The effect of macroeconomic variables on the robustness of the traditional Fama-French model: A study for Mexico using different portfolios

Saucedo, Eduardo; González, Jorge Article The effect of macroeconomic variables on the robustness of the traditional Fama-French model: A study for Mexico using different portfolios Journal of Economics, Finance and Administrative Science Provided in Cooperation with: Universidad ESAN, Lima Suggested Citation: Saucedo, Eduardo; González, Jorge (2021) : The effect of macroeconomic variables on the robustness of the traditional Fama-French model: A study for Mexico using different portfolios, Journal of Economics, Finance and Administrative Science, ISSN 2218-0648, Emerald Publishing Limited, Bingley, Vol. 26, Iss. 52, pp. 252-267, https://doi.org/10.1108/JEFAS-03-2021-0010 This Version is available at: https://hdl.handle.net/10419/253822 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ The effect of macroeconomic variables on the robustness of the traditional Fama–French model. A study for Mexico using different portfolios Eduardo Saucedo EGADE Business School, Tecnol ogico de Monterrey, Monterrey, Mexico, and Jorge Gonz alez Instituto Econofinanzas, Monterrey, Mexico Abstract Purpose –Fama–French model (FFM) has been successful in helping to predict the financial markets, but investors have been interested in creating more sophisticated models to better predict the performance of the stock market. The objective of the extended version is to create a more robust econometric model to better predict the performance of the Mexican Stock Market. Design/methodology/approach –The study divides the Mexican Stock Market into six different portfolios. The criteria to build those portfolios are the same one used in Fama–French (1992). The study comprises 78 stocks listed in the Mexican Stock Market that are analyzed monthly during 1997–2018. The study analyzes the period before and after the 2008–2009 financial crisis to identify whether there are important changes. The estimation applies the traditional and an extended version of the FFM that include macroeconomic variables such as country risk, economic activity, inflation rate, and exchange rate and some financial variables recommended in the literature. Findings –Results indicate that classic FFM variables are statistically significant in most cases, but relevant macroeconomic variables such as the interest rate, exchange rate and country risk stand out for being weakly relevant in most of the portfolios. However, it is noticed that some of these macroeconomic variables became relevant for different portfolios only after the 2008–2009 crisis, especially in portfolios which include small market capitalization firms. Research limitations/implications –The study includes the stocks listed in the Mexican Stock Market. One limitation is the small number of stocks available, which reduces the possibility of creating well diversified portfolios. This study includes 78 stocks. The stocks removed from the sample are from firms that were not listed during six consecutive months or whose market capitalization did not change in the same period. Outlier data were removed from the sample to capture in better way the general performance of the stock market. Practical implications –The objective of the extended version is to create a more robust econometric model than the traditional model. It is expected that such estimations can be helpful to investors to make better decisions when they try to predict performance in the stock market. Social implications –An extended version of the FFM can be helpful to investors to make better decisions when they try to predict performance in the stock market. Originality/value –To the best of our knowledge there are no more studies in the literature of the Mexican financial market that apply the same methodology. Keywords Fama–French model, Extended Fama–French model, Mexican Stock Market, Macroeconomic variables Paper type Research paper JEFAS 26,52 252 JEL Classification —C58, G11, G14, G15 © Eduardo Saucedo and Jorge Gonz alez. Published in Journal of Economics, Finance and Administrative Science. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence maybe seen at http:// creativecommons.org/licences/by/4.0/legalcode. The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/2077-1886.htm Received 23 March 2021 Revised 24 May 2021 Accepted 24 May 2021 Journal of Economics, Finance and Administrative Science Vol. 26 No. 52, 2021 pp. 252-267 Emerald Publishing Limited e-ISSN: 2218-0648 p-ISSN: 2077-1886 DOI 10.1108/JEFAS-03-2021-0010 1. Introduction The Fama–French Model (1992) (FFM) is a well-known asset pricing model in finance that uses size, book-to-market equity and other variables such as beta (market size), leverage and earning-price ratios to capture the stock return of different companies. In the original study, the authors claim that beta has little or even no ability to