Journal of Financial Economics 145 (2022) 642–664
Contents lists available at ScienceDirect
Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec
Sustainable investing with ESG rating uncertainty
R
Doron Avramov
a , ∗
, Si Cheng
b
, Abraham Lioui
c
, Andrea Tarelli
d
a
Interdisciplinary Center (IDC), Herzliya, Israel
b
Chinese University of Hong Kong, Hong Kong
c
EDHEC Business School and EDHEC & Scientific Beta Research Chair, Nice, France
d
Catholic University of Milan, Milan, Italy
a r t i c l e i n f o
Article history:
Received 9 February 2021
Revised 26 June 2021
Accepted 25 July 2021
Available online 17 September 2021
JEL classification:
G11
G12
G24
M14
Q01
Keywords:
ESG
Rating uncertainty
Portfolio choice
Capital asset pricing model
a b s t r a c t
This paper analyzes the asset pricing and portfolio implications of an important barrier
to sustainable investing: uncertainty about the corporate ESG profile. In equilibrium, the
market premium increases and demand for stocks declines under ESG uncertainty. In ad-
dition, the CAPM alpha and effective beta both rise with ESG uncertainty and the nega-
tive ESG-alpha relation weakens. Employing the standard deviation of ESG ratings from six
major providers as a proxy for ESG uncertainty, we provide supporting evidence for the
model predictions. Our findings help reconcile the mixed evidence on the cross-sectional
ESG-alpha relation and suggest that ESG uncertainty affects the risk-return trade-off, social
impact, and economic welfare.
©2021 Elsevier B.V. All rights reserved.
1. Introduction
The global financial market has experienced exponen-
tial growth in sustainable investing, an investment ap-
proach that considers environmental, social, and gover-
R
Bill Schwert was the editor for this article. We especially thank an
anonymous referee for insightful comments and suggestions. We also
thank Bill Schwert, Yakov Amihud, Marcin Kacperczyk, Lubos Pástor, Lasse
Heje Pedersen, Luke Taylor, seminar participants at Catholic University of
Milan, Ben-Gurion University of the Negev, Bar-Ilan University, Bocconi
University, and EDHEC Business School, and conference participants at the
2021 North American and European Summer Meetings of the Economet-
ric Society for useful comments and discussions. We are solely responsi-
ble for any remaining errors.
∗
Corresponding author.
E-mail addresses: doron.avramov@idc.ac.il (D. Avramov),
sicheng@cuhk.edu.hk (S. Cheng), abraham.lioui@edhec.edu (A. Lioui),
andrea.tarelli@unicatt.it (A. Tarelli).
nance (ESG) factors in portfolio selection and management.
Since the launch of the United Nations Principles for Re-
sponsible Investment (PRI) in 2006, the number of signato-
ries has grown from 734 in 2010 to 1384 in 2015 and 3038
in 2020, with total assets under management of US$21 tril-
lion in 2010, US$59 trillion in 2015, and US$103 trillion in
2020.
1
In line with the increasing concerns about global
warming, BlackRock CEO Larry Fink wrote in a recent an-
nual letter that climate change will force businesses and
investors to shift their strategies, leading to a “fundamental
reshaping of finance” and “significant reallocation of capi-
tal.”
2
As the ESG objective is becoming a primary focus in as-
set management, the reallocation of capital has major im-
1
See, https://www.unpri.org/pri .
2
See, https://www.blackrock.com/corporate/investor-relations/larry-
fink- ceo- letter .
https://doi.org/10.1016/j.jfineco.2021.09.009
0304-405X/© 2021 Elsevier B.V. All rights reserved.
D. Avramov, S. Cheng, A. Lioui et al. Journal of Financial Economics 145 (2022) 6 42–66 4
plications for portfolio decisions and asset pricing. How-
ever, ESG investors often confront a substantial amount of
uncertainty about the true ESG profile of a firm. In the ab-
sence of a reliable measure of the true ESG performance,
any attempt to quantify it needs to cope with incomplete
and opaque ESG data and nonstructured methodologies. A
meaningful illustration of uncertainty about the ESG score
is the pronounced divergence across ESG rating agencies.
