Making Profit on Human Vice – an Investigation on The
Performance of Sin Stocks in the U.S
ABSTRACT
This paper researches the performance of three sinful industries in order to determine whether they outperform the market. Two time periods are investigated – first from 1963 until 2017 and second from 2004 until 2017. The three sinful industries considered are the alcohol, tobacco and defense, focusing on companies active in the U.S market. The performance of the sin portfolios is evaluated using the Fama-French (2015) market, size, value, investment, profitability and Cahart’s (1997) momentum factors. Evidence for an outperformance of the tobacco and defense industry portfolios for the second period is found consistent with previous research.
Bachelor thesis Finance and Organization Author: Olya Andonova
Student number: 11019891 Supervisor: dr. L. (Liang) Zou Date: 31.01.2018
2 Statement of Originality
This document is written by Student Olya Andonova who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is 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.
Table of Contents
I. Introduction 4
II. Literature review 6
III. Methodology 10
1. Capital Asset Pricing Model 2. Fama-French Three-Factor Model
3. Fama-French Three-Factor Model and Cahart’s Momentum Factor 4. Fama-French Five-Factor Model
IV. Data 14
1. Sin portfolios
2. Variables from models 3. Summary statistics V. Results 18 1. Discussion 2. Regression tables VI. Conclusion 27 VII. References 28 VIII. Appendix 30
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I.
Introduction
Certain norms exist in society concerning moral behavior and action. These norms are believed to influence market outcomes as they govern conduct and their presence in the market at times overrides the profit maximizing goal of agents. The existence of social norms can explain why economic agents, such as institutional investors, are less willing to hold sin stocks in their portfolios (Hong & Kacperczyk, 2009). What are commonly referred in literature as “sin” stocks are precisely stocks of companies involved in what society believes is immoral and unethical human behavior, consequently making profit on human vice. Sin industries are comprised of activities, both production and services, involving alcohol, tobacco, gaming, defense, nuclear power and adult entertainment (Blitz & Fabozzi, 2017; Statman & Glushkov, 2009).
Researching sin stocks and their influence in the market, Hong and Kacperczyk (2009) postulate that sin stocks have higher expected returns than comparables. This result is consistent with investors’ unwillingness to include them in their portfolios. Meaning that in order to adhere to social norms, investors forgo possible higher returns from holding stocks in vice industries (Hong & Kacperczyk, 2009). Academics research both social and non-social factors for this phenomenon such as religion, political identification, cultural characteristics, litigation risk and financial reporting quality. The results are consistent and demonstrate the negative impact of social views on the demand for sin stocks, while this demand is not explained by a poorer performance reflected by lower quality of financial reports or lower returns (Hong & Kacperczyk, 2009; Kim & Venkatachalam, 2006; Salaber, 2007). However, in their research published in 2017, Blitz and Fabozzi find that when controlling for exposures to the two new Fama and French (2015) quality factors - profitability and investment, sin stocks do not bring higher risk-adjusted returns, a result that is conflicting with the research done so far on this topic. Consequently, due to these contradicting results more research should be carried out to understand the relative performance and returns of vice stocks.
Therefore, the aim of this paper is to examine whether investing in sin stocks leads to different risk-adjusted returns than when investing in the market. This leads to the research question of this paper - whether sin stocks in the U.S, which are stocks of companies involved in immoral or unethical activities, outperform the market?
In order to answer this question, three portfolios of sin stock industries from companies that are active in the US stock market are obtained from the Kenneth R. French database, gathering data for the period from 1963 until 2017. Following, the excess return of the three sin portfolios – namely beer, smoke and guns, is evaluated using The Capital Asset Pricing Model (Sharpe, 1964; Linter, 1965), the Fama-French (2015) factors of size, value, profitability and investment, as well as Carhart’s (1997) momentum factor. Furthermore, this evaluation is performed twice – once for the entire period, and a second time for the period between 2004 until 2017. During the sub-period, there is a considerable increase in socially responsible investment screening by investors in the U.S, leading to shunning of sin stocks, thus the impact on their performance in this period could be substantial and gives reason to investigate this time frame.
The first null hypothesis states that stocks of companies involved in unethical or immoral activities do not outperform the market during the period between 1963 to 2017 as well as during the sub-period from 2004 until 2017. This means that there are no abnormal returns for investors holding portfolios of sin stocks and the market is efficient. Consequently, the alternative hypothesis states that investing in portfolios constructed of sin stocks provides a risk-adjusted abnormal return during the period between 1963 to 2017 as well as during the one from 2004 until 2017.
The regression results for the sub-period show an outperformance of the smoke and guns portfolio, thus the models are unsuccessful in explaining the returns of the two portfolios. The findings lead to a rejection of the null hypothesis, meaning the market is inefficient and holding sin stocks in the smoke and guns industry in the years 2004 until 2017 leads to an abnormal risk-adjusted return for investors. For the beer portfolio, once including the investment and profitability factors, alpha is insignificant therefore the null hypothesis is not rejected and there is market efficiency for both periods under investigation.
The remainder of this paper is organized in five sections. Section II continues with a literature review. In Section III, a description of the method used is presented. Section IV comprises of a description of the data and of the selection of the sin portfolios. The empirical results are presented in Section V along with a discussion of the findings. Section VI concludes.
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II.
Literature review
In this section, a review of past literature and research on the effect of norms on sin stock performance is presented along with literature on responsible investment.
Early research into the effect social norms have on economic behavior focuses on the labor market. The taste-based model of discrimination presents a situation where agents choose not to enter into contracts with hiring a subset of individuals based on their race or gender, even if doing so means incurring a financial cost (Becker, 1957). In an unemployment setting, in spite of incurring costs from following social norms, agents still choose to do so due to a perceived loss of reputation from diverging (Akerlof, 1980). Therefore, the presence of social values in economic activities can be costly for agents as norms are not necessarily outcome oriented (Elster, 1989). There are two reasons why this is the case. First reason concerns the firm - production that is sustainable is also not cheap, and adherence to all social standards not only for production but for all other actions executed in a firm takes a lot of time and resources. The second reason concerns the constraint resulting from the task of investing in only virtue stocks on an investor’s ability to diversify his portfolio, which can lead to underperformance when compared to an unconstrained portfolio (Fabozzi, Ma & Oliphant, 2008). In order to invest only in virtue stocks a common definition of “vice” stocks is needed in order to make a distinction between the two. In their paper, Fabozzi, Ma & Oliphant (2008) discuss the meaning of “sin” or “vice” as well as “sinful” used in relation to economic behavior. The authors argument that “sinful” behavior is determined by the religious characteristics of the place where the action is performed. Therefore, what each society determines as boundaries of “good” and “bad” differs and is subject to change over time, and what is considered to be a sin investment varies with different societies. Nevertheless, even with the presence of this constant change, there exist social norms against supporting companies that offer products and services considered as sinful, and investors may not want to be associated with such actions.
