Is ESG An Additional Risk Factor Contributing To Excess Returns?

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Is ESG An Additional Risk Factor Contributing To Excess Returns?

Written by: Jaimy Duinkerken*

MSc. Thesis Finance University of Groningen Faculty of Economics and Business

Supervisor: A. Dalὸ

Abstract

This study examines traditional risk factors and implements a self-constructed ESG factor to analyze the patterns of risk and returns, pricing anomalies and risk premiums of 25 test portfolios, during a sample period from 2008-2018. Portfolios with higher ESG scores are able to capture more excess returns than the portfolios with low ESG scores. Furthermore, pricing anomalies exists across all the existing and self-constructed ESG models and no ESG risk premium is found. By changing the value-weighted method for the equally-weighted method to construct portfolios, the results on the existence of pricing anomalies and ESG risk premiums prove to be robust. Further analysis on the effect of ESG on individual securities is recommended.

Key words: Factor Investing, ESG, Pricing Anomalies, Risk Premiums

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have experienced a 6-year compounded annual growth rate (CAGR) of 52 percent in Europe during a period ranging from 2013 to 2018. In numbers, this amounts to an increase from €20 billion to €108 billion of responsible assets under management. From a global perspective, one of the largest asset managers Amundi incorporates €280 billion of responsible investments in its portfolio (Eurosif, 2018). An important factor contributing to this growth over the past decades is ethical consumerism. This can be defined as the willingness of consumers to pay a premium for products and/or services that align with personal values (Renneboog et al., 2008). Other factors contributing to the increasing amount invested in the SRI sector are changes in regulation, media and external pressure from NGOs (Escrig-Olmedo et al., 2010). An example of changes in regulation is the research conducted by Capelle-Blancard et al. (2014), about the effect of United Nations Principles for Responsible Investment on financial performance. The effect of these principles on financial performance of firms are neutral, although the signees are obliged to satisfy the need for ESG in the investment making decision process. The majority of studies on factor investing are focused on the traditional multi-factor models (Carhart, 1997; Fama & French, 2014). This study aims to extend these traditional multi-factor models by constructing an ESG risk factor. First of all, the possibility of patterns across returns and risk of 25 test portfolios are examined. Moreover, the existence of pricing anomalies across portfolios for the traditional and self-constructed multi-factor models are analyzed. Finally, this paper aims to conduct research on the existence of an ESG risk premium. As both the benefits of factor investing and the importance of the ESG factor are stressed, the research question of this paper can be written as follows:

Is ESG an additional risk factor contributing to excess stock returns?

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4 2. Literature review

2.1 Factor investing

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high ratios (Fama & French, 1992), implying that investors are compensated most for undervalued stocks. Afterwards, Carhart (1997) extended this model (CH4) by including the additional factor momentum. This fourth factor states that investors or mutual funds tend to buy securities that have proved to be profitable in the short-term past, while securities with losses are not sold (Jegadeesh & Titman, 1993). Furthermore, the FF3 model was extended with the two additional factors profitability and investment resulting in the five-factor model, in 2015 (FF5). The profitability factor is the difference between returns on portfolios of stocks with robust and weak profitability, whereas the investment factor is the difference on portfolios between firms that invest conservatively and aggressively (Fama & French, 2014). By assessing all the factors described above, the investors can generate diversification benefits of securities (Quance, 2018).

2.2 Factor investing and ESG

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from 2014 until 2017, responsible investing outperformed the market on all of the ESG aspects in both Europe and North America. As described in the previous section, the CAPM states that by having a well-diversified portfolio the unsystematic risk can be reduced to a minimum. By selecting firms based on certain ESG criteria, the number of firms in a portfolio might be reduced. Accordingly, there is a possibility of higher unsystematic risk than if the excluded firms were included in the portfolio (Rudd, 1981). Generally, if an investor is exposed to more risk, it should be compensated in terms of higher returns (Sharpe, 1964; Lintner, 1965; Black, 1972). Investing in firms that score low on the ESG dimension, results in more risk of environmental, social or governance issues. The investors are only willing to bear this risk if there they are compensated with a higher premium. Therefore, ESG risk is an interesting risk factor with the possibility of a risk premium.

2.3 Hypotheses tested

The objective of this paper is to conduct research on the excess returns of responsible firms based on ESG criteria. Thereafter, the focus is on whether pricing anomalies are present in the existing multi-factor models and a self-constructed ESG factor will be added to a combination of the CH4 and FF5 models. To analyze the patterns and pricing anomalies, the approach developed by Fama & French (2015) is used to identify size, value, momentum, profitability and investments. By constructing portfolios based on market equity (ME) and ESG quintiles, excess stock return patterns in relation to ESG scores can be exposed. Accordingly, these patterns might imply that there are pricing anomalies not yet covered by the existing literature. Therefore, the following hypothesis can be stated:

𝐻_0,1: the ESG test portfolios are correctly priced

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𝐻_0,2: ESG risk factors are not priced in the cross-section of stock returns

To test this hypothesis, the two-step cross-sectional regression procedure of the Fama-Macbeth (1973) methodology is used.

3. Methodology

3.1 Portfolio construction

In order to test the possibility of pricing anomalies, I create 25 ESG test portfolios by constructing quintiles based on ME and ESG scores. Every year at the end of June, the stocks are independently sorted into quintiles based on ME and ESG scores. In sorting the stocks at the end of June in year t, the ME at the end of December of year t-1 and ESG scores of June of year t are used. The end of June is chosen to rebalance, because then firms are expected to have all the available accounting data included in the stock price (Dennis et al., 1995). Once the firms are sorted, the intersection of these sorts are used to produce 25 value-weighted ME-ESG portfolios. The weights 𝑊_𝑖,𝑡 of each security i at time t for all portfolios can be calculated as follows:

𝑊_𝑖,𝑡 = 𝑀𝐸𝑖,𝑡 ∑𝑁𝑖=𝑛𝑀𝐸𝑖,𝑡

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Furthermore, the return can be calculated using the following equation:

𝑟_𝑝,𝑡 = ∑ 𝑤_𝑖,𝑡𝑟_𝑖,𝑡

𝑁

𝑖=1

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where 𝑟𝑝,𝑡 denotes the return of portfolio p at time t, 𝑤𝑖,𝑡 is the weight of security i at time t,

and 𝑟𝑖,𝑡 is the return of security i at time t.

