DP2023-01

Sustainable Investing Under
Delegated Investment Management
Meg ADACHI-SATO
Hiroshi OSANO

Revised October 13, 2023

Sustainable Investing Under Delegated
Investment Management∗
Meg Adachi-Sato† and Hiroshi Osano‡
Initial version: January 2, 2023
Revised version: October 10, 2023∗

The authors would like to thank Yuuichi Fukuta, Keiichi Hori, Shinsuke Ikeda, Jason Vladusic, andseminar participants at the Asset Pricing Workshop (Osaka University) for their helpful comments andsuggestions.
†
Faculty of Business Administration, Osaka University of Economics, 2-2-8, Osumi, Higashiyodogawaku, Osaka 533-8533, Japan and Research Institute for Economics and Business Administration, Kobe
University, Kobe 657-8501, Japan. E-mail: m-sato@osaka-ue.ac.jp; work phone number: +81-6-63282431.
‡
Corresponding author. Faculty of Economics, Konan University, 8-9-1, Okamoto, Higashinada-ku,
Kobe 658-8501, Japan. e-mail address: osano@kier.kyoto-u.ac.jp; work phone number: +81-78-431-3024.

1

Sustainable Investing Under Delegated Investment Management
Abstract
This paper considers how profit-motivated fund managers of sustainable and passive
funds govern the firms in the portfolios that they construct using the capital collectedfrom socially responsible investors. The fund managers choose their level of engagementwith these firms to increase their profit and to reduce any negative externalities. Using
the search model framework between fund managers and investors, we derive several novel
implications regarding the eﬀects of growing interest in environmental, social, and governance (ESG) investments, the limited impact of shareholder ESG engagement in firms
with high-ESG proxies, and the eﬀects of improvements in ESG engagement cost on the
ESG and financial performances generated by portfolio firms.
JEL Classification: D83, G23, G32, M14.
Keywords: delegated asset investment, ESG, passive fund, social impact, socially responsible investing, sustainable fund.

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1. Introduction
In recent decades, growing preferences for environmental, social, and governance (ESG)
investments have been observed among investors who derive non-pecuniary benefits fromthese investments; as a result, a rapid expansion in socially responsible or sustainable
investment has occurred.1 However, a large proportion of sustainable investments are
made by institutional investment funds, such as sustainable funds (S-funds), the dominant
investing strategy of which is to buy only the stocks of firms with high-ESG performance.
These funds are often managed by asset managers who may pursue their own pecuniary
profits. Therefore, it is of the utmost importance to motivate fund managers to engage inmanaging their portfolio firms not only to enhance pecuniary returns, but also to improve
ESG performance. Furthermore, some scholars (e.g., Hartzmark and Shue, 2022) showthat a sustainable investing strategy directing capital away from firms with low-ESG
performance toward firms with high-ESG performance may be counterproductive in thatit leads the former firms to lower their ESG performance without leading the latter firms
to raise their ESG performance.
In recent years, the presence of passive funds (P-funds) has been significant.2 P-fundmanagers create market portfolios aligned with an index and hence are considered tohave little or no governance role in their portfolio firms. Many practitioners and scholars
suggest that ESG activists have a big P-fund investment problem; that is, ESG activists
who convince investors to ditch stocks with low-ESG characteristics are at risk of seeing
their eﬀorts undermined by the presence of P-funds.3 However, the empirical evidence
about the governance role of P-funds is mixed.4 Thus, the governance role of the P-fund
1

According to Alyssa Stankiewicz (Sustainable Fund Flows Reach New Heights in 2021’s First
Quarter, Morningstar, April 30, 2021, https://www.morningstar.com/articles/1035554/sustainable-fundflows-reach-new-hights-in-2021s-first-quarter), as of March 21, 2021, assets in US sustainable funds totaled
nearly $266 billion, which is a 12% increase over the previous quarter and a 125% increase year over year.
2
The fraction of P-funds grew to just under 40% of the US fund market at the end of 2019 (Investment
Company Institute 2020 Factbook).
3
For example, see Billy Nauman (How Passive Investment Dulls the Green Wave, Financial Times,
February 7, 2022, https://www.ft.com/content/ abd2a946-48d5-11ea-aee2-9ddbdc86190d). This problem
is also related to the passive funds’ incentive problem of underinvestment in stewardship (see Bebchukand Hirst, 2019).
4
See the literature cited in Corum, Malenko, and Malenko (pages 2—3, 2021). Indeed, Fichner,
Heemskerk, and Garcia-Bernardo (2017) find that the top three US passive index fund companies that arelarge stakeholders in most of the Standard & Poor’s (S&P) 500 firms–BlackRock, Vanguard, and State
Street–do use coordinated voting strategies and influence the management of their invested companies
through private engagements. McCahery, Sautner, and Starks (2016) report that large institutional in-3managers is becoming increasingly important.
This paper considers the governance role of profit-motivated managers of S- and P-funds
when they must attract capital from investors with ESG preferences. The governance roleof both fund managers is twofold: first, to engage in the management of their portfolio
to improve ESG performance (i.e., to reduce any negative externalities), and second,
to improve pecuniary returns. Both the eﬀorts to reduce the portfolio firms’ negative
externalities and to increase their pecuniary returns are referred to as the fund manager’s
engagement eﬀorts.
In this setting, we address the following questions. First, how does growing interest
in ESG aﬀect the negative externalities and pecuniary returns of various types of firms
through a change in the S- and P-fund managers’ engagement eﬀorts toward their portfolio
firms? Does growing interest in ESG really have a counterproductive eﬀect in the presenceof S- and P-funds? Second, we address the same questions when the impact of ownershipengagement regarding ESG in firms with high-ESG performance is limited and further
decreases relative to that in firms with low-ESG performance. It is our understandingthat this paper is the first theoretical paper to examine how fund managers’ engagement
eﬀorts toward their portfolio firms aﬀect the negative externalities and pecuniary returns
for various types of firms in the presence of S- and P-funds under growing interest in ESG,or the increasing tendency for shareholder ESG engagement to have a limited impact onfirms with high-ESG performance. Finally, we examine how the ownership engagement
eﬀorts are aﬀected when the cost of such eﬀorts for each fund manager decreases.
To address these questions, we build an asset management market model in which
ESG-conscious fund investors allocate their wealth between an S-fund, a P-fund, andoutside investment opportunities, such as public bonds. These fund investors can invest
their wealth in firms only via funds.5 However, these funds are managed by for-profit
fund managers who may not be keen on ESG. If fund investors decide to invest in an
S-fund, P-fund, or both, they must search for these funds, which incurs a search cost.
After matching, fund investors and the fund manager bargain over the asset management
fee. Then, the fund manager invests in firms that diﬀer in the sustainability of theirvestors with a longer time horizon and less concern about stock liquidity intervene more intensively withmanagement through private engagements.
5
We also consider liquidity investors, who directly invest in firms for various reasons but do not engage
in the governance of the firms.