explain cross-sectional variation in equity returns, but variables such as book-to-market value and market firm capitalization (firm size) can explain such variation. Empirical evidence suggests that, in some cases, FFM has been successful in helping to predict the financial markets, but investors have been interested in creating more sophisticated models to better predict the performance of the stock market. Therefore, in the last few years, some extensions of the FFM have emerged. Besides the traditional variables included in the FFM, Fama–French extensions comprise the inclusion of variables related to either macroeconomic conditions or firm performance, such as momentum, profitability, dividends, fundamentals, etc. Studies by Bali et al. (2015),Aretz et al. (2005),Adcock et al. (2019) and Bergbrant and Kelly (2016) are good examples of Fama–French extensions that include macroeconomic conditions, while studies by Roy and Shijin (2018) and Djamaluddin and Roffi (2017) are extensions that include variables related to firm performance. Regarding the literature about Mexico on this matter, only a few research studies have applied either the traditional or an extension of the FFM to analyze the performance of the Mexican Stock Market. Most of such literature centers its analysis on the FFM and just adds the interest rate as an additional explanatory variable, as found in Velarde (2004) and Trevi~ no (2011). To the best of our knowledge, there are no other research studies that apply an extended version of the FFM to analyze the performance of the Mexican Stock Market across different periods. The objective of this study is to provide some new evidence that contributes to the literature and at the same time provides important signals that can be helpful for investors interested in the Mexican Stock Market. The study divides the Mexican Stock Market into different portfolios, according to specific characteristics that are explained in the following sections, and then applies the traditional FFM and an extended version of the same, which include some macroeconomic and financial variables recommended in the literature. The purpose of the extended version is to explore if the inclusion of economic fundamentals is helpful in creating a more robust econometric model to better predict stock market returns in Mexico. To explore how the 2008–2009 financial crisis affected local markets, the sample has been divided into two periods, one of them without the effect of the crisis. The study uses a database that spans from June 1997 to January 2018 and creates portfolios using Mexican stocks, according to the amount of the returns generated by firms in previous periods, as in Fama and French (1992). The structure of the study is as follows: Section 2 analyses relevant literature regarding the FFM applied to Mexico and international markets. Section 3 presents the methodology and econometric model implemented in this study. Results are presented in Section 4 and, lastly, Section 5 includes the discussion and conclusion parts of the research. 2. Literature review This study is based on Fama and French (1992), which uses different portfolios classified according to market book value and the market capitalization of each firm. Different literature, such as O’Brien (2007) and Blanco (2012), supports the idea that by incorporating firms according to market firm capitalization and market book equity, FFM becomes more robust than the traditional Capital Asset Pricing Model (CAPM). One characteristic that makes FFM preferable to CAPM is that the latter incorporates only the market risk premium and disregards whether portfolios are made up of small or large firms or according to market value books. A study for Mexico using different portfolios 253 2.1 FFM in the Mexican Stock Market and other markets Velarde (2004) works on an extension of the FFM and develops an analysis with additional variables, such as unexpected inflation, exchange rate, long-and-short interest rate spreads, spreads between corporative and government bonds to identify if these risk variables help to explain returns in the Mexican Stock Market. The author concludes that those variables do not explain Mexican Stock Market behavior, since most of them are not statistically significant. Valencia-Herrera (2015) also implements the FFM and analyzes the performance of the Mexican Sustainability Index during the period from 1995 to 2012. Results indicate that such an index generated not only smaller returns but also smaller risk than the entire Mexican Stock Market. Results also indicate that market risk premium, beta market capitalization and year momentum beta are all statistically different from zero. G omez (2006) analyzes the effect of local and external factors in the returns of different Mexican portfolios from 1995 to 2003. The author finds that the exchange rate is relevant to explain market returns, while country risk does not have any effect on