Fuzzy confrontations of models of ESG investing versus non-ESG investing based on artificial intelligence algorithms

ABSTRACT

ESG (Environmental, social, and corporate governance) parameters are involved in investing-related decision-making. DESG (Dominantly ESG) related investing represents a complex tasks studied under severe information shortages. NESG (Non-dominantly ESG) investing either ignores ESG parameters completely or it takes it as less important. ESG investing is partially DESG and partially NESG. A very simple fuzzy reasoning algorithm is used to find out the similarity between DESG and NESG in this paper. A similarity graphs is generated. An edge represents a fuzzy similarity between two nodes / conditional statements. Each statement specifies fuzzy conditions under which some DESG/NESG tools are mutually similar or totally dissimilar. Examples of investing tools are Developed Markets, Emerging Markets Small Caps, Sustainability Index and Environmental Social Governance Index. The following five parameters of investing tools are Risk, Cost, Return, Drop, and Correlation. Low pairwise fuzzy similarities between DESG and NESG are detected.

KEYWORDS:

• Fuzzy similarity
• environmental
• social and governance
• ESG
• sustainable investing
• common sense

1. Introduction

A broad spectrum of different models of investing decisions under different objective functions exist, see, e.g. Andersen et al. (2015) and Stermole and Stermole (2006). Many investors make their investment decisions only on the basis of different versions of financial criteria. However, for an increasing number of investors, this is not enough (Ballestero et al. 2012).

Standard finance theory suggests that when two portfolios yield identical returns, an investor will be indifferent between investing in either one, see Dam and Heijdra (2011). Investors could recognize the positive effect on future cash flows created by enlightened managers, see Whittaker (2011). This leads to a strengthening of ethical management, see Ballestero et al. (2012) and Ortas and Moneva (2013).

DESG investing represents a complex and multidimensional task studied under severe information shortages. DESG time series are usually short. More and more sophisticated methods, e.g. applied artificial intelligence – fuzzy and rough sets, are therefore used to extract useful items of information, which cannot be analysed by conventional statistical methods, see, e.g. Aboura and Chevallier (2017) and Ahi, Searcy, and Jaber (2018) and Mohammed (2021).

Any currently active investor has to contra-balance DESG versus NESG. This makes any feasible investing more problematic. An inevitable shortage of information items results in desperate attempts to extract all relevant data sets from the available information/knowledge. This leads to more and more sophisticated algorithms, see, e.g. Bilbao-Terol et al. (2016) and Escrig-Olmedo et al. (2017).

There are very few studies on non-professional DESG investors. However, this segment is gradually growing (Hafenstein and Bassen 2016; Mousavi and Ouenniche 2018).

A simple formal method(s) must available to support decisions and not ignore information/knowledge items, which are (in)directly hidden within available (semi) subjective information inputs. Unfortunately, these algorithms are not available in a form of user’s friendly software systems, see, e.g. Parsons and Dohnal (1992) and Vesely, Klöckner, and Dohnal (2016). Moreover, mathematical/logical/artificial intelligence-based theories are often out of reach of investors who are not mathematicians. ESG-oriented investor has no intention of going into mathematical details. Therefore, the simplicity of used formal tools is inevitable.

In addition, any investor requires transparency of formal reasoning. Investors want to use simple common sense to reach similar conclusions as these reached by applied formal theories. Therefore, simple and consequently transparent algorithms must be used to support ESG investing decisions (Weston and Nnadi 2021).

AI (Artificial Intelligence) has developed a large number of formal tools, see, e.g. Elliott (2021) and Gao et al. (2021). Frequently used tools are neural networks, genetic algorithms, vague reasoning (fuzzy, qualitative, semi-qualitative, rough, and probabilistic), neural networks and genetic algorithms. Artificial intelligent systems, e.g. common sense reasoning and fuzzy/rough sets genetic algorithm are used to utilize such available vague information/knowledge items, which cannot be treated by, e.g. classical statistical and numerically oriented algorisms.

