Market-Wide Cost of Capital Impacts on the Aggregate EarningsReturns Relation: Evidence from Japan*
YUTO YOSHINAGA†
Graduate School of Commerce and Management,
HITOTSUBASHI UNIVERSITY

ABSTRACTThis study aims to clarify the mechanism of the surprising earnings-returns relation
observed at the aggregate level by offering evidence from Japan. Unlike firm-level
evidence, recent Macro-Accounting research reports that when earnings changes andstock returns of individual firms are cross-sectionally aggregated, a significantly positive
relation cannot be observed in the U.S. market. To explain this puzzling finding,
Kothari et al. (2006) propose a hypothesis that negative effects of changes in themarket-wide cost of capital cancel out positive effects of aggregate earnings changes onaggregate stock returns. Although this hypothesis is empirically supported in the U.S
market, the validity of this hypothesis has not been sufficiently investigated in theJapanese market. Thus, we test the hypothesis and find it robustly supported in Japan.
Our results show that positive effects of aggregate earnings changes on aggregate stock
returns are canceled out by the effects of the market-wide cost of capital. We also find
* Acknowledgements: I would like to convey my gratitude to Hidetoshi Yamaji, the editor in chief of The Japanese
Accounting Review and two anonymous reviewers for providing insightful comments. I am grateful for helpful advice
from Toyohiko Hachiya, Makoto Nakano, and my colleagues at Hitotsubashi University. I also thank Souhei Ishida,
Tetsuyuki Kagaya, Tomohiro Suzuki, Yusuke Takasu at the 12th Youth Academic Seminar, Konari Uchida at Japan
Finance Association Finance Camp 2015, Hiroyuki Ishikawa, Takuma Kochiyama, Shoichi Tsumuraya, Tatsushi
Yamamoto at the 74th Japan Accounting Association Annual Conference, Simone Kelly, Yoshinori Shimada at the27th Asian-Pacific Conference on International Accounting Issues, Keishi Fujiyama, Akinobu Shuto at the 5thInternational Conference of The Japanese Accounting Review, Masato Hirota, Hyonok Kim, Kiichiro Kojima, Akira
Mizobuchi, Katsuhiko Muramiya, Noriyoshi Yanase, Yukihiro Yasuda, Yasushi Yoshida at the 31st TKU FinanceResearch Center Research Workshop, and all the participants at these conferences for beneficial comments. These
names are written in alphabetical order of family names and in chronological order of the conferences’ dates. I
appreciate Grant-in-Aid for Research Fellows of the Japan Society for the Promotion of Science (JSPS KAKENHI
Grant number 15J00015) and financial supports by the Graduate School of Commerce and Management,
Hitotsubashi University. All possible errors in this paper are my own.
†
Corresponding Author. Address Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, JAPAN.
Telephone +81-42-580-8000 E-mail cd151004@g.hit-u.ac.jp
Received October 31, 2015; accepted November, 9, 2016; available online December 27, 2016 (Advance publications by JSTAGE)
DOI: 10.11640/tjar.6.2016.04
Copyright©2016 Research Institute for Economics & Business Administration – Kobe University.

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that these canceling effects stem from the market risk premium in Japan. An additional
test we conduct shows that expected aggregate earnings changes and changes in themarket risk premium are not negatively related. This result indirectly supports the
hypothesis proposed by Kothari et al. (2006), because it undermines the competing
hypothesis proposed by Sadka and Sadka (2009). These results should contribute to
the related research areas, Macro-Accounting and accounting research on the cost ofcapital.
JEL Classification: E44, G12, G14, M41
Keywords: aggregate earnings, earnings-returns relation, cost of capital, market risk
premium

1. Introduction
This study aims to clarify the mechanism of the surprising earnings-returns relation observedat the aggregate level by offering evidence from Japan. In the traditional accounting and financeresearch, many researchers have studied the relation between accounting earnings and stock
returns, beginning with Ball and Brown (1968). In this stream of research, a robust positive
relation between earnings changes and contemporaneous stock returns is observed at the firmlevel1 (Ball and Sadka 2015). Earnings changes are often regarded as earnings surprises.2 Positive(negative) earnings surprises indicate that reported earnings are higher (lower) than expected andearnings are financial resources for payout. Thus, investors will increase (decrease) the expectedcash flows from stocks of the firm and trade them based on their modified expectations. This
results in a positive earnings-returns relation at the firm level.3
Turning our attention to recent studies, there is a new and growing research area called
Macro-Accounting. According to Konchitchki (2016a), there are two typical Macro-Accounting
areas, “Macro-to-Micro” and “Micro-to-Macro.” The former research area, “Macro-to-Micro,”tackles how various types of macroeconomic information affect or improve the firm-level
prediction of future performance or stock valuation (e.g., Konchitchki 2011, 2013; Li et al. 2014;
Williams 2015; Konchitchki et al. 2016). “Micro-to-Macro,” the latter research area, focuses on
how accounting contributes to informing and predicting various macroeconomic aspects (e.g.,
Shivakumar 2007; Arif and Lee 2014; Shivakumar and Urcan 2014; Konchitchki and Patatoukas
2014a, b, 2016a, b; Gallo et al. 2016; Konchitchki 2016b).
“Micro-to-Macro” research often investigates information contents of cross-sectionally
aggregated earnings of listed firms. Following this research stream, we focus on the informationalrole of these “aggregate earnings” in the capital market. Let us consider the following question:
when earnings changes and stock returns of individual firms are cross-sectionally aggregated,
what relation would be observed between aggregate earnings changes and aggregate stock
returns? These aggregate-level variables represent general trends of all listed firms in the market.
1

We describe “contemporaneous” variables as variables at the earnings announcement period in this paper.
Assuming that expected earnings at the current period are equal to realized earnings at the previous period[] =(), earnings surprises at the current period become equal to the earnings changes at the
[
]=∆
[
]=
[
], ∆
∵
−
=
−
).
current period (3
We use the description “earnings-returns relation” as the relation between earnings changes and corresponding stock
returns at earnings announcement periods.
2

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan

97

When positive (negative) aggregate earnings changes are observed, listed firms will generally
experience a rise (drop) in performance. Subsequently, the economic impacts of positive(negative) firm-level earnings surprises should be dominant in the market, resulting in higher(lower) stock prices. According to this logic, a positive earnings-returns relation should also be
observed at the aggregate level.
However, recent U.S. Macro-Accounting studies, such as Kothari et al. (2006) (referenced as
KLW henceforth), present evidence contrary to this prediction. By running a simple regression,
they report that a significantly positive earnings-returns relation cannot be detected at theaggregate level.4 Furthermore, they indicate that even a significantly negative relation can beobserved. Several other U.S. studies report that the observed aggregate earnings-returns relation
is not significantly positive in a simple regression or in a pairwise correlation5 (KLW; Anilowski
et al. 2007; Bali et al. 2008; Hirshleifer et al. 2009; Sadka and Sadka 2009; Uysal 2010;
Patatoukas 2014; Gallo et al. 2016; Konchitchki 2016a).
To clarify this puzzling earnings-returns relation, KLW develop a hypothesis based onomitted variable bias. KLW suppose that investors generally increase (decrease) the discount rate
when aggregate earnings changes are positive (negative). If this hypothesis is correct, positiveeffects of aggregate earnings changes on contemporaneous aggregate stock returns will beconcealed by negative effects of changes in the contemporaneous discount rate. The discount rateis the cost of capital (Brealey et al. 2014), so KLW assume that negative effects of changes in themarket-wide cost of capital cause the negative aggregate earnings-returns relation.
Although several prior U.S. studies empirically support this hypothesis (e.g., Patatoukas2014), the validity of this hypothesis in the Japanese market has not been sufficiently investigated.
He and Hu (2014) is the only study that investigates whether some components of the marketwide cost of capital affect the aggregate earnings-returns relation outside the U.S. market. They
reveal that the aggregate earnings-returns relation does not change after controlling forcontemporaneous changes in interest rates and inflation in non-U.S. markets, which differs fromthe U.S. evidence (Uysal 2010; Gallo et al. 2016). However, it is still not clear whether themarket-wide cost of capital cancels out the positive aggregate earnings-returns relation in theJapanese stock market for three reasons. First, He and Hu (2014) do not consider the market risk
premium in their analysis. In other words, they do not control for all the necessary variables intheir regression model. Second, their evidence is for the average non-U.S. market, and not for a
specific stock market. This is because He and Hu (2014) use a pooled regression of country/year
observations. Third, He and Hu (2014) use only annual data, although quarterly data provide
more precise results because of the shorter window of returns. Accounting for these points, wetest the KLW hypothesis using Japanese quarterly data based on the research design ofPatatoukas (2014), whose regression models contain all components of the market-wide cost ofcapital. This research design also clarifies whether and which components bias the aggregate
earnings-returns relation in the Japanese market.
Our results fulfill three requirements for the KLW hypothesis. First, aggregate earnings
4

We also observe an insignificant and negative aggregate earnings-returns relation in the Japanese stock market byrunning a simple regression, as shown in Table 3.
5
Despite a robust positive earnings-returns relation at the firm level (the micro level), a positive earnings-returns
relation cannot be detected at the aggregate level (the macro level) when running a simple regression. This puzzling
earnings-returns relation is referred to as the “Micro-Macro-Puzzle” in Japan (Nakano 2012, 2014; Yoshinaga 2016).

