The pricing of climate transition risk? Investigating a 'green' premium in US equities using multi-factor models.

MSc Finance - Quantitative Finance Master's Thesis

The pricing of climate transition risk?

Investigating a 'green' premium in US equities using multi-factor models.

Written by Giovanni Ruggero Facchini

(Student no. 13873075)

Thesis supervisor: Cyriel de Jong

University of Amsterdam, Amsterdam Business School

June 2022

Statement of originality

This document is written by student Giovanni Ruggero Facchini, who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Acknowledgements

There are many people whom I would like to thank and am grateful to. I am sure, though, that they will excuse me if I choose to dedicate this space entirely to my grandmother, nonna Mati, who passed away last April 24^th. Sadly, I was unable to return to Italy quick enough to say goodbye. Nonna Mati taught me and my mother many things: from her immense strength in facing, on her own, a troublesome early life, to her lovingkindness towards all human beings. Giving to others was her source of happiness.

To this day, I often cannot believe that she is gone forever, but this is probably why I found the strength to put my head down and keep working hard. In fact, I like to think that nonna Mati has gifted me with her strength, without which I would not have been able to write this paper and all the underlying computer code, in such a limited amount of time.

My thoughts are only for you, nonna, I hope to see you again one day.

Abstract

The transition to a low-carbon economy entails risks for the profitability and value of businesses, particularly the environmentally negligent. Consequently, if the risk-return tradeoff holds, investors may expect to earn comparatively less on a ‘greener’ asset allowing them, ceteris paribus, to hedge transition risks. This would translate into a negative ‘green’

premium. My study provides evidence against the existence of such a premium in the US equity market, while speculating that the mispricing may in part result from the historical laxness of US environmental policy relative to Europe’s major economic powers. A synthetic

‘greenness’ indicator, weighted for both firm-reported emission intensity and third-party- assessed environmental transparency, is used to sort S&P 500 stocks into ‘green’ and ‘brown’

portfolios. The performance difference between the latter is defined as the ‘green’ factor which, incorporated into traditional multi-factor models, is used in a two-pass regression to estimate time-invariant ‘green’ premia for different specifications. An initial replication yields significant negative premia, but a first robustness check, aimed at reducing the bias caused by undiversified idiosyncratic risk, is enough for these estimates to cease being significant. A second check adapts the initial sorting methodology, to control for the observed relationship between ‘greenness’ and firm size, yielding even less significant premia. Also, the smallest magnitude and significance are found to concur with the case in which ‘greenness’

determinants are equally weighted. Besides confirming the absence of an unbiased ‘green’

premium in US equities, these results appear to highlight the importance of a balanced definition of ‘greenness’ for reducing estimation biases. This paper contributes to the literature on ‘green’ premia in the United States, which has thus far failed to find a common ground on the systematic pricing of climate risk. By addressing the biases and quality issues of ESGs and emissions data, in the footsteps of an existing study performed for the European market, my study seeks to pave the way for more transparent definitions of ‘greenness’, which can better reflect an asset’s exposure to climate transition risk.

Key Words: Climate Risk, Transition Risk, Multi-factor Model, Greenness, Green Premium, Emission Intensity, Environmental Transparency, Environmental Policy Stringency.

Table of Contents

Tables and Figures ... 6

Section 1: Introduction ... 7

Section 2: Literature Review ... 10

Section 3: Hypothesis and Methodology ... 15

3.1 Hypothesis and motivation ... 15

3.2 Methodology ... 17

Ø 3.2.1 Theoretical background ... 17

Ø 3.2.2 Constructing a synthetic ‘greenness’ indicator ... 19

Ø 3.2.3 Portfolio sorting and ‘green’ factor determination ... 21

Ø 3.2.4 Obtainment of the cross-sectional parameters 𝜐_! ... 22

Ø 3.2.5 Robustness checks ... 24

Section 4: Data, empirical results and robustness checks ... 25

4.1 Data ... 26

4.2 Univariate portfolio sorting: ‘greenness’ only (2003-2020) ... 26

Ø 4.2.1 Descriptive statistics ... 27

Ø 4.2.2 Empirical results ... 34

4.3 Robustness checks ... 39

Ø 4.3.1 Restricting the time frame (2010-2019) ... 40

Ø 4.3.2 Bivariate portfolio sorting: ‘greenness’ conditional on firm size 42 Ø 4.3.3 Sensitivity analysis for γ: the relative weighting of ‘greenness’ 48

Section 5: Discussion and Conclusions ... 53

Appendix ... 60

References ... 62

Tables and Figures

Table 1: Econometric forms of linear multi-factor model specifications. ... 23

Table 2: Descriptive statistics portfolios, initial replication (4.2). ... 27

Table 3: Descriptive statistics risk factors, initial replication (4.2). ... 28

Table 4: Portfolio constituents’ characteristics, initial replication (4.2). ... 30

Table 5: Portfolio sizes and diversification levels, initial replication (4.2). ... 31

Table 6: Cross-sectional parameters, 𝜐

Table 7: Risk premia estimates, for all risk factors, initial replication (4.2). .... 37

Table 8: OLS regression of ‘green’ factor on existing factors, initial rep. (4.2). 38 Table 9: Risk factor statistics and ‘green’ premia estimates, 1

Table 10: ‘Green’ factor statistics, 2

Table 11: OLS regression of ‘green’ factor on existing factors, 2

Table 12: ‘Green’ premia estimates, 2

Table 13: ‘Green’ premia estimates, 3

Table 14: OLS regression of ‘green’ factor on existing factors, 3

Figure 1: OECD’s ‘Environmental Policy Stringency Index’: US vs. EU. ... 16

Figure 2: Portfolios’ average industrial compositions, initial replication (4.2). 32 Figure 3: Graphical comparison of results between different replications. ... 47

Figure 4: Graphical representation of the sensitivity analysis for 𝛾. ... 53

Figure 5: Timeseries comparisons of US vs. EU standard risk factors. ... 61

Section 1 : Introduction

According to standard asset pricing theory, the risk premium of an investment is measured by the excess expected return, with respect to the risk-free rate, required by an investor to hold a risky asset. This is known as the ‘risk-return trade-off’ and lies at the heart of several factor models that have been proposed to model risky returns. Sharpe’s CAPM model (1964) used the excess return of the market portfolio as the only explanatory variable, Fama &

French (1993) added the ‘size’ (‘small minus big’) and ‘value’ (‘high minus low’) factors, while Carhart (1997) added ‘momentum’ (‘winners minus losers’) as a fourth factor. These ‘risk factors’ supposedly account for systematic patterns of risk that, on average and in the long- run, associate with excess returns. Although these models are considered finance classics, much academic debate has followed their publications, with researchers often disagreeing on the choice and/or definition of risk factors. A new factor (e.g. ‘size’) can be tested by sorting a large sample of stocks into two well-diversified (subset) portfolios, distinguished by the associated characteristic (e.g. market capitalisation). Any significant (long-run) performance difference between the portfolios can then, ceteris paribus, be ‘explained’¹ by that characteristic, and constitutes a ‘premium’ associated with the factor. If the portfolios are indeed well-diversified, such that idiosyncratic² risk can be thought to be minimised, the factor is thought to account for some element of systematic risk, provided it cannot itself be

‘explained’ by existing, well-established risk factors (as those mentioned).

