Ben R. van Arem – 11851325 – BA Finance Universiteit van Amsterdam
Faculty of Economics and Business
June 30th 2020
Statement of Originality
This document is written by Student Ben van Arem who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
Much research has been done on the Fama-French models on non-financial firms. This study aims to add more empirical evidence on the effectiveness of the Fama-French 5-factor model over the Fama-French 3-factor model by analyzing financial service firms. The data comes from firms traded on European markets. A Fama-MacBeth regression on monthly stock returns results in no significant difference in explanatory power between the two models. They do however outperform the q-factor model and the Carhart model. Significance was found for the book-to-market value premium.
Introduction
In the past, researchers have tried to create models that predict the behavior of asset prices. Building on Markowitz’s (1952) fundamental theory on diversification and modern portfolio theory, Treynor (1961), Sharpe (1964), Linter (1965), and Mossin (1966),
independently introduced the capital asset pricing model (CAPM). This was revolutionary at the time. Fast forward two decades later and Fama and French (1992) introduced an extension of the CAPM, called the Fama-French 3-factor model, by adding two new risk factors, namely size and value. Then another two decades later, Fama and French (2015) extended their own model by adding two additional risk factors, namely profitability and investment. This new model was coherently termed the Fama-French 5-factor model. They successfully proved the added explanatory power of the Fama-French 5-factor model over their previously created 3-factor model.
The Fama-French factors have been applied to most developed markets including European markets, which is the focus of this research. A major shortfall of their study is the exclusion of financial firms in their analyses. Hence, the consequent research of this paper is: “A comparison of the Fama-French 5-factor model to the Fama-French 3-factor model. Evidence from financial firms in Europe.” A Fama-MacBeth analysis is executed on a sample of monthly observations from a 10-year period between 2010 and 2020 (Fama & MacBeth, 1973).
The research hypothesis is that the Fama-French 5-factor model will outperform the Fama-French 3-factor model in terms of adding more explanatory power. In other words, the former compared to the latter is better at explaining the variance of stock returns for European financial firms.
The next section gives a review of relevant literature. The data section lays out the sampling procedure for the collection of the stock returns as well as the Fama-French factors. The methodology section continues with the procedure of the Fama-MacBeth analysis. Then the results are reported, which are further explored in the discussion section that ends with the conclusion.
Literature
Carhart (1997) attempted to improve the previously created Fama-French 3-factor model by adding a momentum factor. The momentum factor was first introduced by Jagadeesh and Titman (1993). This momentum is described as amplification of stock price movements over time. More specifically, if a stock price rises, it will more likely continue to rise rather than fall thereafter and vice versa. Carhart (1997) analyzed performance of mutual funds from January 1962 to December 1993. He reported the following pattern: top performing mutual funds showed noticeable short-term performance persistence and equivalently, bad performing mutual funds showed noticeable short-term underperformance persistence. If an investor buys the top performing fund and sells the bad performing fund, she would profit from the resulting spread described above, albeit a majority of the gains on this spread was expensed through fees that mostly stemmed from transaction costs. According to the analysis, the momentum factor explains more than half of this spread.
Hou, Xue, and Zhang (2015) critiqued Fama and French on their 3-factor model. Hou et al. (2015) published an extensive study analyzing return anomalies in stocks traded on the New York Stock Exchange. In total, they analyzed 80 variables that each cover a unique set of anomalies. They claimed that the Fama-French 3-factor model, which was initially applied by Fama and French (1992) on stock returns in the 90s, does not account for the anomalies that
occurred during the two decades leading up to 2015. Hence, Hou et al. (2015) decided to run similar regressions using a 4-factor model that is at its essence the Fama-French 5-factor model, but excludes the book-to-market value factor. This book-to-market value factor is a principal component of the Fama-French 3- and 5-factor model. The 4-factor model, which was termed the q-factor model, includes a market factor, a size factor, an investment factor, and a return on equity factor (ROE), which is the equivalent of the profitability factor. They found the q-factor outperformed the Fama-French 3-factor model and the Carhart (1997) 4-factor model in terms of better accounting for approximately half of the 80 anomalies analyzed. The other half were reported as being insignificant and exaggerated anomalies across the broad cross section.
Additionally, Fama and French have been criticized to only include non-financial firms in the portfolios they constructed. There is no theoretical reason to leave out financial firms.
Modigliani and Miller (1958, 1963) propose the idea that increasing the leverage of a firm does not refute the CAPM; it merely changes its beta.
Initially, Barber and Lyon (1997) and later Baek and Bilson (2015) applied the 3-factor model to financial firms in their respective papers, as they think Fama and French unjustly left out financial firms and overly focused on non-financial firms. In their line of reasoning, this is not perfect representation nor ideal for making generalizations. Both find that the 3-factor model does indeed apply to financial firms, in that empirical asset pricing tests report the existence of size and value premia. Additionally, considering that financial firms are sensitive to interest rate changes, Baek and Bilson (2015) find an interest rate premium. This extra risk factor is beyond the scope of this study to investigate; however, it is a very interesting variable to analyze, considering the nature of its financial firm specific relationship.