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The Japanese Accounting Review, 6 (2016), 95-122

changes are significantly positively related to contemporaneous changes in the market-wide costof capital. Second, the latter have a significantly negative relation with aggregate stock returns.
Third, a significantly positive aggregate earnings-returns relation appears only after controllingfor contemporaneous changes in the market-wide cost of capital. These results show that
contemporaneous changes in the market-wide cost of capital cause a puzzling aggregate earningsreturns relation in the Japanese market. In addition, when we decompose the market-wide cost ofcapital, we find that only contemporaneous changes in the market risk premium affect therelation, while those in the other components do not.
Sadka and Sadka (2009) (referenced as SS henceforth) develop a competing hypothesis
regarding the aggregate earnings-returns relation. To confirm the validity of the KLW
hypothesis in Japan, we also investigate the SS hypothesis. The SS hypothesis is composed of twoarguments. One is an argument relating to the high predictability of aggregate earnings and theother relates to investors’ attitudes toward risk. Our main results undermine the former argument,
because they show that aggregate earnings changes convey positive cash-flow news to investors
during earnings announcement periods. On the other hand, we do not obtain implications on thelatter argument from our main tests. Thus, we investigate the latter argument with an additional
test and show results inconsistent with the argument. Consequently, our main and additional
results indirectly support the validity of the KLW hypothesis, because they are not consistent
with both arguments of the competing hypothesis proposed by SS.
This study makes two contributions to a related research area called Macro-Accounting, andspecifically to the research area of the aggregate earnings-returns relation. This study is the firstthat supports KLW hypothesis outside the U.S. market, as far as we know. “Studies of aggregate
earnings tend to be U.S. centric in their focus (Shivakumar 2010, p.339)” and the external
validity of the KLW hypothesis is not proven yet. We show that the KLW hypothesis explains
the aggregate earnings-returns relation in the Japanese market. Thus, this study contributes toexpanding the external validity of the hypothesis. As the second contribution, our results suggest
the importance of focusing on an argument regarding investors’ risk-avoidance in the SS
hypothesis, although prior studies supporting the SS hypothesis mainly focus on the otherargument regarding the higher predictability of aggregate earnings (Ball et al. 2009; He and Hu
2014). Our results suggest that showing predictability is insufficient to support the SS hypothesis.
Our study also contributes to the stream of accounting research regarding the cost of capitalin two ways. First, we confirm that accounting information is related to the cost of capital at theaggregate level. Recent studies on the cost of capital show that accounting information is useful
to investors’ decision making, and is therefore related to the firm-level cost of capital (e.g.,
Francis et al. 2004; Barth et al. 2013; Konchitchki et al. 2016). We confirm that the relation
between accounting information and cost of capital in the Japanese market exists, even at theaggregate level. Second, our results indicate the strength of the market-wide cost of capital’s
impacts and identify the component that produces the impacts in the Japanese market. Our
results show that these impacts are so strong that the positive effects of aggregate earnings
changes on aggregate stock returns are canceled out. We also find that these impacts stem fromthe market risk premium, not risk-free rates or expected inflation. These findings improve ourunderstanding of the economic impacts of the market-wide cost of capital in the Japanese capital
market.
Additionally, our results have an implication for future international research. He and Hu(2014) report that interest rates and inflation do not affect the aggregate earnings-returns relation

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan99

outside the U.S. market. However, they do not consider the market risk premium. To reveal themechanism of the aggregate earnings-returns relation, this study suggests that futureinternational research should consider the effects of the market risk premium.
This study proceeds as follows. Section 2 summarizes related studies and introduces the
KLW hypothesis. Our research design is provided in Section 3. Sample selection, correlation
matrix, and descriptive statistics are described in Section 4. Section 5 details our empirical results
and interpretations. Finally, Section 6 concludes this study.

2. Prior studies and research question
2.1. Macro-Accounting, the related research area
In this subsection, we present information on a research area called Macro-Accounting andexplain how this study is related to this area. Recently, Konchitchki (2016a) introduced a new
and growing research area called Macro-Accounting. Konchitchki (2016a, p.27) stated, “Thisnew research area focuses on addressing real-life world problems using the value added that
accounting can bring to various macro-level topics that are at the forefront of the academic andprofessional discussions.” To understand this area deeply, he proposes two types of MacroAccounting research: 6 “Macro-to-Micro” and “Micro-to-Macro.” We first summarize priorMacro-Accounting studies in line with his classification.
The first research area, described as “Macro-to-Micro,” investigates how various types ofmacroeconomic information affect or improve the firm-level prediction of future performance orstock valuation. For example, Konchitchki (2011, 2013) shows that considering the effects ofinflation on the accounting figures of individual firms helps to predict their future cash flows andimproves their stock valuations. Li et al. (2014) reveal that combining firm-level exposures withcountries and their forecasted economic performance is useful to predict the profitability of
individual firms. Williams (2015) indicates that investors respond more strongly to bad earnings
news than good earnings news when the recent macro economy is more uncertain. He also findsthat this asymmetric response becomes stronger when stocks have higher sensitivity to macrouncertainty. Konchitchki et al. (2016) report that earnings downside risk, which is related tosensitivity to macroeconomic shock, captures incremental risk information that other risk
variables do not contain. They show that earnings downside risk has an incremental ability to
explain subsequent stock returns.
On the other hand, the latter research stream called “Micro-to-Macro” focuses on how
accounting contributes to informing and predicting various macroeconomic aspects. For example,
Shivakumar (2007), Shivakumar and Urcan (2014), Konchitchki and Patatoukas (2014a), andGallo et al. (2016) propose evidence that aggregate earnings contain various aspects of the future
macro economy (e.g., real and nominal GDP growth, inflation, and monetary policy). Some
recent research aggregates firm-level earnings in unique ways. Konchitchki (2016b) aggregatesearnings changes at the regional level. He finds that regional-level profitability conveys timely
information on the valuation of real estate and stock returns of Real Estate Investment Trusts(REIT). Konchitchki and Patatoukas (2014b, 2016a, b) aggregate earnings information of only
the largest firms to propose a cost-effective aggregating method. They show that their cost-

6

Konchitchki (2016a) recognizes that there are other Macro-Accounting studies that do not belong to the two typesof research. He calls such research “other Macro-Accounting.”

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The Japanese Accounting Review, 6 (2016), 95-122

effective aggregate earnings are useful to nowcast and forecast GDP growth. In addition toearnings information, Arif and Lee (2014) report that higher aggregate investment predicts lower
corporate profitability and economic growth.
We investigate the earnings-returns relation at the aggregate-level. We believe that this kindof research is related to the latter stream, because the issues of whether aggregate earnings are
informative and what they inform are discussed by investigating the relation. Prior studies reportthat a significantly positive earnings-returns relation cannot be observed at the aggregate level. As
an interpretation of this result, KLW argue that aggregate earnings changes convey two kinds ofnews (i.e., cash-flow news and discount-rate news), although SS argue that they are notinformative due to their high predictability. In addition, the discount rate in this context is closely
related to the macro economy, because it affects all stock prices in the market. Thus, our study
belongs to the latter stream of Macro-Accounting research.

2.2. The explanation of the KLW hypothesis on the aggregate earnings-returns relation
Unlike firm-level evidence, the aggregate earnings-returns relation is not significantly
positive. Some existing studies report that even a negative earnings-returns relation can beobserved at the aggregate level. To explain why such a surprising relation can be observed, KLW
propose a hypothesis based on omitted variable bias. In this subsection, we explain the KLW
hypothesis. Hecht and Vuolteenaho (2006) present a formula in which three components explain
realized returns, based on Campbell (1991) who decomposes unexpected returns into two
components.
[ ]+(

≈

[ ]+

=

)

−

,

−

∆

−(

−

)

(1)

,

is the realized log return at period .
is the expectation operator with expectations
conditional on the information available at the end of period -1 (the beginning of period ).
)[ ]
Thus,
[ ] denotes stock return at period expected at the end of period -1. ( −represents the modified expectation for based on the news released at period . ∆ is the log
dividend growth at period . is the inverse of 1 plus the dividend yield ( < 1). Consequently,
( −
)∑
∆
(=
, ) means the modified expectation for subsequent dividend)∑=
growth, which is caused by “cash-flow news.” Further, ( −, is themodified expectation for the subsequent cost of capital, which is caused by “discount-rate news.”7[∆]) and unexpected
Next, we split earnings changes into expected earnings changes ([]∆).
earnings changes (earnings surprises:
∆
7

=

[∆

]+

[∆

]

(2)

)∑
Though Hecht and Vuolteenaho (2006) denote ( −as “expected-return news,” we describe it
as news on “cost of capital,” because expected return is normally equal to cost of capital in the efficient market. If the
expected return of a security is higher (lower) than its cost of capital, investors will be eager to buy (sell) the security.
Then the security price will move upward (downward) until the expected return becomes equal to the cost of capital.