them. Similarly, Trevi~ no (2011) examines the determinants of the Mexican Stock Market returns from 1994 to 2010. The author constructs Fama–French portfolios and finds that the exchange rate has a clear impact on risk returns. Trejo-Pech et al. (2012) analyze the Mexican Stock Market from 1991 to 2010 and implement the FFM. The study includes nine portfolios, and their results are aligned with stock market returns. However, when 25 portfolios are created, the model is no longer functional to predict stock market returns due to the small sample size in each portfolio. Regarding the literature about Latin America, Sanvicente et al. (2017) examine the Brazilian stock market from 2004 to 2014. The authors find that country risk is not statistically significant to explain stock returns. Duarte et al. (2013), in a study for Colombia during the period from 2004 to 2012, use a CAPM model to explain whether the firm size is relevant to determine the size premium in local stock markets. Their results indicate that size premium is not relevant; thus, the market does not award any premium for investing in either small or big companies. In the case of the United States (US), Aretz et al. (2010) develop an extended version of the FFM and incorporate additional variables to the traditional FFM model. They include macroeconomic variables such as economic expectations, unanticipated inflation rate, and changes in the spread between short- and long-term interest rates. They conclude that portfolios constructed according to book market value are overly sensitive to changes in economic fundamentals, while portfolios created according to firm capitalization value are more sensitive to changes in interest rate and exchange rate. Later, Fama and French (2015) developed a different study for the US stock market, from 1963 to 2013, where besides the variables from their seminal model, they include additional variables related to profitability and investment patterns. They create three portfolios and find that this new extended model explains between 71 and 94%, respectively, of the total variance generated by these portfolios. Among the relevant FFM literature that has been developed about Asia, Chiang et al. (2017) analyze nine Asian stock markets from 1995 to 2015 and compare those using different variations of the traditional FFM. The authors include profitability, investment, momentum, P/E ratio and dividend yield variables. They find that FFM with eight explanatory variables is more effective to explain the performance of the stock market than the traditional FFM. Manjuantha and Mallikarjunappa (2018) use data from 1996 to 2010 to test the FFM in the Indian Stock Market. They find that portfolios composed of medium and high book value firms are well explained by the FFM, but portfolios composed of small book value firms only respond to market premium and not to the other two explanatory variables included in the model. Lastly, Chowdhury (2017), in an analysis for Bangladesh during 2010–2014, uses the Fama–French three-factor model. The main finding is that stocks with a small market JEFAS 26,52 254 capitalization value perform better than those with a large capitalization value. Results also indicate that big firms have an ambiguous effect on portfolio returns. 3. Methodology and econometric model This study includes the stocks listed in the Mexican Stock Market. One limitation of this study is the small number of stocks available in the Mexican market, which reduces the possibility of creating well-diversified portfolios. This study includes 78 stocks [1], a number obtained after eliminating financial stocks, as well as the least liquid stocks listed in the stock market [2] (the stocks removed from the sample are from firms that were not listed during six consecutive months or whose market capitalization did not change in the same period). The database used in this study comprises monthly data from June 1997 to January 2018 [3]. The stock market data are obtained from Bloomberg and already include dividends. After robustness and residual tests in each regression, outlier data were removed from the sample when the results changed significantly between periods, or when residuals were located outside the confidence interval threshold. This allowed us to capture the general performance of the Mexican Stock Market in a better way. The study includes the financial risk environment prevailing in the country as an explanatory variable called country risk. Such variable is used to capture the exposure of the stock market to the country’s risk factors. The country risk variable is expressed as the difference between the long-term Mexican bonds categorized in dollars and the long-term US treasury bonds. The long-term premium variable is included afterward and is obtained from the difference between the 10-year Mexican bond return and the 91-day CETE (CETE means Certificado de la Tesoreria, which is a treasury government bond