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Tilburg University
Financial reporting, debt contracting and valuation
Nikolaev, V.
Publication date:2007
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Financial Reporting, Debt Contracting
and Valuation
Financial Reporting, Debt Contracting
and Valuation
Proefschrift
ter verkrijging van de graad van doctor aan de Universiteit van Tilburg, op
gezag van de rector magnificus, prof. dr. F.A. van der Duyn Schouten, in
het openbaar te verdedigen ten overstaan van een door het college voor
promoties aangewezen commissie in de aula van de Universiteit op vrijdag
1 juni 2007 om 14.15 uur door
Valeri Vasilievich Nikolaev
geboren op 30 december 1977 te Minsk, Wit-Rusland.
PROMOTORES: Prof. Dr. S.P. Kothari
Prof. Dr. L.A.G.M van Lent
to my teachers
vii
Acknowledgements
My way towards the Ph.D. degree was both challenging and exciting; it was an unmatched and
unforgettable life experience resulting in this thesis and much more. I would like to acknowledge and
extend my heartfelt gratitude to the following persons who made the completion of this thesis possible and
from whom I learned. First of all my special words of appreciation go to my thesis supervisors S.P. Kothari
and Laurence van Lent, whose guidance, encouragement and strong support have been extremely important
in my professional development.
Laurence is the most responsible for helping me in completing my thesis as well as for involving me into
active research and stimulating the progress I was making. He helped me to make my first steps in the
Ph.D. program and was always eager to listen, to discuss my ideas, and to give his insightful advice and
feedback. Laurence invested a lot of effort and patience in educating me; he commented extensively on
multiple versions of my written work and put immense effort into teaching me how to communicate my
ideas in writing for an academic audience. As I was furthering into the program, Laurence became my
friend. I am deeply grateful to him for supporting and believing in me in the moments of doubt and
difficulty I had and for encouraging me in the moments I was facing challenges.
I am most genuinely grateful and obliged to S.P. He agreed to become my external supervisor after I
visited the Sloan School of Management at the Massachusetts Institute of Technology. I benefited
enormously from S.P.’s invaluable expertise and his generous willingness to teach me his insights into our
field of study as well as his insights about doing research and writing papers. His mentorship significantly
shaped my thinking and helped me to evolve and to become much more mature. I am deeply indebted to
S.P. for the confidence and trust he had in me, and for giving me an opportunity to come to MIT and to get
involved in a joint research project. Needless to say, I am truly honored working with him.
My sincere gratefulness also extends to Jan Bouwens, Philip Joos, and Jeroen Suijs for being members of
my dissertation committee and for their willingness to read and evaluate this thesis. I highly appreciate
valuable feedback they provided at various stages of this dissertation. I am also thankful to all other
colleagues at the Department of Accounting for the interaction we had and for making my stay at Tilburg
University pleasant.
Parts of this thesis were written during a year I spent in the U.S. visiting MIT’s Sloan School of
Management and the University of Chicago’s Graduate School of Business. I am grateful to their faculty
viii
and to the Ph.D. students I met while in the U.S. for being kind and eager to discuss my work. I am
particularly thankful to Ray Ball and Peter Easton for their help and encouragement. Both visits were
extremely influential in terms of stimulating my thinking and motivating me to work hard, as well as in
shaping my academic interests. I acknowledge financial support I received from the Netherlands
Association for Scientific Research (NWO) which made these visits possible (grants: R46-570 and R46-
541).
Many thanks go to fellow Ph.D. students: Stephan Hollander, Flora Kuang, Yuping Jia, Peter Kroos for
their patience towards me and for many nice moments we shared during our studies. I am thankful to
Marina Martynova, Andrei Medvedev, Romana Negrea, and Viorel Roscovan for being my dear friends in
Tilburg and for making my life here enjoyable; as well as to all other friends I met during my studies here
and in Prague. Romana encouraged me to apply to Tilburg, for which I am particularly grateful. My
“thank you” also goes to Maryia Fedzechkina for her tenderness and empathy towards me. Finally, I am
particularly grateful to Andrei Borovoi, Andrei Gritsuk, Vladislav Kamluk, Vitaliy Korotenko, Alexei
Koscheev, Elena Loutskina, and Vladislav Shilov for remaining my closest and dearest friends ever since
our days in Minsk despite the distance. Elena influenced my decision to go to graduate school, while
Andrei Borovoi was always eager to inquire about the progress I was making.
The way towards a Ph.D. degree is not always very smooth. There are many crossroads at which the
decision to take is not obvious. I am thankful to all my teachers from the past for educating and preparing
me to resist the difficulties in such moments.
Most deeply I am grateful to my parents Ludmila Nikolaeva and Vasiliy Nikolaev for educating me and for
giving me their love and kindness, as well as to my sister Lena. In addition to her love and enthusiasm
about me she often gave me her little push when I most needed it.
Tilburg,
April 2007
ix
Table of Contents
Acknowledgements ...................................................................................................................... vii
Chapter 1
Introduction .................................................................................................................................. 1
Chapter 2
Debt Covenants and Accounting Conservatism: Complements or Substitutes?................................. 4 2.1. Introduction.................................................................................................................................... 4
2.2. Background and Related Literature................................................................................................. 7 2.2.1. Role of debt covenants .............................................................................................................. 7 2.2.2. What determines the degree of restrictiveness?.......................................................................... 8 2.2.3. Distress and timely loss recognition .......................................................................................... 9 2.2.4. Covenants as a signaling device and timely loss recognition...................................................... 9
2.3. Hypothesis .....................................................................................................................................10
2.4. Research Design.............................................................................................................................11
2.5. Data and Sample Construction........................................................................................................13 2.5.1 Variable definitions...................................................................................................................16
2.6. Results ...........................................................................................................................................17 2.6.1. Covenant equation ...................................................................................................................17 2.6.2. Main results .............................................................................................................................19
2.7. Conclusions and Limitations...........................................................................................................31
2.8. References......................................................................................................................................32
2.A. Examples of timely accounting policies .........................................................................................35
2.B. Index Construction.........................................................................................................................37
Chapter 3
Agency Theory of Overvalued Equity as an Explanation for the Accrual Anomaly......................... 40 3.1. Introduction....................................................................................................................................40
3.2. Hypothesis Development and Empirical Predictions .......................................................................45 3.2.1. Hypothesis Development .........................................................................................................45 3.2.2. Related evidence......................................................................................................................47 3.2.3. Empirical Predictions...............................................................................................................48
3.3. Data and Sample Selection .............................................................................................................50 3.3.1. Sample Selection .....................................................................................................................50 3.3.2. Total and Discretionary Accruals Variables..............................................................................51 3.3.3. Descriptive Statistics................................................................................................................51
x
3.4. Empirical Tests and Results............................................................................................................53 3.4.1. Abnormal Stock Returns ..........................................................................................................53 3.4.2. Analyst Optimism....................................................................................................................61 3.4.3. Insider Trading Behavior .........................................................................................................64 3.4.4. Investment-Financing Decisions ..............................................................................................68 3.4.5. Relation between Stock Returns and Accruals..........................................................................74
3.5. Summary and conclusions ..............................................................................................................79
3.6. References......................................................................................................................................79
Chapter 4
The Endogeneity Bias in the Relation between Cost-of-Debt Capital and Corporate Disclosure Policy................................................................................................................................................... 84
4.1. Introduction....................................................................................................................................84
4.2. A note on endogeneity....................................................................................................................87 4.2.1. Sources of ‘econometric’ endogeneity.....................................................................................88
4.3. Omitted variables in the relation between cost-of-debt capital and disclosure .................................92 4.3.1 Unobservable firm characteristics ............................................................................................93 4.3.2. Joint determinants of disclosure and cost-of-debt capital ..........................................................94
4.4. Research design and variable definitions.........................................................................................95 4.4.1. Caveats. ...................................................................................................................................99
4.5. Sample and summary statistics .......................................................................................................99
4.6. Results .........................................................................................................................................108
4.7. Discussion and conclusion............................................................................................................120
4.8. References....................................................................................................................................121
4.A. Variable definitions. ....................................................................................................................126
4.B. Mundlak’s (1978) approach .........................................................................................................127
Chapter 5
Implied Cost of Capital When Future Expected Returns Are Stochastic ...................................... 129 5.1. Introduction..................................................................................................................................129
5.2. Valuation with Stochastic Expected Returns .................................................................................132 5.2.1.Why Does Uncertainty Matter?...............................................................................................132 5.2.2. Pricing Equation ....................................................................................................................133
5.3. Implementation ............................................................................................................................135 5.3.1. Assessment of the bias ...........................................................................................................135 5.3.2. Variance of the innovations in expected returns......................................................................138 5.3.3. Standard Models and Uncertainty Adjustment........................................................................140
5.4. Data and Sample Construction......................................................................................................142 5.4.1. Equilibrium Rates of Return Variance Data............................................................................142 5.4.2. Implied Cost of Capital Data..................................................................................................143
5.5. Implied Risk Premia .....................................................................................................................143
5.6. Future work..................................................................................................................................158
5.7. Conclusions..................................................................................................................................159
xi
5.8. References....................................................................................................................................160
5.A. Appendix A.................................................................................................................................161
5.B. Appendix B .................................................................................................................................163
xii
1
Chapter 1
Introduction
An important insight from the current accounting literature is that the quality of accounting
information is predominantly determined by economic incentives provided to managers and not by
accounting standards per se. While, in the light of recent accounting scandals, the need for quality of
financial reporting cannot be underestimated, the concept of accounting quality is hard to define or to study
comprehensively. Nevertheless, it is convenient to think of reporting quality from a user’s viewpoint.
Specifically, as long as the properties of accounting information satisfy the needs of a firm’s stakeholders
the information can be considered of good quality. Many gaps still exist in the literature that examines how
economic demands and incentives of economic agents shape the properties of accounting information.
Much can be learned by isolating stakeholders’ demands and managerial incentives for high quality
financial reports. While each of the studies in the later chapters is somewhat differently themed, they are
unified around the idea that a full understanding of incentives generates powerful insights about the
behavior of economic agents and how it shapes the properties of accounting information.
In Chapter 2, I focus on how contracting demands from public debt market motivate managers to
adopt timely reporting policies with respect to the recognition of economic losses. While the general
economic mechanism through which debt contracting affects accounting information is well documented,
still little research exists on how the microeconomic factors influence the properties of accounting
information. The incentives for timely loss recognition arise in public debt market because bondholders
need to be protected from managers behaving opportunistically and expropriating bondholders’ wealth as a
firm approaches financial difficulties. To achieve this, debt contracts include accounting-based covenants
limiting managerial control over a distressed firm. However, as distress is detected by assessing the
accounting performance, covenants will protect bondholders only to the extent that manager’s discretion to
postpone the recognition of economic losses into earnings is limited.
It follows from this argument that covenants are more valuable in constraining managerial
opportunism if the accounting system generates timely signals of a firm’s economic health. Thus, the
efficiency of the debt contracting technology can be improved if firms choosing to rely on protective
covenants adopt a set of accounting policies improving timely loss recognition ex ante. Consistent with this
conjecture, I find evidence that the reliance on covenants in lending agreements is positively associated
2
with the demand for timely loss recognition. The analysis reveals that firms with more covenants in their
debt contracts are considerably more timely in their recognition of economic losses. This documented link
suggests that the use of covenants increases the demand for timely loss recognition. This helps us to
understand how a particular set of stakeholders, namely public bondholders, create incentives for firm
management to improve a particular dimension of reporting quality. One has to keep in mind, however,
that managers are self-interested and it may be hard to align their incentives with stakeholders’ needs. This
is investigated next.
In Chapter 3 of this thesis, I use the agency theory of overvalued equity (Jensen, 2005) to
understand why some managers fail to recognize and record economic losses in their financial statements.
One of the predictions of the theory is that once a firm becomes substantially overvalued, perhaps because
adverse information is withheld from the market, firm’s managers have strong incentives to manipulate
their reported performance. Such incentives arise because overvalued firms cannot sustain high
performance expectations dictated by the market participants and this leads to a severe conflict of interest
between management and stakeholders.
Earnings management in overvalued firms is likely to be forged via accruals and therefore the
agency theory has important implications for the accrual anomaly (a predictable relation between current
accruals and future returns) documented by Sloan (1996). Since overvalued firms aggressively manage
accruals upwards following a period of overvaluation, a sample of high accrual firms is over-represented
with overvalued companies. However, since overvaluation and superior reported performance cannot last
indefinitely, negative abnormal returns are subsequently realized, on average, for the high accrual portfolio
companies. The analysis is important because previously the accrual anomaly was attributed to functional
fixation of investors, suggestive of inherently poor quality of accrual reporting. However, this chapter
suggests that investors do not simply fixate on accruals but are being purposefully misled by management.
The analysis in the third chapter highlights an important problem when the manager’s reporting
incentives are not aligned with those of the firm’s stakeholders. To discipline the management a strong
corporate governance system must be in place. A central attribute of the corporate governance system,
which helps to align reporting incentives, is the transparency of corporate disclosure. Enhanced
transparency places stricter constraints on a manager’s ability to hide the consequences of their
unsuccessful efforts from outside investors. This mitigates information asymmetry problems, which gives
rise to information risk and, in turn, reduces the cost of capital.
Chapter 4 of the thesis investigates the role of transparency of financial reporting in reducing the
cost of debt capital. While prior research has established an inverse association between transparency and
the cost of debt, the analysis here focuses on establishing a causal link and exploits both cross-sectional and
time series variation in transparency proxies. The chapter also discusses methodological difficulties in
establishing causality. A stronger than previously thought causal link between dimensions of corporate
disclosure quality and cost of debt is documented. This chapter generates additional insights about how
incentives that shape reporting quality arise in capital markets.
3
Chapter 5 of my thesis is mainly methodological. Measures of the cost of equity capital employed
in the empirical literature to examine the impact of corporate governance on a firm’s cost of capital are
subject to substantial measurement difficulties, which jeopardize causal inferences. In this chapter, I
identify a substantial downward bias in traditional measures of the implied cost of equity capital, which
arises due to uncertainty about the future expected returns. As expected returns are stochastic, the
traditional valuation models based on accounting information (such as the residual income model) do not
apply to securities valuation. I develop a simple way to generalize the traditional valuation models and I
then invert the derived valuation model to compute the implied cost of equity. The analysis explains why a
number of prior studies find implied equity premia to be substantially lower than those historically realized.
In addition, uncertainty about the future expected returns differs across firms resulting in an important
omitted factor in extant empirical research.
The thesis links economic incentives facing managers and problems of corporate governance with
the properties of accounting information. The focus is on timely loss recognition, earnings management
and transparency all of which have received a lot of attention in the literature. The findings aim at
advancing our understanding of the role of accounting information in the economy and its impact on
contracting, valuation and the cost of capital.
4
Chapter 2
Debt Covenants and Accounting Conservatism: Complements or Substitutes?
2.1. Introduction
I examine whether firms with more covenants in their public debt contracts recognize economic
losses in earnings in a more timely fashion. Covenants are designed to limit a manager’s ability to take
actions leading to bondholder wealth expropriation when a firm approaches financial distress. In particular,
covenants are designed to protect bondholders from management opportunistically making unwarranted
distributions to shareholders or non-optimal investments (Jensen and Meckling, 1976, Myers, 1977, Smith
and Warner, 1979). However, because covenants typically become binding when accounting performance
deteriorates below a pre-specified threshold, they protect bondholders only to the extent that a manager’s
discretion to postpone the recognition of economic losses in earnings is limited.
The literature recognizes that accounting information is useful in contracting and that the demands
of contracting parties shape its properties (Watts and Zimmerman, 1986). Specifically, debt contracting
creates demand for timely loss recognition, an important property of accounting information also referred to
as conditional conservatism (Watts, 2003a, Holthausen and Watts, 2001, Ball, Robin, and Sadka, 2005). It
is more difficult for outsiders to monitor and control a manager’s actions in firms that rely on public rather
than private debt. As a result, the conflicts of interest between bondholders and management are more
severe for public firms. To mitigate the presence of such conflicts, that is, to limit managerial ability to
expropriate bondholder wealth, policies adopted by the accounting system recognize economic losses in
earnings more promptly (Ball, Kothari, and Robin, 2000, Ball and Shivakumar, 2005).
While the general mechanism through which debt contracting affects accounting information is
well understood, relatively little research exists on how the microeconomic foundations of debt contracting
influence the properties of accounting information (e.g., Sloan, 2001, Guay and Verrecchia, 2006). In this
paper I focus on the role of timely loss recognition in debt contracts, and more specifically on the direct link
between debt covenants and the degree of conditional conservatism in annual reports (Guay and Verrecchia,
5
2006).1 Following Basu (1997), I measure timely loss recognition via a piecewise linear regression of
earnings on positive returns (as a proxy for good news) and negative returns (as a proxy for bad news).
Two opposing views on how the demand for timely loss recognition is resolved in practice exist in
the literature. The first view maintains that the timely recognition of losses facilitates the early transfer of
decision rights from shareholders to bondholders as a firm approaches financial difficulties and thus
reduces the likelihood of bondholder wealth expropriation (Watts, 2003a, Ball and Shivakumar, 2005, Ball,
Robin, and Sadka, 2005). This view is also consistent with Levine and Hughes (2005), who argue that
covenants are more valuable when losses are recognized in a timely manner because this allows for more
effectve bonding against ex post sub-optimal actions. Conservative recognition of news induces early
truth-telling about future cash flows and allows a company with lower default risk to signal its type.
Without timely accounting signals about a firm’s economic health, the efficiency of protective covenants in
curbing the agency costs of debt is lower, i.e., timely loss recognition complements and reinforces the
effectiveness of covenants. As a result, debtholders wishing to reduce the potential for losses include
covenants in contracts and insist on more conservative recognition of economic losses in debtor’s accounts.
This implies that covenants and accounting conservatism should be positively associated.
The second view holds that while firms can meet the demand for timely loss recognition by
adopting conservative accounting policies, bondholders can alternatively adjust GAAP-based accounting
information to fit contract-specific needs for conservatism (Guay and Verrecchia, 2006). In other words,
firms can substitute the adoption of conservative accounting policies within GAAP with pre-specified
modifications to accounting numbers within a contract (Beatty, Weber, and Yu, 2006). If making contract-
specific modifications is indeed more cost effective, then no association between covenants and timely loss
recognition should be observed. By testing these alternative predictions, I provide evidence that
distinguishes between the complementarity and substitution views on conditional conservatism and
accounting-based covenants.
I use the Mergent Fixed Investment Securities Database to retrieve information about covenant
stipulations in public debt contracts. Covenant information is available for a large cross-section of debt
issues by industrial companies. The data allow me to construct five indices of debt contract restrictiveness.
These indices measure: (1) the overall restrictiveness of the contract, (2) restrictions on new investments,
(3) restrictions on the distribution of funds to shareholders, (4) restrictions on future financing, and finally,
(5) the transfer of control to bondholders when default becomes probable. Since most of the covenants
depend on accounting information, these indices are used to proxy for the extent to which a contract is
linked to accounting information.
The findings suggest that firms with more covenants in their debt contracts are considerably more
timely in their economic loss recognition. Indeed, companies with the most restrictive debt contracts, as
1 From a debt contracting perspective, there is less demand for timeliness in gain recognition (e.g., Ball and Shivakumar, 2005, Guay and Verrecchia, 2006).
6
judged by the overall restrictiveness index, are about twice as timely in recognizing economic losses as are
firms with the least restrictive contracts. The results are similar when I separately examine each of the four
indices of restrictiveness. Furthermore, the correlation between the rank of contract restrictiveness and the
estimates of timely loss recognition is as high as 0.71 for the overall restrictiveness index, 0.78 for the
investment restrictions index, 0.70 for the payout restrictions index, and 0.66 for financing restrictions. The
results are somewhat weaker for the transfer of control covenant index. Overall, the results are consistent
with the use of covenants increasing the demand for more timely loss recognition.
In a related study, Beatty, Weber, and Yu (2006) examine how conservative modifications of
accounting information specified in debt covenants are related to conditional conservatism. They find that
conservative net worth covenant modifications do not fully meet lenders’ demand for conservative
reporting: the modifications are further complemented by within-GAAP choice of timelier loss recognition.
This study differs from that of Beatty et al. in that I consider how the inclusion of debt covenants relates to
conservative accounting practices, whereas Beatty et al. (2006) study conservative modifications of net
worth covenants conditional on their presence in a debt contract. Their evidence is consistent with my
findings. In another related study, Begley and Chamberlain (2005) do not find evidence that unconditional
conservatism (one of the dimensions of accounting quality they consider) benefits debt contracting. This
result is consistent with Ball and Shivakumar (2005), who argue that unconditional conservatism is of lower
value for debt contracting. Finally, a number of studies examine how conservatism affects the cost of debt
capital and the degree of information asymmetry between bondholders and the firm (Ahmed et al., 2003,
Zhang, 2005, Moerman, 2005).
While these findings are important for our understanding of accounting conservatism, the exact
mechanism through which the benefits of timely loss recognition are captured has not yet been investigated
empirically. A widely held view is that a substantial part of the improvement in contract efficiency (due to
a higher degree of conditional conservatism) is realized via the use of covenants that are included in
indentures (Watts, 2003, Ball and Shivakumar, 2005, Ball, Robin, and Sadka, 2005). However, a direct
link between timely loss recognition and debt contract design has yet to be established.
This study’s main contributions to the literature are twofold. First, I shed light on the role of accounting
choice and information properties in debt contract design.2 Prior research focuses on firms’ incentives to make
ex post accounting choices that decrease the likelihood of costly covenant violation. While some studies
find evidence that accounting choices are made to avoid covenant violations, others are inconclusive (see
Fields, Lys, and Vincent, 2001 for a review and discussion). One reason for these relatively weak findings
is that debt providers anticipate managerial incentives to make opportunistic accounting choices and thus
restrict the set of acceptable accounting practices (Watts and Zimmerman, 1990, 1986). I examine how
accounting that limits managerial choices ex post relates to the design of debt contracts ex ante. The 2 Debt contract design in the context of accounting also has received attention in Begley (1994), Bharath, Sunder, and Sunder (2006), Begley and Chamberlain (2005), Begley and Feltham (1999), Beatty, Ramesh, and Weber (2002), Beatty and Weber (2003), Press and Weinthrop (1990), and Sweeney (1994), among others.
7
analysis suggests that timely loss recognition can reduce the agency costs of debt via the use of protective
covenants.
The second contribution of this study relates to the empirical literature on the demand for financial
reporting quality (Ball, Kothari, and Robin 2001, Ball and Shivakumar 2005, Ball, Robin, and Sadka 2005).
Although it has been recognized that debt contracting is causally linked to conditional conservatism (Watts,
2003a, Holthausen and Watts, 2001), empirical evidence remains limited to cross-country and cross-market
examinations. More work is needed to investigate whether, while holding constant the properties of
accounting information at the macro level, a firm’s debt contracts influence its accounting choices. The
analysis in this study suggests that firm-level debt contracts put specific demands on the properties of
accounting information.
The next section reviews the related literature and describes the empirical predictions. Section III
develops the hypothesis and Section IV outlines the research method used in the paper. In Section V I
describe the data sources and variable definitions. Section VI reports the empirical findings, and finally, in
Section VII, I discuss limitations and conclude the study.
2.2. Background and Related Literature
The literature argues that debt markets create demand for conservative accounting. Evidence at the
aggregate level strongly supports this argument (Ball, Kothari, and Robin, 2000, Ball, Robin, and Sadka,
2006, Ball and Shivakumar, 2005). At the firm level, conservatism has been shown to improve contracting
efficiency via reductions in both the cost of debt (Ahmed et al., 2002, Zhang, 2005) and the degree of
information asymmetry (Moerman, 2006). In this section, I first discuss the role of debt covenants when
companies approach financial distress. Subsequently, I discuss the role of timely loss recognition in light of
positive accounting theory and argue that in order for covenants to be an effective contracting device, it is
necessary to have timely loss recognition policies in place. Consistent with the evidence in Beatty et al.
(2006), who find that the demand for conservatism is not entirely met via conservative contract
modifications, the discussion assumes that it is costly to substitute within-GAAP conditional conservatism
for a comprehensive set of adjustments to accounting numbers in a contract.
2.2.1. Role of debt covenants When a firm approaches financial distress, bondholders become more vulnerable to wealth
expropriation by managers or shareholders (Bodie and Taggert, 1978, Smith, Smithson, and Wilford, 1989,
Nash, Netter, and Poulsen, 2003). For instance, debt overhang (Myers, 1977), asset substitution (Jensen
and Meckling, 1976), and claim dilution (e.g., Nash et al., 2003) are well known conflict-of-interest
problems that become elevated in financially-troubled firms.3,4 Covenant restrictions reduce the ability of
3 Debt overhang, for example, is associated with a project requiring a sequence of investments. After the initial investments are sunk, managers do not internalize the losses that accrue to the debtholders if late investments are not
8
managers or owners to take actions in key areas such as investments, dividend payouts, and financing that
would benefit managers/owners at the expense of bondholders. For instance, covenants limiting
distributions of dividends to shareholders effectively force levered firms to invest and therefore alleviate
debt overhang associated with the potential unwillingness of managers to undertake positive net present
value projects. Covenants that restrict a firm’s asset sales, mergers and acquisitions, or lines of business
reduce the likelihood of asset substitution, that is, they represent obstacles for management to over-invest in
risky projects after obtaining debt financing. Finally, covenants that place restrictions on leases and sales-
and-lease back transactions as well as negative pledge covenants reduce claim dilution when firms issue
additional debt (possibly of higher priority), diluting the value of current bondholder claims due to a higher
probability of default.
2.2.2. What determines the degree of restrictiveness?
Because covenants that protect bondholders do not detect distress perfectly, they can become
binding while the firm is still financially healthy. As a result, covenants potentially decrease a manager’s
ability to make decisions that benefit the firm. Managers may have to forsake good investment projects
because they are not allowed to obtain additional financing, for instance, or they may not distribute excess
cash to shareholders because of the payout restrictions. Moreover, the costs of technical default and
renegotiation are significant (Beneish and Press, 1993, 1995). The trade-off between the costs and benefits
of covenants therefore plays a key role in the design of debt contracts (Smith and Warner, 1976, Begley,
1994, Nash et al., 2003).
Existing evidence is generally consistent with the trade-off view on the use of covenant restrictions.
On the one hand, covenants are used frequently when agency costs are expected to be high. Thus, default
risk, managerial entrenchment, corporate governance, and firm size are all associated with the use of
covenants (Malitz, 1986, Begley, 1994, Begley and Feltham, 1999, Chava, Kumar, and Warga, 2005).
Covenants also help reduce the cost of debt capital, presumably due to reduced agency costs of debt
(Chava, Kumar, and Warga, 2005, Bradley and Roberts, 2005, Reisel, 2005, Goyal, 2005).
On the other hand, firms forgo covenant use when the costs of restricting managerial discretion are
high. Thus, firms with growth opportunities (Nash, Netter, and Poulsen, 2003, Reisel, 2005, Chava,
Kumar, and Warga, 2005, Khan and Yermack, 1998) or firms in volatile environments (Anderson, 1999)
impose fewer debt covenants.5 Breadley and Roberts (2005) find that while high-growth companies restrict
the use of obtained funds, in line with the trade-off view they avoid constraints limiting their ability to raise
additional funds. made and the project lapses. This is more likely to happen in financial distress. More generally, debt overhang reduces incentives to invest and exert effort. 4 Asset substitution is an over-investment problem that arises when shareholders substitute riskier assets from the firms’ existing assets and expropriate value from the debtholders. 5 However, a number of studies suggest that high-growth, volatile firms may be perceived as more risky and thus that these firms include covenant constraints in their debt contracts (Nash, Netter, and Warga, 2005).
9
Next I discuss the role of timely loss recognition in contracts that include protective covenants.
Timely loss recognition enhances the efficiency of covenant use in two ways, namely, (1) by facilitating
early transfers of decision rights to bondholders and (2) signaling a firm’s credit quality.
2.2.3. Distress and timely loss recognition Timely loss recognition (conditional conservatism) represents a salient dimension of accounting
quality and is believed to play an efficiency-enhancing role in contracting. Recognizing losses in earnings
in a timely manner brings forward covenant violations in financially distressed firms. Thresholds specified
in covenants are commonly based on accounting information that is directly linked to reported earnings and
book values of assets, liabilities, and equity. Covenants are likely to be more efficient in mitigating the
agency problems associated with financial distress if the accounting numbers incorporate adverse economic
events in a more timely fashion, ensuring the early transfer of decision rights from managers to bondholders
when bondholders face greatest expropriation risk. As timely loss recognition increases the usefulness of
accounting information in debt contracts with accounting-based covenants, this creates a demand for
timeliness in recognizing economic losses. Consistent with this idea, economies in which public debt
financing plays a relatively more important role exhibit timelier loss recognition (Ball, Kothari, and Robin,
2000, Ball, Robin, and Sadka, 2005, Ball and Shivakumar, 2005, 2006b).
2.2.4. Covenants as a signaling device and timely loss recognition A helpful step towards understanding the concurrent use of covenants and conservative accounting
has been made by Levine and Hughes (2005), who model the use of accounting-based debt covenants in
tandem with the choice of conservative reporting. The authors demonstrate that the use of covenants
together with (conditionally) conservative reporting is an optimal contracting mechanism.6 In their model,
a firm seeks debt financing and signs two different contracts, a compensation contract with the manager and
a debt contract with lenders. The compensation contract aims at aligning managerial incentives. In the
absence of a bond covenant, firms with a lower risk of default can choose to design incentive compensation
sub-optimally (to signal its type to lenders) and thus engage in costly distortions relative to optimal
operating decisions. The introduction of a bond covenant based on earnings combined with conservative
measurement of earnings overcomes the need to incur these signaling costs. Bond covenants force the
“lesser type” firm into costly default early because the latter cannot mimic the covenant threshold set by the
“better type” firm.
More generally, the literature recognizes the signaling role of debt (Jensen, 1986, Harris and Raviv,
1990, Zwiebel, 1996) and of debt covenants in particular (Garleanu and Zwiebel, 2005, Chava et al., 2005,
Sridhar and Magee, 1996). Since default is costly, managers who are privately informed about a firm’s poor
future profitability or managers of firms suffering from agency problems will separate themselves by not
including performance-based covenants into their debt contracts; consequently, these firms will be forced to pay 6 In their stylized model, no distinction is made between conditional and unconditional conservatism. Nevertheless, conditional conservatism arguably fits the spirit of the model better as their result is driven by the downside risk bondholders face.
10
a higher risk premium. However, signaling through debt contracts with accounting-based covenants is unlikely
to be successful unless the accounting information exhibits timely loss recognition. Since reported performance
is directly related to a manager’s welfare, he has incentives to introduce bias and noise into accounting measures
used in contracts (Watts and Zimmerman, 1986, 1990, Watts, 2003a). Conditional conservatism curbs
managerial ability to bias accounting numbers upwards and enables covenants to perform the signaling role
better. In the absence of this property, lenders are unlikely to rely on covenant restrictions and will look for
other (costly) ways to mitigate agency problems that include increasing the risk premium, reducing the maturity
of the debt issue, or providing funds in small instalments.7
2.3. Hypothesis
The discussion in the preceding section suggests that the ability of covenant restrictions to detect
and prevent agency problems hinges crucially on the ability of the accounting information system to
generate conditionally conservative earnings numbers. To the extent this complementarity view obtains,
the inclusion of covenant restrictions in public debt contracts should be associated with a higher demand for
timely recognition of economic losses. Under an alternative view that firms can substitute timely loss
recognition with contract modifications, no (or even negative) association between covenants and timely
loss recognition is expected.
There are several potential mechanisms through which a positive association may obtain. First,
companies seeking to benefit from covenants as a contractual mechanism should anticipate the demand for
timely reporting and accordingly adopt timelier, i.e., more conditionally conservative, financial reporting ex
ante. 8 The rationale is that because debt contracts require consistency of accounting practices, the adoption
of more conservative policies is expected to take place in the years prior to the year in which a contract is
signed. There are many examples of conditionally conservative accounting policies. For example, a
company can commit ex ante to account for bad debts using the aging of receivables method. Under this
method bad debt expense is based on the age of accounts receivable, which brings the recognition of
adverse conditions forward more quickly than the percentage of sales method, which expenses a fixed
percentage of credit sales irrespective of their collectibility. An increase in collection periods (possibly due
to deteriorated financial health of major customers or to relaxed credit-granting policies) potentially is an
early signal of default. The aging of receivables method therefore is preferable from the lender’s
viewpoint. Appendix A provides a number of additional examples of timelier loss recognition policies.
Second, because the quality of firm-lender relationships can be of significant value to the company,
lenders can punish untimely loss recognition ex post. In particular, a firm failing to recognize losses in a
timely manner will tarnish its reputation and will subsequently suffer higher risk premia and/or more severe 7 See Nash et al. (2003) for a detailed discussion. 8 The restrictions in the form of timely loss recognition are placed on the set of accounting practices that ex ante are likely to decrease the likelihood of ex post managerial opportunism (Watts and Zimmerman, 1986, 1990).
11
contract terms upon future borrowing or renegotiations to waive the covenants. Additionally, if a firm
deviates from timely recognition of incurred losses, bondholders can discipline management by appealing
to the court. This implies that borrowers will be more careful in recognizing losses that would probably be
overlooked in the absence of accounting-based debt contracts.
The above discussion leads to the following hypothesis:
H1: Ceteris paribus, timely recognition of economic losses is increasing in the use of covenant
restrictions in public debt contracts.
2.4. Research Design
I begin by constructing four indices of debt contract restrictiveness to examine the relation between
restrictions placed on key managerial actions and the degree of asymmetric timeliness. Each index captures
the degree to which a debt contract is linked to accounting information. Thus, each index serves as a proxy
for (the inverse of) managerial flexibility in decision making.9 The individual indices are based on
restrictions of the following four types of restrictions:
1) Investment covenants. Covenants of this type restrict capital allocation, mergers and acquisitions,
and disposal of assets.
2) Distribution or payout covenants – restrict payments to shareholders or other entities.
3) Financing covenants – limit managerial ability to raise funds by issuing additional debt or
common/preferred stock or by conducting sale-and-leaseback transactions.
4) Control transfer covenants – facilitate transfer of control from shareholders to bondholders when
the company approaches financial distress.
I then construct an overall index of contract restrictiveness, which is the sum of the four individual indices.
For more details on the covenant restrictions that are used to construct each index, see Appendix B.
The costs and benefits of covenant use are likely to be determined in part by environmental
characteristics and characteristics specific to the firm. These characteristics are likely to reflect market
forces that also influence conservative reporting. For example, prior research shows that the book-to-
market ratio is correlated with the degree of asymmetric timeliness of loss recognition (Roychowdhury and
Watts, 2005) and, as a proxy for growth, also with covenant use (Nash et al., 2003). Other characteristics
such as size, volatility, leverage, and probability of default may be similarly correlated with both the
reliance on covenants and timely loss recognition. To control for these factors, I follow a two-stage
regression procedure. In the first stage I orthogonalize the indices of contract restrictiveness by regressing
the indices on firm-specific characteristics and separating out the unexplained variation in covenant use in
the form of a residual. Specifically, I regress the following model:
9 While I cannot observe whether a particular covenant is accounting-based, I rely on earlier evidence (e.g., Leftwich and Holthausen, 1983, Leftwich, 1981), which documents that many covenants (including covenants limiting distributions, financing, and mergers and acquisitions) are accounting-based or are associated with accounting numbers in an indirect fashion (see also Beneish and Press, 1993).
12
(1), DummiesYear Amount) alln(Princip*y)ln(Maturit*EI)Std.Dev(IBscore-Z*Losses ofNumber *
turns)Std.Dev(Re*Growth Assets*tBook/Marke*Leverage*Yield Dividend*ROA*ln(Assets)* Index enessRestrictiv
12
111098
7654
3210
ξααααααααααααα
+++++++
+++++++=
where the dependent variable is one of the five restrictiveness indices described above.
Intuitively, the residual in (1) proxies for situations in which the benefits of covenant use outweigh
their costs, i.e., the covenants are chosen to constrain (unobserved) agency problems. Identifying such
situations, while randomizing with respect to other factors that influence reporting incentives, is required to
address the research question.
The control variables in Equation (1) are included as prior research shows that they affect the use of
covenants (and hence are likely to be correlated with reporting properties). In particular, size, profitability,
volatility of returns, financial leverage, and Altman’s bankruptcy score (Z-score) are expected to be
correlated with protective covenants as they proxy for the probability of financial distress. Book-to-market
and growth in assets are likely to be associated with higher costs of covenant use, as retaining flexibility is
especially valuable in these firms, and variability of accounting income is expected to be associated with
higher costs of violating covenants. Dividend yield controls for costs (i.e., negative stock price effects)
associated with the inability to pay out a normal level of dividends. In addition, I include two debt contract
features that are used to overcome agency problems (and thus that could substitute for covenants), namely,
maturity and issue size. Finally, I include year dummies to control for possible trends in covenant use.10,11
In the second stage, I sort companies on unexplained variation in covenant use, ξ, and allocate them
to 10 decile portfolios. The degree of timely loss recognition is assessed for all firms in each portfolio.
Note that running the first-stage model to control for confounding factors avoids numerous interaction
terms and allows for a parsimonious second-stage model.12 Following Basu (1997), I measure timeliness of
loss recognition by regressing accounting income scaled by lagged price on annual returns, conditioning the
relationship on the sign of economic news (as proxied by the sign of the returns). Specifically, I estimate
the following model across covenant restrictiveness deciles:
10 Begley and Freeman (2004) show that the use of covenants in public debt contracts has declined. However, this does not seem to be the case for all types of restrictions. Using FISD data, the evidence in Billett, King, and Mauer (2005) and Chava, Kumar, and Warga (2005) suggests that while some covenants (e.g. dividend constraints) have become less popular, the frequency with which others (certain types of investing, financing, and control transfer restrictions) have been adopted has increased over time. 11 Developing a comprehensive set of variables that potentially affect the use of covenants is outside the scope of the paper; the primary reason for including these control variables is that they are potentially related to reporting quality and conservatism. 12 I do not follow a pooled one-stage approach with interaction terms for the following reasons: (i) the number of interaction terms in a single-stage model would equal four (the number of variables in the Basu (1997) model) times the number of control variables in Equation (1), which would lead to an over-parametrized specification; (ii) there is no reason to expect a linear increase in timely loss recognition across restrictiveness deciles; and (iii) the standard errors from a pooled regression would suffer from cross-sectional dependencies. See also, Kothari and Shanken (1992, p.186) for a discussion of single-stage versus two-stage regression models.
13
)2(,)0Ret(RetRet)0Ret(P/E 10101 ttttttt DD εββαα +<×++<+=−
where D(.) is an indicator dummy taking the value of unity when the condition inside the parentheses is
true, Et stands for year t earnings, Pt-1 is the price at the end of year t-1, and Rett is the annual market-
adjusted return over year t. The degree of asymmetric timeliness is measured by the coefficient β1 (or
alternatively, by β0+β1).
I employ several measurement time horizons (windows) surrounding the debt issue. Specifically, I
estimate the second-stage equation, Equation (2), over years –3 to –1, year –1, year +1, and years +1 to +3
relative to the year of issue. The purpose of examining pre-issue period is twofold. First, since lenders
scrutinize prior financial statements, pre-issue analysis reveals whether companies anticipating debt issues
change their accounting beforehand in an effort to enhance their reputation or simply to pre-commit to more
conservative accounting practices ex ante (Ball and Shivakumar, 2006b). Second, it is more difficult to
document asymmetric timeliness ex post as managers have incentives to introduce additional noise into
accounting numbers when trying to minimize the likelihood of covenant violations within the accepted set.
2.5. Data and Sample Construction
The data are taken from the Mergent Fixed Investment Securities Database (FISD), which is a
comprehensive database of publicly traded U.S. bonds. FISD contains information on a number of bond
characteristics including a bond’s principal amount, maturity, and price, but its distinguishing feature is that
it also contains detailed information about the presence of covenants in the bond indenture. Specifically, I
use 41 indicators of various types of covenants to construct the five contract restrictiveness indices
discussed in the previous section. I then cumulate the covenant indicators related to investment (INVEST),
financing (FINAN), distribution (DIST), and control transfer (CONTROL) decisions to compute the scores
for each of the four separate indices. The sum of these four indices represents the overall restrictiveness
index (OVERALL). Appendix B provides more details on the covenants used to construct the indices.
Balance sheet and income statement data are taken from the COMPUSTAT Industrial Annual
database and monthly return data are retrieved from CRSP. Panel A of Table 1 summarizes the sample
construction. Covenant information is available in FISD for 11,947 bond issues by 4,394 industrial
companies. I exclude financial firms because they are subject to different accounting rules and regulations.
After merging the remaining FISD data with COMPUSTAT and retaining only the first debt issue in a
given year (in order to give equal weight to all companies), the sample is reduced to 5,036 debt issues by
2,367 firms over the 1980-2004 period.13 Data availability requirements reduce the sample to 3,382 issues.
13 FISD data are very incomplete prior to 1980.
14
T a b l e 1 Sample and Descriptive Statistics
Note: Both Compustat and FISD variables are winsorised at the 1% population level
Panel A: Sample Construction No. Obs. Issues by industrial companies with available covenant data before merging to Compustat 11,947 Number of firms before merging to Compustat 4,394 Number of issues that merge to Compustat 7,310 Number of issuers that merge to Compustat 2,367 Number of issues after retaining only one issue per year 5,036 Number of issues after requiring non-missing data for control variables 3,382
Panel B: Descriptive Statistics Variable No. Obs. Mean St. Dev. Min Max OVERALL 4,999 8.370 4.565 0 26 INVEST 4,999 2.236 0.941 0 6 DISTR 4,999 0.736 0.944 0 3 FINAN 4,999 3.026 2.502 0 15 CONTROL 4,999 2.372 1.108 0 5 ln(Assets) 4,734 7.331 1.670 -0.805 10.41 Assets 4,734 4,895 7,784 0.447 33,207 ROA 4,564 -0.003 0.274 -2.896 0.488 Dividend Yield 4,386 0.011 0.017 0 0.091 Leverage 4,726 0.333 0.224 0 1.001 Book-to-Market 4,124 0.455 0.659 -4.17 4.584 Assets Growth 4,281 1.436 1.103 0.297 10.80 Std.Dev. of Returns 4,067 0.029 0.015 0.007 0.143 Number of losses over the last 5 years (nloss) 4,281 0.941 1.369 0 5 Altman’s Z-score 4,176 1.672 2.421 -46.28 9.08 Std. Dev. of IBEI 4,018 0.078 0.239 0 3.698 ln(Maturity) 4,987 2.274 0.589 0 4 ln(Principal Amount) 4,999 6.851 0.438 3.219 6.908
15
T a
b l
e 2
Cor
rela
tion
Stat
istic
s
The
tabl
e re
ports
Pea
rson
cor
rela
tion
stat
istic
s com
pute
d fo
r the
var
iabl
es u
sed
in E
quat
ion
(1).
See
Sect
ion
III o
f the
pap
er fo
r mor
e de
tails
on
varia
ble
defin
ition
s.
(1
) (2
) (3
) (4
) (5
) (6
) (7
) (8
) (9
) (1
0)
(11)
(1
2)
(13)
(1
4)
(15)
(1
6)
(1) O
VER
ALL
1.
00
(2) I
NV
EST
0.77
1.
00
(3) D
ISTR
0.
85
0.66
1.
00
(4) F
INA
N
0.93
0.
59
0.73
1.
00
(5) C
ON
TRO
L 0.
65
0.42
0.
43
0.43
1.
00
(6) l
n(A
sset
s)
-0.2
0 -0
.19
-0.3
7 -0
.08
-0.1
4 1.
00
(7) R
OA
-0
.07
-0.0
7 -0
.08
-0.0
1 -0
.11
0.18
1.
00
(8) D
ivid
end
Yie
ld
-0.2
0 -0
.22
-0.2
4 -0
.06
-0.3
3 0.
33
0.13
1.
00
(9) L
ever
age
0.38
0.
31
0.43
0.
31
0.24
-0
.16
-0.1
2 -0
.13
1.00
(10)
Boo
k-to
-Mar
ket
0.01
-0
.03
0.03
0.
04
-0.0
6 0.
05
0.07
0.
13
-0.1
9 1.
00
(11)
Gro
wth
in A
sset
s 0.
05
0.03
0.
07
-0.0
1 0.
11
-0.1
8 -0
.30
-0.1
8 0.
07
-0.0
4 1.
00
(12)
Std
.Dev
. (R
etur
ns)
0.17
0.
18
0.23
0.
03
0.28
-0
.38
-0.3
8 -0
.37
0.14
-0
.12
0.31
1.
00
(13)
Num
ber o
f los
ses
over
the
last
5 y
ears
0.
17
0.19
0.
21
0.07
0.
20
-0.2
3 -0
.28
-0.3
0 0.
32
-0.1
5 0.
14
0.42
1.
00
(14)
Altm
an’s
Z-s
core
-0
.09
-0.0
9 -0
.10
-0.0
4 -0
.12
0.07
0.
57
0.10
-0
.26
0.10
-0
.19
-0.3
0 -0
.42
1.00
(15)
Std
.Dev
.(IB
EI)
0.00
0.
03
0.02
-0
.05
0.07
-0
.21
-0.2
8 -0
.14
0.05
-0
.08
0.65
0.
27
0.29
-0
.28
1.00
(16)
ln(M
atur
ity)
-0.2
0 -0
.13
-0.1
5 -0
.15
-0.2
3 0.
02
0.11
0.
13
-0.0
8 0.
02
-0.0
6 -0
.24
-0.1
1 0.
10
-0.0
3 1.
00
(17)
ln(P
rinci
pal A
mou
nt)
0.06
0.
04
0.06
0.
07
0.01
-0
.06
0.00
-0
.02
0.00
-0
.01
0.01
-0
.01
-0.0
1 0.
04
0.01
-0
.05
16
2.5.1 Variable definitions
Income before extraordinary items (COMPUSTAT item data18) scaled by beginning of fiscal year
price (data199) times shares outstanding (data25) is used to measure the dependent variable in Equation (2)
( 1-/PE tt ). Returns (Rett) are compounded over a 12-month period starting three months after the beginning
of the fiscal year and are adjusted by subtracting the compounded return on a value-weighted market index.
The control variables in Equation (1) are measured in the year prior to the debt issue and are
defined as follows:
ln(Assets) = natural logarithm of total assets (data6);
ROA = return on assets, defined as income before extraordinary items (data18) divided by total assets
(data6);
Dividend Yield = dividends (data21) divided by end of year market value (data199 times data25);
Leverage = ratio of long-term debt (data9) to total assets (data6);
Book-to-Market = book value of equity (data60) divided by market value of equity (data199 times
data25);
Assets Growth = growth rate of total assets (data6);
Std.Dev.(Returns) = standard deviation of monthly returns in CRSP;
Std.Dev.(IBEI) = standard deviation of income before extraordinary items (data18) scaled by total
assets (data6), measured over the five years preceding the issue;
Number of Losses = number of times the company had a loss over the five years preceding a debt
issue;
Z-score = Altman’s bankruptcy score;14
ln(Maturity) = Natural logarithm of years to maturity;
ln(Principal Amount) = Natural logarithm of the amount to be repaid at maturity.
Table 1, Panel B provides summary statistics for these variables. To mitigate the influence of
outliers, I winsorize 1% of the extreme observations at the population level. The mean value of the overall
restrictiveness index (OVERALL) indicates that, on average, firms include 10 out of 41 restrictions in their
contracts. The standard deviation is 4.6, which suggests substantial cross-sectional variation; indeed, the
maximum number of covenant restrictions used by a single firm in the sample is 27, while the minimum is
zero. The average company has $4.9 billion in total assets, leverage of 33%, and book-to-market of 0.45.
Correlation statistics are provided in Table 2. The restrictiveness indices INVEST, DISTR,
FINAN, and CONTROL (respectively, investing-, distribution-, financing-, and control-related covenant
restrictions) exhibit high cross-correlations, ranging from 0.42 to 0.73. The correlations of these indices
with the overall restrictiveness index (OVERALL) are as high as 0.93. The evidence also suggests that the
correlations between debt contract restrictiveness and the control variables employed in the analysis are
14 See Nash et al. (2002) for details.
17
substantial. For example, the correlation coefficients between the overall index and leverage or size are
0.38 and -0.20, respectively.
2.6. Results
In this section I first present the results from estimating the first-stage model (Equation (1)). I then
turn to the second-stage analysis of the relation between asymmetric timeliness and different levels of
contract restrictiveness using the return-earnings specification (Equation (2)). Finally, I repeat the second-
stage analysis using instead the accrual-cash flow relation – an alternative measure of asymmetric
timeliness (Ball and Shivakumar, 2005).
2.6.1. Covenant equation Table 3 presents results of the first-stage estimation (Equation (1)) for each of the five restriction
indices used as the dependent variable. The model’s explanatory power is 32% for the overall restriction
index and ranges between 19% (financing restrictions) and 62% (transfer of control restrictions) for the
other four indices, indicating that there is a substantial amount of unexplained variation in covenant use that
can be exploited in the subsequent analysis.
As can be seen from the table, the coefficient on size indicates that in all models covenant restrictions are
used significantly less in larger firms. In contrast, ROA is positively associated with the use of covenants.
The dividend yield is not related to overall contract restrictiveness, although examination of its components
reveals that while dividend-paying firms try to avoid restrictions on distributions, investment activities, and
the use of other control-related covenants, they constrain financing activities more frequently. Leverage
and book-to-market are both positively related to covenant use. Firms in a fast changing environment, as
measured by the standard deviation of returns, avoid financing restrictions, but they include covenants on
distributions, investments, as well as other covenants.15 The evidence further suggests that growth in assets,
the frequency of past losses, and Z-score do not influence the use of covenants significantly in the presence
of other controls. Finally, the coefficient on maturity is significantly negative, whereas the principal
amount is significantly positively related to the inclusion of covenant restrictions.
These findings are broadly consistent with firms trading off the costs and benefits of covenant
restrictions. More frequent reliance on covenants among small firms (Malitz, 1986, Begley, 1994) and
among firms with high leverage (Begley, 1994, Nash et al., 2003) is consistent with the more pronounced
agency problems. Similarly, dividend-paying firms impose restrictions on investment and financing
activities, but at the same time seem to find it costly to constrain their dividend policy. In line with Levine
and Hughes (2005) and Chava et al. (2005), who argue that “good” firms signal their type via covenant
inclusion, while firms with higher default risk will find this costly, firms with stronger profitability have
15 This parallels the evidence in Breadley and Roberts (2005), who show that high-growth firms restrict the use of funds, while avoiding restrictions on future financing. Firms with more volatile income also appear to avoid the use of covenants, in their study.
18
T a b l e 3 Determinants of Covenant Restrictiveness
Covenant data are taken from Fixed Income Securities Database (which contains more than 40 covenant indicators). Five different contract restrictiveness indexes are constructed: an overall covenant restriction index, an investment covenant restrictions index, a distribution covenant restrictions index, a financing covenant restrictions index, and a transfer of control covenant restrictions index. Each index is constructed by cumulating corresponding covenant indicators for a particular contract. The following multiple regression is estimated:
(1), DummiesYear Amount) alln(Princip*y)ln(Maturit*EI)Std.Dev(IBscore-Z*Losses ofNumber *
turns)Std.Dev(Re*Growth Assets*tBook/Marke*Leverage*Yield Dividend*ROA*ln(Assets)* Index enessRestrictiv
12
111098
7654
3210
ξααααααααααααα
+++++++
+++++++=
Dependent Variable
Independent Variable Statistic
Overall Restrictions
Investment Restrictions
Distribution Restrictions
Financing Restrictions
Control Covenants
ln(Assets) Estimate -0.350*** -0.061*** -0.133*** -0.054* -0.101*** t-value (-7.34) (-5.95) (-13.38) (-1.88) (-11.05)
ROA Estimate 1.062** 0.171* 0.260*** 0.566** 0.065 t-value (2.40) (1.79) (2.81) (2.11) (0.76)
Dividend Yield Estimate 1.186 -3.272*** -2.163** 10.894*** -4.274*** t-value (0.26) (-3.27) (-2.23) (3.87) (-4.81)
Leverage Estimate 6.444*** 0.934*** 1.512*** 3.282*** 0.716*** t-value (19.17) (12.88) (21.48) (16.08) (11.13)
Book-to-Market Estimate 0.730*** 0.093*** 0.187*** 0.347*** 0.104*** t-value (7.02) (4.14) (8.59) (5.49) (5.20)
Assets Growth Estimate -0.012 -0.029 0.019 -0.025 0.022 t-value (-0.14) (-1.54) (1.07) (-0.47) (1.32)
Std. Dev. Of Returns Estimate 10.121* 2.679* 5.396*** -0.521** 2.567* t-value (1.77) (2.18) (4.52) (-0.15) (2.35) Number of losses over the last 5 years Estimate 0.058 0.022* 0.018 -0.003 0.020* t-value (0.06) (0.02) (0.02) (0.00) (0.02)
Altman’s Z-score Estimate 0.030 -0.004 -0.002 0.017 0.019** t-value (0.74) (-0.44) (-0.21) (0.69) (2.39)
Std. Dev. (IBEI) Estimate -0.944*** -0.035 -0.268*** -0.432** -0.210*** t-value (-2.87) (-0.49) (-3.89) (-2.16) (-3.32)
ln(Maturity) Estimate -0.490*** -0.027 -0.082*** -0.345*** -0.036* t-value (-4.71) (-1.21) (-3.76) (-5.46) (-1.81)
ln(Principal) Estimate 0.607*** 0.078** 0.056* 0.360*** 0.114*** t-value (3.99) (2.37) (1.76) (3.89) (3.90) Adjusted R-squared 31.6/% 19.9/% 27.6/% 19.2/% 62.1/% Number of Observations 3,382 3,382 3,382 3,382 3,382
19
more restrictive debt contracts. The findings also suggest that firms with unexercised growth options will
prefer to retain managerial flexibility and thus will avoid the use of covenants (Begley, 1994, Nash et al.,
2003, Khan and Yermack, 1998). Volatile firms value flexibility and avoid the inclusion of financing
restrictions, while at the same time these firms are perceived as risky and thus they include other types of
restrictions in their lending contracts. Finally, contract design choices such as the size of issue seem to
substitute for covenants and hence appear to help mitigate possible conflicts of interest.
2.6.2. Main results
Table 4 presents the parameters of Equation (2) estimated across ten restrictiveness deciles. The
deciles are based on the residual from the first-stage model (Equation (1)) and are labeled Q1 (lowest
restrictiveness) through Q10 (highest restrictiveness). Panel A and Figure 1 report the evidence based on
the overall contract restrictiveness index, while the evidence in Panels B through E is based on the separate
analyses of investment, distribution, financing, and control transfer covenants, respectively. For brevity, β1
and R2 statistics are reported in Panel A only.
From Panel A it can be seen that across all four time horizons around the debt issue that I consider
(first column), β1 is both statistically and economically higher for the tenth decile (Q10) of the overall
restrictiveness index as compared to the first decile (Q1). More specifically, for companies in Q1 the
estimates of β1 are 0.28 for years –3 to –1, 0.30 for year –1, 0.25 for year +1, and 0.34 for years +1 to +3,
while their Q10 counterparts are 0.53, 0.66, 0.53, and 0.50, respectively.
The same pattern arises when examining each of the other restrictiveness indices. The analysis of
the investment restrictions (Panel B) indicates that the differences calculated by subtracting the estimate of
β1 for companies in Q10 from the estimate of β1 for those in Q1 are 0.12, 0.29, 0.27, and 0.22 for years –3
to –1, year –1, year +1, and years +1 to +3, respectively. Similarly, the differences based on the index of
financing constraints (Panel D) are 0.26, 0.35, 0.58, and 0.39, respectively, for the same horizons. All these
differences are statistically significant at conventional levels. The evidence based on the distribution
restrictiveness index (Panel C) suggests that differences in the Q10 and Q1 estimates of β1 are positive but
small in magnitude and statistically insignificant. This result is driven by the very large coefficients for Q1
firms, which drop considerably in magnitude in the second decile of distribution restrictions (Q2) and
suggest an increasing pattern in β1 as we move towards the higher distribution restrictiveness deciles.