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activities; the S-fund buys only the stocks of firms with high-ESG performance and the
P-fund invests all of its money in the value-weighted market portfolio.6 After investing,each fund manager chooses his costly ownership engagement eﬀort levels to mitigate thenegative externalities and to increase the profits of his portfolio firms.
Our first main results are as follows. When investors’ ESG preferences are strengthening, the following three results are obtained. (i) If the investors are not very ESG
conscious, the expected negative externality decreases but the expected profit increases
for the high-ESG firms (hereafter referred to as G-firms) and all the firms in the market
portfolio. (ii) When the investors are highly ESG conscious, the expected negative externality may decrease for G-firms and all the firms in the market portfolio. This occurs
where the S-fund managers have a comparative advantage over the P-fund managers in
improving firms’ profit performance over improving their ESG performance. (iii) Growinginterest in ESG always reduces the expected negative externalities but raises the expected
profit for the low-ESG firms (B-firms).
The intuition behind these results is broken down into two parts: the direct eﬀect andthe fund ownership eﬀect. To delineate the direct eﬀect, note that the fund manager’s
engagement eﬀorts are determined at the point where his expected marginal return equals
his marginal cost of eﬀort.7 As the eﬀort cost parameters are fixed, the fund manager’s
incentives are determined by his expected marginal return. For the ESG engagement
eﬀort, this is equal to the (degree of investors’ ESG preferences)×(fund fee)×(fund ownership stake) established under bargaining between investors and the fund manager. Thus,
stronger ESG preferences of investors directly raise fund managers’ incentives for ESG effort. Later, we show that growing interest in ESG does not aﬀect the asset management
fee of either type of fund. However, the fund ownership eﬀect that occurs through achange in the fund ownership stake is more complicated, as it involves investors’ capital
allocation among assets.
Indeed, if the ESG preferences of investors are not strong initially, fund investors’
allocation of their wealth to both the S- and P-funds increases when the ESG preferencesof investors are strengthened. This increases the S-fund (P-fund) ownership stake in G6

In Appendix B.2, we introduce a non-sustainable fund that buys only the stocks of firms with low-ESG
performance. Under certain conditions, our main results are unaﬀected.
7This holds for the eﬀort to reduce the negative externality and the eﬀort to increase pecuniary returns
for both the S- and P-funds.

5firms (both G- and B-firms) and reduces the ownership of liquidity investors in both Gand B-firms. This ownership change motivates both the S- and P-fund managers to exert
more eﬀorts on their portfolio firms, thus reducing the negative expected externalities andraising the expected profit for each firm. Note that the liquidity investors do not makeengagement eﬀorts.
By contrast, if the ESG preference of investors is initially strong, the fund investors may
allocate less of their wealth to the S-fund as the ESG preference of investors increases,
because the fund investors’ rate of expected return from the S-fund may decrease. Then,the fund ownership eﬀect arising from the reduction of the S-fund’s ownership weakens
the S-fund manager’s engagement eﬀort levels. However, if the S-fund managers have acomparative advantage in improving profit performance over ESG performance to the Pfund managers, the fund ownership eﬀect from the reduction of ownership by the S-fund
is dominated by the eﬀect of the rise of ownership by the P-fund. Then, the expected
negative externality decreases for both G-firms and market portfolio firms. However, for
B-firms, the fund ownership eﬀect works only through the changes in the ownership of
the P-fund and liquidity investors. Consequently, growing interest in ESG always reduces
the expected negative externality but raises the expected profit.
Regarding the fund fee, a strengthened ESG preference of investors changes fund investors’ expected returns for both funds because it aﬀects the expected disutilities ofinvestors. However, the eﬀects of such changes are canceled out by the changes in the
expected profits of their portfolio firms to restore capital allocation conditions in equilibrium. Hence, a growing interest in ESG has no eﬀect on fund investors’ expected rates
of returns for either type of funds, which implies that it has no eﬀects on the fund feesfor either fund with such fees determined through bargaining when investors’ bargaining
power is fixed.
Our second main result examines what happens when the impact of shareholder engagement regarding ESG in G-firms is limited and decreases relative to that in B-firms.
The increasing tendency for shareholder ESG engagement to have a limited impact in Gfirms increases both the expected negative externality and the expected profit for G-firms
and market portfolio firms, but does not aﬀect the expected negative externality or the
expected profit for B-firms.
Intuitively, the increasing tendency for shareholder ESG engagement to have a limited
6

