Examination of Fama-French Five-Factor Model by inclusion of corporate variables

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1 Examination of Fama-French Five-Factor Model by inclusion of corporate variables Ali Asghar Anvary Rostamy Professor of Finance, Tarbiat Modares University, Tehran, Iran Shahla Rowshandel Phd Candidate of Finance Management, Islamic Azad University Dubai Branch, United Arab Emirates Iraj Noravesh Professor of Accounting, Tehran University, Tehran, Iran Roya Darabi Associate Professor, Accounting Department, Islamic Azad University, South Tehran Branch, Tehran, Iran Abstract: Prediction of stock returns has always been one of the most important issues in financial markets. In this regard, the investors in financial markets have attracted to use of Fama-French Five-Factor Model as one of the newest methods in this field among various theories and methods for pricing financial assets and predicting the stock return rate in order to choose the best investment and most appropriate portfolio. Therefore, the improvement in predictive power of firm returns due to inclusion of corporate variables of companies listed on Tehran Stock Exchange to Fama-French Five-Factor Model is the main objective of this study. Among all companies listed on Tehran Stock Exchange during , 75 companies are considered as statistical samples of this research through random sampling method. The results of panel data test in this research indicate a positive significant effect of all variables in Fama-French Five-Factor Model (book to market value ratio, company size, growth opportunity, profitability, and investment) and corporate variables (cash holding, dividend rate, and free cash flow). However, the investment variable has negative impact due to initial estimate of primary Fama and French model. Therefore, the hypothesis based on which the inclusion of corporate variables improves predictive power of firm returns is accepted. Keywords: Stock return, Fama-French Five-Factor Model, cash holding, dividend, free cash flow 1- Introduction Various models have been proposed over years for evaluation of risk and stock return since the investment is one of the important factors of development in this century, and the mobility and prosperity of Stock Exchange are among the indices of economic dynamism and health in all countries; and the numerous researchers have paid attention to capital asset pricing model and Fama-French Five and Three-Factor Model among various models. Undoubtedly, this issue has entered a new scene due to the development of economic 195

2 activities, and there is a need to create more accurate and closer-to-reality methods. This need has become a basis for creating new assessment methods and completing the older methods. In this regard, after introduction of CAPM by Trainer (1961), Sharpe (1964) and Lintner (1965), numerous studies have explained the expected stock return and CAPM promotion such as the research by Fama and French ( 1993) (Eslami and Khojasteh, 2008). William Sharpe (1960) defined the systematic risk or beta coefficient as the only factor for determining the stock return difference. The deviations of CAPM were revealed during 1975 to 1990; and according to the researchers, the use of multi-factor models in explaining stock returns was gradually replaced by the One-factor Capital Asset Pricing Model. After CAPM, Fama and French provided the evidence for empirical failure of CAPM (Babalouyan and Mozaffari, 2016). In 1993, Fama and French investigated the impact of factors associated with firm features such as size, book-to-market value, leverage, et c on stock return and proposed a three-factor model for explaining the stock return (Akbari- Moghaddam et al., 2009). In Fama and French model (1993), the stock return is affected by three factors namely beta, firm size, and book to market value ratio in order to predict the stock return (Izadinia et al., 2014). Adding two new variables of profitability and investment to previous three-factor model, Fama and French (2015) studied the explanatory power of their new Five-Factor Model in New York, U.S and NASDAQ Stock Exchange during According to important results of multivariate regression for Fama-French Five-Factor Model, different coefficients of determination (R 2 ) are obtained according to different categories of portfolios. According to obtained results, Fama-French Five-Factor Model has 63% to 93% of explanatory power of stock return. 196 Maxim (2015) compared the predictive power of 6 models namely the CAPM, DCAPM, twofactor, APT, and three and five-factor Fama and French models in Bucharest Stock Exchange (BVB) during According to results of this study, the explanatory power of stock return in Fama-French Five-Factor Model is higher than other studied models, so that the highest and lowest coefficients of determination (R 2 ) are related to Fama-French Five-Factor Model and DCAPM respectively. In a research entitled "The q- factor Model and the Redundancy of the Value Factor: An Application to Hedge Fund during 1995 to 2012", Racicot and Theoret (2015) tested the Fama-French Five-Factor Model for Hedge Fund during a period of According to results of this study and unlike the findings of Fama-French Five-Factor Model, the value factor is significant in most of the Hedge Fund strategies. Nusret Cakici (2015) examined the three and five-factor Fama and French models in 23 advanced stock markets during 1992 to The obtained results indicate strong evidence in North American, European and global markets similar to results of U.S stock market. However, the impact of profitability and investment factors is very low on portfolios of Japan, Asia, and Oceania. The results suggest that the regional models are better than the global models. However, this study seeks to find answer to this question whether adding corporate variables to Fama and French five-factor model increases the predictability of stock return, and also seeks to investigate the impact of each

