NET OPERATING ASSETS AS A PREDICTOR
FOR FUTURE STOCK RETURNS
-----AN INDUSTRY ANALYSIS
DISSERTATION
Presented in Partial Fulfillment of the Requirement for
The Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Yinglei Zhang, M.A.
****
The Ohio State University
2005
Dissertation Committee:
Professor Siew Hong Teoh, Advisor
Approved by
Professor Anne Beatty
Professor Kewei Hou
Professor Douglas Schroeder
_______________________________
Advisor
Graduate Program in Accounting and MIS
ABSTRACT
Hirshleifer et al. (2004) argue that scaled Net Operating Assets (NOA) measure the
extents to which operating/reporting outcomes provoke excessive investor optimism.
In this paper, I argue that at least part of the information conveyed by NOA is
industry common and cannot be diversified away when forming industry portfolios
conditioning on NOA. If investors do not see through NOA that come in part from
inter-industry differences, then investor misperceptions should be related to both the
industry and the firm-specific components of NOA. Consistent with this hypothesis,
in the 1964-2002 sample, both the cross industry and the within industry components
of NOA are strong negative predictors for future stock returns. In contrast, I find that
the Accruals effect of Sloan (1996) comes entirely from the industry-adjusted
component of Accruals. The industry NOA trading strategy survives the statistical
arbitrage test introduced by Hogan et al. (2004), which is designed to distinguish
between risk premium and mispricing explanations. I also examine the importance of
the time series aggregation property of NOA and its inclusion of investment
information, and provide evidence that the industry NOA effect is independent of the
industry price momentum effect (Moskowitz and Grinblatt, 1999), and it is not driven
by the clustering of either new equity issuance or M&A activities within industries.
ii
To my parents, Dacheng Zhang and Shuxian Liu and my husband, Guang Yang
iii
ACKNOWLEDGMENT
I am deeply grateful to my advisor, Siew Hong Teoh, for her intellectual
support, encouragement ,and on-going enthusiasm in research at every step of my
program. I also wish to thank the other members of my committee, Anne Beatty,
Kewei Hou and Douglas Schroeder, for their stimulation, helpful comments, and
valuable time spent with me. Finally, I thank my parents and my husband for their
love, their emotional support and their patience.
iv
VITA
May 13, 1974
Born—Harbin, Heilongjiang Province, China
1993-1997
B.A. Economics, Nan Kai University
Tianjin, China
1997-1998
Credit Analyst,
Banque Nationale de Paris, Tianjin Branch
Tianjin, China
1998-2000
M.A. Economics,
The Ohio State University, Columbus, Ohio
2000-2005
Graduate Teaching and Research Associate,
The Ohio State University
Columbus, Ohio
PUBLICATION
Do Investors Overvalue Firms with Bloated Balance Sheets? Journal of Accounting
and Economics (2004) (With D. Hirshleifer, K. Hou and S. H. Teoh)
FIELDS OF STUDY
Major Field: Accounting and Management Information System
Minor Field: Microeconomics and Econometrics
v
TABLE OF CONTENTS
Page
Abstract………………………………………………………………………………..ii
Dedication………………………………………………………………………….....iii
Acknowledgment……………………………………………………………………..iv
Vita……………………………………………………………………………...…….v
List of Tables…………………………………………………………………………ix
List of Figures……………………………………………………………………..…xi
Chapters:
1.
Introduction…………………………………………………………..………..1
2.
Industry NOA as a Misperception Index………………………………….. ..11
2.1
2.2
2.3
2.4
3.
Efficient Market Hypothesis and Behavioral Finance……………….11
Limited Attention and the NOA Effect………………………………14
Industry Variations of NOA and Future Stock Returns………...........18
2.3.1 What Causes Cross Industry Variations of NOA?…………...18
2.3.2 The Industry Common Component of NOA
and Future Stock Returns………………………………….…20
The Industry Adjusted Component of NOA and Future
Stock Returns……………………………………………….…….….24
Sample Selection and Descriptive Data…………………………..………….28
3.1
3.2
3.3
3.4
Sample …………………………………………………………….....28
Industry Classification…………………………………………….. ..28
Financial Variable Measurement………………………………….....29
Calculation of Abnormal Returns………………………….………..31
vi
3.5
4.
Empirical Tests……………………………………………….……………...43
4.1
4.2
4.3
5.
The Persistence of Industry NOA Strategy………………………......67
The Sharpe Ratio……………………………………………………..67
The Statistical Arbitrage Test………………………………………..68
The Industry NOA Strategy and The Business Cycle……………….72
Robustness Analyses and Discussion…………………………………...…...79
6.1
6.2
6.3
6.4
7.
The Implications of Industry NOA and Industry Accruals
for Future Industry Earnings…………………………….…………...43
Portfolio Tests…………………………………………..……………44
4.2.1 Industry Portfolio Tests………………….............…………...44
4.2.2 Random Industry Portfolio Tests………….………...….……49
4.2.3 Industry-Adjusted Profits…………………….…….…….…..51
The Fama-Macbeth Regression Tests...……………….…….….……53
Mispricing or Risk?..........................................................................................66
5.1
5.2
5.3
5.4
6.
Descriptive Statistics………………………………………………....32
Sample Selection Bias and the Influence of Extreme Stock Returns..80
6.1.1 Sample Selection Bias…………………………………….….80
6.1.2 The Impact of Influential Observations….…………………..81
The Influence of Transaction Costs and Small Size Firms……….….82
6.2.1 The Influence of Transaction Costs………………..…...........82
6.2.2 The Influence of Small Size Firms…………………….…….84
Are Industry NOA and Industry Accruals One Effect or Two?..........86
Is the Industry NOA Effect Driven by the Cluster of Equity
Issuance and Merge and Acquisition Activities?.................................88
Conclusion…………………………………………………………………...94
Appendices A
A.1
A.2
A.3
Supplementary Tables……………………………………….97
Definition of Industry Classification………………………………...98
Alternative Industry Classification—Portfolio Tests……………….100
Alternative Industry Classification—Regression Tests…………….102
vii
Appendices B
B.1
B.2
Technical Notes…………………………………………….103
The Fama-Macbeth Monthly Cross-Sectional
Regression Procedure……………………………………………….104
Independent Double Sorts vs. Sequential Double Sorts…..……......107
References…..……………………………...………………………………….……112
viii
LIST OF TABLES
Table
Page
Table 3.1
Mean Values of Industry Characteristics
for Each Industry Portfolio…………………………………….….…36
Table 3.2
Frequency of an Industry in Extreme Industry NOA and
Industry Accruals Portfolio and the Intra-Industry NOA
and Intra-Industry Accruals Strategies..………………………..……39
Table 3.3
Mean Values of Industry Characteristics for Portfolios Sorted by
Industry NOA and Industry Accruals …………….…………………41
Table 3.4
Pearson (Spearman) Correlation Coefficients above (below)
the Diagonal………………………………………………………….42
Table 4.1
The Implications of Current Industry NOA and Industry Accruals
for Future One to Four Year ahead Industry Earnings ……………...56
Table 4.2
Average Monthly (Abnormal) Returns for Portfolios Sorted
by Industry NOA, Industry Accruals, Random Industry NOA
and Random Industry Portfolios One Year after the
Portfolios’ Formation……...……………………………...………….57
Table 4.3
Average Monthly (Abnormal ) Returns for Portfolios Sorted
by Industry-adjusted NOA, Industry-adjusted Accruals, NOA
and Accruals One Year after the Portfolios’ Formation………….....59
Table 4.4
Fama-Macbeth Monthly Regressions of Stock Returns on
Industry NOA, Industry Adjusted NOA, Industry Accruals,
Industry-Adjusted Accruals and other Characteristics……………....61
Table 4.5
Fama-Macbeth Monthly Regressions of Industry Portfolio
Returns on Industry NOA, Industry Accruals and Other
Industry Characteristics……………………………………………...63
ix
Table 5.1
The Constrained Mean Statistical Arbitrage Test……….…..……….76
Table 5.2
Regression of 12-Month ahead Growth in GDP on 12-month
Compounded Hedge Returns of Industry NOA Strategy and
Fama-French Factors………………………………..……………….77
Table 6.1
Average Monthly Raw Returns for Portfolios Sorted First by
Industry Size, then by Industry NOA One Year after the Portfolios’
Formation…………………………………………..………………...90
Table 6.2
Average Abnormal Monthly Returns for Portfolios Sorted by
Industry NOA and Industry Momentum Simultaneously One
Year after the Portfolios’ Formation …………………………...……91
Table 6.3
Average Abnormal Monthly Returns for Portfolios Sorted by
Industry NOA for Equity Issuance and/or M&A vs. NonEquity Issuance and/or M&A Sub-Sample One Year after the
Portfolios’ Formation………………………………..………….……92
Table A.1
Definition of Industry Classification……………..………………….98
Table A.2
Alternative Industry Classification—Portfolio Tests……………….100
Table A.3
Alternative Industry Classification—Regression Tests…….………102
x
LIST OF FIGURES
Figure
Page
Figure 4.1
Time-Series Property of Average Abnormal Returns
for the Highest vs. the Lowest Industry NOA Portfolios……………64
Figure 4.2
Time-Series Property of Average Abnormal Returns
for the Highest vs. the Lowest Industry Accruals Portfolios………...65
Figure 5.1
The Persistence of Industry NOA and Industry Accruals
Strategy………………………………………………………………78
xi
CHAPTER 1
INTRODUCTION
The Statement of Financial Accounting Concept No.1 specifies that one of the
objectives of financial reporting is to provide information that is useful to current and
potential investors in making rational investment decisions. Implicit in this objective is an
overall societal goal of facilitating the efficient functioning of capital markets. How
efficiently investors use financial statement information affects how efficiently resources
are allocated in the economy, and is therefore an important concern for accounting
regulators when setting reporting standards. A large body of empirical research has, by
now, documented that accounting variables predict stock returns.1 If risk effects are
adequately controlled for in these studies, these results suggest that investors do not
process accounting information efficiently.
In this study, I focus on two of these variables, accruals and net operating assets.
1
See Ou and Penman (1989a and b), Bernard and Thomas (1989), Abarbanell and Bushee (1991), Lev and
Thiagarajan (1993), Sloan (1996), Frankel and Lee (1998), Teoh, Welch, and Wong (1998a and b),
Fairfield, Whisenant, and Yohn (2003), Hirshleifer et al. (2004), as well as the comprehensive surveys of
Kothari (2000), and Daniel, Hirshleifer, and Teoh (2002).
1
Sloan (1996) reports annual abnormal profits of about 10%, using a trading strategy
based on operating accruals, and Hirshleifer, Hou, Teoh and Zhang (2004) report
abnormal profits of 15% (annualized), using a trading strategy based on net operating
assets. In this paper, I examine whether these abnormal profits derive from the firm
idiosyncratic or the common industry component of accruals and net operating assets.
Firms within an industry tend to be highly correlated in several respects: they
exhibit similar behaviors in business operations and accounting choices; they operate in
the same regulatory environments; they are similarly sensitive to macroeconomic shocks
and are exposed to similar supply and demand fluctuations. Therefore, a firm’s balance
sheet may be industry dependent for a number of reasons. First, industries are endowed
with different production functions and are characterized by various lengths of operating
cycles, which I define as the cash-accruals-cash conversion cycle.2 Second, industries are
subject to different guidance of accounting regulations such as the choice of capitalizing
vs. expensing. Moreover, firms within the same industry share similar economic shocks
and their balance sheets may contain information about the business environment that is
common to the industry. Choy (2003) documents that the level of net operating assets
(NOA) inversely predicts a firm’s ability to meet analyst’ forecasts (Barton and Simko,
2003), and the predictive ability of NOA largely derives from industry variations in net
operating assets.
2
In textbook presentations, the days of account receivables turnover plus the days of inventory turnover
minus the days of account payables turnover is a proxy for the cash-accruals-cash conversion cycle.
2
Industry analysis serves many useful purposes for both academics and
practitioners. Academics commonly seek out comparable firms from the same industry
and use industry averages or medians as benchmarks to isolate firm specific variables to
study. For example, Defond and Jiambalvo (1994) pioneer the use of a two-digit SIC
code benchmark to estimate discretionary accruals from a cross-sectional Jones model.
Many studies in the earnings management area have followed this path. Gebhardt et al.
(2000) assume that industry averages or medians are appropriate targets for the mean
reversion of various financial ratios. Soliman (2003) uses industry-adjusted ratios to
perform a Dupont analysis to improve the earnings forecast. In practice, investors use the
industry comparison method as a parsimonious way to value firms. When analysts
forecast essential variables, such as sales growth and profit margin ratios, they usually
apply comparable firms from the same industry as benchmarks.
In essence, all of the above research focus on the firm-specific components of the
accounting variables and assume that the industry common levels of these variables
represent some optimum. In other words, the strategic behavior being studied at the firm
level is presumed absent at the industry level, either because the average firm does not
engage in the behavior or individual firm’s actions within the industry offset each other.
The deviation from the industry average, therefore, is assumed to capture adequately the
behavior under study. Few studies look closely at the industry-wide variations of these
accounting variables. Whether the industry levels of these variables are indeed optimal
and whether they are well understood by investors hasn’t been formally investigated. One
of the objectives of this study is to fill this gap.
3
Several accounting anomalies have been explained based upon the premise that
investors are not able to fully assimilate the financial information available to them due to
their limited cognitive processing abilities (Hirshleifer and Teoh, 2003). A balance sheet
contains information beyond that contained in an income statement, which is useful for
evaluating the financial prospects of firms. Hirshleifer et al. (2004) argue that if investors
with limited attention anchor only on some salient cues (such as income statement
earnings), but fail to appreciate the rich information contained in both accounting value
added (operating income) and cash value added (free cash flow), then a parsimonious
variable derived from a balance sheet, net operating assets—defined as the difference
between all operating assets and all operating liabilities — measures the extent to which
operating/reporting outcomes provoke excessive investor optimism. They find that the
financial position of a firm with high net operating assets indicates a lack of sustainability
of recent good earnings performance. Consistent with their argument, they find that net
operating assets (scaled by lagged total assets)3 negatively predict future stock returns at
the firm level. I will refer to this finding as the NOA effect.
In this paper, I report robust evidence that both the industry common and the
firm-specific components4 of NOA are strong negative predictors of future stock returns
in a 1964-2002 sample. A trading strategy based upon buying the lowest industry NOA
portfolio and selling short the highest industry NOA portfolio is profitable at 0.73% per
3
I will refer to lagged total assets scaled net operating assets and operating accruals as NOA and Accruals
respectively in the rest of the paper.
4
I will use “industry-common”, “industry-wide” and ‘inter-industry” interchangeably throughout the paper
to refer to the equal average of an attribute within industry. I will also use “industry adjusted”, “firmspecific” and “intra-industry” interchangeably to refer to the difference between a firm’s attribute and its
corresponding industry common attribute.
4
month, highly significant, both economically and statistically. To ensure that the industry
effect is not spuriously driven by grouping firms based on the characteristics documented
to predict future returns at the firm level, namely NOA here, I adopt the random industry
portfolio test design (Moskowitz and Grinblatt, 1999) to isolate the key role of industries
in the industry NOA strategy. A trading strategy based upon random industry portfolios,
which preserve the same magnitude of NOA as the industry NOA portfolios, but contain
stocks from various industries, generate considerably less profits than that based upon
industry NOA information. At the same time, the average hedge profits from the industry
adjusted NOA strategy significantly decline by about one quarter from those of their
unadjusted counterparts-NOA, indicating a loss of valuable information about future
stock returns contained in the industry common component of NOA, The above three
portfolio tests are complementary with each other and paint the same picture—both the
industry common component and the industry adjusted component of NOA contain
information that is not fully impounded into current stock prices.
In contrast, I find that the Accruals effect (Sloan, 1996) is entirely driven by the
firm-specific component of Accruals, and the industry common component of Accruals is
not associated with future returns. A trading strategy utilizing industry Accruals
information can produce almost nil profit, which is only 0.04% per month and
insignificant. Meanwhile, a strategy based upon the industry adjusted (firm-specific)
component of Accruals earns exactly the same profits as the one based on Accruals.
The empirical results of this study have implications for several strands of
research in the accounting and finance literature. First, it identifies a new conditional role
5
for industries in asset prices. Ex post, people observe that returns of stocks within the
same industry tend to move together, that there are large cross-sectional differences in
industry returns at a particular time, and that no industry can be a consistent winner over
time (Moskowitz and Grinblatt,1999). Yet, there is limited research focusing on industry
returns in both the theoretical and empirical asset pricing literature. From the current
literature, industry returns are notoriously difficult to predict. Fama and French (1997)
find that loadings on the asset pricing variables are not stationary when considering
industries, and conclude that industries are not a factor in expected stock returns and
industry effects influence stock prices in a seemingly random way that can be diversified.
Consistent with the above view, previous literature (Cohen and Polk, 1998; Asness et al.,
2000) find that asset pricing factors such as size, book-to-market, and cash flow-to-price
are not associated with future returns at the industry level. Ayers and Freeman (1997)
also assert that the post earnings announcement drift is driven by firm-specific events, not
by industry-wide events. The only exception is Moskowitz and Grinblatt (1999), which
document that industry portfolios exhibit significant price momentum.5 Here, I find a
systematically strong industry influence on stock prices, when conditioning returns on the
historically and publicly available financial information-NOA. Industry NOA profits may
be indicative of an important role for industries in understanding asset pricing.
5
They further find that the industry momentum explains most of the individual firm momentum effects.
Subsequent studies confirm the presence of an industry momentum factor in asset pricing, although they
disagree on whether individual momentum is completely subsumed by industry momentum. Asness et al.
(2000) and Lee and Swaminathan (1999) find that within-industry momentum has predictive power for the
firm’s subsequent stock returns beyond that captured by the industry momentum.
6
The results of this paper also extend the accounting literature on the usefulness of
fundamental analysis in predicting stock returns. While there is abundant empirical
evidence demonstrating the success of fundamental analysis in predicting future returns
at the firm level, there exists no systematic evidence that fundamental analysis can be
effective in identifying mispriced industry groups. This seems surprising given that
industry analysis is often the second major step, after a market analysis, for a top-down
analysis of a firm. Furthermore, there are more than 600 funds in the US, specializing in
industry or economic sector investments (Investment 2002). The results of this study
have implications for sector investors who seek mean-variance optimization.
Furthermore, the existence of the industry NOA trading profits provides
additional support for behavioral models in explaining return anomalies. The industry
level anomalous return pattern documented in this study is hard to reconcile with riskbased explanations because there is no wide support for an industry risk factor in the
asset pricing literature, also because the latest technology for isolating risk versus
mispricing explanations has been employed. The documented industry NOA strategy is
profitable in 31 out of 38 years during the sample period. The annualized Sharpe ratio
based on the characteristics adjusted returns of the industry NOA strategy is 0.92, 2.6
times higher than the Sharpe ratio for holding the market for the same sample period,
indicating a reward to risk that is very attractive relative to holding the stock market as a
whole. Moreover, the industry NOA strategy survives the statistical arbitrage test
introduced recently by Hogan, Jarrow, Teo and Warachka (2004), which is designed to
encompass the specification of any equilibrium asset pricing model to distinguish
7
between risk premium and mispricing explanations for abnormal trading profits. I also
document a counter-cyclical relationship between the industry NOA payoff and future
GDP growth; this raises the doubt that macroeconomics factors are explanations for the
documented industry NOA effect.
Instead, the results are more consistent with the behavioral prediction based on
limited investor attention. The results suggest that investors are unable to adjust
adequately for industry common information contained in financial statements. To the
extent that industry-common information is more readily accessible to market
participants than the firm-specific information, the industry-NOA abnormal trading
profits are more troubling for market efficiency proponents.