impact in G-firms directly weakens the incentives for ESG eﬀort for both S- and P-fundmanagers in G-firms, but it does not aﬀect this incentive for the P-fund managers in
B-firms. We also need to consider the impact on the fund managers’ eﬀort incentive ofa fund ownership eﬀect occurring through a change in fund ownership stakes. However,in this case, the fund investors’ expected rate of return can be adjusted in equilibrium
so that it does not change in either fund, although the fund ownership eﬀect operates
in G-firms. As a result, management fees for both the S- and P-funds are unaﬀected.
Furthermore, the increasing tendency for shareholder ESG engagement to have a limited
impact in G-firms has no eﬀect on the expected negative externality or the expected profit
for B-firms because it does not directly aﬀect the P-fund manager’s ESG eﬀort in B-firms,
and the fund ownership eﬀect does not operate in B-firms either.
Our third main result shows what happens when the ESG engagement cost becomes
lower for the S- and P-fund managers, respectively. For both G-firms and market portfolio
firms, in the case of either S- or P-funds, the reduction in the ESG engagement cost reduces
both the expected negative externality and the expected profit. For B-firms, the reductionin the ESG engagement cost for the P-fund managers reduces both the expected negative
externality and the expected profit.
Intuitively, the lower ESG engagement cost for one fund manager directly strengthens
his incentives for ESG eﬀorts, but it does not aﬀect these incentives for the other fundmanager, nor does it aﬀect the asset management fee for either fund. Hence, the arguments
for the case in which there is an increasing tendency for shareholder ESG engagement tohave a limited impact on G-firms apply to deriving the above result for G-firms andmarket portfolio firms. Furthermore, as the S-fund does not buy B-firms, only the lower
ESG engagement cost of the P-fund manager aﬀects B-firms.
The theoretical implications of our results are as follows. Given that growing interest
in ESG creates S-fund growth, our first results show that the eﬀect of S-fund growth on
the expected negative externality in the presence of the S- and P-funds depends on how
keen the investors are on ESG and/or on the comparative advantage between each fund in
improving ESG or achieving profit, because S-fund growth aﬀects fund ownership stakes.
Thus, under certain conditions, S-fund growth contributes to reducing the expected negative externality in all types of firms. However, if the conditions are not satisfied, S-fundgrowth may not contribute to reducing the expected negative externality except in the7case of B-firms. This is because the fund ownership eﬀect works, unlike the argument ofHartzmark and Shue (2023), which mainly depends on a limited ESG impact on G-firms.
The increasing tendency for shareholder ESG engagement to have a limited impact on
G-firms has a direct eﬀect on both the ESG eﬀorts of the S- and P-fund managers in
G-firms. Given a possible eﬀect from a change in fund ownership stakes, the derivation of
the results is not straightforward. However, we can show that the fund ownership eﬀect
works only in G-firms. Hence, the interaction of the direct eﬀect and the fund ownershipeﬀect in G-firms leads to our second result in the presence of the S- and P-funds.
Our results have several empirical implications as a result of imposing restrictions on
the model parameters that cause S- and P-funds to have diﬀerent types of costs andspecialize in diﬀerent types of engagement. To this end, we define expected financial
returns as [expected profit of the firm] - [price of the firm]. Suppose that improving ESG
performance can be achieved to a certain degree by setting broad, market-wide standards
for ESG, rather than focusing on firm-specific operational improvements. Then, as will
be discussed in Section 5, the S-fund has a more cost advantageous position to improve
profit performance over ESG performance compared with the P-fund.
Under this environment, growing interest in ESG always improves ESG performance inany type of firm, and is likely to increase expected financial returns in any type of firm
if investors’ ESG preferences are not strong initially. In addition, it creates a positive
association between ESG scores and the earnings before interest, taxes, depreciation,
and amortization (EBITDA) attained by any type of firm if investors are not very ESG
conscious initially. However, if these environmental conditions are not satisfied, thesepredictions do not necessarily hold.
Second, the increasing tendency for shareholder ESG engagement to have a limited
impact on firms with high-ESG scores reduces ESG performance, but improves expectedfinancial returns in firms with high-ESG scores and all the firms in the market portfolio. Furthermore, it causes a negative association between ESG scores and the EBITDA
attained by firms with high-ESG scores and all the firms in the market portfolio.
Third, the lower ESG engagement cost of the S-fund (P-fund) improves ESG performance but reduces expected financial returns in firms with high-ESG scores and all thefirms in the market portfolio (in any type of firm). The lower engagement costs of the
S-fund (P-fund) also cause a negative association between ESG scores and the EBITDA
8attained by firms with high-ESG scores and all the firms in the market portfolio (by any
type of firm).
The remainder of the paper is organized as follows. Section 2 reviews the related literature, and Section 3 presents the basic model. Sections 4.1 and 4.2 examine fund managers’
eﬀorts and trading decisions, taking management fees and investment decisions by fundinvestors as given. Section 4.3 derives the asset management fees and the investment allocation decisions by fund investors. Section 4.4 characterizes the equilibrium and Section
4.5 discusses the comparative static results. Section 5 considers the empirical implications of our main results. The final section concludes the paper. Appendix A provides
the proofs of all propositions. Appendix B discusses the robustness of our main resultsin the case of multiple S- and P-funds and in the presence of non-sustainable funds, andprovides additional comparative static results regarding P-fund growth.
2. Related Literature
The analysis in this paper is related to the delegated asset management literature on theinteraction between active and passive funds in general equilibrium (Gârleanu and Pedersen, 2018, and Corum, Malenko, and Malenko, 2021). In particular, by extending themodel of Gârleanu and Pedersen (2018) with shareholder engagement, Corum, Malenko,
and Malenko (2021) mainly examine how the fund managers’ governance incentives toimprove the expected profit of their portfolio firms are aﬀected by passive fund growthevidenced by a decrease in fund investors’ search costs for the P-fund.8 By contrast, basedon the model of Corum, Malenko, and Malenko (2021), we consider multiple task-settingby S- and P-fund managers who make engagement decisions to improve not only the expected profit but also the social performance (i.e., impact) of their portfolio firms wheninvestors have an ESG preference. Our paper focuses on how these engagement decisions
under the multitask setting are aﬀected by growing interest in ESG, the increasing tendency for shareholder ESG engagement to have a limited impact on high-ESG firms, andthe reduction in ESG engagement cost when investors have ESG concerns.
Our model is related to theoretical studies of sustainable investing and provides impli8

Kakhbod, Loginova, Malenko, and Malenko (2023) discuss the eﬀect of shareholder engagement;that is, shareholders communicating their views to management, under growing ownership by passively
managed funds. However, they do not consider the agency relationship between fund investors and fundmanagers.

