New Evidence on the Applicability of Fama and French Three-Factor Model to the Japanese Stock Market.

Transcription

1 New Evidence on the Applicability of Fama and French Three-Factor Model to the Japanese Stock Market. Elhaj Mabrouk Walid * Elhaj Mohamed Ahlem ** Abstract: This paper investigates the applicability of the Fama and French (FF) three-factor model to size and Book-to-Market (BM) characterized-sorted portfolios from the Japanese stock market over a recent daily data set from 00 to 007, which is not addressed on the existing literature. The new results are derived from the generalized method of moments (GMM). There is evidence that both the firm size and book-to-market ratio are negatively and positively significantly related to average return premiums. The intercepts from the regression over FF model and CAPM, as cross-check model, suggest better applying the first model over all the portfolios except those grouping stocks of value and small market capitalization. Moreover, the analysis gives stronger support to FF model rather than the CAPM as more reflective of the return dynamics in the Japanese stock market. Keywords: Fama-French three-factor model, CAPM, Size, Book-to-Market, Japanese Stock Market JEL Classifications: G10, G1 The Authors thanks all of the members of Nishina Seminar, Pr.Kanemi Ban, and Pr.Wee Yeap Lau for extensive discussion on issues rose in this paper and for substantive suggestions for improving this paper. Finally, we acknowledge the financial support for this project from MEXT (Ministry of Education, Culture, Sports, Sciences and Technology, Japan). * Graduate School of Economics, Osaka University, Japan, 1-7 Machikaneyama, Toyonaka, -Osaka Japan. Phone/Fax: egb008mw@mail.econ.osaka-u.ac.jp ** Faculté de Droit et des Sciences Politiques et Economiques de Sousse, Cité Erriadh-403, Sousse, Tunisia. 1

2 1. Introduction: The financial professional and academic surroundings have identified during the last thirty years, several variables susceptible to allow some investors to construct profitable investments strategies: size, book value over market value (book-to-market ratio), price earning ratio (PE), price cash flow ratio, long term returns, short term returns (momentum strategies), etc. These variables are generally considered as many of the market anomalies. Among these anomalies, two occupy our attention: size and BM. According to Fama and French (199), the associated risk premium of the size and BM variables is easily measurable, significantly negative and positive, respectively, whereas the systematic risk premium is null. In other words, when some portfolios are constructed based on firm size sorting (measured by the market capitalization), the return of small size firms is significantly more high than the one of big size firms. At the opposite, when BM ratio sorted portfolios are constructed, the return of stocks called of value (High BM) is more significant than the one of stocks called of growth (small BM). However, there is no difference between the significant returns of the different portfolios sorted based on market risk, this contradicts the CAPM. Based on these results, Fama and French (1996) construct a model in which they added to the excess market return (CAPM) two supplementary risk factors related to the firm size and the BM ratio. This model is the FF three-factor pricing model (TFPM). Comparing the capacity of the unconditional form of the CAPM, the FF model explains return difference among portfolios built on a set of variables, Fama and French conclude that most of the market anomalies disappear once the risk associated to the firm size and BM ratio are taken into account. It should be also noted that earlier evidence on the Japanese stock market from Kubota and Takehara (1997) on a monthly data set from 1981 to 1993 indicates that the FF three-factor model captures well the common risk factors for individual stocks listed on the First Section of Tokyo Stock Exchange. Whereas, our study focuses on the capacity of FF model to capture common risk factors in size and BM characterized-sorted portfolios. Besides, the question remains as to whether this evidence on the FF model is still significant over more recent period from 00 to 007, following the Japanese economic recession. This paper is structured as follows. In the second section, we examine the returns based on the firm s market capitalization and the BM ratio in the Japanese stock market, on the period from the 1 st of October 00 to the 30 th of September 007. In the third section, following Fama and French (1996), we construct two risk factors related to the firm size and BM ratio. We examine the return and the risk associated to these two factors. In the fourth section, we derive the potential from the applicability of the TFPM that may be

