Does the Fama and French Five- Factor Model Work Well in Japan?*

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1 International Review of Finance, :1, 2018: pp DOI: /irfi Does the Fama and French Five- Factor Model Work Well in Japan?* KEIICHI KUBOTA AND HITOSHI TAKEHARA Graduate School of Strategic Management, Chuo University, Tokyo, Japan and Graduate School of Business and Finance, Waseda University, Tokyo, Japan ABSTRACT In this study, we investigate whether the five-factor model by Fama and French (2015) explains well the pricing structure of stocks with long-run data for Japan. We conduct standard cross-section asset pricing tests and examine the additional explanatory power of the new Fama and French factors; robust-minus-weak profitability factor and conservative-minus-aggressive investment factor. We find that robust-minus-weak and the conservativeminus-aggressive factors are not statistically significant when we conduct generalized method of moments (GMM) tests with the Hansen Jagannathan distance measure. Thus, we conclude that the original version of the Fama and French five-factor model is not the best benchmark pricing model for Japanese data during our sampling period from the year 1978 to the year I. INTRODUCTION To date, the Fama and French three-factor model has been considered adequate to explain the risk and return structure of stock data both for the USA (Fama and French 1993) and Japan (Jagannathan et al. 1998, Kubota and Takehara 2010). However, Fama and French (2015) claim that their five-factor model is superior to their original three-factor model (Fama and French 2015) for US firms with new and longer data from July 1963 to December This paper explores the plausibility of this five-factor model proposed by Fama and French (2015) to determine whether this new model explains the long-run data of Tokyo Stock Exchange firms from January 1978 to December We duplicate the original definitions of the new two factors by Fama and French (2015) in the context of financial statements disclosed by Japanese firms following Japanese GAAP and explore the explanatory power of their five-factor model when applied to Japanese data. We employ standard methodologies to choose the best asset pricing model (Hansen and Jagannathan 1997, Gibbons et al. 1989, Cochrane 2005, Kubota and Takehara 2015). * The authors acknowledge financial support from the Grant-in-Aid for Scientific Research ((A) ) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Hitoshi Takehara acknowledges financial support from the Grant-in-Aid for Scientific Research ((C) 15 K03690). All remaining errors are our own.

2 International Review of Finance The Section II defines the five-factor model as proposed by Fama and French (2015), and the Section III explains the data construction method. The Section IV reports the results of asset pricing tests, and the last section concludes. II. FORMULATION OF THE FAMA AND FRENCH FIVE-FACTOR MODEL The Fama and French three-factor model is composed of value-weighted excess market returns (abbreviated as MKT hereafter), size-related portfolio return spreads (referred to as the SMB factor), and book-to-market ratio (B/M)-related portfolio return spreads (also known as the HML factor). The basic Fama and French three-factor model can be written as follows. r jt r ft ¼ βi M r Mt r ft þ β SMB i SMB t þ βi HML HML t þ ε jt : (1) In equation ((1)), r jt is the return of security j in month t, r Mt is the return of the market portfolio, r ft is the risk-free rate, and SMB t and HML t are the Fama and French small-minus-big and high-minus-low factors in month t, and ε jt is the error term. Extant literature shows evidence that this three-factor model can well explain the cross-sectional variation of stock returns both in the USA and in Japan. However, the theoretical background of the SMB and HML factors has not been provided. For this reason, Fama and French (2015) extended their three-factor model based on the dividend discount model, and, at the same time, they tried to explain why the book-to-market is related to stock returns. Let MV j,t, d j,t, and r E,j denote firm j s market value of equity, dividend, and cost of equity capital and consider the following simple dividend discount model (2). d j;tþτ MV j;t ¼ τ (2) ¼1 1 þ r E;j Let Y j,t and BV j,t denote net income and book value of firm j and suppose that clean surplus relation (3) holds. ΔBV tþ1 ¼ BV j;tþ1 BV j;t ¼ Y j;t d j;t (3) Then, by combining model (2) and clean surplus relation (3), we obtain the following equation (4). τ Y j;tþτ ΔBV j;tþτ = 1 þ re;j MV j;t BV j;t ¼ τ¼1 BV j;t (4) Thus, book-to-market is a function of future profitability (=Y j,t+τ /BV j,t ), and investment (ΔBV j,t+τ ) and profitability and asset growth will be related to average stock returns

