Capturing Profitability in Asset Pricing Models for Japanese Equities 1994-2016

We follow Ball et al. (2015) to investigate and compare firms’ gross profit, operating profit, and net income as predictors of returns for a cross-section of traded Japanese equities spanning 1994-2016. We test the predictive power of profit measures on cross-sectional stock returns using portfolio tests and Fama-MacBeth regressions, find that gross-profit-to-book-equity significantly predict returns on sampled stocks. Consistent with Novy-Marx (2013), we also find that sorting portfolios by gross profitability and book-to-market ratios outperform in the Japanese market. Hence, we create a Market-Profitability-Value model that captures value and profitability premium among returns of sampled stocks. Based on Gibbons-Ross-Shanken test and economic value, we demonstrate that our enhanced model outperforms Fama–French multiple-factor model in isolating influences on equity returns.


Introduction
The question of what drives stock returns is perennial in modern finance.The Fama-French (1992,1993) three-factor model has been the benchmark to explain expected returns during the past two decades because the book-to-market ratio (a measure of Value) and market capitalization (Size) have strong explanatory power in empirical analysis.Nonetheless, profitability effects have attracted attention of researchers seeking to explain cross-sectional variations in stock returns.Researchers attend to profitability effects because they can be used to assess the quality of firms and investment decisions.
This study originates with Novy-Marx (2013), who shows that gross profitability relates significantly to stock returns after controlling for book-to-market ratio.Profitability earns a high positive premium and helps to capture most asset-pricing anomalies that plague the Fama-French (1993) three-factor model.Fama and French (2015) add operating profitability to create a five-factor model that outperforms their three-factor model in explaining cross-sections of stock returns.Ball et al. (2015Ball et al. ( , 2016) ) present a more refined test for profitability effects.First, they re-evaluate whether gross profitability has greater predictive power over returns than net income and operating profitability.Second, they compare the effects of gross profitability, operating profitability, and net income using identical denominators (book value of total assets, book equity, and market capitalization).
These studies show that profitability exerts power in predicting returns among US equities, but scant literature investigates Japanese equities.First, retesting Fama-French's five-factor model by examining years of monthly data for shares on the first and second sections of the Tokyo Stock Exchange (TSE), Kuboda and Takehara (2017) find that operating profitability is not a statistically significant predictor of Japanese equity returns.Maeda (2017) tests q-factor (Note 1) model (market, profitability, and investment), finds that profitability (net income) is not a significant predictor of returns on Japanese equities.These studies, however, merely retest whether an asset-pricing model is appropriate for the Japanese market.By ignoring profitability effects their conclusions lack force.This study resolves this deficiency in earlier literature.We characterize firms' profits comprehensively using gross profit, operating profit, and net income to assure robustness in predicting equity returns.We confirm that gross-profit-to-book-equity is a superior proxy for predicting equity returns.Our results endorse those of Novy-Marx (2013) and support existence of a gross profitability premium for Japanese equities.In addition, we mirror Fama-French three-factor (1993) and five-factor models (2015), delete the redundant factor, and create a Market-Profitability-Value (MKT-RMW-HML) model to explain expected returns on Japanese equities.This paper proceeds follows.Section 2 describes our data and variable.Section 3 presents methods and empirical results.Section 4 concludes.

Data and Variable
Financial statement data are from the FactSet database (Note 2).Empirical research covers Japanese equities listed on the first section of the Tokyo Stock Exchange(TSE) that have usable data during 1994-2016 (260 months).Financial firms (industry codes: 7050, 7010, 7100, and 7150) are excluded for their distinctive high-leverage/low-equity capital structures.Our samples cover 834 companies in 1994, and, adjusted yearly, reach 1,658 in 2016.
To construct factors that might influence equity returns, we assemble annual financial statement data for sales (SALE), cost of goods sold (COGS), sales-general-administrative expenses (SGA), book value of total assets (AT), and book equity(BE) measured as AT minus total liabilities (LT).We measure investment patterns (INV) as changes in total assets (AT) every year.Log(ME) is the log of market capitalization (ME).B/M indicates the book-to-market ratio (BE/ME).Gross profit (GP) is SALE minus COGS.Operating profit (OP) is SALE minus COGS and SGA.Bottom-line profit (NP) is net income.

Fama-MacBeth Univariate Regressions on Measures of Profitability
We use monthly Fama and MacBeth (1973) cross-sectional regressions to examine whether profitability convincingly forecasts stock returns.Table 1 shows regressed monthly returns of individual stocks on lagged profitability.We focus on t-values to compare the explanatory power of measures of profitability.
Deflating by total assets, GP, OP, and NP have no significant predicting power, while deflating by book equity, GP and NP have significant predicting power.
Deflating by market capitalization, GP and OP also have power in predicting return significant.Note, however, we admit that a market capitalization-based measure conflates a productivity proxy with B/M ratios.Hence, based on empirical tests for the sampled equities, we choose profit deflated by book equity as a proxy variable.

