are ranked by performance. The percentile rank is
then mapped by a payout function from percentile or rank to the payout to the executive.
For example, the 2008 Proxy Statement for Allete (ALE)9 states that Donald J. Shippar,
the CEO, was granted an RPE award on February 1, 2008. The award is based on a rank-order
tournament among Allete and 16 named peer firms. Total Shareholder Return (TSR), meaning
total stock return including dividends, is the measure of performance by which the firms were to
be compared after a three-year period. Thus, 𝑋𝑡 = 𝑃𝑡 and ⃑⃑⃑⃑
𝑌𝑡 is the 16-vector of stock prices for
the members of the peer group. The TSR calculation is embedded in the grant schedule using the
functional definition of TSR, as represented by 𝑇𝑆𝑅𝑡 = 𝑅(𝑃𝑡 ) . The award has a target payout of
8,282 shares of stock. After the three-year measurement period, Allete’s percentile rank among
the peers will be determined and the payout function shown in Panel A of Figure 2 will determine
⃑⃑⃑⃑𝜏 ), for τ =
the percent of the target shares that is actually paid out to recipient, 𝑝𝑐𝑡 𝑝𝑎𝑦𝑜𝑢𝑡 (𝑋𝜏 |𝑌
3. For example, if Allete ranks 5th (73.5th percentile) for TSR from February 2008 to January 2011,
then the recipient receives 150% of the target, which is 12,423 shares. There is a severe drop-off
for performance below the 44.1st percentile, the payout step size increases at the 61.8th percentile,
and the award is capped at 200% payout of target (16,564 shares) if Allete TSR is in the top three.
Allete (http://www.allete.com/our_businesses/) offers the following description. “ALLETE (NYSE: ALE) is wellpositioned as a reliable provider of competitively-priced energy in the upper Midwest, and has a strategic investment
in the American Transmission Company. ALLETE's Minnesota Power electric utility serves 144,000 residents, 16
municipalities and some of the nation's largest industrial customers. Other businesses include BNI Coal in North
Dakota; ALLETE Clean Energy, a developer of energy projects with limited environmental impact; ALLETE
Properties, which owns 10,000 acres of real estate in northeast Florida; Superior Water, Light & Power in Superior,
Wisconsin; and ALLETE Renewable Resources, which operates and maintains wind generation facilities in North
Dakota for ALLETE's utility and nonutility companies.”
9
23
While the above description is a complete account of how the Allete RPE award works, it
is useful to depict the grant schedule in terms of three-year TSR rather than as a percentile of TSR
in the peer group. Ex ante, in 2008, one will not know the ex post (2011) distribution of peer
performance. One possibility is that peer returns will be uniformly distributed three years hence.
Suppose peer group performance realized in 2011 is distributed evenly in 5% increments from a
minimum at -40%% to a maximum of 35%. Under this assumption, the payout schedule for the
Allete CEO as a function of scaled three-year TSR is depicted in Panel B of Figure 2. Note that
in a rank-order tournament the percentage payout only changes as Allete displaces with one of its
peers, thus creating ranges of return with the same percentage payout. The ex post grant schedule
is lumpy with steps. The example in Panel B also suggests that for some realizations of returns by
Allete’s peers, it is possible for Allete TSR to be negative and for the CEO still to receive a positive
payout of shares. Of course, it is highly unlikely that the distribution of peer performance three
years from the initial grant date will be so well-behaved. Panel C of Figure 2 depicts an example
in which ex post peer returns are distributed less evenly.
Allete’s stock price on the grant date was $39.10. The market value of this payout, at τ =
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 ) = 8,282 × 𝑝𝑐𝑡 𝑝𝑎𝑦𝑜𝑢𝑡 (𝑋𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) × $39.10 × (1 + 𝑇𝑆𝑅𝜏 )𝜏 , assuming for
3, is 𝑁(𝑋
the present no dividends (or the award is dividend-protected), where the percent of target share
payout is given by the grant schedule and initial share value is multiplied by one plus three-year
⃑⃑⃑⃑𝜏 ) = 8,282 × 𝑝𝑐𝑡 𝑝𝑎𝑦𝑜𝑢𝑡 (𝑋𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) and 𝑉(𝑋𝜏 ) = $39.10 ×
scaled TSR. Restated, at τ = 3, 𝑁(𝑋𝜏 |𝑌
(1 + 𝑇𝑆𝑅𝜏 )𝜏 . If ex post returns for peers are distributed as in Panel B, then Panel D of Figure 2
depicts the ex post value of the award. In Panel B, each step is associated with more shares.
Holding shares constant on each step, until Allete TSR surmounts TSR of the adjacent peer leading
24
Allete, the value of the number of shares granted rises linearly in ex post stock price. In terms of
the ex post value of the award, each step in Panel D has positive slope, with the slope increasing
for higher steps because the number of shares granted will have been larger for higher steps.
Panels B through D are based on a specific set of assumed returns for the peers. Holding
constant peer relative performance (as in Panel B), Panel E depicts ex post award value depending
on whether the peer group performs well or not, with the ex post spread in TSR maintained across
all peer group members. Better peer group performance means that Allete TSR must be higher,
all else equal, for the CEO to receive the same ex post award value. Of course, this is only one of
an infinity of possible ex post award value functions. An infinite number of curves and surfaces,
with the location and size of steps depending on the realizations of TSR for the set of peer firms,
are possible.
V.D.2. Example of Performance Net of a Benchmark: American Express
In contrast to the rank-order tournament, about 12% of our sample compares firm
performance to a single peer group statistic, such as the weighted average return. For example,
the 2008 Proxy Statement for American Express (AMEX) states that Kenneth I. Chenault, the
CEO, was granted an RPE award on January 31, 2008. The award pays out cash (as compared to
stock in the previous example) based on adjusted three-year return, defined by the AMEX total
shareholder return net of the S&P 500 TSR. The target payout is $1,636,593. At the end of the
performance period, the CEO is paid 25%, 100%, or 350% of target for an adjusted return of -9%,
0%, or 13%, respectively, with interpolation between points. There is no payout for a benchmarkadjusted return below -9%. This grant function is depicted in Panel A of Figure 3. Panel B restates
the award in more familiar terms of award value versus absolute return for an assumed index
25
return. Finally, Panel C provides a three-dimensional representation of the award value versus
absolute return for all possible index returns.
For all three panels, because the back-end instrument is cash, the ex post value of the award
and the grant schedule are the same. If, instead, the back-end instrument were stock or options,
the flat portions of ex post value above threshold would be increasing in stock price (or
performance) and, for all parts of the schedule below the ceiling except at steps, would be convex
in stock price.
V.D.3. More Complex Grant Schedules and Back-End Instruments
The RPE awards for Allete and American Express are representative of the most typical
awards, but awards do vary along many dimensions. Of course, the functional form 𝑁(𝑋𝜏 |𝑌𝜏 )
accommodates more complex comparisons of 𝑋𝜏 versus 𝑌𝜏 and more complex grant schedules than
the piecewise linear schedules in Figures 2 and 3. Some awards use multiple performance
measures and benchmarks that interact. For example, an award can specify that both an industryadjusted accounting hurdle and a peer-group-adjusted TSR hurdle be satisfied for threshold
performance to be surmounted and the threshold number of back-end units to be conveyed to the
executive. Other multiple-metric grants use “or” conditions. Some awards mix RPE and APE
conditions. Some RPE awards are granted alongside single or multiple APE p-v awards or
alongside other RPE awards.
The framework accommodates more complex incarnations of cash, stock, and options as
back-end instruments. Aspects of a time-based vesting schedule that are relevant would be
discounting, the probability of dismissal and forfeiture of the unvested portion, and the likelihood
that the board would accelerate some of the unvested units even conditional on dismissal (e.g.,
26
without cause) or departure.
These features require estimated parameters on departure
probabilities from the company in question. For options, we can model the interaction of the
effects of early exercise on value with the above-mentioned effects on value of time-vesting
subsequent to the performance period. See Bettis, Bizjak, and Lemmon (2005) on early exercise.
In many cases, the executive receives warrants rather than call options. Standard methods allow
us to value warrants and stock grants that are dilutive. This does not seem to make a large
difference (Anderson and Core, 2013). It also is possible to approximate value for a back-end
instrument that has no or diminished voting rights. While we see no evidence of such in the data,
it is possible to imagine cash payments or stock or option grants for which the value of each unit
depends on At. For example, the back-end unit at the end of the performance period could be
another p-v grant with the performance-vesting provision contingent on both At and Pt. In addition
to setting aside the above complexities, we value the back-end instrument from the point of view
of the diversified investor. See Hall and Murphy (2002) and Ingersoll (2006) on the subjective
value perceived by a risk-averse, undiversified executive.
V.E. Grant Date (Ex Ante) Discounted Expected Value of Ex Post Realized Value
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 ), the product of the number of units
Let ρ be the discount rate applied to 𝑁(𝑋
of the back-end security conveyed times value per unit, both at the end of the performance period.
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) is not exposed to systematic risk and risk of the back-end instrument can be hedged
If 𝑁(𝑋
away, a risk-neutral pricing framework is applicable. Or if investors can fully hedge away the risk
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 ), then it is appropriate to use a risk-neutral pricing framework.
of 𝑁(𝑋
27
In general it is unlikely that a p-v RPE provision joined with the back-end instrument,
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 ), can be perfectly hedged. First, in many cases, there are no instruments and
𝑁(𝑋
strategies one might use to hedge the relevant state variables, such as accounting performance,
market share, FDA approval, or the benchmarks for such metrics. These state variables are
imperfectly correlated with stock price and any hope of an approximation hedge with stock-price
instruments is unlikely to be realized. Second, even if the p-v RPE provision is based solely on
stock performance, the ex post payoff function is often nonlinear and complex and the hedging
strategy complex and correspondingly expensive to execute.
Accordingly, we construct and implement an approach that uses drift rates predicted from
an asset pricing model (APM) and risk-adjusted discounting using that APM. Our approach will
be familiar. Alongside the risk-neutral approach, Black and Scholes (1973) allude to a basic
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 ), not just
version of our approach. The discount rate is based on exposure of 𝑁(𝑋
⃑⃑⃑⃑⃑𝜏 ), to priced risk, per the logic in standard APMs.
𝑉(𝑋
Because the applicable discount rate potentially varies across realizations of the state
⃑⃑⃑⃑⃑𝜏 , ⃑⃑⃑⃑
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 )𝑉(𝑋
⃑⃑⃑⃑⃑𝜏 )/(1 +
variables, we write 𝜌(𝑋
𝑌𝜏 ). Ex ante expected value at the grant date is 𝐸[𝑁(𝑋
⃑⃑⃑⃑⃑⃑𝜏 ,𝑌
⃑⃑⃑⃑⃑⃑𝜏 )𝜏
⃑⃑⃑⃑⃑𝜏 , ⃑⃑⃑⃑
⃑⃑⃑⃑⃑𝜏 )/𝑒 𝜌(𝑋
𝜌(𝑋
𝑌𝜏 ))𝜏 ], or in continuous time 𝐸[𝑁 (⃑⃑⃑⃑⃑⃑
𝑋𝜏 |⃑⃑⃑⃑⃑
𝑌𝜏 ) 𝑉(𝑋
], where the expectation is
taken across the joint distribution function of (𝑟⃑⃑⃑⃑,
𝑟𝑌 )~𝐹(𝜇⃗, Σ), estimated parameters (𝜇⃗, Σ), and
𝑋 ⃑⃑⃑⃑
⃑⃑⃑⃑⃑0 , ⃑⃑⃑⃑
initial values (𝑋
𝑌0 ).10
⃑⃑⃑⃑⃑𝜏 |𝑌
⃑⃑⃑⃑𝜏 ) is resolved, the grant is worth
Once the performance period is complete and uncertainty embedded in 𝑁(𝑋
𝑁𝑉(𝑃𝜏 ) and risk-neutral valuation methods can be applied.