More recent research on the effect social norms have on economic behavior is carried out in the stock market as it is ideally suited for investigating how social norms affect decisions due to the abundance of data and the costs an investor, seeking to create an optimal portfolio, incurs when he constrains his investment pool (Hong & Kacperczyk, 2009). In their research on sin stocks, Fabozzi and al. (2008) use data from 21 national markets for the period of 1970 until 2007.
Using the Capital Asset Pricing Model, the authors focus on stocks of companies involved in tobacco, alcohol, and gaming – the so-called ‘‘Triumvirate of Sin’’, as well as stocks of firms active in adult entertainment, biotech and weapons industry. They find a significant return premium from investing in six vice portfolios. Their results show a 3% yearly outperformance of sin stocks when compared to the market on a raw basis, and nearly 6% yearly outperformance on a beta-adjusted basis. Thus, their findings are consistent with the existence of an economic benefit from investing in sin stocks. The main reason for these results, the authors contribute to the lack of necessity for sinful companies to comply with the costly, implicit or explicit, social standards. The conclusion from this research is that even though sin industries are the hardest to start, monitored quite closely and largely affected and disciplined by social opinion and more precisely scrutiny, the ones that have survived enjoy a positive monopolistic return as proven by the positive risk-adjusted returns.
Previous literature examines the existence of neglect towards sin stocks by institutional investors who rely on Socially Responsible Investment (SRI) screens. The reason for this neglect can be ascribed to the “norm-constrained hypothesis” which states that investors who are constrained by certain norms disregard firms from sinful industries (Hong & Kacperczyk, 2009). This action of shunning sin stocks, along with their defensive nature resulting from the addictive traits of sinful products, is proposed by Hong and Kacperczyk (2009) as an explanation to the outperformance of sin stocks. In their paper, Hong and Kacperczyk (2009) find that vice stocks in the US market outperform their comparables by 26 basis points in the period from 1965 until 2006, even after controlling for the three factors from the Fama-French three-factor asset pricing model combined with the momentum factor. Kim and Venkatachalam (2006) research the possible causes of the neglect effect, more precisely whether it can be attributed to information risk due to poor financial reporting quality. However, the conclusion is that the reporting quality of vice companies is in fact superior to a control group of firms, thus the investors’ disregard of sin stocks is doubtfully due to financial reporting characteristics. Apart from institutional investors neglecting vice stocks, certain individual investors, free to make their own investment decisions, do not invest in sinful industries as that is not in line with their moral values (Fabozzi et al., 2008). Thus, investing in sin stocks is an action undertaken by only a subset of investors having the willingness or permission to incur the social cost. The conclusion from these studies is that investors who neglect sin stocks despite their higher returns and superior financial reporting quality, are in fact
8 basing their portfolio choices on non-financial tastes.
Apart from social norms affecting the willingness of investors to hold sin stocks, political identification is considered as a possible explanation of the neglect effect. Using a large sample of U.S. mutual fund managers, their political contributions and the score of corporate social responsibility by the KLD statistic, tracking controversial business issues, Hong and Kostovetsky (2012) examine this possible explanation. The authors find that for the period from 1992 until 2006 Democrats who make donations are less willing to hold socially irresponsible stocks from firms active in tobacco, guns, defense and natural resource services than either non-donators or Republican donors. This result leads from a sample comprised of large professional managers, who are considered to be price setters in markets, leading to the conclusion that as SRI screening is applied by an ever-increasing number of investors globally, it’s impact on asset prices could be considerable (Hong & Kostovestky, 2012). Furthermore, social views also impact firm specific variables. Research shows that a firm conforming to social norms has higher equity valuation than a firm that does not abide by them, a finding consistent across G20 nations (Fauver & McDonald, 2014).
The majority of studies on vice stock performance focus mostly on U.S. publicly traded stocks. Salaber (2007) researches sin stocks in three industries namely tobacco, alcohol and gambling, and their performance in 18 European countries over the period between 1975 and 2006. In her research, Salaber (2007) focuses on other non-social reasons causing investors’ neglect of sin stocks namely the effect of religion, legal and cultural environment. The results from the paper show evidence that religion affects investment choices – Protestants refrain from investing in sin stocks more than Catholics, and demand a significant premium in order to do so. Moreover, the presence of high excise taxation and litigation risk leads to an outperformance of sin stocks, even when controlling for market capitalization and book-to-market ratio (Salaber, 2007). Thus, the returns on sin stocks depend on the legal and religious characteristics of the country considered.
While previous research provides support for a significant outperformance of sin socks, a recent paper contradicts these findings. Blitz and Fabozzi (2017) analyze U.S sin stocks over the period of 1963 until 2016 and European, Japanese and Global sin stocks over the period of 1990 until 2016. The authors investigate the performance of three sinful industries– the alcohol, tobacco and weapons or defense industry. Blitz and Fabozzi (2017) use as explanatory variables the market excess return, the Fama-French factors of size, value, investment and profitability, as well as the
momentum factor and the low-versus high-beta BAB factor. When using all factors in their regression, the results show no abnormal return from holding sin stocks, however alpha remains positive. The authors emphasize that excluding vice stocks still has an effect on performance. The positive exposure sin stocks have to factors that enjoy positive premiums such as the Fama-French factors, implies that the raw expected return of sin stocks remains higher when compared to the market one, and shunning sin stocks negatively affects the raw expected return of an investor’s portfolio (Blitz & Fabozzi, 2017).
