Factor Models: an analysis of the
Fama and French Factors on industry
characteristics
Noah van Grinsven (10501916)
Supervisor: Lingwei Kong
University of Amsterdam
Abstract
Only a little research has been done on the application of the three-factor model on industry portfolios. Therefore in this paper, the primary purpose was to examine the behaviour of specific industry characteristics with respect to three-factor model. The data consisted of all the listed stocks on NYSE, AMEX and Nasdaq divided over 48 industry portfolios on the period from 2000 - 2010. What was found was an upward trend in the relation between average book-to-market ratio and the HML risk loading and a downward trend in the relation between average firm size and the SMB factor loading. Also, a higher standard deviation of industry returns appeared to have higher loadings on the Excess Market Return factor, and non-cyclical firms showed lower loadings on the Excess Market Return and SMB factors.
Statement of Originality
This document is written by Student Noah van Grinsven 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.
Contents
I Introduction 1
II Theoretical background 2
II.I Modern Portfolio Theory . . . 3
II.II Capital Asset Pricing Model . . . 5
II.III Three-factor Model . . . 6
II.IV Industry-based portfolios . . . 7
III Data & Methods 8 III.I Data . . . 8
III.II Methods . . . 10
IV Results 11
I. Introduction
The three-factor model of Fama and French (1993) posits that expected stock returns can be explained by the Excess Market Return, a book-to-market equity factor (HML), and a size factor (SMB). This model expands on the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), which only uses the market risk factor to explain the return on stocks.
In their regression they use SMB(t) (Small Minus Big) as the difference between the returns on (diversified) portfolios of small stocks and big stocks, and HML(t) (High minus Low) as the difference between the returns on portfolios of high book-to-market (value) stocks and low book-to-market (growth) stocks. The purpose of adding the SMB and HML factors is to mimic the risk factor in returns related to size and book-to-market ratio (BE/ME). Fama and French apply this three-factor model on excess stock returns of 25 portfolios formed as the intersections of five size and five BE/ME groups. The 25 portfolios are used to determine whether the mimicking portfolios SMB and HML capture common factors in stock returns related to size and book-to-market ratio. The results of their research confirm that portfolios constructed to mimic risk factors related to size and BE/ME add substantially to the variation in stock returns explained by a market portfolio (CAPM).
One way to further examine the application possibilities of this factor model is to use this model on portfolios sorted by industry category. Only a little research has been done on the application of factor models on industry portfolios. Research of Fama and French (1997) and Moerman (2005) has shown that pricing assets on an industry level cause problems. Both the CAPM and 3-factor model show a reduction in R2as well as an increase in the pricing error when they are applied to industry-based portfolios. Also, Fama and French (1997) find that the factor loadings on the size and book-to-market factors are not stationary through time. In this article, the primary purpose is to examine the behaviour of specific industry characteristics with respect to three-factor model in more detail. In order to carry out this research U.S. stock data on all listed stocks on NYSE, AMEX and Nasdaq of the period from 2000 - 2010 is used.
The purpose of the industry classification is to split the firms into manageable groups with comparable characteristics. The main focus of this paper is to look at characteristics like the average BE/ME, average market capitalisation (ME) and volatility of returns of an industry. Also, sorting all listed stocks in 48 different subcategories (industries) makes it possible to find patterns in groups of industry portfolios that share the same characteristics. Other characteristics that will be looked at are portfolio groups based on cyclicality and financial versus non-financial industry portfolios. Cyclicality of an industry is based on the principle that some industries are less affected by economy-wide changes during business cycles, while others are more affected. Non-cyclical industries include producers of essential goods such as food and beverages which are regarded as recession-proof. Cyclical industries such as those involved in the manufacturing of durable goods are severely impacted by economic downturns. Here, there are six industries that will be considered as certainly non-cyclical, these industries are Food Products, Utilities, Pharmaceutical Products, Healthcare, Tobacco Products and Beer & Liquor. Also, the four industries in the data used that span up the financial sector are Banking, Insurance, Real Estate and Financial.
The rest of the paper is organised as follows. Section II discusses theoretical background of the model used by Fama, French (1997) and preceding models. Section III explains the data, descriptive statistics and methods used in this paper. Section IV discusses the results for the different industries relative to results of similar papers. A summary and conclusions can be found in Section V.
II. Theoretical background
People always search for better, faster and more efficient solutions to problems. New invented tools or techniques that stand on top of older ones are published constantly. This applies to every field including the finance field. In this manner, many different models have been developed that help explain the return on portfolios using risk factors. The Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) which was developed to measure portfolio performance since the early 1960s is the basis for many of these models. This model was in turn based on work of Markowitz (1952) in which
he proposed his Modern Portfolio Theory. In the following decades, many different researchers have tried to extend the basic CAPM. A major breakthrough came in 1992 when Fama and French argued that the CAPM is not comprehensive enough and they propose a better three-factor model. The latter is the model that is used in this paper. A description of the methods and data that is used used is given in the next section.