2. ESG common sense

Simple, straightforward and easily understandable common sense algorithms, of different natures, represent a significant advantage, see, e.g. Miller et al. (2013). ESG experts, especially at the very beginning of any analysis/decision making, do not use mathematical/formal models as the basic framework for their reasoning. ESG experts and/or investors draw heavily on knowledge represented by common sense, see, e.g. Bredeweg and Salles (2009) and Forbus (1996).

One of the most important features of human thinking is the ability to extract, from a huge collection of masses of heterogeneous data/knowledge sets, only such items of knowledge that are relevant to the task at hand (Dohnal 1991). Moreover, the goal of this study is to examine some factors that influence the use of sustainable investing in sustainable companies by non-professional ESG investors (Hafenstein and Bassen 2016).

Complex DESG decisions are information poor, see, e.g. Blasi, Caporin, and Fontini (2018). Different datasets are constructed by merging different data sources. The resulting set is usually very heterogeneous. DESG is an evolving concept that is, by its nature, ambiguous, uncertain and imprecise, see, e.g. Lamata, Liern, and Pérez-Gladish (2018).

To determine the cost of each investment instrument, as well as the scaling of risk and return variables, data from Morningstar inc. (“Morningstar. and Empowering Investor Success” 2021) and, as a supplement (taking into account the requirements of the EU legislative framework for investment products intended for private investors), data from financial servers covering mainly ETF financial products traded on European exchanges were used. These servers are www.justetf.com and www.extra-funds.de, which provide an overview of the costs of individual investment funds or ETFs and also categorise these costs, including by asset class or by sector or geography.

The parameters of investment instruments meeting the ESG criteria have been established on the basis of the methodologies provided by MSCI and S&P. Time series for each index was also used from both of these companies, including for determining the return, risk, downside and also correlations (Pearson correlation).

The MSCI World ESG Universal Index was chosen as a proxy for general ESG stocks. Environmental data were used based on MSCI information and methodology (“MSCI ESG Indexes” 2021)

Data for water stocks were used based on the S&P information and methodology (“S&P Global Water Index. S&P Dow Jones Indices” 2021) and (“Core ESG – Indices. S&P Dow Jones Indices” 2021). The S&P Global Water Index (“S&P Global Water Index. S&P Dow Jones Indices” 2021) was selected as a specific proxy.

This is the key reason why experts do not use numbers to quantify studied DESG/NESG relations. Quantifiers based on numbers are prohibitively information intensive and therefore not applicable to many DESG decisions. Precisely defined and easily measurable quantification units, as, e.g. kg, m, sec, are not available for DESG/NESG tasks. This is another important reason why numbers as quantificators cannot be easily used.

DESG investing is an interdisciplinary task, see Table 1. It means that a heterogeneous team of experts must be engaged. This fact makes the DESG decisions even more difficult. Examples of DESG issues are given below.

Table 1. DESG issues.

Environmental Issues	Social Issues	Governance Issues
Climate change and carbon emission	Customer satisfaction	Board composition
Air and water pollution	Data protection and privacy	Audit committee structure
Biodiversity	Gender and diversity	Bribery and corruption
Deforestation	Employee engagement	Executive compensation
Energy efficiency	Community relations	Lobbying
Waste management	Human rights	Political contributions
Water scarcity	Labour standards	Whist blower schemes

Source: (“CFA Institute” 2021).

The above-mentioned DESG related features indicate that the most information-intensive numerical quantification is not the best variant. However, DESG tasks are not so information poor to justify the least information quantifications, i.e. trends – positive/increasing, zero/constant, negative/decreasing (Dohnal 2016; Doubravsky and Dohnal 2018). Therefore, medium information-intensive quantifiers are used in this paper. This is the reason why fuzzy sets are introduced, see, e.g. Prato (2007) and Remig (2015).