3
While such uncertainty could be an important barrier to
sustainable investing, to date, little attention has been de-
voted to the role of ESG uncertainty in portfolio decisions
and asset pricing.
This paper aims to fill this gap by analyzing the equi-
librium implications of ESG uncertainty for both the ag-
gregate market and the cross section. To pursue this
task, we consider brown-averse agents who extract non-
pecuniary benefits from holding green stocks, following
Pástor et al. (2021a) . We first study the aggregate market
through a mean-variance setup that consists of the market
portfolio and a riskless asset. Due to uncertainty about the
ESG profile, equities are perceived to be riskier. In addition,
the demand for equities consists of two components: (1)
the usual demand when ESG preferences are muted and
(2) a demand for a pseudo-asset with a positive payoff for
a green market and a negative payoff for a brown market
as well as volatility that evolves from uncertainty about
the market ESG score. Aggregating these components, we
show that the overall demand for equities falls due to ESG
uncertainty, even when the market is green.
We then formulate the market premium in equilibrium.
While the higher risk due to ESG uncertainty essentially
commands a higher market premium, there is an offsetting
force when the market is green because ESG investors ex-
tract nonpecuniary benefits from holding green stocks. The
ultimate implications of ESG preferences with uncertainty
for the market premium are thus inconclusive. When the
market is green neutral, however, the equity premium rises
with ESG uncertainty. For perspective, when ESG uncer-
tainty is not accounted for and the market is green (green
neutral), the market risk does not change, the demand for
risky assets rises (does not change), and the market pre-
mium drops (does not change) relative to ESG indifference.
We further derive a CAPM representation in which both
alpha and the effective beta vary with firm-level ESG un-
certainty. The effective beta differs from the CAPM beta
in the following way. While the CAPM beta is based on
the covariance and variance of actual returns, the effec-
tive beta reflects the notion that both the market and in-
dividual stock returns are augmented by a random ESG-
based component, which is positive for a green asset and
negative otherwise. Thus, the effective beta is based on
the covariance and variance of ESG-adjusted returns. Re-
garding alpha, when ESG uncertainty is not accounted for,
the CAPM alpha exclusively reflects the willingness to hold
green stocks due to nonpecuniary benefits, and the ESG-
3
Berg et al. (2020) report that the average correlation among six ma-
jor rating providers is only 0.54. They also find that, even when the cat-
egories of attributes considered for the evaluation of a firm’s ESG profile
are fixed, raters largely disagree on the measurement of these granular
characteristics.
alpha relation is, hence, negative.
4
Accounting for ESG un-
certainty, the equilibrium alpha increases with ESG uncer-
tainty and the ESG-alpha relation weakens.
We move on to empirically test the model implications
using U.S. common stocks from 2002 to 2019. We collect
ESG ratings from six major rating agencies, namely, As-
set4 (Refinitiv), MSCI KLD, MSCI IVA, Bloomberg, Sustain-
alytics, and RobecoSAM. We employ the average (standard
deviation of) ESG ratings across rating agencies to proxy
for the firm-level ESG rating (ESG uncertainty). Consistent
with existing studies, we confirm that there are substan-
tial variations across different rating providers, while the
average rating correlation is 0.48. The variations are quite
persistent throughout the entire sample period.
We first examine how the ESG rating and uncertainty
affect investor demand. To better capture the demand from
ESG-sensitive investors, we consider three distinct types
of institutions: norm-constrained institutions, hedge funds,
and other institutions. Norm-constrained institutions, such
as pension funds as well as university and foundation en-
dowments, are more likely to make socially responsible
investments compared to hedge funds or mutual funds
that are natural arbitrageurs ( Hong and Kacperczyk, 2009 ).