Foerster and Sapp (2005) analyzed the effect of exclusion of financial firms in not only the Fama-French 3-factor model, but other valuation models too. They found that the models cannot be rejected when financial firms are included and reject models when they are excluded. Their evidence comes from the G7 countries plus the Netherlands and Switzerland.
Fama and French have mostly focused their work on the US stock market. Cakici (2015) replicated the Fama-French 5-factor model analysis and applied it, among other regions, to North America, Europe, and the global market. He found that for all these, so including European stock returns, it adds explanatory power. For Japan and Asia pacific markets, it failed to do so. This implies that markets are still not fully integrated internationally. A published master thesis by Amézola (2017) shows that the profitability and investment risk factors are also significant indicators of expected return on assets in Europe.
The three main points the literature suggests is that the Fama-French 5-factor model outperforms the Fama-French 3-factor model, the Fama-French 5-factor model is applicable to European markets, and stocks of financial firms are important assets to include in valuation models. Thus, the topic of comparing the Fama-French 5-factor to the Fama-French 3-factor model of financial firms in Europe is a good fit in this body of research. Hereby, the purpose is to add more empirical evidence and add to the Fama-French 5-factor model’s generalizability. Hence, the relevance of this text.
Data
The data collection method has two facets. For both facets a 10-year period of monthly observations results in a total of 120 observations for each asset that is included in the analysis. The 10 year-period will be taken from January 2010 to December 2019. Considering the
characteristics of the data, namely multiple assets and multiple time periods, the data to be worked with is panel data. The first facet is to collect right-hand side (RHS) data and the second facet is to collect left-hand side (LHS) data.
RHS
The RHS data collection step is retrieving the monthly factor returns for all the 5 regressors and the risk-free rates from Kenneth French’s online database.1 The Fama-French 5 factors and Fama-French 3 factors data sets for Europe can be downloaded and saved into two separates spreadsheets.2 In essence of further processing in python, a final step is to remove all the unnecessary rows in both of these files.
LHS
The LHS data collection procedure is extracting the returns of all the stocks of European financial firms from yahoo finance.3 The first stage is to download data on publicly traded European firms though the Wharton Research Data Services (WRDS) offered by the Wharton School of the University of Pennsylvania. WRDS offers Compustat from which the global security codes can be extracted. After downloading the data to a spreadsheet, the next step is to select all the relevant European countries. A comprehensive list is provided in Table 1.
1http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html
2 When accessing the Kenneth French website, the next step is to select ‘Data Library’, then ‘Developed Market Factors and Returns’, and subsequently the ‘Fama/French European 3 Factors’ and the ‘Fama/French European 5 Factors’ can be downloaded.
Table 1
Pool of 15 European countries included in the analysis
Austria (AUT) Germany (DEU) Netherlands (NLD)
Belgium (BEL) Great Britain (GBR) Norway (NOR)
Denmark (DNK) Ireland (IRL) Spain (ESP)
Finland (FIN) Italy (ITA) Sweden (SWE)
France (FRA) Luxemburg (LUX) Switzerland (CHE)
Note. The three-letter codes in parentheses are the country codes indicated by Compustat After a careful selection of the respective European countries, the following step is to select the appropriate Global Industry Classification Standard sector code.4 At this point, the file contains a list of financial service firms that stem from the European countries listed in Table 1. The next stage is to copy the names of the companies in a new spreadsheet. Subsequently, the respective yahoo finance tickers are to be collected for all the companies in the list. The next step is extracting the monthly stock returns for these firms through a simple web application. In this research, jasonsrimpel web application is utilized.5 This web application downloads data on multiple stocks in a single request. On the web application, the ticker symbols are filled in an input statement, the frequency is set to monthly, and the range is set from January 2010 to December 2019. Before initiating the download, the web application indicates for each ticker how many observations are available. For 50 of the initial 70 companies, yahoo finance contains the full 120 monthly stock returns. The other 20 companies contain less than 100 observations. The web application downloads the 50 comprehensive companies to a spreadsheet. Upon
opening the new spreadsheet, it becomes clear that the file contains one company that consists of
4 The GIC code corresponding to the financial industry is 40. This includes banks, thrifts & mortgage
finance, diversified financial services, consumer finance, capital markets, mortgage real estate investment trusts (REITs), and insurance.
approximately 80 out of the 120 observations with the value of 0%. This company is removed from the file. What is left are 49 European financial service firms with monthly data ranging from January 2010 to December 2019.
The procedure subtracts the risk-free rates from the stock returns to create the excess returns. The RHS data collection procedure described above collects the risk-free rate for all the 120 monthly periods. Before the data is analyzed, the excess returns are winsorized to limit extreme returns and reduce the effect of these potential spurious outliers. The winsorization is at the 10% level, where both ends of the distribution are clipped at equal lengths. This limits the distribution at the 5th and 95th percentile. Before winsorization, the minimum excess return is -460.95% and the maximum excess return is 465.14%. After winsorization, the minimum excess return is -13.97% and the maximum excess return is 12.85%. Lastly, in essence of processing in python, the procedure transposes the returns into three columns: Date, Ticker, and Return.