2.1. Simple fuzzy multidimensional reasoning

Ancient philosophers understood classical problems related to, e.g. definition of a bald head – how many hairs may have a bald head. There is a clear gradual transition from bald to no-bald as the total number of hairs is increasing, see, e.g. Dubois (2014) and Gaines (1976).

The concept of fuzzy sets was introduced relatively recently (Zadeh 1965). However, fuzzy logic is a relatively well established formal tool, see, e.g. Dubois et al. (2014) and Dubois, Fargier, and Guyonnet (2013). In its most basic sense, a fuzzy set is a set where objects have a gradual transition from membership to non-membership, see, e.g. Kaufmann (1975).

A linguistic value is a value that is given by words, e.g. High, Low, Medium, Approximately 5. A linguistic value is transformed into a fuzzy set by the specification of a grade of membership. For example, a Medium Profit is transferred into a fuzzy set by the grade of membership function given in Figure 1.

Figure 1. Fuzzy set Medium Profit P – Grade of membership function.

There are many different fuzzy reasoning, see, e.g. Dubois and Prade (1997). Unfortunately, the majority of the published reasoning algorithms is prohibitively complex and not suitable for routine applications of ECG experts, see, e.g. Armengol, Dellunde, and García-Cerdaña (2016).

A typical medium profit P, see Figure 1: (1) $b<P<c.$(1) The Profit P (1) belongs to the fuzzy set Medium with the grade of membership equals 1. (2) ${\mu }_M(P)=1,$(2) where P is the profit, index M is Medium and μ is the grade of membership. There are two fuzzy intervals, namely (3) $\begin{array}{c}a<P<b\\ c<P<d\end{array}$(3) The intervals (3) represent profits P that belong to the fuzzy set Medium partially.

A real number is represented by a special fuzzy grade of membership where (4) $a=b=c=d.$(4) There are different definitions of fuzzy similarities of two fuzzy sets for the same variable, see, e.g. Radhakrishna et al. (2018). The simplest possible definition of a similarity s of the fuzzy sets Medium (M) and High (H) for the variable P is demonstrated by Figure 2. (5) $s(M,H)=s_{MH}$(5) A fuzzy model, as it is used in this paper, is a set of m n-dimensional conditional statements: (6) $\begin{array}{c}\mathrm{if}{\mathrm{A}}_{1,1}\mathrm{and}\dots \mathrm{and}{\mathrm{A}}_{1,n}\mathrm{then}{\mathrm{B}}_1\mathrm{or}\\ \mathrm{if}{\mathrm{A}}_{2,1}\mathrm{and}\dots \mathrm{and}{\mathrm{A}}_{2,n}\mathrm{then}{\mathrm{B}}_2\mathrm{or}\\ ⋮\\ \mathrm{if}{\mathrm{A}}_m,1\mathrm{and}\dots \mathrm{and}{\mathrm{A}}_m,\mathrm{n}\mathrm{then}{\mathrm{B}}_m\end{array}$(6) where sets Ai,j, for i = 1,2, … , m and j = 1,2, … , n, are fuzzy sets, see Figure 1. They can be easily specified or/and modified using the relevant points a, b, c, d (see Figure 1). The evaluation of fuzzy sets A is a task for a team of experts. Unfortunately, it is partially subjective.

Figure 2. Graphical definition of fuzzy similarity s.