Of all the factor characteristics, ‘greenness’³ (or, more generally, environmental performance) has certainly been amongst the most debated in recent years, first and foremost because there is much ambiguity surrounding its definition. There are multiple aspects to consider when judging a firm’s environmental performance, many of which are difficult to quantify.

Emissions and ESG metrics have often been used to measure the level of ‘greenness’ of a firm,

1 Note that risk factors are correlational. Since correlation does not imply nor prove causation, the extent to which they deterministically cause the excess returns, with which they empirically associate, is debatable.

Throughout this publication, I use ‘explain’ (and, often, also ‘determine’) in inverted commas to express this implied ambiguity, though an associative terminology would technically be more appropriate.

2 I.e. specific to a firm or industry. The contrary of systematic risk.

3 Throughout my entire research, I use inverted commas around ‘green’ and ‘greenness’ to stress that their definition is not universal. These should be treated as mere names, used to describe one or more aspects relating a business or product to the environment, whose specific meaning may vary depending on the context.

but the methods used for calculations and assessments are prone to inaccuracies and subjectivity. Further, the systematic risk supposedly embodied by ‘greenness’ is still very much abstract, since it is difficult to assess the relationship between a firm’s ‘greenness’ and its effective exposure to environmental regulation. Indeed, despite the rising awareness of climate change and first developments in environmental law, the potential effects of ‘climate’

risk on the financial system were first warned only a few years ago, in a famous speech held by the ex-governor of the Bank of England (Carney, 2015). Climate risk can be divided into many channels, the two most important of which are ‘physical’ and ‘transition’ risks. Physical risks include the effects of extreme weather events on businesses. While the consequences may be felt by the rest of the economy due to spillover effects, the risk of natural disasters is tied to a firm’s specific location, hence may be considered idiosyncratic⁴. As such, this risk can be addressed by diversifying the geographical location of investments, and is hence not of primary interest to asset pricing models. Transition risk, on the other hand, includes the effects of a potential increase in the scope and stringency of environmental regulation during a low-carbon transition. This may impact the profit margins and even reputations of firms, especially those who are less environmentally-friendly, ultimately reducing their market values. Some industries are inevitably more exposed to environmental regulation, but stocks are priced based on expectations; stricter regulations could potentially be stretched to the broader economy as countries strive to fulfil their ambitious Paris NDCs⁵. Therefore, the extent to which climate transition risk may be deemed systematic also depends on expectations regarding the extensiveness and rigidity of future environmental policies, which are highly uncertain. Past, current, domestic and international trends in environmental policy and diplomacy may play a major role. It therefore comes as no surprise that the literature finds patterns relating the geographical variation in ‘green’ premia with the international heterogeneity in policy stringency. From a theoretical standpoint, a better environmental performance should reduce a stock’s exposure to transition risk, resulting in (again, ceteris

4 This is of course debatable, especially if we consider effects such as rising sea levels and droughts, which can potentially affect entire continents. However, unless large-scale catastrophes produce spillover effects for multiple countries (which is entirely possible), the economic impacts may be manageable. It is undoubtable that some areas will be harder-hit from climate change than others, in which case physical risks may be diversifiable.

5 Nationally determined contributions (NDCs) from the Paris Agreement are voluntary pledges made by countries, with the general target of becoming ‘net zero’ by 2050. Intermediate targets, to be fulfilled by 2030, also exist.

paribus) lower expected returns from investors. In other words: if climate transition risk is indeed systematic and priced by the market, it should be reflected in a ‘green’ risk premium, i.e. a performance difference between two (well-diversified) portfolios distinguished by

‘greenness’ only. If this difference is defined as ‘green’ minus ‘non-green’ (or ‘brown’), the premium should be negative as, according to standard asset pricing theory, investors would accept to earn comparatively less on an asset allowing them to hedge transition risk. That is, of course, if ‘greenness’ (as has been conceived) is indeed a ‘determinant’ of an asset’s exposure to systematic risk, just like ‘market’, ‘size’, ‘value’ and ‘momentum’ factors.

My research uses S&P 500 firm-reported emission intensities, weighted by an ESG indicator capturing the transparency of a firm’s environmental disclosure, to construct a synthetic

‘greenness’ indicator. Having defined ‘greenness’, I can then sort stocks into ‘green’ and

‘brown’ portfolios. A key objective of this methodology is to account, as far as possible, for biases in firms’ environmental disclosures. If a firm reports low emissions, but its environmental transparency indicator is also low, this will impact its overall ‘greenness’ score.

The synthetic indicator also seeks to address biases in third-party estimation, since ESG data itself is often far from accurate and consistent. In such sense, diversifying between data sources (firms’ own reporting, and third-party assessments) is beneficial. Having constructed the portfolios, I then define the performance difference between ‘green’ and ‘brown’ as the

‘green’ factor, which I use to test for the existence of a time-invariant ‘green’ premium. This methodology is an adaptation of that used by Alessi et al. (2021) whom, performing it for the European market, obtained a robustly negative premium. The model used is the time- invariant exception of the generic dynamic model developed by Gagliardini et al. (2016). It is based on the idea that the premium is obtained from the sum of two terms: the unconditional expectation of the ‘green’ factor (i.e. its average over the chosen timeframe) and a cross- sectional parameter accounting for market imperfections. The latter is obtained from a two- pass estimation methodology, similar in essence to the well-known Fama & Macbeth method (1973). Having estimated the ‘green’ premium, I then assess whether it can indeed be seen as evidence of systematic returns associated with ‘greenness’, as an intrinsic characteristic embodying an asset’s exposure to climate transition risk. It could be that the premium is in fact largely driven by correlations between ‘greenness’ and other, established, risk factors, and/or by idiosyncratic biases caused by limited portfolio diversification.

