STOCKHOLM SWEDEN 2020,
Sustainability scores for portfolio performance
FELIX STERN
KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES
Sustainability scores for portfolio performance
FELIX STERN
Degree Projects in Financial Mathematics (30 ECTS credits) Degree Programme in Applied and Computational Mathematics KTH Royal Institute of Technology year 2020
Supervisor at KTH: Boualem Djehiche Examiner at KTH: Boualem Djehiche
TRITA-SCI-GRU 2020:386 MAT-E 2020:093
Royal Institute of Technology School of Engineering Sciences KTH SCI
SE-100 44 Stockholm, Sweden URL: www.kth.se/sci
In this thesis, the traditional methods of only using ESG scores to screen stocks for sustainable portfolios is broadened. The selection of securities for portfolios will instead depend on aggregation, weighting and normalization of a wider set of sustainability variables, in turn creating more all-encompassing sustainability scores.
Using these scores, the aim is to implement them in index tracking portfolios. These portfolios combines a hybrid approach between active and passive investment, with the aim of creating sustainable enhanced index funds that can beat the index without adding significant risk. Additionally, this allows for comparison of how different combinations and levels of sustainability affects returns, risk and index tracking.
The results that are obtained shows that in the scenario presented in the thesis, it is possible to create a sustainability score which both increases the average sus- tainability of portfolios, and yields risk adjusted returns. We also studied how a net increase in sustainability scores over a control portfolio results in higher active returns, and eventually a small drop off in information ratio as we apply too strong of a sustainability constraint to our portfolios. The combination of sustainability scores which showed the highest risk adjusted returns was created using equal parts z-scored ESG ratings, ESG risk ratings and ESG momentum.
i
Detta examensarbete breddar de traditionella metoderna f¨or att skapa h˚allbara portf¨oljer. Genom att basera urvalet av aktier p˚a aggregering, viktande och nor- malisering av ett st¨orre set av h˚allbarhetsvariabler, j¨amf¨ort med traditionell screen- ing baserad p˚a endast ESG betyg, skapas mer omfattande h˚allbarhetsbetyg. Syftet med studien ¨ar att implementera dessa h˚allbarhetsbetyg vid skapandet av index- portf¨oljer och analysera resultaten. Dessa portf¨oljer kombinerar d˚a b˚ade aktiva och passiva investeringsprinciper, med m˚alet att skapa h˚allbara indexn¨ara fonder som kan prestera b¨attre ¨an indexet, utan signifikant h¨ojd risk. Dessa h˚allbarhetsbetyg till˚ater ¨aven j¨amf¨orelse av hur olika kombinationer och niv˚aer av h˚allbarhet p˚averkar avkastning, risk och n¨arhet till index.
Resultaten visar tydligt att det, inom uppsatsens avgr¨ansningar, ¨ar m¨ojligt att skapa h˚allbarhetsbetyg som ¨okar b˚ade h˚allbarheten av portf¨oljer i snitt, och skapar riskjusterad avkastning. Det visar ¨aven hur en relativ h¨ojning av h˚allbarhetsbetygen resuterar i h¨agra aktiv avkastning j¨amf¨ort med en kontroll-portf¨olj. Vid en viss niv˚a av h¨ojning sker dock en avtappning av den riskjusterade avkastningen. Den kom- binationen av h˚allbarhetsvariabler som visar h¨ogst riskjusterad avkastning n¨ar de aggregeras till ett h˚allbarhetsbetyg ¨ar en kombination, i lika delar, av ESG betyg, ESG risk och ESG momentum.
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List of Figures vi
List of Tables vii
1 Introduction 1
1.1 Mutual funds . . . 1
1.2 Index funds and hybrid funds . . . 1
1.3 Sustainable investing and ESG implementation . . . 2
1.3.1 Screening . . . 2
1.3.2 Other methods . . . 3
1.4 Previous research . . . 3
1.5 Aim and Research question . . . 4
2 Background and theory 5 2.1 Sustainability and sustainability variables. . . 5
2.1.1 ESG . . . 5
2.1.2 ESG momentum . . . 6
2.1.3 ESG risk . . . 6
2.1.4 Carbon emissions . . . 6
2.1.5 UN development goals . . . 7
2.2 Portfolio theory . . . 8
2.2.1 Markowitz portfolio theory . . . 8
2.3 Index tracking . . . 9
2.4 MSCI ACWI . . . 10
2.5 Factor models . . . 10
2.5.1 Modeling returns and risk . . . 12
2.6 GEMLT . . . 14
2.6.1 Style Factors . . . 14
2.6.2 Country and world factors . . . 16
2.6.3 Industry factor . . . 16
2.7 Performance measures . . . 16
2.7.1 Alpha . . . 16
2.7.2 Beta . . . 18
iii
2.7.3 Active return . . . 18
2.7.4 Active risk - Tracking error . . . 19
2.7.5 Information ratio . . . 20
2.7.6 Turnover . . . 20
2.7.7 Additional performance measures . . . 20
3 Data 22 3.1 Sustainability data . . . 22
3.1.1 ESG data . . . 22
3.1.2 ESG Risk data . . . 22
3.1.3 Co2 data . . . 23
3.1.4 Climate impact data . . . 23
3.2 Stock prices and risk data . . . 23
4 Method 24 4.1 Software . . . 24
4.2 Data aggregation . . . 25
4.2.1 Sorting data by date . . . 25
4.2.2 Data matching . . . 25
4.2.3 Transformations . . . 26
4.3 Sustainability score . . . 27
4.3.1 Uploading sustainability scores . . . 28
4.4 Portfolio creation . . . 28
4.4.1 Stock universe creation . . . 28
4.4.2 Portfolio rebalancing . . . 30
4.4.3 Control portfolio . . . 30
4.4.4 Implementing sustainability scores . . . 30
4.4.5 Varying sustainability score requirements . . . 31
4.5 Scope . . . 31
5 Results and analysis 33 5.1 Initial portfolios . . . 33
5.1.1 Control portfolio . . . 33
5.1.2 ESG portfolios . . . 36
5.1.3 ESG risk portfolios . . . 37 iv
5.1.6 Climate impact portfolios . . . 40
5.1.7 All combined portfolios . . . 41
5.1.8 Number of assets in each portfolio . . . 42
5.1.9 Performance measures . . . 42
5.2 RM and ERM portfolios . . . 43
5.3 ERM portfolio over different levels of sustainability score . . . 44
5.4 Further measurements . . . 46
6 Discussion and conclusions 47 6.1 Conclusion . . . 47
6.2 Discussion and future work . . . 47
6.3 Future work . . . 48
References 50
A Appendix 54
v
List of Figures
1 ACWI and related indexes, (MSCI 2020) . . . 10
2 ACWI markets, (MSCI 2020) . . . 11
3 Security characteristic line (J. M. Chen 2016) . . . 17
4 Portfolio creation process . . . 29
5 Active risk of control portfolio . . . 34
6 Relative performance to MSCI ACWI . . . 35
7 Relative performance of ESG portfolios to MSCI ACWI . . . 36
8 Relative performance of Risk portfolios to MSCI ACWI . . . 37
9 Relative performance of Co2 portfolio to MSCI ACWI . . . 38
10 Relative performance of ESG momentum portfolios to MSCI ACWI . 39 11 Relative performance of Climate impact portfolios to MSCI ACWI. . 40
12 Relative performance of All variables portfolios to MSCI ACWI . . . 41
13 Relative performance of RM, ERM portfolios to MSCI ACWI . . . . 44
14 Active returns and risk for various levels of sustainability scores . . . 45
15 Information ratios for various levels of sustainability scores . . . 46
16 Various risk return measurements . . . 55
17 Various risk return measurements . . . 56
vi
1 Nr. of matching datapoints for the rebalancing dates . . . 26
2 Control portfolio . . . 33
3 ESG portfolios . . . 36
4 ESG risk portfolios . . . 37
5 Co2 portfolio . . . 38
6 ESG momentum portfolios . . . 39
7 Climate impact portfolios . . . 40
8 All combined . . . 41
9 Nr of assets in initial portfolios . . . 42
10 Active risk. return and IR of initial portfolios . . . 43
11 RM, ERM and All combined portfolios at +0.5 . . . 44
12 ESG, risk and momentum portfolios at various levels of net increase in sustainability score . . . 45
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1 Introduction
Currently, general sustainability and the issue of climate change are some of the most significant and high-profile global issues. Across every industry everywhere in the world, action will have to be taken in order to create a more sustainable society and deal with climate change. The financial sector is uniquely positioned to influence other sectors with its services and monetary capital, making it a key arena in this sustainability transformation. A financial sector which prioritizes sustainability will also bring it to the forefront in other industries.