equivalent to the US 3-month Treasury bill). The information for each of these instruments is obtained from Mexico’s Central Bank (Banxico) website. The econometric model also includes fundamental macroeconomic variables, such as exchange rate, an indicator of the economic activity at a country level (IGAE) and the inflation rate. The exchange rate is available daily on Banxico’s website and was calculated using the average value in the entire month. The economic activity index, Indicador Global de la Actividad Economica (IGAE) and the inflation rate (INPC) are available monthly at the National Institute of Statistics and Geography (INEGI). Lastly, the study also includes the SPY500 variable, which measures the performance in the US stock market and was obtained from Bloomberg. The construction of the six portfolios included in this study starts with the Fama and French (1992) methodology. This process consists of sorting the stocks according to market firm capitalization and then dividing them into two categories: B (Big) and S (Small). The category for each firm is obtained considering the average value in the Mexican Stock Market Index during the analyzed period. For example, if a company is among the 50% most capitalized companies in the Mexican Stock Market, then it is considered as a big company, otherwise, it is considered a small company [4]. This exercise allows modifications if market capitalization changes across participant firms. As a result, the portfolios for small and big companies could be consisted of different companies every year. Once the stocks are separated according to firm capitalization (small and big), they are divided according to the book-to-market ratio of each analyzed company. Fama and French (1992) in their study organize the stocks by high, medium and low categories, where the abbreviation H stands for high, M for medium and L for low. It is important to mention that H represents 30% of the company stocks with the highest book-to-market ratio among all the 78 stocks included in the analysis, L stands for the companies with the 30% lowest ratio and M takes the remaining 40% of the stocks in the sample. The book-to-market ratio information comes from the financial statements reported in December from the previous year. Similarly, A study for Mexico using different portfolios 255 portfolios are rebalanced each year to allow for changes if any stock suffers a modification in its book value during the analyzed period. Due to sample size, we did not split the estimations into quintiles, as is presented in the original Fama and French (1992) study. The six portfolios constructed for this study are shown in Table 1. These portfolios are regressed against the traditional variables included in the Fama and French (1992), and then in a second model, they are regressed against the traditional variables plus some additional relevant macroeconomic variables supported by the literature. This process is then followed by the construction of the SMB (Small Minus Big) variable, which is the average return of the three portfolios composed of small-capitalization companies in the Mexican Stock Market (50% smallest market capitalization companies) minus the average yield of the three biggest portfolios (50% biggest market capitalization companies). That is, SMB 5[1/3 (S/L þS/M þS/H)] –[1/3 (B/L þB/M þB/H)]. SMB refers to the firm size premium and is expected to have a positive sign for small firm returns because in the short run small firms traditionally generate larger returns than big firms to compensate by size risk. Next, the HML variable is constructed. HML, which stands for High Minus Low, is the average yield of the two portfolios together with the highest book-to-market ratio (S/H and B/H) minus the average yield of the two portfolios with the smallest ratio (S/L, B/L). That is, HML 5[½(S/H þB/H)] –[½(S/L þB/L)]. The HML coefficient is expected to be positive for the portfolios with the highest ratio, granting higher profitability and value. In this sense, the stocks with the highest valuation are expected to provide higher returns for investors. Therefore, if the portfolio consists of high valuation stocks, then an increase in the return in this kind of stock leads to a better performance of the portfolio. The market return (RM) is constructed by weighting the monthly stock returns listed according to their respective size. We subtract the market risk-free government bond (91-day CETE bond) from the stock market return during the same period. Such difference is called the market risk premium, which is a yield obtained for investing in stocks rather than investing in assets without any risk, such as government bonds. Descriptive statistics are shown in Table 2. The whole period indicates that the B/H portfolio shows the highest returns among all portfolios constructed in this study, while the B/L portfolio shows the smallest returns. Moreover, when the sample is split among the 