Investing in sin stocks is commonly referred in literature as socially (ir)responsible investment, thus implying it is the exact opposite of socially responsible investment (SRI). Socially responsible investment considers the environmental, social and corporate governance (ESG) criteria to simultaneously have market competitive returns and a positive impact on society.1 A growing number of investors follow SRI screens in their portfolio selection. According to a 2016 report2 by The Forum for Sustainable and Responsible Investment (US SIF), in the U.S 22 % of the $40.3 trillion in total assets under management is involved in SRI. The statistics confirm the existence of an excess demand for socially responsible stocks and a shortage for irresponsible stocks (Galema, Plantinga & Scholtens, 2008). This dynamic is theorized to lead to an overpricing of socially responsible stocks and underpricing of socially irresponsible stocks. Thus, the returns from investing in a SRI should be lower than the returns from investing in a non-SRI or unconstrained assets - for example, a portfolio consisting of sin stocks (Fabozzi, Ma & Oliphant, 2008). Galema et al. (2008) research the impact that performance, rated on the basis of social responsibility criteria, has on US portfolio returns, book-to-market values and excess stock returns. Their results show SRI as having a lowering effect on book-to-market ratios, which consequently affects stock returns without in fact generating positive alphas (Galema et al, 2008).
There are two types of screening an investor can apply in his portfolio selection– positive and negative. When companies have a strong record, including them in the portfolio and/or increasing their weights is referred as positive screening, and negative screening implies the opposite – excluding or reducing the weights of companies with weak social responsibility scores (Statman & Glushkov, 2009). Statman and Glushkov (2009) analyze the performance of stocks rated on social responsibility characteristics using the KLD statistics, tracking controversial
1
See http://www.ussif.org/sribasics
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business issues, for the years 1992 until 2007. The results from their research are twofold. First, investors who hold stocks in companies with high rating in the KLD statistics have an advantage compared to conventional investors. However, shunning certain stocks leads to a lower return than conventional investors. This disadvantage offsets the positive impact of holding highly rated companies, thus in total the effect of screening is negative. The conclusion that arises is that it is in investors’ best interest to include and increase the weights of highly rated stocks without neglecting the stocks of any company (Statman & Glushkov, 2009).
III. Methodology
In this section, a description of the method used for constructing the sin portfolio is presented along with the models used to measure the portfolio’s performance.
The method of research on sin stock performance in this thesis is based on the paper by Blitz and Fabozzi (2017). In their paper, the authors conduct six different regressions. The research in this paper uses the same choices of explanatory variables, with the exception of low-versus high-beta factor (BAB). In total, there are four models. Starting with the Capital Asset Pricing Model (CAPM), following the Fama-French Three-Factor Model, Fama-French Three-factor Model in combination with Carhart’s Momentum Factor, and lastly the Fama-French Five-Factor Model.
In order to use each of the models, three sin portfolios, involved in the tobacco, alcohol or defense industry, are obtained from the Kenneth R. French library. The excess return of each portfolio is calculated by subtracting the risk-free rate from the return of the respective portfolio 𝑅",$− 𝑅&,$. In all of the regressions, White’s (1980) heteroscedasticity robust standard errors are used.
To answer the research question of this paper, the following hypotheses are going to be evaluated using the four models mentioned above. Each refers to both the entire period and the sub-period.
Hypothesis 0: There is no risk-adjusted abnormal return from holding one of the three sin portfolios during the period under investigation
Hypothesis 1: There is risk-adjusted abnormal return from holding one of the three sin portfolios during the period under investigation
The statistical hypotheses are as follows: 𝐻(: 𝛽+ = 0
𝐻.: 𝛽+ ≠ 0
The methodology section of this paper continues with four subparts, presenting academic literature on each of the main models applied along with the regression equations used in this research and an explanation of the meaning of the variables. The methodology section ends with Table 1 summarizing the models and variables.
1. Capital Asset Pricing Model
Prior to the Capital Asset Pricing Model, the absence of a way to account for different conditions of risk made attempts to predict the behavior of capital markets problematic (Sharpe, 1964). The CAPM introduces a way to describe the relationship between the systematic risk notated with b and the expected return of assets. The model uses the systematic risk as part of the total risk, namely the idiosyncratic risk, can be diversified away. The investor is compensated only for the time value of money represented by the risk-free rate or 𝑅& and the systematic risk. Following the development of CAPM, Jensen (1968) presents a direct application of the theory that can be used for the evaluation of the predictive abilities of portfolio managers. Jensen’s alpha can be described as follows:
𝑅",$ = 𝛼"+ 𝑟&,$+ 𝛽" 𝑅3,$ − 𝑅&,$ + 𝜀$ (1)
Here, 𝑅",$ is the rate of return on portfolio p or alternatively asset i at time t, 𝑅&,$ is the risk-free rate of return and 𝑅3,$ is the return of the market proxy. The Market Risk Premium is calculated by subtracting 𝑅3,$− 𝑅&,$ , which is the excess return an investor would receive by investing in the market portfolio above the risk-free rate. The systematic risk is represented by the coefficient b and the disturbance term 𝜀$ has an expected mean of zero. When estimating whether there is a risk-adjusted abnormal return, we look at the alpha coefficient. Alpha is the abnormal return of the portfolio and it can be both positive or negative, depending on whether the returns of a portfolio or stock are above or below a well-diversified market portfolio.
12 The regression equation looks as follows:
𝑅",$− 𝑅&,$ = 𝛼"+ 𝛽. 𝑅3,$ − 𝑅&,$ + 𝜀$ (2)
Where, 𝛽. represents the sensitivity of the portfolio’s returns to the return on the market - a measure of volatility. The market beta is equal to one. When all else is held constant, if 𝛽. is
significantly lower than zero, the portfolio’s returns are noncyclical, meaning they are less volatile than the market, and if 𝛽. significantly higher than zero the returns are cyclical, thus more volatile than the market. An evaluation of the significance of the intercept of the regression or 𝛽+ is needed in order to assess whether the sin portfolios outperform the market. If 𝛽+ is significantly different
from zero, the null hypothesis, stating that sin stocks do not outperform the market, is rejected.
2. Fama-French Three-Factor Asset Pricing Model
The Capital Asset Pricing Model is widely used in empirical research in finance, however when explaining returns of stocks, it does not capture anomalies unexplained by the systematic risk component (Fama & French, 1992). A development that provides other explanatory factors is the Fama-French Three-Factor Model. The model includes two new components – the Small minus Big (SMB) and High minus Low (HML). The two factors capture the risk related to firm size and firm value and provide a greater explanatory power when measuring stock performance. The model looks as follows:
𝑅",$− 𝑅&,$ = 𝛼"+ 𝛽" 𝑅3,$− 𝑅&,$ + 𝑠"𝑆𝑀𝐵$+ ℎ"𝐻𝑀𝐿$+ 𝜀$ (3)
Here, apart from the components also present in the CAPM – the rate of return on the portfolio, the risk-free rate of return, the market premium, the coefficient beta and the disturbance term, 𝑆𝑀𝐵$ represents the size factor and 𝐻𝑀𝐿$ represents the value factor. In this model as well, alpha is the abnormal return left unexplained by the other factors.