3.2 Evidence of pricing anomalies

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is zero, this implies that there is no variation in excess return in practice compared with theoretical statements (Jensen, 1967). Therefore, the following models are estimated:

𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡+ 𝜀_𝑝,𝑡 (CAPM) 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡+ 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝜀_𝑝,𝑡 (FF3) 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡+ 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝛽_𝑝𝑟𝑅𝑀𝑊_𝑡+ 𝛽_𝑝𝑐𝐶𝑀𝐴_𝑡+ 𝜀_𝑝,𝑡 (FF5)

𝑅𝑝,𝑡𝑒 = 𝛼𝑝+ 𝛽𝑝𝑚𝑘𝑅𝑚,𝑡+ 𝛽𝑝𝑠𝑆𝑀𝐵𝑡+ 𝛽𝑝ℎ𝐻𝑀𝐿𝑡+ 𝛽𝑝𝑟𝑅𝑀𝑊𝑡+ 𝛽𝑝𝑐𝐶𝑀𝐴𝑡+ 𝛽𝑝𝑚𝑀𝑂𝑀𝑡+ 𝜀𝑝,𝑡 (FFC)

Where 𝑅_𝑝,𝑡𝑒 is the excess return of the portfolio p in month t, 𝛼𝑝 is the pricing error of portfolio

p, 𝛽_𝑝𝑚𝑘 is the systematic risk factor of the market together with the excess return of the stock market index in month t. Furthermore, 𝜀𝑝,𝑡 implies the error term for portfolio p and month t.

Additionally, the variables 𝑆𝑀𝐵_𝑡, 𝐻𝑀𝐿_𝑡, 𝑅𝑀𝑊_𝑡, 𝐶𝑀𝐴_𝑡 and 𝑀𝑂𝑀_𝑡, represent the factors size, value, profitability, investment and momentum, at month t, respectively. The model in equation FFC represents a combined model by adding the momentum factor to the FF5 model.

The Gibbons, Ross and Shanken (1989) test statistics (GRS) can be used to summarize the results for the ME-ESG test portfolios. This GRS test is a time-series regression used to verify whether all the portfolios alphas are simultaneously equal to zero. This test is originally designed to test the portfolios using the CAPM; however, the model can be extended for multi-factor models. The equation used to estimate the alphas in the multi-multi-factor model can be found below:

𝐹

_𝐺𝑅𝑆

= (

𝑇 𝑁

) [

𝑇−𝑁−𝐿 𝑇−𝐿−1

] (

𝛼̂_𝑝′∑̂−1𝛼̂_𝑝 1+𝑟̅𝑝′Ω̂−1𝑟̅𝑝

)

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where T is the number of time-series observations, N is the number of assets, L is the number of factors, 𝛼̂_𝑝′ _{= (𝛼̂}

1, 𝛼̂2, … , 𝛼̂𝑁), ∑̂ is the covariance matrix of residual returns, 𝑟̅𝑝 is the vector

of mean factor returns and Ω̂ is the variance-covariance matrix for the factor returns. A large value for the 𝐹𝐺𝑅𝑆 test statistic implies that the null hypothesis of all the alphas of the portfolios

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3.2 Constructing the ESG risk factor

The ESG risk factor is constructed according to the same methodology as Fama & French (2015) used for the investment and profitability risk factors. This implies the use of 2x3 sorts based on the ME and ESG dimensions of the securities, respectively. The ME is sorted with a 50th percentile cut-off rate whereas ESG is sorted based on 30th and 70th percentile cut-off rates.

Similar to the construction of the 25 test portfolios, this procedure is repeated at the end of June of each year with an value-weighted approach. Small (S) and Big (B) are the size groups whereas Low (L) and High (H) imply the low and high scoring groups in terms of ESG, respectively. The intersections between the ME and ESG scoring groups are used to construct the portfolios. The formula to construct the monthly value-weighted ESG factors can be found in the ESG factor equation below:

𝐸𝑆𝐺 = (𝑆𝑚𝑎𝑙𝑙 𝐻𝑖𝑔ℎ + 𝐵𝑖𝑔 𝐻𝑖𝑔ℎ)/2 − (𝑆𝑚𝑎𝑙𝑙 𝐿𝑜𝑤 + 𝐵𝑖𝑔 𝐿𝑜𝑤)/2 (4)

After constructing the ESG risk factor, a combination with the FFC model is provided in the equation below. This model includes all the factors in the CH4 and FF5 models by appending the self-constructed ESG risk factor.

𝑅_𝑝,𝑡𝑒 _{= 𝛼}

𝑝+ 𝛽𝑝𝑚𝑘𝑅𝑚,𝑡 + 𝛽𝑝𝑠𝑆𝑀𝐵𝑡+ 𝛽𝑝ℎ𝐻𝑀𝐿𝑡+ 𝛽𝑝𝑟𝑅𝑀𝑊𝑡+ 𝛽𝑝𝑐𝐶𝑀𝐴𝑡+

𝛽_𝑝𝑚𝑀𝑂𝑀_𝑡+ 𝛽_𝑝𝑒𝐸𝑆𝐺_𝑡+ 𝜀_𝑝,𝑡

(ESG)

in which 𝐸𝑆𝐺_𝑡 represents ESG as an additional risk factor.

3.3 Risk premiums

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𝑅_𝑝,𝑡𝑒 = 𝜆0,𝑡+ 𝜆1,𝑡𝛽̂𝑝𝑚𝑘+ 𝜆2,𝑡𝛽̂𝑝𝑠+ 𝜆3,𝑡𝛽̂𝑝ℎ+ 𝜆4,𝑡𝛽̂𝑝𝑚+ 𝜆5,𝑡𝛽̂𝑝𝑟+ 𝜆6,𝑡𝛽̂𝑝𝑐+ 𝜆7,𝑡𝛽̂𝑝𝑒+ 𝜈𝑝,𝑡 (5)

In model (5), 𝜆_0,𝑡 is the monthly constant. Furthermore; 𝛽̂_𝑝𝑚𝑘, 𝛽̂_𝑝𝑠, 𝛽̂_𝑝ℎ, 𝛽̂_𝑝𝑚, 𝛽̂_𝑝𝑟, 𝛽̂_𝑝𝑐, and 𝛽̂𝑝𝑒 are the estimated factor loadings on the risk factors market, size, value, momentum,

profitability, investment and ESG respectively. These factors load on portfolio p in which 𝜆1,𝑡,

𝜆2,𝑡, 𝜆3,𝑡, 𝜆4,𝑡, 𝜆5,𝑡, 𝜆6,𝑡, and 𝜆7,𝑡 are the monthly risk premiums for market, size, value,

momentum, profitability, investment and ESG risk at month t, respectively. Finally, the error term of portfolio p is shown as 𝜈𝑝,𝑡.

4. Data and descriptive statistics

4.1 Data sources

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After extracting the return index, the monthly return can be calculated as follows:

𝑟𝑖,𝑡 = 𝑅𝐼𝑖,𝑡

𝑅𝐼𝑖,𝑡−1− 1

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in which 𝑟𝑖,𝑡 is the return for security i at month t and 𝑅𝐼𝑖,𝑡 is the return index of security i at

month t. The sample of this research ranges from the beginning of July 2008 until end of June 2018 (120 months).