Descriptive Statistics
Table 2 shows the descriptive statistics of the Fama-French 5 factors and the excess return. This analysis uses a total of n = 5880 observations. These are all the observations in the panel data where time periods equal 120 and number of stocks equal 49, hence 120 x 49 = 5880. The average excess return, that is the stock return minus the corresponding risk-free rate, is .31% with a standard deviation of 24.60%. This standard deviation indicates there is quite sizable variability in the 5880 stock returns. The average risk premium for being exposed to the market is .57% with standard deviation of 4.68%; for high minus low book-to-market value firms is -.24% with standard deviation of 2.26%; for small minus big firms is .17% with a standard deviation of 1.59%. To note is that the average premium for conservative minus aggressive
investment policies is -.05% with standard deviation of 1.12%. This is incredibly small. The average premium for robust minus weak profitability is .39% with standard deviation of 1.54%.
Table 2
Descriptive Statistics Fama-French 5-factors and excess returns
n Mean SD Min. 25th Median 75th Max.
Excess-Return 5880 .0031 .2460 -.1397 -.0361 .0067 .0492 .1285 Mkt-RF 5880 .0057 .0468 -.1231 -.0249 .0057 .0379 .1188 HML 5880 -.0024 .0226 -.0498 -.0184 -.0042 .0113 .0636 SMB 5880 .0017 .0159 -.0432 -.0095 .0010 .0122 .0468 CMA 5880 -.0005 .0112 -.0300 -.0077 -.0010 .0079 .0295 RMW 5880 .0039 .0153 -.0385 -.0055 .0045 .0148 .0348 Note. n = number of observations, SD = standard deviation, Min. = minimum, 25th = 25th percentile, 75th = 75th percentile, Max. = maximum.
Methodology
The objective is to compare the Fama-French 5-factor to the Fama-French 3-factor model. The dependent variable is the excess return of an asset on the left-hand side of the model. Moreover, it is the return on asset minus the risk-free rate for month t. The independent variables are the 5 risk factors or regressors on the right-hand side of the model. These are explicated in table 3.
Table 3
RHS regressors
Abbreviation Explication Explanation
Mkt Market The value-weighted market portfolio
SMB Small Minus Big Size by market capitalization
HML High Minus Low Book to market value
RMW Robust Minus Weak Profitability
CMA Conservative Minus Aggressive Investment policy
Note. Mkt, SMB, & HML are included in the 3-factor model and Mkt, SMB, HML, RMW, & CMA are included in the 5-factor model.
The construction of the 5 RHS regressors (2x3) in Table 3 is done through creating 18 portfolios in total. These consist of 6 portfolios based on size and book-to-market value, 6 portfolios based on size and profitability, and 6 portfolios based on size and investment. The construction of the SMB size factor is the most complex. It is the difference of the average return of the 9 small portfolios and the average return of the 9 big portfolios:
𝑆𝑀𝐵(𝐻𝑀𝐿) =𝑆𝑚𝑎𝑙𝑙 𝑉𝑎𝑙𝑢𝑒 + 𝑆𝑚𝑎𝑙𝑙 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝑆𝑚𝑎𝑙𝑙 𝐺𝑟𝑜𝑤𝑡ℎ 3 − 𝐵𝑖𝑔 𝑉𝑎𝑙𝑢𝑒 + 𝐵𝑖𝑔 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝐵𝑖𝑔 𝐺𝑟𝑜𝑤𝑡ℎ 3 𝑆𝑀𝐵(𝑅𝑀𝑊) =𝑆𝑚𝑎𝑙𝑙 𝑅𝑜𝑏𝑢𝑠𝑡 + 𝑆𝑚𝑎𝑙𝑙 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝑆𝑚𝑎𝑙𝑙 𝑊𝑒𝑎𝑘 3 − 𝐵𝑖𝑔 𝑅𝑜𝑏𝑢𝑠𝑡 + 𝐵𝑖𝑔 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝐵𝑖𝑔 𝑊𝑒𝑎𝑘 3 𝑆𝑀𝐵(𝐶𝑀𝐴) =𝑆𝑚𝑎𝑙𝑙 𝐶𝑜𝑛𝑠𝑒𝑟 + 𝑆𝑚𝑎𝑙𝑙 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝑆𝑚𝑎𝑙𝑙 𝐴𝑔𝑔𝑟𝑒𝑠 3 − 𝐵𝑖𝑔 𝐶𝑜𝑛𝑠𝑒𝑟 + 𝐵𝑖𝑔 𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝐵𝑖𝑔 𝐴𝑔𝑔𝑟𝑒𝑠 3 𝑆𝑀𝐵 =𝑆𝑀𝐵(𝐶𝑀𝐴) + 𝑆𝑀𝐵(𝑅𝑀𝑊) + 𝑆𝑀𝐵(𝐶𝑀𝐴) 3