3 useful and appropriate for the professional and academic community in finance. Finally, we conclude the paper.. Empirical Framework:.1 Data: In this paper, we are using daily data set of all stocks listed on both first and second section of the Tokyo Stock Exchange (TSE) 1 along five year period, from the 1 st of October 00 to the 30 th of September 007. The daily data sets of Price Book ratios (P/B ratios), market capitalization (size), and closed stock prices including dividends are obtained from the Nikkei Economic Electronic Databank System (NEEDS). The daily Gensaki rate is used as proxy for the risk-free rate. This data is also collected from the NEEDS data base. Following Daniel, Titman and Wei (001), it is assumed that the financial results are publicly available before the end of September. Indeed, most Japanese firms listed on the first and second sections of the Tokyo Stock Exchange are required to publicly announce their financial results within the time period starting from the end of the fiscal year in March through September. Therefore, portfolios are constructed on the first trading day of October and held for the subsequent year. For each firm, the average BM ratio is calculated using observations from April of year t 1 to March of yeart. Similarly, the average logarithm of size is estimated using prices from the beginning of October of year t 1 to the end of September of yeart. This measurement procedure allows for the construction of portfolios at the beginning of October in each year.. The size: To take into consideration the relation between firm-size and its ex-ante weighted excess returns, we sort every year, at the end of September, five portfolios constructed on the basis of firms market capitalization. Subsequently, we compute excess weighted daily returns of each portfolio. The first portfolio (Small size) groups stocks with the smallest market capitalization and the fifth portfolio (Big size) groups equities with the biggest market capitalization. Panel A of Table I shows a negative and perfectly monotonous relationship between the market capitalization and portfolios excess returns. The difference between average daily excess returns of the first portfolio (Small size) and the fifth (Big size) is of 1 Firms were delisted from the sample when they were subject to non-continuous price quotation for more than three consecutive days. Previously Daniel et al (001) and Chiao and Hueng (005) used 30-day gensaki rates as a proxy for the risk-free rate on a Japanese data set.. 3

4 0.054% per day. This important difference is nevertheless reduced by less than the half Table I: Descriptive Statistics on Average Weighted Daily Excess eturns of five Portfolios Constructed through Sorting their Market Capitalization and Book-to-Market atio. At the end of September of every year, firms are sorted out in 5 groups according to their market capitalization (Panel A) and at the end of March according to their Book-to-market ratio (Panel B). Average weighted daily excess returns are calculated for every portfolio from the 1 st of October of year t to the 30 th of September of year t+1. Test statistics are computed as follows: Mean daily excess returns * number of observations ^ 0.5 / Standard Deviation. Panel A: Size Mean (%) Std (%) t statistic.4** 1.80* 1.67* Panel B: Book-to-Market Mean (%) Std (%) t statistic *.10**.07**.7** *, **, *** show the level of signif icance at 1%, 5%, and 10%, respectively. when it crosses to portfolio two. Therefore, the effect of size on excess returns is principally attributable to portfolios with the smallest market capitalization. The volatility exam linked to these portfolios is also informative. In fact, the relationship between market capitalization and standard deviation is negative. The volatility of the first portfolio is about 4% superior to that of the fifth portfolio. The portfolio composed of stocks with small market capitalization is, therefore, much more lucrative, but encloses more risk (high volatility). In order to take into account risk and return at the same time, we perform a test to assess if the returns are statistically significant, different from zero. This test proves that the returns linked to portfolio one are indeed at 95% confidence level, while those of big size firms are only at less than 90% confidence level..3 Book-to-market ratio: We proceed to analyze the relationship between BM ratio and average excess returns through computing the average daily excess returns of the five BM sorted portfolios. The first portfolio (Low-BM) groups stocks with small BM ratio (called of growth) and the fifth 4