2.2. Similarities graphs

The similarity (5) is a one-dimensional similarity, i.e. a similarity based on profit P. However, a multidimensional similarity quantifies the similarity of the multidimensional set, e.g. similarity of two n-dimensional fuzzy sets Ω₁ and Ω₂. (7) $\begin{array}{c}{\mathrm{\Omega }}_1={\mathrm{A}}_{1,1}\mathrm{and}\dots \mathrm{and}{\mathrm{A}}_{1,n}\\ {\mathrm{\Omega }}_2={\mathrm{A}}_{2,1}\mathrm{and}\dots \mathrm{and}{\mathrm{A}}_{2,n}\end{array}$(7) There are n one-dimensional similarities (8) $\begin{array}{c}{s}_1=s({\mathrm{A}}_{1,1},{\mathrm{A}}_{2,1}),\\ s_2=s({\mathrm{A}}_{1,2},{\mathrm{A}}_{2,2}),\\ ⋮\\ s_n=s({\mathrm{A}}_{1,n},{\mathrm{A}}_{2,n}).\end{array}$(8) The n-dimensional similarity λ_{1, 2} of two n-dimensional fuzzy sets Ω₁ and Ω₂ is (9) ${\lambda }_{1,2}=\min (s_1,s_2,\dots ,s_n).$(9) The similarity of the first two A segments of the conditional statements (8) can be easily modified for similarity of any pair of A segments of vth and wth statements s_vw.

A similarity graph G is an oriented graph. It has m nodes. Its edgiest are pairwise similarities λ. Each similarity λ represents an edge leading from node v to node w.

3. Results and discussion

A team of experts and PhD students developed the fuzzy model using traditional methods of knowledge bases for fuzzy expert systems. This model was one of the outputs of the research with the title of Modelling and simulation of sustainable investing decision-making (registration No. 17-23448S), which was supported by the Czech Science Foundation. The model is five dimensional, n =  5, and there are 17 statements, m =  17 (6).

There are chosen 17 investing’s tools, two of them are bonds indices and the rest equity indices, see Table 2. The single stock index follows a unique investing strategy, such as focusing on small stock companies, companies with small fluctuations of their equity, or strategies focusing on the specific industry sector (Table 3).

Table 2. List of investing’s tools.

Variable	Investing tool	Type of investing’s tool
BO	Bonds	NESG
BOE	Bonds Emerging Markets	NESG
CF	Click Investing Funds	NESG
MVI	Minimum Volatility Index	NESG
MVE	Emerging Markets Minimum Volatility Index	NESG
DIV	Dividend Index	NESG
DIS	Dividend Index - Focus Select	NESG
DIE	Dividend Index Emerging Markets Small Caps	NESG
SEC	Sector Rotation Index	NESG
INF	Infrastructure Sector Index	NESG
REI	Real Investing Trust	NESG
IPO	Initial Public Offering Index	NESG
MSC	Developed Markets	NESG
MSE	Emerging Markets Small Caps	NESG
CEI	Central Europe Focus	NESG
WAT	Water Sector Index	DESG
ESGI	Environmental Social Governance Index	DESG

Table 3. Variables used to characterise the investing tools.

Variable	Meaning	Units	Definition
RIS	Risk	Percent	Long-term expected return on an investing (asset), expressed as a standard deviation from the mean value.
COS	Cost	Percent	The cost of holding an investing, reflects the percentage reduction in long-term expected return from the investor's perspective.
RET	Return	Percent	Long-term expected return on investing.
DRO	Drop	Percent	Maximum decrease of investing value during the entire period.
COR	Correlation	–	Correlation of a pair of long-term investing.

Each investing tool, see Table 2, has the following fuzzy descriptions, see Table 4.

Table 4. Set of statements.

No	RIS	COS	RET	DRO	COR	Investing tool	Weight
1	VLO	LOW	LOW	LOW	LOW	BO	1.0
2	MED	MED	LOW	MED	LOW	BOE	0.8
3	LOW	MED	LOW	LOW	LOW	CF	0.8
4	LOW	LOW	MED	MED	HIG	MVI	0.8
5	HIG	MED	HIG	HIG	MED	MVE	0.8
6	MED	MED	HIG	HIG	HIG	DIV	0.8
7	MED	LOW	VHI	MED	HIG	DIS	0.8
8	VHI	MED	HIG	HIG	LOW	DIE	0.8
9	MED	HIG	VHI	MED	MED	SEC	0.9
10	LOW	MED	VHI	MED	MED	WAT	0.9
11	LOW	MED	VHI	MED	MED	INF	0.9
12	HIG	MED	HIG	HIG	MED	REI	0.7
13	VHI	MED	VHI	HIG	MED	IPO	0.7
14	MED	MED	HIG	MED	HIG	ESGI	0.7
15	HIG	LOW	MED	HIG	HIG	MSC	0.8
16	VHI	MED	HIG	HIG	LOW	MSE	0.8
17	HIG	MED	MED	HIG	LOW	CEI	0.8

The dictionaries used in Table 4 are given in Table 5.