There has been a long time concern about the potential sampling errors and
econometric problems associated with anomaly findings (Kothari, 2001). Kraft, Leone
and Wasley (2005) document that after eliminating extreme return observations at the 1%
level, there is an inverted U-shaped relationship between future one year buy-and-hold
size-adjusted abnormal returns (BHAR) and magnitude of Accruals or NOA. Thus, the
hedge returns from Accruals and NOA strategies dramatically drop. They argue that this
finding challenges the behavioral explanation that anomalies are likely due to investors’
inabilities to process accounting information. After repeating the industry portfolio test
by deleting the observations with extreme returns, I don’t observe the inverted U shape
relationship between the magnitude of industry NOA and future abnormal returns. This
implies the documented industry NOA effect is not driven by observations with extreme
returns.
8
People also concern that anomaly findings may disappear after considering
transaction costs and the findings may be driven by small stocks, which are less liquid
and more likely to be subject to the return mismeasurement problem through trading
frictions such as bid-ask spread and poor liquidity (Ball et al., 1995). I present evidence
that the payoffs from the industry NOA strategy are beyond the range of transaction
costs, and that the industry NOA effect is not just driven by small stocks.
Stock prices incorporate a broad set of information including financial
information. Therefore, a relevant question would be whether investors’ overreaction to
industry NOA can be explained by their underreaction to industry returns (Moskowitz
and Grinblatt 1999), or vice versa. If investors have limited attention, then not all
currently available accounting information is fully impounded into stock prices and
industry NOA and industry momentum may be complementary in terms of predicting
future stock returns. I provide evidence that industry NOA provide information
incremental to industry momentum that investors fail to fully appreciate.
In contrast to asset pricing literature, the corporate finance literature has long
recognized the impact of industries in explaining hot and cold IPO and SEO markets,
merger and acquisition (M&A) activities (Mitchell and Mulherin, 1996) and other
corporate investment policies. Prior literature documents that firms issuing stocks and
engaging in M&A activities will suffer long run negative abnormal returns (Loughran
and Ritter,1995; Rau and Vermaelen 1998). In addition, all of the above corporate events
have a direct impact on a firm’s balance sheet and the magnitude of the NOA. Therefore,
it is important to examine whether the industry NOA effect is driven by an industry-wide
9
clustering of corporate events such as new equity issuances and M&A activities. I offer
evidence that the industry NOA effect is incremental to the effect of clustering of these
corporate events within industry members.
The rest of this study is organized as follows: Chapter 2 reviews the related
literature and develops the main hypothesis. Chapter 3 presents sample selection and data
description. Chapter 4 outlines the methodology and major findings. Chapter 5
discriminates between the mispricing and risk explanations for the industry NOA effect.
Chapter 6 performs robust tests and differentiates the industry NOA effect from both the
industry momentum effect and the industry clustering of equity financing activities.
Chapter 7 offers a conclusion.
10
CHAPTER 2
INDUSTRY NOA AS A MISPERCEPTION INDEX
2.1
Efficient Market Hypothesis and Behavioral Finance
The efficient markets hypothesis (EMH) has been the central proposition of
finance since the mid 1960s. Fama (1970) defines an efficient financial market as one in
which security prices always fully reflect the available information. Whether a market is
efficient or not has important economic consequences. An inefficient market implies not
only a redistribution of wealth between noise traders and arbitrageurs; it also has
implications for corporate finance (Teoh et al., 1998a and b; Loughran and Ritter, 1997)
and real investment (Morck et al., 1990) decisions. The degree to which stock markets
are informationally efficient also affects the demand for accounting research in
investment decisions, performance evaluation programs, corporate disclosure decisions,
and regulatory standard setting decisions (Lee, 2001).
The basic theoretical case for the EMH rests on three arguments (Shleifer, 2000;
Hirshleifer, 2001). First, investors are assumed to be rational and hence to value
securities rationally. Second, to the extent that some investors are irrational, their trades
11
are random and therefore cancel each other out without affecting prices. Third, to the
extent that investors are irrational in similar ways, they are met in the market by rational
arbitrageurs who eliminate their influence on prices.
The psychological evidence shows that people do not deviate from rationality
randomly, but in a systematic way. First, individuals do not assess risky gambles
following the precepts of von Neumann-Morgenstern utility (Kahneman and Tversky,
1979). Second, individuals systematically violate Bayes rule and other maxims of
probability theory in their prediction of uncertain outcomes (Kahneman and Tversky,
1973). For example, the famous Allais paradox (Allais, 1953) claims that the assumptions
made in conventional expected utility theory contradict real life decisions. The idea
introduced by Allais is that there is a systematic relationship between an agent's attitude
towards risk and the "degree of certainty". In addition, individuals make different
choices depending on how a given problem is presented to them; therefore framing
influences decisions.
The last twenty years have also seen a rise in Behavioral Economics and
Behavioral Finance. Based on the systematic psychological evidence and theory,
proponents of Behavioral Finance argue that investors wouldn’t trade randomly with each
other, but rather that many of them would try to buy the same securities or to sell the
same securities at roughly the same time. Investor sentiment reflects the common
judgment errors made by a substantial number of investors, rather than uncorrelated
random mistakes (Hirshleifer, 2001; Daniel et al., 2002).
12
If the theory of efficient markets relied entirely on the rationality of individual
investors, then the psychological evidence would by itself present a serious challenge for
the theory. However, this is not the case. The EMH is built upon arbitrage, which claims
that even if sentiment is correlated across unsophisticated investors, the arbitrageurs
should take the other side of demand and bring prices back to fundamentals immediately.
The other central argument of behavioral finance states that, in contrast to the efficient
market theory, real-world arbitrage is risky and therefore limited (Shleifer and Vishny
1997). The effectiveness of arbitrage relies crucially on the availability of close
substitutes for securities whose prices are potentially affected by noise trading. Moreover,
even when securities do have perfect substitutes, the arbitrageurs may face the risk of the
possibility that the mispricing may become worse before it disappears. Therefore, limited
arbitrage explains why some anomalies persist for quite a time.
Researchers have uncovered numerous variables that can predict stock returns.
The variables can be classified into three categories. First, the variables are pure marketbased variables such as size, price momentum and return volatility. They provide direct
challenges to the weak form market efficiency. Second, the variables are constructed as
price-scaled ratios such as the book-to-market ratio (B/M), the earnings-to-price ratio(E/P)
and the value-to-price ratio(V/P, V is an estimation of fundamental value derived form
the residual income model, see Frankel and Lee, 1998). Financial variables here serve as
the proxy for fundamentals in the literature. The rationale here is that the extreme values
of the ratios represent the greatest divergence between fundamental values and market
values, and therefore represent mispricing. Finally, the variables can be pure financial
13
variables such as standard unexpected earnings (SUE), Accruals and NOA. The common
theme is that investors are unable to fully digest the information in financial variables.
Accounting literature plays an important role in the second and third categories of
research discussed above. The post earnings announcement drift (Ball and Brown, 1968;
Bernard and Thomas, 1989 and 1990) has been regarded as the most serious challenge to
the efficient market hypothesis (Fama, 1998). Lee (2001) points out that one of the
comparative advantages of accountants in the market efficiency research area is “to
generate alpha”, that is to identify the potential profitable trading strategy. Given the
noisy prices and costly arbitrage, accounting research can add value by improving the
cost-effectiveness of the arbitrage mechanism. The end goal is to improve the allocation
efficiency of markets through the most cost-effective use of accounting information to
solve significant problems in financial economics.
2.2
Limited Attention and the NOA effect
The accounting recognition rule defines the mapping of what a firm knows about
transactions to what is recorded into its accounting system (Christensen and Demski
2003). Accrual accounting differs from cash basis accounting by the timing of when
revenues and expenses are recognized into income. As a result of double entry
bookkeeping, balance sheet items capture the differences between accrual accounting and
cash basis accounting, inherent in the revenue recognition and (expense) matching
principles, through the accumulation of accruals. Penman (2003) recommends
reformulating the balance sheet into operating and financing sides and observes that the
14
change in net operating assets is equal to the difference between operating income and
free cash flows, which is defined as the difference between cash flow from operations
and the investment accruals.
∆Net Operating AssetsT = Operating IncomeT − Free Cash FlowsT
(2.1)
Hirshleifer et al. (2004) argue that both operating income and free cash flows may
be informative about the value of a firm.6 The operating earnings number may contain
information about future performance that is not available in free cash flows through the
choice of accruals (Christensen and Demski, 2003). For example, accrual accounting
system can record a restructuring charge if managers anticipate future bad news,
therefore it provides more information to financial information users than a simple cash
accounting system. Likewise, free cash flows may also capture the information not
currently reflected in operating earnings. For example, conditional on the information of
accruals, cash flow from investment provides additional information about future
performance (See Hirshleifer et al., 2004). A fully rational investor would want to use
both pieces of information to value a firm.
If time and attention are costly, investors may only focus on salient cues and
ignore some useful information when making decisions. Such behavior may be
reasonable and is a necessary consequence of the vast amount of information available in
6
See also Christensen and Demski (2003) for a theoretical modeling on how cash and accruals provide
information content incremental to each other.
15
the environment. If investors have limited attention, they may anchor on only one piece
of information (either the most recent current operating income or the most recent free
cash flows), but ignore the other piece of information. Furthermore, important
information conveyed by the difference between the two variables is ignored. Detailed
analysis of balance sheets is required to gauge the information embodied in the difference
between operating income and free cash flows to determine the implications for future
operating performance. Arya et al. (2000) and Christensen and Demski (2003) point out
that figuring out the information embodied in the accounting variables can be described
as a decoding process. However, decoding is not without cost; it demands mental powers
as well as considerable professional training (Hirshleifer and Teoh, 2003).
Accounting stock variables provide information useful for the valuation purpose
in addition to accounting flow variables (Ohlson, 1995; Christensen and Demski, 2003)
and the misperceptions of accounting items may have been built up over time (Hirshleifer
et al., 2004). Net operating assets, from equation (2.1), can be interpreted as the
cumulative difference over time between the accounting value added (operating income)
and the cash value added (free cash flows). It is, therefore, a parsimonious measure of
cumulative investors’ misperceptions of accounting information (balance sheet bloat).
This is why a cumulative variable, net operating assets, is more powerful than flow
operating accruals or change in net operating assets to identify mispriced stocks.7
7
Hirshleifer et al. (2004) show that profits from NOA strategies (1.23% per month) are on average 60%
higher than those from Accruals strategies (0.72% per month) for their 1964-2002 sample.
16
Net Operating AssetsT = ∑0 Operating Incomet − ∑0 Free Cash Flows t . (2.2)
T
T
Net operating assets may reflect information about firms’ opportunistic
accounting choices. For example, a large account receivables balance may exist due to
aggressive revenue recognition and/or the underestimation of the provision for bad debts.
In the same spirit, firms may engage in overproduction to take advantage of the
absorption costing system to report lower cost of goods sold and to boost the bottom
earnings number. Consequently, a bigger ending inventory number will show up on the
balance sheet.
Net operating assets can also convey information about the economic
environment that may affect a firm’s current and future operations. For example, a high
account receivables balance may actually reveal a firm’s inferior status on the product
market. A high closing inventory level may also contain information about demand shifts,
as is suggested in Thomas and Zhang (2002). On the liabilities side of the balance sheet, a
shift from operating to financing liabilities, accompanying an increase in net operating
assets, may signal the beginning of a liquidity crisis. The reduced access to trade credit
results in increased reliance on external borrowing.
In summary, the higher the net operating assets, the larger the cumulative
difference between historical accounting value added and cash value added, possibly due
to either consistent upward earnings manipulation and/or adverse business conditions.
17
Thus it is more likely that future financial performance will be adverse.8 Therefore, if
investors with limited attention only anchor on one piece of information, earnings, they
tend to overvalue firms whose balance sheets are ‘bloated’, and undervalue firms when
accounting value added falls short of cash value added. Therefore, NOA is a negative
predictor for future returns.
2.3 Industry Variations of Net Operating Assets and Future Stock Returns
2.3.1
What Causes Cross-Industry Variations of Net Operating Assets?
To understand the determinants of investor perceptions in greater depth,
Hirshleifer et al. (2004) provide an alternative decomposition of net operating assets as
follows:
Net Operating AssetsT = ∑0 Operating Incomet − ∑0 (Operating Cash Flowt − Investmentt )
T
T
= ∑0 (Operating Income Before Depreciationt − Operating Cash Flowt )
T
+ ∑0 (Investment t − Depreciationt ).
T
(2.3)
Equation 2.3 indicates that net operating assets are the sum of two cumulative differences
between accounting and cash value added: (Operating Income before Depreciation −
Operating Cash Flow), and (Investment − Depreciation). Thus, firms with high net
operating assets have high cumulative deviations between accounting and cash
profitability that are derived from both operating and investing activities. I will refer to
8
Hirshleifer et al. (2004) show that firms with high (low) net operating assets tend to experience downward
(upward) trends in operating earnings during the following five years.
18
the first sum as working capital and the second sum as investment assets. Both the
working capital and the investment assets components of firm level net operating assets
may be industry dependent, for the following reasons.
First, industries are characterized by different production functions, which will
affect both the working capital level and the investment assets level. Some industries
have inherently shorter operating cycles than other industries. For example, firms in the
retail industry, in general, have small account receivables and small inventory balances
and rely heavily on trade credits as a way of financing. Therefore, the retail industry
tends to have low working capital. In contrast, industries such as manufacturing usually
carry high inventories and high account receivables balances, due to the credits offered to
customers. Thus, the result is usually high working capital. In terms of the investment
assets level, fixed assets investments (Plant Property and Equipment) in capital intensive
industries such as transportation, energies and utilities typically represent the majority of
their assets and contribute to high NOA. Industries such as services, that require human
capitals as the major input of their production functions will have low capital investment
assets, since human capitals are not capitalized on the balance sheet.
Second, cross-industry variations of NOA are impacted by industry-wide
exposure to accounting regulations. For example, high tech industries, such as computers
and pharmaceuticals, invest heavily in R&D, which are mandated to be expensed as
incurred under the current GAAP; consequently, those industries tend to have low
investment assets.
19
Third, firms within the same industry share similar demand shifts, as well as
technical and institutional innovations. Both the working capital and the investment
assets components of NOA can reflect those shocks. Thus, the industry common NOA
may contain information about favorable vs. adverse business environments common to
the industry. If one firm experiences an unusually prolonged operation cycle, (which is
defined as the day of account receivables turnover, plus the day of inventory turnover,
minus the day of account payables turnover), this prolonged operation cycle may be due
to firm-specific reasons, such as inefficient operation or it may be due to
industry/economic wide factors. If prolonged operation cycles are industry-wide
phenomena, a rational investor can infer that the industry’s current and future
performances are likely to be impacted by some common adverse factors. For example,
increases in raw material prices can affect industry wide inventory level. In the same
spirit, variations in the industry wide investment assets may also carry information
regarding the common business environment. For example, if many competitors rush to
implement new productive technologies, without considering whether the high aggregate
supply of the products can be absorbed by current or future product demands, the high
industry wide investment level will signal future poor performance (Jensen, 1993).
2.3.2 The Industry Common Component of NOA and the Future Stock Returns
In this section, I investigate, whether the NOA effect is at least partly driven by
investors’ misunderstandings of cross-industry variations in NOA. Put another way, I
20
examine whether industries characterized by extreme NOA will, on average, experience
abnormal stock returns.
It may be intuitive to think that if one variable predicts returns at the firm level,
then a portfolio of firms grouped by industries with the extreme level of this variable
would also experience future abnormal returns. In the previous literature, however, this
has generally not been the case. Cohen and Polk (1998) and Asness et al. (2000) find that
asset pricing characteristics, such as size, book-to-market ratio, and cash flow-to-price
ratio, are not associated with future returns at the industry level. The fact that the firm
level return predictabilities don’t necessarily carry over to the industry level elicits one
question, which is, whether the underlying information investors don’t fully digest that is
conveyed by the variable of interest is firm-specific or industry-common.
If the information that fails to be fully impounded into stock prices is only firmspecific, the pricing predictive ability of a particular characteristic may increase when the
intra-industry component is measured (Cohen and Polk, 1998). In contrast, the interindustry component will lose return predictability. The number of firms being overvalued
(conditional on the characteristic) would roughly equal the number of firms being
undervalued (conditional on the characteristic), on average over time, by the law of large
numbers within a specific industry. Thus, the industry average of the characteristic is still
a good benchmark, even though the characteristic itself is mispriced at the firm level.
Here, the distinction between the return predicting variable itself (observable) and
the underlying information conveyed by the variable (usually not directly unobservable)
is important. Although size and the book-to-market ratio variables themselves tend to be
21
correlated within the same industry, it is not clear in the literature what information (or
risk factor) is contained in the size and the book-to-market ratio that investors do not
fully understand9 and it is also not clear whether the information is firm-specific or
industry-common. The findings of Cohen and Polk (1998) and Asness et al. (2000) seem
to suggest that the information is firm-specific.
If the information contained in a financial variable that investors fail to fully
assimilate is at least partially industry common, investors tend to make similar valuation
mistakes for firms within the same industry. Therefore, the industry average of the
characteristic would capture investors’ “common” mistakes and wouldn’t represent an
optimal level. That is, the number of firms being overvalued dominates the number of
firms being undervalued, on average over time, or vice versa. The industry common
component of the characteristic should be useful in predicting future stock returns.
From the discussion in the last section, we can see that the industry common
component of NOA carries information regarding industry wide business environments.
A high industry common component of NOA may indicate that an adverse business
environment is prevailing in the industry. If investors with limited attention fail to
appreciate the information contained in the firm level NOA, this together with the fact
that the information contained in NOA is partly industry-common implies that industry
portfolio conditioning on NOA won’t be able to diversify the valuation mistakes that are
made by investors at the firm level. Investors tend to overvalue the industries with high
NOA and to undervalue the industries with low NOA. Thus, the industry component of
9
See Fama and French (1992; 1993) and Lakonishok et al. (1994).
22
NOA can serve as an investors’ optimism provocation index at the industry level. The
above discussions lead to the first part of my hypothesis:
H1(a): The industry common component of NOA is negatively related to future
stock returns.
As discussed in section 2.2.1, differences in information about the industry-wide
business environment cannot fully account for variations in the industry common
component of NOA. Informationally equivalent accounting choices may also impact the
magnitude of the industry component of NOA. When two accounting choices provide
financial statement users with the same information about the assessment of probabilities
of future states of the world, they are considered informationally equivalent even though
they may have different impacts on a firm’s income statement and balance sheet. This is
referred as the “scaling effect” in Christensen and Demski (2003). For example, it makes
no difference whether depreciation schedules are straight line or accelerated, as long as
they are predetermined and utterly mechanical.
If investors are fully rational, informationally equivalent accounting choices
shouldn’t make a difference in their decision making. However, if investors have limited
attention, they may not be able to fully penetrate the scaling effect from a purely
informational effect; therefore, accounting choices with equivalent information may have
23
vast impacts on investors’ perceptions of firms’ current and future performances.10
Investors with limited attention may have more severe problems in gauging information
from the financial reports of long operating cycle industries, which tend to have relatively
high industry NOA, since such industries, in general, have complex business operations
and accounting practices. I leave it to future research to investigate to what extent
accounting based anomalies, including the industry NOA effect, are attributable to
investors’ inabilities to understand the accounting scaling effects.