The construction of the HML book-to-market value factor is calculating the difference between the average return of the two value portfolios and the average return of the two growth portfolios:
𝐻𝑀𝐿 =𝑆𝑚𝑎𝑙𝑙 𝑉𝑎𝑙𝑢𝑒 + 𝐵𝑖𝑔 𝑉𝑎𝑙𝑢𝑒
2 −
𝑆𝑚𝑎𝑙𝑙 𝐺𝑟𝑜𝑤𝑡ℎ + 𝐵𝑖𝑔 𝐺𝑟𝑜𝑤𝑡ℎ 2
The RMW profitability factor is similarly constructed by taking the difference between the average return of the two robust portfolios and the average return of the two weak portfolios:
𝑅𝑀𝑊 =𝑆𝑚𝑎𝑙𝑙 𝑅𝑜𝑏𝑢𝑠𝑡 + 𝐵𝑖𝑔 𝑅𝑜𝑏𝑢𝑠𝑡
2 −
𝑆𝑚𝑎𝑙𝑙 𝑊𝑒𝑎𝑘 + 𝐵𝑖𝑔 𝑊𝑒𝑎𝑘 2
The CMA investment factor is also similarly constructed by taking the difference between the average return of the two conservative portfolios and the average return of the two aggressive portfolios:
𝐶𝑀𝐴 =𝑆𝑚𝑎𝑙𝑙 𝐶𝑜𝑛𝑠𝑒𝑟 + 𝐵𝑖𝑔 𝐶𝑜𝑛𝑠𝑒𝑟
2 −
𝑆𝑚𝑎𝑙𝑙 𝐴𝑔𝑔𝑟𝑒𝑠 + 𝐵𝑖𝑔 𝐴𝑔𝑔𝑟𝑒𝑠 2
The construction of the Mkt market factor differs. It is the risk premium associated with holding the value weighted European market portfolio.
Fama-French 5-factor Fama-MacBeth two-stage regression:
This research utilizes the Fama-MacBeth method (Fama & MacBeth, 1973). The two formulas below show the MacBeth method, which consists of two stages, for the Fama-French 5-factor model. In essence of comparison, this research runs similar regressions for the Fama-French 3-factor model, leaving out the RMW and CMA regressors.
First Stage: Time-Series Regression
𝑅𝑖,𝑡− 𝑅𝑓,𝑡 = 𝛽0,𝑖+ 𝛽1,𝑡𝑀𝑘𝑡𝑡+ 𝛽2,𝑡𝑆𝑀𝐵𝑡+ 𝛽3,𝑡𝐻𝑀𝐿𝑡+ 𝛽4,𝑡𝑅𝑀𝑊𝑡+ 𝛽5,𝑡𝐶𝑀𝐴𝑡+ 𝑒𝑖,𝑡 Second Stage: Cross-Section Regression
𝑅𝑖,𝑡− 𝑅𝑓,𝑡 = 𝛼𝑖+ 𝛾1,𝑡𝛽̂ + 𝛾1,𝑡 2,𝑡𝛽̂ + 𝛾2,𝑡 3,𝑡𝛽̂ + 𝛾3,𝑡 4,𝑡𝛽̂ + 𝛾4,𝑡 5,𝑡𝛽̂ + 𝜖5,𝑡 𝑖,𝑡
𝑅𝑖,𝑡 is the return of company i, which ranges from 1 to 49, over period t, which ranges form 1 to 120. 𝑅𝑓,𝑡 is the risk-free rate over period t. For each factor, the betas are estimated for the 49 stocks. These betas are the sensitivity of the price of the stock in question to the respective risk factor. The estimation process runs 49 regressions of excess returns on the 5 factors in the Fama-French 5-factor model and the 3 factors in the Fama-French 3-factor model. This results in 120 betas for each individual regressor. The procedure prepares the betas for the second stage by averaging the 120 betas for each regressor. They are referred to as the estimated betas in the remainder of this text.
At the second stage, for each month, the model runs a cross-section regression of the same set of excess returns on the estimated betas. This may be termed as factor loading. Each regression uses the same set of estimated betas from the first stage. Lastly, the model averages the estimated gammas and alphas. These gammas represent the estimated risk premiums for each respective risk factor. And the alpha for both the French 5-factor model and the Fama-French 3-factor model represents the unexplained part of the model.
Newey-West Standard Errors
For the reason that the Fama-MacBeth method only corrects for cross-section correlation, this research uses Newey-West standard errors that assume heteroskedasticity instead of regular standard errors, which assume homoskedasticity (Newey & West, 1987). The Newey-West procedure’s initial application was singular time-series regressions. In due course, modifications were made to accompany the analysis of panel data through means of estimation of lagged residuals within clusters (Bertrand, Duflo, & Mullainathan, 2004). This is for the purpose to additionally correct for the time-series autocorrelation that is inherent in the two-stage
regression. This serial correlation is not sizable for small holding periods like daily or weekly periods; however, the longer the period, the more serial correlation becomes an issue.