3 Fama and French Five-factor Model in Japan Fama and French (2015) define the measure of operating profitability, OP,as annual revenues minus the cost of goods sold, interest expense, selling, and general and administrative expenses during the previous fiscal year divided by the end book value of equity. The authors 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. 1 Then, Fama and French construct the size and OP-ranked six benchmark portfolios at the end of June of each year and compute the robust-minus-weak (RMW) profitability factor in a similar manner with the construction of the HML factor. Fama and French also construct size and INV-ranked six benchmark portfolios and conservative-minus-aggressive (CMA) investment factors. Adding two factors, RMW and CMA, to the three-factor model, gives the Fama and French five-factor model shown in equation (2). r jt r ft ¼ βi M r Mt r ft þ β SMB i SMB t þ β HML i HML t þ βi RMW RMW t þ β CMA i CMA t þ ε jt : There are other alternative multifactor models proposed by Kubota and Takehara (1997, 2010) and Hiraki et al. (2014) for Japanese data. However, the exploration of these models is outside the scope of this short study. Using macroeconomic variables, an alternative multifactor model using the CAPM with human capital was also proposed by Jagannathan and Wang (1996). The authors demonstrate that the CAPM cannot adequately explain the risk and return structure of US stocks, and the CAPM with human capital model performs as satisfactorily as the Fama and French three-factor model (Fama and French 1993). For Japanese data, Jagannathan et al. (1998) also find that the CAPM cannot explain the cross-sectional variations of stock returns adequately, and their CAPM with human capital is as satisfactory as the Fama and French threefactor model. Again, the investigation of this type of model is outside the scope of this research. (5) III. DATA CONSTRUCTION METHOD The source of the financial statement data was the Nikkei NEEDS Database provided by Nikkei Digital Media Incorporated. Stock returns and the market value of equity (MV) were retrieved from the NPM database provided by Financial Data Solutions Incorporated. The observation period was from January 1978 to December 2014, and we used monthly return series to measure stock returns, factor portfolio returns, and annual frequency data for financial statement data. 1 From equation (4), OP should be based on net income and INV on book value of equity. However, we define OP and INV as we explain here to make the empirical results comparable to those in Fama and French (2015)

4 International Review of Finance For the variable OP in this study, we used current earnings for Japanese data as a numerator divided by the end book value of equity and 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. We used current earnings because the current earnings number is widely used by financial analysts in Japan, and the only difference from Fama and French (2015) is that we include net interest received, which should eventually accrue to stockholders. To construct Fama and French s six benchmark portfolios and two other factors for the sample period, we used all firms listed in the first and second sections of the Tokyo Stock Exchange (TSE). The fiscal year-end for more than 90% of the firms listed on the TSE is the end of March. Accordingly, the sample firms were sorted at the end of August each year, which is five months after their fiscal year-end, to ensure the public availability of both the number of shares issued and the book value of equity data for investors. For the firms that did not have a March fiscal year-end, we used earlier data from their financial statements. At the end of August of each year t from 1977 through 2014, all firms listed on the TSE first and second sections were ranked by their size (=market value of equity, MV). Firms were also ranked by their BM, and the 30th and 70th percentiles of TSE first section firms were computed as data breakpoints. Using the median MV and the 30th and 70th percentiles of BM, the firms were divided into six size and BM-ranked groups, thus allowing for the formation of six value-weighted portfolios. The Fama and French factors, MKT, SMB, and HML were then computed by applying a method similar to that of Fama and French (1993). The RMW factor portfolio and the CMA factor portfolio were constructed in the same way as the HML factor portfolios using the 30th and 70th percentiles of TSE first section firms as computed by data breakpoints. For the risk-free interest rate, the monthly average of the overnight call-money rate without collateral as reported by Bank of Japan was used. Additionally, at the end of August for the years t = 1977,, 2014, firms listed in TSE first and second sections were sequentially sorted by their size and BM, and 15 (=3 5) equally weighted portfolios were constructed. 2 We also constructed size and OP-ranked 15 portfolios and size and INV-ranked 15 portfolios. Returns from these 45 portfolios (size-bm ranked 15 portfolios, size-op ranked 15 portfolios, and size-inv ranked 15 portfolios) were used in the asset pricing tests described in the next section. 3 2 We introduced sequential two-stage sorting to construct these 15 portfolios. In the first stage, we use one-thirds and two-thirds of the market value of equity as thresholds. Then, in the second stage, we use the 20, 40, 60, and 80 percentile of the BM (OP or INV) as thresholds. As a result, almost the same number of firms is included in each of the 15 portfolios. 3 Cochrane (2005, p.225) recommends keeping the number of test portfolios to less than 10% of the number of observations in the GMM test. Because we have 444 monthly observations (01/ /2014), the number of test portfolios, 45 in this study, approximately meets that condition. We also conducted a GMM test using size and BM ranked 25(=5 5) portfolios; however, the conclusion is not subjected to the difference of the test portfolios