10
28
For
illustration,
consider
the
simple
two-by-two
case
with
state
variables
((𝐴𝑡 , 𝑃𝑡 ), (𝐵𝑡 , 𝑄𝑡 )) drifting according to 𝐹(𝜇⃗, Σ), with 𝜇⃗ = (𝜇𝐴 , 𝜇𝑃 , 𝜇𝐵 , 𝜇𝑄 ) and Σ =
{𝑐𝑜𝑣(𝑟𝐶 , 𝑟𝐷 )}𝐶,𝐷=𝐴,𝑃,𝐵,𝑄 . Define 𝜀𝐶𝐷 = (𝐷⁄𝐶 )(𝜕𝐶 ⁄𝜕 𝐷) as the elasticity of C in D, where C, D =
A, B, P, Q, M, V, or N and C ≠ D. Performance metrics, A and P, and benchmarks, B and Q, are
defined as above, while M is value of the market portfolio. V and N are functions given by 𝑉(𝑃𝜏 )
and 𝑁((𝐴𝜏 , 𝑅𝜏 )|(𝐵𝜏 , 𝑄𝜏 )). Then the sensitivity of return on the p-v grant to return on the market
is

  d ( N ( A , P ) | B , Q ) V ( P ))  M P
P



dP
 N ( A , P | B , Q ) V ( P )  
 P M
(1)
where Mτ is value of the market at time t = τ and (Mτ/Pτ)(∂Pτ/∂Mτ) = βPM, which is the traditional
CAPM beta of the firm’s stock return with stock market return.
Turn now to providing an expression for the two bracketed terms of equation (1), which
together represent the full elasticity of 𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 ))𝑉(𝑃𝜏 ) in Pτ through all channels. By
all channels, we mean directly through 𝑃𝜏 in the grant schedule and value of the back-end
instrument and also by way of the statistical association between Pτ and the accounting metric, Aτ,
and the benchmarks for stock and accounting performance, Bτ, Qτ. Time subscripts are suppressed
when the meaning is clear and it is convenient. In general, the derivatives are taken at the end of
the performance period, t = τ.
Differentiating fully, the elasticity of 𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 ))𝑉(𝑃𝜏 ) in Pτ is
29
 P   d ( N V )   P    V 
 N N A N B N Q  
 N V   dP    N V   N  P   V  P  A P  B P  Q P  
 




  
This expression can be rewritten as
 P   d (N V )  



  VP   NP   NA AP   NB BP   NQ QP 
 N V   dP  
(2)
The sensitivity of the return on the p-v grant to return on the market is given by
 P   d ( N V )  M P
 N V   dP  P M  VP   NP   NA AP   NB BP   NQ QP   PM



(3)
Restated, the beta of return on 𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 ))𝑉(𝑃𝜏 ) relative to return on the market is
 NV ,M  VP   NP   NA AP   NB BP   NQ QP   PM
(4)
The elasticities 𝜀𝐴𝑃 , 𝜀𝐵𝑃 , and 𝜀𝑄𝑃 can be measured using historical data on ((𝐴, 𝑃), (𝐵, 𝑄)). 𝜀𝑁𝑃 ,
𝜀𝑁𝐴 , 𝜀𝑁𝐵 , and 𝜀𝑁𝑄 are based on the functional form of the grant schedule, 𝑁((𝐴𝜏 , 𝑃𝜏 )|(𝐵𝜏 , 𝑄𝜏 )),
and 𝜀𝑉𝑃 is based on the ex post value of the back-end instrument, 𝑉(𝑃𝜏 ). These elasticities
potentially can vary across realizations of (𝐴𝜏 , 𝑃𝜏 , 𝐵𝜏 , 𝑄𝜏 ).
For example, if the back-end security is a simple vested call option and adjusted BlackScholes
is
appropriate,
𝜀𝑉𝑃
would
be
based
on
the
derivative
of
𝑉(𝑃𝜏 ) =
𝑐(𝑃𝑡 , 𝐾, 𝜎𝑟 , 𝑑(Ŧ𝑡 ), 𝑇 – 𝑡, 𝑟𝑓 ) in 𝑃𝜏 , a derivative that varies in 𝑃𝜏 . On the other hand, 𝜀𝑉𝑃 = 1 if the
back-end instrument is stock and there are no complications, such as an additional time-vesting
restriction or dilution. Note that if there is no RPE then 𝜀𝑁𝐵 = 𝜀𝑁𝑄 = 0, and if there is no
30
performance-vesting at all then 𝜀𝑁𝑃 = 𝜀𝑁𝐴 = 0, and (4) reduces to the expression, 𝛽𝑉𝑁,𝑀 =
𝜀𝑉𝑃 𝛽𝑃𝑀 , which is equation (15) in Black and Scholes (1973).
The application of this discounting approach seems simple for the sort of grant schedule
depicted in Figure 3. The only problem arises at the threshold where the grant function has infinite
slope, though this occurs only for a subset of realizations in the state space of firm and
peer/benchmark performance that has measure zero. This problem is more apparent for percentilebased RPE grant schedules. For example, the Allete, Inc. grant schedule exposes the recipient to
systematic risk because it depends on Allete stock performance and also peer stock performance.
But, per Figure 2 (Panels A, B, C), if the ex post schedule were treated as certain, the measured
discount rate would reflect zero additional systematic risk on the flat part of each step and infinite
exposure to systematic risk for the few realizations of Allete TSR that exactly match a realization
for one of the peer firms (the small number of vertical parts of the steps). On the other hand, given
that own performance and peer performance are uncertain (or trembling) just prior to the end of
the performance period, so is the ex post location of the steps in the ex post grant function. To
accommodate this aspect of percentile grant schedules, for purposes of discounting only we
approximate exposure to systematic risk by smoothing the grant function, with smoothing to
depend on each ex post realization. For each step above threshold in each possible ex post grant
function we linearize using the corner of each step. We also smooth at the first step, threshold, by
anchoring the lower end of the smoothing line at performance of the adjacent trailing peer. If there
is no trailing peer, we create a synthetic trailing peer that trails the threshold peer by the same
amount as the adjacent peer above threshold exceed threshold performance.
31
To illustrate, for steps above threshold suppose there is a percentile grant function using
stock price of the firm and peers as the metric. For a given step in the grant schedule there are two
immediately adjacent peers, one leading in performance (designated L) and the other following
(F). Assume the follower and leader firms have final stock prices of $1.25 and $1.50 respectively.
If trading places with the follower firm would induce a payout of 40% of target, and trading places
with the leader firm would induce a payout of 50%, then we assume that the firm in question is
paid linearly between 40% and 50% of target for final prices ranging between $1.25 and $1.50.
Similarly, if the leader (follower) receives 𝑁𝐿 (𝑁𝐹 ) units for performance of 𝑃𝐿 (𝑃𝐹 ), then, under
the linearization, for stock price 𝑃 the executive receives 𝑁 = [(𝑃 − 𝑃𝐹 )/(𝑃𝐿 − 𝑃𝐹 )](𝑁𝐿 − 𝑁𝐹 ).
The linearized grant schedule captures systematic risk through a positive derivative in own
performance (𝑃) and negative derivatives in performance of each peer (𝑃𝐿 , 𝑃𝐹 ). Then for each step
and associated adjacent peers, exposure to the market return is given by equation (4) above, with
𝑁 representing the smoothed grant function, absence of an accounting metric, 𝐵 = 𝑃𝐿 , and 𝑄 =
𝑃𝐹 , which is written as  NV ,M  VP   NP   NP  P P   NP  P P   PM .
L
L
F
F
⃑⃑⃑⃑⃑𝜏 , ⃑⃑⃑⃑
The form of 𝜌(𝑋
𝑌𝜏 ) (or 𝜌(𝐴𝜏 , 𝑃𝜏 , 𝐵𝜏 , 𝑄𝜏 )) depends on the asset pricing model. The above
calculations of beta, sensitivity of the value of the grant at the end of the performance period to
return on the market, are oriented towards a CAPM or CAPM-like market model.11 We employ
the CAPM, 𝑟 = 𝑟𝑓 + 𝛽𝑁𝑉,𝑀 [𝐸(𝑟𝑀 ) − 𝑟𝑓 ] + 𝑒̃ , where 𝑒̃ is the error term. Then
 ( A , P , B , Q )  rf  VP   NP   NA AP   NB BP   NQ QP   PM [ E (rM )  rf ]
11
We can extend our approach to a Fama-French 3-factor model or Carhart 4-factor model.
32
(5)
Then, again, ex ante expected value at the grant date is
E[ N ( A , P | B , Q )V ( A , P ) / (1   ( A , P , B , Q )) | ( A0 , P0 , B0 , Q0 )]
(6)
To empirically generate the expectation, for each grant schedule in each firm we simulate 10,000
paths in the vector of state variables.
⃑⃑⃑⃑⃑𝝉 , ⃑⃑⃑⃑⃑
V.F. Evolution of the State Variables, (𝑿
𝒀𝝉 )
⃑⃑⃑⃑⃑𝑡 , ⃑⃑⃑⃑
A probabilistic model of how the state variables (𝑋
𝑌𝑡 ) (or ((𝐴𝑡 , 𝑃𝑡 ), (𝐵𝑡 , 𝑄𝑡 ))) evolve
⃑⃑⃑⃑⃑0 , ⃑⃑⃑⃑
from initial values (𝑋
𝑌0 ) (or ((𝐴0 , 𝑃0 ), (𝐵0 , 𝑄0 ))) over the performance period, t = 0 to t = τ,
⃑⃑⃑⃑⃑𝑡 , ⃑⃑⃑⃑
and beyond to any other t > τ of interest, is required. We assume that the rate of change in (𝑋
𝑌𝑡 )
has a stationary multivariate cumulative distribution, (𝑟⃑⃑⃑⃑,
𝑟𝑌 )~ F(𝜇⃗, Σ), with (I+J) x 1 vector of
𝑋 ⃑⃑⃑⃑
expected values given by 𝜇⃗ = (𝜇
⃑⃑⃑⃑⃑,
𝜇𝑌 ) and the (I+J) x (I+J) covariance matrix by Σ. Think of the
𝑋 ⃑⃑⃑⃑⃑
⃑⃑⃑⃑⃑𝑡 , ⃑⃑⃑⃑
parameters as determining the drift and volatility of (𝑋
𝑌𝑡 ) per unit time. In the simple two-bytwo case, state variables ((𝐴𝑡 , 𝑃𝑡 ), (𝐵𝑡 , 𝑄𝑡 )) drift according to F(𝜇⃗, Σ), with 𝜇⃗ = (𝜇𝐴 , 𝜇𝑃 , 𝜇𝐵 , 𝜇𝑄 )
and Σ = {𝑐𝑜𝑣(𝑟𝐶 , 𝑟𝐷 )}𝐶,𝐷=𝐴,𝑃,𝐵,𝑄 .
V.G. Estimating the Parameters
The expectation in (6) requires 𝛽𝑃𝑀 , the joint distribution function of (𝑟⃑⃑⃑⃑,
𝑟𝑌 ~ F(𝜇⃗, Σ),
𝑋 ⃑⃑⃑⃑),
initial values (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ), estimated parameters (𝜇⃗, Σ), and length of the performance period
𝜏. We assume that drift rates for most accounting metrics are normally distributed and drift rates
for stock price and other truncated performance measures, such as sales, costs, and dividends, are
⃑⃑⃑⃑⃑𝑡 , 𝑌
⃑⃑⃑⃑𝑡 ), for the granting firm
log-normally distributed. For any specific vector of state variables (𝑋
we estimate the parameters (𝜇⃗, Σ) using five years of quarterly data on (𝑟⃑⃑⃑⃑,
𝑟𝑌 over t = -5 to t = 𝑋 ⃑⃑⃑⃑)
33
1, with the last observation from the quarter just prior to the quarter containing the grant date. We
do the same for each other firm in the same Fama French 48 (FF48) industry over the same 20
quarters. Because the data are noisy and the time series is short, for the granting firm we estimate
(𝜇⃗, Σ) as the average across all firms in the same FF48 industry.12
13
For the granting firm we
estimate 𝛽𝑃𝑀 = 𝑐𝑜𝑣(𝑟𝑝 , 𝑟𝑀 )/𝑐𝑜𝑣(𝑟𝑀 , 𝑟𝑀 ) using three years of weekly data on firm stock return
(including dividends) and return on the market. We use the S&P 1500 as the market index. The
risk-free rate is the Treasury bill rate with the maturity date closest to the end of the performance
period.
VI. The Incentive Properties of RPE Awards
For simplicity, the following discussion is based primarily on the simple two-by-two
model. The approach to measuring the incentive properties of RPE grants can be extended easily
to the case of I performance metrics and J benchmarks.
12
A technical problem arises because earnings drift is not well defined for companies with either zero or negative
lagged earnings. If lagged earnings is positive, then we define drift in earnings as change in earnings divided by
lagged earnings. If lagged earnings is less than zero then we use the absolute value in the denominator. We do not
have this difficulty with sales, which also is frequently used in practice, as it is strictly positive. These assumptions
are discussed in Bens, Nagar, Skinner and Wong (2003).