2.4
The Industry Adjusted Component of NOA and Future Stock Returns
The next question is, after the removal of the industry effect, whether the
industry-adjusted component of NOA will still contain information that investors don’t
fully appreciate. Here, I argue that at least two types of information, contained in the firm
level NOA, are essentially firm-specific. First, information about the firm-specific
economic environment is lost when aggregating NOA at the industry level but it is still
retained in the industry-adjusted component of NOA. Second, information regarding
firm-specific opportunistic accounting choices is largely embedded in the industryadjusted component of NOA.
The first point is self-evident. With regard to the second point, there is no prior
belief or empirical evidence that the stimuli for earnings management are highly and
consistently correlated within the same industry. Various incentives for earnings
10
For example, even if the difference in earnings between firm A and firm B is entirely due to different
predetermined depreciation methods, some naïve investors may simply anchor on the earnings number and
interpret one firm as having better performance than the other, although the underlying economic
performance may be exactly the same.
24
manipulation are examined in the literature (Healey and Wahlen, 1999). Numerous
studies report evidence that firms opportunistically manage earnings to meet certain
thresholds, such as zero earnings and analyst consensus forecasts (Burgstahler and
Dichev, 1997; Degeorge et al., 1999). It is reasonable to assume that firms below the
threshold may have incentives to boost their bottom numbers up to avoid the torpedo
effect (Skinner and Sloan, 2002). Firms that are too far below the benchmark may engage
in taking big baths. Firms that are far above the benchmark may also choose to defer
earnings to avoid ratcheting up investors’ expectations (Graham et al., 2004) and to
reserve for possible future bad years. For capital market financing purposes, DeAngelo
(1998) reports that managers of buyout firms have incentives to understate earnings prior
to the buyout while Teoh et al. (1998a;b) find that managers overstate earnings in periods
surrounding equity offers. For management compensation contract induced earnings
management, prior studies show that firms may increase reported earnings (Dechow and
Sloan, 1991) or they may defer incomes through accruals, when firms with caps on bonus
reach the cap (Holthausen et al., 1998). For regulation related motivation, some firms
may overstate earnings to avoid failing regulatory tests (Collins et al., 1995) and some
firms may understate earnings to reduce risks associated with political visibilities such as
investigation and intervention by anti-trust regulation (Watts and Zimmerman, 1986).
Firms from the same industry may be influenced by different incentives at a
particular time. In addition, a firm’s opportunistic accounting choices may reflect the
trade offs among various incentives. Therefore, it is not very likely that firms within the
same industry will simultaneously and consistently engage in (the same direction of)
25
upwards or downwards earnings manipulation.11 In short, the industry adjusted
component of NOA retains information about firm-specific economic shocks and
opportunistic accounting choices, which is largely washed out in the industry common
component of NOA. A high industry adjusted component of NOA indicates a higher
likelihood that a firm may engage in consistently upward earnings manipulation and/or is
subject to firm-specific adverse business shocks. As discussed in Section 2.1, investors
with limited attention tend to overvalue firms with a high industry adjusted component of
NOA and they tend to undervalue firms with a low industry adjusted component of NOA.
The above discussions lead to the second part of my hypothesis:
H1(b): The industry adjusted component of NOA is negatively related to future
stock returns.
For the purposes of comparison, I also examine industry return predictabilities for
Accruals (Sloan, 1996), which is an important return regularity documented in the
accounting literature. Accruals, which reflect the one time difference between the
operating income and cash flow from operation, should also convey information about a
firm’s opportunistic accounting choices as well as about its business environment. Here, I
don’t make ex ante predictions for Accruals return predictabilities at the industry level for
the following two reasons.
11
The claim does not preclude the possibility that stimuli for earnings management can be correlated within
industry at a particular time, but the chance for this is relatively small and the industry correlated stimuli,
excluding some special industries, if any, won’t be highly persistent over time.
26
First, as one slice of NOA, Accruals is a flow variable, and thus doesn’t capture
the cumulative effect of investors’ misperceptions as NOA. For each period, Accruals
doesn’t contain the investment information, which tends to be correlated among firms
within the same industry to reflect the demand shifts, technology innovations, and
organizational changes common to industry (Jensen, 1993). Therefore, the information
regarding industry common business environments contained in Accruals is likely to be
considerably less than that contained in NOA.
Second, previous literature shows that the return predictabilities of Accruals are
largely attributable to shocks to the discretionary accruals, rather than to the nondiscretionary accruals (Teoh et al., 1998; Xie, 2001). They also provide evidence that the
shocks to discretionary accruals are consistent with earnings management incentives.
Since discretionary accruals are likely firm specific as discussed above, I expect that
Accruals are less likely to predict returns at the industry level. Therefore, I leave it up to
empirical tests to determine whether Accruals can predict returns at the industry level.
For completeness, I further decompose the industry NOA into the industry
working capital and the industry investment components. Working capital is time-series
aggregation of Accruals. This decomposition is designed to investigate the following
question: Does the time series aggregation property of NOA and/or the investment
information that is not available to Accruals make a difference in return predictabilities,
between industry NOA and industry Accruals, if any?
27
CHAPTER 3
SAMPLE SELECTION AND DESCRIPTIVE DATA
3.1
Sample
The sample covers the NYSE, AMEX and NASDAQ firms with available data
from July 1964 to December 2002, from the intersection of CRSP and Compustat
datasets. All observations are required to have sufficient financial data to compute net
operating assets, accruals, firm size, book-to-market ratio and 11-month return
momentum. The initial sample consists of 166,145 firm-year observations and 1,612,268
firm-month observations. The sample size varies slightly across analyses due to different
data restrictions.
3.2
Industry Classification
I follow the industry classification algorithm of Fama and French (1997), which
re-categorizes firms based on four–digit SIC codes and rearranges the SIC codes from
production and technology oriented (supply side) to principal business oriented (demand
side). Using a partial log-linear approach employed by Lev (1969), Soliman (2003)
28
demonstrates that the Fama-French classification is superior to the two-digit and the
three-digit SIC code grouping schemes in explaining whether the industry medians
represent reasonable targets for a variety of financial ratios. Appendix A-1 reproduces the
Fama French (1997) industry classification for the reader’s convenience.
In a recent paper, Bhojraj et al. (2003) recommend adoption of the Global
Industry Classifications Standard (GICS), which is based on firms’ principal business
activities (demand based), due to its superior abilities to explain contemporaneous stock
return co-movements, cross-sectional variations in valuation multiples and a variety of
financial ratios such as P/E. I therefore repeat the majority of the analyses for the GICS
industry classification12. I also repeat the majority analyses by adopting two other widely
used industry classification schemes--a 14-industry categorization used in Beaver et al.
(2002), and a 20-industry delineation used in Moskowitz and Grinblatt (1999).
Appendices A-2 and A-3 report summary results for the GICS, 14 industries and
20 industries classifications and they show that the findings of this study are robust to the
choice of those industry grouping schemes. 13
3.3
Financial Variables Measurements
Net operating assets are calculated as the difference between operating assets and
operating liabilities (Barton and Simko, 2002; Hirshleifer et al., 2004), where
12
The GICS classification schemes are available for the majority of the firms from the Compustat PDE file
and they match about 82% of my original sample. The data manual points out that the GICS classification
for inactive firms has not been reviewed by Morgan Stanley yet. Therefore, I still report the results for the
Fama-French 48 industries classification in the main tables.
13
I don’t exclude firms in financial industries or regulatory industries. The untabulated results show that
the results reported in this paper are not sensitive to the inclusion/exclusion of those industries.
29
Operating Assetst=Total Assetst-Cash and Short Term Investmentt
Operating Liabilitiest=Total Assetst-Short Term Debtt-Long Term Debtt
-Minority Interestt-Preferred Stockt-Common Equityt
(4)
I calculate operating accruals using the indirect balance sheet approach (Sloan,
1996) for all fiscal years in my sample, since the data coverage starts before 1987, when
SFAS 95 was effective and cash flow from operations numbers can be directly pulled out
from Compustat (Hribar and Collins, 2002).
Accrualsbs = (∆Current Assets-∆Cash and Short Term Investment)
- (∆Current Liabilities -∆Short-term debts-∆Tax Payable)-Depreciation (5)
Both net operating assets and operating accruals are scaled by the fiscal year
beginning total assets (Compustat #6). 14 To avoid the extremely small denominator
problem, I delete observations with lagged total assets smaller than one million dollars.
When calculating NOA and Accruals, if short-term debt, tax payable, long-term debt,
minority interest or preferred stock has missing values, I treat these values as zeros to
avoid unnecessary loss of observations.
14
The main results of this paper are not affected by the choice of ending total assets or average total assets
as deflators for accruals and net operating assets.
30
I use the eleven-month intermediate return horizon starting 12 months to 2 months
prior to the portfolio formation month as the measure of price momentum. Following the
convention with the finance literature, I skip the month just prior to the testing month to
control for potential microstructure influences.
Industry-wide financial variables, such as industry NOA, industry Accruals and
industry Earnings, are constructed each month, using the equally-weighted values across
firms for each industry.15
3.4
Calculation of Abnormal Returns:
I adopt the characteristics approach proposed by Daniel et al. (1997) to control for
the following asset pricing factors -- size, book-to-market (B/M), and momentum effects
--simultaneously to better isolate the anomalous effect investigated. The empirical
evidence provided by Daniel et al. (1997) suggests that characteristics provide better ex
ante forecasts of the cross-sectional patterns for future returns. In their setting to measure
mutual fund performance, characteristics-matching also does a better job in matching
future realized returns, meaning that the average fraction of the variance of the fund
returns explained by the benchmark is higher, and that the standard error of the estimate
of the fund’s abnormal performance is lower.
Specifically, each month, the size-B/M-momentum benchmark portfolios
(5*5*5=125) are formed based on NYSE cutoff points. To calculate monthly
15
Value-weight schemes won’t qualitatively impact the results documented in this paper. The primary
findings of this paper also hold if industry medians instead of industry means are used.
31
characteristics-adjusted returns (hereafter ‘abnormal returns’), I then subtract the equal
weighted returns of the size-B/M-momentum benchmark portfolio to which the firm
belongs from the raw buy and hold returns for each firm each month. To ensure the
availability of the financial information, returns are matched with the financial data
starting from the fifth month to the sixteenth month after fiscal year end.
Industry (abnormal) returns are calculated as the equal-weighted average of
(abnormal) returns across firms for each industry each month.
3.5
Descriptive Statistics
Forty-eight equal-weighted industry portfolios are formed each month from July
1964 to December 2002 following the Fama and French (1997) industry grouping scheme.
Table 3.1 reports the time-series average (unconditional mean) values for selective
financial characteristics as well as the raw annual returns for each industry. The time
series means of industry NOA cluster around the interval from 0.6 to 0.8 with a range
from 0.46 to 0.83. Consistent with previous arguments, industries such as Energy,
Telecommunication and Utilities have relatively high NOA while industries such as
Drugs, Business Services and Computers tend to have low NOA. The time series means
of industry Accruals are from -0.078 to 0.030. Except for Apparel and Wholesale
industries, the industry Accruals are all negative. The industry Earnings are rather
uniform across industries, as suggested by the economics theory that competition will
drive the profitability across industries to converge in the long run (Soliman, 2003).
32
Consistent with Moskowitz and Grinblatt (1999), there is little evidence that
differences in unconditional industry returns exist. An F-test for same mean returns
across the 48 industries cannot be rejected (F=0.49) at the conventional significance
levels for the sample period.
Interestingly, untabulated results show that Business
Service and Computer industries are among the highest NOA industry groups in year
1999, which is coincident with the computer-related bubble, although unconditionally
those two industries have relatively low industry NOA.
Table 3.2 provides the frequency of each industry portfolio in the extreme
industry NOA and industry Accruals groups as well as the results for intra-industry NOA
and intra-industry Accruals strategies. Every month, eight portfolios are formed, each
containing six individual industry portfolio, based on the magnitude of industry NOA or
industry Accruals. Ind_NOA1 (Ind_Acc1) and Ind_NOA8 (Ind_Acc8) represent the
lowest industry NOA (Accruals) and the highest industry NOA (Accruals) portfolios
respectively. Column A and B report the percentage of an industry in the lowest and the
highest industry NOA group during the sample period. Among the 48 industries, 37 and
42 industries show in the lowest and the highest industry NOA group at least once. 15
and 14 industries are in the lowest and the highest industry NOA group 20% or more of
the time during the sample period. Construction, Shipping and Insurance industries
frequently stay in the lowest industry NOA group while Healthcare, Entertainment,
Energy and Telecommunication industries appear in the highest industry NOA group for
more than 30% of the time. Several industries such as Tobacco, Precious Metal,
33
Telecommunication and Personal Service, frequently appear in both the lowest and the
highest industry NOA group.
Columns C and D of Table 3.2 report the probability of an industry being sorted
into the extreme low and high industry Accruals group during the same sample period.
12 and 11 industries are in the lowest and the highest industry Accruals group 20% or
more of the time. Although NOA and Accruals are closely related, the frequency of an
industry in the extreme industry NOA group is often inconsistent with that in the extreme
industry Accruals group. For example, the Energy industry stays in the lowest industry
Accruals for 80% of the time, but only for 4% of the time in the lowest industry Accruals
group. The Entertainment and Restaurant industries are high frequenters for both the
lowest industry Accruals and the highest industry NOA group. The above observations
suggest that the information set captured by industry NOA and industry Accruals are
quite different.
Columns E and F of Table 3.2 report the results of whether the NOA and the
Accruals trading strategies can make statistically significant profits for each individual
industry during the 1964 to 2002 sample period. NOA strategy works for 24 out of 48
industries while Accruals can only make profits for 14 industries. Two observations are
worthy noting here. First, it seems that if Accruals strategy works for an industry, it is
very likely that the NOA strategy will work for the same industry. Second, whether the
NOA (Accruals) strategy works for an industry has little to do with its frequency at the
extreme industry NOA (Accruals) group.
34
Table 3.3 describes (conditional) mean values for selected financial and market
characteristics for eight portfolios, each containing six individual industry portfolios,
sorted by the magnitude of industry NOA and industry Accruals respectively. Panel A
reports the results for industry NOA portfolios. The variations of the industry NOA
across portfolios range from about 0.58 to 1.04. Both the extremely low and high industry
NOA portfolios tend to have smaller industry Earnings. Turning to stock market
characteristics, extreme (both the highest and the lowest) NOA industries have the
smallest B/M ratio. Industries with low NOA are comprised of relatively small firms
while the average size for industries with high NOA is relatively large. Therefore, it will
be important to control for the size and the B/M effects in later empirical analyses.
Panel B of Table 3.3 reports the results for industry Accruals portfolios. In great
contrast to the results reported in Panel A, lower Accruals industries are associated with
higher industry B/M ratios and lower industry market values of equities. The magnitudes
of industry NOA roughly remain constant across the industry Accruals portfolios. The
positive monotonic relationship between Accruals and Earnings at the firm level
portfolios still preserves well here.
Table 3.4 provides the correlation matrix among industry NOA, industry Accruals
and other industry level characteristics at annual frequency. Industry NOA shows
moderately positive correlations with industry Accruals (Spearman/Pearson
Correlation=0.18/0.25), and slightly negative correlation with industry momentum
(Spearman/Pearson Correlation=-0.07/-0.06).
35
Agric
Food
Soda
Beer
Smoke
Toys
Fun
Books
Hshld
Clths
Hlth
MedEq
Drugs
Chems
Rubbr
Txtls
BldMt
Cnstr
Steel
FabPr
Mach
ElcEq
Misc
Autos
Aero
Ships
Guns
Gold
Mines
Coal
Enrgy
Util
Telcm
PerSv
BusSv
Comps
Chips
(A)
Ind_
NOA
0.737
0.720
0.775
0.739
0.752
0.732
0.748
0.693
0.724
0.751
0.828
0.709
0.631
0.718
0.732
0.796
0.742
0.638
0.735
0.725
0.692
0.713
0.667
0.708
0.703
0.641
0.648
0.759
0.796
0.709
0.807
0.772
0.824
0.740
0.616
0.656
0.709
(B)
Ind_
Accruals
-0.028
-0.034
-0.045
-0.031
-0.007
-0.011
-0.058
-0.036
-0.007
0.003
-0.023
-0.001
-0.015
-0.031
-0.027
-0.026
-0.030
-0.016
-0.030
-0.026
-0.013
-0.016
-0.028
-0.023
-0.022
-0.030
-0.020
-0.041
-0.037
-0.071
-0.078
-0.035
-0.065
-0.037
-0.037
-0.016
-0.019
(C)
Ind_
Earnings
0.062
0.124
0.138
0.120
0.144
0.094
0.072
0.144
0.118
0.122
0.103
0.053
0.065
0.112
0.109
0.100
0.103
0.060
0.083
0.091
0.104
0.109
-0.002
0.115
0.094
0.100
0.129
-0.022
0.040
0.043
0.076
0.092
0.102
0.106
0.082
0.078
0.106
(D)
Ind_
B/M
0.683
0.591
0.427
0.544
0.668
0.640
0.560
0.411
0.594
0.807
0.419
0.353
0.263
0.543
0.739
1.076
0.794
0.742
0.929
0.836
0.658
0.659
0.529
0.705
0.731
0.704
0.612
0.480
0.702
0.793
0.590
0.653
0.425
0.490
0.415
0.419
0.535
(E)
Ind_
MV
57
77
187
161
232
24
28
95
39
28
29
38
96
198
22
44
45
33
68
15
32
36
12
82
66
68
179
49
50
85
78
246
111
30
27
41
26
(F)
Ind_
Ret
0.089
0.143
0.220
0.101
0.182
0.097
0.125
0.151
0.117
0.120
0.183
0.159
0.100
0.124
0.138
0.123
0.137
0.098
0.122
0.121
0.124
0.117
0.035
0.110
0.105
0.146
0.132
0.044
0.100
0.052
0.081
0.108
0.106
0.132
0.123
0.092
0.122
Table 3.1: Mean Values of Industry Characteristics for Each Industry Portfolio
(Continued)
36
Table 3.1: Continued
LabEq
Paper
Boxes
Trans
Whlsl
Retail
Meals
Banks
Insure
RlEst
Fin
Average
F-test
0.715
0.742
0.768
0.708
0.725
0.693
0.794
0.704
0.468
0.731
0.681
0.719
-0.009
-0.034
-0.044
-0.067
0.003
-0.018
-0.069
-0.028
-0.037
-0.029
-0.022
-0.030
0.088
0.117
0.116
0.079
0.087
0.112
0.102
0.065
0.096
0.031
0.062
0.090
0.582
0.740
0.629
0.715
0.693
0.613
0.589
0.565
0.398
0.630
0.401
0.610
24
118
196
58
20
57
26
15
65
15
30
70
0.142
0.130
0.095
0.129
0.124
0.091
0.128
0.130
0.194
0.073
0.114
0.119
0.49
The sample consists of a maximum of approximately 1.61 million firm-month
observations covering all NYSE, AMEX and Nasdaq firms with available data from July
1964 to December 2002.