Considering the monthly holding periods that are used in this research, the Newey-West standard errors seem more appropriate.
The Newey-West procedure adjusts the estimated covariance matrix of parameters that results from the multivariate regressions of this research. It does so to improve the accuracy of the t-statistics of the parameter estimates that result after the second stage. Consequently, the significance of the parameter estimates is more accurate as well. Building on White’s (1980) robust standard errors that are unconditional, Newey-West standard errors are calculated
conditional on the maximum lag length. The maximum lag length in this analysis is one less the number of months for each firm: T - 1 = 120 – 1 = 119. The following formula depicts the process of calculating the Newey-West standard errors:
𝑆∗ =1 𝑇∑ 𝑒𝑡 2 𝑇 𝑡=1 𝓍𝑡𝓍𝑡′+ 1 𝑇∑ ∑ 𝓌ℓ𝑒ℓ 𝑇 𝑡=ℓ+1 𝐿 ℓ=1 𝑒𝑡−ℓ(𝓍𝑡𝓍𝑡−ℓ′ + 𝓍𝑡−ℓ𝓍𝑡′) where 𝓌ℓ= 1 − ℓ 𝐿+1 .
The weight 𝓌ℓ in the formula is to assure the prevention of an estimated covariance matrix that is not positive definite. The assumption is that 𝓌ℓ > 1, because if 𝓌ℓ = 1, then the 𝑆∗ estimated covariance matrix will result in White standard errors. The OLS residuals 𝑒𝑡 are used instead of the residuals from the second stage of the Fama-MacBeth regression 𝜖𝑖,𝑡, which are unobservable. This has no asymptotic consequences.
Hypothesis Testing
The null hypothesis is that the alpha, or the unexplained part, of the Fama-French 5-factor model is equal to or greater than that of the Fama-French 3-factor model. This indicates no improvement in explanatory power. The main hypothesis is that the alpha, or the unexplained part, of the Fama-French 5-factor model is smaller than that of the Fama-French 3-factor model. This indicates an improvement in explanatory power.
The following statistics are reported: average alphas, average gammas, Newey-West standard errors, average observations, average adjusted R-squared, average total premium, average total return. Additionally, the analysis examines the extent of equivalence of the average estimated gammas to the averages of each individual factor premium.
Results
Table 4 shows the correlations between the variables. In accordance with prior literature, the market factor has the largest correlation with excess return. All factors have a significant correlation with the excess return at a 1% level except for excess return & size factor and market & investment factor, which are significant at a 5% level. What is noticeable is the large
correlation between the market factor and the value factor. It stands significant at .473. This is due to the fact that low book-to-market firms are more sensitive to market movements as their
relative market value is large compared to their high book-to-market value counterparts. The size factor has significant negative correlations, largest with the market factor, because small firms are more sensitive to market movements than their larger counterparts.
For the investment factor, it can be seen that it has low correlations with all but the value factor. This correlation of .569 is quite sizable and is most likely due to the fact that low market value firms tend to have more aggressive investment policies than their high book-to-market counterparts. The profitability factor has a negative correlation with excess return of -.131, because the more profitable a firm becomes, the lower the return on the stock usually is. This is because more investors are eager to invest in companies that have more robust profits and thus trading out the potential gains on a stock. The correlation of the profitability factor and the market factor of -.413 is also negative, because more robust profits mean less sensitivity to market movements.
Table 4
Correlation Matrix Fama-French 5-factors and excess returns Excess-Return Mkt-RF HML SMB CMA Mkt-RF .181*** _ HML .137*** .473*** _ SMB -.032** -.119*** -.045*** _ CMA .038*** .030** .569*** -.097*** _ RMW -.131*** -.413*** -.824*** -.047*** -.466*** Note. * p < 0.1. ** p < 0.05. *** p < 0.01.
Something very noteworthy is that the profitability factor is strongly correlated with the value factor. This correlation of -.824 is both large and negative for the reason that low book-to-market value firms tend to be more profitable than their high book-to-book-to-market value counterparts. And the final thing to note is the correlation between the profitability and investment factor of
-.466, which is both quite sizable and negative. This is most likely due to that more conservative investment policies are associated with more robust profits.
Table 5 shows the parameter estimates for the alpha and the regressors from 5 respective models, which all result from two-stage Fama-MacBeth regressions. The next sections report on these multifactor models. After starting with the French 5-factor model and the Fama-French 3-factor model, the q-factor model and the Carhart model are outlined in the additional results section.