Sustainable investment is defined as investing practices that includes non-financial sustainability data compared to conventional investing that only relies on financial data (Jin 2018). One way in which this is already being done is through sustain- able mutual funds. These allow investors to invest sustainably, without sacrificing returns or increase risk. Additionally, as more and more industries and companies prioritize sustainability, sustainable mutual funds will capture these general trends.
There are many ways in which the sustainability of stocks and funds can be mea- sured when crafting this type of fund. The most common measurement is called Environmental, Social and Governance (ESG), and measures sustainability through different criterion within these three sectors. ESG will be presented in more detail in section 2.1.1. The majority of research using ESG scores are focused on investi- gating the correlation between the inclusion of these criteria and the yielded returns (Steve Lydenberg 2016).
1.1 Mutual funds
Mutual funds represent a significant portion of all money invested in the stock market. In Sweden alone this amounted to over 2.5 trillion SEK in the year 2014 (Konkurrensverket 2015). As such, it represents a significant amount of capital which can have wide-reaching influence. By investing more sustainably, the worlds response to climate change could be sped up. Additionally, other aspects of sustain- ability could also be improved globally.
1.2 Index funds and hybrid funds
Index funds are a type of fund that aim to replicate a certain chosen index’s per- formance. These types of funds are considered passive, in that no active decisions
1 INTRODUCTION 2 are made by the portfolio manager, and instead the portfolio optimization is done algorithmically. Due to their passive nature, they are cheaper for investors and their fees are significantly lower compared to actively managed funds.
In addition to pure index funds, there are a number of related portfolio types refered to as smart beta or enhanced index funds which have gained significant popularity in recent years (FT-adviser 2016). These aim at replicating an index but use an actively defined strategy in order to beat the index. This can be done by using a different index or implementing a factor strategy, representing an investment style.
These are cheaper compared to traditionally actively managed portfolios, but offer comparatively moderate increase of returns. They also offer additional transparency, by clarifying how they differentiate themselves from regular index funds to investors (Kahn 2016).
The size of the smart beta market has grown rapidly over the last few years, with Morningstar reporting a total increase in assets under management by 257% over the time period 2012-2017, to a total size of 1 trillion USD. This includes both mutual funds and Exchange Traded Funds (ETF) (FTSE-Russell 2018).
1.3 Sustainable investing and ESG implementation
Socially responsible investment (SRI) is a type of investment that takes into account non-financial data, providing an alternative to purely financially driven investment.
SRI started in the 1960s and 1970s and has, at the time of writing, developed into a large field (Eccles, L.-E. Lee, and Stroehle 2020). By 2015, over 50% of assets in Europe were invested in portfolios which took sustainability into consideration in some form (Global-sustainable-investment-alliance 2016)
1.3.1 Screening
The most common method for applying sustainability into the portfolio creation process is the process known as ”screening”. This is done by applying certain re- quirements to stock that are considered for the stock universe for a portfolio, typi- cally avoiding the worst ESG performers. By doing this the fund managers can avoid investing in potentially ”bad” companies, thus increase its appeal to customers (Qi and Li 2020).
1.3.2 Other methods
Apart from screening, there are a number of other methods for integrating sustain- ability into portfolios. These strategies include smart beta, quantitative, enhanced index strategies and factor based approaches (UNPRI 2016). This is, however, a fairly new field and significant amount of research is ongoing.
1.4 Previous research
Despite the large prevalence of SRI, its profitability compared to regular investment practices is still debated, both in research and amongst fund managers. Tradi- tionally, there has been a consensus in both academia and amongst investors that sustainable investment has sacrificed financial performance for the sustainability in- crease they provide (Derwall et al.2005). This has been argued for on a theoretical level, by maintaining that non-financial information restricts financial performance, per portfolio theory. On the other hand, there are those that argue that any ex- tra information on potential investments is beneficial and can increase performance (Kaur 2018).
An argument against simple screening practices is made by Fabozzi, Ma, and Oliphant 2008, and Kacperczyk and Hong 2009, who find that divesting from industries such as weapons, tobacco or gambling is costly, due to these industries better than aver- age performance. There are also studies which have found sustainable indexes to be outperformed by their non-sustainable counterparts, for example Lean and Nguyen 2014.
However, in recent years other research has pointed in the direction of sustainable investing performing well compared to conventional investment. An example of this is the meta analysis by Clark, Feiner, and Viehs 2015 which found that 33 out of the 41 included studies provided positive correlation between higher levels of sustainability and increased stock prices. They also found that each pillar of ESG, enviromental, social and governance provide positive stock returns. It only found one study in which negative correlation between a high ESG score and stock returns was presented (D. D. Lee and Faff2009). The remaining seven studies found mixed or no relation (Clark, Feiner, and Viehs 2015).
There is however comparatively little research in how different sustainability metrics can be combined, and this report aims to help fill this gap. Studies such asibid.look at which of the ESG pillars perform best, but few reports have combined different
1 INTRODUCTION 4 types of sustainability metrics in a portfolio creation process to compare. There are studies which have looked at this question using regression, but few using portfolios (Torre et al. 2020; Chang et al. 2020).