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan

101

[∆
]+
[∆
] in Equation 1 and deleting
Substituting ∆intouncorrelated terms in the definition, 8 we can rewrite the earnings-returns relation)) in the following way.
( ,∆
(
( ,∆

)≈

[ ],

(

[∆

])
(3)

+

, ,

[∆

] −

, ,

[∆

]

In Equation 3, the earnings-returns relation is decomposed into three components: (1) the
[ ],
[∆
])),
(
relation between expected earnings changes and expected returns ((2) the relation between earnings surprises and contemporaneous modified expectation for[∆] ), and (3) the relation between earnings
subsequent dividend growth (, ,surprises and contemporaneous modified expectation for the subsequent cost of capital
[∆
] ).
(
, ,
In an economic boom (economic recession), when aggregate earnings changes are positive(negative), positive (negative) firm-level earnings surprises should be dominant in the market,
yielding higher (lower) stock prices. Thus, earnings changes should have positive effects oncontemporaneous stock returns at the aggregate level, comparable to the firm level[∆] > 0). However, what if aggregate earnings changes are positively(, ,[∆] > 0 )?
related to changes in the market-wide cost of capital 9 (, ,Changes in the market-wide cost of capital are generally negatively related to the movement ofstock prices.10 Additionally, KLW (p.542) argue that “discount rates should be strongly correlated
across stocks, largely driven by business conditions, while cash flows are likely to have a larger
idiosyncratic component.” Based on their argument that idiosyncratic components will be offset
through aggregation, the negative effects of changes in the cost of capital on thecontemporaneous stock returns will be stronger than the positive effects of earnings surprises at
[∆
] ≤
[∆
] ). Therefore, in a
the aggregate level (, ,, ,simple regression model that does not control for changes in the market-wide cost of capital,
omitted variable bias will make the earnings-returns relation insignificant or negative) ≤ 0).11
( ,∆
(

8

We delete uncorrelated terms in the following way. Earnings changes expected at period -1 are not related to news[∆
] ≈ 0,[∆] ≈ 0). Earnings surprises occur at
released at period t (
, ,
, ,
[ ],
[∆
]) ≈ 0).
(period . Thus, they are not correlated to stock returns expected at period -1 (9
To understand the KLW hypothesis more deeply, we propose a possible economic story behind the positive relation
between aggregate earnings changes and changes in the risk-free rate or expected inflation. In an economic boom
(economic recession) when positive (negative) aggregate earnings changes are observed, the demands for money,
goods, and services will increase (decrease), causing higher (lower) interest rates and inflation.
10
Based on valuation models such as the Dividend Discount Model, the increase (decrease) of the discount rate (thecost of capital) drives the stock prices downward (upward). Therefore, changes in the market-wide cost of capital
have a negative effect on aggregate stock returns.
11
Additionally, the relation between expected earnings changes and expected returns should not affect the aggregate[∆] ≈ 0, ∴[ ],[∆]) ≈ 0), because this hypothesis assumes(
earnings-returns relation (that aggregate earnings changes are largely unpredictable.

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The Japanese Accounting Review, 6 (2016), 95-122

FIGURE 1 CONCEPTUAL DIAGRAM OF KLW HYPOTHESIS
Requirement 3 (3’)

aggregate earnings changes

aggregate stock returns
Requirement 1 (1’)
changes in(the component of)market-wide cost of capitalcancel out

Requirement 2 (2’)

earnings announcement period

2.3. Empirical evidence on the aggregate earnings-returns relation
There are three requirements for the KLW hypothesis, as follows.
Requirement 1 (1’): aggregate earnings changes are significantly positively related tocontemporaneous changes in (components of) the market-wide cost of capital.
Requirement 2 (2’): contemporaneous changes in (components of) the market-wide cost of capital
have a significantly negative relation with aggregate stock returns.
Requirement 3 (3’): a significantly positive aggregate earnings-returns relation appears only after
controlling for contemporaneous changes in (components of) the market-wide cost of capital.
Figure 1 illustrates the KLW hypothesis and its requirements. Prior U.S. studies mainly
investigate whether these requirements are supported by two regression tests. In the firstregression, they focus on the relation between aggregate earnings changes and contemporaneouschanges in (components of) the market-wide cost of capital to check Requirement 1 (1’). In thesecond regression, they regress aggregate stock returns on aggregate earnings changes andcontemporaneous changes in (components of) the market-wide cost of capital used in the firstregression to detect whether Requirement 2 (2’) is achieved. They also concentrate on thecoefficient of aggregate earnings changes in the second regression to investigate Requirement 3(3’).
KLW show that aggregate earnings changes are positively related to contemporaneouschanges in the one-year T-bill rate. Uysal (2010) reports that, although the aggregate earningsreturns relation is insignificant in a simple regression, a significantly positive aggregate earningsreturns relation occurs after controlling for two or more discount-rate proxies. Patatoukas (2014)
observes that aggregate earnings changes are positively related to changes in the market-wide costof capital. In addition, he shows that a significantly positive aggregate earnings-returns relation
appears after controlling for changes in the market-wide cost of capital, although this significant
relation does not appear in a simple regression. Gallo et al. (2016) find that aggregate earnings

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan103

changes convey news regarding the federal fund rate. They show that when they control for
federal fund rate news, the aggregate earnings-returns relation changes from significantly
negative to insignificant. To the contrary, He and Hu (2014) report that, though aggregate
earnings changes are positively correlated with contemporaneous changes in interest rates andinflation, the aggregate earnings-returns relation does not change even after controlling for thesevariables outside the U.S. market. In summary, these studies support the validity of the KLW
hypothesis in the U.S. market, while it is not proven outside of the U.S. market.
In addition to the KLW hypothesis, SS present the other hypothesis regarding the aggregate
earnings-returns relation. Their hypothesis is composed of two arguments. One is an argument
regarding the high predictability of aggregate earnings and the other is regarding investors’ riskavoidance. It is assumed that aggregate earnings changes do not modify investors’ expectations at
earnings announcement periods, because they are almost completely predicted and priced in before[∆] ≈ 0,[∆]
earnings announcement periods (
, ,
, ,
[∆
] ≈ 0, ∆ ≈[∆] ). In addition, SS explain that aggregate≈0∵
earnings changes can be negatively related with ex ante expected returns due to the negative
relation between expected aggregate earnings changes and the market risk premium[ ],[∆]) ≤ 0).
((Prior evidence that supports the SS hypothesis focuses mainly on the former argument: highpredictability of aggregate earnings (changes). SS and Ball et al. (2009) show that aggregate
earnings (changes) are significantly related to past aggregate returns.12 He and Hu (2014) study
28 non-U.S. stock markets and show that the aggregate earnings-returns relation is weaker (frompositive to negative) in countries with more transparent financial disclosure, because suchdisclosure helps investors forecast future earnings more precisely. These results suggest that
aggregate earnings changes are at least partially reflected in past aggregate returns. Therefore, ourempirical tests use surprising information in aggregate earnings changes (aggregate earnings
surprises) in addition to “raw” aggregate earnings changes.

2.4. Motivation and research question
As far as we know, the He and Hu (2014) study is the only non-U.S. study that investigates
whether several components of the market-wide cost of capital affect the aggregate earningsreturns relation. However, it is not clear whether their evidence explains the aggregate earningsreturns relation in the Japanese market for three reasons. First, He and Hu (2014) do not include
all components of the market-wide cost of capital in their regression model. As Patatoukas(2014) states, the market-wide cost of capital has three components: the real risk-free rate,
expected inflation, and market risk premium. He and Hu (2014) control for only inflation andchanges in nominal interest rates, and do not consider the market risk premium.
Second, though He and Hu (2014) propose evidence regarding the effects of inflation andinterest rates on the aggregate earnings-returns relation, the evidence is for the average non-U.S.
market and not for a specific stock market. He and Hu (2014) cover 28 non-U.S. stock markets
and run a pooled regression of their country/year observations. Consequently, their results show
the average effects of inflation and interest rates on the aggregate earnings-returns relation inthese countries. They do not sufficiently investigate whether the aggregate earnings-returns
12

In existing studies supporting the SS hypothesis, it is argued that aggregate earnings changes contain positive cashflow news, but such news is priced in before earnings announcement periods.

