The Market-Wide Cost of Capital Impacts on the Aggregate Earnings-Returns Relation-Evidence from Japan-*Yuto Yoshinaga†
Doctoral Student
Graduate School of Commerce and Management
Hitotsubashi University

October 2015*

I am grateful for helpful advice from Toyohiko Hachiya, Makoto Nakano, Yusuke Takasu, and my colleagues at
Hitotsubashi University. I also thank Tetsuyuki Kagaya, Tomohiro Suzuki 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 and all theparticipants at these conferences for beneficial comments. These people are written in alphabetical order of thefamily names and in chronological order of the dates of the conferences. I appreciate Grant-in-Aid for Research
Fellows of Japan Society for the Promotion of Science (JSPS KAKENHI Grant number 15J00015) and financial
supports by Graduate School of Commerce and Management, Hitotsubashi University. Finally, I would like toconvey my gratitude to the committee of The 6th International Conference of The Japanese Accounting Review forproviding me the fruitful opportunity of making the presentation.
†
Yuto Yoshinaga, Doctoral Student (JSPS Research Fellow DC), Graduate School of Commerce and Management,
Hitotsubashi University. Contact: cd151004@g.hit-u.ac.jp

Abstract
Prior studies have observed a significantly positive relation between earnings changes and thecontemporaneous stock returns at the firm level. However, when they are cross-sectionally
aggregated, even a negative relation can be observed. Through clarifying this puzzling relation,
U.S. studies have shown that risk-free rate and expected inflation, which are components of themarket-wide cost of capital, cause strong omitted variable bias against the relation. On the other
hand, the economic impacts of these components are trivial in Japan due to “zero-interest-rate
policy” and stable prices, such that the market-wide cost of capital can be weak. Therefore, we
test whether changes in the market-wide cost of capital still have a strong bias against theaggregate earnings-returns relation in Japanese stock market. First, we find that aggregate
earnings changes are positively correlated to the contemporaneous changes in the market-wide
cost of capital. Second, a significantly positive aggregate earnings-returns relation appears after
controlling for changes in the market-wide cost of capital, though this relation cannot be
detected running a simple regression. Third, these results are not caused by risk-free rate or
expected inflation but caused by market risk premium, the other component of the market-wide
cost of capital.

Keywords: aggregate earnings, earnings-returns relation, implied cost of capital
JEL Classification: E44, G12, G14, M41

1. Introduction
The purpose of this paper is to contribute to clarifying the mechanism of the surprisingearnings-returns relation observed at the aggregate level. In accounting and finance research,
many researchers have studied the relation between accounting earnings and stock returns,
beginning with Ball and Brown (1968). In this stream of studies, a robust positive relation
between earnings changes and the contemporaneous stock returns is observed at the firm level1(cf. Ball and Sadka 2015). Earnings changes are often regarded as earnings surprises2. Positive(negative) earnings surprises indicate that reported earnings are higher (lower) than expected
and these earnings are financial resources for payout. Thus, investors will increase (decrease)
the expected cash 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 level3.
If this explanation holds true and when earnings changes and stock returns of individual
firms are cross-sectionally aggregated, what relation should be observed between “aggregate”
earnings changes and “aggregate” stock returns? These aggregate variables represent thegeneral trends of the listed firms. When positive (negative) aggregate earnings changes areobserved, listed firms will generally experience a rise (drop) in performance. Subsequently, theeconomic impacts of positive (negative) firm-level earnings surprises should be dominant in themarket, hence resulting in higher (lower) stock prices. According to this logic, positive
earnings-returns relation should also be observed at the aggregate level. However, recent U.S.
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
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 the realized earnings at the previous period(𝐸𝑡−1 [𝑋𝑡 ] = 𝑋𝑡−1 ), earnings surprises at the current period become equal to the earnings changes at the current
period (𝑈𝐸𝑡−1 [∆𝑋𝑡 ] = ∆𝑋𝑡 ∵ 𝑈𝐸𝑡−1 [∆𝑋𝑡 ] = 𝑋𝑡 − 𝐸𝑡−1 [𝑋𝑡 ], ∆𝑋𝑡 = 𝑋𝑡 − 𝑋𝑡−1 ).
3
We use the description, “earnings-returns relation” as the relation between earnings changes and thecontemporaneous corresponding stock returns.
2

1

positive earnings-returns relation cannot be detected at the aggregate level4. Furthermore, somestudies indicate that even a significantly negative relation can be observed5. In order to clarify
this puzzling earnings-returns relation, KLW develop a hypothesis based on the omitted
variable bias. KLW suppose that investors increase (decrease) the discount rate generally whenaggregate earnings changes are positive (negative). If this is correct, the positive effect ofaggregate earnings changes on the contemporaneous aggregate stock returns can be concealedby the negative effect of changes in the discount rate. This hypothesis can explain the puzzling
aggregate earnings-returns relation.
Discount rate is the cost of capital (Brealey et al. 2014) and market-wide cost of capitalcan be decomposed into real risk-free rate, expected inflation, and market risk premium(Patatoukas 2014). Among these components, prior U.S. studies supporting KLW’s hypothesis(Kothari et al. 2006; Uysal 2010) mainly have focused on risk-free rate and expected inflation.
They show that when controlling for risk-free rate and expected inflation, which are thecomponents of the market-wide cost of capital, a positive aggregate earnings-returns relation
appears. Therefore, these two components should cause a strong bias against aggregate
earnings-returns relation in the U.S. market. However, turning our eyes to our country, theeconomic impacts of these components should be trivial due to the “zero-interest-rate policy”
and stable prices. These differences can reduce the economic significance of the market-wide
cost of capital. Thus, whether the market-wide cost of capital works as an omitted variable that4

Most existing U.S. studies report that a significantly positive aggregate earnings-returns relation cannot be
detected in a simple regression or in a pairwise correlation (Kothari et al. 2006; Anilowski et al. 2007; Bali et al.
2008; Hirshleifer et al. 2009; Sadka and Sadka 2009; Uysal 2010; Patatoukas 2014). We also observe an
insignificant and negative (-0.638) aggregate earnings-returns relation in Japanese stock market by running asimple 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. Such a
puzzling earnings-returns relation is introduced as “Micro-Macro-Puzzle” in Japan (cf. Nakano 2012, 2014).

2

bias against the aggregate earnings-returns relation in Japanese stock market is not clear6. In
this paper, we investigate whether changes in the market-wide cost of capital bias the aggregate
earnings-returns relation even in Japanese stock market.
This study proceeds as follows. Section 2 introduces two hypotheses to explain theaggregate earnings-returns relation. One is proposed by KLW and the other is proposed by
Sadka and Sadka (2009) (referenced as SS henceforth). We state our research design in Section
3, and our sample selection and variable definition are described in Section 4. Section 5 details
our empirical results and interpretations. Finally, Section 6 concludes this study and describes
our implications for the future research.
2. Prior research and our research questions
There are two primary hypotheses on the aggregate earnings-returns relation. One is
proposed by KLW and the other is by SS. In this section, we introduce these two hypotheses
and propose our research questions.
Hecht and Vuolteenaho (2006) present a formula that three components explain realized
returns, based on Campbell (1991) who decomposes unexpected returns into two components.
∞∞

𝑅𝑡 ≈ 𝐸𝑡−1 [𝑅𝑡 ] + (𝐸𝑡 − 𝐸𝑡−1 ) [∑ 𝜌 𝑗 ∆𝑑𝑡+𝑗 ] − (𝐸𝑡 − 𝐸𝑡−1 ) [∑ 𝜌 𝑗−1 𝑅𝑡+𝑗 ]
𝑗=0

𝑗=0

= 𝐸𝑡−1 [𝑅𝑡 ] + 𝑁𝐶𝐹,𝑡 − 𝑁𝐷𝑅,𝑡(1)

𝑅𝑡 is realized return at period t. 𝐸𝑡−1 is the expectation operator with expectations
conditional on the information available at the end of period t-1 (the beginning of period t).
Thus, 𝐸𝑡−1 [𝑅𝑡 ] denotes stock return at period t expected at the end of period t-1.
6

He and Hu (2014) report that the interest rate and inflation do not produce omitted variable biases against theaggregate earnings-returns relation in the non-U.S. markets, including Japanese stock market. However, He and Hu(2014) use “pooled regression” to check whether these have any effect on the aggregate earnings-returns relation.
Therefore, their evidence is for the average non-U.S. market, not for a specific stock market.