My choice of transposing an existing methodology (Alessi et al., 2021) to a different country is not casual. Since the early 1990s, the US has notably lagged behind Europe’s major economic powers in terms of environmental policy stringency (OECD, 2016). This raises major concerns, since it is hard to justify the world’s second largest emitter of CO2. The US’s recent reinstatement of its Paris commitments has replenished some optimism, though one may still expect decades of weak environmental policy to be reflected in what remains by far the world’s most advanced financial market. How? In a ‘green’ premium that is not statistically different from zero. Therefore, my research seeks to address the following questions:

§ Is there evidence of a ‘green’ premium in the US equity market?

§ If so, how far can we consider ‘greenness’, as an independent characteristic (supposedly) embodying an asset’s exposure to climate transition risk, to systematically ‘explain’¹ such premium?

Section 2 : Literature Review

Several studies have compared the performance of ‘green’ stocks with respect to ‘brown’

stocks, yielding significant though often contradictory results. Some have taken a much broader perspective on the topic, by using ESG scores as a distinguishing characteristic defining ‘greenness’. Derwall et al. (2005) were among the first to do this, using ‘eco- efficiency’ scores⁶ as an indicator of environmental performance. They found that the most eco-efficient portfolio sizeably outperformed its counterpart, though it remained unclear whether this could be explained in terms of exposure to risk. Further, the indicator’s comprehensiveness and the limited sample period (1997-2003) raised validity concerns. More recently, Jin (2018) replicated the two-pass approach by Fama and Macbeth (1973) to test whether an ESG factor (ESG-weighted minus unweighted) is priced in US mutual funds. A positive premium was found while, through similar methods, Maiti (2021) found reinforcing evidence for the individual ESG ‘pillars’. While these studies seemingly contradict the prediction that a ‘green’ premium should be negative, ESG scores are very comprehensive;

they are usually weighted sums of numerous other sub-scores, each of which correlates with different aspects of a firm’s business. As such, it is difficult to discern the aggregate channel through which ESGs impact a portfolio’s exposure to climate risk. In fact, Jin (2018, p.2) warned that “weighting processes practiced on the basis of ESG criteria” may ironically increase portfolio risk, since ESG scores often correlate with firm/industry characteristics that may hamper the effectiveness of diversification. This may partially explain the surprising results mentioned above. Nonetheless, it remains clear that overly comprehensive ESGs are not ideal for proxying climate risk.

Fortunately, studies focusing on the carbon footprint of firms have also been carried out, since greenhouse gas emissions are the main driver of climate change. Bolton & Kacperczyk (2021a) found a significantly positive ‘carbon’ premium (hence, negative⁷ ‘green’ premium) upon sorting a cross-section of over 3000 US stocks by CO2 emission levels, while controlling

6 The ratio of the value a company adds to the waste it generates.

7 We define the ‘green’ premium as the difference in returns between well-diversified ‘green’ and ‘brown’

portfolios which, based on climate risk considerations, we would expect to be negative. Hence, a ‘carbon’ (or

‘brown’, ‘pollution’, etc.) premium is its inverse, i.e. the excess return earned by a ‘brown’ portfolio with respect to a ‘green’ portfolio. Theory would consequently predict it to be positive.

for firm size. They could not explain this using existing risk factors, implying that the level of emissions could indeed be a systematic ‘determinant’ of the observed premium. However, when emission intensity (emissions on sales) was used instead of levels, the ‘carbon’ premium ceased to be significant. This puzzled the authors, but not Aswani et al. (2022, p.3), who showed that while “unscaled emissions are strongly correlated with firm size, industry composition and time… emission intensity does not correlate nearly as highly.” This finding stresses the need to look deeper into the root causes of ‘green’ premia, since emissions are often correlated with other (financial) variables. In this regard, normalising emissions by sales is a good way of controlling for elements of profitability and firm size that are correlated with emission levels, and that may bias the resultant premium. In light of this, Hsu, Li, & Tsou (2022) sorted a large sample of US stocks, conditional on the industry sector, by toxic emission intensity, and found a robust ‘pollution’ premium of 4.42% (hence, - 4.42% ‘green’ premium).

They also showed that the premium could not be explained by existing risk factors. This could be interpreted as evidence of the systematic pricing of pollution risk, especially as the conditional sorting methodology ensured that undiversified idiosyncratic risk tied to industry concentrations would be minimised. However, the inclusion of a broader range of toxic emissions other than greenhouse gases (which are by far the culprits of climate change) reduces the relevance of this study with respect to climate transition risk. Their premium could, for instance, be pricing the physical and reputational risks tied to toxic leakages. The importance of accounting for firm and industry characteristics was also highlighted by In et al. (2019), who (contrary to theoretical predictions) initially found a significantly positive

‘green’ premium for a sample of 736 US firms, sorted by emission intensity. In the only case where the sorting was conditional on firm size (market capitalisation), the authors found the premium to be “close to zero and not statistically significant.” This is an important finding, since size is an established risk factor (‘small minus big’) which, if unaccounted for, may bias the ‘green’ premium. Such premium should only be pricing the heterogeneity in ‘greenness’;

if ‘greenness’ is itself driven by size differences, then there would be no new element of systematic risk inherent in it.

A final note is on studies performed at the global level. Görgen et al. (2020, p.62) found, for a sample of 1657 stocks, that while their ‘brown minus green’ factor did “move asset prices systematically”, there was no significant premium to be detected. Contrarily, Bolton and

Kacperczyk (2021b) obtained a negative ‘green’ premium for a huge cross-section of 14,400 firms, from a total of 77 different countries. Further, they found larger premia in countries implementing stricter environmental policies. This finding is particularly interesting, since it suggests that investors do indeed adapt their expectations based on a country’s environmental stance or, as the authors describe it (pp. 22-23), “carbon policies are seen by investors as permanent shocks to carbon-transition risk.” However, rather unorthodoxly with respect to the broader asset-pricing literature, but due to cross-country comparability concerns and a highly unbalanced panel (i.e. many countries with very low data availability), the authors chose not use a risk-factor approach to estimate the premium. Also, as in their previous research for the US market (2021a), they performed the analysis on emission levels and rates of growth, not intensity, thereby raising similar robustness concerns. As such, their findings appear weak when it comes to proving that it is indeed emissions, and not some omitted variable, ‘explaining’ the premium.

