MSCI Climate Paris Aligned Indices: A quantitative study comparing the performance of SR indices and their conventional benchmark indices

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MSCI Climate Paris Aligned Indices

A quantitative study comparing the performance of SR indices and their

conventional benchmark indices

Linnéa Casselryd, Agnes Lantto, Alicia Julienne Zanic

Department of Business Administration

International Business Program; Civilekonomprogrammet Bachelor Thesis, 15 Credits, Spring2021

Supervisor: Oben K. Bayrak

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Acknowledgements

First of all, we would like to thank our supervisor Oben K. Bayrak. We deeply

appreciate your help all around the clock and your valuable suggestions that helped us write this thesis. Not only your experiences and knowledge but also your calming and encouraging words of support helped us tremendously.

Further, we would like to express our gratitude for each other. During the whole process of writing this thesis, we enjoyed the teamwork greatly. Without the ideas and contributions of each of us, this project would not have been possible.

Umeå, May 27, 2021 Agnes, Linnea & Julienne

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Abstract

There is no clear consensus about whether green investments perform better, worse or equal to conventional brown investments. With the rising popularity of social

investments, it becomes increasingly important to understand these investments. The recent launch of the MSCI Climate Paris Aligned Indices (CPAI) aim to illustrate the development of an economy that is in line with the requirements and goals of the Paris Agreement from 2015. In this research we aim to find out whether the MSCI Europe, USA and EM Climate Paris Aligned Indices outperform their parent indices. We do this by comparing performance measures such as the net return, standard deviation of net returns and Sharpe ratio. We further conduct an ordinary least squares regression to test whether the betas and Jensen´s alphas of the CPAI differ significantly from their parent indices.

The results show that only the USA CPAI clearly outperforms its parent index. This is due to it having a higher Sharpe Ratio and Jensen’s alpha as well as higher monthly net returns and a lower standard deviation compared to its parent index. The regression shows that it does perform better than the parent index. The results for the EM CPAI show that it performs in a similar way as its parent index. It has a higher monthly net return but also slightly higher standard deviation which leads to an equally large Sharpe ratio. Neither the estimated Jensen’s alpha nor the beta are significantly different from those of its parent index and thus the hypothesis of it performing equally as well as its parent index cannot not be rejected. Lastly, the Europe CPAI has a higher Sharpe ratio, Jensen’s alpha and monthly net returns than its parent index, but it also exhibits a higher standard deviation. The regression indicated that it performs in a similar way as its parent index, no difference could be proven. In conclusion, this means that all CPAI perform at least equally as well as their parent indices, if not better.

Keywords: MSCI Climate Paris Aligned Indices, Socially Responsible Investments, Sustainable Indices, Performance, Beta, Sharpe Ratio, Jensen´s Alpha, Spanning Test, Ordinary Least Squares

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List of Figures

Figure 1. Scatterplots of excess return of the CPAI ... 25

Figure 2. Time series plots ... 27

Figure 3. Residual vs. Fitted plots ... 29

Figure 4. Histograms ... 30

Figure 5. Normal probability plots ... 32

Figure 6. MSCI EM and MSCI EM Climate Paris Aligned Index Performance ... 38

Figure 7. MSCI Europe and MSCI Europe Climate Paris Aligned Index Performance 38 Figure 8. MSCI USA and MSCI USA Climate Paris Aligned Index Performance ... 38

List of Tables

Table 1. Correlation matrix of excess return of the parent indices and the error term ... 26

Table 2. Breusch-Godfrey LM test ... 27

Table 3. Durbin-Watson test ... 28

Table 4. Shapiro-Wilk test ... 31

Table 5. Average monthly net returns ... 33

Table 6. Monthly standard deviation of net returns... 34

Table 7. Sharpe ratios ... 34

Table 8. Regression Results... 35

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Glossary

CPAI

Climate Paris Aligned Index is the name of the eight recently launched indices designed to be in line with the requirements set in the Paris Agreement in 2015.

ESG

Environmental, Social and Governance criteria are a set of standards guiding companies´ operations. Environmental criteria are about a company´s dealings with environmental issues. Social criteria are about their relationships to employees, customers, suppliers and other stakeholders. Lastly, Governance criteria cover a company´s treatment of leadership and internal control.

Indices

An index is a measurement of the change in an economy as it shows a weighted average representative sample of the market. It measures the performance of a selection of stocks, by measuring these stocks collectively. Therefore, they track the overall

performance of the market better than just looking at the performance of a single stock.

Each index helps measure how the overall market is doing trough the performance of the securities it tracks.

MSCI

The Morgan Stanley Capital International is an American finance company. They are providing several financial tools such as equity, fixed income, portfolio-analysis and indices.

NDC

The Nationally Determined Contributions are a set of actions and regulations every signed country of the Paris Agreement has to formulate themselves and submit every five years.

SRI

Socially responsible investments are investments that take environmental, sustainable, social and ethical issues into consideration.

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1. Introduction

In the introductory chapter we present the topic of this research by providing a research background and identifying the research gap we are attempting to fill. After stating and explaining the research question we explain the limitations of this study and provide a disposition as well as a glossary.

1.1. Research Background

In 2020 Morgan Stanley Capital International (MSCI), an investment research firm that provides indices and other financial services, created eight new indices, the so-called Climate Paris Aligned Indices (CPAI). Each of these indices is based on a parent index which covers different economies around the world. In this study we will focus on six of them, i.e. MSCI Europe Climate Paris Aligned Index, MSCI USA Climate Paris Aligned Index and the MSCI EM Climate Paris Aligned Index and their parent indices the MSCI Europe, MSCI USA and MSCI Emerging Market Index, respectively. The latter three parent indices are popular benchmarks as they represent a major part of the economy in their respective area. What distinguishes the CPAI from their respective parent indices, is that they are in line with the requirements set by the Paris Agreement in 2015. The Paris Agreement is an international treaty signed by 191 countries to reduce carbon dioxide emissions and limit global warming. The CPAI are adapted to the requirements by a redistribution of the securities within the indices and the exclusion of securities that operate within environmental damaging industries. Each of the CPAI are based on a parent index and are adapted to meet the requirements of the Paris

Agreement. Many studies we introduce in Section 2.2. investigate the performance of such socially responsible indices in comparison with conventional benchmark indices.

Yet, none of them focus on the CPAI in particular and how they perform compared to their parent indices. Providing an answer to this question might help investors to build portfolios in a profitable way while also aligning them with social values and beliefs.