104

The Japanese Accounting Review, 6 (2016), 95-122

relation in the Japanese market is affected by these components of the market-wide cost of capital.
Third, He and Hu (2014) use only annual data while U.S. studies that test the KLW
hypothesis also often use quarterly data to investigate the aggregate earnings-returns relation (e.g.,
KLW). Quarterly earnings constitute more timely information. Quarterly returns are calculated
by a shorter window, which is useful in excluding more of the effects of uninterested events. Thus,
quarterly analyses will capture the aggregate earnings-returns relation in the Japanese market
more precisely.
Based on these three reasons, we set our research question as whether the KLW hypothesis
explains the quarterly aggregate earnings-returns relation in the Japanese market. To answer thisquestion, we use the research design of Patatoukas (2014), whose regression model contains allcomponents of the market-wide cost of capital.
If the KLW hypothesis explains the aggregate earnings-returns relation in the Japanesemarket, Requirements 1, 2, and 3 will all be fulfilled. Thus, we investigate whether theserequirements are achieved in our empirical tests. Additionally, we decompose the market-wide
cost of capital into three components to clarify which components bias the aggregate earningsreturns relation in the Japanese market. If a component of the market-wide cost of capital makes
the aggregate earnings-returns relation not significantly positive, the component will satisfy all
three Requirements 1’, 2’, and 3’.

3. Research design
3.1. Model description
We adopt two main tests to investigate whether changes in the market-wide cost of capitaland changes in its components bias the aggregate earnings-returns relation in the Japanese stock
market. In the first test, we check Requirement 1 (1’). We use the regression models shown inEquations 4 through 6.
∆

=

+

∆

+

∆

=

+

∆

+

∆

+

∆

=

+

∆

+

∆

+

(4)
(5)
∆

+

(6)

is a variable of aggregate earnings changes. ∆represents changes in the∆
represents changes in the implied market risk premium.
market-wide cost of capital. ∆∆represents changes in the nominal risk-free rate. ∆represents changes in the real
represents changes in expected inflation. In Equation 4, we investigate
risk-free rate. ∆the relation between aggregate earnings changes and contemporaneous changes in the marketwide cost of capital. If the KLW hypothesis reflects the reality of the Japanese stock market,
in Equation 4 should be significantly positive (Requirement 1).
Equations 5 and 6 are used to investigate whether and which components of changes in themarket-wide cost of capital fulfill Requirement 1’. We split ∆into ∆and ∆into ∆
and ∆in Equation 6. If thesein Equation 5. We divide ∆components bias the aggregate earnings-returns relation, their coefficients should be significantly
positive.

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan105

In the second test, we focus on Requirements 2 and 3 (2’ and 3’). We use the regression
models described in Equations 7 through 10.
=

+

∆

+

=

+

∆

+

∆

+

=

+

∆

+

∆

+

∆

+

=

+

∆

+

∆

+

∆

+

(7)
(8)
(9)
∆

+

(10)

represents aggregate stock returns during earnings announcement periods. According
to prior studies, the quarterly aggregate earnings-returns relation is observed to be insignificant orsignificantly negative with a simple regression model both in Japan (Yoshinaga 2016) and in the
U.S. (e.g., KLW; SS; Patatoukas 2014). Therefore, we expect that in Equation 7 is not
significantly positive. As an interpretation of this earnings-returns relation, KLW argue that thepositive effects of aggregate earnings changes are canceled out by the negative effects ofcontemporaneous changes in the market-wide cost of capital (∆). We control for ∆in Equation 8 to test this argument. If the KLW hypothesis reflects reality in Japan, should besignificantly positive (Requirement 3) and should be significantly negative (Requirement 2).
into its components and investigate whether
In Equations 9 and 10, we decompose ∆and which components satisfy Requirements 2’ and 3’. If the components fulfill theRequirements, coefficients of the components should be significantly negative (Requirement 2’)
and coefficients of ∆should be significantly positive (Requirement 3’).

3.2. Variable definition
We use quarterly data. As a proxy for aggregate stock returns, we use equally-weighted
averages of firm-level quarterly buy-and-hold returns ( ). Before calculating the firm-level
returns, we adjust stock prices for price movements due to ex-rights and ex-dividends. The
measurement window of the stock returns is from the beginning to the end of the quarter.
Though cumulative total net incomes during the fiscal year are typically announced on aquarterly basis in Japan, we define firm-level quarterly earnings as net income of firm achieved
during quarter (, ). If quarter is the first quarter of each fiscal year for firm , we use its.
If quarter is not the first quarter, we treat the quarter-on-quarter
net income as,change in its net income as, . We use two variables of aggregate earnings changes in ourempirical tests.13 The first is the “raw” aggregate earnings changes (∆), which are equallyweighted averages of the year-on-year change in firm-level quarterly earnings deflated by theprevious-year book value of equity (

,

,
,

).

The second is the estimated aggregate earnings surprises (13). We defineas

We estimate the aggregate earnings surprises () and use the estimate in our tests, because prior studies suggestthat aggregate earnings changes are predicted before earnings announcement periods. We use ∆in addition
tobecause our results may depend on our specific estimation model of aggregate earnings surprises.

106

The Japanese Accounting Review, 6 (2016), 95-122

residuals of the following Equation 11.14 15 Untabulated results of Equation 11 indicate that theestimated andin Equation 11 are all significantly positive ( = 0.655 [ =7.031], = 0.028[ = 2.673]) and the adjusted R-square is 0.464 using adjusted standard errors presented bydoes not contain information reflected in stock
Newey and West (1987). We confirm thatprices before earnings announcement periods in Appendix (A).
∆

=

+

∆

+

+

(11)

∆

represents changes in the market-wide implied cost of capital (∆=−). We apply the estimating method offered by Easton and Sommers (2007) to calculate). Our estimation method for this variable is detailed in
the market-wide cost of capital (Appendix (B). ∆represents changes in the nominal risk-free rate, which is the quarter-onquarter change in yield of the 10-year Japanese government bond at the end of each quarter=−). ∆represents changes in the market risk premium and is defined as(∆
the difference between ∆and ∆, following Patatoukas (2014) (∆=∆−∆).
represents changes in expected inflation in Japan. This variable is measured as the averages∆
of expected year-on-year growth of the core Consumer Price Index (CPI) released in the ESP
forecast16 issued at the end of each quarter as expected inflation17 (∆=−).
represents the difference between ∆and ∆Following Patatoukas (2014), ∆=∆−∆). Figure 2 is the timeline of our main variables.
(∆

14

Yoshinaga (2016) shows that aggregate earnings changes have a significantly positive relation with aggregate stock
returns just before earnings announcement periods in the Japanese stock market. KLW report positive
autocorrelation of aggregate earnings changes (earnings persistence), and our untabulated results confirm that thefirst-order autocorrelation is observed in Japanese aggregate earnings changes. These results can be interpreted as
evidence that aggregate earnings changes are somehow predictable. To exclude the effects of expected aggregate
earnings changes on expected returns as SS assume, we extract surprising information in aggregate earnings changes
using Equation 11.
15
According to KLW, aggregate earnings changes have the first to the third order significantly positive autocorrelation,and this autocorrelation is mainly caused by the first order partial autocorrelation. In our untabulated tests, we
also has the first to the second order significantly positive autocorrelation, and thisconfirm that ∆autocorrelation is mainly caused by the first order partial autocorrelation. (The relation between ∆and∆becomes insignificant after controlling for ∆.) Thus, we adjust aggregate earnings changes for.
only the first order autocorrelation in calculating
16
ESP forecast is the survey issued by the Economic Planning Association since its origin in 2004, and it was takenover by the Japan Center for Economic Research in April 2012. These authorities send approximately 40 private
economists a questionnaire about their expectations of important economic indicators, such as stock prices and yen
exchange rates, each month. They publish their answers monthly to clarify the consensus on future economic trends
and the persistence of business conditions (http://www.jcer.or.jp/esp/index.html).
17
In April 2014, the consumption tax rate was increased from 5% to 8% in Japan. To exclude the effects of the tax
increase on expected inflation, we use the average core CPI after adjusting for the rise in the consumption tax rate(the adjusted average core CPI) starting at Q2:2013. However, at Q2:2013 and at Q3:2013, the ESP forecast has
not announced the adjusted average core CPI. Consequently, we subtract 0.02 from the non-adjusted average yearon-year growth of the core CPI in these quarters to rule out the effect of the consumption tax rate increase, because
Bank of Japan (2013) estimates the effects of the rise in the consumption tax on the CPI in 2014 to be 2.0%. The
Japanese central bank states: “The effects of the two scheduled consumption tax hikes on prices can be mechanicallyestimated by assuming that the rise in consumption taxes will be fully passed on for all currently taxable items. On
this basis, the CPI will be pushed up by 2.0 percentage points in fiscal 2014.”

