FSA InstituteDiscussion Paper Series

ESG/Green Investment andAllocation of Portfolio Assets

YOSHINO Naoyuki and YUYAMA Tomonori

DP 2020-9
December 2020

Financial Research Center (FSA Institute)Financial Services Agency
Government of Japan
3-2-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8967, JapanYou can download this and other papers at the FSA Institute’s Web site:
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The views expressed in this paper are those of the authors and do not necessarily reflect the views of the
Financial Services Agency or the FSA Institute.

＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

ESG/Green Investment and Allocation of Portfolio Assets

YOSHINO Naoyuki

YUYAMA Tomonori

December 7, 2020

Abstract
This article examines the current portfolio allocation in ESG and Green projects. Traditional
investments focus on rates of return and risks associated with investment. Environmental, Socialand Governance (ESG) or Green factors are additional components that investors have to pay
attention to. Environmental protection is very important. However, as we see the current different
definitions of ESG or Green factors lead to distorted allocations in portfolio investments. In orderto bring portfolio allocations to a desirable direction, global taxation on pollution or creation ofan accurate Green credit rating based on emissions of various pollutants are recommended.
Keywords: ESG (Environmental, Society and Governance); Green investment; Green
credit rating; optimal portfolio allocation and GHG taxation.

Professor Emeritus (Economics) of Keio University, Director of Financial Research Center at Japan
Financial Services Agency, and Visiting Professor at GRIPS, Tokyo Japan.
e-mail: yoshino@econ.keio.ac.jp
Director, Macroeconomic and Market Analysis Office, Strategy Development and Management Bureau,
Japan Financial Services Agency.
e-mail: tomonori.yuyama@fsa.go.jp
The views expressed in this paper are based on the personal views of the authors and not the views of theorganizations to which they belong.
The authors would like to thank participants in the “research reporting session” at the FSA for their valuablecomments, and would also like to thank Prof. Tokuo Iwaisako (Hitotsubashi University), Prof. Yoshiaki
Ogura (Waseda University), and participants in the Nippon Finance Association 2nd Fall Conference(2020) for their valuable comments. The authors are thankful to Director Jun Yasuno and his team in the
FSA for giving detailed comments to our draft. We also thank Junko Aoki for her help in creating thefigures in the paper and Mariko Takeda for her help with the English editing.

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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

1. ESG Investment
In recent years, “ESG investment” has become a popular trend in the field of asset management.
ESG stands for Environmental, Society, and Governance, and investments that take ESG factors
into account are called ESG investments. ESG investments are investments in companies thatvalue these ESG factors and investments that take these factors into account when investing.
The United Nations set up 17 Sustainable Development Goals (SDGs) with a target to achieveby 2030. The main agenda is to “leave no one behind.” SDGs provide a shared blueprint for peace
and prosperity of people and the planet for the current generation and future generations. The
creation of the SDG targets has been a major factor in the progress of ESG investments. The UN
global agenda clarified the importance of the development of Green energy and reducing
pollutants, such as CO2, NOx, and plastics; however, data show that, based on the current
mechanism, it is not possible to achieve these goals. If the current trajectory of global fossil-fueluse continues, the planet’s temperature is likely to rise by 4–6 C above the pre-industrial level.
Greenhouse gas (GHG) emissions cause climate change, and global warming is now indisputable.
In order to reduce GHG emissions, investors are requested to make their investment decisions
based not only on the rate of return but also the ESG or “greenness” of companies. The mostdisappointing aspect of the contemporary global Green economy is the low rate of investment(Sachs et al. 2019).
In order to increase the rate of return in Green investment, a tax should be levied on emissionsof CO2, NOx, and plastics, and the revenues can be distributed to Green sectors in order toincrease the rate of return on Green investment so as to attract more investors. Another proposal
is to establish an accurate credit rating of greenness of each company by measuring emission ofCO2, NOx, plastics etc. which is disclosed to achieve optimal portfolio allocation.
Institutional investors use the services of different ESG rating companies, which define thecriteria of ESG. Traditionally, investors watched (1) rate of return from investments and (2) risks
associated with investments. The ESG component is an additional factor that investors must
consider. Investors now make their portfolio allocations by studying three factors: (i) risk, (ii) rateof return, and (iii) ESG. As the criteria of ESG by each ESG rating company are different, theirmeasurements are also different, and these can distort optimal portfolio investments. Much
academic literature has been produced on the importance of Green finance and investment in the
deployment of renewable energy projects for GHG emission reduction. However, we could not
find any study that developed a model for calculating optimal portfolio allocations for investment
in ESG. This article shows that the best policy will be to tax on emission of GHGs and pollutants
such as CO2, NOx, and plastics globally by applying the same tax rate, forcing investors to focus
on rate of return and risk after tax. Alternative method to achieve best policy for environment is
to make accurate credit rating based on emissions of CO2, N2O, plastics etc.
Figure 1 shows a portfolio frontier between asset H and Green investment G. It also shows an
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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