9cations for the existence of socially responsible investors. Pástor, Stambaugh, and Taylor(2021b) derive an ESG factor in an equilibrium asset-pricing model when investors havean ESG preference. They show that sustainable investing brings about a positive social impact by making firms greener and by shifting real investment toward green firms.
Goldstein, Kopytov, Shen, and Xiang (2022) develop a rational expectations equilibrium
model with socially responsible and traditional for-profit investors, and suggest that anincrease in the fraction of socially responsible investors and an improvement in the ESG
information quality can reduce price informativeness about the financial payoﬀ and raise
the financial returns for investors.
Under the interaction between socially responsible investors and traditional for-profit
investors when firms are subject to financing constraints, several papers consider the effect of socially responsible investors providing more capital to sustainable investment.
Chowdhry, Davies, and Waters (2019) indicate that socially responsible investors must
hold financial claims to counterbalance project owners’ tendencies to overemphasize profits, if project owners cannot commit to social objectives when they finance capital fromprofit-motivated investors alone. Green and Roth (2021) examine the situation in whichsocially responsible and commercial investors compete to finance for-profit entrepreneurs,
and characterize alternative strategies for socially responsible investors that result inhigher social welfare and higher financial returns. Oehmke and Opp (2020) identify optimal investment choices for socially responsible investors who bargain with the entrepreneur with ESG preferences, and show that socially responsible and for-profit financial
investors are complementary. Using the model in which entrepreneurs search for capital,
Landier and Lovo (2022) indicate that a firm’s incentive to reduce negative externalities
increases with the size of socially responsible capital.
Heinkel, Kraus, and Zechner (2001) and Edmans, Levit, and Schneemeier (2022) derive conditions concerning whether holding stocks of a “brown” firm taking a corrective
action dominates divestment of stocks of “brown” firms. Broccardo, Hart, and Zingales(2022) find that engagement (i.e., through voting rights) is more eﬀective than divesting
stocks to make firms internalize negative externalities. Inderst and Opp (2022) investigate
a situation in which the social planner sets a minimum susceptibility standard that all
investment and production must satisfy, and ask whether such labeling is socially optimal. Hartzmark and Shue (2022) discuss that the current sustainable investment strategy
10mainly rewards green firms for trivial reductions in their already low levels of emissions.
By contrast, our paper is the first to consider how the expected negative externality andthe expected profit of firms in the presence of the S- and P-funds vary with (i) investors’
ESG preferences, (ii) the limited impact of shareholder ESG engagement in high-ESG
firms, and (iii) the ESG engagement cost for each fund manager. In particular, these
problems are examined not only when profit-motivated fund managers face a multitask
agency situation where they exert engagement eﬀorts to improve ESG and profit levels forsocially responsible investors, but also when the impact of shareholder ESG engagementin high-ESG firms is limited. Although the direct eﬀects of the key parameters in these
problems have important eﬀects, one of the significant factors in our paper is the interaction of the fund investors’ reallocation of investments across assets and the fund managers’
reallocation of engagement eﬀorts across tasks, which may lead to S-fund growth failingto contribute to improving ESG performance.
3. The Basic Model
3.1. Firms, fund managers, and investors.–
The model considers a single period, from time 0 to time 1, in which there are three typesof agents: fund managers, who invest in firms on behalf of fund investors but are purelyinterested in their monetary payoﬀs; fund investors, who indirectly invest in firms throughthe fund managers and consider both firm profit and ESG performances; and liquidity
investors, who directly invest in firms for various reasons, and consider both firm profit
and ESG performances. In Appendix B.2, we extend the basic model by incorporating
non-socially responsible investors, who do not care about ESG performance. All agentsare risk neutral.
There is a mass one of firms with observable high-ESG performance (which we referto as G-firms), and a mass one of firms with observable low-ESG performance (B-firms).
G-firms generate lower negative externalities (e.g., they are cleaner and pollute the environment less) than B-firms. We index G-firms (B-firms) by Gj ∈ [0, 1] (Bj ∈ [0, 1]).

Each firm’s stock is in unit supply because the initial owners of the firm have suﬃciently
low valuations such that they are willing to sell their shares regardless of the price.

11

The observable profit of firm Gj is represented by
MGjeGj ≡ RGj + ²RGj = R0 + P eiGj + ²RGj ,
R

(1)

i=1

where R0 is the base profit without shareholder engagement, MGj is the number of shareholders of firm Gj , eiGj is the amount of unobservable eﬀort exerted by shareholder i to
improve the profit of firm Gj , and ²RGj is unobservable noise that has a mean of zero.9
Similarly, the observable profit of firm Bj is
MBjeB ≡ RB + ²BG = R0 + P eiB + ²RB ,
R
j
j
j
j
j

(2)

i=1

where MBj is the number of shareholders of firm Bj , eiBj is the amount of unobservableeﬀort exerted by shareholder i to improve the profit of firm Bj , and ²RBj is the unobservable noise that has mean zero. For simplicity, note that the base profit is the same forboth G- and B-firms.
The observable negative externality released by firm Gj is given by
MGj

P
aiGj + ²ZGj ,ZeGj ≡ ZGj + ²ZGj = ZG0 − λ

(3)

i=1

where ZG0 is the negative externality of G-firms without shareholder engagement, λ ∈ [0,1) is a constant parameter, aiGj is the amount of unobservable eﬀort exerted by shareholder
i to improve the ESG performance of firm Gj , and ²ZGj is the unobservable noise thathas mean zero. Similarly, the observable negative externality released by firm Bj is
MBj

PZeBj ≡ ZBj + ²ZBj = ZB0 −aiBj + ²ZBj ,

(4)

i=1

where ZB0 is the negative externality of B-firms without shareholder engagement, aiBj isthe amount of unobservable eﬀort exerted by shareholder i to improve the ESG performance of firm Bj , and ²ZBj is the unobservable noise that has mean zero.
9
The noise terms ²RGj and ²RBj (²ZGj and ²ZBj ) prevent fund investors from stipulating eiGj andeiBj (aiGj and aiBj ) for i ∈ (S, P ) for their fund managers directly by observing RGj and RBj (ZGj andZBj ).

