Are the Fama French factors treated as risk? Evidence from CEO compensation

Published date01 November 2018
Date01 November 2018
DOI: 10.1111/eufm.12172
Are the Fama French factors treated as risk?
Evidence from CEO compensation
Jeremy Bertomeu
Edwige Cheynel
Michelle Liu-Watts
Rady School of Management,
University of California, San Diego
Hunter College, City University of
New York (CUNY)
Asset pricing theory postulates that a risk factor correlates
with individuals' marginal utility of consumption. Hence,
under plausible preferences, individuals should become
more risk tolerant given favorable factor returns. We
show that this wealth effect predicts a positive association
between performance pay and factor returns. Our results
support the hypothesized relationship for the market,
book-to-marketand momentum factors. Factors constructed
from bond prices are positively associated to incentives,
incrementally to the Fama French factors, but we obtain
mixed evidence for higher-order market factors, liquidity
factors or factors constructed from national income
accounts, including pricing kernels.
G1, G3
This paper develops a non-conventional approach to test whether commonly-used empirical risk
factors capture individual consumption risks. A challenge in testing asset pricing theory is that
individual consumption and wealth are difficult to measure. We bypass this measurement problem by
testing the theory in the context of executive compensation, in which detailed data about incentives are
J. Bertomeu is an associate professor and E. Cheynel is an assistant professor both at Rady School of Management,
University of California, San Diego, and M. Liu-Watts is an associate professor at Hunter College CUNY. Contact author:
J. Bertomeu, 9500 Gilman Dr, La Jolla, CA 92093; email: We received helpful comments from
participants at workshops at Baruch College, the University of Paderborn and the University of Mannheim.
© 2018 John Wiley & Sons, Ltd. Eur Financ Manag. 2018;24:728774.
available. Incentive contracts should allocate risk to states of the world in which the agent has lower
absolute risk-aversion whi ch, under standard asset pricin g assumptions, are states with lo wer
marginal utility of wealth and higher factor returns (Coch rane, 2009). Under the joint hypo thesis of
market and contract efficie ncy, incentives in observed co ntracts will be positively a ssociated with
factor returns.
A motivation for our approach is given by Harvey, Liu, and Zhu (2014), who observe that standard
test procedures for a new factor, which rely on the existence of unexplained returns, do not take into
account the extensive statistical mining for factors. While Harvey, Liu, and Zhu suggest increasing the
desired significance level based on standard-errors adjusted for multiple hypotheses testing, we
propose a closely related solution, that is, to combine existing empirical asset pricing tests with tests
relying on observed real contracting decisions. Under multiple hypothesis testing, the less correlated
the noise in a test to noise in existing tests, the higher the joint significance of both tests. Because
incentives in contracts need not be correlated to expected returns, evidence from contracts may
increase confidence in a risk factor and should be read together with existing asset pricing tests from
which we borrow the set of factors under consideration.
For our empirical tests, we use two datasets. The first dataset is the sensitivity of managerial wealth
to stock price movements (Delta) for top executives from 19922014, as described in Coles, Daniel,
and Naveen (2013). Since this dataset contains the total Delta but not its option and stock components,
we also examine a second dataset using newly available data from the Execucomp compensation
database in Compustat. Starting with the fiscal year-end 2006, this database collects detailed
information about top management's portfolio of equity and options, which allows us to estimate the
sensitivity of managerial wealth to stock price movements for the stock option delta and stock delta.
Because our test relies on a predicted characteristic of the contract, it does not require a measurement of
other sources of managerial wealth separate from the firm. Hence, this approach offers an asset pricing
test with limited knowledge of the manager's consumption or wealth portfolio, as long as the researcher
observes sensitivity to firm-specific risks.
Overall, we find robust evidence that contracts treat the market, book-to-market (Fama & French,
1993) and momentum factors (Carhart, 1997) as risk, that is, factor returns are positively associated
with incentives over various time periods and specifications. We also find evidence that the size factor
is associated with incentives over the full sample (19922014), but the relationship no longer holds for
the recent period (20062014) and in many supplementary tests.