investor’s utility function by a red curve. If the rate of return from Green investment is lower thanasset H and if the risk associated with investing in Green energy is higher than asset H, no investor
would like to invest in Green projects. It is important to increase the rate of return from Green
projects by injecting collected taxes from CO2, NOx, and plastics so that private investors will
be interested in investing in Green projects.

Rate of Return

e
H
G

σ
Risk
Source: Authors’ depiction.

Figure 1: Low rate of return on Green investment

2. Different Definitions of ESG
When institutional investors make ESG investments, they often refer to ESG scores provided by
ESG rating agencies, and they often invest in companies with high ESG scores. The ESG indexes
such as MSCI and FTSE used by institutional investors are composed of companies with high
ESG scores. However, it has been noted that ESG scores for the same companies differ widelyfrom one assessment agency to another, and that they do not tend to converge (GPIF 2019,
Chatterji et al. 2016, Berg et al. 2019).
The reason for this is that the evaluation methodologies and criteria for ESG scores vary fromone evaluating organization to another. For example, (1) some agencies use its own criteria toevaluate a company’s ESG efforts, (2) some agencies assign a score based on the degree of
disclosure, (3) some agencies use a score based on whether or not the company has an ESG policy,(4) some agency uses a score based on actual ESG activities such as CO2reduction by judging
from performance, and so on (Table 1). It also raises issues whether ESG scores actually reflect
ESG activities and outcomes of companies (Chatterji et al. 2009, Drempetic et al. 2019). Table 1
summarizes the definition of ESG scores and evaluation methodologies provided by the major
ESG rating agencies.
The different standards on ESG and SDGs are not only a problem for ESG rating agencies at
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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

the corporate level. Recently, even on a country basis, the EU, China and the International
Organization for Standardization (ISO) have been trying to establish separate standards for green
finance and other issues (MUFJ Research and Consulting, 2020). In particular, the EU has aclassification of activities, called the EU Taxonomy, and is said to be a strict regulation that aims
for a strict definition of sustainable economic activity. In China, the National Development andReform Commission and the People’s Bank of China have also formulated a catalog of green
industry guidance, which sets green standards to be applied nationwide and defines green
eligibility. However, too many disparate and rigid definitions of what is green and what
contributes to ESG and SDGs in different countries can affect investment activities not only ineach country, but also at the global level.

Table 1: ESG scores and evaluation methodologies of major ESG rating agencies
ESG Scores

Overview of Rating Methodology

Bloomberg ESG Disclosure Scores

Evaluating by degree of ESG disclosure

FTSE Russell’s ESG Ratings

Evaluating by ESG risks based on disclosure and commitment to policy
development and improvement

ISS Quality Score

Evaluating governance (board composition, shareholder and takeover
defenses, compensation and remuneration, and audit and risk
monitoring)

MSCI ESG Ratings

Evaluating by 37 key ESG issues

RobecoSAM Corporate Sustainability
Assessment

Evaluating by economy, environment and society. Governance isincluded in the economy.

Sustainalytics’ ESG Risk Ratings

Evaluating by ESG measures, disclosures, and the level of the problem

Thomson Reuters ESG Scores

Evaluating by 10 categories (environment [resource use, emissions, andinnovation], society [employees, human rights, local communities, andproduct responsibility], and governance [management, shareholders, andCSR strategy]).