4.2 Data selection procedure

In line with Fama & French (2012), this study includes firms operating in 23 developed countries that can be subdivided in four regions consisting of North America, Japan, Asia Pacific and Europe. The countries belonging to each region are specified in table 1 and will be elaborated on in the next section. Consequently, the data is filtered on the availability of ESG data on June of year t and ME data at the end of December of year t-1. Firms without data on one of these two variables are excluded. Thereupon, the return index is extracted from Thomson Reuters Datastream and only firms with at least 12 consecutive returns from July of year 1 until June of year t+1 are included in the sample. Finally, securities having the same return index at least three months in a row at the end of a year are excluded. The explanation behind this is that firms can still be registered in the database, although they do not operate anymore.

4.3 Descriptives

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12 Table 1

Summary Statistics Total Sample

The table reports the 23 countries within the four regions North-America, Japan, Asia Pacific and Europe. The first column shows the abbreviation of the country which is fully written out in the second column. Furthermore, the horizontal ax shows the years of the sample ranging from 2008 until 2017 from left to right, respectively. The final row is used to describe the total number of securities in the sample for each year. Note: each year starts in July of year t and ends in June of year t+1.

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13 Table 2

Descriptive Statistics ESG Scores

This table reports the descriptive statistics of the ESG scores. From left to right: the average, standard deviation, minimum, maximum, skewness and kurtosis are provided per year. Note: as the portfolios are constructed at the end of June, a full year of consecutive returns refers to two years in the table.

Average St.dev. Min. Max. Skew Kurtosis 2008/2009 4.99 2.57 0.00 10.00 0.13 2.29 2009/2010 5.05 2.63 0.00 10.00 0.03 2.28 2010/2011 4.97 2.60 0.00 10.00 0.08 2.29 2011/2012 5.21 2.53 0.00 10.00 -0.05 2.29 2012/2013 4.97 2.57 0.00 10.00 -0.02 2.34 2013/2014 4.40 2.39 0.00 10.00 0.25 2.46 2014/2015 4.61 2.25 0.00 10.00 0.14 2.43 2015/2016 4.78 2.18 0.00 10.00 0.07 2.38 2016/2017 4.77 2.15 0.00 10.00 0.09 2.46 2017/2018 4.86 2.16 0.00 10.00 0.09 2.42

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14 Table 3

Descriptive Statistics Per Portfolio

This table reports the average monthly excess return (Panel A), standard deviation (Panel B), average yearly ESG scores (Panel C) and average number of firms (Panel D) for each of the 25 constructed test portfolios. The horizontal axes show the five quintiles based on ME with “Small” being the quintile with the smallest firms and “Big” as the quintile with the largest firms. Additionally, the vertical axes display the ESG scores based on five quintiles as well, in which “A” is the quintile with firms scoring the lowest and “E” with firms scoring highest.

Panel A Panel B

Average monthly excess returns per portfolio (%) Sharpe Ratio

Small 2 3 4 Big Small 2 3 4 Big

Low 1.23 1.25 0.98 0.90 0.75 Low 0.1501 0.2045 0.1546 0.1626 0.1345 B 1.38 1.11 0.98 0.74 0.63 B 0.2231 0.1896 0.1798 0.1458 0.1170 ESG C 1.44 0.89 0.80 0.77 0.82 ESG C 0.2173 0.1392 0.1478 0.1426 0.1482 D 1.01 1.20 0.81 1.03 0.69 D 0.1526 0.2399 0.1587 0.2144 0.1179 High 1.39 1.04 1.09 1.04 0.57 High 0.2034 0.2131 0.2496 0.2612 0.1030 Panel C Panel D

Average yearly ESG scores per portfolio Average yearly number of firms per portfolio

Low 1.81 1.71 1.65 1.61 1.83 Low 75 70 55 55 39

B 3.57 3.55 3.62 3.59 3.60 B 72 70 61 47 46

ESG C 4.98 4.95 4.98 4.91 4.96 ESG C 59 63 62 53 58

D 6.40 6.32 6.34 6.39 6.41 D 50 51 62 62 69

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ESG dimensions. Again, this implies that the larger securities are, the less returns these provide indifferently from in which ESG quintiles the securities are based. Furthermore, from the first until the fourth ME quintile, the pattern of larger returns for securities scoring high on ESG becomes even more clear. As shown in Panel C and Panel D, the average ESG scores ranges from 1.61 to 8.46 across all quintiles whereas the average numbers of firms per portfolio ranges from 39 to 83. According to Statman (1987), a portfolio should include at least more than 30 securities to benefit from diversification. Therefore, it can be stated that the 25 test portfolios in this paper are well-diversified.

Panel A in Table 4 outlines the correlation across all factors used to estimate the models in this paper. It can be stated that multicollinearity is not an issue that is affecting the multi-factor model with inclusion of ESG as a risk factor. Furthermore, the ESG risk factor is positively correlated across the value, profitability, investment and momentum factor, with the exception for the market and size factor. In panel B of Table 4, it is shown that both the market and profitability factors have the largest positive returns on average. Accordingly, this suggests that much of the variation found in the models can be explained by these two factors.

Table 4

ESG Risk Factor Construction and Descriptive Statistics

Every year at the end of June, the portfolios are constructed based on 50th percentile cut-off rate for the ME dimension and a 30th and 70th percentile cut-off rate for the ESG dimension. Small (S) and Big (B) are the ME size groups whereas High (H) and Low (L) imply the high and low scoring groups in terms of ESG, respectively. Value-weighted returns for each portfolio are calculated from July of year t until June of year t+1. The variables 𝑅𝑚, 𝑆𝑀𝐵, 𝐻𝑀𝐿, 𝑅𝑀𝑊, 𝐶𝑀𝐴, 𝑀𝑂𝑀, and 𝐸𝑆𝐺

are the market, size, value, profitability, investment, momentum and ESG risk factor, respectively. Panel A: risk factor correlations

𝑅_𝑚 𝑆𝑀𝐵 𝐻𝑀𝐿 𝑅𝑀𝑊 𝐶𝑀𝐴 𝑀𝑂𝑀 𝐸𝑆𝐺 𝑅𝑚 1.0000 𝑆𝑀𝐵 0.0754 1.0000 𝐻𝑀𝐿 0.2391 0.0465 1.0000 𝑅𝑀𝑊 -0.4152 -0.3201 -0.5523 1.0000 𝐶𝑀𝐴 -0.3696 -0.1610 0.4347 -0.1278 1.0000 𝑀𝑂𝑀 -0.3973 -0.1400 -0.3942 0.3188 0.2645 1.0000 𝐸𝑆𝐺 -0.2930 -0.1338 0.0608 0.0318 0.1365 0.1602 1.0000

Panel B: average returns and standard deviation risk factors

𝑅_𝑚 𝑆𝑀𝐵 𝐻𝑀𝐿 𝑅𝑀𝑊 𝐶𝑀𝐴 𝑀𝑂𝑀 𝐸𝑆𝐺

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On the other hand, a negative average return of -0.09 and -0.13 can be found for the HML and ESG risk factors, respectively. The negative ESG risk factor implies that, on average, the sample is tilted towards low scoring ESG securities. Table 5 in the appendix shows the diagnostic tests on the time-series data for the ESG model on autocorrelation, heteroscedasticity and non-stationarity. These tests include the Godfrey, Breusch-Pagan and Dick-Fuller tests, respectively. I find that several portfolios have either a form of autocorrelation or heteroscedasticity. Therefore, I use standard robust errors when estimating the regressions. Furthermore, the Dickey-Fuller test is significant at the 5 percent level for all portfolios, rejecting the null hypothesis that there is a unit root. Accordingly, non-stationarity is not an issue for the data in this sample, implying that in the results no wrong inferences will be made about the relationship between variables.