Finally, the analysis of transfer of control covenants (Panel E) reveals that over years –3 to –1 and over year
–1, Q10-Q1 differences in β1 are positive and statistically significant (0.22 and 0.30, respectively). These
differences become statistically indistinguishable from zero for years +1 and years +1 to +3, but they still
remain positive.
Overall, the evidence in Table 4 supports the hypothesis that firms that rely more on covenants
exhibit increased levels of timely loss recognition. In addition, an examination of the coefficients of
determination (R2) reveals patterns that are generally increasing. This evidence provides additional support
20
T a
b l
e 4
A
sym
met
ric
Tim
elin
ess o
f Ear
ning
s: S
tock
Ret
urn
Evi
denc
e Es
timat
es fr
om a
pie
cew
ise-
linea
r reg
ress
ion
of e
arni
ngs
on re
turn
s, co
nditi
onal
on
the
sign
of
“eco
nom
ic n
ews,”
are
est
imat
ed a
cros
s te
n de
cile
s of
con
tract
restr
ictiv
enes
s, Q
1 to
Q10
. Fiv
e ty
pes
of c
oven
ant r
estri
ctio
n in
dice
s are
con
side
red:
ove
rall
restr
ictio
ns, i
nves
tmen
t res
trict
ions
, dist
ribut
ion
restr
ictio
ns, f
inan
cing
restr
ictio
ns, a
nd tr
ansf
er o
f co
ntro
l res
trict
ions
. Eac
h in
dex
is b
ased
on
the
resi
dual
from
mod
el (1
) as
repo
rted
in T
able
3. I
n pa
rticu
lar,
each
inde
x is
con
struc
ted
by c
umul
atin
g th
e co
vena
nt in
dica
tors
pr
esen
t in
a gi
ven
cont
ract
. Ear
ning
s ar
e m
easu
red
by in
com
e be
fore
ext
raor
dina
ry it
ems
(dat
a18)
sca
led
by y
ear -
1 m
arke
t val
ue (C
ompu
stat
item
s da
ta19
9*da
ta25
); re
turn
s ar
e co
mpo
unde
d ov
er th
e 12
mon
ths s
tarti
ng th
ree
mon
ths a
fter t
he fi
scal
yea
r-en
d ar
e ad
just
ed b
y su
btra
ctin
g th
e re
turn
on
the v
alue
-wei
ghte
d m
arke
t ind
ex c
ompo
unde
d ov
er
the
sam
e pe
riod.
To
miti
gate
the
influ
ence
of o
utlie
rs 0
.5/%
of s
cale
d ea
rnin
gs a
nd re
turn
s ar
e ex
clud
ed fr
om b
oth
tails
. ***
, **,
* in
dica
te th
e si
gnifi
canc
e at
the
1/%
, 5/%
, an
d 10
/% le
vels
, res
pect
ivel
y. T
he m
odel
is:
.)0
Ret
(*
Ret
*R
et*
)0R
et(
*P/
Et
t1
t0
t1
01
tt
tD
Dε
ββ
αα
+<
++
<+
=−
Yea
rs R
elat
ive
to I
ssue
C
oef.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q
10-Q
1 Pa
nel A
: Ove
rall
Res
tric
tions
-3
to -1
β 0
-0
.044
-0
.041
-0
.026
-0
.004
-0
.013
-0
.041
-0
.022
-0
.031
-0
.014
-0
.054
-0
.010
β 1
0.27
9 0.
217
0.19
7 0.
252
0.19
4 0.
242
0.23
6 0.
221
0.35
8 0.
525
0.24
5***
R2 0.
06
0.06
0.
06
0.09
0.
05
0.05
0.
06
0.04
0.
07
0.10
-1
β 0
-0
.016
-0
.004
-0
.017
-0
.050
0.
002
-0.0
56
-0.0
46
-0.0
40
0.02
5 -0
.109
-0
.093
***
β 1
0.
295
0.21
5 0.
257
0.29
5 0.
033
0.15
6 0.
281
0.19
6 0.
254
0.66
1 0.
366*
**
R2
0.06
0.
08
0.09
0.
10
0.01
0.
05
0.06
0.
02
0.06
0.
13
+1
β 0
-0.0
95
-0.0
40
-0.1
83
-0.1
08
0.04
2 -0
.070
0.
019
-0.0
23
-0.0
59
-0.0
05
0.09
0
β 1
0.24
8 0.
296
0.39
8 0.
322
0.09
1 0.
299
0.21
9 0.
257
0.60
2 0.
525
0.27
7**
R2
0.04
0.
12
0.23
0.
11
0.03
0.
14
0.10
0.
06
0.22
0.
20
+1 to
+3
β 0
-0.0
95
-0.0
76
-0.1
30
-0.0
91
-0.0
37
-0.0
20
-0.0
15
-0.0
20
-0.1
05
-0.0
48
0.04
8
β 1
0.33
9 0.
364
0.31
8 0.
390
0.24
6 0.
232
0.26
0 0.
520
0.62
1 0.
501
0.16
2*
R2
0.06
0.
11
0.09
0.
11
0.07
0.
08
0.08
0.
12
0.20
0.
11
Pa
nel B
: Inv
estm
ent R
estr
ictio
ns
-3 to
-1
β 1
0.31
9 0.
277
0.19
6 0.
144
0.18
4 0.
242
0.25
4 0.
374
0.29
7 0.
444
0.12
4*
-1
β 1
0.27
5 0.
279
0.17
5 0.
116
0.04
4 0.
261
0.21
8 0.
322
0.27
6 0.
567
0.29
2***
+1
β 1
0.
374
0.25
2 0.
136
0.49
0 0.
131
0.31
1 0.
362
0.53
6 0.
381
0.64
5 0.
271*
+1
to +
3 β 1
0.
356
0.30
0 0.
263
0.35
8 0.
284
0.26
5 0.
405
0.55
3 0.
519
0.58
0 0.
224*
*
21
Tab
le 4
: Con
tinue
d
Yea
rs R
elat
ive
to I
ssue
C
oef.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q
10-Q
1 Pa
nel C
: Dis
trib
utio
n R
estr
ictio
ns
-3 to
-1
β 1
0.36
8 0.
171
0.14
1 0.
142
0.10
8 0.
169
0.38
8 0.
367
0.39
5 0.
320
-0.0
49
-1
β 1
0.31
6 0.
128
0.11
3 0.
144
0.01
7 0.
100
0.41
0 0.
295
0.40
7 0.
444
0.12
8 +1
β 1
0.
374
0.09
0 0.
331
0.18
7 0.
358
0.42
7 0.
280
0.48
7 0.
448
0.43
9 0.
065
+1 to
+3
β 1
0.43
0 0.
239
0.26
0 0.
228
0.30
6 0.
292
0.54
5 0.
558
0.52
0 0.
429
-0.0
01
Pane
l D: F
inan
cing
Res
tric
tions
-3
to -1
β 1
0.
299
0.20
4 0.
208
0.27
3 0.
259
0.24
8 0.
141
0.24
1 0.
305
0.55
6 0.
257*
**
-1
β 1
0.29
9 0.
237
0.15
4 0.
226
0.21
8 0.
120
0.29
5 0.
262
0.25
1 0.
644
0.34
5***
+1
β 1
0.
224
0.15
3 0.
666
0.18
2 0.
221
0.13
8 0.
274
0.23
9 0.
405
0.80
5 0.
581*
**
+1 to
+3
β 1
0.33
2 0.
236
0.56
4 0.
284
0.22
4 0.
239
0.42
5 0.
299
0.48
7 0.
719
0.38
7***
Pa
nel E
: Con
trol
Cov
enan
ts
-3 to
-1
β 1
0.23
0 0.
356
0.31
0 0.
300
0.26
9 0.
333
0.21
6 0.
133
0.31
4 0.
450
0.21
9***
-1
β 1
0.
188
0.26
5 0.
384
0.28
3 0.
169
0.28
5 0.
275
0.11
4 0.
416
0.48
3 0.
295*
**
+1
β 1
0.30
6 0.
438
0.37
9 0.
596
0.23
0 0.
565
0.41
7 0.
185
0.37
9 0.
345
0.03
9 +1
to +
3 β 1
0.
466
0.38
8 0.
460
0.46
5 0.
346
0.52
7 0.
407
0.18
3 0.
311
0.43
9 -0
.027
22
Figure 1: Timely Loss Recognition and Overall Contract Restrictiveness: Return-Earnings Evidence
The figure depicts the β1 coefficients from the piecewise-linear regression estimated over ten deciles, Q1 to Q10, and based on the orthogonalized overall contract restrictiveness index. The evidence, based on Table 4, comes from the following regression:
.)0Ret(*Ret*Ret*)0Ret(*P/E tt1t0t101 ttt DD εββαα +<++<+=−
Figure 1a: Years –3 to –1
0.00
0.10
0.20
0.30
0.40
0.50
0.60
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
Figure 1b: Year –1
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
Figure 1c: Year +1
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
1 2 3 4 5 6 7 8 9 10Deciles, Q1 to Q10
Figure 1d: Years +1 to +3
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
23
to the hypothesis that covenant usage is positively related to the timeliness with which negative economic
news is reported in accounting income.
The discussion thus far has been on the highest and the lowest deciles of debt contract
restrictiveness. Note that the pattern in β1 estimates does not appear to be linear. Specifically, the pattern in
the coefficients for the lower part of the restrictions’ distribution is rather flat and in some cases it is even
slightly downward sloping, but we observe a substantial increase in the estimates of β1 as we approach the
highest restrictions’ deciles.16 The increase is consistent with complementarity: as the timely loss
recognition increases, the marginal gain in contracting efficiency due to covenants also increases and hence
both mechanisms reinforce each other. In contrast, the slightly downward-sloping relation in the lowest
restrictiveness portfolios is consistent with covenants being a substitute for the asymmetric timeliness at the
other extreme.17 Figure 1 illustrates these patterns and reveals further that the estimated parameters from
Equation (2) are quite volatile.18 To assess formally whether there is a significant trend in the asymmetric
timeliness estimates across restrictiveness deciles, I perform additional correlation and regression analyses
as discussed next.
For each combination of time horizon and type of restriction index in Table 4, using ten
observations I form the decile rank d, which ranges from 1 for the lowest restrictiveness decile (Q1) to 10
for the highest decile of contract restrictiveness (Q10). I then calculate both the Pearson and the Spearman
correlations between d and β1, d and β0+β1, as well as d and R2. I also run the regression
υφφβ +⋅+= ddr 10
ˆ ,
where d ∈ 1,…,10 is the restrictiveness decile rank and drβ ∈β0, β1, β0+β1, R2 measures the degree of
timely loss recognition. The coefficient 1φ gives the average increase in the timeliness of loss recognition
that occurs by moving to the next contract restrictiveness decile.
Table 5 presents the results of this analysis. Panel A reports correlations based on the overall
restrictiveness index. The results reveal that the decile rank (d) is strongly correlated with estimates of β1
(and β0+β1), with Pearson correlation coefficients of 0.60, 0.38, 0.47, and 0.54 (0.63, 0.34, 0.72, and 0.71)
for years –3 to –1, year –1, year +1, and years +1 to +3, respectively. The evidence based on Spearman
correlations yields very similar results. Turning to the regression analysis, the estimates of 1φ for the
overall restrictiveness index are similar across all time horizons and imply that as contract restrictiveness 16 A related issue is whether there is a certain threshold beyond which further increases in conditional conservatism become prohibitively costly as they would provoke too frequent covenant violations. The findings suggest, however, that even if such a threshold exists, in practice it is not binding. 17 This substitution may be due to the usefulness of conservatism in curbing agency problems unrelated to debt contracts (e.g., compensation contracts), which in turn may diminish the overall level of the agency problems and lead to a lesser use of covenants. 18 This is not necessarily surprising as the number of observations in the analysis is rather limited, while the estimates in the piecewise linear regression of returns on earnings are substantially influenced by the extremes of the distribution.
24
T a b l e 5 Trends in Asymmetric Timeliness Estimates from the Basu (1997) model estimated across 10 Debt
Contract Restrictiveness Deciles This table analyzes trends in coefficients and R2s (reported in Table 4) from the piecewise-linear regression of earnings on returns (allowing for a differential effect of positive versus negative returns on earnings) estimated around the year of a debt issue across 10 deciles of each of five contract restrictiveness proxies. In particular, the table reports Pearson and Spearman correlations between abnormal contract restrictiveness decile ranks and their corresponding estimated coefficients (from Table 4). In addition, the table reports the slope from the regression of estimated regression coefficients from Table 3 on their decile ranks. The following model is estimated:
υφφβ +⋅+= dd10
ˆ ,
where d ∈ 1,..,10 is the decile rank and βd∈β0, β0, β0+β1, R2 is the decile estimate for the given type of restrictiveness measure. Significance levels for Pearson and Spearman correlation coefficients are based on ten observations (i.e., eight degrees of freedom); for coefficient φ 1 the significance is reported based on a Normal distribution, as φ1 is a linear combination of asymptotically normal estimates. Panel A: Overall Restrictiveness Horizon Statistic ρPearson
P-value ρSpearman P-value φ1 t-stat P-value -3 to t-1 β0 -0.009 (0.981) -0.006 (0.987) 0.000 -0.02 (0.981) β1 0.604 (0.064) 0.418 (0.229) 0.020 2.14 (0.032) β0+β1 0.639 (0.047) 0.527 (0.117) 0.020 2.35 (0.019) R2 0.265 (0.458) 0.139 (0.701) 0.002 0.78 (0.436)
-1 β0 -0.391 (0.264) -0.297 (0.405) -0.005 -1.20 (0.229) β1 0.382 (0.276) -0.006 (0.987) 0.020 1.17 (0.242) β0+β1 0.340 (0.337) 0.200 (0.580) 0.015 1.02 (0.307) R2 0.032 (0.931) 0.018 (0.960) 0.000 0.09 (0.929)
+1 β0 0.485 (0.156) 0.503 (0.138) 0.011 1.57 (0.117) β1 0.471 (0.169) 0.358 (0.310) 0.023 1.51 (0.131) β0+β1 0.723 (0.018) 0.624 (0.054) 0.034 2.96 (0.003) R2 0.359 (0.308) 0.261 (0.467) 0.009 1.09 (0.276)
+1 to +3 β0 0.458 (0.183) 0.394 (0.260) 0.006 1.46 (0.145) β1 0.544 (0.104) 0.406 (0.244) 0.023 1.83 (0.067) β0+β1 0.711 (0.021) 0.600 (0.067) 0.030 2.86 (0.004) R2 0.531 (0.114) 0.539 (0.108) 0.007 1.77 (0.076)
Panel B: Correlations for Separate Restriction Types Investment Restrict. Distribution Restrict. Financing Restrict. Control Transfer Horizon Statistic ρPearson
P-value ρPearson P-value ρPearson
P-value ρPearson P-value
-3 to -1 β0 0.006 (0.99) -0.014 (0.97) -0.066 (0.86) 0.637 (0.05) β1 0.513 (0.13) 0.47 (0.17) 0.461 (0.18) 0.13 (0.72) β0+β1 0.582 (0.08) 0.496 (0.15) 0.497 (0.14) 0.406 (0.24)
-1 β0 -0.715 (0.02) -0.464 (0.18) -0.566 (0.09) 0.08 (0.83) β1 0.509 (0.13) 0.581 (0.08) 0.495 (0.15) 0.391 (0.26) β0+β1 0.362 (0.30) 0.52 (0.12) 0.351 (0.32) 0.43 (0.22)
+1 β0 0.242 (0.50) 0.408 (0.24) 0.198 (0.58) 0.46 (0.18) β1 0.571 (0.09) 0.617 (0.06) 0.406 (0.24) -0.175 (0.63) β0+β1 0.757 (0.01) 0.734 (0.02) 0.59 (0.07) 0.208 (0.56)
+1 to +3 β0 0.154 (0.67) 0.339 (0.34) 0.203 (0.58) 0.613 (0.06) β1 0.774 (0.01) 0.614 (0.06) 0.484 (0.16) -0.403 (0.25) β0+β1 0.782 (0.01) 0.677 (0.03) 0.667 (0.04) 0.003 (0.99)
25
increases by 10% (one decile), on average the magnitude of β1 (β0+β1) increases by approximately 0.02
(0.015 to 0.03, depending on the horizon). The magnitude of this effect is economically substantial and,
while based on only ten observations, the estimates in Panel A are mostly statistically significant.
Next, I repeat the analysis separately for each of the component indices that comprise the overall
restrictiveness index and find similar results. For brevity, Panel B reports Pearson correlations only. The
evidence on investing restrictions indicates that the asymmetric timeliness estimates are positively
correlated with the decile rank d. The correlation coefficients depend on the time horizon and are as high as
0.51, 0.51, 0.57, and 0.77 for β1 and 0.58, 0.36, 0.75, and 0.78 for β0+β1 for years –3 to –1, year –1, year
+1, and years +1 to +3. Over the same four horizons, analysis of restrictions on distributions yields
correlation coefficients of 0.47, 0.58, 0.62, and 0.61 for β1 and 0.50, 0.52, 0.73, and 0.68 for β0+β1, and the
evidence based on financing restrictiveness yields correlation coefficients of 0.46, 0.50, 0.41, and 0.48 for
β1 and 0.50, 0.35, 0.59, and 0.67 for β0+β1. The magnitudes of 1φ (not tabulated) are similar across the
investing, distribution, and financing restrictiveness indices and range from 0.015 to 0.038 across the three
panels. Finally, as in Table 4, the results based on the transfer of control covenants indicate a positive
correlation between decile rank d and asymmetric timeliness estimates only for years –3 to –1 and year –1.
Together the evidence in Tables 4 and 5 suggests that we cannot reject the positive association
between covenant use and asymmetric timeliness. This evidence is consistent with the hypothesis that the
use of accounting-based covenants creates demand for timely loss recognition and that firms respond by
limiting their discretion ex ante.19
2.6.3. Accrual-based measure of asymmetric timeliness Following Ball and Shivakumar (2005), I also use an alternative measure of asymmetric timeliness
based on the relation between cash flows and accruals. Accruals are used to incorporate revisions of the
present value of future cash flows into the income statement. Therefore, in addition to reducing the noise in
cash flows from operations (Dechow, 1994), accruals allow for the timely recognition of economic gains
and losses. Since the demand for economic loss recognition is higher than that for gains, accruals are used
to recognize economic losses in a timely manner while economic gains are more likely to be accounted for
on a cash basis, i.e., when realized. As a result, a positive but asymmetric correlation arises between cash
flows and accruals. I estimate the following piecewise-linear regression to measure the degree of
asymmetric timeliness of loss recognition, 1β .
)3(,)0CFO(CFOCFO)0CFO(ACC 1010 tttttt DD εββαα +<×++<+=
19 It may happen that this effect is due in part to prior debt issues, as contracts usually do not differ substantially within the same firm. A direct examination of this issue is difficult because of truncation and limited coverage of FISD before the 1990s, while some maturities exceed 50 years.
26
T a
b l
e 6
A
sym
met
ric
Tim
elin
ess a
nd th
e Sm
ooth
ing
Effe
ct o
f Ear
ning
s: A
ccru
als E
vide
nce
Estim
ates
from
a p
iece
wis
e lin
ear
regr
essi
on o
f acc
rual
s on
cas
h flo
ws,
cond
ition
al o
n “c
ash
flow
new
s,” a
re e
stim
ated
acr
oss
the
deci
les
of c
ontra
ct r
estri
ctiv
enes
s, Q
1 to
Q
10. F
ive
type
s of
cov
enan
t res
trict
ion
indi
ces
are
cons
ider
ed: o
vera
ll re
stric
tions
, inv
estm
ent r
estri
ctio
ns, d
istri
butio
n re
stric
tions
, fin
anci
ng r
estri
ctio
ns a
nd o
ther
con
trol
cove
nant
s. Ea
ch in
dex
is b
ased
on
the
resi
dual
from
mod
el (1
) as r
epor
ted
in T
able
3. I
n pa
rticu
lar,
each
inde
x is
con
stru
cted
by
cum
ulat
ing
the
cove
nant
indi
cato
rs p
rese
nt in
a
give
n co
ntra
ct. A
ccru
als
are
mea
sure
d by
sub
tract
ing
cash
flow
from
ope
ratio
ns (d
ata3
08) f
rom
cas
h flo
w s
tate
men
t ear
ning
s (d
ata1
23),
both
sca
led
by la
gged
tota
l ass
ets.
To m
itiga
te th
e in
fluen
ce o
f out
liers
0.5
/% o
f sca
led
earn
ings
and
retu
rns
are
excl
uded
from
bot
h ta
ils. *
**, *
*, *
indi
cate
the
sign
ifica
nce
at th
e 1/
%, 5
/%, a
nd 1
0 /%
leve
ls,
resp
ectiv
ely.
The
mod
el is
: .
)0C
FO(
*A
sset
s/
CFO
*A
sset
s/
CFO
*)0
CFO
(*
Ass
ets
/A
ccru
als
11
10
10
1t
tt
tt
tt
tt
DD
εβ
βα
α+
<+
+<
+=
−−
−
Yea
rs R
elat
ive
to I
ssue
C
oef.
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q
10-Q
1 Pa
nel A
: Ove
rall
Res
tric
tions
-3
to -1
β 0
-0
.285
-0
.431
-0
.288
-0
.504
-0
.527
-0
.432
-0
.527
-0
.486
-0
.588
-0
.657
-0
.372
***
β 1
0.
451
0.31
6 0.
586
0.80
8 0.
864
1.07
1 0.
816
0.84
7 0.
923
1.00
4 0.
552*
**
R
2 0.
05
0.09
0.
11
0.22
0.
15
0.19
0.
18
0.14
0.
23
0.14
-1
β 0
-0
.288
-0
.365
-0
.412
-0
.556
-0
.506
-0
.46
-0.5
32
-0.6
09
-0.6
38
-0.8
66
-0.5
78**
*
β 1
0.34
3 0.
35
0.97
7 1.
216
0.73
5 1.
264
1.73
7 1.
167
1.77
7 1.
346
1.00
2***
R2
0.05
0.
03
0.28
0.
29
0.07
0.
25
0.13
0.
28
0.49
0.
26
+1
β 0
-0.4
52
-0.3
07
-0.3
76
-0.3
94
-0.7
97
-0.4
17
-0.3
62
-0.4
73
-0.5
22
-0.4
5 0.
002
β 1
0.
425
0.49
3 0.
2 -0
.13
0.52
8 0.
291
0.98
2 0.
491
0.46
6 0.
772
0.34
8
R2
0.06
0.
02
0.17
0.
09
0.29
0.
26
0.09
0.
07
0.12
0.
09
+1 to
+3
β 0
-0.4
84
-0.3
42
-0.4
24
-0.4
18
-0.5
87
-0.4
46
-0.3
03
-0.3
86
-0.5
10
-0.4
81
0.00
4
β 1
0.67
4 0.
575
0.26
0 0.
071
1.12
3 0.
266
0.35
8 0.
407
0.36
3 1.
087
0.41
3**
R
2 0.
08
0.05
0.
18
0.08
0.
32
0.22
0.
08
0.06
0.
14
0.12
Pane
l B: I
nves
tmen
t Res
tric
tions
-3
to -1
β 1
0.
508
0.53
7 0.
654
0.79
8 0.
941
0.06
7 0.
663
0.51
5 0.
826
1.30
3 0.
795*
**
-1
β 1
0.41
9 0.
253
0.82
3 1.
229
1.17
2 -1
.018
1.
124
0.80
4 1.
083
1.81
7 1.
398*
**
+1
β 1
0.31
5 -0
.18
0.57
3 0.
348
0.12
5 0.
569
0.33
5 -0
.291
0.
546
0.97
4 0.
660*
**
+1 to
+3
β 1
0.62
4 -0
.17
0.79
7 0.
495
0.76
5 0.
392
0.42
8 -0
.188
0.
477
1.11
1 0.
487*
**
27
Tab
le 6
. Con
tinue
d.
Yea
rs R
elat
ive
to I
ssue
C
oef
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q
10-Q
1 Pa
nel C
: Dis
trib
utio
ns R
estr
ictio
ns
-3 to
-1
β 1
0.55
8 0.
516
0.56
2 0.
761
0.73
6 0.
326
1.29
9 0.
7 0.
829
1.15
3 0.
596*
**
-1
β 1
0.66
4 0.
545
1.17
1 0.
993
1.27
6 0.
083
0.79
9 1.
379
1.57
8 0.
002
-0.6
62**
* +1
β 1
0.
382
0.57
0.
583
0.2
0.23
-1
.826
0.
631
0.45
8 1.
371
0.49
3 0.
112
+1 to
+3
β 1
0.52
7 0.
781
0.43
1 0.
842
0.29
1 -1
.269
0.
687
0.55
7 0.
891
0.57
0.
043
Pane
l D: F
inan
cing
Res
tric
tions
-3
to -1
β 1
0.
435
0.59
0.
523
0.51
8 0.
935
0.89
7 0.
524
1.36
5 0.
869
0.90
6 0.
471*
**
-1
β 1
0.58
3 0.
715
0.49
4 0.
639
1.03
1.
254
1.49
5 1.
754
1.38
1 1.
05
0.46
7**
+1
β 1
0.48
2 0.
316
0.60
6 0.
386
0.57
9 0.
155
-0.8
02
0.11
4 0.
799
0.43
7 -0
.045
+1
to +
3 β 1
0.
745
0.53
6 0.
193
0.95
1 0.
503
0.20
9 -0
.086
0.
864
0.50
9 0.
867
0.12
1 Pa
nel E
: Con
trol
Cov
enan
ts
-3 to
-1
β 1
0.36
4 0.
543
0.81
6 0.
612
1.02
0.
688
0.81
1 1.
023
0.80
1 0.
949
0.58
5***
-1
β 1
0.
403
0.49
7 0.
931
0.74
1 0.
609
1.55
1 1.
206
1.23
8 1.
188
1.46
9 1.
067*
**
+1
β 1
0.70
8 0.
39
0.41
7 0.
422
0.47
3 0.
468
0.17
5 0.
364
0.40
5 0.
542
-0.1
66
+1 to
+3
β 1
0.49
4 0.
431
0.38
1 0.
857
0.68
5 0.
386
0.83
6 0.
088
0.47
8 0.
453
-0.0
41
28
Figure 2: Timely Loss Recognition and Overall Contract Restrictiveness: Accruals-Cash Flow Evidence
The figure displays the β1 coefficients from the accrual-cash flow piecewise-linear regression estimated over ten deciles, Q1 to Q10, and based on the orthogonalized overall contract restrictiveness index. The evidence, based on the coefficients in Table 6, comes from the following regression:
.)0CFO(*Assets/CFO*Assets/CFO*)0CFO(*Assets/Accruals 1110101 ttttttttt DD εββαα +<++<+= −−−
Figure 2a: Years –3 to –1
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
Figure 2b: Years –1
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
Figure 2c: Years +1
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
Figure 2d: Years +1 to +3
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1 2 3 4 5 6 7 8 9 10
Deciles, Q1 to Q10
29
T a b l e 7 Trends in Asymmetric Timeliness Estimates from the Accrual-Return Model Estimated across 10
Debt Contract Restrictiveness Deciles This table analyzes trends in coefficients and R2s (reported in Table 6) from the piecewise-linear regression of accruals on cash flow (allowing for a differential effect of positive versus negative cash flows on accrual component of earnings) estimated around the year of a debt issue across ten deciles for each of five contract restrictiveness proxies. In particular, the table reports Pearson and Spearman correlations between abnormal contract restrictiveness decile ranks and their corresponding estimated coefficients (from Table 6). In addition the table reports the slope from the regression of estimated regression coefficients from Table 5 on their decile ranks. The following model is estimated:
υφφβ +⋅+= dd10
ˆ ,
where d ∈ 1,..,10 is the decile rank and βd∈β0, β0, β0+β1, R2 is the decile estimate for the given type of restrictiveness measure. Significance levels for Pearson and Spearman correlation coefficients are based on ten observations (i.e., eight degrees of freedom); for coefficient φ 1 the significance is reported based on a Normal distribution, as φ1 is a linear combination of asymptotically normal estimates Panel A: Overall Contract Restrictions Horizon Statistic ρPearson
P-value ρSpearman P-value φ1 t-stat P-value -3 to -1 β0 -0.836 (0.003) -0.855 (0.002) -0.033 -4.30 (0.000) β1 0.814 (0.004) 0.806 (0.005) 0.065 3.97 (0.000) β0+β1 0.525 (0.119) 0.673 (0.033) 0.032 1.74 (0.081) R2 0.594 (0.070) 0.539 (0.108) 0.011 2.09 (0.037) -1 β0 -0.904 (0.000) -0.915 (0.000) -0.048 -5.97 (0.000) β1 0.809 (0.005) 0.830 (0.003) 0.134 3.89 (0.000) β0+β1 0.628 (0.052) 0.503 (0.138) 0.085 2.28 (0.022) R2 0.620 (0.056) 0.552 (0.098) 0.029 2.24 (0.025) +1 β0 -0.204 (0.571) -0.370 (0.293) -0.009 -0.59 (0.555) β1 0.455 (0.186) 0.442 (0.200) 0.045 1.45 (0.148) β0+β1 0.344 (0.330) 0.333 (0.347) 0.036 1.04 (0.300) R2 0.096 (0.792) 0.297 (0.405) 0.003 0.27 (0.785) +1 to +3 β0 -0.104 (0.775) -0.103 (0.777) -0.003 -0.30 (0.768)
β1 0.155 (0.668) 0.103 (0.777) 0.018 0.44 (0.657) β0+β1 0.146 (0.687) 0.103 (0.777) 0.015 0.42 (0.676) R2 0.042 (0.908) 0.139 (0.701) 0.001 0.12 (0.905)Panel B: Correlations for Separate Restriction Types Investment Restrict. Distribution Restrict. Financing Restrict. Control Transfer Horizon Statistic ρPearson
P-value ρPearson P-value ρPearson
P-value ρPearson P-value
-3 to -1 β0 -0.668 (0.035) -0.817 (0.004) -0.854 (0.002) -0.418 (0.230) β1 0.408 (0.242) 0.589 (0.073) 0.659 (0.038) 0.718 (0.019) β0+β1 0.225 (0.533) 0.356 (0.312) 0.429 (0.216) 0.632 (0.050) -1 β0 -0.668 (0.035) -0.663 (0.037) -0.770 (0.009) -0.741 (0.014) β1 0.378 (0.281) 0.019 (0.959) 0.769 (0.009) 0.826 (0.003) β0+β1 0.262 (0.464) -0.140 (0.700) 0.495 (0.146) 0.728 (0.017) +1 β0 -0.136 (0.709) -0.055 (0.880) 0.141 (0.697) 0.007 (0.984) β1 0.347 (0.325) 0.117 (0.747) -0.145 (0.690) -0.325 (0.360) β0+β1 0.358 (0.310) 0.098 (0.788) -0.115 (0.751) -0.226 (0.531) +1 to +3 β0 0.088 (0.810) 0.112 (0.758) 0.147 (0.686) -0.437 (0.206) β1 0.155 (0.670) -0.007 (0.985) 0.046 (0.900) -0.149 (0.682) β0+β1 0.189 (0.601) 0.013 (0.971) 0.101 (0.780) -0.286 (0.423)
30
where CFOt is year t cash flow from operations (COMPUSTAT item data308) and ACCt are accruals,
which are measured by subtracting CFOt from cash flow statement earnings (data123), and 0)(CFO <tD is
a dummy variable that takes the value of unity when CFOt is negative and zero otherwise. The variables
CFOt and ACCt are scaled by lagged total assets. The coefficient 1β is expected to be positive as accruals
are used to recognize economic losses in a more timely fashion (Ball and Shivakumar, 2005a, 2005b).20
Note that following Ball and Shivakumar (2005b) and Collins and Hribar (2002), in the above regression I
use cash flow statement information available in COMPUSTAT for the period of 1987-2004.
Equation (3) is estimated over ten restrictiveness deciles constructed based on the five indices of
contract restrictiveness. The results are reported in Table 6 and also depicted in Figure 2. The tenor of the
results is the same as in Table 4. In particular, analysis of the overall restrictiveness index reveals that in
the highest restrictiveness decile (Q10) the magnitudes of 1β are 1.00, 1.34, 0.77, and 1.09 for years –3 to –
1, year –1, year +1, and years +1 to +3, respectively, while their lowest decile (Q1) counterparts are 0.45,
0.34, 0.42, and 0.67. The differences between these estimates are both statistically and economically
significant.
The differences in asymmetric timeliness estimates between Q10 and Q1 are especially pronounced
for investing restrictions, attaining values of up to 1.40, and are significant at the 1% level. The evidence
based on the distribution and financing restrictiveness indices, as well as on the index of control transfer
covenants, indicates that in years prior to a debt issue there is a substantial and statistically significant
increase in asymmetric timeliness from decile Q1 to Q10.21 In the post-issue periods (year +1 and years +1
to +3), on average 1β increases in smaller increments moving from Q1 to Q10.
Finally, Table 7 presents correlations of the decile ranks with the estimated parameters. The
correlations between the decile rank and 1β based on the overall restrictions (Panel A) are 0.81 for years –3
to –1 and year –1, statistically significant at 1%. However, the correlation coefficients decline to 0.46 and
0.16 for year +1 and years +1 to +3, respectively, and are no longer statistically significant (based on ten
observations). A similar pattern obtains when I examine the different types of restrictions separately (Panel
B). Overall, the correlation coefficients computed for the horizons prior to the debt issue (years –3 to –1
and year –1) are substantial, at about 0.50 on average, whereas in years following the issue, the trends in the
estimates of β1 or β0+β1 become weaker. These findings are consistent with management introducing noise
into accounting formation.
20 The coefficient 0β is predicted to be negative, suggesting a noise-reducing role for accruals (Dechow et al., 1998). 21 One exception is the payout restriction in year –1, where the difference between Q10 and Q1 is negative. However, examination of Q9 and Q8 strongly indicates an increasing pattern, so the result is likely to be driven by noise in the estimation.
31
2.7. Conclusions and Limitations
I argue that the use of restrictive covenants in public debt contracts is associated with higher
demand for the timely recognition of economic losses in accounting income. The purpose of covenants is
to transfer control rights from shareholders to bondholders when a firm approaches financial distress,
thereby limiting the ability of a manager to take actions leading to bondholder wealth expropriation. As
most covenants depend either explicitly or implicitly on accounting information and become binding when
accounting performance deteriorates, I argue that covenants are more effective in constraining opportunistic
behavior by the manager (and in preventing the associated agency problems) when a firm’s accounting
system is designed in a way such that it produces timely signals of the firm’s economic health. Therefore,
when contracts rely on covenants as a contractual mechanism to protect bondholders, higher demand with
respect to timely loss recognition in financial statements should arise.
The analysis shows that companies with the most restrictive contracts are about two times as timely
in recognizing economic losses in earnings as companies with the lowest restrictions. The results are robust
to measures of asymmetric timeliness derived from return-earnings and accrual-cash flows relations.
Overall, I conclude that the demands of contracting parties, at the firm level, are predictably associated with
the degree of timeliness in the recognition of economic losses.
My evidence is consistent with complementarity between conditionally conservative accounting
and debt covenants. While I argue that a company that relies on covenants will adopt more timely loss
recognition ex ante, the debt contracts themselves may require that accounting information satisfy certain
conditions, in which case they may specify modifications or adjustments to accounting information (Core
and Verrecchia, 2006). Leftwich (1983) presents early evidence that debt contracts adjust accounting
information to be more conservative. However, such accounting information is usually backed out from
GAAP numbers. Since it is likely to be very costly to specify a comprehensive set of accounting
adjustments in a contract (Holthausen and Leftwich, 1983), self-imposed constraints in the form of
conditional conservatism should prove useful. This conjecture is consistent with Beatty, Weber, and Yu
(2006), who find that the demand for conservatism is not entirely met via conservative adjustments to
accounting information.
This study is subject to several potential limitations. First, no attempt is made to determine
causality in the relation between timely loss recognition and debt contract restrictiveness, that is, I do not
establish whether timely loss recognition affects covenant design or whether the contractual features, i.e.,
the covenants influence companies’ decisions with respect to the timely recognition of losses.
Nevertheless, under both scenarios the lenders relying on covenants, as a contractual mechanism to reduce
agency problems, are concerned with timely loss recognition. Thus, the latter is positively linked to
contract design, which suggests that contract restrictiveness and asymmetric timeliness are complements.
The second potential limitation to this study relates to the ability to pre-commit to conditionally
conservative accounting practices. Specifically, the empirical evidence presented above suggests that
32
companies adjust their accounting in the years preceding a debt issue. This observation is consistent with
Ball and Shivakumar (2006b), who argue that initial public offerings experience a great degree of scrutiny
by investors and hence adopt timelier reporting. However, in the years following the debt issue, I find
weaker evidence of timely loss recognition when I rely on accrual-based regressions. A possible
explanation for this finding is that firms exert discretion over accounting as well as real activities to reduce
the likelihood of covenant violations. To the extent that this introduces additional noise into accruals, and
more importantly into cash flows, an errors-in-variables problem exists. This problem makes it more
difficult to find significant changes in asymmetric timeliness when moving from one level of covenant
restriction to the next.
Finally, the restrictiveness indices I use in the analysis count the number of covenants included in
debt contracts. A higher number of covenants need not imply more restrictive contracts per se, as the
contracts may provide a slack in meeting covenant thresholds. Sridhar and Magee (1997) show that
accounting information quality and covenant tightness are substitutes. In contrast, consistent with the
arguments in Levine and Hughes (2005) and others, I argue that covenant restrictions and timely loss
recognition are complements. The analysis of Sridhar and Magee applies to the tightness of covenants and
not to their inclusion, which is the focus in this paper. If the restrictiveness indices above are positively
correlated with the tightness of covenants, this may bias my results. However, the bias should generally
work against finding the hypothesized relation.
2.8. References
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2.A. Examples of timely accounting policies
In general, firms can recognize losses in a more timely fashion by choosing to implement
accounting policies that slow down the recognition of gains while speeding up the recognition of losses.
The following discussion provides several examples of ways in which companies can move the recognition
of losses forward.
First, materiality principle implies that transactions of less than material amounts need not be
accounted for by using principles of financial accounting. This means that managers have a fair amount of
discretion in accounting for immaterial transactions and implies that investors will often miss important
information because companies deem such details “immaterial.” Because the abuse of materiality may help
a company avoid covenant violations, a commitment to decrease materiality thresholds in relation to
accounting for losses and adverse economic events (e.g., treating virtually any loss as material unless it
becomes prohibitively costly to do so) would be another way to commit to timelier loss recognition.
In a similar vein, in the context of accounting for pensions, SFAS 87, which is designed to smooth
the volatility of income due to fluctuations of the value of the fund, leaves room for improvements in timely
loss recognition. Realized returns on a pension fund’s assets virtually always differ from the expected
return used to calculate the pension expense. This, together with a number of other factors, such as changes
in actuarial assumptions with respect to life expectancy, turnover, and salary growth, results in deferrals,
i.e., the presence of unrecognized gains or losses. Unless deferred gains or losses exceed (a substantial)
materiality threshold,22 firms are not required to recognize (amortize) the gain/loss. A firm may adopt a
policy to expense a loss (or start its amortization) whenever the deferred gain evolves into a deferred loss
22 Ten percent of the greater of the projected benefit obligation or the market-related value of plan assets.
36
(i.e., whenever it has been absorbed). While such a policy may be extreme, nothing prevents a firm from
implementing a policy to recognize deferred losses resulting from pension accounting sooner then deferred
gains, for example, by using faster depreciation rates for losses than for gains.
Additionally, managers often have a choice over the parameters used to calculate pension expense.
Comprix and Muller (2006) provide evidence consistent with managers manipulating expected rates of
returns to increase their compensation. In a similar fashion, assumptions about expected returns can be
used to avoid covenant violations. A firm can move the recognition of economic losses forward by
specifying ex ante the rules for the determination of the expected returns on a fund’s assets. For instance,
some firms use a moving average over actual realizations, which increases a firm’s expense when the fund
is performing poorly. Such a policy may be considered as consistent with more timely loss recognition
over a cross-section of firms.
Accounting for marketable securities also leaves room for timeliness of losses recognition as firms
have discretion with respect to reclassifying marketable securities as available for trading or available-for-
sale. Unrealized losses for the latter do not enter the income statement as presumably the company
presently has no intention of selling these securities. These need not be true intentions, however, and may
just be a way to increase reported income and thereby avoid covenant violations. Adoption of a policy not
to reclassify available-for-sale securities as trading securities whenever doing so results in increased
income, or alternatively, a commitment not to classify trading securities as available-for-sale whenever
doing so avoids recording unrealized loss in the income statement, would be consistent with more timely
recognition of losses. Moreover, companies have discretion in whether to treat unrealized losses associated
with available-for-sale securities as permanent or temporary. The former necessitates expensing, which
creditors would generally prefer. A commitment to always treat unrealized losses as permanent would be
another way to adopt timelier loss recognition.
Contingent liabilities represent yet another area in which firms can demonstrate more timely loss
recognition. Consider a situation in which a court jury finds a company liable for punitive damages of $7
million (with a subsequent settlement for $5 million) and the company files an immediate appeal but does
not recognize any of the liability on the balance sheet or income statement (instead, the firm makes only a
footnote disclosure). The lenders are likely to prefer the alternative treatment of recognizing an immediate
loss of $7 million and revising the loss downward if subsequent court decisions warrant such changes. It is
often the case that while a liability’s exact amount cannot be determined, the maximum amount is well
defined (e.g., fines for environmental pollution), in which case adopting a policy to recognize the maximum
liability would clearly represent timely accounting for losses.
Finally, as Basu (1997) points out, firms may revise their estimates of an asset’s useful life
upwards, which would have a positive impact on income over multiple years. Since these revisions are
subjective, creditors would prefer that a company commit against following such a practice.
The remaining examples concern pre-commitments against overstating inventory and fixed assets.
Accounting for changes in the replacement cost of obsolete inventory often requires estimating its net
37
realizable value, which in turn leads to (subjective) assessments of future demand, market conditions, etc.
An optimistic assessment would prevent a timely write-down of inventory (to the replacement cost). In
contrast, a policy to assume, for example, that future demand for obsolete inventory is zero would avoid
problems associated with discretionary assessments of future demand and would result in the recognition of
economic losses being moved forward. In addition, the choice of LIFO over FIFO to value inventory is
consistent with more timely expense recognition in the context of increasing inventory prices.
When accounting for maintenance and betterments of long-lived assets, firms often have a choice
over whether to capitalize large maintenance expenses necessitated by the deterioration of an asset’s
condition (which would result in higher income) or to expense them. Since the discretion over this choice
may be used to avoid the recognition of economic losses, a commitment to treat the costs associated with
betterments as maintenance expenses (rather than to capitalize them) whenever, e.g., the betterments do not
involve a purchase of new equipment would be consistent with more timely loss recognition.
2.B. Index Construction
The Investment Restrictions Covenant Index includes indicators for the following covenants:
1. Restrictions on consolidations or mergers between an issuer and other entities
(consolidation_merger).
2. Restrictions on an issuer's investment policy in an effort to prevent risky investments (investments).
3. Restrictions on the ability of an issuer to sell assets or restrictions on the issuer's use of the proceeds
from the sale of assets (sale_assets).
4. Restrictions on subsidiaries' investments (su_investments_unrestricted_subs).
5. Restrictions on an issuer’s business dealings with its subsidiaries (transaction_affiliates).
6. Restrictions on the use of proceeds from the sale of a subsidiaries' assets to reduce debt
(su_sale_xfer_assets_unrestricted).
The Distributions Restrictions Covenant Index includes indicators for the following covenants:
1. Restrictions on payments made to shareholders or other entities; payments may be limited to a
certain percentage of net income or some other ratio (dividends_related_payments).
2. Restrictions on an issuer's freedom to make payments (other than dividend-related payments) to
shareholders and others (restricted_payments).
3. Restrictions on a subsidiary’s payment of dividends to a certain percentage of net income or some
other ratio (su_dividends_related_payments).
The Financing Restrictions Covenant Index includes indicators for the following covenants:
1. Restrictions on an issuer from issuing additional funded debt (funded_debt).
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2. Restrictions on additional debt issues; the issuer must have achieved or maintained certain
profitability levels (net_earnings_test_issuance).
3. Restrictions on incurring additional debt, with limits on the absolute dollar amount of debt
outstanding or the percentage total capital (indebtedness).
4. Restrictions on the type or amount of property used in a sale leaseback transaction and on the use of
proceeds from a sale (sales_leaseback).
5. Restrictions on the amount of senior debt an issuer may issue in the future (senior_debt_issuance).
6. Restrictions on issuing additional common stock (stock_issuance_issuer).
7. Restrictions on issuing secured debt unless the issues secures the current issue on a pari passu basis
(negative_pledge_covenant).
8. Restrictions from transferring, selling, or disposing of the issuer’s own common stock or the
common stock of a subsidiary (stock_transfer_sale_disp).
9. Restrictions on the issuance of junior or subordinated debt (subordinated_debt_issuance).
10. Restrictions on the total indebtedness of subsidiaries (su_indebtedness).
11. Restrictions on subsidiary borrowing, except from the parent (su_borrowing_restricted).
12. Restrictions on subsidiaries issuing additional funded debt (su_funded_debt).
13. Restrictions on issuing additional common stock in restricted subsidiaries (su_stock_issuance).
14. Restrictions on subsidiaries' ability to issue preferred stock (su_preferred_stock_issuance).
15. Restrictions on a subsidiary issuing guarantees for the payment of interest and/or principal of
certain debt obligations (su_subsidiary_guarantee).
16. Restrictions on subsidiaries from selling lease back assets that provide security for the debtholder
(su_sales_leaseback).
17. If an issuer's net worth (as defined) falls below a minimum level, certain bond provisions are
triggered (declining_net_worth).
18. Requirement that an issuer maintain a minimum specified net worth (maintenance_net_worth).
19. Requirement that an issuer have a ratio of earnings available for fixed charges of at least a
minimum specified level (fixed_charge_coverage).
20. Restrictions on an issuer’s total indebtedness (leverage_test).
21. Restrictions on subsidiaries' leverage (su_leverage_test).
22. Requirement that in the case of default, the bondholders have the legal right to sell mortgaged
property to satisfy their unpaid obligations.(liens).
23. Restrictions on subsidiaries from acquiring liens on their property (su_liens).
24. Requirement that subsidiaries maintain a minimum ratio of net income to fixed charges
(su_fixed_charge_coverage).
39
The Control Covenant Index includes indicators for the following covenants:
1. A bondholder protective covenant that will activate an event of default in their issue if an event of
default has occurred under any other debt of the company (cross_default).
2. A bondholder protective covenant that allows the holder to accelerate their debt if any other debt of
the organization has been accelerated due to an event of default (cross_acceleration).
3. A covenant whereby upon a change of control in the issuer, bondholders have the option of selling
the issue back to the issuer (change_control_put_provisions).
4. A covenant whereby the issue's change of control provisions are triggered if an investor controls
more than a given percentage of the issuer's stock (voting_power_percentage).
5. A covenant whereby the issue's change of control provisions are triggered if the issuer's employee
retirement plan controls more than a given percentage of the issuer's stock
(voting_power_percentage_erp).
6. A covenant whereby a decline in the credit rating of the issuer (or issue) triggers a bondholder put
provision (rating_decline_trigger_put).
7. A covenant whereby property acquired after the sale of current debt issues will be included in the
current issuer's mortgage (after_acquired_property_clause).
8. A covenant that indicates whether restricted subsidiaries may be reclassified as unrestricted
subsidiaries (su_subsidiary_redesignation).
40
Chapter 3
Agency Theory of Overvalued Equity as an Explanation for the Accrual Anomalyπ
3.1. Introduction
The prevailing hypothesis in the literature is that investor fixation causes the Sloan (1996) accrual
anomaly, i.e., a predictable negative relation between accounting accruals and subsequent stock returns.
Our tests show that the agency theory of overvalued equity, the agency hypothesis, explains the accrual
anomaly, whereas the evidence does not support the investor-fixation hypothesis. A large body of research
articulates the agency theory of overvalued equity and its implications for corporate investment, financing,
and financial reporting decisions.23 One of the predictions of the theory is that overvalued firms’ managers
attempt to boost their firms’ reported performance to meet investor expectations. We therefore expect
overvalued firms to aggressively engage in earnings management, and as a result, following a period of
overvaluation, such firms gravitate toward the high accrual deciles of the population of firms. Therefore,
when firms are sorted according to accruals, firms with prior over-valuation are likely to be over-
represented in the high accrual decile portfolios. However, since overvaluation and superior reported
performance cannot last indefinitely, we expect, and find, negative abnormal returns for the high accrual
decile portfolio.24
In contrast, undervalued firms are not expected to actively under-report accruals, i.e., manage
earnings downwards. In fact, under-valued firms might also attempt to manage earnings upward to correct
the misevaluation. Therefore, such firms are unlikely to be concentrated in the low accrual deciles of the
population of firms; instead they might be dispersed across various accrual deciles of firms. Hence, the low
π Based on the paper co-authored with S.P. Kothari (MIT) and Elena Loutskina (University of Virginia). 23 See Jensen, Murphy, and Wruck (2004), Jensen (2005), Shleifer and Vishny (2003), Baker, Stein, and Wurgler (2003), Polk and Sapienza (2004), Moeller, Schlingemann, and Stulz (2005), Ritter (1991), Loughran and Ritter (1995), Graham and Harvey (2001), Dong, Hirshleifer, Richardson, and Teoh (2006), and others. 24 Preceding discussion raises at least two questions. First, how do some firms end up being overvalued (or undervalued) in an efficient market, the maintained assumption underlying the agency theory of overvalued equity? Second, why do managers of overvalued firms attempt to prolong overvaluation and thus face potential adverse consequences when prices revert to their normal level? We address these questions below in section 2.
41
accrual decile portfolios’ future stock-price performance is expected to be normal. This prediction differs
from that of the investor-fixation hypothesis for the accrual anomaly.
The fixation and agency hypotheses both imply that investors misunderstand company
fundamentals for some firms, which leads to mispricing. However, under fixation, accruals cause
mispricing, whereas under the agency hypothesis high accruals are, in part, a byproduct of overvaluation.
Overvalued firms’ managers likely engage in earnings management and report high accruals. The fixation
and agency hypotheses therefore generate different predictions. (i) Fixation predicts a linear relation
between accruals and future returns. In contrast, the agency hypothesis predicts a kink in the relation
between accruals and future returns, with negative future returns for the high, but not positive returns for
the low accrual decile portfolios. (ii) Since earnings management is motivated in part by prior
overvaluation, the agency hypothesis also predicts an asymmetric relation between past returns and current
accruals. We expect high returns to precede high accrual decile portfolios, but not particularly low returns
preceding the low accrual decile portfolios. The fixation hypothesis does not make predictions about past
returns and current accruals. A systematic past return behavior that is consistent with the agency
hypothesis constitutes evidence against fixation.25
Previous research also reports an asymmetry, but only in the relation between accruals and future
returns.26 We offer an economic rationale for this asymmetry, and also predict an asymmetric relation
between accruals and past returns. The latter is the result of agency incentives stemming from prior
overvaluation.
We complement the predictions of stock price performance surrounding the year of accrual
measurement with predictions of asymmetry in the degree of analyst optimism, insider trading activity, and
distortions in firms’ investment and financing decisions, i.e., expect these among firms in the high, but not
the low, accrual deciles. The predictions about analyst optimism, about distortions in firms’ investment-
financing decisions, or about unusual amount of insider trading activity among the high-accrual decile firms
are distinct from the investor fixation explanation for the accrual anomaly. The differing predictions based
on the agency hypothesis versus investor fixation are helpful in discriminating between the competing
explanations for the anomaly. We find evidence consistent with all of our predictions based on the agency
25 This is much like systematic positive or negative abnormal performance following an event is inconsistent with market efficiency, which does not predict such systematic return behavior. Also see Friedman (1950, p. 9) on choosing between alternative theories based on evidence contradicting and not contradicting the predictions. 26 See Barth and Hutton (2004), Beaver, McNichols, and Price (2005), Beneish and Vargus (2002), Chan, Chan, Jegadeesh and Lakonishok (2006), D’Avolio, Gildor, and Shleifer (2001), Desai, Rajgopal and Venkatachalam (2004), Hirshleifer, Teoh and Yu (2005), Houge and Loughran (2001), Kraft, Leone, and Wasley (2006), Lesmond and Wang (2005), Lev and Nissim (2006), Teoh and Zhang (2006), and Thomas and Zhang (2002). Sloan (1996) also finds an asymmetric pattern when abnormal stock performance is measured using Jensen’s alpha.
42
hypothesis. Collectively, the evidence casts doubt on the prevailing hypothesis that market naïvely fixates
on reported financial performance in generating the accrual anomaly.27
Background. Following Sloan (1996), the accrual anomaly has received tremendous attention in
the literature, with Xie (2001), Thomas and Zhang (2002), Hirshleifer, Hou, Teoh, and Zhang (2004), and
Richardson, Sloan, Soliman, and Tuna (2005) replicating and extending the anomaly. The most common
explanation for the anomaly is that investors naively fixate on accounting accruals without fully
recognizing the lesser persistence of accruals (see Sloan, 1996, Hirshleifer and Teoh, 2003, and Dechow,
Richardson, and Sloan, 2006). We label this explanation the fixation hypothesis.
Many studies reexamine the accrual anomaly and document evidence that undermines the naïve
investor fixation hypothesis, e.g., the evidence of asymmetry in the accrual-return relation. While such
evidence is damaging to the fixation hypothesis, the literature does not explain this asymmetry. We
propose the agency theory of overvalued equity as an economic rationale for the asymmetric relation
between returns and accruals.
Under the agency hypothesis, overvalued firms’ managers not only resist market “correction,” but
they proactively attempt to prolong the overvaluation. Thus, instead of disseminating information that
would disappoint capital markets, shareholders, and even the board, managers are likely to take actions
designed to meet the market’s optimistic performance expectations and sustain the overvaluation.28 Among
the actions, earnings management is expected to feature prominently, which leads to overvalued firms being
over-represented among the high accrual firms. In addition, overvalued firms’ managers are expected to
make excessive debt and equity issues, capital expenditures, acquisitions paid for using equity, and they are
likely to engage in insider trading.29
Considerable anecdotal evidence suggests managers do indeed attempt to mask bad news and
engage in earnings management in the hope of prolonging a favorable assessment of the firm in the
investment community. Below we describe two such episodes. 30 First, the software giant, Computer
Associates (CA), in the 1990s backdated sales contracts to shift forward the revenues. In 1995, CA
awarded nearly $1 billion in shares to top company officers, with the shares vesting when the stocks price
hits and stays at a target level. This benchmark was met in 1998. But the sales slowed down subsequently,
dragging CA stock down. The company’s top executives tried to sustain the overvaluation by engaging in
fraudulent practices over 1998-2000, including about $1 billion in sales due to fraudulent and premature 27 While finding asymmetry in returns (as well as investment-financing decision, analyst forecasts errors, and insider trading) does not per se reject fixation hypothesis, observing systematic patterns in returns consistent with the agency hypothesis undermines the fixation hypothesis. 28 See Kothari, Shu, and Wysocki (2006) for systematic evidence that managers delay the dissemination of bad news. 29 See Jensen et al. (2004), Jensen (2005), Moeller et al. (2005), Baker and Wurgler (2002), Baker et al. (2003), and Polk and Sapienza (2004). 30 Additional examples of firms inflating earnings to sustain stock price, and thus benefit from option exercise or share sales, include Xerox, Tyco, and Waste Management (see Bergstresser and Philippon, 2006).