We first confirm that norm-constrained institutions display
preferences for greener firms. Consistent with the model
prediction, we find that in the presence of uncertainty
about the ESG profile, ESG-sensitive investors lower their
demand for risky assets. For instance, among the high-ESG-
rating portfolios, norm-constrained institutions hold 22.8%
of the low-uncertainty stocks but only 18.1% of the high-
uncertainty stocks, indicating a 21% decline. The results are
particularly strong among high-ESG stocks, suggesting that
rating uncertainty matters the most for ESG-sensitive in-
vestors in their ESG investment. Notably, even with grow-
ing ESG awareness, their demand for green assets has con-
tinued to diminish with rating uncertainty over the past
decade. In addition, while hedge funds invest more in low-
ESG stocks, rating uncertainty plays a similar role in dis-
couraging stock investment.
We next examine the cross-sectional implications of
ESG uncertainty. We first sort stocks into quintile portfolios
based on their ESG uncertainty. Within each uncertainty
group, we further sort stocks into quintile portfolios ac-
cording to their ESG ratings. We find that the ESG rating
is negatively associated with future performance among
stocks with low ESG uncertainty, providing empirical sup-
port for the predictions of Pástor et al. (2021a) , who rely
on deterministic ESG scores. For instance, brown stocks
outperform green stocks by 0.59% per month in raw re-
turn and 0.40% per month in CAPM-adjusted return. How-
ever, in the presence of ESG uncertainty, our model shows
that the ESG-alpha relation can be nonlinear and ambigu-
ous. Indeed, we demonstrate empirically that the negative
return predictability of ESG ratings does not hold for the
remaining firms. The results are robust to adjusting returns
for alternative risk factors and controlling for firm charac-
teristics in Fama and MacBeth (1973) regressions.
4
See, e.g., Heinkel et al. (2001) and Pástor et al. (2021a) .
643
D. Avramov, S. Cheng, A. Lioui et al. Journal of Financial Economics 145 (2022) 6 42–66 4
Finally, we calibrate the model for plausible values of
market volatility and risk aversion. The investment uni-
verse consists of a riskless asset and the market portfo-
lio. Our calibration considers two types of agents who ob-
serve the returns on investable assets. One type of agents
accounts for ESG preferences with uncertainty in assess-
ing the risk-return profile of the optimal portfolio, while
the other type is ESG indifferent. Accounting for ESG un-
certainty significantly reduces the demand for the mar-
ket portfolio and the certainty equivalent rate of return of
ESG-sensitive agents. The calibration results reinforce the
notion that ESG uncertainty could negatively, and signif-
icantly, affect the risk-return trade-off, social impact, and
economic welfare.
This paper contributes to several strands of the litera-
ture. First, we explicitly account for uncertainty about the
ESG profile in equilibrium asset pricing for both the ag-
gregate market and the cross section. Prior work has fo-
cused on investors’ ESG preferences (e.g., Heinkel et al.,
2001; Pástor et al., 2021a ), while our model predictions
and calibration results highlight the importance of consid-
ering ESG uncertainty when analyzing sustainable invest-
ing. Specifically, the perceived equity risk increases with
ESG uncertainty, while the demand for equity falls. ESG
uncertainty also affects the market premium in aggregate,
as well as the CAPM alpha and effective beta in the cross
section.
Second, we contribute to the growing literature on
the cross-sectional return predictability of the ESG profile.
Prior studies show weak return predictability of the over-
all ESG rating (e.g., Pedersen et al., 2021 ) and mixed evi-
dence based on different ESG proxies (e.g., Gompers et al.,
20 03; Hong and Kacperczyk, 20 09; Edmans, 2011; Bolton
and Kacperczyk, 2020 ). Our contribution is to propose that
ESG uncertainty could tilt the ESG-performance relation
and serve as a potential mechanism to explain the op-
posing findings. We show that ESG ratings are negatively
associated with future performance when there is little
uncertainty and that the ESG-performance relation could
be insignificant or positive when uncertainty increases.
