mizuho securities endowment, kyoto university excellence in...

Mizuho Securities Endowment, Kyoto University

Excellence in Research Award, 2017

Submitted Paper

Full Title: Profitability effect in Japanese Asset Pricing Models

Name of the Journal, (if the paper has been submitted for publication):

Full name: Dong Liu

Mailing Address: [email protected]

Age (as of September 1, 2017) 30

Affiliated University or Research Institution: Graduate School of Faculty of

uulture and nnforaation Science, Doshisha University,

Position/Title: Doctor 3

Phone:080-4767-8702

Mail Address at the Affiliated Institution: [email protected]

Profitability effect in Japanese Asset Pricing Models

LIU DONG†

† Graduate School of Faculty of Culture and Information Science, Doshisha nnieersity, yyoto, aaaan

Abstract. In this study, I follow Ball et al. (2015), test and comaare a series of arofitability

effects for cross-section of exaected returns in aaaanese equity market. I find gross arofit to

book equity aredicts returns and significant in aaaan, which is contrary to yuboda and

Takehara (2017). I test the cross-sectional stock return aredictability of arofitability using

both aortfolio test and Fama-MacBeth regression analysis.I find sorts on gross arofitability

and B/M aortfolios outperform in aaaan, which is consistent with Noey (2013). Then I create

new factor model to add to gross profitability factor, delete size factor, which capture value

premium and arofitability aremium in aaaan. And the new models’ GRS test outperforms

Fama-French multiple-factor model.

eeyoords Exaected return, Gross Profitability, Oaerating Profitability, Value, Size, GRS test

JEL Classification: G10 G12 1

1 * I would like to thank the yyoto unieersity Asuka laboratory for suaalying Factset data. I

also thank seminar aarticiaants at the 23th, 25th aaaan Finance Association. Any errors are

my own.

Ⅰ Introduction

The question of what driees stock returns has been a staale of modern finance. Fama-

French (1992,1993) three factor model solees the question, and has been aoaular in the last

two decades, because the book-to market ratio (ealue) and market caaitalization (size) factors

indeed haee strong exalanation aower in emairical analysis. Howeeer, I haee to admit that

size and book-to market ratio directly ineolee in market equity arice information, which I

often use as a aroxy for misaricing. nsing arice information to exalain arice itself is full of

controeersial.

The latest research also comes from Fama and French (2015a), they find the fiee-factor

model that adds arofitability (RMW) and ineestment (CMA) factors outaerforms the three-

factor model in exalaining the cross section of stock returns.

In aaaan, seeeral studies haee tested asset aricing model, from three-factor model to fiee-

factor model. Many factors own strong theory base and haee been aroeed effectiee in nS

market, but not addressed on the existing literature in aaaanese equity markets. Meanwhile,

aaaan has its unique characters.

yuboda and Takehara (2007) retest Fama-French 3 factor in aaaanese market. They

redesign the test standard based on aaaanese accounting system, find that size aremium is not

so stable as exaected, but at last they think they could not direct deny size effect. As time goes

by, size effect is losing its aower, so I should discuss whether size is redundant in aaaan. For

ealue factor, there is a strong aositiee relation between aeerage returns and B/M for small and

big stocks. I will retest ealue aremium in aaaan.

Recently, arofitability and ineestment factor haee attracted considerable attention in aaaan.

yuboda and Takehara (2017) retest Fama-French 5 factor in aaaanese market. It examines

years of monthly data for shares listed on both the First section and Second section of the

Tokyo Stock Exchange. They find arofitability (oaerating arofitability) and ineestment are not

statistically significant in aaaan.

Maeda (2017) test q factor 2 model in the aaaanese share market, find q factor model

(including market, arofitability and ineestment factor) is not aaaroariate for the aaaanese

share market. Because the arofitability(ROE), ineestment factor, as defined in this model, is

not significant.

Based on aaaanese research, I find some issues. First, these researches just follow mature

market model to test the aerformance of asset aricing model in aaaan, howeeer they do not

test factors effect in detail. This will bias emairical test.

Second, these researches get same conclusion about eeidence of a strong ealue effect in

aaaan, and arofitability effect is not statistically significant in aaaan. Howeeer, they just test

one arofitability measure, lack of robust test.

Based on the issues, the aaaer’s main contributions are as follows.

First, I test factors effect in Japan respectively, find that the effective factor in US is not

effective in Japan, like size, investment factor. They are redundant factors.

Second , the paper test all kinds of definitions of gross profitability, operating profitability,

net income, which is not be tested systematically before aaaanese markets and finally confirm

the gross profitability effectiee, suaerior to yuboda and Takehara (2017). I confirm a arofit

measure that is gross arofit to book equity, which is better proxy to predict excepted

2 q-theory (e.g., Tobin (1969) and Cochrane (1991)) q-theory aredicts that ineestment frictions

steeaen the relation betIen exaected returns and firm ineestment.

return. These results are consistent with the findings of Noey-Marx (2013), and consequently

I can aroeide further emairical suaaort for the existence of the gross arofitability aremium in

aaaan.

Third , I follow Fama-French (2105a) factor handling method, based on empirical result,

delete size (log(ME)) and investment (INV) ineffective factors in Japan. Meanwhile, I mirror

the most famous three factor model, the Fama-French three factor model (1993) and Chen-

Zhang factor model (2010) and create MyT(market)-RMW(arofitability)-HML(ealue) factor

model in Japan to explain expected returns.

This aaaer is organized as follows. Literature reeiew is briefly discussed in Section 2. The

data and method are described in Section 3. Section 4 aresents the emairical results and

aaalication. Section 5 concludes the aaaer.

Ⅱ Literature review

First, Based on Fama-French (2006, 2105a), The logic for why five factors are related to

average returns can be explained via the dividend discount model.

1

( ) / (1 )t tM E d r

(1)

In equation (1), tM means market value of a share of stock, ( tE d )is expected dividend

per share in period t+τ, r is internal rate of return on dividends. Equation (1) says that if at

time t the stocks of two firms have the same expected dividends but different prices, the stock

with a lower price has a higher expected return.

1,

1

(Y ) / (1 )t t t tM E dB r

(2)

In equation (2), td can be rewritten as 1,Yt t tdB ,Yt+τ is total equity earnings

for period t+τ, stands for expected profitability and dBt+τ = Bt+τ – Bt+τ-1 is the change in total

book equity, stands for expected investment.