43
revenue recognition practices. The company’s stock price declined by more than 50% followed by the SEC
investigation and numerous lawsuits alleging management fraud contributing to stock price inflation. In
2004, U.S. District Judge Leo Glasser said that the “central goal” of CA accounting practice was to meet or
exceed “revenue expectations.” In 2006, the SEC investigation led to the former CEO pleading guilty to
orchestrating $2.2 billion accounting fraud (for further detail, see Bloomberg, September 22, 2004; and
CFO magazine, April 09, 2004).
The second example is Shell Corporation, one of the world’s largest and most profitable firms (and
also one of the most conservative and reliable firms, see Guardian, April 20, 2004), which overstated its oil
reserves over the period 1997-2001. The company’s management began to realize this problem as early as
2000, but was unwilling to disclose this to the market and strived to find new oil reserves in order to back
up their overly optimistic estimates.31 One of the executives wrote to the CEO that he felt they were
“caught in a box” due to aggressive booking of reserves over 1997-2000. In 2002, the CEO, Sir Philip
Watts, who had a sterling career with the company, sent an internal email emphasizing that it was vital not
to take a write-down for the unproven reserves until new reserves had been found to replace them. He
suggested the executive to consider the whole spectrum of possibilities and “ to leave no stone unturned”
(The Independent, April 20, 2004).32 Eventually in 2004, Shell acknowledged that their reserves were
overstated. The CEO and several executives subsequently resigned. The stock price declined by more that
10%, the firm was fined, and S&P downgraded Shell’s credit rating.
While the anecdotal evidence is consistent with overvalued firms’ managers seeking to prolong
their firms’ valuation through favorable disclosures and/or earnings management, we now turn to providing
systematic evidence consistent with the agency hypothesis as an alternative to the fixation hypothesis to
explain the accrual anomaly.
Summary of results. Consistent with the predictions of the agency hypothesis, we find (i) an
asymmetric relation between accruals and past, current, and future returns, (ii) asymmetry in the optimism
of analysts’ long-term growth forecasts, (iii) asymmetric insider trading behavior, and (iv) asymmetric
distortion in the investment-financing decisions. Specifically, we report significant return reversals for the
high accrual-decile firms, but weak/insignificant for the low accrual-decile firms. To further discriminate
between the fixation and agency hypotheses, we examine stock-price performance of the accrual-decile
firms for three years prior to the year in which we classify firms into accrual deciles. The high accrual-
decile firms’ abnormal returns for the prior three years are significantly positive at about 18% per year
compared to only -3.6% for the low accrual-decile firms. The asymmetric return-accrual relation in the 31 For example, Financial Services Authority, August 24, 2004, Final Notice (to Shell investigation). 32 “I am becoming sick and tired about lying about the extent of our reserves issues and the downward revisions that need to be done because of far too aggressive/optimistic bookings,” van de Vijver (CEO of Shell’s Exploration & Production) wrote in a November 2003 e-mail to Mr. Watts, the CEO. Still, in a subsequent email, when legal advisers sent van de Vijver a memo (saying that Shell should disclose the problems), he responded to Exploration&Production CFO: “This is absolute dynamite, not at all what I expected and needs to be destroyed.” (The Associated Press, April 19, 2004; Financial Director, May 2004).
44
prior years is not predicted under the fixation hypothesis. We also observe return reversals only for the
high accrual decile firms. This evidence is consistent with over-valuation prompting managers to engage in
earnings management, which leads such firms to gravitate towards the high accrual deciles.
In addition, we observe unusually high levels of analyst optimism, insider-trading activity, debt and
equity issues, capital expenditures, and M&A activity among the high accrual-decile firms prior to and
during the year of high accruals compared to the low accrual-decile firms. These phenomena, and their
asymmetric relation to accruals, are predicted under the agency hypothesis, but not the fixation hypothesis.
Finally, we conduct Mishkin market efficiency tests separately for companies with income-
increasing accruals (deciles 6 through 10) and income-decreasing accruals (deciles 1 through 5). The
results confirm the asymmetry as predicted under the agency hypothesis in that pricing is as if investors
overestimate accrual persistence only for the high accrual deciles. This asymmetry does not support
investor fixation.
Alternative explanations. The fact that predictable stock price reversals follow equity
overvaluation and earnings management among firms in the high accrual deciles is consistent with many
explanations, including market inefficiency, limited arbitrage (see DeLong, Shleifer, Summers, and
Waldmann, 1990, and Shleifer and Vishny, 1997) and trading frictions preventing a speedy adjustment of
overvalued firms’ stock prices, survival biases, risk misestimation, etc. These are explored in a large
stream of research that focuses on survivor biases, risk misestimation, and distributional properties of the
data as explanations for the abnormal performance of the accrual strategy (see Zach, 2004, Kraft et al. 2006,
Khan, 2005, Kothari, Sabino, and Zach, 2005, etc.). Related research also examines whether trading
frictions and arbitrage risk account for the apparent slow price adjustment to accrual information (e.g., Ali,
Hwang, and Trombley, 2000, Lesmond and Wang, 2005, Hirshleifer, Teoh, and Yu, 2005, Mashruwala,
Rajgopal, and Shevlin, 2006, and Pontiff, 2006).33 Our study does not pursue any of the above lines of
inquiry.
We believe it is unlikely that limited arbitrage due to higher costs of short-sale constraints for the
high accrual firms would explain the observed asymmetry. Short sale constraints can generate the
asymmetry because the constraints will impede shorting of the high accrual decile firms, but not affect
investors’ ability to exploit the mispricing among the lowest accrual decile firms. However, D’Avolio
(2002) finds that short-sale constraints are unlikely for 91% of the stocks, and Asquith, Pathak, and Ritter
(2005, p. 243) conclude that “For the overwhelming majority of stocks, short interest and institutional
ownership levels make short interest constraints unlikely.” Therefore, short selling constraints are unlikely
to explain three years of subsequent stock underperformance of the high accrual firms.34
33 There is no consensus in the literature whether limited arbitrage can explain asset pricing anomalies, e.g., see Brav and Heaton (2006). 34 An additional relevant factor is that difficulties to borrow the stock are likely to exist when there is a divergence of opinion in investor valuation (Miller, 1977) and thus overvaluation itself (not necessarily accruals) likely contributes to the difficulty of borrowing a stock for short-selling. D’Avolio (2002) argues that investor optimism can limit
45
Outline of the paper. Section 2 summarizes the relevant literature, develops testable hypotheses,
and outlines the empirical predictions. Section 3 describes sample selection and variable construction.
Section 4 presents our empirical tests and results. We summarize and conclude in Section 5.
3.2. Hypothesis Development and Empirical Predictions
In this section we examine the accrual anomaly in the context of the agency theory of overvalued
equity. We describe some of the existing evidence surrounding the accrual anomaly, which accords with
the implications of the theory of overvalued equity rather than investor fixation on accruals. We then
present a set of testable hypotheses and empirical predictions that would discriminate between the agency
theory of overvalued equity and fixation as the driving force behind the accrual anomaly.
3.2.1. Hypothesis Development The accrual anomaly is that a zero-investment strategy with a short position in the highest accrual-
decile firms and a long position in the lowest accrual-decile firms earns an economically significant
magnitude of abnormal return. Sloan (1996) and others attribute the abnormal performance to investors’
fixation on accruals. Under the fixation hypothesis, investors overestimate the persistence of the accrual
component of earnings. Investors thus overvalue high accrual firms and undervalue low accrual firms.
This systematic mispricing is corrected in future years, thus generating predictable price reversals for the
extreme accrual stocks.
We advance an alternative explanation for the accrual anomaly, namely, agency cost of overvalued
equity (see references in the Introduction). Even in an efficient market, some firms can get overvalued for a
number of reasons. Optimistic assessment of or withholding of adverse internal information about (i) the
demand for a firm’s products, (ii) a firm’s profitability from revenue growth and cost and scale efficiency,
(iii) the prospects of a new technology, (iv) the quality of management, and/or (v) macroeconomic
implications for the company’s business are some of the reasons that can lead to a particular firm to be
overvalued. The management might also genuinely share the optimism about the firm’s future and/or might
even have proactively contributed to the market’s optimistic assessment. Under these circumstances, the
management is expected to make investment, operating, and financing decisions that might validate their
and the market participants’ expectations.
However, at some point, the management might come to the realization that it would be a challenge
to meet the expectations. At this juncture, the agency hypothesis predicts that an overvalued firm’s
management has many reasons to generate signals (e.g., via managed earnings) that would maintain the
overvaluation. First, the management benefits from the firm’s continued growth and overvaluation through
arbitrage via the loan market mechanism. When market is overly optimistic about a company, non-lending optimists are likely to absorb a large fraction of shares, which leads to higher costs of shorting.
46
higher compensation and high valuation of their stock and options in the firm.35 Second, the incentive
might also come from the managerial labor-market – managers with superior past performance are in
demand. A stock-price decline, even if it’s a correction, would tarnish the manager’s record and thus
reduce his/her cache in the labor market. Third, earnings management might also be due in part a CEO’s
attempt to fulfill the market’s expectation of high performance in line with the overvalued stock price.
Managers might be hopeful that they will be able to ride out future reversals of current earnings
management with good news that will roll in and offset the reversals. Finally, managers engaging in
earnings management might have a high discount rate such that they heavily discount the potential future
downturn and/or adverse consequences in favor of their high utility for continued good times resulting from
the firm’s overvaluation. This is consistent with managers’ utility function displaying significant loss
aversion.
The unwinding of the overvaluation and the earnings management, however, are inevitable, on
average. Thus, under the agency hypothesis, the predictability of subsequent underperformance for the
high accruals portfolio is rooted in the prior overvaluation motivating managers to report upward managed
earnings.36 That is, when firms are sorted according to accruals, overvalued firms are likely to be over-
represented at the high end of the accrual distribution in part because over-valued firms’ managers are
expected to have managed earnings up. We emphasize that not all of the accruals of the high accrual
portfolio are due to earnings management motivated by prior overvaluation. In fact, a large fraction of a
firm’s accruals are likely to be an outcome of its underlying economic fundamentals (e.g., sales growth,
capital intensity, etc.). It is just that the combination of (i) relatively high levels of accruals due to good
economic performance (e.g., high growth), and (ii) upward managed earnings due to the incentives facing
managers of overvalued firms makes it likely that overvalued firms will be over-represented in the high-
accrual portfolios formed on the basis of ranking the population of stocks on accruals.
In contrast, low accrual firms’ subsequent price performance is not predicted to be superior under
the agency hypothesis. Low accruals are typically a result of slow-down in growth and poor operating
performance, which likely is reflected in adverse prior stock-price performance. Like some over-valued
firms, some of these firms might even be undervalued. However, the undervalued firms’ managers do not
face incentives to under-report their accruals, i.e., lower their performance through earnings management.
In fact, managers of undervalued firms might be motivated to manage earnings upward (i) to signal their
superior fundamentals relative to the market’s valuation and thus attempt to correct the misevaluation, and
35 Several studies suggest equity incentives as a motive for earnings management (see Cheng and Warfield, 2005, Burns and Kedia, 2006, and Bergstresser and Phillipon, 2006). 36 In an efficient market, the correction should take place quickly after the public release of information such that even for the high accrual stocks future performance should not be predictably negative for one or more years. The observed evidence of negative abnormal performance for the high-accrual portfolios has multiple potential explanations. They include (i) market inefficiency, (ii) limited arbitrage, trading frictions, and arbitrage risk, which prevent a speedy price adjustment, (iii) survival and hindsight biases, and (iv) risk misestimation, i.e., the fact that inferences from estimated abnormal performance are tests of the joint hypothesis of market efficiency and a model of equilibrium expected returns. Relevant references appear in the Introduction section of the paper.
47
(ii) for the usual agency incentives stemming from management and/or debt contracts. Such actions could
cause these stocks to migrate away from the lowest accrual decile portfolio. Therefore, undervalued firms
are unlikely to gravitate toward the low end of the distribution of firms ranked according to accruals. They
are more likely to be dispersed among several of the accrual-decile portfolios, probably among the middle
and low accrual portfolios. Thus, we do not expect the lowest accrual decile portfolio to be over-
represented with undervalued stocks. Hence, the agency hypothesis does not predict positive abnormal
future stock-price performance for the low accrual firms. Overall, the agency hypothesis predicts an
asymmetric relation between accruals and future returns.
3.2.2. Related evidence
There is voluminous prior research on the accrual anomaly. While we are unaware of any research
linking the accrual anomaly to the agency hypothesis, we note that some of the findings in the accrual
anomaly literature are consistent with the agency hypothesis. We classify these findings into five streams.
First, Xie (2001), Thomas and Zhang (2001), and DeFond and Park (2001) find that the accrual strategy’s
success in predicting subsequent returns is primarily related to the discretionary component of accruals.
The agency hypothesis directly ties overvaluation to discretionary accruals, i.e., earnings management,
motivated in part by a desire to prolong the overvaluation.
Second, mispricing of the accrual component of earnings is observed primarily among specific
subsets of the population of firms: (i) firms whose insiders were abnormal sellers of their equity (see
Beneish and Vargus, 2002), (ii) glamour stocks (see Desai, Rajgopal, and Venkatachalam, 2005), and (iii)
firms engaged in mergers, acquisitions, or divestures (Zach, 2003). These all three subsets of firms are
likely to be overvalued. For example, insiders of overvalued firms sell equity (e.g., Jenter, 2005), glamour
stocks are hypothesized to be overvalued (e.g., Lakonishok, Shleifer, and Vishny, 1994), and, as pointed
out earlier, overvalued firms excessively engage in M&A activities. The evidence in Zach (2003), though
not directly implying overvaluation, is consistent with overvalued firms’ managers (i) using equity as cheap
currency to make acquisitions to satisfy growth expectations, and (ii) raising external capital to over-invest
in risky green-field projects. Additionally, Teoh, Welch and Wong (1998a, 1998b) find that long-term
underperformance of initial or seasoned public offerings is associated with high accruals at the time of the
issue. Such evidence is consistent with these firms timing the market, i.e., issuing the equity during the
periods of overvaluation, while at the same time managing accruals to sustain market’s expectations at high
level.
Third, research suggests sophisticated and individual investors process accrual information
similarly (e.g., Bradshaw, Richardson, and Sloan, 2001, Barth and Hutton, 2004, and Ahmed, Nainar, and
Zhou, 2001). This is inconsistent with the naïve fixation hypothesis in which sophisticated investors are
more discerning. However, the lack of difference between naïve and sophisticated investors is consistent
with the agency hypothesis. Analysts and other sophisticated investors might have fueled the market’s
expectations about firm performance and led to some firms being overvalued. Therefore, when these firms’
48
managements report superior financial performance, both real and managed, sophisticated investors might
find it in line with their expectations and thus might not immediately conclude that it represents earnings
management. It is also possible that high performance expectations of sophisticated investors and analysts
exert pressure on management to report high performance to meet those expectations (see Degeorge, Patel,
and Zechauser, 1999). An overvalued company with more extensive analyst coverage faces more pressure
to deliver the expected superior performance. Ali et al. (2000) find the negative association between
accruals and future returns is more pronounced for firms with extensive analysts’ coverage and greater
institutional ownership.
Fourth, stock underperformance is observed subsequent to periods of high investments, particularly
those leading to high current accruals and, more generally, high net operating assets, (Fairfield, Whisenant
and Yohn, 2003, Richardson and Sloan, 2003, Wei and Xie 2004, Titman, Wei and Xie, 2004). As the
agency hypothesis predicts, in addition to accrual management, overvalued firms to over-invest to increase
the probability of meeting market’s expectations.
Finally, accrual mispricing is observed primarily among the firms reporting income increasing
accruals.37 While inconsistent with fixation, this asymmetry in the accrual-return relation is suggestive of
the agency hypothesis, as described earlier.
3.2.3. Empirical Predictions To empirically distinguish between investor fixation, i.e., the fixation hypothesis, and the agency
hypothesis, we test four sets of predictions with respect to: (i) the return-accrual relation, (ii) analysts’
forecasts, (iii) insider trading, and (iv) firms’ investment and financing decisions.
Return predictions. We make predictions about return behavior in the year of, years prior to, and
years following the accrual measurement year, year zero. Under the fixation hypothesis, returns in year
zero are increasing in accruals, and in years one and beyond, the return-accrual relation is negative. The
fixation hypothesis is silent with respect to the pattern of stock returns in the years leading up to year zero.
The agency hypothesis implies an asymmetry in the relation between year zero accruals and stock
returns of all periods. Specifically, we expect a price run up in the years leading up to and in year zero
among the higher accrual decile firms because these portfolios are likely to be over-represented with over-
valued firms that might have attempted to prop up reported earnings through accruals.38 For the high
accrual decile firms, this produces a positive relation between leading period returns and year zero accruals.
In addition, a contemporaneous positive return-accrual association is expected in year zero. Some of the 37 See Barth and Hutton (2004), Beaver, McNichols, and Price (2005), Beneish and Vargus (2002), Chan et al. (2006), D’Avolio, Gildor, and Shleifer (2001), Desai et al. (2004), Houge and Loughran (2001), Hirshleifer et al. (2005), Kraft et al. (2006), Lesmond and Wang (2005), Lev and Nissim (2006), Teoh and Zhang (2006), and Thomas and Zhang (2002). 38 Some of the price run up is rational anticipation of superior future accounting performance capturing economic fundamentals of the firm. This is stock prices anticipating future accounting performance, which has been long documented in the literature going back to Ball and Brown (1968) and Beaver, Lambert, and Morse (1980). Unlike overvaluation, the rational price run up is not expected to reverse in the future.
49
high accrual decile firms’ performance represents earnings management, which is managers’ response to
overvaluation that began to occur in the years prior to year zero. Therefore, in the years leading up to year
zero, we expect positive abnormal returns for the high accrual decile firms, but not the low accrual decile
firms. The return reversals in years one and beyond are also expected primarily for the high accrual decile
firms because these were overvalued firms that engaged in accrual management to prolong the
overvaluation. Overall, asymmetry in the accrual-return relation is predicted under the agency hypothesis,
but not under the fixation hypothesis.
Since the agency hypothesis is premised on the assumption that overvaluation motivates earnings
management, we expect the subset of relatively more overvalued firms to bear out the return predictions of
the agency hypothesis more compellingly than other firms. Using prior one year’s abnormal price run-up
as a (crude) proxy for overvaluation, we test whether the reversals in stock prices are more pronounced in
future years, i.e., years one and beyond, for the highly overvalued stocks. In contrast, the fixation
hypothesis implies that current period’s accruals, not prior abnormal returns, predict return reversals in
future years.
Analysts’ optimism. The optimistic assessment of the prospects of the overvalued firms is likely to
be shared by analysts and thus reflected in their forecasts of the firms’ future performance. Therefore,
under the agency hypothesis, because we expect over-valued firms to be over-represented in the high
accrual portfolios, analysts will exhibit an optimistic bias in forecasting the prospects of the high accrual
firms, but not the low accrual firms, in the year of and years prior to the accrual measurement year.
Predictions under the naïve fixation hypothesis depend on the maintained hypothesis about analysts’
sophistication. If analysts are assumed to be sophisticated, then we would not predict a systematic variation
in the degree of analyst optimism across high and low accrual firms. On the other hand, if analysts are also
naively fixated on accruals, then we expect analysts to be pessimistic about the low accrual firms and over-
optimistic about the high accrual firms. This implies a symmetric relation.
Insider trading. The agency hypothesis predicts asymmetry in the insider trading activity across
the accrual deciles. Insiders among the high accrual decile firms are predicted to be net sellers because
those firms are overvalued.39 The agency hypothesis does not expect insiders of the low accrual-decile
firms to exhibit abnormal buying of firm equity in the years surrounding year zero of the accrual anomaly.
In contrast, under the fixation hypothesis, we expect insiders to be net sellers of firm equity among the high
accrual decile firms and net buyers of firm equity among the low accrual decile firms. Thus, insider trading
activity is predicted to be symmetric in its occurrence and magnitude across the accrual deciles under the
fixation hypothesis.
Investment-financing decisions. The agency hypothesis makes several predictions about
corporations’ investment-financing decisions, which are distinct from the behavior predicted under the 39 Insiders are likely to sell equity on average, and/or it may be more costly for them to purchase additional stock when they believe their firm is undervalued, which may lead to asymmetric insider trading patterns. To address this concern, we adjust our measures of insider trading for mean insider selling of companies of similar size, so that executives who refrain from selling will appear to be net buyers.
50
fixation hypothesis. Specifically, the agency hypothesis predicts that in year zero and prior years the high
accrual decile firms will (i) excessively tap the debt and equity markets; (ii) excessively use (overvalued)
equity as currency to pay for mergers and acquisitions; and (iii) over-invest in property, plant, and
equipment (i.e., capital expenditures) and R&D. Once again, these investment-financing decisions are
expected to be asymmetric, i.e., observed among the high accrual decile firms, but not the low accrual
decile firms. The fixation hypothesis does not predict (especially discretionary) accruals to impact firms’
investment-financing decisions. It also does not predict an asymmetry in the relation between accruals and
investment activity.
We acknowledge the possibility that investors are naively fixated on accruals, but managers
recognize that stocks are misvalued and that they take actions to exploit the misevaluation. In this scenario,
managers of over-valued firms might excessively tap the equity and debt markets, which means both
agency and fixation hypotheses make the same prediction. However, (i) we do not expect over-valued
firms to make over-investments under the fixation hypothesis, and (ii) we would expect managers of both
over- and under-valued firms to engage in insider trading to exploit the misevaluation under the fixation
hypothesis. Thus, (i) some of the predictions of the agency and fixation hypotheses differ, and (ii) when
they are similar, the predicted behavior under the fixation hypothesis requires an agency relationship to
influence management’s behavior much like that under the agency hypothesis.
3.3. Data and Sample Selection
3.3.1. Sample Selection
We analyze all firms with available data on Compustat and CRSP files excluding closed-end funds,
investment trusts and foreign companies. Our initial sample contains 42 years of financial data beginning
in 1963 and ending in 2004. Due to the difficulties involved in interpreting accruals for financial firms,
consistent with the literature in this area, we drop companies with SIC codes from 6000 to 6999. These
procedures yield 157,456 firm-year observations with non-missing total accruals data and 156,000 firm-
year observations with discretionary accruals data, where discretionary accruals are estimated using the
within-industry cross-sectional modified-Jones model. We do not require firms in our sample to survive
through the period of our analysis. We include all valid firm-year observations irrespective of their fiscal-
year-end, though some tests in our analysis require December year-end firms (e.g., buy-and-hold abnormal
returns). In each sub-section we specify the additional sample restrictions we impose.
For the purpose of our analysis, each year we divide the sample of firms into decile portfolios based
on the magnitude of either total accruals or discretionary accruals. We do not restrict our analysis only to
discretionary accruals because (i) naïve fixation as a behavioral theory underlying the accrual anomaly is
not specified in a particular measure of discretionary accruals, but likely to be in total accruals as distinct
from cash flows; and (ii) discretionary accruals as a measure of managed earnings are well-known to
contain estimation error, which might induce a bias and/or reduce the power of our tests. Hence, we also
51
use total accrual portfolios. The results are qualitatively similar using the two different measures. For any
given measure, the assignment of firm-years to the accrual deciles remains constant throughout the analysis
to insure comparability of results across different sets of tests even though some tests (e.g., insider trading
behavior) impose additional filters on our primary sample.
3.3.2. Total and Discretionary Accruals Variables We use the balance-sheet method to compute total accruals. Collins and Hribar (2002) show that
total accruals measured from the balance-sheet data contain a measurement error while those measured
directly from the statement of cash-flows are more accurate. To account for the error, we also implement
our empirical tests using the total accruals estimated via statement of cash flows for the sample of financial
statements after 1987. The results are qualitatively the same. The total accruals (TAj,t) for a firm j in year
t are computed as follows:
tjtjtjtjtjtjtj DepTPSTDebtCLCashCATA ,,,,,,, )()( −∆−∆−∆−∆−∆= (1)
where ∆CAj,t is change in current assets (Compustat item #4),
∆Cashj,t is change in cash/cash equivalents (Compustat item #1),
∆CLj,t is change in current liabilities (Compustat item #5),
∆STDj,t is change in debt included in current liabilities (Compustat item #34),
∆TPj,t is change in income taxes payable (Compustat item #71), and
Depj,t is depreciation and amortization expense (Compustat item #14).
For comparability across sample firms, the dollar amount of total accruals is deflated by the
beginning of the year total assets (Compustat item #6).
Further, we use cross-sectional modified-Jones model to separate discretionary and non-
discretionary accrual components (Jones, 1991, and Dechow et al., 1995). We estimate the following cross-
sectional regression for each of 48 Fama-French industry groups in each year t:
tjtj
tj
tj
tjtj
tjtj
tj
AssetsPPE
AssetsARv
AssetsAssetsTA
,1,
,3
1,
,,2
1,1
1,
, )Re(1 εααα ++∆−∆
+=−−−−
(2)
where ∆Revj,t is change in sales revenues (Compustat item #12),
∆ARj,t is change in accounts receivable (Compustat item #2), and
PPEj,t is gross property, plant and equipment (Compustat item #7).
We denote the predicted values of the modified-Jones model as non-discretionary accruals
( tjNDA , ) and the residuals as discretionary accruals ( tjDA , ).40
3.3.3. Descriptive Statistics
Table 1 reports descriptive statistics for several variables of interest. Panel A presents the analysis
by total accrual decile portfolio and Panel B by discretionary accrual decile portfolio. All variables are
40 The modified-Jones model likely yields biased estimates of discretionary accruals for firms experiencing extreme growth rates. We nonetheless use the model to maintain comparability with past research.
52
Tab
le 1
Su
mm
ary
of th
e Sa
mpl
e Fi
rms F
inan
cial
Cha
ract
eris
tics
The
tabl
e pr
esen
ts su
mm
ary
stat
istic
s for
var
ious
firm
cha
ract
erist
ics i
n ou
r sam
ple.
Pan
el A
pre
sent
s the
mea
n (m
edia
n) c
hara
cter
istic
s for
tota
l acc
rual
-dec
ile p
ortfo
lios,
and
pane
l B fo
r di
scre
tiona
ry a
ccru
al d
ecile
por
tfolio
s. To
tal a
ccru
als
are
com
pute
d us
ing
the
bala
nce-
shee
t met
hod
and
disc
retio
nary
acc
rual
s us
ing
the
with
in in
dustr
y, c
ross
-se
ctio
nal m
odifi
ed-J
ones
mod
el.
Des
crip
tive
stat
istic
s ar
e re
porte
d: (i
) mar
ket c
apita
lizat
ion
(Com
pusta
t dat
a ite
m #
24*i
tem
#25
), (ii
) tot
al a
sset
s (C
ompu
stat
dat
a ite
m #
6),
(iii)
leve
rage
(C
ompu
stat
dat
a ite
m #
142/
item
#6)
, (iv
) mar
ket-t
o-bo
ok r
atio
(C
ompu
stat
dat
a ite
m #
24*i
tem
#25
/item
#60
), an
d (v
) in
com
e be
fore
ext
raor
dina
ry i
tem
s (C
ompu
stat
dat
a ite
m #
18/ i
tem
6).
The
sam
ple
cont
ains
all
firm
-yea
rs fr
om 1
963
to 2
004.
To
be in
clud
ed in
the
sam
ple,
a fi
rm-y
ear s
houl
d co
ntai
n su
ffici
ent i
nfor
mat
ion
in
Com
pust
at to
cal
cula
te o
f the
pre
sent
ed c
hara
cter
istic
s and
be
pres
ent i
n th
e C
RSP
Mon
thly
Ret
urns
file
.
Pane
l A: T
otal
Acc
rual
Dec
ile P
ortf
olio
s 1
23
45
67
89
10
-26.
37
-12.
55
-8.6
9 -6
.28
-4.3
6 -2
.57
-0.5
3 2.
27
7.21
31
.27
Tota
l Acc
rual
s, %
of T
otal
Ass
ets
(-22
.40)
(-12
.59)
(-8.
91)
(-6.
49)
(-4.
53)
(-2.
75)
(-0.
66)
(2.2
3)(7
.18)
(21.
01)
493.
42
1053
.18
1526
.34
1672
.11
1728
.15
1558
.34
1287
.55
925.
52
508.
45
315.
60
Mar
ket C
apita
lizat
ion,
$ m
il.
(18.
60)
(41.
24)
(68.
59)
(100
.66)
(121
.08)
(109
.69)
(88.
68)
(65.
35)
(48.
26)
(38.
91)
339.
68
1031
.49
1501
.26
1754
.26
1876
.27
1708
.06
1198
.94
873.
80
427.
17
200.
00
Tota
l Ass
ets,
$ m
il.
(24.
41)
(62.
16)
(100
.16)
(146
.54)
(167
.84)
(148
.88)
(108
.55)
(75.
87)
(50.
90)
(31.
84)
17.8
5 19
.50
20.6
5 21
.25
21.5
8 20
.71
20.1
8 16
.81
16.5
0 14
.25
Leve
rage
, in
%
(6.1
1)(1
2.03
)(1
5.64
)(1
7.49
)(1
8.08
)(1
6.69
)(1
4.58
)(1
1.53
)(8
.70)
(5.1
1)
3.41
2.
66
2.04
3.
10
2.42
2.
18
2.43
2.
76
3.14
3.
97
Mar
ket-t
o-B
ook
Rat
io
(1.4
2)(1
.40)
(1.3
9)(1
.43)
(1.4
3)(1
.44)
(1.5
2)(1
.61)
(1.7
5)(2
.29)
-2
1.83
-5
.33
-1.4
5 0.
58
1.30
1.
81
2.06
2.
40
1.87
-3
.71
Inco
me
Bef
ore
Extra
ordi
nary
item
s, %
of T
otal
Ass
ets
(-7.
00)
(2.0
8)(3
.50)
(4.0
6)(4
.35)
(4.5
3)(4
.87)
(5.5
2)(6
.21)
(7.5
3)
Pa
nel B
: Disc
retio
nary
Acc
rual
Dec
ile P
ortf
olio
s 1
23
45
67
89
10
-25.
66
-10.
74
-6.3
4 -3
.65
-1.6
3 0.
11
1.87
4.
12
7.98
26
.39
Dis
cret
iona
ry A
ccru
als,
%
of T
otal
Ass
ets
(-21
.60)
(-10
.50)
(-6.
28)
(-3.
60)
(-1.
59)
(0.1
4)(1
.86)
(4.0
3)(7
.67)
(18.
34)
452.
95
774.
56
1022
.48
1364
.80
1559
.26
1737
.18
1554
.80
1422
.63
849.
97
363.
38
Mar
ket C
apita
lizat
ion,
$ m
il.
(19.
00)
(34.
75)
(56.
57)
(84.
59)
(108
.90)
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53
measured contemporaneously with accruals. We find the characteristics of firms in our sample to be similar
to those reported in earlier studies. First, we find that firms with extreme accruals, those in the lowest and
highest accrual deciles, are smaller than the firms in the middle accrual deciles. Both market capitalization
and total assets exhibit an inverted U-shaped pattern with respect to the accrual deciles. Moreover, the
median size of the lowest accrual decile firms is smaller than that of the highest accrual decile firms, but the
mean size of the lowest accrual decile firms is larger than the mean size of the highest accrual decile firms.
Second, firms with extreme income increasing accruals have higher market-to-book ratios than firms with
income-decreasing accruals. Third, firm performance, measured by median income before extraordinary
items as a percentage of total assets, hereafter earnings, is increasing monotonically with accruals. Median
earnings increase from -7% for the lowest total accrual decile portfolio to 7.5% for the highest total accrual
decile portfolio. Finally, leverage of extreme accrual decile firms is lower than that of firms in the middle
of the accrual distribution.
3.4. Empirical Tests and Results
In this section we present the results of our empirical tests that are designed to distinguish between
the agency and fixation hypotheses. We analyze the pattern of abnormal stock performance, analysts’
earnings growth forecasts, insider trading behavior, and firms’ investment-financing decisions in event time
period centered on the year in which we form accrual decile portfolios, year 0. We then describe results of
the Mishkin market efficiency tests separately for firms with income-increasing and income-decreasing
accruals. Finally, we perform quantile regression tests of the relation between accruals and returns.
3.4.1. Abnormal Stock Returns We begin by analyzing abnormal stock return performance in the year of, years prior to, and years
following the accrual measurement year using two methodologies. First, we compare the size and book-to-
market adjusted annual buy-and-hold returns computed by following the procedure outlined in Barber,
Lyon, and Tsai (1999). Second, we estimate annualized alphas from Fama-French three factor model based
on the calendar-time monthly accrual portfolio returns. In each case we use CRSP monthly stock returns
adjusted to include delisting returns using the method detailed in Beaver, McNichols, and Price (2005).
Buy-and-Hold Abnormal Returns
This sub-section summarizes results using size and book-to-market adjusted abnormal buy-and-
hold returns. The benchmark portfolio returns are constructed as follows. Each year we compute end of
April capitalization quintile cutoffs for the sample of NYSE firms. Based on these cutoff points we assign
all of the sample firms to size quintile portfolios. Since the lowest size quintile contains roughly half of
firm-year observations, we further divide this quintile into five additional portfolios. Each of the resulting
nine size portfolios is then divided into quintile portfolios based on book-to-market ratio, where book value
is taken as of previous fiscal year end and market value is as of the end of the following April. This
54
procedure yields 45 benchmark portfolios. Annual abnormal return for each firm-year is computed as one-
year buy-and-hold return (12-month return starting May 1) less average annual return of the corresponding
size and book-to-market portfolio. The start date of May 1 for calculating annual return ensures that the
market has information about the prior year’s financial performance. For consistency between benchmark
returns and individual firm returns we limit our sample to December fiscal-year-end firms.
Table 2 presents time-series means and Fama-MacBeth t-statistics for annual abnormal buy-and-
hold returns. Average abnormal returns for each accrual decile portfolio are calculated for nine annual
periods from event-year -4 to year +4, where event-year 0 is the accrual measurement year. Panel A
presents the results for total accrual portfolios while Panel B presents the results for discretionary accrual
portfolios. We illustrate the results graphically in Figures 1a and 1c, where we graph annual buy-and-hold
abnormal returns for the 1st, 5th, and 10th accrual decile portfolios.
Firms with the highest income increasing accruals (both discretionary and total) experience
significant abnormal price run-up prior to the accrual measurement year, i.e., year 0, and underperform
subsequently. In case of total accruals, the highest accrual decile portfolio experiences 29.43% abnormal
return in year -1, which is followed by -7.63% abnormal return (reversal) in year +1. Similarly, the highest
discretionary accrual decile portfolio earns 18.3% abnormal return in year -1, which is followed by -8.3%
of underperformance in year +1. Superior performance prior to firms recording high accruals, i.e., high
earnings growth, is consistent with the market anticipating strong earnings performance, i.e., returns leading
earnings (e.g., Beaver et al. 1980, and Collins, Kothari, and Rayburn, 1987).41 However, the evidence is
also consistent with the agency hypothesis that a portion of the price run-up is overvaluation and that the
overvalued firms engage in accrual management, and experience market correction in years +1 and beyond.
This latter evidence of return reversal suggests that the prior price run up was not due entirely to rational
anticipation of future earnings, i.e., prices leading earnings, but due in part to overvaluation.
The performance behavior of the lowest accrual portfolio in the years subsequent to and prior to
year 0 lends further credence to the agency hypothesis and helps us in discriminating between the fixation
and agency hypotheses. Specifically, consistent with prior research, the lowest accrual decile portfolio’s
performance in years +1 and beyond is not significantly positive. In fact, the point estimates of average
abnormal return for the lowest accrual decile portfolio are insignificantly negative. Turning to the
performance in years prior to 0, the lowest accrual decile portfolio experiences considerably smaller
magnitude of negative abnormal performance compared to the highest accrual-decile portfolio. Panel A of
Table 1 shows that, in year -1, the lowest accrual decile portfolio’s abnormal return is -11.8% compared to
29.4% for the highest decile accrual portfolio. Corresponding numbers when portfolios are formed on the
basis of discretionary accruals in Panel B are -5.3% and 18.33%, which again reveals the large disparity in
performance in prior years. 41 Consistent with the earnings anticipation explanation for the price run-up, we do not observe high levels of accruals in years -4 to -1 for the highest accrual decile portfolio. Thus, past price run up for the high accrual stocks is not due to extraordinary past accounting performance. The accrual behavior in years -4 to -1 is also not unusual for the lowest accrual decile firms.
55
T a b l e 2 Buy-and-Hold Abnormal Returns
This table presents time-series means, with associated Fama-MacBeth t-statistics, for annual abnormal returns on 10 accrual portfolios. The accrual portfolios are constructed in year zero, and abnormal returns are computed as follows. Each year we use end of April market capitalization to allocate all companies in our sample into size quintiles based on cutoffs computed for NYSE sub-sample. We further allocate lowest size quintile firms into another 5 quintiles. Subsequently each of the resulting nine size portfolios is allocated into quintiles based on book-to-market ratio, which results in 45 benchmark portfolios in total. The book value is measured as of December of the previous (fiscal) year. The annual abnormal return for each stock is computed as one-year buy-and-hold return (12 month return starting in April) less average annual return of the corresponding size – book-to-market portfolio. Panel A presents the results for total accruals portfolios. Total accruals are computed using the balance sheet method. Panel B presents results for discretionary accruals portfolios. Discretionary accruals are estimated using the within industry, cross-sectional modified Jones model. ***, **, and * indicate significance of the t-statistics for the tests of difference in means at 1, 5, and 10 percent levels, respectively. The sample contains all firm-years from 1963 to 2004. To be included in the sample, a firm-year should contain sufficient information in Compustat to calculate of the presented characteristics and be present in the CRSP Monthly Returns file.
Year With Respect to Accrual Measurement Accrual Decile -4 -3 -2 -1 0 1 2 3 4
Panel A: Case of Total Accruals Lowest 0.49 -2.35 -7.02 -11.82 -7.22 -1.92 -1.29 -0.83 0.57
2 -0.29 -1.02 -5.24 -8.74 -3.23 1.17 -1.11 -0.50 -1.93 3 1.87 -0.92 -3.42 -5.91 -1.20 -0.43 0.33 -0.72 -0.03 4 0.49 -0.94 -2.60 -4.87 -0.95 0.14 0.28 -0.98 -1.57 5 -0.69 0.28 -0.92 -3.09 -1.61 0.57 -1.15 0.25 -0.81 6 1.02 1.29 0.54 -2.03 -1.71 -0.19 -0.53 -0.97 -0.96 7 1.33 1.12 1.06 -0.28 -1.60 -1.22 -1.24 -1.57 -2.40 8 3.33 3.19 5.05 2.86 -2.40 -1.69 -0.20 -0.71 -1.12 9 4.46 3.38 9.74 10.23 0.28 -4.07 -2.40 -2.09 -0.98
Highest 0.41 7.48 14.83 29.43 5.45 -7.63 -5.53 -3.34 -0.84
10th - 1st -0.08 9.82*** 21.84*** 41.25*** 12.66*** -5.70*** -4.23** -2.50 -1.41 1st - 5th 1.17 -2.63 -6.09 -8.72 -5.61 -2.48 -0.14 -1.07 1.37 10th - 5th 1.09 7.19*** 15.74*** 32.52*** 7.05*** -8.19*** -4.37*** -3.58** -0.03
Panel B: Case of Discretionary Accruals
Lowest -0.38 -1.20 -2.10 -5.29 -2.19 0.21 -2.18 -1.91 -2.06 2 -0.47 -0.23 -4.36 -6.53 -0.96 0.11 -0.96 -0.30 -0.54 3 2.49 1.11 -2.22 -4.28 -1.32 0.16 0.24 0.25 -1.56 4 2.72 0.42 -1.14 -3.53 -0.02 0.07 -0.13 -1.57 -1.01 5 1.25 1.76 -1.27 -1.39 -0.95 0.41 -0.09 -0.33 0.07 6 1.52 -0.76 -0.29 -1.34 -2.66 -0.20 1.50 -0.38 -1.29 7 -0.04 1.02 0.63 -1.32 -1.77 -1.48 -0.75 -0.30 -1.64 8 0.67 1.62 2.39 -0.49 -2.28 -1.79 -2.96 -0.87 -0.17 9 2.77 1.16 5.63 2.78 -2.46 -2.39 -2.85 -1.77 -2.86
Highest -1.22 3.46 9.57 18.33 0.33 -8.36 -4.91 -3.97 0.13
10th - 1st -0.84 4.65** 11.67*** 23.63*** 2.51 -8.57*** -2.73 -2.07 2.20 1st - 5th -1.63 -2.96 -0.83 -3.90 -1.24 -0.20 -2.09 -1.57 -2.14 10th - 5th -2.46* 1.69 10.84*** 19.73*** 1.27 -8.76*** -4.82*** -3.64** 0.06
56
Figu
re 1
a. A
nnua
l Buy
-and
-Hol
d A
bnor
mal
Ret
urns
Fo
r T
otal
Acc
rual
Por
tfol
ios
-15
-10-505101520253035
-3-2
-10
12
3Ye
ar w
ith R
espe
ct to
Acc
rual
Mea
sure
men
t
Return (%)
1st A
ccru
al D
ecile
5th
Acc
rual
Dec
ile10
th A
ccru
al D
ecile
Figu
re 1
c. A
nnua
l Buy
-and
-Hol
d A
bnor
mal
Ret
urns
Fo
r D
iscr
etio
nary
Acc
rual
Por
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ios
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-3-2
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12
3
Yea
r with
Res
pect
to A
ccru
al M
easu
rem
ent
Return (%)
1st A
ccru
al D
ecile
5th
Accr
ual D
ecile
10th
Acc
rual
Dec
ile
Fi
gure
1b.
Ann
ualiz
ed A
lpha
s Fro
m F
ama-
Fren
ch T
hree
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tor
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el F
or
Tot
al A
ccru
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ortf
olio
s
-10-5051015202530
-3 to
-1-1
01
1 to
3In
vets
men
t Hor
izon
Annualized Alphas (%)
1st a
ccru
al d
ecile
5th
accr
ual d
ecile
10th
acc
rual
dec
ile
Fi
gure
1d.
Ann
ualiz
ed A
lpha
s Fro
m F
ama-
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ch T
hree
Fac
tor
Mod
el F
or
Dis
cret
iona
ry A
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ortf
olio
s
-10-505101520
-3 to
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01
1 to
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Inve
stm
ent H
oriz
onAnnualized Alphas (%)
1st a
ccru
al d
ecile
5th
accr
ual d
ecile
10th
acc
rual
dec
ile
Fi
gure
1 g
raph
s th
e ab
norm
al s
tock
per
form
ance
of a
ccru
al (t
otal
and
dis
cret
iona
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truct
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nly
1st, 5
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nd 1
0th d
ecile
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rual
por
tfolio
s ar
e de
pict
ed.
Fig
ures
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and
1b g
raph
per
form
ance
of
the
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l ac
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ls p
ortfo
lios,
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reas
Fig
ures
1c
and
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raph
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ance
for
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cret
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ry a
ccru
al
portf
olio
s. Th
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turn
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res
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The
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ails
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pear
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able
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The
estim
atio
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ualiz
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izon
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phed
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igur
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b an
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, is d
escr
ibed
in T
able
3.
57
As a test of asymmetry in the performance of the highest and lowest accrual decile portfolios in
prior years, we compare their performance against that of accrual decile portfolio 5. Portfolio 1’s, i.e., the
lowest accrual decile portfolio’s performance is statistically indistinguishable from that of portfolio 5 in
years -1 and -2, whereas portfolio 10 statistically outperforms portfolio 5 in years -1 and -2. The
considerable asymmetry in abnormal returns across the highest and lowest accrual decile portfolios coupled
with the absence of significantly positive subsequent abnormal return for the portfolio of income decreasing
accruals is inconsistent with the fixation hypothesis but supports the agency hypothesis.
Annualized Alphas from Fama-French Three-Factor Model
Below we repeat the abnormal return analysis using annualized alphas as a measure of the accrual
decile portfolios’ abnormal return performance. We estimate the Fama-French three factor model using
calendar-time monthly portfolio returns. Intercepts from these regressions for each of the 10 accrual
portfolios are estimates of abnormal performance. We estimate the regression over five different event-
time horizons: event years -3 to -1, year -1, year zero, year +1, years +1 to +3. As before, the return
measurement period is four months after the fiscal year end for each firm included in the analysis. To
estimate abnormal performance, i.e., alphas, we regress monthly equal-weighted accrual portfolio returns
on the three Fama-French factors, namely market, size, and book-to-market. Similar to Table 2, Panel A of
Table 3 reports results for the total accrual portfolios and Panel B for the discretionary accrual portfolios.
Figures 1b and 1d present the results graphically.
The tenor of the results based on alphas as a measure of abnormal performance is similar to that
based on buy-and-hold abnormal returns. The highest accrual-decile portfolio earns significantly positive
abnormal returns prior to year zero and significantly negative abnormal returns beyond year zero. Prior to
year 0, the annualized value of estimated alpha for the highest total-accrual-decile portfolio is 25.58% for
year -1 and 17.82% when averaged over years -3 to -1. In contrast, the estimated alphas for the lowest
accrual decile firms are negative prior to year 0, but they are remarkably smaller in magnitude when
compared to alphas of the highest accrual decile firms. Specifically, in Panel A, the abnormal alpha is -
3.92% for the lowest decile versus 17.82% for the highest decile using total accrual portfolios, and, in Panel
B, it is -0.06% versus 12.88% using discretionary accrual portfolios.
The asymmetry in the performance of the highest and lowest accrual decile portfolios is also
observed in year +1 and beyond. In Panel A, the estimated annualized alphas for the highest total accrual
portfolio are -8.12% for year +1, and -5.36% when averaged over years +1 to +3. In contrast, the lowest
accrual decile portfolio’s year +1 or year +1 to +3 alphas are statistically and economically insignificant.
Furthermore, while the highest accrual decile portfolio alphas are significantly different from those of the
5th accrual decile portfolio, the lowest decile portfolio’s alphas are not. The above conclusions are also
applicable to the results using discretionary accruals as reported in Panel B of Table 3.
58
T a b l e 3 Annualized Alphas from Fama-French Three Factor Model
This table presents annualized Jensen’s alphas for 10 accrual portfolios and for different holding horizons. The accrual portfolios are constructed in Year t. The alphas are estimated from calendar time regressions based on Fama-French’s three-factor model using monthly returns: ( )pt ft mt ft t t tR R R R s SMB h HMLα β ε− = + − + ⋅ + ⋅ + , where Rpt is the return on the accrual portfolio in month t; Rmt is the return on the CRSP value-weighted index in month t; Rft is the 3-month T-bill yield in month t; SMBt is the return on small firms minus the return on large firms in month t; and HMLt is the return on high book-to-market stocks minus the return on low book-to-market stocks in month t. The factor definitions are described in Fama and French (1993). The accrual portfolios are constructed in the following way. For companies in each accrual decile in year t, we include monthly returns earned over five different horizons (around year zero): Years -3 to -1, Year -1, Year zero, Year 1, Years 1 to 3. Monthly returns are included starting from 4 months after the beginning and 4 months after the end of each horizon. Panel A presents results for total accruals portfolios. Total accruals are computed using balance sheet data. Panel B presents results for discretionary accruals portfolios. Discretionary accruals are estimated using the within industry, cross-sectional modified Jones model. The sample contains all firm-years from 1963 to 2004. To be included in the sample, a firm-year should contain sufficient information in Compustat to calculate of the presented characteristics and be present in the CRSP Monthly Returns file. T-statistics are presented in parentheses. ***, **, and * indicate significance of the t-statistics for the tests of difference in means at 1, 5, and 10 percent significance levels.
Panel A: Case of Total Accruals
Accrual Decile Years -3 to -1 Year -1 Year 0 Year 1 Years 1 to 3
Alpha T-Stat Alpha T-Stat Alpha T-Stat Alpha T-Stat Alpha T-Stat Lowest -3.92 (1.97)** -8.03 (3.70)*** -3.94 (1.74)* 2.11 (0.98) 1.64 (0.87)
2 -2.79 (2.29)** -6.12 (4.41)*** 0.12 (0.08) 3.80 (2.76)*** 3.45 (2.82)*** 3 -1.65 (1.66)* -4.09 (3.60)*** 1.66 (1.37) 4.57 (4.24)*** 3.98 (4.14)*** 4 -1.14 (1.37) -2.73 (2.88)*** 0.46 (0.47) 2.77 (3.05)*** 2.23 (2.85)*** 5 -0.39 (0.51) -2.35 (2.74)*** 0.36 (0.39) 1.57 (1.83)* 1.78 (2.37)** 6 0.82 (1.09) -0.27 (0.32) 1.03 (1.13) 2.25 (2.23)** 1.99 (2.52)** 7 3.00 (3.50)*** 2.17 (2.32)** -0.15 (0.17) 1.83 (2.02)** 1.65 (1.99)** 8 5.08 (6.04)*** 4.96 (5.23)*** 0.91 (0.99) 0.22 (0.24) 1.19 (1.34) 9 8.59 (8.21)*** 10.74 (9.90)*** 1.50 (1.44) -2.13 (1.80)* -0.87 (0.77)
Highest 17.82 (12.29)*** 25.58 (17.06)*** 4.88 (3.62)*** -8.12 (5.18)*** -5.36 (3.51)***
10th - 1st 21.73 (8.82)*** 33.61 (12.75)*** 8.82 (3.35)*** -10.24 (3.84)*** -7.00 (2.89)*** 1st - 5th -3.52 (1.65)* -5.69 (2.44)** -4.30 (1.76)* 0.54 (0.23) -0.14 (0.07) 10th - 5th 18.21 (11.11)*** 27.93 (16.17)*** 4.51 (2.74)*** -9.69 (5.42)*** -7.14 (4.20)***
Panel B: Case of Discretionary Accruals
Accrual Decile Years -3 to -1 Year -1 Year 0 Year 1 Years 1 to 3
Alpha T-Stat Alpha T-Stat Alpha T-Stat Alpha T-Stat Alpha T-Stat Lowest -0.06 (0.04) -1.40 (0.73) 0.94 (0.45) 1.30 (0.65) 1.12 (0.63)
2 -1.04 (0.80) -3.10 (2.13)** 2.49 (1.63) 4.35 (2.90)*** 3.74 (2.90)*** 3 -0.34 (0.33) -1.82 (1.56) 1.34 (1.17) 3.53 (3.19)*** 2.82 (2.73)*** 4 0.33 (0.39) -1.42 (1.55) 0.69 (0.64) 2.08 (2.09)** 2.09 (2.25)** 5 0.48 (0.62) -0.71 (0.80) 0.64 (0.66) 3.07 (3.54)*** 2.43 (3.11)*** 6 0.88 (1.29) 0.14 (0.17) -0.13 (0.16) 0.70 (0.86) 1.57 (2.09)** 7 1.49 (2.25)** 0.54 (0.73) -0.24 (0.30) 0.87 (1.06) 1.26 (1.76)* 8 2.46 (3.09)*** 1.52 (1.74)* 0.40 (0.45) 0.02 (0.02) 0.55 (0.66) 9 5.21 (5.14)*** 5.88 (5.66)*** 0.16 (0.16) -0.35 (0.27) 0.13 (0.13)
Highest 12.88 (9.02)*** 17.04 (11.46)*** 1.10 (0.84) -7.10 (4.58)*** -4.48 (3.02)***
10th - 1st 12.94 (5.71)*** 18.44 (7.60)*** 0.16 (0.06) -8.40 (3.33)*** -5.60 (2.42)** 1st - 5th -0.54 (0.28) -0.69 (0.32) 0.30 (0.13) -1.77 (0.82) -1.31 (0.68) 10th - 5th 12.40 (7.62)*** 17.76 (10.24)*** 0.46 (0.28) -10.17 (5.73)*** -6.91 (4.13)***
59
Accrual Anomaly Conditioning on Prior Return Performance
Below we examine whether the extent of future return reversal for the accrual decile portfolios
varies with the firms’ prior stock-price performance. The fixation hypothesis predicts price reversals as a
function of accruals regardless of prior stock price performance.42 In contrast, under the agency hypothesis,
prior performance as a proxy for misvaluation predicts subsequent reversals, especially for the high-accrual
portfolios. To perform the tests, we subdivide accrual decile portfolios each year into quartiles based on the
annual abnormal buy-and-hold return (calculated by adjusting for size and book-to-market) in year -1. The
goal here is to maintain roughly equal accrual performance for the quartile portfolios within each accrual
decile portfolio, but form the quartiles to segregate firms into portfolios on the basis of prior price
performance. In Table 4 we report return performance in year +1 for the quartile portfolios within each of
the accrual-decile portfolios 1, 5, and 10.43 We present time-series means and Fama-MacBeth t-statistics
for the abnormal returns. Panels A and B of Table 4 present results for total and discretionary accrual-
decile portfolios.
Table 4 shows that return reversals in Panels A and B both are predominantly observed for the
extreme prior return quartiles Q4 and Q3 and that too prominently only within the highest accrual decile
portfolio. Specifically, in Panel A, the highest return quartile Q4 within accrual decile portfolio 10 earns an
average annual abnormal return of -10.57% compared to -3.99% for Q4 within the lowest accrual decile
portfolio. The Q4 portfolio within the lowest accrual decile portfolio earns negative, not positive, abnormal
returns in year +1. This is inconsistent with low accrual firms earning positive abnormal returns according
to the accrual anomaly. Average abnormal returns of the Q3 portfolios within accrual deciles 1 and 10 are
consistent with return reversals, but the magnitudes are markedly smaller. Specifically, Q3 portfolios
within accrual deciles 1 and 10 earn average annual abnormal returns of 2.13%and -3.84. The abnormal
return magnitudes for Q1 and Q2 portfolios are small in absolute magnitude, particularly for those within
the lowest accrual decile portfolio. These results reveal the asymmetry in return performance of the high
and low accrual portfolios, which is consistent with the agency, but not the fixation, hypothesis. The
concentration of reversals in the extreme high prior return portfolio, particularly, conditioning on high
accruals, is also consistent with the agency, not fixation, explanation for the accrual anomaly.
As further evidence of the asymmetry, we compare abnormal returns of quartile portfolios within
deciles 1 and 10 with those of the quartile portfolios within the 5th decile. The fifth decile portfolio is used
as the benchmark to assess whether performance of the portfolios within decile 1 and 10 is asymmetric as
predicted under the agency hypothesis. The results in Panels A and B both reveal that only the performance 42 To the extent past returns predict future return reversals, the year +1 performance of the portfolios is influenced by not only investor fixation on accruals or the agency hypothesis, but also by predictability of returns as a function of past price performance. This concern, however, is muted by the fact that we form quartile portfolios on price performance in year -1, whereas the future return performance is for year +1. Thus, we skip year 0 in which most of the effects of predictability based on past price performance are expected to be observed. 43 In this subsection we only include December fiscal year-end firms. This is similar to the previous analysis using buy-and-hold returns in section 4.1.1.
60
T a b l e 4 Magnitude of the Accrual Anomaly and Prior Overvaluation
This table presents time-series means and Fama-MacBeth t-statistics for the average annual abnormal stock return in year +1 for accrual portfolios constructed in year 0. The abnormal returns are size and book-to-market adjusted as described in Table 2. Within each decile accrual portfolio, we assign sample companies to quartile portfolios based on their abnormal return in year -1, i.e., they year prior to the accrual measurement year. We report abnormal returns for each quartile portfolio within selected accrual-decile portfolios. The sample contains all firm-years from 1963 to 2004. To be included in the sample, a firm-year should contain sufficient information in Compustat to calculate of the presented characteristics and be present in the CRSP Monthly Returns file. Panel A presents the results for total accruals portfolios. Total accruals are computed using the balance sheet method. Panel B presents results for discretionary accrual portfolios. Discretionary accruals are estimated using the within industry, cross-sectional modified Jones model. T-statistics are reported in parentheses. ***, **, and * indicate significance of the t-statistics for the tests of difference in means at 1, 5, and 10 percent significance levels.