Literature comparing the performance of sustainable and conventional investments dates back to a study by Moskowitz in 1972 (cited in Schröder 2007, p.331). He recognized that there is no standardized definition of a socially responsible company and therefore it is hard to make an investment decision based on social and ethical values (Moskowitz, 1972, p.71). This could be one of the reasons for why the results of previous literature are mixed. Studies such as the ones conducted by Schröder (2004), Consolandi et al. (2009) and Revelli and Viviani (2015) find that there is no difference in performance between socially responsible investment (SRI) and conventional investments. On the other hand, Rocchia and Bechet (2011) found that SRI in the US, the Eurozone and the UK exhibit lower returns than their conventional counterparts.

However, a study by Ibikunle and Steffen (2017) as well as Climent and Soriano (2011) suggest that the performance of green funds increases over time. In other words, they might have performed worse in the past in a limited time period but it could be expected that they perform better in the future. Studies by Monasterolo and de Angelis (2018;

2020) and Kruse et al. (2020) further show that the Paris Agreement and publications concerned with it have a positive effect on the performance of green investments.

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Considering the disagreement in the literature the aim of this study is to revisit the subject with the recently launched CPAI and investigate whether they outperform their conventional parent indices or not. Furthermore, it is worth to mention that while some of the previous research focuses on funds, others investigate indices and some even a mixture of both. We decided to limit this research to the investigation of indices because focusing on indices enables a relatively more direct measure of the performance of the underlying equities. As argued by Schröder (2004), a performance analysis of funds inevitably includes the performance and the quality of the fund management, for example through market timing and the use of publicly available information alongside with the performance of the underlying equities. On the other hand, a performance analysis focusing on indices avoids this problem and provides relatively clearer picture of whether the underlying SRI equities achieve superior, inferior or similar outcomes than conventional brown ones.

1.2. Research Gap

As mentioned in Section 1.1., there is no consensus among the studies comparing the performance of sustainable and conventional indices. One way to contribute to the solution of this issue is to conduct further research with newly available data. The recent launch of the MSCI CPAI brings an opportunity to look at the performance of a relevant topic. Since they were launched on October 26, 2020, they are rather young indices. The inconsistency of results from previous research comparing sustainable and conventional indices, makes it difficult to find a commonly agreed upon theory that can explain the performance of SR indices. When searching through the existing literature, we

could not find any studies that focused on the performance of the MSCI CPAI specifically.

The Paris Agreement requires the member countries to submit their Nationally

Determined Contributions (NDCs) every five years, starting in 2020. The NDCs are set of goals and measures that are to be implemented to reach these goals, formulated by each member country. The coming years will show how the countries then live up to their self-formulated goals and regulations and how these will affect the performance of the companies operating in the respective countries (Kruse, 2020, p.27). Considering this, our research can provide a starting point for analysis of how the indices based on the Paris Agreement might develop in the future.

1.3. Research Question

The lack of consensus regarding the performance of sustainable indices in comparison with conventional indices, suggests a need to conduct further research. There are three possible scenarios: the CPAI could perform worse, better or the same as their parent indices. It is our aim to investigate these three possibilities and identify which of them is the case for the CPAI. Derived from the introductory thoughts and the research gap identified, we investigate the following research question:

Do the MSCI Climate Paris Aligned Indices perform worse, better or the same as their parent indices?

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3 1.4. Research Purpose

Since previous research has not come to a consensus about whether sustainable investments perform differently than conventional benchmarks, we see this as an opportunity to further develop the knowledge in that area. We do so by looking at three of the MSCI CPAI which are indices specifically constructed to follow the requirements of the Paris Agreement signed in 2015. We compare performance measures such as net returns, standard deviation and the widely used Sharpe ratio of the CPAI and their parent indices. Furthermore, we are conducting ordinary least squares regression to estimate the CPAIs´ Jensen´s alphas and betas. From these figures and comparisons, we derive an answer to our previously stated research question.

1.5. Limitations

Since the CPAI have just been launched in October 2020, which as of now was 6 months ago, there is not a lot of historical performance data which we can rely our research upon. Therefore, to be able to compare measurements of the CPAI with their parent indices and conduct regressions, we rely on the back-tested data provided by MSCI. Back-tested data unlike historical data is hypothetical and calculated under certain assumptions. These assumptions and their drawbacks are discussed in Section 4.2. of this paper.

Another limitation would be to which extent our results are applicable to other green indices. As we discuss in the theoretical framework chapter, there is no uniform

definition of socially responsible investments and therefore no standardized set of rules for what counts as an SRI. The results of this study should therefore not be generalized to all kinds of SR indices. The CPAI in particular can be considered socially responsible because they undergo a screening in which all companies engaging in socially or

environmentally harming activities are excluded from the index. This leaves them only with companies that are in line with the Paris Agreement requirements. However, the issue of generalization is a problem that every research faces. The extent to which a study can be generalized is custom to each study.

1.6. Disposition

This thesis begins with an introductory chapter describing the research background, the research gap and its limitations with the purpose to position the research within the relevant theoretical field and also emphasize the need for it. It further identifies the research question and the purpose this research is supposed to fulfil. Following the introduction, a description of the relevant theoretical framework is provided. Previous research is described and discussed in detail and connected theories and concepts are explained and linked to our specific topic. After setting the theoretical framework in Section 2, Section 3 of this thesis presents a methodology chapter. This chapter aims to identify our research paradigm which explains how we are going interpret our findings and results. That is followed by Chapter 4 which discloses our methods of data

collection and statistical analysis while also describing alternative ways and our reasons of deciding against them. Next, Chapter 5 presents all results obtained from the

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calculations and statistical tests. In Chapter 6, these results are then discussed and evaluated in the context of the theoretical framework. Lastly, a conclusion is provided in Chapter 7 where the quality criteria are discussed and ideas for future research are presented.

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2. Theoretical Framework

In the theoretical framework the main terms, existing theories and performance

measurements that this thesis is based on are explained alongside with their connection to this thesis. Previous literature is reviewed in-depth, followed by a summarizing table.

The definition of SRI and possible reasons for different results are discussed.

2.1. Socially Responsible Investments

Interest and awareness regarding social and environmental issues in investing is rising (Ernst & Young LLP, 2017). The accounting firm Ernst & Young states that sustainable investment strategies have grown 107.4% annually since 2012 and links this to the wish of the generation of millennials to align their investments with their sustainable values and beliefs (2017, p. 2.) The increased interest in sustainable investments can also be seen on the growing number of studies focussing on “Socially Responsible

Investments” (SRI) which is the term commonly used to describe all kinds of investments that consider social topics such as environmental care, gun control or animal abuse. Yet, it seems like this term is vaguely perceived by people, for example Berry and Junkus (2013, p.715) interviewed over 4,000 investors on their view of SRI.