1.5 Aim and Research question
In this essay, the traditional method of using ESG scores is broadened. The selection of securities for portfolios will depend on aggregation, weighting and normalization of a wider set of sustainability variables, in turn creating more all-encompassing sus- tainability scores. Using these scores, the aim is to implement them in index tracking portfolios, in an enhanced index approach. This is a hybrid approach between ac- tive and passive investment, with the hope of creating sustainable enhanced index portfolios which can beat the index without adding significant risk. The creation of these portfolios is the tool used to study how the different sustainability scores affect portfolio performance. As such the portfolio creation process is kept simple, using index replication with an extra requirement on the end portfolio. Additionally, this adds to the replicability of the study. This requirement is implemented by setting an average sustainability score requirement for the created portfolios. The total net sustainability score of the portfolios must pass the sustainability score requirement.
The sustainability score requirement is relative to a reference portfolio. This thesis thus aims to study how varying the sustainability score affects sustainability, returns and risk.
Following this reasoning, two research questions are posed,
• Is it possible to define a total sustainability score which improves the financial performance of a portfolio?
• How is financial performance affected by increasing the requirements on derived total sustainability score?
The aim is to answer these questions and thus contribute to the research on the crafting of sustainable funds.
2 Background and theory
2.1 Sustainability and sustainability variables
Defining sustainability is a difficult task. The obvious starting point is to look at greenhouse gas emissions and its effect on the climate, but there is more to sustainability then just Co2 emissions. As such, a number of sustainability variables have been developed over the last 50 years. This section will introduce some of these variables and other ways to approach sustainability.
2.1.1 ESG
Starting in the 1960s investors began to implement non-financial information in the creation of portfolios. Demand for this kind of information has risen ever since. Some of this information served as the start for SRI. Based on these socially responsible investment strategies, more clearly defined sustainability data was developed in the form of ESG (Eccles, L.-E. Lee, and Stroehle 2020). This data has gained more and more interest in the last few decades.
As mentioned, ESG stands for Enviromental, social and governance issues. These are three separate pillars, each representing a separate group of issues. The term first appeared in the United Nations Global Compact report ”Who Cares Wins:
Connecting financial markets to a changing world” (Compact 2004). This report was endorsed by a number of key players in the financial market and served to clarify the general definitions of the concept (Eccles, L.-E. Lee, and Stroehle2020) . ESG data is, however, not a fixed concept, and how it is applied and scored depends on the source of the data. There are a number of sources for ESG ratings, as can be seen in, for example, the 170 different ESG indexes around the world, (Steve Lydenberg 2016), along with 100s of ESG rankings and standards (Eccles, L.-E.
Lee, and Stroehle 2020).Thus having ESG data from a well established source is crucial, but one also has to understand that one entity’s definition of ESG might be different from another’s. This is one of the reasons why this report does not singularly focus on ESG ratings.
2 BACKGROUND AND THEORY 6
2.1.2 ESG momentum
ESG momentum is defined as the change of ESG. Usually this means the relative change in an ESG score over a certain period of time. If this is positive, it indicates a general increase in sustainability of a company, which is usually good for stock performance. It is thus similar in nature to the Momentum investment strategy that is commonly used (MSCI 2020). There is academic evidence from a number of sources supporting that ESG momentum is a reliable indicator of future stock performance (H.-Y. Chen and Yang 2020; Kaiser 2020)
2.1.3 ESG risk
ESG is a measurement and way too asses a number of issues; these issues come with a certain risk. Managing ESG related risk is a crucial part of any company’s sustainability work, and as such should be considered. These are risks in the negative sense, not just high variance that is commonly described as risk in finance.
ESG risk is especially interesting from a risk minimization perspective, as negative ESG events generally correlates to a large drop in stock prices. An example of this is the Volkswagen emission scandal, where the stock price dropped by 18% in one of Europe’s biggest industrial companies (Torre et al. 2020).
2.1.4 Carbon emissions
Carbon dioxide emissions are a key factor in any sustainability work. We all know the importance of minimizing our carbon emissions, and this extends also to companies and enterprises. Whilst greenhouse gas emissions is represented in the environmental pillar of ESG, its crucial role in the challenges the world faces due to global warming warrants its inclusion as a separate variable in financial data.
Carbon dioxide emissions produced by companies is classified into three categories.
Scope 1, which is the emissions occurring directly at the companies facilities. Scope 2, which are emissions related to the energy consumption of the company. Scope 3, which is emissions related to other factors, for example the lifecycle of produced goods (Hertwich and Wood 2018).
2.1.5 UN development goals
The United Nations’ (UN) sustainable development goals (SDG) are a continuation of the millennium goals outlined at the turn of the millennium. These goals include 17 different sustainability goals to strive for, namely:
1 ”End poverty in all its form everywhere”
2 ”End hunger, achieve food security and improved nutrition and promote sustain- able agriculture”
3 ”Ensure healthy lives and promote well-being for all at all ages”
4 ”Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all”
5 ”Achieve gender equality and empower all women and girls”
6 ”Ensure availability and sustainable management of water and sanitation for all”
7 ”Ensure access to affordable, reliable, sustainable and modern energy for all”
8 ”Promote sustained, inclusive and sustainable economic growth, full and produc- tive employment and decent work for all”
9 ”Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation”
10 ”Reduce inequality within and among countries”
11 ”Make cities and human settlements inclusive, safe, resilient and sustainable”
12 ”Ensure sustainable consumption and production patterns”
13 ”Take urgent action to combat climate change and its impacts”
14 ”Conserve and sustainably use the oceans, seas and marine resources for sus- tainable development”
15 ”Protect, restore and promote sustainable use of terrestrial ecosystems, sus- tainably manage forests, combat desertification, and halt and reverse land degradation and halt biodiversity loss”
2 BACKGROUND AND THEORY 8 16 ”Promote peaceful and inclusive societies for sustainable development, provide access to justice for all and build effective, accountable and inclusive institu- tions at all levels”
17 ”Strengthen the means of implementation and revitalize the global partnership for sustainable development”
(UN 2020; WHO 2020)
All of these goals are considered under ESG in general: However, two goals are of special importance in this thesis - goal number seven and goal number thirteen. This does not mean the other goals have less value, but this enables the sustainability scores to take into account how well a company is working to combat climate change, other than its own emissions. As these goals mainly relate to the climate, how a company integrates their work in relation to them will be referred to as ”Climate Impact” in this thesis.
2.2 Portfolio theory
In order to explain the creation of portfolios which incorporate sustainability as a goal, the fist step is to outline the traditional index portfolio creation process.