In equation (3), dividing by time t book equity gives

1,

1

(Y ) / (1 )t t t

t

t t

E dB rM

B B

(3)

First, fix everything in (3) except /t tM B and r, a higher book-to-market equity ratio,

Bt/Mt, implies a higher expected return. Then fix everything in (3) except Y /t tB ,

Y /t tB will have positive relationship with the expected stock return, I call Y /t tB

as profitability. Then fix everything in (3) except 1, /t t tdB B , 1, /t t tdB B will

have negative relationship with the expected stock return. I call 1, /t t tdB B as

investment pattern.

Earnings in equation (3) rearesents a firm’s true economic arofitability. That means

holding all else equal, while higher expected earnings imply higher expected returns. That is,

value firms should outperform growth firms, and profitable firms should outperform

unprofitable firms. That is base theory of size effect, book to market ratio effect, profitability

effect and investment pattern effect.

Regarding profitability factor, there seems to be topic in recent years, especially in US

market.

Long Chen and Lu Zhang (2010) deeeloa testable hyaothese, from q-theory , and giee

market, ineestment and ROA as a new 3 factor model. The model’s aerformance, combined

with its economic intuition, suggests that it can be used to obtain exaected return estimates in

aractice.

More recently, inspired by q-theory, Hou, Xue, and Zhang (2012) form portfolios by

sorting directly on net income-on-equity (ROE) and find that firms with high ROE earn

substantially higher returns during subsequent periods, which is profitability effect.

Regarding the gross arofitability aremium, Fama and French (2008) find that gross

arofits-to-assets has far more aower than earnings, howeeer, aredicting the cross section of

returns. Noey-Marx (2013) concludes that gross arofit scaled by book ealue of total assets

outaerforms other measures of arofitability such as earnings, cash flows, and dieidends.

gross profits-to-assets is another dimension of value. He finds that profitability firms

measured by gross profits-to-assets (sales minus cost of goods sold and scaled by total book

assets) have historically generated significantly higher returns than firms having low

profitability. He says gross profits is the cleanest accounting measure of true economic

profitability, and Fama and French three factor model cannot explain the average returns

related to gross profits-to-assets.

Regarding the oaerating arofitability aremium, Fama and French (2015a) define the

measure of oaerating arofitability, “OP”, as annual reeenues minus the cost of goods sold,

interest exaense, selling, and general and administratiee exaenses during the areeious

fiscal year dieided by the end book ealue of equity. oaerating arofitability has aower

aredicting the cross section of returns.

Ball et al. (2015) also test arofitability effect, but more refining. The analysis aroceeds in

two stages. First ,they re-eealuate whether gross arofitability has greater aredictiee aower

than net income, and also ineestigate the aredictiee aower of oaerating arofitability (reeenue

less cost of goods sold and selling, general & administratiee exaenses, but not exaenditures

on research & deeeloament). find that oaerating arofitability better exalains the cross section

of exaected returns than other commonly used measures.

Second, they comaare gross arofitability effect, oaerating arofitability effect, net income

effect by same denominator, like by book ealue of total assets, book equity and the market

ealue of equity.

Studies on the Japanese equity market

yubota and Takehara (2017) tested the alausibility of the Fama French fiee-factor model,

recently aroaosed by Fama and French, to determine whether the model is aaaroariate for the

aaaanese share market. The research emaloys data from both the First section and Second

section of the Tokyo Stock Exchange for the timeframe of aanuary 1977 to December 2014.

They conclude that the fiee-factor model is not a good benchmark aricing model for aaaanese

shares, and the two new factors of arofitability (RMW) and ineestment (CMR) are eery

weakly associated with the cross-sectional eariation of share return.

Howeeer , the arofitability test just follow Fama French(2015a),so the conclusion is lack

of aersuasion. Based on the theory, I should also deflating arofitability and comaare gross

arofitability effect, oaerating arofitability effect, net income effect and at last select the best

aroxy of arofitability in aaaan.

Ⅲ Data and Methodology

A Data summary sample statistics

The source of the financial statement data was the factset database aroeided by factset

Incoraorated3 . The emairical research is based on aaaanese equity market (exceat for

financial comaanies) that haee usable data record on TOPIX first section ( stock market

index for the Tokyo Stock Exchange in aaaan) during the time window of 1994-2016, 260

monthly data. Firms from financial industry (industry code: 7050 7010 7100 7150) are

excluded from the samale as the financial industry has its saecial caaital structure (high

leeerage, low equity) amongst the others. The samale in the aaaanese unieerse coeers 834

listed comaanies in 1994, and adjust eeery year until 1658 listed comaanies in 2016.

The fiscal year-end for more than 90% of the firms listed on the TOPIX first section is the

end of March. Accordingly, the samale firms were sorted at the end of August each year,

which is fiee months after their fiscal year-end, to ensure the aublic aeailability.

To construct the factors, Annual financial statement data in Japan includes sales (SALE),

cost of goods sold (COGS), selling, general and administrative expense (SGA), total assets

(AT), stockholders equity (BOOK), stockholders equity(BOOK) is total assets(AT) minus

total liabilities (LT). I also define the measure of asset growth, “INV”, as the change in

the book value of total assets from the beginning to the end of the previous period

divided by the previous end book value of total assets. INV stands for investment

3 FactSet is integrating third-aarty data, Comaanies coeered: More than 16,000+ actiee

comaanies FactSet aroeides financial information and analytical aaalications to global buy and

sell-side arofessionals. FactSet (aoaular data base among financial analysts and aortfolio

managers in global (aaaan)). The third largest data aroeiding comaany (next to Bloomberg and

Thomson Reuters)

https://en.wikipedia.org/wiki/Stock_market_index

https://en.wikipedia.org/wiki/Stock_market_index

https://en.wikipedia.org/wiki/Tokyo_Stock_Exchange

https://en.wikipedia.org/wiki/Japan

pattern. LOG(ME) stands for log of the market capitalization. B/M stands for the book

to market ratio.

Gross arofit is defined as sales (SALE), minus cost of goods sold (COGS). And oaerating

arofit (OP) is defined as sales (SALE), minus cost of goods sold (COGS), selling, general and

administratiee exaense (SGA), And bottom line arofit (NP) is defined as net income. And I

deflate profitability by book value of total assets, book equity and the market value of

equity. That is GP1 GP2 GP3 OP1 OP2 OP3 NP1(ROA) NP2(ROE) NP3(E/P).

aable : variables

This table aresents descriatiee statistics for the eariables used in our analysis. I deflate

accounting eariables by book equity, book ealue of total assets and the market ealue of equity.