5 Fama and French Five-factor Model in Japan IV. FACTOR RETURNS FOR JAPANESE DATA AND ASSET PRICING TESTS Before exploring the behavior of the five-factor model in Japan, we report the average returns from the 45 portfolios (size-bm ranked 15 portfolios, size-op ranked 15 portfolios, and size-inv ranked 15 portfolios), which are used as dependent variables in asset pricing tests, to investigate the operating profit effects and asset growth effects in Japan. Fama and French (1993) write that The bottom-line results in that two empirically determined variables, size and book-to-market equity do a good job explaining the cross-section of average returns on NYSE, Amex, and NASDAQ stocks for the period. (Fama and French 1993, p. 4). Thus, we first go back to Fama and French (1992) and examine whether the two new characteristics, OP and INV, can explain the cross-sectional return variations of Japanese stocks. Table 1 reports the average monthly realized returns from the 45 portfolios. First, we reconfirm the existence of strong value effects in Japan. For largeand medium-sized stocks, return spreads (P1 P5) are very high at and 0.826% per month, and they are statistically significant at the 5% level. By contrast, OP seems unrelated to the stock returns. We observe no clear tendency between OP and stock returns in Table 1, and the magnitude of return spreads are relatively small and not significant without exception. Finally, as for firms Table 1 Average returns from 45 portfolios Size and B/M ranked 15 portfolios P1 (High) P2 P3 P4 P5 (Low) Diff. p-value Large Mid Small Size and OP ranked 15 portfolios P1 (Robust) P2 P3 P4 P5 (Weak) Diff. p-value Large Mid Small Size and Inv ranked 15 portfolios P1 (Aggressive) P2 P3 P4 P5 (Conservative) Diff. p-value Large Mid Small Average monthly returns of size-b/m, size-op, and Size-INV ranked 15 portfolios. Numbers in column Diff. are average return spreads (P1 P5), and their corresponding probability values in Welch s two-sample t-test are reported in column p-value. The sample period is from January 1978 to December

6 International Review of Finance investments (INV), they are negatively related to stock returns, as Fama and French expected. However, we can expect only limited effects on the stock market as the return spreads are significant only in medium and small capital categories. To put it more succinctly, the two new variables, OP and INV, cannot explain the cross-sectional variation of Japanese stock. Thus, the validities of the RMW and CMA factors constructed using OP and INV are questionable. Table 2 reports the basic statistics of the factors we used for the final factor model tests with four and five-factor models. In Panel A, we report the basic statistics, and, in Panel B, we report the correlation numbers among these candidate five factors. The observation period of our monthly data was January 1978 through December The numbers reported are in percentages, and for the excess market return, MKT, the average monthly return is 0.314%, which is equivalent to 3.768% per annum. All the factor returns have positive average values except the operating profit factor, RMW, with 0.088%. For the standard deviation, MKT shows the highest variability. We also report the 25th percentile, the median, and the 75th percentile figures in the right-hand four columns. For the median, we find that the RMW factor is positive in contrast with the mean. Otherwise, the differences between the means and medians are not substantial. Panel B reports the correlation numbers between the five factors. The lower-left Table 2 Descriptive statistics of the Fama and French five factor model Panel A. Summary statistics Mean (p-value) SD 25%ile Median 75%ile MKT SMB HML RMW CMA Panel B. Correlation matrix among the Fama and French five factors MKT SMB HML RMW CMA PRC PRC PRC PRC PRC PRC PRC MKT, excess returns from the value-weighted market index; SMB, small-minus-big factor; HML, high-minus-low factor; RMW, robust-minus-weak factor; CMA, conservative-minus-aggressive factor. Mean is an arithmetic average of monthly return from factors (in %), and p-value is a probability value from Student s t-test in which the null hypothesis is the arithmetic average of the risk factor equal to zero. SD is a standard deviation of risk factors. 25%ile,, median, and 75%ile denote the 25 percentile, median, and 75 percentile of risk factors, respectively. In Panel B, Pearson correlations among the five factors are shown in the lower-left triangular part of the matrix, and Spearman rank correlations are shown in the upper-right triangular part