13
We use the industry-level approach for the large-sample analysis in this paper. [Since this study involves large
firms, we use the Incentive Lab universe of firms (which encompasses the Execucomp universe) to compute industry
averages.] The benefit of the industry-level approach, absent large differences across companies, is additional
precision in the estimates. The cost is that this assumes that all firms in the same industry have the same process
generating the state variables. Accordingly, in analyzing awards for some individual firms, one can implement an
approach that customizes the parameter estimates to better reflect the circumstances of the specific company. Among
other things, the method can use a mix of industry and firm parameters, characteristics of prior grants (including
threshold, target, ceiling, and type of metric), and whether the firm achieved critical performance levels specified in
prior grants, so as to enhance the precision of the forecast of (𝜇⃗, Σ).
34
VI.A. Marginal Sensitivity of Grant Value to Stock and Net Stock Performance
One conventional way to calculate the pay-performance sensitivity of a stock or option
grant (delta) is to calculate the change in value of that grant arising from a 1% change in stock
price.14 Likewise, for an RPE grant of stock, options, or cash we perturb initial 𝑃0 by 1%, simulate
ex ante value (per equation (6)) based on the different initial condition (𝐴0 , (1.01)𝑃0 , 𝐵0 , 𝑄0 ), and
take the difference between the simulated values based on different initial starting points,
(𝐴0 , (1.01)𝑃0 , 𝐵0 , 𝑄0 ) versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ). This difference indicates the effect of changing the
stock price by 1% on the ex ante expected discounted value of the RPE grant, holding (𝐴0 , 𝐵0 , 𝑄0 )
constant. We call this the marginal delta in own stock performance and denote it as 𝛿𝑃 .
The intuition for RPE implies a focus on stock performance net of any benchmark(s). As
a first step, note that expected discounted value of the award depends on the benchmark 𝑄, with
the dependence likely to be negative. Perturb initial 𝑄0 by 1%, simulate ex ante value based on
the different initial condition (𝐴0 , 𝑃0 , 𝐵0 , (1.01)𝑄0 ), and take the difference between the simulated
values based on different initial starting points, (𝐴0 , 𝑃0 , 𝐵0 , (1.01)𝑄0 ) versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ). This
difference indicates the effect of changing the stock price by 1% on the ex ante expected discounted
value of the p-v grant, holding (𝐴0 , 𝑃0 , 𝐵0 ) constant. We call this the marginal delta in stock
performance benchmark and denote it as 𝛿𝑄 . In the simple two-by-two case, there is a single stock
performance benchmark, but when there are multiple benchmarks, such as for a percentile grant,
the approach applies in the same manner to the benchmarks for the group of peers together. For
example, if there are 16 peers, with initial benchmark values (𝑄01 , 𝑄02 , … , 𝑄016 ), then we generate
14
For example, see Coles, Daniel, and Naveen (2006) for usage of the semi-elasticity form of pay-performance
sensitivity (delta) in the absence of vesting provisions.
35
𝛿𝑄
based
on
the
change
in
ex
ante
expected
value
of
the
grant
for
(𝐴0 , 𝑃0 , 𝐵0 , (1.01)𝑄01 , (1.01)𝑄02 , … , (1.01)𝑄016 ) versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄01 , 𝑄02 , … , 𝑄016 ).
For the second step, note that 𝑃 and 𝑄 covary. Indeed, it is precisely this covariation that
the inclusion of the benchmark 𝑄 can be intended to remove, so that the inference problem yields
a cleaner signal and the incentive contract can be written to be more effective by focusing on
performance the executive can affect or control. The statistical relation between 𝑃 and 𝑄 is given
by 𝜀𝑄𝑃 = 𝑐𝑜𝑣(𝑄, 𝑃)/𝑐𝑜𝑣(𝑃, 𝑃). Thus, for a 1% change in 𝑃 one would on average expect an
𝜀𝑄𝑃 % change in 𝑄. Perturb initial 𝑃0 by 1% and initial 𝑄0 by 𝜀𝑄𝑃 %, simulate ex ante value based
on the different initial condition, (𝐴0 , (1.01)𝑃0 , 𝐵0 , (1 + .01𝜀𝑄𝑃 )𝑄0 ), and take the difference
between the simulated values based on the different initial starting points, (𝐴0 , (1.01)𝑃0 , 𝐵0 , (1 +
.01𝜀𝑄𝑃 )𝑄0 ) versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ). We call this difference the marginal RPE delta in stock
𝑅𝑃𝐸
performance and denote it as 𝛿𝑃𝑄
.
In this simple case, with a single stock performance benchmark, a linear approximation of
𝑅𝑃𝐸
this incentive effect is 𝛿𝑃𝑄
≅ 𝛿𝑃 + 𝜀𝑄𝑃 𝛿𝑄 . Based on the logic for RPE in contract design, in
general we expect 𝜀𝑄𝑃 > 0 and 𝛿𝑄 < 0, insofar as 𝑄 is meant to remove the variation in 𝑃 over
𝑅𝑃𝐸
which the executive has no control. Thus, we have 𝛿𝑃𝑄
< 𝛿𝑃 .
For percentile grants with multiple peers, the analogous calculation is to perturb initial 𝑃0
𝑅𝑃𝐸
by 1% and initial 𝑄0𝑘 by 𝜀𝑄𝑘𝑃 %, for each peer k = 1, …,K. Then to generate 𝛿𝑃𝑄
we simulate ex
ante value based on the different initial condition, (𝐴0 , (1.01)𝑃0 , 𝐵0 , (1 + .01𝜀𝑄1𝑃 )𝑄01 , … , (1 +
.01𝜀𝑄𝐾𝑃 )𝑄0𝐾 ) and take the difference between the simulated values based on the different initial
starting
points,
(𝐴0 , (1.01)𝑃0 , 𝐵0 , (1 + .01𝜀𝑄1𝑃 )𝑄01 , … , (1 + .01𝜀𝑄𝐾𝑃 )𝑄0𝐾 )
36
versus
(𝐴0 , 𝑃0 , 𝐵0 , 𝑄01 , 𝑄02 , … , 𝑄0𝐾 ). To the extent that the effect on value of increasing the benchmark for
𝑅𝑃𝐸
each peer individually is negative, and supposing 𝜀𝑄𝑘𝑃 > 0 for k = 1, …,K, then again 𝛿𝑃𝑄
< 𝛿𝑃 .
VI.B. Marginal Sensitivity of Grant Value to Gross and Net Accounting Performance
It is possible to extend the above approach to accounting performance or any other
performance metric. As above, one could perturb initial 𝐴0 by 1%, simulate ex ante value based
on the different initial condition ((1.01)𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ) versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ), and take the
difference between the simulated values at the different starting points. The difference indicates
the effect of changing accounting performance (or some other performance metric) by 1% on the
ex ante expected discounted value of the p-v grant, holding (𝑃0 , 𝐵0 , 𝑄0 ) constant. We call this the
marginal delta in own accounting (or other) performance, denoted as 𝛿𝐴 . Likewise, perturbing
the accounting performance benchmark by 1% gives the marginal delta in accounting benchmark,
which we denote 𝛿𝐵 . For accounting-based percentile grants with multiple peers, as for stockbased grants, marginal delta in the accounting benchmark is based on a 1% perturbation of all
benchmarks.
To construct the RPE delta in accounting performance, perturb initial 𝐴0 by 1% and initial
𝑄0 by 𝜀𝐵𝐴 %, simulate ex ante value based on the different initial condition, ((1.01)𝐴0 , 𝑃0 , (1 +
.01𝜀𝐵𝐴 )𝐵0 , 𝑄0 ), and take the difference between the simulated values based on the different initial
starting points, ((1.01)𝐴0 , 𝑃0 , (1 + .01𝜀𝐵𝐴 )𝐵0 , 𝑄0 ) versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ). We call this difference
𝑅𝑃𝐸
the marginal RPE delta in accounting (or other) performance and denote it as 𝛿𝐴𝐵
. A linear
𝑅𝑃𝐸
approximation of this incentive effect is 𝛿𝐴𝐵
≅ 𝛿𝐴 + 𝜀𝐵𝐴 𝛿𝐵 . For 𝜀𝐵𝐴 > 0 and 𝛿𝐵 < 0, we have
𝑅𝑃𝐸
𝛿𝐴𝐵
< 𝛿𝐴 . For percentile grants with multiple peers, the construction is analogous to that for
37
stock-price-based percentile grants, with the perturbation of each peer benchmark determined by
the elasticity of that benchmark in the accounting metric of the granting firm.
VI.C. Aggregate Sensitivity of RPE Grant Value to Stock Performance
Presumably stock performance and other performance metrics, such as accounting
performance, are related. For example, it can be precisely through observable improvements in
accounting performance that price discovery and formation in stock markets leads to increased
stock price. Moreover, the benchmarks can be correlated with stock performance. Empirically,
the parameters, estimated using historical data, used to construct F(𝜇⃗, Σ), represent the relation.
For each 1% change in stock price, on average there will have been some associated change in the
accounting metric, 𝜀𝐴𝑃 %, where 𝜀𝐴𝑃 is the historical elasticity of 𝐴 in 𝑃. Similarly, when the award
contains RPE, 𝜀𝐵𝑃 and 𝜀𝑄𝑃 , which are likely to be positive, represent the association between the
benchmarks and the stock price metric. Thus, the marginal RPE delta in stock price is an
incomplete measure of the sensitivity of the ex ante value of the p-v RPE grant to stock price.
Accordingly, when we perturb initial 𝑃0 by 1%, the expected associated perturbations in
accounting performance and the benchmarks are: 𝐴0 by 𝜀𝐴𝑃 %, 𝐵0 by 𝜀𝐵𝑃 %, and 𝑄0 by 𝜀𝑄𝑃 %.
Simulate ex ante value based on the initial condition ((1 + .01𝜀𝐴𝑃 )𝐴0 , (1.01)𝑃0 , (1 +
.01𝜀𝐵𝑃 )𝐵0 , (1 + .01𝜀𝑄𝑃 )𝑄0 ), and take the difference between the simulated values based on the
different initial starting points, ((1 + .01𝜀𝐴𝑃 )𝐴0 , (1.01)𝑃0 , (1 + .01𝜀𝐵𝑃 )𝐵0 , (1 + .01𝜀𝑄𝑃 )𝑄0 )
𝑅𝑃𝐸
versus (𝐴0 , 𝑃0 , 𝐵0 , 𝑄0 ), to obtain the aggregate RPE delta in stock performance, denoted 𝛿𝐴𝑔𝑔
.
𝑅𝑃𝐸
The obvious linear approximation is 𝛿𝐴𝑔𝑔
≅ 𝛿𝑃 + 𝜀𝐴𝑃 𝛿𝐴 + 𝜀𝐵𝑃 𝛿𝐵 + 𝜀𝑄𝑃 𝛿𝑄 , which is the
𝑅𝑃𝐸
𝑅𝑃𝐸
𝑅𝑃𝐸
approximately the same as 𝛿𝐴𝑔𝑔
≅ 𝛿𝑃𝑄
+ 𝜀𝐴𝑃 𝛿𝐴𝐵
when 𝜀𝐵𝑃 ≅ 𝜀𝐵𝐴 𝜀𝐴𝑃
38
For percentile grants with multiple peers, we apply the same procedures as above. For
example, consider a percentile grant based on an accounting metric and a stock-price metric, J peer
benchmarks in accounting performance, and K peer benchmarks in stock performance. To
𝑅𝑃𝐸
generate 𝛿𝐴𝑔𝑔
we take the difference in value based on ((1 + .01𝜀𝐴𝑃 )𝐴0 , (1.01)𝑃0 , (1 +
.01𝜀𝐵1 𝑃 )𝐵01 , … , (1 + .01𝜀𝐵𝐽𝑃 )𝐵0𝐽 , (1 + .01𝜀𝑄1 𝑃 )𝑄01 , … , (1 + .01𝜀𝑄𝐾𝑃 )𝑄0𝐾 )
versus
(𝐴0 , 𝑃0 , 𝐵01 , 𝐵02 , … , 𝐵0𝐽 , 𝑄01 , 𝑄02 , … , 𝑄0𝐾 ).