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan

107

FIGURE 2 THE TIMELINE OF OUR MAIN VARIABLES

∆

∆

∆
∆
∆
∆
∆

:
Before earnings announcement: +1
Earnings announcement period

is aggregate stock returns. ∆is aggregate earnings changes. ∆is changes in theis changes in the market risk premium. ∆is changes inmarket-wide cost of capital. ∆real risk-free rate. ∆is changes in expected inflation.

3.3. Statistical issues: heteroskedasticity and serial correlation
Many empirical studies in accounting and finance adjust for heteroskedasticity. Researchers
often calculate standard errors with the method of White (1980) to reduce statistical problems
due to heteroskedasticity. Additionally, considering Durbin-Watson statistics, serial correlation
may bias some of our results. 18 Therefore, we use heteroskedasticity- and autocorrelationconsistent standard errors proposed by Newey and West (1987). We set the maximum lag length
for calculating Newey-West standard errors as two, which is an integer part of 0.25 power of thesample size, based on related studies (Konchitchki and Patatoukas 2014a) and practicalconvention (Ota 2012).

18

Stanford University releases "Critical Values for the Durbin-Watson Test" based on the method presented by Savinand White (1977) (http://web.stanford.edu/~clint/bench/dwcrit.htm). We use the critical values presented on thiswebpage to judge whether and how strongly the serial correlation biases our results.

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The Japanese Accounting Review, 6 (2016), 95-122

4. Sample selection, correlation matrix, and descriptive statistics
4.1. Sample selection
Our data source is primarily “Nikkei NEEDS Financial Quest 2.0,” which contains financial
data of listed firms and macroeconomic data in Japan. We obtain all the required data except
expected inflation from Nikkei NEEDS. Expected inflation is manually collected from the ESP
forecast.
We define Q1 as the quarter from January to March, Q2 as April to June, Q3 as July to
September, and Q4 as October to December. Using this description, we collect financial data andstock price data from Q1:2003 to Q1:2015.19 We impose the following six data requirements on
firm/quarter observations for these periods:
I.

Firm/quarter observations that have non-missing data to construct all the firm-level
and aggregate-level variables required in our empirical tests.
II. Firm/quarter observations of industrial firms (not financial firms: banks, insurance,
brokerage, and asset management firms)
III. Firm/quarter observations that use positive book values to construct the variables
IV. Firm/quarter observations whose stock price at the beginning of the quarter is
100JPY or higher
V. Firm/quarter observations whose fiscal year-ends are March, June, September, or
December
VI. Firm/quarter observations that release a quarterly Summary of Financial Statementsby 60 days after the beginning of the earnings announcement periods
Data requirement I is required to remove observations that have missing variables or thatcannot be used to construct aggregate-level variables. We establish Data requirement II becausesome accounting items of financial firms are different from those of industrial firms. Datarequirement III is set to avoid variables whose deflators are zero or negative. Data requirement IV
is imposed to exclude outliers of stock returns. If stock prices are near the minimum monetary
unit (1JPY), the stock returns tend to be highly volatile. Thus, it is supposed that KLW and SS
exclude observations with stock prices below 1USD to reduce the effects of outliers of stock
returns. Our sample covers listed firms adopting March as the fiscal year-end, because March is
the most popular fiscal year-end in Japan. As stated in data requirement V, we add firms withfiscal year-ends of June, September, or December to our sample to increase the generality of ourresults. Data requirement VI is set for reported earnings changes to be priced in during earnings
announcement periods.
In addition to imposing these data requirements, we regard the top and bottom 1% of our
firm/quarter observations as ranked by ∆

19

, ,

,
,

, and

,

,
,

each quarter as

The first quarter in which Nikkei NEEDS includes quarterly financial data from the Summary of Financial
Statements (Kessan-Tanshin in Japanese) is Q2:2002. We do not, however, use data before Q1:2003, because thenumbers of firms whose quarterly (3-months) earnings can be calculated are less than 500 before Q2:2003 and somedata at Q1:2003 is required to calculate firm-level variables after Q1:2003.

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan109

TABLE 1 CORRELATION MATRIX AND DESCRIPTIVE STATISTICS
is aggregate stock returns. ∆is aggregate earnings changes.
is surprisinginformation in aggregate earnings changes. ∆is changes in the market-wide cost of capital.
∆
is changes in the market risk premium. ∆is changes in nominal risk-free rate. ∆is changes in real risk-free rate. ∆is changes in expected inflation. In Panel A, Pearson(Spearman) correlations are below (above) diagonal. Significant correlation at 5% level is bold.
Panel A Correlation matrix (N=42)
∆
0.082
∆
-0.057-0.0210.714∆-0.3480.889∆-0.370
0.866
∆
0.290
-0.232∆-0.081-0.487
∆
0.276
0.368

0.664
0.670
-0.317-0.2960.113

0.988-0.368-0.3960.186-0.508-0.436
0.137

0.410
0.210

-0.806

Panel B Descriptive statistics
Mean
S. D.
0.023
0.101
∆
0.002
0.010
0.000
0.007
∆
0.000
0.010
∆
0.001
0.010
∆
0.000
0.002
∆
-0.001
0.003
∆
0.000
0.003

Min
-0.169-0.027-0.019-0.024-0.024-0.003-0.008-0.01225%-0.049-0.002-0.003-0.006-0.005-0.002-0.0020.000

Median
0.012
0.002
0.000
0.000
0.001
0.000
-0.001
0.001

75%
0.085
0.007
0.003
0.007
0.008
0.001
0.001
0.001

Max
0.266
0.035
0.025
0.028
0.031
0.003
0.009
0.005

-0.1690.575∆-0.341
0.792
0.656

∆
-0.360
0.760
0.683
0.977

∆
0.369
-0.168-0.415-0.357-0.517∆0.041-0.283-0.082-0.322-0.399
0.572

∆
0.225
0.227
-0.167
0.105
0.066
0.146
-0.594

N
43
43
43
43
43
43
43
43

outliers, and exclude them from our sample. 20 After deleting outliers, we obtain 104,971
firm/quarter observations from Q2:2004 to Q1:2015 to calculate aggregate-level variables. We
exclude a quarter observation at Q2:2004, because we cannot calculate some aggregate-levelvariables in Q2:2004 (,∆,∆,∆, and ∆).21 Our final sample consists of
43 quarter from Q3:2004 to Q1:2015.

4.2. Correlation matrix and descriptive statistics
Table 1 shows the correlation matrix and descriptive statistics. The correlation between

,

20
,

21

and

,

,
,

are used to estimate the market-wide cost of capital. Please see Appendix (B) for more

information.
requires ∆
; ∆
and ∆
require; and ∆
and ∆requirefor thecalculation. Our sample covers firm/quarter observations from Q2:2004 and expected inflation written in the ESP) is available from Q2:2004. Therefore,,∆,∆,∆, and ∆
are available fromforecast (Q3:2004.

110

The Japanese Accounting Review, 6 (2016), 95-122∆
and ∆is almost one, probably because movements of both the risk-free rate andexpected inflation in Japan do not change drastically.22 Consistent with this supposition, theand ∆are less than one third of those of ∆. Somestandard deviations of ∆explanatory variables have strong correlations with one another. Therefore, we judge whether our
empirical results are biased by multicollinearity based on the Variance Inflation Factor (VIF). We
confirm that the VIF of each variable in all regression models is lower than 10 in the following
Tables. Thus, we conclude that statistical problems due to multicollinearity do not affect our
results severely.
We conduct the unit root tests proposed by Phillips and Perron (1988) for all variables
described in Table 1. According to Okimoto (2010), when we regress an explained variable thathas a unit root on an explanatory variable that also has a unit root, a significant relation between
them can be observed, even though they have no rational relation.23 All results of the PhillipsPerron type unit root tests reject the null hypothesis that variables contain a unit root at the 1%
level (untabulated). Therefore, our regressions in Section 5 should not be “spurious regressions.”