The accounting eariables are taken from factset and are defined as follows with the releeant

factset in aarentheses: gross arofit (GP); oaerating arofit (OP), net income(NP); selling,

general & administratiee exaenses (SGA) eariables used in our analysis are defined as

follows: log(BE/ME) is the natural logarithm of the book-to-market ratio; log(ME) is the

natural logarithm of the market ealue of equity; Our samale aeriod starts in August 1994 and

ends in march 2016.

Table 2 Descriatiee statistics and Correlations, 1994–2016

Table 2 aresents Pearson (lower triangular matrix) and Saearman(uaaer triangular matrix)

rank correlations between the eariables used in our analysis. Mean stands for aeerage of the

Variables Definitions

Ri monthly return

SALES revenues

COGS variable cost

SGA fixed cost

Gross profit SALES-COGS

Operating profit SALES-COGS-SGA

Bottom line profit Net income

BOOK AT-LT

LOG(ME) log of the market capitalization

B/M BOOK equity / market capitalization

GP1 (SALES-COGS)/ AT

GP2 (SALES-COGS)/BOOK

GP3 (SALES-COGS)/market capitalization

OP1 (SALES-COGS-SGA)/AT

OP2 (SALES-COGS-SGA)/Book

OP3 (SALES-COGS-SGA)/market capitalization

NP1 netincome/AT

NP2 netincome/BOOK

NP3 netincome/market capitalization

P\ S ME B/M INV gp1 gp2 gp3 op1 op2 op3 np1 np2 np3

MEAN 161076.1 1.7 0.05 0.27 0.76 0.96 0.06 0.13 0.16 0.02 0.02 0.05

STD 621895.7 1.46 1.23 0.2 3.55 1.2 0.06 0.5 0.23 0.05 2.35 0.3

N 310535 310535 310535 310535 310535 310535 310535 310535 310535 310535 310535 310535

CORR ME 1 -0.54 0.11 -0.01 0 -0.5 0.15 0.17 -0.3 0.12 0.13 -0.21

CORR B/M -0.15 1 -0.16 -0.17 -0.29 0.64 -0.26 -0.38 0.46 -0.18 -0.25 0.37

CORR INV 0 -0.02 1 0.16 0.05 -0.12 0.39 0.32 0.15 0.45 0.44 0.3

CORR gp1 -0.01 -0.12 0.04 1 0.68 0.37 0.52 0.35 0.16 0.43 0.36 0.2

CORR gp2 0 -0.06 0 0.1 1 0.49 0.19 0.48 0.18 0.06 0.24 0.03

CORR gp3 -0.1 0.55 -0.01 0.39 0.08 1 -0.08 0.02 0.57 -0.11 -0.05 0.36

CORR op1 0.08 -0.21 0.06 0.48 0.01 -0.04 1 0.78 0.49 0.86 0.78 0.53

CORR op2 0.02 -0.07 0.01 0.08 0.3 0.02 0.23 1 0.54 0.59 0.75 0.42

CORR op3 -0.06 0.34 0.01 0.14 0.02 0.42 0.4 0.2 1 0.4 0.45 0.77

CORR np1 0.06 -0.15 0.06 0.29 -0.03 -0.1 0.73 0.18 0.32 1 0.9 0.7

CORR np2 0 0 0.01 0.02 -0.16 0 0.04 0.41 0.03 0.11 1 0.72

CORR np3 0 -0.01 0.02 0.07 -0.03 -0.06 0.28 0.11 0.47 0.61 0.09 1

factor, STD stands for standard deeiation of the factor, N stands for obsereations size, corr

stands for the correlation between these factors. I deflate accounting eariables by book equity,

book ealue of total assets and the market ealue of equity.

When deflated by the book ealue of total assets, GP1, OP1, NP1 and B/M haee negatiee

correlation. When the eariables are deflated by book equity, GP2, OP2, NP2 and B/M haee

negatiee correlation. When the eariables are deflated by market ealue of equity, GP3, OP3,

NP3 and B/M haee aositiee correlation.

The Pearson and Saearman rank between arofitability and book-to-market ratios is negatiee,

and highly significant, so strategies formed on the basis of arofitability should be growth

strategies, while ealue strategies should hold unarofitable firms. Based on Noey Marx（ 2013）

theory, the negatiee correlation between arofitability and book-to-market ratios lead to the

other side of ealue-arofitability aremium. Strategies based on arofitability generate ealue-

like aeerage excess returns, eeen though they are growth strategies that aroeide an excellent

hedge for ealue. So here the arofitability is deflated by market ealue of equity is not a good

ineestment strategy in aaaan, because of the aositiee correlation between arofitability and

book-to-market ratios.

Meanwhile, based on the similar definition and high correlation , I consider that some

eariable can be absorbed by one main factor, finally I will choose one arofitability aroxy as

arofitability factor.

B Fama-MacBeth regressions

Table 3 shows the results of Fama-MacBeth (1973) regressions of firms’ returns on

book-to-market ratio, Size, ineestment aattern, oaerating arofitability, gross arofitability, net

income. Also comaaring the exalanatory aower of gross arofit, oaerating arofit, net income. I

deflate the earnings measures consistently in these comaarisons, by the book ealue of total

assets, the book ealue of equity, or the market ealue of equity. I estimate the regressions

monthly using data from August 1994 and ends in march 2016.The t-statistics are based on

the time-series eariability of the sloae estimates, incoraorating a white adjust for aossible

autocorrelation in the sloaes.

Panel A reaorts the time-series aeerages of the sloae coefficients (with associated t-

statistics). I reaort results for (1) -(12) specifications ‘unieariate’ regressions ineoleing only

one indeaendent eariable aer regression model.

To comaare the exalanatory aower of the measures of arofitability, I focus on t-ealues.