Table 5. Fuzzy dictionaries, see Tables 3 and 4 and Figure 1.

Variable	Fuzzy values	Description	a	b	c	d
RIS – Risk	VLO	Very low	0	1	9	11
	LOW	Low	10	12	15	16
	MED	Medium	15	17	19	20
	HIGH	High	19	21	23	25
	VHI	Very high	24	26	100	101
COS – Costs	LOW	Low	0	0.1	0.3	0.4
	MED	Medium	0.3	0.4	0.6	0.7
	HIGH	High	0.6	0.7	10	11
RET – Return	VLO	Very low	0	3	5	5.5
	LOW	Low	5	6	6	7.5
	MED	Medium	6.5	8	9	9.5
	HIGH	High	9	10	10	12
	VHI	Very high	11	13	16	20
DRO – Drop	LOW	Low	0	7	11	15
	MED	Medium	12	16	20	23
	HIGH	High	21	24	100	101
COR – Correlation	LOW	Low	0	0.1	0.3	0.4
	MED	Medium	0.3	0.4	0.6	0.7
	HIGH	High	0.6	0.8	10	11

The results, see Table 5, were based on interviews with experts from Assets Management of financial institutions, investment companies and banks (Patria Finance, Erste Premier, KBC, Societe General), and previous research was also taken into account, see, e.g. Bilbao, Parra, and Cañal-Fernández (2012) and Kocmanova et al. (2017). Unfortunately, some fuzzy sets are very fuzzy. It means that the range of the relevant interval a–d is large. This high level of fuzziness reflects the fact that the experts were not able to reach a meaningful consensus.

All non-zero pairwise similarities λ (9) are given in Table 6. For example, statement No. 2 is similar to statements 3 and 17. It means that BOE is similar to CF and CEI. Both similarities are the same 0.267.

Table 6. Pairwise similarities, zero similarities are not given.

Statement No., see Table 4	Statement No.	Similarities	Statement No.	Statement No.	Similarities
1	3	0.222	10	9	0.3
2	3	0.267		11	0.9
	17	0.267		14	0.197
3	1	0.222	11	6	0.212
	2	0.267		7	0.277
4	6	0.267		9	0.3
	14	0.243		10	0.9
5	6	0.267		14	0.197
	7	0.2	12	5	0.7
	8	0.2		6	0.243
	9	0.212		7	0.187
	12	0.7		8	0.187
	13	0.187		9	0.197
	14	0.24		13	0.175
	15	0.267		14	0.233
	16	0.2		15	0.243
	17	0.267		16	0.187
6	4	0.267		17	0.243
	5	0.267	13	5	0.187
	7	0.2		8	0.187
	9	0.212		12	0.175
	10	0.212		16	0.187
	11	0.212	14	4	0.243
	12	0.243		5	0.243
	14	0.249		6	0.249
	15	0.267		7	0.187
7	5	0.2		9	0.197
	6	0.2		10	0.197
	10	0.277		11	0.197
	11	0.277		12	0.233
	12	0.187		15	0.243
	14	0.187	15	5	0.267
8	5	0.2		6	0.267
	12	0.187		12	0.243
	13	0.187		14	0.243
	16	0.8	16	5	0.2
	17	0.2		8	0.8
9	5	0.212		12	0.187
	6	0.212		13	0.187
	10	0.3		17	0.2
	11	0.3	17	2	0.267
	12	0.197		5	0.267
	14	0.197		8	0.2
10	6	0.212		12	0.243
	7	0.277		16	0.2

The similarity graph G, based on Table 6, is given in Figure 3. There are just two investing tools DESG, namely WAT, statement No. 10, Table 4 and ESGI, statement No. 14. Both, see Table 6 and Figure 3.