5. Empirical results
5.1. Main results
Table 2 shows the results of the first main test, and Table 3 of the second main test. First,
we focus on Requirements 1, 2, and 3 to reveal whether the KLW hypothesis explains theaggregate earnings-returns relation in Japan. In Table 2, the coefficients of ∆aresignificantly positive, which means that aggregate earnings changes have a significantly positive
relation with contemporaneous changes in the market-wide cost of capital. Thus, Requirement 1
is fulfilled in the Japanese market. In Table 3, the coefficients of ∆andareinsignificant and negative in a simple regression, which means that a significantly positive
earnings-returns relation is not observed at the aggregate level when running a simple regression.
On the other hand, when controlling for ∆, the coefficients of ∆and, whichbecome significantly positive. Table 3 also describes the negative coefficients of ∆means that changes in the market-wide cost of capital have a significantly negative relation withaggregate returns (). These results prove that Requirements 2 and 3 are satisfied in theJapanese market. In summary, our results indicate that the KLW hypothesis is valid in theJapanese market, because Requirements 1 through 3 are all fulfilled. In other words, negative
effects of contemporaneous changes in the market-wide cost of capital cancel out positive effects
of aggregate earnings changes in Japan.
Next, we target results for components of the market-wide cost of capital to reveal which
components bias the aggregate earnings-returns relation in Japan. In Tables 2 and 3, the signs
and significance of coefficients of ∆are the same as those of ∆
.∆
and

22

The average absolute value of the quarterly yield changes in the 10-year government bond from Q2:2003 to Q1:2015
is 0.153% in Japan, while it is 0.397% in the U.S. In addition, the average absolute value of year-on-year changes in
the quarterly Consumer Price Index for all items less food and energy from Q2:2003 to Q1:2014 is 0.590% in Japan,
while it is 1.920% in the U.S. This slight change in risk-free rates and expected inflation may be caused by the “zerointerest rate policy” in Japan. The yield of 10-year government bonds in the U.S. is collected from the website of the
U.S. Department of the Treasury and the Consumer Price Index in the U.S. is from the website of the U.S. Bureauof Labor Statistics. The Japanese data is collected from Nikkei NEEDS.
23
Granger and Newbold (1974) caution about this kind of nonsense and spurious regression.

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan

111

TABLE 2 THE RELATION BETWEEN AGGREGATE EARNINGS CHANGES AND CHANGES IN
THE MARKET-WIDE COST OF CAPITAL AND THOSE IN ITS COMPONENTS
The table shows the results obtained by ∆= + ∆+ (Equation 4),
∆
= + ∆
+ ∆
+
(Equation 5), ∆
= + ∆
+
∆
+ ∆
+ (Equation 6). ∆is replaced by ∆or.
∆is aggregate earnings changes.
is aggregate earnings surprises. ∆is changes
in the market-wide cost of capital. ∆is changes in the market risk premium. ∆ischanges in nominal risk-free rate. ∆is changes in real risk-free rate. ∆is changes in
expected inflation. The left three columns indicate the results by the regression whose explained
variable is ∆. The right three columns indicate the results by the regression whose
explained variable is. We report t-statistics using heteroskedasticity- and autocorrelationconsistent standard errors proposed by Newey and West (1987) in the brackets. ***, ** and *denote statistical significance at the 1%, 5% and 10% level respectively, using two-tailed tests.
0.002**[2.250]0.888***[8.207]∆∆∆0.002**[2.707]0.920***[8.177]1.432***[3.157]

∆
∆
∆
.
.

.

0.785
67.363***
1.607
1.000
42

0.787
33.891***
1.739
1.314
42

0.002**[2.654]0.000[0.095]0.472***[4.627]0.858***[10.465]0.980**[2.557]1.714***[4.828]0.821
39.250***
1.923
4.200
42

0.426
21.406***
2.174
1.000
42

0.000
[-0.030]0.000[-0.054]0.448***[3.687]0.054[0.083]0.443***[3.485]0.420
15.737***
2.136
1.314
42

0.019
[0.026]0.076[0.120]0.405
10.432***
2.145
4.200
42

have a significantly positive relation with ∆in Table 2 (Requirement 1’).
Coefficients of ∆are significantly negative in Table 3 (Requirement 2’). Coefficients ofandbecome significantly positive after controlling for ∆in Table 3∆(Requirement 3’). These results show that changes in the market risk premium meet
Requirements 1’, 2’, and 3’. To the contrary, though some coefficients of ∆,∆, andare significantly positive in Table 2, coefficients of ∆,∆, and ∆
are∆not significantly negative in Table 3. These results mean that changes in the risk-free rate andexpected inflation do not meet Requirement 2’, at least. In untabulated results, when we exclude∆
from Equations 9 and 10, the coefficients of ∆andare insignificant and,∆, and ∆
are not significantly negative. These untabulated
those of ∆results show that changes in risk-free rates and expected inflation do not meet Requirements 2’
and 3’. On the other hand, when we regresson ∆orcontrolling for only
, the coefficients of ∆andbecome significantly positive and those of∆

112

The Japanese Accounting Review, 6 (2016), 95-122

TABLE 3 EFFECTS OF CONTROLLING FOR CHANGES IN THE MARKET-WIDE COST OF
CAPITAL ON AGGREGATE EARNINGS-RETURNS RELATION

The table shows the results obtained by= + ∆+ (Equation 7),
= +
∆
+ ∆
+
(Equation
8),
= + ∆
+ ∆
+
∆
+
(Equation
9),
= + ∆
+ ∆
+ ∆
+
∆
+ (Equation 10). ∆is replaced by ∆or.
is aggregate stock
returns. ∆is aggregate earnings changes.
is aggregate earnings surprises. ∆ischanges in the market-wide cost of capital. ∆is changes in the market risk premium. ∆is changes in nominal risk-free rate. ∆is changes in real risk-free rate. ∆is changes in
expected inflation. We report t-statistics using heteroskedasticity- and autocorrelationconsistent standard errors proposed by Newey and West (1987) in the brackets. ***, ** and *denote statistical significance at the 1%, 5% and 10% level respectively, using two-tailed tests.
0.026[1.400]-0.586[-0.392]

∆

∆

0.002
[0.184]11.903***[4.241]

0.004[0.285]
11.647***[3.808]0.025[1.444]0.024[1.340]0.027[1.627]0.023[1.470]-0.307[-0.202]5.229**[2.636]-5.935***[-3.279]

5.682**[2.536]5.511***[3.009]-5.409**[-2.652]6.689[0.688]-6.358***[-3.012]-14.039***[-4.795]∆-13.574***[-3.840]-9.679[-0.784]

∆
∆
∆
.
.

0.005
[0.320]10.437***[2.994].

-0.022
0.154
1.606
1.000
42

0.359
11.504***
2.185
4.764
42

0.346
11.797***
2.191
6.127
42

-12.871***[-3.625]-10.963[-0.851]-6.062[-0.502]0.343
11.805***
2.197
6.553
42

-0.025
0.041
1.636
1.000
42

0.143
5.382***
1.248
1.787
42

0.160
5.373***
1.314
2.142
42

-0.839[-0.083]
11.406[1.510]0.243
6.885***
1.430
4.200
42

∆
∆

are significantly negative. These untabulated results support the conclusion thatmeets Requirements 2’ and 3’.
In summary, we find that the KLW hypothesis explains the aggregate earnings-returns
relation in the Japanese market. In other words, contemporaneous changes in the market-wide
cost of capital cause omitted variable bias against the aggregate earnings-returns relation.
Additionally, decomposing the market-wide cost of capital, we find that only changes in themarket risk premium cause such bias in Japan.

5.2. Robustness checks
In this subsection, we check the robustness of our main results by using different standard
errors, a different regression method, a different aggregating method, and different periods. We

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan113

do not tabulate the results of these robustness checks due to space considerations. Briefly
speaking of the conclusion of these tests, we confirm the robustness of the interpretation of ourmain results.
5.2.1. Robustness checks on serial correlation and heteroskedasticity
We calculate the heteroskedasticity- and autocorrelation-consistent Newey-West standard
errors in our main tests. In calculating these standard errors, we set the maximum lag length as
two. Despite this treatment, we may not be able to reduce statistical problems due to serial
correlation, because this lag length is based only on academic and practical conventions.
Therefore, we check the robustness of our main results in two ways. First, we vary the maximum
lag length from zero to four and check the sensitivity of our results. Second, we adopt thegeneralized least-squares method presented by Prais and Winsten (1954) and use theheteroskedasticity-consistent standard errors presented by White (1980). All results of theserobustness checks are similar to our main results.
5.2.2. Robustness checks on the other aggregating method: value-weighted averages
Existing studies on the aggregate earnings-returns relation use value-weighted crosssectional averages as aggregate-level variables, in addition to equally-weighted cross-sectional
averages. Therefore, we employ value-weighted averages based on market values as ouraggregation method and run the same regressions as in the main analysis. In this robustness
check, we estimate the average cost of capital separately for each industry and calculate the valueweighted average of the cost of capital based on the total market value of each industry. We
regard it asin this test. Untabulated results using these value-weighted averages
demonstrate that almost all signs and statistical significance of coefficients are similar to those of
our main results, with one differing result. When we check the relation between
and,(Equation 8) or its components (Equations 9 and 10) with Newey-West
controlling for ∆are insignificant. To the contrary, when we adopt thestandard errors, the coefficients ofgeneralized least-squares method presented by Prais and Winsten (1954) and theheteroskedasticity-consistent standard errors proposed by White (1980), significantly positivecoefficients ofare observed, consistent with our main analysis. Therefore, we
comprehensively judge that positive effects of value-weighted aggregate earnings surprises on thecontemporaneous aggregate stock returns exist, but they are somewhat weaker.24
5.2.3. Robustness checks on the sample period
Aggregating fewer firms can cause inadequate diversification of firm-specific information.
Due to data restriction, our sample size is limited to roughly 1,000 firm/quarter observations
before Q2:2005, although over 2,000 firm/quarter observations are available starting at Q2:2005.
Thus, we limit the sample periods to those beginning with Q2:2005 and run the regressions. The
24

One of the reasons why positive effects of value-weighted aggregate earnings surprises are weaker is that the impactsof large firms become stronger when we use value-weighted averages. Collins et al. (1987) suggest that earnings
changes in larger firms are more predictable. Therefore, the value-weighted averages of earnings changes will beusing equallypredicted more easily than equally-weighted averages. By running Equation 11 to calculate
weighted averages, the adjusted R-Square is 0.464 (untabulated). On the other hand, when we use value-weighted
averages, the adjusted R-Square is 0.568 (untabulated). This difference suggests that value-weighted aggregate
earnings changes are more predictable than equally-weighted aggregate earnings changes.