12

It follows from (3) and (4) that in response to an increase in the eﬀort of each shareholder, there is a marginal improvement in the ESG performance of G-firms that is smaller
than that of B-firms. Thus, λ indicates the limited impact in G-firms relative to B-firms
in response to each fund manager’s ESG eﬀort. This formulation reflects the observationthat the shareholder eﬀort would be more valuable for firms that lag behind in terms of
ESG; that is, for B-firms (for empirical evidence, see Hartzmark and Shue, 2023).
We assume that ²RGj , ²RBj , ²ZGj , and ²ZBj are distributed independently. It follows
eGj , ReBj , ZeGj , andfrom (1)—(4) that RGj , RBj , ZGj , and ZBj are the expected values of R

ZeBj , respectively. As G-firms have better ESG performance than B-firms, we focus on
the case of ZGj > ZBj , which implicitly assumes that ZB0 is suﬃciently larger than ZG0 .

In the subsequent analysis, we focus on the case of (ZGj , ZBj ) > 0.

We assume that the stocks of firms can be accessed by fund investors only throughtwo fund types: namely, S-funds and P-funds. For simplicity, there is one fund managerof each type of fund, although we can easily extend to any number of S-funds and Pfunds, NS and NP .10 The S-fund is restricted to holding stocks of firms with high-ESG
performance, whereas the P-fund is restricted to holding a value-weighted portfolio of
all stocks according to a mechanical rule. In our framework, the S-fund can be taken as
either sustainable active funds or ESG-indexed funds. In Appendix B.2, we consider a nonsustainable fund (N-fund) that only invests in stocks of firms with low-ESG performance.
The fund manager of each fund oﬀers to invest the wealth of fund investors in stocks offirms in exchange for an asset management fee.
The fund manager of type i ∈ (S, P ) chooses the amount of unobservable eﬀorts(eihj , aihj ) to improve the profit and ESG performance of his portfolio firms hj at time 0,

where h ∈ (G, B). If he exerts an eﬀort regarding the firm profit eihj , he incurs a private

cost cRi (eihj ) for i ∈ (S, P ) and h ∈ (G, B). However, if he exerts an eﬀort regarding ESG

performance aihj , he incurs a private cost cZi (aihj ) for i ∈ (S, P ) and h ∈ (G, B). We
assume that cki (0) = 0, c0ki (·) > 0, c00ki (·) > 0, c0ki (0) = 0, and c0ki (∞) = ∞ for k ∈ (R, Z)

and i ∈ (S, P ). These standard assumptions ensure an interior solution to (eihj , aihj ) fori ∈ (S, P ) and h ∈ (G, B).
10

Although we extend our model to the case of multiple S- and P-funds, the only things that matterfor fund managers’ engagements with portfolio firms are the combined holdings of all S-funds and thoseof all P-funds. The individual fund’s ownership stakes do not matter; therefore, our results continue tohold. See Appendix B.1 for further details.

13

The eﬀort eihj (aihj ) exerted by the fund manager i for i ∈ (S, P ) and h ∈ (G, B)

includes any actions, such as communicating with management, submitting shareholder
proposals, nominating directors, and voting on proxy contests. Although large P-funds
charge substantially smaller management fees than actively managed funds, the large
amount of assets under their management and ownership stakes can compensate for their
low management fees and strongly incentivize their fund managers to exert managerial
eﬀort (see Brav, Malenko, and Malenko, 2022, for a numerical discussion; and Kahn andRock, 2020, and Lewellen and Lewellen, 2022, for empirical evidence regarding financial
incentives of P-funds). In particular, recently, fund managers of large P-funds have been
involved in engagement through voting and communications with management (see theliterature review of Section 4.2 in Brav, Malenko, and Malenko, 2022, for the empiricalevidence). Hence, greater ownership of P-funds has various eﬀects on governance. In thesubsequent analysis, we focus on the case of (eSGj , aSGj ) > 0 and (eP hj , aP hj ) > 0 for h ∈(G, B) and any j. Note that the S-fund does not hold stakes in B-firms.

There is a large mass of homogeneous fund investors, who have a certain amount ofwealth to invest, ε.11 We denote their aggregate wealth by W , which is given exogenously. Although fund investors want to receive more pecuniary investment returns, theyalso derive disutility from holding stocks of firms generating negative externalities. For
simplicity, we assume that the amount of disutility incurred by fund investors per unit of
their stock holdings is equal to η × (the negative externality generated by their holding

firms per unit of their stock holdings), where η (> 0) is a scalar measuring the degree ofinvestors’ “ESG” preference.12

At time 0, each fund investor chooses whether to invest in the S-fund and/or the P-fund
by delegating her wealth to the fund manager, and whether to invest in an alternative
investment opportunity such as public bonds that generates a fixed return of 0. Wheneach fund investor with wealth ε seeks an S-fund (a P-fund) manager, she must search forand vet fund managers by incurring a search cost ψS ε (ψP ε). Fund investors are assumed
11

Fund investors typically include pension funds, sovereign wealth funds, and wealthy retail investors
who have invested in family oﬃces in which hedge funds manage their covert operations.
12
The utility of fund investors depends on the pecuniary returns that they receive and the social value
created by firms they have financed through funds. Green and Roth (2021) refer to these investors asvalue-aligned social investors. The assumption that investors prefer socially responsible performance issupported by empirical studies in the mutual fund literature. For example, see Riedl and Smeets (2017)
and Hartzmark and Sussman (2019).