Drawing random stocks from a group of stocks and purchasing an arbitrary amount of them until the portfolio has run out of money is not a scientific approach. There needs to be a structure and clear method to creating portfolios if we are to investigate their potential for sustainability integration. As such this thesis will follow the framework of Modern portfolio theory (MPT), and how we can use variations of it to track a reference index or benchmark.
2.2.1 Markowitz portfolio theory
Harry Markowitz laid the groundwork for what we now call MPT in 1952. It defined the portfolio optimization problems as a trade off between expected returns and risk.
The fundamental assumption that is made is that a rational investor would always choose the portfolio that either minimizes risk for their level of expected return, or maximized the expected return for their chosen level of risk. This level of risk and return is judged based on the portfolio as a whole, where individual assets’ expected returns, risk and their dependence on each other play the key roles in maximizing the portfolio performance (H. Markowitz 1952; Fabozzi, Gupta, and H. M. Markowitz
2002). Whilst many consider MPT to have lost some of its explanatory power over the years, it nevertheless plays a key role as a foundation of modern finance (J. M.
Chen 2016; Fabozzi, Gupta, and H. M. Markowitz 2002).
2.3 Index tracking
Whilst certain investment strategies consist of maximizing return for a set level of risk, or minimizing risk for a set level of return, another common approach is to replicate a certain index. These indexes are usually used as indicators of the whole or portions of the financial markets. An example is the SP 500, which consists of 500 of the largest companies traded in the USA. Regardless of which index is chosen as a benchmark, the goal is to minimize the tracking error of a portfolio relative to the chosen benchmark portfolio (Edirisinghe 2013).
This can be viewed as an extension of the classical minimization of variance problem found in MPT, where instead of minimizing the variance of the portfolio, it aims to minimize the tracking error. This is done by minimizing the square of the tracking error (variance of the difference between benchmark and portfolio). The first step is defining the beta between an asset i and the benchmark (ibid.).
βi = Cov(ri, rb)
σb2 . (1)
The optimization problem then becomes:
minimize
w
1
2wTV w − σb2βTw subject to
n
X
i=1
µiwi = rb
n
X
i=1
wi = 1.
The optimization problem is convex and solvable provided that the covariance matrix is positive-semidefinite (ibid.).
If we are to remove the second term in the optimization problem, we would get the definition of the minimum variance portfolio for a situation with no risk free asset from MPT (H. Markowitz 1952).
2 BACKGROUND AND THEORY 10
2.4 MSCI ACWI
MSCI All country world index (MSCI ACWI, or ACWI) is MSCIs flagship global equity index. It is designed to represent the combination of developed markets and developing markets. It consists of between 2450 and just over 3000 constituents which are large- and mid-cap stocks throughout the period 2016-2019. These span 23 developed markets and 26 developing markets. Large- and mid-cap stocks are defined as stocks with a market capitalization of over 2 billion USD. This is used as an index as it represents a global benchmark, with stocks easy to invest in.
This index covers approximately 85% of the global investable equity opportunity set (MSCI 2020).
Figure 1: ACWI and related indexes, (MSCI 2020)
2.5 Factor models
MPT relies entirely on the estimations being made for the expected return and variance of the assets considered for the portfolio. As such, a key component in the effectiveness of the creation of any portfolio is how these are estimated for the future.
Traditional approaches may consist of looking at historical stock data of assets, their mean values, variances and correlations. This is based on the assumption that past performance is the only indicator of future performance. This also comes with the added problem of calculation cost. While variance and means of a large number of
Figure 2: ACWI markets, (MSCI 2020)
potential assets scales linearly with the size of the selection, the correlations scale with the square. As such, with long and detailed price histories and a large selection universe, the computational costs become very expensive. One way to address not only this concern but also bring in other considerations than just previous stock prices is by applying factor models to model both expected return and variance (Fama 1992).
One of the key components in MPT is the capital asset pricing model (CAPM).
The CAPM defines returns of an asset as a function of the risk. Traditionally, by modeling this risk as a factor of how an asset depends on the markets fluctuations, β is defined. This is the beta that is referenced in section 2.5.1 (J. M. Chen2016).
Factor models are based on the CAPM, but expands it by including more than just the β as a factor.
In the early 1990s, (Fama 1992) laid the groundwork for what we now call factor models. Their regression model described how different factors and the market contributed to the return and risk of an asset. Fama and French first developed a 3-factor model but then expanded it to 5 factors (Fama and French 2015). In this
2 BACKGROUND AND THEORY 12 work we will use variations of these original 5 factors but include MSCIs expansion of this model into the factor model used in this report.
2.5.1 Modeling returns and risk
Modelling the returns of a portfolio requires modeling the returns of the individual stocks, and then summing these returns with their respective weights in the portfolio to get the total return. We can start with a simple example of a two asset portfolio:
rp = h1r1+ h2r2. (2)
Where:
rp = Return of the entire portfolio.
ri = Return of the asset i.
hi = Weight of asset i in the portfolio.
We can also express the portfolio’s risk as:
σp2 = h21σ12+ h22σ22+ 2h1h2ρ1,2σ1σ2. (3) Where:
σi = Standard deviation of the returns of asset i.
ρi,j = Correlation between returns of the assets i and j.
By expanding this expression to include n number of assets, we can instead rewrite this using the covariance matrix and vectors:
σp2 = hTVh. (4)
Where:
h = A nx1 vector of all the assets in the portfolios weights.
V = The nxn covariance matrix of all the assets.
Now we introduce factors into the model. We can start with the most basic factor model, basing the model on a factor that depends on the market. We can then model
the returns and risks proportional to the market, but we also get a residual return and risk that is independent of the market. We also need to define the exposure of an asset to this factor, beta in this simple model. Using this we can then model the exposure of a certain asset to our market factor. When the market moves in a certain direction, the greater the beta of the asset is the more it follows this market movement. This is the basic model that is used in the Capital Asset Pricing Model (J. M. Chen 2016).
ri = βirmarket+ ri,residual. (5)
σi2 = βi2σ2market+ σ2i,residual. (6) Where:
ri = Total return of asset i.
rmarket = Return of the overall market.
ri,residual = Residual return of asset i independent of the market.
σi = Total risk of asset i.
σmarket = Risk of the market.
σi,resiudal = Residual risk of asset i independent of the market.
βi = Exposure of asset i to market factor.
This model is a simplification, but it sets the framework for how we can develop this model for a larger number of factors (Fama 1992). We can then expand this to include other factors and get a much closer estimation of an assets behaviour when exposed to these factors.
By expanding this risk expression to include several factors, we get an expression on the following form.
F = XVXT + ∆. (7)
F = Variance and Covariance matrix of the assets.
X = The exposure matrix of the system.
V = The covariance matrix of all the factors returns.
∆ = Matrix of the residual variances.