5. Results

5.1 Pricing anomalies across existing models

The aim of the first part of this study is to conduct research on the existence of pricing anomalies across multi-factor models. Table 6 until 9 in the appendix show the findings for the CAPM, FF3, FF5 and FFC model, whereas the results for the self-constructed ESG model are presented in table 10 of this section.

The CAPM model in table 6 shows significant alphas for 7 out of the 25 ESG test portfolios, implying that the model is unable to correctly explain all of the variation in excess returns. Furthermore, the table shows that the betas for all test portfolios are significant and become smaller from lowest to the largest ME quintile. Accordingly, this implies that the test portfolios with large securities are less sensitive to market volatility compared to test portfolios with small securities.

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afterwards to the largest quintile in terms of ME. Therefore, it can be stated that in terms of ME, portfolios in the median quintile are tilted towards growth stocks. From a financial point of view, this implies that in this sample the portfolios with a median ME tend to be growth stocks and have lower excess returns compared with value stocks. Furthermore, it can be found that the portfolios in the smallest and largest quintiles, in terms of ME, are more tilted towards value stocks and therefore tend to have higher excess returns compared to portfolios with more growth stocks. This is in line with the theory of Fama & French (2012) stating that value stocks outperform growth stocks in the long term.

Table 8 of the FF5 model presents 4 portfolios with significant alphas, implying that more of the variation of the excess returns is captured than in the CAPM and FF3 models. The size and value factors show similar patterns as in the FF3 model. The profitability risk factor does not show a clear pattern and the investment factor is negative on average with no clear pattern as well. The negative investment factor implies that most of the firms in the portfolios used in the sample invest aggressively instead of conservatively.

Table 9 presents the results of the FFC model, in which 5 portfolios show a significant alpha. Again, the factors market, size, value, profitability, investment show similar patterns as in the previous models. Across all ESG quintiles, the additional momentum factor shows an increasing value from the lowest to the highest quintile in terms of ME. This implies that portfolios with securities with low ME are tilted more towards low performing stocks. On the other hand, portfolios including securities with a large ME are tilted more towards high performing stocks, ceteris paribus.

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18 Table 10

ESG Pricing Anomalies and Risk Factor Betas For 25 ESG Test Portfolios

The self-constructed ESG model is estimated for the 5x5 ESG test portfolios sorted on the ESG and ME dimension using the following equation: 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡 + 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝛽_𝑝𝑟𝑅𝑀𝑊_𝑡+ 𝛽_𝑝𝑐𝐶𝑀𝐴_𝑡+ 𝛽_𝑝𝑚𝑀𝑂𝑀_𝑡+ 𝛽_𝑝𝑒𝐸𝑆𝐺_𝑡+ 𝜀_𝑝,𝑡

where 𝑅_𝑝,𝑡𝑒 is the excess return of the portfolio p in month t, 𝛼_𝑝 is the pricing error of portfolio p in percentages, 𝛽_𝑝𝑚𝑘 is the systematic risk factor of the market together with the excess return of the stock market index in month t. Additionally, the variables 𝑆𝑀𝐵_𝑡, 𝐻𝑀𝐿_𝑡, 𝑅𝑀𝑊_𝑡, 𝐶𝑀𝐴_𝑡, 𝑀𝑂𝑀_𝑡 and 𝐸𝑆𝐺_𝑡 represent the factors size, value, profitability, investment and ESG at month t, respectively.

Test portfolios with an alpha corresponding to a t-statistic with a p-value < 0.05 appear in bold.

Panel A Panel B

𝛼̂𝑝 t-statistic

Low 0.58 0.58 0.10 0.44 0.65 1.04 2.24 0.44 1.43 1.69 B 0.76 0.37 0.26 0.16 0.47 1.99 1.34 1.23 0.61 1.36 C 0.85 0.17 0.21 0.18 0.83 2.49 0.51 1.00 0.56 2.17 D 0.37 0.45 0.17 0.41 0.54 1.00 1.91 0.80 1.70 1.43 High 0.58 0.29 0.57 0.51 0.58 1.77 1.61 2.57 2.78 1.56 𝛽̂_𝑝𝑚𝑘 t-statistic

Low 0.9230 0.9440 1.0820 0.8740 0.7200 5.49 13.06 19.15 10.62 7.36 B 0.8840 1.0110 0.9460 0.8590 0.7850 10.26 12.40 16.63 11.39 8.24 C 1.0150 1.0150 0.9490 0.9100 0.7510 11.76 15.66 17.84 13.87 7.51 D 1.0050 0.9600 0.9170 0.9110 0.8620 11.41 13.26 15.49 13.24 9.44 High 1.0710 0.9800 0.8060 0.7780 0.7790 11.63 15.08 12.21 15.31 8.20 𝛽̂𝑝𝑠 t-statistic

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19 B 0.6130 0.3760 0.1450 0.0787 -0.1960 -2.18 1.53 0.76 0.29 -0.71 C 0.4940 0.4440 -0.1550 -0.0452 -0.5770 1.91 1.56 -0.81 -0.15 -1.80 D 0.4190 0.4930 0.0760 -0.1040 -0.2720 1.30 2.47 0.42 -0.43 -0.87 High 0.8170 0.2870 -0.0475 -0.1010 -0.3100 2.79 1.77 -0.27 -0.59 -1.09 𝛽̂𝑝ℎ t-statistic

Small 2.0000 3.0000 4.0000 Big Small 2 3 4 Big

Low 0.2790 0.1570 0.0631 0.1540 0.6290 0.52 0.66 0.34 0.59 2.50 B 0.3670 -0.1450 0.0547 0.2490 0.2460 1.24 -0.57 0.31 1.08 0.96 C 0.3500 0.2680 -0.0698 0.5050 0.3820 1.28 1.18 -0.44 2.40 1.44 D 0.3640 -0.1110 0.0785 0.1280 0.4270 1.39 -0.55 0.42 0.74 1.66 High 0.3160 -0.0593 -0.0604 0.1090 0.4550 0.99 -0.30 -0.34 0.71 1.87 𝛽̂𝑝𝑟 t-statistic