Variable Measurement
Raw NOA = Operating Assets (OA)-Operating Liabilities (OL), where
(Compustat item numbers in parentheses)
OA
= Total Assets (#6) – Cash and short term investment (#1)
OL
= Total Assets – STD – LTD – MI – PS - CE
STD = Debts included in current liabilities (#34)
LTD = Long term debts (#9)
MI
= Minority interests (#38)
PS
= Preferred stocks (#130)
CE
= Common equity (#60)
NOA
= Raw NOA /Lagged total assets
Ind_NOA
=Equal weighted NOA within each industry each industry month
Earnings
= Income from continuing operations (#178)/lagged total assets
Ind_Earning = Equal weighted Earnings within each industry each month
Raw Accruals = (∆CA-∆Cash)-(∆CL-∆STD-∆TP)-Dep, where ∆ is the annual change,
CA = Current assets (#4)
CL = Current liabilities (#5)
TP
= Income tax payable (#71)
Dep = Depreciation and amortization (#14)
Accruals
= Raw accruals / Lagged total assets
(Continued)
37
Table 3.1: Continued
Ind_Accruals = Equal weighted Accruals within each industry each month
MV
= Fiscal year end closing price*shares outstanding (#199*#25)
Ind_MV
= Equal weighted MV within each industry each month
B/M
= The ratio of BV divided by MV (as defined above)
Ind_B/M
= Equal weighted B/M within each industry each month
Momentum = The previous year’s stock return from month t-12 to t-2
Ind_Momentum =Equal weighted Momentum within each industry each month
Ret
= Monthly raw buy and hold return
Ind_Ret
= Equal weighted Ret within each industry each month
Adjret
= Size, book to market and momentum adjusted return*
* The monthly abnormal return for any individual stock is calculated by subtracting the
equal-weighted return of a benchmark portfolio (5*5*5) matched by size, B/M and
momentum from the monthly buy and hold raw return of that stock.
38
Short
Name
Agric
Food
Soda
Beer
Smoke
Toys
Fun
Books
Hshld
Clths
Hlth
MedEq
Drugs
Chems
Rubbr
Txtls
BldMt
Cnstr
Steel
FabPr
Mach
ElcEq
Misc
Autos
Aero
Ships
Guns
Gold
Mines
Coal
Enrgy
Util
Telcm
PerSv
BusSv
(A)
(B)
(C)
(D)
(E)
(F)
%
%
%
%
ind_NOA1 ind_NOA8 ind_Acc1 ind_Acc8 NOA Accruals
2.44%
2.44%
7.32%
4.88%
N
N
0.00%
7.32%
0.00%
2.44%
N
N
12.20%
7.32%
N
N
24.39%
19.51%
9.76%
9.76%
9.76%
4.88%
N
N
17.07%
9.76%
N
N
26.83%
19.51%
9.76%
4.88%
7.32%
36.59%
Y
Y
2.44%
12.20%
N
36.59%
34.15%
Y
2.44%
2.44%
4.88%
26.83%
Y
Y
2.44%
2.44%
0.00%
9.76%
Y
Y
0.00%
4.88%
0.00%
N
46.34%
Y
2.44%
2.44%
N
N
78.05%
29.27%
7.32%
0.00%
N
N
19.51%
51.22%
4.88%
0.00%
14.63%
N
N
41.46%
2.44%
4.88%
4.88%
0.00%
N
Y
4.88%
4.88%
2.44%
0.00%
N
N
0.00%
7.32%
0.00%
4.88%
N
N
0.00%
4.88%
0.00%
0.00%
N
Y
4.88%
7.32%
14.63%
N
N
46.34%
0.00%
2.44%
0.00%
0.00%
N
N
4.88%
9.76%
17.07%
14.63%
N
Y
0.00%
4.88%
2.44%
9.76%
Y
Y
0.00%
0.00%
2.44%
7.32%
N
N
12.20%
17.07%
17.07%
N
N
24.39%
0.00%
0.00%
2.44%
2.44%
Y
Y
14.63%
0.00%
2.44%
14.63%
Y
Y
4.88%
14.63%
9.76%
N
N
51.22%
7.32%
12.20%
14.63%
N
N
46.34%
4.88%
N
N
21.95%
19.51%
31.71%
0.00%
14.63%
7.32%
4.88%
N
N
2.44%
N
N
21.95%
24.39%
51.22%
2.44%
2.44%
N
31.71%
80.49%
Y
0.00%
2.44%
0.00%
N
29.27%
Y
2.00%
N
20.00%
32.00%
50.00%
Y
9.76%
9.76%
N
26.83%
19.51%
Y
7.32%
7.32%
4.88%
24.39%
Y
Y
Table 3.2: Frequency of an Industry in the Extreme Industry NOA and Industry
Accruals Portfolio and the Intra-Industry NOA and Accruals Strategies
(Continued)
39
Table 3.2: Continued
Boxes
Comps
Chips
LabEq
Paper
Boxes
Trans
Whlsl
Retail
Meals
Banks
Insure
RlEst
Fin
6.98%
7.32%
2.44%
0.00%
0.00%
6.98%
2.44%
0.00%
21.95%
0.00%
12.20%
78.05%
2.44%
31.71%
2.33%
19.51%
2.44%
4.88%
2.44%
2.33%
4.88%
14.63%
2.44%
24.39%
12.20%
4.88%
21.95%
12.20%
11.63%
2.44%
2.44%
0.00%
0.00%
11.63%
68.29%
0.00%
0.00%
60.98%
7.32%
19.51%
7.32%
9.76%
2.33%
48.78%
24.39%
26.83%
2.44%
2.33%
2.44%
46.34%
4.88%
2.44%
34.15%
4.88%
7.32%
17.07%
N
Y
Y
Y
N
N
Y
Y
Y
Y
N
Y
Y
Y
N
Y
Y
N
N
N
N
Y
Y
N
N
N
N
Y
NOA and Accruals are defined in Table 3.1. Every month, 48 industries are sorted into 8
portfolios based on the magnitude of industry NOA and industry Accruals. Ind_NOA1
(8) represents the lowest (highest) industry NOA portfolio. Ind_Acc1(8) represents the
lowest (highest) industry Accruals portfolio. For column E (F), Y indicates that the
NOA (Accruals) strategy earns significantly positive stock returns during the sample
period for the particular industry.
40
Ind_
Ind_
Ind_
Ind_
Portfolio
NOA
Accruals Momentum Earnings
Rank
Panel A: Portfolios sorted by industry NOA
0.576
-0.031
0.177
0.088
1
0.683
-0.017
0.160
0.090
2
0.725
-0.013
0.148
0.091
3
0.753
-0.009
0.140
0.098
4
0.780
-0.007
0.127
0.102
5
0.810
-0.006
0.136
0.100
6
0.859
0.000
0.124
0.097
7
1.043
-0.004
0.141
0.081
8
Panel B: Portfolios sorted by industry Accruals
0.801
-0.085
0.159
0.070
1
0.764
-0.049
0.147
0.075
2
0.751
-0.032
0.143
0.090
3
0.744
-0.020
0.151
0.091
4
0.765
-0.008
0.136
0.099
5
0.760
0.006
0.139
0.100
6
0.781
0.025
0.126
0.103
7
0.861
0.076
0.150
0.120
8
Ind_
MV
Ind_
B/M
684
720
623
722
757
671
823
879
0.648
0.831
1.024
1.096
1.351
0.934
1.801
0.836
958
722
736
724
693
776
697
575
1.015
0.880
0.955
0.909
1.112
1.814
0.975
0.861
Table 3.3: Mean Values of Industry Characteristics for Portfolios Sorted by
Industry NOA and Industry Accruals
All variables are defined in Table 3.1. Every month between July 1964 to December 2002,
48 industry portfolios are formed according to the Fama French (1997) industry
classification scheme. Then, eight portfolios are constructed, each containing 6 industries,
based on Ind_NOA (Panel A) and Ind_Accruals (Panel B) respectively. The mean values
of each industry characteristics for each industry NOA and industry Accruals portfolio
across 474 months are reported.
41
42
Ind_Earnings Ind_NOA Ind_Accruals Ind_MV Ind_B/M Ind_Momentum Ind_Adjret
Ind_Earnings
1.000
-0.001
-0.025
0.257
-0.221
0.077
0.019
0.000
<.0001 <.0001
0.906
<.0001
0.005
Ind_NOA
1.000
0.011
0.000
0.198
0.180
-0.069
-0.057
<.0001
<.0001
0.097
0.993
<.0001
<.0001
Ind_Accruals
1.000
-0.011
0.003
0.354
0.253
-0.180
-0.115
<.0001
<.0001
<.0001
0.115
<.0001
0.664
Ind_MV
1.000
0.000
-0.228
-0.090
-0.237
-0.027
-0.035
<.0001
<.0001
<.0001
<.0001
<.0001
0.946
Ind_B/M
1.000
0.001
0.126
-0.014
-0.061
-0.384
0.025
<.0001
0.042
<.0001 <.0001
0.000
0.925
Ind_Momentum
1.000
0.109
-0.130
-0.071
-0.058
0.105
0.028
<.0001
<.0001
<.0001 <.0001
<.0001
<.0001
Ind_Adjret
-0.006
0.001
0.000
1.000
0.022
-0.052
0.051
0.001
<.0001
0.337
0.835
0.959
<.0001
Table 3.4: Pearson (Spearman) Correlation Coefficients above (below) the Diagonal
All variables are defined in Table 3.1. Bold numbers indicate significance at less than 5% level (2-tailed).
42
CHAPTER 4
EMPIRICAL TESTS
4.1
The Implications of Industry NOA and Industry Accruals for Future Industry
Earnings
Table 4.1 provides the results of the annual Fama-Macbeth (1973) regression of
one to four year ahead industry Earnings on current industry Earnings and industry
NOA (Panel A) or industry Accruals (Panel B). Consistent with my argument in
Chapter 3, a high industry NOA indicates an adverse industry-wide future performance
(proxied by industry Earnings) for up to four years ahead conditional on current
industry Earnings information. In contrast, industry Accruals provide no reliable
information in addition to industry Earnings for future industry-wide performance.
The results, together with the following return tests, are consistent with the
behavioral argument. If investors have limited attention and are unable to fully digest
the information contained in Accruals or NOA about future financial performance
(Hirshleifer et al., 2004), it won’t hurt their overall assessment of the future industry
43
performance by ignoring the Accruals information. However, they will overestimate the
future industry wide financial performance for high NOA industries and underestimate
the performance for low NOA industries. Therefore, industries with extremely high
NOA are overvalued and the industries with extremely low NOA are undervalued. If so,
NOA can be a predictor for stock returns at the industry level.
4.2
Portfolio Tests
4.2.1
Industry Portfolio Tests
The industry portfolio tests directly address the question of whether the industry
component of NOA is a predictor of future stock returns. Every month from July 1964
to December, 2002, 48 industries are sorted into eight portfolios, each containing 6
individual industries, based on the industry NOA. Then, a hedging strategy of going
long equally in the bottom six industries (lowest NOA industries) while shorting equally
the top six industries (highest NOA industries) is implemented. The time series average
means of the hedge returns along with the associated t-stat are reported.
For the rest of the paper, the portfolios are rebalanced monthly and the time
series means for 474 months are reported. The annually rebalanced portfolio technique
is widely used in the accounting literature (Sloan, 1996; Xie, 2001). There are three
advantages to performing statistical tests based on monthly portfolios instead of on
annual portfolios. First, it can easily line up firms by calendar time rather than by fiscal
time, so as to insure both the freshness of the information and the feasibilities of a
trading strategy. Second, it reduces the survivor-ship bias inherent in portfolios
44
rebalanced annually. Third, it avoids compounding annual buy and hold returns
(BHAR). Fama (1998) points out that market efficiency is tested jointly with a model
for expected (normal) returns. Therefore, tests of efficiency can be contaminated by a
bad model problem. The bad model problem is less serious in shorter return window
studies, but grows with the return horizon, and is most acute with long term BHAR,
which compound (multiply) an expected returns model’s problem.
As reported in Panel A of Table 4.2, the strategy yields an average monthly
profit (abnormal returns) of 0.73% (8.76% annualized, t=5.73), for the zero-cost
investment portfolio. As argued in Moskowitz and Grinblatt (1999), aggregating stocks
into the industry portfolios largely eliminates the firm-specific components of returns,
due to the large number of firm members in each portfolio. In the next chapter, I
investigate whether concentration of industries exposes the portfolios to systematic
macro level risk factors.
The results are consistent with hypothesis H1(a) that investors’ misperceptions
of NOA can impact industry asset pricing. In addition, the industry NOA strategy
generates equally strong and significant abnormal returns for both the long
(Adjret=0.38%, t=4.34) and short (Adjret=0.35%, t=-4.21) sides of the trading strategy,
indicating that short sales constraints cannot fully explain the anomalous industry NOA
effect.
Panel B of Table 4.2 indicates that Accruals fail to predict returns at the industry
level. The average monthly abnormal return for the industry Accruals strategy is only
0.04% (t=0.49). Interestingly, a close examination of the descriptive data (Panel B of
45
Table 2) reveals that it is not a lack of variations in Accruals between the lowest and
highest industry Accruals portfolios that is responsible for the finding. The dispersion of
industry Accruals (ranging from -0.085 to 0.090 to lagged total assets), is about the
same as that of Accruals portfolios formed at the firm level.
The results are consistent with the argument that the Accruals anomaly is driven
by investors’ inabilities to digest idiosyncratic information such as firm specific
opportunistic accruals manipulation. This result gives credence to the assumption in
previous literature that Accruals aggregated at the industry level serve as an appropriate
benchmark for measuring non-discretionary accruals, and do not predict future stock
returns.
As robustness checks, I also apply the time-series approach of Fama and French
(1993). The time series approach estimates risk measures (factor loadings) and then
evaluates the overall fit of a factor pricing model in a simultaneous test. It thereby
mitigates the errors-in-variables problem associated with separate estimations of risk
measures. Unreported results show that the regression of the payoffs from the industry
NOA strategy on the value-weighted or equal-weighted market portfolio return alone
yields an insignificant coefficient on the market return and an adjusted R2 of about zero.
This suggests that the industry NOA portfolio is a zero-beta portfolio relative to the
market. The intercept of this regression, which is the CAPM alpha, is almost identical
to the raw hedge return (CAPM alpha=0.84%, t-stat=4.82)
Fama and French (1993) expand the traditional CAPM model to a three factor
model. Their time series model says that the excess expected return on a zero-
46
investment portfolio is explained by the sensitivity of its return to the three factors as
followings:
E(Ri)t-Rf=bi[E(Rm)-Rf]t+siE(SMB)t+hiE(HML)t,
(4.1)
where E(Rm)-Rf, E(SMB) and E(HML) are expected premia and the factor
loadings are the slopes in the following time-series regression,
Ri-Rf=a+bi(Rm-Rf)+siSMBt+hiHMLt+ei.
(4.2)
Rm-Rf, SMB and HML are market, size and book to market factors obtained
from the Kenneth French data library. The dependent variable is the excess payoff from
the zero-investment industry NOA portfolio. If the three factors model can fully explain
the industry NOA effect, one will observe an intercept which is indifferent from zero.
The empirical result shows that the Fama-French 3-factor α, and its associated t-stat, are
quite similar to the characteristics-adjusted hedge return and the t-stat (three factor
alpha=0.72%, t-stat=5.47).
Since the momentum effect cannot be explained by the Fama-French three
factor model (Fama and French 1996), Carhart (1997) extends the model into a four
factor one by incorporating the momentum factor. I also report the intercept for the four
factor model, which is 0.64% (t-stat=4.76). This suggests that the industry NOA effect
cannot be explained by the expanded 4 factor either.
47
Table 4.2 also reports the CAPM, Fama-French 3-factor α and the 4-factorα α
for industry Accruals strategy. Again, the results are consistent with the hedge returns
from the industry Accruals portfolio tests.
Panel A of Figure 4.1 plots the time-series abnormal returns starting from 5
years before to 5 years after the portfolio formation year for the highest and the lowest
industry NOA portfolios respectively. The high NOA industries experience steady
increases in abnormal returns from year -5 to -1, and then the abnormal returns start
dropping at year 0, but are still positive. In contrast, the low NOA industries on average
exhibit downward trends in returns from year -4 to -1, then there is a bounce back at
year 0. At year 0, there is no significant difference between the abnormal returns
earned by the highest industry NOA portfolio and those earned by the lowest industry
NOA portfolio.
This pattern suggests that investors partially understand the positive effects
associated with the low NOA industries and adjust the valuations upwards
correspondingly. In contrast, investors are still too optimistic about the high NOA
industries, although to a much less extent than in previous years. The abnormal returns
for the industry groups with the highest (lowest) NOA continue to drop (increase) in the
next several years. In addition, the pattern is also consistent with the notion of price
convergence that the prices do not adjust to fundamental value instantly by fiat. Price
convergence toward fundamental value is better characterized as a process and this
process requires time (Lee, 2001).
48
Panel 2 of Figure 4.1 provides the plot of cumulative abnormal returns (CAR),
corresponding to the same time periods. The low NOA industry group eventually
outperforms the high NOA industry group after year +1.
Panels 1 and 2 of Figure 4.2 plot similar graphs based on the industry Accruals
strategy. The pattern described above for industry NOA does not present here for
industry Accruals.
4.2.2
Random Industry Portfolio Tests
The above industry portfolio test provides direct evidence that industry NOA
negatively predict future abnormal returns. However, this test doesn’t preclude the
possibility that the anomalous returns associated with industry portfolios are just due to
grouping firms based on firm-level characteristics documented to predict returns. That
is, the results may be spurious because of the positive correlations between industry
NOA and firm level NOA.
In this section, I adopt the random industry portfolio technique recommended by
Moskowitz and Grinblatt (1999), which is designed to isolate the role of industry in an
industry portfolio test. Specifically, each month t, every true stock in industry j is
replaced with another stock that has virtually the same NOA (Accruals) level but is
drawn from a random industry.16 In essence, random industry portfolios preserve the
same magnitude of NOA (Accruals) as the industry NOA (Accruals) portfolios, but
contain stocks from various industries.
16
Please refer to the notes for Table 4.2 for the detailed construction of random industry portfolios.
49
Since the construction of random industry NOA (Accruals) portfolios destroys
the industry grouping, a random industry NOA (Accruals) strategy will exhibit no
anomalous returns if the industry common component of NOA (Accruals) is the only
driving force for the NOA (Accruals) effect. In contrast, the random industry NOA
(Accruals) strategy will generate more abnormal returns than the industry NOA
(Accruals) strategy, if the firm-specific component of NOA (Accruals) is fully
responsible for the NOA (Accruals) effect, since the construction relaxes the restrictions
imposed by the industry NOA (Accruals) portfolios. Otherwise, the random industry
NOA (Accruals) strategy will be less profitable than the industry NOA (Accruals)
strategy, if both the industry-common and the firm-specific component of NOA
(Accruals) account for the NOA (Accruals) effect.
As demonstrated in Panel C of Table 4.2, the average monthly profit from the
random industry NOA portfolio strategy is 56% less than that from the industry NOA
strategy (0.32% vs. 0.73% monthly abnormal return). The t-stat for the difference
between the mean payoffs from these two strategies is significant at the 0.01 level
(difference=0.41% per month, t-stat=3.58), indicating that the industry NOA effect is
significantly driven by industry. As expected, the random industry Accruals strategy
produces significantly abnormal returns (average abnormal return=0.17%, t=3.89),
consistent with the conjecture that the Accruals effect reflects firm-specific information
that investors fail to fully understand. However, the t-stat for the difference between the
industry Accruals and the random industry Accruals strategy is not significant.
50
4.2.3
Industry-Adjusted Profits
In the previous two sub-sections, I presented evidence that the industry NOA
effect exists, even after controlling for the known asset pricing factors such as size, B/M,
and momentum. In this subsection, I test hypothesis H1(b), which states that the
industry adjusted component of NOA can still predict returns after removing the
industry effect, due to its ability to retain firm specific information. To address the
question, I form portfolios based on the industry adjusted component of NOA, which is
constructed by subtracting each stock’s contemporaneous industry common component
of NOA from its own NOA.