5 portfolio (high-bm) is composed of stocks where the BM ratio is high (called of value). Table II: Descriptive Statistics on Average Weighted Daily Excess eturns of 5 Portfolios Constructed through Sorting their Market Capitalization and Book-to-Market atio. The 5 portfolios are constructed at the breakpoints of portfolios formed independently on the basis of the market capitalization and on Book-to-market ratio. Test statistics are calculated as follows: Mean daily excess returns * number of observations ^ 0.5 / Standard Deviation. Book-to Market Low High Size Mean (%) Small Std (%) t statistic 1.97**.84***.71***.64*** 3.08*** Mean (%) Std (%) t statistic **.4**.78*** 3.16*** Mean (%) Std (%) t statistic **.7***.10**.99*** Mean (%) Std (%) t statistic **.5**.18** 1.50 Mean (%) Big Std (%) t statistic **.03**.44** 1.59 *, **, *** show the level of s ignificance at 1%, 5 %, and 10%, respectively. Panel B of the table I shows a strictly monotonous and positive relationship between the BM ratio and excess returns. The total variation between average daily excess returns of high BM and low BM portfolios is of 0.037%. This variation is weaker than in the case of size grouping. In addition, unlike portfolios formed on the basis of market capitalization, more than 70 percent of this difference is assigned to the two portfolios on the extremities. In fact, the difference between portfolio two and one is 0.0% and that between the portfolio five and four is 0.008%. The return volatility of the portfolio of low BM is the highest (1.3%). There is no clear relationship between the BM ratio and standard deviation: the volatility of portfolio two 5

6 and five is of the same range. The comparison of the statistical tests associated to various BM sorted portfolios does not bring out a relationship as clear as in the case of market capitalization grouping. However, stocks with high BM ratio are more competitive..4 Excess returns, size and BM: Table I encloses separately the characteristics of returns of portfolios sorted through market capitalization and/or BM ratio. This paragraph considers jointly the size and BM dimensions. In table II, we carry out two independent sorting and form five portfolios on the break points of the market capitalization and five others on the break point of BM ratio. The combination of these portfolios allows building twenty-five portfolios. The excess return of the portfolio sorted of firms with small market capitalization and high BM ratio is relatively high with 0.117% per day. Contrary, the average excess return of the portfolio sorted of stocks with big market capitalization and low BM ratio is weak of 0.049% per day. The difference in excess return between the two portfolios is important, that is to say of 0.068% per day. The results above show that equity return is influenced by risk factors other than of the market. Starting from this observation, it is then possible to build a normative model which will replace the CAPM to evaluate the performance of portfolios and to estimate the equity cost of firms. It is the objective of the following section. 3. Market anomalies: 3.1 The three-factor pricing model: For Fama and French, the size and BM effects represent a risk premium. The weak market capitalization can be linked to the lack of liquidity and information. The BM ratio is associated to a financial distress indicator. In fact, the firms whose BM ratio is high (weak) are generally more small (strong) and are characterized by more (less) important profits. According to Fama and French, investors would require compensation to cover additional risk incurred from holding small size stocks of high BM ratio, whereas they would accept a discount for the big size stocks of high BM ratio. Thus the equity return should not only be explained by the market risk premium, as the CAPM conceives it, but also by the two other risk factors, the first related to the firm-size and the second related to the BM ratio. Fama and French (1996) TFPM model captures the majority of the differences in return between portfolios formed on the basis of various 6