Low -0.4760 0.0103 0.3080 -0.5630 -0.5030 -0.52 0.04 1.16 -1.72 -1.39 B 0.0254 -0.0861 0.2520 0.0537 -0.6820 0.07 -0.30 1.21 0.18 -1.84 C -0.0256 0.3470 -0.0560 0.3800 -0.9580 -0.07 1.18 -0.27 1.18 -2.66 D 0.3680 0.1580 0.2640 0.1050 -0.6110 0.99 0.68 1.14 0.38 -1.50 High 0.5020 0.3700 0.1770 0.2330 -0.7010 1.32 1.63 0.85 1.14 -1.98 𝛽̂_𝑝𝑐 t-statistic

Low 0.1600 -0.1910 -0.1560 -0.1030 -1.3090 0.31 -0.48 -0.53 -0.35 -4.45

B -0.1810 0.3580 -0.1940 -0.1920 -0.6220 -0.40 0.96 -0.66 -0.60 -2.09

C -0.3340 -0.4380 -0.2720 -0.5700 -0.6050 -0.85 -1.10 -0.96 -2.08 -1.81

D -0.4470 0.3740 -0.1350 0.0843 -0.7500 -1.04 1.27 -0.41 0.37 -2.33

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20

𝛽̂_𝑝𝑚 t-statistic

Low -0.2250 -0.2440 -0.2260 0.0627 0.2290 -1.03 -2.44 -2.41 0.63 2.47 B -0.2300 -0.2120 -0.1560 0.0154 0.1040 -1.77 -2.19 -2.10 0.17 1.02 C -0.2890 -0.3250 -0.1390 -0.0147 0.1580 -1.75 -3.04 -1.86 -0.13 1.36 D -0.4450 -0.1180 -0.1790 0.0419 0.1780 -2.95 -1.48 -2.13 0.50 1.66 High -0.5160 -0.2360 -0.1760 -0.0047 0.1490 -3.23 -2.63 -2.36 -0.06 1.38 𝛽̂_𝑝𝑒 t-statistic

Low -0.5730 -0.7320 -0.8200 -0.7240 0.1360 -1.25 -2.49 -3.25 -3.55 0.56

B -0.4270 -0.4520 -0.4750 -0.2950 0.3670 -1.20 -1.50 -2.13 -1.48 1.55

C 0.0349 -0.1590 -0.4070 -0.0104 0.5270 0.11 -0.53 -1.72 -0.05 1.95

D 0.2000 -0.0166 -0.0658 -0.0520 0.8380 0.67 -0.07 -0.25 -0.27 3.13

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21

Table 11 summarizes the results of the Gibbons, Ross & Shanken test (1989). According to this test, all the models can be rejected at the five percent significance level. Consequently, this implies that none of the tested models is able to correctly price the test portfolios simultaneously. This evidence suggests that there is not enough evidence to state that all of the ESG test portfolios are priced correctly. The lowest GRS statistics of 1.70 for both the FF5 and FFC model implies that these models are best in pricing excess stock returns of all the portfolios simultaneously. As expected, the mean alpha for all 25 test portfolio is positive and has the largest values for the FF5 and ESG model. Furthermore, the fourth column shows that the adjusted 𝑅2_{increases from the CAPM until the ESG model with a value of 0.7215, stating that}

the ESG model is able to capture most of the variance.

Table 11

Gibbons, Ross & Shanken Test

5.2 Risk premiums

As shown in the previous section, all of the existing multi-factor models are not able to capture the excess stocks returns for at least 4 out of the 25 constructed test portfolios. The Fama-Macbeth procedure is used to determine the premiums for each of the variables used in the multi-factor models. The results of these cross-sectional regressions are provided in table 12 on the next page. Again, the return of the risk-free asset 𝜆_0,𝑡 across all the models is positive, implying a positive risk-free rate. The other risk factors in presented in the tables are not statistically significant. Thus, there is not a variable that is standing out in terms of premiums that can be derived. Furthermore, it can be found that the ESG risk factor does not yield a premium contributing to excess stock returns with its insignificant premium of 0.000. This suggests that there is not enough evidence for an ESG risk factor premium for all the ME-ESG test portfolios simultaneously. A possible explanation for the absence of a premium on all test

For all 25 test portfolios, this table provides the following for the CAPM, FF3, CH4, FF5 and ESG models: the GRS test statistic, absolute mean alpha in percentages, the standard error of the alpha and the average 𝑅2_{of the time}

series.

GRS statistics with a p-value < 0.05 appear in bold. GRS Mean alpha Standard Error 𝑅2

CAPM 1.88 0.34 0.0029 0.6867

FF3 2.10 0.35 0.0029 0.6952

FF5 1.70 0.45 0.0032 0.7033

FFC 1.70 0.44 0.0031 0.7130

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22

portfolios might be due to the fact that ESG scores are observable and thus already priced by the market.

Table 12

Fama-Macbeth Monthly Cross-Sectional Regressions For all 25 test portfolios, the following regression is estimated:

𝑅_𝑝,𝑡𝑒 = 𝜆0,𝑡+ 𝜆1,𝑡𝛽̂𝑝𝑚𝑘+ 𝜆2,𝑡𝛽̂𝑝𝑠+ 𝜆3,𝑡𝛽̂𝑝ℎ+ 𝜆4,t𝛽̂𝑝𝑟+ 𝜆5,𝑡𝛽̂𝑝𝑐+ 𝜆6,𝑡𝛽̂𝑝𝑚+ 𝜆7,𝑡𝛽̂𝑝𝑒+ 𝜈𝑝,𝑡

where 𝑅_𝑝,𝑡𝑒 is the excess return of the portfolio p in month t in percentages, and 𝜆_0,𝑡 is the monthly constant. Furthermore; 𝛽̂_𝑝𝑚𝑘, 𝛽̂_𝑝𝑠, 𝛽̂_𝑝ℎ, 𝛽̂_𝑝𝑟, 𝛽̂_𝑝𝑐, 𝛽̂_𝑝𝑚 and 𝛽̂_𝑝𝑒 are the estimated factor loadings on the risk factors market, size, value, profitability, investment, momentum and ESG respectively. These factors load on portfolio p in which 𝜆_1,𝑡, 𝜆_2,𝑡, 𝜆_3,𝑡, 𝜆_4,𝑡, 𝜆_5,𝑡, 𝜆_6,𝑡 and 𝜆_7,𝑡 are the monthly risk premiums for market, size, value, profitability, investment, momentum, ESG risk at month t, respectively. Finally, the error term of portfolio p is shown as 𝜈𝑝,𝑡.