The purpose of this chapter is to discuss the financial theories mentioned above. First, the Modern Portfolio Theory (MPT) will be explained. In the next section, the Capital Asset Pricing Model (CAPM) is discussed. This is followed by an explanation of the Fama-French Three-Factor Model, and its expansion on different portfolios based on industry.
II.I. Modern Portfolio Theory
As mentioned above, the Modern Portfolio Theory as described by Markowitz (1952) can be seen as the basis for CAPM and other subsequent models. It is also known as the mean-variance analysis because it is based on the expected returns (mean) and the standard deviation (variance) of different portfolios. The theory was developed as a mathematical framework for assembling a portfolio that maximises the expected return for a given level of risk over a holding period. The theory made two fundamental assumptions about investor behaviour. The first assumption is that all investors are rational and want to maximise the expected return of their portfolio. The second assumption is that all investors are risk-averse. This means they will try to keep the variance, or fluctuation, of these expected returns as low as possible. This does not mean that investors do not want to take any risk, but means that they will always prefer the less risky asset if they can choose between two assets. Contrarily, an investor will take on increased risk only if compensated by higher expected returns (Markowitz (1952)).
Given this first assumption, an investor will always try to maximise its profit. An investor will always choose to invest all its capital in the asset with the highest expected net present value (NPV). This implies diversification would not be used. If the second assumption saying that all investors are risk-averse is added, this changes. It is not likely an investor would invest in only one asset risking to lose it all. More likely is that
he would invest in a portfolio with multiple assets which would lower this risk while gaining the same expected return. He would minimise his variance and at the same time maximise his expected return. Markowitz (1952, pp.79) combined these two important assumptions to show that using the correlation between different assets could be used to lower the variance of his expected returns. This is called diversifying a portfolio.
To show how the correlation among individual asset returns affects portfolio risk, consider investing in two risky assets, A and B (example from Perold (2004), pp. 7). Assume that the risk of an asset is measured by its standard deviation of return, which for assets A and B is denoted by σA and σB, respectively. Let ρ denote the correlation between the returns on assets A and B; let x be the fraction invested in asset A and y (= 1−x) be the fraction invested in asset B. When the returns on assets within a portfolio are perfectly positively correlated (ρ = 1), the risk of the total portfolio can be expressed as:
σP = xσA+ yσB (1)
Saying the portfolio risk is the weighted average of the asset risks in the portfolio. The more interesting case is when the assets are not perfectly correlated (ρ<1). Then there is a nonlinear relationship between portfolio risk and the risks of the underlying assets. In this case, at least some of the risk from one asset will be offset by the other asset. Then, the standard deviation of the portfolioσPis always less than the weighted average ofσA andσB. This can be shown using the variance formula:
σ2
P = (xσA+ yσB)2−2xy(1−ρ)σAσB (2)
Whenρ<1, the size of the second term will increase asρ declines, and so the standard deviation of the portfolio will fall as ρ declines. While risks combine non linearly (because of this diversification effect), expected returns do combine linearly. That is, the expected return on a portfolio of investments is just the weighted average of the expected returns of the underlying assets. For instance, by combining two assets with the same expected return and standard deviation in a portfolio, one can obtain a return that is the same as either one of them but a standard deviation that is lower than any
one of them individually. Diversification thus leads to a reduction in risk without any sacrifice in expected return.
There will be many combinations of assets that will result in the same expected return but different risk. Vice versa, there will be many combinations of assets with the same risk but different expected return. By optimising, it can be computed what Markowitz called the ’efficient frontier’. For each level of expected return, there is a combination of assets that has the smallest risk. Contrarily, for each level of risk there is a combination that has the highest expected return. The efficient frontier consists of all optimal portfolios.
II.II. Capital Asset Pricing Model
The CAPM model as described by Sharpe (1964) and Lintner (1965) builds on Markowitz his Modern Portfolio Theory. Sharp and Lintner show that the correlation between the market portfolio and all other assets is only caused by their common dependence on the state of the economy. Here, the Market portfolio is a portfolio that consists of all available assets in the market. With this information, investors could diversify all specific risk, but not the risk inherent to the entire market, also known as systematic risk. Thus, investors should not be granted a higher return for bearing specific risk because this kind of risk can be minimised and in most cases even eliminated by diversification. Therefore, the CAPM says the expected return of a portfolio only depends on one risk factor, the overall market risk. The model is defined as:
E[Ri] = rf +β(E[Rm]−rf) (3)
Here, E[Ri] and E[Rm] are the expected return on the asset and the market portfolio, respectively, and β is the sensitivity of the assets return to the return on the market portfolio.