3 corporate variables namely the cash holding, dividend, and free cash flow on improving the predictability of stock return based on Fama and French five-factor model by examining this model in companies listed on Tehran Stock Exchange. 2- Theoretical principles: Introduction of Fama and French five-factor model According to numerous studies, the mean stock return is related to ratio of equity book to market value (B/M). There is also evidence under which the investment and profitability can increase the power of explaining the mean stock return created by B/M ratio. The rationale for connecting these variables to mean return can be explained by dividend discount model. According to this model, the market value of a share is equal to current value of expected earnings per share during a period according to the following equation: (Equation 1) (Equation 1) In this equation, mt is the share price at time t; E(dt+r): expected dividends for period of t+τ; and r is the approximate mean of long term stock return or more precisely the internal rate of expected dividend return. According to equation (1), if the stock of two companies has the same expected dividends but different prices, the share with lower price will have higher expected return. If pricing is reasonable, the future dividend of stock with lower price will have higher risk. Forecast based on model (1) focuses on price of mt here and in the next section; and the forecasts will be the same whether pricing is reasonable or not. A little manipulation can lead to extracted concept of equation (1) from relations between expected returns, expected profitability, expected investment and B/M. According to Miller and Modigliani (1961), the total market value is obtained from the total stock value of company at time t as explained in equation (2): (Equation 2) In this equation, Yt+τ is the total equity dividends for period of t+τ and dbt+τ=bt+τ-bt+τ-1 refers to the changes in equity book value calculated through dividing by equity book value at time t according to Equation (3). 197

4 (Equation 3) Equation (3) refers to three points about expected stock returns. First, except the current stock value (Mt) and mean expected return (r), the rest of cases are constant in equation (3). Therefore, the lower value of Mt or higher book to market value (Bt/Mt) refers to higher expected returns. Second, Mt and all values in equation (3) except for future earnings and stock returns are constant. According to this equation, the higher expected future earnings mean higher expected returns. Finally, despite the constant Bt, Mt and expected earnings, there is a need for more growth in ratio of book value to investment; and this means lower expected returns. Challenges of equation (3) have led to identification of experimental criteria for expected future earnings and investment. A recent study by Novy and Marx (2012) introduced an index for expected profitability which has a strong relationship with mean return. Aharoni, Grundy, and Zeng (2013) identified a statistical weaker but reliable relationship between investment and the mean return. Due to these results and aims of equation (3), Fama and French decided to investigate a complementary version of Fama-French Three-Factor Model French (1993), and thus they added two factors namely the profitability and investment to market factors, size and B/M to their three-factor model and proposed a five-factor model according to equation 4: Where: ( ) (Equation 4) HMLt: is book to market value factor which means the difference between stock return with high book to market value ratio and stock return with low book to market value ratio. RMWt: It is the profitability factor which is obtained from difference between stock returns of companies with high profitability and stock of companies with low profitability. CMAt: It is the investment factors which is obtained from difference between stock returns of companies with high investment (venture) and stock of companies with low investment (conservative). 198

5 are respectively the market factors, size, book-to-market value, profitability and investment of portfolio i, and is the specific return of portfolio assets with zero mean. 3- Research methodology This research has a quasi-experimental-basic type. Panel Data is the data analysis method including the year of company. Therefore, F Limer and Hausman tests are used in this regard. The content related to research literature is collected from library studies such as books, scientific journals, proceedings, doctoral theses, reviewed documents, and electronic research resources such as the Internet, etc. Data of statistical research section is directly obtained from official reports, documents, financial statements and notes issued by companies. EVIEWS software is used to fit the model. 3-1-Research questions The main question of this study is as follows: Are the corporate variables able to significantly improve the predictability of firm returns according to Fama and French 5-factor model in Tehran Stock Exchange? According to the main question, the sub-questions of this study are as follows: Does the addition of difference in portfolio return with high and low cash holdings able to improve the predictability of firm return according to Fama and French 5- factor model in Tehran Stock Exchange? (Does the cash holding rate have information content?) Does the addition of difference in portfolio return with high and low free cash flow able to improve the predictability of firm return according to Fama and French 5- factor model in Tehran Stock Exchange? (Does the free cash flow have information content?) Does the addition of difference in portfolio return with high and low cash dividend able to improve the predictability of firm return according to Fama and French 5- factor model in Tehran Stock Exchange? (Does the cash dividend have information content?) 3-2- Research hypotheses According to the research questions, hypotheses of this study are as follows: 199