The monthly average risk premium are reported per variable and the Fama-Macbeth test statistic is shown in square brackets. 𝜆0,𝑡 𝜆1,𝑡 𝜆2,𝑡 𝜆3,𝑡 𝜆4,𝑡 𝜆5,𝑡 𝜆6,𝑡 𝜆7,𝑡 𝑅2 CAPM 0.28 0.72 0.2052 [0.35] [0.76] FF3 0.89 0.00 0.26 0.23 0.3877 [1.37] [0.00] [0.64] [0.51] FF5 0.89 0.02 0.15 0.58 -0.04 0.35 0.5000 [1.67] [0.03] [0.43] [1.49] [-0.21] [1.56] FFC 1.25 -0.39 0.07 0.43 -0.13 0.34 -0.76 0.5576 [2.26] [-0.52] [0.19] [1.03] [-0.78] [1.49] [-0.96] ESG 1.29 -0.45 0.05 0.47 -0.13 0.36 -0.80 0.00 0.5928 [2.57] [-0.66] [0.14] [0.88] [-0.78] [1.40] [-1.15] [0.02] 5.3 Robustness test

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23

6. Conclusion

ESG has become an increasingly relevant subject over the past few years. Besides profit maximization, firms are nowadays expected to contribute to society’s stakeholders. This paper aimed to conduct research on whether patterns of returns and risk, pricing anomalies and risk premiums are present for existing multi-factor models and a self-constructed ESG model. The main findings on these three topics are presented below.

As shown in the descriptive data section, the sample has a pattern of higher excess returns for portfolios with securities scoring high on ESG, compared to the test portfolios having a low ESG score. This finding is contrary to most of the existing literature on the relationship between risk and return, as one would expect higher premiums for portfolios with low scores on ESG due to higher risk.

With regards to the testing of pricing anomalies, this study finds that none of the existing and self-constructed multi-factor models are able to correctly price all of the 25 test portfolios. Accordingly, this implies that the multi-factor models do not explain all of the variation in excess returns. Moreover, for all the multi-factor models, the market beta is found to become smaller when the Market Equity (ME) of portfolios increase. Therefore, it can be stated that the securities of large firms are less sensitive to market volatility, compared with small firms. Furthermore, the betas corresponding to the existing risk factors show similar patterns as in the existing literature.

After testing for the pricing anomalies for each test portfolio individually, the analysis proceeded with conducting research on the risk factors premiums for all the test portfolios simultaneously. Although the test portfolios in the descriptive data section showed that ESG and excess returns have a positive relationship, it is found that the ESG risk factor in general does not contribute to excess stock returns for the sample period from 2008 until 2018.

As a robustness test, the constructed portfolios are formed as equally-weighted test portfolios rather than value-weighted test portfolios. This test confirmed the results on the pricing anomalies and risk premium of the ESG model and therefore the findings are robust.

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individual securities level. However, research has still not included ESG as a potential risk factor at individual securities level. Further research on this topic might be conducted to create an ESG-savvy market, leading to new insights for a sustainable economy.

7. References

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8. Appendix

Figure 1

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28 Figure 2

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29 Table 5

Diagnostic Tests of Sample

This table reports the diagnostic test run on the data of the sample testing for autocorrelation (Breusch-Godfrey), heteroscedasticity (Breusch-Pagan) and non-stationarity (Dickey-Fuller) for the following model: 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡+ 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝛽_𝑝𝑟𝑅𝑀𝑊_𝑡+ 𝛽_𝑝𝑐𝐶𝑀𝐴_𝑡+ 𝛽_𝑝𝑒𝑀𝑂𝑀_𝑡+ 𝛽_𝑝𝑒𝐸𝑆𝐺_𝑡+ 𝜀_𝑝,𝑡 where 𝑅_𝑝,𝑡𝑒 _{is the excess return of the portfolio p in month}

t, 𝛼_𝑝 is the pricing error of portfolio p in percentages,

𝛽_𝑝𝑚𝑘 is the systematic risk factor of the market together with the excess return of the stock market index in month

t. Additionally, the variables 𝑆𝑀𝐵𝑡, 𝐻𝑀𝐿𝑡, 𝑅𝑀𝑊𝑡,

𝐶𝑀𝐴𝑡 𝑀𝑂𝑀𝑡, and 𝐸𝑆𝐺𝑡 represent the factors size, value,

profitability, investment, momentum and ESG at month

t, respectively. Note: Test portfolios with an alpha

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30 Table 6

CAPM Pricing Anomalies and Risk Factor Betas for 25 ESG Test Portfolios

The Capital Asset Pricing Model (CAPM) is estimated for the 5x5 ESG test portfolios sorted on the ESG and ME dimension using the following equation: 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡+ 𝜀_𝑝,𝑡

where 𝑅_𝑝,𝑡𝑒 is the excess return of the portfolio p in month t, 𝛼_𝑝 is the pricing error of portfolio p in percentages, 𝛽_𝑝𝑚𝑘 is the systematic risk factor of the market together with the excess return of the stock market index in month t. Furthermore, 𝜀𝑝,𝑡 implies the error term for portfolio p and month t.

Panel A Panel B

𝛼̂_𝑝 t-statistic

Low 0.51 0.53 0.20 0.26 0.18 0.88 1.86 0.79 0.97 0.52 B 0.70 0.42 0.31 0.15 0.06 2.05 1.53 1.38 0.63 0.20 C 0.68 0.14 0.12 0.14 0.27 2.11 0.46 0.61 0.57 0.78 D 0.25 0.60 0.19 0.46 0.10 0.81 2.65 0.86 2.13 0.26 High 0.62 0.44 0.57 0.56 0.03 1.85 2.11 2.80 3.24 0.09 𝛽̂𝑝𝑚𝑘 t-statistic

Low 1.1280 1.1210 1.2170 0.9980 0.8880 9.48 16.46 20.39 15.62 10.25

B 1.0550 1.0770 1.0380 0.9200 0.8830 11.75 16.49 21.01 15.78 11.95

C 1.1840 1.1760 1.0530 0.9870 0.8500 12.70 13.77 21.36 15.28 11.26

D 1.1800 0.9390 0.9740 0.8920 0.9200 10.93 21.10 18.88 16.96 12.94

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31 Table 7

FF3 Pricing Anomalies and Risk Factor Betas For 25 ESG Test Portfolios

The Fama-French three factor model (FF3) is estimated for the 5x5 ESG test portfolios sorted on the ESG and ME dimension using the following equation: 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡+ 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝜀_𝑝,𝑡

where 𝑅_𝑝,𝑡𝑒 _{is the excess return of the portfolio p in month t, 𝛼}

𝑝 is the pricing error of portfolio p in percentages, 𝛽𝑝𝑚𝑘 is the systematic risk factor of the market

together with the excess return of the stock market index in month t. Furthermore, 𝜀_𝑝,𝑡 implies the error term for portfolio p and month t. Additionally, the variables 𝑆𝑀𝐵𝑡 and 𝐻𝑀𝐿𝑡 represent the factors size, and value at month t, respectively.