To our knowledge, all but the marginal delta in stock price, 𝛿𝑃 , are new constructs for
measuring incentive alignment. In implementation, we focus for now on percentile awards based
on a single stock or accounting performance metric. J and K are the number of peers. For ex post
𝑅𝑃𝐸
𝑅𝑃𝐸
value given by 𝑁(𝑃𝜏 | 𝑄1,𝜏 , … , 𝑄𝐾,𝜏 )𝑉(𝑃𝜏 ), we calculate 𝛿𝑃 , 𝛿𝑄 , and 𝛿𝐴𝑔𝑔
= 𝛿𝑃𝑄
, while noting
𝑅𝑃𝐸
that 𝛿𝐴 = 𝛿𝐵 = 𝛿𝐴𝐵
= 0. For ex post value given by 𝑁(𝐴𝜏 | 𝐵1,𝜏 , … , 𝐵𝐽,𝜏 )𝑉(𝑃𝜏 ), we calculate
𝑅𝑃𝐸
𝑅𝑃𝐸
𝑅𝑃𝐸
𝑅𝑃𝐸
𝛿𝑃 = 𝛿𝑃𝑄
, 𝛿𝐴 , 𝛿𝐵 , 𝛿𝐴𝐵
, and 𝛿𝐴𝑔𝑔
, while noting that 𝛿𝑄 = 0. Also note that 𝛿𝑃 = 𝛿𝑃𝑄
= 0 if
cash is the back end instrument for a percentile grant based on a (single) accounting metric. We
set aside for now, to be analyzed in a forthcoming draft, the more complex case of percentile grants
with multiple performance metrics and the simpler case of benchmark-adjusted awards.
VI.D. Marginal Sensitivity of RPE Grant Value to Performance and Benchmark Volatility
The sensitivity of expected value of an award to the volatility of stock performance is seen
as a measure of the incentive conveyed by the award to the executive to take risk on behalf of
shareholders (e.g., Core and Guay. 2002; Guay, 1999). One measure of vega is the change in
expected value of the award associated with a 1% proportional change in the annualized standard
deviation of stock return (see Anderson and Core, 2013, for example). In the absence of vesting
39
provisions, in general the convexity in payoff arising from options is large relative to any convexity
arising from shares (Core and Guay, 2002), so historically almost all of vega in an executive’s
portfolio arose from the accumulation of options net of dispositions. More recently, as illustrated
in Figures 2 and 3 for RPE awards and per BBCK (2010, 2013) for APE awards, there appears to
be significant local convexity in vesting provisions, though often there are other portions of the
grant schedule with significant concavity.
To measure vega incentives, the increased usage of p-v poses two problems. First, even
for p-v provisions using APE, the usage of one or more accounting performance metrics, either on
their own or in conjunction with stock performance metrics, requires an adjustment for variation
in the accounting measure(s) and covariation in the accounting measure(s) with stock return.
BBCK (2013) have addressed this problem for p-v APE awards based on accounting performance.
Second, using RPE in a p-v award introduces the question of volatility of the benchmarks and
covariation in the benchmarks with the accounting and stock performance metrics. We adopt a
modified version of the BBCK (2013) solution to covariation in accounting and stock performance
and develop a new approach to address the benchmark question. In both instances, unlike BBCK
(2013), we suppose that the correlation matrix, rather than the covariance matrix, represents the
underlying primitive relation among performance metrics and benchmarks.
Consider the two-by-two case. Recall that (𝑟𝐴 , 𝑟𝑃 , 𝑟𝐵 , 𝑟𝑄 )~F(𝜇⃗, Σ), based on estimated
parameters.
For
𝛲 ≡ {𝑐𝑜𝑟𝑟(𝑟𝐶 , 𝑟𝐷 )}𝐶,𝐷=𝐴,𝑃,𝐵,𝑄 ,
{𝑐𝑜𝑟𝑟(𝑟𝐶 , 𝑟𝐷 )√𝑐𝑜𝑣(𝑟𝐶 , 𝑟𝐶 )√𝑐𝑜𝑣(𝑟𝐷 , 𝑟𝐷 )}𝐶,𝐷=𝐴,𝑃,𝐵,𝑄 .
we
can
write
Σ=
For a given p-v RPE grant of stock or
options, we proportionally increase √𝑐𝑜𝑣(𝑟𝑃 , 𝑟𝑃 ), by 1%. Note that this means that, in addition to
40
the variance of stock return, we also perturb some off-diagonal elements of the covariance matrix.
We then simulate ex ante value based on the different initial condition based on
(1.01)√𝑐𝑜𝑣(𝑟𝑃 , 𝑟𝑃 ) and take the difference between the simulated expected values based on
different initial starting points, (1.01)√𝑐𝑜𝑣(𝑟𝑃 , 𝑟𝑃 ) versus √𝑐𝑜𝑣(𝑟𝑃 , 𝑟𝑃 ), holding all other
parameters constant). For the covariance matrix, note that this change multiples 𝑐𝑜𝑣(𝑟𝑃 , 𝑟𝑃 ) by
(1.01)2 and 𝑐𝑜𝑣(𝑟𝑃 , 𝑟𝐶 ) by (1.01) for C = Q, A, B. This difference indicates the effect of changing
the stock return volatility proportionally by 1% on the ex ante expected discounted value of the pv grant. We call this the marginal vega in own stock performance and denote it as νP.
Likewise, following BBCK (2013), we calculate the effect of a change in volatility of the
accounting (or other) performance metric. We proportionally increase √𝑐𝑜𝑣(𝑟𝐴 , 𝑟𝐴 ) by 1%. This
change multiples 𝑐𝑜𝑣(𝑟𝐴 , 𝑟𝐴 ) by (1.01)2 and 𝑐𝑜𝑣(𝑟𝐴 , 𝑟𝐶 ) by (1.01) for C = P, Q, B. The difference
between the simulated expected values based on different
initial
starting points
((1.01)√𝑐𝑜𝑣(𝑟𝐴 , 𝑟𝐴 ) versus √𝑐𝑜𝑣(𝑟𝐴 , 𝑟𝐴 ), holding all other parameters constant, indicates the
effect of changing the volatility of drift in the accounting metric proportionally by 1% on the ex
ante expected discounted value of the p-v grant. We call this the marginal vega in own accounting
performance and denote it as νA.
In similar manner, to calculate the effects of an increase in riskiness of the performance
benchmarks, we proportionally increase the standard deviation of the accounting or stock
performance benchmarks. If there are multiple peers in a percentile grant, then we increase by 1%
either √𝑐𝑜𝑣(𝑟𝐵𝑗 , 𝑟𝐵𝑗 ), for all j = 1, …,J, or √𝑐𝑜𝑣(𝑟𝑄𝑘 , 𝑟𝑄𝑘 ), for all k = 1,…,K. This scales up the
corresponding diagonal and cross elements of the covariance matrix, some by 1.01 and others by
41
(1.01)2. We then compare the value of the RPE grant based on the different starting conditions.
We denote the marginal vega in the accounting performance benchmark(s) as 𝜈𝐵 and the marginal
vega in the stock performance benchmark(s) as 𝜈𝑄 .
If convexities in the grant schedule and back-end instrument are sizable relative to
concavities in the grant schedule (e.g., at threshold or ceiling), then 𝜈𝐴 , 𝜈𝑃 , 𝜈𝐵 , and 𝜈𝑄 are likely to
be positive. If concavities dominate, then these measures can be negative.
One caveat is required. Anderson and Core (2013) assert, contrary to conventional wisdom
(Core and Guay, 2002), that managerial holdings of debt and levered equity also provide
significant vega. If this analysis survives further inspection, then our model can be adjusted to
include these sources of vega.
VI.E. Aggregated Sensitivity of RPE Grant Value to Performance and Benchmark Volatility
To aggregate all sources of volatility and, we apply the analogous procedure to all elements
of the covariance matrix. That is, we scale up all elements of the covariance matrix per (1.01)2 Σ,
which is the same as multiplying every √𝑐𝑜𝑣(𝑟𝐶 , 𝑟𝐷 ), C, D = A, P, B, Q, by 1.01. This procedure
both acknowledges the covariation of the accounting and stock performance metrics and
benchmarks and also maintains the elements in the covariance matrix in the same proportions. We
then simulate ex ante grant value based (1.01)2 Σ versus Σ and take the difference. We call this
aggregate RPE vega and denote it as 𝜈Σ .
While 𝜈𝑃 is well-known, to our knowledge the marginal vega in accounting (or other)
metric, 𝜈𝐴 , marginal vegas in performance benchmarks, 𝜈𝐵 and 𝜈𝑄 , and aggregate 𝜈Σ are new
constructs for measuring executive incentives to take risk. Again, in implementation we focus for
42
now on percentile awards based on a single stock or accounting performance metric. For ex post
value given by 𝑁(𝑃𝜏 | 𝑄𝜏1 , … , 𝑄𝜏𝐾 )𝑉(𝑃𝜏 ), we calculate 𝜈𝑃 , 𝜈𝑄 , and 𝜈Σ , while noting that 𝜈𝐴 = 𝜈𝐵 =
0. For ex post value given by 𝑁(𝐴𝜏 | 𝐵𝜏1 , … , 𝐵𝜏𝐽 )𝑉(𝑃𝜏 ), we calculate 𝜈𝑃 , 𝜈𝐴 , 𝜈𝐵 , and 𝜈Σ , while
noting that 𝜈𝑄 = 0. Also note that 𝜈𝑃 = 0 if cash is the back end instrument for a percentile grant
based on a (single) accounting metric. Again, we set aside for now the more complex case of
percentile grants with multiple performance metrics and the simpler case of benchmark-adjusted
awards.
VII. Outcomes, Value, and Incentives for Percentile P-V RPE Grants to Executives
In this section we apply the methods developed in the prior two sections to characterize the
outcomes, value, and incentive properties of RPE awards. For now we focus on the largest part of
the sample, percentile awards of stock and/or cash based on accounting or stock performance. For
simplicity, in this draft we restrict the analysis to awards based on a single performance metric and
a single measurement period.
To derive payouts and estimate grant date value, delta, and vega of RPE awards, we
simulate stock price (and accounting) drift over the specified performance period for the granting
firm and its stated RPE peer group. Motion is based on a vector of drift rates and a covariance
matrix for drift rates.15 For any grant, we simulate 10,000 paths for the state (performance)
15
Some additional details follow. We determine the drift rates using the CAPM model. We estimate firm-specific
beta for all firms in the CRSP universe by regressing weekly returns in excess of the 10-year government bond against
weekly returns of the CRSP value-weighted market portfolio in excess of the same risk-free rate. The estimation
period is a three year window and is repeated at the end of the every calendar year available from 1973 to 2012. To
utilize the most stable value, we take the median beta for each firm as the firm beta. We winsorize the CRSP universe
of betas at the 5th and 95th percentiles. Each firm is classified by two-digit SIC and size quintile as of mid-date of
our sample. If data are not available on that date, we take the closest available date. We then assume every firm in
43
variables. For each simulation, we find the final percentile rank of the granting firm, apply the
payout multiplier as defined in the proxy, and determine the value of the award at the end of the
performance period (𝜏).16 For cash awards the value of the award at 𝑡 = 𝜏 is the product of the
target amount and the multiplier. For stock awards it is the product of the target number of shares,
the multiplier, and the ending stock price as determined by each individual simulation. For some
comparisons it is useful to equalize all initial stock prices to a value of $1 at the beginning of the
performance period.
VII.A. Distribution of Grant Schedule Performance Rank and Payout Rate at Threshold,
Target, and Ceiling
We first examine the magnitude of payout (as a percentage of target payout) at threshold,
target, and ceiling. One possibility is that these milestones are “cream-puff” hurdles and payout
at any performance milestone is a high proportion of target. An alternative is that the milestones
provide meaningful objectives. We consider single-step or “cliff” schedules on their own because
in essence threshold and ceiling (and target) are all located at the same step. Multi-step percentile
grant schedules all have a different threshold and ceiling.
each industry/size group share the same median value for that group. If the value is missing for any firm we repeat
the process based on industry only. The CAPM estimation is completed by using the contemporaneous 10-year
government bond rate and a market premium of 4.1%. To estimate the volatility of each firm, for each industry/size
group we calculate the average 5-year annualized standard deviation of monthly returns for each firm in the CRSP
database. The minimum number of observations is 36 months per firm and five firms per industry/size group. The
estimation window spans the 5-year period ending the month before the awards grant date. As with the drift rate, we
match the estimated volatility to each firm in the simulation by industry and size. If the value is missing, we repeat
the process based on industry only. To estimate the correlation matrix for the firms in the simulation, we rely again
on historical returns. For each possible combination of firms in an RPE simulation, we develop a list of firms for each
of the two firms. The lists consist of all CRSP firms in the same industry/size group as the simulation firm. We then
find the correlation of returns among all combinations of firms between the two lists, discarding any observation with
less than 36 observations. When five or more correlations are present, the average correlation among the remaining
observations is the estimated correlation between the two firms. The correlation of any firm to itself is set to one. If
the value is missing we repeat the process based on industry only.