3

(𝐸𝑡 − 𝐸𝑡−1 )[𝑋] represents the modified expectation for 𝑋 based on the news released atperiod t. ∆𝑑𝑡 is log dividend growth at period t. 𝜌 is the inverse of 1 plus the dividend yield𝑗(𝜌 < 1). Then, (𝐸𝑡 − 𝐸𝑡−1 )[∑∞
𝑗=0 𝜌 ∆𝑑𝑡+𝑗 ](= 𝑁𝐶𝐹,𝑡 ) means the modified expectation for

subsequent dividend growth, which is caused by “cash-flow news.” Further,𝑗−1(𝐸𝑡 − 𝐸𝑡−1 )[∑∞
𝑅𝑡+𝑗 ](= 𝑁𝐷𝑅,𝑡 ) is the modified expectation for the subsequent cost of
𝑗=0 𝜌

capital, which is caused by “discount-rate news7.” Next, we split earnings changes into
expected earnings changes (𝐸𝑡−1 [∆𝑋𝑡 ]) and unexpected earnings changes (earnings surprises:
𝑈𝐸𝑡−1 [∆𝑋𝑡 ]).
∆𝑋𝑡 = 𝐸𝑡−1 [∆𝑋𝑡 ] + 𝑈𝐸𝑡−1 [∆𝑋𝑡 ](2)

Substituting ∆𝑋𝑡 into 𝐸𝑡−1 [∆𝑋𝑡 ] + 𝑈𝐸𝑡−1 [∆𝑋𝑡 ] in Equation 1 and deleting theuncorrelated terms in definition8, we can rewrite the earnings-returns relation (𝑐𝑜𝑣(𝑅𝑡 , ∆𝑋𝑡 )) in
the following way.
𝑐𝑜𝑣(𝑅𝑡 , ∆𝑋𝑡 ) ≈ 𝑐𝑜𝑣(𝐸𝑡−1 [𝑅𝑡 ], 𝐸𝑡−1 [∆𝑋𝑡 ]) + 𝑐𝑜𝑣(𝑁𝐶𝐹,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ])−𝑐𝑜𝑣(𝑁𝐷𝑅,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ])(3)

In Equation 3, earnings-returns relation is decomposed into three components: (1) the
relation between expected earnings changes and expected returns (𝑐𝑜𝑣(𝐸𝑡−1 [𝑅𝑡 ], 𝐸𝑡−1 [∆𝑋𝑡 ]));
(2) the relation between earnings surprises and the contemporaneous modified expectation forthe subsequent dividend growth (𝑐𝑜𝑣(𝑁𝐶𝐹,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ])); and, (3) the relation between
earnings surprises and the contemporaneous modified expectation for the subsequent cost of𝑗−1
Though Hecht and Vuolteenaho (2006) denote (𝐸𝑡 − 𝐸𝑡−1 )[∑∞
𝑅𝑡+𝑗 ] as the “expected-return news,” we
𝑗=0 𝜌describe it as the news modifying investors’ expectations about the subsequent “cost of capital,” because theexpected return is normally equal to the cost of capital in the efficient market. If the expected return of a security ishigher (lower) than the cost of capital, investors will be eager to buy (sell) the security. Then, the security pricewill move upward (downward) until the expected return becomes equal to the cost of capital.
8
We delete the uncorrelated terms in the following way. Earnings changes expected at period t-1 are not related to
the news released at period t (𝑐𝑜𝑣(𝑁𝐶𝐹,𝑡 , 𝐸𝑡−1 [∆𝑋𝑡 ]) = 0, 𝑐𝑜𝑣(𝑁𝐷𝑅,𝑡 , 𝐸𝑡−1 [∆𝑋𝑡 ]) = 0). Since earnings surprises
occur at period t, they are not correlated to stock returns expected at period t-1 (𝑐𝑜𝑣(𝐸𝑡−1 [𝑅𝑡 ], 𝑈𝐸𝑡−1 [∆𝑋𝑡 ]) = 0).
74capital (𝑐𝑜𝑣(𝑁𝐷𝑅,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ])). In the following subsections, we introduce two hypotheseson the aggregate earning-returns relation based on these three components.
2.1. KLW’s hypothesis
Figure 1 illustrates KLW’s hypothesis. In an economic boom (economic recession) whenaggregate earnings changes are positive (negative), positive (negative) firm-level earnings
surprises should be dominant in the market, hence yielding higher (lower) stock prices. Thus,earnings changes should have a positive effect on the contemporaneous stock returns at theaggregate level, comparable to the firm level (𝑐𝑜𝑣(𝑁𝐶𝐹,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ]) > 0). However, what if
aggregate earnings changes are positively related to changes in the market-wide cost of capital(𝑐𝑜𝑣(𝑁𝐷𝑅,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ]) > 0)? Changes in the market-wide cost of capital are generally
negatively related to the movement of the stock prices9. Additionally, according to KLW,
“discount rates should be strongly correlated across stocks, largely driven by businessconditions, while cash flows are likely to have a larger idiosyncratic component.” Based on theargument that idiosyncratic components will be offset through aggregation, the negative effectof changes in the cost of capital on the contemporaneous stock returns will be stronger than thepositive effect of earnings surprises at the aggregate level (𝑐𝑜𝑣(𝑁𝐶𝐹,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ]) ≤𝑐𝑜𝑣(𝑁𝐷𝑅,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ])). Therefore, in a simple regression model that does not control forchanges in the market-wide cost of capital, an omitted variable bias will make earnings-returns
relation insignificant or negative (𝑐𝑜𝑣(𝑅𝑡 , ∆𝑋𝑡 ) ≤ 0)10.
Patatoukas (2014) observes that aggregate earnings changes are positively related to9

Based on valuation models such as the Dividend Discount Model, the increase (decrease) of the discount rate(the cost of capital) drives the stock prices downward (upward). Therefore, changes in the market-wide cost ofcapital have a negative effect on the aggregate stock returns.
10
Additionally, as SS describe, since this hypothesis assumes that aggregate earnings changes are largely
unpredictable, the relation between expected earnings changes and expected returns should not affect the aggregate
earnings-returns relation (𝐸𝑡−1 [∆𝑋𝑡 ] ≈ 0, ∆𝑋𝑡 ≈ 𝑈𝐸𝑡−1 [∆𝑋𝑡 ] ∴ 𝑐𝑜𝑣(𝐸𝑡−1 [𝑅𝑡 ], 𝐸𝑡−1 [∆𝑋𝑡 ]) ≈ 0).

5

changes in the market-wide cost of capital. He shows that significantly positive aggregate
earnings-returns relation appears after controlling for the changes in the market-wide cost ofcapital, though this significant relation does not come out in a simple regression. Patatoukas(2014) also decomposes the market-wide cost of capital into three components: real risk-freerate, expected inflation, and market risk premium. Out of these components, existing U.S.
studies mainly focus on risk-free rate and expected inflation. KLW show that aggregate
earnings changes are positively related to changes in the one-year T-bill rate. They also indicatethat a significantly positive aggregate earnings-returns relation can come up after controlling forchanges in the T-bill rate, although this relation does not appear by running a simple regression.
Uysal (2010) reports that although the aggregate earnings-returns relation is insignificant in a
simple regression, a significantly positive aggregate earnings-returns relation occurs after
controlling for these two variables. Based on these studies, risk-free rate and expected inflation
will have a strong bias against the aggregate earnings-returns relation in the U.S. market11.
2.2. SS’s hypothesis
Figure 2 illustrates the other hypothesis proposed by SS to explain the aggregate
earnings-returns relation. In this hypothesis, it is assumed that aggregate earnings changes arealmost completely predicted and priced before the earnings announcement period12(𝑈𝐸𝑡−1 [∆𝑋𝑡 ] ≈ 0, ∆𝑋𝑡 ≈ 𝐸𝑡−1 [∆𝑋𝑡 ]). Thus, this hypothesis assumes that aggregate earnings
changes do not modify investors’ expectations at the earnings announcement period13(𝑐𝑜𝑣(𝑁𝐶𝐹,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ]) ≈ 0, 𝑐𝑜𝑣(𝑁𝐷𝑅,𝑡 , 𝑈𝐸𝑡−1 [∆𝑋𝑡 ]) ≈ 0). SS also suppose that when
11

To understand KLW’s hypothesis more deeply, we propose the possible economic story behind the positive
relation between aggregate earnings changes and changes in risk-free rate or expected inflation. In an economic
boom (economic recession) when positive (negative) aggregate earnings changes are observed, the demands formoney, goods, and services will increase (decrease), hence causing higher (lower) interest rates and inflation.
12
Strictly speaking, SS’s hypothesis assumes that aggregate earnings changes announced at period t are priced in
before the beginning of period t.
13
Existing research supporting SS’s hypothesis interprets aggregate earnings changes as cash-flow news priced in
before the earnings announcement period, not aggregate earnings surprises at the earnings announcement period.