Source: Bloomberg, ESG rating organization websites, and Yuyama et al. (2020).

Table 2: Examples of ESG/SDG-related standard development movements in different
countries.
Standard Development Movement
EU

Through the EU Taxonomy, the criteria for classifying economic activity as
environmentally compatible or not have been established

China

Develop a green industry guidance catalog and green standards to be applied
nationallyInternational Organization forStandardization (ISO)Moves to set standards for greenhouse gases, environmental performance, andgreen financeSource: MUFJ Research and Consulting (2020).

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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

Source: Authors’ depiction.

Figure 2: Comparison between traditional portfolio investment and ESG investment
Figure 2 shows a comparison between traditional portfolio investment and investment taking ESG
factors into account. The red curve denotes the utility curve of investors when they focus only on(i) rate of return and (ii) risks associated with investment. The blue curve between A and B denotes
the efficiency frontier of two investments A and B in the first quadrant. The optimal portfolio
allocation can be achieved at point “e”. When investors have to take ESG factors into account, an
additional second quadrant must be added for the allocation of portfolio investments. The second
quadrant measures the degree of ESG criteria. Suppose investment in B achieves higher ESG
points compared to investment A. Investors have to allocate more to B compared to investment
A. The chart shows that the optimal portfolio allocation is not point “e” but has to be point “F”
where much more investment is allocated to company B.
However, the degree of ESG differs depending on which ESG scores each investor uses, as isshown in Table 1. Point “F” is not a unique point, but there can be many different patterns ofallocations based on the ESG rating agencies. Therefore, optimal portfolio allocations would be
distorted by the different definitions of consulting companies. A detailed mathematicalexplanation is provided in Section 4.

3. Green Bonds
A similar argument can be applied to Green bond investment. Table 3 shows the Green Bond
Principles defined by the International Capital Market Association (ICMA). In Japan, theDevelopment Bank of Japan (DBJ) has issued green bonds for the construction of commercial
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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

buildings that reduce CO2 and are environment friendly. The Japan Housing Finance Agency has
issued green bonds for the construction of environment friendly housing. Both of these bonds
satisfy the criteria defined by the ICMA. However, they do not accurately indicate by how much
CO2, NOx and other polluting gases are reduced. It can be said that some green bonds are 80%
green and 20% gray, and others 90% green and 10% gray. But as long as the criteria defined by
the ICMA are met, a green bond can be issued.

Table 3: Green Bond Principles (GBP) 2018(i) renewable energy(ii) energy efficiency(iii) pollution prevention and control(iv) environmentally sustainable management of living natural resources and land use(v) terrestrial and aquatic biodiversity conservation(vi) clean transportation(vii) sustainable water and wastewater management(viii) climate change adaptation(ix) eco-efficient and/or circular economy adapted products, production technologies andprocesses(x) green buildings
Source: The Green Bond Principles: Voluntary Process Guidelines for Issuing Green Bonds, ICMA, June 2018

Figure 3 shows the greenness index in the second quadrant. As in the case of ESG investment,
investors are now taking greenness into account in addition to the rate of return and risks
associated with investments. Since a green bond is not necessarily 100% green, portfolio
allocations can be distorted by current definitions of such bonds depending on consulting
companies.

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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

Source: Authors’ depiction.

Figure 3: Utility function: rate of return, riskiness and green bonds

4. Theoretical Model of ESG Investment and Portfolio Selection
4.1 Model by incorporating the ESG indicator in the investors’ utility function
In this subsection, we modify the conventional portfolio utility function by incorporating the ESG
indicator1. First, equation (1) represents the traditional portfolio utility function, which includes
risk and rate of return.
𝑈(𝑅𝑡 , 𝜎𝑡2 )=𝑅𝑡 − 𝛽𝜎𝑡2

(1)

Where Rt is the rate of return and σ is risk, coefficient β represents the relative weight byinvestors to risk compared to the rate of return. If investors focus more on the rate of return
compared to the risk, the value of β becomes small. On the other hand, if investors care more
about risks compared with the rate of return, the value of β will be larger.
Rate of Return:𝑅𝑡 = 𝛼𝑡 𝑅𝑡𝐴 + (1 − 𝛼𝑡 )𝑅𝑡𝐵 ,where A = Company (or asset) A, B = Company (or asset) B(2)

Risks:
𝜎𝑡2 = 𝛼𝑡2 (𝜎𝑡𝐴 )2 + (1 − 𝛼𝑡 )2 (𝜎𝑡𝐵 )2 + 2𝛼𝑡 (1 − 𝛼𝑡 )𝜎𝑡𝐴𝐵

1(3)This part of the discussion is an extension and application to the case of ESG of the theoretical model
shown by Yoshino et al. (2020).