16
The payout percentages are normalized so that the average payout percentage, equally weighted across all percentile
ranks, is 100%. This facilitates comparability.
44
Table 5 reports the distribution of payout as a proportion of target across percentile grant
schedules. For the median multi-step percentile RPE grant schedule, threshold payout is 27% of
target shares or cash and ceiling payout is 200% of target. For the median multi-step percentile
RPE grant, the percentile performance required to earn threshold, target (100% of target), and the
maximum are 30th percentile, 50th percentile, and 90th percentile, respectively. Less onerous grant
schedules, such as the 10th percentile among schedules) hit the maximum (75th percentile
performance) and threshold (20th percentile performance) payouts at lower performance
percentiles.
Table 6 tabulates the distribution across the sample of single-step and multi-step percentile
grant schedules of the simulated likelihood of achieving threshold, target, and ceiling performance.
For each grant, based on 10,000 simulated paths for the state variables based on historical
parameters, we calculate the percentage of those paths for which the realization of performance
implied payout at threshold or better, target or better, and ceiling. By way of illustration, among
multi-step saw-blade RPE grant schedules that pay shares as the back-end instrument the median
proportion of the 10,000 simulated paths for which such grants cleared threshold is 0.73. The
median (across such grant schedules) likelihood time that ceiling (target) payout is attained is 0.12
(0.51).
VII.B. Simulated Ex Post Value of Percentile RPE Awards of Stock and Cash
Table 7 describes the distribution of ex-post payout for the sample of percentile RPE
awards of cash and stock by whether the p-v RPE award is contingent on a (single) stock price or
accounting metric. Consider awards based on stock price. For cash awards, the median RPE
award has an average payout of $1.01 per $1.00 of target value. For stock awards the multiplier
45
is the fraction of target shares that are granted to the award recipient ex-post. Similar to cash
awards, on average the median firm receives 100.8% of the target, but the median normalized stock
price after the measurement period has increased from $1.00 to $1.23. The average payout for the
median firm is $1.62 per $1.00 of grant target value. The reason this exceeds the product of the
average target payout rate and average ex post value of the back-end instrument (stock) is that
often there is significant convexity in the product of a grant schedule that depends on stock price
and the stock price.
This effect does not appear for grant schedules dependent on accounting performance. For
the median across simulations of percentile p-v RPE grants based on accounting performance that
pays shares, the average simulated payout is 105.9% of target, ex post average stock price is $1.25
per dollar of initial stock price, and average payout per dollar of initial stock price is $1.31. Though
such grant schedules often have significant convexity, at least locally, induced convexity is small
because accounting and stock performance are not highly correlated. Of course, if cash is the
back-end instrument there is no convexity induced beyond what is embedded in the grant schedule
as a function of performance.
VII.C. Ex Ante Value of Percentile RPE Awards of Stock and Cash versus Disclosed FMV
For percentile RPE awards of stock and cash, we now report ex ante value for the instances
in which we have a full characterization of the ex post grant schedule and compare that estimate
of ex ante economic award fair market value to the FMV disclosed by the company in the DEF
14A. Table 8 presents the results.17
17
We lose some observations because of incomplete reporting. Prior to the enhanced reporting requirements
implemented in 2006 reporting on FMV and the target number of back-end units was often incomplete. In the latter
case, for example, this means that calculations per $1 of target value are possible but aggregate value can’t be
46
Consider percentile RPE awards of shares based on a single stock price performance
metric. The present value at the grant date of the median stock award is $1.17 per $1 of initial
stock value. Unnormalized, the ex ante value of the median percentile RPE grant is $1,125,378.
The median difference between ex ante value and fair market value reported by the company is a
modest $70,948. But for awards with value below the median, reported FMV exceeds the grant
date present value by much more, such as by about $1.2 million at the 10th percentile in grant date
present value. In contrast, RPE stock awards with higher grant date present value exceed reported
FMV by significant amounts, such as by more than $400,000 at the 90th percentile in grant date
present value. There is a significant disconnect in the economic value of the awards versus FMV
reported by companies. This disconnect extends all four subsets of awards depicted in Table 8.
One possible reason is that for awards contingent on stock performance firms are required
to report an FMV using standard, risk-neutral simulation methods. We make the same calculation
for purposes of comparison. The median difference of grant date value versus risk-neutral value
is -$0.14, which is a significant difference per dollar of initial stock price. Our valuation
framework delivers estimates of economic value that differ substantially from value estimated
using standard risk-neutral methods.
While these differences are largest for stock grants
contingent on stock performance, they are significant as well for grants of cash and grants
contingent on accounting performance.
To isolate the effect of RPE, we calculate the average number of back-end units, as
determined by the simulation, multiplied by the present value of the back-end award. The present
calculated. Attrition due to missing disclosed FMV is even worse for grants based on accounting performance and
grants of cash, because firms likely are not required to report figures for these classes of grants.
47
value of the back-end instrument is the grant date stock price for stock awards and $1 discounted
by the risk-free rate over the performance period for cash awards. Table 8 indicates that, for stock
awards, RPE adds value to the grant, while the reverse is true for cash awards.
VII.D. Incentive Properties of Percentile RPE Awards of Stock and Cash
Tables 9 and 10 report, for single-metric percentile RPE awards of stock and cash, our
results on the incentives of executives to increase shareholder value and incentives to take risk.
Table 9 confirms that the RPE delta in stock performance is less than the delta in own stock
performance. The reason is that stock performance is measured in comparison to peer stock
performance, higher peer stock performance is negatively related to the number of back-end units
of stock or cash (and ex post value) conveyed to the executive (𝛿𝑄 < 0), and own-firm and peerfirm stock performance are positively correlated (𝜀𝑄𝑃 > 0). Of course, the benefit of this effect is
to allow the firm to use higher-powered contracts with larger 𝛿𝑃 than would otherwise be optimal.
RPE strips out variation in performance over which the executive has no control. Note that this
effect is much smaller for stock and cash awards based on a single accounting performance
measure.
The reason is that the correlation between own-firm and peer-firm accounting
performance tends to be quite small (𝜀𝐵𝐴 ≅ 0). Accounting RPE does little to remove common
shocks.
For all four classes of awards, there is large variation across RPE grants in delta incentives.
For example, for a p-v RPE grant of stock contingent on stock performance, the aggregate RPE
incentive to increase shareholder value varies from $3,449 at the 10th percentile to $71,773 at the
90th percentile, approximately a factor of 20. The other three categories of awards in Table 9
reflect large differences of the same order of magnitude for the 90th versus 10th percentiles.
48
The literature provides very little opportunity to assess the economic importance of RPE
award incentives. One reason is that most prior empirical studies measure delta and vega without
including the effects of any p-v provision that might be employed (e.g., Jensen and Murphy, 1990,
and Coles, Daniel, and Naveen, 2006). One exception is BBCK (2013), which measures marginal
and aggregate delta and vega incentives for p-v absolute performance evaluation grants. For stock
grants based on a single stock performance metric, median aggregate RPE delta calculated herein
($19,947) exceeds slightly the median APE delta ($16,335, per BBCK, 2013, Table 6). For stock
grants contingent on accounting performance only, the median aggregate RPE delta ($7,223) is
more than twice that of the median APE award ($3,268, per BBCK, 2013, Table 6). RPE grants
convey to executives as much or more incentive to increase shareholder wealth, through the direct
stock price channel, indirectly through accounting performance of the firm, and indirectly through
competing with peers to affect peer performance, than APE awards.
In terms of risk-taking incentives, it is not clear as to whether increased variability should
increase or decrease the value of a p-v RPE grant. Grant schedules and ex post value, as functions
of the state variables, meaning the performance metrics and the associated benchmarks, tend to
contain both concavities and convexities. Table 10 indicates that RPE grants tend to increase the
appetite of executives for volatile firm and peer returns. Particularly for RPE grants of stock, for
only a small proportion of awards is aggregate RPE vega negative and, when it is, the vega is close
to zero. Otherwise, 𝜈Σ tends to be positive and large. Moreover, for awards of stock contingent
on stock performance, the median RPE award conveys 𝜈Σ = $5,081, as compared to the median
aggregate vega from an APE grant of $891 (BBCK, 2013, Table 7). For stock grants based on a
single accounting metric, median aggregate vegas are almost the same ($429 for RPE versus $417
49
for APE (BBCK, 2013)). Also note that aggregate vega tends to be discernibly larger than the
marginal vega in stock price performance. This comparison reinforces the notion that including
RPE is likely to increase the appetite of executives for risk. Note that even RPE awards of cash
contingent on stock performance convey positive aggregate vega. The median is $498. In contrast,
median vega for cash awards contingent on accounting performance appears to be negligible.
In terms of executive incentives, however, it is important to focus on what executives can
control. In this respect, because executives are unlikely to be able to affect the risk characteristics
of peer performance, perhaps the most relevant incentive measures are the marginal vegas in stock
and accounting performance. From BBCK (2013, Table 7), for APE awards of stock based on a
stock performance metric, median stock performance vega is $891, as compared to the median of
$3,808 in Table 10. For stock awards based on accounting performance, median APE marginal
accounting vega is $211, as compared to the RPE median of $2,305, while APE aggregate vega in
stock performance is $417 versus $971 for RPE awards. Based on median grants, it appears that
percentile RPE grants of stock based on either accounting or stock performance, relative to
analogous APE awards, convey significant marginal incentives to executives to take risk. This
conclusion, however, is tentative, insofar as a significant proportion of RPE grants have negative
marginal accounting and stock performance vegas.
VIII. Conclusion
The intuition for the use of RPE contracts is compelling. Nonetheless, empirical tests
rarely detect usage of RPE in contract design.
Likely reasons include various forms of
misspecification. Specification problems likely include: assuming that all firms use RPE when
50
some do not; incorrect performance metric(s); incorrect benchmark(s); incorrect peer groups or
industry; and usage of an incorrect functional form. In this context, our data indicate persistent,
common usage of RPE in executive compensation contracts in large U.S. companies. Consistent
with the paucity of prior evidence supporting the use of RPE, the level of detail in our data
demonstrates that implicit tests for RPE suffer from all of the above-mentioned forms of
misspecification.
We examine a full spectrum of issues pertaining to the use of RPE in compensation contract
design. In particular, we address: the frequency and persistence of RPE usage by firms; the
functional form of RPE grant schedules in firm and peer/benchmark performance; the performance
metrics and benchmarks employed; who receives RPE awards; the economic determinants of RPE
usage; the significance in value of RPE awards; and the incentive properties, for value creation
and risk-taking, of RPE awards. These last two contributions require that we develop and
implement new models for valuation and new measures of executive incentives.
In short, RPE awards tend to be used more often when the product market is more
competitive and when it is possible to remove common shocks by using RPE. In terms of the form
of the grant schedule, the milestones in RPE grants, including thresholds and ceilings based on
percentile or relative stock or accounting performance, represent significant hurdles that are
achievable by executives with at best modest likelihood. Using our valuation approach, our
simulations indicate that in general the grant date value of an RPE grant differs significantly from
the fair market value of the grant reported by the firm in public disclosures. The accuracy and
utility of reported FMV, as an indicator of the economic value of p-v RPE awards of stock, cash,
and options to executives, appear to be low. Many RPE awards convey significant incentives to
51
executives to increase shareholder value and at least some incentives to increase the volatility of
firm stock and accounting returns. Some of these incentives appear to be significant compared to
p-v APE awards with otherwise-similar attributes.
52
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55
Appendix A: Variable Definitions
Definitions of RPE Usage (all variables dichotomous at the firm-year level)
ADOPT
This variable equals one the first year a firm grants RPE to any individual.
We exclude all occurrences where the first year is before 2000 to reduce the
likelihood of incorrectly identifying a repeat RPE observation as the initial
observation. The value is set to zero for all years for firms with no RPE
observations or for observations at least three years before initial adoption.
For each firm we keep only one randomly selected firm-year where ADOPT
equals zero.
DROP
This variable equals one if the firm granted RPE to any individual the prior
year and granted no RPE for the current year. The value is set to zero if the
firm granted RPE in both the prior and the current year.