The regression equation used is as follows: 𝑅",$ – 𝑅&,$ = 𝛼" + 𝛽.(𝑅3,$− 𝑅&,$) + 𝛽?𝑆𝑀𝐵$ + 𝛽@𝐻𝑀𝐿$ + 𝜀$ (4)
In order to capture the effect of market, size and value, the coefficients represented by 𝛽., 𝛽? and 𝛽@ are included. The latter two can be interpreted in the following way – when holding all else constant, if 𝛽? is negative the sin portfolio correlates more with big capitalization companies than
book-to-market equity firms than with low book-to-market equity firms.
3. Fama-French Three-Factor Asset Pricing Model and Carhart’s Momentum Factor
Jegadeesh and Titman (1993) find that in stock returns there is a risk caused by a momentum factor or so-called “hot hand” factor. Carhart (1997) expands the Fama-French 3 Factor Model with the momentum (MOM) factor representing the possibility to have superior performance by buying stocks that performed well in the past 3-12 months, called winners, and selling stocks that performed poorly in the same time span, called losers (Carhart, 1997). The model equation for a portfolio is as follows:
𝑅",$ − 𝑅&,$ = 𝛼"+ 𝛽" 𝑅3,$− 𝑅&,$ + 𝑠"𝑆𝑀𝐵$+ ℎ"𝐻𝑀𝐿$+ 𝑚"𝑀𝑂𝑀$+ 𝜀$ (5)
Where the difference with the Fama-French Three-Factor model is presented by 𝑀𝑂𝑀$ - the average return on past winners minus past losers.
The regression equation used:
𝑅",$ − 𝑅&,$ = 𝛼"+ 𝛽. 𝑅3,$− 𝑅&,$ + 𝛽?𝑆𝑀𝐵$+ 𝛽@𝐻𝑀𝐿$+ 𝛽C𝑀𝑂𝑀$+ 𝜀$(6)
Here, the coefficient 𝛽C represents the effect of the “hot hand” factor, and when all else is held constant, if 𝛽C is positive then the sin portfolios correlate more with recent winners or good performers than with losers or bad performers. The other variables’ meaning remains the same as described before.
4. Fama-French Five-Factor Asset Pricing Model
Research in previous years by Titman, Wei and Xie (2004) as well as Novy-Marx (2013) finds that Fama-French 3 Factor model is incomplete in terms of predicting the expected returns as it misses the variation in average returns related to profitability and investment. Consequently, in order to improve the predictive powers of the three-factor model, Fama and French (2015) present a new Five-Factor asset pricing model that includes precisely the two missing factors. The Fama-French 5 Factor model:
𝑅",$− 𝑅&,$ = 𝛼"+ 𝛽" 𝑅3,$ − 𝑅&,$ + 𝑠"𝑆𝑀𝐵$+ ℎ"𝐻𝑀𝐿$+ 𝑟"𝑅𝑀𝑊$+ 𝑐"𝐶𝑀𝐴$+ 𝜀$ (7)
14 The regression model used:
𝑅",$ − 𝑅&,$ = 𝛼"+ 𝛽. 𝑅3,$ − 𝑅&,$ + 𝛽?𝑆𝑀𝐵$+ 𝛽@𝐻𝑀𝐿$+ 𝛽C𝑅𝑀𝑊$+ 𝛽H𝐶𝑀𝐴$+ 𝜀$ (8) Where the effect of the two newly introduced factors on the excess return on the portfolios is captured by the coefficients 𝛽C and 𝛽H. When all else is held constant, if 𝛽C is significantly positive it means the sin portfolios correlate more with companies with high profitability, and if 𝛽H is significantly positive it means the sin portfolios correlate more with companies with conservative investment.
In total eight regressions are performed for each of the three sin stock portfolios- four for the entire period and four for the sub-period. Table 1 summarizes the variables included in the models.
Table 1. Summary of models and variables
Model Variable Type Definition
(1) CAPM 𝑅_𝑚 − 𝑅_𝑓 Independent The market risk premium
𝑅_𝑓 Independent The risk-free rate of return on U.S Treasury Bills
(2) FF3 SMB Independent The size factor
HML Independent The value factor
(3) FF3+MOM MOM Independent The momentum factor
(4) FF5 RMW Independent The profitability factor
CMA Independent The investment factor
𝑅_𝑏 Dependent Daily return on beer industry portfolio
𝑅_𝑠 Dependent Daily return on smoke industry portfolio
𝑅_𝑔 Dependent Daily return on guns industry portfolio
IV. Data
In this section, a description of the necessary data and the method for its collection is presented along with summary statistics.
When investigating the performance of vice stocks, important tasks are to first define which industries are to be categorized as sinful, and consequently identify the companies active in them,
whose stocks are viewed as sin stocks. The definition in this paper is based upon the choice of sinful industries in previous literature, namely industries involving the production and services of alcohol, tobacco, gaming, military or defense (Statman & Glushkov, 2009). The U.S market is investigated as the majority of sin companies are based in the country, thus dominating the overall sin market (Lobe & Walkshäus, 2016).
Past papers on sin stock performance select companies based on Kenneth R. French’s database, the KLD Statistics or self-selection based on multiple criteria. This paper selects portfolios of sin industries available in the Kenneth R. French data library3. The library contains all companies traded on NYSE, AMEX or NASDAQ and groups them into different portfolios based on industry involvement. The database classifies stocks based on their Standard Industrial Classification (SIC) codes into 49 industries. Three of the industry portfolios are selected and defined as sinful. Namely, the beer, smoke and guns industry portfolios. Companies having SIC codes 2100-2199 are allocated to the beer group, 2080-2085 in the smoke group and 3795 along with 3480-3489 in the guns group. The beer industry includes manufacturers and distributers of malt beverages, along with producers, distillers and shippers of wine, brandy and brandy spirits. The smoke industry comprises of companies engaged in the manufacturing or distributing of cigarettes, cigars, chewing tobacco or engaged in the stemming and redrying of tobacco. The guns industry represents manufacturers and distributers of guns, ammunitions, missiles and bombs among others4. The daily return on the three portfolios are average value-weighted and are updated annually at the end of June. The Kenneth R. French’s database for industry portfolios for entertainment stocks does not separate gaming stocks from others, thus no separate portfolio exists for gaming and this leads to its exclusion from this investigation on sin stocks.