Panel A: Abnormal Returns in Year +1 for Total Accruals Portfolios (%) For quartile portfolios formed on the basis of abnormal return in year -1
Accrual Decile Q1 Q2 Q3 Q4 1 0.48 -0.25 2.13 -3.99 (0.20) (0.10) (0.74) (1.49) 5 2.34 -1.21 0.54 0.34 (1.30) (1.11) (0.49) (0.18)
10 -1.54 -1.14 -3.84 -10.57 (0.43) (0.33) (1.41) (6.34)
10th-1st -2.02 -0.89 -5.97 -6.58** (0.47) (0.21) (1.51) (2.08)
1st-5th -1.86 0.96 1.59 -4.33 (0.61) (0.36) (0.52) (1.32)
10th-5th -3.88 0.07 -4.38 -10.91*** (0.97) (0.02) (1.49) (4.34)
Panel B: Abnormal Returns in Year +1 for Discretionary Accruals Portfolios (%)
For quartile portfolios formed on the basis of abnormal return in year -1 Accrual Decile Q1 Q2 Q1 Q4
1 2.70 2.11 2.10 -4.92 (0.80) (0.56) (0.69) (1.57) 5 -0.27 1.64 2.09 -2.27 (-0.13) (1.32) (1.53) (1.38)
10 -2.94 -6.19 -3.98 -11.68 (0.86) (2.97) (1.47) (7.19)
10th-1st -5.64 -8.30* -6.07 -6.76*
(1.18) (1.92) (1.49) (1.91) 1st-5th 2.97 0.47 0.00 -2.65
(0.75) (0.12) (0.00) (0.75) 10th-5th -2.67 -7.83*** -6.07** -9.41***
(0.66) (3.25) (2.00) (4.07)
61
of the Q4 portfolio within decile 10 is significantly different from that of Q4 within decile 5. Once again,
the asymmetry and concentration of abnormal performance in Q4 are consistent with the agency
hypothesis, and inconsistent with the fixation hypothesis.
3.4.2. Analyst Optimism The second prediction under the agency hypothesis is about analyst optimism across the accrual
decile portfolios. In the interest of brevity, we only report results using total accruals. However, the
evidence based on discretionary accruals is similar.
We analyze analysts’ forecasts of long-term earnings growth (LTG) each year over a 9-year
window centered on the accrual measurement year (year 0). LTG forecast error is a measure of analyst
optimism, measured as the realized long-term earnings growth rate minus the forecasted long-term earnings
growth rate. Unbiased estimates of this measure are difficult to calculate (see Kothari, 2000).
Acknowledging that growth forecast errors are likely to be upward biased as a function of firm size and
earnings volatility, we adjust them by subtracting the average forecast error for the companies in the same
beginning-of-the-year market capitalization decile. Following Dechow and Sloan (1997) and Dechow,
Hutton, and Sloan (2000), the realized earnings growth is computed as the slope coefficient of an ordinary
least squares regression of the natural logarithm of annual earnings per share on a constant and a time trend
over 5-year moving window (e.g., from the beginning of year 0 to the end of year 5) using a maximum of 6
annual observations. This estimation procedure restricts the sample of firms to those with at least three
non-missing earnings per share observations within this 5-year moving window. Negative earnings per
share observations are excluded because growth rates with negative earnings denominator are not
interpretable. The forecasted long-term earnings growth rate is taken from IBES summary file as of the
beginning of each fiscal year (specifically within 4th month after prior fiscal year end). We also leave out
outliers by trimming 1% of observations at both tails of the distribution.44 Since IBES data is sparse before
1980, we restrict our analysis to the period from 1980 to 2004.
Table 5 and figure 2 present the results of LTG forecast error analysis. Panels A and B report
annual average and median size-adjusted LTG forecast errors for 10 total accrual portfolios. The results
show that around the year of accrual measurement (i.e., in the beginning of years -1 through 1) analysts
significantly overestimate long-term growth for the highest accrual decile firms compared to the firms in
deciles 1 and 5. In year 0, decile 10 firms enjoy 8.15% (8.06%) positive mean (median) analysts’ growth
forecasts errors. These errors are significantly different from the errors of firms in 1st and 5th accrual
deciles. Analysts’ over-optimism regarding prospects of the highest accrual decile firms is noticeable in
years -1 and -2, peaks in year 0, and is virtually unobservable from the beginning of year +2 onwards.
The asymmetry in analyst optimism becomes apparent when we compare the errors for the tenth
decile against the lowest accrual decile. Both mean and median size-adjusted forecast errors of portfolio 1
44 The annual means of forecast errors are sensitive to the inclusion of outliers, but the results remain qualitatively similar if outliers are not deleted.
62
T a b l e 5 Long-Term Earnings Growth: Analysts’ Forecast Errors
This table presents the analysis of the relation between total accruals and analysts’ long-term earnings growth forecast errors (LTG forecast error). LTG forecast error is computed as a difference between forecasted by analysts and realized long-term earnings growth rates. Subsequently LTG forecast errors are size adjusted by subtracting the average LTG forecast error of companies in the same year and size decile portfolio. Panels A and B present the time-series means of the annual size-adjusted mean and median LTG forecast errors respectively, conditional on year 0 accrual decile. Analysts’ forecasts of long term growth rate are from the IBES summary file as of the beginning of each fiscal year (specifically within 4th month after prior fiscal year end). Following Dechow and Sloan (1997) and Dechow, Hutton, and Sloan (2000), we compute realized long-term growth rate from the slope coefficient of the OLS regression of natural log of realized EPS on a constant and the time trend over 5-year moving window (using maximum of 6 annual observations). This estimation procedure restricts the sample of firms to those with at least three non-missing and positive earnings per share observations within the 5-year moving window. Furthermore, since IBES data is sparse before 1980 we restrict our analysis to the period from 1980 to 2004. To reduce the influence of outliers 1% of observations is left out from each tail of the distribution before any statistics are computed. ***, **, and * indicate significance of the t-statistics for the tests of difference in means at 1, 5, and 10 percent significance levels.
Panel A: Mean Size-adjusted LTG Forecast Error (%) Accrual Decile Year With Respect to Accrual Measurement
-4 -3 -2 -1 0 1 2 3 4 Lowest 1.32 0.47 -1.03 -2.54 -2.13 0.68 -0.58 0.10 0.00
2 2.35 0.60 -1.86 -2.59 -2.61 -0.69 -0.12 1.20 0.92 3 0.10 -0.87 -1.83 -1.66 -2.54 -1.58 -1.78 -2.60 -1.90 4 -0.80 -1.60 -2.04 -2.46 -2.34 -1.70 -1.03 -0.98 -1.37 5 -1.55 -1.46 -1.06 -1.37 -1.89 -1.90 -1.82 -1.99 -1.34 6 -2.28 -1.65 -1.44 -1.31 -1.03 -1.20 -0.99 -1.19 -1.66 7 -0.94 0.22 0.52 1.17 1.04 0.15 -0.40 -0.21 -0.88 8 -0.37 0.16 1.75 3.03 3.01 2.02 1.63 0.49 -0.12 9 -1.12 1.54 3.44 5.41 5.47 2.86 1.83 1.32 1.40
Highest -1.80 1.49 2.70 7.63 8.15 5.38 1.25 2.38 1.84
10th - 1st -3.12 1.02 3.73** 10.17*** 10.28*** 4.71*** 1.83 2.28 1.85 1st - 5th -2.86 -1.92 -0.03 1.17 0.24 -2.57* -1.24 -2.09 -1.34 10th - 5th -0.25 2.95** 3.75*** 9.00*** 10.04*** 7.28*** 3.07** 4.37*** 3.19***
Panel B: Median Size-adjusted LTG Forecast Error (%) Lowest 2.18 2.54 0.12 -0.61 -0.91 2.34 0.24 -0.66 0.47
2 3.33 2.15 -0.08 -0.40 -0.91 0.78 1.41 1.91 1.43 3 1.32 -0.21 -0.92 -1.17 -0.84 -0.62 -0.71 -1.08 -1.51 4 0.05 -0.48 -0.82 -1.63 -1.15 -1.06 -0.25 -0.33 -0.86 5 -0.26 -0.47 -0.61 -0.51 -0.73 -0.97 -1.57 -1.54 -1.30 6 -1.46 -1.09 -0.87 -0.74 -0.62 -0.47 -0.44 -0.38 -1.11 7 0.14 0.65 0.69 1.50 1.24 0.59 0.78 0.55 0.10 8 0.13 1.16 2.26 2.52 3.35 2.37 2.07 1.28 1.12 9 -0.23 2.17 4.40 5.57 4.82 3.95 3.17 2.46 1.81
Highest 2.78 2.64 5.57 7.91 8.06 7.10 2.06 4.08 3.54
10th - 1st 0.59 0.10 5.45*** 8.52*** 8.97*** 4.75** 1.82 4.74*** 3.08 1st - 5th -2.44 -3.01** -0.73 0.10 0.18 -3.31** -1.81 -0.88 -1.77 10th - 5th 3.04** 3.11* 6.18*** 8.42*** 8.79*** 8.06*** 3.63*** 5.63*** 4.84***
63
Figure 2a. Mean Size-adjusted LTG Forecast Error (%)
-4
-2
0
2
4
6
8
10
-4 -3 -2 -1 0 1 2 3 4
1st accrual decile 5th accrual decile 10th accrual decile
Figure 2b. Median Size-adjusted LTG Forecast Error (%)
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
-4 -3 -2 -1 0 1 2 3 41st accrual decile 5th accrual decile 10th accrual decile
Figure 2 graphs time-series means (Panel A) and medians (Panel B) of analysts’ long-term earnings growth forecast errors (LTG forecast error) for firms in 1st, 5th, and 10th total accrual deciles. The total accruals portfolios are formed in the accrual measurement year zero by ranking stocks according to total accruals calculated using the balance sheet method. LTG forecast error is computed as the difference between LTG forecasted by analysts and realized long-term earnings growth. The LTG forecast errors are size adjusted by subtracting the average LTG forecast error of companies in the same year and size decile portfolio. The sample contains firm-years from 1980 to 2004.
64
do not appear noticeably different from portfolios 2 through 5 or to its own forecast errors in the prior or
future years. In addition they are statistically indistinguishable from the forecast errors for the 5th accrual
decile. Thus, the forecast errors also exhibit an asymmetry as predicted under the agency hypothesis.
The earlier evidence of a substantial price run-up experienced by the highest accrual decile
portfolio coupled with the evidence of significant analyst optimism for the highest decile portfolio is
consistent with the hypothesis that the high accrual decile portfolios are overvalued and exhibit accrual
behavior as predicted under the agency hypothesis. Overall, the evidence of asymmetry in analyst
optimism and earlier evidence of asymmetry in the return behavior with respect to the accrual decile
portfolios support the agency hypothesis.
3.4.3. Insider Trading Behavior The agency hypothesis implies differences in the insider trading behavior for the firms in different
accrual deciles. The data for the insider-trading analysis comes from Thomson Financial Insider Filing
Form 4 that provides all common and ordinary shares transactions of insiders (purchases and sales only).
Our definition of insiders includes CEO, COO, CFO, president, and chairman of the board. For firms in
each accrual-decile, we analyze insiders’ equity transactions over 9 years from year -4 to year 4, where year
0 is the year of accrual measurement. For each year we include transactions occurring during the fiscal
year. Consistent with the earlier literature (see, e.g., Lakonishok and Lee, 2001), we exclude small
transactions defined as those with the number of shares traded less than 100. Due to the unavailability of
the Thomson Financial Insider Filing Data prior to 1986, the analysis in this subsection covers activities
from 1986 to 2004.45
Table 6 presents evidence on three measures of insider trading. Figure 3 presents the results
graphically comparing insider trading across 1st, 5th, and 10th accrual-decile portfolios. Panel A presents the
average net purchase ratio calculated according to Lakonishok and Lee (2001) as the number of shares
purchased minus the number of shares sold, divided by the total number of shares traded by the insiders.
The second measure is the net purchase dollar volume (see Lakonishok and Lee, 2001) calculated as the
dollar volume of purchases minus the dollar volume of the sale transactions, divided by the total dollar
volume of all transactions by the insiders (Panel B). Finally, we use the average net shares traded (see
Beneish and Vargus, 2002), which is calculated as the number of shares purchased by insiders minus
number of shares sold by insiders, divided by the total number of shares outstanding (Panel C). All three
measures are size adjusted by subtracting the average insider trading characteristic of all the companies
with the same fiscal year and belonging to the same size decile portfolio.
Management of firms in the highest accrual decile engage in insider trading behavior consistent
with firm overvaluation prior to and during the year of accrual measurement, i.e., year 0. Specifically, the
insiders are abnormal sellers of their equity in the firm in years -1 and 0, and continue to do so in year +1.
45 The limited number of years for which the data is available also prevents us from presenting Fama-MacBeth standard errors in our analysis. Instead we present means and t-statistics based on pooled sample.
65
T a b l e 6 Insider Trading By Total Accrual Deciles
This table presents insider trading activity for companies in different total accruals deciles. Total accruals are computed in year t using balance sheet data. Panel A presents mean net purchase ratio as number of shares purchased minus number of shares sold divided by total number of shares traded by the insiders. Panel B presents mean net purchase volume ratio as volume of purchase transactions minus volume of sale transactions divided by total volume of shares traded by the insiders. Panel C presents mean net shares traded as number of shares purchased by the insiders minus number of shares sold by the insiders divided by total number of shares outstanding. All three measures are size adjusted by subtracting the average insider trading characteristic of companies in the same year and size decile portfolio. The definition of insiders includes: CEO, COO, President, Chairman of the board, and CFO. The insider trading data is the common shares transactions (purchases and sales only) recorded in Form 4 from Thomson Financial Insider Filing Data. We exclude small transactions with number of shares traded less than 100. The sample period is 1986-2004. ***, **, and * indicate significance of the t-statistics for the tests of difference in means at 1, 5, and 10 percent significance levels.
Year With Respect to Accrual Measurement Accrual Decile -4 -3 -2 -1 0 1 2 3 4
Panel A: Size Adjusted Net Purchase Ratio (%) Lowest -0.389 -3.726 -6.806 -1.718 2.848 4.968 -0.804 3.356 0.903
2 -10.367 -7.520 -6.012 -1.701 2.333 -1.250 -1.213 -2.192 -0.845 3 -4.383 -2.395 -4.215 -1.531 1.974 -1.035 -3.087 -2.334 -3.025 4 -6.039 -0.974 -1.009 2.443 7.633 6.437 3.700 0.929 5.599 5 -3.024 -0.117 1.828 9.075 8.649 5.801 3.318 5.349 3.975 6 1.797 2.471 4.782 3.980 6.698 6.477 4.545 5.050 2.439 7 -2.425 -2.590 1.091 0.762 2.275 -1.173 -2.206 -1.475 -1.103 8 -8.741 -6.696 -8.483 -5.031 -2.152 -5.882 -3.261 0.144 -4.918 9 -8.488 -12.765 -16.412 -17.465 -11.031 -9.406 -8.370 -7.690 -4.842
Highest -8.899 -8.168 -8.919 -11.686 -19.374 -15.670 -9.029 -6.944 -4.270 10th - 1st -8.509 -4.442 -2.113 -9.969 -22.223*** -20.638*** -8.225*** -10.300** -5.173** 1st - 5th 2.635 -3.609 -8.634 -10.793** -5.801*** -0.833** -4.122 -1.993 -3.072 10th - 5th -5.874 -8.051 -10.747* -20.761*** -28.024*** -21.471*** -12.347*** -12.294*** -8.245***
Panel B: Size Adjusted Volume Net Purchase Ratio (%) Lowest 0.024 -3.352 -6.980 -2.536 2.393 3.738 -1.742 2.534 -0.084
2 -10.318 -7.452 -6.298 -2.429 2.186 -1.279 -1.819 -2.399 -0.177 3 -5.017 -2.841 -5.187 -1.834 1.738 -1.533 -3.372 -2.262 -3.047 4 -6.603 -1.208 -0.763 2.260 7.819 5.924 3.554 0.828 5.245 5 -2.904 0.012 2.159 9.189 8.669 6.270 3.591 5.484 4.464 6 2.070 2.432 5.019 4.074 6.793 6.723 4.927 4.843 2.622 7 -2.099 -2.621 0.871 0.534 2.451 -0.983 -2.260 -1.652 -1.119 8 -8.835 -6.400 -8.415 -4.755 -2.010 -6.428 -3.552 -0.387 -5.648 9 -8.765 -13.058 -16.340 -17.389 -11.049 -9.946 -9.140 -8.183 -4.439
Highest -8.920 -8.913 -9.364 -12.409 -19.221 -16.365 -9.986 -7.758 -4.862 10th - 1st -8.943 -5.562 -2.383 -9.873 -21.614*** -20.103*** -8.243*** -10.291** -4.777** 1st - 5th 2.928 -3.364 -9.140 -11.725** -6.276*** -2.532** -5.334 -2.950 -4.548 10th - 5th -6.015 -8.926 -11.523* -21.598*** -27.890*** -22.635*** -13.577*** -13.241*** -9.326***
66
Table 6. Continued. Panel C: Size Adjusted Net Shares Traded (%)
Lowest 0.881 -0.585 -0.897 1.599 1.661 2.173 -0.591 -1.124 -1.8612 -1.842 0.144 -1.184 -1.552 0.021 -0.376 0.831 -0.048 -1.403 3 -1.544 -1.047 -0.495 -0.375 -1.568 -1.543 -0.018 -0.430 -0.256 4 -0.522 0.666 2.911 1.096 1.510 2.956 2.928 2.519 2.695 5 0.693 -1.157 0.583 2.143 1.820 0.952 1.126 2.152 2.974 6 0.239 2.442 2.265 2.505 2.238 1.648 3.231 3.473 2.761 7 0.277 0.036 0.845 1.506 2.136 1.234 0.431 1.157 0.861 8 1.044 0.442 -0.520 -0.468 0.328 0.141 0.580 1.697 0.682 9 1.394 -0.564 -5.172 -5.363 -2.294 -1.734 0.662 1.638 2.073
Highest 0.512 0.140 -1.203 -3.736 -5.848 -7.318 -5.789 -2.451 -2.235 10th - 1st -0.369 0.725 -0.306 -5.335 -7.508*** -9.491*** -5.198** -1.327* -0.374 1st - 5th 0.188 0.572 -1.480 -0.544 -0.160 1.222 -1.716 -3.276 -4.835** 10th - 5th -0.181 1.297 -1.786 -5.879 -7.668*** -8.270*** -6.915*** -4.603*** -5.209***
67
Figure 3a. Size Adjusted Net Purchase Ratio
-25
-20
-15
-10
-5
0
5
10
15
-4 -3 -2 -1 0 1 2 3 4Year with Respect to Accrual Measurement
1st accrual decile 5th accrual decile 10th accrual decile
Figure 3b. Size Adjusted Volume Net Purchase Ratio
-25
-20
-15
-10
-5
0
5
10
15
-4 -3 -2 -1 0 1 2 3 4Year with Respect to Accrual Measurement
1st accrual decile 5th accrual decile 10th accrual decile
Figure 3c. Size Adjusted Net Shares Traded
-8
-6
-4
-2
0
2
4
-4 -3 -2 -1 0 1 2 3 4Year with Respect to Accrual Measurement
1st accrual decile 5th accrual decile 10th accrual decile
Figure 3 graphs the abnormal frequency of insider trading for firms in total accruals deciles 1, 5, and 10. Total accruals are calculated in year 0 using the balance sheet method. Figure 3a graphs the average net purchase ratio, Figure 3b the average net purchase volume, and Figure 3c presents the average net shares traded. All three measures are size adjusted (see Table 6 for calculation details). Insiders include: CEO, CO, President, Chairman of the board, and CFO. The insider trading data is the common/ordinary shares transactions (purchases and sales only) recorded in Form 4 of Thomson Financial Insider Filing Data.
68
As seen from Figure 3 and Table 6, the selling activity of insiders of decile 10 firms is the highest of all the
portfolios using all three measures of insider selling. In year 0, the highest accrual decile firms’ insiders
sell around 19% more shares (in terms of number of shares and dollar volume) than they buy. This
isequivalent to selling, on average, 3.7% of company shares outstanding (see Panel C), which likely
represents a substantial fraction of the insiders’ stake in the company. To assess statistical significance, we
compare decile 10 insider selling with that of decile 5. In year 0, all three measures indicate insiders of
decile 10 firms sell more equity than insiders of decile 5. In years -1 and -2, the net purchase ratio and the
net dollar volume of transactions ratio in Panels A and B for decile 10 are significantly greater than those
measures for decile 5. The third measure has a negative point estimate, as predicted, but they are not
statistically significant in years -1 and -2.
The insiders of the lowest accrual decile firms do not exhibit a consistent buying or selling behavior
around year 0. They are net buyers of company stock in year 0, but the magnitude is neither economically
nor statistically different from the buying behavior of the insiders of decile 5 firms. In fact, the buying of
firm equity by the insiders of the firms in decile 1 is generally lower than that of decile 5 insiders. If low
accruals were to indicate undervaluation, the insiders of firms with extreme low accruals, i.e., decile 1,
should be more aggressive in acquiring equity than the insiders of the firms with the average magnitude of
accruals, i.e., decile 5, which should not be mispriced, on average.
The insider trading evidence described above is consistent with the agency hypothesis. The
asymmetry in the insider behavior across the high and low accrual-decile portfolios is as predicted under
the agency hypothesis. Decile 1 insiders’ net selling prior to year 0 also suggests the management of these
firms were aware of overvaluation and attempt to take advantage of it by unloading their ownership stake in
the firm. The fixation hypothesis does not predict such asymmetry.
3.4.4. Investment-Financing Decisions
Management might attempt to prolong the overvaluation by making certain investment-financing
decisions that are not necessarily value-maximizing for the shareholders. Managers of overvalued firms are
likely to (i) raise excessive amount of equity cheaply, (ii) use overvalued equity as currency in merger and
acquisition transactions; and (iii) overinvest in capital assets, i.e., PP&E, and in R&D. Table 7 and figure 4 report the investment and financing decisions of the firms in various accrual
deciles. In Panel A we report firms’ average external equity issues as a percentage of total assets (Compustat
data item #108/item #6). Panel B summarizes the contribution of new equity through mergers and acquisitions,
as a percentage of total assets (Compustat data item #129/item #6). Finally, Panel C examines the firms’
intensity of investment in capital assets and R&D, which we measure as the growth in the sum of capital assets
and R&D expenditures (Compustat data item #128 + item #46). All three investment-financing variables are
size adjusted by subtracting the average investment-financing amount for the portfolio of companies in the same
year and size decile portfolio of the sample firms. The sample contains all CRSP-Compustat firm-years from
1963 to 2004 for which sufficient data exists to construct considered firm characteristics. Figure 4 presents our
69
results where we graphically compare firms’ investment and financing decisions across 1st, 5th, and 10th accrual-
decile portfolios.
T a b l e 7 Financing and Investing Decisions of Firms in Total Accrual Deciles
This table presents time-series means and Fama-McBeth t-statistics for the operating decision of companies in different total accruals deciles. The deciles are formed in the accrual measurement year zero using balance sheet data. Panel A presents portfolio means of equity issues as a percentage of total assets (Compustat data item 108/item 6). Panel B presents mean contributions from acquisitions as a percentage of total assets (Compustat data item 129/item 6). Panel C presents mean growth in capital and R&D expenditures (Compustat data item 128 + item 46). All three measures are size adjusted by subtracting the average operating decision characteristic of companies in the same year and size decile portfolio. The sample contains all firm-years from 1963 to 2004. To be included in the sample, each firm-year observation should contain sufficient Compustat data to calculate the presented characteristics and also have data on the CRSP Monthly Returns file. ***, **, and * indicate significance of the t-statistics for the tests of difference in means at 1, 5, and 10 percent significance levels.
Year With Respect to Accrual Measurement Accrual Decile -4 -3 -2 -1 0 1 2 3 4
Panel A: Equity Issues as Percentage of Total Assets (%) Lowest 8.42 9.03 8.06 6.64 7.21 3.66 0.97 -0.03 -1.18
2 3.26 3.16 2.15 1.66 -1.43 -1.80 -2.38 -2.83 -3.25 3 1.46 1.31 0.75 -0.35 -2.93 -2.31 -2.80 -3.15 -3.71 4 0.09 1.28 0.67 -0.10 -2.92 -2.97 -3.07 -3.29 -3.78 5 0.37 0.41 0.62 0.49 -2.75 -2.47 -2.75 -2.76 -3.13 6 0.47 0.61 0.88 1.22 -2.92 -2.89 -2.60 -3.07 -3.40 7 1.32 1.12 2.01 1.81 -2.65 -2.69 -2.68 -3.23 -3.61 8 1.86 2.09 2.65 3.17 -2.12 -2.37 -3.22 -3.66 -3.75 9 2.67 3.04 3.22 4.73 2.76 -1.71 -2.68 -3.69 -4.00
Highest 7.98 7.60 8.32 9.14 30.62 1.77 -0.06 -0.95 -1.73 10th - 1st -0.435 -1.427 0.258 2.500 23.415*** -1.888** -1.034 -0.915 -0.550 1st - 5th 8.046*** 8.623*** 7.449*** 6.155*** 9.959*** 6.130*** 3.722*** 2.731*** 1.945***
10th - 5th 7.611*** 7.196*** 7.707*** 8.655*** 33.375*** 4.241*** 2.689*** 1.816*** 1.394**
Panel B: Contribution from Acquisition as Percentage of Total Assets (%) Lowest 0.09 0.08 0.03 -0.06 0.28 0.01 0.06 0.07 0.08
2 0.01 0.11 0.07 -0.07 -0.30 -0.11 -0.15 -0.19 -0.18 3 0.06 0.01 0.02 -0.10 -0.55 -0.18 -0.24 -0.15 -0.17 4 0.17 0.22 0.12 0.06 -0.68 -0.19 -0.24 -0.25 -0.42 5 0.03 0.07 0.05 0.04 -0.62 -0.18 -0.22 -0.34 -0.28 6 0.02 0.07 0.00 -0.01 -0.62 -0.27 -0.32 -0.39 -0.42 7 0.02 0.02 0.13 0.14 -0.36 -0.15 -0.19 -0.32 -0.35 8 0.00 0.00 0.15 0.21 0.04 -0.10 -0.21 -0.22 -0.28 9 -0.03 -0.09 0.17 0.29 0.83 0.24 0.03 -0.13 -0.22
Highest -0.11 -0.02 0.01 0.41 2.82 0.41 0.02 -0.10 -0.26 10th - 1st -0.196* -0.103 -0.016 0.471*** 2.541*** 0.402*** -0.039 -0.169* -0.340***1st - 5th 0.056 0.007 -0.022 -0.103 0.905*** 0.186** 0.283*** 0.406*** 0.360***
10th - 5th -0.140 -0.097 -0.038 0.368*** 3.446*** 0.589*** 0.244*** 0.237** 0.020
Panel C: Growth in Capital Expenditures and R&D (%) Lowest 8.67 13.04 12.34 2.38 9.55 -1.22 6.21 1.89 -0.70
2 6.93 7.81 3.84 -3.85 -7.20 -6.83 -3.62 -3.50 -4.76 3 5.53 2.60 0.98 -3.39 -11.18 -5.45 -5.68 -5.77 -5.86 4 3.01 2.10 1.19 -2.96 -10.63 -5.81 -6.10 -7.06 -10.36 5 -0.02 -1.10 -0.35 -1.62 -10.74 -4.73 -4.86 -7.80 -6.46 6 -1.98 0.86 -1.15 -0.12 -9.15 -6.14 -6.56 -5.96 -8.24 7 3.42 0.65 3.07 3.50 -5.87 -4.34 -7.04 -7.22 -7.73 8 3.82 3.54 5.36 8.32 2.38 -2.37 -7.13 -6.43 -7.40 9 4.61 6.16 7.55 13.85 13.93 0.66 -5.33 -6.82 -5.41
Highest 11.21 12.62 18.38 30.84 61.48 20.03 -3.29 -3.37 -1.10 10th - 1st 2.539 -0.427 6.040 28.469*** 51.929*** 21.247*** -9.501*** -5.257* -0.402 1st - 5th 8.689*** 14.143*** 12.684*** 3.998 20.290*** 3.516 11.067*** 9.691*** 5.760**
10th - 5th 11.228*** 13.717*** 18.724*** 32.467 72.220*** 24.762 1.567*** 4.434*** 5.357**
70
Figure 4a. Equity Issues as a Percentage of Total Assets (%)
-5
0
5
10
15
20
25
30
35
-4 -3 -2 -1 0 1 2 3 4
1st accrual decile 5th accrual decile 10th accrual decile
Figure 4b. Contribution from Acquisition as a Percentage of Total Assets (%)
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-4 -3 -2 -1 0 1 2 3 41st accrual decile 5th accrual decile 10th accrual decile
Figure 4c. Growth in Capital Expenditures and R&D (%)
-20
-10
0
10
20
30
40
50
60
70
-4 -3 -2 -1 0 1 2 3 4
1st accrual decile 5th accrual decile 10th accrual decile Figure 4 graphs the time-series means of the operating decision characteristics for firms in the 1st, 5th, and 10th total accrual deciles. The total accruals portfolios are formed in the accrual measurement year zero, with total accruals calculated using the balance sheet method. Figure 4a graphs the firm’s equity issues as a percentage of total assets (Compustat data item 108/item 6), Figure 4b the contributions from acquisitions as a percentage of total assets (Compustat data item 129/item 6), and Figure 4c the growth in capital expenditures and R&D (Compustat data item 128 + item 46). All three measures are size adjusted. The sample contains firm-years from 1963 to 2004.
71
Panels A-C of Table 7 demonstrate that firms in decile 10 exhibit very high levels of investment-
financing activity in year 0 and in prior years compared to decile 5. In Panel A, mean amount of equity
issued as a percentage of total assets is 30.62% for decile 10 compared to -2.75% for decile 5 in year 0, and
the difference is highly significant. While the decile 10’s equity issues are of considerably smaller
magnitudes in year -4 through -1, they are nonetheless significantly greater than those of the firms in decile
5. The lowest accrual decile firm, contrary to the fixation hypothesis, also raises equity in year 0, but the
magnitude is considerably smaller at 7.21% of its total assets.46 Overall, the evidence on firms’ equity
issues reinforces the asymmetric pattern as predicted under the agency hypothesis.
Besides equity issues, the M&A activity as well as the growth in capital expenditures and R&D
expenditures for decile 10, but not decile 1, are high in year 0. The differences between the highest and the
lowest accrual firms increase in years prior to and peak in year zero, when the highest accrual-decile firms
have 10 times larger levels of M&A activity, and 6 times higher growth in capital and R&D expenditures
compared to the lowest accrual decile firms. This supports the overvaluation hypothesis, but the
asymmetry in the investment-financing decisions is not predicted under the fixation hypothesis.
Mishkin Test
In addition to documenting the predictability of returns using accruals, the literature shows that
investors overestimate the persistence of the (discretionary) accrual component of earnings. Such evidence
is consistent with the fixation hypothesis. Following the literature, in this sub-section we use the Mishkin
(1983) test to determine whether the relation between accruals and stock returns is asymmetric, i.e., non-
linear. Evidence of asymmetry would be inconsistent with the fixation hypothesis. We apply the
Mishkin (1983) framework of testing the rational expectations hypothesis and estimate the following
system of simultaneous equations:
12101 Accruals Total FlowsCash Earnings ++ +++= tttt ξγγγ (3)
1**
1*
1101 ) AccrualsTotal FlowsCash Earnings(Returns Abnormal20 +++ +−−−+= ttttt ζγγγββ (4)
Equation (3) is the forecasting equation for predicting one-year-ahead earnings and γ coefficients
reflect the persistence of the earnings components. Equation (4) is the valuation equation and γ*
coefficients reflect the market persistence beliefs in valuing stocks. Sloan (1996) and others document that
market underestimates the persistence of cash flows ( *11 γγ > ) and overestimates the persistence of accruals
( *22 γγ < ), which contributes to the predictability of returns using accruals. Under the fixation hypothesis,
investors are expected to overestimate the persistence of accruals in a similar fashion for income-increasing
and income-decreasing accrual firms. That is, fixation should be symmetric. Hence, we predict *22 γγ − of
a similar magnitude across sub-samples under the fixation hypothesis. In contrast, the agency cost of
46 The surprising positive equity issues for the 1st decile could be due in part to the low value of assets of the firms reporting losses, i.e., low accruals.
72
T a b l e 8 Mishkin Test of the Market Pricing of Cash Flows and Accruals
This table presents results of the Mishkin test. Panel A reports the market pricing of the cash flow and total accrual components of earnings. Panel B reports the market pricing of the cashflow, discretionary accrual, and non-discretionary accrual components of earnings. We present two sets of estimates: (i) the coefficients estimated via the iterated non-linear least squares using full sample of firm-years (“Pooled Estimates”); and (ii) Fama-MacBeth coefficients and t-statistics generated from annual estimates of the iterated non-linear least squares. In addition, we implement the Mishkin test for two subsets of the sample. Based on accruals in year t (total accruals in Panel A and discretionary accruals in Panel B) we separate the sample into bottom five accrual decile firm-years (1st through 5th deciles) and top five accrual decile firm-years (6th through 10th deciles). The sample contains all non-financial firms from 1963 to 2004 with data on both CRSP and Compustat in year t and t+1 for which abnormal buy-and-hold returns can be calculated. The t-statistics for the difference in the coefficients are reported in round parentheses and the chi-square statistics for the difference in the estimated coefficients are reported in square parentheses. ***, **, and * indicate significance of the test statistics for the difference in estimates at 1, 5, and 10 percent significance levels.
Panel A: Total Accruals
1**
1*
1101
12101
) AccrualsTotal FlowsCash Earnings(Returns Abnormal AccrualsTotal FlowsCash Earnings
20 +++
++
+−−−+=
+++=
ttttt
tttt
ζγγγββξγγγ
Pooled Estimates Fama-MacBeth Estimates
Full
Sample
1st to 5th Accrual Decile Firm-
Years
6th to 10th Accrual Decile
Firm-Years Full
Sample
1st to 5th Accrual Decile Firm-
Years
6th to 10th Accrual Decile
Firm-Years γ1 0.746 0.763 0.732 0.761 0.764 0.770 γ1* 0.613 0.620 0.663 0.677 0.595 0.722 γ1 - γ1* 0.133 0.143 0.069 0.084 0.169 0.047
[38.17]*** [18.35]*** [5.61]** (1.85)* (3.71)*** (0.69)
γ2 0.703 0.701 0.713 0.706 0.695 0.709 γ2* 0.796 0.411 0.899 0.833 0.454 0.698 γ2 - γ2* -0.092 0.291 -0.186 -0.127 0.240 0.011
[6.34]** [11.12]*** [13.14]*** (1.03) (3.33)*** (0.18)
Panel B: Discretionary and Non-discretionary Accruals
1*3
*2
*1
*01101
132101
)lsary Accruadiscretion-Non lsary AccruaDiscretion FlowsCash Earnings(Returns Abnormal
lsary Accruadiscretion-Non lsary AccruaDiscretion FlowsCash Earnings
+
++
++
+−
−−−−+=
++++=
tt
tttt
ttttt
ζγγγγββ
ξγγγγ
Pooled Estimates Fama-MacBeth Estimates
Full
Sample
1st to 5th Accrual Decile Firm-
Years
6th to 10th Accrual Decile
Firm-Years Full
Sample
1st to 5th Accrual Decile Firm-
Years
6th to 10th Accrual Decile
Firm-Years γ1 0.746 0.762 0.726 0.760 0.758 0.770 γ1* 0.612 0.617 0.647 0.636 0.596 0.686 γ1 - γ1* 0.134 0.145 0.079 0.124 0.163 0.084
[38.99]*** [16.33]*** [8.97]*** (3.08)*** (3.42)*** (1.79)*
γ2 0.709 0.705 0.683 0.710 0.703 0.699 γ2* 0.837 0.500 0.860 0.692 0.481 0.697 γ2 - γ2* -0.128 0.204 -0.177 0.018 0.222 0.002
[9.91]*** [4.44]** [9.80]*** (0.41) (2.08)** (0.04)
γ3 0.685 0.648 0.710 0.688 0.675 0.704 γ3* 0.668 0.449 0.756 0.617 0.547 0.671 γ3 - γ3* 0.017 0.199 -0.047 0.071 0.129 0.033
[0.07] [2.81]* [0.43] (0.75) (0.92) (0.37)
73
overvalued equity hypothesis predicts that *22 γγ − would be negative for high accrual firms and zero for
the low accrual firms.
We briefly comment on whether potential differences in the persistence of low and high accrual
firms due to accounting conservatism might generate the observed asymmetry and thus confound with the
predictions of the agency hypothesis. Low accrual firms typically report losses. As reported in table 1,
mean and median earnings before extraordinary items for the lowest accrual decile firms are negative.
Because of accounting conservatism, losses often represent a capitalized amount of accruals, including asset
write-offs and impairments, which are less persistent than gains. Therefore, naïve investor fixation on
earnings and over-estimation of persistence are expected to be a more severe problem with low accruals
than high accruals.47 Thus, the conservatism phenomenon is likely to bias against finding the hypothesized
asymmetric relation predicted under the agency hypothesis.
Table 8 presents results of the Mishkin test for the full sample and two sub-samples of firm-years in
the top and bottom five deciles of the accrual distribution. Panel A reports results of the market pricing for
the cash flow and accrual components of earnings. Panel B further decomposes the accruals into
discretionary and non-discretionary components. In panel B, we split the full sample into sub-samples at
the median of the discretionary-accrual distribution. We report coefficients estimated using the pooled
sample regressions as well as the Fama-MacBeth coefficient estimates of the non-linear system (3)-(4) and
test whether *11 γγ = and *
22 γγ = .
We find that investors’ mis-processing of the persistence of accruals differs dramatically between
income-increasing and income-decreasing accruals. Surprisingly, investors underestimate, not
overestimate, the persistence of accruals for the low accrual decile portfolios 1 through 5. For these firms,
( *22 γγ − ) is positive 0.29 when estimated for the pooled-sample and 0.24 using the Fama-MacBeth
estimates, both significant at the 1% level. Similarly, when we decompose accruals into discretionary and
non-discretionary components, the bias is due mostly to investors underestimating the persistence of
discretionary accruals. In contrast, investors overestimate the persistence of accruals for the high accrual
decile portfolios 6 through 10. Based on the pooled-sample estimates, ( *22 γγ − ) is -0.18 for total accruals
in Panel A and -0.17 for discretionary accruals in Panel B, both significant at the 1% level. The Fama-
MacBeth estimates suggest that investors’ pricing of total and discretionary accruals is indistinguishable
from rational pricing in an efficient market.
We also performed the Mishkin test by each decile. We do not find a consistent pattern of over- or
under-estimation of the persistence of accruals across the deciles. This is not surprising. There is very little
variation in the independent variable (accruals) when the analysis is conducted by deciles formed on the
47 Alternatively, investor naiveté varies systematically across accrual deciles, which makes it impossible to predict ex ante how it will affect the relation between accruals and future returns.
74
basis of accruals, which econometrically leads to imprecise estimation and large standard errors. Naturally,
a consistent pattern in the results fails to emerge.
Overall, results using the Mishkin test reinforce the asymmetry in investors’ pricing of income-
increasing and income-decreasing accruals. Since we are able to replicate the accrual anomaly for the full
sample, the evidence of asymmetry is unlikely to be due to some unusual attributes of our sample. The
observed asymmetry is inconsistent with investor fixation on accruals. The results are consistent with the
agency hypothesis in that investors over-estimate the persistence of high accrual firms. Surprisingly,
however, we also find that investors underestimate the persistence when accruals are low. This result is not
predicted under the agency hypothesis or the fixation hypothesis.
3.4.5. Relation between Stock Returns and Accruals To further discriminate between the fixation and agency hypotheses, in this section we test for the
causality implications of the two hypotheses. The fixation hypothesis implies that investors’ over-
estimation of accrual persistence leads to stock-price over-reaction, especially in the extreme accrual
portfolios. This means extreme accruals should forecast future return reversals, whereas past returns should
not predict future accruals. The agency theory, on the other hand, contends that it is over-valuation in the
first place that leads to overstated accruals. Below we discriminate between the hypotheses by first
performing an instrumental variable analysis, which shows that overvaluation causes earnings management.
Second, we perform quantile regressions (described below), which demonstrate a striking asymmetry in the
relation between accruals and past and current returns.
Instrumental Variables Analysis
We regress accruals on past and present abnormal returns, with abnormal returns as a crude proxy
for overvaluation. However, we recognize that returns contain information about (future) earnings and
hence accruals (see Beaver et al. 1980, and Collins et al. 1987), so past returns’ predictive ability can be due
to returns leading earnings, not just overvaluation. To enhance the quality of abnormal returns as a proxy
for overvaluation, we propose instruments that are likely to be correlated with overvaluation, but not with
the information about future unmanaged accruals or earnings. This set of instruments, when used in the
two-stage least squares framework, allows us to identify the causal relation between overvaluation and
future accruals as implied by the agency hypothesis.
One set of instruments is managerial actions, except earnings management, which firms are likely
to take to prolong the overvaluation. Our instruments include: (i) equity issuance as a percentage of total
assets, (ii) acquisitions as a percentage of total assets, (iii) growth in PPE and PPE as a fraction of total
assets, (iv) growth in R&D and R&D as a fraction of total assets, (v) growth in capital expenditures and
capital expenditures as a fraction of total assets, (vi) dummy for a positive income contribution from
acquisitions, and (vii) dummy for a positive change in goodwill. Under the agency hypothesis, an increase
in each of these variables is indicative of overvaluation, but is unlikely to be correlated with future
unmanaged accruals.
75
Table 9 reports the results of 2SLS regressions of accruals on one year lagged returns (Panel A) and
contemporaneous returns (Panel B), where the returns are instrumented using firm characteristics above. In
our analysis we require non-missing data on the instrumental variables and buy-and-hold abnormal returns
(described in Section 4.1.1).48 The instruments are measured contemporaneously with the independent
variable (abnormal return). The table presents time-series average coefficients and associated Fama-
MacBeth test statistics.
T a b l e 9 Relations between Returns, Accruals, and Operating Decisions
This table presents evidence of a causal relation between prior/present returns (as proxies for overvaluation) and current accruals and operating decision characteristics. Panel A reports time series means of slope coefficients from cross-sectional regressions of accruals at time t on annual buy-and-hold abnormal returns at time (t-1) where the returns are instrumented using instrumental variables measured at time (t-1). Panel B reports time series means of slope coefficients from cross-sectional regressions of accruals at time t on annual buy-and-hold abnormal returns at time t where the returns are instrumented using instrumental variables measured at time t. Annual buy-and-hold abnormal returns are size and book-to-market adjusted as described in Table 2. In both panels the instrumental variables are (i) equity issuance as percentage of total assets, (ii) acquisitions as percentage of total assets, (iii) growth in PPE and PPE as a fraction of total assets, (iv) growth in R&D and R&D as a fraction of total assets, (v) growth in CapEx and CapEx as a fraction of total assets, (vi) dummy for positive income contributions from acquisitions, and (vii) dummy for positive change in good-will. Panel C reports the time series means of the slope coefficient of the cross-sectional regression of operating decisions at time t on annual buy-and-hold abnormal returns at time (t-1). We consider six operating decisions characteristics: (i) equity issues as a percentage of total assets (Compustat data item 108/item 6), (ii) debt issues as a percentage of total Assets (Compustat data item 111/item 6), (iii) contributions from acquisitions as a percentage of total assets (Compustat data item 129/item 6), (iv) growth in capital expenditures (Compustat data item 128), (v) growth in R&D expenditures (Compustat data item 46), and (vi) growth in property plant and equipment (Compustat data item 7). The sample contains all non-financial firms from 1963 to 2004 with data available on both CRSP and Compustat in year t and (t-1). T-statistics are based on Fama-MacBeth standard errors.
Panel A: 1Accruals Abnormal Returnt t tα β ε−= + ⋅ +
1 1 1Abnormal Return Instrumental Variablest t tc D ξ− − −= + ⋅ +
Coefficient (β) T-stat P-value Number of
observations Total Accruals 0.0764 2.556 0.015 38 Discretionary Accruals 0.0390 2.111 0.041 38
Panel B:Accruals Abnormal Returnt t tα β ε= + ⋅ + Abnormal Return Instrumental Variablest t tc D ξ= + ⋅ +
Coefficient (β) T-stat P-value Number of
observations Total Accruals 0.1568 4.101 0.001 38 Discretionary Accruals 0.1240 4.014 0.001 38
Panel C: 1Operating Decision Abnormal Returnt t tα β ε−= + ⋅ +
Coefficient (β) T-stat P-value Number of
observations Equity Issues (% of Total Assets) 0.0565 6.468 0.001 32 Debt Issues (% of Total Assets) 0.0268 6.444 0.001 32 Acquisitions (% of Total Assets) 0.0086 7.691 0.001 32 Growth in Capital Expenditures 0.5610 11.157 0.001 38 Growth in R&D 0.0725 10.906 0.001 38 Growth in PPE 0.1356 11.157 0.001 38
48 Since we use the buy-and-hold abnormal return we limit our consideration to December fiscal-year-end firms.
76
Panel A shows year -1 abnormal returns’ effect on year zero total and discretionary accruals. The
coefficients on lagged returns are 0.076 (p-value 0.02) for total accruals and 0.039 (p-value 0.04) for
discretionary accruals. The coefficient magnitudes imply one percentage point increase in lagged buy-and-
hold abnormal returns leads to a 7.6 basis-point increase in total accruals as a percentage of total assets and
a 3.9 basis-point increase in discretionary accruals. Since the highest accrual-decile firms exhibit 29.5%
abnormal buy-and-hold return in year -1, it translates into a 2.24% increase in total accruals as a percentage
of assets. Panel B reports contemporaneous 2SLS regression of year zero accruals on year zero returns.
The coefficient magnitudes more than double to 0.157 and 0.124 in the total and discretionary accrual
cases, with both being significant at the 1% level. Since the return variable in these regressions is the fitted
value of returns using proxies for overvaluation, the evidence supports our conjecture that the agency
hypothesis contributes to the accrual anomaly.
Finally, Panel C of Table 9 shows that overvaluation proxies predict managements’ investment-
financing decisions. We show that lagged buy-and-hold abnormal returns lead to increased levels of equity
and debt issuance, participation in acquisitions, and investments in capital and R&D. This evidence
validates our choice of instrumental variables and also provides evidence consistent with the agency
hypothesis.
Relation between Accruals and Returns: Quantile Regression Results
We evaluate the symmetry in the accrual-return relation by examining the effect of returns on the
tails of accrual distribution. This is done using the Quantile regression framework. Similar to an OLS
regression, which models the relation between regressors and conditional mean of the distribution of the
dependent variable, a quantile regression estimates the relation between regressors and the conditional
quantiles of the distribution of interest (see Koenker and Hallock, 2001, for details and economic
applications). Specifically, a Quantile regression estimates the linear conditional quantile function
qxqxyFyxqQ β')|(|min)|( =≥≡ , where the estimated ∑=
−=n
iiiq
q xy1
)'(minargˆ βρββ
, where
)1()( 0 <−= zq qzzρ .
For each quantile q ∈0.05, 0.1, 0.2, 0.3, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95 of the dependent variable, we
estimate the following models:49 qtt
qqt ζβα ++= −1ReturnsAbnormalAccruals (5)
qtt
qqt ζβα ++= ReturnsAbnormalAccruals (6)
49 Although we estimate the quantile regression model for each quantile of the dependent variable, quantile regressions are not equivalent to the OLS regressions estimated over subsets of observations partitioned on the dependent variable into quantiles. It’s well-known that the latter lead to biased and inconsistent slope coefficient estimates because the regression errors are likely to be non-zero for different partitions of the data on the dependent variable. In contrast, quantile regressions employ all of the data when fitting the quantiles and therefore produce unbiased and consistent effects of the independent variables on conditional quantiles.
77
Table 10 presents time-series average coefficient estimates and Fama-MacBeth t-statistics for the
quartile regressions. Panel A and Panel B report the slope coefficients for the cases of total and
discretionary accruals. Figure 5 presents our results graphically showing not only Fama-MacBeth slope
coefficient estimates but also pooled sample estimates plotted against different quantiles q.50
T a b l e 10 Quantile Regression Analysis of the Relation between Returns and Accruals
The table reports the time series means and Fama-MacBeth t-statistics for the slope coefficients from cross-sectional regressions: (i) of accruals in year 0 on annual abnormal buy-and-hold return in year -1, and (ii) of annuals abnormal buy-and-hold return in year +1 on accruals in year 0. The coefficients for each quantile q regression are estimated as follows:
−=
−=
<
=∑
)1()(
)'(minargˆ
0
1
zq
n
iiiq
q
qzz
xy
ρ
βρββ
Panel A presents the results for total accruals, whereas Panel B presents the results for discretionary accruals. Annual buy-and-hold abnormal returns are size and book-to-market adjusted as discussed in Table 2. The total accruals are computed using the balance sheet data. The discretionary accruals are estimated via within industry, cross-sectional modified Jones model. The sample contains all non-financial firms that are present in both CRSP and Compustat in years -1, 0, and 1 and covers period from 1963 to 2004.
Accrualsit = α + β Retit-1+εit Accrualsit = α + β Retit+εit Quantile of Distribution
q Slope
Coefficient T-Stat Slope
Coefficient T-Stat Panel A: Total Accruals
5% 0.021 (4.88) 0.006 (1.37) 10% 0.020 (5.39) 0.004 (1.28) 20% 0.021 (6.83) 0.004 (1.40) 30% 0.022 (7.89) 0.002 (0.88) 40% 0.024 (8.78) 0.001 (0.49) 50% 0.027 (9.59) 0.001 (0.47) 60% 0.031 (11.44) 0.002 (0.75) 70% 0.036 (11.50) 0.003 (1.20) 80% 0.045 (12.43) 0.006 (1.97) 90% 0.067 (13.45) 0.015 (3.29) 95% 0.092 (13.93) 0.026 (3.79)
95%-5% 0.071 (13.23) 0.019 (2.59) 95%-50% 0.066 (12.17) 0.024 (4.18) 5%-50% -0.005 (1.69) 0.005 (1.37)
Panel B: Discretionary Accruals 5% 0.010 (2.69) -0.003 (0.58)
10% 0.011 (3.89) -0.003 (0.91) 20% 0.013 (5.32) -0.004 (1.83) 30% 0.013 (6.22) -0.004 (2.23) 40% 0.013 (7.00) -0.004 (2.59) 50% 0.013 (8.33) -0.003 (1.87) 60% 0.014 (9.72) -0.003 (1.64) 70% 0.017 (11.76) -0.003 (1.69) 80% 0.021 (12.68) -0.003 (1.29) 90% 0.033 (12.93) 0.001 (0.01) 95% 0.054 (9.68) 0.003 (0.52)
95%-5% 0.045 (8.78) 0.006 (0.87) 95%-50% 0.042 (8.08) 0.006 (1.18) 5%-50% -0.003 (1.17) 0.001 (0.01)
50 In this section of our analysis we use December fiscal-year-end firms for which the data on total (discretionary) accrual and returns in years -1, and 0.
78
Figure 5a. Quantile Regressions of Total Accruals on Past Returns
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.02 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.98Quantile
Slop
e C
oeff
icie
nt E
stim
ates
Fama MacBeth Pooled Sample
Figure 5b. Quantile Regressions of Discretionary Accruals on Past Returns
- 0.02
0
0.02
0.04
0.06
0.08
0.1
0.02 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.98Quantile
Slop
e C
oeff
icie
nt E
stim
ates
Fama MacBeth Pooled Sample
Figure 5c. Quantile Regressions of Total Accruals on Contemporaneous Returns
0
0.01
0.02
0.03
0.04
0.05
0.06
0.02 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.98Quantile
Slop
e C
oeff
icie
nt E
stim
ates
Fama MacBeth Pooled Sample
Figure 5d. Quantile Regressions of Discretionary Accruals on Contemporaneous Returns
- 0.01
- 0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.02 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.98Quanti le
Slop
e C
oeff
icie
nt E
stim
ates
Fama MacBeth Pooled Sample
Figure 5 graphs the slope coefficients for quantile regressions of accruals in year 0 on annual abnormal buy-and-hold returns in year -1 (Figures 5a and 5b), and slope coefficients for the quantile regressions of accruals in year 0 on annual abnormal buy-and-hold returns in year 0 (Figures 5c and 5d). The slope coefficients are estimated for the following set of percentiles: 2%, 5%, 10% through 90%, 95%, and 98%. The buy-and-hold annual abnormal returns are size and book-to-market adjusted (see Table 2 for calculation details). Figures 5a and 5c graph results for the total accrual portfolios, while Figures 5b and 5d present for the discretionary accrual portfolios.
Estimation of model (5) reveals that high abnormal returns of year -1 positively impact year 0
accruals, but this phenomenon is observed primarily for the upper tail of the accrual distribution. In case of
total accruals, the slope coefficient 95.0β is 0.09, which is 4.5 times as large as the 05.0β coefficient of
0.02. A similar order of magnitude difference is observed when the regressions use discretionary accruals.
Figures 5a and 4b reveal striking patterns in quantile coefficients where the relation appears to grow
geometrically as we approach the tail of the income increasing accruals. The evidence suggests that
variation in prior returns drives higher accrual quantiles to a much greater extent. This is consistent with
abnormal price run-ups driving accruals of those firms that are likely to be manipulate them.
Estimation of model (6) shows that contemporaneous return-accrual relation is weak over the range
of accrual distribution except for its highest quantiles. The evidence is in line with that of the predictive
79
model (5) and confirms pronounced asymmetry in the accruals-return relation. Overall the results of this
section confirm the pronounced asymmetry in the relation between abnormal returns and accruals.
3.5. Summary and conclusions
Agency theory of overvalued equity predicts that the overvalued firms are likely to engage in
income increasing earnings management in order to meet the unrealistic performance expectations
incorporated in the stock prices. This prediction suggests an alternative explanation for accrual anomaly as
we expect that a sub-sample of firms with upward managed accruals will be more heavily populated with
overvalued firms and the subsequent negative stock performance of such companies is a mere overvaluation
reversal. We formulate a number of testable predictions that allow us to distinguish between the agency
theory of overvalued equity and the traditional naïve investor fixation hypothesis as the driving force
behind the accrual anomaly.
Consistent with the agency theory of overvalued equity, we find an asymmetry in the relation
between accruals and returns, accruals and analyst optimism, accruals and insider-trading patterns, and
accruals and corporate investment-financing decisions. Such asymmetry is not predicted under the naïve
investor fixation on accruals. We find that companies in the highest income increasing accrual decile
experience an economically large abnormal price run-up prior to the accrual management year, which is
followed by stock underperformance in the subsequent years. This type of relation is not observed for the
lowest accrual decile portfolio. Finally we find evidence consistent with the prediction of the agency
theory of overvalued equity using the instrumental variable framework which allows us to isolate a casual
relationship from overvaluation to accrual management.
Overall, the evidence in our study casts doubt on the prevailing hypothesis that market naively
fixates on accruals or earnings. In contrast to earlier studies that merely present evidence inconsistent with
fixation, we provide an alternative economic mechanism rooted in the agency theory of overvalued equity
to explain the relation between returns and accruals.
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Chapter 4
The Endogeneity Bias in the Relation between Cost-of-Debt Capital and Corporate Disclosure Policyπ
4.1. Introduction
Corporate disclosure policy is one of the most widely researched topics in accounting. Theory has
generally suggested a negative causal relation between the quality of information disclosed by a firm and its
cost of capital (Verrecchia, 2001, Dye, 2001, Easley and O’Hara, 2004). The basic idea is that disclosure
reduces both the information differences and incentive problems between the firm and its investors (Healy
and Palepu, 2001). Investors, then, ‘reward’ firms for high-quality disclosures with lower required returns.
In recent years, however, both the existence and sign of the relation between disclosure and cost-of-
capital has been called into question not in the least because the empirical literature has provided
conflicting results. While some studies find strong negative associations consistent with theoretical
predictions (Welker, 1995, Leuz and Verrecchia, 2000, Sengupta, 1998), other fails to document a
significant relation (Botosan and Plumlee, 2002, Botosan and Frost, 1998), find only partial evidence
(Botosan, 1997, Healy et al., 1999, Richardson and Welker, 2001) or even report a positive association
(Heiflin, Shaw and Wild, 2003).