From this the Security Market Line can be constructed, this is the graphical representation of the linear relation between all assets β’s and expected returns. It is also said by (Sharpe (1964) and Lintner (1965)) this line has the most optimal sharpe-ratio. When
shown graphically with the risk ’beta’ on the horizontal axis and return on the vertical axis, all securities should form a single line, this line is called the Securities Market Line. If the market is in equilibrium, all assets must lie on this line. If this is not the case, there is a possibility for investors to improve and obtain a higher Sharpe Ratio, this was used by Black, Jensen Scholes (1972). In their research the distance that the actual returns lie above or below the SML prediction for the expected return is calledα, this is seen as the pricing error of the model. They argued that if the CAPM was true, α should never be significantly different from 0.
II.III. Three-factor Model
The three-factor-model introduced by Fama and French (1992) is an expansion on the CAPM, adding a size factor and a value factor to the model. This is the model that will be used in this paper, in the next section is discussed what other researchers found by using this model on industry-based portfolios. Before this model was invented, many academics had tried to add new factors to the CAPM. Among them Banz (1981), who found that adding a size factor to the model contributed to explaining stock returns. His results showed that using the market beta as the only explanatory variable gave small firms too low returns and large firms too high returns. The conclusion is that some asset characteristics other than market beta have explanatory power on expected returns. These anomalies lead to the invention of the three-factor model. The three-factor model can be described as:
Ri−Rf = ai+ bi[RM−RF]−siSMB + hiHML +ϵi (4)
In this regression, Ri is the return on portfolio i, RF is the risk-free rate, RM−RF is the market return in excess of the risk-free rate, SMB (Small Minus Big) is the difference between the average returns on (diversified) portfolios of small stocks and big stocks, and HML (High minus Low) is the difference between the average returns on portfolios of high (value) and low (growth) book-to-market ratio (BE/ME) stocks. Here SMB is used to mimic the risk factor in returns related to size. Similarly, HML mimics the risk
factor in returns related to book-to-market equity. For the dependent variable, Fama and French use excess stock returns on 25 portfolios formed as the intersections of five size and five BE/ME groups. The 25 portfolios are used to determine whether the mimicking portfolios SMB and HML capture common factors in stock returns related to size and book-to-market equity. The results of their research confirm that portfolios constructed to mimic risk factors related to size and BE/ME add substantially to the variation in stock returns explained by a market portfolio (CAPM).
Fama and French (1993, 1995) argue that both of these firm characteristics for size and book-to-market ratio are measures of profitability. They found that stocks with a low BE/ME are more profitable than stocks with a high BE/ME. Low BE/ME is characteristic of firms with a high average return on book-equity and a high BE/ME signals low earnings compared to book-equity. Fama and French (1993, 1995) have interpreted their three-factor model as evidence for a "distress premium". Small stocks with high book-to-market ratios are firms that have performed poorly and are vulnerable to financial distress, and hence investors command a risk premium. This financial distress can be explained by a number of causes, for instance, firm inefficiency or cash flow problems (Chan & Chen, 1991). Concluding, while BE/ME ratios and size are not by definition risk factors, they seem to act like risk factors which can help explain a stock’s expected return.
II.IV. Industry-based portfolios
Research has shown that accurately pricing assets with CAPM or 3-factor model (FF3) on an industry level cause problems (Fama & French, 1997, Moerman, 2005). Both the CAPM and FF3 models show a reduction in R2 as well as a significant increase in α when applied on industry-based portfolios. Besides, Fama and French found that the estimated cost of equity becomes imprecise. Their standard errors become more than three percent for both CAPM and FF3. This means that when the models are used to form a prediction interval for the cost of equity using a one-standard-error bounded interval the interval becomes quite large which makes it practically useless (Fama & French, 1997). Furthermore, the estimates of the CAPM and FF3 differ more than two
percent for many industries. These differences are likely driven by uncertainty about true risk factors and imprecise estimates of period by period risk loadings (Fama & French, 1997). This uncertainty in the prediction of the cost of equity cause problems for companies when these estimates are used to evaluate investment opportunities.
III. Data & Methods
This section explains the structure of the data that is used, the empirical model that is estimated and tests used in this paper.