6 1. Addition of difference between the portfolio return with high and low cash holdings to Fama and French 5-factor model can significantly improve the predictability of firm returns in Tehran Stock Exchange. 2. Addition of difference between the portfolio return with high and low free cash flow to Fama and French 5-factor model can significantly improve the predictability of firm returns in Tehran Stock Exchange. 3. Addition of difference between the portfolio return with high and low cash dividend to Fama and French 5-factor model can significantly improve the predictability of firm returns in Tehran Stock Exchange Introduction of statistical population, sample and its determination The statistical population of this study consists of companies listed on Tehran Stock Exchange. The reasons for this choice is the easy access to financial information of these companies, the regulations and standards provided by organization, and also more homogeneous and reliable financial information of these companies. The studied sample includes the companies in Tehran Stock Exchange during a 12-year period from the beginning of 2003 to the end of Therefore, we have used the random sampling (screening) by taking into account several selective criteria as follows: They should be accepted on Tehran Stock Exchange since To enhance the comparability, the fiscal period of sample companies should be finished at the end of March. They should not have any changed activity or financial year during the target financial years. The selected companies should not be the members of banks, financial institutions and investment, financial intermediation, holding and leasing companies because they have different financial disclosures and structures of strategic principles. And finally, it should be noted that the dismissed companies, the firms transferred to subsidiary boards, and those which do not have the minimum sessions according to acceptance time, are excluded from statistical population Research model and introduction of its variables In this study, the following primary model is used to test Fama and French five-factor model of explain the role of corporate variables in improving the prediction accuracy of Fama and French five-factor model. (1) 200

7 Where, indicates the stock return; BM: book to market value ratio; Size: firm size; growth: growth opportunity; Profit: profitability factor; and Invest: investment factor. To test each research hypothesis, first each of the corporate variables are added to this model and finally all variables are added to each other, and the model is estimated. The target models are as follows: (2) (3) (4) (5) The variables are calculated as follows: Annual stock return: The annual stock return is defined as follows: The change in price of beginning and end of stock period in addition to other proceeds from stock purchase such as benefits of priority, bonus shares, and dividend shares divided by the stock price in the beginning of period. ( ) ( ) Kt = Total stock return to ratio of first stock price Pt = Stock price at the end of fiscal year Pt-1 = Stock price at the beginning of fiscal year Pn = Nominal value of share Dt = Gross dividend per share Ne = Number of increased shares by reserves or retained earnings Nc = Number of shares increased by cash Nt = Number of shares before capital increase The variables of Fama and French five-factor model are calculated as follows: Firm size (SIZE): It refers to a two-dimensional variable which receives value of 1 if the firm size is lower than the median of sample firms and those with financial limitations, otherwise it giants value of zero and is measured by logarithm of firm assets. Book to market value (BV/MV): 201

8 The book value refers to the value of each asset in balance sheet of company. Book value per share is calculated as follows: First, the entire debt is subtracted from all assets, and the remainder is divided by number of shares issued by company and given to people. The stock refers to the total market value of number of issued shares to the current price of market value of a share. If these two are divided by each other, BV/MV or the ratio of book to market value is obtained. Growth opportunity: ( ) BVEit = Book value of equity in company i at the end of year t MVEit = Market value of equity in company i at the end of year t and it is equal to number of stock issued by company at the last traded price of stock at the end of year t. TAit = Book value of total assets of company i at the end of year t Profitability factor It is obtained from the difference between stock returns of companies with high profitability and stock returns of companies with low profitability. Investment factor It is obtained from difference between stock returns of companied with high investment (venture) and stock returns of companied with low investment (conservative). The corporate variables are calculated as follows: Cash holding: Linear relationship between changes in cash holdings and operating cash flows, either positive or negative, assume that the change in cash holdings is regardless of cash flow direction. When companies are faced with positive operating cash flow, the sensitivity of cash holdings to operating cash flows will have normal situation. On the contrary, when companies are faced with negative operating cash flows, the sensitivity of cash holdings to operating cash flows is different from positive operating cash flows. Free cash flow to equity (FCFF): 202