Some commentators have pointed to the possibility of endogeneity bias as a potential explanation
why empirical findings are not consistent with theory and report contradicting results with regard to the
sign of the relation (Healy and Palepu, 2001, Core, 2001, Zhang, 2001).51 It is well know that endogeneity
causes Ordinary Least Squares regressions to be biased and inconsistent (Wooldridge, 2002). Findings from
OLS regressions of cost-of-capital onto disclosure are difficult to interpret in the presence of endogeneity
and this may very well account for the lack of agreement in the empirical literature on the sign of the
relation.
π Based on the paper co-authored with Laurence van Lent (Tilburg University) and published in European Accounting Review, Vol. 14, 2005. 51 Other potential explanations for these conflicting results are the current high standards of mandatory disclosure (rendering voluntary disclosure choices of second order importance) and measurement problems in the somewhat elusive key constructs of ‘information problems’ and ‘disclosure quality’ (Leuz and Verrecchia, 2000, Healy and Palepu, 2001, Zhang, 2001).
85
We document the effect of endogeneity bias on the relation between disclosure and cost-of-debt
capital. We define endogeneity bias broadly as any situation where the disturbance term of the structural
equation is correlated with one or more independent variables.52 Intuitively, our reasoning is that
differences exist in the cost of debt that are correlated with the firm’s disclosure policy, but that are not
necessarily caused by this policy. Instead, these differences are caused either by (1) unobservable
heterogeneity among firms in a cross sectional sample or (2) observable determinants of cost-of-debt capital
which are correlated with disclosure but omitted from the analysis. Note that these two sources of
endogeneity bias are both variations of the correlated omitted variable problem and are in fact theoretically
equivalent. To an empirical researcher they are different, however, because the first source is unobservable
and should be roughly constant over time, while the second is observable and may change over the period
of investigation. We will provide an illustration of both sources of endogeneity bias in turn.
One example of unobserved heterogeneity is the difference in ‘costs of disclosure’53 among firms.
High costs of disclosure will reduce the optimal level of disclosure and at the same time increase the
equilibrium cost-of-capital (Zhang, 2001). While in a cross sectional analysis, it will appear as if disclosure
is causally related to cost-of-capital, what we observe in fact are equilibrium changes of both disclosure
level and cost-of-capital each caused by the unobservable firm-specific characteristic of ‘costs of
disclosure’.
At least some of the determinants of a firm’s disclosure choice would appear to be also related to
the default risk of the firm (Jaffee, 1975, Kidwell et al. 1984, Fung and Rudd, 1986), and as such impact on
the cost-of-debt.54 For example, larger firms are generally considered less risky and therefore enjoy lower
cost-of-debt capital (Fama and French, 1992, 1993). Larger firms also benefit from economies of scale in
producing information. They usually have specialized departments set up to deal with investors’
information needs and it will generally be less costly for them to compile more information and disclose it
to the capital market. Empirically, size is significantly correlated with disclosure in many studies. In sum,
size is associated both with cost-of-debt and with disclosure. When omitted from the analysis, one may find
52 This definition is consistent with the econometrics literature (Greene, 2000, Wooldridge, 2002) and with the proposal in Chenhall and Moers (2004). 53 Often these costs of disclosure are defined to include the costs of collecting, processing, reporting and verifying information and the cost due to loss of competitiveness (see, e.g., Wagenhofer, 1990, Guo, Lev and Zhou, 2004). Potentially interesting definitions also refer to the costs associated with uncertainty about investor reactions to a certain disclosure (Fishman and Hagerty, 2003, Verrecchia, 2001) or litigation costs (Skinner, 1997). 54 Within standard asset pricing models, such as the CAPM, only undiversifiable risk is priced on the market, and therefore we have to assume that the proposed joint determinants of ‘cost-of-debt capital’, such as the firm’s default risk, are at least partly correlated across firms. Indeed, an often-heard critique on studies that relate disclosure to cost of capital is that differences in disclosure quality are idiosyncratic and therefore should not ‘survive the forces of diversification’ (Leuz and Verrecchia, 2005: 1) nor impact on the cost-of-capital. Leuz and Verrecchia (2005), in contrast, argue that disclosure improves the coordination between the firm and its investors with respect to capital investment decisions. As such, poor disclosure quality can lead to misaligned investments and higher cost-of-capital. Other studies have suggested that disclosure may impact on cost-of-capital, even if it is idiosyncratic, because it improves market liquidity (Verrecchia, 2001, Leuz and Verrecchia, 2000), reduces estimation risk (Barry and Brown, 1985) or increases the investor base (Merton, 1987).
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a negative relation between cost-of-debt and disclosure policy, but this association is likely driven by firm
size.
After a brief review of the econometrics of endogeneity, we discuss in more detail the sources of
endogeneity bias in the relation between disclosure and cost of capital. We then document empirically the
effect of endogeneity bias in regressions of cost-of-debt capital on disclosure policy. Specifically, we use
Sengupta’s (1998) original model55 as a starting point of our analysis and replicate this study’s results in a
sample similar to his. As in Sengupta, we establish a strong negative association between disclosure and
cost-of-debt capital. We then augment Sengupta’s model with variables that are known to be associated
with a firm’s disclosure policy and which are likely to affect cost-of-debt capital in order to address the
endogeneity bias caused by omitted variables. Our results show that the coefficient on disclosure is reduced
to approximately 50% of its former magnitude in the benchmark model and disclosure is no longer
significantly related to cost-of-debt capital in the augmented version of our regressions. The omitted
variable effect seems substantial.
Next, we evaluate both sources of endogeneity bias at the same time and use panel data techniques
to estimate the augmented model. We find that once observable determinants of disclosure and cost-of-debt
capital are included in the regression and the estimation technique controls for firm-specific effects, we re-
establish the negative association between disclosure and cost-of-debt capital. The association is stronger
than before and the difference is economically significant – the fixed effects coefficient on disclosure is
over 200% larger than the OLS coefficient in the same model – which suggests that the cost-of-capital
benefits of increased disclosure are much larger than previously thought and economically significant.
Based on these analyses, our beliefs about the existence of endogeneity bias in the benchmark model are
reinforced. We then suggest a simple procedure to directly assess whether the independent variables in the
regression (in particular, the disclosure policy variable) are associated with unobservable firm heterogeneity
and document that, in fact, disclosure policy is strongly positively correlated with firm heterogeneity.
Synthesizing our findings, we show that at the level of the individual firm, increases in disclosure
are causally56 associated with lower cost-of-debt capital. However, in cross-sectional analyses that do not
control for endogeneity bias, a negative association between these two variables should not be interpreted
causally and is likely caused by firm heterogeneity effects, which are compounded in the disclosure
variable. The resulting association between disclosure and cost-of-capital is (at least partly) spurious.
Together these results speak strongly in favor of dealing explicitly with endogeneity when
investigating the relation between disclosure policy and cost-of-capital. Note that while endogeneity has 55 Sengupta’s model provides a convenient vehicle to illustrate the effect of endogeneity bias in disclosure research. It is also to some extent an arbitrary choice since endogeneity bias is present in many contexts in (financial) accounting research and many potential candidates exist for similar analysis as is conducted in this paper. Chenhall and Moers (2004), Ittner and Larcker (2001), and Larcker and Rusticus (2005) provide helpful discussions of endogeneity in accounting research. 56 We recognize that causal statements cannot be made based on statistical considerations, but only on theory. When we refer to a causal relation, we use this as shorthand for ‘a causal relation as suggested by theory and underpinned by empirical evidence’.
87
been identified as the ‘most important limitation’ (Healy and Palepu, 2001, 430) of disclosure studies, few
attempts have been made to address the issue empirically (Cohen, 2003).
The remainder of this paper is organized into six sections. Section 2 provides a self-contained
discussion of the econometrics of endogeneity bias in the context of financial accounting research. Section
3 discusses firm heterogeneity and correlated omitted determinants as two sources of endogeneity bias in
the relation between cost-of-debt capital and disclosure. Section 4 outlines the research design and provides
the variable definitions. Section 5 describes the sample and some summary statistics. Section 6 presents the
empirical results on the extent of endogeneity bias in the association between disclosure and cost-of-debt
capital. The final section summarizes the results and discusses the limitations to our analyses.
4.2. A note on endogeneity
The traditional textbook definition of endogeneity we used so far requires the disturbance term in
the structural equation to be correlated with one or more explanatory variables. This rather arcane definition
is not very helpful to applied researchers. We therefore propose a more intuitive definition (following
Heckman, 2000), which is closer to the practice of economists. Economics “undertakes to study the effect
which will be produced by certain causes, not absolutely, but subject to the condition that other things are
equal and that causes are able to work out their effects undisturbed” (Marshall 1961, p. 36). Researchers
aim at identification of these causal effects, which is done by measuring the effect of a certain cause while
holding all the other causes in the model constant. This in itself is not a straightforward task since many
causes will not vary independently. Our intuitive definition of endogeneity then is any situation where the
ceteris paribus condition is not fulfilled whenever the independent variable of interest is changed.
Empirical researchers typically use an economic model or informal reasoning to arrive at a
structural model, which represents the causal relations between the variables of interest. Although theory or
earlier empirical work will often suggest that many of these variables cannot be said to be truly exogenous,
empirical researchers will have to assume some are, to estimate the parameters of the structural model. A
careful justification of why certain variables are exogenous is therefore required. In his presidential address,
Demski (2004) advocates to explicate the micro foundations (preferences, expectations) of the choice
behavior of economic actors in the relation under study and to apply equilibrium reasoning to derive a
structural model. Such procedure allows for a better understanding of how all the salient aspects of
behavior, such as causal effects, are captured into the model.
Suppose an empirical researcher is interested in the following structural model:
uxxxy kk ++++= ααα ...2211 (A)
where y, x1, x2, … xk are observable random scalars and u is the unobservable random disturbance.
An explanatory variable xj is said to be endogenous in equation A if it is correlated with the disturbance
term u; xj is exogenous if it is uncorrelated with the disturbance term. It is important to stress that in this
‘empirical’ or econometric definition, variables are inherently neither exogenous nor endogenous; instead
88
their nature is conditional on the way the structural model is written (Greene, 2000). An empirical
researcher will be interested in estimating the parameters in the structural model. It is important to the
researcher to know whether an explanatory variable is endogenous in a specific structural equation because
it affects the way in which its parameter should be estimated. The upshot of all this is that it is paramount to
be careful when using the words ‘endogenous’ or ‘exogenous’, since these designations are context-
specific. The litmus test of the econometric form of endogeneity is whether the parameters of interest in the
context of a specific structural model are affected by correlation between any explanatory variables and the
disturbance term (Maddala, 2001). If they are the variable is said to be endogenous, if not it is exogenous.
Since there is no clean-cut statistic or diagnostic instrument available to ‘test’ for endogeneity, the
econometrics literature often advises empirical researchers to apply introspection (Wooldridge, 2002) or the
criterion of reasonableness57 (Greene, 2000, Kennedy, 2003) as a way to determine whether there is an
endogeneity problem. It would appear that researchers are left rather vulnerable against allegations that
their model suffers from ‘endogeneity problems’. In the end, researchers have to determine which variables
they care about (i.e., are the focus of their analysis) and should therefore be as free from bias as possible,
and which variables they do not care about and are only in the model as a control. Bias in the estimates of
the latter variables are less of a problem and should not be weighted to heavily when evaluating the
soundness of empirical work.
4.2.1. Sources of ‘econometric’ endogeneity The source of correlation between the structural disturbance and an explanatory variable is
important because it provides clues how endogeneity can be addressed. Wooldridge (2002) lists three
common sources of endogeneity: (1) omitted variables, (2) simultaneity and (3) measurement error. Our
discussion will focus on the first two of these. Considerable advances have been made to mitigate
measurement error in variables using latent variables techniques. While some of the methods to address
endogeneity we discuss below may also reduce measurement error, the literature seems to move towards
the use of these latent variables techniques (Larcker and Rusticus, 2005), and we defer further elaboration
here. Note that each source of econometric endogeneity will affect the consistency of the estimation in a
similar fashion and as such confound the interpretation of the regressions.
4.2.1.1. Omitted variables: causes
The first source of endogeneity arises if the structural disturbance term consists of omitted variables
and these variables are correlated with one or more of the explanatory variables. This may occur because
data is not available on those variables the researcher would like to include additionally into the model.
These omitted variables are said to be unobservable to the researcher.58 Omitted variables also may be due
to a failure of the researcher to include all the observable factors theory suggest to be important in 57 One test is that the choices made should be palatable to the researcher’s peers. 58 While the disturbance term then includes variables that are unobservable to the researcher, these factors may very well be observable to the economic agent under study. Indeed, endogeneity arises when the explanatory variables represent decisions made by the agent on the basis of such factors (Hayashi, 2000).
89
explaining the dependent variable. Economic relations are often such that two factors that are determinants
of the same dependent variable will be mutually associated. If one such factor is omitted from the analysis
and thus included in the disturbance term, the latter will be correlated with the included factor. One special
case of omitted observable variables arises when the omitted variable is a function of an explanatory
variable in the model. This type of omitted variable problem is often referred to as ‘functional form
misspecification’.
In sum, omitted variables can be either observable or unobservable to the researcher. Omitted
variables are captured by the disturbance term in the structural equation. When these omitted variables are
correlated with explanatory variable xi, then xi is endogenous in that particular structural equation.
4.2.1.2. Omitted variables: potential ‘solutions’
We emphasized that omitted variables may be either observable or unobservable to the researcher
because this dimension matters when trying to mitigate the problems associated with estimating the
parameters in the structural model. It should be noted that it is unlikely for any of the methods we describe
to resolve fully the issues associated with endogeneity.
Omitted observable variables. This source of endogeneity can be addressed by including all factors
that are important in explaining the dependent variable and, at the same time, are associated with one of the
explanatory variables, into the structural equation. Factors that are associated with both dependent and one
or more explanatory variables are said to be ‘joint determinants’. In practical terms, this will usually
require the researcher to conduct a thorough review of the extant theoretical and empirical literatures to
identify these joint determinants. Once included in the structural model, the disturbance term is purged
from the source of its correlation with the explanatory variables and the estimation of the parameters of
interest should no longer be affected by endogeneity.
Omitted unobservable variables. Since the researcher will not be able to gather data on omitted
variables that are unobservable, our earlier recipe of including any joint determinants will no longer work.
We will discuss two distinct instances of omitted unobservable variables and methods to address these,
which are relevant to the accounting literature, (1) self-selection and (2) firm-specific heterogeneity.
4.2.1.3. Self or sample-selection
Self or sample-selection arises if the probability that a firm is included into the sample and the
dependent variable are both affected by an (omitted unobservable) variable. As a result the sample is no
longer random. Alternatively, the omitted unobservable variable may affect the way in which an
observation is categorized within the sample, although all observations are included.59 A good example in
an accounting context is provided by Leuz and Verrecchia (2000). These authors study a sample of firms
that have switched from a German to an international reporting regime. They are interested in the question
whether a commitment to increased disclosure, as required under international standards, has tangible 59 Self selection bias will also arise when the sample is truncated or censored, or sampling is on the dependent variable. When sampling is on one of the exogenous variables, the sample will not be random but estimation of the structural model is unaffected (Wooldridge, 2002). See also Shehata (1991) for a discussion of selection bias issues in an accounting context.
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benefits in the form of lower cost-of-capital. Firms will decide on disclosure based on the expected
consequences with regard to their cost-of-capital. Therefore, the factors that determine the disclosure choice
(expected net cost-of-capital benefit) are likely to also affect the dependent variable, current cost-of-capital.
Simply regressing cost-of-capital on disclosure would not do in this context because it ignores the fact that
only those firms with positive expected net cost of capital benefits will have selected to switch reporting
regime. As Leuz and Verrecchia are careful to point out, without discounting this selection effect the
association between disclosure and cost-of-capital will be overstated for those firms that have switched
regimes and understated for the firms that have not. Although, the expected net benefits of increased
disclosure to the firm are unobservable to the researcher, they should be accounted for when estimating the
structural model of interest. This is usually done by modeling the selection mechanism explicitly and
adjusting the estimation of the parameters in the structural model for the selection effect. Heckman’s (1979)
procedure offers an often-used, easily implemented approach to achieve this.
4.2.1.4. Firm-specific heterogeneity
Unobserved omitted variables often represent features of the firm that are given and do not change
over the period in question. Specifically, firm characteristics like managerial ability, structural
arrangements, and employee skills can be thought of as roughly constant over time. As before, if these firm
characteristics impact on both the dependent variable and one or more explanatory variables, the structural
disturbance (which captures heterogeneity across units of observation) will be correlated with those
explanatory variables. For example, more talented managers may prefer high-quality disclosures and, at the
same time, the market may think these managers better ‘risks’ and charge a lower cost-of-capital. The talent
of management is difficult to observe for a researcher and should be relatively constant. Regressions of
cost-of-capital onto disclosure are affected by firm-specific heterogeneity bias if the talent of managers is
not properly discounted.
Firm-specific heterogeneity can be addressed in several ways. Researchers may find a proxy
variable for the firm characteristic and plug this into the structural equation. Alternatively, instruments
might be available for those explanatory variables that are correlated with the unobservable firm
characteristic and instrumental variable (IV) estimation can be used to estimate the parameters of the
structural equation consistently (see, Wooldridge, 2002). Often, it will be the case that accounting
researchers can observe a firm at different points in time. If so, panel data techniques are available to
account for heterogeneity.
Since the choice of which method to use to address firm-specific heterogeneity directly impinges
on our empirical work and is of practical concern in many other settings as well, we digress briefly from the
main topic and discuss the tradeoffs involved when using IV versus panel data techniques.60
60 This discussion is geared towards one panel data technique in particular: fixed effect estimation.
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Asymptotically, IV and fixed effects estimation must agree,61 which makes it relevant to compare their
properties in applied settings.62 Panel data techniques address a narrower problem because they can only
deal with time-invariant omitted variables. IV estimation does not assume that firm characteristics are
constant and hence admits modelling the impact of a broader set of unobservable variables. Nevertheless,
IV estimation is vulnerable to producing misleading results when the instruments used are not valid or
weak. Instrument variables must be independent of the (unobservable) structural disturbance term and as
highly correlated as possible with the explanatory variable they represent. The first condition cannot be
tested; the second is frequently not met in practice (Larcker and Rusticus, 2005). Not only is it often
difficult to find valid and strong instruments in applied settings, the choice between alternative candidate
instruments is subjective and may impact on the robustness of the empirical work.63 Panel data techniques,
on the other hand, are easy to implement and do not involve a subjective choice by the researcher. They
assume, however, that the relation under study is essentially driven by changes within the firm, not by
differences between firms. In other words, the cross-sectional variation should be limited compared to
changes within firms. Since panel data techniques require multiple observations of a firm, the likelihood of
a selection bias is higher than when IV estimation is applied. In sum, neither IV estimation nor panel data
techniques dominate when trying to solve for endogeneity. The final choice between the two methods will
depend on the specifics of the research design.
We conclude this section on omitted variables with an often-misunderstood fact. The mere fact that
some variable represents a decision (or choice) to the firm or, more generally, an economic agent, is not in
itself sufficient for ‘econometric endogeneity’ to arise. Only if the factors that impact on the decision by
the economic agent, whether observable or nor, are also inter-related with the dependent variable will
endogeneity exist.
4.2.1.5. Simultaneity: causes
In many settings of interest to accounting researchers, the data generating process is essentially
such that variables are simultaneously determined and interdependent. Simultaneity arises when at least one
of the explanatory variables is determined simultaneously along with the dependent variable (Wooldridge,
2002). If so, the structural disturbance and the explanatory variable will be correlated. Intuitively, one can
think of simultaneity as describing instantaneous feedback relations among variables. An accounting
example is provided in Welker (1995). This author is interested in the relation between disclosure policy
and liquidity in equity markets. He notes that effective corporate disclosure will mitigate information
61 If fixed effects and IV estimation do not agree, the implication is that the model is misspecified (e.g., the instruments are invalid or endogeneity is not alleviated by fixed effects estimation. A Hausman-type test may be used to discriminate between the estimators. 62 It is not immediate which estimator will be more efficient asymptotically. This will depend on the number and quality of instruments and the amount of within-variation. 63 It is often not immediate whether including more than one instrumental variable is beneficial in finite sample settings. See, e.g., Kennedy (2003) for a discussion. A Sargan (1958) - Hansen (1982) test is available to evaluate whether extra instruments should be used.
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problems in the market and thus increase liquidity. At the same time, corporate disclosure may be
influenced by the information differences between the firm and the market and thus by current liquidity.
There is an ‘equilibrium feedback mechanism’ (Griffiths et al. 1993) operating on disclosure and liquidity
to determine the equilibrium outcomes for both variables.
4.2.1.6. Simultaneity: potential ‘solutions’
To capture instantaneous feedback relations, researchers write a system of equations that consists of
separate structural equations for each endogenous variable. When variables y1 impacts on y2 and vice versa,
y2 would be included as an explanatory variable in the structural equation for y1; y1, in turn, is an
explanatory variable in the structural equation of y2. Estimation of this system of equations is possible,
provided it is identified – i.e., rank and order conditions are met – using (inefficient) single equation
methods (indirect least squares, two-stage least squares, or LIML) or (efficient) system methods (three-
stage least squares, FIML).64 Most econometric textbooks contain detailed discussions of the estimation of
systems of equations (e.g., Greene, 2000).
In conclusion, we support Heckman’s (2000) suggestion that it is sensible to think of endogeneity
as the case where the ceteris paribus condition does not hold while manipulating one of the explanatory
variables. Sources of endogeneity include omitted variables and simultaneity. Potential solutions for
endogeneity following from both causes are available, but their success in applied settings varies greatly.
4.3. Omitted variables in the relation between cost-of-debt capital and
disclosure
The previous section emphasized two main sources of endogeneity bias: (1) correlated omitted
variables and (2) simultaneity. We will concentrate in the remainder of this paper on the first source
because earlier literature has already investigated simultaneity bias in the relation between cost-of-capital
and disclosure (Welker, 1995, Hail, 2002) and found that simultaneity bias does not appear to invalidate the
results of OLS estimation.65
We first discuss (1) costs of disclosure66 and (2) management reputation67 as examples of
unobservable firm characteristics that are likely correlated with disclosure and relatively fixed over time.
64 The tradeoff between single equation and system methods is that the latter are more susceptible to misspecification since they require the correct specification of all equations in the system. As an equivalent alternative one may estimate the reduced form of the structural model and then solve for the structural parameters in terms of reduced form parameters. 65 We choose a research design that allows us to investigate endogeneity caused by omitted variables in relative isolation from endogeneity caused by simultaneity. We provide more details on this in Section 4. In short, we rely on the pre-determinedness of most of our RHS variables to argue that simultaneity is less likely to be severe. Nevertheless, we cannot exclude the possibility that simultaneity bias is present and our results should be interpreted with this caution in mind. One possible explanation why these earlier studies have not found that OLS is inconsistent might be that the instrument variables that were used in prior work were weak (see also, Larcker and Rusticus, 2005) 66 Recent studies have pointed explicitly to the failure of many disclosure studies to take between-firm differences in costs of disclosure into account (Fields et al., 2001, Cohen, 2003).
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Next, we review the literature in search of joint, observable determinants of both disclosure and cost-of-
debt capital that were omitted in Sengupta (1998).
4.3.1 Unobservable firm characteristics Costs of disclosure. While it is likely that the direct costs of disclosure (gathering and reporting
information) differ between firms, some recent papers have focussed on a potentially interesting source of
firm heterogeneity, i.e., the costs associated with investor uncertainty about the disclosure of information
(Verrecchia, 2001). This uncertainty can originate from differences in technical expertise to understand the
disclosure among the firm’s investors (Fishman and Hagerty, 2003) or because it is unclear whether
withholding disclosure results from firms having no information or having unfavourable information (Dye,
1985, 1998, Jung and Kwon, 1988). Whatever its origin, these models suggests that the extent of
uncertainty affects the optimal disclosure policy of the firm. Intuitively, the firm may benefit from
uncertainty because (unsophisticated) investors cannot distinguish between the two reasons for withholding
information and, as a result, such investors may over value the firm.68 The idea that investors differ in terms
of their sophistication has found general recognition in the empirical literature (Hand, 1990). Usually,
sophistication is proxied by the proportion of institutional investors. Several papers document how capital
market reactions differ depending on the composition of the firm’s investor base (Kim et al., 1997, Walther,
1997, Bartov et al. 2000). Thus, the uncertainty of firms about the way the market will react to their
disclosures is likely to differ. Not only will this uncertainty affect the optimal disclosure, but it will also
affect cost-of-capital. Given that investors are uncertain about the nature of non-disclosure they need to be
compensated in expected return. Therefore, both disclosure and costs of capital are affected by the
unobservable firm-specific characteristic of the sophistication of investors.
Management reputation. Disclosure has been modelled as a device through which managers signal
their talent (Trueman, 1986, Healy and Palepu, 2001). The reasoning usually is that more talented managers
will reveal their type through making voluntary disclosures, although Nagar (1999) offers a model in which
even talented managers may opt for non-disclosure in some cases. This author assumes that managers are
differently talented and that they are uncertain about the market’s response to the disclosure of their
performance. Depending on the extent of the penalty the market puts on non-disclosing performance and
the manager’s discomfort from the uncertainty about the market’s reaction to disclosure, the optimal
disclosure policy will vary. Regardless of the supposed chain of events, managerial talent or discomfort are
unobservable sources of firm heterogeneity.
67 We would like to stress that these are indeed examples and many other reasonable theories exist. Agency costs are a clear alternative illustration. These costs are unobservable but likely differ among firms. Agency costs are likely to affect both the disclosure decision and the cost-of-capital. Yet another alternative is firm (as opposed to management) reputation. We do not aim at providing an exhaustive list of firm heterogeneity. 68 See Hirshleifer and Teoh (2003) for a model in which pro forma disclosures are used to misdirect the attention of investors with limited cognitive abilities. To the extent that cognitive abilities among investors vary we expect different optimal levels of disclosure.
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It seems very likely that a manager’s talent also affects the cost-of-debt capital. For example, more
talented managers might make more persuasive propositions when seeking debt capital. Investors will
consider the default risk of firms managed by talented managers to be lower. Their road shows should be
more interesting to investors and they might attract bigger crowds eager to jump on the bandwagon of a
talented manager and his or her firm. In sum, both cost-of-debt capital and disclosure are influenced by the
manager’s talent, and talent is likely to differ between firms but is also relatively constant over time in any
one firm.
4.3.2. Joint determinants of disclosure and cost-of-debt capital
Lang and Lundholm (1993) suggest three categories of variables that will impact on the disclosure
decision (1) performance variables, (2) structure variables, and (3) offer variables. These categories are
motivated by theoretical arguments in which disclosing information reduces adverse selection problems
between investor and firm, decreases transaction costs associated with trading on capital markets and limits
potential litigation costs caused by withholding information relevant to investors. Each of these variables
will likely also affect the firm’s cost-of-debt capital. We will briefly discuss each category in turn and
indicate its effect on disclosure and cost of capital.
It is well recognized that performance is related to disclosure, albeit that the exact nature of the
relation between the two is complex (Miller, 2002). Some theoretical models (e.g., Verrecchia, 1983 and
Lanen and Verrecchia, 1987) suggest that firms will withhold negative news but disclose positive news, a
concern that is often voiced by regulators as well (see, e.g., Levitt, 1998). The empirical evidence so far is
not consistent with these contentions, as some authors have shown that bad news is rushed forward to avoid
legal action (Skinner, 1994, 1997), to warn investors about earnings disappointments (Kasznik and Lev,
1995) or to improve the conditions surrounding stock option grants (Aboody and Kasznik, 2000).
Nevertheless, the evidence suggests that disclosure is associated with performance.
Firms that perform well are likely to meet more favourable conditions when vying for capital.
Investors perceive firms with sustained superior performance as less risky or they attribute better prospects
to these firms. Performance will therefore be negatively associated with the cost-of-debt capital.
Structure variables refer to the economies of scale in producing information and to the extent of
information asymmetry between investors and firm. One structural variable is the size of the firm; the idea
is that larger firms will have comparatively lower (accounting) costs to produce the same amount
information than smaller firms. Larger firms will thus disclose more information.
The adverse selection problem between the firm and its investors will be larger when information
asymmetry between the two parties is greater (Healy and Palepu, 2001, Dye, 2001, Diamond and
Verrecchia, 1991). Since disclosure is an instrument to reduce information asymmetry, disclosure will be
more extensive when information asymmetry (prior to disclosure) is perceived to be substantial.
As large firms are generally thought to be less risky, size is expected to be negatively associated
with cost-of-debt capital (Fama and French, 1992, 1993). Similarly, information asymmetry increases the
95
(default) risk an investor is exposed to when providing capital to a company (Amihud and Mendelson,
1986, Easley and O’Hara, 2004). The cost-of-capital is therefore increasing in the extent of information
asymmetry.
Finally, the last category of factors that impact on the disclosure decision refers to the offer
variable. Theory suggests that managers who consider making capital market transactions have incentives
to disclose information to reduce information asymmetry problems (Myers and Majluf, 1984). Lang and
Lundholm (1993, 1996) and Healy et al. (1999) find evidence consistent with this idea for equity and debt
offerings, respectively and Frankel et al. (1995) for both.69
The extent of a firm’s capital market transactions may also affect its cost-of-capital because the
market may interpret the frequency of these transactions as a signal about the firm’s performance (Myers
and Majluf, 1984). For example, frequent, sizable public debt issues may change the market’s assessment
of the default risk of the firm. Offerings are therefore likely to be associated with the cost-of-debt.
In conclusion, we have described 1) some unobservable firm characteristics (costs of disclosure and
management reputation) that are correlated with the firm’s disclosure policy and 2) joint determinants that
are likely to impact on both disclosure and cost-of-capital. When omitted from the analysis of the relation
between cost-of-capital and disclosure, the results are likely to be misleading. In the following sections, we
document the severity of the bias in analyses that do not incorporate unobservable firm characteristics or
joint determinants of disclosure and cost-of-capital and suggest a methodology to mitigate the bias.
4.4. Research design and variable definitions
We start the analysis by replicating Sengupta’s (1998) results on the relation between disclosure
and cost-of-debt capital. Specifically, we estimate the following regression equation using Ordinary Least
Squares:
(1) 11 itiiitit ControlDisclosureInterceptYIELD εββ +++= ∑+
where
YIELD = The effective yield to maturity at the moment of a public bond issue. This is our measure
of the cost-of-debt capital. Yield to maturity is defined as the discount rate that equates the
current value of all future interest and principal payments to the capital provided by the
lender at the moment of the bond issue.
Disclosure = Joint label for our four measures of corporate disclosure policy: (1) PCTRNK, the
percentage rank of overall corporate disclosure policy, (2) PCTREL, the percentage rank of
69 Lang and Lundholm (2000) on the other hand provide evidence that increasing disclosure prior to a seasoned equity offering may be interpreted as ‘hyping’ the stock and firms experience continued negative returns subsequent to the offering announcement. This effect is probably difficult to witness in our sample since we do not have a continuous measure of disclosure policy, but instead rely on annual assessments of disclosure. See also, Jog and McConomy (2003) and Mak (1996)
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investor relations disclosure policy, (3) PCTANL, the percentage rank of disclosure
through the firm’s annual report and (4) PCTOPB, the percentage rank of quarterly and
other publications disclosures. Percentage ranks are constructed from the assessment of
corporate disclosure policy by the AIMR Corporate Information Committee in their Annual
Reviews of Corporate Reporting Practices.70 Percentage ranks for each disclosure measure
are computed by ranking each firm from 1 to N within each industry, such that N is
assigned to the firm with the highest AIMR disclosure score, etc. Subsequently, each firm’s
rank is divided by the total number of firms rated within its industry to obtain the
percentage ranks.
Control = These measures include leverage, coverage of interest expense, return-on-sales, the log of
total assets, volatility of firm performance, the size of the bond issue, the issue’s time to
maturity, the call option properties of the security, the interest on constant maturity US
treasury bills, the time-series variation in risk premium over that contained in treasure bills,
and dummy variables for convertible bonds and subordinate debt. These controls intend to
take into account firm and issue specific factors as well as macroeconomic circumstances.
For brevity we refer the reader to Sengupta (1998) for a further justification of their
inclusion in the analysis. Appendix A provides measurement details. Since it is our purpose
to replicate Sengupta’s findings and then investigate the potential endogeneity bias in the
relation between cost-of-debt capital and disclosure, we defer discussion of these control
variables.
The time subscripts are of importance. We measure cost-of-debt capital at t+1, while Disclosure
and all control variables that are not bond issue specific are measured at t. We can therefore consider these
right hand side variables as predetermined; although these variables may be contemporaneously (at t)
determined jointly, with regard to future values (t+1) of cost-of debt capital they may be regarded as having
already been determined (Greene, 2000). This is a common method to make plausible that innovations in
the dependent variable are uncorrelated with the explanatory variables (i.e., to reduce the likelihood of
simultaneity bias). Bond-issue specific controls are not predetermined and we cannot exclude the possibility
that they are endogenous. Moreover, to the extent that autocorrelation is present, we can no longer assume
that the disturbance term is uncorrelated with the explanatory variables. Results should be interpreted with
this possibility in mind.
Next, we evaluate the importance of the first source of endogeneity bias in the OLS regression of
Equation (1), i.e., the impact of omitted variables known to be a determinant of both cost-of-debt capital
and disclosure policy. For this purpose, we augment Equation (1) with variables that intend to capture those
categories listed in Lang and Lundholm (1993) and summarized above as joint determinants of disclosure
policy and cost-of-capital. Specifically, we estimate the following equation using OLS: 70 These ratings have been frequently used in earlier disclosure studies and are discussed in some detail elsewhere (Lang and Lundholm, 1996, Healy and Palepu, 2001, Core, 2001).
97
(2) 11
itllkk
jjiiitit
ControlOffer
StructureePerformancDisclosureInterceptYIELD
εββ
βββ
++
++++=
∑∑∑∑+
where
Performance variables71:
GROWTH = Average future growth in sales (item #12) between t+1 and t+3.
FROS = Average future return-on-sales (as defined earlier) between t+1 and t+3.
LOSS = Dummy variable that is unity for firms with negative current net income (item
#18), and zero otherwise.
MTB = Market-to-book ratio at the end of the year, defined as market value of equity
(item #24×item #25) divided by the book value of equity (item #60).
FROS×GROWTH = Interaction term between future return-on-sales and future growth rate. We
include this variable to capture the potentially non-linear relation between
performance and disclosure as suggested in Miller (2002). Before computing the
interaction between FROS and GROWTH each of the variables is demeaned in
order to make main effects interpretable.
Structure variables:72
CAPEXP = Capital expenditures in the current year (item #128) scaled by total assets (item
#6). This variable captures information asymmetry about the firm’s strategy and, in
particular about its investment opportunities.
MOODRNK = Moody’s ranking of the firm’s bond. MOODRNK equals 100 if the bond is rated
A1 by Moody’s and 1 if the bond has rating Caa1. MOODRNK declines linearly
from 100 to 1. We include MOODRNK as a proxy for amount of information
asymmetry between the firm and its investors. The idea is that high levels of
information asymmetry will make the firm’s securities more risky and will prompt
Moody’s to downgrade the firm’s ranking (see, e.g., Bhojraj and Sengupta, 2003,
Ziebart and Reiter, 1992, Kaplan and Urwitz, 1979, Fisher, 1959).73
71 Sengupta (1998) includes two variables as control variables in his regression that would otherwise have been included into this category. These variables (current income and interest coverage) are therefore part of the specification of our Equation 1 as ROS and COVER, respectively. 72 Sengupta (1998) includes the logarithm of total assets as a control variable in his regression. This variable (LASSETS) was therefore included as control in our Equation 1. Otherwise, it would have been included in the category of structure variables to proxy for the economies of scale in producing information. 73 The inclusion of MOODRNK as a determinant of cost-of-debt capital is contentious. While some prior studies have added credit ratings as a control variable (Mansi et al., 2003, Campbell and Taksler, 2003, Bagnani et al., 1994), other have not. Sengupta (1998) argues that credit rating agencies consider the quality of disclosure when deciding on a firm’s credit rating. Including the rating alongside a measure of disclosure may therefore create multicollinearity problems and it might become difficult to separate out the effects of disclosure and of credit ratings. We decided to include MOODRNK not only because it is an established proxy of information asymmetry, but also because we
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Offer variable:
ISSUES = Number of bond issues by firm i in the current year.
If omitted variables are a source of endogeneity bias in Equation (1) then including the variables
described above will reduce the amount of bias and OLS estimation of the augmented equation should be
consistent (in the absence of firm heterogeneity effects). Therefore we document changes in the coefficient
estimate on Disclosure in Equations (1) and (2) to evaluate the extent of the endogeneity bias caused by
omitted variables.
Finally, we investigate both sources of endogeneity bias simultaneously. We use panel data
techniques (fixed effects) 74 to estimate the following equation:
(3) 11
itillkk
jjiiitit
ControlOffer
StructureePerformancDisclosureInterceptYIELD
εαββ
βββ
+++
++++=
∑∑∑∑+
where
iα = Any unobservable firm-specific variable that remains fixed over time, and all other variables are
as defined above.
Since the firm-specific variable iα is assumed to remain constant, an alternative approach to fixed
effects estimation is to re-specify Equation (3) in first differences and estimate it with OLS. Differencing
provides researchers with an easy to implement solution to the heterogeneity bias (Wooldridge, 2002).
Taking differences in Equation (3) will cause the firm-specific variable iα to drop out of the equation. Note
that differencing requires at least two consecutive years of data for each firm. We use first-differences
estimation as a robustness check on our fixed effects findings.
Finally, we provide further evidence on the nature of the correlation, which theory suggests exists
between Disclosure (as well as other independent variables) and the firm heterogeneity variable iα using a
believe it is important to try to establish if the market reacts to disclosure directly or to credit ratings which (indirectly) reflect disclosure quality. We have also conducted the empirical analyses without MOODRNK and we report these results in footnote 32. If MOODRNK is construed as a proxy for information asymmetry then a more appropriate measurement is before the firm discloses its information. Since MOODRNK is an issue-specific rating, it is not straightforward to implement this in the regressions. We check the robustness of our results to the timing of the measurement of information asymmetry by replacing MOODRNK by S&P long term debt rating (Compustat item 280), which is available for all firm-years in the sample. We use a lagged (t-1) value of this rating to ensure that it is measured before the disclosure at t. We report the results for this specification in footnote 32 as well. 74 In principle, Equation (3) could be estimated using fixed and random effects, respectively. The appropriateness of each estimator depends on assumptions about the correlation between αi and the included independent variables. If the firm-specific characteristics captured in αi are independent of the regressors, random effects estimation is consistent and efficient. However, if the firm-specific characteristics are correlated with any of the regressors this estimation procedure is inconsistent and fixed effects is preferred. Since we have strong theoretical reasons to believe that firm-specific characteristics are correlated with the disclosure variable, our priors are that fixed effects estimation is the most appropriate when estimating Equation 3. In fact, unreported results of a Hausman test of the consistency of random and fixed effects estimation support the choice for fixed effects. This is further evidence that firm heterogeneity is important in the current setting and should be taken into account (using fixed effects) when estimating the relation between disclosure and cost-of-debt capital.
99
procedure suggested by Mundlak (1978). We provide a brief and informal description of Mundlak’s (1978)
approach in Appendix B. Combined, the results for Equations 1-3 provide us with evidence on the
magnitude of endogeneity bias caused by firm-specific heterogeneity and omitted variables. Note that while
we focus on the effect of endogeneity on the coefficient on Disclosure, any of the RHS variables may
(potentially) be correlated with the error term in the structural equation, and thus be endogenous. In fact, we
show below this to be the case for CALL and RISK. To the extent that endogeneity is caused by time-
invariant firm heterogeneity, the fixed effects estimation will alleviate the bias in all RHS variables.
4.4.1. Caveats.
The use of panel data techniques (especially, fixed effects or differencing) when multiple
observations of a firm over time are available has become pervasive practice in the economics and finance
literatures, although accounting researchers have been somewhat slow to emulate the example. This
literature strongly demonstrates the importance of controlling for unobservable firm (or economic agent)
heterogeneity in many settings.75 Fixed effects estimation will, however, not always be successful in
mitigating the problem of unobserved firm heterogeneity. Zhou (2001), for example, draws attention to the
observation that if the relation under study is essentially a cross-sectional phenomenon, fixed effects
estimation will not be effective. Indeed, since fixed effects estimation removes all cross-sectional (between)
variation, one of its underlying assumptions is that over-time changes within each firm are driving the
relation of interest. In the context of our setting, we need to establish that disclosure quality changes
substantially over time for individual firms and that it is this within variation that impacts on cost-of-debt
capital. Changes in disclosure should be indicative of substantive changes in disclosure policy. The next
section provides evidence to underpin the validity of using fixed effects in our context.76
4.5. Sample and summary statistics
The sample comprises 358 firm-year observations from 100 firms during 1986-1996.77 To be
included in the sample, the firm needs to fulfil the following criteria: (1) public debt is issued during the
75 Seminal studies include Mundlak (1961, 1978), Hoch (1962), Ben-Porath (1973), Griliches (1977), Ashenfelter (1978), Chamberlain (1978), Hausman (1978), Hausman and Taylor (1981). More recent applications in finance include Doidge (2004), Campbell and Taksler (2003), Himmelberg et al. (1999), Ashenfelter and Kruger (1994). In accounting, Francis et al. (2004), Hail and Leuz (2004) provide fixed effect results. 76 Zhou (2001), Himmelberg et al. (1999) and Griliches and Hausman (1986) note that the fixed effect estimator may suffer from bias, which is associated with measurement error. Griliches and Hausman (1986) point out that measurement error will have a different impact on the fixed effects estimator and the first-differences estimator. Since we report fixed effects and first-differences results that are very close, it is unlikely that measurement error is a major issue here. 77 Sengupta’s (1998) sample consists of 103 observations (and as many firms, since he only retains one observations per firm). We have, due to our design, multiple observations for each firm, and consequently cannot claim that our observations are independent. To ascertain the extent of this problem we have compiled a sample in which each firm enters only once, and ran the benchmark model on this sample. Our results remained qualitatively unchanged and we conclude that any potential downward bias of the standard errors, due to dependent observations, is likely to be minor.
100
T a b l e 1 Sample Characteristics
PANEL A Sampling Procedure Subsample # firms # of Obs.AIMR rated companies (1986-1996) 932 4705i. AIMR companies in COMPUSTAT/CRSP 778ii. AIMR rated companies that issued debt 508 1604i. and ii. Companies Merged (by year) 331 892Net of Non-Industrial companies 237 604After deletion of missing values 180 438Companies with more than one observation 100 358 PANEL B Distribution of the Number of times a given firm appears in the sample # of times # Of Firms # of Obs. %2 35 70 19.63 23 69 19.34 17 68 19.05 9 45 12.66 9 54 15.17 5 35 9.88 1 8 2.29 1 9 2.5Total: 100 358 100 PANEL C Number of companies used in the analysis by year YEAR # of Obs. %1986 17 4.751987 13 3.631988 26 7.261989 29 8.101990 68 18.991991 52 14.531992 52 14.531993 19 5.311994 35 9.781995 32 8.941996 15 4.19Total: 358 100.00
101
Table 1: Continued
PANEL D Number of companies used in the analysis by Industry INDUSTRY # of Firms # of Obs. % Aerospace 2 4 1.12Airline 4 17 4.75Apparel 1 7 1.96Chemical 4 16 4.47Construction 1 2 0.56Container and Packaging 2 4 1.12Diversified Companies 2 4 1.12Domestic Oil 5 14 3.91Electrical Equipment 4 11 3.07Food, Beverage and Tobacco 17 48 13.41Health Care 9 35 9.78Independent Oil 2 5 1.40International Oil 1 5 1.40Machinery 3 13 3.63Natural Gas Distributors 2 9 2.51Natural Gas Pipeline 6 30 8.38Nonferrous and Mining 2 5 1.40Paper and Forest Products 12 47 13.13Precious Metals 1 2 0.56Publishing and Broadcasting 4 15 4.19Railroad 3 12 3.35Retail Trade 11 47 13.13Specialty Chemicals 1 4 1.12Textiles 1 2 0.56Total: 100 358 100
102
T a b l e 2 Descriptive Statistics
Table provides summary statistics for the variables used in subsequent analyses. The sample includes 100 companies, which amount to 358 firm-year observations. In order to avoid double counting we use only the first debt issue in a given year to measure YIELD. Bond attributes including YIELD are forwarded by one year since regressions use period t+1 debt issues when looking at period t disclosures. Disclosure score used to construct percentage rankings (PCTRNK, PCTREL, PCTANL, PCTOPB) are collected from AIMR-FAF reports over the period 1986-1996. The firm-level control variables are taken from CRSP/COMPUSTAT Merged database; debt issues information is taken from SDC Platinum Database; Macroeconomic variables come from FRED II. See Appendix A for variable definitions.
Variable Mean St. Dev. 75th pct Median 25th pct YIELD 8.138 1.331 9.125 8.065 7.105 PCTRNK 0.578 0.284 0.824 0.632 0.375 PCTREL 0.559 0.271 0.793 0.598 0.360 PCTANL 0.571 0.278 0.806 0.618 0.375 PCTOPB 0.548 0.285 0.800 0.585 0.308 LEV 0.240 0.104 0.313 0.238 0.173 COVER 4.372 5.340 4.925 2.952 1.868 ROS 0.173 0.087 0.209 0.159 0.114 ASSETS 9817 11766 12130 7801 3000 LASSET 8.747 0.967 9.403 8.962 8.006 RISK 0.394 0.172 0.458 0.361 0.275 SIZE 179.2 123.5 225.0 149.8 99.7 LMATUR 16.293 11.193 30.000 10.000 10.000 CALL 0.174 0.308 0.300 0.000 0.000 CONVER 0.036 0.187 0.000 0.000 0.000 SUBOR 0.034 0.180 0.000 0.000 0.000 TBILL 7.311 1.017 8.110 7.340 6.570 RISKPR 0.669 0.126 0.760 0.650 0.590 MOODRNK 72.302 28.236 94.737 84.211 36.842 GROWTH 1.068 0.089 1.109 1.055 1.017 FROS 0.170 0.085 0.211 0.158 0.110 MTB 2.755 2.175 3.148 2.039 1.386 CAPEXP 0.087 0.049 0.110 0.076 0.054 FROSXGR 0.000 0.007 0.002 0.000 -0.002 LOSS 0.056 0.230 0.000 0.000 0.000 ISSUES 2.251 2.405 3.000 2.000 1.000
103
T a
b l
e 3
Pe
arso
n co
rrel
atio
ns (b
elow
dia
gona
l) an
d th
eir
signi
fican
ce le
vels
(abo
ve d
iago
nal)
Tabl
e re
ports
Pea
rson
cor
rela
tions
bel
ow th
e di
agon
al a
nd th
eir s
igni
fican
ce le
vels
abo
ve th
e di
agon
al. S
ampl
e co
nsis
ts o
f 358
firm
-yea
r obs
erva
tions
. See
App
enid
x 1
for
varia
ble
defin
ition
s.
(1
) (2
) (3
) (4
) (5
) (6
) (7
) (8
) (9
) (1
0)
(11)
(1
2)
(13)
(1
4)
(15)
(1
6)
(17)
(1
8)
(19)
(2
0)
(21)
(2
2)
(23)
(2
4)
(25)
(1) Y
IELD
0.04
0.
10
0.00
0.
16
0.00
0.
00
0.01
0.
20
0.00
0.
34
0.02
0.
37
0.00
0.
06
0.00
0.
00
0.09
0.
00
0.00
0.
00
0.53
0.
16
0.82
0.
60
(2) P
CTR
NK
-0
.11
0.
00
0.00
0.
00
0.37
0.
01
0.33
0.
22
0.83
0.
04
0.70
0.
41
0.84
0.
46
0.31
0.
80
0.00
0.
00
0.11
0.
47
0.01
0.
00
0.96
0.
01
(3) P
CTR
EL
-0.0
9 0.
74
0.
00
0.00
0.
80
0.03
0.
22
0.04
0.
24
0.01
0.
33
0.76
1.
00
0.34
0.
40
0.63
0.
01
0.01
0.
15
0.10
0.
07
0.00
0.
27
0.00
(4) P
CTA
NL
-0.1
6 0.
85
0.51
0.00
0.
08
0.16
0.
59
0.36
0.
35
0.15
0.
46
0.10
0.
77
0.58
0.
03
0.93
0.
00
0.00
0.
39
0.22
0.
01
0.03
0.
83
0.01
(5) P
CTO
PB
-0.0
7 0.
80
0.46
0.
66
0.
28
0.05
0.
31
0.60
0.
76
0.04
0.
66
0.63
0.
48
0.27
0.
57
0.84
0.
00
0.04
0.
10
0.56
0.
03
0.04
0.
41
0.08
(6) L
EV
0.18
-0
.05
0.01
-0
.09
-0.0
6
0.00
0.
15
0.88
0.
08
0.89
0.
37
0.94
0.
16
0.79
0.
97
0.16
0.
00
0.02
0.
19
0.00
0.
12
0.13
0.
00
0.01
(7) C
OV
ER
-0.2
0 -0
.14
-0.1
1 -0
.08
-0.1
1 -0
.55
0.
00
0.80
0.
37
0.05
0.
11
0.98
0.
84
0.56
0.
23
0.78
0.
01
0.01
0.
00
0.00
0.
09
0.04
0.
00
0.10
(8) R
OS
-0.1
3 -0
.05
-0.0
6 -0
.03
-0.0
5 -0
.08
0.23
0.04
0.
02
0.08
0.
19
0.80
0.
87
0.40
0.
21
0.81
0.
92
0.12
0.
00
0.00
0.
00
0.55
0.
00
0.30
(9) L
ASS
ET
-0.0
7 0.
06
0.11
0.
05
0.03
-0
.01
0.01
-0
.11
0.
00
0.00
0.
61
0.02
0.
00
0.00
0.
04
0.00
0.
25
0.00
0.
12
0.10
0.
00
0.21
0.
12
0.01
(10)
RIS
K
0.21
0.
01
-0.0
6 0.
05
0.02
0.
09
-0.0
5 -0
.13
-0.2
1
0.39
0.
93
0.35
0.
11
0.12
0.
01
0.02
0.
01
0.05
0.
00
0.01
0.
00
0.18
0.
44
0.80
(11)
SIZ
E -0
.05
0.11
0.
14
0.08
0.
11
0.01
0.
11
-0.0
9 0.
41
-0.0
5
0.11
0.
86
0.27
0.
99
0.22
0.
14
0.78
0.
67
0.03
0.
00
0.01
0.
27
0.76
0.
05
(12)
LM
ATU
R
0.13
-0
.02
-0.0
5 -0
.04
-0.0
2 0.
05
0.08
-0
.07
0.03
0.
00
0.09
0.00
0.
53
0.30
0.
03
0.52
0.
57
0.01
0.
57
0.65
0.
14
0.01
0.
46
0.20
(13)
CA
LL
0.05
0.
04
0.02
0.
09
0.03
0.
00
0.00
0.
01
-0.1
2 0.
05
-0.0
1 0.
39
0.
00
0.00
0.
01
0.42
0.
90
0.79
0.
29
0.14
0.
59
0.80
0.
52
0.04
(14)
CO
NV
ER
-0.2
4 0.
01
0.00
0.
02
0.04
0.
07
-0.0
1 -0
.01
-0.2
4 0.
09
0.06
0.
03
0.40
0.00
0.
02
0.34
0.
03
0.11
0.
80
0.75
0.
01
0.00
0.
12
0.06
(15)
SU
BO
R
-0.1
0 0.
04
0.05
0.
03
0.06
0.
01
-0.0
3 -0
.04
-0.1
7 0.
08
0.00
0.
05
0.23
0.
54
0.
10
0.74
0.
00
0.13
0.
36
0.87
0.
94
0.02
0.
67
0.09
(16)
TB
ILL
0.81
-0
.05
-0.0
4 -0
.12
-0.0
3 0.
00
-0.0
6 -0
.07
-0.1
1 0.
13
-0.0
7 0.
11
0.14
0.
12
0.09
0.00
0.
25
0.06
0.
01
0.00
0.
03
0.99
0.
05
0.13
(17)
RIS
KPR
0.
23
-0.0
1 -0
.03
0.00
0.
01
-0.0
7 0.
02
0.01
-0
.16
0.12
-0
.08
-0.0
3 0.
04
0.05
0.
02
0.26
0.08
0.
32
0.34
0.
03
0.48
0.
27
0.10
0.
57
(18)
MO
OD
RN
K
-0.0
9 0.
19
0.14
0.
20
0.20
-0
.35
0.14
-0
.01
0.06
-0
.14
-0.0
1 0.
03
0.01
-0
.12
-0.1
7 0.
06
0.09
0.23
0.
77
0.21
0.
92
0.39
0.
01
0.24
(19)
GR
OW
TH
-0.2
0 0.
16
0.15
0.
18
0.11
-0
.12
0.14
-0
.08
-0.2
0 0.
11
0.02
-0
.14
0.01
0.
09
0.08
-0
.10
0.05
0.
06
0.
25
0.00
0.
21
0.01
0.
82
0.76
(20)
FR
OS
-0.2
0 -0
.08
-0.0
8 -0
.05
-0.0
9 -0
.07
0.23
0.
91
-0.0
8 -0
.16
-0.1
1 -0
.03
0.06
-0
.01
-0.0
5 -0
.14
-0.0
5 -0
.02
-0.0
6
0.00
0.
04
0.32
0.
01
0.11
(21)
MTB
-0
.36
0.04
0.
09
0.07
0.
03
-0.2
4 0.
47
0.16
0.
09
-0.1
4 0.
22
-0.0
2 -0
.08
-0.0
2 -0
.01
-0.2
6 -0
.11
0.07
0.
22
0.23
0.51
0.
26
0.25
0.
53
(22)
CA
PEX
P 0.
03
0.14
0.
09
0.13
0.
12
-0.0
8 0.
09
0.17
-0
.23
0.15
-0
.14
-0.0
8 -0
.03
0.14
0.
00
0.11
0.
04
-0.0
1 0.
07
0.11
0.
03
0.
00
0.25
0.
48
(23)
FR
OSX
GR
0.
07
-0.1
6 -0
.17
-0.1
2 -0
.11
-0.0
8 0.
11
-0.0
3 0.
07
-0.0
7 -0
.06
0.14
-0
.01
-0.1
9 -0
.12
0.00
-0
.06
0.05
-0
.14
-0.0
5 -0
.06
-0.2
4
0.22
0.
75
(24)
LO
SS
-0.0
1 0.
00
-0.0
6 0.
01
0.04
0.
21
-0.1
8 -0
.20
0.08
0.
04
0.02
0.
04
0.03
0.
08
0.02
-0
.10
-0.0
9 -0
.14
0.01
-0
.14
-0.0
6 -0
.06
0.06
0.29
(25)
ISSU
ES
-0.0
3 0.
15
0.16
0.
14
0.09
0.
13
-0.0
9 -0
.06
0.36
-0
.01
0.11
-0
.07
-0.1
1 -0
.10
-0.0
9 -0
.08
0.03
0.
06
0.02
-0
.09
-0.0
3 0.
04
-0.0
2 0.
06
104
T
a b
l e
4
Yea
r-to
-Yea
r T
rans
ition
Pro
babi
litie
s Mat
rix
(for
PCT
RN
K)
Tabl
e co
ntai
ns th
e ye
ar-to
-yea
r tra
nsiti
on p
roba
bilit
ies
mat
rix, w
hich
show
s th
e pr
obab
ilitie
s of
a fi
rm m
ovin
g fr
om q
uant
ile i
in y
ear t
(sho
wn
in th
e co
lum
ns) t
o qu
antil
e j i
n ye
ar t+
1 (s
how
n in
the
row
s). P
anel
A c
onta
ins
the
trans
ition
mat
rix fo
r the
ent
ire A
IMR
sam
ple
(198
6-19
96),
whi
ch in
clud
es o
nly
firm
s with
at l
east
two
cons
ecut
ive
obse
rvat
ions
(362
4 fir
m-y
ears
). Pa
nel B
con
tain
s tra
nsiti
on m
atrix
for o
ur fi
nal s
ampl
e w
ith a
t lea
st tw
o co
nsec
utiv
e ob
serv
atio
ns (1
56 fi
rms)
.