Following, all data on the variables included in the models is also obtained through Kenneth French’s database. The data from Kenneth R. French’s website is in basis points, commonly used for percentage change in financial instruments, where one basis point represents one hundredth of a percentage. The data on the Fama-French (2015) five-factors – market, size, value, profitability and investment as well as Carhart’s (1997) momentum factor is daily from 1963-2017 for the U.S. Using six value-weighted portfolios formed on either size and book-to-market, size and operating profitability or size and investment, the Fama-French five-factors are
3 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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constructed. The size factor is constructed using the returns of two types of companies – ones with big market value of equity and ones with small market value of equity, where the breakpoint between the two is the NYSE median market capitalization. The value factor represents two different stock categories – value and growth, and is constructed using the 30th and 70th percentile of the B/M ratio (book-value of equity/market-value of equity) for NYSE listed stocks. The value companies lie above the 70th percentile, whilst the growth companies are below the 30th percentile. The profitability and investment factors are constructed in a similar way to the value factor. The profitability factor is the difference between the return on robust profitability portfolios on day t and the return on weak profitability portfolios on day t. It classifies firms into two categories – those with robust operations, meaning they have the highest profits, and those with weak operations. The investment factor is the difference between the return on conservative investment portfolios on day t and the return on aggressive investment portfolios on day t, where, conservative investment implies less investment in asset growth. The profitability and investment factors are meant to capture the influence high/low profitability, conservative/aggressive investment have on returns of stocks (Fama & French, 2015).
The momentum factor is constructed using six value-weighted portfolios formed on size – market value of equity, and prior two to twelve monthly returns, including all stocks listed on NYSE, AMEX or NASDAQ with prior returns available. MOM is the average return on the two top winners (highest prior portfolios) minus the two bottom losers (lowest prior portfolios) using the NYSE median market capitalization for the size breakpoint and 30th and 70th percentile for the prior return breakpoint. The research in this paper uses as market proxy the one present in the Kenneth French’s database, constructed with the value-weighted returns of all companies in the Center for Research in Security Prices (CRSP) database, having a share code of 10 or 11, and traded on the NYSE, AMEX or NASDAQ. The excess return or the Market Risk Premium is the difference between the returns of the market proxy and the risk-free rate of return on the one-month Treasury bill. Following, the excess returns of each of the three sin portfolio are calculated using the same risk-free rate.
This paper investigates the performance of the three sin industries as far back as data is available on industry returns and factors. In Kenneth R. French’s library, the data on all variables needed is available from 1963 until October 2017. Thus, 1963 is the starting point of the sin stock performance evaluation. The sub-period under investigation starting from 2004 until 2017 is
chosen on the basis of a report from The US SIF Foundation's Center for Sustainable Investment Education published in 2014. The choice for the beginning of the sub-period is based on the growth of SRI in the US from 2004 onwards, visible from Figure A below. As SRI investment implies negative screening of sin companies and putting more weight on ESG responsible companies, it is interesting to examine whether in this period there is a significant risk-adjusted abnormal return from holding the three sin portfolios.
Summary statistics are presented in Table 2. For the entire period, all of the portfolios earned an average daily excess return higher than the market, however all three had a higher standard deviation than the market as well. Thus, for the overall period it seems the higher return compensates for higher risk. However, for the sub-period, both the beer and smoke industry portfolios provide an excess return higher than the market whilst their standard deviation is lower than the market one. This points to a possible positive outperformance of the two respective sin portfolios. In the Appendix 1, Table A presents a correlation matrix between all the variables used in the models for the entire period of 1963 until 2017 as well as for the sub-period 2004-2017. The market risk premium is negatively correlated with value, profitability and investment factors. The two value and investment factors exhibit positive correlation of 0.56 over the entire period and 0.23 over the sub-period, the existence of which is present as well in the paper by Fama and French (2015). A negative correlation exists between the value and momentum factor of -0.53 for the
18
entire period and -0.25 for the sub-period, a relation consistent with previous research on the co-movement of the two factors (Moskowitz & Pedersen, 2013). No sign of multicollinearity is present.
Sub-period 2004-2017
Variable Average daily return Standard deviation Min Max
𝑅M− 𝑅& 0.0392% 0.9318% -7.70% 10.12% 𝑅N− 𝑅& 0.0633% 1.1491% -8.29% 13.31% 𝑅O− 𝑅& 0.0623% 1.2737% -9.00% 10.22% 𝑅3− 𝑅& 0.0361% 1.1727% -8.95% 11.35% SMB 0.0066% 0.5619% -3.41% 4.48% HML 0.0035% 0.6311% -4.22% 4.83% MOM 0.0063% 0.9446% -8.20% 7.01% RMW 0.0130% 0.3691% -2.60% 1.94% CMA -0.0018% 0.2977% -1.70% 1.97%
Observations for entire period n = 13679, for sub-period n = 3483. 𝑅M− 𝑅& is the Return on beer portfolio – risk free rate, 𝑅N− 𝑅&is the Return on smoke portfolio – risk free rate, 𝑅O− 𝑅& is the Return on guns portfolio – risk free rate, 𝑅3− 𝑅& is the market risk premium; SMB, HML, MOM, RMW, CMA are size, value, momentum, profitability and investment factors respectively.
V.
Results and Discussion
In this section, the results from the four regressions performed are presented along with a discussion of the findings.
Table 2. Summary statistics Entire period 1963-2017
Variable Average daily return Standard deviation Min Max
𝑅M− 𝑅& 0.0356% 1.1141% -14.76% 10.12% 𝑅N− 𝑅& 0.0482% 1.3554% -14.02% 14.97% 𝑅O − 𝑅& 0.0379% 1.3788% -19.52% 14.90% 𝑅3− 𝑅& 0.0252% 0.9834% -17.44% 11.35% SMB 0.0086% 0.5186% -11.21% 6.11% HML 0.0172% 0.5010% -4.22% 4.83% MOM 0.0307% 0.7018% -8.20% 7.01% RMW 0.0124% 0.3709% -3.03% 4.52% CMA 0.0138% 0.3646% -5.93% 2.53%
For each of the three sin portfolios, namely beer, smoke and guns, eight regressions are performed – four for the entire period of 1963 until 2017 and four for the sub-period of 2004 to 2017. Two additional tests are performed in an attempt to explain market inefficiency. In total, 26 regressions are performed. The four regression equations are based on The Capital Asset Pricing Model, The Fama-French Three-Factor Model, The Fama-French Three-Factor Model combined with Carhart’s Momentum Factor and The Fama-French Five-Factor Model. The results from all of the regressions are summarized in Tables 3, 4, 5 for the respective sin industry portfolios in the U.S. market. In all of the regressions the coefficient 𝛽., measuring the sensitivity of the stock returns to the return of the market, is tested against one, all other coefficients are tested against zero, and significance levels are shown with respect to the two different tests. For each regression, the null hypothesis is 𝐻+: 𝛼 = 0, thus testing whether each of the three portfolios for either the entire period or sub-period, outperforms the market or whether there is market efficiency. If 𝐻+ is not rejected, there is market efficiency, in the case where 𝐻+ is rejected, market is inefficient and there is a risk-adjusted abnormal return from holding one of the sin portfolios. In each regression, White’s (1980) heteroscedasticity robust standard errors are used, presented between parentheses in the tables below.