They found that the majority of investors see environmental factors as the key issue when it comes to evaluating whether a company can be seen as socially responsible.

The second and third most important factors were business policy and company products, respectively. This shows that a wide range of investments can be considered socially responsible, as their efforts in a lot of different areas fall under the term SRI.

This vagueness in understanding the scope of SRI leads to an issue when constructing an SR index. The question of which companies to include and which to exclude arises.

When constructing the CPAI, MSCI overcomes this issue by following a strict list of criteria. They exclude companies that engage in activities such as animal testing or other environmentally or socially damaging acts. In this way they are in line with the Paris Agreement and can be considered socially responsible indices. The lack of a standardized definition of SRI could also be one factor contributing to the mixed results of the previous research.

2.2. Literature Review

There is an extensive amount of research investigating the financial effects of sustainability, as well as the performance of SRIs in comparison to conventional

investments. In this section we review parts of this literature. An overview of all studies discussed can be found in Appendix 5. Although the results are mixed, the reviewed literature points towards social responsibility having a positive impact on financial performance. However, this does not seem to translate into the stocks of the firms, as the majority of the reviewed studies do not show significant difference in performance of SRIs compared to conventional investments. We further show that the performance of SRIs might improve over time, as well as react to publications concerning the Paris Agreement.

One possible explanation to the mixed results can be the lack of a standardized definition of SRI, as explained in the previous section. Thus, there are many possible

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approaches to take when constructing SR funds and indices, as well as when conducting research on the topic. For example, one can evaluate whether an investment is socially responsible or not by considering the ESG score, Morningstar’s sustainability rating or CSR score. One can further focus on different sub-categories of SRI, such as

environmental, social or governance criteria (ESG criteria). Depending on the definition and criteria used, the results may vary drastically (Revelli & Viviani, 2015, p.162). This can be seen in a study by Reboredo et al. (2017), in which the performances of

alternative energy funds are compared to that of SR mutual funds and corporate mutual funds. Alternative energy mutual funds can be seen as a sub-set of SRI. These funds were shown to underperform compared to the funds solely categorized at SRIs, as well as the corporate mutual funds. This result was reached by Juan et al.´s approach to categorize funds and shows that different categorization might lead to different outcomes.

In addition to the lack of a standardized SRI definition, another potential explanation for the mixed results could be the wide range of methodologies and measurements used to examine the impact of sustainability practices. This is suggested by Alshehhi et al.

(2018), who provide a review of the literature analyzing corporate sustainability’s impact on financial performance. They count the different methodologies used in

previous studies and find that regression analysis is the most common methodology as it is used in 48 out of the 132 included articles. They further find that 45 out of the 132 articles are conducted though unique methodologies that are not used in any of the other included studies (p.11-12). These findings emphasize the wide selection of

methodologies.

Alshehhi et al. (2018) further explain two contradicting theories that may explain the effect of sustainability on financial performance; value creating and value destroying.

The value creating theory argues that adapting social and environmental sustainability may reduce the risk of the firm, while the value destroying theory argues that such adaptation will make the corporation lose focus on profitability. Moreover, out of the 132 articles they analyzed, 78 % showed a positive relationship between corporate sustainability and financial performance, advocating the value creating theory.

Another comprehensive research is made by Friede et al. (2015), who examine 60 review studies resulting in a sample of more than 2200 unique primary studies investigating the relation between Environment, Social and Governance (ESG) and financial performance. The study includes a wide range of articles focusing on each of the three E, S and G aspects, as well as portfolio studies. The majority of the examined studies found a positive relationship between ESG and financial performance, whereas less than 10 % found a negative relation. Moreover, the share of studies showing a positive relationship is found to be substantially larger within emerging markets compared to developed markets. Among the developed markets, the share of positive findings is greater in North America compared to Europe and the combination of Asia and Australia. Although the overall findings show a positive relationship, portfolio related studies are an exception to these findings, as these on average show a mixed or neutral relation. This is an interesting result indicating that the financial benefits of social responsibility may not be reflected into the firms’ stocks. According to the authors, this exception could be a cause of the common misperception that ESG has a negative or neutral effect on financial performance, in line with the neoclassical view of

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financial markets. The conjecture is that the misperception can be limiting the expansion of SRI.

When focusing solely on research targeting SRI, one can see that a common focus is SR mutual funds, whereas previous research on SR indices is somewhat limited. This can be connected to SR indices being a rather new phenomenon. After having reviewed parts of the previous research, we decided to focus our research on the comparison of indices. As Schröder explains in his study, a fund's performance is influenced by its management and occurring transaction costs (2004, p.125). On the other hand, when looking at an index, the performance of the underlying assets can be evaluated relatively more directly without having to take management or transaction costs into account.

Even though we focus on the investigation of indices in this research, both SR funds and SR indices are assessed in the remaining of this subsection. This is done because both are closely related and findings from research on funds are relevant to

understanding indices as well.

Schröder has conducted several studies within the area of SRI. In his study from 2004, he compares 16 German and Swiss SR funds, 30 American SR funds and 10 SR indices to conventional benchmarks (p.130). He finds that the risk-adjusted performance of the sustainable funds and indices is neither significantly worse nor significantly better than their benchmarks. He concludes that SRIs exhibit a performance similar to conventional investments (p.131). In a follow-up study, Schröder (2007) focuses solely on 29 SR indices for the reasons mentioned above. The results are in line with the previous study, finding that there is no significant difference between the performance of the SR indices and the benchmark indices. Moreover, his findings suggest that most of the SR indices are more volatile than their benchmark, meaning that they exibit a higher risk (Schröder, 2007, p.344).

On the other hand, there are also studies which contradict Schröder’s findings. For example, a relatively more recent study by Rocchia and Bechet (2011) compares the performance of 30 sustainable and 30 conventional indices in the time period from 2001 until 2011. They find that in all examined areas, the US, the Eurozone and the UK, the sustainable indices realize lower returns than the conventional benchmark indices.

A very recent study by Alda (2021), finds that integration of ESG factors in

conventional funds increases over time. This suggests that SR funds and conventional funds may be approaching each other and becoming more similar. Although, they also conclude that SR funds still fulfill higher ESG standards compared to conventional funds, keeping their ethical purpose. The possible correlation between companies included in SRI and conventional funds or indices have been highlighted before by Consolandi et al. (2008), who describes it as a factor blurring the results of the research.