III.I. Data
All the variables used in this paper are measured at monthly frequencies over the period from January 2001 to January 2010, in other words there are 120 time points. The data comes directly from Kenneth French’s Web site1. The explanatory variables, R
M−RF,
HML and SMB, follow the same methodology as the one used in Fama and French (1992, 1993, 1997). The risk-free interest rate is based on the one-month U.S. Treasury Bill rate. The independent variable is measured in value-weighted returns per industry. Here, all listed stocks on NYSE, AMEX and Nasdaq are assigned each June of year t to one of 48 industry portfolio based on its four-digit SIC code. Appendix 1 lists the range of SIC codes that define each industry. These SIC codes come from the Compustat database, whenever Compustat SIC codes are not available, CRSP SIC codes are used. These 48 industries can be grouped by characteristics like cyclicality. A cyclical industry can be seen as an industry that is sensitive to the business cycle, such that revenues are generally higher in periods of economic prosperity and lower in periods of economic contraction. Here, industries that are considered as cyclical are Food Products, Utilities, Pharmaceutical Products, Healthcare, Tobacco Products and Beer & Liquor.
To summarise the data that is used, table 1 shows the average of value-weighted average monthly returns, standard deviation, average number of firms, average total market capitalisation (ME) and the average of value-weighted averages of book-to-market ratio of each industry over the 120 months.
The top-performing industries from this sample are Coal (2.93%/month), Tobacco Products (1.82&) and Industrial Metal Mining (1.70%). The poorest performing industries are Communication (-0.50%) Electronic Equipment (-0.25%) and Printing and Publishing (-0.23%). The monthly standard deviations range from highs of 14.23% (Coal) and 10.59% (Textiles) to lows of 4.14% (Food Products) and 4.39% (Consumer Goods). These are quite high standard deviations, this volatility in returns could be caused by the financial crisis in the last three years of this sample. Other characteristics of the industries are the average number of firms in the industry portfolio, average firm size (ME) and Book-to-market ratio (BE/ME). As Fama and French (1997) pointed out, industries with a low average BE/ME tend to be growth industries and high BE/ME tend to have performed poorly and are vulnerable to financial distress. In this sample, industries with a low BE/ME are Beer Liquor (0.15%), Pharmaceutical Products (0.20%) and Consumer Goods (0.20%). Industries with a high BE/ME are Automobiles and Trucks (1.13%), Fabricated Products (0.80%) and Coal (0.79%).
Table 1: Descriptive statistics
Return Other characteristics Industry Average Std deviation Avg. nr of firms Avg. firm size Avg. BE/ME Agric 1,15 6,10 12 2549,4 0,37 Food 0,65 4,14 67 3962,0 0,32 Soda 0,98 7,65 8 2816,3 0,39 Beer 0,46 4,58 14 16692,4 0,15 Smoke 1,82 7,56 5 29478,6 0,28 Toys 0,35 6,85 36 651,9 0,40 Fun 0,56 8,96 57 2548,3 0,56 Books -0,23 6,29 37 2284,4 0,38 Hshld 0,34 4,39 60 4702,5 0,20 Clths 0,96 6,88 62 1215,1 0,36 Hlth 0,81 6,51 73 1139,6 0,39 MedEq 0,66 4,58 161 1437,4 0,26 Drugs 0,26 4,40 305 3749,6 0,20 Chems 0,64 6,36 77 2709,8 0,42 Rubbr 0,40 6,90 33 628,3 0,48 Txtls 0,73 10,59 14 969,1 0,78 BldMt 0,52 7,11 71 1172,7 0,43 Cnstr 1,00 7,78 49 1399,5 0,59
Descriptive statistics continued...