Table 5
Parameter estimates CAPM model, Fama-French 3-factor model, Fama-French 5-factor model, q-factor model, & Carhart model
Estimates
CAPM FF 3-factor FF 5-factor q-factor Carhart
Alpha .0061*** (.0018) .0036** (.0017) .0036** (.0016) .0043*** (.0016) .0038** (.0016) Mkt-RF -.0034 (.0050) .0046 (.0047) .0047 (.0049) .0038 (.0044) .0047 (.0045) HML -.0060** (.0026) -.0059** (.0028) -.0058** (.0026) SMB -.0025 (.0021) -.0027 (.0022) -.0028 (.0022) -.0025 (.0021) CMA -.0018 (.0013) -.0025 (.0015) RMW .0035* (.0021) .0044** (.0019) MOM .0037 (.0037) R-squared .0003 .0025 .0025 .0024 .0026 n 5880 5880 5880 5880 5880
Note. Number of stocks = 49, number of observations per stock = 120, n = number of observations, Newey-West standard errors in parentheses, averaged R-squared. * p < 0.1. ** p < 0.05. *** p < 0.01.
Fama-French 5-factor model
The first model to run is the Fama-French 5-factor model. Table 6 reports the beta
estimates that were obtained after the first stage of the Fama-MacBeth regression. The regression calculates all the betas for each firm and subsequently averages them per factor. The last column shows its respective standard deviation.
Table 6
Beta estimates Fama-French 5-factor model
i Mean SD ß0 (Constant) 49 .0031 .0058 ß1 (Mkt-RF) 49 .6214 .2772 ß2 (SMB) 49 -.1004 .5272 ß3 (HML) 49 .2875 .5641 ß4 (RMW) 49 -.6310 .6810 ß5 (CMA) 49 -.2872 .5325
Note. i = number of stocks, SD = standard deviation.
Table 5 shows the parameter estimates for the Fama-French 5-factor model. It shows a significant alpha and value factor at the 5% level. The market, size, and investment factor show no significance. The profitability is just significant at the 10% level. The 95% confidence interval for the market factor, the SMB size factor, the CMA investment factor, and the RMW profitability factor estimates include the value 0, hence they cannot be assumed to be significant at a 5% level.
Lastly, this research compares the average risk premiums from the database (Table 2) and the average gammas from the Fama-MacBeth regression (Table 5). The average risk premium for the market factor is greater than its respective average gamma: .57% > .47%. The average risk premium for the value factor is lower in absolute terms than its respective average gamma: |-.24%| < |-.59%|. The average risk premium for the size factor is lower in absolute terms than its respective average gamma, but they are in opposite directions: |.17%| < |-.27%|. The average risk
premium for the investment factor is lower in absolute terms than its respective average gamma: |-.05%| < |-.18%|. The average risk premium for the profitability factor is greater than its
respective average gamma: .39% > .35%.
Fama-French 3-factor model
The second model to run is the Fama-French 3-factor model. Table 7 reports the beta estimates that were obtained after the first stage of the Fama-MacBeth regression. The regression calculates all the betas for each firm and subsequently averages them per factor. The last column reports its respective standard deviation.
Table 7
Beta estimates Fama-French 3-factor model
i Mean SD
ß0 (Constant) 49 .0010 .0057
ß1 (Mkt-RF) 49 .6524 .2856
ß2 (SMB) 49 -.0158 .4835
ß3 (HML) 49 .5329 .6410
Note. i = number of stocks, SD = standard deviation.
Table 5 shows the parameter estimates for the Fama-French 3-factor model. It is clear from the 5% significance level view point that only the alpha and the value factor are significant. The alpha amounts to .36% with a Newey-West standard error of .0017. The parameter estimate for the value factor amounts to -.60% with a Newey-West standard error of .0026. The 95% confidence interval for both the market factor and the size factor estimate contain the value 0, thus we cannot conclude that these have significant effects in this model at the 5% level. Moreover, the market factor and size factor are insignificant at the 10% level.
Again, this research compares the average risk premiums from the database and the average gammas from the Fama-MacBeth regression. The average risk premium for the market factor is greater than its respective average gamma: .57% > .46%. The average risk premium for
the value factor is lower in absolute terms than its respective average gamma: |-.24%| < |-.60%|. The average risk premium for the size factor is lower in absolute terms than its respective average gamma, but they are in opposite directions: |.17%| < |-.25%|.
Comparison of the Fama-French models and CAPM
When viewing Table 5, the most important thing to note for the purpose of this research is that the alpha does not change between the Fama-French 5-factor model and the Fama-French 3-factor model. Additionally, there are only minor changes in effect sizes and these are most often offset by its respective change in standard error.
As Table 5 indicates, the CAPM alpha, or the unexplained part of the model, is almost 1.7 times the alpha of the Fama-French 5- and 3-factor model. With the estimate sitting at .61% and a Newey-West standard error of .0018, it is highly significant at the 1% level. The final thing to note is that the average adjusted R-squared does increase from .0003 for the CAPM model to .0025 for both the Fama-French 5- and 3-factor model. The average adjusted R-squared for the models are quite low compared to Baek and Bilson’s (2015) average adjusted R-squared of .30 (> .0025).