Asness et al. (2000) argue that a firm’s probability of earning economic rents is
more a function of its position within its industry, rather than its position relative to all
firms in the economy. They find that profits from hedge portfolios sorted by industry
adjusted variables such as industry adjusted size, industry adjusted B/M ratio and
industry adjusted cash flow-to-price ratio are relatively higher (with smaller standard
errors) than those sorted by their unadjusted counterparts.
Therefore, if the cross-industry variation component is well understood by
investors, the information about future returns in a variable is best measured as the
difference from its industry mean. Investments based on the industry adjusted
component of NOA (Accruals) will make similar or more profits than those based on
the unadjusted NOA (Accruals). If both the industry-common and the firm-specific
components of NOA (Accruals) account for the NOA (Accruals) effect, one would
expect that a trading strategy based on industry-adjusted NOA (Accruals) alone will
51
make less profit than one based on its unadjusted counterpart, since it only explores one
piece of information. Otherwise, zero profit is expected if the industry-common
component of NOA (Accruals) is the only driving force for the anomalous returns.
For comparison, Panels C and D of Table 4.3 replicate firm level NOA and
Accruals strategies in my sample, both of which yield significant monthly profits of
1.33% (t=11.41) and 0.72% (t=7.47) respectively.
Panels A and B of Table 4.3 report the profits of the hedge portfolios sorted by
the industry adjusted NOA and the industry adjusted Accruals respectively. As the table
shows, the average hedge profits from the industry adjusted NOA strategy decline about
one quarter to 103 basis points per month from those of their unadjusted counterparts
(133 basis points). The difference in payoffs between the industry adjusted NOA
strategy and the NOA strategy is significant at the 0.01 level for both raw return
(difference=-0.37%, t=-3.92) and adjusted return (difference=0.30%, t=-4.29).The
findings are consistent with the argument that the firm-specific component of NOA
contains information that is not fully impounded into current stock prices and that the
pricing ability of NOA declines because of the loss of information about future returns
in the industry component of NOA.
The monthly average profit from the industry adjusted Accruals strategy exhibits
the same magnitude (even with the same t-statistics), as that from the Accruals strategy.
The difference between these two strategies is not significant at all. Therefore, Accruals
won’t lose any pricing abilities by focusing only on the firm specific component of
Accruals. This, together with the empirical evidence in Table 4.2, implies that the
52
Accruals effect is essentially driven by investors’ misperceptions of the firm-specific
information (Teoh et al., 1998a, b; Xie, 2001).
Appendix A-2 outlines the results from the industry portfolio test, the random
industry portfolio test, the industry adjusted portfolio test, and the firm level portfolio
test for the 14 industries, the 20 industries and the GICS classification respectively. The
results reported in this section are robust with respect to all of the above three industry
grouping schemes and are particularly strong for the GICS industry classification.
4.3
Fama-Macbeth Monthly Cross-Sectional Regression Tests
In this section, I apply Fama-Macbeth monthly cross-sectional regressions to
investigate the relationship between industry NOA and subsequent returns subject to an
expanded set of risk controls. These controls consist of size, B/M, the intermediate 11month returns (for the Jegadeesh and Titman (1993) momentum effect), the short-term
one-month return (for the Jegadeesh (1990) contrarian effect), and the long-run 3-year
returns (using returns from month -36 to -13 for the DeBondt and Thaler (1985) reversal
effect). Further advantages of the Fama-Macbeth regression method include being able
to control for cross-sectional correlations of the error terms and to use all available
observations rather than focusing only on extreme value portfolios. 17
The evidence in Table 4.4, Panel A, confirms previous findings in the literature:
There are a strong short-term return reversal, a long-term return reversal, Accruals and
NOA effects at the firm level after controlling for the size, B/M and momentum effects.
17
Please refer to Appendix B-I for a detailed discussion on the Fama-Macbeth procedure.
53
One may notice that the coefficient for NOA is smaller than that for Accruals. This is
not inconsistent with the result of the portfolio test that NOA has stronger return
predictabilities than Accruals. The magnitude of the coefficient itself cannot be directly
interpreted as profits from the underlying trading strategy (Bernard and Thomas, 1990).
One should go for the results from the portfolio test to interpret the economic
significance of the predicted variable. The smaller coefficient, together with the larger tstat for NOA, implies that NOA is more reliable than Accruals in predicting future
returns.
Panel B of Table 4.4 reports the same cross-sectional regression results as in
Panel A by decomposing individual NOA (Accruals) into the industry-common and the
industry-adjusted components. The t-statistics associated with Ind_NOA and
Ind_Accruals are -5.13 and -0.96 respectively. The Adj_NOA and Adj_Accruals remain
highly significant (t=-11.68 and -8.73 respectively).
Panel C of Table 4.4 reports the results of the further decomposition of the
industry NOA into the industry working capital and the industry investment
components, and also the decomposition of the industry adjusted NOA into the industry
adjusted working capital and the industry adjusted investment components. The
decompositions are designed to investigate the following question: Does the time series
aggregation property of NOA or the investment information that is not available to
Accruals make the difference in the return predictabilities between industry NOA and
industry Accruals? Working capital is the time series aggregation of operating accruals.
The fact that the industry working capital component of NOA can predict returns at the
54
industry level (t=-6.23) while industry Accruals cannot indicates that the time series
aggregation property of NOA is one of the key sources of the industry NOA return
predictabilities. The industry investment assets component itself is also a strong
negative predictor for future returns (t=-5.28), indicating the important contribution of
investment information to the industry NOA strategies.
Table 4.5 provides the Fama-Macbeth monthly regression tests at the industry
portfolio level. This test directly addresses the question of whether the industry NOA
and the industry Accruals can be determinants for industry returns.
For every monthly regression, the dependent variable of the regression is equal
weighted industry return, and the independent variables are industry size, industry B/M
ratio, one month ahead industry return, 12 month industry momentum, 36 month
industry returns, industry NOA and/or industry Accruals. Therefore, each month, there
are 48 cross-sectional observations. Then, the time-series averages of coefficients along
with their t-statistics are reported. Consistent with the earlier literature, size and B/M
play no role in industry asset pricing (Asness at al., 1997), one month reversal at the
firm level turns to be one month continuation at the industry level (Grinblatt and
Moskwitz, 1999) potentially due to the microstructure effects, momentum effects still
remain strong at the industry level.
The result also confirms the findings from the previous section that the stock
returns of high NOA industries as a group will outperform those of low NOA industries
even subject to an expanded set of asset pricing controls.
55
Panel A: The implications of current Ind_NOA for future 1 to 4 year head Ind_Earnings
Dependent Variable
1-Year ahead Ind_Earnings
2-Year ahead Ind_Earnings
3-Year ahead Ind_Earnings
4-Year ahead Ind_Earnings
Intercept Ind_Earnings
0.057
0.600
5.30
11.97
0.080
0.510
7.71
9.93
0.076
0.458
5.82
8.34
0.091
0.444
8.05
7.93
Ind_NOA
-0.026
-2.30
-0.041
-3.91
-0.029
-2.44
-0.047
-4.29
Adjust R2
59%
43%
34%
33%
Panel B: The implications of current Ind_Accruals for future 1 to 4 year ahead
Ind_Earnings
Dependent Variable
1-Year ahead Ind_Earnings
2-Year ahead Ind_Earnings
3-Year ahead Ind_Earnings
4-Year ahead Ind_Earnings
Intercept Ind_Earnings Ind_Accruals
0.036
0.607
-0.025
-0.77
5.25
11.91
0.046
0.521
-0.067
-1.35
5.46
9.75
0.053
0.463
-0.036
-0.70
5.54
8.29
0.053
0.453
-0.089
-1.86
5.14
7.82
Adjust R2
58%
43%
36%
32%
Table 4.1: The Implications of Current Industry NOA and Industry Accruals for
Future One to Four Year ahead Industry Earnings
All variables are defined in Table 3.1. Each year, the cross-section one to four year
ahead industry Earnings are regressed on current Industry Earnings and current industry
NOA (Panel A) or current industry Accruals (Panel B). The time-series average of the
annual coefficients estimates and their associated time-series t-statistics (in italics) are
reported. Bold numbers indicate significance at less than 5% level (2-tailed t-test).
56
Portfolio
1 (Lowest)
2
3
4
5
57
6
7
8(Highest)
Hedge
(L-H)
Difference
t-stat
Panel A: Ind_NOA Panel B: Ind_Accruals
Ret
Adjret
Ret
Adjret
0.0165
0.0038
0.0114
-0.0009
-0.95
4.91
4.34
3.67
0.0164
0.0034
0.0129
0.0002
0.27
5.17
4.71
4.54
0.0136
0.0005
0.0153
0.0014
0.77
4.78
5.50
2.02
0.0125
-0.0009
0.0130
0.0005
-1.68
0.90
4.34
4.72
0.0110
-0.0018
0.0130
0.0003
0.57
3.96
-3.04
4.43
0.0119
-0.0008
0.0141
0.0009
-1.23
1.56
4.28
4.59
0.0116
-0.0005
0.0115
-0.0008
-0.71
-1.34
4.09
3.78
0.0080
-0.0035
0.0110
-0.0015
2.49
-4.21
3.42
-2.14
0.0085
0.0073
0.0004
0.0004
0.24
0.49
4.95
5.64
Ind_NOA/Random
Ind_Accurals/Random
Industry NOA
Industry Accruals
0.0049
0.0041
-0.0032
-0.0013
-1.22
-0.92
3.36
3.58
Panel C : Random
Industry NOA
Ret
Adjret
0.0141
0.0016
4.55
4.32
0.0132
0.0004
1.44
4.52
0.0132
0.0004
1.50
4.64
0.0133
0.0005
1.95
4.63
0.0122
-0.0003
-0.93
4.29
0.0114
-0.0010
4.02
-3.64
0.0119
-0.0006
4.13
-2.19
0.0105
-0.0015
3.49
-4.89
0.0036
0.0032
5.04
5.66
Panel D : Random
Industry Accruals
Ret
Adjret
0.0141
0.0006
4.55
2.01
0.0132
0.0004
1.21
4.52
0.0132
0.0005
1.76
4.64
0.0133
-0.0002
-0.59
4.63
0.0122
0.0002
0.86
4.29
0.0114
-0.0002
-0.75
4.02
0.0119
-0.0003
-1.19
4.13
0.0105
-0.0011
3.49
-3.90
0.0036
0.0017
5.04
3.89
Table 4.2: Average Monthly (Abnormal) Returns for Portfolios Sorted by Industry NOA, Industry Accruals, Random
Industry NOA and Random Industry Accruals, One Year after the Portfolios’ Formation
(Continued)
57
Table 4.2: Continued
CAPM α
3-Factor α
4-Factor α
0.0084
4.82
0.0082
4.72
0.0064
4.76
0.0072
5.48
0.0072
5.47
0.0064
4.76
0.0006
0.40
0.0013
0.83
0.0017
1.02
0.0010
0.75
0.0098
0.76
0.0012
0.86
0.0036
4.90
0.0037
5.16
0.0035
4.65
0.0031
5.53
0.0032
5.53
0.0032
5.39
0.0023
4.30
0.0025
4.25
0.0028
4.87
0.0018
4.11
0.0018
4.08
0.0021
4.66
58
All variables are defined in Table 3.1. For Panel A and Panel B, every month between July, 1964 and December, 2002, firms
are assigned into 8 portfolios, each containing 6 individual industries, based on Ind_NOA and Ind_Accruals of the nearest
available fiscal year respectively. To allow for a minimum of a four-month lag between the fiscal year end and the return
month, all returns are measured from the 5th month to the 16th month after the fiscal year end. The hedge portfolio consists of a
long position in the highest ranked portfolio and an offsetting short position in the lowest ranked portfolio. The intercepts,
α, from time-series regressions of the returns of the hedge portfolio on the CAPM model, which employs excess return of the
market portfolio, the Fama-French three factor model, which contains the market portfolio and two factor-mimicking
portfolios associated with the size effect (SMB) and the book-to-market effect (HML) and a four factor model which adds a
momentum factor-mimicking portfolio to the previous factors, are also reported. For Panel C and Panel D, the random
industries are generated by replacing return for each stock in the industry portfolio with an equal weighted average of the
stocks ranked above and below it based on the overall NOA and Accruals ranking respectively. To avoid endpoint problems,
stock 1 and N is replaced by stock 2 and N-1respectively. In essence, the random industry portfolios have the same industry
NOA/industry Accruals magnitude as the true industry portfolios, but contain stocks from various industries. The values in
italics are t-statistics based on the time-series of the monthly portfolio abnormal stock returns. Bold numbers indicate
significance at less than 5% level (2-tailed t-test).
58
Portfolio
1 (Lowest)
2
3
4
5
59
6
7
8(Highest)
Hedge
(L-H)
Difference
t-stat
Panel A: Adj_NOA
Ret
Adjret
0.0156
0.0038
4.47
6.19
0.015
0.0023
4.8
5.52
0.0144
0.0014
5.04
4.48
0.0139
0.0009
5.13
2.53
0.0138
0.0005
1.37
5.19
0.0128
-0.0004
-1.04
4.76
0.0104
-0.002
3.67
-5.27
0.0043
-0.0065
1.29
-13.15
0.0113
0.0103
10.29
12.05
Adj_NoA / NOA
-0.0037
-0.0030
-3.92
-4.29
Panel B: Adj_Accruals
Ret
Adjret
0.0146
0.0020
4.04
2.91
0.0151
0.0018
5.14
5.07
0.0142
0.0013
5.23
3.69
0.0138
0.0010
5.32
2.97
0.0127
0.0002
0.55
5.02
0.0124
0.0000
-0.11
4.53
0.0113
-0.0010
3.73
-2.79
0.0060
-0.0052
1.72
-10.63
0.0086
0.0072
7.24
7.47
Adj_Accruals / Accruals
0.0001
0.0000
0.24
-0.12
Panel C : Firm NOA
Ret
Adjret
0.0177
0.0057
4.85
6.95
0.0163
0.0032
5.08
6.92
0.0150
0.0016
5.20
4.59
0.0143
0.0011
5.26
2.90
0.0133
0.0000
0.01
4.99
0.0118
-0.0010
4.49
-2.59
0.0093
-0.0028
3.38
-6.65
0.0027
-0.0077
0.78
-12.97
0.0150
0.0133
9.67
11.41
Panel D : Firm Accruals
Ret
Adjret
0.0144
0.0018
3.89
2.36
0.0148
0.0015
5.13
3.94
0.0145
0.0017
5.47
4.81
0.0134
0.0007
5.26
2.04
0.0132
0.0004
1.13
5.12
0.0127
0.0001
0.35
4.56
0.0114
-0.0008
3.75
-2.16
0.0059
-0.0054
1.64
-10.28
0.0085
0.0072
7.27
7.47
Table 4.3: Average Monthly (Abnormal) Returns for Portfolios Sorted by Industry adjusted NOA, Industry
adjusted Accruals, NOA and Accruals, One Year after the Portfolios’ Formation
(Continued)
59
Table 4.3: Continued
CAPM α
0.0116
10.50
0.0105
12.25
0.0089
8.66
0.0071
8.12
0.0152
9.69
0.0133
11.35
0.0088
7.41
0.0071
7.32
0.0123
11.38
0.0108
12.06
0.0087
8.30
0.0070
7.91
0.0159
10.54
0.0138
12.02
0.0086
7.12
0.0069
6.99
0.0125
11.20
0.0110
12.43
0.0087
8.05
0.0070
7.95
0.0146
9.50
0.0135
11.33
0.0089
7.12
0.0072
7.06
3-Factor
α
4-Factor
α
60
NOA, Accruals, Ret and Adjret are defined in Table 3.1. Adj_NOA (Adj_Accruals) for each individual stock is calculated by
subtracting equal weighted mean NOA/Accruals of the industry to which the stock belongs from its NOA (Accruals). For
Panel A and B, every month between July, 1964 and December, 2002, firms are assigned into eight portfolios based on
Adj_NOA (Adj_Accruals) of the nearest available fiscal year. To allow for a minimum of a four-month lag between the fiscal
year end and the return month, all returns are measured from the 5th month to the 16th month after the fiscal year end. The
hedge portfolio consists of a long position in the highest ranked portfolio and an offsetting short position in the lowest ranked
portfolio. The same procedures apply to Panel C and Panel D except that the sorting variables are NOA and Accruals. The
values in italics are t-statistics based on the time-series of the monthly portfolio (abnormal) stock returns. Bold numbers
indicate significance at less than 5% level (2-tailed t-test).
60
61
Panel A: Firm-Level NOA and Accruals
Ln
Ln
Ret
Ret
Ret
Intercept
(size)
(btm)
(-1:-1)
(-12:-2) (-36:-13)
NOA
Accruals
0.0306
-0.0010 0.0034 -0.0693
0.0058
-0.0020 -0.0067
4.43
-2.16
4.45
-16.30
3.45
-3.16
-11.82
0.0265
-0.0011 0.0031 -0.0689
0.0060
-0.0022
-0.0090
3.84
-2.22
4.13
-16.17
3.54
-3.50
-7.91
0.0296
-0.0011 0.0033 -0.0695
0.0058
-0.0017 -0.0052 -0.0090
4.26
-2.27
4.34
-16.34
3.43
-2.78
-7.60
-4.81
Panel B: Decomposition of NOA (Accruals) into industry NOA (Accruals) and industry adjusted NOA (Accruals)
Ln
Ln
Ret
Ret
Ret
Ind_
Adj_
Ind_
Adj_
Intercept
(size)
(btm)
(-1:-1)
(-12:-2) (-36:-13)
NOA
NOA
ACC
Acc
0.0378
-0.0009 0.0035 -0.0698
0.0057
-0.0019 -0.0173 -0.0066
4.95
-2.02
4.81
-16.57
3.41
-3.03
-5.13
-11.68
0.0263
-0.0011 0.0032 -0.0698
0.0059
-0.0018
-0.0091 -0.0131
-0.96
3.86
-2.37
4.24
-16.45
3.56
-3.03
-8.75
0.0373
-0.0010 0.0034 -0.0708
0.0055
-0.0016 -0.0161 -0.0051 -0.0183 -0.0087
-1.92
4.85
-2.18
4.71
-16.87
3.35
-2.72
-4.59
-8.78
-5.56
Panel C: Decomposition of NOA into Working Capital and Investment
Ln
Ln
Ret
Ret
Ret
Ind_
Adj_
Ind_
Adj_
Intercept
(size)
(btm)
(-1:-1)
(-12:-2) (-36:-13)
WC
WC
Invest
Invest
0.0410
-0.0011 0.0037 -0.0710
0.0053
-0.0018
-0.0227
-0.0100
-0.0169 -0.0050
5.51
-2.35
5.26
-16.79
3.22
-2.98
-6.23
-9.11
-5.28
-7.89
Table 4.4: Fama-MacBeth Monthly Regressions of Stock Returns on Industry NOA, Industry-adjusted NOA, Industry
Accruals, Industry-adjusted Accruals and other Characteristics
(Continued)
61
Table 4.4: Continued
62
Accruals, NOA, Ind_Accruals and Ind_NOA are defined in Table 3.1. Adj_NOA and Adj_Accruals are defined in Table 4.3.
WC denotes working capital, which is calculated as the difference between non-financial current assets (#4-#1) and nonfinancial liabilities (#5-#34) over lagged total assets. Ind_WC denotes the industry equal-weighted average of working capital.