To avoid this problem, Consolandi et al. (2008) took a somewhat new approach in their research on the Dow Jones Stoxx 600 Index between the years of 2001 and 2006. They start by analyzing the performance of the index and compare it to its sustainable counterpart, the Dow Jones Sustainability Stoxx Index (DJSSI). The results show no significant difference in performance. Then, they create a new index, which consists of all the companies in the Dow Jones Stoxx 600 Index but excludes those companies that are featured in the DJSSI. This new index is called Surrogate Complementary Index (SCI). While the DJSSI holds all green and sustainable securities from the Dow Jones, the SCI now holds all the securities that are not green. The argument for this approach is

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that results might otherwise be blurred by the fact that the compared indices to a large extent include the same stocks. They argue this approach will generate a more correct size difference in performance. When comparing these two indices, the researchers find that the sustainable DJSSI outperforms the SCI. Therefore, by clearly separating brown and green securities they find that the green securities constitute a better investment.

These three authors/author teams, Schröder, Rocchia and Bechet as well as Consolandi et al., all find different results regarding the performance of SRIs in comparison to conventional or brown investments. Each of the results can be explained by different theories. Modern portfolio theory provides possible reasons for why SRIs perform worse than conventional investments, since the possibility to diversify is limited within SRIs. This is further elaborated in Section 2.2. of this paper. On the other hand, SRIs outperforming the conventional indices could be explained by investor behaviour.

Renneboog et al. (2008) finds that investors value the effort companies undertake to be socially and environmentally responsible. This has long-term beneficial effects on the company´s stock performance. Therefore, sustainable indices holding these SR stocks would benefit from investors favouring these stocks.

Due to the inconsistency of results in previous research, in 2015, Revelli and Viviani conducted a meta-analysis in which they evaluate if socially responsible investments perform better than conventional investments. The meta-analysis consists of 85 studies and 190 experiments, each comparing the performance of either SR mutual funds, SR indices or SR portfolios, to the performance of non-SR funds, indices or portfolios. The result implies that there is no significant difference between the performance of socially responsible investments and conventional investments.

More recent studies continue to show mixed results. Although, the majority of the examined literature is in line with the result of Revelli and Viviani, finding no significant difference in performance of SRIs and conventional investments. One example of such a study is conducted by Jain et al. (2019), who compare sustainable ESG indices with conventional MSCI benchmark indices. In addition to finding no significant difference in performance, the study investigates the volatility and volatility spill-over between the indices. It shows that there is indeed a spill-over between the indices, meaning that since the market is integrated with each other there is a flow of information between the indices. The information of one index can help forecast the performance of the other index. This is evaluated using an auto-regressive

heteroscedasticity modelling. The results of no significant difference might also be connected to the modern portfolio theory and investors behaviour, and that these two contrary effects even out the performance. The study also finds that in order to

minimize risk, investors should diversify their portfolios by using both the sustainable ESG and conventional MSCI indices.

A very recent study by Yue et al. (2020) compares sustainable funds with conventional funds. They do so by constructing two portfolios and comparing their performance. One portfolio holds 30 sustainable funds and the other one holds 30 conventional funds.

They further include the MSCI Europe Index in their study as a benchmark index. The study cannot confirm that sustainable funds generate higher returns than the

conventional funds or the benchmark index. Regarding risk, they find that sustainable funds exhibit a smaller market risk compared to the conventional funds, which

contradicts the findings of Schröder in 2007.

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There is also research suggesting that the performance of SRIs improve over time.

Ibikunle and Steffen (2017) compared the risk-adjusted performance of green mutual funds to conventional funds and black mutual funds, between the years of 1991 and 2014. During the full period, the green funds were shown to significantly underperform the conventional funds, while no significant difference was identified between the green and the black mutual funds. However, the risk-adjusted return of the green funds was shown to improve over time. For the three last years of the studied period, 2012-2014, the green funds statistically outperformed the black funds, while showing no significant difference compared to conventional funds. These results are similar to those of Climent and Soriano (2011), who examined US mutual funds during the period 1987-2009. They found that green funds significantly underperformed their conventional peers when examining the full period. However, when solely examining the later period, 2001- 2009, no significant difference between the performances of green and conventional funds were found. These findings suggest that the performance of green investments is increasing over time which reflects the increased awareness of and sensibility towards sustainable investing.

A factor possibly influencing investment performance is the announcement of and news around green agreements, such as the Paris Agreement. This is supported by the study of Kruse et al. (2020) which investigates the influence of the announcement of the Paris Agreement on green and brown stocks. The event study finds that in response to the announcement, green stocks significantly outperform the brown ones. They further show that while the announcement has a positive effect on the green stock´s

performances, there is no significantly negative effect on the brown stocks. This

indicates that investors exploit opportunities arising from low-carbon transitions but do not let go of investing into companies with high emissions.

Earlier, in 2018, Monasterolo and de Angelis conducted a study to investigate the effects of the Paris Agreement on green and brown indices and found that the agreement led to an increase in performance of green indices due to a decrease in risk. Their study finds that announcements such as the agreement, lead to investors considering green investments less risky while at the same time considering brown indices riskier. This leads to them demanding a higher risk premium for brown investments. In a more recent study Monasterolo and de Angelis conducted in 2020 they find that due to the decreased risk, a higher weight of green indices in a portfolio is favourable. These findings

suggests that investors on the stock market find low carbon assets as attractive investments, but that investors yet not have turned down intensive carbon assets.

In summary, there is no consensus about whether green indices perform any different than conventional ones. However, we do find that the majority of researchers conclude that there is no significant difference in performance. Yet, it is important to investigate whether this is true for the CPAI as they are a rather new kind of index. As studies have shown that events surrounding the Paris Agreement have a positive influence on an investment´s performance, it is interesting to see whether the CPAI are in line with the findings of previous researchers.

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10 2.3. Modern Portfolio Theory

The Modern Portfolio Theory is an investment model created by Harry M. Markowitz during the 1950s and 1970s. The model describes how investors should construct their portfolios in order to take advantage of the diversification effect. Diversification means spreading risk by investing into different securities, preferably including different industries as well as geographic areas.

In the model it is assumed that investors are risk-averse and given the choice between two assets that generate the same return, a rational investor will choose the one with lower risk. The only reason for investors to choose assets with higher risk would be if they were compensated with a higher return. Therefore, it is possible to construct a portfolio aiming to maximize the expected return based on a given level of risk, or in contrary minimize the level of risk for a given level of expected return. This gives investors the opportunity to create an efficient portfolio. An efficient portfolio is one that consists of assets that generate the highest possible return to the lowest risk. The portfolio return is the weighted return of all the assets included, which all have a variance and an expected return. The risk in the portfolio is the standard deviation. ‘ Diversification is one strategy for investors to spread out their risks. By including several assets in a portfolio, the risk reduces since the return is not dependent on only one asset. For this to be successful the assets should have no covariance with each other since they then respond to market dynamics in opposite ways. This will provide the investor with a protection from market dynamics. Furthermore, the portfolio should be diversified both across asset classes and geographically in order to maximize the diversification effect (Markowitz, 1971).