6

investors predict an economic boom (economic recession), they will take more (less) risks14,
resulting in a lower (higher) market risk premium. Since the market risk premium is one of thecomponents of the market-wide cost of capital, a lower (higher) market risk premium will leadto a lower (higher) market-wide cost of capital. Then, stock prices will move upward(downward) until the “expected returns from buying stocks on current prices” get equal to thecorrespondent cost of capital15. Assuming that they correspond before the earnings
announcement period, “expected returns from buying stocks on current prices” at the beginningof the earnings announcement period will be lower (higher) and will have a negative relation
with the predicted aggregate earnings changes (𝑐𝑜𝑣(𝐸𝑡−1 [𝑅𝑡 ], 𝐸𝑡−1 [∆𝑋𝑡 ]) ≤ 0). In conclusion,
if positive (negative) aggregate earnings changes are sufficiently predicted, expected returns
will decrease (increase), causing realized returns to decrease (increase) (𝑐𝑜𝑣(𝑅𝑡 , ∆𝑋𝑡 ) ≤ 0).
Existing literature supporting SS’s hypothesis argues that aggregate earnings changes are
more predictable than firm-level earnings changes, and that the earnings-returns relation will
get weaker (from positive to negative) as the number of firms aggregated increases16. SS report14

We tentatively present the economic background behind the negative relation between the predicted aggregate
earnings changes and risk appetite of investors to understand SS’s hypothesis more deeply. When expected cash
flows are modified upward (downward), the possibility of capital loss of buying stocks will decrease (increase) as
long as the volatilities of stock prices are stable.
15
Although expected returns are ordinarily equal to the cost of capital, “expected returns from buying stocks oncurrent prices” can be different from the cost of capital temporally due to cash-flow news or discount-rate news.
When “expected returns from buying stocks on current prices” become higher than the cost of capital, it means thatthe expected cash flows are higher (lower) than required. Since investors are eager to buy (sell) such stocks, stock
prices will move upward (downward). As stock prices move upward (downward), “expected returns from buying
stocks on current prices” get lower (higher) and finally, “expected returns from buying stocks on current prices”
become equal to the cost of capital.
16
SS name Chen (1991) as a supporter of their hypothesis. However, we suspect that he may not be a proper
supporter for their hypothesis. Chen (1991) shows that the recent growth of Gross National Product is negat ively
correlated to the future market return. If the effects of cash-flow news and discount-rate news stay constant,realized return is equal to the expected return on average. Thus, his results may suggest a negative relation between
the economic growth and the market-wide cost of capital (which is equal to the expected return). Since aggregate
earnings changes have a positive relation with the contemporaneous economic growth (e.g., Konchitchki andPatatoukas 2014), aggregate earnings changes can be regarded as reflecting the contemporaneous economic growth.
Therefore, the result by Chen (1991) may indicate the negative relation between aggregate earnings changes andchanges in the market-wide cost of capital. Assuming that the economic growth and changes in the market-wide
cost of capital are positively correlated, KLW's hypothesis can explain the results by Chen (1991).

7

that aggregate earnings changes have more components that can be explained by thecorrespondent stock returns before the earnings announcement period than the firm-levelearnings changes. They also show that the more number of firm-level earnings changes areaggregated, the more information about aggregate earnings changes are priced in before theearnings announcement period. This causes a weaker (from positive to negative) aggregate
earnings-returns relation. Ball et al. (2009) report a positive correlation between aggregate
earnings and the previous aggregate stock returns. This positive correlation suggests that the
information in aggregate earnings is priced in before the earnings announcement period. He andHu (2014) run a pooling regression of the country/year observations made from the financial
data of listed firms in 28 non-U.S. stock markets. They show that the aggregate earnings-returns
relation is weaker (from positive to negative) in countries with more transparent financial
disclosure because such disclosure helps investors forecast future earnings more precisely.
2.3. Research questions
As described, prior U.S. studies supporting KLW’s hypothesis suggest that risk-free rateand expected inflation are important components of the market-wide cost of capital that bias theaggregate earnings-returns relation. However, the economic significance of these components
will be trivial in Japan due to the “zero-interest-rate policy” and stable prices. For example, theaverage absolute value of the quarterly yield changes in 10-year government bond over oursample period (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 the year-over-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.17

17

The yield of 10-year government bond in the U.S. is collected from the website of the U.S. Department of theTreasury and the Consumer Price Index in the U.S. is from website of the U.S. Bureau of Labor Statistics. The

8

Thus, changes in the market-wide cost of capital may not function as an omitted variable.
Therefore, our research question is whether the market-wide cost of capital still biases theaggregate earnings-returns relation in Japanese stock market. To answer this question, we focus
on three points. The first is whether aggregate earnings changes are positively related tochanges in the market-wide cost of capital. If changes in the market-wide cost of capital cause
the omitted variable bias, they must have a positive relation.
Second, we focus on whether changes in the market-wide cost of capital have asignificantly negative relation with aggregate stock returns and whether a significantly positive
aggregate earnings-returns relation appears after controlling for changes in the market-wide
cost of capital in Japanese stock market. If changes in the market-wide cost of capital are an
omitted variable, they should have a significantly negative effect on the aggregate stock returns.
Additionally, a significantly positive earnings-returns relation should appear at the aggregate
level after controlling for them.
Finally, we decompose changes in the market-wide cost of capital into three components
following Patatoukas (2014), and investigate which components bias the aggregate
earnings-returns relation in Japanese stock market. Due to the slight changes of risk-free rateand expected inflation during our sample periods, their economic impacts will be trivial in
Japanese stock market. Therefore, we predict that these two components do not cause an
omitted variable bias against the aggregate earnings-returns relation in Japan.
3. Research design
3.1. Model description
We adopt two main tests to investigate whether the market-wide cost of capital biases
aggregate earnings-returns relation in Japanese stock market. In the first test, we check theJapanese data is collected from “Nikkei NEEDS Financial Quest 2.0.”