RPE
This variable equals one if the firm grants RPE to any individual and zero
otherwise.
PV-RPE
Equals one if the firm grants RPE to any individual and zero if the uses a p-v
grant to any individual but uses APE and no RPE.
MEASRET
For an RPE contract, the variable equals 1 if the contract relies on one or
more performance metrics based on stock price, equals 0 otherwise.
STOCKPAY
For an RPE contract, equals 1 if the back-end instrument uses only stock as
the back-end instrument, equals 0 otherwise.
STOCKRET
The product of MEASRET and STOCKPAY.
Other Explanatory Variables
BOARD_SIZE
The number of members on the board of directors
CF_VOL
The standard deviation of the quarterly operating cash flows divided by sales
for the previous five years
CONSULT
Dichotomous variable equal to one if the firm used a compensation
consultant and equal to zero otherwise (for the limited years of data
available).
DIV_YIELD
Dividends paid over the fiscal year divided by the market value of equity at
the end of the fiscal year
56
IND_HERF
The sum of the squared values of firm sales for the fiscal year divided by
total industry sales, where the industry is defined by three-digit SIC code
INDADJ_RET
Stock return of the firm for the fiscal year less the median industry stock
return for the same time period, where the industry is defined by two-digit
SIC code
INDADJ_RO
A
Firm ROA for the fiscal year less the median ROA for the industry, where
ROA is operating income divided by assets and industry is defined by twodigit SIC code
INSTOWN
The aggregate percentage ownership of all shareholders with 5% or more
ownership average over the fiscal year
INV
The sum of R&D, capital expenditures, and advertising for the fiscal year
divided by total assets
LN_ASSETS
The natural log of total assets
M/B
Market value of equity divided by book value of equity
MKT_RISK
The R2 from regressing monthly stock returns for the firm against monthly
stock returns for the value-weighted market returns for the CRSP universe
OPTGRANT
Options granted during the fiscal year divided by total shares outstanding as
of the end of the fiscal year
OPTOUT
Options outstanding at the end of the fiscal year divided by total shares
outstanding as of the end of the fiscal year
OPTPRICE
The value of an option grant at the end of the fiscal year divided by the stock
price at the end of the fiscal year
PCT_INSIDE
Number of board of director members who are firm employees divided by
the total number of members
RET
Total stock return for the fiscal year
RET_VOL
Standard deviation of daily stock returns for the firm for the fiscal year
ROA
Operating income divided by total assets
SALES_GR
The percentage growth in sales for the fiscal over the prior fiscal year
57
SEG_HERF
The sum of the squared values of sales per segment divided by total firm
sales
58
Time Trend in Incentive Pay
Firm-Year Usage for NEOs
1
0.8
0.6
0.4
0.2
0
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Time Vest Options
Time Vest Restricted Stock
All P-V Awards
RPE Awards
Figure 1: Yearly Usage Rates for Large US Firms of Time-vesting,
Performance-vesting (P-V), and P-V RPE Grants of Stock, Options,
and Cash to Executives
59
Figure 2. Example of RPE Award - Allete, Inc.
This figure depicts possible payouts for a stock award based on an RPE performance vesting provision.
The performance measure is three-year annualized total stock return (TSR). The number of shares granted,
defined as a proportion of a target number, depends on the relative percentile rank of Allete TSR as
compared to a group of 16 peer firms. The target number of Allete shares is 8, 282. The grant was made
to the CEO of Allete, Donald J. Shippar, on February 1, 2008.
Panel A: Payout as a Function of Relative Percentile Rank
Payout
Rank
Percentile
11 - 17
<44.12
0%
10
44.12
50%
7
61.76
100%
1-3
≥85.29
200%
Percent Payout of Target
250%
Target
Payout
200%
150%
100%
50%
0%
0.00
20.00
40.00
60.00
Percentile Rank
80.00
100.00
Panel B: Payout as a Function of Return Assuming an Even Ex Post Distribution of Peer Returns
Percent Payout of Target
250%
200%
150%
100%
50%
0%
-50%
-40%
-30%
-20% -10%
0%
10%
Measurement Period Return
60
20%
30%
40%
Panel C: Payout as a Function of Return Based on a Less Even Ex Post Distribution of Peer
Returns
Percent Payout of Target
250%
200%
150%
100%
50%
0%
-50%
-40%
-30%
-20% -10%
0%
10%
Measurement Period Return
20%
30%
40%
Panel D: Ex Post Market Value of Payout (Based on an Even Ex Post Distribution of Peer
Returns)
Ex-Post Market Value of
Payout ($)
1,000,000
800,000
600,000
400,000
200,000
0
-50%
-30%
-10%
10%
Measurement Period Return
61
30%
Panel E: Market Value of Payout for Various Returns of Peers
(Based on an Even but Movable Ex Post Distribution of Peer Returns)
Ex-Post Value
of Payout ($)
Median Peer
Return
Allete
Measurement
Period Return
62
Figure 3. Example of Benchmark-Adjusted-Return RPE Award – American
Express
This figure depicts the possible payouts for the RPE award of cash granted to the CEO of American Express on January
31, 2008.
Panel A: Payout as a Function of Benchmark-Adjusted Return
Payout
Target
Payout
< -9%
0%
-9%
25%
0%
100%
>= 13%
350%
Percent Payout of Target
400%
TSR –
RetS&P500
350%
300%
250%
200%
150%
100%
50%
0%
-25% -20% -15% -10% -5% 0%
5% 10% 15%
Measurement Period Return – RetS&P500
20%
25%
Panel B: Market Value of Payout Assuming 12% Return for S&P 500
Ex-Post Market Value of Payout ($)
$7,000,000
$6,000,000
$5,000,000
$4,000,000
$3,000,000
$2,000,000
$1,000,000
$0
-10%
-5%
0%
5%
10%
15%
20%
Measurement Period Return
63
25%
30%
35%
Panel C: Market Value of Payout as a Function of Index Return
Ex-Post Value
of Payout ($)
S&P 500 Wtd
Avg Return
AMEX
Measurement
Period Return
64
Table 1: RPE Usage Statistics
The following tables provide descriptive statistics of RPE usage in our sample. Panel A reports the portion
of firms using at least some options, stock, and performance-vested awards. In addition Panel A provides
the fraction of total compensation that RPE represents for RPE-granting firms. To determine the portion
of total compensation, RPE ex-ante value is the reported Fair Market Value or the value of the target at the
time of grant. Panel B reports the back-end instrument of at least some of the RPE awards for each firmyear when reported. Panel C describes the depth of RPE awards among the named executive officers and
directors. Year represents the calendar year of the end of the fiscal year. Note that for all tables it is possible
for a firm to have multiple types of compensation and even multiple RPE awards with varying
characteristics. Thus rows do not necessarily add up to 100%. Appendix A provides all variable definitions.
Panel A: Usage of Plan-based Awards
All P-V Awards
LongAnnual
term
Incentive
Incentive
Plan
Plan
22.8%
23.3%
RPE P-V Award
LongAnnual
term
Incentive
Incentive
Plan
Plan
4.5%
9.9%
N
(RPE
Details
Reported)
62
RPE
as Pct
of Tot
Comp
44.1%
7.7%
63
33.4%
4.3%
8.0%
52
33.6%
3.7%
7.8%
58
36.5%
20.1%
4.0%
8.9%
57
30.5%
27.3%
23.4%
3.7%
10.4%
63
45.7%
27.6%
28.8%
3.7%
12.9%
71
34.3%
42.3%
26.3%
33.8%
3.9%
14.6%
107
37.3%
51.8%
61.1%
46.5%
4.8%
17.1%
220
31.9%
70.5%
63.8%
73.2%
53.3%
5.7%
18.9%
256
31.6%
1,253
70.3%
63.8%
75.9%
55.9%
5.4%
20.2%
266
31.7%
1,232
67.1%
65.9%
75.1%
55.8%
6.1%
21.5%
284
32.8%
2010
1,210
65.1%
68.3%
77.8%
60.3%
6.3%
25.2%
320
33.6%
2011
1,182
63.2%
69.1%
77.0%
66.6%
6.4%
28.2%
349
32.1%
2012
1,149
56.7%
64.8%
76.8%
69.9%
6.2%
34.0%
386
Year
N
T-V
Options
T-V
Restricted
Stock
1998
1,134
84.0%
18.1%
1999
1,417
84.6%
17.9%
22.3%
19.8%
3.5%
2000
1,406
84.3%
21.2%
24.6%
19.4%
2001
1,393
86.5%
22.0%
23.0%
19.8%
2002
1,390
84.5%
26.1%
25.8%
2003
1,374
81.4%
29.9%
2004
1,368
79.2%
38.0%
2005
1,348
73.2%
2006
1,306
71.1%
2007
1,273
2008
2009
31.8%
(Continued)
65
Table 1-Continued
Panel B: Back-end Instrument for RPE Awards
Year
Stock
Options
Cash
1998
52.8%
4.2%
53.5%
1999
48.6%
2.9%
56.4%
2000
50.3%
2.0%
58.3%
2001
47.3%
0.0%
60.3%
2002
52.8%
0.0%
55.8%
2003
61.3%
1.7%
49.7%
2004
63.1%
2.0%
48.3%
2005
64.8%
0.9%
43.2%
2006
68.7%
3.5%
42.1%
2007
69.9%
2.9%
43.7%
2008
73.9%
2.1%
39.1%
2009
73.4%
3.6%
39.3%
2010
76.1%
2.0%
34.6%
2011
79.1%
1.6%
30.3%
2012
82.4%
1.9%
27.5%
Panel C: Individuals Receiving RPE
95.1%
Directors
Granted
RPE
7.7%
Avg Number of
NEOs Granted
RPE
4.5
1999
95.7%
5.7%
4.6
2000
94.7%
7.9%
4.5
2001
96.6%
10.3%
4.6
2002
94.5%
10.4%
4.6
2003
94.2%
7.5%
4.6
2004
93.1%
7.9%
4.6
2005
94.3%
9.3%
4.5
2006
91.5%
6.2%
4.6
2007
92.8%
6.1%
4.5
2008
91.2%
6.3%
4.5
2009
92.5%
5.8%
4.5
2010
93.1%
6.9%
4.6
2011
95.4%
9.1%
4.6
2012
95.1%
6.4%
4.6
Year
CEOs
Granted RPE
1998
(Continued)
66
Table 2: Determinants of RPE Usage
Panel A provides maximum likelihood estimates from a logistic regression for various factors associated
with the propensity to use, adopt, or discontinue RPE. Panel B does the same for the propensity to pay
stock (versus cash) as the back-end instrument (STOCKPAY), the propensity to use stock (versus
accounting) performance in the grant schedule (STOCKRET), and the length of the measurement period
(MEASRET). All variable definitions are provided in Appendix A. All continuous variables are
Winsorized at the 2nd and 98th percentiles. The standard errors are calculated after adjusting for firm-level
clustering in all models with the exception of model three (firms do not have repeating observations). We
report absolute values of Z-statistics in parentheses. Significance is denoted by ***, **, and * at less than
1%, 5%, and 10% levels, two-tailed tests, respectively. The coefficient for the constant is not shown.