Panel A Panel B

𝛼̂_𝑝 t-statistic

Low 0.49 0.53 0.17 0.27 0.20 0.93 1.88 0.68 1.02 0.57 B 0.71 0.41 0.29 0.16 0.08 2.17 1.55 1.30 0.66 0.26 C 0.70 0.13 0.11 0.17 0.35 2.22 0.43 0.52 0.66 1.00 D 0.27 0.59 0.19 0.48 0.14 0.89 2.65 0.85 2.26 0.39 High 0.65 0.48 0.58 0.58 0.09 2.04 2.28 2.89 3.32 0.25 𝛽̂_𝑝𝑚𝑘 t-statistic

Low 1.0270 1.0950 1.2110 0.9790 0.8880 8.78 15.31 20.63 14.88 9.13 B 1.0000 1.0530 1.0380 0.9070 0.8680 11.49 14.37 20.72 14.47 10.81 C 1.1310 1.1470 1.0660 0.9760 0.8260 13.14 13.61 20.86 14.35 9.88 D 1.1340 0.9200 0.9680 0.8870 0.9000 11.01 18.62 18.94 16.04 11.69 High 1.1300 0.8970 0.8140 0.7510 0.8120 12.60 21.26 16.15 16.47 9.59 𝛽̂_𝑝𝑠 t-statistic

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32 B 0.7070 0.4150 0.1950 0.1220 0.0222 2.70 1.76 1.10 0.64 0.09 C 0.5940 0.4940 -0.0170 -0.0658 -0.3210 2.52 2.29 -0.11 -0.32 -1.17 D 0.4580 0.3960 0.0710 -0.1560 -0.1260 1.87 2.32 0.48 -0.92 -0.46 High 0.7460 0.1080 -0.0859 -0.1850 -0.1450 2.79 0.79 -0.63 -1.42 -0.54 𝛽̂𝑝ℎ

Low 0.7500 0.1910 -0.0094 0.1770 0.0463 2.80 1.14 -0.06 1.11 0.24

B 0.4540 0.1720 -0.0407 0.1190 0.1530 2.38 1.09 -0.31 0.94 0.92

C 0.4590 0.2070 -0.1310 0.1350 0.3270 2.21 1.29 -1.06 0.85 1.83

D 0.4030 0.1230 0.0504 0.0851 0.2420 2.49 0.98 0.42 0.81 1.27

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33 Table 8

FF5 Pricing Anomalies and Risk Factor Betas For 25 ESG Test Portfolios

The Fama-French Five Factor Model (FF5) is estimated for the 5x5 ESG test portfolios sorted on the ESG and ME dimension using the following equation: 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡 + 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝛽_𝑝𝑚𝑀𝑂𝑀_𝑡+ 𝛽_𝑝𝑟𝑅𝑀𝑊_𝑡+ 𝛽_𝑝𝑐𝐶𝑀𝐴_𝑡+ 𝜀_𝑝,𝑡

where 𝑅_𝑝,𝑡𝑒 is the excess return of the portfolio p in month t, 𝛼_𝑝 is the pricing error of portfolio p in percentages, 𝛽_𝑝𝑚𝑘 is the systematic risk factor of the market together with the excess return of the stock market index in month t. Additionally, the variables 𝑆𝑀𝐵_𝑡, 𝐻𝑀𝐿_𝑡, 𝑀𝑂𝑀_𝑡 𝑅𝑀𝑊_𝑡, and 𝐶𝑀𝐴_𝑡 represent the factors size, value, momentum, profitability, and investment at month t, respectively.

Test portfolios with an alpha corresponding to a t-statistic with a p-value < 0.05 appear in bold

Panel A Panel B

Low 0.57 0.57 0.09 0.41 0.65 0.98 1.94 0.33 1.29 1.70 B 0.76 0.37 0.25 0.16 0.47 1.87 1.20 1.09 0.58 1.41 C 0.86 0.18 0.21 0.18 0.84 2.49 0.51 0.89 0.57 2.23 D 0.40 0.46 0.18 0.41 0.56 1.02 1.92 0.81 1.72 1.45 High 0.61 0.31 0.58 0.52 0.60 1.76 1.69 2.57 2.87 1.55 𝛽̂_𝑝𝑚𝑘 t-statistic

Low 1.0030 1.0430 1.1910 0.9570 0.6930 5.90 13.04 17.54 11.63 6.99 B 0.9460 1.0760 1.0100 0.8940 0.7360 10.76 12.45 16.86 12.31 7.84 C 1.0250 1.0500 1.0050 0.9120 0.6800 12.99 17.86 17.51 15.56 7.01 D 1.0030 0.9680 0.9340 0.9150 0.7530 12.99 14.45 16.74 13.86 7.55 High 1.0760 0.9490 0.7960 0.7610 0.6290 12.20 16.95 12.72 15.34 6.17 𝛽̂_𝑝𝑠 t-statistic

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34 B 0.6980 0.4650 0.2340 0.1280 -0.2650 2.24 1.71 1.06 0.50 -0.97 C 0.5030 0.4880 -0.0786 -0.0427 -0.6750 1.85 1.67 -0.37 -0.15 -2.11 D 0.4080 0.5020 0.0965 -0.0968 -0.4250 1.22 2.50 0.50 -0.42 -1.31 High 0.8150 0.2390 -0.0643 -0.1260 -0.5210 2.61 1.47 -0.36 -0.79 -1.69 𝛽̂𝑝ℎ t-statistic

Low 0.4720 0.3550 0.2300 -0.0008 0.3810 1.09 1.37 1.07 0.00 1.51 B 0.5830 0.0476 0.1800 0.1980 0.1690 2.30 0.20 1.02 0.97 0.76 C 0.6870 0.6240 0.0441 0.5210 0.2590 1.92 2.67 0.27 2.66 1.00 D 0.9000 0.0229 0.2770 0.0738 0.3180 2.59 0.13 1.66 0.44 1.35 High 0.9300 0.2530 0.1600 0.1320 0.4190 2.57 1.50 0.92 0.92 1.89 𝛽̂𝑝𝑟 t-statistic

Low -0.4150 0.0926 0.4050 -0.4520 -0.5000 -0.45 0.31 1.43 -1.33 -1.33 B 0.0649 -0.0412 0.3060 0.0980 -0.7250 0.18 -0.13 1.37 0.33 -1.93 C -0.0592 0.3380 -0.0106 0.3800 -1.0190 -0.15 1.03 -0.05 1.22 -2.72 D 0.2950 0.1490 0.2560 0.1170 -0.7150 0.68 0.64 1.08 0.43 -1.66 High 0.4260 0.2950 0.1380 0.2110 -0.8590 0.95 1.16 0.59 1.08 -2.24 𝛽̂_𝑝𝑐 t-statistic