9relation between aggregate earnings variables (∆𝐴𝑔𝑔𝐸𝑞 ) and the contemporaneous changes in
the market-wide cost of capital (∆𝐼𝐶𝐶𝑞+1 ). We use two aggregate earnings variables: aggregate
earnings changes (∆𝐸𝐴𝑅𝑁𝑞 ) and aggregate earnings surprises18 (𝑆𝑈𝑅𝑞 ). Following Patatoukas(2014), we use the regression model as shown in Equations 4 through 6.
∆𝐴𝑔𝑔𝐸𝑞 = 𝛼 + 𝛽1 ∆𝐼𝐶𝐶𝑞+1 + 𝜀(4)∆𝐴𝑔𝑔𝐸𝑞 = 𝛼 + 𝛽1 ∆𝐼𝑅𝑃𝑞+1 + 𝛽2 ∆𝑅𝐹𝑞+1 + 𝜀(5)∆𝐴𝑔𝑔𝐸𝑞 = 𝛼 + 𝛽1 ∆𝐼𝑅𝑃𝑞+1 + 𝛽2 ∆𝑅𝑅𝐹𝑞+1 + 𝛽3 ∆𝐼𝑁𝐹𝑞+1 + 𝜀(6)In Equation 4, we investigate the relation between aggregate earnings variables andchanges in the market-wide cost of capital. If KLW’s hypothesis grasps the reality of Japanesestock market, 𝛽1 in Equation 4 should be significantly positive. In Equations 5 and 6, weinvestigate which components of changes in the market-wide cost of capital cause an omitted
variable bias. In Equation 5, we split changes in the market-wide cost of capital into changes in
the market risk premium (∆𝐼𝑅𝑃𝑞+1) and changes in the nominal risk-free rate (∆𝑅𝐹𝑞+1 ). In
Equation 6, we divide changes in the nominal risk-free rate into the real risk-free rate(∆𝑅𝑅𝐹𝑞+1 ) and those of expected inflation (∆𝐼𝑁𝐹𝑞+1 ). If these components are omitted
variables, their coefficients should be significantly positive.
In the second test, we focus on the bias of changes in the market-wide cost of capital andthose in its components against the aggregate earnings-returns relation. We use the regression
model described in Equations 7 through 10.
18

SS construct the hypothesis that aggregate earnings changes are predicted before the earnings announcement
period. Consistent with their hypothesis, Yoshinaga (2015) show that aggregate earnings changes have asignificantly positive relation with aggregate stock returns before earnings announcements in Japanese stock
market. Additionally, KLW report that aggregate earnings changes have a positive autocorrelation (earnings
persistence). According to these studies, aggregate earnings changes may be correctly predictable and may mainly
be composed of expected earnings changes (𝐸𝑡−1 [∆𝑋𝑡 ]), not of unexpected earnings changes (𝑈𝐸𝑡−1 [∆𝑋𝑡 ]). Thus,
we extract surprising information in aggregate earnings changes (aggregate earnings surprises) to use in ourempirical analysis. If the results are not largely different whichever aggregate earnings variables we use, we canjudge that aggregate earnings changes mainly reflect aggregate earnings surprises.

10𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝜀(7)

𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝛾2 ∆𝐼𝐶𝐶𝑞+1 + 𝜀(8)

𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝛾2 ∆𝐼𝑅𝑃𝑞+1 + 𝛾3 ∆𝑅𝐹𝑞+1 + 𝜀(9)

𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝛾2 ∆𝐼𝑅𝑃𝑞+1 + 𝛾3 ∆𝑅𝑅𝐹𝑞+1 + 𝛾4 ∆𝐼𝑁𝐹𝑞+1 + 𝜀(10)

According to prior studies, observed aggregate earnings-returns relation is insignificant
or negative with a simple regression model both in the U.S. (e.g., KLW; SS; Patatoukas 2014)
and in Japan (Yoshinaga 2015). Therefore, we expect that 𝛾1 in Equation 7 will not besignificantly positive. However, KLW’s hypothesis argues that this earnings-returns relation isbiased by the negative effect of the contemporaneous changes in the market-wide cost of capital(∆𝐼𝐶𝐶𝑞+1 ). Then, in Equations 8 through 10, we control for the contemporaneous changes in
the market-wide cost of capital or their components, and test whether and how 𝛾1 changes. If
KLW’s hypothesis reflects reality, 𝛾1 should be significantly positive and 𝛾2 should besignificantly negative in Equation 8. In Equations 9 and 10, we decompose changes in themarket-wide cost of capital and investigate which components have significantly negative
coefficients. If the coefficient of a component is significantly positive in the first test andsignificantly negative in the second test, the component is suggested to bias the aggregate
earnings-returns relation. Based on the unique Japanese economic situation, we predict that atleast risk-free rate and expected inflation will not meet both requirements.
3.2. Variable definition
We use quarterly data. As a proxy for aggregate stock returns, we use theequally-weighted averages of the quarterly buy-and-hold returns (𝑅𝑞 ). Before calculating thefirm-level stock returns, we adjust stock prices for the price movements due to the ex-rights andex-dividends. Aggregate earnings changes (∆𝐸𝐴𝑅𝑁𝑞 ) are the averages of the seasonally11differenced quarterly earnings deflated by the book value of equity one year before(

𝐸𝐴𝑅𝑁𝑖,𝑞 −𝐸𝐴𝑅𝑁𝑖,𝑞−4
𝐵𝑉𝑖,𝑞−4). We define aggregate earnings surprises (𝑆𝑈𝑅𝑞 ) as the residuals of thefollowing Equation 1119.
∆𝐸𝐴𝑅𝑁𝑞 = 𝛼 + 𝛽1 ∆𝐸𝐴𝑅𝑁𝑞−1 + 𝛽2 𝑅𝑞 + 𝜀(11)Easton and Sommers (2007) run a cross-sectional regression to determine the implied
cost of capital for a portfolio. We estimate that 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 this as themarket-wide cost of capital in our analysis (𝐼𝐶𝐶𝑞 ). Their method is derived from the following
residual income model (Equation 12).
∞𝑣𝑖,𝑡 = 𝑏𝑝𝑠𝑖,𝑡 + ∑𝜏𝑒𝑝𝑠𝑖,𝑡+𝜏 − 𝑟𝑖,𝑡 × 𝑏𝑝𝑠𝑖,𝑡+𝜏−1(1 + 𝑟𝑖,𝑡 )𝜏

(12)𝑣𝑖,𝑡 is the intrinsic value per share of firm i at period t. 𝑏𝑝𝑠𝑖,𝑡 is the book value per shareof firm i at period t. 𝑒𝑝𝑠𝑖,𝑡 is the earnings per share of firm i at period t. 𝑟𝑖,𝑡 is the cost ofcapital of firm i at period t. We transform Equation 12 into Equation 13 by setting the following
two assumptions: (1) the perpetual growth rate of the residual earnings starting from period t+1(𝑔𝑖 ) is constant, and (2) the intrinsic value is equal to the contemporaneous stock price(𝑣𝑖,𝑡 = 𝑝𝑖,𝑡 ).
𝑝𝑖,𝑡 = 𝑏𝑝𝑠𝑖,𝑡 +𝐸𝑡 [𝑒𝑝𝑠𝑖,𝑡+1 ] − 𝑟𝑖,𝑡 × 𝑏𝑝𝑠𝑖,𝑡(𝑟𝑖,𝑡 − 𝑔𝑖 )(13)

In Equation 13, 𝑝𝑖,𝑡 is stock price of the firm i at period t, and 𝐸𝑡 [𝑒𝑝𝑠𝑖,𝑡+1 ] is the19

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 test, we confirm that ∆𝐸𝐴𝑅𝑁𝑞 also has the first order to the second order significantly positive
autocorrelation and this autocorrelation is mainly caused by the first order partial autocorrelation. (The relation
between ∆𝐸𝐴𝑅𝑁𝑞 and ∆𝐸𝐴𝑅𝑁𝑞−2 turns into insignificant after controlling for ∆𝐸𝐴𝑅𝑁𝑞−1 , although the relation
is significantly positive when running a simple regression.) Thus, we adjust aggregate earnings changes for only
the first order autocorrelation in calculating 𝑆𝑈𝑅𝑞 .