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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

We can consider ESG investments in the new portfolio utility function by the following equations:
ESG levels are described as follows:
𝐸𝑆𝐺𝑡𝐴 = 𝑎1𝑡 (𝐶𝑂2𝐴 𝑡 ) + 𝑎𝑡2 (𝑁𝑂𝑋𝐴 𝑡 )(4)

𝐸𝑆𝐺𝑡𝐵 = 𝑏𝑡1 (𝐶𝑂2𝐵 𝑡 ) + 𝑏𝑡2 (𝑁𝑂𝑋𝐵 𝑡 )(5)where 1 is the CO2, and 2 is the NOx exposed by companies A and B. In equations (4) and (5),the coefficients of (𝑎1𝑡 , 𝑎𝑡2 ) and (𝑏𝑡1 , 𝑏𝑡2 ) are different from one consulting company to another.
Next, we set the utility function in equation (6), which includes all the three elements discussed;
the rate of return, risk and ESG. The new variable ESG subject to the constraints are presented inequation (9):U(𝑅𝑡 , 𝜎𝑡2 , 𝐸𝑆𝐺𝑡 ) = 𝑅𝑡 − 𝛽𝜎𝑡2 + 𝛾(𝐸𝑆𝐺𝑡 )(6)s.t. 𝑅𝑡 = 𝛼𝑡 𝑅𝑡𝐴 + (1 − 𝛼𝑡 )𝑅𝑡𝐵

(7)

𝜎𝑡2 = 𝛼𝑡2 (𝜎𝑡𝐴 )2 + (1 − 𝛼𝑡 )2 (𝜎𝑡𝐵 )2
𝐸𝑆𝐺𝑡 = 𝛼𝑡 (𝐸𝑆𝐺𝑡𝐴 ) + (1 − 𝛼𝑡 )(𝐸𝑆𝐺𝑡𝐵 )

(8)
(9)

Substituting equations (7), (8), and (9) into equation (6), we obtain the optimal level of portfolio
function, expressed in equation (10).
𝑈 = 𝛼𝑡 𝑅𝑡𝐴 + (1 − 𝛼𝑡 )𝑅𝑡𝐵 − 𝛽{𝛼𝑡2 (𝜎𝑡𝐴 )2 + (1 − 𝛼𝑡 )2 (𝜎𝑡𝐵 )2 + 2𝛼𝑡 (1 − 𝛼𝑡 )𝜎𝑡𝐴𝐵 } +𝛾{𝛼𝑡 (𝐸𝑆𝐺𝑡𝐴 ) + (1 − 𝛼𝑡 )(𝐸𝑆𝐺𝑡𝐵 )}(10)

Obtaining the first-order conditions for the ratio between asset A (share = 𝛼𝑡 ) and asset B(share = 1-𝛼𝑡 ), equation (11) can be shown as follows:𝜕𝑈𝜕𝛼𝑡= (𝑅𝑡𝐴 − 𝑅𝑡𝐵 ) − 𝛽{2𝛼𝑡 (𝜎𝑡𝐴 )2 + 2(1 − 𝛼𝑡 )(𝜎𝑡𝐵 )2 } + (2 − 4𝛼𝑡 )𝜎𝑡𝐴𝐵 + 𝛾(𝐸𝑆𝐺𝑡𝐴 − 𝐸𝑆𝐺𝑡𝐵 )=0(11)