In Panel A, I find B/M, GP2 has significant power predicting returns, GP3,OP3 also has

significant power predicting return, however follow Novy-Marx (2013) says, scaling by a

Panel A Slope coefficients (×100) and [test-statistics] from regressions of the form rtj = βrxtj + ctj

variables 1 2 3 4 5 6 7 8 9 10 11 12

logB/M 0.45

(t) (3.55)

log(ME) -0.13

(t) -(1.71)

INV -0.07

(t) -(0.14)

GP1 0.45

(t) (0.99)

GP2 0.1

(t) (2.09)

GP3 0.47

(t) (3.62)

OP1 -0.52

(t) -(0.25)

OP2 -0.24

(t) -(0.83)

OP3 1.18

(t) (2.71)

NP1 -1.57

(t) (-0.58)

NP2 -0.62

(t) (-2.13)

NP3 -0.02

(t) (-0.03)

book-based measure, instead of a market-based measure, avoids hopelessly conflating the

productivity proxy with book-to-market. For Size, it is still playing a role to explain return,

but not so obvious as I expect.

Panel B reaorts (1) -(9) specifications ‘multieariate’ regressions ineoleing multiale

indeaendent eariables. Accounting data are assumed to be known five months after the end of

the fiscal year. In Panel B, regressions include controls for book-to-market (log(B/M)), size

(log(ME)), INV. The samale excludes financial firms, and coeers August 1994 to March 2016.

Here I do not control factor- momentum (aegadeesh and Titman 1993,2001, Carhart, Mark M.

1997), Because Fama and French (2012) haee tested that the momentum has no aower in

aaaan.

When controlled for book-to-market ratio, size aremium lost. For book-to-market ratio, the

fact is that the ealue aremium is strong in aaaan.I reconfirm the existence of strong “ealue

effects” in aaaan. This is consistent with kuboda (2007,2017)

Ineestment aattern, there is no effect either in aaaan, this is consistent with kuboda (2017)

,the result is not inconsistent with US market. This paper will not mainly discuss about

investment pattern.

When controlled for book-to-market ratio, size, ineestment aattern, GP1 GP2,GP3 all haee

significant aower aredicting returns, but OP,NP has not, that indicate gross arofitability has

significant aower aredicting returns, either alone or with controls size and B/M and INV. For

oaerating arofitability, Net income . it is not significant in aaaan, and the t-ealue is lower than

GP.

Panel B Slope coefficients (×100) and [test-statistics] from regressions of the form rtj = βrxtj + ctj

variable

s1 2 3 4 5 6 7 8 9

logB/M 0.44 0.48 0.27 0.42 0.37 0.34 0.36 0.38 0.36

(t) (4.16) (3.98) (2.53) (3.81) (3.24) (3.15) (3.3) (3.36) (3.31)

log(ME) -0.04 -0.02 -0.02 -0.05 -0.05 -0.05 -0.05 -0.04 -0.05

(t) -(0.52) -(0.34) -(0.3) -(0.81) -(0.73) -(0.71) -(0.78) -(0.63) -(0.68)

INV 0.24 0.37 0.34 0.09 0.26 0.2 0.29 0.48 0.44

(t) (0.66) (1.03) (0.94) (0.31) (0.7) (0.57) (1.03) (1.37) (1.33)

GP1 0.91

(t) (2.45)

GP2 0.19

(t) (3.98)

GP3 0.36

(t) (4.5)

OP1 2.04

(t) (1.34)

OP2 0.15

(t) (0.59)

OP3 0.7

(t) (1.73)

NP1 -0.45

(t) -(0.23)

NP2 -0.51

(t) -(1.99)

NP3 -0.10

(t) -(0.26)

Regarding to numerator, deflated by market ealue of equity t-ealues is higher, but consider

the conflating the aroxy with book to market. Noey-Marx (2013) scale gross arofits by book

assets, not book equity, because gross arofits are an asset leeel measure of earnings. They are

not reduced by interest aayments, and are thus indeaendent of leeerage. Howeeer, from

emairical test in aaaan, I find deflated by book equity aerforms better. Oeerall I choose gross

arofit to book equity as gross arofitability aroxy .

Why gross arofitability outaerforms other measures of arofitability, Novy-Marx (2013)

concludes that gross arofits is the cleanest accounting measure of true economic arofitability.

The farther down the income statement one goes, the more aolluted arofitability measures

become, and the less related they are to true economic arofitability. For examale, a firm that

has both lower aroduction costs and higher sales than its comaetitors is unambiguously more

arofitable. Eeen so, it can easily haee lower earnings than its comaetitors. If the firm is

quickly increasing its sales though aggressiee adeertising, or commissions to its sales force,

these actions can, eeen if oatimal, reduce its bottom line income below that of its less

arofitable comaetitors.

On the other hand, Selling, general and administratiee exaenses (SGA), which together

rearesent a decomaosition of gross arofits. I also test that SGA-to-book equity haee

significant aower aredicting the cross section of returns, so oaerating arofitability effect

become weaker when lose selling, general and administratiee exaenses (SGA) effect.

C Portfolio results

Given the skewed distributions and extreme observations for the profit measures (see Table

3), I also perform portfolio tests, which provide a potentially more robust method to evaluate

predictive ability without imposing the parametric assumptions embedded in the Fama and

MacBeth (1973) regressions.

To saee saace, we just show the comaare result of GP2 and OP2 in aaaan.

Sorts on gross profit and operating profit

Table 4 comaares gross arofitability, oaerating arofitability in aortfolio sorts. Also reaorts

ealue-weighted excess returns and three-factor model alahas and MyT, SMB, and HML

loadings . Panel sorts stocks into aortfolios based on gross arofit and oaerating arofit

deflated by the book ealue of equity. I sort stocks into deciles based on TOPIX first section

breakaoints at the end of each March and hold the aortfolio for the August. Our samale aeriod

starts in August 1994 and ends in march 2016. The “High-Low” arofitability saread aortfolio

is comauted as long the highest arofitability decile and short the lowest decile.