9 The Free cash flow to equity is an index for measuring the performance of companies and refers to cash flow which is available for company after spending expenditure for maintenance or development of assets. In fact, the cash flow is resulted from operations of company which is excess of capital expenditures necessary for company to perform existing operations or increase production capacity. Free cash flow to equity (FCFE) refers to cash flow available to shareholders after necessary capital expenditure and costs related to finance from debt. Dividend per share (DPS): Earnings per share (EPS), as one of the important financial statistics for investors, is obtained from dividing the earnings after subtracting the firm tax from the total number of shares, and indicates the earnings which is obtained by company in return for a normal share within a specified period (Neveu, 2006). Dividend per share (DPS) refers to earnings divided by company and given to shareholders in cash; in other words, the DPS is a part of earnings after subtracting the tax per share paid by company. Dividend per share is obtained from dividing the total paid dividend (approved by Annual Ordinary Assembly) by the number of company shares. 4 -Research findings Table 1 represents the descriptive statistics for research variables. It should be noted that these results are related to all research data of studied period and for all sample companies. Table 1: Descriptive statistics of research variables Variable Mean Standard deviation Median Size BV/MV Growth Profit Invest RCF FCFF DPS The first column indicates the mean data of target variable for studied years (2003 to 2014) and for the whole studied companies. The standard deviation is a dispersion or variability index of scores; and the greater values will lead to higher variability, and vice versa, the lower values will lead to lower variability and dispersion, Another column represents the median which is another value of central tendency and as a parameter which divides the frequency of values or distribution of scores into two groups; and it receives the middle 203

10 score; in other words, the middle score refers to median if data is sorted in ascending or descending order. Answer to research questions The stability (fixed variable distribution over time) of variables should be studied before estimating model in studies on time-series data in order to prevent the false regression. This study uses Levin, Lin, and Chu test for examining the stability of variables. Since the obtained significance level for Levin, Lin, and Chu test is less than 0.05 for all variables, it can be concluded that the research variables are stable, and thus there will not be the problem of false regression due to the stable variables in regression analysis (Table 2). Table 2: Stability test of research variables Levin, Lin and Chu test Variable Statistic value level Size BV/MV Growth Profit Invest RCF FCFF DPS F limer test is used to study which one of the pooled or panel models are appropriate for estimating the regression models of research. The results of this test for all studied models ((second model (study on impact of cash holdings), third model (study on free cash flow to equity), fourth model (study on impact of dividend), and final model (study on all corporate variables)) are presented in Table 3. Since the significance level of F limer test is lower than 0.05 all models, the null hypothesis of this test will be rejected. Therefore, this test indicates that the panel model is appropriate for estimation of all models. According to F limer test, which indicates the model of estimation by panel data, there are two methods of estimation with fixed or randomized effects models for estimation with panel data. Hausman Test is used to determine whether the fixed or randomized-effects models should be used for estimating the parameters of model. The null hypothesis of Hausman Test indicates the appropriate randomized-effects model for estimating the regression models of panel data. The results of Hausman Test for selection of fixed or randomized effects models are presented in Table 3. Since significance level of Hausman Test is less than 0.05 for model, so the null hypothesis based on appropriate randomized effects is rejected in model; and the panel method with fixed effects is used to estimate the regression model. 204

11 Table 3: F Limer and Hausman tests on second, third, fourth and final models Model name Tests Test statistic Test result level F Statistic F Limer test Fama-French Chi-square Primary Model Hausman test statistic Second model: (adding the cash holdings) Third model: (adding the free cash flow to equity) Fourth model: (adding the dividend) Final model: (Adding all three corporate variables) F Limer test Hausman test F Limer test Hausman test F Limer test Hausman test F Limer test Hausman test F Statistic Chi-square statistic F Statistic Chi-square statistic F Statistic Chi-square statistic F Statistic Chi-square statistic accepted panel model accepted fixed effect accepted panel model accepted fixed effect accepted panel model accepted fixed effect accepted panel model accepted fixed effect accepted panel model accepted fixed effect Fama and French five-factor model is first examined to respond to research questions, and then all corporate variables are added to this model, and the result is provided, and finally all corporate variables are added two by two and investigated. The results of all estimated models are presented in Table 4. According to Table 4, the significance of F-statistic for relevant model is less than 0.05, and we can conclude that there is a linear relationship between independent and dependent variables in this model. Therefore, it is concluded that the whole model is significant. Durbin-Watson test is utilized to investigate the independence of errors from each other. The lack of correlation between errors will be accepted if Durbin-Watson statistic is close to 2. According to Table 4, Durbin-Watson statistic has proper value for all models. Therefore, all studied variables have significant relationships according to results of estimated Fama and French 5-factor model. Among the studied variables, only the capital factor has a negative relationship, but the other variables have positive relationships. According to the results of estimated second model and the second hypothesis based on the improved predictability of corporate return in Tehran Stock Exchange due to added difference between portfolio return with high and low 205