2 BACKGROUND AND THEORY 14 We then expand this over all assets in a portfolio, using the expression for the weighted average of the assets’ exposures. We have K factors in the model and N assets in the portfolio. We also use ui as the specific return of asset i, called rresidual in the simple model:
xP k =
N
X
l=1
hlxlk. (8)
rP =
K
X
k=1
xP kfk+
N
X
i=1
hiui. (9)
We can now replace our covariance matrix V in the expression with our new expres- sion for the variance using these factors:
σP2 = hTVh = hT(XFXT + ∆)h. (10)
2.6 GEMLT
MSCI:s Global equity model for long term investors (GEMLT) is the factor model used in the portfolio creation for this thesis. It consists of style factors, industry factors, country factors and a world factor (Bonne et al. 2018).
2.6.1 Style Factors
There are eight total style factors in GEMLT. These are factors that are independent of country and/or industry but represent a certain investment style. These styles all have different characteristics. A number of these can be traced back to the work of Fama and Frenchs five and three factor models (Fama and French 2015; Fama 1992), but GEMLT brings some additional factors. Some of the style factors consist of several different measurements in order to improve their accuracy (Bonne et al.
2018).
Value The Value factor consists of three different sections. The first part is Book- to-price, which represents 30% of the Value factor. It is calculated as the last reported value on the books divided by current market capitalization. The second part is Earnings yield, which represent 60% of the Value factor. It describes differences in the return of a stock based on the company’s earnings
in relation to its stock price. The last 10% of the Value factor consists of long-term reversal, which aims to explain common variation in the returns of a stock based on the behaviour of the long-term stock price. It is orthogonal to the momentum factor.
Size Size consists of two different components. 90% of this value comes from the size measurement. The size measurement attempts to capture the phenom- ena that stocks with smaller market capitalization generally outperform large capitalization stocks. The other component of the size factor is the mid- capitalization component. It attempts to capture the stocks with medium sized market capitalization.
Momentum Momentum is the factor that captures how well stocks have performed in their last twelve months. It is often one of the most exposed factors in a portfolio due to its history of being able to produce risk adjusted returns.
Quality Quality is the factor with the highest number of different components.
It consists of: investment quality (25% of the contribution), earnings quality (25%), profitability (25%), earnings variability (12.5%) and leverage (12.5%) .Investment quality captures the growth in assets, capital expenditure and net issuance. Earnings quality represent the quality of the earnings. Profitability considers the efficiency of a company’s operation. Earnings variability repre- sent the variability of the earnings and the cash flows of the company. Leverage captures the differences in returns between low and high leverage stocks, for example market-leverage and dept-to-assets ratio.
Yield Yield is based on the differences between the returns in a stock from the last twelve-months dividends, and the predicted returns.
Volatility Volatility consists of Beta (60%) and residual volatility (40%). Beta captures the market risk that cannot be explained by the world factor. Resid- ual volatility consists of the volatility of the daily returns, both excess and residual, and the range of the stock over the last year.
Growth Growth rewards stocks based on the prospects on the growth of the stocks.
Main contribution to this is what analysts predict the long term growth should be, in combination with growth over the past 5 years.
Liquidity Liquidity has to do with the relative trading activity, i.e. how much the stock has been traded recently.
2 BACKGROUND AND THEORY 16 (Bonne et al. 2018)
2.6.2 Country and world factors
GEMLT includes two different geographic factors, one world factor and one specific country factor. By including both, a company can be exposed to both the world markets and a country’s specific factor. This avoids any issues with a company being too dependent on a single country’s factor when it is an internationally focused company, and vice versa (ibid.).
2.6.3 Industry factor
The risk model also models an industry factor. This is done using GICS codes. One feature of GEMLT is its ability to expose a company to several different industries.
For example, a car manufacturer might not only be exposed to the their car man- ufacturing division, but their financial services that provides car financing will also be exposed to appropriate financial factors relative to their assets and income in that sector (ibid.).
2.7 Performance measures
In order to evaluate any portfolio, a set of portfolio measurements is required. There are a number of measurements that can be called upon. The primary evaluation measurements in this thesis will be active risk, active return and information ratio.
Our goal is to generate as high of an information ratio as possible from our portfolio, as this represents an appropriate risk/return measurement for this sort of portfolio.
If a portfolio was not based in index replication, other measurements such as the Sharpe ratio might be of more interest for comparison. Nevertheless, this report will discuss and include other measurements of risk and returns, as it provides further analysis of produced portfolios.
2.7.1 Alpha
Fundamental to analysis of any portfolio is understanding it’s risks and returns.
As predicted by MPT, returns depends on the risk taken; as such, the goal for a rational investor is to minimize risk and maximize returns. Consequently, portfolio
managers will seek to generate returns that are in excess to what is expected for a certain level of risk.
By writing a more comprehensive statement of the CAPM, we get this (J. M. Chen 2016):
rp = rf + βp(rm− rf) + αp. (11)
rp− rf = βp(rm− rf) + αp. (12) Where
rp = Returns of the portfolio.
rf = Risk free interest rate.
rm = Returns of the benchmark/market.
αp = Alpha of the portfolio.
βp = Beta of the portfolio.
This expression is the excess return of an asset, which dependent on α. As such, we can view this as the following:
Figure 3: Security characteristic line (J. M. Chen 2016)
As such, α represents excess risk adjusted returns yielded by a portfolio. This is in practice difficult to achieve, and can be viewed as an investors’ ”skill” or the
2 BACKGROUND AND THEORY 18 effectiveness of the investing strategy implemented. Ideally, an efficient market would only generate returns based on risk and chance, thus α would not exist, as per the so called ”efficient market hypothesis” (J. M. Chen 2016).
The actual measurement of α that is used in this report is the so called ”Jensens Alpha”, which will be discussed in section 5.1.9. Other return/risk measurements will also be included.
2.7.2 Beta
As was described in section 2.7.1 and 2.5.1, β represents how an asset follows the market. Defining what constitutes ”the market” plays a significant role here. Since this thesis aims to track an index and minimize the tracking error, the choice is made to have ACWI represent ”the market”, as per section 2.4. As described in section 2.5.1, this can be generalized to an entire portfolio, p from a single asset:
βp = Cov(rp, rb)
σb2 . (13)
This is similar to the Pearson’s correlation coefficient (ibid.). As such, if β is positive, it indicates that the portfolio or asset follows the benchmark in its swings. If β is 0 there is no correlation between it and the benchmark. If its negative it moves opposite of the benchmark.
β is however not a complete risk measurement, as it only represents risk relative to the market. As such it needs to be combined with other risk measurements such as standard deviation in order to build a complete picture. This is in addition to the simplicity of the risk model.