Results
In all of the regressions for the three sin industry portfolios, the coefficient of the market 𝛽. is tested against one, evaluating whether the portfolio of stocks is more or less volatile than the market, where the market beta equals one. The results for the beer, smoke and guns industry portfolio show that the beta coefficient on the market remains consistently significant at the 1% level and is lower than one, indicating the less volatile nature of sins stocks when compared to the market.
The first regression performed is based on the Capital Asset Pricing Model. The findings are consistent with previous research – for the entire period as well as for the sub-period, there exists a significant alpha for the beer and smoke portfolio. The situation differs for the guns portfolio, where considering the entire period the CAPM alpha is insignificant, however when looking at the sub-period only, the alpha is significant at the 5% level and positive. The first finding results in the conclusion of market efficiency, the second in the rejection of the null hypothesis thus market inefficiency is present.
20
The second regression includes the size and value factors. The coefficients on the size and value factors are negative and significant at the 5% level across the tables with some exceptions, indicating that the return of sin stocks correlate more with large market capitalization stocks and with low equity-to-market companies, or growth stocks. This result is consistent with previous findings where vice stocks present the same relation with the two factors (Blitz & Fabozzi, 2017). For the beer portfolio, the model successfully explains the returns indicated by an insignificant, albeit positive alpha, whereas for the entire period the null hypothesis is rejected due to the highly significant coefficient at the 1% level. The three-factor model is unsuccessful in explaining the returns of the smoke industry, where in the two periods the alpha remains significant at the 1% level. Finally, the pattern exhibited previously for the guns portfolio is present in this model regression as well – for the entire period, the abnormal return is insignificant, whereas for the sub-period it remains significant at the 5% level.
Following, the four-factor model – including size, market, value and momentum factor, provides similar results. A pattern is also present in the regression results for the beer portfolio- the entire period results lead to a rejection of the null hypothesis with a 1% level of significance, whereas for the sub-period no evidence of risk-adjusted abnormal return is present. The regression performed on the smoke portfolio, provides consistent results – the model is unsuccessful in explaining the portfolio returns in both the entire period and the sub-period, where alpha remains significant at the 1% level. The regression on the guns portfolio results in an insignificant alpha for the entire period and a significant alpha for the sub-period at the 5 % level.
Lastly, the five-factor model introducing the two investment and profitability factors, successfully explains the return of the sin industries in almost all scenarios. For the beer industry portfolio, the five-factor alpha is insignificant in both the entire and the sub-period window of investigation. For the smoke portfolio, a distinction is present – the model is successful in explaining the portfolio returns for the entire period, however in the sub-period the five-factor alpha remains significant at the 5% level. The situation for the guns portfolio is similar. These results lead to the rejection of the null hypothesis, thus the market is inefficient and there exists a significant risk-adjusted abnormal return from holding either the smoke or guns industry portfolios during the period from 2004 until 2017. Two additional tests are performed in an attempt to explain these abnormal returns.
The model used is the following:
𝑅",$− 𝑅&,$ = 𝛼"+ 𝛽. 𝑅3,$− 𝑅&,$ + 𝛽?𝑆𝑀𝐵$+ 𝛽@𝐻𝑀𝐿$+ 𝛽C𝑅𝑀𝑊$+ 𝛽H𝐶𝑀𝐴$+ 𝛽P𝑀𝑂𝑀$+ 𝜀$ (9)
Where, the Fama-French (2015) Five-Factor model is combined with Cahart’s (1997) Momentum factor. The results from this additional test are presented in Table 6. The fit of the two tests is higher than with the five-factor model at 0.430, however alpha is still positive and significant at the 5 % level. Thus, the conclusion remains the same. The null hypothesis stating that there is no risk-adjusted abnormal return from holding one of the three sin portfolios during the sub-period under investigation, is rejected in terms of the smoke and guns portfolio. Therefore, the smoke and guns industry outperform the market during the years 2004-2017, however there is no evidence for outperformance of the beer portfolio.
Discussion
In all of the regressions, the results for the beer, smoke and guns industry portfolio show a significant beta coefficient on the market that is lower than one at the 1% level. Thus, sin industry portfolios tend to be less volatile that the market. The evidence for this defensive nature of sin stocks is also present in previous research (Hong & Kacperczyk, 2009). With small exceptions, the size, value, profitability, investment and momentum factors are significant in explaining the returns of the portfolios. For the beer and smoke portfolio, a negative beta coefficient on size and on value remains in all of the regressions, thus indicative of a correlation between the sin portfolios and large market capitalization companies and growth stocks. This relation is also present in previous work (Hong & Kacperczyk, 2009). For the guns portfolio, there is a similar pattern, however for the entire period the value factor returned a positive coefficient, thus the guns portfolio correlates more with value stocks than with growth stocks. The highly significant and positive momentum coefficient in all of the regression implies that the return performance of recent winners adds value in estimating the sin industry returns.