In the meta-analysis of Revelli and Viviani (2014) it is stated that sustainable investment portfolios cannot diversify in an equally broad way as conventional

investment portfolios. Since sustainable investments exclude investment opportunities within certain industries, the ability to diversify decreases. Schröder (2004) also draws connection to the modern portfolio theory and states that since SRIs are limited in their ability to diversify, they can only perform just as good as traditionally investments at best and should result in a lower risk-adjusted return. The CPAI are indeed restricted from investing into certain industries. As specified in Section 2.4, this is to ensure their alignment with the Paris requirements, and has resulted in each of the examined CPAI containing significantly fewer constitutions compared to their respective parent index.

This would imply a lower level of diversification for the CPAI compared to their benchmarks. According to modern portfolio theory, it means the CPAIs´ performance cannot be better than the performance of the parent indices. Instead, their performance should be equal at best.

2.4. Paris Agreement

In 2013, the European Commission published an announcement stating that they were planning to construct an international contract in 2015 dedicated to the fight of global warming (European Commission, 2013a). Along with this announcement came the Consultative Communication which specified the goals and the purpose of the future contract. The highest goal is to limit global warming to ideally 1.5°C but a maximum of

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2°C compared to pre-industrial level (European Commission, 2013b, p.3). It further aims to decrease the emission of greenhouse gases. The contract´s purpose is to set up a legally binding framework and encourage countries all around the world to work together in an effort of solidarity and integrity (p.5). The contract aims to build on the achievements of the Kyoto protocol while also learning from its shortcomings. A main improvement should be an accounting system which shall increase the ambitions of each country to set high sustainability goals for themselves (p.9).

The result of the negotiations conducted in 2015 is the Paris Agreement, which was set into force on November 4, 2016 and as of today, is ratified by 191 countries around the globe (UNFCCC, n.d.). The agreement does not include any specified mandatory actions a country has to undertake to counteract global warming. However, what is required is the submission of the individual nationally determined contributions (NDCs) every five years, with the first submission deadline being in 2020. In the NDCs each country has to specify a list of actions and regulations that it is planning to implement in order to fulfil the goals set by the agreement. These actions and regulations might affect companies and the way they operate. The MSCI indices which are specifically

constructed to track the performance of an economy which is consistent with the Paris Agreement could be a tool to evaluate how the agreement makes progress in the future.

2.5. MSCI Climate Paris Aligned Indices

MSCI, an investment research firm that provides indices and other financial services, created eight indices in response to the Paris Agreement, which launched on October 26, 2020. They cover different regions around the world and are designed for investors who wish to decrease their exposure to risk arising from natural disasters and global warming. At the same time, they provide the opportunity for the investor to benefit from the efforts companies undertake to decrease their carbon emissions (MSCI, 2020b, p.3).

Each of the Climate Paris Aligned Indices (CPAI) is based on their respective

conventional parent index. For instance, the MSCI Europe Climate Paris Aligned Index is based on the MSCI Europe Index. What distinguishes the CPAI from their parent indices is that in order to be in line with the Paris requirements, the weight of securities is shifted. The weight of companies that face a higher risk due to global warming or produce a high amount of carbon emissions is decreased while the weight of companies who embrace the opportunities of climate change and actively decrease their carbon emissions is increased. Therefore, in all three of the CPAI that are being examined in this research, the weight of industries such as information technology and real estate is higher compared to their parent index while the weight of the material and energy industries got reduced. Furthermore, companies involved in controversial weapons, ESG controversies, tobacco, environmental harm, thermal coal mining, oil and gas and companies deriving more than 50 percent from thermal coal-based power generation are completely excluded (MSCI, 2020b, p.6). To maintain the CPAI, they are rebalanced on a semi-annual basis and go through an optimization process to ensure a constant

alignment with the requirements (MSCI, 2020b, p.7). The last rebalance date was on February 26, 2021.

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As mentioned above, this research focuses on three out of the eight CPAI. The first one is the MSCI Europe Climate Paris Aligned Index with its parent index, the MSCI Europe Index. These indices capture securities in 15 developed European markets. The Europe CPAI contains 271 constituents while its parent index contains 434 (MSCI, 2021c; 2021d). The second index is the MSCI USA Climate Paris Aligned Index with its parent index, the MSCI USA Index. They contain 350 and 621 constituents

respectively. All securities within these indexes are located in the United States (MSCI, 2021e; 2021f). Lastly, we include the MSCI EM Climate Paris Aligned Index which is based on the MSCI Emerging Markets Index. They cover 27 emerging market countries all around the world. The EM CPAI consists of 565 constituents whereas its parent index consists of 1392 (MSCI, 2021a; 2021b).

We chose to focus on these three particular indices for several reasons. Since we all live and study in the European Union, it is particularly interesting to us to conduct research that is concerned with our domestic economy. With the European Union and the United States constituting the biggest economies in the world, it seems only logical to compare them. To capture a broader range of countries than only Europe and the US, we wanted to include another index into the research. Since both the MSCI World Climate Paris Aligned Index and the MSCI ACWI Climate Paris Aligned Index consist over 50% of securities within the US (MSCI, 2021g; 2021h), we decided to not include these indices in our research since the performance might be too heavily correlated with the MSCI USA Index. The same reasoning applies to the exclusion of the MSCI World ex USA Climate Paris Aligned Index and the MSCI EMU Climate Paris Aligned Index, as they mainly cover European developed economies (MSCI, 2021i; 2021j) and therefore might correlate heavily with the MSCI Europe Index. Out of the remaining two indices, the MSCI Japan Climate Paris Aligned Index and the MSCI Emerging Markets Climate Paris Aligned Index, we decided to include the latter because it covers emerging economies all across the world. We find it extremely interesting to compare the development of sustainable indices of the two major economies in the world with an index that captures the performance of the most rapidly developing economies. That way this study is able to cover brought regions all around the globe.