Pane
l A: E
ntir
e A
IMR
sam
ple
(198
6-19
96)
Q
1
Q 2
Q
3
Q 4
Q
5
Q 6
Q
7
Q 8
Q
9
Q 1
0 A
ll Q
1
0.45
0.
22
0.13
0.
06
0.04
0.
04
0.02
0.
01
0.02
0.
01
1.00
Q
2
0.24
0.
31
0.16
0.
11
0.06
0.
06
0.02
0.
02
0.02
0.
01
1.00
Q
3
0.11
0.
17
0.26
0.
16
0.08
0.
07
0.05
0.
04
0.03
0.
02
1.00
Q
4
0.06
0.
11
0.18
0.
22
0.14
0.
12
0.05
0.
07
0.03
0.
03
1.00
Q
5
0.05
0.
06
0.13
0.
16
0.19
0.
15
0.10
0.
06
0.06
0.
03
1.00
Q
6
0.04
0.
08
0.08
0.
09
0.14
0.
19
0.16
0.
11
0.07
0.
04
1.00
Q
7
0.01
0.
02
0.06
0.
09
0.10
0.
16
0.20
0.
17
0.11
0.
07
1.00
Q
8
0.01
0.
03
0.04
0.
03
0.10
0.
11
0.18
0.
21
0.19
0.
11
1.00
Q
9
0.01
0.
02
0.04
0.
03
0.05
0.
09
0.12
0.
19
0.23
0.
22
1.00
Q
10
0.01
0.
02
0.01
0.
02
0.05
0.
05
0.08
0.
12
0.21
0.
46
1.00
Pa
nel B
: Fin
al sa
mpl
e (u
sed
to e
stim
ate
our
OL
S/FE
reg
ress
ions
) (19
86-1
996)
Q
1
0.42
0.
16
0.05
0.
16
0.05
0.
11
0.00
0.
05
0.00
0.
00
1.00
Q
2
0.14
0.
29
0.36
0.
14
0.07
0.
00
0.00
0.
00
0.00
0.
00
1.00
Q
3
0.12
0.
24
0.24
0.
18
0.00
0.
06
0.12
0.
00
0.06
0.
00
1.00
Q
4
0.00
0.
16
0.16
0.
05
0.21
0.
21
0.16
0.
05
0.00
0.
00
1.00
Q
5
0.00
0.
08
0.00
0.
08
0.15
0.
31
0.23
0.
00
0.00
0.
15
1.00
Q
6
0.00
0.
00
0.06
0.
11
0.11
0.
11
0.11
0.
17
0.33
0.
00
1.00
Q
7
0.00
0.
00
0.00
0.
07
0.14
0.
07
0.50
0.
14
0.00
0.
07
1.00
Q
8
0.00
0.
00
0.00
0.
05
0.16
0.
05
0.11
0.
21
0.26
0.
16
1.00
Q
9
0.00
0.
00
0.00
0.
00
0.14
0.
14
0.21
0.
00
0.29
0.
21
1.00
Q
10
0.00
0.
00
0.11
0.
00
0.00
0.
00
0.00
0.
22
0.33
0.
33
1.00
105
sample period and data on yield-to-maturity and other issue characteristics are available on the SDC
Platinum Database, (2) the firm’s disclosure policy is rated by the AIMR, (3) accounting data is available
on the CRSP/COMPUSTAT Merged Database and (4) future sales and earnings data is available to
compute FROS and GROWTH. We excluded 80 firms with only one observation in the sample due to the
requirements of the panel data techniques and we deleted firms in the financial industry. Table 1 documents
the effect of each of the sample filters and breaks down the sample by year and by industry. The data
necessary to compute the variables TBILL and RISKPR are taken from the Federal Reserve Database
(FREDII).
Table 2 contains sample summary statistics. The average (median) value of our cost-of-debt capital
measure [YIELD] is 8.14 (8.07), which is similar to Sengupta’s (1998) findings. The average percentage
rank of disclosure is (for all four measures) just above 0.5, indicating that our sample firms disclose more
information than the average firm in their industry. The standard deviation of each disclosure score is about
0.27, which indicates that we have substantial disclosure variation in our sample. AIMR’s disclosure ratings
tend to focus on larger and better known firms. This bias is reflected in our sample since sample firms are
large (mean (median) of total assets is $9.81($7.80) billion). Our sample is less skewed than Sengupta’s
who reports a mean (median) value of total assets of $10.1 ($6.02) billion.
Table 3 reports Pearson correlations (below the diagonal) and their p-values (above the diagonal).
YIELD is significantly, negatively associated with three disclosure measures and negatively, but not
significantly with the measure PCTOPB. The three specific disclosure measures (PCTREL, PCTANL and
PCTOPB) are positively and significantly associated with the overall measure of disclosure (PCTRNK),
which suggests that disclosure practices via investor relations, the annual report and other publications are
complementary.
We mentioned in the previous section that substantial over-time variation in each firm’s disclosure
quality is a precondition for applying fixed effects estimation. We conduct a first analysis of whether our
sample fulfils this precondition in Table 4. The table contains the year-to-year transition probabilities
matrix, which shows the probability of a firm moving from decile i in year t (shown in the first column) to
decile j in year t+1 (shown in the first row). Panel A contains the transition matrix for entire AIMR sample
(1986-1996). Panel B contains the transition matrix for our final sample. The findings suggest that the final
sample is representative of the entire AIMR population. More importantly, the probability of staying in the
same disclosure quality category from year to year generally does not exceed 25% (diagonal entries in each
panel). Therefore, about 75% of firms either improve or worsen their disclosure over time. It would seem
that the within variation is substantial and fixed effects estimation should be appropriate in the current
setting. We address the requirement of substantial over-time variation in the firm’s disclosure quality
further in the Additional Analysis section.
106
T a
b l
e 5
R
eplic
atio
n of
the
Seng
upta
’s fi
ndin
gs fo
r di
ffere
nt D
isclo
sure
mea
sure
s
it
kk
itit
Con
trol
Dis
clos
ure
Inte
rcep
tYI
ELD
εβ
β+
++
=∑
+1
1
Tabl
e pr
ovid
es e
stim
ates
for
Equ
atio
n (1
) us
ing
pool
ed O
LS r
egre
ssio
ns. T
he m
odel
is a
n eq
uiva
lent
of t
hat e
stim
ated
by
Seng
upta
(19
98).
Col
umn
A o
f th
e ta
ble
repl
icat
es S
engu
pta’
s re
sults
usin
g th
e m
easu
re o
f tot
al d
iscl
osur
e qu
ality
(PC
TRN
K).
The
follo
win
g th
ree
colu
mns
, res
pect
ivel
y, u
se m
easu
res
of q
ualit
y of
inve
stor
re
latio
ns (
PCTR
EL),
annu
al r
epor
ts (
PCTA
NL)
, and
qua
rterly
and
oth
er p
ublic
atio
ns (
PCTO
PB).
All
four
mea
sure
s of
dis
clos
ure
are
cons
truct
ed u
sing
AIM
R-FA
F di
sclo
sure
sco
res
for t
he p
erio
d 19
86-1
996.
The
dis
clos
ure
scor
es a
re c
onve
rted
to w
ithin
indu
stry
perc
enta
ge ra
nkin
gs in
ord
er to
ach
ieve
bet
ter c
ompa
rabi
lity
acro
ss
indu
strie
s and
ove
r tim
e: fo
r eac
h ye
ar a
nd e
ach
indu
stry
the
firm
s are
rank
ed b
ased
upo
n di
sclo
sure
sco
re, t
hen
the
rank
ings
are
div
ided
by
the
num
ber o
f firm
s bei
ng
rank
ed. S
ampl
e in
clud
es 1
00 c
ompa
nies
, whi
ch a
mou
nt to
358
firm
-yea
r obs
erva
tions
. In
orde
r to
avoi
d do
uble
cou
ntin
g w
e us
e on
ly fi
rst d
ebt i
ssue
in a
giv
en y
ear t
o m
easu
re Y
IELD
. St
anda
rd e
rror
s are
Whi
te h
eter
osce
dast
icity
con
sist
ent.
See
App
endi
x A
for v
aria
ble
defin
ition
s.
Type
of D
iscl
.
(A) T
OT
AL
RA
NK
(PC
TR
NK
) (B
) IN
V. R
EL
AT.
(PC
TR
EL
) (C
) AN
NU
AL
(PC
TA
NL
) (D
) OT
HE
R P
UB
L. (
PCT
OPB
)
Vari
able
Si
gnC
oeff.
St
. Dev
. P-
valu
e C
oeff.
St
. Dev
. P-
valu
e C
oeff.
St
. Dev
. P-
valu
e C
oeff.
St
. Dev
. P-
valu
e D
isclo
sue
- -0
.332
0.
122
[.007
] -0
.292
0.
102
[.005
] -0
.318
0.
133
[.017
] -0
.196
0.
115
[.090
] LE
V
+ 2.
170
0.33
8 [.0
00]
2.29
8 0.
351
[.000
] 2.
174
0.33
7 [.0
00]
2.25
0 0.
345
[.000
] C
OV
ER
- -0
.015
0.
006
[.011
] -0
.013
0.
006
[.025
] -0
.014
0.
006
[.020
] -0
.013
0.
006
[.031
] RO
S -
-0.7
06
0.39
6 [.0
75]
-0.7
40
0.39
3 [.0
61]
-0.7
05
0.40
1 [.0
80]
-0.7
18
0.39
8 [.0
72]
LASS
ET
- -0
.099
0.
043
[.021
] -0
.098
0.
043
[.024
] -0
.098
0.
043
[.022
] -0
.102
0.
043
[.018
] SI
ZE
+ 0.
001
0.00
0 [.0
25]
0.00
1 0.
000
[.027
] 0.
001
0.00
0 [.0
31]
0.00
1 0.
000
[.031
] RI
SK
+ 0.
732
0.21
5 [.0
01]
0.69
0 0.
212
[.001
] 0.
756
0.22
2 [.0
01]
0.72
2 0.
220
[.001
] LM
ATU
R +
0.00
0 0.
003
[.880
] 0.
000
0.00
3 [.9
83]
0.00
0 0.
003
[.965
] 0.
001
0.00
3 [.8
60]
CA
LL
+ 0.
353
0.13
8 [.0
11]
0.35
1 0.
136
[.010
] 0.
373
0.14
3 [.0
10]
0.33
9 0.
136
[.013
] C
ON
VER
-
-2.9
71
0.32
0 [.0
00]
-2.9
83
0.32
6 [.0
00]
-2.9
72
0.32
2 [.0
00]
-2.9
60
0.33
3 [.0
00]
SUBO
R +
0.08
8 0.
311
[.778
] 0.
102
0.31
7 [.7
48]
0.07
9 0.
313
[.801
] 0.
082
0.32
7 [.8
03]
TBIL
L +
1.06
9 0.
028
[.000
] 1.
073
0.02
8 [.0
00]
1.06
3 0.
029
[.000
] 1.
073
0.02
8 [.0
00]
RISK
PR
+ 0.
395
0.27
3 [.1
50]
0.39
5 0.
276
[.153
] 0.
405
0.27
4 [.1
39]
0.40
1 0.
281
[.154
] C
0.39
2 0.
523
[.454
] 0.
313
0.51
2 [.5
42]
0.40
2 0.
534
[.451
] 0.
286
0.50
2 [.5
69]
Adj
-R2
0.
848
0.84
7
0.
848
0.84
5
N
OB:
358
358
358
358
107
T a
b l
e 6
D
eter
min
ants
of D
isclo
sure
In P
anel
A th
e de
term
inan
ts (
DET
ERM
INAM
TS)
for
each
of t
he f
our
disc
losu
re q
ualit
y m
easu
res
(PC
TRN
K, P
CTR
EL, P
CTA
NL,
PC
TOPB
) ar
e in
vest
igat
ed. T
he
mai
n pu
rpos
e of
thes
e re
gres
sion
s is
to d
emon
strat
e th
at v
aria
bles
w
e id
entif
ied
as d
eter
min
ants
of d
iscl
osur
e an
d cl
assi
fied
into
Per
form
ance
, Stru
ctur
e an
d O
ffer
grou
ping
s re
late
to th
e le
vel o
f dis
clos
ure
(in a
dditi
on to
the
varia
bles
in S
engu
pta
(199
8)).
Pane
l B re
ports
F-s
tatis
tics
from
an
AN
OV
A a
naly
sis
to d
emon
strat
e th
at
firm
-spe
cific
effe
cts
alon
e ex
plai
n a
larg
er p
ropo
rtion
of v
aria
tion
in th
e di
sclo
sure
pro
xies
as
the
dete
rmin
ants
in th
e re
gres
sion
s in
Pan
el A
. An
F-te
st is
use
d to
test
fo
r the
sign
ifica
nce
of th
e di
ffere
nces
in fi
rm-s
peci
fic d
iscl
osur
e le
vels
. The
sam
ple
incl
udes
100
com
pani
es a
nd 3
58 fi
rm-y
ear o
bser
vatio
ns. S
tand
ard
erro
rs a
re W
hite
he
tero
sced
astic
ity c
onsi
sten
t. Se
e A
ppen
dix
A fo
r var
iabl
e de
finiti
ons.
PAN
EL
A: O
LS
Est
imat
ion
itk
kit
TSD
ETER
MIN
ANIn
terc
ept
Dis
clos
ure
εβ
++
=∑
Type
of D
iscl
.
(A) T
OT
AL
RA
NK
(PC
TR
NK
)(B
) IN
V. R
EL
AT
ION
S (P
CT
RE
L)
(C) A
NN
UA
L (P
CT
AN
L)
(D) O
TH
ER
PU
BL
. (PC
TO
PB)
Vari
able
Si
gn
Coe
ff.
St. D
ev.
P-va
lue
Coe
ff.
St. D
ev.
P-va
lue
Coe
ff.
St. D
ev.
P-va
lue
Coe
ff.
St. D
ev.
P-va
lue
C
-0
.252
0.
258
[.330
] -0
.209
0.
263
[.428
] -0
.295
0.
252
[.241
] 0.
028
0.26
8 [.9
16]
GRO
WTH
+
0.41
8 0.
176
[.018
] 0.
362
0.17
0 [.0
34]
0.47
3 0.
171
[.006
] 0.
238
0.17
9 [.1
86]
ROS
+/-
0.49
9 0.
415
[.229
] 0.
089
0.38
3 [.8
17]
0.27
4 0.
389
[.481
] 0.
548
0.43
4 [.2
07]
FRO
S -
-0.7
22
0.40
8 [.0
78]
-0.3
57
0.37
5 [.3
42]
-0.3
82
0.40
5 [.3
46]
-0.7
86
0.43
7 [.0
73]
LOSS
+
0.03
9 0.
074
[.598
] -0
.060
0.
072
[.407
] 0.
048
0.06
8 [.4
79]
0.09
8 0.
070
[.162
] FR
OSX
GR
- -5
.306
2.
454
[.031
] -5
.378
1.
804
[.003
] -3
.204
1.
988
[.108
] -3
.698
2.
680
[.169
] M
TB
+ 0.
001
0.00
7 [.8
60]
0.00
7 0.
008
[.377
] 0.
003
0.00
7 [.6
45]
0.00
3 0.
007
[.674
] LA
SSET
+
0.02
3 0.
016
[.136
] 0.
030
0.01
6 [.0
59]
0.01
8 0.
016
[.257
] 0.
009
0.01
7 [.5
83]
CA
PEX
P +
0.65
6 0.
276
[.018
] 0.
425
0.28
3 [.1
34]
0.65
1 0.
273
[.018
] 0.
562
0.28
0 [.0
45]
MO
OD
RNK
-
0.00
2 0.
001
[.001
] 0.
001
0.00
1 [.0
28]
0.00
2 0.
001
[.001
] 0.
002
0.00
1 [.0
00]
ISSU
ES
+ 0.
010
0.00
5 [.0
23]
0.01
1 0.
005
[.023
] 0.
010
0.00
5 [.0
32]
0.00
6 0.
007
[.400
]
A
dj-R
2
0.09
6
0.
082
0.08
1
0.
065
NO
B:
35
8
35
8
35
8
35
8
PA
NE
L B
: A
naly
sis o
f Var
ianc
e (A
NO
VA
) of D
iscl
osur
e qu
ality
pro
xies
T
OT
AL
RA
NK
(PC
TR
NK
) IN
V. R
EL
AT
ION
S (P
CT
RE
L)
AN
NU
AL
(PC
TA
NL
) O
TH
ER
PU
BL.
(PC
TOPB
) A
dj-R
2
0.61
7
0.
523
0.55
7
0.
642
H0: α I
=α
F(
99,2
58)
6.82
1 [0
.000
0]
F(99
,258
) 4.
948
[0.0
000]
F(
99,2
58)
5.54
1 [0
.000
0]
F(99
,258
) 7.
492
[0.0
000]
108
4.6. Results
Benchmark model. Table 5 contains the results from pooled OLS regressions of Equation (1) for each of the
four measures of Disclosure. These regressions replicate and extend Sengupta’s original analysis. As in
Sengupta (1998, Table 6)78, we find a negative and strongly significant association (coefficient=-0.33,
s.e.=0.12)79 between the measure of overall disclosure policy (PCTRNK) and cost-of-debt capital. We also
consistently find negative and significant associations between the three other measures of Disclosure
(PCTREL, PCTANL and PCTOPB) and cost-of-debt capital. Note that this finding is somewhat in contrast
with Botosan and Plumlee (2002) who report that the sign of the relation between disclosure and cost-of-
capital is conditional on the type of disclosure (i.e., through investor relations, the annual report or other
publications). Although not the focus of our attention, we find that most control variables are significant in
all four regressions and have the same sign as in Sengupta (1998). Together the independent variables have
good explanatory power; the adjusted R-squared is about 84%.
Main findings. We investigate the endogeneity bias caused by omitted ‘joint determinants’ in Tables 6
through 8. Recall that our claim is that Sengupta’s model omits several variables theory suggests are
correlated with both disclosure and cost-of-debt capital. We first evaluate whether these ‘joint
determinants’ are indeed associated with Disclosure in Table 6 – Panel A. We report on regressions of each
of our four Disclosure measures on those variables suggested in earlier literature, including Performance,
Structure and Offer variables. The results show that all joint determinants (except for LOSS, LASSET and
MTB) are significantly associated with our overall measure of Disclosure, PCTRNK. Although the results
for the other three measures (PCTREL, PCTANL and PCTOPB) are somewhat mixed, we conclude that the
complete set of variables has significant explanatory power for each Disclosure measure.80 Table 5 – Panel
B shows the results of an ANOVA analysis of the four Disclosure measures. We find that allowing firm-
specific intercepts to explain disclosure accounts for much more of the variation in each of the Disclosure
measures than our complete set of ‘joint determinants’ (the adjusted R-squared in the ANOVA analysis
averages about 60% versus 9% in the regressions of Panel A). Our interpretation of this finding is that
unobserved firm-specific factors are a very important consideration in explaining differences in disclosure
policy. In addition, these results indicate that augmenting the benchmark model with the joint determinants
alone may not suffice to eliminate the endogeneity bias in the results, if in fact unobserved firm
heterogeneity is correlated with cost-of-debt capital.
78 Note that the magnitudes of our coefficients are not directly comparable to those in Sengupta (1999) because our variable definitions are sometimes different. 79 Standard errors throughout the paper are White (1980) heteroskedasticity consistent. 80 The simple correlations in Table 2 between each of the ‘joint determinants’ (and their best linear combination) and our disclosure variables are low and there is little reason to be concerned about multicollinearity being an issue in our subsequent analyses (see also Griffiths et al. 1993).
109
T a
b l
e 7
A
ugm
ente
d M
odel
est
imat
ed fo
r Fo
ur D
isclo
sure
mea
sure
s us
ing
Ord
inar
y L
east
Squ
ares
itl
lk
kj
ji
iit
itC
ontr
olO
ffer
Stru
ctur
ee
Perf
orm
anc
Dis
clos
ure
Inte
rcep
tYI
ELD
εβ
ββ
ββ
++
++
++
=∑
∑∑
∑+
11
Type
of D
isclo
sure
Si
gn
(A) T
OT
AL
DIS
CLO
SUR
E
(B) I
NV
REL
. (PC
TR
EL
) (C
) AN
NU
AL
(PC
TA
NL
) (D
) OT
HE
R (P
CT
OPB
)
Vari
able
C
oeff.
St
.Dev
P-
valu
e C
oeff.
St
.Dev
P-
valu
e C
oeff.
St
.Dev
P-
valu
e C
oeff.
St
.Dev
P-
valu
e D
iscl
osur
e -
-0.1
72
0.11
1 [.1
22]
-0.0
95
0.09
6 [.3
20]
-0.1
54
0.11
8 [.1
93]
-0.0
62
0.10
2 [.5
43]
Perf
orm
ance
GRO
WTH
-
-1.2
00
0.33
7 [.0
00]
-1.2
37
0.34
7 [.0
00]
-1.2
10
0.33
5 [.0
00]
-1.2
60
0.35
0 [.0
00]
FRO
S -
-1.0
32
1.00
5 [.3
05]
-0.9
32
0.99
5 [.3
50]
-0.9
78
0.98
9 [.3
23]
-0.9
39
1.00
8 [.3
52]
LOSS
+
0.32
9 0.
206
[.111
] 0.
319
0.20
8 [.1
26]
0.33
0 0.
205
[.107
] 0.
332
0.20
4 [.1
05]
MTB
-
-0.0
47
0.01
4 [.0
01]
-0.0
48
0.01
4 [.0
01]
-0.0
48
0.01
5 [.0
01]
-0.0
49
0.01
5 [.0
01]
FRO
SXG
R +/
- 1.
051
3.87
3 [.7
86]
1.34
3 3.
963
[.735
] 1.
403
3.95
2 [.7
23]
1.57
3 3.
942
[.690
] St
ruct
ure
C
APE
XP
- 0.
484
0.83
1 [.5
61]
0.39
7 0.
838
[.636
] 0.
460
0.83
8 [.5
83]
0.37
7 0.
839
[.654
] M
OO
DRN
K
- -0
.005
0.
001
[.000
] -0
.005
0.
001
[.000
] -0
.005
0.
001
[.000
] -0
.005
0.
001
[.000
] O
ffer
IS
SUES
-
0.00
7 0.
011
[.510
] 0.
006
0.01
1 [.5
55]
0.00
7 0.
011
[.528
] 0.
006
0.01
1 [.5
92]
Con
trol
s
LEV
+
1.60
7 0.
330
[.000
] 1.
664
0.33
4 [.0
00]
1.61
1 0.
330
[.000
] 1.
645
0.33
1 [.0
00]
CO
VER
-
-0.0
02
0.00
5 [.6
44]
-0.0
01
0.00
5 [.9
08]
-0.0
01
0.00
5 [.7
76]
0.00
0 0.
005
[.946
] RO
S -
0.13
8 1.
042
[.895
] 0.
034
1.03
6 [.9
74]
0.09
4 1.
029
[.928
] 0.
054
1.04
9 [.9
59]
LASS
ET
- -0
.135
0.
046
[.003
] -0
.136
0.
046
[.003
] -0
.135
0.
045
[.003
] -0
.138
0.
046
[.003
] SI
ZE
+ 0.
001
0.00
0 [.0
04]
0.00
1 0.
000
[.005
] 0.
001
0.00
0 [.0
05]
0.00
1 0.
000
[.005
] RI
SK
+ 0.
563
0.20
5 [.0
06]
0.54
9 0.
203
[.007
] 0.
576
0.21
0 [.0
07]
0.56
1 0.
207
[.007
] LM
ATU
R +
-0.0
01
0.00
3 [.7
64]
-0.0
01
0.00
3 [.7
22]
-0.0
01
0.00
3 [.7
15]
-0.0
01
0.00
3 [.7
40]
CA
LL
+ 0.
386
0.12
4 [.0
02]
0.37
9 0.
122
[.002
] 0.
393
0.12
9 [.0
02]
0.37
5 0.
121
[.002
] C
ON
VER
-
-3.0
44
0.29
4 [.0
00]
-3.0
38
0.29
7 [.0
00]
-3.0
41
0.29
6 [.0
00]
-3.0
30
0.29
7 [.0
00]
SUBO
R +
0.02
1 0.
292
[.942
] 0.
015
0.29
7 [.9
60]
0.01
5 0.
293
[.958
] 0.
009
0.29
6 [.9
76]
TBIL
L +
1.
050
0.02
8 [.0
00]
1.05
3 0.
028
[.000
] 1.
047
0.02
9 [.0
00]
1.05
2 0.
028
[.000
]
110
Tab
le 7
. Con
tinue
d
a. In
add
ition
to c
ontro
l var
iabl
es in
Sen
gupt
a’s m
odel
( Con
trol),
the
mod
el in
clud
es th
ree
addi
tiona
l gro
upin
gs o
f con
trol v
aria
bles
: Per
form
ance
, Stru
ctur
e an
d O
ffer.
Perf
orm
ance
cap
ture
s th
e fu
ture
pro
spec
ts o
f th
e co
mpa
ny.
Stru
ctur
e ca
ptur
es i
nfor
mat
ion
asym
met
ries
betw
een
inve
stor
s an
d th
e fir
m a
nd t
he e
cono
mie
s of
sco
pe i
n pr
oduc
ing
info
rmat
ion.
Offe
r mea
sure
s the
ext
ent o
f cap
ital m
arke
t tra
nsac
tions
. All
thre
e gr
oups
are
rela
ted
in th
eory
to th
e le
vel o
f dis
clos
ure
and
to Y
IELD
. b.
Equ
atio
n (2
) is
estim
ated
usin
g po
oled
OLS
. The
col
umns
A-D
of t
he ta
ble
repo
rt on
eac
h of
fou
r di
sclo
sure
qua
lity
prox
ies
resp
ectiv
ely:
tota
l dis
clos
ure
qual
ity
(TO
TRN
K),
qual
ity o
f inv
esto
r re
latio
ns (P
CTR
EL),
qual
ity o
f ann
ual r
epor
ts (P
CTA
NL)
, and
qua
lity
of q
uarte
rly a
nd o
ther
pub
licat
ions
(PCT
OPB
). A
ll fo
ur m
easu
res
of
disc
losu
re a
re c
onstr
ucte
d us
ing
AIM
R-FA
F di
sclo
sure
sco
res
for t
he p
erio
d 19
86-1
996.
The
dis
clos
ure
scor
es a
re c
onve
rted
to w
ithin
indu
stry
perc
enta
ge ra
nkin
gs in
ord
er
to a
chie
ve b
ette
r co
mpa
rabi
lity
acro
ss in
dustr
ies
and
over
tim
e: f
or e
ach
year
and
eac
h in
dustr
y th
e fir
ms
are
rank
ed b
ased
upo
n di
sclo
sure
sco
re, t
hen
the
rank
ings
are
di
vide
d by
the
num
ber o
f firm
s be
ing
rank
ed. S
ampl
e in
clud
es 1
00 c
ompa
nies
, whi
ch a
mou
nt to
358
firm
-yea
r obs
erva
tions
. In
orde
r to
avoi
d do
uble
cou
ntin
g w
e us
e on
ly
first
deb
t iss
ue in
a g
iven
yea
r to
mea
sure
YIE
LD.
Stan
dard
err
ors a
re W
hite
het
eros
ceda
stic
ity c
onsi
sten
t. Se
e A
ppen
dix
A fo
r var
iabl
e de
finiti
ons.
RISK
PR
+ 0.
454
0.26
7 [.0
91]
0.46
0 0.
269
[.088
] 0.
462
0.26
7 [.0
84]
0.46
4 0.
270
[.086
] C
2.58
1 0.
787
[.001
] 2.
571
0.79
0 [.0
01]
2.59
3 0.
792
[.001
] 2.
595
0.79
8 [.0
01]
Adj
-R2
0.
872
0.87
2
0.
872
0.87
1
111
T a
b l
e 8
A
ugm
ente
d M
odel
est
imat
ed fo
r Fo
ur D
isclo
sure
mea
sure
s us
ing
Fixe
d E
ffect
s
iti
ll
kk
jj
ii
itit
Con
trol
Offe
rSt
ruct
ure
ePe
rfor
man
cD
iscl
osur
eIn
terc
ept
YIEL
Dε
αβ
ββ
ββ
++
++
++
+=
∑∑
∑∑
+1
1
Type
of D
isclo
sure
Si
gn
(A) T
OT
AL
DIS
CLO
SUR
E
(B) I
NV
REL
. (PC
TR
EL
) (C
) AN
NU
AL
(PC
TA
NL
) (D
) OT
HE
R (P
CT
OPB
)
Vari
able
C
oeff.
St
.Dev
P-
valu
e C
oeff.
St
.Dev
P-
valu
e C
oeff.
St
.Dev
P-
valu
e C
oeff.
St
.Dev
P-
valu
e D
iscl
osur
e -
-0.4
00
0.13
0 [.0
02]
-0.3
77
0.11
8 [.0
02]
-0.3
48
0.13
4 [.0
10]
-0.2
23
0.13
3 [.0
94]
Perf
orm
ance
GRO
WTH
-
-0.5
75
0.41
0 [.1
62]
-0.6
85
0.41
2 [.0
98]
-0.6
36
0.41
6 [.1
28]
-0.7
13
0.42
5 [.0
95]
FRO
S -
-0.1
92
1.15
3 [.8
68]
0.06
1 1.
159
[.958
] -0
.197
1.
169
[.866
] -0
.143
1.
158
[.902
] LO
SS
+ 0.
162
0.14
6 [.2
68]
0.12
1 0.
152
[.425
] 0.
176
0.14
8 [.2
35]
0.16
7 0.
153
[.276
] M
TB
- -0
.020
0.
024
[.402
] -0
.014
0.
025
[.564
] -0
.021
0.
025
[.394
] -0
.023
0.
024
[.341
] FR
OSX
GR
+/-
5.12
3 4.
713
[.278
] 5.
082
4.68
5 [.2
79]
5.04
3 4.
728
[.287
] 5.
719
4.76
2 [.2
31]
Stru
ctur
e
CA
PEX
P -
0.41
0 1.
044
[.695
] 0.
167
1.06
3 [.8
75]
0.38
2 1.
047
[.716
] 0.
361
1.06
2 [.7
34]
MO
OD
RNK
-
-0.0
01
0.00
3 [.6
97]
-0.0
01
0.00
3 [.8
09]
-0.0
01
0.00
3 [.6
53]
-0.0
01
0.00
3 [.6
20]
Offe
r
ISSU
ES
- 0.
007
0.01
2 [.5
65]
0.00
7 0.
012
[.569
] 0.
007
0.01
2 [.5
40]
0.00
7 0.
012
[.600
] C
ontr
ols
LE
V
+ 1.
585
0.63
8 [.0
14]
1.68
2 0.
646
[.010
] 1.
594
0.64
1 [.0
14]
1.70
3 0.
651
[.010
] C
OV
ER
- 0.
000
0.01
0 [.9
67]
0.00
1 0.
010
[.918
] -0
.005
0.
010
[.604
] -0
.002
0.
010
[.797
] RO
S -
-3.0
21
1.17
2 [.0
11]
-3.2
04
1.19
3 [.0
08]
-2.8
96
1.16
3 [.0
13]
-3.1
10
1.18
0 [.0
09]
LASS
ET
- -0
.107
0.
141
[.452
] -0
.126
0.
142
[.378
] -0
.144
0.
137
[.294
] -0
.143
0.
134
[.290
] SI
ZE
+ 0.
001
0.00
0 [.0
06]
0.00
1 0.
000
[.004
] 0.
001
0.00
0 [.0
06]
0.00
1 0.
000
[.006
] RI
SK
+ 0.
193
0.16
5 [.2
44]
0.16
7 0.
160
[.296
] 0.
202
0.16
5 [.2
22]
0.17
9 0.
164
[.277
] LM
ATU
R +
0.00
0 0.
003
[.960
] -0
.001
0.
003
[.737
] 0.
000
0.00
3 [.9
39]
-0.0
01
0.00
3 [.7
39]
CA
LL
+ 0.
237
0.09
7 [.0
15]
0.25
7 0.
098
[.009
] 0.
250
0.09
6 [.0
10]
0.23
9 0.
097
[.014
] C
ON
VER
-
-3.0
99
0.44
6 [.0
00]
-3.1
21
0.44
5 [.0
00]
-3.1
30
0.44
7 [.0
00]
-3.1
02
0.45
2 [.0
00]
SUBO
R +
0.23
7 0.
364
[.515
] 0.
226
0.36
6 [.5
38]
0.23
9 0.
370
[.519
] 0.
190
0.37
4 [.6
11]
112
T
able
8. C
ontin
ued
a. In
add
ition
to c
ontro
l var
iabl
es in
Sen
gupt
a’s
mod
el (
Con
trol
), th
e m
odel
her
e in
clud
es th
ree
addi
tiona
l gro
upin
gs o
f con
trol v
aria
bles
: Per
form
ance
, Stru
ctur
e an
d O
ffer.
Perf
orm
ance
cap
ture
s th
e fu
ture
pro
spec
ts o
f the
com
pany
. Stru
ctur
e ca
ptur
es in
form
atio
n as
ymm
etrie
s be
twee
n in
vest
ors
and
the
firm
and
the
econ
omie
s of
sco
pe in
pr
oduc
ing
info
rmat
ion.
Offe
r mea
sure
s the
ext
ent o
f cap
ital m
arke
t tra
nsac
tions
. All
thre
e gr
oups
are
rela
ted
in th
eory
to th
e le
vel o
f dis
clos
ure
and
to Y
IELD
. b.
The
col
umns
A-D
of t
he ta
ble
repo
rt on
eac
h of
fou
r di
sclo
sure
qua
lity
prox
ies
resp
ectiv
ely:
tota
l dis
clos
ure
qual
ity (
TOTR
NK
), qu
ality
of i
nves
tor
rela
tions
(PC
TREL
), qu
ality
of a
nnua
l rep
orts
(PCT
AN
L), a
nd q
ualit
y of
qua
rterly
and
oth
er p
ublic
atio
ns (P
CTO
PB).
All
four
mea
sure
s of
dis
clos
ure
are
cons
truct
ed u
sing
AIM
R-FA
F di
sclo
sure
sc
ores
for t
he p
erio
d 19
86-1
996.
The
dis
clos
ure
scor
es a
re c
onve
rted
to w
ithin
indu
stry
perc
enta
ge ra
nkin
gs in
ord
er to
ach
ieve
bet
ter c
ompa
rabi
lity
acro
ss in
dustr
ies
and
over
tim
e: fo
r eac
h ye
ar a
nd e
ach
indu
stry
the
firm
s are
rank
ed b
ased
upo
n di
sclo
sure
scor
e, th
en th
e ra
nkin
gs a
re d
ivid
ed b
y th
e nu
mbe
r of f
irms b
eing
rank
ed.
c. T
he d
ispl
ayed
resu
lts a
re th
e es
timat
es fr
om F
ixed
Effe
cts r
egre
ssio
n fo
r Equ
atio
n (3
).
d. S
ampl
e in
clud
es 1
00 c
ompa
nies
, whi
ch a
mou
nt to
358
firm
-yea
r obs
erva
tions
. In
orde
r to
avoi
d do
uble
cou
ntin
g w
e us
e on
ly fi
rst d
ebt i
ssue
in a
giv
en y
ear t
o m
easu
re
YIE
LD.
Stan
dard
err
ors a
re W
hite
het
eros
ceda
stic
ity c
onsi
stent
. See
App
endi
x A
for v
aria
ble
defin
ition
s.
TBIL
L +
1.
060
0.02
9 [.0
00]
1.06
8 0.
029
[.000
] 1.
055
0.02
8 [.0
00]
1.06
2 0.
028
[.000
] RI
SKPR
+
0.59
9 0.
264
[.024
] 0.
595
0.26
6 [.0
26]
0.59
9 0.
264
[.024
] 0.
642
0.27
0 [.0
18]
C
A
dj-R
2
0.92
0
0.
920
0.91
9
0.
918
113
Table 7 contains the results of the OLS estimation of the augmented Sengupta model, Equation (2) for each
of the four Disclosure measures. These regressions only attempt to mitigate the endogeneity bias caused by
omitted joint determinants. The Performance, Structure and Offer variables we included based on the extant
literature are generally associated with cost-of-debt capital. The weakest results are obtained for FROS, the
interaction FROS*GR, CAPEXP and ISSUES, which do not obtain significance in any of the four
regressions. However, GROWTH, MTB and MOODRNK (LOSS) are strongly (marginally) associated
with cost-of-debt capital. An F-test on the incremental explanatory power of all Performance, Structure and
Offer variables together suggests that these variables are helpful in explaining cost-of-debt capital (in the
overall disclosure measure regression, PCTRNK, F=10.31, p-value<1%)81. We find that Disclosure and
cost-of-debt capital are no longer significantly associated once these ‘joint determinants’ are included in the
regression. Note that the loss of significance is due to a reduced magnitude of the OLS coefficient on
Disclosure compared with Equation (1) and not because of an increase in the standard errors and thus lack
of power. From comparing these results with those of Equation (1), it would seem that in the latter
equation Disclosure subsumes part of the effect of the joint determinants on cost-of-debt capital, which
results in an upward bias of the coefficient on Disclosure in Sengupta’s original model.82
Table 8 contains the findings for the fixed effects estimation of the augmented Sengupta model, i.e.,
Equation (3) for each of the Disclosure measures.83 These regressions attempt to simultaneously control for
firm-specific heterogeneity bias and for endogeneity caused by omitted variables. The findings are
consistent throughout the table. Cost-of-debt capital is strongly negatively associated with disclosure policy
at the level of the individual firm. The coefficient estimates range between -0.22 and -0.40 for each of the
four Disclosure measures. In particular, we find that the fixed effect coefficient in Equation (3) on
PCTRNK is -0.40 (s.e.=0.13) compared with the OLS coefficient in Equation (1), which is –0.33. The
implication is that the cost-of-debt capital benefit from increased disclosure is larger than previously
reckoned. For a median size debt issue of $149.8 million, an improvement of disclosure score from the 25th
to the 75th percentile, may reduce interest payments by about $10.4 million.84
So far, while we have directly documented the effect of omitted ‘joint determinants’, we have only
indirectly shown that unobservable firm-specific factors exist that are associated with both cost-of-debt
81 The (unreported) results for the other three disclosure measures are similar to those for PCTRNK. 82 We also estimated the model without MOODRNK. Unreported results show that in the augmented OLS regressions Disclosure remains significant, but the size of the coefficient is smaller than in a model without any control variables included. Replacing MOODRNK by the lagged value of S&P’s long term debt rating did not affect the main findings and our conclusions remained unchanged. 83 Random effects estimates for PCTREL, PCTANL and PCTOPB are available from the authors upon request. 84 It should be noted, however, that the incremental explanatory power of the Disclosure variable is small (and below 1%). This is not unexpected though, since our model already explains almost 90% of the variation in cost-of-debt capital. What is more, the incremental explanatory power of Disclosure is of similar magnitude as our leverage variable, which is always very significant. Therefore, we believe that adding Disclosure to the model is meaningful regardless of its low incremental explanatory power.
114
capital and disclosure. When these unobservable factors remain unaccounted for, the disclosure variable
will subsume part of their effect on cost-of-capital. In such case, the reported association between cost-of-
debt capital and disclosure is a mixture of the true association between these variables and a spurious part
due to not accounting properly for unobservable firm-specific factors. We use Mundlak’s (1978) approach
to investigate directly how unobservable firm-specific factors are associated with disclosure (or other
independent variables). Table 9 holds the results of this analysis for all four Disclosure measures. We find
that our measure of overall disclosure (PCTRNK), disclosure via investor relations (PCTREL), and
marginally disclosure via annual reports (PCTANL) and other publications (PCTOPB) are positively
associated with unobservable firm-specific factors.85 Note that several of the control variables in Sengupta’s
original model are also related with these firm-specific factors (especially, RISK and CALL), which
reinforces the need for taking these effects into account when investigating the relation between cost-of-
debt capital and disclosure.
These results confirm the presence of endogeneity bias and imply that firms with higher cost-of-
capital levels are also the firms that happen to disclose more information. This occurs not because
disclosure is causally related to cost-of-capital, but because both variables are driven by omitted factors.
The resulting endogeneity bias works against finding a relation in the cross-sectional OLS regressions we
report in Table 7. As such, our results offer an explanation why some earlier studies fail to find a relation
between cost-of-capital and disclosure.
Based on these findings, we evaluate the bias in Sengupta’s model by comparing the fixed effects
estimation of the coefficient on disclosure in Equation (3) with the OLS estimation of the same coefficient
in Equation (1). While the difference between the two estimates is sizable at about 21%, this number does
not fully convey the magnitude of the bias in Equation (1). Considering our earlier analyses together, the
biases caused by firm heterogeneity and by omitted variables are of opposite sign, partially cancelling each
other out in this specific setting.
Additional Analyses. To show that our results do not depend on the specifics of fixed-effect estimation we
also use OLS to estimate Equation (3) in first differences. The additional data requirement of two
consecutive years of data reduces the number of firm-year observations to 258. The results (reported in
Table 9) show that the coefficient on each of our Disclosure measures is similar in magnitude to the fixed
effects estimates. We also tested whether our results are sensitive to using unadjusted (‘raw’) AIMR
disclosure scores and whether the relation between disclosure and cost-of-debt capital is different for firms
that increase vs. decrease disclosure over time. Our results do not change when using raw disclosure
scores86 and we do not find differences for firms with increasing or decreasing over time disclosure.
85 We also used feasible generalized least squares to estimate the relation between unobservable firm-specific factors and disclosure and our results (not reported, but available on request) were qualitatively similar and did not change our conclusions. 86 Indeed, signs and significance remain similar in all cases except for the regressions of PCTANL.
115
T a
b l
e 9
A
uxili
ary
regr
essio
n pr
opos
ed b
y M
undl
ak (1
978)
1
∑∑
∑∑
++
++
=l
lk
kj
ji
iit
iC
ontr
olO
ffer
Stru
ctur
ee
Perf
orm
anc
Dis
clos
ure
κκ
κκ
κα
Tabl
e pr
ovid
es e
stim
ates
of a
n au
xilia
ry re
gres
sion
intro
duce
d by
Mun
dlak
(197
8) a
nd th
eir s
igni
fican
ce le
vels
bas
ed o
n t-t
est.
An
uppe
r bar
ove
r the
var
iabl
es in
clud
ed in
th
e m
odel
ind
icat
es t
he f
irm-s
peci
fic a
vera
ges
of r
egre
ssor
s. Te
st s
tatis
tics
cons
truct
ed u
sing
hete
rosc
edas
ticity
con
sist
ent
stan
dard
err
ors
from
With
in a
nd B
etw
een
estim
ator
s (de
scrib
ed in
mor
e de
tail
in A
ppen
dix
B) a
nd u
sing
the
fact
that
the
latte
r and
the
form
er a
re in
depe
nden
t und
er th
e nul
l hyp
othe
sis o
f no
mis
spec
ifica
tion.
The
re
sults
sugg
est a
pos
itive
cor
rela
tion
betw
een
the
erro
r ter
m a
nd th
e de
pend
ent v
aria
ble.
See
App
endi
x A
for v
aria
ble
defin
ition
s.
Type
of D
iscl
.
TO
TA
L R
AN
K
RE
LA
TIO
NS
AN
NU
AL
O
TH
ER
Va
riab
le
Sign
C
oeff.
S
t Dev
P-
valu
e C
oeff.
St
Dev
P-
valu
e C
oeff.
St
Dev
P-
valu
e C
oeff.
St
Dev
P-
valu
e D
iscl
osur
e
0.31
9 0.
166
0.05
6 0.
542
0.15
9 0.
001
0.21
2 0.
172
0.21
9 0.
241
0.16
5 0.
146
Perf
orm
ance
GRO
WTH
-1.3
50
0.85
8 0.
117
-1.3
27
0.86
2 0.
125
-1.2
62
0.86
5 0.
146
-1.2
36
0.87
2 0.
157
FRO
S
-4.6
09
4.70
8 0.
328
-4.5
64
4.69
2 0.
332
-4.6
58
4.70
3 0.
323
-4.5
29
4.72
6 0.
339
LOSS
0.15
9 0.
219
0.47
0 0.
224
0.22
4 0.
318
0.13
0 0.
222
0.55
9 0.
165
0.22
6 0.
464
MTB
-0.0
21
0.02
5 0.
398
-0.0
32
0.02
5 0.
201
-0.0
19
0.02
5 0.
453
-0.0
20
0.02
5 0.
434
FRO
SXG
R
-7.2
51
50.5
29
0.88
6 -6
.822
50
.387
0.
892
-6.8
62
50.4
96
0.89
2 -7
.794
50
.670
0.
878
Stru
ctur
e
CA
PEX
P
-1.0
51
2.34
2 0.
654
-1.1
26
2.35
3 0.
633
-0.9
73
2.32
7 0.
676
-1.1
29
2.32
9 0.
628
MO
OD
RNK
-0
.004
0.
003
0.13
4 -0
.005
0.
003
0.07
8 -0
.004
0.
003
0.16
1 -0
.004
0.
003
0.14
8 O
ffer
IS
SUES
0.00
1 0.
013
0.94
8 -0
.007
0.
013
0.58
3 0.
002
0.01
3 0.
900
-0.0
02
0.01
3 0.
871
Con
trol
s
LEV
-0.6
51
0.95
8 0.
497
-0.6
84
0.95
4 0.
474
-0.6
77
0.95
7 0.
480
-0.7
12
0.97
2 0.
464
CO
VER
-0.0
06
0.01
0 0.
556
-0.0
02
0.01
0 0.
810
-0.0
01
0.01
0 0.
945
-0.0
01
0.01
0 0.
930
ROS
7.
144
4.34
8 0.
101
7.10
0 4.
333
0.10
2 7.
078
4.32
8 0.
103
7.11
8 4.
378
0.10
5 LA
SSET
0.00
1 0.
146
0.99
5 0.
024
0.14
7 0.
873
0.04
0 0.
141
0.77
6 0.
040
0.13
9 0.
776
SIZE
0.00
0 0.
000
0.54
0 0.
000
0.00
0 0.
885
0.00
0 0.
000
0.52
5 0.
000
0.00
0 0.
688
RISK
1.47
7 0.
373
0.00
0 1.
545
0.36
9 0.
000
1.50
9 0.
376
0.00
0 1.
491
0.37
3 0.
000
LMA
TUR
-0
.002
0.
003
0.42
8 -0
.001
0.
003
0.77
6 -0
.003
0.
003
0.37
0 -0
.001
0.
003
0.67
0 C
ALL
0.53
1 0.
156
0.00
1 0.
475
0.15
7 0.
003
0.54
4 0.
158
0.00
1 0.
512
0.15
6 0.
001
CO
NV
ER
0.
263
0.62
6 0.
674
0.36
0 0.
625
0.56
5 0.
288
0.62
5 0.
646
0.29
3 0.
632
0.64
3 SU
BOR
-0
.534
0.
501
0.28
8 -0
.544
0.
503
0.28
1 -0
.555
0.
508
0.27
5 -0
.489
0.
512
0.34
1 TB
ILL
-0
.065
0.
036
0.06
7 -0
.082
0.
036
0.02
4 -0
.066
0.
034
0.05
8 -0
.072
0.
035
0.04
2 RI
SKPR
-0.1
60
0.66
7 0.
810
-0.1
88
0.66
6 0.
778
-0.1
31
0.66
8 0.
844
-0.2
15
0.67
3 0.
749
116
T a
b l
e 10
R
elat
ions
hip
betw
een
diffe
rent
type
s of d
iscl
osur
e qu
ality
and
cos
t of d
ebt:
Mod
el in
Diff
eren
ces
itl
lk
kj
ji
iit
itC
ontr
olO
ffer
Stru
ctur
ee
Perf
orm
anc
Dis
clos
ure
Inte
rcep
tYI
ELD
εβ
ββ
ββ
+∆
+∆
+∆
+∆
+∆
+=
∆∑
∑∑
∑+
11
Type
of D
iscl
.
TO
TA
L R
AN
K
RE
LA
TIO
NS
AN
NU
AL
O
TH
ER
Va
riab
le
Sign
C
oeff.
S
t Dev
P-
valu
e C
oeff.
St
Dev
P-
valu
e C
oeff.
St
Dev
P-
valu
e C
oeff.
St
Dev
P-
valu
e ∆D
iscl
osur
e -
-0.4
18
0.14
4 [.0
04]
-0.3
79
0.12
8 [.0
04]
-0.3
93
0.13
0 [.0
03]
-0.1
68
0.14
0 [.2
33]
∆Per
form
ance
∆GRO
WTH
-
-0.2
81
0.43
6 [.5
20]
-0.3
49
0.43
6 [.4
25]
-0.2
78
0.44
3 [.5
30]
-0.3
79
0.44
6 [.3
96]
∆FRO
S -
0.17
2 1.
346
[.899
] 0.
592
1.31
5 [.6
53]
0.26
5 1.
349
[.845
] 0.
341
1.35
1 [.8
01]
∆LO
SS
+ 0.
288
0.12
6 [.0
23]
0.23
9 0.
130
[.068
] 0.
290
0.12
4 [.0
20]
0.27
8 0.
138
[.044
] ∆M
TB
- -0
.032
0.
025
[.210
] -0
.025
0.
025
[.324
] -0
.033
0.
026
[.196
] -0
.033
0.
025
[.189
] ∆F
ROSX
GR
+/-
11.4
85
5.86
2 [.0
51]
11.7
15
5.70
9 [.0
41]
11.5
95
5.74
1 [.0
45]
13.2
67
5.87
9 [.0
25]
∆Str
uctu
re
∆C
APE
XP
- 1.
580
1.23
5 [.2
02]
1.33
0 1.
266
[.294
] 1.
673
1.24
4 [.1
80]
1.55
8 1.
272
[.222
] ∆M
OO
DRN
K-
0.00
1 0.
003
[.645
] 0.
002
0.00
3 [.5
74]
0.00
1 0.
003
[.717
] 0.
001
0.00
3 [.8
71]
∆Offe
r
∆ISS
UES
-
0.00
7 0.
015
[.629
] 0.
005
0.01
5 [.7
26]
0.00
8 0.
015
[.596
] 0.
008
0.01
5 [.5
83]
∆Con
trol
s
∆LEV
+
1.04
8 0.
751
[.164
] 1.
154
0.76
0 [.1
31]
1.07
4 0.
757
[.157
] 1.
110
0.76
6 [.1
49]
∆CO
VER
-
-0.0
03
0.00
9 [.7
71]
-0.0
03
0.01
0 [.7
42]
-0.0
06
0.00
9 [.5
04]
-0.0
05
0.01
0 [.5
94]
∆RO
S -
-3.7
02
1.04
7 [.0
00]
-3.9
00
1.03
2 [.0
00]
-3.5
76
1.03
8 [.0
01]
-3.7
49
1.03
8 [.0
00]
∆LA
SSET
-
0.28
4 0.
199
[.155
] 0.
295
0.20
2 [.1
47]
0.26
0 0.
206
[.207
] 0.
260
0.20
1 [.1
98]
∆SIZ
E +
0.00
1 0.
000
[.088
] 0.
001
0.00
0 [.0
59]
0.00
1 0.
000
[.077
] 0.
001
0.00
0 [.0
83]
∆RIS
K
+ -0
.311
0.
285
[.275
] -0
.336
0.
280
[.231
] -0
.333
0.
280
[.236
] -0
.329
0.
288
[.255
] ∆L
MA
TUR
+ 0.
003
0.00
3 [.4
33]
0.00
2 0.
003
[.601
] 0.
003
0.00
3 [.4
10]
0.00
2 0.
003
[.610
] ∆C
ALL
+
0.13
6 0.
093
[.142
] 0.
172
0.09
3 [.0
65]
0.14
5 0.
092
[.117
] 0.
158
0.09
2 [.0
87]
∆CO
NV
ER
- -2
.897
0.
361
[.000
] -2
.927
0.
358
[.000
] -2
.910
0.
358
[.000
] -2
.906
0.
365
[.000
] ∆S
UBO
R +
0.29
5 0.
316
[.351
] 0.
280
0.31
0 [.3
68]
0.31
9 0.
324
[.325
] 0.
266
0.32
7 [.4
18]
∆TBI
LL
+
1.07
7 0.
033
[.000
] 1.
082
0.03
3 [.0
00]
1.06
4 0.
031
[.000
] 1.
075
0.03
3 [.0
00]
117
T
able
10.
Con
tinue
d
a. T
he E
quat
ion
(3) m
odel
is e
stim
ated
in d
iffer
ence
s. D
iffer
enci
ng is
alte
rnat
ive
met
hod
to re
mov
e un
obse
rved
het
erog
enei
ty b
ias
sinc
e th
e fir
m s
peci
fic e
ffect
s dr
op o
ut f
rom
the
mod
el. T
he r
esul
ts a
re s
imila
r to
Fix
ed E
ffect
s tre
atm
ent.
Col
umn
A r
epor
ts th
e fin
ding
s fo
r th
e m
easu
re o
f to
tal
disc
losu
re q
ualit
y (P
CTR
NK
). C
olum
ns B
-D r
epor
t on
mea
sure
s of
qua
lity
of i
nves
tor
rela
tions
(PC
TREL
), an
nual
rep
orts
(PC
TAN
L),
and
quar
terly
and
oth
er p
ublic
atio
ns (
PCTO
PB).
All
four
m
easu
res
of d
iscl
osur
e ar
e co
nstru
cted
usin
g A
IMR-
FAF
disc
losu
re s
core
s fo
r the
per
iod
1986
-199
6. T
he d
iscl
osur
e sc
ores
are
con
verte
d to
with
in in
dustr
y pe
rcen
tage
ra
nkin
gs in
ord
er to
ach
ieve
bet
ter c
ompa
rabi
lity
acro
ss in
dust
ries
and
over
tim
e: fo
r eac
h ye
ar a
nd e
ach
indu
stry
the
firm
s ar
e ra
nked
bas
ed u
pon
disc
losu
re s
core
, the
n th
e ra
nkin
gs a
re d
ivid
ed b
y th
e nu
mbe
r of f
irms b
eing
rank
ed.
b. In
add
ition
to c
ontro
l var
iabl
es in
Sen
gupt
a’s
mod
el (C
ontr
ol),
the
mod
el h
ere
incl
udes
thre
e ad
ditio
nal g
roup
ings
of c
ontro
l var
iabl
es: P
erfo
rman
ce, S
truct
ure
and
Offe
r. Pe
rfor
man
ce c
aptu
res
the
futu
re p
rosp
ects
of t
he c
ompa
ny. S
truct
ure
capt
ures
info
rmat
ion
asym
met
ries
betw
een
inve
stor
s an
d th
e fir
m a
nd th
e ec
onom
ies
of
scop
e in
pro
duci
ng in
form
atio
n. O
ffer m
easu
res t
he e
xten
t of c
apita
l mar
ket t
rans
actio
ns. A
ll th
ree
grou
ps a
re re
late
d in
theo
ry to
the
leve
l of d
iscl
osur
e ba
nd to
YIE
LD.
Sam
ple
incl
udes
100
com
pani
es, w
hich
am
ount
to 2
58 fi
rm-y
ear o
bser
vatio
ns. I
n or
der t
o av
oid
doub
le c
ount
ing
we
use
only
firs
t deb
t iss
ue in
a g
iven
yea
r to
mea
sure
Y
IELD
. St
anda
rd e
rror
s are
Whi
te h
eter
osce
dast
icity
con
siste
nt. S
ee A
ppen
dix
A fo
r var
iabl
e de
finiti
ons.
∆RIS
KPR
+
0.91
7 0.
281
[.001
] 0.
932
0.28
0 [.0
01]
0.90
5 0.
283
[.002
] 0.
995
0.28
9 [.0
01]
C
-0
.030
0.