Low -0.0489 -0.4050 -0.3370 0.0607 -1.0430 -0.10 -1.05 -1.05 0.18 -3.47

B -0.4130 0.1500 -0.3300 -0.1370 -0.5380 -0.96 0.43 -1.18 -0.41 -1.94

C -0.6950 -0.8210 -0.3950 -0.5870 -0.4720 -1.51 -1.85 -1.38 -1.91 -1.43

D -1.0200 0.2300 -0.3480 0.1420 -0.6300 -1.86 0.94 -1.16 0.55 -1.98

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35 Table 9

FFC Pricing Anomalies and Risk Factor Betas For 25 ESG Test Portfolios

The Fama-French-Carhart (FFC) model is estimated for the 5x5 ESG test portfolios sorted on the ESG and ME dimension using the following equation: 𝑅_𝑝,𝑡𝑒 = 𝛼_𝑝+ 𝛽_𝑝𝑚𝑘𝑅_𝑚,𝑡 + 𝛽_𝑝𝑠𝑆𝑀𝐵_𝑡+ 𝛽_𝑝ℎ𝐻𝑀𝐿_𝑡+ 𝛽_𝑝𝑟𝑅𝑀𝑊_𝑡+ 𝛽_𝑝𝑐𝐶𝑀𝐴_𝑡+ 𝛽_𝑝𝑚𝑀𝑂𝑀_𝑡+ 𝜀_𝑝,𝑡

where 𝑅_𝑝,𝑡𝑒 is the excess return of the portfolio p in month t, 𝛼_𝑝 is the pricing error of portfolio p in percentages, 𝛽_𝑝𝑚𝑘 is the systematic risk factor of the market together with the excess return of the stock market index in month t. Additionally, the variables 𝑆𝑀𝐵_𝑡, 𝐻𝑀𝐿_𝑡, 𝑅𝑀𝑊_𝑡, 𝐶𝑀𝐴_𝑡 and 𝑀𝑂𝑀_𝑡 represent the factors size, value, profitability, investment and momentum at month t, respectively.

Panel A Panel B

Low 0.56 0.56 0.08 0.41 0.66 1.01 2.00 0.29 1.29 1.72 B 0.74 0.36 0.24 0.16 0.48 1.93 1.24 1.09 0.58 1.42 C 0.85 0.17 0.20 0.18 0.85 2.53 0.50 0.90 0.56 2.24 D 0.38 0.45 0.17 0.41 0.57 1.04 1.92 0.80 1.71 1.48 High 0.58 0.31 0.57 0.52 0.61 1.83 1.68 2.63 2.87 1.59 𝛽̂_𝑝𝑚𝑘 t-statistic

Low 0.9900 1.0290 1.1770 0.9580 0.7050 5.89 13.42 17.57 11.51 7.09 B 0.9340 1.0640 1.0010 0.8940 0.7420 11.05 12.64 17.11 12.25 7.85 C 1.0110 1.0330 0.9970 0.9120 0.6900 13.48 18.95 17.80 15.33 7.17 D 0.9820 0.9620 0.9250 0.9170 0.7650 13.16 14.60 17.39 13.87 7.82 High 1.0520 0.9390 0.7880 0.7610 0.6400 12.67 17.85 12.79 15.37 6.27 𝛽̂𝑝𝑠 t-statistic

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36 B 0.6850 0.4520 0.2240 0.1280 -0.2580 2.31 1.71 1.06 0.50 -0.95 C 0.4880 0.4710 -0.0871 -0.0435 -0.6650 1.96 1.73 -0.42 -0.15 -2.09 D 0.3860 0.4950 0.0871 -0.0948 -0.4130 1.31 2.51 0.48 -0.41 -1.28 High 0.7890 0.2280 -0.0729 -0.1260 -0.5090 2.91 1.52 -0.43 -0.78 -1.66 𝛽̂𝑝ℎ t-statistic

Low 0.1710 0.0193 -0.0916 0.0176 0.6540 0.31 0.07 -0.44 0.06 2.50 B 0.2860 -0.2300 -0.0350 0.1940 0.3150 0.95 -0.85 -0.18 0.80 1.22 C 0.3560 0.2380 -0.1460 0.5030 0.4810 1.30 1.00 -0.83 2.29 1.74 D 0.4020 -0.1150 0.0661 0.1180 0.5850 1.48 -0.60 0.35 0.65 2.17 High 0.3470 0.0075 -0.0318 0.1380 0.6790 1.12 0.04 -0.18 0.86 2.69 𝛽̂𝑝𝑟 t-statistic

Low -0.3890 0.1210 0.4320 -0.4530 -0.5230 -0.43 0.46 1.69 -1.34 -1.46 B 0.0903 -0.0174 0.3240 0.0984 -0.7370 0.26 -0.06 1.58 0.33 -1.99 C -0.0309 0.3710 0.0057 0.3820 -1.0380 -0.09 1.33 0.03 1.24 -2.90 D 0.3380 0.1600 0.2740 0.1130 -0.7380 0.95 0.71 1.25 0.42 -1.71 High 0.4760 0.3160 0.1540 0.2110 -0.8820 1.31 1.36 0.74 1.07 -2.26 𝛽̂_𝑝𝑐 t-statistic

Low 0.2740 -0.0458 0.0072 0.0410 -1.3360 0.52 -0.12 0.02 0.12 -4.45

B -0.0960 0.4480 -0.0997 -0.1330 -0.6950 -0.23 1.27 -0.34 -0.40 -2.36

C -0.3410 -0.4070 -0.1910 -0.5680 -0.7100 -0.89 -1.05 -0.68 -2.23 -2.11

D -0.4860 0.3770 -0.1220 0.0947 -0.9160 -1.15 1.37 -0.38 0.41 -2.60

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37

𝛽̂_𝑝𝑚 t-statistic

Low -0.2620 -0.2910 -0.2790 0.0160 0.2370 -1.25 -3.25 -3.24 0.13 2.52

B -0.2570 -0.2410 -0.1860 -0.0036 0.1270 -1.99 -2.45 -2.62 -0.04 1.27

C -0.2870 -0.3350 -0.1650 -0.0154 0.1920 -1.78 -2.94 -2.15 -0.13 1.68

D -0.4320 -0.1190 -0.1830 0.0385 0.2320 -2.72 -1.59 -2.22 0.43 1.84

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38 Table 13

Pricing Anomalies & Risk Premiums of Equally-Weighted Test Portfolios

Panel A of this table shows the alphas and corresponding t-statistics of the ESG model by using equally-weighted instead of value-weighted portfolios. Additionally, Panel C shows the risk premium of the ESG model in which 𝜆1,𝑡, 𝜆2,𝑡, 𝜆3,𝑡, 𝜆4,𝑡, 𝜆5,𝑡, 𝜆6,𝑡 and 𝜆7,𝑡 are the monthly risk

Is ESG An Additional Risk Factor Contributing To Excess Returns?