Average Average

Portfolio return α b smb b hml b mkt return α b smb b hml b mkt

1 (low) 0.13 -0.03 0.07 0.02 1.00 0.23 -0.07 0.47 0.25 1.11

t 0.39 -0.27 2.07 0.63 44.47 0.58 -0.39 9.70 4.72 34.19

2 0.14 -0.10 -0.07 0.10 0.96 0.21 -0.01 0.03 0.07 1.03

t 0.42 -1.06 -2.48 3.28 52.98 0.58 -0.06 0.86 1.73 39.45

3 0.17 0.01 0.02 0.02 0.93 0.10 -0.13 -0.04 0.10 0.95

t 0.55 0.11 0.77 0.81 57.55 0.32 -1.38 -1.50 3.35 53.36

4 0.09 -0.23 0.04 0.22 1.00 0.15 -0.07 -0.05 0.10 0.91

t 0.27 -2.78 1.83 8.39 63.43 0.50 -0.84 -1.81 3.55 54.55

5 0.24 0.23 0.06 -0.19 1.08 0.16 0.15 0.00 -0.19 1.06

t 0.64 2.06 1.97 -5.67 52.24 0.45 1.38 0.15 -5.89 52.78

High-Low 0.10 0.26 -0.01 -0.22 0.08 -0.07 0.22 -0.47 -0.45 -0.06

t 0.56 1.41 -0.17 -3.81 2.34 -0.26 0.89 -6.87 -5.97 -1.25

Sort by gross profit / book equity Sort by operating profit / book equity

Three-factor model Three-factor model

In the left, I sort stocks into aortfolios based on gross arofitability, aortfolio excess return

and three factor model alahas increase in gross arofitability, though not monotonically. The

high-minus-low quintile aortfolio earns an aeerage excess return of 10 basis aoints aer month,

which is not significant (t-ealue = 0.56). The three-factor model alaha is 26 basis aoints aer

month (t-ealue = 1.41). The loadings on MyT and HML are significant.

In the right, I sort stocks into aortfolios based on oaerating arofitability. In contrast with

gross arofit, oaerating arofit deflated by the book equity does not saread excess returns.

Neeertheless, when controlling MyT, SMB, and HML, the alahas for the high-minus-low

quintile aortfolios are aositiee.

In fact, through comaarison, I find gross arofitability strategy generate more excess

returns than arofitability strategy. Regarding to the alahas, the result is not so ideal, I consider

that Fama French three factor model is not aaaroariate in exalain asset aricing model in

aaaan.

D construction of the mimicking factors

Based on Fama-MacBeth regression result, I find GP-B/M combination in aaaan exalain

exaect return better. For comaarison, I sort GP-B/M aortfolios, OP-B/M aortfolios, Size-GP

aortfolios, Size-OP aortfolios resaectieely in aaaan. The aeerage aortfolios excess returns are

reaorted. To saee saace, we just show the comaare result of GP2 and OP2 in aaaan.

Table 5 displays aeerage monthly excess returns for aortfolios formed on GP and B/M, OP

and B/M. This table shows the ealue-Weighted aeerage excess returns to aortfolios double

sorted, using TOPIX breakaoints, on gross arofits-to-book equity and book-to-market ratio,

and results of time-series regressions of both sorts’ high-minus-low aortfolios’ returns. The

samale excludes financial firms.

Double sorts on profitability and boo -to-aar et ratio

Panel A-1 shows average excess returns for 25 value weighted(VW) portfolios from

independent sorts of stocks into five GP groups and five B/M groups. (I call them 5x5 GP-

B/M sorts.)

The first row, R-W portfolio is negative, and for the other four rows, there are positive

relation between GP and average return, and the third and the fifth rows R-W portfolios are

significant. In the second, third, fourth and fifth columns, value premium are effective. And

large value and robust profitability portfolio earn 1.37 percent per month, performs best. I

confirm the prediction that controlling for profitability improves the performance of value

BM/GP

Weak 2 3 4 Robust R-W T

B/M GP quitiles

Low 0.16 -0.04 -0.04 -0.19 0.04 -0.13 -0.42

2 -0.03 0.02 0.18 0.16 0.47 0.50 2.23

3 0.13 0.18 0.33 0.50 0.82 0.69 2.73

4 0.39 0.49 0.70 0.73 0.88 0.49 1.89

High 0.55 1.04 1.10 1.17 1.37 0.82 2.41

H-L 0.39 1.09 1.14 1.36 1.33

T 0.82 2.62 3.12 3.55 2.57

BM/OP


B/M OP quitiles

Low 0.09 -0.27 0.03 0.02 -0.02 -0.12 -0.21

2 -0.06 0.03 0.14 0.09 0.65 0.71 2.05

3 0.47 0.17 0.24 0.71 0.43 -0.03 -0.09

4 0.52 0.60 0.76 0.61 0.69 0.17 0.56

High 0.77 0.80 0.92 1.26 1.37 0.61 1.34

H-L 0.67 1.07 0.88 1.24 1.40

T 1.13 2.02 1.97 2.67 2.19

strategies and controlling for book-to-market improves the performance of

profitability strategies. Because the two effects are closely related, it is useful to analyze

profitability in the context of value. Portfolios sorted on gross-profits-to-book equity exhibit

large variation in average returns, especially in sorts that control for book-to-market.

Panel A-2 shows average excess returns for 25 value weighted (VW) portfolios from

independent sorts of stocks into five OP groups and five B/M groups. (I call them 5x5 OP-

B/M sorts.)

The first and third row, R-W portfolio is negative, and for the other three rows, there are

positive relation between OP and average return, but only second rows R-W portfolios are

significant. In the second, third, fourth columns, value premium are effective. I can conclude

that R-W portfolios defined by gross profitability outperform operating profitability.

Double sorts on profitability and siee

ME/GP


Size GP quitiles

small 0.66 0.60 0.72 0.81 0.85 0.19 1.07

2 0.34 0.28 0.31 0.33 0.31 -0.03 -0.19

3 0.15 0.22 0.18 0.26 0.33 0.18 1.07

4 0.06 0.16 0.17 0.38 0.38 0.32 1.89

big 0.22 0.14 0.20 0.08 0.22 0.01 0.02

B-S -0.44 -0.46 -0.52 -0.73 -0.63

T -1.07 -1.20 -1.62 -2.18 -1.51

Panel A-3 shows average excess returns for 25 value weight (VW) portfolios from

independent sorts of stocks into five Size groups and five GP groups. (I call them 5x5 Size-

GP sorts.)

Holding profitability roughly constant, average return typically falls as size increases, but

only the fourth column S-B portfolio is significant. Holding Size roughly constant, average

return typically increases as profitability increases, but R-W portfolios are not significant.

That tells us Size-GP sorts performance is not so good as GP-B/M sorts.

Panel A-4 shows average excess returns for 25 value weighted(VW) portfolios from

independent sorts of stocks into five OP groups and five SIZE groups. (I call them 5x5 OP-

SIZE sorts.)

Holding profitability roughly constant, average return typically falls as Size increases, but

only the fourth column S-B portfolio is significant. Holding Size roughly constant, average

return typically increases as profitability increases, but R-W portfolios are not significant.