2.7.3 Active return
In this thesis, the focus is on tracking an index with the aim of generating excess returns compared to the benchmark, whilst still keeping close to the benchmark. As such, we are not strictly interested in only the returns of the portfolio, but also the active return compared to our benchmark. This is defined as (Satchell and Scowcroft 2016):
AR = rp− rb. (14)
2.7.4 Active risk - Tracking error
Tracking error or active risk, is a measurement of how well a portfolio tracks a benchmark portfolio. This can mean either how well it tracks the market, or for example how well a passively managed portfolio follows its benchmark. Tracking error and active risk are synonyms, and as such they will be used interchangeably in this thesis. The standard definition of this is as follows:
T E = std(rp− rb). (15)
As such, it is the measurement of the standard deviation between the return of the portfolio rp and benchmarks return rb (Dunis and Ho 2016). This can be calculated in practice using the following formula:
T E = s
PT
t=1(Rp,t− Rb,t)2
T − 1 . (16)
Where:
rp,t= Return of our portfolio over the return time period t.
rb,t = Return of our benchmark over the return time period t.
T = Total time.
t = Return period.
However, this method is based on measuring the tracking error over historical data.
In order to make accurate predictions of what the portfolios tracking error is at any given time, a more general formula is used:
T Et = q
wTP,tV wP,t. (17)
Where:
wp,t= Weights of assets in portfolio at time t.
V = Covariance matrix of assets.
We can then replace the covariance matrix with our approximation from the factor model.
V = XFXT + ∆. (18)
2 BACKGROUND AND THEORY 20
2.7.5 Information ratio
In order to understand how our resulting portfolios compare to our benchmarks, we need a risk-return measurement. Both due to the interest rates over the time period being looked at, and the fact that we are actively tracking a benchmark portfolio- we will not use the commonly used Sharpe ratio. Instead we will use the information ratio. The information ratio is a measurement of how well a portfolio can generate excess returns compared to a certain benchmark, whilst not exposing itself to a greater risk. It is defined as following (Satchell and Scowcroft 2016):
IR = AR
T E. (19)
2.7.6 Turnover
Turnover ratio is another key statistic when studying portfolios and their perfor- mance. Ideally, one would set a portfolio which would not need to be rebalanced while continuously maintaining optimal performance. In reality there is constant change in the assets’ characteristics. Thus, no portfolio position will be optimal for long. Additionally, the transaction costs connected to managing a portfolio adds costs every time a change is made in the portfolio. Therefore, it is of interest to analyze the turnover ratio of a portfolio (Tucker 2018).
T O = Change in portfolio
Average value over last year. (20) This can be used to illustrate how much a portfolio is altered during a given time- span. In this project, a total of 4 rebalances are done each year. As such, some turnover ratio is expected.
2.7.7 Additional performance measures
Sharpe ratio The Sharpe ratio is the creation of Nobel laureate William Sharpe, and is a standard risk/return measurement. It is defined as the average excess returns relative to the risk free rate per unit of volatility (J. M. Chen 2016):
Sharpe = rp− rf
σp . (21)
Due to the nature of the portfolios being created, the Sharpe ratio was not prioritized in favour of Information ratio.
Sortino The Sortino ratio can be viewed as a variation of the Sharpe ratio. It only considers the ”downside deviation”, which is the negative risk in its equation.
As such, it rewards positive risk, whilst punishing negative risk (Capitani 2014).
Sortino = rp− rf
σd . (22)
Jensens Alpha Jensens Alpha is a measurement of how well a portfolio or asset outperforms their expected returns, as predicted by the capital asset pricing model (CAPM). This is the definition of α that is used in the results. It can be viewed as the excess risk adjusted returns as compared to the market (Peterson 2012).
αp = rp− [rf + βp(rb − rf)]. (23)
3 DATA 22
3 Data
3.1 Sustainability data
The sustainability variables included in this thesis are supplied by MSCI and Sus- tainalytics. They consist of ESG ratings, ESG momentum, ESG risk rating, Co2 emission and climate impact data. Data is available for four full calendar years, from 2016 through 2019.
3.1.1 ESG data
ESG data is supplied by MSCI. It is the largest dataset that is available and is updated monthly throughout the four investigated years. Each data point consists of not only an ESG rating, but also its momentum and its individual pillars scores.
These are scored from 0-10, which represent the ratings C to AAA.
3.1.2 ESG Risk data
ESG risk data comes from Sustainalytics. It is a rating that aims to model the risk of an ESG rating on a scale from 0 to 50. A higher risk rating corresponds to a higher likelihood of an negative ESG event, for example an oil spill or scandal.
This kind of events usually have a significant negative impact on a company’s stock price, since investing in a company with a high ESG risk rating could expose one to negative returns (Kacperczyk and Hong 2009).
The data is split into two sections, the data from 2016-2018 and the data from 2019. The data from 2019 is updated monthly and contains a significant amount of the variables that the risk rating is built on. The data for 2016-2018, however, is different. It comes from a simulation, where Sustainalytics has used historical data along with their risk model to estimate the ESG risk rating. This rating is comparable to the full risk rating from 2019, but has slightly lower accuracy.
Compared to known scores, the simulated data accurately predicts the ESG risk rating of the full rating with a frequency of 88%. It has a 90% confidence interval of ±2.7 points of the company’s Risk score. This data is reported yearly.
3.1.3 Co2 data
Data on the emissions of carbon dioxide (Co2) emissions is provided by MSCI. They are reported as an intensity consisting of the combined scope 1 and scope 2 tons Co2 emissions per million USD of revenue. Ideally, scope 3 emissions would also have been included, but this was not available for the full time span. If a company does not report carbon dioxide emissions publicly, MSCI uses a proprietary method for estimating the emissions instead. This data set is updated yearly, primarily towards the end of the year. As a result, the previous year’s Co2 data will be used in the data aggregation.
The companies in the dataset are identified by their ISIN code.
3.1.4 Climate impact data
This data is supplied by MSCI and aims to capture the percentage of revenue of a company that goes towards goal seven and thirteen of the UN sustainable develop- ment goals. These two goals represent ”climate action” and ”affordable and clean energy”. This data is related to Co2 emissions, but allows the capture of other factors. There are many companies with negligible Co2 emissions that differ in how they invest their revenue. By using climate impact data a company’s actions that not only affect their own Co2 emissions but bring a positive impact to the climate can be captured.
3.2 Stock prices and risk data
Data on the stock prices along with the data for the risk model (GEMLT) are provided by MSCI. They are accessed in Barra Portfolio Manager for the purpose of this thesis.
4 METHOD 24
4 Method
In order to create portfolios that track an index and include sustainability factors, there are two main problems that need to be overcome. First, we need to create sustainability scores for each date on which we rebalance the portfolios. Second, we need to create portfolios and rebalance them over the time frame. These portfolios are simplistic in their creation, and not aimed to be implemented in a real financial market. They nevertheless provide the toolset for comparing how a sustainability score requirement effects results.
How often you rebalance a portfolio will affect the number of dates for which you generate the sustainability scores. In real life, there are many factors to consider.