Thus, the sin premium ( Hong and Kacperczyk, 2009 ) and
carbon premium ( Bolton and Kacperczyk, 2020 ) could
be attributed to the notion that sin stocks (i.e., com-
panies involved in producing alcohol, tobacco, and gam-
ing) and carbon emissions are clearly defined and thus
subject to minimal uncertainty among investors. On the
other hand, other ESG profiles could be more challeng-
ing to measure or rely on nonstandardized information
and methodologies, thereby displaying more uncertainty
and mixed evidence on return predictability. A recent work
by Pástor et al. (2021b) further highlights the distinction
between ex ante expected returns and ex post realized
returns, and shows that U.S. green stocks outperformed
brown stocks during the last decade, due to unexpect-
edly strong increases in environmental concerns. While our
model is static in nature and formulates expected returns,
we also confirm that our findings are stronger in the pre-
2011 period. This suggests that the equilibrium outcome
over longer horizons could be even stronger than the full
sample evidence we report, due to the unexpected out-
comes realized over the last decade.
To the extent that ESG uncertainty will decrease with a
better understanding of a firm’s true ESG profile, our work
enriches academic and policy discussions in that context.
Despite the rapid growth in the sustainable investing and
ESG data markets,
5
the comparability of ESG information
remains a critical issue. Due to the lack of standards gov-
erning the reporting of ESG information, it is not a triv-
ial task to compare the ESG data of two different com-
panies ( Amel-Zadeh and Serafeim, 2018 ). In addition, the
construction of ESG ratings is nonregulated, and method-
ologies can be opaque and proprietary, leading to sub-
stantial divergence across data providers (e.g., Mackintosh,
2018; Berg et al., 2020 ). Our findings imply that the lack
of consistency across ESG rating agencies makes sustain-
able investing riskier and hence reduces investor participa-
tion and potentially hurts economic welfare. This has im-
portant normative implications. For instance, it would be
useful for policy makers to establish a clear taxonomy of
ESG performance and unified disclosure standards for sus-
tainability reporting. It would be especially instructive to
identify which investments are really green. Doing so could
mitigate ESG uncertainty, thus reducing the cost of equity
capital for green firms, leading to higher social impact.
Our study of the equilibrium implications of ESG un-
certainty owes a debt to the innovative setup developed
by Pástor et al. (2021a) , although our focus is different.
Pástor et al. (2021a) comprehensively analyze the equilib-
rium implications of sustainable investing and conduct an
analysis of welfare and social impact. They also account
for the possibility that ESG investors can disagree about a
firm’s ESG profile and analyze cases in which the market
is green neutral or green. Notably, in their setup, the ESG
score is certain because investors are dogmatic about their
ESG perceptions and can observe each other’s perceived
ESG values. Relative to their important work, we study the
implications of uncertainty about the corporate ESG pro-
file. In particular, the investors in our model agree that the
ESG scores are uncertain and they also agree on the un-
derlying distribution of the uncertain scores. The empirical
proxy for uncertainty is the dispersion, or disagreement,
across raters. We show that ESG uncertainty affects the eq-
uity premium, investor’s demand for risky assets, economic
welfare, and the alpha and beta components of stock re-
turns.
The remainder of this paper is organized as follows.
Section 2 presents the model. Section 3 describes the
data and the main variables used. Section 4 empirically
examines how ESG ratings and uncertainty affect in-
vestor demand and cross-sectional return predictability.
Section 5 calibrates the model and explores its quantita-
tive implications. The conclusion follows in Section 6 .
2. ESG and market equilibrium
The theory section develops the economic setup. We
start with a single risky asset, i.e., the market portfolio,
and a riskless asset. We derive the optimal portfolio and
5
The estimated spending on ESG data was US$617 million in 2019
and could approach US$1 billion by 2021. See, http://www.opimas.com/
research/547/detail/ .
644
D. Avramov, S. Cheng, A. Lioui et al. Journal of Financial Economics 145 (2022) 6 42–66 4
discuss the implications of uncertainty about the ESG pro-
file for the market premium and welfare. The single-asset
setup is then extended to consider multiple risky assets.
We analyze the implications of ESG uncertainty for the de-
mand of individual stocks, derive an asset pricing model
for the cross section of stock returns, and discuss incre-
mental effects of ESG uncertainty on the alpha and beta
components of returns.