Adj_WC denotes industry adjusted working capital, which is calculated as the difference between WC and Ind_WC. Invest
denotes investment assets, which is calculated as the difference between NOA and WC. Ind_Invest denotes the industry equal
weighted average investment assets. Adj_Invest denotes the industry adjusted investment assets, which is calculated as the
difference between Invest and Ind_Invest. The Fama-MacBeth procedure is as follows: Every month t between July, 1966 and
December, 2002, the cross-section of stock returns are regressed on ln(size) where size is defined as the log of the firm’s
market capitalization; ln(B/M) which is the log of the book-to-market ratio; the previous month’s return on the stock, denoted
ret(-1: -1); the previous year’s return on the stock from month t-12 to t-2, denoted ret (-12: -2); the return on the stock starting
from month t -36 to t-13, denoted ret( -36: -13) and financial variables interested. There is a minimum of a four-month gap
between the fiscal year end and the return month in month t regressions. The time-series average of the monthly coefficient
estimates and their associated time-series t-statistics (in italics) are reported. Bold numbers indicate significance at less than
5% level (2-tailed t-test).
62
Intercept
Ln(Ind_
MV)
Ln(Ind_ Ind_Ret
B/M)
(-1:-1)
Ind_Ret
(-12:-2)
Ind_Ret
(-36:-13)
63
Model1
0.0124
1.85
-0.0002
-0.51
-0.0018
-1.17
0.0570
4.33
0.0227
6.15
-0.0039
-2.02
Model2
0.0132
2.02
-0.0003
-0.74
-0.0023
-1.52
0.0553
4.27
0.0226
6.07
-0.0032
-1.67
Model3
0.0219
3.04
-0.0003
-0.76
-0.0016
-1.07
0.0571
4.42
0.0225
6.22
-0.0027
-1.40
Model4
0.0210
2.98
-0.0004
-0.91
-0.0021
-1.38
0.0565
4.43
0.0225
6.16
-0.0023
-1.20
Ind_Accruals Ind_NOA
-0.0112
-1.76
-0.0103
-3.94
-0.0116
-1.54
-0.0089
-3.34
Table 4.5 Fama-Macbeth Monthly Regression of Industry Portfolio Returns on Industry NOA, Industry Accruals
and Other Industry Characteristics
Ind_MV, Ind_B/M, Ind_Accruals and Ind_NOA are defined in Table 3.1. Ind_m1 denotes the previous month’s industry
equal weighted average return; Ind_m12 denotes the previous year’s industry equal weighted average return from month t12 to t-2; Ind_m36 denotes the equal weighted average return for each individual industry starting from month t-36 to t13.The time-series average of the monthly coefficient estimates and their associated time-series t-statistics (in italics) are
reported. Bold numbers indicate significance at less than 5% level (2-tailed t-test).
63
Panel A: Time Series Property of Average Abnormal Returns
for the Highest vs. Lowest Industry NOA Portfolios
0.06
0.05
Abnormal Returns
0.04
0.03
0.02
0.01
0
-0.01
-5
-4
-3
-2
-1
0
1
2
3
4
5
-0.02
-0.03
-0.04
Year
Lowest Ind_NOA
Highest Ind_NOA
Cumulative Abnormal Returns
Panel B: Cumulative Abnormal Returns for the Highest vs. Lowest
Industry NOA Portfolios
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.02
-5
-4
-3
-2
-1
0
1
2
3
4
5
Year
Lowest Ind_NOA
Highest Ind_NOA
Figure 4.1: Time-series Properties of Abnormal Stock Returns
based on Industry NOA
Ind_NOA is defined in Table 3.1. Abnormal returns are annualized
characteristics adjusted returns starting four months after fiscal year
end. Year 0 is the year in which firms are ranked and assigned into 8
portfolios based on Ind_NOA.
64
Panel A: Time Series Property of Average Abnormal Returns for
the Highest vs. Lowest Industry Accruals Portfolos
Abnormal Returns
0.06
0.04
0.02
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
-0.02
-0.04
Year
Lowest Ind_Accruals
Highest Ind_Accruals
Cumulative Abnormal Returns
Panel B: Cumulative Abnormal Returns for the Highest vs. Lowest
Industry Accruals Portfolios
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.02
-5
-4
-3
-2
-1
0
1
2
3
4
5
Year
Lowest Ind_Accruals
Highest Ind_Accruals
Figure 4.2 Time-series Properties of Abnormal Stock Returns based
on Industry Accruals
Ind_Accruals is defined in Table 3.1. Abnormal returns are annualized
characteristics adjusted returns starting four months after fiscal year end.
Year 0 is the year in which firms are ranked and assigned into 8 portfolios
based on Ind_Accruals.
65
CHAPTER 5
MISPRICING OR RISK?
Both the portfolio test and the regression test are hindered by the joint hypothesis
problem. The risk adjustment process for returns requires an underlying model of market
equilibrium. Therefore, abnormal returns from trading strategies don’t necessarily imply
the rejection of market efficiency, since they could be due to a misspecification of the
equilibrium asset pricing model (Fama, 1998).
Researchers in Accounting and Finance have continually sought methods to
distinguish between the above two competitive explanations (Bernard and Thomas, 1989;
Bernard et al., 1997; Daniel et al., 1997; Campbell, 1997; Cochrane and Saa-Requejo
2000 etc.). The Accounting literature provides compelling evidence that the anomalous
returns findings are very hard to reconcile with risk explanations. For example, healthier
firms, as measured by various accounting fundamentals, often earn higher subsequent
returns (Piotroski, 2000), which is inconsistent with the intuition of risk explanations.
The evidence that a substantial portion of the abnormal returns are earned around future
66
earnings announcement dates is also difficult to explain in a risk context (Bernard and
Thomas, 1989; Sloan, 1996; Ali et al., 2003).
My results thus far are consistent with the view that industry NOA serves as an
index of investors’ misperception at the industry level and so affects industry asset
pricing. In this chapter, I consider an alternative explanation for my findings that high
NOA industries are less risky than low NOA industries, and therefore earn lower risk
premia.
5.1
The Persistence of Industry NOA Strategy during the Sample Period.
Bernard et al. (1997) propose a volatility test to disentangle the risk vs. mispricing
explanations. They argue that mispricing is indicated if anomalous returns on zeroinvestment portfolios are consistently positive, period by period. If the mean returns from
the zero-investment portfolio reflect compensation for risk, it will cause returns to be
volatile and negative in particular periods.
Panels A and B of Figure 5.1 graph year by year profits from the trading strategies
based on industry NOA and industry Accruals respectively. The industry NOA strategy is
consistently profitable in 31 out of 38 years. In great contrast, the industry Accruals
strategy generates positive returns for only half the years (19 out of 38 years).
5.2
The Sharpe Ratio of the Industry NOA Strategy
The Sharpe ratio is a traditional measure in the Finance literature to value rewards
to uncertain payoffs. The annualized Sharpe ratio of the industry NOA strategy is 0.92
67
based on the characteristic adjusted returns, offering investors a very attractive reward
relative to the risk. For comparison, the Sharpe ratio associated with the market excess
return (holding the market) is only 0.36 during the same period of time. If one views the
CAPM theory and market proxy for the wealth portfolio as approximations, then the
Sharpe ratio of other portfolios should not be dramatically higher than that of the market
portfolio (Cochrane and Saa-Requejo, 2001).
The size of the achievable Sharpe ratio raises some serious initial doubts about the
rational risk explanation for the industry NOA effect. There is a long tradition in finance
that regards high Sharpe ratios as “good deals”. Ross (1976) bounds asset pricing theory
residuals by assuming that no portfolios can have more than twice the market Sharpe
ratio. Previous research on the equity premium puzzle (Mehra and Prescott, 1985)
indicates that the high expected return on the stock market raises a difficult challenge for
rational asset pricing models and requires an unreasonably high marginal rate of
substitution of utility to justify it.
5.3
A Statistical Arbitrage Test
In a recent paper, Hogan et al. (2004) introduced the concept of statistical
arbitrage, a long horizon trading opportunity that generates a riskless profit.18 Statistical
arbitrage circumvents the joint hypothesis dilemma of the traditional market efficiency
tests because its definition is independent of any equilibrium model. Statistical arbitrage
is defined as a long horizon trading opportunity that generates a riskless profit. As such,
18
See Hogan et al. (2004) for a detailed discussion on statistical arbitrage.
68
statistical arbitrage is a time series analog of the limited arbitrate opportunity contained in
Ross (1976). The difference between the two concepts is that a statistical arbitrage is a
limiting condition over time, while Ross’s APT is a cross-sectional limit at a specific
time.
A statistical arbitrage satisfies four conditions: (1) it is a zero initial cost selffinancing trading strategy that in the limit has (2) positive expected discounted profits, (3)
a probability of a loss converging to zero, and (4) a time-average variance converging to
zero, if the probability of a loss does not become zero in finite time. In economics terms,
the fourth condition implies that a statistical arbitrage opportunity eventually produces
riskless incremental profit, with an associated Sharpe ratio increasing monotonically
through time. Overall, to generate statistical arbitrage, it is essential that a trading
strategy’s time-averaged variance falls over time.
Statistical arbitrage rejects the market as being in any economic equilibrium, an
important prerequisite for an efficiency market (Jarrow, 1988). A statistical arbitrage will
induce investors to engage in trading and consequently, will prevent the market from
reaching equilibrium. The existence of a single trader operating under a finite time
horizon who is willing to pursue a statistical arbitrage is sufficient for one to conclude
that these trading opportunities reject the market efficiency hypothesis.19
In this section, I investigate whether the industry NOA strategy survives the
statistical arbitrage test. If the industry NOA profit is not a statistical arbitrage
19
The investor increases his expected utility by pursuing a statistical arbitrage opportunity. Taking an
infinitely large position in the zero cost self-financing asset is possible. Hence, the economy cannot be in
equilibrium if such trading strategies exist.
69
opportunity, then the significant abnormal returns documented in the previous section
may be premium(s) compensating for industry-related risk(s). Otherwise, the result tends
to reject the market efficiency hypothesis.
The test of statistical arbitrage requires no information beyond the traditional
intercept test. An investment of $1 is maintained in the portfolios at all times. The selffinancing condition is enforced by investing (borrowing) trading profits (losses)
generated by the trading strategy at the risk free rate. Specifically, monthly time series
hedge (raw) returns (Hret(ti))are first generated from the industry NOA (industry
Accruals) strategy. Then, the trading profits V(ti-1) accumulate at the risk free rate r(ti) to
yield cumulative trading profits: V(ti)=Hret(ti)+V(ti-1)*[1+r(ti-1)] (V(t0)=0). This
cumulative trading profit is then discounted by B(ti)=exp{∑ r(ti)} to construct discounted
cumulative trading profits v(ti). Let ∆vi= v(ti)-v(ti-1) denote increments of the discounted
cumulative trading profits. Under the assumption that ∆vi evolves according to the
following process20
∆vi=µiθ+δiλzi
(5.1)
for i=1, 2 ,…, n, where zi are i.i.d N(0,1) random variables with z0=0. Both v(t0) and ∆v0
are zero, the discounted cumulative trading profits generated by the trading strategy are
distributed as
20
The functional form of the coefficients in Eq. (6) allows for a large variety of potential changes to the
mean and variance. Moreover, misspecification of the incremental trading profit process will increase the
likelihood of accepting the null hypothesis of no statistical arbitrage (Hogan et al. 2004)
70
n
n
n
i =1
i =1
i =1
v (t n ) = ∑ ∆v i ~ dN ( µ ∑ i θ , δ 2 ∑ i 2 λ )
(5.2)
while the log likelihood function for the increments in (5.1) equals
log L( µ , δ 2 , λ , θ | ∆v) = −
1 n
1
log(δ 2 i 2 λ ) − 2
∑
2 i =1
2δ
n
1
∑ i λ (∆v
i =1
2
i
− µi θ ) 2 ,
(5.3)
using the maximum likelihood estimation method to generate the four parameters. Under
the constrained mean test (θ=0)21 and Theorem 1 of Hogan et al. (2004), a trading
strategy generates a statistical arbitrage with 1-α percent confidence, if the following
conditions are satisfied:
H(1): u>0
H(2): λ<0,
The sum of the individual p-values forms an upper bound of the test’s type I error
by Bonferroni inequality. For λ<0, the marginal decrease in the portfolio’s volatility itself
declines over time, which ultimately satisfies the fourth condition of the statistical
21
Hogan et al. (2004) demonstrate that the constrained mean model is more appropriate for modeling the
observed incremental trading profits, because the unconstrained mean model spreads the information
contained in trading profits over an additional variable without offering an improved fit, thereby weakening
the power of the statistical arbitrage test. See Hogan et al. (2004) for a more detailed discussion of the
constrained mean vs. unconstrained mean statistical test.
71
arbitrage. In contrast, the traditional single t-test for trading profits only considers the
mean effect and is not sufficient for statistical arbitrage.
Table 5.1 reports the statistical arbitrage test results for the industry NOA and the
industry Accruals strategy respectively. The risk free rates are obtained from Kenneth
French’s website. The mean discounted incremental profit (µ) associated with industry
NOA strategy is 0.20% per month (p-value<0.0001) with an estimated growth rate of
standard deviation of -0.56 (p-value<0.0001). Thus, the sum of p-value is still <0.0001,
implying that the industry NOA strategy satisfies the requirements of the statistical
arbitrage.
In contrast, the discounted incremental profit for the industry Accruals strategy is
not significantly differently from 0 (µ=-0.0001, p-value=0.65). The significant negative
growth rate of standard deviation of the industry Accruals strategy simply means that the
probability of making no money converges to 1.
The limitation of the statistical arbitrage test is that it is still an in-sample test. The
test in this section provides evidence that investors overlooked the arbitrage opportunities
associated with the industry NOA during the sample period.
5.4
The Industry NOA Strategy and the Business Cycle
The analyses in the above sections largely alleviate the concerns that the (omitted)
risk factors associated with firm level characteristics can explain the industry NOA
anomaly. In Chapter 2, I argue that NOA contains information about firms’ business
environments. Since business environments tend to correlate for firms within the same
72
industry, the industry common component of NOA will carry information about industry
wide business conditions. Therefore, it is relevant to examine whether the industry NOA
effect is a manifestation of the macroeconomics risk(s) associated with business cycles.
More recent studies investigate the issues of macroeconomics factors as
determinants for future stock returns (Chen et al., 1986). Fama (1981) documents the
presence of a positive and statistically significant relation between the market factor and
future economic growth in the United States. Liew and Vassalou (2000) document the
global evidence that the HML (book to market factor) and SMB (size factor) are
positively related to future growth in the real economy. They claim their findings support
HML and SMB as state variables in the context of Merton’s intertemporal capital asset
pricing model. The evidence for momentum effect is mixed. Chordia and Shivakumar
(2002) find that the profits of momentum strategy disappear once stock returns are
adjusted for their predictabilities based on the macroeconomic variables; therefore, they
propose that the role for time-varying expected returns as an explanation for momentum
effect. In contrast, Liew and Vassalou (2000) and Griffin et al. (2003) find little evidence
for a relationship between the momentum factor and the real economy.
In this section, I first uncover an interesting time variation in profits from the
industry NOA strategy. Adjusted returns to the strategy are much higher during the
recession periods22 with an average payoff of 1.10% per month (t-stat=4.14). During
expansion, the average profit is 0.67% per month (t-stat=4.41). This is in great contrast to
the findings of Chordia and Shivakumar (2002) about the momentum effects, which are
22
The business cycle data are obtained from the National Bureau for Economic Research (NBER) website.
73
only significant during the expansion periods. The finding also reveals that the industry
NOA strategy works reasonably well for both good and bad states.
Then, following Liew and Vassalou (2000), I examine the relation between the
industry NOA payoff and future GDP growth using univariate and multivariate
regression analysis. The regression use the quarterly data
GDPgrowth(t,t+4)=α+β*FactorRet(t-4,-t)+e(t,t+4)
(5.4)
where GDPgrowth is the compounded growth rate in real GDP over quarter t to t+4. The
real GDP growth data is obtained from the website of the Bureau of Economic Analysis
(www.bea.gov). Factors are payoffs from Ind_NOA strategy (PInd_NOA), Market, SMB,
HML, and Momentum. E(t,t+4) is the residual term of the regression. GDP growth rates are
only available at quarterly frequency; therefore, consecutive annual growth rates have
overlapping quarters. I use Newey and West (1987) estimators and set the lag equal to 3
to correct the potential serial correlation problems.
The results from the above regression are presented in Table 5.2. Consistent with
prior literature, the excess market factor and the SMB factor are positively associated
with future GDP growth. As in Liew and Vassalou (2000), I find no significant
relationship between momentum factor and future economic growth. The coefficient on
ind_NOA payoff is significantly negative irrespective of whether Fama and French
factors are included as control variables or not. The negative coefficient suggests that the
variation of industry NOA payoff is counter-cyclical to the business cycle. Chordia and
74
Shivakumar (2004) also uncover a negative relationship between the post earnings
announcement drift (PEAD) and future economic states.
If the underlying anomalous effect is driven by the macroeconomics factors, one
would expect a positive relationship between the payoff from a zero-investment portfolio
(factor mimicking portfolio) and the future GDP growth. For example, Liew and
Vassalou (2000) argue that a positive relationship would exist, if high returns in HML
and SMB are associated with the future good state of the economy. This would mean that
high B/M and small capitalization stocks are better able to prosper than low B/M and big
capitalization stocks when periods of high economic growth are expected. The observed
positive relationship between HML and SMB and future GDP growth makes sense.
Presumably, investors would rather hold stocks whose returns are relatively high when
they discover that the economy is in a bad state. Therefore, they hold low B/M and big
capitalization stocks.
The observed negative relationship between industry NOA payoff and the future
GDP growth indicates that low NOA industries are better able to prosper than high NOA
industries when the future looks grim. It is less plausible. If low NOA industries are
indeed riskier than the high NOA industries, the opposite should have happened.
In summary, the observed counter-cyclical relationship raises the doubt that
macroeconomics factors are explanations for the documented industry NOA effect.
Rather, it is consistent with that the industry NOA effect is still based on characteristics
instead of factor risks (Hirshleifer et al. 2005).
75
δ
(standard
tstatistics deviation)
Portfolio
µ
(mean)
Ind_NOA
Ind_Accruals
0.0021 6.95
-0.0001 -0.44
0.033
0.192
λ (growth
rate of
standard
deviation)
H2
H1
Sum
(µ>0)
(H1+H2) Statistical
(λ<0)
arbitrage
p-value p-value p-value
-0.55
-0.71
0.000
0.654
0.000
0.000
0.000
0.654
Yes
No
Table 5.1: The Constrained Mean (CM) Statistical Arbitrage Test
77
Ind_NOA and Ind_Accruals are defined in Table 3.1. The sample period is from July 1964 to December 2002. Every
month, firms are sorted into eight portfolios according to the magnitude of Ind_NOA and Ind_Accruals respectively. The
risk free asset is used to finance the portfolio. H1 and H2 denote the p-values from the constrained mean statistical
arbitrage tests, which test whether the portfolio’s mean monthly discounted incremental profit is positive and whether its
time-averaged variance is declining over time. The sum of the H1 and H2 columns is the p-value for the statistical arbitrage
test.
76
Intercept PInd_NOA
0.0787
52.43
Mkt
SMB
HML
MOM
-0.0325
-4.49
0.074
54.00
ADJ_R2
4.51%
0.0200
2.60
0.0733
56.11
1.22%
0.0582
5.85
0.0758
53.72
6.77%
-0.0150
-1.62
0.0765
43.81
0.36%
-0.0129
-1.28
0.0776
50.35
-0.0325
-4.72
0.0200
2.97
0.0785
37.32
-0.0397
-5.36
0.0122
1.31
0.13%
5.74%
0.0622
6.10
0.0086
0.01
-0.0181
-1.04
13.29%
Table 5.2: Regression of 12-Month ahead Growth in GDP on 12-month
Compounded Hedge Returns of Industry NOA Strategy and Fama-French Factors
The regression uses quarterly data, since data on GDP is available only on a quarterly
basis. The dependent variable is the continuous compounded growth in real GDP over
months t to t+12. PInd_NOA refers to the raw hedge returns from the industry NOA
strategy. Since the regression use overlapping data, the t-stats, which are reported in
italics, are based on Newey-West standard errors. Fama French factors are obtained from
the Kenneth French website. The GDP data is obtained from the website of the Bureau of
Economic Analysis (www.bea.gov).