042
[.468
] -0
.042
0.
042
[.317
] -0
.036
0.
043
[.399
] -0
.038
0.
043
[.380
] A
dj-R
2
0.87
2
0.
871
0.87
2
0.
868
NO
B:
25
8
25
8
25
8
25
8
118
T a b l e 6 Substantive Changes in Total Disclosure
itillkkjjiiitit ControlOfferStructureePerformancDisclosureInterceptYIELD εαβββββ +++++++= ∑∑∑∑+ 11
Table reports the results of OLS and fixed effects estimation of equation (3), but restricts the sample to observations with substantive changes in disclosure. Substantive changes are defined as cases when a firm moves between two consecutive observations from disclosure quality decile k to decile k±i , where i is greater or equal to two. Sample consists of 68 firms with 182 observations. Deciles are formed on the entire set of companies ranked by AIMR in a given year.
Estimator: Sign OLS (αi=0) WITHIN (FIXED EFFECTS)
Variable Coeff. St.Dev P-value Coeff. St.Dev P-value PCTRNK - -0.188 0.181 [.300] -0.324 0.149 [.032] Performance
GROWTH - -0.997 0.439 [.025] -0.732 0.552 [.188] FROS - -1.607 1.323 [.226] -1.520 1.747 [.387] LOSS + 0.531 0.286 [.065] 0.177 0.204 [.389] MTB - -0.041 0.024 [.093] -0.048 0.030 [.115] FROSXGR +/- -1.281 4.470 [.775] -1.869 8.806 [.832]
Structure CAPEXP - -0.175 1.130 [.877] -1.156 1.627 [.479] MOODRNK - -0.656 0.001 [.000] -0.973 0.003 [.781] Offer ISSUES - 0.041 0.032 [.198] 0.040 0.039 [.308]
Controls LEV + 1.342 0.432 [.002] 1.537 1.162 [.189] COVER - -0.242 0.010 [.804] -0.497 0.020 [.807] ROS - 1.275 1.314 [.333] -3.786 1.804 [.039] LASSET - -0.212 0.070 [.003] -0.218 0.197 [.273] SIZE + 0.001 0.000 [.141] 0.001 0.000 [.051] RISK + 0.395 0.282 [.164] -0.218 0.199 [.277] LMATUR + -0.176 0.004 [.648] 0.001 0.004 [.778] CALL + 0.509 0.177 [.005] 0.137 0.138 [.322] CONVER - -2.806 0.434 [.000] -2.776 0.233 [.000] SUBOR + -0.756 0.407 [.065] -0.434 0.481 [.369] TBILL + 1.046 0.039 [.000] 1.057 0.040 [.000] RISKPR + 0.787 0.379 [.039] 1.198 0.368 [.002] C 3.024 1.007 [.003] Adj-R2 0.857 0.942
119
Finally, we reported transition probabilities in Table 4 and argued that the amount of within-firm
variation is sufficient to warrant fixed-effects analysis. At the same time, however, since many firms appear
to be changing from one disclosure quality decile to another, these changes may not reflect the necessary
substantial changes in disclosure policy. Theory (e.g., Verrecchia, 2001) emphasizes that cost-of-capital
effects are mainly expected when a firm commits to a higher standard of disclosure (as opposed to a
transitory change in disclosure quality in any given year). Any ex-ante commitment to a specific disclosure
quality will translate into a systematic component of disclosure quality and this component will be
eliminated in the fixed effects estimation.87 If we were to take theory literally, we should not find a cost-of-
debt capital effect after removing the systematic component of disclosure via fixed effects estimation. Our
main findings, however, indicate that the changes in our Disclosure metric are such that they have a cost-
of-debt capital effect. Our metric apparently captures substantial disclosure policy changes. On the other
hand, since so many firms change disclosure policy (in Table 4), one might ask if this interpretation is
reasonable. Sceptics may argue that if disclosure policy changes happen this often, ex-ante commitment is a
rather hollow concept.88 We therefore consider next disclosure quality changes that are more exceptional
(than movements to adjacent deciles) and which are more likely to capture disclosure policy changes. We
conduct the following analyses to provide some evidence on this issue. We create disclosure quality deciles
based on the sample of all AIMR firms (as in Table 4, Panel A). We then retain only those pairs of
observations in the sample for which it is more likely that they reflect a change in the firm’s commitment to
a disclosure policy. Specifically, we retain two consecutive observations if a firm is grouped in decile k
first and subsequently is grouped in decile k ± i where i ≥ 2. Thus, the new sample contains only those
observations where the firm ‘jumps’ over adjacent disclosure quality deciles. This restriction results is a
final sample of 68 firms with 182 observations. We then run our main analysis again on this sample of
firms with disclosure policy changes. Table 11 holds the details. As expected, we continue to find that
disclosure policy affects the cost-of-debt capital. As before, OLS estimation of the augmented model
produces an insignificant coefficient on Disclosure, but after adjusting for firm heterogeneity this
coefficient is about twice larger than in the OLS regressions and strongly significant. We conclude from
this that our original findings are similar to the findings for a sample of firms for which we can be more
certain that they changed their disclosure policy. Interpreting the original findings as evidence for what
87 Indeed, this is precisely why we use fixed effects estimation. The decision to commit to a disclosure policy is likely to be part of a portfolio of simultaneous firm choices on strategy, business profile, risk and environmental segments, compensation, and customer/supplier relates policies (Core, 2001). As such, the systematic component is likely to be endogenous and should be eliminated from the analysis. 88 One alternative explanation for our findings could be that our Disclosure measure captures mostly random noise or performance-related variation in disclosure quality (either because good performance leads to better disclosure or because its leads to better perceived disclosure). Noise will attenuate the regression coefficient, but the performance part can induce a negative relation between disclosure and cost-of-debt capital. While the performance control variables should control for this, the net effect could still be a negative observed relation between disclosure and cost of capital.
120
happens if a firm changes its commitment to a certain disclosure policy would, consequently, not seem
unreasonable.
4.7. Discussion and conclusion
Theory prescribes the following steps to address endogeneity. First, researchers should develop a
theoretical model for the choice being examined. Next, researchers should determine which variables are
considered exogenous in the setting under study and a reduced form model should be derived. Given that
the model is identified, the reduced form can be estimated and the structural parameters can be recovered.
This prescription appears to be ignored in many empirical studies. In particular, the requirement to
formulate explicitly the underlying model for the choice being examined is, in our observation, seldom met
in practice. Such model does not have to be formal, but should be based on a rigorous survey of what is
known about the choice under investigation. Only once the underlying model is made explicit can the
econometric properties of the estimated results be understood.
We argue that our understanding of the relation between cost-of-capital and disclosure is precarious
because of the existence of an endogeneity bias in extant work. We investigate two important sources of
endogeneity bias, (1) unobservable firm heterogeneity and (2) observable omitted variables. Theory
suggests that firm heterogeneity may arise due to differences in costs of disclosure between firms or
because management reputation varies among firms. Cost of disclosure as well as management reputation
impacts on both cost-of-debt capital and disclosure. Neither is directly observable to the researcher and
when omitted from the empirical analysis causes endogeneity bias. Earlier empirical and theoretical work
has suggested that variables reflecting firm performance, structure and offerings are related to disclosure
policy. These variables also affect cost-of-debt capital. Similar as before, when omitting these variables
from the analysis an endogeneity bias is likely to arise.
We investigated how each of these two endogeneity biases affect the estimation of the relation
between cost-of-debt capital and disclosure and documented substantial effects for both, albeit that firm
heterogeneity appears to be the more important one. It also appears that in the current setting the two
sources of bias are of opposite sign, which makes the net effect underestimate the true magnitude of the
bias. We further investigate firm heterogeneity and show that disclosure is positively and significantly
associated with unobservable firm-specific factors that cause heterogeneity. This reinforces our claim that
the association between disclosure and cost-of-debt capital is partially driven by the disclosure variable
reflecting omitted firm-specific factors.
We attempt to mitigate endogeneity bias by relying on theory to identify additional variables
correlated with both disclosure and cost-of-debt capital and by applying fixed effects estimation. Fixed
effects estimation is only expected to be helpful if the relation of interest between two variables is driven by
changes over time within the firm. The relation under investigation should not be a cross-sectional
phenomenon, since between variation is eliminated in the fixed effects approach. Empirically, we show that
121
in our setting over-time changes in firm disclosure are substantial, which speaks to the fact that the relation
between disclosure and cost-of-debt capital is surely not just a cross-sectional attribute. This finding is
substantiated by the results of the fixed effects estimation, which demonstrate that after removal of the
cross-sectional variation, a strong association exists between disclosure and cost-of debt capital. Implicitly,
fixed effects estimation assumes that the changes in our disclosure measure are an indication of substantive
changes in disclosure policy. Some theoretical studies suggest that cost-of-capital effects are expected to be
most strongly when a firm commits to a certain level of disclosure ex ante. Since such commitment would
lead to a relatively constant level of disclosure over time for any one firm, its effect would be subsumed by
the variable iα and drop out in the fixed effects estimation. In contrast, we established a strong relation
between cost-of-debt capital and disclosure in the fixed effects estimation which is consistent with (1)
changes in our disclosure measure being indicative of substantive changes in (ex ante commitment to)
disclosure policy – and therefore not subsumed in iα , or (2) changes in disclosure matter even after
controlling for a firm’s overall ex ante commitment to a specific level of disclosure. The latter explanation
assumes that ex ante commitment to disclosure is not the only way to obtain cost-of-capital effects (see for
a similar opinion: Dye, 2001). Earlier empirical work seems to concur. Healy et al. (1999) and Lundholm
and Myers (2002), for example, show that changes in disclosures impact on stock return and stock liquidity.
While we readily concede that the burden of proof is on the researcher to make sure that fixed effect
estimation is appropriate in a specific setting to address endogeneity, we also believe that in our setting it
clearly is a helpful method to mitigate at least some of endogeneity’s confounding effects.
Based on our findings, we recommend that researchers collect multiple observations for each firm
in their sample and use either a first-differences specification and OLS or fixed effects estimation to address
the endogeneity bias in the relation between cost-of-debt capital and disclosure. Without explicitly
accounting for endogeneity in this relation, any causal inference is likely to be fraught with problems.
Some may argue that using fixed effects estimation to address endogeneity in this or other settings
is too simple a solution for a complex problem. Perhaps this is true, but at a minimum researchers should be
warned that some concern is warranted if they find that OLS results change dramatically after the inclusion
of fixed-effects. If nothing else, fixed effects may function as a crude diagnostic that the findings need
additional scrutiny.
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4.A. Variable definitions.
YIELD = The effective yield to maturity at the moment of bond issue.
PCTRNK = The percentage rank of overall corporate disclosure policy.
PCTREL = The percentage rank of investor relations disclosure policy.
PCTANL = The percentage rank of disclosure through the firm’s annual report.
PCTOPB = The percentage rank of quarterly and other publications disclosures.
GROWTH = Average future growth in sales (item #12) between t+1 and t+3.
FROS = Average future return-on-sales (see, below) between t+1 and t+3.
LOSS = Dummy variable that is unity for firms with negative current net income (item #18), and
zero otherwise.
MTB = Market-to-book ratio at the end of the year, defined as market value of equity (item
#24×item #25) divided by the book value of equity (item #60).
FROS×GROWTH = Interaction term between future return-on-sales and future growth rate.
CAPEXP = Capital expenditures in the current year (item #128) scaled by total assets (item #6).
MOODRNK = Moody’s bond rating converted into the linear scale.
ISSUES = Number of bond issues by firm i in the current year.
LEV = Leverage, defined as long-term debt (Compustat item #9) divided by total assets
(Compustat item#6).
COVER = Coverage of interest expenses, a measure of the firm’s ability to meet its debt service
requirements, computed as income before extraordinary items and interest expense
(item#18+item #15) divided by interest expense (item #15).
ROS = Return-on-Sales, as a measure of the firm’s operating performance, computed as earnings
before interest, taxes, depreciation and amortization (item #13) divided by sales (item #12).
ASSET = Total assets (item #6).
127
LASSET = Log of total assets, to proxy for the size of the firm. Computed as the logarithm of total
assets (item #6).
RISK = Volatility of the firm’s performance, defined as the firm’s highest stock price in year t
(item #23) minus the firm’s lowest stock price in year t (item #22) divided by the end-of-
year stock price (item #24).
SIZE = Size of the bond issue in millions of dollars. This is the amount of capital received by the
borrower.
TTM = Time to maturity.
CALL = The callability of the security, ranging between zero and unity. It the bond is callable
form the moment of issue CALL equals unity. CALL is zero for non-callable securities.
CALL is computed as the bond’s maturity minus the time from the moment that the bond
first becomes callable divided by the bond’s time to maturity.
CONVER = Bond convertibility. Dummy variable that takes the value of unity if the bond is
convertible and zero otherwise.
SUBOR = Bond subordination. Dummy variable that takes the value of unity for subordinate debt
and zero otherwise.
TBILL = Interest on constant maturity US treasury bonds. These bonds are matched with treasury
bills by maturity. A time weighted average is computed if the maturity of the bond does not
match with that of the treasury bill.
RISKPR = Measure of the time-series variation in risk premium over that contained in TBILL.
Defined as the difference between the yield on a Moody’s Aaa bond and a treasury bill
with 30 years maturity.
4.B. Mundlak’s (1978) approach
In the random effects framework, a fundamental assumption is that the firm-specific effects are
treated as strictly exogenous to present, future and past values of explanatory variables (Hsiao, 2003).
Mundlak (1978) criticized the random effects specification precisely because there is usually very little
reason to assume that firm-specific effects αi are uncorrelated with the regressors explicitly controlled for.
If one neglects such correlation the inferences are incorrect. Mundlak (1978) relaxes the assumption of
strict exogeneity by allowing the individual effects to depend linearly on the average values of individual-
specific means of the explanatory variables. Specifically:
][...11 Mxxy itikitkitit εαβββ +++++=
][... ..11 regressionAuxiliaryxx ikikii ωκκα +++=
where ..1 ,..., kii xx are average values of regressors for each individual i.
128
The coefficients kκκ ,...,1 capture the extent of the correlation between the explanatory variable and
the error term iα . Mundlak demonstrated that the GLS vector of coefficients ],...,[ 1 kκκ is equal to the
following difference: withinbetween ββ ˆˆ − , where betweenβ is a vector of slope coefficients from the regression
where individual specific means in the dependent variable .iy are regressed on the individual specific
means in the independent variables ..1 ,..., kii xx ; and withinβ is the Fixed Effects estimator. Moreover,
Mundlak (1978) showed that GLS vector of coefficients in model M given the auxiliary regression equals
the Fixed Effects estimator. On these grounds he claimed that there is only one correct estimator, which is
the F.E. estimator.
Under the null hypothesis of no endogeneity betweenβ and withinβ , are independent and it is easy to
construct test statistics in order to test the significance of kκκ ,...,1 coefficients. We use a simple t-test:
( ) ( )withink
betweenk
withink
betweenk
VarVarTstat
ββββ
ˆˆ
ˆˆ
+
−= .
129
Chapter 5
Implied Cost of Capital When Future Expected Returns Are Stochastic
5.1. Introduction
Uncertainty about the future expected (equilibrium) rates of return used to discount future cash flows
affects the value of equity. Traditional valuation models used to calculate the implied cost of capital (such
as the dividend discount model, the discounted cash-flows model or the residual income model) do not take
this into account. Instead these models assume constant discount rates. This study provides both evidence
that such an assumption may lead to a substantial downward bias in the implied cost of capital estimates,
and a way to adjust for this bias. The bias is especially pronounced for companies in uncertain
environments.
Standard expressions of the present value of expected future cash flows presuppose non-stochastic
discount rates (Fama, 1977). Such assumption is unlikely to hold in practice however, as the risk profiles of
many companies are changing. The literature has recognized that equilibrium rates of return are uncertain
(e.g., Samuelson, 1961, Campbell and Shiller, 1989, Campbell, 1991, Fama and French, 2002, Feltham and
Ohlson, 1999, Vuolteenaho, 2002). Campbell (1991) finds that 91.6% of aggregate returns variance is due
to changes in expectations about future returns. Evidence in Vuolteenaho (2002) suggests that changes in
expected cashflows diversify at the aggregate level but, at the same time, the variance in expected returns
remains large.
The time-variation in the expected rates of return which arises from macroeconomic shocks, causes
changes in risk-free rates and aggregate equity premia, i.e., the price of risk (e.g., Blanchard, 1993,
Jagannathan, McGratten, and Scherbina, 2001). Besides macroeconomic causes of uncertainty in expected
returns, firms' individual risk factors and price of risk vary over time. This, for example, happens naturally
over a firm's life cycle when a company exercises its growth options (and it becomes clearer how the future
of the firm will evolve), enters new industries, undertakes new investments, experiences shocks to their
productivity, or develops new growth options.
While modern finance theory may easily accommodate the assumption of stochastic discount rates,
the present value models do not represent a convenient and substantially general tool from a theoretical
130
perspective. As a result, little progress has been made to generalize the standard (present value) valuation
models with respect to the uncertainty about future discount rates (one exception is Ang and Liu 2004).89
A vast body of recent empirical literature relies on the estimates of firm-specific implied cost of
capital (Botosan, 1997, Botosan and Plumlee, 2002, 2005, Brav, Lehavy, and Michaely, 2004, Chen,
Jorgensen and Yoo, 2004, Easton and Monahan, 2005, Francis, LaFond, Olsson, and Schipper, 2004, Gode
and Mohanram, 2002, Guay, Kothari and Shu, 2004, Hail, 2003, Hail and Leuz, 2004a, 2004b, Lee, Ng and
Swaminathan, 2004 among others). The benefit of doing so is that the implied cost of capital is based on
forward looking information and is believed to exhibit less noise than the estimates derived from realized
returns (e.g., risk factor models) or cash flows.90
Studies have documented that the equity premia implied by residual income models are significantly
lower than those historically realized. Specifically, Claus and Thomas (1998), and Gebhardt, Lee and
Swaminathan (2000) (hence on CT and GLS) report average implied equity premia of 3.40 and 2.50%,
respectively, while the corresponding historical risk premium equals, in the CT sample, 7.16%.
In an efficient market, where risks are appropriately priced, the historical average risk premium
should yield an unbiased estimate of the equity premium (Claus and Thomas, 2001). Thus, the evidence of
a gap between the realized average risk premium and the average implied cost of capital is puzzling and the
question of why it exists remains unsettled. Practitioners, such as Ibbotson Associates, suggests that the
equity risk premium lies in the region of 7 to 9%, which differs substantially from the documented implied
equity premia.
I use three standard valuation models (described in GLS, CT and Easton (2004)) to estimate the
implied cost of capital. I replicate the findings reported in earlier work before augmenting each of these
three models with an uncertainty-adjustment factor, which accounts for the stochastic nature of the future
expected returns. The uncertainty in future expected returns is expected to vary across industries and with
size and book-to-market proxies. Therefore, I measure the uncertainty in expected returns across 48 Fama-
French industries, as well as across 25 portfolios based on size and book-to-market quintiles. To determine
the variance of the future expected returns, I build up the work of Campbell (1990) and Vuolteenaho
(2002).91 I find substantial differences in the variance of expected returns (across industry, size and book-
to-market portfolios): high-tech industries and smaller firms with lower book-to-market face higher
uncertainty about expected returns.
89They develop a practitioner-oriented model to value future cash flows when expected returns are stochastic. The model provides a rich framework to capture uncertainty in expected returns and incorporates the effect of changing market risk premiums, risk-free rates and conditional betas in a context of conditional CAPM. The model however is not practical to determine the implied cost of capital as it yields a series of different discount rates which are applied to future cash flows, i.e., the term structure of future discount rates. 90For example, Fama and French (1997) demonstrate that expected return estimates are notoriously noisy even at the industry level. 91I do not perform a variance decomposition as it captures the capitalized effect of shocks to the interest rate. Instead, I estimate the variance of the year to year innovations in expected returns.
131
The results suggest that all three standard valuation models examined here suffer from a bias in the
implied cost of capital of about 3.5% at the aggregate level. The implied risk premia range between
5.961% ( 6.301% ) and 8.91% ( 9.27% ) when the uncertainty in the expected returns is modeled by
industry (by size and book-to-market ratio). Once adjusted for this bias, the implied cost of capital is close
to historically realized returns and to practitioners' assessments.
The contribution of this study is threefold. First, it demonstrates that uncertainty in the future
expected rates of return, used to discount future expected cash flows, needs to be taken into account when
inverting a present value model (e.g., DDM, DCF, or RIM) to estimate the implied cost of capital. Ignoring
this uncertainty in valuation, results in a significant downward bias in the implied cost of capital. The
degree of the bias correlates with firm specific characteristics (e.g., industry, size and book-to-market) and
failure to adjust for the bias can easily lead to a correlated omitted variable problem and thus to spurious
relations between conventional implied cost of capital metrics and their economic determinants. This may
lead to incorrect inferences and is particularly important in the light of findings in Easton and Monahan
(2004) that implied cost of capital estimates are highly unreliable.
The findings can explain several counterintuitive results in prior research. Specifically, GLS find that
the implied cost of capital is (i) positively associated with book-to-market ratio and (ii) negatively
associated with the dispersion in analysts' forecasts. A priori one may expect the opposite. Note, however,
that book-to-market (high forecast dispersion) is negatively (positively) associated with the uncertainty
about future expected rates of return, which in turn implies that book-to-market (dispersion) is negatively
(positively) related with the downward bias in the implied cost of capital. Thus, low book-to-market ratio
(high dispersion) generally means lower cost of capital when the bias is not taken into account.
Second, I offer an easy to implement way to incorporate uncertainty about future expected returns
into standard valuation models. The proposed model differs in that it pre-multiplies the present value of
future expected dividends (cash flows) by a factor increasing in the variance of expected returns. The model
is of interest because, in addition to abundant empirical evidence that expected returns change over time,
the study by Lee, Myers, and Swaminathan (1999) shows that the inclusion of time-varying discount rates
is essential to the success of the intrinsic value estimates in the sense of their ability to detect deviations
from fundamental value.92
Third, I offer an explanation for why a number of recent studies that evaluate the performance of
commonly used valuation models have documented that the predicted firm value is biased downwards (e.g.,
Frankel and Lee, 1998, Dechow, Hutton and Sloan, 1999, Lee, Myers and Swaminathan, 1999, Myers,
1999, Francis, Olsson and Oswald, 2000, Choi, O'Hanlon and Pope, 2006). The downward bias is
particularly pronounced for companies that went public (Chemmanur and Loutskina, 2005). This evidence
may be explained by incorporating the uncertainty with respect to future expected returns into the valuation
model, because this type of uncertainty implies that firm value consists of the present value of future 92The analysis in the study shows that intrinsic value estimates that do not include time-varying interest rates (i) have little power in predicting returns and (ii) exhibit the ability to track the fundamental value better.
132
expected cash flows plus an additional term, which will generally be positive. This is consistent with the
analysis in Ang and Liu (2004) who show that ignoring the stochastic nature of expected returns may result
in up to 50% undervaluation.
The remainder of the paper is organized as follows. Section 2 provides examples that further motivate
the analysis and develops a model that incorporates the uncertainty in expected returns. Section 3
implements the model by relying on a variance decomposition approach. Section 4 describes the data used
to conduct the empirical analysis. Section 5 lays out the empirical findings. Section 6 discusses future work
related to generalizing the model, and the final section concludes the paper.
5.2. Valuation with Stochastic Expected Returns
This section begins by providing intuitive examples of how uncertainty in expected returns may
affect prices. Subsequently it provides a general valuation model that incorporates the uncertainty in the
expected returns and discusses its implications for computing the cost of capital.
5.2.1.Why Does Uncertainty Matter?
Uncertainty about future expected rates of return ( r ) can be valued because gains from
unanticipated decreases in discount rate, on average, outweigh losses due to unanticipated increases in r .
Therefore, uncertainty about future discount rates must be reflected by the stock price.
Consider the following example. A firm generates constant perpetual dividends d and thus,
conditional on r , has value of rd/ . Further, assume that due to some unforseen economic shock, r may
go either up or down by α , with equal probabilities. The loss (gain) when r increases (decreases) by α is
)(=
αα
α +−−
+ rrd
rd
rd
−
−− )(
=α
αα rr
drd
rd
. In percentage terms this means that firm value
decreases (increases) by %)( α
α+r
−
%)( α
αr
. Clearly, the gains of changes in return outweigh the
losses and the differences can be substantial. For instance, for 20%=r and 10%=α , firm value will
decrease by 33.3% when the discount factor r goes up, while it will increase by 100% when r goes down.
In this simplified example investors benefit, on average, when r is random and prices will reflect the
uncertainty in r .
I show, next, that the implied cost of capital, as it is conventionally computed, cannot be compared
directly to the expected rate of return that we observe over a long time span. Consider another example and
for simplicity assume that a firm has constant expected perpetual dividends D independent of discounting.
Also assume that investor does not know r but rather has a prior belief about its distribution. In this case
firm's value will be given by:
)~(
>~=)~(1
=1=
0 rED
rDE
rD
EPconvexityceindependen
tt
t
+∑∞
(1)
133
The last inequality follows from the convexity of the function under the expectation operator. In
order for the price to be equal to the last term in (1), it is necessary to subtract a positive number from the
denominator. That is:
arE
DEP−)~()(=0 (2)
where arEi −≡ )~( is the definition of the internal rate of return or the implied cost of capital. It
follows that )~(< rEi . Note that the parameter a will be proportional to the variance of the required rate of
return. This, in turn, implies that the degree of bias in the implied cost of capital will vary across firms and
across industries as the uncertainty in expected returns will differ among them as well.
5.2.2. Pricing Equation A fundamental asset pricing equation is written as
))((= 111 +++ + ttttt DPmEP (3)
where tP is stock price at time t , 1+tD is the amount of dividends at 1+t , and 1+tm is a pricing
kernel. The pricing kernel is a market wide random variable that reflects future state prices and from an
empirical perspective represents a set of risk factors.93 It follows from equation (3) that expected return on a
security is given by the following equation:
)),((1)(=)( 111
11 ++−
++ − ttttttt RmCovmERE (4)
Since a state independent payoff of unity in 1+t should be priced at one over the risk free rate at
time t (4) can be written as
ttf
ttt rRRE +≡++ 1)(1=)( 1 λ (5)
where ),(= 11 ++− tttt RmCovλ and reflects the price(s) of risk and conditional beta(s) of a security.
To incorporate uncertainty about the future expected rates of return into a stock valuation model
consider the following definition of expected return:
++ ++
t
tttt P
DPEr 11=1 (6)
Restating (6) in terms of tP and iterating it forward once gives
++
++
+ +
+++
+
1
221
1
111
1=
t
ttt
tt
ttt r
DPE
rrD
EP (7)
++
++
+ +
+++
))(1(11=
1
221
tt
tt
t
tt rr
DPr
DE (8)
93In conditional CAPM, for example, m
tttt Rbam 11 = ++ + , where mtR 1+ is the return on the market portfolio.
134
with the last equality following from the law of iterated expectations. Repeating the iterations and
assuming the transversality condition to hold the price of a security can be written as
)()(1
= 1
=
1=tts
t
s
tstt VE
r
DEP ≡
+∏∑ −
∞
+τ
τ
(9)
Since the future risk-free rates, prices of risk, and the firms' conditional betas are stochastic, equation
(5) implies that rates sr are random for ts > and thus we cannot assume them constant and therefore we
cannot take them out of the expectation in (9). To see the implications for this with respect to valuation
denote 11= −+ ss rR , fix 0=t , and conduct a second order Taylor series expansion around the
unconditional mean ρ≡)( sRE (by differentiating with respect to the whole vector
,...),,,(=' 4321 RRRRR ). This yields:94
00
1=
02
00
1=
02
0
1=00
)(
|'
'21)(
=
|'
'21|
'
QDE
GRR
VGE
DE
GRR
VGG
RVD
EP
tt
t
tt
t
tt
t
+≡
∂∂∂
+
∂∂∂
+
∂∂
+≈
∑
∑
∑
∞
∞
∞
ρ
ρ
ρ
ρ
ρρ
(10)
where RERG (= 0− ).
It follows that the firm value at time t may be written as:
ttt
tt QDEP +≈ −
∞
+∑ τ
τ
τ ρ1= (11)
Thus the price equals to the usual present value of future dividends discounted using unconditional
expected return (i.e., long run expected return) plus an additional term tQ , which is generally positive. Note
that when the variance in the future expected returns is zero, the equation (11) reduces to the traditional
valuation formula. The last term Q in (10) and (11) involves a large number of covariances and to obtain a
closed form solution requires an assumption about expected return generating process. This is developed in
Section 3.
As traditional valuation models ignore the term tQ in (11), this potentially explains that they value
estimates that are too low (see references in the Introduction). For the same reason, the difference between
94The second order term in the approximation will have a first order effect on our results since the variance of r is non-zero. The higher order terms in the Taylor series will be of second order importance and should not materially affect the results.
135
implied cost of capital (as documented in GLS, CT and others) and historically realized returns can emerge.
Intuitively, suppose we observe two firms with future expected dividends (or book-value and future
expected earnings) and expected rates of returns. Also assume that the first firm exhibits uncertainty about
future expected returns, while the second does not. The price of the first firm must be larger due to a
positive term tQ in (11). Therefore, DMD, DCF or RIM models will result in a lower implied rate of return
for the first company, since tQ is positive and thus we need to increase the implied cost of capital in order
to satisfy (11). By assumption, the expected rates of returns of both companies are the same, it is the
uncertainty that differs between two cases.
5.3. Implementation
In this section, I evaluate the bias in the implied cost of capital which results from overlooking the
uncertainty in future expected rates of return. I begin by making a number of assumptions to assess
empirically the magnitude of tQ in equation (11). While some of these assumptions may seem ad hoc, the
purpose is (not to develop the most comprehensive model, but rather) to propose a simple model that allows
researchers to assess the importance of the uncertainty about future expected returns when measuring the
implied cost of capital. Subsequently, I consider the implications of the model on a practical example of
Jonson&Jonson. I proceed with estimating the variance of the innovations in expected rates of return
(which is necessary to compute tQ ) by using the methodology of Campbell (1991). I end this section by
outlining three commonly used valuation models and how to adjust them for the uncertainty in expected
returns.
5.3.1. Assessment of the bias
Following Campbell (1990) and others, I assume that future expected returns follow a first order
autoregressive process ttt RR εαρα ++− −1)(1= where tε is i.i.d with mean zero and variance 2
tεσ . The
unconditional expectation and variance of tR are ρ=)( tRE , )/(1=)( 22 ασε −ttRVar respectively with
(0,1)∈α .95 An autoregressive process is appropriate for the following reason. When a company
undertakes new investments, decides to exercise its growth opportunities, or successfully launches a new
product its expected return will change. These shock to the expected rate of return are likely to persist over
a number of periods. For this reason, I expect the α parameter to be relatively high.96, 97
95See also Campbell and Ammer (1993), Vuolteenaho (2004) Callen and Segal (2004) for a similar assumption. 96Campbell (1991) considers α in the range of 0.5 to 0.9. 97A higher order autoregressive processes may also be used instead of AR(1) process. However, the benefit of doing so will not benefit a practitioner substantially because the higher order autoregressive process, which exhibits positive decaying auto-correlation structure, should be reasonably well approximated by AR(1) process.
136
For tractability purposes, I also assume that the innovations in future dividends are uncorrelated with
the innovations in the future expected returns.98 This avoids the need to make assumptions about a process
describing the evolution of the dividends, and the model is much easier to solve in a closed form. This
assumption may be justified by the findings of Campbell (1991) that almost 92% of the variance in
aggregate returns is due to changes in expected returns and only 7% is due to the covariance between
changes in expected returns and dividends. With this in mind, the assumption of zero correlation should not
be harmful for my purposes, at least at the aggregate level (in Section 7, I explicitly model the correlation
between the innovations in expected dividends and expected returns). Under these assumptions, Appendix
A demonstrates that 0Q in (10) can be expressed as:
00 1= PQ
θθ+
(12)
where ))(1))((1(
)(=αρρ
θgg
rVar t
+−+− and g is a growth rate in tQ .
When a company operates in a steady state, the growth rate g equals to zero or to the inflation rate.99
Actual growth rates may in fact be higher, however choosing g more conservatively works against finding
any bias in the implied cost of capital. For this reason such assumption is appropriate in order to assess (the
lower bound of) the bias in the implied cost of capital.
Equation (12) represents the term necessary to augment the traditional present-value-based models.
Following equations (11) and (12), firm value can be expressed as follows:
ttt
t PDE
Pθθ
ρττ
τ +++
∞
∑ 1=
1=
(13)
ττ
τ ρθ +
∞
∑+⇔ ttt
DEP
1=
)(1= (14)
Equation (14) is a simple and intuitively appealing formula. The only difference between equation
(14) and the traditional valuation model is that the standard model is pre-multiplied by a factor that adjusts
for uncertainty in the future expected rates of return.
It is useful to quantify the effect of uncertainty with respect to the implied cost of capital ( ρ ). I do so
based on data from the numerical example of Johnson and Johnson, described in the appendix to GLS. The
variance of the yearly innovations in tr is set to 0.005, 0.010 and 0.020% respectively. The following
parameters are used as of November 30th, 1995: price P =$86.63, book value 0B =11.08, EPS 3.68=1FY ,
98E.g. price of risk may change, while expected dividends stay the same. Alternatively, the variance (and thus covariances of future cash flows with the market) may change without impacting on their expected value. 99Similar assumptions is made by all traditional valuation models when calculating the expression for terminal value at a certain future date.
137
4.18=2FY , long term growth in earnings LTG=12.53%, dividend payout ratio k=36.2%, target industry
ROE=18%.100
Figure 1: Year t difference between actual and predicted prices for various ρ . Calculations are based on
Gebhardt, Lee, and Swaminathan (2001)
First, I consider RIM model as implemented in GLS. 101 Each curve in the Figure 1 shows the
difference (valuation error) between the actual price and value predicted by the RI model conditional on ρ
varying from 5 to 20%, and on different levels of variance of expected returns εσ . The cost of capital is
determined at the point where each line crosses the zero level on the vertical axis. The first bold line is the
solution that follows from the RI model of GLS. It yields an implied cost of capital estimate of 7.12%
which is the same as reported in Appendix of GLS.
The results are strikingly different once the model incorporates uncertainty about future expected
returns. The cost of capital increases considerably and ranges between 10 to 13%, depending on the
variance 2
tεσ . This suggests that J&J faces a risk premium that is much larger than suggested by the
standard RI model. 100Here I set g to zero, i.e.
)1)(()(=αρρ
θ−−tRVar .
101GLS rely on explicit analysts' forecasts of EPS for the first three years and thereafter assume that a firm's ROE performance will return to the industry median ROE over the years 4 to 12. Eventually, at time 12=T , GLS assume that residual income remains constant.
138
Figure 2: Year t difference between actual and predicted prices for various ρ . Calculations are based on
Claus and Thomas (2001).
Next, I consider the same example but now using the RIM implemented in CT.102 Figure 2 yields cost
of capital estimates similar to GLS. As in previous case, the variance in future expected returns
substantially affects the solution. Year t difference between actual and predicted prices for various ρ
based on Claus and Thomas (2001).
Finally, the J&J data are used to implement the model outlined in Easton (2004).103 The results based
on this model are displayed in Figure 3 and are similar to the cases of CT and GLS. Overall, the analysis
suggests that the bias in the implied cost of capital can be sufficiently large to explain why prior studies
found relatively low equity premia.
5.3.2. Variance of the innovations in expected returns
The model proposed in Section 3.1 requires estimation of the variance of the innovations in expected
returns. I follow the approach taken in Campbell (1991, see also Vuolteenaho, 2002, Callen and Segal,
102Their model is outlined in detail in the next section. It uses analysts' forecasts to predict the residual income for the five years following 0=t . For the period thereafter, CT determine the terminal value of residual income by assuming that residual income grows at the inflation rate. For consistency, the same payout ratio is used as in the GLS example. 103This version of Ohlson and Juettner-Nauroth (2005) [OJ] model uses only two years of analyst forecasts data and then assumes that the growth rate in the `economic' income is zero.
139
2004). A vector-autoregressive (VAR) specification is used to decompose stock returns into two
Figure 3: Year t difference between actual and predicted prices for various ρ . Calculations are based on
Easton (2004)
components: shocks to expected returns (expected return news) and shocks to expected dividends (cash-
flow news). As before, expected rates of return follow an AR(1) process
11021~=~
++++ ++ ttttt RERE εαα (15)
where 211~)( +++ −≡ tttt REEε is the innovation in one-period-ahead expected return.
Firms are assumed to follow a linear information dynamics given by the following VAR system:
1,,01, = ++ +Γ+ tititi uzz γ (16)
where tiz , is a vector of firm-specific state variables with the first element of firm's realized stock return
( tiR ,~≡ ). Then, we may write
)(=~)(= 1,001211 ++++ Γ+Γ+− tttttt ueREE γγε (17)
2111 '=)( εσε ≡Γ′ΓΣ+ eeVar t (18)
where )'(= ,, titi uuEΣ and 1e is the unit vector, which has the first element equal to one and zeros
elsewhere.
140
Note that prices (and realized stock returns) will reflect the capitalized effect of the changes in the
future expected returns and therefore the variance decomposition of returns is not performed. Instead, I
estimate the parameter 2εσ given by (18).
Following Vuolteenaho (2002), I include the following state variables into the vector tiz , :
)~(= ,, titi Rlogr – natural log of realized (raw) return; )/(=/ ,, titi MBlogmb – log of book-to-market ratio;
)/(1= 1,,, −+ tititi BXlogroe – log of return on equity; tr – year-industry median tir , ; tmb/ – year-industry
median timb ,/ ; troe – year-industry median tiroe , ; tf – risk-free rate measured by the rate of return on a
T-bill with 10-year maturity. 104
Parameters 0γ , Γ and Σ may not be the same across firms and therefore they are allowed to vary
depending either on industry or on size and book-to-market quintiles. The vector autoregression in (16) is
estimated using an iterative SUR procedure.
5.3.3. Standard Models and Uncertainty Adjustment In this subsection, I briefly describe three models commonly used in the literature to estimate the
implied cost of capital and their implementation.
The model in GLS relies on current book value 0B , historical payout ratio k and 12 years ahead
forecasts of earnings per share (EPS). Actual analysts' forecasts are used for the first three years. To
forecast the remaining 9 EPS values, it is assumed that return on equity (ROE) decays towards the industry
median ROE. After year 12=t residual income remains constant. Hence, the firm value at time t=0 is
given by
1,...,12,~)(=
)(1)(1=
1
1112
11
1=00
∈−
++
++
−
∑tBrROEae
rrae
raeBV
tGLStt
GLSGLSt
GLS
t
t (19)
where tROE and tB~ are forecasted return on equity and future book value.
The model in CT is somewhat different. It relies on analysts' forecasts for five initial years and then
assumes a constant growth in the residual income, which is set equal to the inflation rate. Since CT
aggregate data before computing the implied risk premia, their model assumes 50% dividend payout.105 As
this need not hold at individual firm level, I use firm-specific historical dividend payout ratios. The
valuation is given by
104I do not use market adjusted returns or excess returns because the variation in expected returns is in part due to market and economy-wide movements. 10550% is close to the historical average payout rates.
141
1,...,5,~~=
))(1()(1
)(1=
1
55
5
1=00
∈−
+−++
++
−
∑tBrXae
rgrgae
raeBV
tCTtt
CTaeCT
aet
CT
t
t (20)
where tX~ is forecasted future earnings and aeg is growth in RI after 5=t .
Finally, the OJ model (Ohlson and Juettner-Nauroth, 2005) implemented in Easton (2004) does not
rely on book values but instead uses EPS forecasts for two consecutive years to determine the economic
income. From year 2 onwards, the model assumes that economic income remains constant, which yields the
following valuation model
21220 )/~~(= mpegmpeg rXdrXV −− (21)
All three models are used as benchmark when evaluating the cost of capital. Their uncertainty-
adjustment is implemented in the following way. Since the term tt
t
dE−
∞
+∑ ττ
τ ρ1= in (14) (at 0=t ) may be
restated in the form of 0V given by either of (19), (20), and (21) we may write
,)(1= 00 VP θ+ (22)
,,
,))(1))((1(
)(=
mpegCTGLS
t
rrrgg
RVar
∈+−+−
ραρρ
θ (23)
where, Var( tR ) is the unconditional variance in the expected returns ( )/(1 22 ασε − ) and α is the
autoregressive parameter. The long-run average expected return or the implied cost of capital is given by ρ .
At this point, it becomes necessary to make an assumption about the autoregressive parameter α .
Following Campbell (1991), I set α equal to 0.75, which implies that today's shock (almost entirely) fades
away over the following 10 years.106, 107 When implementing the model empirically, I assume g to equal
the long run inflation rate of 3%.
I use a grid search procedure in order to solve (22) and determine the implied cost of capital for each
company. This is done conditional either on restricting θ to zero (traditional model estimates) or allowing
for the uncertainty in the expected returns (i.e. non-zero θ ). The search is done over the range between the
106More precisely, if we normalize today's shock to 100% then only 23.7% of this shock will persist over the next 5 years and only 5.6% will persist over a 10 year horizon. 107Albeit it arbitrary, to model the impact of shock to the equilibrium rate of return to persist for 10 years seems descriptive of many firm events. Consider for example the time period involved when a firm launches a new product or enters a new market. Most of the shock will probably disappear during the early years due to the entry of competitors.
142
long run inflation rate (assumed 3%) and 50%. Observations that did not converge in this range are left
out.108 I censor any negative equity premia at zero.109
5.4. Data and Sample Construction
First, I describe the data used to estimate the variance of the innovations in the future expected rates
of return. Then I proceed with the data used to estimate the implied equity premia.
5.4.1. Equilibrium Rates of Return Variance Data The intersection of CRSP monthly stock and COMPUSTAT combined industrial annual datasets for
the period 1970-2003 represents the population. Further, the following conditions must be met for
observations to be included in the analysis: (1) December must be the month of the fiscal year end (because
the aggregate variables are measured over a fixed interval), (2) each firm must have positive book value of
equity and at least three non-missing observations of book value.
The monthly stock returns are compounded over a 12 month period starting three months after the
beginning of the fiscal year. I require all 12 monthly returns to be non-missing. Book-to-market ratio is
calculated as the ratio of book value of equity (data item 60) to the product of end of year price (data item
24) and the number of shares outstanding (data item 25). The return on equity is calculated as the ratio of
net income (data item 172) over the previous year book value.
Since the log transformation for returns close to -1 may result in outliers I require that the log of one
plus compounded return is greater than 4101 −× . Further, in order to mitigate the influence of outliers I
winsorize all the variables (after log transformation) at 1% (symmetrically). This leaves me with 80,947
non-missing firm-year observations.
The aggregate values of ROE, size and book-to-market are calculated by taking the median for each
year and each Fama-French industry of a log transformed variable. The risk-free rate is calculated as annual
average of daily 10-year (constant maturity) treasury rates taken from Federal Reserve Economic Data
(FRED II).
Following Fama and French (1993) I use NYSE listed companies in COMPUSTAT in order to
calculate size (end of year market value) and book-to-market breakpoints. These breakpoints are used to
classify firms into 25 portfolios based on their average size and book-to-market. For each of these
portfolios as well as for each Fama-French industry I estimate the variance of the equilibrium rate of return,
which is subsequently used to calculate the implied cost of capital.
108Note that setting the cost of capital smaller than the rate of growth in dividends or residual income will invalidate the valuation equation as the series will not converge. 109Otherwise the price of a firm must be zero as no one will invest in a company offering compensation for risk lower than risk-free return.
143
5.4.2. Implied Cost of Capital Data
Next, I describe the data used to implement the model developed in the Section 3.1 and to compute
the implied cost of capital. I use COMPUSTAT, CRSP and I/B/E/S to retrieve accounting data, prices and
analyst forecasts, respectively. Based on COMPUSTAT data I measure income before extraordinary items
– tX (data item 18), dividends – td (data item 21), book value of equity – tB (data item 60), total assets
(data item 6), and number of shares (data item 25).
The I/B/E/S summary data file is used to obtain consensus forecasts as of the middle of each
month.110 I retrieve the earnings forecasts for two consecutive years ( 1FY and 2FY ) and the long term
forecasted growth rate in earnings (LTG). Only the observations with at least two future earnings forecasts
are included. In order to ensure that information about book value is publicly available, the forecasts and
the prices are taken three months after the fiscal year end. Specifically, I/B/E/S forecasts are taken as of the
third week of the fourth month after the fiscal year end. The price is measured at the end of fourth month
after fiscal year end. I leave out observations with negative current book value of equity and observations
with negative 2FY forecasts. Further I consider observations with forecasted EPS 2 greater or equal than
forecasted EPS 1 as this is required by the model in Easton (2004). Data availability in I/B/E/S limits the
sample to the period of 1981-2003.
The clean surplus relation ( tttt dXBB −+−1= ) is employed to forecast the future book values. To
forecast earnings per share more than 2 years ahead, I use the long term growth (LTG). If LTG is missing it
is interpolated from the trend in one- and two-year EPS forecasts (FY1 and FY2). I use the ratio of average
dividends to average earnings over the last three years to compute the current dividend payout ratio. If the
actual earnings are negative the denominator is replaced by 0.06× (Total Assets).111 Payout ratios are
restricted to [0, 1] interval and otherwise are censored at the boundary.
The median return on equity (ROE, used by GLS) is calculated over the 10-year moving window for
each Fama-French industry. Following GLS, loss firms are excluded. I assume that long term inflation rate
equals to 3%.112 The number of observations for the final sample varies from 486 to 2646.
5.5. Implied Risk Premia
Table 1 provides the estimated variances of the innovations in the expected rates of return 2εσ , given
by (18). The variances are estimated across 55× subsamples created on size and book-to-market ratio. The
110Thursday following the second Friday. 111Such assumption was maintained in GLS who argued that ROA in U.S. is six percent on average 112This assumption is used in CT to capitalize residual income at the terminal date. I also assume that g (expected
growth rate in tQ ) equals the inflation rate.
144
T a
b l
e 1
Ann
ual V
aria
nce
of th
e In
nova
tions
to E
xpec
ted
Ret
urn
(σε2 )
Low
B/M
Hig
h B
/M
Q1
Q2
Q3
Q4
Q5
Smal
l Q
1 0.
045
0.03
9 0.
028
0.02
0 0.
009
Q
2 0.
060
0.03
3 0.
021
0.01
1 0.
009
Q
3 0.
033
0.03
7 0.
011
0.01
1 0.
019
Q
4 0.
026
0.01
6 0.
006
0.00
5 0.
007
Lar
ge
Q5
0.01
0 0.
009
0.00
6 0.
003
0.00
6
Var
ianc
e of
the
inno
vatio
ns in
the
expe
cted
rate
of r
etur
n '
'1
12
eeΓΣΓ
=εσ
whe
re e
1 is
a co
lum
n ve
ctor
with
firs
t ele
men
t equ
al to
on
e an
d ze
ros
else
whe
re; Γ
and
Σ a
re p
aram
eter
s es
timat
ed w
ithin
eac
h qu
intil
e of
com
pani
es a
lloca
ted
by a
vera
ge S
ize
(mar
ket c
ap)
and
Book
-to-M
arke
t usin
g th
e fo
llow
ing
VA
R m
odel
(bre
akpo
ints
are
calc
ulat
ed u
sing
NY
SE fi
rms o
nly)
1,
,0
1,
++
+Γ+
=ti
titi
uz
zγ
and
)'
(,
,ti
tiu
uE=Σ
Th
e V
AR
is e
stim
ated
usin
g ite
rate
d SU
R. F
irst e
lem
ent o
f zi,,
t is
log
of o
ne p
lus
raw
sto
ck r
etur
n an
d th
e ot
her
elem
ents
are
log
of
book
-to-m
arke
t; lo
g of
one
plu
s re
turn
on
equi
ty;
year
-indu
stry
med
ian
log
of s
tock
ret
urns
; ye
ar-in
dustr
y m
edia
n lo
g of
boo
k-to
-m
arke
t; ye
ar-in
dustr
y m
edia
n lo
g of
ret
urn
on e
quity
and
ris
k-fr
ee r
ate.
I ta
ke in
ters
ectio
n of
CRS
P an
d C
OM
PUST
AT
annu
al t
o cr
eate
the
stat
e ve
ctor
s z i,
t. Th
e sa
mpl
e is
restr
icte
d to
dat
a af
ter 1
970
and
to fi
rms
with
Dec
embe
r fis
cal y
ear e
nd. I
furth
er re
quire
at
leas
t 3
non-
mis
sing
obse
rvat
ions
for
boo
k va
lue
and
12 n
on-m
issin
g ob
serv
atio
ns f
or m
onth
ly s
tock
ret
urns
. O
bser
vatio
ns a
re
win
soriz
ed s
ymm
etric
ally
at 1
% le
vel.
The
final
dat
aset
con
tain
s 80
,947
obs
erva
tions
. Ind
ustry
gro
ups
are
defin
ed a
s in
Fam
a an
d Fr
ench
(199
7).
145
T a
b l
e 2
Impl
ied
Cos
t of C
apita
l by
Yea
r
(A) S
tand
ard
Mod
el
(B) V
aria
nce
by F
-F In
dust
ry
(C) V
aria
nce
by S
ize
and
B/M
N
r GLS
r C
T r m
peg
ff GLS
r
ff CT
r
ff mpe
gr
sb
mG
LSr
sb
mC
Tr
sb
mm
peg
r
ALL
35
977
8.66
8.
98
11.7
5 12
.63
12.7
6 15
.55
12.9
7 13
.14
15.9
1 19
81
486
11.6
6 11
.15
14.8
4 15
.42
14.8
4 18
.50
15.3
4 14
.77
18.4
1 19
82
660
9.34
9.
00
13.2
4 13
.39
12.7
6 17
.00
13.4
2 12
.82
17.0
3 19
83
935
10.2
7 10
.41
14.2
6 14
.31
14.3
6 18
.13
14.3
6 14
.41
18.1
7 19
84
876
9.93
9.
82
12.7
6 13
.95
13.7
2 16
.67
14.0
9 13
.89
16.8
1 19
85
870
8.75
8.
24
11.3
5 12
.84
11.9
8 15
.26
12.9
6 12
.16
15.4
0 19
86
1018
8.
55
8.18
11
.43
12.5
9 11
.82
15.2
8 12
.75
12.0
4 15
.46
1987
94
0 9.
46
9.14
11
.88
13.4
7 12
.88
15.7
7 13
.66
13.1
3 15
.98
1988
98
8 9.
06
8.64
10
.91
12.9
8 12
.26
14.7
2 13
.19
12.5
3 14
.94
1989
10
89
9.38
8.
93
11.7
4 13
.17
12.4
4 15
.40
13.4
9 12
.82
15.7
5 19
90
1112
8.
93
8.33
11
.84
12.8
0 11
.87
15.5
2 13
.14
12.2
4 15
.87
1991
12
70
8.37
8.
19
11.5
7 12
.40
11.8
6 15
.37
12.7
1 12
.21
15.7
1 19
92
1457
8.
16
8.37
11
.26
12.2
5 12
.12
15.1
1 12
.58
12.5
0 15
.46
1993
17
98
8.33
8.
59
11.3
2 12
.32
12.2
9 15
.10
12.7
3 12
.76
15.5
7 19
94
1965
8.
56
8.95
11
.32
12.4
9 12
.68
15.0
8 12
.90
13.1
5 15
.54
1995
22
01
8.17
8.
60
10.8
5 12
.14
12.3
7 14
.66
12.6
4 12
.91
15.2
1 19
96
2523
8.
49
9.07
11
.52
12.4
9 12
.98
15.4
2 12
.91
13.4
5 15
.90
1997
26
51
7.83
8.
72
11.0
1 11
.92
12.6
4 14
.90
12.3
2 13
.07
15.3
3 19
98
2475
8.
80
9.65
12
.22
12.7
5 13
.54
16.0
4 13
.16
13.9
7 16
.46
1999
22
54
9.16
10
.07
12.5
6 13
.04
13.9
2 16
.34
13.3
5 14
.26
16.6
7 20
00
1932
8.
58
9.29
11
.83
12.4
9 13
.15
15.6
0 12
.72
13.3
8 15
.83
2001
20
43
8.06
8.
57
11.7
8 12
.00
12.3
5 15
.53
12.3
6 12
.72
15.8
9 20
02
2204
8.
89
9.17
12
.15
12.7
5 12
.93
15.9
0 13
.22
13.4
2 16
.38
2003
22
30
7.93
8.
51
11.0
2 11
.89
12.3
2 14
.82
12.3
8 12
.82
15.3
1 Th
is ta
ble
prov
ides
impl
ied
cost
of e
quity
est
imat
es a
vera
ged
over
eac
h ye
ar. T
he e
stim
ates
are
com
pute
d so
lvin
g th
e fo
llow
ing
mod
el
)(
))(
1(r
Vr
Pt
tθ+
= ,
)1)(
1()
1/()
(2
2
αα
σθ
ε
gr
gr
r−
+−
+−
=
146
whe
re V
t(r) i
s va
lue
of th
e fir
m a
s gi
ven
by e
ither
GLS
, CT,
Eas
ton
(200
4) (o
r any
oth
er d
isco
unte
d ca
sh fl
ow/d
ivid
ends
) mod
els
(see
sec
tion
4 of
the
pape
r fo
r mor
e de
tails
on
each
mod
el);
r is t
he im
plie
d co
st o
f cap
ital m
etric
s; g
is e
xpec
ted
grow
th ra
te in
pric
es se
t to
long
run
cons
erva
tive
infla
tion
rate
of 3
%;
α is
aut
oreg
ress
ive
para
met
er in
the
equi
libriu
m ra
te o
f ret
urn
set e
qual
to 0
.75.
Pane
l A p
rovi
des
the
impl
ied
cost
of c
apita
l for
m th
e sta
ndar
d m
odel
s, w
hich
restr
ict θ
(r) t
o ze
ro. S
ubsc
ripts
GLS
, CT,
and
rm
peg
next
to r
ref
er
GLS
, CT
and
East
on’s
mod
els u
sed,
resp
ectiv
ely,
to e
xpre
ss V
t(r) i
n te
rms o
f res
idua
l (or
eco
nom
ic) i
ncom
e in
stea
d of
div
iden
ds. P
anel
B c
onta
ins a
djus
ted
impl
ied
cost
of
capi
tal
estim
ates
, whe
re θ
(r)
varie
s ac
ross
Fam
a-Fr
ench
48
indu
stry
grou
ps b
ased
on
with
in in
dustr
y va
rianc
e of
the
inno
vatio
ns in
the
equi
libriu
m ra
te o
f ret
urn
('
'1
12
eeΓΣΓ
=εσ
). Pa
nel C
con
tain
s the
impl
ied
cost
of e
quity
cal
cula
ted
whe
n θ(
r) is
allo
wed
to v
ary
acro
ss 5×5
siz
e an
d bo
ok-to
-m
arke
t dec
iles b
ased
on σ ε
2 est
imat
e.
A
naly
sts’
con
sens
us f
orec
asts
for
m I
/B/E
/S a
nd h
istor
ical
CO
MPU
STA
T da
ta a
re u
sed
to p
redi
ct f
utur
e ea
rnin
gs,
divi
dend
s an
d bo
ok v
alue
s re
quire
d by
the
res
idua
l in
com
e m
odel
s. D
ivid
end
payo
ut r
atio
ns a
re c
alcu
late
d ba
sed
on 3
yea
rs o
f hi
storic
al d
ata.
I c
onsi
der
obse
rvat
ions
with
EPS
1 fo
reca
st g
reat
er o
r eq
ual
than
EPS
2 fo
reca
st a
s re
quire
d by
mod
el i
n Ea
ston
(200
4);
addi
tiona
lly I
res
trict
to
posi
tive
EPS 2
for
ecas
t us
ed t
o in
terp
olat
e ea
rnin
gs in
to th
e fu
ture
. Fo
reca
stin
g fu
ture
ear
ning
s in
GLS
mod
el a
ssum
es f
utur
e re
turn
on
equi
ty d
ecay
s to
war
ds th
e in
dustr
y m
edia
n RO
E ov
er 1
2 ye
ars.