12earnings per share of firm i at period t+1 that are expected at period t. Then Equation 13 can be
reduced to Equation 14.
𝐸𝑡 [𝑒𝑝𝑠𝑖,𝑡+1 ]𝑝𝑖,𝑡= 𝑟𝑖,𝑡 + (𝑟𝑖,𝑡 − 𝑔𝑖 ) ×
𝑏𝑝𝑠𝑖,𝑡𝑏𝑝𝑠𝑖,𝑡(14)

If we assume that the analyst forecast of earnings per share is the proxy for the expected
earnings per share (𝐸𝑡 [𝑒𝑝𝑠𝑖,𝑡+1 ]), we can substitute all items for the specific values in Equation
14 except 𝑟𝑖,𝑡 and (𝑟𝑖,𝑡 − 𝑔𝑖 ). Furthermore, if we replace these two variables by the intercept
parameter and the slope parameter respectively (𝛼 = 𝑟𝑖,𝑡 , 𝛽 = (𝑟𝑖,𝑡 − 𝑔𝑖 )), and run across-sectional regression, we can simultaneously estimate the averages of the cost of capitalfor the stocks in the portfolio and those of the perpetual growth rate for the listed firms whose
stocks are in the portfolio each period.
Nonetheless, it is known that the estimated cost of capital by using the analysts’ forecastof future earnings is biased upward since analysts tend to forecast future earnings optimistically(Easton and Sommers 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 offorecasted future earnings. Assuming that the perpetual growth rate of residual earnings startingfrom period t (𝑔′𝑖 ) is stable and that the intrinsic value is equal to the contemporaneous stock
price (𝑣𝑖,𝑡 = 𝑝𝑖,𝑡 ), we transform Equation 12 into Equation 15. Further, Equation 15 can be
reduced to Equation 16.
∞

𝑝𝑖,𝑡 = 𝑏𝑝𝑠𝑖,𝑡 + ∑(𝑒𝑝𝑠𝑖,𝑡 − 𝑟𝑖,𝑡 × 𝑏𝑝𝑠𝑖,𝑡−1 )(1 + 𝑔′𝑖 )𝜏
(1 + 𝑟𝑖,𝑡 )𝜏

𝜏= 𝑏𝑝𝑠𝑖,𝑡 +(𝑒𝑝𝑠𝑖,𝑡 − 𝑟𝑖,𝑡 × 𝑏𝑝𝑠𝑖,𝑡−1 )(1 + 𝑔′𝑖 )(𝑟𝑖,𝑡 − 𝑔′𝑖 )

13

(15)

𝑟𝑖,𝑡 − 𝑔′ 𝑖 𝑝𝑖,𝑡 − 𝑏𝑝𝑠𝑖,𝑡𝑒𝑝𝑠𝑖,𝑡⇔= 𝑟𝑖,𝑡 +×
𝑏𝑝𝑠𝑖,𝑡−1
1 + 𝑔′ 𝑖𝑏𝑝𝑠𝑖,𝑡−1
By replacing 𝑟𝑖,𝑡 and𝑟𝑖,𝑡 −𝑔′ 𝑖1+𝑔′ 𝑖(16)with the intercept parameter and the slope parameter

𝑟 −𝑔′

𝑖,𝑡
𝑖
), we can simultaneously estimate the average cost of capital
respectively (𝛼 = 𝑟𝑖,𝑡 , 𝛽 = 1+𝑔′𝑖

for the stocks in the portfolio and the average perpetual growth rates of the listed firms whose
stocks are in the portfolio each period. Although Easton and Sommers (2007) estimate theimplied cost of capital each year using annual earnings, we have to estimate it each quarterbecause our analysis is quarterly based. So we sum up the recent four quarterly earnings of eachfirm and regard such total earnings as the quasi annual earnings of the firm. Using these quasi
annual earnings, we estimate the implied market-wide cost of capital each quarter. Considering
the timing of the quarterly earnings announcement20 and multiplying per share items by the
number of outstanding shares, we transform Equations 15 and 16 into Equations 17 and 18,
respectively.
(𝑆𝑈𝑀𝐸𝐴𝑅𝑁𝑖,𝑞−1 − 𝐼𝐶𝐶𝑖,𝑞 × 𝐵𝑉𝑖,𝑞−5 )(1 + 𝐺 ′𝑖,𝑞 )(𝐼𝐶𝐶𝑖,𝑞 − 𝐺 ′𝑖,𝑞 )(17)

𝑆𝑈𝑀𝐸𝐴𝑅𝑁𝑖,𝑞−1
𝐼𝐶𝐶𝑖,𝑞 − 𝐺 ′𝑖,𝑞 𝑀𝑉𝑖,𝑞 − 𝐵𝑉𝑖,𝑞−1= 𝐼𝐶𝐶𝑖,𝑞 +×+𝜀
𝐵𝑉𝑖,𝑞−5
1 + 𝐺 ′𝑖,𝑞
𝐵𝑉𝑖,𝑞−5(18)

𝑀𝑉𝑖,𝑞 = 𝐵𝑉𝑖,𝑞−1 +𝑀𝑉𝑖,𝑞 is the market value of firm i at the end of quarter q. 𝐵𝑉𝑖,𝑞−1 is the book value offirm i stated in the earnings briefing at quarter q-1 (released at quarter q). 𝑆𝑈𝑀𝐸𝐴𝑅𝑁𝑖,𝑞−1 isthe quasi annual earnings of firm i at quarter q-1. 𝐼𝐶𝐶𝑖,𝑞 is implied cost of capital of firm iestimated at the end of quarter q. 𝐺′𝑖,𝑞 is the perpetual growth rate of residual quasi annual
earnings starting from quarter q. Using Equation 19 as derived from Equation 18, we run the20

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

14

cross-sectional regression and estimate the implied cost of capital for the market portfolio eachquarter.
𝑆𝑈𝑀𝐸𝐴𝑅𝑁𝑖,𝑞−1
𝑀𝑉𝑖,𝑞 − 𝐵𝑉𝑖,𝑞−1= 𝛼𝑞 + 𝛽𝑞 ×+𝜀
𝐵𝑉𝑖,𝑞−5
𝐵𝑉𝑖,𝑞−5(19)

Changes in the nominal risk-free rate are the differenced yield of the 10-year government
bond (∆𝑅𝐹𝑞 = 𝑅𝐹𝑞 − 𝑅𝐹𝑞−1 ). We define the difference between changes in the market-wide
cost of capital and changes in the nominal risk-free rate as the market risk premium (∆𝐼𝑅𝑃𝑞 =∆𝐼𝐶𝐶𝑞 − ∆𝑅𝐹𝑞 ), following Patatoukas (2014). Changes in expected inflation are the expected
year-on-year growth of the core Consumer Price Index (CPI) (∆𝐼𝑁𝐹𝑞 = 𝐼𝑁𝐹𝑞 − 𝐼𝑁𝐹𝑞−1 ).
Following Patatoukas (2014), we use the real risk-free rate as the difference between thenominal risk-free rate and expected inflation (∆𝑅𝑅𝐹𝑞 = ∆𝑅𝐹𝑞 − ∆𝐼𝑁𝐹𝑞 ). Figure 3 is the timelineof our main variables.
3.3. Statistical issues: heteroskedasticity, serial correlation, and multicollinearity
Many empirical studies in accounting and finance adjust for heteroskedasticity. For
example, researchers often calculate standard errors by the method of White (1980) to reduce
the statistical problems due to heteroskedasticity. Additionally, considering the Durbin-Watson
statistics, some of our main results may be biased by the serial correlation21. Therefore, we use
the heteroskedasticity- and autocorrelation-consistent standard errors proposed by Newey andWest (1987). We set the maximum lag length for calculating the Newey-West adjusted standard
errors as two, which is the integer part of the 0.25 power of the sample size, based on related
studies (Konchitchki and Patatoukas 2014) and practical convention (Ota 2012). We judge if
our empirical results are biased by multicollinearity based on the Variance Inflation Factor
21

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

15

(VIF). Since the VIF of each variable is lower than 10 in all models, we suppose that thestatistical problems due to multicollinearity are trivial.
4. Sample selection and Data source
4.1. Sample selection
Our data source is primarily “Nikkei NEEDS Financial Quest 2.0,” which contains thefinancial data of listed firms and macroeconomic data in Japan. We define Q1 as the quarter
from January to March, Q2 as that from April to June, Q3 as that from July to September, andQ4 as that from October to December. Using this description, our sample covers 48 quartersfrom Q2:2003 to Q1:2015. Although the first quarter which Nikkei NEEDS includes financial
data from the quarterly Summary of Financial Statements (Kessan-Tanshin in Japanese) is
Q2:2002, we exclude the periods before Q2:2003, because available firm/quarter observations
are only less than 500 for these periods. Additionally, we impose the following six datarequirements.
I.