Return Other characteristics Industry Average Std deviation Avg. nr of firms Avg. firm size Avg. BE/ME Steel 0,54 10,34 53 1815,0 0,64 FabPr 0,37 8,02 15 407,0 0,80 Mach 0,82 7,69 139 1966,1 0,39 ElcEq 0,39 7,17 71 1436,4 0,36 Autos 0,03 9,57 56 1898,0 1,13 Aero 0,74 7,30 18 8203,9 0,36 Ships 1,29 7,76 9 2610,9 0,45 Guns 1,32 6,95 9 3662,1 0,38 Gold 1,33 10,54 7 2625,2 0,41 Mines 1,70 8,86 13 2392,7 0,38 Coal 2,93 14,23 7 2390,0 0,79 Oil 1,04 6,00 150 5867,7 0,43 Util 0,82 4,79 114 4043,4 0,60 Telcm -0,50 6,09 127 6246,5 0,57 PerSv 0,70 5,51 54 934,7 0,39 BusSv -0,16 7,49 610 2192,3 0,23 Comps 0,07 9,86 192 3244,4 0,27 Chips -0,25 10,21 285 2494,3 0,35 LabEq 0,30 8,36 104 912,5 0,37 Paper 0,44 5,78 48 3320,0 0,36 Boxes 0,91 6,73 11 1714,8 0,49 Trans 0,58 5,56 98 2628,7 0,47 Whlsl 0,49 5,20 157 1071,0 0,46 Rtail 0,23 5,24 231 3821,8 0,32 Meals 0,72 5,28 82 1680,3 0,32 Banks 0,15 6,73 658 2162,8 0,52 Insur 0,34 6,35 152 4547,3 0,62 RlEst 0,69 9,77 26 707,1 0,50 Fin 0,51 8,18 122 3383,9 0,45 Other -0,21 6,79 55 7723,2 0,45 Mean 0,63 7,21 100 3504,4 0,44 III.II. Methods
Here, the three-factor model of Fama and French model is used by doing a time-series regression of the industry’s excess return on three factors. The three factors are: excess return of the market portfolio, the difference between the return on a portfolio of small stocks and big stocks (SMB) and the difference between the return on a portfolio of
stocks with a high BE/ME and low BE/ME (HML). The estimated model is described as:
Rit−Rf t = ai+ bi[RMt−RFt]−siSMBt+ hiHMLt+ϵit (5) Where Rit is the rate of return on portfolio (industry) i at time t, Rft is the risk-free rate at time t and RMt is the rate of return on the market portfolio at time t. The estimates give coefficients bi, si and hi which are the factor risk loadings for industry i. The coefficient of the intercept ai is the measure of the pricing error. In total there are N (= 48) time series regressions.
To ensure the validity of this model a test is carried out on the joint significance of the intercept coefficient. This test is also known as the GRS-test of Gibbons, Ross and Shanken (1989). The null hypothesis H0 : (a1, ..., aN) = 0 is tested against Ha : (a1, ..., aN)̸= 0 using the GRS-statistic:
GRS = ( T N ) ( T−N−L T−L−1 ) [ ˆ α′ˆΣ−1αˆ 1 + ¯µ ˆΩ−1µ¯ ] ∼ F(N, T−N−L) (6)
Here, ˆα is a Nx1 vector of estimated intercepts, ˆΣ is the residual covariance matrix, ¯µ is a Lx1 vector of the industry’s factor sample means and ˆΩ is the industry’s factor covariance matrix. T is the total timeframe of 120 months. If H0 is statistically rejected,
there is a significant pricing error present in the estimation.
IV. Results
The goal of this paper is to find patterns in explaining industry portfolios by looking at industry characteristics. As explained in the data section, among the characteristics that will be used are average return, standard deviation of return, average firm size, average BE/ME and cyclicality of the industries. If the data follows the same pattern as in that of Fama and French (1993) it is expected that an industry’s SMB loading will increase if firms in the industry become smaller. Also, it is expected that the HML loading will increase when an industry’s book-to-market ratio increases.
Table 2 shows the estimated factor loadings obtained by estimating equation (6) on each industry over the whole sample (120 months). By looking at this table directly