Writing equation (11) for the 𝛼𝑡 results in equation (12):1𝛾(𝑅 𝐴 − 𝑅𝑡𝐵 ) − (𝜎𝑡𝐵 )2 − 𝜎𝑡𝐴𝐵 +(𝐸𝑆𝐺𝑡𝐴 − 𝐸𝑆𝐺𝑡𝐵 )
2𝛽 𝑡
2𝛽
𝛼𝑡 =
(𝜎𝑡𝐴 )2 − (𝜎𝑡𝐵 )2 − 2𝜎𝑡𝐴𝐵(12)8

＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

Equation (12) indicates the share of the allocation to asset A. The last term in the numerator is anadditional component that affects the allocation between asset A and asset B. If 𝐸𝑆𝐺𝑡𝐴 is larger
than 𝐸𝑆𝐺𝑡𝐵 , the portfolio allocation to asset A will become more significant, as shown in Figure
2. Figure 4 shows the traditional portfolio investment, determined by the rate of return and risks.
Point “e” is the optimal portfolio allocation. Figure 2 shows the case where ESG is included in
the utility function, where point “F” becomes the optimal portfolio allocation because asset A
shows a higher ESG score compared to asset B.

Rate

𝑅

𝑅𝐵

𝑅𝐴

𝑒

𝐵

𝐴

𝜎𝐴

𝜎𝐵

𝜎

Risk

Source: Authors’ depiction.

Figure 4: Traditional portfolio investment selection

However, the measure of ESG differs from one ESG rating company to another. Investors selectan ESG rating company to allocate their portfolio based on its definition of the ESG. The asset
allocation of each investor results in distorted portfolio allocation based on the different weightsof (𝑎1𝑡 , 𝑎𝑡2 ) and (𝑏𝑡1 , 𝑏𝑡2 ) as in equations (4) and (5). Thus, each investor will choose a different
portfolio based on the consulting company they chose.
In the second quadrant ESG score is measured together with the rate of return and risks associatedin portfolio investment in the first quadrant in Figure 5.

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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

Source: Authors’ depiction.

Figure 5: Portfolio allocation when ESG factors are taken into accountMarkowitz (2005) states the following assumptions in the above simple CAPM model: (A1)
Transaction costs and other illiquidities can be ignored. (A2) All investors hold mean-varianceefficient portfolios. (A3) All investors hold the same (correct) beliefs about means, variances, andcovariances of securities. (A4) Every investor can lend all she or he has or can borrow all she or
he wants at the risk-free rate. Brennan and Lo (2010) claim that the result for two assets as is usedin the above model cannot be generalized for many assets, as some assets/portfolios will certainly
have negative weights as n →∞. Therefore, the above model used in this paper has to have
limited number of assets rather than infinity number of assets. DeMiguel, Garlappi and Uppal(2009) find that naive diversification (1/n allocation to each asset) often beats simple optimal
allocation as is used in this model. Even if naïve 1/n allocation to each asset were introduced,
additional allocation of ESG investment will distort the original allocation of 1/n by the amountof ESG investment. Therefore, similar argument can be applied to naïve 1/n asset allocation
explained in this section.

5. Empirical Application of the Theory
Stock prices of two companies are selected to show theoretical application of the model inprevious section to real data. Company A shows rate of return as 0.067 (=RA) and its risk, whichis measured by standard error of stock price (σA), is 1.537. Company B shows the rate of returnas 0.003 (=RB) and its risk as 1.316 (=σB). Covariance of these two stocks are -0.087 (σAB).
ESG scores of these two companies are different by the ESG rating agencies as is summarized inTable 4.

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Table 4: Empirical application of the theory
ESG Score

No Rating

RobecoSAM

Sustainalytics

Bloomberg

ESG score of company A

-

8.6

9.6

2.9

ESG score of company B

-

1.8

1.3

3.9

0.57

0.71

0.74

0.54

Value of αNote: Each ESG score is converted to a 10-point scale for comparison.
Source: Based on each company’s 2019 actual stock returns, standard deviation, covariance, and ESG score. Author’s
calculations based on equation (12) from Bloomberg data