77
Panel A: Hedge Returns Based on Industry NOA Strategy
Abnormal Returns
0.7
0.5
0.3
0.1
-0.1
-0.3
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02
Year
Ind_NOA
Panel B: Hedge Returns Based on Industry Accruals Strategy
Abnormal Returns
0.7
0.5
0.3
0.1
-0.1
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02
-0.3
Year
Ind_Accruals
Figure 5.1: Persistence of Industry NOA and Industry Accruals Strategy
All variables are defined in Table 3.1. Every month, firms are assigned into 8 portfolios,
each containing 6 individual industries, based on Ind_NOA/Ind_Accruals of the nearest
available fiscal year. Equal-weighted abnormal returns for each Ind_NOA/Ind_Accruals
portfolio are then computed monthly. The annual abnormal returns are calculated as the
sum of the monthly hedge abnormal returns from January to December for each
calendar year from 1965-2002.
78
CHAPTER 6
ROBUSTNESS ANALYSES AND DISCUSSION
6.1 Sample Selection Biases and the Influence of Extreme Stock Returns
Since the advent of market efficiency theory, researchers have debated over
whether anomaly findings are robust to potential sampling errors and econometric
problems (Kothari, 2001). Specifically, regarding the Accruals and NOA anomaly, Kraft,
Leone and Wasley (2005) recently argue the importance of performing robust tests and
avoiding sample selection bias when testing economic or behavioral explanations for
apparent accounting-related mispricing. They state that correcting for common sample
selection biases not only reduces the magnitude of the abnormal returns to the hedge
portfolio based on the Accruals strategy, but also dramatically alters the abnormal returns
attributable to the high and low Accruals portfolio.
They document that after eliminating outliers, there is an inverted U-shaped
relationship between Accruals and one year ahead buy-and-hold size-adjusted abnormal
returns (BHAR). This finding challenges the behavioral explanation that the anomaly is
likely due to investors’ inabilities to process accounting information. They also find that
79
the same outliers they identify for the Accruals anomaly have a similar effect on the
NOA anomaly in their 1988 to 1999 sample.
6.1.1 Sample Selection Biases
Kraft et al. (2005) argue that several sources for selection biases may affect the
statistical inference of anomaly research. First, most studies limit analyses to
NYSE/AMEX firms and may depend on either ZLIST (from Compustat) or HEXCD
(from CRSP) to identify the exchange listing23. However, only the EXCHCD (from
CRSP) variable provides the right historical identification. They document that this subtle
choice may have a great impact on the documented Accruals hedge returns. Second,
exclusion of firm-year observation not reporting Earnings or Accruals in year (t+1) due to
the requirement of the Mishkin (1983) test may introduce a survivorship bias. Another
selection bias is excluding firm-year observations with missing returns during the BHAR
accumulation period.
Both Hirshleifer et al. (2004) and this study are free from the problem of potential
sample selection biases raised by Kraft et al. (2005). First, the samples for both studies
consist of both NYSE/AMEX firms and Nasdaq firms. Therefore, there is no
misidentification problem across exchange lists. Second, since the main results of
Hirshleifer et al. (2004) and this study don’t rely on the Mishkin (1983) test, there is no
constraint for the availability of future Earnings or NOA data. Finally, the portfolios
23
Both ZLIST and HEXCD only report a firm’s exchange listing at the time the particular when version
(i.e. year) of the database was constructed (Kraft et al. 2005).
80
examined in Hirshleifer et al. (2004) and in this study are rebalanced monthly; thereby
avoiding the problems associated with the calculation of BHAR.
6.1.2 The Impact of Influential Observations
After conducting the Least Trimmed Squared regression at 1% or excluding the
observations with BHAR exceeding 200%, Kraft et al. (2005) find that there is an
inverted U shape relationship between the magnitude of Accruals and NOA and the
subsequent one year BHAR. They draw the conclusion that the functional fixation
hypothesis, which predicts the monotonic relationship between Accruals and future
returns, is only driven by the 1% of outliers. Thus, it is not likely to be responsible for the
anomaly.
In this section, I first verify their results by forming the monthly portfolios based
on the samples with deletion of the extreme 1% raw returns at both tails of monthly
return distribution in my 1964-2002 sample. Consistent with their results, I also find an
inverted U relationship between Accruals or NOA and the subsequent hedge returns. The
hedge returns from the Accruals anomaly is dramatically reduced from 0.74% per month
to 0.21% per month.
Next, I repeat the Industry NOA trading strategy for the same constrained sample.
The hedging abnormal returns only drop modestly from 0.73% per month to 0.60% per
month (t-stat=5.19). The purpose of a trading strategy is to identify extreme future stock
returns, and so it is not surprising that hedge returns do drop when observations with
extreme returns are excluded from the sample. More importantly for our understanding of
81
the source of the anomaly, the inverted U shape relationship is not observed here. The
lowest industry NOA group still earns the highest future abnormal returns (abnormal
return=0.30%, t-stat=3.85) and the highest industry NOA portfolio experiences the lowest
future abnormal returns (abnormal return=-0.30%, t-stat=-4.22).
Finally, I rerun the Fama-Macbeth regression test (Model 3 of Panel B, Table 4.4)
with the Least Trimmed Square method recommend by Kraft et al. (2005). In particular,
every month, the cross-sectional OLS regression is performed; I then drop the 1% of the
observations with the largest squared residual and re-estimate the regression with the
remaining 99% of the sample. The untabulated results show that the industry NOA effect
is virtually unaffected. The coefficient associated with ind_NOA is -0.0132 with a t-stat
of -5.07, while the coefficient and t-stat for ind_NOA for the full sample is -0.0119 and 4.36 respectively.
In summary, the Kraft et al. (2004) critique for the empirical methodology
associated with testing accounting related mispricing does not hold for the industry NOA
effect documented in this study.
6.2 The Influence of Transaction Costs and Small Size Firms
6.2.1 The Influence of Transaction Costs
A common critique of return anomalies is that such anomalies may disappear after
adjusting for transaction costs facing the arbitrageur including bid-ask spread, short sale
cost, brokerage commissions, price impact cost, and other immediacy cost. Bhushan
(1994) presents evidence indicating that the magnitude of the post earnings
82
announcement drift is positively related to the direct and indirect costs of trading.
Lesmond et al. (2004) argue that the momentum strategy requires frequent trading in
disproportionately high cost securities; such that generates large trading costs and
prevents profitable strategy execution. Both articles imply that the documented anomalies
cannot be regarded as evidence against market efficiency since the costs do not justify
investors’ endeavors to pursue such strategy.
In contrast, Korajczyk and Sadka (2004) find that transaction costs do not appear
to fully explain the return persistence of the momentum effect. Some researchers view the
existence of transaction costs, together with the lack of complete and perfect substitutes,
limit arbitrage, and so deepen the mispricing in the short run and may also be sufficient
for the persistence of seemingly profitable trading strategies. (Lakonishock and Vishny,
1997; Mashruwala et al., 2004).
Following Hogan et al. (2004), I estimate the impact of transaction costs on the
industry NOA strategy as follows. Each month, I first estimate the average monthly
turnover rate by taking a ratio of the sum of the number of “buy” firms and the sum of the
number of “sell” firms over two times the total number of firms for both the long and
short portfolios, since the portfolios are equally weighted. This estimates the number of
round-trip transactions as a percentage of the number of stocks held. Then I multiply this
measure of monthly turnover by an estimate of the round-trip transaction costs given by
Chan and Lakonishok (1997). According to Chan and Lakonishok (1997), the average
83
stock in the NYSE and Nasdaq has a roundtrip transactions cost of 1.34% and 1.55%24
respectively. Finally, I adjust the monthly profits downward by the transactions costs.
The average monthly turnover ratio of the industry NOA strategy during the sample
period is 10.92%. The monthly transaction cost adjusted hedge returns are 0.59% (tstat=4.50) and 0.56% (t-stat=4.32) when the roundtrip cost of 1.34% or 1.55% are
applied respectively. Therefore, the payoffs of industry NOA strategy are not only
statistically significant, but are also economically significant in that they are well above
the range of estimated transaction costs. The analysis doesn’t explicitly consider the short
selling cost. However, as reported in Table 4.2, unlike most firm-level anomalies, the
industry NOA strategy generates equally strong and significant abnormal returns for both
the long and short sides of the trading strategy.
6.2.2 The Influence of Small Size Firms
Previous literature documents that the PEAD (Bernard and Thomas, 1990), B/M
effect (Ali et al., 2003), and momentum effect (Hong et al., 2000) are all strongest for
small size firms. It is well known that small stocks are less liquid and have greater
transactions costs than large stocks (Chan and Lakonishok, 1997). People argue that the
“penny stock” could lead to return mismeasurement problems through trading frictions
such as bid-ask spread, poor liquidity. Conrad and Kaul (1993) and Ball et al. (1995)
suggest that apparent long term market overreaction may be driven by the computational
problems associated with the returns on low price loser stocks.
24
The transaction costs which are explicitly considered in Chan and Lakonishok (1997) are commissions
and market impact costs.
84
On the other hand, the above findings are also consistent with the behavioral
argument that there is less information available for small size firms and/or small size
firms tend to more unattractive to investors, especially the institutional investors (Ali et
al., 2003; Hong et al., 2001). To investigate the impact of small size firms on the industry
NOA strategy, I first examine whether the strategy works particularly well for industry
portfolios characterized by small firms.
Table 6.1 presents the results of sequential double sorts by industry size first, then
by industry NOA.25 Industry size is the equal weighted average market capitalization,
which is measured at the fiscal year end. The evidence here indicates that industry NOA
strategy works for every industry size group and that the profit from the strategy is
actually smallest for the small size industries.
Second, I remove stocks in the sample with market capitalizations below the 50th
NYSE and AMEX market equity percentile each period. This reduces my sample size by
more than two-thirds because there are many more small stocks than large stocks and
there are relatively more small stocks traded in the Nasdaq than in the NYSE. I then
retest the industry NOA trading strategy for this restricted sample. Results from the test
suggest that the payoff of industry NOA trading strategy is only marginally smaller
without the bottom 50th NYSE percentile. The monthly adjusted return is 0.62% (tstat=4.15), compared to 0.73% for the whole sample.
25
Here, the sequential double-sorts method is an appropriate method to address the conditional information
content problem. Please refer to Appendix B-2 for further discussion on independent double sorts vs.
sequential double sorts.
85
Lastly, I separate the sample into the AMEX/NYSE and the Nasdaq subsamples.
The previous literature shows that the Nasdaq firms tend to be small, growth and less
liquid firms. Hirshleifer, Teoh and Yu (2005) find NOA anomaly is much stronger for
Nasdaq firms. Consistent with their finding, the average abnormal hedge return of
industry NOA strategy for AMEX/NYSE firms is 0.45% (t=4.16), which is considerably
lower that that for the Nasdaq firms (hedge return=1.03%, t=4.03). This is consistent with
the limited arbitrage argument (Shleifer and Vishny 1997). Industry Accruals strategy
doesn’t work for either sub-sample.
In summary, the payoff from the industry NOA strategy is beyond the range of
transaction costs, and the industry NOA effect is not driven by small stocks.
6.3
Are Industry NOA and Industry Momentum One Effect or Two?
Considering the close relationship between operating accruals and earnings as
well as operating accruals and cash flow from operations, researchers have investigated
whether the Accruals effect is independent of the post earnings announcement drift
(PEAD, Bernard and Thomas, 1989) and the cash flow effect documented in the literature.
Collins and Hribar (2000) conclude that the Accruals and PEAD effects are independent.
In contrast, Desai et al. (2004) argue that the Accruals effect is subsumed by the cash
flow-to-price effect.
Here, a similar question arises: Do the industry momentum effect and the industry
NOA effect capture the same underlying mispricing phenomenon (substitutes)? There
exists the possibility that the two effects are closely related, since stock returns are driven
86
by changes in underlying fundamentals such as earnings in excess of expectations. An
alternative hypothesis would be that the two effects are incremental to each other. Stock
returns incorporate a broader set of information than the financial accounting information.
Meanwhile, not all currently available accounting information is fully impounded into the
stock prices, if investors have limited attention. Then, industry NOA and industry
momentum can provide complementary information for future returns.
To empirically address this issue, I adopt an independent double-sorts technique.
For every month between July 1964 and December 2002, firms are ranked by industry
momentum into four groups. At the same time, firms are also ranked by industry NOA
into four groups. Then sixteen portfolios are formed monthly for each combination
(intersection) of the industry Momentum rank and the industry NOA rank.
If the industry NOA effect and the industry momentum effect are substitutes for
each other, the investment strategy of going long the portfolio with both the lowest
industry NOA and the highest industry momentum rankings and shorting the portfolio
with both the highest industry NOA and the lowest industry momentum rankings will
produce similar profits as a strategy utilizing either one of them. Put another way, the
two-way sort essentially degenerates into a one way sort. If the two effects are
complementary, the profits from the independent dual-ranking strategy would be roughly
equal to the sum of the profits from the individual ranking strategies, based on industry
NOA and industry Momentum separately, since the strategy exploits both pieces of
information. Otherwise, one will make profits anywhere in between the above two
scenarios, depending on the extent to which the two effects are correlated.
87
Table 6.2 reports the monthly average abnormal returns from the independent
double-sorts strategy one year after the portfolio formations. The industry momentum
strategy makes profits for every industry NOA quartile portfolio, and the industry NOA
strategy earns significant abnormal returns for all except the second lowest industry
momentum quartile portfolios. Most importantly, the strategy produces an average 1.26%
monthly abnormal return, which is almost the sum of the profits from the separate
industry NOA and the industry momentum strategies.26 The empirical evidence here is
consistent with the argument that the industry NOA effect and the industry momentum
effect are complementary. Untabulated results from Fama-Macbeth regression are
consistent with those from the dual-ranking portfolio test.
6.4
Is the Industry NOA Effect Driven by the Cluster of New Equity Issues and/or
M&A Activities?
It is possible that the industry NOA effect presented in this paper is potentially
related to the evidence that equity issuers (Loughran and Ritter, 1995) and firms engaging
in M&A activities (Rau and Vermaelen, 1998) tend to exhibit negative long-run
underperformance. Prior literature has documented the clustering of new equity issuance
and M&A activities in time as well as within industries (Mitchell and Mulherin, 1996).
One potential explanation for the herding of corporate events within industries is
that firms from the same industry have similar sensitivities to common economic factors
and shocks (Mitchell and Mulherin, 1996). Moreover, the above corporate events will
26
Untabulated results show that the average monthly hedge abnormal return from the quartile industry
NOA (industry momentum) portfolios is 0.63% (0.66%).
88
have a direct impact on a firm’s balance sheet and the magnitude of NOA. For example,
the magnitude of NOA tends to increase (through the increase of net current assets) when
a firm acquires another company to reflect the balance of the merged equities or when a
firm uses the proceeds from stock issuance to invest in operating assets. Therefore, if
extreme NOA firms have recently issued new equity or have engaged in M&A activities,
the documented anomalous industry NOA effect in this study may simply capture the
clustering of these known anomalies related to corporate events.
Zach (2002) investigates a similar question of whether the Accruals effect is
driven by corporate events. He excludes new financing and M&A firms from the sample,
and finds that although the profits earned by the Accruals strategy decline by
approximately 10%, they still remain highly significant. I adopt a similar approach by
partitioning the sample into two sub-samples. If the firm engages in a new equity
issuance or an M&A activity in the portfolio formation year, then the binary variable
E&M is set equal to 1; otherwise E&M is 027. I employ the industry NOA strategy for
each sub-sample for the 1971 to 2002 period28. If the industry NOA effect is driven by
the clustering of the corporate events, one would expect that the industry NOA strategy
will make no profits for the non-event sample.
The empirical results of Table 6.3 (E&M=1 subsample) confirm the new issues
and the M&A effects. On average, firms suffer negative abnormal returns after the year
of these special activities, regardless of the magnitude of industry NOA. The industry
NOA strategy is able to predict future abnormal returns for both the E&M=1 and E&M=0
27
28
Please see the notes for Table 6.3 for a detailed data description.
Compustat variables for New Equity Issuance and M&A are only available from 1971.
89
sub-samples, indicating that the industry NOA effect is not totally driven by the cluster of
corporate events for firms in the same industry. The results also reveal that industry NOA
has stronger return predictabilities for the E&M=1 sub-sample than for the E&M=0 subsample.
90
Ind_
MV
1
2
3
4
Spread
t-stat
1
0.0161
0.0151
0.0159
0.0165
-0.0004
-0.23
2
0.0135
0.0149
0.0131
0.0096
0.0039
2.42
Ind_NOA
3
4
0.0125 0.0127
0.0136 0.0088
0.0106 0.0092
0.0114 0.0108
0.0011 0.0018
0.60
0.86
Spread
0.0034
0.0063
0.0067
0.0057
t-stat
2.43
4.19
3.68
2.24
Table 6.1 Average Monthly Raw Returns for Portfolios, Sorted First by other
Industry Size, Then by Industry NOA, One Year after the Portfolios’ Formation
Ind_MV and Ind_Moment are defined in Table 3.1. Every month between July, 1964 and
December, 2002, 48 industries are assigned into 4 portfolios according to Ind_MV, each
containing 12 portfolios. Then, within each Ind_MV quintile portfolio, industries are
sorted by Ind_NOA into 4 portfolios. Equal-weighted raw returns are then computed
monthly for each of the 16 portfolios. The time series average returns and associated tstatistics of these portfolios, as well as the differences in returns between quartile 1 and 4
for each row and column are reported. Bold numbers indicate significance at less than 5%
level (2-tail t-test).
91
Ind_
Momentum
1
2
3
4
Spread
t-stat
1
0.0002
0.0009
0.0034
0.0068
0.0066
3.23
Industry NOA
2
3
4
-0.0034 -0.0025 -0.0058
-0.0021 -0.0030 -0.0016
-0.0005 -0.0004 -0.0006
0.0033 0.0011 0.0021
0.0067 0.0036 0.0079
3.91
2.20
4.33
Spread
0.0060
0.0025
0.0040
0.0047
t-stat
3.29
1.61
2.67
2.61
Table 6.2: Average Abnormal Monthly Returns for Portfolios, Sorted by Industry
NOA and Industry Momentum Simultaneously, One Year after the Portfolios’
Formation
Ind_NOA and Ind_Momentum are defined in Table 3.1. Every month between July, 1964
and December, 2002, 48 industries are assigned into 4 portfolios according to Ind_NOA.
Simultaneously, industries are sorted by Ind_Momentum into 4 portfolios. Then 16 (4*4)
portfolios are formed for each combination (intersection) of Ind_NOA and
Ind_Momentum rankings. Equal-weighted (abnormal) returns are then computed monthly
for each of the 16 portfolios. The time series average returns and associated t-statistics of
these portfolios, as well as the differences in returns between quartile 1 and 4 for each row
and column are reported. Bold numbers indicate significance at less than 5% level (2-tail ttest).