1997–2010 period (to capture the effect of economic crisis) and 2010–2018 (without crisis), the average return for all portfolios is, in general, higher for the pre-crisis period than for the after-crisis period, except for the S/L and SMB portfolios, which show opposite results. Table 2 also shows that when the average return between big-capitalization (BL, BM, BH) and small-capitalization (SL, SM, SH) portfolios is contrasted, a clear dominance cannot be stated among them. Table 2 also indicates that volatility during the period after the financial crisis is smaller than the period before the crisis. This happens for almost all portfolios, regardless of the stock composition in the portfolio. Lastly, Market Risk Premium (MRP) is small, but positive for all samples, indicating that the average return in the financial stock market is not higher than risk-free instruments such as government bonds (CETES). The second period shows practically zero returns for a market premium; such results could be explained due to a local monetary tightening policy and a weak performance in the Mexican Book value Market capitalization Small Big Low Small/Low (S/L) Big/Low (B/L) Medium Small/Medium (S/M) Big/Medium (B/M) High Small/High (S/H) Big/High (B/H) Source(s): Own estimations using data from Bloomberg Table 1. Portfolios created for this study JEFAS 26,52 256 Whole period June 1997 to January 2018 Before and during financial crisis June 1997 to May 2010 After financial crisis June 2010 to January 2018 Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Big firms B/H 1.45 24.87 38.33 7.38 1.66 24.87 38.33 9.28 1.09 11.67 9.01 4.42 B/M 0.81 18.96 32.58 6.62 1.02 18.96 32.58 7.88 0.45 7.41 9.09 3.61 B/L 0.71 19.54 44.08 7.53 0.97 19.54 44.08 8.84 0.26 13.27 23.67 4.52 Small firms S/H 0.97 45.83 38.53 8.81 0.98 45.83 38.53 10.60 0.97 11.12 10.85 4.39 S/M 1.44 22.55 30.62 6.79 1.59 22.55 30.62 8.13 1.17 9.21 8.43 3.52 S/L 0.90 14.51 30.55 5.92 0.81 14.51 30.55 6.98 1.04 9.67 6.37 3.50 SMB, HML and market risk premium SMB 0.11 13.27 15.26 4.52 0.09 13.27 15.26 5.37 0.46 7.15 6.50 2.49 HML 1.13 29.26 38.64 7.38 1.26 29.26 38.64 8.99 0.91 14.40 9.23 5.35 MRP 0.21 14.26 32.20 6.39 0.34 14.26 32.20 7.71 0.01 7.59 11.01 3.17 Source(s): Authors’estimations using data from Bloomberg. MRP is equal to RMt−rft, that is, market risk minus risk-free interest rate Table 2. Descriptive statistics A study for Mexico using different portfolios 257 Stock Market. Table 3 shows the correlation matrix and indicates that correlation among portfolios is not a relevant problem. The base model for this study is an adaptation from the Fama and French model (1992) with the inclusion of factors, such as credit and macroeconomic variables, as presented by Simpson and Ramchander (2008). rit rft¼ α iþβ1ðRMtrftÞþβ2SMBtþβ3HMLtþγ1Termtþγ2Country Riskt þδ1ExcRatetþδ2Ytþδ3 π tþ f 1SPYtþ ε it (1) Where, SMB refers to a portfolio composed of small-minus big-capitalization companies and HML refers to a portfolio with high minus low book-to-market ratio companies. Both generated variables are consistent with the Fama–French methodology. The variable RM in Eqn 1 refers to the average market return of the 78 stocks in this study. The 91-day CETE is a proxy for the risk-free rate of return, this variable is denoted as rft; then, ðRMt−rftÞand refers to excess returns or market risk premium. The rit −rftis the dependent variable and refers to the excess return of each of the portfolios constructed in this study (S/L, S/M, S/H, B/L, B/M, B/H). Note that βis estimated for the common FFM variables. Then, we focus on the long-term risk premium variable, which is obtained throughout the estimation of the spread of the 10-year Mexican Treasury bond and the 91-day Treasury bond (CETE). The structure term reflects the expectations of market participants about future changes in interest rate. Another variable included in the model is called country risk, which refers to the spread between the long-term Mexican bonds in US dollars and the long-term US Treasury bond. An increase in country risk reflects a higher risk to invest in Mexico; therefore, investors need to be compensated with a higher premium in returns to be willing to invest. For these variables (further to FFM model), it is estimated γ, which refers to how each portfolio reacts to changes in the interest environment. Now, δmeasures the impact of three macroeconomic variables (Exc Rate, Yand π ) that refer to exchange rate, economic activity and the local inflation rate. According to results obtained in the literature, a depreciation of the Mexican peso is expected to lead to fewer portfolio returns (Adcock et al., 2019;Aretz et al., 2010). A similar effect on each portfolio return is expected to be generated by increases in the inflation rate (Kelly, 2003;Zhang et al., 2009). Lastly, an increase in economic activity is also expected to increase returns across portfolios (Kelly, 2003;Zhang et al., 