By setting the values of γ=0.015, and β=0.005, the optimal portfolio allocation are different forscores based on RobecoSAM, Sustainalytics and Bloomberg, as shown in Table 4. Values of α
(where α denotes allocation of portfolio between two assets A and B, equation (12)) are different
from one agency to another. The allocation of assets between A and B changes depending on
which ESG rating agencies’ ESG score is used for the portfolio allocation. Higher the ESG scoreis, higher the α, and thus higher the investment allocation. For example, since Sustainalytics isthe highest ESG score for Company A, investors following this rating will have the highest
allocation to Company A. On the other hand, the Bloomberg score is lower for Company A thanfor Company B, resulting in a smaller investment allocation. If we do not take into account the
ESG score, the investment allocation to Company A is 0.57. The example shown here proves thevalidity of the theoretical model developed in Section 4. In this empirical analysis, very small
weight for greenness factor or ESG factor will make a big difference in portfolio asset allocation
as is shown in Table 4.

6. GHG Taxation, Green Credit Rating and Optimal Portfolio Allocation
for ESG Investment
6.1 GHG Taxation
A standard global GHG taxation (taxing CO2 and NOx) will give us a new rate of return on assets
A and B, presented in this sub-section 2 . Tax rates can be adjusted based on the progress ofpollution reduction. If the pollution reduction is slow compared to the target, the global tax rate
can be adjusted by the same rate.
𝑈(𝑅̃𝑡 , 𝜎̃𝑡2 )=𝑅̃𝑡 − 𝛽𝜎̃𝑡2

𝑇𝑡𝐴 =

(13)

𝐴
𝑡1 (𝐶𝑂2𝐴 𝑡 )+𝑡2 (𝑁𝑂𝑋
𝑡)

(14)

𝑌𝑡𝐴

2

This part of the discussion is also an extension and application to the case of ESG of the theoreticalmodel shown by Yoshino et al. (2020).

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𝑇𝑡𝐵 =

𝐵
𝑡1 (𝐶𝑂2𝐵 𝑡 )+𝑡2 (𝑁𝑂𝑋
)
𝑡

(15)

𝑌𝑡𝐵

Equation (13) shows the new utility function of investors based on the “after-tax rate of return”
and “after-tax risk.” In equations (14) and (15), 𝑇𝑡𝐴 and 𝑇𝑡𝐵 denote the GHG tax rate charged tocompanies A and B, respectively. 𝑌𝑡𝐴 and 𝑌𝑡𝐵 are the total outputs of companies A and B,
respectively. 𝑡1 and 𝑡2 show the tax rate on CO2 and NOx, which have the same rates globally.
The tax rate on CO2 is the same for companies A and B, and the tax rate of NOx is the same forcompanies A and B. These rates need to be the same globally to avoid distortion of investments
between different countries.
𝑅̃𝑡𝐴 = 𝑅𝑡𝐴 − 𝑇𝑡𝐴(16)

𝑅̃𝑡𝐵 = 𝑅𝑡𝐵 − 𝑇𝐵𝑡(17)

Equations (16) and (17) show the “after-tax rate of return” of company A and company B. The
optimal allocation of assets between company A and B is computed as equations (18) and (19)that show the optimal rate of return and risk, respectively:𝑅̃𝑡 = 𝛼̃𝑡 𝑅̃𝑡𝐴 + (1 − 𝛼̃𝑡 )𝑅̃𝑡𝐵(18)

𝜎̃𝑡2 = 𝛼̃𝑡2 (𝜎̃𝑡𝐴 )2 + (1 − 𝛼̃𝑡 )2 (𝜎̃𝑡𝐵 )2 + 2𝛼̃𝑡 (1 − 𝛼̃𝑡 )𝜎̃𝑡𝐴𝐵(19)

Next, to find the optimal portfolio allocation ratio between asset A and asset B, we obtain thefirst-order condition of the utility function for 𝛼̃:
𝜕𝑈
̃𝑡
𝜕𝛼

= (𝑅̃𝑡𝐴 − 𝑅̃𝑡𝐵 ) − 𝛽{2𝛼̃𝑡 (𝜎̃𝑡𝐴 )2 + 2(1 − 𝛼̃𝑡 )(𝜎̃𝑡𝐵 )2 } + (2 − 4𝛼̃𝑡 )𝜎̃𝑡𝐴𝐵 = 0(20)