A key issue which arises from the ambiguous picture painted so far is that the quality and form of ESG and emissions data play a major role in determining the outcome of a study. The sourcing of data, i.e. whether emissions are disclosed directly by firms or estimated by data vendors, is also important, yet this distinction is largely ignored by the literature. For instance, Busch et al. (2022) showed that different data vendors’ estimates of emissions only displayed a correlation coefficient of 0.67, unlike firms’ own disclosures which, reported by different vendors, correlated at around 0.97. Vendors tend to provide emission estimates if firm disclosures are unavailable, yet their different estimation methods lead to research results which are hardly comparable between themselves. Worse still, as pointed out by Aswani et al. (2022, p.27), data vendors “place a high weight on financial fundamentals when estimating carbon emissions”, meaning that studies using such estimates (which, according to the authors, are a vast proportion of the relevant literature) are more likely to find associations between stock returns and emissions. This is not to say that self-reported emissions are unexposed to inaccuracies or other biases (e.g. ‘self-reporting’ bias), but that collectively they are less prone to inconsistencies and omitted variables. Heterogeneity in estimation methodologies is a huge problem for environmental accountability. The need for a global, standardised reporting is stressed by Yu et al. (2021, p. 3975), since comparability strengthens the accountability of firms and stimulates their disclosure efforts. In fact, the authors found

evidence that “more environmental disclosure decreases a firm’s ex ante cost of equity”, due to reduced information asymmetries. In practice, firm-level environmental auditing and reporting remain, at present, largely unregulated and unscrutinised. Whether self-reported or estimated by vendors, emissions data collected in the last decades is likely to be highly inaccurate and/or biased. It follows that, like ESG scores, emissions data alone appears to be an inadequate proxy for climate transition risk. A potential solution to this, though largely ignored by the literature at present, is to construct a synthetic indicator for ‘greenness’, weighed for both firm-reported greenhouse gas emission intensity and data vendor estimates of the transparency of such environmental disclosure. The intention is to factor the transparency (or quality) of a firm’s environmental reporting into the measure of its

‘greenness’, in the attempt to reduce the concentration of biases, while also diversifying between data sources. Like emission estimates, ESG indicators obviously include elements of subjectivity. However, provided there is consistency of judgement, one can trust them to carry information on firms’ disclosure efforts. While discrepancies may exist between data vendors, there should be less disagreement on the relative rankings of firms.

Unfortunately, none of the studies mentioned so far explicitly accounts for the transparency and quality of firms’ reported emissions, and very few stress the difference between self- reporting and third-party estimation. This is not the case for Alessi et al. (2021). In their publication, the authors sorted 942 stocks from the ‘STOXX Europe Total Market Index’ into subset ‘green’ and ‘brown’ portfolios, using a synthetic ‘greenness’ indicator weighed for both Bloomberg’s ‘Environmental Disclosure Score’ (‘E-score') and firm-reported emission intensity. They then defined the performance difference between portfolios as the ‘greenness and transparency factor’⁸. This was included as an extra risk factor within traditional multi- factor models, to estimate the time-invariant ‘green’ premium for the European market, based on the procedure outlined by Gagliardini et al. (2016). The premium was found to be robustly negative and significant, a fact which the authors interpreted as “evidence of climate risk being viewed as significant, with the market seeing value in investing in greener assets as a hedging strategy towards worse environmental outcomes” (Alessi et al., 2021, p.2), coherently with what classical asset pricing theory would predict.

8 For simplicity, I choose to reduce this to ‘green’ factor in my research.

Section 3: Hypothesis and Methodology

In this section, I offer a detailed overview of my research process. I begin (3.1) by providing my one-sentence hypothesis, motivating the reasoning that led to this assertion, while also linking it to previous sections. I then focus on the methodology used to test the hypothesis, starting from the theoretical background (3.2.1) necessary to derive and understand the main equations used in the process. Referring to these equations, I then (3.2.2 - 3.2.4) explain the practical steps that are required. More specifically: I provide a quantitative definition of

‘greenness’ (in line with Alessi et al., 2021), describe the portfolio sorting methodology, and uncover the econometric forms of the regressions that are implemented. In the final section (3.2.5), I describe the three robustness checks which I use to seek confirmation (or disproval) of the initial findings, and address potential biases in the estimation procedure.

3.1 Hypothesis and motivation

One-sentence hypothesis: An unbiased estimate of the time-invariant ‘green’ premium in the S&P 500 index, obtained via annual sorting by a synthetic ‘greenness’ indicator, equally weighted for firm-reported greenhouse gas intensity and third-party-assessed environmental transparency, is not statistically significant at the 5% level.

Note that expecting the risk premium to be insignificant is not equivalent to doubting the existence of climate transition risk itself (in the United States). Rather, it predicts that, notwithstanding its reality, climate risk has thus far not been priced by the US equity market.

Also, the word ‘unbiased’ is used to distinguish between statistical significance and unbiasedness; a ‘green’ premium could well be significant, yet be driven by the dependency of ‘greenness’ on other risk factors (which I refer to as ‘systematic bias’) or by the presence of undiversified idiosyncratic risks (‘idiosyncratic bias’). To test the proposition, I adapt the aforementioned study by Alessi et al. (2021) (henceforth, often referred to as the ‘reference paper’) to the S&P 500 index, in its composition as of March 2022. The comparison between the US and EU markets is interesting, since the European Union is (by many) considered to be a leader in environmental policy. This may be reflected in the result obtained in the reference paper, since a robustly negative ‘green’ premium may suggest that market participants pay

close attention to transition risk. On the other hand, the United States failed to ratify the Kyoto Protocol at the time (2005) when the European Union was launching the world’s first ever emissions trading system. This system has consolidated and been expanded since, and was followed by the announcement in 2019 of a ‘European Green Deal’ set to make the continent carbon neutral by 2050. At the same time the United States was formalising its withdrawal from the Paris Agreement (a decision later reversed by the Biden administration).

Figure 1 below confirms these trends in quantitative terms, by comparing the evolution of the US’ ‘Environmental Policy Stringency Index’ (as constructed by the OECD, 2016) with Europe’s G8 countries. My research may provide insights relating the comparative laxness of US environmental policy with the time-invariant ‘green’ premium that I estimate. While a causal interpretation is beyond my scope, I do speculate that this laxness will be reflected in US market participants’ expectations on transition risk. Hence, I derive my hypothesis that the

‘green’ premium is zero in the United States. The financial implications of this regard both small-scale and institutional investors. This is because the underestimation of climate risk may lead to asset mispricing, which impacts portfolio management. If a low-carbon transition were to be brought forward more abruptly, for instance due to greater pressure by the public opinion or due to an event which increases the saliency of climate change, ‘brown’ assets may eventually become stranded. In turn, this could result in non-performing loans, with potentially catastrophic spillovers for the rest of the economy.

Figure 1: Comparative time series for the OECD ‘Environmental Policy Stringency Index’ (EPS), between the United States, Italy, Germany and France, 1990-2015. The index measures “the degree to which environmental policies put an explicit or implicit price on polluting or environmentally harmful behaviour” (OECD, 2016). The comparison reveals that, since the signing of the world’s first international convention on climate change in 1992 (the

‘UNFCC’, signed in Rio), on average the US has lagged behind the EU’s main industrial powers. Together, these make up a large proportion of the EU’s total market capitalisation. Such policy trends could be reflected in market participants’ expectations regarding climate transition risk. The graph was produced in Excel.