2.6. Sharpe Ratio

The Sharpe ratio, originally introduced by Sharpe in 1966 to evaluate the performance of mutual funds, is a popular measure of “the expected differential return per unit of risk” (Sharpe, 1994). In contrast to solely measuring return, Sharpe is a risk-adjusted measure indicating the return of assets in relation to its risk. Since investors are commonly assumed to want to maximize returns and minimize risk, risk-adjusted measures are often seen as good estimations of performance. The Sharpe ratio can be calculated as follows:

(1) 𝑆𝑅 =

𝑆𝑅 = Sharpe ratio for index i 𝑟 = average return of index i

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𝜎 = standard deviation of the excess return of index i

Mathematically, the Sharpe ratio separates the total return of an investment from its risk-free rate, therefore deriving its excess return. The excess return is then divided by the investment´s standard deviation. The standard deviation is a measure of volatility which means it is an indicator of risk. Ultimately, the Sharpe ratio provides the risk- adjusted return per risk taken. The higher the excess return, the higher the Sharpe ratio will be. The opposite is true for the standard deviation. As it gets bigger, the Sharpe ratio will decrease. A higher Sharpe Ratio indicates a higher return per risk taken and therefor characterizes a better investment. Therefore, when choosing between two investments, the one with the higher Sharpe Ratio is to be preferred (Dowd, 2000, p.212).

Apart from the traditional Sharpe ratio, there are modified versions such as the normalized Sharpe ratio and the modified Sharpe ratio. These modified versions are appropriate in times of a downward market, as the traditional may give misleading results under such circumstances. This research investigates the full period from November 26, 2013 until February 26, 2021, during which the overall market has gone up which is reflected in all six of the investigated indices. Therefore, solely the

traditional Sharpe ratio is used. Furthermore, our calculations are based on monthly data, thus the Sharpe ratio is expressed as a monthly value. The values are possible to be annualized by multiplying with the square root of 12. However, we chose against doing so because we solely aim to compare the performance of each CPAI with its respective parent index. Thus, the timeframe in which the ratios are expressed does not matter as long as it is the same for all indices included in the comparison.

There are some limitations of the Sharpe ratio that must be considered. The Sharpe ratio is based on the standard deviation of a portfolio which is assumed to have a normal distribution of pay offs (Goetzmann et al., 2002, p.1). However, in reality the pay offs of a portfolio are not always normally distributed which will lead to a misleading Sharpe ratio. Furthermore, when calculating the Sharpe ratio managers can choose a period of returns that will generate a higher Sharpe ratio instead of choosing a long look back that would be a more natural reflection (Goetzmann et al., 2002, p. 25-26). In this thesis we will therefore evaluate the distribution of the standard deviation of all CPAI and choose a long period in order to obtain as valid results as possible.

2.7. Jensen´s Alpha

Jensen’s alpha is a measure of risk-adjusted return, which was developed by Jensen (1968) with the purpose to evaluate the performance of fund managers. The value of Jensen´s alpha is the average return of a portfolio that exceeds the expected return which in turn is based on the Capital Asset Pricing Model (CAPM). The CAPM is a popular method used to assess the risk of cash flows and deriving the expected return of investments (Jagannathan & Wang, 1996, p.4). A positive Jensen´s alpha indicates a performance superior to the benchmark, while a negative Jensen´s alpha indicates a performance inferior to the benchmark. The formula used to calculate Jensen’s alpha is the following:

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(2) 𝛼 = 𝑟 − 𝑟 + 𝛽 𝑟 − 𝑟

𝛼 = estimated return not explained by the level of risk 𝑟 = return of asset i

𝑟 = risk-free rate of return 𝛽 = systematic of asset i 𝑟 = return of the market

As can be seen, one of the variables affecting Jensen’s alpha is beta. Beta is a measure of systematic risk, as it measures volatility in relation to the market. By definition, the market has a beta of one. A beta greater than one indicates a risk greater than the market and a beta below one indicates a lower risk compared to the market. By rearranging the equation above, it can be used to estimate Jensen´s alpha and beta for each of the CPAI.

We will use ordinary least squares to conduct a linear regression for each of the three CPAI. The dependent variable is the excess return of the CPAI and the independent variable is excess return of the corresponding benchmark. Thus, the following equation is estimated:

(3) 𝑟_, − 𝑟 = 𝛼 + 𝛽 𝑟_, − 𝑟_, + ℰ_,

𝑟_, = logarithmic monthly return of the CPAI i at time t 𝑟 = monthly risk-free rate at time t

𝛼 = estimated monthly return of the CPAI i, not explained by the level of risk 𝛽 = estimated systematic risk for Climate Paris Aligned Index i

𝑟_, = monthly logarithmic return of the benchmark index i at time t ℰ_, = error term for index i at time t

2.8. Risk-free Rate

The models used in this study include a risk-free rate in order to measure the excess return, thus, the risk-free rate needs to be defined. The risk-free rate is the return one can get from an asset containing no risk. An asset without risk is one where the return does not vary, which would imply an expected return equal to the actual return. In most developed economies, the government can be seen as default free, and the typical assets seen as risk-free are therefore government bonds (Damodaran, 1999). There are two common ways to determine what government’s bonds to use as the risk-free asset. The decision could be based on either the currency used in the research, or on the

geographic area examined. We found the second alternative most appropriate and therefore used three different risk-free rates, one for each of the three geographic areas covered by the indices. The reason for this decision is that risk-free assets can be seen as the alternative to investing in risky assets and thus the return exceeding that of the risk- free asset is the gain for taking on risk. It would be reasonable if the alternative to investing in US risky assets, would be US bonds, the alternative to European risky

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assets would be EU bonds and the alternative to EM risky assets would be EM bonds.

Thus, we used the US Treasury bill interest rate as the US risk-free rate. For the European indices and the EM indices we calculated a weighted average bond interest rate based on the five countries with the largest shares within the respective index. In Appendix 2 we provide a table which shows the shares of the countries within the indices. It further shows the risk-free rate for each country, which we retrieved from Fernandez et al. (2020). Furthermore, due to the statistical tests and the Sharpe ratios being based on monthly returns, the risk-free rates are converted from annual returns into monthly returns using the following formula.

(4) 𝑟𝑒𝑡𝑢𝑟𝑛 = (1 + 𝑟𝑒𝑡𝑢𝑟𝑛 ) − 1

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3. Methodology

In the methodology chapter we present the paradigm of our research and the

assumptions we made about reality and knowledge. Furthermore, we elaborate on the choice of sources we used and the ethical and moral aspects to consider when

conducting research.

3.1. Authors´ Background

Our authors´ team consists of Linnea Casselryd, Agnes Lantto and Julienne Zanic. All of us are Bachelor´s students in business administration at Umeå School of Business, Economics and Statistics in Sweden. Both Linnea and Agnes are born and raised in Sweden. Besides the studies in business administration, they are currently studying towards a Master’s degree in economics. Linnea has experience in finance from working at a Swedish bank and Agnes is planning to work within the finance sector in the future. Julienne was born and raised in Germany, then came to Sweden to pursue her Bachelor´s degree. She has experiences in finance as she worked in two German banks.

All three authors are greatly interested in finance which is why a topic within that area was chosen. Further, each of them highly value sustainability and environmental care.