Finally, we obtain the optimal level of portfolio allocation as in equation (21):1 ̃ 𝐴 ̃𝐵
− 𝑅𝑡 ) − (𝜎̃𝑡𝐵 )2 − 𝜎̃𝑡𝐴𝐵
2𝛽 (𝑅𝑡𝛼̃𝑡 =(𝜎̃𝑡𝐴 )2 − (𝜎̃𝑡𝐵 )2 − 2𝜎̃𝑡𝐴𝐵(21)

Evidently, as in equation (21), investors do not need to consider ESG as an additional item, as
shown in equation (12). Instead, investors maximize their utility based only on the rate of returnand the risk after tax. The optimal portfolio allocation is as shown in equation (21). The 𝛼̃𝑡12＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

indicates the optimal portfolio as shown in Figure 6 by point f. f is the optimal point after the
adoption of the international GHG taxation scheme.

Rate

𝑅

𝑒
𝑓

𝜎Risk
Source: Authors’ depiction.

Figure 6: International GHG taxation scheme

6.2 Green credit rating
Another way is to make a credit rating of a company based on its greenness, which is a comparable
measure of its GHG emission. If company A’s GHG emission is zero, it is rated AAA, but one
with a large emission would be rated as BB, etc. An accurate measuring of GHG will provide an
accurate green credit rating of each company to investors. Table 5 shows an example of green
credit rating based on emissions of CO2, NOx, and plastics. These ratings will facilitate investors
to decide on investment in Green projects by watching a single green credit rating without being
concerned about different criteria.
Table 5: Green Credit Rating (Example)
Credit Rating

Greenness (%)

CO2

NOx

Plastic

N2O etc

AAA

100 ～ 90

AAA

AAA

AAA

……

AA

90 ～ 80

A

AA

AAA

……

A

80 ～ 70

A

AA

BBB

……

BBB

70 ～ 60

BBB

BB

A

……

BB

60 ～ 50

BB

BB

BB

……

B

50 ～ 40

B

B

B

……

CCC

40 ～ 30

CCC

B

CCC

……

CC

30 ～ 20

CC

C

CCC

……

C

20 ～ 10

C

C

C

……

Source: Authors’ depiction.

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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

U(𝑅𝑡 , 𝜎𝑡2 , 𝐺𝑟𝑒𝑒𝑛𝑡 ) = 𝑅𝑡 − 𝛽𝜎𝑡2 + 𝛾(𝐺𝑟𝑒𝑒𝑛𝑡 )(22)

𝑅𝑡 = 𝛼𝑡 𝑅𝑡𝐴 + (1 − 𝛼𝑡 )𝑅𝑡𝐵

(23)

𝜎𝑡2 = 𝛼𝑡2 (𝜎𝑡𝐴 )2 + (1 − 𝛼𝑡 )2 (𝜎𝑡𝐵 )2
𝐺𝑟𝑒𝑒𝑛𝑡 = 𝛼𝑡 (𝐺𝑟𝑒𝑒𝑛𝑡𝐴 ) + (1 − 𝛼𝑡 )(𝐺𝑟𝑒𝑒𝑛𝑡𝐵 )

(24)

s.t.

(25)

Where greenness index is based on the following two equations.
𝐺𝑟𝑒𝑒𝑛𝑡𝐴 = 𝑎1𝑡 (𝐶𝑂2𝐴 𝑡 ) + 𝑎𝑡2 (𝑁𝑂𝑋𝐴 𝑡 )(26)

𝐺𝑟𝑒𝑒𝑛𝑡𝐵 = 𝑏𝑡1 (𝐶𝑂2𝐵 𝑡 ) + 𝑏𝑡2 (𝑁𝑂𝑋𝐵 𝑡 )(27)

Optimal portfolio allocation now depends not only on rate of return and risks but also depends
on greenness index 𝐺𝑟𝑒𝑒𝑛𝑡𝐴 and 𝐺𝑟𝑒𝑒𝑛𝑡𝐵 .
1𝛾(𝑅 𝐴 − 𝑅𝑡𝐵 ) − (𝜎𝑡𝐵 )2 − 𝜎𝑡𝐴𝐵 +(𝐺𝑟𝑒𝑒𝑛𝑡𝐴 − 𝐺𝑟𝑒𝑒𝑛𝑡𝐵 )
2𝛽 𝑡
2𝛽
𝛼𝑡 =
(𝜎𝑡𝐴 )2 − (𝜎𝑡𝐵 )2 − 2𝜎𝑡𝐴𝐵(28)

Unique value of αt is obtained from a single green credit rating.