Panel A: Logit Estimates for RPE Usage
(1)
RPE/no RPE
-0.607**
(-2.42)
(2)
RPE/no RPE
-0.710**
(-2.16)
(3)
RPE/APE
-0.529**
(-2.07)
(4)
RPE/APE
-0.630*
(-1.88)
(5)
ADOPT
-0.592
(-1.64)
(6)
DROP
-0.295
(-0.72)
IND_HERF
-1.041*
(-1.90)
-1.270*
(-1.83)
-1.006*
(-1.85)
-1.050
(-1.44)
-1.076
(-1.56)
-0.181
(-0.25)
MKT_RISK
0.959***
(2.92)
0.885
(1.46)
-0.0714
(-0.21)
0.740
(1.18)
2.537***
(4.06)
-1.380**
(-2.43)
LN_ASSETS
0.329***
(5.35)
0.297***
(3.49)
0.337***
(5.24)
0.379***
(4.20)
0.130
(1.38)
-0.135
(-1.38)
M/B
-0.0823***
(-2.81)
-0.0158
(-0.38)
-0.0790***
(-2.64)
-0.0396
(-0.83)
-0.124***
(-2.59)
0.0409
(1.09)
ROA
2.530**
(2.21)
1.449
(0.99)
1.601
(1.40)
1.616
(1.10)
3.045
(1.60)
-0.514
(-0.30)
INDADJ_ROA
-1.583*
(-1.77)
-0.671
(-0.64)
-1.380
(-1.59)
-0.324
(-0.30)
-0.926
(-0.74)
1.199
(1.03)
0.111
(1.08)
0.408**
(2.18)
0.162
(1.44)
0.545***
(2.70)
0.254
(1.02)
-0.185
(-0.78)
-0.0523
(-0.46)
-0.198
(-0.95)
-0.0610
(-0.50)
-0.325
(-1.44)
-0.510*
(-1.88)
-0.293
(-1.19)
-0.874***
(-3.17)
-0.131
(-0.30)
-0.173
(-0.60)
0.168
(0.37)
-1.159*
(-1.91)
0.582
(1.14)
0.0957
(0.60)
0.236
(1.00)
0.539***
(3.03)
1.189***
(2.91)
-0.0921
(-0.39)
-0.187
(-0.56)
-0.449***
(-2.83)
-0.663**
(-2.03)
-0.482***
(-2.95)
-0.847**
(-2.47)
-0.375
(-0.70)
-0.309
(-0.81)
SEG_HERF
RET
INDADJ_RET
RET_VOL
CF_VOL
SALES_GR
67
INV
-3.616
(-0.86)
-9.042*
(-1.74)
-5.002
(-1.18)
-9.995*
(-1.87)
6.032
(1.21)
1.714
(0.31)
DIV_YIELD
22.09***
(6.37)
19.14***
(4.63)
19.57***
(5.26)
19.76***
(4.39)
4.689
(0.72)
-13.60**
(-2.28)
PCT_INSIDE
-3.806***
(-5.38)
-2.152*
(-1.87)
-2.555***
(-3.50)
-1.936
(-1.59)
-4.120***
(-4.36)
-1.412
(-1.16)
BOARD_SIZE
-0.0147
(-0.48)
-0.0648
(-1.36)
-0.0212
(-0.63)
-0.0850*
(-1.74)
0.0283
(0.55)
0.0473
(0.88)
DUALITY
-0.0932
(-0.78)
0.190
(1.05)
0.102
(0.81)
0.204
(1.10)
-0.677***
(-3.39)
0.114
(0.59)
INSTOWN
0.433
(0.76)
0.0785
(0.10)
0.223
(0.38)
0.273
(0.34)
1.274
(1.42)
0.430
(0.44)
701
0.150
1355
0.033
CONSULT
N
Pseudo-R2
0.667**
(2.33)
7517
0.160
1858
0.118
0.523*
(1.87)
4720
0.117
1677
0.133
Panel B: Characteristics of the RPE Contract
(7)
STOCKPAY
(Stock is paid at
back end)
-0.249
(-0.55)
(8)
MEASRET
(Stock price
metric)
-0.943*
(-1.92)
(9)
STOCKRET
IND_HERF
-0.309
(-0.31)
-0.146
(-0.15)
-0.926
(-0.98)
MKT_RISK
1.590***
(2.61)
-1.214**
(-2.12)
0.158
(0.28)
LN_ASSETS
-0.00849
(-0.07)
-0.110
(-0.79)
-0.0363
(-0.29)
M/B
-0.0616
(-1.19)
-0.0339
(-0.74)
-0.0930*
(-1.81)
SEG_HERF
68
(Both)
-0.310
(-0.70)
ROA
0.207
(0.09)
-2.356
(-1.07)
-0.426
(-0.19)
INDADJ_ROA
0.714
(0.48)
1.682
(1.19)
1.911
(1.34)
RET
0.0905
(0.43)
-0.139
(-0.69)
-0.151
(-0.72)
INDADJ_RET
-0.0372
(-0.16)
0.143
(0.64)
0.132
(0.59)
RET_VOL
-1.083**
(-2.02)
-1.335**
(-2.34)
-1.266**
(-2.47)
CF_VOL
-0.0812
(-0.33)
1.204
(1.39)
0.0942
(0.37)
SALES_GR
-0.0154
(-0.06)
0.0667
(0.23)
-0.104
(-0.42)
9.511
(1.15)
3.582
(0.53)
8.908
(1.26)
DIV_YIELD
18.39***
(2.86)
11.34
(1.49)
17.58***
(2.90)
PCT_INSIDE
-4.629***
(-3.39)
-2.130
(-1.47)
-3.182**
(-2.31)
BOARD_SIZE
-0.0970
(-1.62)
0.0775
(1.17)
-0.0373
(-0.63)
DUALITY
-0.117
(-0.56)
-0.301
(-1.26)
-0.0768
(-0.37)
INSTOWN
0.842
(0.84)
-0.175
(-0.16)
-0.375
(-0.37)
N
Pseudo-R2
1314
0.074
1312
0.062
1290
0.060
INV
69
Table 3
RPE Peer Groups
The following table describes the type of peer group used for measuring relative performance. Select Peers means the firm has
identified the constituents of its peer group by name. Broad Index means the firm is using the constituents of a pre-defined broad
index such as the S&P 500. Industry Index means the firm is using the constituents of a pre-defined industry-specific index.
Panel A: Peer Group Type
Broad Index or
Industry Index or
Year
Select Peers
Peer Group
Peer Group
1998
65.4%
17.6%
25.0%
1999
62.3%
21.0%
26.1%
2000
64.0%
16.7%
27.3%
2001
63.4%
18.3%
29.6%
2002
64.8%
12.3%
29.6%
2003
66.9%
16.0%
28.4%
2004
71.0%
15.0%
24.5%
2005
67.6%
17.8%
22.7%
2006
71.2%
19.1%
21.4%
2007
73.3%
18.4%
19.1%
2008
70.5%
19.9%
19.9%
2009
72.5%
17.7%
19.0%
2010
75.9%
16.6%
17.4%
2011
74.7%
19.0%
15.8%
2012
72.3%
19.9%
17.1%
70
Table 4
Performance Evaluation
The following table describes how firm performance is measured for RPE awards. Panel A reports the firm performance metric
used. Panel B provides further details for awards based on accounting results. Panel C describes representation of RPE by
functional form. Panel D describes the performance period length, the existence of any ex-post vesting after the performance
period, and the average time to vest.
Panel A: Performance Metric
Year
N
Stock Return
Accounting
1998
139
79.1%
36.0%
1999
140
75.0%
34.3%
2000
150
76.7%
36.0%
2001
145
70.3%
43.4%
2002
163
72.4%
39.3%
2003
173
74.6%
41.6%
2004
202
75.7%
35.6%
2005
226
76.1%
35.4%
2006
257
73.9%
38.1%
2007
275
75.6%
36.4%
2008
278
74.8%
34.2%
2009
301
75.4%
35.2%
2010
338
78.1%
34.3%
2011
365
80.0%
32.1%
2012
417
83.2%
28.5%
Panel B: Accounting Metric
Year
N
Earnings
Growth
Return on
X
1998
50
38.0%
70.0%
Cash
Flow
Growth
4.0%
1999
48
43.8%
70.8%
2000
52
46.2%
67.3%
2001
61
52.5%
2002
59
2003
69
2004
2005
EVA
Growth
Other
Profit
Margin
Sales
Growth
0.0%
14.0%
4.0%
16.0%
2.1%
2.1%
20.8%
2.1%
14.6%
7.7%
1.9%
13.5%
1.9%
13.5%
65.6%
6.6%
4.9%
11.5%
3.3%
16.4%
50.8%
61.0%
6.8%
5.1%
11.9%
0.0%
10.2%
55.1%
50.7%
5.8%
1.4%
13.0%
1.4%
14.5%
70
60.0%
54.3%
2.9%
0.0%
7.1%
1.4%
17.1%
78
60.3%
50.0%
2.6%
1.3%
10.3%
2.6%
15.4%
2006
98
55.1%
45.9%
6.1%
1.0%
17.3%
3.1%
15.3%
2007
101
48.5%
43.6%
6.9%
1.0%
19.8%
2.0%
22.8%
2008
96
43.8%
43.8%
4.2%
1.0%
24.0%
4.2%
20.8%
2009
107
44.9%
35.5%
4.7%
1.9%
22.4%
4.7%
24.3%
2010
117
42.7%
38.5%
0.0%
1.7%
26.5%
7.7%
18.8%
2011
117
38.5%
40.2%
1.7%
1.7%
28.2%
7.7%
23.1%
2012
122
37.7%
44.3%
0.8%
1.6%
24.6%
6.6%
20.5%
(Continued)
71
Table 4-Continued
Panel C: Functional Form of RPE Grant
Year
Percentile
Rank
BenchmarkAdjusted
1998
79.1%
26.7%
1999
78.7%
26.6%
2000
76.8%
25.3%
2001
85.5%
18.1%
2002
84.9%
18.3%
2003
86.5%
15.4%
2004
89.6%
12.8%
2005
88.3%
13.1%
2006
86.3%
15.1%
2007
88.9%
12.3%
2008
86.9%
15.5%
2009
85.8%
15.3%
2010
89.3%
13.3%
2011
87.4%
14.4%
2012
87.3%
15.8%
Panel D: Performance Period and Ex-Post Vesting
Year
1-Year
2-Year
3-Year
4-Year
5+ Years
Multiple
Perf
Periods
Use of
Ex-Post
Vesting
Avg Ex-Post
Vest
(Months)
1998
36.9%
5.0%
58.9%
10.6%
8.5%
9.8%
9.4%
25.3
1999
36.4%
2.9%
60.0%
10.7%
5.0%
9.3%
9.4%
24.2
2000
39.1%
6.0%
63.6%
6.6%
6.0%
10.6%
9.3%
21.2
2001
34.2%
2.1%
67.1%
6.8%
4.1%
8.2%
4.1%
26.3
2002
33.7%
6.1%
66.9%
4.3%
3.7%
7.4%
7.5%
21.0
2003
34.9%
5.2%
66.9%
6.4%
4.7%
6.9%
11.1%
29.8
2004
28.2%
6.4%
74.8%
4.0%
4.5%
7.4%
10.5%
29.4
2005
27.1%
5.8%
74.2%
3.6%
4.4%
7.5%
9.4%
27.9
2006
28.3%
4.3%
74.4%
6.2%
1.9%
11.6%
12.5%
26.5
2007
29.9%
2.9%
74.8%
4.7%
2.5%
15.1%
9.7%
30.4
2008
27.1%
2.8%
75.7%
6.3%
2.1%
14.8%
9.3%
29.9
2009
26.0%
4.5%
75.6%
4.2%
1.9%
16.6%
7.5%
28.0
2010
26.0%
4.9%
78.9%
3.2%
0.9%
13.8%
8.8%
27.6
2011
24.7%
4.6%
78.0%
3.8%
1.6%
14.5%
8.4%
25.5
2012
22.7%
5.0%
79.0%
3.8%
1.7%
13.7%
12.1%
29.1
72
Table 5
Payout Function for RPE Percentile Grants of Stock, Cash, or Options
This table describes how relative performance translates to the ex-post payout. We limit this table to
percentile grant schedules.