7 criteria, they conclude that firm-size and BM ratio correspond to variables that are evaluated by the market. In particular, Fama and French three-factor model can be expressed for each asset i as follows. it ft = i + bi ( mt ft ) + si SMB, t + hi HML, t α Eq (1) where it ft is the realized excess return of asset i at time t, Mt ft is the excess market return, SMB, t is the realized return on the size-factor portfolio, HML, t is the return on the BM-factor portfolio, and b i, si, and h i are coefficients of sensitivity of the different forms of risk. Equation (1) can be estimated from the set of assets, the number of which n is assumed to be significantly larger than the number of factors. The empirical tests of equation (1) focus on the interceptsη which are expected to be insignificant. The construction of the factor portfolios follows the methodology proposed by Fama and French (1993). All stocks are ranked on the basis of BM and size values and portfolios are constructed using the 30 percent and 70 percent breakpoints for the BM and 50 percent breakpoint for size. The three book-to-market groups including stock below 30 percent breakpoint, above 70 percent breakpoint, and medium 40 percent are referred to as L, H and M portfolios, respectively. With respect to size, stocks that are below and above the 50 % breakpoint are referred to as S and B, respectively. The combination of these two size-groups and three capitalization-groups results in six value-weighted portfolios SL, SM, SH, BL, BM and BH, the returns of which are denoted as SL, SM, SH, BL, BM, and BH, respectively. Thus, the returns on the size-factor portfolio, which is neutral with respect to book-to-market, are measured as the difference between the equal-weighted averages of the returns on the three small stock portfolios and the three big stock portfolios SMB = ( SL + SM + SH BL BM BH ) / 3. The returns on the BM-factor portfolio, which is neutral with respect to size, can be computed as difference between the averages on the two high book-to-market portfolios and the two low book-to-market portfolios = ( + ) / BL. HML SH BH SL 3. isk and return from risk factors: Panel A of Table III describes returns of the three risk factors over the period from 1 st October 00 to 30 th of September 007. The average daily market premium is 0.03%. With a relatively high volatility, it does not significantly differ from zero at 99% degree of confidence, but only at 95%. The daily premium linked to the SMB risk factor is 0.046%. It is significant at 99% degree of confidence. The SMB portfolio is much less risky than 7

8 Table III: Descriptive Statistics elated to the Three isk Factors ( m f, SMB, and HML ) Over the Period From the 1 st of October 00 to the 30 th of September 007. m represents the market return calculated out of our sample. f represents the risk-free rate. SMB represents the return of the portfolio in which firms of small market capitalization are detained and those of big market capitalization are shortly sold. HML represents the return of the portfolio in which firms with high Book-to-Market ratio are detained and those with low Book-to-market are sold. Test statistics are calculated as follows: Average daily returns / Standard error. Panel A: Daily mean returns m f SMB HML Mean (%) Std (%) t statistic.15** 3.70***.1** % Positive Panel B: Correlations m f SMB HML m f 1 SMB HML *, **, *** show the level of significance at 1%, 5%, and 10%, respectively. the excess market return: 0.51% and 0.44%. The daily premium associated to the HML risk factor is almost the double of that associated to the market risk factor, 0.060%. It is also significant at 95% degree of confidence. The HML portfolio has the highest level of risk and excess return. In fact, on a five-year period of time, it appears clearly that market return premium is positive in 57% of the cases, the SMB factor in 54% of the cases and the HML factor in 56% of the cases. Panel B of Table III presents the correlations between risk factors. The correlation coefficients are weak. The correlation between the market premium and the SMB risk factor is diminutive and positive. However, the correlation between HML risk factor, market premium and SMB risk factor is negative. This negative correlation is interesting for any kind of investment strategy which would combine the SMB and HML risk factors. The correlation between the HML and SMB is only Hence, the HML factor appears to provide a measure of the BM premium comparatively free of the size effect, and the SMB factor provides a measure of the size premium free of the BM effect. 8