there is not much out of the ordinary to see. For the four financial industries, Banking, Insurance, Real Estate and other Financials, it can be seen that their factor loadings do not differ significantly from loadings of other industries.
Table 2: Factor loadings per industry by estimating (6)
Intercept Market SMB HML Industry a t(a) b t(b) s t(s) h t(h) R2 Agric 0,87 1,71 0,55 5,15 0,21 1,5 0,04 0,31 0,23 Food 0,38 1,17 0,43 6,41 -0,19 -2,17 0,31 3,45 0,33 Soda 0,33 0,52 0,67 5,08 0,23 1,39 0,64 3,66 0,26 Beer 0,26 0,65 0,35 4,24 -0,2 -1,85 0,18 1,62 0,17 Smoke 1,48 2,25 0,54 3,97 -0,2 -1,14 0,45 2,44 0,17 Toys -0,34 -0,8 0,96 11,07 0,42 3,76 0,63 5,42 0,59 Fun 0,09 0,2 1,54 16,69 0,23 1,93 0,56 4,51 0,73 Books -0,74 -2,11 1,01 13,86 0,16 1,71 0,55 5,71 0,66 Hshld -0,03 -0,09 0,49 6,76 0,01 0,09 0,32 3,39 0,33 Clths 0,51 1,35 1,1 14,05 -0,1 -0,95 0,67 6,4 0,67 Hlth 0,08 0,16 0,52 4,99 0,06 0,45 0,86 6,21 0,35 MedEq 0,26 0,81 0,61 9,29 0,19 2,23 0,27 3,11 0,48 Drugs 0,24 0,68 0,53 7,39 -0,2 -2,19 -0,04 -0,44 0,32 Chems 0,4 1,17 1,1 15,6 -0,18 -2 0,4 4,3 0,69 Rubbr -0,39 -0,94 0,93 10,95 0,58 5,32 0,65 5,74 0,62 Txtls -0,43 -0,68 1,4 10,52 0,55 3,23 1,37 7,71 0,6 BldMt -0,16 -0,41 1,1 13,69 0,22 2,18 0,79 7,37 0,68 Cnstr 0,31 0,65 1,12 11,27 0,39 3,1 0,69 5,24 0,59 Steel 0,44 0,89 1,8 17,51 0,28 2,13 0 0,03 0,75 FabPr -0,15 -0,28 1,08 9,58 0,41 2,83 0,4 2,66 0,5 Mach 0,66 1,92 1,39 19,36 0,13 1,44 0,12 1,2 0,78 ElcEq 0,28 0,85 1,32 19,04 -0,05 -0,52 0,15 1,64 0,76 Autos -0,52 -0,89 1,46 12,02 0,1 0,62 0,77 4,74 0,59 Aero 0,41 0,88 1,09 11,23 -0,21 -1,73 0,57 4,38 0,56 Ships 0,67 1,26 0,97 8,71 -0,03 -0,22 0,85 5,72 0,48 Guns 0,66 1,15 0,42 3,46 -0,02 -0,12 0,77 4,83 0,24 Gold 1,02 1,03 0,37 1,8 0,08 0,31 0,14 0,52 0,03 Mines 1,41 2,25 1,24 9,58 0 -0,02 0,38 2,22 0,46 Coal 2,26 1,83 1,05 4,1 0,63 1,92 0,46 1,35 0,18 Oil 1,01 2,16 0,73 7,57 -0,32 -2,58 0,1 0,81 0,34 Util 0,53 1,39 0,51 6,52 -0,16 -1,56 0,33 3,14 0,32 Telcm -0,35 -1,12 1,09 16,6 -0,25 -2,94 -0,15 -1,68 0,71 PerSv 0,31 0,7 0,59 6,37 0,09 0,77 0,32 2,59 0,29 BusSv 0,22 0,91 1,31 25,76 0,02 0,36 -0,67 -9,88 0,88 Comps 0,47 1,15 1,59 18,68 0,25 2,25 -0,8 -7,04 0,81 Chips 0,07 0,15 1,62 17,14 0,32 2,67 -0,72 -5,7 0,78
Factor loadings per industry continued... Intercept Market SMB HML Industry a t(a) b t(b) s t(s) h t(h) R2 LabEq 0,32 0,87 1,33 17,51 0,42 4,29 -0,39 -3,82 0,79 Paper 0 -0,01 0,89 13,09 -0,12 -1,39 0,63 6,94 0,65 Boxes 0,69 1,61 1,06 11,96 -0,08 -0,71 0,29 2,46 0,56 Trans 0,17 0,53 0,87 12,82 0 -0,02 0,48 5,34 0,62 Whlsl 0,08 0,25 0,82 13,16 0,16 1,96 0,37 4,42 0,64 Rtail -0,02 -0,07 0,84 12,42 -0,06 -0,64 0,27 3 0,58 Meals 0,39 1,17 0,8 11,62 -0,14 -1,58 0,45 4,88 0,58 Banks -0,45 -1,43 1,04 15,89 -0,16 -1,91 0,94 10,71 0,76 Insur -0,06 -0,18 1,01 15,36 -0,3 -3,55 0,72 8,27 0,73 RlEst -0,41 -0,66 1,21 9,38 0,68 4,08 1,15 6,66 0,56 Fin 0,49 1,44 1,52 21,36 0,03 0,35 -0,01 -0,06 0,81 Other -0,45 -1,02 1,04 11,27 -0,1 -0,86 0,33 2,71 0,54 Mean 0,29 0,55 0,98 11,50 0,08 0,49 0,37 2,90 0,54
To ensure the validity of the estimated model the GRS-test is done to test the joint significance of the intercept coefficient. The null hypothesis H0 : (a1, ..., aN) = 0 is tested against Ha : (a1, ..., aN)̸= 0. The result of the test is displayed in table 3. This table shows the H0 is not rejected, this means there are no significant pricing errors with estimating
this model.