92
E&M=1
E&M=0
Difference (0-1)
t-stat
Ind_NOA
1
2
3
4
-0.0002 -0.0056 -0.0070 -0.0077
0.0053 0.0006 -0.0005 -0.0004
0.0055 0.0062 0.0075 0.0081
4.22
5.08
7.01
7.18
Spread
0.0075
0.0057
t-stat
3.80
4.63
Table 6.3: Average Abnormal Monthly Returns for Portfolios Sorted by Industry
NOA for New Equity Issuance and/or M&A vs. Non-New Equity Issuance and/or
M&A Sub-sample One Year after the Portfolios’ Formation
Ind_NOA is defined in Table 3.1. E&M=1 if a firm has equity issuance (#129>=lagged
total assets*10%) and/or M&A activities (#108>=lagged total assets*10%) in the
portfolios formation year; otherwise E&M=0. Both #129 and #108 are available from
fiscal year 1971. Every month between January 1972 and December 2002, 4 portfolios
are formed based on Ind_NOA for both the E&M=1 and the E&M=0 sub-sample.
Equal-weighted abnormal returns are then computed monthly for each portfolio. The
time series average returns and associated t-statistics for these portfolios, as well as the
differences in returns between quartile 1 and 4 for each row and those between the
E&M=1 and the E&M=0 sub-sample for each column are reported. Bold numbers
indicate significance at less than 5% level (2-tail t-test).
93
CHAPTER 7
CONCLUSION
Net operating assets measure the cumulative difference between accounting value
added and cash value added since a firm’s startup and retain rich information, such as the
history of a firm’s accounting choices, as well as its business conditions. Hirshleifer et al.
(2004) argue that NOA measures the extent to which operating/reporting outcomes
provoke excessive investor optimism. In this study, I show that the industry common
component of NOA carries industry wide information beyond that contained in the
current income statement and could be a source of investors’ misperceptions of balance
sheet information at the industry level. I, then, investigate whether the NOA effect is
driven by investors’ misperceptions of the cross-industry variations of NOA or the firmspecific component of NOA.
I argue for the important distinction between return predictive variables
(observable) and the information underlying those variables (not directly observable). As
accounting researchers, we have advantages to interpret what the information underlies
financial variables. Utilizing the knowledge of financial statement analysis, I argue that at
94
least part of the information conveyed by NOA is industry-common and that investors’
misperceptions of NOA cannot be diversified away when forming portfolios
conditioning on industry NOA; thus the industry common component of NOA can
predict future returns. At the same time, firm-specific economic shocks and opportunistic
accounting choice behaviors are largely retained in the firm specific component of NOA.
Therefore, the industry-adjusted component of NOA is also a negative predictor of future
returns.
Consistent with my hypothesis, in the1964-2002 sample, both the cross industry
and the within industry components of NOA are strong negative predictors for future
stock returns. In contrast, I show that investors’ misperceptions of Accruals are entirely
driven by the industry-adjusted (firm-specific) component of Accruals, which is likely a
manifestation of a firm’s idiosyncratic accounting choices and the economic environment.
By decomposing industry NOA into industry working capital and industry investment
components, I show that both the time series aggregation property and the retention of
investment information of NOA contribute to the difference in return predictabilities
between industry NOA and industry Accruals.
The finding of the industry NOA effect is robust with the treatment of outliers,
beyond the range of transaction costs, and it is not driven just by small size firms. I also
provide empirical evidence that the industry NOA effect is independent of the industry
price Momentum effect and that it is distinct from the clustering of new equity issuance
and/or M&A activities within industries.
95
Together with Hirshleifer et al. (2004), the evidence in this paper suggests that
investors’ misperceptions of balance sheet information are more severe than their
misperceptions of income statement information. The abnormal returns for a trading
strategy based on a financial stock variable are much larger (Hirshleifer et al. 2004) and
investors’ misperceptions of balance sheet information impact asset pricing, not only at
the firm level, but also at the industry level. These findings suggest that firms, the
business media, and policymakers should consider possible ways to make balance sheet
information more salient and transparent to investors to facilitate the efficient functioning
of capital markets.
96
APPENDICES A:
SUPPLEMENTARY TABLES
97
Short
Name
1 Agric
Long Name
Agriculture
2
3
4
5
6
7
8
Food Products
Candy and Soda
Alcohol Beverage
Tobacco Products
Recreational Products
Entertainment
Printing and Publishing
Food
Soda
Beer
Smoke
Toys
Fun
Books
9 Hshld
10 Clths
11 Hlth
12 MedEq
Consumer Goods
15 Rubbr
16 Txtls
Apparel
Healthcare
Medical Equipment
Pharmaceutical
Products
Chemicals
Rubber and Plastic
Products
Textiles
17 BldMt
Construction Materials
18
19
20
21
Construction
Steel Works, Etc.,
Fabricated Products
Machinery
13 Drugs
14 Chems
Cnstr
Steel
FabPr
Mach
22 ElcEq
Electrical Equipment
SIC Code
0100-0799, 2048
2000-2046,2050-2063,2070-2079,20902095,2098-2099
2064-2068,2086-2087,2096-2097
2080-2085
2100-2199
0900-0999, 3650-3652, 3732,3930-3949
7800-7841,7900-7999
2700-2749,2770-2799
2047,2391-2392,2510-2519, 2590-2599,28402844,3160-3199,3229-3231,
3260,3263,3269,3630-3639,37503751,3800,3860-3879,
3910-3919, 3960-3961,3991,3995
2300-2390,3020-3021,3100-3111,31303159,3965
8000-8099
3693, 3840-3851
2830-2836
2800-2839,2850-2899
3000, 3050-3099
2200-2295, 2297-2299,2393-2395, 2397-2399
0800-0899,2400-2439,2450-2459,24902499,2950-2952,
3200,3219, 3240-3259,3261,3264,32703299,3420-3442,
3446-3452,3490-3499,3996
1500-1549,1600-1699,1700-1799
3300-3369,3390-3399
3400,3443-3444,3460-3479
3510-3536,3540-3569,3580-3599
3600-3621,3623-3629,3640-3646,36483649,3660,3691-3692,3699
Table A.1: Industry Classification
(Continued)
98
Table A.1: Continued
23 Misc
31 Energy
32 Util
33 Telcm
Miscellaneous
Automobiles and
Trucks
Aircraft
Shipbuilding, Railroad
Equipment
Defense
Precious Petals
Nonmetallic Mining
Coal
Petroleum and Natural
Gas
Utilities
Telecommunications
34 PerSv
Personal Services
35 BusSv
Business Services
36 Comps
37 Chips
Computers
Electronic Equipment
Measuring and Control
Eq
24 Autos
25 Aero
26
27
28
29
30
Ships
Guns
Gold
Mines
Coal
38 LabEq
39
40
41
42
43
Paper
Boxes
Trans
Whlsl
Retail
44
45
46
47
48
Meals
Banks
Insure
RlEst
Fin
Business Supplies
Shipping Containers
Transportation
Wholesale
Retail
Restaurants, Hotel,
Motel
Banking
Insurance
Real Estate
Trading
3900,3990,3999,9900-9999
2296,2396,3010-3011,3537,3647,3694,37003716,3790-3792,3799
3720-3729
3730-3731,3740-3743
3480-3489,3760-3769,3795
1040-1049
1000-1039,1060-1099,1400-1499
1200-1299
1310-1389,2900-2911,2990-2999
4900-4999
4800-4899
7020-7021,7030-7039,7200-7212,72157299,7395,7500,
7520-7549, 7600-7699,8100-8499,86008699,8800-8899
2750-2759,3993,7300-7372,73747394,7397,7399,7510-7519,
8700-8748,8900-8999
3570-3579,3680-3689,3695,7373
3622,3661-3679,3810,3812
3811, 3820-3830
2520-2549,2600-2639,2670-2699,27602761,3950-3955
2440-2449,2640-2659,3230-3221,3410-3412
4000-4299,4400-4799
5000-5199
5200-5736,5900-5999
5800-5813,5890,7000-7019,7040-7049,7213
6000-6199
6300-6411
6500-6553
6200-6299,6700-6799
99
Industry
Classification
Number of
Portfolios
Sorting Variable
(Hedge
Adj_ret)
Industry-14
Industry-20
GICS-26
7 Portfolios
10 Portfolios
8 Portfolios
NOA
Accruals
NOA
Accruals
NOA
Accruals
100
Industry
Portfolios
(H-L)
t-statistics
0.0063
3.50
0.0005
0.35
0.0047
3.23
-0.0001
-0.07
0.0091
5.24
0.0004
0.76
Random Industry
Portfolios
(H-L)
t-statistics
0.0025
4.26
0.0005
0.97
0.0030
5.23
0.0011
2.23
0.0029
4.06
0.0013
1.97
Industry Adjusted
Portfolios
(H-L)
t-statistics
0.0099
12.16
0.0067
8.56
0.0128
12.02
0.0088
8.36
.0103
11.26
0.0074
8.51
Firm Level
Portfolios
(H-L)
t-statistics
0.0124
11.46
0.0067
7.57
0.0145
11.37
0.0095
7.54
.0131
10.99
.0068
6.85
Table A.2: Alternative Industry Classifications- Portfolio Tests
(Continued)
100
Table A.2: Continued
All variables are defined in Table 3.1. Procedures for forming the industry portfolio, the random industry portfolio,
the industry adjusted portfolio and the firm level portfolio are described in Tables 4.2 and 4.3 respectively.
Industry-14 classifications are based on the 4-digit SIC code as follows: Agriculture (0-999), Mining & Construction
(1000-1299, 1400-1999), Food (2000-2001), Textiles and Printing/Publishing (2200-2790), Chemicals (2800-2824,
2840-2899), Pharmaceuticals (2830-2836), Extractive (1300-1399, 2900-2999), Durable Manufacturers (3000-3569,
3580-3669, 3680-3999), Computers (3570-3579, 3670-3679, 7370-7379), Transportation (4000-4899), Utilities
(4900-4999), Retail (5000-5999), Financial and Others (6000-6999,2111-2199) and Services (7000-7360, 73809999).
101
Industry-20 classifications are based on the 2-digit SIC code as follows: Mining (10-14), Food (20), Apparel (20-23),
Paper (26), Chemical (28), Petroleum (29), Construction (32), Primary Metals (33), Fab.Metals (34), Machinery (35),
Electrical Equipment (36), Transport Equipment (37), Manufacturing (38-39), Railroads (40), Other Transportation
(41-47), Utilities (49), Department Stores (53), Retail (50-52, 54-59), Financial (60-69) and Other (other).
GICS-26 classification is based on the first 6 digits of the Global Industry Classification Standard obtained from the
Compustat PDE file. There are 26 industry groups and 82% of my original sample matched the GICS code in the
Compustat PDE file.
101
Ret
Ret
Ret
Ind_
Adj_
(-1:-1)
(-12:-2)
(-36:-13)
NOA
NOA
Accruals Accruals
0.0385 -0.0010
0.0036
-0.0752
4.84
-2.28
5.57
-18.19
Panel B: 20 Industry Classification:
0.0048
2.99
-0.0016
-2.78
-0.0221
-3.64
-0.0051
-8.81
-0.0227
-1.53
-0.0093
-5.79
0.0379
-0.0011
0.0034
-0.0751
4.87
-2.36
5.00
-17.91
Panel C: GICS 26 Industry Classification:
0.0046
2.85
-0.0015
-2.67
-0.0196
-4.09
-0.0052
-8.64
-0.0104
-0.86
-0.0094
-6.05
0.0047
2.91
-0.0015
-2.86
-0.0102
-3.00
-0.0058
-8.20
-0.0115
-1.25
-0.0086
-5.41
Intercept
Ln(size)
Ln(btm)
Ind_
Adj_
Panel A: 14 Industry Classification:
102
0.0287
4.19
Table A.3:
-0.0010
-2.21
0.0033
5.32
-0.0786
-18.47
Alternative Industry Classifications –Regression Tests
Ind_m1 denotes the previous month’s equal-weighted industry average return; Ind_m12 denotes the previous year’s
equal-weighted industry average return from month t-12 to t-2; Ind_m36 denotes the equal weighted average return for
each individual industry starting from month t-36 to t-13. Please refer to Table 4.4 for other variable definitions and for
details of the Fama-Macbeth regression procedure. Alternative industry classification definitions are described in Table
A.2.
102
APPENDICES B:
TECHNICAL NOTES
103
B.1
THE FAMA-MACBETH MONTHLY CROSS
SECTIONAL REGRESSION PROCEDURE
Fama and Macbeth (1973) first developed the cross-sectional regression approach,
which is widely adopted in the following literature. Assuming that the asset pricing
factors are known, the regression model for the tth cross section of N assets is
Rt=γ0tι+βm’γt +ηt
(A-1)
Where Rt is the (Nx1) vector of return or excess asset returns for time period t, ι
is an (Nx1) vector of ones, and βm(NxM) is the vector of M asset pricing factors, ηt are
random errors, which are assumed to be normally identical and independently distributed.
Implementation of the Fama-Macbeth approach involves two steps. First,
equation (A-1) is estimated by using OLS for each time period t, t=1…..T, giving the T
estimates of γ0t (scalar) and γt(γ1,γ2,…γM). 29In the second step, the following statistics are
formed:
29
Usually, people run the Fama-Macbeth regression on a monthly basis since monthly stock returns
conform the best to the normality assumptions (Fama and Macbeth, 1973).
104
ω (γˆ j ) =
γˆ j
δˆγ
j=0,1,…,M
(A-2)
j=0,1,…,M
(A-3)
j
Where,
γˆ j =
1 T
∑ γˆ jt
T t =1
and
σˆ γ2j =
T
1
(γˆ jt − γˆj ) 2
∑
T (T − 1) t =1
j=0,1,…,M
(A-4)
The distribution of ω(γj) is student T, with (T-1) degrees of freedom and is
asymptotically distributed as standard normal.
The Fama-Macbeth procedure is very intuitive and easy to implement. It is
particularly useful because it can easily be modified to accommodate additional asset
pricing factors beyond the CAPM beta. The approach has several advantages. First, it is
an improvement over a naïve OLS approach since the nonscalar covariance structure of
returns is reflected in the variance of the monthly estimates (Shanken, 1992). That is, it
relaxes the constraint of constant covariance put by OLS regression. Second, researchers
only need the t-values of the cross-sectional variables; it does not require the estimation
of covariance among returns on different assets. This makes it suitable for studying a
large cross section of individual stocks (Jagannathan and Wang, 1998).
However, the Fama-Macbeth methodology, while useful, does present several
problems. First, if asset pricing factors are not observable (such as market beta), the
105
error-in-variables problem arises. Second, Janannathan and Wang (1998) find that firm
characteristics might be significant in the Fama-Macbeth regression because the linear
beta-pricing model is misspecified, not because the firm characteristics are priced.
Therefore, it is important to conduct complementary tests (such as portfolio tests) for the
robustness of empirical findings.
106
B.2 INDEPENDENT DOUBLT SORTS VS.
SEQUENTIAL DOUBLE SORTS
There are two widely used methods to conduct the dual ranking investment
strategy, independent or sequential double-sorts. The two different methods are designed
to address different questions. The independent double-sorts method is more appropriate
for determining whether anomaly A and anomaly B capture the same underlying
mispricing phenomena. Put another way, whether signal A contains information in
additional to signal B that investors fail to fully appreciate (Collins and Hribar, 2000).
The sequential double-sorts method is designed to investigate the interaction effects
between two anomalies, that is, whether the abilities of signal A to predict future returns
depending on signal B (Bernard and Thomas, 1990).
To implement the independent double-sorts strategy, every time period, stocks are
ranked by signal A into N groups. Simultaneously, stocks are also ranked by signal B into
N groups. Then N*N portfolios are formed each period for each combination
(intersection) of signal A ranking and signal B ranking. To perform the sequential
double-sorts strategy, one sorts the firms into N portfolios according to signal A first,
107
then sorts the firms into N sub-portfolios according to signal B within each of the N
portfolios. Again, N*N portfolios are formed.
If anomaly A and anomaly B essentially capture the same underlying mispricing
phenomena (substitute effects)30, through the construction of independent double-sorts
portfolios, there will be very few or zero number of observations for off-diagonal
portfolios while the compositions of the upper most left and lower right portfolios are
(almost) the same as the highest and lowest Signal A (Signal B) portfolio as in the one
way sort. That is the two-way sort method essentially degenerates into a one way sort. In
contrast, sequential double-sorts method is not appropriate in this setting. In essence, the
sequential double sort method is just a refinement of the one way sort by forming N*N
portfolios, and it will appear that signal A can make profits for each signal B portfolio
and vice versa; thus creating an illusory impression that A and B are complementary.
This contrast can be illustrated by the following example:
Suppose that there are 9 stocks and two signals A and B capturing the same
underlying mispricing effect. That is, sorting the 9 stocks into 3 portfolios according to
signal A is equivalent to sorting 9 stocks into 3 portfolios according to signal B. Suppose
x1 to x9 are ranked according to magnitude of signal A (signal B). A1(B1) is the
portfolio consisting of the stocks with the lowest signal A(signal B) and A3(B3) is the
highest portfolio with the highest signal A(signal B). Therefore,
30
Or in other words, sorting firms according to signal A is equivalent to sorting firms according to signal B,
or A itself is almost perfectly correlated with B, |corr(A,B)|=1
108
A1={x1, x2, x3}, A2={x4, x5, x6}, A3={x7, x8, x9}, and
B1={x1, x2, x3}, B2={x4, x5, x6}, B3={x7, x8, x9}
Then, each of the 9 portfolios from the independent double-sorts C11 to C33
composes the following stocks:
B
A
C11=A1∩B1={x1, x2, x3}, C12=A1∩B2={Ø},
C13=A1∩B3={Ø}
C21=A2∩B1={Ø},
C22=A2∩B2={x4, x5, x6},
C23=A2∩B3={Ø}
C31=A3∩B1={Ø},
C32=A3∩B2={Ø},
C33=A3∩B3={x7, x8, x9}
Therefore, under the independent double sorts, if two effects are essentially
substitutes, the two way sorts essentially degenerates to a one way sort (the plane
collapses to a line-diagonal)31 and the abnormal returns from implementing this strategy
(shorting portfolio C11 while longing portfolio C33) is exactly the same as that from
shorting portfolio A1(B1) while longing portfolio A3(B3). Therefore, one can conclude
that A and B are the same underlying mispricing effects (substitutes). Moreover, one will
observe a U shape relation of abnormal returns for implementing the investment strategy
based on signal A (B) across signal B (A).
In contrast, under the sequential double-sorts strategy, the compositions of the 9
portfolios C11 to C33 are as follows:
31
If corr(A,B)=-1, then the plane will collapse to the opposite diagonal.
109
B
A
C11={x1}
C12={x2}
C13={x3}
C21={x4}
C22={x5}
C23={x6}
C31={x7}
C32={x8}
C33={x9}
Therefore, the abnormal returns from implementing this strategy (shorting
portfolio C11 and longing portfolio C33) will be higher than that from shorting portfolio
A1 (B1) while longing portfolio A3 (B3) since it refines the sample into 9 portfolios from
the original 3. Moreover, it also “appears” that exploiting signal B (A) can yield
abnormal returns within each portfolio sorted by signal A (B). In short, sequential
double-sorts can create the illusion that two anomalies are complementary while actually
they are substitutes.
If the research question is whether the abilities of one signal to predict future
returns depend on the magnitude of the other signal, that is if the objective is to
investigate the interaction effects between the two anomalies, then the sequential doublesorts method is conceptually more appropriate subject to the condition that the two
signals are not fully substitutes. For example, it is well known that the PEAD effect is
110
strongest for small size groups. Bernard and Thomas (1990) partition the sample into
three groups first, then conduct the one way sort for each sub-sample.32
32
Other examples using the sequential double-sorts include Ali et al. (2003).
111
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