114

The Japanese Accounting Review, 6 (2016), 95-122

results are not largely different from the main results in signs and significance of the coefficients.
The bankruptcy of Lehman Brothers and the subsequent financial crisis occurred during oursample period. Since this financial crisis seriously damaged the Japanese economy, someobservations can be outliers. Therefore, we exclude quarter observations from Q3:2008 (theperiod in which Lehman Brothers declared bankruptcy) to Q1:2010 (the first trough of thebusiness cycle following the bankruptcy of Lehman Brothers according to the Cabinet Office ofJapan) to reduce the effect of the financial crisis on our results. In this skipped sample period, we
run the same regressions as in our main tests using the generalized least-squares method of Prais
and Winsten (1954) and the heteroskedasticity-consistent standard errors proposed by White(1980). As a result, two points are largely different from our main results.
First, when we regress ∆
on ∆
and ∆
in Equation 5 or regress it on,∆, and ∆
in Equation 6, the coefficients of ∆
,∆
, and
∆
become insignificant. These results mean that changes in risk-free rates (∆,∆∆) and expected inflation (∆) do not fulfill all Requirement 1’. These results are
consistent with our interpretation that these variables do not fulfill all Requirements 1’ through 3’.
on ∆,∆, and ∆
in Equation 9 and when
Second, when we regress
we regress
on ∆
,∆
,∆
, and ∆
in Equation 10, the coefficients,∆, and ∆
become significantly negative and the coefficients ofof ∆become significantly positive. These results may mean that changes in risk-free rates∆
and expected inflation meet Requirements 2’ and 3’. However, three other results indicate thatchanges in risk-free rates and expected inflation do not meet all three Requirements 1’, 2’, and 3’.
First, as we state in the previous paragraph, the risk-free rates and expected inflation do notsatisfy Requirement 1’. Second, the coefficients of ∆
,
,∆
,∆
, and
become insignificant when we do not control for ∆in Equations 9 and 10,∆
which is inconsistent with the interpretation that changes in risk-free rates and expected inflation
fulfill Requirement 2’ and 3’. Third, when we replace ∆within Equations 9 and 10,,∆, and ∆
become insignificant and negative. Thesethe coefficients of ∆results also suggest that changes in risk-free rates and expected inflation do not satisfy
Requirement 2’. Therefore, we conclude that changes in risk-free rates and expected inflation do
not satisfy all the requirements. Consequently, our main results are robust when we reduce theeffects of the financial crisis.

5.3. Discussion of SS hypothesis
As noted in Section 2, SS propose the other hypothesis regarding the earnings-returns
relation at the aggregate level. In this subsection, we discuss how our findings are related to their
hypothesis. Furthermore, we make an additional test to investigate the validity of the SS
hypothesis in the Japanese market.
The SS hypothesis is composed of two arguments. One is an argument regarding the highpredictability of aggregate earnings and the other addresses investors’ attitudes toward risk. They
argue that aggregate earnings changes are almost completely predictable and investors will
become less (more) risk-averse when they predict future positive (negative) aggregate earnings
changes.
At first, our main results undermine the former argument. We extract surprising informationin aggregate earnings changes () using Equation 11 and check whether
hassignificantly positive effects on aggregate stock returns at earnings announcement periods ()

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan115

after controlling for changes in the market-wide cost of capital (∆) in Equation 8. If theformer argument of the SS hypothesis is valid in the Japanese market, the observed relation will
not be significant, because the SS hypothesis argues that aggregate earnings changes do notconvey any news to investors during earnings announcement periods. However, Table 3 indicates
thatis significantly positively related within Equation 8. This result suggests that
aggregate earnings changes convey positive cash-flow news to investors during earnings
announcement periods, inconsistent with the SS hypothesis.
On the other hand, we do not obtain implications on the latter argument from our main
tests. Thus, we investigate the latter argument with an additional test. We focus on how themarket risk premium changes when aggregate earnings changes are predicted. In Japan, quarterly
aggregate earnings changes have a significantly positive relation with aggregate returns just before
earnings announcement periods (Yoshinaga 2016). We confirm this with regression results using
Equation 11. We obtain a significantly positive relation between aggregate earnings changes(∆) and aggregate returns just before earnings announcement periods ( ). Interpreting
this significant relation as quarterly aggregate earnings changes are predicted just before earnings
announcement periods, we can investigate the latter argument of the SS hypothesis by focusing
on the relation between expected aggregate earnings changes and changes in the market risk
premium during the periods (∆). If this argument is right, we will observe a significantly
negative relation between them.
To clarify the validity of the latter argument of SS hypothesis, we regress ∆on ∆is a fitted value of Equation 11. We regard it as ausing a simple regression model. ∆on ∆toproxy for expected aggregate earnings changes. In addition, we regress ∆address the concern that results using ∆may depend on the specific estimation model of
expected aggregate earnings changes.
are both significantly
and that of ∆As a result, the estimated coefficient of ∆positive using Newey-West standard errors (1.029 [ =5.153] and 0.459 [ =3.176]). When we dothe robustness checks provided in Subsection 5.2, significantly negative coefficients are notobserved. Therefore, our results suggest that investors do not become less (more) risk-averse
when expected aggregate earnings changes are positive (negative). Though this additional test is
simple, the results suggest that the latter argument of the SS hypothesis will not be valid, at leastin the Japanese market.
In summary, our main and additional results oppose two arguments of the SS hypothesis.
The discussion in this subsection supports the KLW hypothesis indirectly, because the SS
hypothesis competes with the KLW hypothesis.

6. Conclusion
There is a new and growing research area called Macro-Accounting. Konchitchki (2016a)
explains that there are two research areas in Macro-Accounting research. One, called “Macro-toMicro,” tackles how various types of macroeconomic information affect or improve the firm-level
prediction of future performance or stock valuation (e.g., Konchitchki et al. 2016). The other,
described as “Micro-to-Macro,” focuses on how accounting contributes to informing andpredicting various macroeconomic aspects (e.g., Gallo et al. 2016).
Prior studies in the “Micro-to-Macro” stream frequently use cross-sectionally aggregatedearnings in empirical tests. Some of them analyze the earnings-returns relation with aggregate

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The Japanese Accounting Review, 6 (2016), 95-122