Table 3:Gibbons-Ross-Shanken test The GRS test statistic GRS =
( T N ) ( T−N−L T−L−1 ) [ ˆ α′ˆΣ−1αˆ 1+ ¯µ ˆΩ−1µ¯ ] ∼ F(N, T−N−L) is tested for H0 : (a1, ..., aN) = 0
against Ha: (a1, ..., aN)̸= 0; Here, N = 48 (industries), T = 120 (months) and L = 3 (factors)
GRS test for joint significance ofα Nr. of observations: 48
Value df P-value
GRS statistic 0,7808 (48, 69) 0,8169 H0:α = 0 is not rejected
To ease the quest for certain patterns in the estimated factor loadings figure 1 shows three plots. These plots show the relation between average BE/ME, estimated factor
loadings of equation (6) and standard deviation of returns of an industry. The data had one outlier for Automobiles and Trucks with an average BE/ME of 1.13. This outlier is removed to get a clearer view of the trend line. The first thing that stands out is the trend line. For all three plots there is a clear upward trend line on the relation between BE/ME and the estimated factor loadings for Market Return, SMB and HML. When looking at the plotted points of plot a) and b) the upward trend is less visible, a possible cause of the upward slope of the trend line could be due to outliers in the data. However, the plotted points in c) shows a clear upward trend. This is in line with results of Fama and French (1995) where they show that weak firms tend to have high BE/ME and positive slopes on HML, and strong firms tend to have low BE/ME and negative slope on HML. Also, a third variable is used, standard deviation of industry returns, which is shown by the color gradient. In plot a) this shows that higher standard deviations in returns correspond to higher risk loadings for Market Return. Intuitively this should be correct, because higher volatility in returns leads to a higher risk when investing in that particular industry. This cannot be completely confirmed because there are still a few exceptions, this is probably due to an industries idiosyncratic element that is specific to the industry.
Figure 1:BE/ME vs factor loadings
The relation between Average BE/ME, factor loadings estimated by equation (6) and standard deviation of returns of an industry. On the x-axes of all three plots are the average BE/ME, on the y-axes are the estimated factor loadings and standard deviations of returns is displayed by the color gradient. Also, a trend line is plotted. Nr. of data points:
47
In figure 2 the relation between average firm size, factor loadings estimated by equation (6) and a categorical distribution on cyclicality of the industries is shown. The data had two outlier for the Tobacco Products (Avg. ME = 29478, 6) and Beer Liquor (Avg. ME = 16692) industry. These outliers are removed to get a clearer view of the trend line. As stated earlier, it is expected that an industry’s SMB loading will increase if firms in the industry become smaller. this can be confirmed by plot b) which shows a downward trend line of the relation between average firm size and
SMB loading. Another pattern emerges when looking at cyclicality of the industries, four industries which can be seen as non-cyclical industries are marked red in the plots. These are the industries for Food Products, Utilities, Pharmaceutical Products and Healthcare. The two removed industries for Tobacco Products and Beer & Liquor can also be seen as cyclical industries. Noticeable is that these industries have significant low risk loadings for Market return and SMB relative to their size. As can be seen in table 2 the two removed industries also show considerably low risk loadings (Tobacco: b = 0, 54; s =−0, 2; Beer & Liquor: b = 0, 35; s =−0, 2). However, this pattern does not apply to the HML factor loadings. There is a possibility that this pattern is just sheer luck, because only 6 of the 48 were considered to be non-cyclical which is quite a small sample group.
Figure 2:Firm size vs factor loadings
The relation between Average firm size, factor loadings estimated by equation (6) and a categorical distribution of the industries. On the x-axes of all three plots are the average BE/ME, on the y-axes are the estimated factor loadings and non-cyclical industries are displayed by a red color. Also, a trend line is plotted. Nr of data points: 46
V. Conclusion
The three-factor model of Fama and French (1993) posits that expected stock returns can be explained by the Excess Market Return, a book-to-market equity factor (HML), and a size factor (SMB). Only a little research has been done on the application of this factor model on industry portfolios. Therefore, in this paper this model was applied to 48
different industry portfolios using data that ranged from 2000 to 2010 (120 months). The primary purpose was to examine the behaviour of specific industry characteristics with respect to three-factor model in more detail. The idea behind sorting firms on industry classification was to create more manageable groups with comparable characteristics. These characteristics were then used to find certain patterns in explaining these portfolios with the FF3 model. Central in this paper were characteristics like average BE/ME, average market capitalization (ME) and volatility of returns of an industry. Also, having 48 different industries made it possible to find patterns in groups of industry portfolios that share the same characteristics. Therefore, this paper looked into industry groups based on cyclicality and financial versus non-financial industries.