Firm/quarter observations that have non-missing data to construct the variables

II. Firm/quarter observations of industrial firms (not financial firms: banks; insurance;
brokerage; asset management firms)
III. Firm/quarter observations that have positive market values and positive book values
used to construct the variables
IV. Firm/quarter observations whose stock price at the beginning of the quarter is ¥100and over
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 Statements16

by 60 days after the beginning of the earnings announcement period
Data requirement I is required to remove observations that have missing values. Datarequirement II is established because the accounting items of financial firms are different fromindustrial firms. Data requirement III is set to avoid negative deflators and financially abnormal
observations. Data requirement IV is imposed to exclude the outliers of stock returns. If stock
prices are near the minimum monetary unit (¥1), the stock returns tend to be highly volatile.
Thus, it is supposed that KLW and SS exclude observations with stock prices below $1 to
reduce the effects of the outliers of stock returns. We cover the listed firms adopting March as
the fiscal year-end because March is the most popular fiscal year-end in Japan. Additionally,
data requirement V is required to increase the number of sample firms by covering firms thathave fiscal year-ends of June, September, or December. Data requirement VI is set so reported
earnings are priced in at the earnings announcement period.
After imposing these data requirements, we regard the top and bottom 1% of thefirm/quarter observations as ranked by the ∆𝐸𝐴𝑅𝑁𝑖,𝑞 ,𝑆𝑈𝑀𝐸𝐴𝑅𝑁𝑖,𝑞−1
𝐵𝑉𝑖,𝑞−5and𝑀𝑉𝑖,𝑞 −𝐵𝑉𝑖,𝑞−1
𝐵𝑉𝑖,𝑞−5eachquarter as the outliers, and exclude them from our sample. Our final sample contains 43 quarter
observations aggregated by 102,877 firm/quarter observations.
We collect macroeconomic data during our sample periods. The nominal risk-free rate is
the yield of the 10-year government bond at the end of each quarter obtained from Nikkei
NEEDS. We manually collect the averages of the expected year-on-year growth of the core CPI
from the ESP forecast22 issued at the end of each quarter as expected inflation23.

22

The ESP forecast is the survey issued by the Economic Planning Association originally and was taken over by
the Japan Center for Economic Research after April 2002. 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 submit their answers each month to clarify the consensus on the future economic
trends and the persistence of the business condition (cf. http://www.jcer.or.jp/esp/index.html).
23
In April 2014, the consumption tax rate was increased from 5% to 8% in Japan. To exclude the effect of this, we

17

4.2. Correlation matrix and descriptive statistics
Table 1 shows the correlation matrix and descriptive statistics. The correlation between
𝑆𝑈𝑅𝑞 and 𝑅𝑞 is almost zero because 𝑆𝑈𝑅𝑞 is the residuals estimated using the regression
model that contains 𝑅𝑞 as an independent variable (Equation 11). The correlation between∆𝐼𝐶𝐶𝑞 and ∆𝐼𝑅𝑃𝑞 is almost one probably because of the trivial movements of risk-free rateand expected inflation in Japan. Consistent with this supposition, the standard deviations of∆𝑅𝐹𝑞 and ∆𝐼𝑁𝐹𝑞 are less than one third of those of ∆𝐼𝑅𝑃𝑞 .
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 a dependent variable thathas a unit root on an independent variable that also has a unit root, significant relation between
them can be observed, even though they have no rational relation (cf. “spurious regression” as
Granger and Newbold 1974 state). All results of the Phillips-Perron 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 details the results from the first main test. At first, aggregate earnings changes
have a significantly positive relation with the contemporaneous changes in the market-wide costof capital, as do aggregate earnings surprises. In this table, we can also observe the significantly
positive relation between aggregate earnings variables and changes in the market risk premium.
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. “The effects of the two scheduled consumption tax hikes on prices can be mechanicallyestimated by assuming that the rise in the 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” (Bank of Japan 2013). Based onthese statements, we subtract 2% from the non- adjusted average year-over-year growth of the core CPI at thesequarters to rule out the effect of the consumption tax rate increase.

18

On the other hand, coefficients of changes in risk-free rates and those of expected inflation are
not consistent.
Table 3 illustrates the results of the second main test. When running a simple regression,a significantly positive aggregate earnings-returns relation cannot be observed. On the other
hand, when controlling for the contemporaneous changes in the market-wide cost of capital,coefficients of aggregate earnings variables dramatically change. They turn into significantly
positive. Additionally, it is indicated that changes in the market-wide cost of capital havesignificantly negative relation with the aggregate stock returns. These results suggest that thecontemporaneous changes in the market-wide cost of capital cause an omitted variable bias
against the aggregate earnings-returns relation in Japanese stock market.
Next, we decompose changes in the market-wide cost of capital and investigate which
components bias the aggregate earnings-returns relation in Japan. Consistent with our
prediction, the coefficients of changes in risk-free rates and expected inflation are allinsignificant. On the other hand, the coefficient of the market risk premium is significantly
negative. Therefore, it is suggested that the market-wide cost of capital causes a strong bias
against the aggregate earnings-returns relation due to the bias from the market risk premium inJapanese stock market24.
Additionally, in Table 3, there are minimal differences between the results with aggregate
earnings changes and those with aggregate earnings surprises in the sign and statisticalsignificance of their coefficients. Thus, although aggregate earnings changes may be predicted
before the earnings announcement period, they reflect surprising information at the earnings
announcement period.

24

We confirm that the observed aggregate earnings-returns relation is still insignificant, even when we control for
only the contemporaneous changes in the real risk-free rate and those in expected inflation (untabulated).

19

5.2. Robustness checks
In this section, we check the robustness of our main results by using different standard
errors, regression method, aggregating method, and sample periods. We do not tabulate theresults of these robustness checks due to space considerations.
5.2.1. Robustness checks on serial correlation and heteroskedasticity
We calculate the heteroskedasticity- and autocorrelation-consistent standard errors
proposed by Newey and West (1987) 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, since this lag length is based only on academic andpractical conventions. Therefore, we check the robustness of the main results in the following
two ways. First, we vary the maximum lag length from zero to four and check the sensitivity of
our results. Second, we adopt the generalized least-squares method presented by Prais andWinsten (1954) and use the heteroskedasticity-consistent standard errors presented by White(1980). All results of these robustness checks are similar to our main results.
5.2.2. Robustness checks on the other aggregating method: value-weighted averages
Existing studies on aggregate earnings-returns relation use not only equally-weighted
cross-sectional averages but also value-weighted cross-sectional averages as aggregate
variables. Therefore, we employ value-weighted averages based on market values as theaggregation method and run the same regressions as conducted in the main analysis. In thisrobustness check, we estimate the cost of capital separately for each industry and calculate thevalue-weighted averages of the cost of capital based on the total market value of each industry
as the market-wide cost of capital. Almost all signs and statistical significances of thecoefficients are similar to those of the main results, with one differing result. When we check20

the relation between aggregate earnings surprises and the contemporaneous aggregate stock
returns after controlling for the contemporaneous changes in the market-wide cost of capital(Equation 8) or those of its components (Equation 9 and 10) with the standard errors by Newey
and West (1987), an insignificant relation is observed. To the contrary, when we adopt thegeneralized least-squares method by Prais and Winsten (1954) and theheteroskedasticity-consistent standard errors proposed by White (1980), a significantly positive
aggregate earnings-returns relation occurs consistent with the main analysis. Therefore, we
comprehensively judge that the positive effect of the value-weighted aggregate earnings
surprises on the contemporaneous aggregate stock returns exists, but is somewhat weaker25.
5.2.3. Robustness checks on the sample period
Due to the data restrictions, our sample is limited to roughly 1,000 firm/quarter
observations before Q2:2005, although we can collect over 2,000 firm/quarter observations
starting from Q2:2005. Before Q2:2005, the aggregated variables may become outliers because
aggregating fewer firms can cause an inadequate diversification of firm-specific information.
Thus, we limit the sample periods starting from Q2:2005 and run our main regression models.
The results are not largely different from the main results in the signs and significances of thecoefficients.
The bankruptcy of Lehman Brothers and the subsequent financial crisis occurred during
our sample period. Since this financial crisis seriously damaged the Japanese economy, someobservations can be outliers due to the crisis. Therefore, we exclude quarter observations from25

The positive effect of value-weighted aggregate earnings surprises is weaker, probably because the impacts oflarge firms will be strong if we use value-weighted averages. Collins et al. (1987) suggest that earnings changes inlarger firms are more predictable. Therefore, value-weighted averages of earnings changes will be predicted moreeasily than equally-weighted averages. By running Equation 11 to calculate 𝑆𝑈𝑅𝑞 using equally-weighted
averages, the adjusted R-Square is 46.54% (untabulated). On the other hand, when we use value-weighted averages,
the adjusted R-Square is 56.01% (untabulated). This difference suggests that the value-weighted aggregate
earnings changes are more predictable than the equally-weighted aggregate earnings changes.