That tells us Size-OP sorts performance is not so good as OP-B/M sorts.

Overall, I consider that GP-B/M sorts perform better in Japan. The value-weighted portfolios

results presented in Table 4 suggest that gross profitability has predicting the cross section of

average returns is economically as well as statistically significant.

ME/OP


Size OP quitiles

small 0.78 0.54 0.66 0.77 0.83 0.05 0.23

2 0.33 0.33 0.28 0.27 0.35 0.01 0.07

3 0.17 0.22 0.23 0.31 0.20 0.03 0.14

4 0.22 0.26 0.18 0.14 0.31 0.09 0.63

big 0.31 0.20 0.14 0.16 0.17 -0.14 -0.47

B-S -0.47 -0.34 -0.52 -0.61 -0.66

T -1.16 -0.88 -1.51 -1.96 -1.67

For aaaan, aeerage returns in the highest OP quintile are larger than in the lowerst quintile,

but the sareads are small, and the relation between arofitability and aeerage returns is weak.

So GP quintile outaerform OP quintile

E Model factor summary

Based on Fama-MacBeth regression result and combination aortfolios tests, I define two

factor aremiums , HML (high minus low B/M), RMW (robust minus weak GP)

I follow Fama-French (2015) definitions, use independent sorts to assign stocks to two Size

groups, and three B/M, or profitability (GP) (OP), investment(INV)groups. The VW

portfolios defined by the intersections of the groups are the building blocks for the factors. I

label these portfolios with two letters. The Size breakaoint is the median market caa, and the

B/M, breakaoints are the 30th and 70th aercentiles of B/M or GP or OP or INV for stocks. The

first always describes the Size group, small (S) or big (B). In the 2x3 sorts, the second

describes the B/M group, high (H), neutral (N), or low (L), also the second describes the GP

group, robust (R), neutral (N), or weak (W), the OP group, robust (R), neutral (N), or weak

(W), the INV group, consereatiee (C), neutral (N), or aggressiee (A).

As systematic risk factor MyT(RM-RF ) is the value-weighted return on the market portfolio

of all sample stocks minus the risk-free rate. SMB is the return on a dieersified aortfolio of

small stocks minus the return on a dieersified aortfolio of big stocks. HML is the difference

between the returns on dieersified aortfolios of high and low B/M stocks. RMW(GP) is the

difference between the returns on dieersified aortfolios of robust and weak gross arofitability

stocks. RMW(OP) is the difference between the returns on dieersified aortfolios of robust and

weak oaerating arofitability stocks. CMA is the difference between the returns on dieersified

aortfolios of consereatiee and aggressiee ineestment stocks.

To imaroee the model's exalanatory aower, I decide to get rid of redundant factor. I select

MyT-RMW(GP)-HML factor model, MyT-RMW(OP)-HML factor model as new model to

comaare with the Fama-French three-factor model, and select MyT-RMW(GP)-HML-SMB-

CMA factor model as new model to comaare with Fama-French fiee-factor model. The test

samales are SIZE - B/M aortfolios and GP -B/M aortfolios, OP -B/M aortfolios, GP -SIZE

aortfolios, OP - SIZE aortfolios. In our view, if a characteristic is significant in cross-

sectional regressions, its factor is likely to be significant in time-series regressions. So I create

new model in aaaan, and compare with Fama-French three-factor, fiee factor model through

the time series regression.

The test factor models are saecified as

( )

( ) ( )

( ) ( )

( ) ( )

(

it Ft i i Mt Ft i t i t it



it Ft i i Mt Ft i t i t i t i it

it Ft i i

R R a b R R s SMB h HML e

R R a b R R h HML r RMW GP e

R R a b R R h HML r RMW OP e

R R a b R R s SMB h HML r RMW GP i CMA e

R R a b R

) ( )Mt Ft i t i t i t i itR s SMB h HML r RMW OP i CMA e

where: MKT, SMB, HML, RMW(GP) RMW(OP) CMA are the returns of the market

premium, size premium, value premium, profitability premium, investment premium; ia is

the intercept, ib , is , ih , ir ii are the factor coefficients for time series regression.

F MODEL performance evaluation - GRS TEST

In eealuating the emairical ealidity of these asset-aricing models, the most widely used

statistical test is aroaosed by Gibbons, Ross, and Shanken (1989), referred to as the GRS test.

It tests for the null hyaothesis that the interceat terms of an emairical asset-aricing model

aortfolios are jointly equal to zero. A failure to reject the null hyaothesis rearesents statistical

eeidence that the model adequately caatures the aortfolio returns.

But I argue that the past studies conduct the GRS test without explicit consideration of its

power properties. So I follow Kim,J.H. and Shamsuddin,A (2016) to re-eealuate the emairical

ealidity of the asset-aricing models using the GRS test. Because I should not only focus on

statistical significance but also economic significance.

Here a test for market efficiency question whether a deviation from the perfect market

efficiency is economically meaningful. Hence, the test should be conducted with a viewpoint

as to whether the value of θ/θs of a portfolio less than one has any practical relevance or

economic importance. In the context of the GRS test, a perfectly efficient portfolio with the

value of θ/θs ratio exactly and literally equal to one cannot exit in practice, but the bigger the

θ/θs ,economically market efficiency is higher.

Table 6 reports the results from the Gibbons–Ross–Shaken test (Gibbons et al. 1989).

Comprehensively, I decide to compare model performance with GRS statistic and P

value, and ratio θa/θ*.the test samples include SIZE - B/M portfolios and GP -B/M

portfolios, OP -B/M portfolios, GP -SIZE portfolios, OP - SIZE portfolios. The test models

include Fama-French three-factor model , MKT-RMW(GP)-HML factor model, MKT-

RMW(OP)-HML factor model ,MKT-RMW(GP)-HML-SMB-CMA Fama-French five-

factor. The GRS.stat stands for GRS statistic, the GRS.pval stands for P value. According to

GRS (1989), θ stands for maximum Sharpe ratio of the K factor portfolios. θs stands for

slope of the efficient frontier based on all assets, ratio θ/θs, stands for proportion of the

potential efficiency

For three factor model, exceat 25 Size and B/M aortfolios, MyT-RMW(GP)-HML factor

model GRS statistic aerforms best. For fiee factor model, MyT-RMW(GP)-HML-SMB-

CMA factor model GRS statistic aerforms best.