First a test was carried out to test whether there was a significant pricing error found in the results. This test did not reject the null hypothesis that there was no pricing error. Next, based on the factor loadings there was not much out of the ordinary to see. Almost all of the estimated coefficient for the Market Return were significant, for HML most of the coefficient were significant and for SMB about half of the coefficient was significant. When plotted these factor loadings against average BE/ME and size a pattern emerged. There was a clear upward trend in the relation between BE/ME and the HML factor loading. Also, there was a clear downward trend in the relation between average firm size and the SMB loading. These findings are a confirmation on the findings of Fama and French (1993). When a third variable for standard deviation of industry return was added to the plot another pattern came to light where a higher standard deviation appeared to have higher factor loadings for the Excess Market Return. The last pattern that was found by this empirical research was that cyclicality also played a role in determining the factor loadings for Market Return and SMB but not for HML. It was found that non-cyclical industries had significant lower factor loadings for Market Return en SMB. Although this pattern was quite clear, it is also possible this was due to the fact there were only six industries that were considered non-cyclical which is quite a small group.
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Appendix I
Fama and French (1997) use four digit SIC codes to assign firms to 48 industries. This appendix lists the range of SIC codes that defines each industry.
Agriculture 0100-0799, 2048-2048
Food Products 2000-2046, 2050-2063, 2070-2079, 2090-2095 2098-2099 Candy and Soda 2064-2068, 2086-2087, 2096-2097
Alcoholic Beverages 2080-2085
Tobacco Products 2100-2199
Recreational Products 0900-0999, 3650-3652, 3732-3732, 3930-3949 Entertainment 7800-7842, 7870-7870, 7900-7999
Printing and Publishing 2700-2749, 2770-2799
Consumer Goods 2047-2047, 2391-2392, 2510-2519, 2590-2599, 2840-2844, 3160-3199, 3229-3231, 3260-3260, 3269-3269, 3630-3639, 3750-3751, 3800-3800, 3860-3879, 3910-3919, 3960-3964, 3970-3970, 3991-3991, 3995-3995 Apparel 2300-2390, 3020-3021, 3100-3111, 3130-3159, 3965-3965 Healthcare 8000-8099 Medical Equipment 3693-3693, 3840-3851 Pharmacetical Products 2830-2836 Chemicals 2800-2829, 2850-2899
Rubber and Plastic Products 3000-3000, 3050-3099
Textiles 2200-2295, 2297-2299, 2393-2395, 2397-2399 30
Construction Materials 0800-0899, 2400-2439, 2450-2459, 2490-2499, 2950-2952 3200-3219, 3240-3259, 3261-3261, 3264-3264, 3270-3299 3420-3442, 3446-3452, 3490-3499, 3996-3996
Construction 1500-1549, 1600-1699, 1700-1799 Steel Works, Etc., 3300-3370, 3390-3399
Fabricated Products 3400-3400, 3443-3444, 3460-3479 Machinery 3510-3536, 3540-3569, 3580-3599
Electrical Equipment 3600-3621, 3623-3629, 3640-3646, 3648-3649, 3660-3660, 3690-3692, 3699-3699
Miscellaneous 3900-3900, 3990-3990, 3999-3999, 9900-9999
Automobiles and Trucks 2296-2296, 2396-2396, 3010-3011, 3537-3537, 3647-3647, 3694-3694, 3700-3716, 3790-3792, 3799-3799 Aircraft 3720-3729 Shipbuilding, Railroad 3730-3731, 3740-3743 Defense 3480-3489, 3760-3769, 3795-3795 Precious Metals 1040-1049, 1101-1101 Non-Metallic Mining 1000-1039, 1060-1099, 1400-1499 Coal 1111-1111, 1200-1299
Petroleum and Natrual Gas 1110-1110, 1310-1390, 2900-2911, 2990-2999
Utilities 4900-4999 Telecommunications 4800-4899 Personal Services 7020-7021, 7030-7039, 7200-7212, 7214-7299, 7395-7395, 7500-7500, 7520-7549, 7600-7699, 8100-8199, 8200-8299 8300-8399, 8400-8499, 8600-8699, 8800-8899 Business Services 2750-2759, 3993-3993, 7300-7372, 7374-7394, 7396-7397, 7399-7399, 7510-7519, 8700-8799, 8900-8999 31 Computers 3570-3579, 3680-3689, 3695-3695, 7373-7373 Electronic Equipment 3622-3622, 3661-3679, 3810-3810, 3812-3812 Measuring and Control Equip. 3811-3811, 3820-3832
Business Supplies 2520-2549, 2600-2639, 2670-2699, 2760-2761, 2950-3955 Shipping Containers 2440-2449, 2640-2659, 3210-3221, 3410-3412 Transportation 4000-4099, 4100-4199, 4200-4299, 4400-4499, 4500-4599, 4600-4699, 4700-4799 Wholesale 5000-5099, 5100-5199 Retail 5200-5299, 5300-5399, 5400-5499, 5500-5599, 5600-5699 5700-5736, 5900-5999
Banking 6000-6099, 6100-6199
Insurance 6300-6399, 6400-6411
Real Estate 6500-6553, 6590-6590