We want to track an index, MSCI ACWI, which exists in a number of different forms. The specific index chosen for replication in this thesis is called MSCI ACWI - monthly. This index portfolio is updated monthly throughout the four studied years. If we are to only track this index, it would be optimal to rebalance each month, provided it did not result in too high turnover, transaction costs and workload. The most frequently updated data used only updates monthly, so this is a good candidate for a rebalance frequency.
However, there needs to be a trade off between the workload that this would lead to and the benefit. In this thesis, it is therefore deemed adequate to rebalance quarterly instead. This means that the workload per portfolio is cut to one third, enabling a larger number of portfolios to be created. As such, the portfolios are rebalanced on the first date of each quarter- the first of January, April, July and October.
4.1 Software
In order to facilitate this analysis, three pieces of software are used. The first is the programming language R, used in the R studio environment. This is used to collect the sustainability data from the various data sets. Excel is then used to calculate and create upload files for the sustainability scores.
The actual portfolio optimization and rebalancing is done in Barra Portfolio manager (BPM), which is supplied by MSCI.
4.2 Data aggregation
4.2.1 Sorting data by date
In order to rebalance our portfolios accurately every quarter, we will need to pull the sustainability data for each of the 16 dates we rebalance on. An R-script was used which selects the appropriate data for a given date. Selecting the sustainability data available for a certain date then simply becomes a task of inputting the date and running the script. The selection of data points relevant to these dates are conducted using two different methods.
Firstly, the climate impact, Co2 and the ESG risk data from 2016-18 are all reported yearly. As such the script simply selects which year’s data set is selected based on the input date. In the case of the ESG risk and Climate impact, that is the current year. In the case of the Co2 data, it is the previous year.
Secondly, for the ESG data and the risk data from 2019 a different approach is required due to the higher, but not completely even, update frequency. This is done by removing all data that is temporally located after the input date. Then it runs through all assets in the data sets, selects all data points for each asset and selects the data point with newest data.
4.2.2 Data matching
As per the previous step, the relevant data from each data set as of the input date is acquired. In order to create our sustainability score we need to match the entries from each data set. This could not done by name due to various different types of formatting of the names in the different data sets. As such, the International Securities Identification Number (ISIN) is used.
An ISIN code consist of a country identifier and a ten digit numeric identifier.
It is provided and defined by the ISIN organisation. Ideally, SEDOL or another identification code should have been used, due to ISIN having the ability to assign several numbers to the same security depending on the stock market it is traded at.
However, this was not available.
This is reported in every data set apart from the ESG risk data from 2019. As such, a workaround is implemented. The ESG risk data from 2019 and the ESG data from 2019 are the two largest data sets available. By converting all names into capital letters, and removing any symbols apart from letters, the ESG data and risk data
4 METHOD 26 can be matched with decent accuracy. We then assign the ISIN codes from the ESG data to the risk data ahead of the final matching.
The data is then added up and matched. At this point we use the complete cases function in R to remove any securities for which we do not have complete data. The total number of securities which are generated at each of the 16 rebalancing dates is presented bellow:
Date Nr. of matching datapoints 1-January-2016 1120
1-April-2016 1135 1-July-2016 1158 1-October-2016 1210 1-January-2017 1519 1-April-2017 1554 1-July-2017 1590 1-October-2017 1619 1-January-2018 4042 1-April-2018 4225 1-July-2018 4303 1-October-2018 4429 1-January-2019 4641 1-April-2019 1865 1-July-2019 1965 1-October-2019 1105
Table 1: Nr. of matching datapoints for the rebalancing dates
4.2.3 Transformations
To create our final sustainability scores, the data from the variables will be trans- formed. This is in theory possible to skip, and it would be possible to create some sort of sustainability score based on the raw variables. This would, however, come with a few caveats. The biggest problem is the nature of the different data points.
ESG rating is measured between 0-10, ESG risk between 0-50 and Climate impact between 0-100 %. Co2 intensity varies wildly as well, from almost 0 to thousands of tons of Co2 emissions per million USD of revenue. An obvious option would be a transformation of everything into percentiles. While this would make the results of the portfolios that only concern one variable easy to contextualise, when you com- bine several percentiles into a weighted score of several percentiles, you would lose some of the explanatory potential.
In this thesis we have instead decided to transform it to a z-score (standard score).
This does come with some drawbacks, including the fact that our variables distribu- tions are not all normally distributed. This transformation is defined as following:
z = x − µ
σ . (24)
Where:
x = The raw data point z = The z-scored data point
µ = The mean of the variable that the data point is
σ = The standard deviation of the variable that the data point is transformed Due to the nature of some of the variables, another aspect has to be considered. In the case of ESG risk and Co2 emissions- we want them to be as low as possible, while a higher value is preferred for the other variables. Since this is a symmetrical transformation, we can use the following formula for ESG risk and Co2 emissions:
z = −x − µ
σ . (25)
Once we have transformed our data points, they can be compared. We can then create sustainability scores where the performance of different companies for certain variables can be aggregated.
4.3 Sustainability score
Since we have transformed our variables, we can then create a sustainability score of each asset that we are interested in. We will then define our sustainability score, S, as following:
Si = fESGzi,ESG+fESGmomzi,ESGmom+fESGriskzi,ESGrisk+fCo2zi,Co2+fSIzi,SI. (26)
Where:
fk = The sustainability score weight of variable K zi,k = The z-scored data point of variable k for asset i Si = The sustainability score of asset i
4 METHOD 28 Using this we can then create a total sustainability score for any portfolio for which we have data for all the assets. This is done by calculating the average sustainability score in regards to asset weight. Asset weight is defined by the value of the stocks held in an asset, not the number of stocks.
Stotal =
N
X
i=1
hiSi (27)
Stotal = Total sustainability score of the portfolio N = Number of different stocks in the portfolio hi = The portfolio weight of stock i
4.3.1 Uploading sustainability scores
In order to use the sustainability scores in Barra Portfolio manager (BPM), they need to be uploaded. This is done by using an upload template. BPM is capable of dealing with imported variables for each rebalancing date. This means that for each of the sustainability scores produced, a total of 16 versions of this sustainability score will need to be uploaded- from 1-january-2016 to 1-october-2019. These uploads do overwrite previous sustainability scores on stock, but they do not remove any old sustainability scores. One concern that this brings is that if a stock loses its sustainability score during a rebalancing period- it would continue to be included at its previous level. This will be addressed by the stock universe that we use later on.
4.4 Portfolio creation
4.4.1 Stock universe creation
In order to only use stocks for which we have both financial data and sustainability data- we need to create a stock universe. Selecting only stocks which we have financial information from becomes trivial in MSCI BPM, since any inputs not found are not included. In order to only include stocks for which we have up-to- date sustainability data, we need to match our stock selection universe with the securities which we have up-to-date sustainability data for at the rebalancing dates.
This is done by creating a stock universe portfolio.