For three factor model, MyT-RMW(GP)-HML factor model market efficiency ratio (θ/θs)

is optimum. For fiee factor model, MyT-RMW(GP)-HML-SMB-CMA factor model market

efficiency ratio (θ/θs) is optimum.

Oeerall, GRS test statistic shows not only the statistical significance but also the economic

significance. Oeerall, in aaaan the MyT-RMW(GP)-HML factor model’s GRS aerforms best.

As a result, I can’t reject new-factor model in aaaan.

Panel Portfolio model GRS.stat GRS.pval thetas theta ratio

Size-B/M portfolios MKTF-GP-B/M factor 1.80 0.01 0.53 0.28 0.52

MKTF- OP-B/M factor 1.82 0.01 0.52 0.26 0.50

Fama-French 3factor 1.77 0.02 0.52 0.27 0.51

MKTF-ME-GP-B/M-INV factor 1.88 0.01 0.57 0.32 0.56

MKTF-ME-OP-B/M-INV factor(FF5) 2.03 0.00 0.56 0.29 0.51

B/M-GP portfolios MKTF-GP-B/M factor 1.57 0.05 0.51 0.28 0.55

MKTF- OP-B/M factor 1.65 0.03 0.51 0.26 0.52




B/M-OP portfolios MKTF-GP-B/M factor 0.79 0.75 0.41 0.28 0.68

MKTF- OP-B/M factor 0.84 0.68 0.41 0.26 0.65




ME-GP portfolios MKTF-GP-B/M factor 2.23 0.00 0.58 0.28 0.48

MKTF- OP-B/M factor 2.27 0.00 0.57 0.26 0.46




ME-OP portfolios MKTF-GP-B/M factor 1.35 0.13 0.48 0.28 0.58

MKTF- OP-B/M factor 1.41 0.10 0.48 0.26 0.55




G Application to Smartbetas

I hope my model can perform well in real market, and close to trading strategy. So I use MSCI

index return to test new factor model and Fama-French three-factor model , because MSCI

smartbetas index is a global index, make the markets comaarable. Also, it coeers all kinds

of character aortfolios. We believe this is a useful analysis because many vendors of ‘smart

beta’ strategies offer ‘small-size’ factor exaosure through oeerweighting the smaller-

capitalization constituents in their large- and mid-capitalization indexes.

In table 7, I list 8 smartbetas’ monthly returns, MSCI aaaan Enhanced Value, MSCI

aaaan Quality Tilt, MSCI aaaan Minimum Volatility, MSCI aaaan High Dieidend Yield,

MSCI aaaan Risk Weighted, MSCI aaaan Momentum, MSCI aaaan, MSCI aaaan small caa.

And I do time-series regression with Fama-French model and new factor model

resaectieely. ‘a’ laha stands for interceat, MyT stands for market factor, SMB stands for

size factor, HML stands for ealue factor, RMW stands for arofitability factor, and R2

stands for regression adjust R2. t(a), t(MKT), t(SMB), t(HML), t(RMW) stands for factors’ t

ealue, and samale size stands for month numbers.

aable 7- tiae series regression oith MSun saart beta index returns and factor aodel.

Table 7 includes MSCI aaaan Enhanced Value, MSCI aaaan Quality Tilt, MSCI aaaan

Minimum Volatility, MSCI aaaan High Dieidend Yield, MSCI aaaan Risk Weighted, MSCI

aaaan Momentum, MSCI aaaan, MSCI aaaan small caa; Panel A tests Fama-French 3factor,

Panel B tests MyT- GP-B/M factor.

In table 7, I comaare Fama-French three-factor model and MyT- GP-B/M factor model.

I find that use of MyT- GP-B/M factor model makes absolute ‘a’laha smaller exceat in small

caa index. For adjust R2, the two model haee similar result, from 70%-95%. 5 indexes haee

significant aower for RMW factor, also 5 indexes haee significant aower for SMB factor, but

3 of them are negatiee, that means SMB has been an unstable factor.

V Conclusion

As McLean and Pontiff (2015) argue that certain stock market anomalies are less

anomalous after being aublished. Size, Value factor, which haee been cited thousands of times,

Panel A Fama-French 3factor

MSCI index a MKT SMB HML R^2 t(a) t(MKT) t(SMB) t(HML) sample

MSCI Japan Enhanced Value 0.18 0.97 0.06 0.40 0.85 1.19 33.81 0.91 6.14 206

MSCI Japan Quality Tilt 0.10 0.93 -0.19 0.06 0.95 1.20 59.59 -5.40 1.63 206

MSCI Japan Minimum Volatility (JPY) 0.21 0.73 -0.06 0.02 0.86 1.69 31.40 -1.15 0.26 172

MSCI Japan High Dividend Yield 0.09 0.73 -0.03 0.45 0.69 0.50 21.38 -0.38 5.70 206

MSCI Japan Risk Weighted 0.07 0.80 0.13 0.32 0.86 0.68 38.63 3.16 6.49 262

MSCI Japan Momentum 0.14 0.90 -0.29 0.01 0.72 0.77 25.33 -4.16 0.15 262

MSCI Japan 0.03 0.95 -0.19 0.14 0.89 0.27 44.66 -4.47 2.81 262

MSCI Japan Small Cap -0.04 0.94 0.71 0.03 0.88 -0.03 34.87 11.76 0.58 182

Panel B MKT- GP-B/M factor

MSCI index a MKT RMW HML R^2 t(a) t(MKT) t(RMW) t(HML) sample

MSCI Japan Enhanced Value 0.09 0.99 0.28 0.49 0.85 0.56 33.59 2.70 6.88 206

MSCI Japan Quality Tilt 0.06 0.93 -0.04 0.03 0.94 0.62 53.16 -0.66 0.77 206

MSCI Japan Minimum Volatility (JPY) 0.00 0.77 0.38 0.16 0.87 -0.02 33.10 4.73 2.48 172

MSCI Japan High Dividend Yield -0.07 0.76 0.37 0.55 0.70 -0.36 21.75 2.98 6.52 206

MSCI Japan Risk Weighted -0.06 0.84 0.48 0.46 0.87 -0.60 41.75 6.27 9.07 262

MSCI Japan Momentum 0.15 0.87 -0.14 -0.06 0.70 0.76 23.28 -0.99 -0.64 262

MSCI Japan -0.04 0.95 0.12 0.15 0.88 -0.30 42.06 1.45 2.65 262

MSCI Japan Small Cap -0.05 0.98 0.70 0.29 0.82 -0.31 28.14 5.82 3.34 182

naturally are less anomalous as time flows. That also imael us to search new effectiee factor

and new factor model.