Additional Results q-factor model
Table 5 also shows the parameter estimates of the q-factor model proposed by Hou et al. (2015). The alpha is significant at the 1% level and sits at .43% with a Newey-West standard error of .0016. To note is the significance of the RMW profitability premium estimate at the 5% level where its estimate is valued at .44% with a Newey-West standard deviation of .0019. The market factor, the SMB size factor, and the CMA investment factor estimates all have 95%
confidence intervals that include the value 0, hence they are insignificant at the 5% level. Moreover, the market factor, the size factor, and the investment factor are insignificant at the 10% level.
Carhart model
Lastly, Table 5 shows the parameter estimates for the Carhart (1997) model in which a MOM momentum factor is added to the Fama-French 3-factor model. The alpha is significant at the 5% level and it sits at .38% with a Newey-West standard deviation of .0016. Comparable to the Fama-French models, the HML factor is the only significant estimate at the 5% level where its coefficient estimate is valued at -.58% with a Newey-West standard deviation of .0026. The 95% confidence interval for the market factor, the SMB size factor, and the newly added MOM momentum factor estimates contain the value 0, hence these estimates are insignificant at the 5% level. These factors are additionally insignificant at the 10% level.
Comparison of additional models
To note about Table 5 is the alpha of the q-factor model, which is .43% and significant at the 1% level and the alpha of the Carhart model is .38% and significant at the 5% level. The alpha of the q-factor model is approximately 1.2 times the alpha of both the Fama-French 3- and 5-factor model and approximately 1.13 times the alpha of the Carhart model. The alpha of the Carhart is approximately 1.05 times the alpha of both the Fama-French 5- and 3-factor model. The order of best performing model in terms of alpha is: CAPM; q-factor; Carhart; with the Fama-French 5-factor and Fama-French 3-factor model tied at the top.
Discussion
The purpose of this research is to compare the Fama-French 5-factor model to its 3-factor predecessor. From the results section, specifically Table 5, it is clear that no difference exists between the alpha of the Fama-French 5-factor model and the alpha of the Fama-French 3-factor model. This satisfies and therefore cannot reject the null hypothesis, which is restated here: The alpha, or the unexplained part, of the Fama-French 5-factor model is equal to or greater than that of the Fama-French 3-factor model, which indicates no improvement in explanatory power. In the outcome of this research, the unexplained part of the two models are equal. Hence, it is invalid to assume the research hypothesis, which is also restated here: The alpha, or the unexplained part, of the Fama-French 5-factor model is smaller than that of the Fama-French 3-factor model.
Cakici (2015) reported improved explanatory power of the Fama-French 5-factor model over the 3-factor model. The analysis from his article does not include financial service firms; however, if financial service firms are eligible to be included in the Fama-French factor analysis in American markets, one might expect an equal eligibility to be include in European markets. In this research no support of such eligibility has been found. Similar conclusions can be drawn against the research by Amézola (2017).
As a result of this nonexistent difference between the models, it was inducive to this research to investigate the difference between the CAPM model, which one may view as a hypothetical Fama-French 1-factor model with the market factor as its sole regressor, and the Fama-French 5- and 3-factor model. The analysis showed improved explanatory power associated with using the Fama-French models over the CAPM model.
The question that arises is: where does this added explanatory power originate? From Table 5, it is clear that this mostly comes from the value factor in terms of both its effect size and its significance. Moreover, it is the only factor that is actually significant. This is a very
surprising result as it contradicts the findings of Fama and French (2015) of their research on their 5-factor model. In their article, they report that the HML value factor is made redundant when adding the CMA investment and the RMW profitability factor to their previously created 3-factor model. No such phenomenon is measured in this research. Without regarding the limitations of this research, a reason could be underlying differences between European markets and American markets. Additionally, discrepancies in the behavior of financial service firms’ stock prices compared to those of non-financial firms. The value factor only shows a slight decrease from the Fama-French 3-factor model to the Fama-French 5-factor model of 1 basis point. Thus, this redundancy of the value factor does not show up in this research.
The explanation Fama and French (2015) give is that the average value premium is captured by its exposure to other factors. Moreover, the value factor’s exposure to the investment and profitability factors. And also, in this research, there is some compelling evidence that the HML factor and the CMA and RMW factors are strongly related to one another, yet the HML value factor is far from being made redundant in the Fama-French 5-factor model compared to the Fama-French 3-factor model.
Hou et al. (2015) exclude the value factor all together in their research and find evidence to support the q-factor model, which includes the market factor, the size factor, the investment factor, and the profitability factor. In the additional results section, it has become clear that for this research, leaving out the HML value factor reduces the performance of the model. To note is that the alpha for the q-factor model is lower than the alpha of the CAPM model, which is mostly
due to the RMW profitability factor of which its estimate has suddenly become significant. This is technically in line with Fama and French’s (2015) explanation of the HML value factor redundancy phenomenon where they claim that this is due to the factor’s exposure to the CMA investment and indeed the RMW profitability factor.
The Carhart (1997) model, which adds a momentum factor to the Fama-French 3-factor model, performed almost as good as the Fama-French models. It performs better than the q-factor model. This is again due to the HML value q-factor, which was the only significant contributor to the performance in that model.