2.1. One risky asset
Consider a single-period economy in which an optimiz-
ing agent trades at time 0 and liquidates the position at
time 1. Let
˜
r
M
denote the random rate of return on the
market portfolio in excess of the riskless rate, r
f
, and let
˜
g
M
denote the true , but unobservable, ESG score of the
market portfolio.
6
We model the excess market return and
the ESG score as
˜
r
M
= μ
M
+ ˜
M
, (1)
˜
g
M
= μ
g,M
+ ˜
g,M
, (2)
where E
(
˜
r
M
)
= μ
M
is the expected market excess return,
E
(
˜
g
M
)
= μ
g,M
is the expected value of the market ESG
score, and ˜
M
and ˜
g,M
are zero-mean residuals. We as-
sume that the residuals obey a bivariate normal distribu-
tion with σ
M
, σ
g,M
, and ρ
g,M
denoting the standard devia-
tion of return, the standard deviation of ESG score, and the
correlation between residuals, respectively.
It is assumed that the agent knows the joint distribu-
tion of return and the ESG score as well as the underly-
ing parameters. In the empirical analysis that follows, μ
g,M
and σ
g,M
are proxied by the average and standard devia-
tion of ESG ratings across six major data vendors, respec-
tively. From an investor’s perspective, a higher σ
g,M
in-
dicates more disagreement among ESG raters and hence
more uncertainty about the true ESG profile of the market.
Following Pástor et al. (2021a) , we consider an optimiz-
ing agent who derives nonpecuniary benefits from hold-
ing stocks based on their ESG characteristics. Moreover,
preferences are formulated through the exponential utility
(CARA) function
V
˜
W
1
, x
= −e
−A
˜
W
1
−BW
0
x
˜
g
M
, (3)
where
˜
W
1
= W
0
1 + r
f
+ x
˜
r
M
is the terminal wealth, W
0
is
the initial wealth, x is the fraction of wealth invested in
the risky asset, A stands for the agent’s absolute risk aver-
sion, and B characterizes the nonpecuniary benefits that
the agent derives from stock holdings. Positive (negative)
B indicates that the agent extracts benefits from holding
green (brown) stocks. Hence, B can be interpreted as the
absolute brown aversion. In the following, we make the
sensible assumption of a nonnegative brown aversion ( B ≥
0
). Slightly departing from Pástor et al. (2021a) , we formu-
late preferences for ESG to be wealth-dependent. Then, the
expression BW
0
represents the relative brown aversion.
In the presence of brown aversion, the correlation be-
tween residuals in Eqs. (1) and (2) , ρ
g,M
, is assumed to
6
Consistent with static setups, we do not formulate intertemporal pref-
erences; hence, the riskless rate is exogenously specified.
be positive. In particular, if the agent learns that the mar-
ket ESG score is higher than previously thought (i.e., ˜
g,M
is positive), the price that he would be willing to pay for
the market will be revised upward (positive ˜
M
), while a
downward price revision applies for a score lower than
previously thought.
7
Observe from Eq. (3) that the investment in the riskless
asset does not contribute to the portfolio’s ESG profile, as
perceived by the agent. This is because the riskless asset
is implicitly assumed to be green neutral. As ESG scores
are ordinal in nature, the choice of considering the riskless
asset as a reference level does not imply loss of general-
ity. In addition, to capture the ESG benefits and costs from
investing in the market, we allow the market portfolio to
depart from green neutrality.
The agent picks x , attempting to maximize the expected
value of preferences in Eq. (3) . The first-order condition
suggests that the optimal portfolio in the presence of ESG
uncertainty is given by
x
∗
=
1
γ
μ
M
+ bμ
g,M
σ
2
M,U
, (4)
where b =
B
A
, γ = AW
0
stands for the relative risk aversion,
and σ
2
M,U
= σ
2
M
+ b
2
σ
2
g,M
+ 2 bσ
M
σ
g,M
ρ
g,M
is the variance of
return, as perceived by the agent. Henceforth, b is referred
to as brown aversion for brevity. The ex ante market vari-
ance, σ
2
M,U
, is no longer equal to σ
2
M
because, with ESG un-
certainty, the risky asset is perceived to be a package of
two distinct securities. The first delivers the market excess
return
˜
r
M
, while the second reflects exposure to ESG uncer-
tainty and yields b
˜
g
M
. The latter component can be inter-
preted as investing b units in a pseudo-asset that pays
˜
g
M
per unit. As b increases, i.e., when the ratio between brown
aversion and risk aversion increases, the ESG component
becomes more meaningful in investment decisions. A suf-
ficient condition for σ
2
M,U
≥ σ
2
M
is that the brown aversion
and the correlation between market return and ESG score
are nonnegative (i.e., b ≥ 0 and ρ
g,M
≥ 0 ). As noted earlier,
these conditions are likely to be satisfied.