Fama-MacBeth Multivariate Regression
Table 2 reports model ( 1)-(3) specifications for multivariate regressions including controls for book-to-market ratio (B/M), size (log(ME)), and INV (investment patterns).When controlled accordingly, the B/M is strong for the sampled equities.We reconfirm the existence of strong value effects among Japanese equities per Kuboda andTakehara (2007, 2018).The size premium sheds predictive power.Investment patterns show no effect on returns of sampled equities, consistent with Kuboda and Takehara (2017) and unlike US equities.GP exhibits significant power to predict returns, whereas the predictive power of OP is not significant.Results show NP has negative power to explain returns, however, motivated by valuation theory, Fama and French (2006) explore the positive relation between profitability and expected returns.Hence, we abandon net income as an investigative variable.
Based on Fama and MacBeth cross-sectional regressions, gross-profit-to-book-equity exerts the most significant power over excepted returns alone or when controlled for size, B/M, and INV.Novy-Marx (2013) concludes that gross profit is the cleanest accounting measure of true economic profitability and therefore outperforms other measures of profitability.Items farther down the income statement are more attenuated measures of profitability and less cogent with respect to true economic profitability.

Sorts on Profitability
We perform portfolio tests as a more predictive exercise that escapes bias of Fama and MacBeth regression.We compare results of gross-profit-to-book-equity, and operating-profit-to-book-equity for the sampled equities.
Table 3. Sorts on gross and operating profitability 1994-2016 Table 3 reports value-weighted excess returns and three-factor model alphas and MKT, SMB and HML loadings.The "High-Low" profitability spread portfolio is computed as long the highest profitability decile and short the lowest decile.We sort stocks into deciles based on TSE first section breakpoints at the end of each March and hold the portfolio for the August.Our sample period starts in August 1994 and ends in March 2016.
In the GP formulation, sorting portfolios' average excess returns are generally increasing with GP.Alphas for the Fama-French-three-factor model increase with GP, although not monotonically.The high-minus-low quintile portfolio earns a statistically insignificant average excess return of 10 basis points per month (t-value = 0.56).Alpha for the three-factor model is 26 basis points per month (t-value = 1.41).Loading for HML is negative significant.That reveals high gross-profit-to-book-equity portfolio generates more excess returns, meanwhile there exists negative relation between GP and B/M ratio.In the OP formulation, in contrast with GP, the high-minus-low quintile portfolio does not spread excess returns.
In fact, comparison reveals that a strategy of pursuing gross profitability generates more excess returns than pursuing operating profitability.

Construction of Mimicking Factors
Based on Novy-Marx ( 2013) and results for Table 3, we find that gross profitability is negatively correlated with book-to-market ratio.That reveals the profitability strategy is a growth strategy, and it provides a great hedge for value strategies.We can explore the performance of portfolios double-sorted by profitability and B/M ratio to generate more excess return.
For comparison, we sort GP-B/M portfolios, OP-B/M portfolios, Size-GP portfolios, and Size-OP portfolios for the sampled equities.Average excess portfolio returns appear.
Table 4 Panel A. Double sort by profitability and B/M Panel A shows average excess returns for 25 value-weighted (VW) portfolios, from independent (5x5 GP-B/M sorting), and (5x5 OP-B/M sorting).The "R-W" profitability spread portfolio is computed as long the most robust profitability decile and short the weakest decile.The "H-L" profitability spread portfolio is computed as long the highest B/M decile and short the lowest decile.We sort stocks into deciles based on TSE first section breakpoints at the end of each March and hold the portfolio for the August.Our sample period starts in August 1994 and ends in March 2016.
In the GP-B/M formulation, except in row 1, GP and average return are positively related in all remaining rows.R-W portfolios (gross profitability premium) in rows 3 and 5 are significant.Value premium is evident in columns 2 through 5. Large value and robust profitability portfolios perform best with 1.37% monthly returns.We confirm that controlling for GP improves performance of value strategies and controlling for B/M ratio improves performance of profitability strategies.
In the OP-B/M formulation, the R-W portfolio (operating profitability premium) is positive in rows 2,4,5.However, only in row 2 is significant.Value premium is effective in columns 2 through 4.
Panel A suggest that GP quintiles outperform OP quintiles.Panel B shows average excess returns for 25 value-weighted (VW) portfolios from independent (5x5 Size-GP sorting), and (5x5 Size-OP sorting).The "R-W" profitability spread portfolio is computed as long the most robust profitability decile and short the weakest decile.The "S-B" profitability spread portfolio is computed as short the biggest size decile and long the smallest decile.We sort stocks into deciles based on TSE first section breakpoints at the end of each March and hold the portfolio for the August.Our sample period starts in August 1994 and ends in March 2016.
In the Size-GP formulation, holding GP roughly constant, average return typically falls as size increases.Only the S-B portfolio (size premium) in column 4 is significant.Holding size roughly constant, average return typically increases with GP, but R-W portfolios (gross profitability premium) are not significant.That finding reveals Size-GP sorting underperforms GP-B/M sorting.In the Size-OP formulation, holding OP roughly constant, average return typically falls as size increases.Only the S-B portfolio (size premium) in column 4 is significant.Holding size roughly constant, average return typically increases with profitability.No R-W portfolio (operating profitability premium) is significant.That finding reveals Size-OP sorting underperforms OP-B/M sorting.
Overall, Panel B suggest value quintiles outperform size quintiles.Results in Table 4 suggest sorting of GP and B/M portfolios outperform among the sampled equities.