2009). Then, f is estimated to capture the impact that the US stock market index (S&P 500) is having on domestic portfolios. A positive relationship between the US and Mexico stock markets is expected, due to the positive cycles between both economies. Lastly, the ε i;tterm refers to the traditional error term that is expected to have a normal distribution with a zero mean and variance, σ 2. BH BM BL SH SM SL SMB HML RMP B/H 1.00 B/M 0.64 1.00 B/L 0.57 0.65 1.00 S/H 0.47 0.42 0.41 1.00 S/M 0.69 0.61 0.60 0.60 1.00 S/L 0.57 0.64 0.48 0.45 0.63 1.00 SMB 0.31 0.36 0.42 0.44 0.13 0.13 1.00 HML 0.77 0.32 0.14 0.66 0.49 0.21 0.09 1.00 RMP 0.52 0.61 0.64 0.48 0.51 0.50 0.17 0.29 1.00 Source(s): Authors’estimations with data obtained from Bloomberg Table 3. Correlation between portfolio returns JEFAS 26,52 258 One of the main purposes of this study is to identify whether the macroeconomic variables included in the model are influencing the stock returns in each of the six portfolios. Variables such as momentum and profitability, among others included in the literature (Fama and French, 2015;Djamaluddin and Roffi, 2017) are excluded from the analysis to keep enough degrees of freedom, as suggested by Trejo-Pech et al. (2012). Additionally, to check the stationarity of the variables used in the model, a table with the unit root test is developed, which is available upon request. Such table shows the Dickey Fuller Extended test with the optimal number lags (according to Schwarz information criterion) and the Phillips–Perron test. Results indicate that all variables are I(1), which allow us to regress all variables in the FFM. Lastly, to check heteroskedasticity problems in the regressions estimated in this study, Breusch–Pagan tests are included for each regression. In general, no problems can be seen with heteroskedasticity or autocorrelation in the distribution of errors. 4. Results 4.1 Whole sample period analysis Two econometric models for each of the portfolios are estimated. The first model refers to the classic FFM, followed by the second model that is an augmented version of the FFM and includes the spread between short- and long-term interest rate, country risk and the macroeconomic variables previously mentioned. Each regression is estimated for the entire analyzed period (June 1997 to January 2018). The study also comprises an analysis for the period before and after the 2008–2009 financial crisis. The reason for dividing the analysis into these two periods is because some relevant changes could be originated in the Mexican Stock Market after the financial crisis. Table 4 shows the portfolio results for small and big market capitalization firms for the whole period analyzed in this study. Such portfolios are divided into low-, medium- and highvalue firms. The table also shows comparatives between the traditional and the extended version of the FFM, which is the main objective of this research paper. Results indicate that coefficients for traditional FFM are all statistically significant and similar to coefficients obtained in the extended FFM. The traditional FFM includes the market risk, SMB and HML variables. Results indicate that excess return or market risk premium ðRMt−rftÞis positive and significant across all regressions. Such results indicate evidence that the Mexican Stock Market demands a premium for investing in risk assets rather than investing in assets without market risk. However, the coefficient is close to 1, a value aligned with a unitary elasticity, except for the BH portfolio, characterized by big capitalization and value. SMB is positive and statistically significant in the case of all small-capitalization firm portfolios. Such coefficients indicate that the Mexican Stock Market grants a size premium for investing in small-capitalization firms where stock variations are higher than big-firm variations. In the case of portfolios composed of big market capitalization firms, results are negative and statistically significant, indicating that an increase in the return of SMB portfolios creates a negative effect on the portfolio’s return since the small portfolios become more attractive with an increase in their returns. In the case of small market capitalization portfolios, the HML coefficient is statistically significant for all portfolios but with mixed signs. It is positive for high and medium book valued firms, but negative for low book valued firms. Findings are relevant because they show a premium for firm size and for firm value. As a result, investors with portfolios composed mainly of small firms could expect to see higher returns than the average market returns; such behavior is replicated for stocks with high books value. 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Corresponding author Eduardo Saucedo can be contacted at: [email protected] For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: [email protected] A study for Mexico using different portfolios 267