Figure 3. The similarity graph based on the 17 statements, see Table 4.

The non-zero similarities of WAT, ESGI and the rest of the investing tools are given in Table 7. The most similar investing tool to DESG is the INF tool. The fuzzy similarity λ (9) is 0.9. This is a surpassingly high similarity.

Table 7. Similarities of WAT and ESGI.

DESG investing tool	NESG investing tool	Similarity λ (9)
WAT	DIV	0.212
WAT	DIS	0.277
WAT	SEC	0.30
WAT	INF	0.90
ESGI	MVI	0.243
ESGI	MVE	0.243
ESGI	DIV	0.249
ESGI	DIS	0.187
ESGI	SEC	0.197
ESGI	INF	0.197
ESGI	REI	0.233
ESGI	MSC	0.243

The investing tools with no fuzzy DESG equivalent are given in Table 8.

Table 8. Investing tools without DESG equivalent.

Variable	Investing tool
BO	Bonds
BOE	Bonds Emerging Markets
CF	Click Investing Funds
DIE	Dividend Index Emerging Markets Small Caps
IPO	Initial Public Offering Index
MSE	Emerging Markets Small Caps
CEI	Central Europe Focus

A trivial investor interpretation of Table 8 is simple – ESG features are not supported by the tools given in Table 8. Table 8 is not based on deep knowledge. It is based exclusively on a partially subjective fuzzy model. Any change of the fuzzy model can lead to modification of Tables 7 and 8.

4. Conclusion

The concept of Socially Responsible Investing and related tasks is known since 1960. Ethical Investing and some other similar approaches arose from the mid twentieth-century political climate of social awareness for the environment, etc.

Real investing processes are complex, integrated, ill known and nearly always difficult to observe in their ECG and macroeconomic environments. They may be subject to complex relations with their surroundings which may make it nearly impossible to isolate them without substantial distortion of the available knowledge.

Therefore, knowledge of such processes is inconsistent, sparse and uncertain and represented by different formal calculi and consequently by different quantifiers. A general strategy for dealing with investing knowledge is to modify it as little as possible, thus reducing information loss.

The presented approach is only one out of many possible modifications. To accommodate flexibly all features of realistic investing problem, an ad hoc fuzzy modification must be implemented. Unfortunately, there is no general methodology as to how to invent the best possible formalization of fuzzy knowledge.

If fuzzy knowledge is to be used in realistic investing complex tasks, it must be heterogeneous. This will inevitably require the integration of many different kinds of knowledge. Therefore, a flexible structure of interrelated sub-models of different nature (fuzzy, qualitative, semi qualitative, rough, conventional) is needed, see, e.g. Parsons and Dohnal (1995).

Realistic applications of information non-intensive calculi, as fuzzy mathematics, require:

• maximal utilization of the conventional methods – development of mixed models,

• suitable integration of fuzzy and classical calculi 0 software – user friendly – man-computer interface – graphic presentation of final results – flexible interface between numerical and fuzzy representation top object experts and top knowledge engineers,

• common sense retrospective analysis of each step It is not clear how to create the best network of different calculi (fuzzy, rough, etc.) to revitalize knowledge.

On the basis of experts’ claims, it can be concluded that most similarity is shown by those stock indexes that are in line with usable investing.

The characteristics of these indices are so different that they cannot be replaced by other indices (or combinations of other indices). According to the expert’s claims, these equity indices are an interesting alternative to index investing in capitalization-weighted indices. Based on comparisons over the past 10 years, these companies have shown higher returns with less risk of fluctuations.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is supported by the Economic management of the business in a period of digital transformation; Registration No. FP-S-20-6345, and Modelling and optimizing business processes under digital transformation conditions; Registration No. FP-S-20-6376.