In what follows, we consider a positive market pre-
mium (i.e., μ
M
> 0 ), which is plausible in the presence
of risk aversion. The brown-aversion assumption is sensi-
ble for ESG-perceptive investors. Additionally, to distill the
incremental effects of ESG uncertainty, we consider two
benchmark cases. In the first, the agent is ESG indiffer-
ent, and in the second, preference for ESG is accounted for,
while the ESG profile is known for certain. The latter case
is studied by Pástor et al. (2021a) in a multiple-security
setup.
Equation (4) presents the optimal stock position in the
presence of uncertainty about the ESG profile. Stock invest-
ment is thus driven by the relative risk aversion, γ , and
the price of risk of the portfolio that yields
˜
r
M
+ b
˜
g
M
. To
give perspective on the optimal equity demand, consider
the case that incorporates ESG preferences but excludes
uncertainty. Then, the perceived volatility of the stock re-
turn is still σ
M
. Conforming to intuition, the demand for
7
We thank the referee for suggesting this avenue.
645
D. Avramov, S. Cheng, A. Lioui et al. Journal of Financial Economics 145 (2022) 6 42–66 4
stocks rises as b rises and the market is green. Essentially,
stocks are more attractive to a green-loving agent.
When ESG uncertainty is accounted for, however, this
intuition is no longer binding. To illustrate, consider two
limiting cases. In the first, b grows with no bound. The in-
vestor then avoids equities, i.e., lim
b→∞
1
γ
μ
M
+ bμ
g,M
σ
2
M,U
= 0 . Simi-
larly, when ESG uncertainty rises with no bound, the de-
mand for stocks evaporates. Thus, both increasing brown
aversion and increasing uncertainty translate into increas-
ing equity risk. In the presence of ESG uncertainty, a
brown-averse agent could substantially reduce stock in-
vesting, even when the market is green, on average.
Moving beyond the two limiting cases, we further ex-
amine portfolio tilts in the presence of ESG uncertainty. For
that purpose, we rewrite the optimal portfolio as
x
∗
=
1
γ
μ
M
σ
2
M
+
1
γ
b
μ
g,M
σ
2
M
−
1
γ
μ
M
+ bμ
g,M
σ
2
M
b
2
σ
2
g,M
σ
2
M,U
+ 2 b
σ
M
σ
g,M
ρ
g,M
σ
2
M,U
. (5)
The first term on the right-hand side of Eq. (5) de-
scribes the benchmark case of ESG indifference. Prefer-
ences for ESG generate the second and third terms. The
term
1
γ
bμ
g,M
σ
2
M
corresponds to the second benchmark case
with ESG preferences when the ESG profile is known for
certain. It suggests that as b rises, the demand for the risky
asset rises and portfolio tilt intensifies. The third term
purely reflects the incremental effect of ESG uncertainty.
The ratio
σ
2
g,M
σ
2
M,U
stands for the contribution of ESG uncer-
tainty to the total, ex ante , market variance. Additionally,
in the presence of a positive correlation between market
return and the ESG profile, the agent employs the market
portfolio to hedge against risk evolving from ESG uncer-
tainty, as captured by the hedge ratio
σ
M
σ
g,M
ρ
g,M
σ
2
M,U
. Hence,
the incremental effect of ESG uncertainty on stock invest-
ing (captured by the third term) is negative.