12 Coefficient Coefficient Coefficient Coefficient Coefficient Examination of Fama-French Five-Factor Model by inclusion of cash holdings to Fama-French Five-Factor Model, all studied variables have shown a significant positive relationship. The Investment factor also indicates a positive and significant effect after adding the cash holdings. The results of estimated third model consistent with third hypothesis based on added free cash flow except for the investment factors, which is insignificant, indicate the positive significant relationship of all variables. The fourth column represents the results estimated Fama-French Model by adding the dividend variable. Like the other models, the obtained results indicate a significant and positive relationship. Finally, the last column of Table 4 represents all three corporate variables added to Fama and French primary model, and all results. In this model, the same results as other models based on their positive and significant impact on corporate return is obtained for all variables (i.e. the ratio of book to market value, company size, growth opportunities, profitability and investment, cash holdings, dividend, and free cash flow). Therefore, according to obtained results, the main hypothesis based on improved predictability of companies listed on Tehran Stock Exchange is accepted in the case of studied influence of corporate variables in Fama-French Five-Factor Model. Method Dependent variable Table 4: Estimated Fama-French Primary Five-Factor Model Fama-French Primary model Second model: Adding the cash holdings Third model: Adding the free cash flow Fourth model: Adding dividend Final model: Adding all three corporate variables Independent variables BM SIZE Growth Profit Invest RCF FCFF DPS C F statistic level Durbin- Watson statistic Coefficient of determination

13 4- Summary and conclusion Given the impact of stock returns on potential and active shareholders' decisions, the researchers need to examine factors influencing the stock returns. This research investigates Fama-French Five-Factor Model test in companies listed on Tehran Stock Exchange and explains the role of skewness coefficient in improving the accuracy of predicting the return on Fama-French Five-Factor Model. The target models are estimated through panel data regression with fixed effects. According to obtained results, all variables of Fama-French Five-Factor Model (book to market value ratios, firm size, growth opportunity, profitability, and investment) have positive and significant impact. According to results of adding the corporate variables cash holdings, dividend, and free cash flow) to Fama and French five-factor model, both the corporate variables and all variables related to Fama and French five-factor model have positive significant effects on predictability of firm returns, and thus the main hypothesis of this study is accepted. References 1. Akbari-Moghaddam, Beytollah; Rezaei, Farzin; Norouzi, Ali (2009), Comparison of predictive power for Fama and French, beta and expected return models; Quarterly of Economic Modeling, Third year, Issue 1, Serial No. 7, Spring 2009, pp Babalouyan, Shahram; and Mozaffari, Mehrdokht (2016). Comparing the predictive power of Fama and French five-factor model with Carhart four-factor and HXZ q- factor models in explaining the stock returns; quarterly of financial knowledge about Analysis of Securities, ninth year, Issue 30, Summer Eslami, Gholamreza; Khojasteh, Mohammad-Ali (2008), Improved portfolio performance based on adjusted returns based on risk in capital-productivity-based investment in Tehran Stock Exchange ( ); Financial research; Vol. 10, Issue 25, Spring and summer 2008, pp Fama, E., French, k. (2015), "A Five-factor Asset Pricing Model", Journal of Financial Economic 116, Izadinia, Naser; Ebrahimi, Mohammad; Hajiannejad, Amin (2014), Comparison of Fama and French main three-factor model with Carhart main four-factor model in explaining stock returns in companies listed on Tehran Stock Exchange; Quarterly of asset management and financing, second year, No. 3, Serial No. 6, fall 2014, pp Maxim, Caudia A. (2015), "The evaluation of CAPM, Fama-French and APT models on the Romanian capital market", Applied Financial Research (DASI). 7. Nusret C. (2015), " the Five-factor Fama-French Model: International Evidence", Available at SSRN: abstract _id= Racicot, F. and Theoret, R. (2015), "The q-factor Model and the Redundancy of the Value Factor: An Application to Hedge Fund", publications/pdf/