7. Relation between ESG Investment and Stock Prices
There are various analysis on the relation between ESG investment and stock prices. One view isthat ESG investment will increase stock prices since it pushes companies to move for better
environment. Another view is that ESG investment does not necessarily push stock prices up
since they are not influenced by ESG investment alone but rather by the performance of thecompany.

7.1 Co-movement of ESG investment and stock prices
Fluctuations of stock prices can be explained as follows. The demand for a stock depends on therate of return (R), risk (σ) and ESG investment. Many investors started to build portfolios basedon environmental concern. The ESG investment will rise until a certain level of ESG investment
is achieved (ESG). Institutional investors have their target level of ESG investment in mind. The
demand for ESG investment would increase as long as the current ESG investment is smaller than
the target level (ESG-ESG). As institutional investors increase their portfolios while ESG-ESG is
positive, stock prices will rise (equation (29)). However, when ESG investment reaches the target
level of ESG, stock prices will stop increasing (Equation (30)). Therefore, the positive correlation
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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞

between ESG investment and stock prices is observed only when current ESG investment is lower
than the target level of ESG.
𝑑𝑝
= 𝑝̇ = 𝜆{𝐷(𝑅, 𝜎, 𝐸𝑆𝐺 − 𝐸𝑆𝐺) − 𝑆(𝑟, 𝑌)}
𝑑𝑡

(29)

when ESG=ESG is achieved(30)

Source: Authors’ depiction.

Figure 7: Fluctuation of stock prices and ESG investment
7.2 ESG investment and the rate of return
Some investors seek for higher rate of return believing that ESG investment will push up theactual rate of return on the companies such as wind power and solar power. Equation (31)describes such a case. ESG investment will expand their business and will push up stock return.

(31)

(32)

If such domestic companies as wind power and solar power are competitive compared to foreigncompanies in the same sector, and if they can sell their products extensively, equations (31) and(32) will hold. However, in the case of wind power, Japanese companies lost their competitivenesscompared to European companies and they have withdrawn from the market.
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＜FSA Institute Discussion Paper Series DP2020-9 (December, 2020)＞(%)

High Ratings

Medium Rating

Low Ratings

1
0
-1
-2
-3
-4
-5
-6
ESG Rating Agency A

ESG Rating Agency B

ESG Rating Agency C

Note: Only stocks covered by each ESG rating agency are aggregated. The estimation period is the first quarter of2020 (December 30, 2019 to March 31, 2020).
Source: Authors’ calculations from Bloomberg data.

Figure 8: ESG score (high-medium-low quintile) and stock returns (first quarter of 2020)
Figure 8 shows the relation between stock performance and the ESG rating. Rating agency B
gives ESG scores that are in parallel with the stock performance. However, rating agencies A andC rank ESG scores un-correlated with stock performances. This example empirically shows that
positive correlations between stock performance and ESG rating cannot be seen.

8. Conclusion & Policy Implications
SDGs, ESG and Green investment are important policy objectives that we have to achieve forsustainable environment and sustainable growth. However, each ESG rating company has its own
criteria for measuring ESG. Investors’ portfolio allocations become distorted due to the lack ofglobal standardized criteria for such measurement. To achieve clean energy and environmentrelated ESG, we recommend the adoption of international GHG taxation systems and the credit
rating of greenness of each company based on GHG emissions to be used by investors.
Finally, although adopting an international taxation system for GHG and plastics is desirable,
it might be difficult for developing countries. Therefore, we recommend starting such a system inregions where economic cooperation and economic integration exist, like the European Union or
the Association of Southeast Asian Nations. Another policy proposal is to make a global green
credit rating of companies based on their emissions of pollutants such as CO2, NOx, plastics etc.,
which will drive investors toward optimal portfolio allocation.

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