3.2 Methodology

Ø _3.2.1 Theoretical background

As mentioned in the previous section, the methodology is based on the paper by Alessi et al.

(2021), which in turn lays ground on the procedure outlined in Gagliardini et al. (2016) for the specific case of time-invariant risk premia. These papers should be used as references for further details, though please note that my notation differs slightly. Also, I choose to make some adaptations in the portfolio sorting methodology, which are explained in later sections.

The current section provides a theoretical background on the estimation procedure for the time-invariant risk premium, to better understand how the main formula (Eq. 5) is derived.

To begin with, a candidate risk factor is defined as the performance difference between two well-diversified portfolios which have been sorted by the factor’s distinctive characteristic. In our case, the ‘green’ factor is defined as:

Eq. 1: 𝑓" = 𝑟_{!,# #}^! − 𝑟_#^$ ,

where rt is the portfolio’s monthly return, and ‘G’ (green) and ‘B’ (brown) are hereby used to label the shades of ‘greenness’ (to be defined later) of the respective portfolios. The ‘hat’

indicates that it is an estimate. Excess stock (‘i’) returns Ri,t (= ri,t-rf , where rf is the risk-free rate of US treasuries) are modelled using the following linear multi-factor model:

Eq. 2: 𝑅_%,# = 𝑎_%+ ∑ 𝑏 _{& %,&}𝑓_&,# + 𝜀_%,# ,

where the set ‘k’ of risk factors is included as ‘explanatory’ variables. ‘k’ varies between different model specifications. Factors are included as explanatory variables because they associate with elements of systematic risk, i.e. risk inherent to the way markets function, which cannot be eliminated by diversification, and are therefore priced by the market. In this paper, I use three traditional factor models for my analysis, augmented by the ‘green’ factor 𝑓_!: the ‘Capital asset pricing’ model (henceforth, ‘CAPM’), the ‘Fama-French 3-factor’ model (‘3 FF’) and the ‘Carhart’ model (‘CAR’). The coefficient bi,k , referred to in the literature as the

‘factor loading’, measures the exposure of asset i to risk factor k. The higher the magnitude,

the greater the performance difference between the asset and the factor, and hence also (in theory) the riskiness of the asset. The intercept of the model, ai, seeks to capture the structural imperfections of markets (e.g. imperfect information, beliefs, transaction costs) affecting all stocks, though to different degrees, whereas the error term 𝜀%,#⁹ contains any undiversified idiosyncratic risk. The ai term is assumed to be further decomposable as follows:

Eq. 3: 𝑎_% = ∑ 𝑏 _{& %,&}𝜐_& ,

where 𝜐& is a cross-sectional parameter specific to factor ‘k’, capturing the systematic imperfections that are associated with it. If we then merge Eq. 3 into Eq. 2, and substitute the result into the standard linear relationship between expected excess returns (𝐸1𝑅_%,#2) and risk premia (𝜆&), given by:

Eq. 4: 𝐸1𝑅_%,#2 = ∑ 𝑏 _{& %,&}𝜆&#([*,+] ,

we obtain the following expression for the time invariant risk premium of risk factor k:

Eq. 5: 𝜆&#([*,+] = 𝐸1𝑓_&,#2 + 𝜐_& ,

In other words: the time-invariant risk-premium associated with risk factor k is the combination of the time-invariant expected value of the factor (i.e. its simple average, 𝑓4444 ) _&,#

over the chosen timeframe (T months), plus the cross-sectional parameter (𝜐_&) which, originating from the relaxation of the assumption that factors are tradable, seeks to incorporate systematic market imperfections. In our case the time-invariant ‘green’ risk premium, 𝜆_!, is therefore defined as:

Eq. 6: 𝜆"_!

#([*,+] = ^-₊∑ 𝑓_# " + 𝜐_!,# 5_! .

9 In the literature, the sum of ai and ε_!,# is frequently referred to as ‘alpha’, i.e. the component of excess returns which cannot be explained by existing factors. By separating the two, we seek to capture those elements of alpha which can potentially be priced due to their origination from structural market imperfections. Indeed ai

is time-invariant, which means that relative differences between stocks are fixed over time, unlike the effects of idiosyncratic headwinds or tailwinds. In fact, we see later that from regressing the ai on the bi in the cross- section of stocks, we obtain the parameter 𝜐$which seeks to capture those systematic inefficiencies.

Time invariance implies that it is a static premium, i.e. assumed to be immutable for the chosen timeframe. If it weren’t the case, the expectation in Eq. 5 would not be unconditional.

Note that the ‘t=[0,T]’ subscript specifies the range of time over which the premium is estimated and hence time-invariance assumed, which for the first part of my analysis I choose to be the months between (fiscal years) 2003-2020. I choose monthly factor data¹⁰ to avoid intra-year loss of information, while increasing the number of observations and hence decreasing the sizes of standard errors. While invariance is a simplifying assumption, it is necessary both due to limited data availability and time constraints, since a dynamic model would have required a much longer, balanced panel as well as a far more laborious methodology. Of course, in practice it is not imaginable that premia remain unaltered, even more so for ‘green’ premia since environmental consciousness and the perceptions of climate risk have evolved rapidly over time.

The rest of Section 3.2 is subdivided into the practical steps required to obtain estimates for time-invariant risk premia, of which the ‘green’ premium is of course the main focus. I begin by defining ‘greenness’ through a synthetic indicator, which I then use to sort the S&P 500 stocks into deciles. I then construct the ‘green’ factor and include it alongside existing factors in the traditional multi-factor models mentioned earlier. I use these models to perform a two- pass cross-sectional regression methodology, giving me an estimate for the cross-sectional parameter 𝜐_!. Finally, I sum this with the ‘green’ factor average, 𝐸1𝑓_.,#2, to obtain an estimate for the overall ‘green’ risk premium 𝜆_!.