7 Fama and French Five-factor Model in Japan triangular part reports Pearson correlations, and we find CMA is positively correlated with HML at and RMW is negatively correlated with HML at Table 3 reports the correlation between the five factors and the first seven principal components estimated from the returns of individual securities listed during the observation period from the year 1978 to the year We find that the first principal component has high correlations with MKT at and SMB at The second principal component is correlated with CMA and RMW at and 0.322, respectively. The third principal component is correlated with SMB and MKT at and 0.414, respectively. The fourth principal component is correlated with SMB at However, surprisingly, the HML factor is not highly correlated with principal components except for the second principal component at 0.304, which is also correlated with CMA and RMW. Table 4 reports the results from Fama & MacBeth (1973) regressions in which we test the following multi-beta model (6). r j r f ¼ γ 0 þ γ 1 β MKT j þ γ 2 β SMB j þ γ 3 β HML j þ γ 4 β RMW j þ γ 5 β CMA j þ ε j : (6) Table 3 Correlation between statistical factors and the five factor model MKT SMB HML RMW CMA PRC PRC PRC PRC PRC PRC PRC MKT, excess returns from the value-weighted market index; SMB, small-minus-big factor; HML, high-minus-low factor; RMW, robust-minus-weak factor; CMA, conservative-minus-aggressive factor. PRC1 through PRC7 are the first seven principal components computed using the returns of individual securities from January 1978 through December Table 4 Results of Fama and MacBeth regressions (1) (2) (3) (4) Intercept (γ0) 1.381*** MKT (γ1) 0.769* SMB (γ2) ** HML (γ3) 0.819*** 1.151*** RMW (γ4) CMA (γ5) 0.529*** Adjusted R γ 0, γ 1, γ 2, γ 3, γ 4, and γ 5 are estimated risk premium for betas. The sample period is from January 1978 through December 2014 (444 months). The dependent variables are returns from 45 test portfolios (which are based on Size-B/M ranked 15, Size-OP ranked 15, and Size-INV ranked 15 portfolios). ***Significant at 1%. **Significant at 5%. *Significant at 10%

8 International Review of Finance The test reveals the factors that are priced among candidate five factors and reports the overall fitness of the model. The MKT is not significant except for the CAPM and the coefficient is negative. However, the evidence is consistent with previous evidence on TSE firms (Jagannathan et al. 1998). The HML beta is significant with positive coefficients for the Fama and French three-factor and five-factor model. However, the coefficients on the SMB beta are all positive while significant only for the four-factor model in which the HML beta is replaced by RMW and CMA betas. We report the results from this four-factor model because Fama and French (2015) find that this four-factor model performs as well as their five-factor model, and we attempt to confirm that this is true for Japanese data also. The significance of the SMB factor, however, can be found only for this four factor model, and the overall HML beta is robust in explaining the cross section of stock returns for Japan. After dropping the HML beta, SMB beta re-emerges again as a strong explanatory variable because the other two factors, RMW and CMA, are not strong explanatory variables judging from the decrease in adjusted R-squared values to 0.678, while the coefficient for CMA is significant. For five-factor models, however, these new two factors are not significant and the sign of the slope for the CMA beta changes to an incorrect negative sign. Table 5 reports the results from a GMM test in which we test the Euler condition (7). E r p;t r f ;t 1 þ δ1 r M;t r f ;t þ δ2 SMB t þ δ 3 HML t þ δ 4 RMW t þ δ 5 CMA t ¼ 0: (7) In the above pricing equation (7), we judge the fitness of the model with Hansen and Jagannathan distance measure (Hansen and Jagannathan 1997). For the distance measures, the Fama and French five-factor model shows the shortest distance at Hansen Jagannathan distance for the Fama and French three-factor model is 0.346, which is much smaller than that of the four-factor model at for which HML is dropped from the five-factor model. Contrary to the case for US data, we find that the four-factor model is inferior to the three-factor model, and HML is not a redundant factor in Japan. Table 5 Results of GMM tests (1) (2) (3) (4) MKT (δ1) ** 1.951** 1.932** SMB (δ2) HML (δ3) 8.052*** 8.316*** RMW (δ4) CMA (δ5) 4.268* HJ-Dist 0.410*** 0.346* 0.396*** 0.345** In the table, δ 1, δ 2, δ 3, δ 4, and δ 5 are the parameter values in equation (7) of the main text. HJ-Dist denotes the Hansen Jagannathan distance measure. The significance level of the coefficients and the significance level of the Hansen and Jagannathan distance measure for the GMM test are shown in the table. In the GMM test, T = 444, N = 45, and K =1,3,4,5.Thep-values are computed by numerically generating χ 2 (1) values 10,000 times. ***Significant at 1%. **Significant at 5%. *Significant at 10%