14

to be homogeneous; therefore, they incur the same search cost ψS ε (ψP ε) when they try tofind an S-fund (a P-fund) manager. Thus, the proportional parameter ε can be interpreted
as a normalization by adjusting the scale of ψS and ψP . These costs indicate that mostfund investors must spend significant resources to find a fund manager whom they trustwith their money, and to examine the funds’ investment strategies and fee structures.13
We assume that ψS ≥ ψP . This assumption can be justified because it takes more timeand eﬀort to understand the investment strategy and fee structure of an S-fund than thatof a P-fund.
After a fund investor finds a fund manager i ∈ (S, P ), they negotiate the fee fi throughgeneralized Nash bargaining at time 0.14 The fund manager of the S-fund (P-fund) has

bargaining power ωS (ωP ) ∈ (0, 1), whereas the fund investor has bargaining power 1 −ωS (1− ωP ). We assume that the fee charged by the fund manager to the fund investor
is a fraction of the sum of the realized values of the profit and the disutility of the negative externality of their portfolio firms, which is assumed to be observable. The pecuniary
amount deducted from the fund manager’s compensation as a result of the negative externality arises directly from bargaining between the fund manager and the fund investor.15
However, it may be viewed as the fund manager’s reward reduction being tied to ESG
criteria and/or the fund manager’s reputation loss from the nonaccomplishment of directcontract commitments on ESG goals or from public sentiment that the fund manager may
impair improvement in firms’ ESG performance.
Finally, there is a large mass of liquidity investors, who directly invest in firms at time
0 for various reasons, such as liquidity need, hedging demand, firms’ issuance, repurchase of shares, or investor sentiment, although they also incur a disutility of amount as
η × (the negative externality generated by their holding firms per unit of their holding

stocks).16 Liquidity investors apply rational expectations in predicting the value of each13

For more information, see Corum, Malenko, and Malenko (2021) and the references listed in footnote
9 in their text.
14
This assumption is also made in Gârleanu and Pedersen (2018) and Corum, Malenko, and Malenko(2021).
15
Note that the deduction amount, fi × (the disutility of the negative externality), in turn, increases
the pecuniary payoﬀ of fund investors, while decreasing the pecuniary payoﬀ of the fund manager. In
addition, the fund manager’s payoﬀ is positive even though this amount is deducted because we impose
the assumption, as discussed below, that the stock price is always positive. Adachi-Sato (2022) clarifies
that a profit-oriented agent pursues improvement in ESG performance under the bargaining between asocially and environmentally aware principal and the agent.
16
These traders include insurance companies and retail investors.

15

stock. However, their valuation is perturbed by an additional factor that captures theamount of liquidity need, hedging demand, firms’ issuance, repurchase of shares, or investor sentiment. As a result, liquidity investors’ expectation of the value of the stockof each firm is equal to the sum of the expected values of the profit and the disutilityof the negative externality generated by the firm hj , Rhj − ηZhj , minus the additional

component, Lhj > 0; that is, Rhj − ηZhj − Lhj for h ∈ (G, B).17
3.2. Equilibrium.–

The equilibrium includes the search and investment allocation strategies of fund investors, management fees, each agent’s trading strategy, each fund manager’s engagement
eﬀort strategy, and the market clearing price, as follows.
At the beginning of time 0, fund investors make their search and investment allocation
decisions with the aim of maximizing the sum of their expected profit and their expected
disutility from negative externalities minus the search cost. After a fund investor finds afund manager, they negotiate the management fee through generalized Nash bargaining.
Then, each fund manager invests the delegated amount of fund investors’ wealth in stocks
according to the trading strategy of each fund, as described below. First, the S-fund isrestricted to holding stocks of firms with high-ESG performance. Specifically, we assume
that the S-fund manager invests only in G-firms. Second, the P-fund is restricted toholding a value-weighted portfolio of all stocks according to a mechanical rule.
However, liquidity investors trade according to their predictions about the stock priceof each firm. Their predictions are made by anticipating the equilibrium eﬀort of fundmanagers under rational expectations.
After trading, each fund manager selects his eﬀort at time 0 to maximize his expectedcompensation minus his eﬀort cost by improving the profit and ESG performance of his
portfolio firms, given his management fee.
Finally, at time 1, the profit and negative externality generated by each firm is realized.
Then, the payoﬀs of the fund manager and fund investors in each fund are determinedaccording to the management fee.
The stock price of each firm is set to clear the market at time 0. Short sales are ruledout. We restrict our analysis to the case in which liquidity investors hold at least some17

All of our results continue to hold even when LGj = LBj .

16

shares of each type of stock.18 The assessment of both the S-fund and the P-fund of eachstock h ∈ (G, B) reflect the fund investors’ valuation of the stock h, which is higher thanthat of the liquidity investors; therefore, the market clearing price of stock h ∈ (G, B)

may be determined by the liquidity investors’ assessment of stock h.19
Figure 1 illustrates the model timing.
4. The Analysis

We solve this model by backward induction. First, we determine the eﬀort decisionsof fund managers and examine the trading decisions of liquidity investors and fund managers. Then, we clarify the investment allocation decisions of fund investors and thedetermination of asset management fees. Finally, the equilibrium is defined as a set ofthese decisions and market clearing conditions.
We drop the subscript j from each variable in the subsequent discussions because Gfirms (B-firms) are all homogeneous and because the S-fund finds it optimal to diversify
equally across all G-firms.20
4.1. Fund managers’ eﬀort decisions.–
Suppose that the S-fund manager charges the management fee fS , holds xSG shares,
and exerts the eﬀorts (eSG , aSG ). Then, the S-fund manager’s expected payoﬀ is given by
fS xSG (RG − ηZG ) − cRS (eSG ) − cZS (aSG ).