Ø _3.2.2 Constructing a synthetic ‘greenness’ indicator

The first step is to define ‘greenness’, so that the S&P 500 stocks can be sorted by this characteristic. In line with Alessi et al. (2021), I construct a synthetic ‘greenness’ indicator ‘GI’

accounting for both the intensity of greenhouse gas emissions and environmental transparency. Observations where such information is missing are dropped, to avoid their interference with the rest of the procedure. Financial firms are also excluded a priori, in line with common practices in the field and with Alessi et al. (2021) themselves. I use annual data

10 Which I then annualize via trivial multiplication by twelve.

on firm-reported ‘Total CO2 Equivalent Emissions To Revenues’ (which I abbreviate to ‘GHG emission intensity’) and the one-year lag of ‘Environmental Pillar Score’ (‘E-score’, 0-100), both downloaded from the Eikon Refinitiv database (though only E-score is estimated by Eikon), to construct ‘GI’. It is important to stress that the emissions data used must have been reported by firms themselves; this comes at the expense of lower data availability, but with the advantage of avoiding estimation inconsistencies between data vendors (recall Section 2), for the benefit of external validity. The lag in ‘E-score’ is used to account for time passing between firm-level disclosure (e.g. through annual reporting) and the data vendor’s own assessment (and publication) of the level of environmental transparency. Note that the ‘E-score’ is normalised to account for industry differences, allowing for better comparability¹¹. This is important because its purpose in this model is not so much to capture sectorial differences in environmental impacts (which are already partly accounted for by emission intensity), but rather to proxy firms’ relative efforts in disclosing environmental information¹². Similarly, intensity is used instead of emission levels, to control for size and profitability (as well as other potential omitted variables mentioned by Aswani et al., 2022). The synthetic ‘greenness’

indicator associated with asset ‘i’ is then defined as:

Eq. 7: 𝐺𝐼_%,/ = 𝛾𝐾_%,/ + (1 − 𝛾)𝐿. 𝐸_%,/ ,

where 𝐾_%,/ and 𝐿. 𝐸_%,/ are, respectively, the reverse ranking and the ranking of firm i in terms of ‘GHG intensity’ and lag of ‘E-score’, in year y. The weight 𝛾 is arbitrary: I used 0.5 for all replications, except for the final robustness check (Section 4.3.3) where a sensitivity analysis is performed specifically for 𝛾.

The purpose of ‘GI’ is to create a less biased indicator of emission intensity at the firm level, attenuating potential inaccuracies caused by biased reporting and estimation practices.

11 Refinitiv (2022a) specifies that “the ESG pillar score is a relative sum of the category weights, which vary per industry for the environmental and social categories.”

12 ‘E’ scores are often erroneously believed to be a (reverse) measure of environmental ‘damage’. While this inevitably plays a part (an oil company’s environmental damage is obviously set to be larger than a software company’s), the degree of reporting transparency and the managerial strategies implemented to reduce the firm’s environmental impact also play a big role in the final score. Refinitiv (2022b) defines top quartile firms as showing “excellent relative ESG performance and high degree of transparency in reporting material ESG data publicly.”

Indeed, high E-scores should only be achieved by highly transparent and environmentally engaged firms, that are not interested in ‘cheating’. Further, ‘GI’ provides a balanced measure of ‘greenness’, since we saw in Section 2 that, when taken individually, both emissions and ESGs appear to be weak proxies of an asset’s exposure to climate risk. Also, the fact that the data used was generated from two different sources (even though downloaded from the same database) is helpful to diversify between biases. One important adaptation made with respect to Alessi et al. (2021) is that the authors preventively split firms into ‘transparent’ and

‘non-transparent’ portfolios, based on whether their E-score is non-zero, and then construct

‘GI’ only for firms in the ‘transparent’ portfolio. Contrarily, I choose to rank the entire index¹³.

Ø 3.2.3 Portfolio sorting and ‘green’ factor determination

In this section and the next, I briefly describe the methodology used for my first replication (Section 4.2), applying univariate sorting by ‘greenness’ only. In Section 4.3.2, the procedure is slightly adapted to control for firm size (conditional bivariate sorting), and in Section 4.3.3 a sensitivity analysis is performed for the ‘greenness’ weight 𝛾, but the methodological essence is unchanged.

Having defined ‘greenness’, for each fiscal year I sort S&P 500 stocks into ‘greenness’ deciles, defining the 10^th decile as the ‘green portfolio’ and the 1^st decile as the ‘brown portfolio’. The portfolios are weighted by market capitalisation¹⁴. Recalling Eq. 1, I define the difference in the monthly returns (unadjusted for dividends) of ‘green’ and ‘brown’ portfolios as the ‘green’

factor 𝑓_!,#. I then merge this timeseries with monthly timeseries of other risk factors¹⁵, and calculate the time-invariant expected values (i.e. the averages) of all¹⁶ factors for the fiscal period 2003-2020. The 𝐸1𝑓_0,#2 are then annualised, for ease of visualisation, via trivial

13 This is based on my reasoning that ‘zero’ entries may sometimes signal data unavailability as opposed to non-disclosure, hence potentially leading to ambiguities. Also, in the sorting style of Alessi et al., it would take very little disclosure effort (e.g. an ‘E-score’ of >1) for a stock to be omitted from the ‘non-transparent’

portfolio.

14The weighted ‘green’ portfolio return is hence: 𝑟_%^&= ∑_+∈&&'$%()*^'$%()*!,#_#∙ 𝑟_+,% .

15 Monthly US Fama-French and ‘momentum’ factors, as well as the 1-month US treasury (risk-free) rate, have been downloaded from Kenneth French’s data library (2022).

16 In fact, only 𝐸*𝑓_-,%, is required to estimate the ‘green’ premium itself, but in my first replication (Section 4.2) I choose to estimate premia for all factors. Regardless, as we’ll see, it is useful to calculate the averages of other factors to analyse potential dependencies of 𝑓-.

multiplication by 12 (while standard deviations are multiplied by √12 ). Note that, in my methodology, ‘brown’ is just a shade of ‘greenness’ (the lowest) unlike Alessi et al. (2021) who predetermine ‘brown’ sectors of the economy (based on historical emissions) and select the ‘non-transparent’ firms belonging to these sectors to form their ‘brown’ portfolios. Their procedure creates ‘brown’ portfolios which not only may ignore low (though non-zero) E- score firms¹⁷, but may also be exposed to (ceteris paribus) a higher level of undiversified idiosyncratic risk, due to limited industrial variation.

Ø 3.2.4 Obtainment of the cross-sectional parameters 𝜐_&

Having calculated the factor averages, the penultimate step is the obtainment of the set of cross-sectional parameters 𝜐_&. Specifically, to obtain the ‘green’ premium, we would only need 𝜐_! but, unlike in 3.2.3 where we had the option to calculate other factors’ averages (recall footnote 16), in this case one unique procedure simultaneously generates the vector 𝜐_&. The need for this extra term is based on the will not to give the tradability of factors for granted, which would further simplify the model. If markets are assumed to be fully efficient, the effects of frictions such as short-selling transaction costs, imperfect or asymmetric information and investors’ beliefs are completely unaccounted for. By relaxing this assumption, I seek to capture at least part of these imperfections into the premia estimates.