9 Fama and French Five-factor Model in Japan Table 6 Results of Gibbons Ross Shanken tests Model CAPM Three-factor model Four-factor model Five-factor model Factors MKT MKT + SMB + HML MKT + SMB + FF3 + RMW + CMA RMW + CMA GRS F-value p-value GRS F-value denotes Gibbons Ross Shanken (1989) s test statistic for mean variance efficiency, and the p-value denotes its corresponding probability values. For the three-factor model, the MKT and HML coefficients show correct negative signs (Jagannathan and Wang 1996). For the four-factor model, CMA is significant at the 10% level and, for the five-factor model, HML is significant at the 1% level, thus deleting the significance of RMW and CMA factors. Null hypothesis of zero pricing error is rejected in all candidate models. Table 6 reports the results from the Gibbons Ross Shaken test (Gibbons et al. 1989). We find all candidate models are rejected in this mean variance efficiency test as was the case in Fama and French (2015) for US data. However, the test statistic is at the minimum for the Fama and French five-factor model at 9.447, and the three-factor model was the next best at 9.491, which implies that the simpler three-factor model functions at a similar level as the five-factor model. The test statistic of the four-factor model is high at 9.988, and it is at almost the same level as that of the CAPM at Although the four-factor model is suitable for the USA and functions as well as the five-factor model (Fama and French 2015), we conclude the performance of the four and five-factor models are inferior to the three-factor model for Japanese data in terms of model simplicity and significance of the coefficients. V. CONCLUSIONS We investigated whether the five-factor model by Fama and French (2015) can adequately explain the pricing structure of long-run stock data for Japan. We find that the historical averages of these new two factors are not large and are statistically insignificant, which is contrary to the evidence for the US by Fama and French (2015). From the asset pricing tests, we find that both the RMW betas and the CMA betas are weakly associated with the cross-sectional variations of stock returns, which is significantly different from the US evidence. Finally, we demonstrate that the coefficients of these two factors are not statistically significant when we conduct GMM tests with the Hansen and Jagannathan distance measure. We conclude that the Fama and French five-factor model, or their four-factor model, which fits US data, cannot be an adequate benchmark pricing model for Japanese data during our sampling period from the year 1978 to the year Further out-of-sample tests, as in Lewellen (2015), are subjects for future research

10 International Review of Finance Hitoshi Takehara Graduate School of Business and Finance Waseda University Shinjyuku-ku Tokyo Japan REFERENCES Cochrane, J. (2005), Asset Pricing, Revised Edn. Princeton, NJ: Princeton University Press. Fama, E. F., and K. R. French (1993), Common Risk Factors in the Returns on Stock and Bonds, Journal of Financial Economics, 33(1), Fama, E. F., and K. R. French (2015), A Five-Factor Asset Pricing Model, Journal of Financial Economics, 116(1), Fama, E. F., and J. MacBeth (1973), Risk, Return, and Equilibrium: Empirical Tests, Journal of Political Economy, 81(3), Gibbons, M., S. Ross, and J. Shanken (1989), A Test of the Efficiency of a Given Portfolio, Econometrica, 57(5), Hansen, L. P., and R. Jagannathan (1997), Assessing Specification Errors in Stochastic Discount Factor Models, Journal of Finance, 52(1), Hiraki, T., Watanabe A., and Watanabe M. (2014). The Investment Value of Earnings Forecasts, SSRN Working Paper, Abstract=id Jagannathan, R., K. Kubota, and H. Takehara (1998), Relationship between Labor Income Risk and Average Return: Empirical Evidence from the Japanese Stock Market, Journal of Business, 71(1), Jagannathan, R., and Z. Wang (1996), The Conditional CAPM and the Cross-Section of Expected Returns, Journal of Finance, 51(1), Kubota, K., and H. Takehara (1997), Common Risk Factors of Tokyo Stock Exchange Firms: Finding Mimicking Portfolios, in T. Boss and T. Fetherston (eds), Advances in Pacific Basin Financial Markets, Vol. 3. Greenwich, CT: JAI Press, Inc., pp Kubota, K., and H. Takehara (2010), Expected Return, Liquidity Risk, and Contrarian Strategy: Evidence from the Tokyo Stock Exchange, Managerial Finance, 36(8), Kubota, K., and H. Takehara (2015), Reform and Price Discovery at the Tokyo Stock Exchange: From 1990 to NYC, NY: Palgrave-Macmillan. Lewellen, J. (2015), The Cross Section of Expected Stock Returns, Critical Finance Review, 4(1),