earnings and obtain interesting results. They report that a significantly positive earnings-returns
relation cannot be observed at the aggregate level. As a response to this finding, KLW propose ahypothesis. They assume that negative effects of changes in the market-wide cost of capitalconceal positive effects of aggregate earnings changes. After KLW, several studies empiricallysupport this hypothesis in the U.S. market. However, the validity of the KLW hypothesis in theJapanese market has not been investigated. Therefore, we test the KLW hypothesis using
Japanese quarterly data based on the research design of Patatoukas (2014), whose regression
models contain all components of the market-wide cost of capital.
Our results robustly support the validity of the KLW hypothesis in Japan. We find that
positive effects of aggregate earnings changes on aggregate stock returns are concealed bynegative effects of changes in the market-wide cost of capital. Of the components of the marketwide cost of capital, we find that only the market risk premium makes the aggregate earningsreturns relation not significantly positive. Including additional results, our results are inconsistent
with the competing hypothesis proposed by SS. Our results indicate that aggregate earnings
changes are not completely priced in before earnings announcement periods. Our additional
results suggest that investors do not change their attitudes toward risks as SS assume. These
results support the KLW hypothesis indirectly, through rejecting the competing hypothesis
constructed by SS.
This study contributes to Macro-Accounting research, especially on aggregate earnings. At
first, our results support the external validity of the KLW hypothesis. It is not sufficiently clear
whether the KLW hypothesis is valid outside the U.S. market. To the best of our knowledge,
this is the first study that supports the hypothesis outside the U.S. market. We show the validityof the KLW hypothesis in the Japanese market. There are many differences in economic
situations between Japan and the U.S. Thus, our results contribute to expanding the external
validity of the hypothesis. As the second contribution, our results suggest the importance offocusing on an argument regarding investors’ risk-avoidance in the SS hypothesis, although priorstudies supporting the SS hypothesis mainly focus on the other argument regarding the higher
predictability of aggregate earnings (Ball et al. 2009; He and Hu 2014). Our results suggest that,even if the former argument is partially supported, the latter can be unsupported.
We contribute to the accounting research on the cost of capital in two ways. The firstcontribution is indicating the significant relation between accounting and cost of capital using
aggregate-level variables. Prior studies show the significant relation at the firm level (e.g., Francis
et al. 2004; Barth et al. 2013; Konchitchki et al. 2016). On the other hand, we focus on theaggregate-level relation between accounting information and cost of capital. After our empiricaltests, the relation is shown to exist in the Japanese market, even at the aggregate level. Second, weclarify the strength of the market-wide cost of capital’s impacts and identify the component that
produces the impacts. Our results show that the powerful impacts of the market-wide cost ofcapital cancel out the positive effects of aggregate earnings changes on aggregate stock returns.
We also reveal that the impacts of the market-wide cost of capital are derived from the market
risk premium in the Japanese capital market. These results will be helpful in understanding theimpacts of the market-wide cost of capital in the Japanese market.
Additionally, these results have an implication for future international research. He and Hu(2014) report that changes in interest rates and inflation do not affect the aggregate earningsreturns relation outside the U.S. market. They do not, however, consider the role of the market
risk premium. We find that the market risk premium has important impacts on the aggregate

Yoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan

117

TABLE 4 THE RELATION BETWEEN AGGREGATE EARNINGS SURPRISES AND
THE PAST AGGREGATE STOCK RETURNS= +∑+ (Equation 12).
is
The table shows the results obtained byaggregate stock returns.
is aggregate earnings surprises. We report t-statistics using
heteroskedasticity-consistent standard errors proposed by White (1980) in the brackets. ***, **and * denote statistical significance at the 1%, 5% and 10% level respectively, using two-tailed
tests.
0.000[-0.000]
0.000[0.000]0.000[-0.068]-0.001[-0.537]0.000[-0.225]

0.004[0.349]0.023*[1.782].
.

-0.024
0.000
1.863
1.000
43

.

-0.022
0.122
1.897
1.000
42

0.093
3.177*
2.031
1.000
41

0.018
[1.534]
0.048
2.352
1.859
1.000
40

-0.001[-0.582]0.000[-0.007]
0.002[0.165]0.020[1.127]0.015[1.053]
0.059
1.594
1.887
1.124
40

earnings-returns relation, even if both the risk-free rates and inflation do not. Considering theeffects of the market risk premium can yield results different from those of He and Hu (2014).
Before concluding this paper, we discuss its limitation. Existing studies including this study
have not sufficiently clarified the mechanism of the positive relation between aggregate earnings
changes and changes in the market risk premium. In our next study, we would like to investigate
this mechanism to understand the aggregate earnings-returns relation more deeply.

Appendix(A) The validity of

as a proxy for aggregate earnings surprises). We
We use the residuals of Equation 11 as a proxy for aggregate earnings surprises (test whether this variable is appropriate to represent aggregate earnings surprises using Equation
12. If the slope parameters of Equation 12 are significant,can contain information priced
in before the earnings announcement period and this variable may not be appropriate foraggregate earnings “surprises.”
=

+

+

(12)

Table 4 indicates the results of the regression using Equation 12. In this table, aggregate

118

The Japanese Accounting Review, 6 (2016), 95-122

earnings surprises are not significantly related to past aggregate stock returns. Thus, we canconclude thatis not priced in before the earnings announcement period and is appropriate
as a proxy for aggregate earnings surprises.
(B) Our estimating method of the market-wide cost of capital
We estimate the market-wide cost of capital by applying the method proposed by Easton
and Sommers (2007). Easton and Sommers (2007) run a cross-sectional regression to determine
the implied cost of capital for a portfolio. We estimate the implied cost of capital for a market
portfolio which is composed of the stocks of all sample firms based on their method, and use it as
the market-wide cost of capital in our analysis (). Their method is derived from thefollowing residual income model (Equation 13).

,

=

,

−
, ×
(1 +
, )

,

+

,

(13)

, is the intrinsic value per share of firm at period .
, is the book value per share ofistheearnings
per
share
of
firm
at
period.
firm at period .
,, is the cost of capitalof firm at period . We can transform Equation 13 into Equation 14 by applying the following
three arguments: (1) the perpetual growth rate of the residual earnings starting at period +1( , ) is constant, (2) the intrinsic value is equal to the contemporaneous stock price ( , =, ), and (3) firm has a positive book value of equity at period (, > 0).

,

=

,

+

,

=

,

+

,

=

,

,

(

−

,

,

−

(

,

−

,

−

+

×
(1 +

, )(1 +

,

×

,

,

)

, )

,

)

,

×

,

,

(14)

,

Investors at period cannot know the realized earnings per share of firm at period +1.
Therefore,
can be regarded as the expected earnings per share of firm at period +1 that,]). We obtain the following Equation 15.
are expected at period ( [
,
[

,
,

]

=

,

+

,

−

,

×

,
,

(15)

Assuming that analysts’ forecast of future earnings per share is a proxy for the expected]), we can substitute all items for the specific values in Equation
earnings per share ( [,15 except ,and. Replacing these two with the intercept parameter and the, − ,) and containing error term inslope parameter, respectively ( = , , =, − ,Equation 15, we can simultaneously estimate the average cost of capital and the average perpetualYoshinaga:Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation: Evidence from Japan119

growth rate for the listed firms in the portfolio each period with a cross-sectional regression( , = + , ,= ). This method is often used to estimate the portfolio-level cost ofcapital (e.g., Easton et al. 2002).
Nonetheless, it is known that the estimated cost of capital based on analysts’ forecast isbiased upward, because analysts tend to forecast future earnings optimistically (Easton andSommers 2007). To handle this upward bias, Easton and Sommers (2007) propose a method that
estimates the implied cost of capital using realized current earnings instead of forecasted future
earnings. Assuming (1) the perpetual growth rate of residual earnings starting from period( , ) is stable, (2) the intrinsic value is equal to the contemporaneous stock price ( , = , ),> 0), we can transformand (3) firm has positive book value of equity at period -1 (,Equation 13 into Equation 16. Further, Equation 16 can be reduced to Equation 17.

,

=

,

+

,

=

,

+

,

⇔

,

,

−

,

=

, )

)(1 +

,

−

−

,

)(1 +

)

)

(16)

)

,
,

×

,

,

−

,

(17)

,

,

with the intercept parameter and the slope parameter,

,

, ,

(1 +

,

1+

,

,

×

,

,

+

,

×

,

(

and

=

respectively

−

,

(

=

,

Replacing

(

,

,
,

and containing error term, we can simultaneously

estimate the average cost of capital and the average perpetual growth rates of the listed firms
whose stocks are in the portfolio each period (

,

=

,

=

,

).

Although Easton and Sommers (2007) estimate the implied cost of capital each year using
annual earnings, we must estimate it each quarter because our analysis is on a quarterly basis.
Thus, we sum up the recent four quarterly earnings of each firm and regard such total earnings as
the quasi-annual earnings of the firm. Using these quasi-annual earnings, we estimate theimplied market-wide cost of capital each quarter. Considering the timing of the quarterly
earnings announcement25 and multiplying per share items by the number of outstanding shares,
we transform Equations 16 and 17 into Equations 18 and 19, respectively.
,

25

=

,

+

(

−

,

(

,
,

×

−

In Japan, quarterly earnings are normally released at the next quarter.

,
, )

)(1 +

, )

(18)

120

The Japanese Accounting Review, 6 (2016), 95-122

,

=

,

,

−

,

+

1+

,
,

,

×

−

,

(19)

,

is the book value of firm
, is the market value of firm at the end of quarter .
,is the quasistated in the earnings briefing at quarter -1 (released at quarter ).
,annual earnings of firm at quarter -1.
isthe
impliedcostofcapitaloffirmestimated at,
the end of quarter . ′ , is the perpetual growth rate of residual quasi-annual earnings startingfrom quarter .
Replacingrespectively

=

,

,

and

,

with the intercept parameter and the slope parameter,

,

, ,

=

,

,

and the containing error term, we obtain Equation,

20 from Equation 19. We run the cross-sectional regression using Equation 20 and estimate theimplied cost of capital for the market portfolio each quarter (=). We regard, =as the market-wide cost of capital in this study.
,
,

=

+

×

,

−
,

,

+

(20)

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