9 4 Performance of the three-factor pricing model: Jensen (1968) was the first to notice that the Sharpe-Lintner version of the relation between the expected return and market beta implies a time-series regression. The Sharpe-Lintner version of the CAPM says that the average value of an asset or a portfolio s excess return is completely explained by its average realized market risk premium. This implies that Jensen s alpha, the intercept term in the time-series regression, it = α + β ( ) + ε, Eq () ft i i Mt ft it is zero for each asset or portfolio. Normally, to measure performance of an asset pricing model we use the coefficient Jensen-alpha estimated from time-series regression of portfolio excess return on market excess return. Indeed, according to the CAPM, this coefficient measures abnormal performance, in other term, measures abnormal return not explained by the market risk. We expect the intercept term to be significantly different from zero and thus confirm that the CAPM will not be the correct pricing model to use in Japan, Kobota and Takehara (1997, 003). The preceding results in table III show that risk premiums associated to size and BM ratio are higher than of the market. Thus, it must be more suitable to estimate cost of equity using the TFPM. With this intention, it is necessary to proceed in the same way as in the case of CAPM, we make time-series regression using GMM method of portfolios excess returns on the three risk factors. We expect Fama and French model to be highly advisable for practitioners than CAPM model. It is to notice that earlier evidence on the Japanese stock market from Kubota and Takehara (1997) indicates that the Fama-French three factor model captures well the common risk factors in Japanese stocks. However, it s rational to think that past performance is not a guide to future performance. For that reason, we should reconsider re-examining Fama and French model s applicability and performance over recent sample period. Estimates of α from the time-series regression of Eq(1) and Eq() over twenty-five i size and BM sort ed portfolios will be used to calibrate how rapidly stock prices respond to new information; Loughran and itter (1995), Mitchell and Stafford (000). The results of the GMM estimation of intercepts using both the CAPM and the TFPM models are presented in table IV. The TFPM alpha coefficients illustrated in Panel A of table IV show that the abnormal performances of portfolios computed from the TFPM are relatively lower than those computed from the CAPM, in most of the cases. This result lends support to the evidence that firm size and BM ratio absorb more additional risk effect into average returns and that it s advisable to use TFPM model. 9

10 Table IV: Time-Series egressions of the 5 Size and Book-to-Market Sorted Portfolios: 1st of October 00 to 30th of September 007. On the left side of this table we present intercepts in percentage and their t-statistics in brackets and on the right side we present the s from the CAPM and the TFPM time-series regressions on the 5 size/bm sorted portfolios. Panel A: Intercepts estimates (t-statistic) and from the TFPM model Size Book-to-Market Book-to-Market Low High Low High Small (0.57) (-1) (-0.77) (-0.43) (.17)** (1.8)* (1.15) (1) (1.3) (.71)*** (1.94)* (0.34) (1.6) (1.17) (1.78)* (1.3) (1.1) (0.7) (0.3) (0.89) Big (1.7)* (0.98) (0.13) (-1.01) (-0.13) Panel B: Intercepts estimates (t-statistic) and from the CAPM model Size Small (0.67) (-0.60) (-1.37) (-.0)** (-1.1) (.31)** (1.57) (0.77) (0.66) (0.57) (.64)*** (1.36) (1.93)* (0.9) (1.1) (.36)** (.7)*** (1.3) (0.87) (1.7) Big (3.56)*** (3.04)*** (.03)** (-0.34) (0.7) *, **, *** show the l evel of significance at 1%, 5%, and 10%, r espectively. It also appears from Tab le IV tha t the intercepts of low book-to-marke t ratio a nd big market capitalization (big cap) portfolios are statistically significant and higher when regressed with CAPM than Fama and French model. Whereas those of high book-to-market ratio and small market capitalization (small cap) portfolios are statistically significant and higher when regressed with Fama and French model than CAPM. This result does not give, for the moment, credibility to neither of the two models. In Fact, The TFPM model considers that value and small cap stocks outperform markets on a regular basis. By including the size and BM factors, the model adjusts for the outperformance tendency, which is thought to make it a better tool for evaluating cost of equities. However, we find that the performance of portfolios with small cap and high BM tend likely to be better outperformed through the CAPM than TFPM. Following our expectations, we find that portfolios made of big cap and growth stocks are more outperformed through the TFPM than CAPM. However, for most of 10