As mentioned earlier, the derivation procedure is based on the two-pass approach by Gagliardini et al. (2016), which closely resembles that by Fama & MacBeth (1973). By recalling Eq. 3, it is seen that, in order to make 𝜐_& the subject, we first need to obtain estimates for the ai and bi,k of each stock ‘i’. Therefore, the first stage of the two-pass procedure consists of running timeseries regressions of a chosen linear factor model (Eq. 2) for individual stocks.

The choice is between the three traditional multi-factor models introduced earlier, whose econometric forms are reported in Table 1 (next page).

17 In fact, any variation in their brown portfolio composition over time relies on ‘brown’ industry firms alternating in their failures to disclose information on their environmental impact (and consequently being sorted into the ‘non-transparent’ portfolio). This may also raise the problem of self-selection bias¹⁷.

Table 1: The three, distinct, linear factor model specifications applied in the first stage of the two-pass approach used to estimate 𝜐_$. The ‘Capital asset pricing’, ‘Fama-French 3-factor’ and ‘Carhart’ models, all traditional asset pricing models in the literature, have been augmented by the ‘green’ factor fG,t , abbreviated to ‘G’ for simplicity.

For each model, time series regressions are run for each individual stock, where the dependent variable is the excess return of each stock ‘i’, in month ‘t’, with respect to the 1-month US treasury bill, and the independent variables are the established risk factors plus fG,t. Note that, recalling Eq. 2, the estimated intercepts of such regressions correspond to ‘ai’, which is then used as dependent variable in the second stage.

The dependent variable is the monthly excess return of stock ‘i’, in month ‘t’, with respect to the one-month US treasury bill ‘rf’ (the ‘risk-free’ rate), and the independent variables are the standard risk factors plus the ‘green’ factor, fG,t , at time ‘t’. Standard factors include the market factor (henceforth abbreviated to ‘MKT’) which is the excess return of the US market portfolio with respect to the risk-free rate, the size factor (or ‘small minus big’, henceforth abbreviated to ‘SMB’) which captures the long-run excess return earned by small-cap stocks with respect to large-cap stocks, the value factor (or ‘high minus low’, henceforth abbreviated to ‘HML’) which seeks to explain the long-run overperformance of stocks with high book-to- market (or low P/E) ratios with respect to ‘growth’ stocks, and the momentum factor (henceforth, abbreviated to ‘MOM’) which captures the tendency of ‘winning’ stocks to continue their positive trend of gains relative to sliding stocks. Recalling Eq. 2, then: for each stock, the regression intercept corresponds to ai , while the factor regression coefficients correspond to the factor loadings bi,k. .

The second stage then involves running a cross-sectional weighted least squares (‘WLS’) regression of the first stage ai on the estimated factor loadings bi,k . ‘Cross-sectional’ implies no time variation (hence, no t subscript), since we are just pooling together all the first stage, stock-specific, estimates. Note that, since the first stage was performed on individual stocks, the number of observations in the second stage cross-section corresponds to the sample size.

Recalling Eq. 3, the econometric form of the second-stage cross-sectional WLS is given by:

Eq. 8: 𝑎_% = 𝜐A 𝑏_{12+ 12+,%}+ 𝜐A𝑏_{31$ 31$,%}+ 𝜐A 𝑏_{415 415,%}+ 𝜐A 𝑏_{161 161,%}+ 𝜐5𝑏_{! !,%} + 𝜀_% Model Dependent variable Independent variables

CAPM + G ri,t - rft fMKT,t, fG,t

Fama-French 3-factor + G ri,t - rft fMKT,t, fSMB,t, fHML,t fG,t,

Carhart + G ri,t - rft FMKT,t, fSMB,t, fHML,t , fMOM,t, fG,t,

Each observation is weighted proportionally to the reciprocal of its variance, using the ‘wls0’

‘Stata’ package downloadable on the web (UCLA, 2022). A WLS regression is preferred to a regular OLS because it accounts for heteroskedasticity in the residuals, which is likely to be applicable in this case. Having run the second stage regression, 𝜐_& then simply corresponds to the estimated regression coefficient of factor loading bi,k. Finally, summing the factor average 𝑓4444 with 𝜐&,# & gives the estimate of the time-invariant risk premium for factor k (Eq. 5).

Having obtained an estimate for the time-invariant ‘green’ premium, 𝜆_!, the difficulty then lies in its interpretation. The major problem is that the premium could be biased, both by the presence of undiversified idiosyncratic risk (due to imperfect portfolio diversification), and/or by virtue of any significant correlation between 𝑓_! and other risk factors. If this were the case, the premium wouldn’t be capturing systematic excess returns associated with ‘greenness’

alone, at least not as an independent characteristic embodying an asset’s exposure to transition risk. This would hinder our ability to interpret 𝜆_! from the perspective of climate risk. Idiosyncratic risk can be diversified by increasing portfolio sizes, while an OLS regression of 𝑓_! on other risk factors may assess the extent to which ‘greenness’, as a unique characteristic, can ‘explain’ the estimated premium.

Ø 3.2.5 Robustness checks

To account for the effects of potential biases mentioned in the previous section, which may hinder our ability to interpret the ‘green’ premium, I perform three distinct robustness checks of the initial replication (Section 3.2.3, with results reported in 4.2) allowing me to test the hypothesis (3.1) that an unbiased ‘green’ premium is not significant in the US. The first check (4.3.1) involves a simple restriction of the timeframe, from the initial 2003-2020 fiscal period, to 2010-2019. The main purpose is to increase the average size of portfolios, excluding the very small ones that are found prior to 2010 (since data availability is found to be particularly low). This should increase the level of diversification, reducing the bias caused by undiversified idiosyncratic risk. Further, the restriction ensures that years of high market volatility (such as the ‘Great Recession’ and the beginning of the Covid-19 pandemic) are excluded, since these may further exacerbate the influence of idiosyncratic risks. The second

check (4.3.2) builds on the first (i.e. the restricted timeframe is kept), but adds an extra step to the sorting methodology described in 3.2.3. More specifically, ‘green’ and ‘brown’

portfolios are now determined through bivariate sorting of stocks by ‘greenness’ (quintiles) conditional on firm size (terciles). This is done to account for the significant size (market capitalisation) differences that are observed between ‘green’ and ‘brown’ portfolio constituents (4.2.1), which may bias the ‘green’ factor and hence the premium. Indeed, size is an established risk factor (recall ‘SMB’); to be able to interpret the premium from the perspective of climate risk, we must seek to isolate the relationship between ‘greenness’ and excess returns¹⁸. The third and final robustness check (4.3.3) involves a sensitivity analysis in which the initial (4.2) and bivariate (4.3.2) replications are iterated for a range of ‘greenness’

weights 𝛾 (recall Eq. 7). This is done to assess how changes in the definition of ‘greenness’

impact the resultant premium, ensuring that the results obtained for 𝛾=0.5 are not merely coincidental.

