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

• Published date: 01 November 2018
• Date: 01 November 2018
• Author: Jeremy Bertomeu,Edwige Cheynel,Michelle Liu‐Watts
• DOI: http://doi.org/10.1111/eufm.12172

DOI: 10.1111/eufm.12172

ORIGINAL ARTICLE

Are the Fama French factors treated as risk?

Evidence from CEO compensation

Jeremy Bertomeu

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Edwige Cheynel

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Michelle Liu-Watts

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1

Rady School of Management,

University of California, San Diego

Emails: jbertomeu@ucsd.edu;

echeynel@ucsd.edu

2

Hunter College, City University of

New York (CUNY)

Email: michelle.liu@hunter.cuny.edu

Abstract

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.

JEL CLASSIFICATION

G1, G3

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INTRODUCTION

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: jbertomeu@ucsd.edu. We received helpful comments from

participants at workshops at Baruch College, the University of Paderborn and the University of Mannheim.

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© 2018 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/eufm Eur Financ Manag. 2018;24:728–774.

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 1992–2014, 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 (1992–2014), but the relationship no longer holds for

the recent period (2006–2014) 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 &

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Mullainathan, 2001; Garvey & Milbourn, 2006).

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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.

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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 1992–2014, 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).

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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

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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).

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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.

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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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