11 the cases, the intercept, used as an evaluation tool, is lower for Fama and French model than CAPM, lending further support to Fama and French model. In fact, market participants mispricing the value of stocks vis-à-vis their size-bm characteristics and the lack of financial risk management may explain the performance of the TFPM over the CAPM in expressing excess return variations. It is also possible to obtain evidence on whether the TFPM or CAPM is more reflective of average excess returns observing the list of coefficients of determination ( ) in the right side of Panel A and B of table IV. The is used to determine the estimate, and significance of the coefficients estimates in Eq (1) and Eq(). The s obtained from the estimate of TFPM are higher in all twenty five portfolios than those derived through the estimate of CAPM. This result approves that the TFPM is better debriefing the evolution of stock returns than the CAPM. This also approves the reason that made Ibbotson Associates Japan 3 and many other Japanese security brokerage firms use the TFPM as an alternative to the CAPM for estimating the cost of equities. 5. Conclusion: 3 Ibbotson Associates is a leading authority on asset allocation with expertise in capital market expectations and portfolio implementation. Approaching portfolio construction from the top-down through a research-based investment process, its experienced consultants and portfolio managers serve mutual fund firms, banks, broker-dealers, and insurance companies worldwide. 11

12 This study shows that there exists in Japan monotonous negative and positive relationship between, on one hand, firm size and stock returns and, on the other hand, BM ratio and stock returns, respectively. However, this relationship established during five year period is not continuously linear. The size effect appears principally in portfolios made of stocks of weak market capitalization. The BM ratio effect appears mainly in the two extreme portfolios. When these two dimensions are combined, this relationship with excess return is less clear, but it remains that portfolios characterized by a bias in favor of firms of small size and high BM ratio dominate portfolios characterized by a bias in favor of firms of big size and low BM ratio. ratio, which are added to the excess market return to constitute a model with three factors: the We build like in Fama and French (1996) two risk factors related to firm size and BM three-factor pricing model (TFPM). It arises from this analysis that the premiums associated to the size factor and BM ratio are respectively equal to 0.046% and 0.060% per day and are higher than the ones associated to the market premium (0.03% per day). This result lumped together all raisons for using the TFPM over the CAPM to estimate cost of equities. The tests preformed over the TFPM and CAPM using the GMM method reveal that the majority of intercepts on the twenty-five book-to-market and size groupings are not significant and relatively low when estimated with TFPM. However, the s obtained from the TFPM are higher in all twenty five portfolios than those derived through CAPM. In fact, this lends stronger support in favor of the TFPM over the CAPM. Our results provide a new insight over the CAPM and TFPM effectiveness over portfolios of Size and BM characteristic groupings. The question remains to whether characteristics and/or risk factor betas are reflective of return dynamics. Future avenues for research may include also volatility spillovers on the characteristics and cross-sectional behavior of returns on domestic stocks. 1

13 eferences: Daniel, K,. Titman, S. and John Wei, K.C., (001), Explaining the cross-section of stock returns in Japan: Factors or characteristics?, Journal of Finance, Vol. 56, No., pp Fama. E.F. and K.. French. (199), The cross-section of expected stock returns, Journal o f Finance, 47, Fama, E.F., and K.. French, (1996), Multifactor explanations of asset pricing anomalies., Journal of Finance, 51, Loughram, Tim and Jay.. itter. (1995), The New Issues Puzzle, Journal of Finance, 50/1, Mitchell, Mark L. and Erik Stafford. (000), Managerial Decisions and Long-Term Stock Price Performance, Journal of Business, 73/3, Jensen, Michael C. (1968), The performance of mutual funds in the period , Journal of Finance, 3/, Jensen, G.., Johnson,.. and Mercer, J. M. (1997), New evidence on size and price-to-book effects in stock returns, Financial Analysts Journal, Nov/Dec, Kubota, K., and H. Takehara, (1997), Common risk factors of Tokyo stock exchange firms, Advances in Pacific Basin Financial Markets, JAI Press, Vol., pp Kubota, K., and H. Takehara, (003), eturn on Equity, the Cost of Capital and Income Taxation: Evidence from the Japanese Industries Working paper, Tsukuba University. 13