The significance of the value premium in the Fama-French 3-factor model in this research confirms the research by Barber and Lyon (1997) and Baek and Bilson (2015), whom both found evidence of the prominence of the value premium in financial service firms. They also found evidence to support a size premium, but this research finds no such significance. Assuming no limitation of this research, the significance of the value factor in the Fama-French 3-factor model can be considered additional evidence from European markets of the prominence of a value premium for financial service firms. Moreover, the same goes for the Fama-French 5-factor model.
To summarize, this research has found evidence for the existence a value premium in the Fama-French 5-factor model, the Fama-French 3-factor model, the Carhart model, and shows a lower performance of the q-factor model that excludes the value factor. All these pieces of evidence on the value premium seem contradictory with prior literature at times. Consequently, this warrants future research on the significance and contribution of the book-to-market value factor to explaining the variance of stock returns. More specifically, the value premium in financial firms.
Besides the value factor, there seems to be an overall lack of significance of the factors in the models. Assuming no manifestations of threats to the validity of this research, a possible explanation could be the well-known efficient market hypothesis (EMH). The EMH initially started with the proposition made by Cowles (1933) that investors are incapable to predict stock market prices and subsequently ‘beat the market’. In the decades after his proposition, more empirical evidence indicated that stock prices seem to take ‘random walks’. Then Fama (1970) wrote a very influential paper reviewing the EMH in which he categorized the now widely adopted three stances: ‘weak-form’, ‘semi-strong-form’, and ‘strong form’. Before linking this with the study at hand, the characteristics of financial models need to be illuminated.
Once an influential financial model becomes well known and subsequently implemented on a wide scale, its effectiveness in predicting stock returns diminishes to an unprofitable extent. This is in line with at least the ‘weak-form’ that the predictive power of historical returns is priced in and the ‘semi-strong-form’ in which all publicly available information related to the specific firm at hand is additionally priced in. Considering the fact that not only the Fama-French and the other models, but the factors themselves have been around for a multitude of time and that this research focused on the decade leading up to 2020, the EMH might explain to some extent the ineffectiveness of the models. Moreover, this research studies financial service firms, therefore a logical deduction to be drawn is that equity investors of financial firms are possibly more equipped and familiar with these models than equity investors of non-financial firms.
Interesting as these findings may be, to what extent are they valid? Before the
generalizability of this research can be inquired, examining the internal validity of this study is a fundamental step. To start off, the majority of the studies on the Fama-French models are done through creating sorts of portfolios of stocks and analyzing them. This study might potentially
yield different results if a similar method is applied. However, taking into account the limiting pool of stocks that are available to analyze in this research, namely 49, the allowance of individual stock analysis is justified to some extent.
Furthermore, efforts in the selection procedure is directed towards extracting the full population of European financial service firms. While advancing through the procedure described in the Data section, a set of roadblocks caused the sample to lose some of its stocks. Firstly, several stocks did not show up in database searches. Secondly, several stocks did show up in database searches; however, there is a serious lack of available returns (less than 100) over the period January 2010 to December 2019. It was decided not to include those stocks. Lastly, one stock showed a vast amount of stock returns of 0% and this can potentially skew the distribution, hence it is taken out too. All in all, this form of selection bias causes potentially adverse effects on the analysis. Additionally, survivorship bias is a common phenomenon in analyzing financial firms, especially investment funds (Brown, Goetzmann, Ibbotson, & Ross, 1992; Fung & Hsieh, 1997; Wermers, 1997). As such, this causes more bias in the selection process.
Lastly, the Newey-West standard errors correct only for a portion of the bias created by OLS/White standard errors. The simulations by Peterson (2005) show that Newey-West standard errors correct for 60% of the bias when a maximum lag of T-1 is taken.
Conclusion
For the monthly stock returns of European financial service firms, there is no evidence to support an improvement of explanatory power of the Fama-French 5-factor model over the previously created Fama-French 3-factor model. Both Fama-French models outperform the q-factor model as well as the Carhart model. The research does potentially suffer from threats to
internal validity through selection bias and survivorship bias. Furthermore, the research design itself diverges from the usual sorts of portfolios analysis that is customary in multifactor model designs as it regresses over individual stock returns. Assuming no such limitations, much support was found for the HML book-to-market value factor in the Fama-French 3-factor model, the Fama-French 5-factor model, the Carhart model, and the q-factor model showed a sizable decrease in explanatory power when the value factor was left out. These findings seem to contradict prior literature, where there is mention of the redundancy of the value factor when investment and profitability factors are introduced. Within this research there is also a slight contradiction as the correlations between the value factor and the investment and profitability factor respectively are quite sizable. Yet the so-called exposure of the value factor to these two factors did not end up digesting the existence of the value premium. The insignificance of the other factors is potentially attributable to the efficient market hypothesis. Future research is warranted to investigate the role of the value premium in explaining variance of the stock returns of financial service firms.
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