21

Q3:2008 (the period 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 byPrais and Winsten (1954) and the heteroskedasticity-consistent standard errors by White (1980).
In the results of this robustness check, aggregate earnings changes are not significantly related
to changes in risk-free rates and expected inflation, unlike the main results. However, this does
not impede the interpretation of our main results, and the other results are similar to our main
results.
5.2.4. Conclusion of the robustness checks
Three main evidences are confirmed again by these robustness checks. First, aggregate
earnings changes are positively related to the contemporaneous changes in the market-wide costof capital. Second, a significantly positive aggregate earnings-returns relation appears after
controlling for the contemporaneous changes in the market-wide cost of capital. Third, theeconomic impacts of the market-wide cost of capital are mainly based on the market risk
premium in Japanese stock market. These results support the robustness of our main results.
6. Conclusion
Contrary to the “common sense” of the research area on accounting and finance, recent
studies report that significantly positive earnings-returns relation cannot be observed at theaggregate level. To explain this puzzling relation, KLW propose that changes in themarket-wide cost of capital cause an omitted variable bias against this relation. Although U.S.
studies suggest that risk-free rate and expected inflation are the important components of themarket-wide cost of capital, the economic impacts of these components are minimal in Japan22

due to its economic situation. Nevertheless, our three results suggest that KLW’s hypothesis still
explains Japanese stock market. First, aggregate earnings changes are positively correlated tochanges in the market-wide cost of capital. Second, after controlling for the contemporaneouschanges in the market-wide cost of capital, a significantly positive aggregate earnings-returns
relation appears. Third, these two results are mainly caused by changes in the market risk
premium, not risk-free rate or expected inflation.
To the best of our knowledge, this paper is the first study to show supportive evidence for
KLW’s hypothesis not only in Japanese stock market but also in another non-U.S. market. Our
results suggest that changes in the market risk premium cause an omitted variable bias against
the aggregate earnings-returns relation in Japanese stock market, where risk-free rate andexpected inflation do not have significant economic impacts. This has some implications for theaggregate earnings-returns relation in foreign stock markets. First, although prior studies
suggest that risk-free rate is one of the important components in the U.S. market, the U.S.
government has adopted the “zero-interest-rate policy” in 2008. Therefore, the economic
impacts of risk-free rate will be weaker in the recent U.S. market. However, related prior U.S.
studies do not cover the sample period after 2008 sufficiently26. Though there are manydifferences between Japanese stock market and the U.S. market, our results will help tounderstand the recent aggregate earnings-returns relation in the U.S. market. Second, our results
suggest the importance of market risk premium in investigating the mechanism of aggregate
earnings-returns relation. Though prior international research (He and Hu 2014) proposes
evidences that interest rates and inflation do not affect the aggregate earnings-returns relation in
the non-U.S. markets, it does not consider the effects of market risk premium. Based on our

26

KLW studies 1970 to 2000 in their main tests. Uysal (2010) studies 1969 to 2008. Patatou1kas (2014) studies
Q1:1981 to Q2:2009.

23

results, market risk premium will strongly bias the aggregate earnings-returns relation in thesemarkets. Therefore, in the future international research, we should control for the changes inmarket risk premium.
Though aggregate earnings-returns relations have been gradually investigated, there aresome unclear points. For example, existing research has not sufficiently clarified why aggregate
earnings changes have positive relation with changes in market risk premium. In our next
research, we would like to investigate this mechanism.

24Appendix(A) The validity of 𝑆𝑈𝑅𝑞 as a proxy for aggregate earnings surprises
We use the residuals of Equation 11 as a proxy for aggregate earnings surprises (𝑆𝑈𝑅𝑞 ).
We test whether this variable is appropriate as aggregate earnings surprises using Equation 20.
If the slope parameters of Equation 20 are significant, 𝑆𝑈𝑅𝑞 can have the information priced
in before the earnings announcement period and this variable may not be appropriate as
aggregate earnings surprises.
3

𝑆𝑈𝑅𝑞 = 𝛼 + ∑ 𝛽𝑘 𝑅𝑞−𝑘 + 𝜀

(20)

k=0

Table 4 indicates the results of the regression using Equation 20. In this table, aggregate
earnings surprises are not significantly related to the past aggregate stock returns. From thisresult, we can interpret that 𝑆𝑈𝑅𝑞 is not priced in before the earnings announcement period.

25

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Table 1 Correlation matrix and descriptive statistics
𝑅𝑞 is aggregate stock returns. ∆𝐸𝐴𝑅𝑁𝑞 is aggregate earnings changes. 𝑆𝑈𝑅𝑞 is aggregate earnings surprises.
∆𝐼𝐶𝐶𝑞 is changes in the market-wide cost of capital. ∆𝐼𝑅𝑃𝑞 is changes in the market risk premium. ∆𝑅𝐹𝑞 ischanges in the nominal risk-free rate. ∆𝑅𝑅𝐹𝑞 is changes in the real risk-free rate. ∆𝐼𝑁𝐹𝑞 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
𝑅𝑞
𝑅𝑞∆𝐸𝐴𝑅𝑁𝑞