Percent of Target Payout
Grant Schedule Percentile
Single-Step Schedule
Percentile Performance
Rank for Threshold
Multi-Step Schedule
Threshold Payout as %
of Target
Maximum Payout as %
of Target
Percentile Performance
Rank for Threshold
Percentile Performance
Rank for Target
Percentile Performance
Rank for Maximum
N
10th
25th
50th
75th
90th
1,689
50%
50%
50%
75%
75%
12,671
0%
23%
27%
50%
50%
12,671
100%
150%
200%
200%
200%
12,671
20%
25%
30%
39%
50%
12,671
50%
50%
50%
60%
74%
12,671
75%
75%
80%
90%
100%
73
Table 6: Simulation Results – Hit Rates
Distribution of Simulated Percentage Hit Rates for Threshold, Target, and Ceiling across Percentile RPE
Grant Schedules by Single- versus Multi-step Schedules and by Shares versus Cash as the Back-end
Instrument
Stock Price Metric; Paid in Stock
Simulated Ex-Ante Avg Pctl/Rank
Single Step Awards - Simulated % times hurdle met
Multi-Step Awards - Simulated % time threshold met
Multi-Step Awards - Simulated % time target met
Multi-Step Awards - Simulated % time max met
Stock Price Metric; Paid in Cash
Simulated Ex-Ante Avg Pctl/Rank
Single Step Awards - Simulated % times hurdle met
Multi-Step Awards - Simulated % time threshold met
Multi-Step Awards - Simulated % time target met
Multi-Step Awards - Simulated % time max met
Accounting Metric; Paid in Stock
Simulated Ex-Ante Avg Pctl/Rank
Single Step Awards - Simulated % times hurdle met
Multi-Step Awards - Simulated % time threshold met
Multi-Step Awards - Simulated % time target met
Multi-Step Awards - Simulated % time max met
Accounting Metric; Paid in Cash
Simulated Ex-Ante Avg Pctl/Rank
Single Step Awards - Simulated % times hurdle met
Multi-Step Awards - Simulated % time threshold met
Multi-Step Awards - Simulated % time target met
Multi-Step Awards - Simulated % time max met
Grant Schedule Percentile
25th
50th
75th
N
10th
1158
55
0.45
28.8%
0.49
44.5%
0.50
50.9%
0.52
58.2%
0.54
62.8%
732
52.3%
62.9%
73.0%
80.2%
89.6%
707
732
40.7%
0.0%
45.2%
0.0%
50.5%
12.0%
55.1%
22.0%
60.0%
25.3%
295
11
0.46
26.5%
0.49
27.6%
0.50
40.7%
0.52
45.4%
0.54
46.0%
162
142
162
45.2%
37.9%
0.0%
54.8%
44.3%
0.0%
68.7%
48.2%
15.2%
77.4%
52.9%
21.4%
87.3%
57.5%
24.3%
361
19
0.40
28.0%
0.48
45.5%
0.51
55.3%
0.56
67.5%
0.61
74.1%
214
199
214
50.6%
31.7%
0.0%
61.6%
40.6%
0.0%
76.0%
52.9%
8.4%
85.7%
61.3%
20.9%
100.0%
69.1%
27.7%
278
17
0.46
14.5%
0.50
20.3%
0.51
34.6%
0.54
53.5%
0.58
78.5%
145
139
145
49.4%
34.9%
0.0%
58.6%
42.8%
0.0%
75.9%
50.5%
14.5%
84.0%
55.7%
22.2%
100.0%
62.5%
25.9%
74
90th
Table 7: Simulation Results – Payout Rates and Value
Distribution of Payout Rates and Values as a Proportion of Target Payout across Percentile RPE Grant
Schedules per Dollar of Initial Stock Price (Stock Grant) or per Dollar of Cash Target (Cash Grant)
Grant Schedule Percentile
25th
50th
75th
N
10th
Stock Price Metric; Paid in Stock
Avg target multiplier
Avg price per $1 of original stock value
Avg payout per $1 of original stock value
Std Dev of payout per $1 of original stock value
787
1158
787
787
87.3%
$1.15
$1.39
$1.25
95.0%
$1.19
$1.49
$1.44
101.0%
$1.23
$1.64
$1.83
105.1%
$1.27
$1.76
$2.36
112.5%
$1.30
$1.87
$3.10
Stock Price Metric; Paid in Cash
Avg payout per $1 target
Std Dev of payout per $1 target
173
173
$0.87
$0.62
$0.95
$0.74
$1.02
$0.83
$1.05
$1.00
$1.09
$1.18
Accounting Metric; Paid in Stock
Avg target multiplier
Avg price per $1 of original stock value
Avg payout per $1 of original stock value
Std Dev of payout per $1 of original stock value
233
361
233
233
69.3%
$1.08
$0.84
$1.02
85.0%
$1.19
$1.06
$1.20
105.9%
$1.25
$1.31
$1.46
119.5%
$1.28
$1.53
$1.82
134.2%
$1.31
$1.78
$2.27
Accounting Metric; Paid in Cash
Avg payout per $1 target
Std Dev of payout per $1 target
162
162
$0.82
$0.59
$0.95
$0.67
$1.03
$0.79
$1.11
$0.98
$1.22
$1.14
75
90th
Table 8: Simulated Ex Ante Value of Percentile P-V RPE Grants of Stock and
Cash versus Fair Market Value Disclosed by the Company
Grant date value is the simulated ex ante present discounted value at the grant date of the percentile p-v
RPE award of stock or cash. The table also reports the present value of the award if risk-neutral methods
are applied and the value of the award disclosed by the company in the proxy statement. The table reports
an estimate of the value of the award if there is no RPE, which is calculated as the average number of backend units granted, as determined by the simulation, multiplied by the present value of the back-end award,
which is grant date stock price for stock awards and $1 discounted by the risk-free rate over the performance
period for cash awards.
Stock Price Metric; Paid in Stock
Elasticity of Grant Date Value to Stock Price
Grant Date Value (per $1 of target)
Grant Date Value - Risk-Neutral Value (per
$1 of target)
Grant Date Value - Value of Award w/o RPE
Grant Schedule (per $1 of target)
Total Grant Date Value
Total Grant Date Value - Disclosed FMV
Stock Price Metric; Paid in Cash
Elasticity of Grant Date Value to Stock Price
Grant Date Value (per $1 of target)
Grant Date Value - Risk-Neutral Value (per
$1 of target)
Grant Date Value - Value of Award w/o RPE
Grant Schedule (per $1 of target)
Total Grant Date Value
Total Grant Date Value - Disclosed FMV
Accounting Metric; Paid in Stock
Elasticity of Grant Date Value to Stock Price
Grant Date Value (per $1 of target)
Grant Date Value - Risk-Neutral Value (per
$1 of target)
Grant Date Value - Value of Award w/o RPE
Grant Schedule (per $1 of target)
Total Grant Date Value
Total Grant Date Value - Disclosed FMV
Accounting Metric; Paid in Cash
Elasticity of Grant Date Value to Stock Price
Grant Date Value (per $1 of target)
Grant Date Value - Risk-Neutral Value (per
$1 of target)
Grant Date Value - Value of Award w/o RPE
Grant Schedule (per $1 of target)
Total Grant Date Value
Total Grant Date Value - Disclosed FMV
Grant Value Percentile
50th
N
10th
25th
75th
90th
707
707
707
2.70
$1.02
-$0.22
3.33
$1.07
-$0.18
4.24
$1.17
-$0.14
5.54
$1.25
-$0.11
7.42
$1.35
-$0.08
707
$0.00
$0.05
$0.13
$0.27
$0.44
578
344
$202,220
-$1,187,007
$529,993
-$443,024
$1,125,738
-$70,948
$2,237,212
$74,611
$4,224,330
$408,458
142
142
142
1.99
$0.67
-$0.18
2.71
$0.73
-$0.15
3.85
$0.77
-$0.12
4.97
$0.82
-$0.09
9.85
$0.90
-$0.07
142
-$0.17
-$0.16
-$0.13
-$0.09
-$0.08
113
9
$36,788
-$3,261,163
$196,639
-$1,167,305
$538,934
-$699,614
$1,411,060
-$674,540
$2,437,508
-$137,918
199
199
199
0.94
$0.71
-$0.14
1.04
$0.84
-$0.07
1.23
$1.05
-$0.02
1.59
$1.18
$0.01
2.25
$1.33
$0.06
199
-$0.02
-$0.01
$0.00
$0.01
$0.02
139
24
$97,476
-$1,609,960
$222,062
-$850,151
$649,662
$9,490
$1,328,209
$240,408
$3,983,840
$629,998
139
139
139
0.00
$0.76
-$0.07
0.04
$0.87
-$0.04
0.35
$0.97
-$0.01
0.79
$1.04
$0.00
1.52
$1.12
$0.03
139
-$0.04
-$0.02
-$0.01
$0.00
$0.00
65
0
$105,847
.
$161,915
.
$328,312
.
$468,685
.
$759,008
.
76
Table 9: Ex Ante Delta Incentive Properties of Percentile P-V RPE Grants of
Stock and Cash Based on a Single Performance Metric
Grant Incentive Percentile
25th
50th
75th
N
10th
620
620
$3,814
-$56,014
$10,552
-$28,475
$23,976
-$12,498
$49,864
-$5,234
$94,458
-$1,873
619
$3,449
$9,046
$19,947
$40,004
$71,773
139
139
$342
-$43,316
$2,289
-$19,001
$7,319
-$6,933
$20,138
-$2,553
$48,149
-$335
139
$278
$1,682
$5,163
$12,324
$26,638
Accounting Metric; Paid in Stock
Marginal Delta in Own Accounting Performance (𝛿𝐴 )
Marginal Delta in Accounting Performance Benchmark(s) (𝛿𝐵 )
𝑅𝑃𝐸
Marginal RPE Delta in Accounting Performance 𝛿𝐴𝐵
Marginal Delta in Own Stock Performance (𝛿𝑃 )
𝑅𝑃𝐸
Aggregate RPE Delta in Stock Performance (𝛿𝐴𝑔𝑔
)
151
151
151
151
151
$262
-$10,922
$266
$971
$992
$719
-$6,152
$720
$2,386
$2,688
$2,305
-$2,500
$2,268
$6,843
$7,223
$6,049
-$812
$6,264
$13,662
$14,495
$12,721
-$252
$12,709
$33,622
$34,219
Accounting Metric; Paid in Cash
Marginal Delta in Own Accounting Performance (𝛿𝐴 )
Marginal Delta in Accounting Performance Benchmark(s) (𝛿𝐵 )
𝑅𝑃𝐸
Marginal RPE Delta in Accounting Performance 𝛿𝐴𝐵
Marginal Delta in Own Stock Performance (𝛿𝑃 )
𝑅𝑃𝐸
Aggregate RPE Delta in Stock Performance (𝛿𝐴𝑔𝑔
)
69
69
69
69
69
$461
-$3,735
$461
$0
-$153
$896
-$2,349
$883
$0
$87
$1,591
-$1,650
$1,589
$0
$377
$2,163
-$726
$2,159
$0
$618
$4,075
-$485
$3,999
$0
$963
Stock Price Metric; Paid in Stock
Marginal Delta in Own Stock Performance (𝛿𝑃 )
Marginal RPE Delta in Stock Price Benchmark(s) (𝛿𝑄 )
Marginal RPE Delta in Stock Performance = Aggregate RPE
𝑅𝑃𝐸
𝑅𝑃𝐸
Delta in Stock Performance (𝛿𝑃𝑄
=𝛿𝐴𝑔𝑔
)
Stock Price Metric; Paid in Cash
Marginal Delta in Own Stock Performance (𝛿𝑃 )
Marginal RPE Delta in Stock Price Benchmark(s) (𝛿𝑄 )
Marginal RPE Delta in Stock Performance = Aggregate RPE
𝑅𝑃𝐸
𝑅𝑃𝐸
Delta in Stock Performance (𝛿𝑃𝑄
=𝛿𝐴𝑔𝑔
)
77
90th
Table 10: Ex Ante Vega Incentive Properties of Percentile P-V RPE Grants of
Stock and Cash Based on a Single Performance Metric
Grant Incentive Percentile
25th
50th
75th
N
10th
Stock Price Metric; Paid in Stock
Marginal Vega in Own Stock Performance (νP)
Marginal Vega in the Stock Performance Benchmark(s) (νQ)
Aggregate RPE Vega (𝜈Σ )
620
620
620
$481
-$712
$723
$1,524
$4
$2,121
$3,808
$848
$5,081
$8,641
$2,551
$10,424
$18,102
$6,001
$22,567
Stock Price Metric; Paid in Cash
Marginal Vega in Own Stock Performance (νP)
Marginal Vega in the Stock Performance Benchmark(s) (νQ)
Aggregate RPE Vega (𝜈Σ )
139
139
139
-$4,686
-$1
-$74
-$1,997
$163
$30
-$393
$1,401
$498
$5
$3,730
$1,891
$436
$9,175
$6,205
Accounting Metric; Paid in Stock
Marginal Vega in Own Accounting Performance (νA)
Marginal Vega in Accounting Performance Benchmark(s) (νB)
151
-$15,878
-$6,768
-$2,788
-$726
-$96,485
$7,262
$243,014
$549,979
Marginal Vega in Own Stock Performance (νP)
Aggregate RPE Vega (𝜈Σ )
151
151
-$38,692
$515,284
$104
-$625
$316
-$36
$971
$429
$1,733
$2,825
$4,380
$8,329
Accounting Metric; Paid in Cash
Marginal Vega in Own Accounting Performance (νA)
Marginal Vega in Accounting Performance Benchmark(s) (νB)
69
-$6,194
-$2,898
-$1,020
-$345
-$78,613
-$2,616
$38,083
$170,765
Marginal Vega in Own Stock Performance (νP)
Aggregate RPE Vega (𝜈Σ )
69
69
-$8,485
$156,114
$0
-$421
$0
-$196
$0
-$6
$0
$339
$0
$1,050
78
151
69
90th