8
In addition, when the market is green neutral (i.e.,
μ
g,M
= 0 ) and when the ESG profile is known for certain,
stock investing is unaffected relative to ESG indifference. In
contrast, when the market is green neutral and ESG uncer-
tainty is accounted for, participation in the equity market
is discouraged, relative to both benchmark cases.
We now turn to analyzing the equilibrium implications
of ESG preferences with uncertainty. It is assumed that, in
equilibrium, the representative agent’s wealth is fully in-
vested in the market portfolio. Thus, equalizing the optimal
stock allocation in Eq. (4) to 1 yields the market premium.
The market premiums for the cases of ESG indifference ( I),
ESG preference with no uncertainty ( N), and ESG prefer-
ence with uncertainty ( U) are given by
μ
I
M
= γσ
2
M
, (6)
μ
N
M
= γσ
2
M
− bμ
g,M
, (7)
8
In the case where
μ
M
+ b
μ
g,M
is negative, the ESG uncertainty effect
on stock investing goes the opposite way. This requires the interaction of
extreme brown aversion along with an extreme brown market.
μ
U
M
= γσ
2
M
− bμ
g,M
+ γ (σ
2
M,U
− σ
2
M
) . (8)
Retaining the assumptions of a green market and a
brown-averse agent, the market premium diminishes rel-
ative to Eq. (6) , as captured by the second term in Eq. (7) .
This is because, as implied by Pástor et al. (2021a) in
a multi-asset context, an agent who extracts nonpecu-
niary benefits from holding green stocks is willing to com-
promise on a lower risk premium relative to an ESG-
indifferent agent. If the market is green neutral, the second
term disappears; hence, the equity premium is unchanged
even when ESG preferences are accounted for.
Further accounting for uncertainty in Eq. (8) , there are
two conflicting forces. On the one hand, the agent extracts
nonpecuniary benefits from holding the green market, a
force leading to diminished market premium. On the other
hand, the market is perceived to be riskier; thus, it com-
mands a higher market premium, as formulated in the
third term of Eq. (8) . The overall effect is inconclusive. If
the market is green neutral, the equity premium increases
relative to both benchmark cases due to the increasing risk
channel.
The same conflicting forces apply to the equilibrium
Sharpe ratio (the slope of the capital allocation line) when
accounting for ESG uncertainty, SR
U
, relative to ESG indif-
ference, SR
I
. Given market return volatility, σ
M
, it follows
that
SR
U
SR
I
=
σ
2
M,U
σ
2
M
−
bμ
g,M
γσ
2
M
. The first term is greater than one
and reflects the increase in perceived equity risk. The sec-
ond captures the decrease in the market premium due to
the nonpecuniary benefits from ESG investing.
In the presence of ESG preferences, the market risk pre-
mium thus incorporates an ESG incremental premium that
can be defined as
μ
N
M
− μ
I
M
= −bμ
g,M
, (9)
μ
U
M
− μ
I
M
= γ
σ
2
M,U
− σ
2
M
− bμ
g,M
. (10)
The no-uncertainty case is associated with a negative
ESG incremental premium when the market is green and
the agent is brown-averse, while the incremental premium
is zero when the market is green neutral. In addition,
it is evident from Eq. (10) that the market premium in-
creases with ESG uncertainty. Collectively, with ESG uncer-
tainty, the incremental premium is positive when the mar-
ket is green neutral. Otherwise, with a green market and a
brown-averse agent, the sign of the incremental premium
is inconclusive due to the conflicting forces.
The single-security economy establishes a solid bench-
mark in which to comprehend the more complex multi-
asset setup to be developed later in the text. While the
cross-sectional ESG-alpha relation is negative when ESG
uncertainty is not accounted for, the single-security case
provides the first clue that (1) the risk premium increases
with ESG uncertainty, and (2) the risk premium of a green
stock could exceed that of a brown stock in the presence
of ESG uncertainty. Taken together, the ESG-alpha relation
in the cross section can be subject to conflicting forces.
Up to this point, we have considered a single-agent
economy for ease of exposition. In what follows, to assess
the welfare implications of ESG uncertainty in the aggre-
gate and to study the multi-asset economy, we extend the
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