We test whether these associations may be tied to a positive association between pay and firm-level
factor betas, as documented by Garvey and Milbourn (2003). This problem is different from ours, in
that we try to control for firm-specific determinants of incentives, which include firm-level betas, and
our test variable is the factor return. In our main regression, we include firm fixed effects to control,
among other things, for the time-invariant component of betas. In supplementary analyses, we include
estimated factor betas in the main regression and, alternatively, run separate regressions by subsamples
of firms within quintiles of size and book-to-market. In these specifications, we find similar results for
the market, book-to-market and momentum factors but do not find a positive relationship between the
size factor and incentives.
Note that identification assumes efficient contracting and, therefore, we cannot distinguish
between market and contract inefficiencies. To examine whether contracting inefficiencies may cause
the relationship, we examine subsamples in which we would expect the contract to be more efficient.
We conjecture that firms with poor governance may be less willing to contract on observable risk
factors in order to conceal the nature of the compensation (Bebchuk & Fried, 2003). In particular, if
compensation arrangements tie incentives to changes in observable factors, it may be more difficult to
justify unexplained reductions in incentives following negative firm performance (Bertrand &
Mullainathan, 2001; Garvey & Milbourn, 2006).
However, we find similar results after partitioning
the sample by various governance variables suggesting that, when governance affects contract
efficiency, this might occur through higher rents to managers rather than a distortion to the
exposure of incentives to factors. Another source of contracting inefficiency may be imperfect
knowledge of the manager's preferred exposure to systematic risks by compensation committees.
We conjecture that both the manager's risk-aversion and the nature of the incentive scheme may
take time to learn. We test this hypothesis in a subsample of firms whose management had at
least two years in office, conducting the analysis separately for year 1 versus year 2. All factors
except the size factor are significant in year 2, but only the momentum factor remains significant
in year 1.
We then broaden the scope of ou r analysis to test a larger un iverse of factors discus sed in
Harvey, Liu, and Zhu (2014) and B erk and Van Binsbergen (2014). Sp ecifically, we examine five
classes of asset pricing fact ors: (i) higher-order marke t spanning factors, (ii) fact ors based on bond
prices, (iii) national inco me accounts variables, (iv) li quidity factors, and (v) facto rs based on
theory-based kernels. To re main consistent with our basel ine regressions, we conduct th ese tests
incrementally to the Fama-Fren ch factors.
We find robust evidence of a positiv e association
between factors based on bond prices and incentives. H owever, other factors, such as factors based
on national income variables, li quidity and kernels, are eithe r insignificant or negativel y correlated
to incentives.
Note that our empirical design cannot rule out two related channels for the association between
factors and performance pay. First, preferences have been found to exhibit cyclical changes in risk-
aversion (Rosenberg & Engle, 2002) with lower risk tolerance during recessions. To the extent that this
explanation also predicts lower performance pay during recessions, it suggests tests similar to ours.
Second, the agency problem may contain cyclical components in, say, cost of effort or information
which would be captured by factors. This channel is difficult to predict because the primitives of the
agency problem are not observable and, therefore, it is very difficult to form testable hypotheses with
context-specific agency problems. Nevertheless, such systematic changes in agency problems would
likely affect aggregate consumption and, thus, would contribute to systematic risk under this
hypothesis. Having noted this, this channel may imply a significant negative association between a risk
factor and performance-pay, and hence, weaken our procedure to test for a significant positive or
negative association between factor and performance-pay rather than, in our baseline, a directional
association. This, in turn, may explain the presence of negative significant associations between
incentives and some of the factors.
Figure 1 presents motivational stylized facts. For the period 19922014, we measure, for firms
listed in Execucomp, the total dollar sensitivity of an executive's portfolio of stock and options for a 1%
change in the firm's stock price (Δ).
For each fiscal period month end, we separate months by
recession, as classified by the National Bureau of Economic Research. The average Δis US$ 0.17
For example, complex contract structures, which condition pay on risk factors unrelated to managerial actions, may cause
special scrutiny by shareholders if they are viewed as a violation of relative performance evaluation (Abowd & Kaplan,
1999; Core, Guay, & Larcker 2003).
In untabulated additional tests, we did not observe that including or excluding the Fama-French factors in these regressions
had noticeable effects on the regressions.
In our analyses, we use the NBER recession variable during the month of each firm's fiscal year-end based on the
assumption that boards could have altered the contract given the most recent available information. However, these insights
are robust to grouping observations by quarters that include at least one month of an NBER recession, or if we calculate the
average delta only for firms that feature a full year of an NBER recession.

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