I ca
lcul
ate
med
ian
ROE
for
each
indu
stry
and
each
yea
r us
ing
10 y
ear
mov
ing
win
dow
exc
ludi
ng lo
ss fi
rms.
Mod
el in
CT
assu
mes
per
petu
al g
row
th ra
te in
res
idua
l in
com
e st
artin
g fr
om y
ear 5
. Thi
s gr
owth
is a
ssum
ed to
be
the
expe
cted
infla
tion
rate
set
equ
al to
3%
. A
naly
sts
fore
cast
s ar
e m
easu
red
in th
e m
iddl
e of
the
four
th m
onth
afte
r the
fisc
al y
ear e
nd. P
rices
are
mea
sure
d at
the
end
of th
e fo
urth
mon
th a
fter t
he fi
scal
yea
r end
to m
ake
sure
the
acco
untin
g in
form
atio
n is
publ
icly
ava
ilabl
e. A
vaila
bilit
y of
I/B/
E/S
data
lim
its th
e sa
mpl
e to
198
1-20
03. C
ost o
f equ
ity e
stim
ates
less
than
3%
(con
serv
ativ
e in
flatio
n ra
te e
stim
ate)
ar
e ce
nsor
ed a
nd th
e ob
serv
atio
ns w
ith c
ost o
f cap
ital m
ore
than
50%
are
left
out f
orm
the
anal
ysis
. Fur
ther
I re
stric
t the
sam
ple
to th
e se
t on
non-
mis
sing
obse
rvat
ions
acr
oss a
ll th
e 9
diffe
rent
type
s of c
ost o
f cap
ital e
stim
ates
.
147
evidence suggests that these variances are substantial (ranging between 0.003 and 0.06). Smaller firms with
lower book-to-market generally exhibit the higher 2εσ and this variance declines when moving to larger
size and higher book-to-market portfolios.
Table 2 reports average implied cost of capital for each year. The three columns in Panel (A) contain
cost of capital measures based on the traditional valuation models presented in GLS, CT and Easton and
denoted by GLSr , CTr and mpegr respectively. Panel (B) provides the uncertainty-adjusted measures based
on these models. The adjustment factor )( ffθθ ≡ is based on 48 industry specific estimates of 2εσ . These
measures are denoted by ffGLSr , ff
CTr , and ffmpegr , respectively. Panel (C) provides the implied cost of capital
with adjustment )( sbmθθ ≡ based on 2εσ estimated across 55× size and book-to-market portfolios. They
are denoted by sbmGLSr , sbm
CTr , and sbmmpegr , respectively.
The evidence in the table indicates that GLSr , CTr and mpegr estimates are on average 8.66, 8.98, and
11.75%, respectively.113 Their uncertainty-adjusted counterparts are considerably larger: ffGLSr , ff
CTr , and
ffmpegr are 12.63, 12.76, and 15.55%, while sbm
GLSr , sbmCTr and sbm
mpegr constitute 12.97, 13.14, and 15.91%,
respectively. This suggests the presence of a substantial downward bias in the implied cost of capital
estimates from traditional valuation model.
Table 3 reports the implied equity premia (calculated as a difference between the implied cost of
capital and the risk-free rate fr ) and the variance of the innovations in the expected returns 2εσ by
industry. Cross-industry differences are substantial. The highest variances belong to Pharmaceutical
Products (13), Lab Equipment (37), Healthcare (12) and Electronic Equipment (36).
The evidence in Panel (A) indicates that the three traditional models generate on average equity
premia of 2.47 (GLS), 2.97 (CT), and 5.40% (Easton). These numbers are comparable to prior findings of
GLS and CT who report average equity premia of 2.5% and 3.4%, respectively. 114
The evidence contained in Panels (B) and (C) reveals substantial differences in equity premia when
the stochastic nature of expected returns is taken into account. When the variance 2εσ is estimated at
industry level, the uncertainty-adjusted equity premia are 5.96, 6.28 and 8.91 for the specifications in GLS,
CT, and Easton, respectively. The corresponding numbers when 2εσ is modelled across size and book-to-
market deciles, are 6.30, 6.66 and 9.27. These findings suggest that when the uncertainty in expected
returns is properly accounted for the implied equity premia are of similar size as those historically realized.
113This is consistent with prior findings (Botosan and Plumlee, 2005) that the model in Easton (2004) yields relatively higher estimates. 114Equity premium is not reported in Easton (2004); the average implied cost of capital there is 11.9% while the estimate in Table 2 is 11.75%
148
T a
b l
e 3
Impl
ied
Equ
ity P
rem
ia in
Exc
ess o
f Ris
k-fr
ee R
ate
by F
ama-
Fren
ch 4
8 In
dust
ry G
roup
s
(A
) Sta
ndar
d M
odel
(B
) Var
ianc
e by
F-F
Indu
stry
(C
) Var
ianc
e by
Siz
e an
d B/
M
F
-F In
dust
ry
N
r GLS
-rf
r CT-
r f r m
peg-r
f ff G
LSr
-rf
ff CT
r-r
f ff m
peg
r-r
f sb
mG
LSr
-rf
sbm
CT
r-r
f sb
mm
peg
r-r
f 2 εσ
A
LL
3597
7 2.
47
2.97
5.
40
5.96
6.
28
8.91
6.
30
6.66
9.
27
0.01
7 1
Agr
ic
832.
68
3.29
5.
29
7.81
8.
49
10.4
9 6.
72
7.38
9.
37
0.02
9 2
Food
69
9 1.
90
2.10
3.
79
3.75
3.
78
5.56
5.
27
5.27
7.
14
0.00
6 3
Soda
80
2.02
2.
01
3.83
3.
48
3.25
5.
20
5.75
5.
24
7.48
0.
004
4A
lcoh
ol
145
1.85
2.
08
3.53
3.
17
3.30
4.
77
5.63
5.
66
7.26
0.
004
5To
bacc
o 38
8.04
6.
31
8.43
12
.81
11.0
6 13
.27
11.4
9 9.
79
11.9
4 0.
019
6To
ys&
Rec
270
2.89
3.
31
6.08
6.
40
6.51
9.
58
6.40
6.
58
9.64
0.
016
7Fu
n&En
tt 44
3 2.
52
3.24
5.
84
6.38
7.
01
9.74
6.
60
7.37
10
.07
0.01
7 8
Boo
k&Pr
nt
487
1.82
1.
77
3.15
3.
81
3.44
5.
01
5.36
4.
92
6.59
0.
007
9H
shld
78
8 2.
34
2.75
4.
71
5.25
5.
40
7.48
6.
37
6.60
8.
73
0.01
1 10
App
arel
54
5 3.
17
3.30
5.
14
4.87
4.
87
6.72
6.
85
6.86
8.
80
0.00
5 11
Hea
lth
604
2.62
3.
23
5.46
8.
50
9.30
11
.89
6.96
7.
73
10.1
2 0.
041
12M
edEq
88
3 2.
13
2.76
5.
10
7.02
7.
69
10.3
8 6.
93
7.71
10
.40
0.03
0 13
Dru
gs
839
1.83
2.
27
3.93
8.
64
8.86
11
.09
5.92
6.
23
8.22
0.
053
14C
hem
ic
933
2.38
2.
62
4.94
5.
05
4.96
7.
35
5.87
5.
81
8.25
0.
009
15Ru
bb&
Plas
25
1 3.
02
3.65
6.
23
5.46
5.
82
8.43
7.
14
7.59
10
.25
0.00
8 16
Txtls
29
1 2.
97
3.68
7.
81
5.99
6.
63
10.7
6 6.
32
7.04
11
.15
0.01
1 17
BldM
t 72
2 2.
44
3.13
6.
29
5.45
5.
97
9.21
6.
16
6.76
10
.00
0.01
1 18
Cns
tr 41
1 4.
01
4.54
6.
69
9.36
9.
93
12.2
4 7.
68
8.15
10
.41
0.03
0 19
Stee
l 59
3 3.
26
4.09
9.
59
6.95
7.
70
13.0
3 6.
38
7.17
12
.51
0.01
4 20
FabP
r 11
3 2.
97
3.42
7.
22
6.08
6.
59
10.2
5 6.
99
7.59
11
.32
0.01
2 21
Mac
h 12
51
2.21
3.
07
6.50
6.
00
6.73
10
.20
6.21
7.
03
10.5
2 0.
016
22El
cEq
450
2.49
2.
90
5.79
6.
17
6.49
9.
39
6.64
6.
98
9.93
0.
015
23A
utos
68
3 3.
30
3.63
6.
36
7.42
7.
62
10.3
2 6.
80
7.10
9.
76
0.01
7 24
Aer
o 18
5 2.
22
2.64
5.
06
4.70
4.
79
7.38
4.
80
5.08
7.
54
0.00
9 25
Ship
&Ra
il 12
3 2.
51
3.16
6.
20
5.20
5.
47
8.41
5.
86
6.17
9.
20
0.00
8 26
Gun
s 55
3.55
2.
26
3.95
7.
43
5.94
7.
69
7.54
6.
11
7.89
0.
016
149
Tab
le 3
. Con
tinue
d.
27G
old
760.
43
1.68
4.
18
3.80
4.
67
9.12
2.
56
3.73
7.
76
0.02
5 28
Min
es
115
2.11
3.
21
7.28
5.
40
6.28
10
.19
5.93
6.
83
10.7
7 0.
010
29C
oal
433.
99
3.80
9.
37
5.35
5.
02
10.4
4 7.
81
7.76
13
.01
0.00
3 30
Oil&
Gas
10
74
1.04
2.
19
6.07
4.
24
5.13
9.
42
4.14
5.
17
9.43
0.
014
31U
til
1486
2.
38
2.46
3.
81
4.73
4.
23
5.70
5.
94
5.30
6.
85
0.00
5 32
Telc
m
757
2.23
2.
15
4.14
4.
82
4.28
6.
60
5.45
4.
97
7.40
0.
009
33Pe
rSv
337
2.00
2.
69
4.74
7.
18
7.88
10
.08
6.48
7.
25
9.37
0.
029
34Bu
sSv
3253
2.
45
2.84
5.
38
6.84
7.
04
9.92
7.
04
7.33
10
.26
0.02
3 35
Com
ps
1597
2.
50
3.18
6.
64
7.77
8.
61
12.4
0 6.
77
7.62
11
.28
0.03
4 36
Chi
ps
1905
1.
97
2.52
5.
82
7.73
8.
11
12.1
6 5.
84
6.27
9.
97
0.04
1 37
LabE
q 72
7 1.
62
2.46
5.
62
7.52
8.
18
12.0
7 5.
84
6.57
10
.13
0.04
3 38
Pape
r 68
6 2.
14
2.57
6.
47
5.14
5.
24
9.19
5.
62
5.89
9.
81
0.01
1 39
Box
es
173
2.83
3.
27
6.00
5.
03
5.21
7.
94
6.58
6.
92
9.62
0.
007
40Tr
ans
1000
3.
02
3.56
6.
78
6.43
6.
85
10.0
3 6.
63
7.09
10
.33
0.01
3 41
Whl
sl
1201
2.
52
3.46
6.
09
5.81
6.
65
9.31
6.
32
7.23
9.
94
0.01
3 42
Rtai
l 24
45
2.48
2.
82
4.70
6.
47
6.64
8.
73
6.04
6.
25
8.32
0.
019
43M
eals
69
5 2.
07
2.96
4.
91
5.60
6.
42
8.49
6.
40
7.33
9.
43
0.01
5 44
Bank
s 36
59
2.89
3.
33
4.65
4.
37
4.54
5.
89
6.68
6.
82
8.18
0.
003
45In
sur
1788
3.
40
3.37
4.
88
5.40
5.
16
6.71
6.
64
6.48
8.
04
0.00
6 46
RlEs
t 54
3.08
6.
38
8.77
5.
17
8.50
10
.73
7.53
11
.01
13.2
6 0.
006
47Fi
nTra
d 54
9 2.
02
3.73
5.
40
3.23
4.
79
6.44
6.
15
7.65
9.
32
0.00
3 48
Mis
cel
392
2.06
2.
98
5.29
4.
09
4.86
7.
22
5.67
6.
64
9.05
0.
007
This
tabl
e pr
ovid
es im
plie
d eq
uity
pre
mia
(def
ined
as
cost
of e
quity
est
imat
es a
vera
ged
min
us th
e ris
k fr
ee ra
te) o
ver
each
of 4
8 Fa
ma
and
Fren
ch (1
997)
in
dustr
y gr
oups
. The
impl
ied
cost
of c
apita
l is c
ompu
ted
solv
ing
the
follo
win
g m
odel
)(
))(
1(r
Vr
Pt
tθ+
= ,
)1)(
1()
1/()
(2
2
αα
σθ
ε
gr
gr
r−
+−
+−
=
whe
re V
t(r) i
s va
lue
of th
e fir
m a
s gi
ven
by e
ither
GLS
, CT,
Eas
ton
(200
4) (o
r any
oth
er d
isco
unte
d ca
sh fl
ow/d
ivid
ends
) mod
els
(see
sec
tion
4 of
the
pape
r fo
r mor
e de
tails
on
each
mod
el);
r is t
he im
plie
d co
st o
f cap
ital m
etric
s; g
is e
xpec
ted
grow
th ra
te in
pric
es se
t to
long
run
cons
erva
tive
infla
tion
rate
of 3
%;
α is
aut
oreg
ress
ive
para
met
er in
the
equi
libriu
m ra
te o
f ret
urn
set e
qual
to 0
.75.
Pa
nel A
pro
vide
s th
e im
plie
d eq
uity
pre
mia
form
the
stan
dard
mod
els,
whi
ch re
stric
t θ(r
) to
zero
. Sub
scrip
ts G
LS, C
T, a
nd r
mpe
g ne
xt to
r r
efer
G
LS, C
T an
d Ea
ston
’s m
odel
s use
d, re
spec
tivel
y, to
exp
ress
Vt(r
) in
term
s of r
esid
ual (
or e
cono
mic
) inc
ome
inst
ead
of d
ivid
ends
. Pan
el B
con
tain
s adj
uste
d im
plie
d eq
uity
pre
mia
est
imat
es, w
here
θ(r
) va
ries
acro
ss F
ama-
Fren
ch 4
8 in
dustr
y gr
oups
bas
ed o
n w
ithin
indu
stry
varia
nce
of t
he in
nova
tions
in th
e
150
equi
libriu
m ra
te o
f ret
urn
''
11
2e
eΓΣΓ
=εσ
(thu
s sup
ersc
ript f
f). P
anel
C c
onta
ins t
he e
quity
pre
mia
cal
cula
ted
whe
n θ(
r) is
allo
wed
to v
ary
acro
ss 5×5
size
and
bo
ok-to
-mar
ket d
ecile
s bas
ed o
n σ ε
2 est
imat
e (th
us su
pers
crip
t sbm
).
Ana
lyst
s’ c
onse
nsus
for
ecas
ts f
orm
I/B
/E/S
and
hist
oric
al C
OM
PUST
AT
data
are
use
d to
pre
dict
fut
ure
earn
ings
, di
vide
nds
and
book
val
ues
requ
ired
by t
he r
esid
ual
inco
me
mod
els.
Div
iden
d pa
yout
rat
ions
are
cal
cula
ted
base
d on
3 y
ears
of
histo
rical
dat
a. I
con
side
r ob
serv
atio
ns w
ith E
PS1
fore
cast
gre
ater
or
equa
l th
an E
PS2
fore
cast
as
requ
ired
by m
odel
in
Easto
n (2
004)
; ad
ditio
nally
I r
estri
ct t
o po
sitiv
e EP
S 2 f
orec
ast
used
to
inte
rpol
ate
earn
ings
into
the
futu
re.
Fore
cast
ing
futu
re e
arni
ngs
in G
LS m
odel
ass
umes
fut
ure
retu
rn o
n eq
uity
dec
ays
tow
ards
the
indu
stry
med
ian
ROE
over
12
year
s. I
calc
ulat
e m
edia
n RO
E fo
r ea
ch in
dustr
y an
d ea
ch y
ear
usin
g 10
yea
r m
ovin
g w
indo
w e
xclu
ding
loss
firm
s. M
odel
in C
T as
sum
es p
erpe
tual
gro
wth
rate
in r
esid
ual
inco
me
star
ting
from
yea
r 5. T
his
grow
th is
ass
umed
to b
e th
e ex
pect
ed in
flatio
n ra
te s
et e
qual
to 3
%.
Ana
lyst
s fo
reca
sts
are
mea
sure
d in
the
mid
dle
of th
e fo
urth
mon
th a
fter t
he fi
scal
yea
r end
. Pric
es a
re m
easu
red
at th
e en
d of
the
four
th m
onth
afte
r the
fisc
al y
ear e
nd to
mak
e su
re th
e ac
coun
ting
info
rmat
ion
is pu
blic
ly a
vaila
ble.
Ava
ilabi
lity
of I/
B/E/
S da
ta li
mits
the
sam
ple
to 1
981-
2003
. Cos
t of e
quity
est
imat
es le
ss th
an 3
% (c
onse
rvat
ive
infla
tion
rate
est
imat
e)
are
cens
ored
and
the
obse
rvat
ions
with
cos
t of c
apita
l mor
e th
an 5
0% a
re le
ft ou
t for
m th
e an
alys
is. F
urth
er I
restr
ict t
he s
ampl
e to
the
set o
n no
n-m
issin
g ob
serv
atio
ns a
cros
s all
the
9 di
ffere
nt ty
pes o
f cos
t of c
apita
l est
imat
es.
151
T a b l e 4
Bias in the Implied Cost of Capital by Fama-French 48 Industry Groups
(A) Variance by F-F Industry (B) Variance by Size and B/M
F-F Industry N ff
GLSr ffCTr ff
mpegr sbmGLSr sbm
CTr sbmmpegr 2
εσ
ALL 35977 3.49 3.31 3.50 3.83 3.69 3.87 0.017 1 Agric 83 5.13 5.20 5.20 4.04 4.09 4.08 0.029 2 Food 699 1.85 1.68 1.77 3.37 3.17 3.35 0.006 3 Soda 80 1.45 1.25 1.37 3.73 3.23 3.65 0.004 4 Alcohol 145 1.31 1.22 1.25 3.77 3.58 3.73 0.004 5 Tobacco 38 4.77 4.75 4.84 3.45 3.48 3.50 0.019 6 Toys&Rec 270 3.50 3.20 3.51 3.50 3.28 3.56 0.016 7 Fun&Entt 443 3.87 3.77 3.90 4.08 4.13 4.24 0.017 8 Book&Prnt 487 1.99 1.67 1.86 3.54 3.15 3.44 0.007 9 Hshld 788 2.91 2.66 2.78 4.02 3.85 4.03 0.011
10 Apparel 545 1.71 1.58 1.58 3.68 3.57 3.66 0.005 11 Health 604 5.88 6.07 6.43 4.35 4.50 4.66 0.041 12 MedEq 883 4.89 4.93 5.28 4.81 4.96 5.30 0.030 13 Drugs 839 6.82 6.59 7.16 4.09 3.95 4.28 0.053 14 Chemic 933 2.67 2.34 2.42 3.49 3.19 3.31 0.009 15 Rubb&Plas 251 2.44 2.17 2.21 4.12 3.95 4.02 0.008 16 Txtls 291 3.02 2.95 2.95 3.35 3.36 3.34 0.011 17 BldMt 722 3.01 2.84 2.93 3.72 3.63 3.71 0.011 18 Cnstr 411 5.35 5.38 5.55 3.67 3.60 3.71 0.030 19 Steel 593 3.69 3.61 3.44 3.12 3.09 2.91 0.014 20 FabPr 113 3.11 3.17 3.03 4.02 4.17 4.10 0.012 21 Mach 1251 3.79 3.66 3.70 4.00 3.96 4.03 0.016 22 ElcEq 450 3.69 3.59 3.60 4.15 4.09 4.14 0.015 23 Autos 683 4.12 3.99 3.96 3.50 3.48 3.40 0.017 24 Aero 185 2.48 2.15 2.31 2.58 2.44 2.48 0.009 25 Ship&Rail 123 2.70 2.32 2.21 3.36 3.01 3.00 0.008 26 Guns 55 3.88 3.69 3.75 3.98 3.85 3.94 0.016 27 Gold 76 3.37 2.99 4.94 2.13 2.05 3.58 0.025 28 Mines 115 3.29 3.07 2.91 3.82 3.62 3.49 0.010 29 Coal 43 1.36 1.22 1.07 3.82 3.96 3.65 0.003 30 Oil&Gas 1074 3.19 2.94 3.34 3.09 2.98 3.36 0.014 31 Util 1486 2.36 1.77 1.89 3.57 2.84 3.03 0.005 32 Telcm 757 2.59 2.13 2.47 3.22 2.82 3.26 0.009 33 PerSv 337 5.18 5.19 5.34 4.48 4.57 4.62 0.029 34 BusSv 3253 4.39 4.20 4.54 4.58 4.48 4.88 0.023 35 Comps 1597 5.27 5.43 5.76 4.26 4.44 4.65 0.034 36 Chips 1905 5.76 5.59 6.34 3.86 3.75 4.15 0.041 37 LabEq 727 5.90 5.72 6.45 4.22 4.11 4.51 0.043 38 Paper 686 3.00 2.67 2.72 3.49 3.32 3.34 0.011 39 Boxes 173 2.20 1.94 1.94 3.75 3.65 3.62 0.007 40 Trans 1000 3.41 3.29 3.25 3.60 3.53 3.55 0.013 41 Whlsl 1201 3.29 3.19 3.22 3.80 3.77 3.85 0.013 42 Rtail 2445 4.00 3.82 4.03 3.56 3.43 3.62 0.019
152
Table 4. Continued. 43 Meals 695 3.53 3.45 3.58 4.34 4.37 4.52 0.015 44 Banks 3659 1.47 1.21 1.23 3.78 3.49 3.52 0.003 45 Insur 1788 2.00 1.79 1.83 3.23 3.11 3.16 0.006 46 RlEst 54 2.09 2.12 1.96 4.45 4.63 4.49 0.006 47 FinTrad 549 1.22 1.06 1.05 4.13 3.92 3.93 0.003 48 Miscel 392 2.02 1.88 1.93 3.61 3.65 3.76 0.007
This table provides the bias in the implied cost of equity estimates averaged 48 Fama-French (1997) industry groups. Bias is defined as the difference between the adjusted implied cost of capital estimate (described below) minus the unadjusted (standard) implied cost of capital estimate. The implied cost of capital is computed solving the following model
)())(1( rVrP tt θ+= , )1)(1(
)1/()(22
αασθ ε
grgrr
−+−+−
=
where Vt(r) is value of the firm as given by either GLS, CT, Easton (2004) (or any other discounted cash flow/dividends) models (see section 4 of the paper for more details on each model); r is the implied cost of capital metrics; g is expected growth rate in prices set to long run conservative inflation rate of 3%; α is autoregressive parameter in the equilibrium rate of return set equal to 0.75. The implied cost of capital form the standard models restrict θ(r) to zero. Subscripts GLS, CT, and rmpeg next to r refer GLS, CT and Easton’s models used, respectively, to express Vt(r) in terms of residual (or economic) income instead of dividends). In Panel A the adjusted implied cost of capital estimates is calculated when θ(r) varies across Fama-French 48 industry groups based on within industry variance of the innovations in the equilibrium rate of return ( '' 11
2 ee ΓΣΓ=εσ ) (thus superscript ff). In Panel B the adjusted implied cost of equity calculated when θ(r) is allowed to vary across 5×5 size and book-to-market deciles based on σε2 estimate (thus superscript sbm). Analysts’ consensus forecasts form I/B/E/S and historical COMPUSTAT data are used to predict future earnings, dividends and book values required by the residual income models. Dividend payout rations are calculated based on 3 years of historical data. I consider observations with EPS1 forecast greater or equal than EPS2 forecast as required by model in Easton (2004); additionally I restrict to positive EPS2 forecast used to interpolate earnings into the future.
Forecasting future earnings in GLS model assumes future return on equity decays towards the industry median ROE over 12 years. I calculate median ROE for each industry and each year using 10 year moving window excluding loss firms. Model in CT assumes perpetual growth rate in residual income starting from year 5. This growth is assumed to be the expected inflation rate set equal to 3%. Analysts forecasts are measured in the middle of the fourth month after the fiscal year end. Prices are measured at the end of the fourth month after the fiscal year end to make sure the accounting information is publicly available. Availability of I/B/E/S data limits the sample to 1981-2003. Cost of equity estimates less than 3% (conservative inflation rate estimate) are censored and the observations with cost of capital more than 50% are left out form the analysis. Further I restrict the sample to the set on non-missing observations across all the 9 different types of cost of capital estimates.
153
The bias in the equity premia estimates for 48 Fama-French industries is reported in Table 4. When
the uncertainty-adjustment θ is based on within industry variance estimates (i.e., ffθθ = ), the average
bias ranges from 3.31 to 3.50%. The bias ranges between 3.69 and 3.83 when θ is based on size and book-
to-market quintiles (i.e., btmθθ = ). Interestingly, all three models yield bias of similar magnitude. As
suggested by cross-sectional variation in the estimates of 2εσ discussed above, the highest bias (averaged
across six different measures), is encountered in Pharmaceutical Products (13), Healthcare (12), Lab
Equipment (37), Medical Equipment (12), Computers (35), and Electronic Equipment (36).
Table 5 provides the evidence of how the adjustment factor sbmθ varies across size and book-to-
market quintals. The three panels in the table provide the adjustment factors sbmGLSθ , sbm
CTθ , and sbmmpegθ for the
models in GLS, CT, and Easton (2004) respectively. These factors are evaluated at the implied rate of
return ρ that solves the valuation equation. The patterns are generally decreasing with size and book-to-
market, i.e. resemble the patterns in the estimated variance of the innovations in the expected returns. The
magnitude of the adjustment factors sbmGLSθ , sbm
CTθ and sbmmpegθ ranges in 0.33-2.99, 0.51-3.08, and 0.29-2.12,
respectively.
This evidence suggests that traditional valuation models ignore a substantial fraction of the value.
The predicted value of equity of the portfolio of the smallest firms with the highest growth opportunities is
about 3 times larger than what is predicted by the traditional valuation models. This is consistent with the
evidence in Chemmanur and Loutskina (2005) that prices of the IPO's exceed the value predicted by the
residual income model 3 times on average (assuming that these are small/high growth firms).
The evidence in Table 6 compares the uncertainty-adjusted implied cost of capital estimates with
their counterparts that ignore the stochastic nature of expected returns. These differences are computed over
size and book-to-market portfolios. The table indicates that the smallest firms with the highest growth
opportunities have equity premia that range from 9.55 (for GLS) to 15.97 (for Easton, 2004) which is
consistent with the assessments of practitioners.
In addition, consistent with the findings in CT, Panels A1-A3 indicate that the unadjusted cost of
capital increases with the book-to-market. This is not intuitive as higher book-to-market (greater assets in
place) suggests less risk. However, when we adjust for uncertainty, the evidence generally reverses. Panels
(B1-B3) show that firms in the lowest book-to-market quintiles have higher risk premia than firms in the
highest book-to-market quintiles. It follows from Panels C1-C3 that this is due to firms in the smallest
book-to-market quintile having the highest θ while this is not the case for the highest book-to-market
firms.
Finally, Table 7 aims to assess the reliability of different cost of capital proxies. The correlations
among the traditional implied cost of capital proxies range from 0.649 to 0.732 when θ is set to zero. At
the same time, the correlation coefficients for the uncertainty-adjusted measures range from 0.718 to 0.783
(0.722 to 0.812) when θ is based on 48 industry groups ( 55× size and book-to-market portfolios). This
154
T a b l e 5 Correction factor θ : by Size and Book-to-Market
Panel A: Average Adjustment Factor for model in GLS ( θGLS)
Low B/M High B/M Q1 Q2 Q3 Q4 Q5 Small Q1 2.142 1.929 1.462 1.060 0.543 Q2 2.992 1.870 1.295 0.716 0.559 Q3 2.179 2.114 0.835 0.747 0.953 Q4 1.997 1.262 0.556 0.429 0.484 Large Q5 1.172 0.917 0.561 0.330 0.472
Panel B: Average Adjustment Factor for model in CT ( θCT)
Q1 Q2 Q3 Q4 Q5 Small Q1 2.075 2.054 1.663 1.262 0.676 Q2 3.086 2.256 1.569 0.895 0.734 Q3 2.429 2.448 1.098 0.978 1.022 Q4 2.309 1.730 0.830 0.602 0.695 Large Q5 1.559 1.468 0.867 0.514 0.732
Panel C: Average Adjustment Factor for model in Easton (2004) ( θmpeg) Q1 Q2 Q3 Q4 Q5 Small Q1 1.368 1.403 1.141 0.823 0.408 Q2 2.141 1.439 1.055 0.589 0.479 Q3 1.697 1.712 0.757 0.658 0.812 Q4 1.565 1.046 0.496 0.389 0.436 Large Q5 0.970 0.821 0.508 0.291 0.433
Table contains the adjustment factors
)1)(1()1/()(
22
αασθ ε
grgrr
−+−+−
=
evaluated at the implied cost of capital that solves the valuation equation )())(1( rVrP tt θ+=
where Vt(r) is value of the firm as given by either GLS, CT, Easton (2004) models (see section 4 of the paper for more details on each model); r is the implied cost of capital metrics; g is expected growth rate in prices set to long run conservative inflation rate of 3%; α is autoregressive parameter in the equilibrium rate of return set equal to 0.75.
Subscripts GLS, CT, and rmpeg next to r refer GLS, CT and Easton’s models used, respectively, to express Vt(r) in terms of residual (or economic) income instead of dividends). The adjusted implied cost of equity calculated when θ(r) is varies across 5×5 size and book-to-market quintiles based on σε2 estimate.
The data is taken form the intersection of I/B/E/S, CRSP and COMPUSTAT. Availability of I/B/E/S data limits the sample to 1981-2003. Cost of equity estimates less than 3% (conservative inflation rate estimate) are censored and the observations with cost of capital more than 50% are left out form the analysis. Further I restrict the sample to the set on non-missing observations across all the 9 different types of cost of capital estimates.
155
T a
b l
e 6
A
djus
ted
vs. S
tand
ard
Equ
ity R
isk
Prem
ia: S
ize
and
B/M
Qui
ntile
s
Si
ze
B/M
B/M
B/M
A
1: r G
LS -r
f
A2:
r CT -r
f
A3:
r mpe
g -r
f
Lo
w
Hig
h
Low
H
igh
Lo
w
Hig
h Sm
all
3.27
2.
82
3.02
3.
38
4.44
4.83
3.
76
3.51
3.
78
4.78
8.90
6.
92
6.64
7.
40
9.18
1.94
2.
29
2.69
3.
19
3.85
3.12
3.
00
3.05
3.
35
3.84
5.47
5.
53
5.78
6.
43
7.29
1.94
2.
23
2.43
2.
90
3.90
2.84
2.
81
2.81
3.
06
4.14
4.83
4.
84
4.74
5.
54
7.00
1.53
1.
76
2.09
2.
76
3.59
2.36
2.
22
2.40
2.
76
3.49
3.89
4.
08
4.32
5.
29
6.71
Standard
Larg
e 1.
15
1.36
1.
95
2.47
3.
34
1.
83
1.94
2.
46
2.75
3.
12
2.
83
3.28
4.
15
4.67
5.
91
B1
: sb
mG
LSr
-rf
B2
: sb
mC
Tr
-rf
B3
: sb
mm
peg
r -r
f
Smal
l 9.
55
8.78
8.
18
7.70
7.
02
11
.49
9.96
8.
80
8.12
7.
47
15
.97
13.4
5 12
.04
11.7
7 11
.68
9.
07
7.85
7.
21
6.37
6.
54
10
.74
8.58
7.
41
6.33
6.
47
13
.48
11.3
9 10
.28
9.44
9.
81
7.
22
8.08
5.
60
6.13
8.
43
8.
12
8.65
5.
57
6.01
8.
66
10
.44
10.9
6 7.
63
8.51
11
.37
6.
20
5.51
4.
05
4.82
5.
97
6.
93
5.58
3.
95
4.41
5.
60
8.
77
7.79
6.
05
7.03
8.
79
Corrected
Larg
e 3.
55
3.75
4.
03
3.94
5.
50
3.
98
3.90
4.
04
3.85
5.
02
5.
24
5.48
5.
91
5.89
7.
81
C
1:
sbm
GLS
r- r
GLS
C2:
sb
mC
Tr
- rCT
C3:
sb
mm
peg
r- r
mpe
g
Smal
l 6.
28
5.96
5.
16
4.31
2.
58
6.
65
6.20
5.
28
4.34
2.
69
7.
07
6.52
5.
41
4.37
2.
50
7.
13
5.56
4.
52
3.18
2.
69
7.
62
5.58
4.
36
2.98
2.
64
8.
01
5.86
4.
51
3.01
2.
52
5.
28
5.85
3.
17
3.23
4.
53
5.
27
5.84
2.
76
2.95
4.
51
5.
61
6.12
2.
89
2.96
4.
37
4.
67
3.76
1.
97
2.06
2.
39
4.
57
3.36
1.
56
1.65
2.
11
4.
88
3.71
1.
73
1.75
2.
08
Difference
Larg
e 2.
40
2.39
2.
08
1.47
2.
16
2.
15
1.95
1.
58
1.10
1.
90
2.
41
2.20
1.
76
1.22
1.
90
This
tabl
e pr
ovid
es im
plie
d eq
uity
pre
mia
(def
ined
as
cost
of e
quity
esti
mat
es a
vera
ged
min
us th
e ris
k fre
e ra
te) a
cros
s 3
stand
ard
and
3 ad
juste
d m
odel
s as
w
ell a
s the
ir di
ffere
nce
calc
ulat
ed o
ver 5×5
Siz
e an
d Bo
ok-to
-Mar
ket q
uint
iles.
The
impl
ied
cost
of c
apita
l is c
ompu
ted
solv
ing
the f
ollo
win
g m
odel
156
)(
))(
1(r
Vr
Pt
tθ+
= ,
)1)(
1()
1/()
(2
2
αα
σθ
ε
gr
gr
r−
+−
+−
=
whe
re V
t(r) i
s val
ue o
f the
firm
as g
iven
by
eith
er G
LS, C
T, E
asto
n (2
004)
(or a
ny o
ther
disc
ount
ed c
ash
flow
/div
iden
ds) m
odel
s (se
e se
ctio
n 4
of th
e pa
per f
or
mor
e de
tails
on
each
mod
el);
r is t
he im
plie
d co
st of
cap
ital m
etric
s; g
is ex
pect
ed g
row
th ra
te in
pric
es se
t to
long
run
cons
erva
tive
infla
tion
rate
of 3
%; α
is
auto
regr
essiv
e pa
ram
eter
in th
e eq
uilib
rium
rate
of r
etur
n se
t equ
al to
0.7
5.
Pa
nels
A1-
A3
prov
ide
the
impl
ied
equi
ty p
rem
ia fo
rm th
e sta
ndar
d m
odel
s, w
hich
restr
ict θ
(r) t
o ze
ro. S
ubsc
ripts
GLS
, CT,
and
rmpe
g ne
xt to
r re
fer G
LS,
CT a
nd E
asto
n’s m
odel
s use
d, re
spec
tivel
y, to
exp
ress
Vt(r
) in
term
s of r
esid
ual (
or e
cono
mic
) inc
ome
inste
ad o
f div
iden
ds. P
anel
s B1-
B3 c
onta
in th
e ad
juste
d im
plie
d eq
uity
pre
mia
esti
mat
es, w
here
θ(r
) is a
llow
ed to
var
y ac
ross
5×5
size
and
boo
k-to
-mar
ket d
ecile
s bas
ed o
n w
ithin
indu
stry
varia
nce
of th
e in
nova
tions
in
the e
quili
briu
m ra
te o
f ret
urn
''
11
2e
eΓΣΓ
=εσ
. Pan
els C
1-C3
giv
e the
bia
s in
the i
mpl
ied
equi
ty p
rem
ia ca
lcul
ated
as t
he d
iffer
ence
bet
wee
n pa
nels
B1-B
3 an
d A
1-A
3.
A
naly
sts’ c
onse
nsus
fore
casts
form
I/B/
E/S
and
histo
rical
CO
MPU
STA
T da
ta a
re u
sed
to p
redi
ct fu
ture
ear
ning
s, di
vide
nds a
nd b
ook
valu
es re
quire
d by
the
resid
ual i
ncom
e m
odel
s. D
ivid
end
payo
ut ra
tions
are
cal
cula
ted
base
d on
3 y
ears
of h
istor
ical
dat
a. I
cons
ider
obs
erva
tions
with
EPS
1 for
ecas
t gre
ater
or e
qual
th
an E
PS2 f
orec
ast a
s req
uire
d by
mod
el in
Eas
ton
(200
4); a
dditi
onal
ly I
restr
ict t
o po
sitiv
e EP
S 2 fo
reca
st us
ed to
inte
rpol
ate
earn
ings
into
the
futu
re.
Fore
casti
ng fu
ture
ear
ning
s in
GLS
mod
el a
ssum
es fu
ture
retu
rn o
n eq
uity
dec
ays t
owar
ds th
e in
dustr
y m
edia
n RO
E ov
er 1
2 ye
ars.
I cal
cula
te m
edia
n RO
E fo
r eac
h in
dustr
y an
d ea
ch y
ear u
sing
10 y
ear m
ovin
g w
indo
w e
xclu
ding
loss
firm
s. M
odel
in C
T as
sum
es p
erpe
tual
gro
wth
rate
in re
sidua
l inc
ome
starti
ng
from
yea
r 5. T
his g
row
th is
ass
umed
to b
e th
e ex
pect
ed in
flatio
n ra
te se
t equ
al to
3%
. A
naly
sts fo
reca
sts a
re m
easu
red
in th
e mid
dle
of th
e fo
urth
mon
th a
fter
the
fisca
l yea
r end
. Pric
es a
re m
easu
red
at th
e en
d of
the
four
th m
onth
afte
r the
fisc
al y
ear e
nd to
mak
e su
re th
e ac
coun
ting
info
rmat
ion
is pu
blic
ly a
vaila
ble.
Ava
ilabi
lity
of I/
B/E/
S da
ta li
mits
the
sam
ple
to 1
981-
2003
. Cos
t of e
quity
esti
mat
es le
ss th
an 3
% (c
onse
rvat
ive
infla
tion
rate
esti
mat
e) a
re c
enso
red
and
the
obse
rvat
ions
with
cos
t of c
apita
l mor
e th
an 5
0% ar
e le
ft ou
t for
m th
e an
alys
is. F
urth
er I
restr
ict t
he sa
mpl
e to
the
set o
n no
n-m
issin
g ob
serv
atio
ns a
cros
s all
the
9 di
ffere
nt ty
pes o
f cos
t of c
apita
l esti
mat
es.
157
T a
b l
e 7
Cor
rela
tions
Am
ong
Diff
eren
t Im
plie
d C
ost o
f Cap
ital p
roxi
es
The
tabl
e co
ntai
ns th
e co
rrel
atio
ns b
etw
een
vario
us im
plie
d co
st of
cap
ital m
etric
s. Fi
rst t
hree
mea
sure
s are
cal
cula
ted
usin
g va
riatio
ns o
f res
idua
l in
com
e m
odel
bas
ed o
n G
LS, C
T an
d Ea
ston
2004
resp
ectiv
ely.
Sec
ond
3 m
easu
res a
re c
alcu
late
d us
ing
the
adju
stmen
t fac
tor w
hich
var
ies o
ver
48 F
ama
and
Fren
ch (1
997)
indu
stry
grou
ps d
epen
ding
on
the
estim
ated
var
ianc
e of
the
inno
vatio
ns o
f the
equ
ilibr
ium
rate
of r
etur
n. T
he la
st 3
mea
sure
s are
bas
ed o
n th
e adj
ustm
ent f
acto
r tha
t var
ies a
cros
s 5×5
size
and
book
-to-m
arke
t dec
iles.
r G
LS
r CT
r mpe
g ff G
LSr
ff C
Tr
ff m
peg
r
sbm
GLS
r
sbm
CT
r
sbm
mpe
gr
r GLS
1.
000
r CT
0.73
2 1.
000
r mpe
g 0.
649
0.68
8 1.
000
ff GLS
r
0.82
2 0.
673
0.64
7 1.
000
ff C
Tr
0.
622
0.91
4 0.
645
0.78
3 1.
000
ff mpe
gr
0.
582
0.64
4 0.
954
0.74
8 0.
718
1.00
0
sbm
GLS
r
0.81
4 0.
719
0.63
0 0.
743
0.65
8 0.
600
1.00
0
sb
mC
Tr
0.
603
0.91
6 0.
615
0.59
6 0.
882
0.60
0 0.
812
1.00
0
sbm
mpe
gr
0.
585
0.67
4 0.
950
0.62
1 0.
658
0.92
7 0.
744
0.72
2 1.
000
158
implies that adjusting for uncertainty improves the ability of different implied cost of capital metrics to
capture the underlying construct.
5.6. Future work
In this section, I extend the model by allowing innovations in expected returns to correlate with the
changes in dividends (or cash flows). An analytically convenient approach is to use continuous
compounding and to assume normal distribution for changes in expected returns (and dividend growth). In
this case expected return at time t is given by:
+ ++
t
tttt P
DPErexp 11=)( (24)
Assuming the transversally condition is met and iterating the expression (24) yields the following
expression for the price of a security115
−∏∑−∞
t
t
tDrexpEP )(=
1
0=1=00 τ
τ (25)
In order for the correlation of time varying expected returns and future cash-flows (dividends) to be
incorporated, it is necessary to assume an evolution tD (in addition to assuming a stochastic process for
tr ). Following Ang and Liu (2004) dividends are assumed to grow at logarithmic growth rate
)/(= 11 ttt DDlng ++ . Both tg and tr are assumed to follow Gaussian AR(1) processes:
ttt rr εαρα ++− −1)(1= (26)
ttt ggg υββ ++− −1)(1= (27)
where )(0,~ 2εσε Nt , )(0,~ 2
υσυ Nt and ευσυε =),( ttCov .
It can be shown that under these assumptions equation (25) can be rewritten as
)(,= 0
1
0=
1
0=0
1
0=0
1=0 t
ttt
tDEgrCovexprexpEP
−
− ∑∑∑∑−−−∞
ττ
ττ
ττ
(28)
As Appendix B shows, calculating the expectation and covariance yields the following expression
)(= 01=
0 tttt
DEtttexpP Ψ−Ω+−∑∞
ρ (29)
where
,11
21
111
21
)(1= 2
2
2
2
−−+
−−−
−Ω
αα
αα
ασ ε tt
t tt (30)
115see also Ang and Liu (2004)
159
)
1))(1(1
1))(1(1
1)((1))(1)(1(1
=
ββαβ
ααβα
βαβααββααβ
σ ευ
−−−−
−−−−
−−++−−−−
Ψ
tt
ttttt t
t (31)
Notice that if ρ=tr for any t , i.e. cost of capital is deterministic, above result reduces to standard
dividend discount formula. This representation has the same form as equation (10) we saw earlier as (29)
can be written as
001=
0 )(= QDEtexpP tt
+−∑∞
ρ (32)
where )(=0 ttexpQ tt Ψ−Ω
Equation (29) can also be stated as
TVDEtttexpP ttt
T
t+Ψ−Ω+−∑ )(= 0
1=0 ρ (33)
where
)(=
)(=
01=
01=
TtttTt
tttTt
DEtgttttexp
DEtttexpTV
∆++Ψ−Ω+−
Ψ−Ω+−
∑
∑∞
+
∞
+
ρ
ρ (34)
and g is the long run expected dividend growth rate and t∆ captures the volatility of dividend
growth. As time t increases →∆ΨΩ ,, ttt ,, ∆ΨΩ . In this case the terminal value may be calculated
in a closed form: 116
1)1)((
)(= 0
−∆−−Ψ+Ω−+− gTexpDETV T
ρ (35)
where 22 )/2(1= ασε −Ω , ))(1/(1= βασευ −−Ψ , 2)/2(1= βσυ −∆ .
5.7. Conclusions
This paper demonstrated that uncertainty about the future expected returns will be reflected by the
stock price and needs to be taken into account by the valuation models. A failure to account for this type of
uncertainty will result into (i) a downward bias in firm value, as yielded by standard valuation models; (ii) a
downward bias in the implied cost of equity capital.
The bias in the implied cost of capital is economically significant and is about 3.5% at the economy
level. In addition, this bias varies with firm-specific characteristics and the investment opportunities set.
The bias is considerably more pronounced in volatile industries and for small firms with large growth
116Otherwise numerical integration is a more precise alternative.
160
opportunities. The findings suggest an explanation for why prior empirical literature found that the implied
equity premia are smaller than their historical counterparts. In addition, preliminary evidence suggests that
the cost of capital measures derived here are more reliable than the measures derived from the standard
valuation models.
The implied cost of capital is a widely used summary measure. The model to calculate the implied
cost of capital proposed here is analogous to the traditional valuation models used in the literature with the
only difference that it includes an adjustment factor for the uncertainty about future expected returns. This
model is straightforward to implement and is of interest to practitioners and empirical researchers in
economics, finance and accounting.
A straightforward step for future research is to evaluate ability of the model proposed here to predict
firm's value (or fundamental value) and compare it with other valuation models used in practice.
5.8. References
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161
Fama, E., F., French, K.,R., 1993, Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3-56.
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5.A. Appendix A
The elements of the Hessian matrix evaluated at ρ , ρ|'0
2
RRVH∂∂∂≡ are given by
)(1=|'
= =2),(max=
02
jitt
jitijij Id
RRVh +
∂∂∂
+
∞
∑ ρρ (36)
where .I is an indicator function.
Also, note that )(=),( ts
stt RVarRRCov α+ where the variance is unconditional. Therefore, under
the assumption that expected returns are uncorrelated with dividends, we may write
( ) ( ) )('21='
21= 0
||00 tijij
ji RVarhEHGGEQ ll −α (37)
162
where l is a column of ones.
From (11) and the law of iterated expectations it follows that we may write
)(1
= 1),(max1),(max01),(max=
0 −−+ −+
jijijiji
ij QPEI
hEρ
(38)
Thus 0Q is the sum of the elements of the following matrix times one half of the unconditional
variance of tR (here td stands for expected dividends to simplify notation)
++++
+++++++
+++++++++
++++++++++
OMMMM
......)(...)(...)(...)(
......)(2...)(...)(...)(
......)(...)(2...)(...)(
......)(...)(...)(2...)(
......)(...)(...)(...)(2
1
551
552
553
554
55
440
55
441
55
442
55
443
55
441
55
44
330
55
44
331
55
44
332
55
442
55
44
331
55
44
33
220
55
44
33
221
55
443
55
44
332
55
44
33
221
55
44
33
2210
2
ρα
ρα
ρα
ρα
ρρα
ρρα
ρρα
ρρα
ρρα
ρρρα
ρρρα
ρρρα
ρρα
ρρρα
ρρρρα
ρρρρα
ρρα
ρρρα
ρρρρα
ρρρρρα
ρ
dddd
dddddddd
ddddddddddd
ddddddddddddd
dddddddddddddd
(39)
Substituting this back into (39) we may obtain the following convenient representation of 0Q
)()(2)()(
)()(2)(
)()()(2
'2
1=222
0
222
1
222
2
222
1
111
0
111
1
222
2
111
1
000
0
020 tRVarQPQPQP
QPQPQP
QPQPQP
EQ l
OMMM
K
K
K
l
−−−
−−−
−−−
ρα
ρα
ρα
ρα
ρα
ρα
ρα
ρα
ρα
ρ (40)
First, sum the elements that have the same tP and note that ααα−− +
∑ 11=
1
0=
ktk
t. Thus we have
1))((1)(1
)(=
)(1)(1
)(=
0
1
0=2
0
1
0=20
−−−
−−
−+∞
+∞
∑
∑
t
ttt
t
t
t
ttt
t
t
t
QPQERVar
QPERVarQ
ρα
αρ
ρα
αρ (41)
The value of tQ must be proportional to price tP as tQ is proportional to the stream of future
expected dividends. This implies that the ratio tt QPq /= is constant and can be replaced by the ratio
00/QP .
163
1))((1)(1
)(=0
00
1
0=20 −−−
+∞
∑ QPQERVarQ tt
t
t
t
ρα
αρ (42)
Assuming tQ grows at rate g+1 , we have tt gQQ )(1= 0 + and thus we may write:
)())(1))((1(
)(=
)()(1)(1)(1
)(=
)()(11)(1
)(=
00
002
00
1
0=20
QPgg
RVar
QPgg
RVar
PQgRVarQ
t
t
tt
t
t
t
−+−+−
−
+−
−+−−
−+−−
+∞
∑
αρρ
αραρ
ρρ
αρ
ρα
αρ
(43)
Thus 0Q is given by the following formula
00 1= PQ
θθ+
(44)
and firm value is given by
ttt
tt PdEP
θθ
ρττ
τ ++−
∞
+∑ 1
=1=
(45)
where ))(1))((1(
)(=αρρ
θgg
RVar t
+−+− depending on whether we assume g .
5.B. Appendix B
By exploiting normal distribution, equation (25) can be expressed as
)(=
)(),(
)(21)(=
)()),(()(=
01=
0
1
0=
1
0=0
1
0=0
1
0=0
1=
0
1
0=
1
0=0
1
0=0
1=0
tttt
t
tt
tt
t
t
ttt
t
DEtttexp
DEgrCov
rVarrEexp
DEgrCovexprexpEP
Ψ−Ω+−
−+
−+−
−−
∑
∑∑
∑∑∑
∑∑∑∑
∞
−−
−−∞
−−−∞
ρ
ττ
ττ
ττ
ττ
ττ
ττ
ττ
(46)
In order to demonstrate the last equality we need to calculate )( 1
0=0 ττrE t∑ −− , )( 1
0=0 ττrVar t∑ −− ,
),( 1
0=
1
0=0 ττττgrCov tt ∑∑ −−− . This is done next.
First note that
ss
sLLr −
−−− ∑+−+−− τ
τ
ττ εαρεαραα1
0=
11 =)(1)(1)(1= (47)
164
and that
ss
t
s
tt
tr −
−−−
∑∑∑ + ττ
ττ
εαρ1
0=
1
0=
1
0== (48)
thus it follows that
ttErE ss
t
s
tt
ρεαρ ττ
ττ
==1
0=
1
0=0
1
0=0
+
−
−−−
∑∑∑ (49)
Second, note that
2
221
0=00 1
)(1==)(αασεα ε
τ
τ −−
−
−
∑t
sts
sVarrVar (50)
and
2
||2(2
0||
1
0=
1
0=00
1))(1=)(=
,=),(
ααασα
εαεα
ντντε
ντντ
ντ
ντ
−−
−∧
∧−
−
−
−
−
∑∑
rVar
CovrrCov sts
sst
s
s (51)
this allows us to compute the following variance
−−+
−−−
−Ω
Ω≡
−−+
−−−
−
−−−++
−−+−
−+
−
−−−
−−
−−
−−−
−+
−−−
−
−
−−−
−+
−−−
−
−−−
−−+
−−−
−
−+
−−−
−
−+
−−−
−
−+−−
−−
∑∑
∑∑
∑∑∑∑
∑∑∑∑
∑∑∑
∑∑
∑∑∑∑∑
−−
−
−
−−
−−−
−−
+−−
−−−
−−−−
∧−−−
−−−−−
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
21
0=
1
0=2
2
2
2
1
0=1
1
0=2
2
2
2
1
0=
1
0=
1
0=
1
0=2
2
2
2
1
0=
1
0=
1
0=
1
0=2
2
2
2
21
0=
1
0=
21
0=2
2
)2(||1
0=
1
0=2
2
0
1
0=
1
0=
1
0=
1
0=0
1
0=0
11
21
111
21
)(1=
211
112
)(1=
))(1(1))(1(1
)(1))(12(1
11
1=
)11
11(
12)
11(
12
11
1=
)(1
2)(112
11
1=
112
112
11
1=
2211
1=
2211
1=
)(12)(11
=
)(11
=
),(=,=
αα
αα
ασ
αα
αα
ασ
αααα
ααα
αα
ασ
αα
αα
ααα
αα
αα
ασ
ααα
ααα
αα
ασ
ααα
ααα
αα
ασ
αααααα
ασ
αααα
ασ
αααασ
ααασ
ε
ε
ε
ε
ττ
τ
τ
τ
ε
ττ
τ
ττ
τ
ε
ντ
ν
τ
τ
ντ
ν
τ
τ
ε
νττ
ντ
νττ
ντ
ε
ννττ
ντ
τ
τ
ε
ντντ
ντ
ε
ντνν
νν
ττ
ττ
tt
t
t
tt
tt
tttt
ttt
ttt
ttt
ttt
tt
tt
ttttt
tt
tt
t
tt
t
t
t
t
rrCovrrCovrVar
(52)
Finally, note that
165
ντ
τττνευ
ντ
ννντευ
νττττν
ντννντ
ντ
ντ
αββαβσ
αββαασ
βα
υβεα
<
<00
1
0=
1
0=00
1)(1
1)(1=
),(),(=
,=),(
II
IgrCovIgrCov
CovgrCov sts
sst
s
s
−−+
−−
+
−
≥
−
−≥
−
−
−
−
−
∑∑ (53)
which allows to calculate the following:
t
t
t
t
tt
t
t
t
t
II
grCovgrCov
t
tt
tttt
tttttt
tttt
tttttt
tt
tttt
tttttt
tttttt
tttttt
ttt
tt
tttt
Ψ≡−−−−
−−−−
−−++−−−−
−−−
−−−
−−−++
−−−+
−−−
−
−−−
−−
−−
−−−
−+
−−−
−−
−−
−−−
−+
−−−
−
−−
−−−
+
−−
−−−
+−−−
−
−−−
−−+
−−−
−−+
−−−
−
−+−+
−−−
−
−+−+
−−−
−
−+−+−−
−−+
−−
∑∑
∑∑
∑∑∑∑
∑∑∑∑∑∑∑∑
∑∑∑∑∑∑∑∑
∑∑∑∑∑
∑∑
∑∑∑∑
−−
−−
−
−
−−−
−
−−
−−−
−−−−−−
−−−
−−−−−
−−
−−−
−−−−
−
≥
−−−
−−−−
)1
))(1(11
))(1(1
1)((1))(1)(1(1
=
))(1
)(1)(1
)(1))(1(1
2))(1(1
1))(1(1
1(1
=
))1
111(
11)
11(
1
)1
111(
11)
11(
111(
1=
))(1
1)(11
)(1
1)(111
1(1
=
11
11
11
11
11
1=
11
1=
11
1=
)(1)(1)(11
=
1)(1
1)(1=
),(=,
22
1
0=
1
0=
1
0=
1
0=
1
0=1
1
0=
1
0=1
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
1
0=
<
1
0=
1
0=
0
1
0=
1
0=
1
0=
1
0=0
ββαβ
ααβα
βαβααββααβ
σβββ
ααα
βαβα
βαβα
βααβ
αβσ
αββα
ββ
αββ
ββ
αββα
αα
βαα
αα
αββα
αβσ
βαβα
βββ
βααβ
ααα
αββα
αβσ
ααβ
βββ
ββα
ααα
αββα
αβσ
αββββααααββα
αβσ
βαββαααββα
αβσ
βαββααβααβσ
αββαβσ
αββαασ
ευ
ευ
ευ
ννν
ν
ν
ν
τττ
τ
τ
τ
ευ
νν
ν
νν
ν
ττ
τ
ττ
τ
ευ
τν
τ
ν
ν
τν
τ
ν
ν
ντ
ν
τ
τ
ντ
ν
τ
τ
ευ
ντν
τν
τνν
τν
νττ
ντ
νττ
ντ
ευ
τττνν
τν
νννττ
ντ
ττ
τ
ευ
ντ
τττνευ
ντ
ννντευ
νν
ντνν
νν
ττ
(54)
This completes the derivation of equation (46).