Summary of Factor Model
We eliminate redundant factors to boost the model's explanatory power.Based on Fama-MacBeth regressions and tests of combination portfolios, we define two main factor premiums: HML (high minus low B/M) and RMW (robust minus weak GP).If a characteristic is significant in cross-sectional regressions, we hypothesized that its factor will be significant in time-series regressions.Hence, we created a new model MKT-RMW(GP)-HML model for the sampled equities and compared time-series regressions with the Fama-French-three-factor model.Test factor models are ( ) Where: R it is the return of portfolio in month t.R Ft is risk free rate.α i is the intercept, b i , s i , h i , r i are factor coefficients for time-series regression, e it is the error term.
Following Fama-French (1993, 2015), to construct factor, we sort independently to assign stocks to two size groups, three B/M groups, and three profitability groups (GP).The Size breakpoint is median market cap.B/M or GP breakpoints are the 30th and 70th percentiles.
MKT (Rm-Rf ) is the value-weighted return on the market portfolio of all sampled stocks minus the risk-free rate.SMB is the return on a diversified portfolio of small-cap stocks minus the return on a diversified portfolio of big-cap stocks.HML is the difference between returns on diversified portfolios of high and low B/M stocks.In addition, RMW(GP) is the difference between returns on diversified portfolios of stocks with robust and weak gross profitability.

Evaluating Model Performance
Gibbons , Ross, and Shanken (1989) propose the most widely used statistical test of empirical validity for asset-pricing models (GRS test).It tests for the null hypothesis that the intercept terms of empirical asset-pricing model portfolios jointly equal 0. Failure to reject the null hypothesis is evidence the model adequately captures portfolio returns.Meanwhile, considering its predictive power properties, we follow Kim and Shamsuddin (2016), add to economic value to evaluate model performance.
The test models include a Fama-French-three-factor model and our MKT-RMW(GP)-HML factor model.The test samples include GP-B/M portfolios, OP-B/M portfolios, Size-GP portfolios, Size-OP portfolios, Size-B/M portfolios.
Table 5. Gibbons-Ross-Shaken Test (Gibbons et al., 1989;Kim & Shamsuddin, 2016) Table 5 reports results from the Gibbons-Ross-Shaken test (Gibbons et al., 1989).Comprehensively, the GRS P value indicates statistical significance.The bigger the P value, the greater the model performance.Economic value indicates proportion between the maximum sharpe ratio of the three factor portfolios and the slope of the efficient frontier based on all assets.The bigger the economic value, the greater the dual economic and market efficiency.For GRS P value, except 5x5 Size-B/M sorting portfolios, our MKT-RMW(GP)-HML factor model outperforms the Fama-French-three-factor model.For economic value, our MKT-RMW(GP)-HML model always provides optimum.Overall, we show our MKT-RMW(GP)-HML model outperforms both the statistical and economic significance for the sampled equities.

Conclusion
McLean and Pontiff (2016) argue that some stock market anomalies are less anomalous after being published.
Repeatedly cited size and value factors naturally are less anomalous over time.That also impels us to seek new effective factors and new-factor models.Our conclusions are as follows.
We find that gross profitability surpasses operating profitability and net income in power to predict returns on the sampled equities.This finding explains why Kuboda and (2017) and Maeda (2017) say profitability is not a significant factor in the Japanese equity market: they choose a flawed proxy for profitability.
As a measure of profitability, gross-profit-to-book-equity better the sampled cross-section of expected returns than operating profitability and net income.We extend Novy-Marx's (2013) intuition about focusing on gross profitability rather than current revenue and construct a measure of gross profit with a stronger link to expected returns on Japanese equities.
Size premium for the sampled equities shed predictive power over time and become redundant.Value premium remain strong among our sampled equities.Hence, we created a new MKT-RMW(GP)-HML factor model and investigated the applicability of a Fama-French-three-factor model on our sampled equities.Tests reveal that the model featuring gross profitability outperforms the Fama-French-three-factor model.

Table 2 .
Fama-MacBeth multivariate regressions of firm returns 1994-2016Multivariate slope coefficients (×100) βs and (t-statistics) from regressions are shown.We estimate regressions monthly spanning August 1994 to March 2016.t-statistics are based on the time-series variability of slope estimates, incorporating a white adjust for possible autocorrelation in the slopes.Fiscal year-end for more than 90% of firms in the TSE first section is March 31.Accordingly, sampled firms were sorted at the end of August each year, five months after fiscal year-end, to assure public availability.

Table 4
Panel B. Double sort by profitability and size