𝑆𝑈𝑅𝑞

∆𝐼𝐶𝐶𝑞

∆𝐼𝑅𝑃𝑞

∆𝑅𝐹𝑞

∆𝑅𝑅𝐹𝑞

∆𝐼𝑁𝐹𝑞

0.250

-0.040-0.318-0.389

0.381

0.049

0.225

0.585

0.352

0.267

0.091

-0.0500.197-0.077-0.120

0.232

0.101

0.055

0.974

-0.344-0.3320.129-0.512-0.407

0.072

0.572

0.146

∆𝐸𝐴𝑅𝑁𝑞

0.245

𝑆𝑈𝑅𝑞

0.000

0.713

∆𝐼𝐶𝐶𝑞

-0.3410.474-0.006∆𝐼𝑅𝑃𝑞-0.361

0.424-0.049

0.988

∆𝑅𝐹𝑞

0.292

0.096

0.267

-0.342-0.481∆𝑅𝑅𝐹𝑞-0.081-0.396-0.058-0.380-0.415

0.410

∆𝐼𝑁𝐹𝑞

0.276

0.487

0.228

0.186

0.136

0.210

-0.806-0.594

Panel B Descriptive statistics
Mean

S. D.

Min

25%

Median

75%

Max

N

𝑅𝑞

0.023

0.100

-0.168-0.049

0.013

0.086

0.265

43

∆𝐸𝐴𝑅𝑁𝑞

0.002

0.009

-0.026-0.002

0.002

0.007

0.033

43

𝑆𝑈𝑅𝑞

0.000

0.007

-0.019-0.003

0.000

0.003

0.024

42

∆𝐼𝐶𝐶𝑞

0.000

0.010

-0.023-0.006

0.000

0.005

0.028

42

∆𝐼𝑅𝑃𝑞

0.000

0.011

-0.023-0.007

0.001

0.007

0.031

42

∆𝑅𝐹𝑞

0.000

0.002

-0.003-0.002

0.000

0.001

0.003

43

∆𝑅𝑅𝐹𝑞

-0.001

0.003-0.008-0.002-0.001

0.001

0.009

43

∆𝐼𝑁𝐹𝑞

0.000

0.003

-0.012

0.000

0.001

0.001

0.005

43

28

Table 2 The relation between aggregate earnings variables and the changes in the market-wide
cost of capital
The table shows the results obtained by ∆𝐴𝑔𝑔𝐸𝑞 = 𝛼 + 𝛽1 ∆𝐼𝐶𝐶𝑞+1 + 𝜀 (Equation 4), ∆𝐴𝑔𝑔𝐸𝑞 = 𝛼 +𝛽1 ∆𝐼𝑅𝑃𝑞+1 + 𝛽2 ∆𝑅𝐹𝑞+1 + 𝜀 (Equation 5), ∆𝐴𝑔𝑔𝐸𝑞 = 𝛼 + 𝛽1 ∆𝐼𝑅𝑃𝑞+1 + 𝛽2 ∆𝑅𝑅𝐹𝑞+1 + 𝛽3 ∆𝐼𝑁𝐹𝑞+1 + 𝜀(Equation 6). ∆𝐴𝑔𝑔𝐸𝑞 is aggregate earnings variable, which is replaced by ∆𝐸𝐴𝑅𝑁𝑞 or 𝑆𝑈𝑅𝑞 . ∆𝐸𝐴𝑅𝑁𝑞 isaggregate earnings changes. 𝑆𝑈𝑅𝑞 is aggregate earnings surprises. ∆𝐼𝐶𝐶𝑞 is changes in the market-wide costof capital. ∆𝐼𝑅𝑃𝑞 is changes in the market risk premium. ∆𝑅𝐹𝑞 is changes in the nominal risk-free rate. ∆𝑅𝑅𝐹𝑞
is changes in the real risk-free rate. ∆𝐼𝑁𝐹𝑞 is changes in expected inflation. The left three rows indicate theresults by the regression whose independent variable is ∆𝐸𝐴𝑅𝑁𝑞 . The right three rows indicate the results by the
regression whose independent variable is 𝑆𝑈𝑅𝑞 . We report t-statistics using heteroskedasticity- andautocorrelation-consistent 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.
∆𝐸𝐴𝑅𝑁𝑞𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡∆𝐼𝐶𝐶𝑞+1

0.002**

0.002**

0.002**

0.000

0.000

0.000

[2.156][2.561][2.500][0.077][-0.065][-0.088]0.857***

0.462***[8.364][4.774]∆𝐼𝑅𝑃𝑞+1∆𝑅𝐹𝑞+10.882***

0.821***

0.435***

0.431***[8.389][10.900][3.784][3.554]1.292***-0.005[2.931][-0.008]∆𝑅𝑅𝐹𝑞+1∆𝐼𝑁𝐹𝑞+1
𝐴𝑑𝑗. 𝑅2

𝑆𝑈𝑅𝑞

0.848**-0.038[2.358][-0.055]

1.574***

0.016[4.928][0.027]

0.776

0.775

0.810

0.434

0.431

0.416

𝐹 𝑠𝑡𝑎𝑡𝑠

69.953***35.553***41.879***22.787***17.119***11.378***𝐷. 𝑊. 𝑠𝑡𝑎𝑡𝑠

1.648

1.743

1.962

2.173

2.128

2.138

𝑁

42

42

42

41

41

41

29

Table 3 The bias of the changes in the market-wide cost of capital against the aggregate
earnings-returns relation
The table shows the results obtained by 𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝜀 (Equation 7), 𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 +𝛾2 ∆𝐼𝐶𝐶𝑞+1 + 𝜀 (Equation 8), 𝑅𝑞+1 = 𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝛾2 ∆𝐼𝑅𝑃𝑞+1 + 𝛾3 ∆𝑅𝐹𝑞+1 + 𝜀 (Equation 9), 𝑅𝑞+1 =𝛼 + 𝛾1 ∆𝐴𝑔𝑔𝐸𝑞 + 𝛾2 ∆𝐼𝑅𝑃𝑞+1 + 𝛾3 ∆𝑅𝑅𝐹𝑞+1 + 𝛾4 ∆𝐼𝑁𝐹𝑞+1 + 𝜀 (Equation 10). ∆𝐴𝑔𝑔𝐸𝑞 is aggregate earnings
variable, which is replaced by ∆𝐸𝐴𝑅𝑁𝑞 or 𝑆𝑈𝑅𝑞 . 𝑅𝑞 is aggregate stock returns. ∆𝐸𝐴𝑅𝑁𝑞 is aggregate
earnings changes. 𝑆𝑈𝑅𝑞 is aggregate earnings surprises. ∆𝐼𝐶𝐶𝑞 is changes in the market-wide cost of capital.
∆𝐼𝑅𝑃𝑞 is changes in the market risk premium. ∆𝑅𝐹𝑞 is changes in the nominal risk-free rate. ∆𝑅𝑅𝐹𝑞 ischanges in the real risk-free rate. ∆𝐼𝑁𝐹𝑞 is changes in expected inflation. We report t-statistics using
heteroskedasticity- and autocorrelation-consistent standard errors proposed by Newey and West (1987) in thebrackets. ***, ** and * denote statistical significance at the 1%, 5% and 10% level respectively, using two-tailed
tests.
𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡∆𝐸𝐴𝑅𝑁𝑞

0.026

0.004

0.006

0.007

0.025

0.025

0.028

0.024

[1.438][0.355][0.489][0.504][1.440][1.350][1.639][1.488]-0.63811.643***11.355***10.068***[-0.417][3.947][3.684][2.779]-0.4135.415**

5.987**

5.812***[-0.257][2.623][2.557][3.043]

𝑆𝑈𝑅𝑞∆𝐼𝐶𝐶𝑞+1-13.477***-5.996***[-4.558][-3.372]∆𝐼𝑅𝑃𝑞+1∆𝑅𝐹𝑞+1-12.910*** -12.213***-5.506*** -6.451***[-3.810][-2.774][-3.530]-7.5347.157[-0.644][0.779]∆𝑅𝑅𝐹𝑞+1∆𝐼𝑁𝐹𝑞+1[-3.091]-9.089-0.338[-0.733][-0.035]-3.82111.932[-0.331][1.632]

𝐴𝑑𝑗. 𝑅2-0.021

0.349

0.339

0.338

-0.025

0.146

0.166

0.250

𝐹 𝑠𝑡𝑎𝑡𝑠

0.174

10.472***

11.494***12.802***0.066

5.691***

5.451***

6.895***

𝐷. 𝑊. 𝑠𝑡𝑎𝑡𝑠

1.607

2.262

2.280

2.274

1.618

1.213

1.265

1.371

𝑁

42

42

42

42

41

41

41

41

30

Table 4 The relation between aggregate earnings surprises and the past aggregate
stock returns
The table shows the results obtained by 𝑆𝑈𝑅𝑞 = 𝛼 + ∑3k=0 𝛽𝑘 𝑅𝑞−𝑘 + 𝜀 (Equation 20). 𝑅𝑞 isaggregate stock returns. 𝑆𝑈𝑅𝑞 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.
𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
𝑅𝑞

0.000

0.000

0.000

0.000

-0.001[0.000][-0.069][-0.529][-0.223][-0.584]

0.000

0.000

[-0.000][-0.014]

𝑅𝑞−1

0.004

0.002

[0.362][0.184]𝑅𝑞−2

0.023*

0.019[1.769][1.113]

𝑅𝑞−3

0.018

0.015

[1.557][1.084]

𝐴𝑑𝑗. 𝑅2-0.025-0.022

0.090

0.050

0.058

𝐹 𝑠𝑡𝑎𝑡𝑠

0.000

0.131

3.129*

2.423

1.625

𝐷. 𝑊. 𝑠𝑡𝑎𝑡𝑠

1.873

1.909

2.046

1.873

1.901

𝑁

42

42

41

40

40

31

Figure 1 Conceptual diagram of KLW’s hypothesis

32

Figure 2 Conceptual diagram of SS’s hypothesis

33

Figure 3 The timeline of our main variables

𝑅𝑞 is aggregate stock returns. ∆𝐸𝐴𝑅𝑁𝑞 is aggregate earnings changes. ∆𝐼𝐶𝐶𝑞 ischanges in the market-wide cost of capital. ∆𝐼𝑅𝑃𝑞 is changes in the market risk
premium. ∆𝑅𝑅𝐹𝑞 is changes in the real risk-free rate. ∆𝐼𝑁𝐹𝑞 is changes in
expected inflation.

34