Since sustainability is a matter of growing importance, they find it necessary to increase awareness of sustainable financial products and consider it an honour to contribute to knowledge in that research area.

3.2. Research Paradigm

The paradigm of a research defines how researchers assume the nature of organizations, how the research should be done and how results should be interpreted (Bryman & Bell, 2007 p.24). There are two main paradigms in research: positivism and interpretivism.

The core of a positivist paradigm is the belief that there is only one true reality which exists independent of its observer (Collis & Hussey, 2013, p.43). Since this approach fails to capture the individual point of view of each person, interpretivism rose as a paradigm. Interpretivism includes the belief that there are multiple realities that are subject to each individual's values (p.45). To be able to answer our research question we decided to conduct this research under the positivist paradigm. This is because

numerical data is compared and analysed in order to ultimately derive one logical answer and a mathematically backed conclusion which is independent of the observer's opinion of it.

Each paradigm states a set of assumptions for a research conducted under the respective paradigm, which are stated in the following sections.

3.3. Ontological Assumption

Ontology is the philosophical debate about how to view reality. It asks what exists that knowledge can be acquired about. Under an interpretivist paradigm, reality is seen as a social construct. Every person sees it through their own eyes and evaluates their reality

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with their own personal values. This means that there are multiple realities which are all subject to a person's individual perception. In contrast, reality under a positivist

paradigm is independent of the person who perceives it. It claims that there is only one reality and this reality is the same for everyone (Collis & Hussey, 2013, p.47).

As this research follows the paradigm of positivism, it is assumed that there is only one reality. This assumption is also in line with the decision to analyse the performance of indices rather than funds or ETFs. As stated above we are eliminating the influence of a fund´s management on its performance by looking at indices. Therefore, it is only fitting to follow the assumption that reality shall not be influenced by the actors within it as we are aiming for objective results. We look at numbers and analyse them statistically without any room for personal interpretation.

3.4. Epistemological Assumption

Epistemology is concerned with what can be accepted as valid knowledge. The research paradigm of interpretivism states that reality is seen subjectively, rather than

objectively. Similarly, knowledge is seen subjectively as well. Under an interpretivist paradigm, the epistemological assumption states that valid knowledge is what can be observed. It does not only want to measure and count, but to understand and explore the reasoning behind what is observed. To be able to do that, researchers who follow an interpretivist paradigm usually apply qualitative methods. With these methods they aim to understand why things are observed in a certain way and how they are perceived by different individuals. The focus here is on wording, phrasing, tone and attitude (Collis

& Hussey, 2013, p.47).

The epistemological assumption under a positivist paradigm is that everything can be explained logically, rationally and mathematically. Therefore, valid knowledge can be acquired by collecting numerical data and testing relationships between variables.

Because of this assumption, studies under a positivist paradigm frequently use

qualitative methods to gather and analyse their data (Collis & Hussey, 2013, p.47). As this study is conducted under a positivist paradigm and follows the according

epistemological assumption, the methods used are of quantitative nature. We believe that collecting numerical data and analysing it in an objective manner is the best way to answer our research question

3.5. Research Logic

The logic of the research is deductive, which means that previous literature is studied thoroughly and existing theories are considered and applied in order to evaluate the findings from this study. The research is moving from general concepts towards our specific topic, as we look at how existing models are able to explain our findings (Collis

& Hussey, 2013, p.7). We decided to follow the deductive logic because we are looking at a very specific and newly introduced type of index, the CPAI. The aim is to

investigate whether the performance of the CPAI is in line with the findings of previous research. To do so we are using established measures such as the Sharpe ratio and

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commonly used statistical models to be able to compare our results with those of previous studies.

In contrast, a research can also follow an inductive logic, which is exactly reversed. In that case, the researcher would start by looking at their specific findings and then develop a theory that aims to be generally applicable. To conduct an inductive study a bigger sample size would be appropriate (Collis & Hussey, 2013, p.7). In our case that means that we would have to analyse a greater number of indices to be able to derive a theory which can explain the performance of green indices.

3.6. Source Criticism

As MSCI is the company running the indices examined in this research, a lot of information and data gathered for the analysis was provided by them. MSCI is a

company that seeks to make profit. This raises the question if information is given with a certain intention or bias in order to benefit the company´s image. On the factsheets they provide for each of their indices, they state values for Sharpe ratios and standard deviations. When calculating these values ourselves, we naturally compared them with the numbers provided by MSCI. As anticipated, we did not get the exact same numbers.

This is caused by us employing different assumptions and most likely different ways of calculating. Since MSCI does not provide a public disclosure of their assumptions and calculations, it is hard to comprehend and replicate their numbers. Furthermore, it is difficult to evaluate whether the numbers might be influenced in a way that makes the indices look better, especially given the fact that all values must have been calculated using back-tested data. Back-tested data itself is subject to a certain bias since it is created in hindsight (see Section 4.2.).

As for the research articles referenced in our research, some of them are popular and widely accepted such as the research by Markowitz (1971) and Sharpe (1994). When searching for other previous research we paid attention to the methods used, the

assumptions made and validity and reliability of results to ensure we are using valuable sources. We further focused on articles that have been peer reviewed or that are

published in credible journals, since this means they have been critically reviewed and need to fulfil certain standards. To evaluate the credibility of a journal, we have used the SCImago Journal & Country Rank (n.d.), which is a portal providing ranking indicators on journals.

3.7. Ethical Aspects

It is important to take ethical considerations into account when conducting a research as the researcher should ensure that no harm is done to the participants or anyone else involved in the research process. This is particularly important when conducting a quantitative research using primary data. Voluntariness of participation, anonymity of the participants and confidentiality of information are issues that need to be addressed (Collis & Hussey, 2013, p.32). Since solely secondary data is used in this study,

voluntariness and anonymity can be neglected. However, confidentiality does need to be considered. To be able to conduct this research, data was requested from MSCI. The

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company kindly agreed to provide the requested data. It is our responsibility to ensure that we respect the conditions of the license given to us and that the data set is not further used or distributed.

Ethics and sustainability are important issues at the Umea School of Business, Economics and Statistics. This is also reflected in this thesis. Firstly, the topic

investigated is sustainable indices which lies within the field of sustainable finance. The authors of this thesis consider it important to contribute to knowledge in this area and increase the awareness of sustainable investments. When it comes to research ethics, we made sure no harm was done to anyone involved. We will further respect the conditions under which the data was provided by MSCI. Those conditions are explained in Section 4.1.

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4. Data and Methods

This chapter serves the presentation of the process of data collection and evaluation.