18 Unless climate risk is in fact already incorporated by the size factor, in which case ‘greenness’ itself would not be accounting for a new element of systematic risk. This discussion is expanded in the relevant section.

Section 4: Data, empirical results and robustness checks

In this section, the longest of the paper, I report the empirical results obtained for the methodology described in Section 3.2. I begin by briefly referencing the data sources used (4.1). I then report descriptive statistics (4.2.1) and results (4.2.2) for the first replication, involving a univariate sorting by ‘greenness’ for the 2003-2020 fiscal period (recall 3.2.3). In the final section (4.3) I report the results for the three robustness checks as described in the previous section (3.2.5), and make comparisons between the replications. Throughout the whole of Section 4, I frequently refer to the distinction between ‘univariate’ (‘greenness’ only) and ‘bivariate’ (‘greenness’ conditional on firm size) portfolio sorting, so it is useful to keep this in mind.

4.1 Data

Monthly returns, outstanding shares and closing prices have been downloaded from the

‘CRSP’ monthly stock database on the Wharton Research Data Services website (‘WRDS’).

Yearly ‘Environmental Pillar’ scores and firm-reported ‘Total CO2 Equivalent Emissions to Revenues’ for S&P 500 firms, used to construct the synthetic ‘greenness’ indicator, have been obtained from the Eikon Refinitiv database. The S&P 500 panel composition reflects the date in which the data was first downloaded, i.e. March 2022. I am aware that the index composition changes on a periodic basis, and that index constituents in earlier years may therefore differ compared to the panel constituents hereby analysed. US monthly factors other than ‘green’ have been downloaded directly from Kenneth French’s data library (French, 2022). The results of my research were obtained by merging and processing such datasets using a combination of ‘Stata 17’ and ‘Python’ codes. All codes and datasets are available on request.

4.2 Univariate portfolio sorting: ‘greenness’ only (2003-2020)

This section outlines the empirical results for the initial replication (Section 3.2.3) of the methodology. The first part (4.2.1) provides descriptive statistics for the risk factors, as well as for ‘green’ and ‘brown’ portfolio returns and composition. Importantly, the average risk

factors for the 2003-2020 period are reported, which (from Eq. 5) make up a large component of the time-invariant premia. The second part (4.2.2) reports the cross-sectional parameters obtained from the two-pass approach (recall 3.2.4). When these are summed with the factor averages reported in 4.2.1, a full set of time-invariant risk premia is obtained. A first attempt to explain the findings is made, though deeper reflections are left for the robustness checks (4.3) and discussion (Section 5).

Ø 4.2.1 Descriptive statistics

Table 2 below displays descriptive statistics for S&P 500 monthly returns of ‘green’ and

‘brown’ portfolios, for fiscal years 2003-2020. The rightmost column displays the t-statistic for the null hypothesis of a mean equal to zero.

Table 2 : Descriptive statistics for monthly S&P 500 ‘green’ and ‘brown’ portfolio excess returns, in % terms, for fiscal years 2003-2020. The portfolios have been weighted by market capitalization, and excess returns are relative to the 1-month US treasury bill. The second column reports the average monthly return of the corresponding portfolio over the entire timeframe (216 months); the difference between ‘green’ and ‘brown’

averages is, by definition (Eq. 1), the ‘green’ factor. The last column to the right displays the t-statistic for a zero average monthly return. ^***indicates statistical significance at the 1% level.

The first thing to note is that, on average, the ‘brown’ portfolio (1.283% return) performed better than the ‘green’ portfolio (1.068%.) The second aspect to consider is that the standard deviation of portfolio returns is almost an order of magnitude larger than in the reference paper (see Table 1 in Alessi et al., 2021, p.7). There are several potential reasons for this, which I tried to investigate. The presence of outliers is one of them, but my attempt to winsorise the data (both at the 1% and 5% levels) only marginally reduced the variability. I also attempted different approaches to annualising the monthly factors, but all of these still returned much larger standard deviations than expected. I then downloaded European factors from Kenneth French’s website but, despite a comparably lower volatility (see Figure 5 in the appendix for a graphical comparison), this still could not explain the large discrepancy in standard deviations. When asked to explain it, Professor Elisa Ossola confirmed the correctness of my numbers, suggesting that perhaps “the reported descriptives (in our paper) might have been computed on re-scaled factors”, although the rescalings used remained

unclear to me. One option to reduce the standard deviations could be to extend the sample period, but unfortunately this is not feasible due to the limited data¹⁹ availability for emissions and E-scores. After intensive reflection, I have concluded that this was a pure case of miscommunication, where Alessi et al. (2021) used the term ‘standard deviation’ as a substitute for ‘standard error’. If this were not the case, converting their standard deviations to standard errors would, in turn, yield t-statistics which largely exceed the values that they report. My standard errors are also comparable to their reported standard deviations, which reinforces my conclusion.

Table 3: Descriptive statistics for US ‘established’ risk factors plus ‘green’ factor 𝑓_𝑮 , in annualized % terms, for fiscal years 2003-2020.The former were downloaded (in monthly terms) from Kenneth French’s data library (2022), while the latter has been constructed using the methodology in Sections 3.2.2-3. The annualization of monthly factors was obtained via simple multiplication by 12, while the annualization of monthly standard deviations required multiplication by √12. The penultimate column to the right is the only one where values are expressed in monthly terms. The last column displays the t-statistic for a mean equal to zero. The asterisks ^***

indicate statistical significance at the 1% level.

Table 3 above displays descriptive statistics for the five factors in my analysis. Once again, only the ‘green’ factor has been constructed by me, as described in the methodology section.

Originally in monthly terms, the factors have been annualised via trivial multiplication by twelve, while the annualization of the standard deviations required multiplication by √12 (in line with common financial practices; see Morningstar, 2022). Comparing the factor means to those reported by Alessi et al. (2021, p.7) we see that the magnitudes differ, but the signs coincide. Specifically, my ‘green’ factor average is 60%, my market factor is 170%, my SMB factor is 85%, my HML factor is 220%, and my MOM factor is 3% of the respective magnitudes.

The skewness and kurtosis are very similar. The observed differences are understandable considering that US factors differ from their European equivalents. Also, the timeframes used

19 For the Eikon Refinitiv database, ESG data is available as far back as 2002, but many ‘gaps’ remain in the early years.