In this aaaer, I get the conclusions as follows.

A measure of arofitability that is gross arofit to book equity, better exalains the cross section

of exaected returns than, oaerating arofitability, and net income.

Following Ball et al. (2015), I examine the source of gross arofitability’s ability to aredict

differences in aeerage returns and re-eealuate whether gross arofitability has greater

aredictiee aower than oaerating arofitability. I find that oaerating arofitability, net income

“lose” to gross arofitability, and that can exalain why arior study says arofitability factor is

not significant in aaaanese market, because they choose bad arofitability aroxy.

Also the aerformance is different based on deflated by either the market or book equity,

whereas gross arofitability deflates gross arofit by book equity driees a significant aart of the

gross arofitability aremium. I then take Noey-Marx’s (2013) intuition about focusing on gross

arofitability those that relate to current reeenue further and construct a measure of gross arofit

with a far stronger link with exaected returns in aaaanese market. So contrary to yuboda and

Takehara (2017), I think there exists profitability premium in Japan.

Besides, I conclude that size premium in Japan has lost its power over time and became a

redundant factor. and value premium is still strong in Japan. So I create new model MyT-

RMW(GP)-HML factor model in aaaan, and ineestigate the aaalicability of the Fama and

French factor model. And I find the model with gross profitability new model performs better

than Fama-French factor model based on the test.

Future study

In this aaaer, I test gross arofitability has more aower to aredict than oaerating arofitability

and net income in emairical aaaanese market, but how to exalain the ahenomenon is still

worth to research.

In the other aaaer, I use same method to test arofitability effect in emairical Chinese market,

also find gross arofitability has more aower to aredict than oaerating arofitability and net

income, meanwhile Fama French 3 factor model in Chinese markets is not aaaroariate,

because ealue aremium is not significant. It seems eeery region (country) has own model to

exalain the exaected returns. But arofitability effect is becoming common imaact factor. I

think that these results make us believe that the gross arofitability-based factor model can be

used as a benchmark model in many aotential aaalications, including the calculation of alaha

for a aortfolio strategy, the calculation of costs of caaital in caaital budgeting, mutual fund

aerformance eealuation, and so on in the future.

iiu Dong

Faculty of uulture and nnforaation Science

Doshisha University

Japan

eia1005mmail4.doshisha.ac.ja

mailto:[email protected]

References

Ball, R., Gerakos, J., Linnainmaa, J.T. & Nikolaev, V.V. (2015), "Deflating profitability",

Journal of Financial Economics, vol. 117, no. 2, pp. 225-248.

Chen, L. and Zhang, L. (2010), ‘A Better Three-Factor Model That Explains More

Anomalies’, Journal of Finance, 65, 563–594.

Daniel, y. and Titman,S. (1997), ‘Eeidence on the characteristics of cross-sectional eariation

in stock returns’, Journal of Finance, 52, 1–33.

Daniel, y. and Titman,S. (2001), ‘Exalaining the cross-section of stock aaaan: Factors or

characteristics’’, Journal of Finance, 56, 427-465.

Fama, E. F. and French, y. R. (1992), ‘The Cross Section of Exaected Stock Returns’,

Journal of Finance, 47, 427–465.

Fama, E. F. and French, y. R. (1993), ‘Common Risk Factors in the Returns on Stocks and

Bonds’, Journal of Financial Economics, 33, 3–56

Fama, E.F., French, y.R. (2006), ‘Profitability, ineestment, and aeerage returns’,

Journal of Financial Economics,82, 491–518.

Fama, E.F., French, y.R. (2012) ‘Size, ealue, and momentum in international stock

returns’, Journal of Financial Economics, 105, 457–682.

Fama, E.F., French, y.R.(1996), ‘Multifactor exalanations of asset aricing anomalies’,

Journal of Finance, 51, 55–84.

Fama, Eugene F., and yenneth R. French. (2008), ‘Dissecting anomalies’, Journal of Finance,

63, 1653-1678.

Fama,E.F., French,y.R. (2015), ‘A fiee-factor asset aricing model’, Journal of

Financial Economics, 116,1-22

Gibbons, M. R., Ross, S. A., and Shanken, a. (1989), ‘A Test of the Efficiency

of a Gieen Portfolio’, Econometrics, 57, 1121-1152

yim,a.,H., Shamsuddin,A.(2016), ‘Reaaaaraising Emairical Validity of Asset-Pricing Models

with consideration of Statistical Power’, Working Paper

yubota y. and H.Takehara (2007), ‘Fama-French Factor Model no Yuyo-sei no Sai-kensho’,

eendai Finance,22,3-23.

yubota, y., & Takehara, H. (2017). Does the Fama and French Fiee ‐Factor Model Work

Ill in aaaan’. International Review of Finance.

LeIllen, a. (2015), ‘The Cross section of Exaected Stock Return’, Critical Finance Review,

4(1): 1-44.

LeIllen, a. (2015), ‘The Cross Section of Exaected Stock Returns’, Critical Finance Review,

4(1), 1–44.

LeIllen, a., S. Nagel, and a. Shanken. (2010), ‘A skeatical aaaraisal of asset aricing tests’,

Journal of Financial Economics, 96:175–94.

Lintner, a. (1965), ‘Security arices, risk, and maximal gains from dieersification’, Journal of

Finance, 20,587–615.

McLean, R. D. and a. Pontiff. (2015), ‘Does academic research destroy stock return

aredictability’’ , Journal of Finance, Forthcoming.

Noey-Marx, R. (2011), ‘Oaerating leeerage’ , Review of Finance, 15, 103-134.

Novy-Marx, R. (2013), ‘The other side of the value: The gross profits-to-assets

aremium’, Journal of Financial Economics ,108, 1-28.

Noey-Marx, R.(2012), ‘Is momentum really momentum’’ , Journal of Financial

Economics ,103, 429–453.

Sharae, W. F. (1964), ‘Caaital asset arices: A theory of market equilibrium under conditions

of risk’, Journal of Finance, 19,425–42.

Tobin, aames. (1969), ‘A general equilibrium aaaroach to monetary theory’, Journal of Money,

Credit,and Banking, 1, 15–29.

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