(5)

Note that the S-fund holds only the stock of the G-firm, and that the sum of the expected
profit and the expected disutility from the negative externality of the G-firm is RG −
ηZG . As discussed in Section 3.1, note that the fund manager’s compensation includes

the pecuniary amount deducted as a result of the negative externality.
Next, suppose that the P-fund manager charges the management fee fP , holds xP hshares, and exerts the eﬀorts (eP h , aP h ) for h ∈ (G, B). Then, the P-fund manager’s
18

Proposition 1 provides a suﬃcient condition for this to hold.
For an alternative justification, we can assume that the S- and P-funds submit a market order,
whereas liquidity investors submit a limit order reflecting their valuation of each stock.
20
We provide a suﬃcient condition for this in Proposition 1.
19

17

expected payoﬀ from firm h is given by
fP xP h (Rh − ηZh ) − cRP (eP h ) − cZP (aP h ),for h ∈ (G, B).

(6)

Note that the P-fund holds stocks of both the G-firm and the B-firm, and that the sumof the expected profit and the expected disutility from the negative externality of firm h
is Rh − ηZh for h ∈ (G, B).

For simplicity, we assume that cRi (eih ) and cZi (aih ) are quadratic; that is,cRi (e) =

cRi 2
cZi 2
e and cZi (a) =a,2
2for i ∈ (S, P ),(7)

where cRi > 0 and cZi > 0 for i ∈ (S, P ). Then, it follows from (1)—(4) that maximizing(5) and (6) yields the following first-order conditions; that is, the optimal eﬀort decisionsof the S- and P-fund managers satisfyeSG =eP h =

fS xSG
ηλfS xSG
and aSG =
,
cRS
cZS

fP xP hηλh fP xP h
and aP h =
,
cRP
cZP

for h ∈ (G, B),

(8)

(9)

where λG = λ and λB = 1. Next, (8) and (9) imply the following: (i) each fund manager
exerts more eﬀort regarding both firm profit and ESG performance in all firms if he holds
more shares of his portfolio firms (i.e., higher xih ) and/or if his management fee is higher(i.e., higher fi ); (ii) each fund manager exerts more eﬀort regarding ESG performance inall firms if the degree of investors’ ESG preference is larger (i.e., larger η); and (iii) eachfund manager exerts more eﬀort regarding ESG performance in G-firms if his eﬀort ismore valuable in G-firms (i.e., higher λ).
4.2. Trading decisions.–
In making their trading decisions, liquidity investors and fund managers rationally
anticipate the fund managers’ eﬀort decisions given by (8) and (9).
Under rational expectations, if liquidity investors expect the S- and P-funds to holdxSG and xP G shares in G-firms, it follows from (1), (3), (8), and (9) that the liquidity

18

investors’ assessment of the stock of G-firms is¶µ
fS xSG fP xP G
ηλfS xSG
ηλfP xP G
RG −ηZG −LG = R0 +−LG . (10)+−η ZG0 − λ
−λ
cRS
cRP
cZS
cZP
Similarly, using (2), (4), and (9), liquidity investors’ assessment of the stock of B-firms is¶µfP xP BηfP xP B
RB − ηZB − LB = R0 +− LB .
− η ZB0 −
cRP
cZP

(11)

Note that the S-fund holds only the stock of G-firms.
Each liquidity investor purchases stock h ∈ (G, B) if his valuation exceeds the price;that is, Rh − ηZh − Lh ≥ Ph for h ∈ (G, B). We focus on the case in which liquidity

investors hold at least some shares of stocks in each type of firm; that is, G- and B-firms.
As mentioned at the end of Section 3.2, this implies that the market clearing price ofstock h ∈ (G, B) is determined by the liquidity investors’ assessment of stock h:
Ph = Rh − ηZh − Lh ,for h ∈ (G, B),(12)

where Rh − ηZh − Lh for h ∈ (G, B) is given by (10) and (11). Here, we assume that R0> max (ηZG0 + LG , ηZB0 + LB ), which is also provided in Proposition 1. Given (10) and(11), this assumption ensures that the price of each stock is always positive.
To characterize the trading decisions of the S- and P-funds, let WS and WP denote thesizes of the S- and P-funds, respectively, which are endogenously determined in equilibrium. The S- and P-fund managers use all of WS and WP delegated to them as long asliquidity investors hold at least positive shares of stocks of each firm.21
The S-fund invests only in G-firms. As mentioned, the S-fund finds it optimal todiversify equally across all G-firms. Given that the S-fund can use all WS to purchasexSG units of the stock of G-firms, we have
xSG =
21

WS
.
PG

(13)

Note that these fund managers evaluate each stock more highly than do liquidity investors or submit
a market order.

19

Because of (12), note that
PG = RG − ηZG − LG .

(14)

The P-fund is restricted to holding a value-weighted portfolio of all stocks, with thismarket portfolio denoted by index M. As there is a mass one of G-firms and a mass
R1
R1
one of B-firms, the price of the market portfolio is PM = 0 PG dj + 0 PB dj = PG + PB .