22 Table 3
Regression results with dependent variable: Return on beer portfolio – risk free rate (𝑹𝒃− 𝑹𝒇) Entire period 1963-2017 Sub-period 2004-2017
(1) (2) (3) (4) (1) (2) (3) (4) 𝑅3− 𝑅& 0.688*** 0.662*** 0.675*** 0.778*** 0.546*** 0.626*** 0.633*** 0.672*** (0.0130) (0.0118) (0.0116) (0.0108) (0.0176) (0.0181) (0.0180) (0.0185) SMB -0.311*** -0.315*** -0.144*** -0.261*** -0.263*** -0.242*** (0.0287) (0.0283) (0.0258) (0.0334) (0.0337) (0.0325) HML -0.0560* -0.0135 -0.179*** -0.224*** -0.192*** -0.254*** (0.0281) (0.0284) (0.0256) (0.0386) (0.0413) 0.0363) MOM 0.104*** 0.0467** (0.0201) (0.0167) RMW 0.673*** 0.242*** (0.0346) (0.0496) CMA 0.455*** 0.460*** (0.0369) (0.0535) Constant 0.0183* 0.0226** 0.0183* 0.00569 0.0194 0.0190 0.0184 0.0150 (0.00757) (0.00748) (0.00757) (0.00714) (0.0114) (0.0111) (0.0111) (0.0109) n 13679 13679 13679 13679 3483 3483 3483 3483 R2 0.369 0.390 0.394 0.448 0.473 0.515 0.517 0.540
In all regressions, 𝛽. , the coefficient on the market risk premium (𝑅3− 𝑅&), is tested against one, all others are tested against zero; SMB, HML, MOM, RMW, CMA are size, value, momentum, profitability and investment factors respectively. Regression (1) refers to regression equation (2) in the methodology section, or CAPM. Regression (2) refers to regression equation (4) or Fama-French Three-Factor Model. Regression (3) refers to regression equation (6) or Fama-French Three-Factor Model combined with Carhart’s momentum factor. Regression (4) refers to regression equation (8) or Fama-French Five-Factor Model. All data is daily. The *, ** and *** mark 5%,1% and 0,1% significance respectively. White’s (1980) heteroscedasticity robust standard errors are presented between parentheses.
Table 4
Regression results with dependent variable: Return on smoke portfolio – risk free rate (𝑹𝒔− 𝑹𝒇)
Entire period 1963-2017 Sub-period 2004-2017
(1) (2) (3) (4) (1) (2) (3) (4) 𝑅3− 𝑅& 0.699*** 0.676*** 0.693*** 0.802*** 0.584*** 0.680*** 0.700*** 0.739*** (0.0162) (0.0148) (0.0143) (0.0144) (0.0247) (0.0245) (0.0244) (0.0268) SMB -0.328*** -0.333*** -0.171*** -0.385*** -0.394*** -0.345*** (0.0291) (0.0295) (0.0293) (0.0413) (0.0409) (0.0437) HML -0.0135 0.0380 -0.195*** -0.217*** -0.119** -0.229*** (0.0352) (0.0366) (0.0353) (0.0405) (0.0417) (0.0450) MOM 0.126*** 0.139*** (0.0275) (0.0223) RMW 0.613*** 0.388*** (0.0487) (0.0575) CMA 0.606*** 0.507*** (0.0542) (0.0716) Constant 0.0306** 0.0342*** 0.0291** 0.0169 0.0422** 0.0420** 0.0402** 0.0356* (0.00997) (0.00993) (0.0100) (0.00972) 0.0156 (0.0151) (0.0150) (0.0148) n 13679 13679 13679 13679 3483 3483 3483 3483 R2 0.257 0.273 0.276 0.314 0.355 0.400 0.409 0.425
In all regressions, 𝛽. , the coefficient on the market risk premium (𝑅3− 𝑅&), is tested against one, all others are tested against zero; SMB, HML, MOM, RMW, CMA are size, value, momentum, profitability and investment factors respectively. Regression (1) refers to regression equation (2) in the methodology section, or CAPM. Regression (2) refers to regression equation (4) or Fama-French Three-Factor Model. Regression (3) refers to regression equation (6) or Fama-French Three-Factor Model combined with Carhart’s momentum factor. Regression (4) refers to regression equation (8) or Fama-French Five-Factor Model. All data is daily. The *, ** and *** mark 5%,1% and 0,1% significance respectively. White’s (1980) heteroscedasticity robust standard errors are presented between parentheses.
24 Table 5
Regression results with dependent variable: Return on guns portfolio – risk free rate (𝑹𝒈− 𝑹𝒇)
Entire Period 1963-2017 Sub-period 2004-2017
(1) (2) (3) (4) (1) (2) (3) (4) 𝑅3− 𝑅& 0.742*** 0.750*** 0.768*** 0.829*** 0.700*** 0.736*** 0.752*** 0.770*** (0.0186) (0.0189) (0.0180) (0.0182) (0.0249) (0.0319) (0.0309) (0.0329) SMB -0.0246 -0.0296 0.0885** -0.118* -0.125* -0.0961 (0.0289) (0.0287) (0.0288) (0.0545) (0.0545) (0.0552) HML 0.0983** 0.155*** 0.0152 -0.0990 -0.0191 -0.109 (0.0348) (0.0334) (0.0407) (0.0548) (0.0571) (0.0572) MOM 0.137*** 0.114*** (0.0243) (0.0251) RMW 0.457*** 0.217** (0.0456) (0.0688) CMA 0.308*** 0.308*** (0.0522) (0.0822) Constant 0.0192 0.0175 0.0119 0.00609 0.0371* 0.0369* 0.0354* 0.0333* (0.0100) (0.0101) (0.0101) (0.00995) (0.0165) (0.0165) (0.0164) (0.0164) n 13679 13679 13679 13679 3483 3483 3483 3483 R2 0.280 0.281 0.285 0.298 0.415 0.420 0.425 0.427
In all regressions, 𝛽. , the coefficient on the market risk premium (𝑅3− 𝑅&), is tested against one, all others are tested against zero; SMB, HML, MOM, RMW, CMA are size, value, momentum, profitability and investment factors respectively. Regression (1) refers to regression equation (2) in the methodology section, or CAPM. Regression (2) refers to regression equation (4) or Fama-French Three-Factor Model. Regression (3) refers to regression equation (6) or Fama-French Three-Factor Model combined with Carhart’s momentum factor. Regression (4) refers to regression equation (8) or Fama-French Five-Factor Model. All data is daily. The *, ** and *** mark 5%,1% and 0,1% significance respectively. White’s (1980) heteroscedasticity robust standard errors are presented between parentheses.