We characterize the data we gathered and identify its advantages as well as

disadvantages. This is followed by a description of the performance measures we use.

Lastly, we provide all assumptions that we made regarding the regression we are conducting.

4.1. Data Collection

Information about the CPAI and their parent indices was retrieved from the factsheets about each index provided by MSCI (2021 a – f). The CPAI were launched October 26, 2020. The hypothetical performance prior to that has been estimated by MSCI using back-tested data. They tracked back the hypothetical performance of each CPAI until November 26, 2013. MSCI states that differences between the calculation and how the indices would have actually performed can occur. Since the performance of the CPAI prior to their launch date is based on back-tested instead of actual historical data, conventional databases do not provide this information. Therefore, we contacted MSCI who kindly agreed to provide us with the back-tested monthly net index levels of the CPAI for the period of November 26, 2013 until February 26, 2021. By using data provided by MSCI, we are basing our research on secondary data. In contrast, primary data would be data that we collect ourselves by e.g. constructing a survey. All

calculations that are conducted are based on the monthly net index levels MSCI

provided us with, as well as the monthly net index level for the parent indices, collected from Refinitiv Eikon. The following paragraph states the conditions under which MSCI granted us the usage of their data.

The MSCI data contained herein is the property of MSCI Inc. (MSCI). MSCI, its affiliates and its information providers make no warranties with respect to any such data. The MSCI data contained herein is used under license and may not be further used, distributed or disseminated without the express written consent of MSCI.

4.2. Back-tested Data

Ideally, an index would have existed for many years when conducting research upon it.

If so is the case, one can look at the historical performance of that index. Examples here are the MSCI Europe and MSCI USA Index. They launched on March 23, 1986 and their performance since then is captured with historical data. The MSCI EM Index launched on January 1, 2001 which also provides us with over 20 years of historical data. Historical data is data about an index´s performance that has actually been collected in the past. Since the CPAI are relatively new indices and just launched on October 26, 2020, the historical performance data is only available until that date. To be able to compare the CPAIs´ performance over a longer period of time, we look at their hypothetical performance prior to that date. This hypothetical performance has been estimated by MSCI using back-tested data. In contrast to historical data, back-tested data is supposed to show the hypothetical performance of an index and how it would have developed, if it had been launched earlier. This is used to create a model which

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shows how the CPAI likely would have performed (Berman et al., 2013). MSCI estimated the performances up until November 26, 2013. They also state that the

hypothetical performance they created for the CPAI is based on the available data that is in line with the index methodology. On the example of the MSCI World Climate Paris Aligned Index they state that the tracking error was 1% (2020 a, p.6). It is important to emphasize that hypothetical performance based on back-tested data has some

limitations. It is not actual performance and it also is no indicator for future

performance. According to Kang and Ung (2012, p.10) another limitation of working with back-tested data is that it is created in hindsight. While it still may be in line with the index methodology and the featured securities, it will never capture the full scope of risk and opportunities of actual trading activities.

4.3. Process of Statistical Tests and Calculations

In order to get comparable values for the net returns, standard deviations and Sharpe ratios, we needed to prepare the data first. Then, before conducting the actual

regression, the data needed to be checked for the OLS assumptions. The following are the steps we undertook to get our results.

1. Calculating log returns of all six indices

2. Computing and comparing mean returns and standard deviations 3. Calculating and comparing Sharpe ratios

4. Checking OLS assumptions and potentially correcting data to fulfil assumptions 5. Estimating Jensen´s alpha and beta though a single factor linear regression 6. Conducting a Lincom test

7. Evaluating R² and possibly adding more factors to the regression to get a better model

8. Conducting a joint hypothesis test 9. Analysing results

These steps are described in detail in the following section. Having collected the

monthly net prices of all six indices, the first step is to calculate the logarithmic monthly returns using the following formula.

(5) 𝑟_, = log ^,

,

𝑟_, = logarithmic monthly return for index i at time t 𝑝_, = price of index i at time t

𝑝_, = price of index i at time t-1

The advantage with logarithmic values over non-logarithmic values is that it takes compounding into account. This way of calculating is therefore appropriate when the

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data consists of returns, as the return of one period is also dependent on past periods returns.

Next, the average logarithmic monthly return of each index is computed, as well as the standard deviations of the logarithmic returns. The returns and standard deviations give a first overview of the performance and risk of each CPAI in comparison to its

corresponding benchmark.

The next step is to closer measure the performances by calculating the Sharpe ratio for each of the six indices. The Sharpe ratios are based on monthly net prices during the period of November 26, 2013 until February 26, 2021. The data used are the average monthly logarithmic returns computed in previous step, risk-free rates for the USA, Europe and emerging markets as described in Section 2.8, and the standard deviations of the excess returns. The last variable is computed by subtracting the risk-free rate from the associated logarithmic return for each month, which results in an excess return for each month. Then, the standard deviation of the new variable, excess return, could be computed.

As explained in Section 2.6., the Sharpe ratio is a risk-adjusted measure, meaning it measures the return of an asset in relation to its risk. This makes it a good estimate of the overall performance of each index, as well as an appropriate way to compare performances. In line with the purpose of this research, the focus is to compare the performance of each CPAI with its parent index. If the respective CPAI exhibits a Sharpe ratio higher than its parent index, it has generated a higher return per unit of risk taken during the examined period. This would indicate a performance superior to its benchmark. If the Sharpe ratio is lower than the corresponding benchmark’s, it would indicate a performance inferior to the benchmark.

To get a more valuable comparison, an OLS linear regression is conducted in order to estimate alpha and beta for each CPAI. When conducting OLS regressions, the data needs to fulfil a number of assumptions in order to generate valid results. Thus, before conducting any regressions, the data is tested to evaluate if the assumptions are fulfilled.

If not, the data or tests need to be corrected. A further description of the assumptions and the process of evaluating the data is described in Section 4.4.

After controlling the assumptions and possibly correcting the data and/or tests, a single model linear OLS regression is conducted for each of the three CPAI, in which the dependent variable is the excess return of the CPAI and the independent variable is the excess return of its corresponding parent index. As explained in Section 2.7., the regression is based on the equation of Jensen´s alpha and the estimated model is the following.

(3) 𝑟_, − 𝑟 = 𝛼 + 𝛽 𝑟_, − 𝑟_, + ℰ_,

The regression results in an estimation of Jensen’s alpha and beta originated from the CAMP model. Jensen’s alpha is an estimation of the average return of the index that exceeds the expected return according to CAPM. If the estimated Jensen´s alpha is positive, the CPAI has outperformed its parent index during the examined period. If

MSCI Climate Paris Aligned Indices: A quantitative study comparing the performance of SR indices and their conventional benchmark indices