Figure 4: Portfolio creation process
4 METHOD 30 The process starts by creating a portfolio on the first of January 2016 which consists of only the stocks for which we have have sustainability data. This creates the stock universe the first rebalancing is performed in. At the second rebalancing date, the stock universe portfolio is updated with a new list of the stocks for which we have up to date sustainability data. This does, however, overwrite the previous stock universe portfolio. As a result we avoid any issues with stocks being included in the next rebalancing that do not have up to date sustainability data. This process is then repeated a further 14 times.
4.4.2 Portfolio rebalancing
Portfolios are rebalanced, as previously mentioned, quarterly. This rebalancing is identical over the 16 times, apart from the first time since this is when the portfolio is created. The portfolios are created by adding 100M SEK to the portfolio on 1- January-2016, and are then rebalanced immediately. Consecutive rebalances do not remove or add cash to the portfolio.
4.4.3 Control portfolio
In order to evaluate our sustainable portfolios we need a reference with no sustain- ability score considerations. This is created by making a portfolio that lacks any sustainability requirement and only aims to replicate the ACWI index.
4.4.4 Implementing sustainability scores
In order to implement our sustainability scores, we want them as a variable of the portfolio as a whole. This is measured as the average sustainability scores of the assets in the portfolio, weighted by the individual asset’s weight in the portfolio as described in 4.3. When we implement our sustainability scores, we then implement them as a requirement to have a net gain in the sustainability score compared to the control portfolio.
For example, if we look at a portfolio with ESG as the only component of its sus- tainability score, with a desired net increase of +0.2, we first check what the sus- tainability score is at each of the 16 rebalancing dates in our control portfolio. Since this control portfolio is not affected by a sustainability score, it will simply pro- vide what it considered to be the optimal portfolio. Then we check what the total
portfolio sustainability score is at the first rebalancing date, 1-jan-16. The total sustainability score in the control portfolio could be, for example, 0.15 at this date.
Then we create and rebalance the portfolio with a sustainability score implemented at that date. When doing so we set a requirement in the rebalancing optimization for the sustainability score to be a minimum of 0.15 + 0.2 = 0.35. Then this process is repeated over the next 15 rebalances. As such, the sustainability score is always raised a net amount compared to the control portfolio.
4.4.5 Varying sustainability score requirements
Two different levels are chosen for the initial portfolios, +0.2 and +0.5 net increases over the control portfolio. These represent a +0.2 and +0.5 standard deviations increase in total sustainability scores, provided the sustainability score is normally distributed.
Srequirement = Scontrol+ x. (28)
Stotal,i = Total sustainability score of the portfolio for portfolio i x = Net increase in sustainability score
Which is then implemented in:
minimize
w
1
2wTV w − σb2βTw subject to
n
X
i=1
µiwi = rb
n
X
i=1
wi = 1
N
X
i=1
wiSi ≥ Srequirement.
4.5 Scope
There are a number of limiting factors to this study. Creating a sustainability score given the data set available could be done in an huge number of ways. Several different transformations could be used. Different methods of aggregating them, for example multiplicatively, could have been used instead of the additive approach as
4 METHOD 32 in this study. Selecting which variables to include and how to weigh them with each other bring the possibility of an enormous amount of additional combinations. Even just sticking to one level of sustainability score, one method of aggregating them and equal weights yields 31 different possible sustainability scores. As such this work aims to provide a starting point, by choosing a simple set of initial sustainability scores and then see if any obvious combinations from those can provide better results.
5 Results and analysis
The results will be divided into three sections. The first section consists of the initial portfolios. These will be created using sustainability scores produced with only one sustainability variable and one score where all are equally weighted.
After this, the single variable portfolios are studied to see which variables seemed most promising for generating greater information ratio. Then, a few extra portfolios are generated including those. After that, the best portfolio in terms of information ratio will be evaluated over a range of possible net increases in sustainability scores.
This intends to give an indication of how performance varies over various levels of this net increase with the most promising sustainability score.
5.1 Initial portfolios
The initial portfolios constructed will consist of the sustainability scores being cre- ated by the z-scored individual sustainability variables and one portfolio with all 5 equally weighted. These will be attempted to be tested at two different levels of average score increases, +0.2 and +0.5 respectively. These intend to represent a small and a moderate sustainability increase in the final portfolios. This will enable us to get an initial overview of how each variable can potentially affect portfolio performance.
In order to set these sustainability scores for each rebalancing date, the first portfolio that was created was the control portfolio. This is then used to find the reference values for the other initial portfolios.
5.1.1 Control portfolio
Nr of assets in starting portfolio 742 Nr of assets in ending portfolio 2425 Active returns (annualized) 0.07%
Active risk (annualized) 0.75%
IR 0.093
Table 2: Control portfolio
The control portfolio provided the baseline for all other portfolios, as any net in- crease would have to be in relation to this. Immediately noticeable in the table 2
5 RESULTS AND ANALYSIS 34 is the relatively high active risk. For an index fund, one generally wants the active risk/tracking error to be as close to 0 as possible. There are however limitations placed on this portfolio that a normal purely index tracking portfolio does not have.
The first is that it is created using the same stock universe as the other initial portfolios, and as such lack significant coverage of MSCI ACWI. The second major factor is that this portfolio is updated quarterly, instead of the index that is updated monthly.
The impact of changes in the number of stocks in the selection universe can be evaluated over time, as the number of assets available for consideration increases over the time period.
We thus plot the active risks over time for each rebalancing date in figure 5:
Figure 5: Active risk of control portfolio
Plotting the relative performance over time compared to the benchmark portfolio yields the following figure 12:
As we can see here in6, the control portfolio is much more stable and tracks ACWI far better during 2018-2019 than during the previous years. This can probably be attributed to the stock selection universe being larger. We also cross under 0.2 in active risk through the time period 2018-2019, which would indicate that our portfolio creation is working well, but performs worse when limited by the data set from 2016-2017.
Figure 6: Relative performance to MSCI ACWI
5 RESULTS AND ANALYSIS 36
5.1.2 ESG portfolios
Sustainability score per stock is set as:
Si = zi,ESG. (29)
ESG +0.2 ESG +0.5 Nr of assets in starting portfolio 716 607
Nr of assets in ending portfolio 2188 1497 Active returns (annualized) 0.29% 0.60%
Active risk (annualized) 0.76% 0.82%
IR 0.381 0.731
Table 3: ESG portfolios
Figure 7: Relative performance of ESG portfolios to MSCI ACWI
5.1.3 ESG risk portfolios
Sustainability score per stock is set as:
Si = zi,ESGrisk (30)
ESG risk +0.2 ESG risk +0.5 Nr of assets in starting portfolio 692 566
Nr of assets in ending portfolio 2094 1237 Active returns (annualized) 0.34% 0.66%
Active risk (annualized) 0.78% 0.90%
IR 0.436 0.733
Table 4: ESG risk portfolios
Figure 8: Relative performance of Risk portfolios to MSCI ACWI