Table 6
Regression results for additional test
Sub-period 2004-2017
Smoke portfolio (𝑅N− 𝑅&)
(5) Mkt-RF 0.750*** (0.0263) SMB -0.351*** (0.0429) HML -0.149** (0.0476) RMW 0.378*** (0.0570) CMA 0.453*** (0.0722) Mom 0.105*** (0.0228) Constant 0.0343* (0.0147) Observations 3483 R2 0.430 Sub-period 2004-2017
Guns portfolio (𝑅O− 𝑅&)
(5) Mkt-RF 0.780*** (0.0320) SMB -0.101 (0.0552) HML -0.0372 (0.0617) RMW 0.208** (0.0686) CMA 0.259** (0.0837) Mom 0.0946*** (0.0254) Constant 0.0321* (0.0164) Observations 3483 R2 0.430
In all regressions, 𝛽. , the coefficient on the market risk premium (𝑅3− 𝑅&), is tested against one, all others are tested against zero; SMB, HML, MOM, RMW, CMA are size, value, momentum, profitability and investment factors respectively. All data is daily. The *, ** and *** mark 5%,1% and 0,1% significance respectively. White’s (1980) heteroscedasticity robust standard errors are presented between parentheses.
The findings from the CAPM model for the beer and smoke industry are consistent with previous work which finds outperformance of sin industries indicated by a significant alpha (Fabozzi et al., 2008). These results remain for the beer and smoke industry for the three-factor model and four-factor model for both time periods – from 1963 until 2017 and 2004 until 2017. The situation differs for the guns portfolio, where a pattern is present - in the entire period there is no sign of outperformance with any of the four models, however in the sub-period there is a significant risk-adjusted abnormal return. The alpha coefficient on the beer portfolio is consistent and insignificant when using the five-factor model in both the entire and the sub-period. For the beer and smoke industry portfolios, only the five-factor model succeeds in explaining the returns
26
indicated by an insignificant alpha coefficient. However, this is only true for the smoke portfolio in the entire period. When looking at the sub-period results, the alpha remains significant for the smoke and guns portfolio accounting for all the five-factors along with an additional regression combining the five-factors with the momentum factor. The contradictory results between the two periods for the five-factor model could be the cause of a more pronounced screening out measures of smoke and gun stocks due to the significant increase of SRI in the sub-period, leading to a higher price and possible higher returns.
Therefore, this paper contributes to existing literature in two distinct ways. Prior research using the market, size, value and momentum factor finds evidence of a sin stock outperformance. A recent paper, including the profitability and investment factors, puts forward results contradicting previous work – namely that the sin stock “anomaly” is explained by the five-factor model (Blitz & Fabozzi, 2017). The research in this paper confirms this finding when considering the beer industry portfolio. However, the results differ when examining the smoke and guns industry portfolios – for the sub-period, the alpha remains significant at the 5 % level even with the combination of the five-factor with the momentum factor, thus there exist risk-adjusted abnormal returns from holding the two sin portfolios during the sub-period from 2004-2017 and the market is inefficient. Therefore, this finding is in line with previous work that finds outperformance of sin stocks, and contradicts the results from the paper by Blitz and Fabozzi (2017). This paper investigated the period between 2004 until 2017, when SRI screening measures grew substantially, and this particular time frame has not been researched before.
Nevertheless, there are limitations to this research. Data issues are present, due to the choice of database for the sin industry portfolio returns. The “Triumvirate of Sin”– the alcohol, tobacco and gaming industry is not investigated in total as no separate portfolio exists for the gaming industry and this paper does not evaluate its performance. Moreover, the performance of the beer, smoke and guns industry is examined as three separate portfolios, whereas regression analysis on a portfolio consisting of the three industries could present different findings.
Results on this topic remain contradicting. More research should be carried out in order to explain the performance of sin stocks. For example, as SRI screening measures increase, corporate governance of sin stocks will perhaps be affected as well. Research on the relation of corporate governance on sin stocks can provide useful information for their outperformance.
VI. Conclusion
Social norms have an influence on economic behavior as agents alter their decisions based on non-financial tastes. This leads to a neglect effect towards sin stocks despite their performance (Hong & Kacperczyk, 2009). However, if the performance of sin stocks is lower relative to the market, this neglect should not harm investors. Therefore, this paper analyzes the performance of sin stocks, represented by the beer, alcohol and defense industry portfolios for the U.S market, with the use of five models. The entire period ranging from 1963 until 2017 and the sub-period from 2004 until 2017, is investigated using The Capital Asset Pricing Model, The Fama-French Three-Factor Model, The Fama-French Three-Factor Model in combination with Cahart’s Momentum factor and The Fama-French Five-Factor Model for each of the three industries. An additional regression is run using the Five-Factor Model in combination with the momentum factor for the smoke and guns portfolio. The results are consistent with previous research as outperformance of sin stocks persists in the years between 2004 until 2017. Therefore, adhering to social norms leads to a cost for investors that neglect sin stocks.
28 VII. References
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30 VIII. Appendix
Table A
Correlation matrix for all variables included in the regression models
𝑅M− 𝑅& 𝑅N− 𝑅& 𝑅O− 𝑅& 𝑅3− 𝑅& SMB HML RMW CMA MOM
𝑅M− 𝑅& 1.00 𝑅N− 𝑅& - 1.00 - -𝑅O− 𝑅& - - 1.00 - - -𝑅3− 𝑅& 0.61 0.51 0.53 1.00 (0.69) (0.6) (0.64) -SMB -0.22 -0.18 -0.07 -0.12 1.00 (0.06) (0.0019) (0.14) (0.29) -HML -0.16 -0.12 -0.08 -0.21 0.08 1.00 (0.11) (0.11) (0.19) (0.36) (0.09) -RMW 0.11 0.07 -0.01 -0.22 -0.29 -0.05 1.00 (-0.13) (-0.07) (-0.18) (-0.39) (-0.33) (-0.38) -CMA -0.14 -0.08 -0.13 -0.37 0.03 0.56 0.07 1.00 (-0.01) (-0.0035) (-0.03) (-0.12) (0.04) (0.23) (-0.09) -MOM -0.01 -0.003 -0.01 -0.12 0.03 -0.25 0.13 0.03 1.00 (-0.14) (-0.08) (-0.14) (-0.34) (-0.06) (-0.53) (0.26) (0.05)
-Entire period considered 1963-2017. The sub-period 2004-2017 correlations are in between brackets. 𝑅M− 𝑅& is the Return on beer portfolio – risk free rate, 𝑅N− 𝑅&is the Return on smoke portfolio – risk free rate, 𝑅O− 𝑅& is the Return on guns portfolio – risk free rate, 𝑅3− 𝑅& is the market risk premium; SMB, HML, MOM, RMW, CMA are size, value, momentum, profitability and investment factors respectively. The regression models do not include two portfolios at the same time, thus their correlation is excluded from the table.