The P-fund purchases xP h units of stock h according to the market portfolio rule, underwhich the proportion of the amount invested in stock h in the fund, xPWhPPh , equals theweight of this stock in the market portfolio, PPMh . This implies that xP h is the same forany h ∈ (G, B) and is equal to

xP =

WP
.
PM

(15)

Furthermore, let RM = RG + RB , ZM = ZG + ZB , and LM = LG + LB . Then, it follows
from (10)—(12) with xP h = xP for any h ∈ (G, B) thatPM = RM − ηZM − LM ,

(16)

where
¶
µ
fS xSG fP xP
ηλfS xSG
ηλfP xP
RM − ηZM − LM = R0 ++− η ZG0 − λ
−λ
cRS
cRP
cZS
cZP
¶
µ
fP xP
ηfP xP− LM .
− η ZB0 −(17)+ R0 +cRP
cZP
Note that from (9) and (15), eP h is the same for any h ∈ (G, B). Thus, (9) is rewritten
so that

eP =

fP xP
ηλh fP xP
and aP =,cRP
cZP

for h ∈ (G, B),(90 )where λG = λ and λB = 1.
4.3. Investment allocation decisions and asset management fees.–
Now, we discuss the investment allocation decision by infinitesimal fund investors, whochoose between investing in the S-fund and/or the P-fund and investing in an alternative
investment opportunity, such as public bonds, that generates the fixed return 0. To
this end, we begin by examining fund investors’ indiﬀerence conditions regarding the20

investment allocation. Consider a fund investor with wealth ε. If the fund investor invests
with the S-fund, the fund manager buys PεG stocks. Then, the fund investor’s expected
payoﬀ is (RG − ηZG ) PεG − fS (RG − ηZG ) PεG − ψS ε = (1 − fS )(RG − ηZG ) PεG − ψS εbecause she incurs a search cost ψS ε and pays the fee fS . Similarly, the fund investor’s

expected payoﬀ with the P-fund is (1 − fP )(RM − ηZM ) PεM − ψP ε.

Under the condition of Proposition 1 derived below, we can ensure that WS + WP <W if the aggregate wealth of fund investors such as pension funds is suﬃciently largethat they purchase public bonds. Then, fund investors make a positive investment inpublic funds with the fixed return of 0. This implies that fund investors earn the samerate of expected net return regardless of whether they invest with S- or P-funds, and thisexpected net return is equal to 1.22 Specifically, the fund investors’ indiﬀerence conditionsare(1 − fS )RG − ηZG
RM − ηZM− ψS = (1 − fP )− ψP = 1.
PG
PM

(18)

Next, we deal with bargaining in the S-fund. After a fund investor with wealth ε incurs
the cost ψS ε and finds an appropriate S-fund, she bargains with the S-fund manager overthe fee fbS . The outcome of the bargaining depends on each player’s expected payoﬀ in
the event of agreement and no agreement. If the fund investor and the fund manager
agree on the fee fbS , the fund investor’s expected payoﬀ is (1 − fbS )(RG − ηZG ) ε . If
PG

no agreement is reached, the fund investor can either find the P-fund by incurring thecost ψP ε and invest with the P-fund or invest in the alternative investment opportunity.

Under (18), the P-fund yields the same rate of net return 1 for the fund investor as thealternative investment opportunity so that her expected payoﬀ is ε when no agreement isreached.
To specify the fund manager’s expected payoﬀ, we must provide his additional expected
payoﬀ from agreeing on the fee fbS and obtaining the additional funds ε. The additional

expected payoﬀ is represented by fbS (RG − ηZG ) PεG .23 However, the fund manager’s gain
22This assumption forces us to neglect the case where the rates of net return from investing with the Sand P-funds are larger than 1, which is analyzed by Corum, Malenko, and Malenko (2021). However, theassumption enables us to focus on the eﬀects that occur through the eﬀort decisions of fund managers on
multiple tasks under the negative externality released by their portfolio firms.
23
By adding ε to the fund with xSG , it follows from (1), (3), and (90 ) that the expected payoﬀ of the
xP
fP xP
P xP
b
S-fund manager is max {fS [RG0 + e + fcPRP− η(ZG0 − λa − λ ηλfcZP )]xSG + fS [RG0 + e + cRP −
e,a

ε
P xP
η(ZG0 − λa − λ ηλfcZP )] PG − cRS (e) − cZS (a)}. Using the envelope theorem, the derivative with respect

21

from no agreement is zero.
Given the fund manager’s (investor’s) bargaining power ωS (1 − ωS ), the bargaining

outcome maximizes the product of the expected payoﬀ gains from agreement with respect
to fbS :∙¸ω¸1−ωS ∙εε S
bbfS (RG − ηZG )−ε.
max (1 − fS )(RG − ηZG )
PG
PG
fS
The solution must satisfy

∙
¸
ε
ε
b
fS (RG − ηZG )= ωS (RG − ηZG )
−ε .
PG
PG

As the S-fund fee is the same for all fund investors, we have fbS = fS . Thus,µfS = ωS 1 −PG
RG − ηZG

¶

.

(19)

Similarly, the P-fund fee is the same for all investors, and is given byµfP = ωP 1 −PM
RM − ηZM

¶

.

(20)

4.4. Characterization of equilibrium.–
The equilibrium is defined as a solution to the following system of equations: (i) thefund managers’ eﬀort decisions (8) and (90 ); market clearing conditions (10) and (13)—(17);fund investors’ capital allocation conditions (18); and fee bargaining conditions (19) and(20). These equations determine the following endogenous variables: the fund managers’
eﬀort decisions, (eSG , aSG , eP , aP G , aP B ); the asset management fees, (fS , fP ); the trading
decisions and investment asset allocations, (xSG , xP , WS , WP ); the total expected payoﬀs,(RG − ηZG , RM − ηZM ); and the asset prices, (PG , PM ).

Now, we obtain the following proposition that characterizes the equilibrium.

Proposition 1: Suppose that R0 > max (ηZB0 + LB , ηZG0 + LG ) and R0 − ηZG0 − LG

> W ≥ W , where W is given by (A9) in Appendix A. Then, we have the following.

S ψS
P ψP
and fP = ψPω+1−ω, and fS ≥ fP if ωS(i) The asset management fees are fS = ψSω+1−ω
SP≥ ωP .

xP
1
P xP
b (RG −ηZG ) .
to ε at ε = 0 yields fbS [RG0 + e + fcPRP− η(ZG0 − λa − λ ηλfcZP )] PG = fS
PG

22

S
(ii) The expected profit of G-stocks and the market portfolio are RG = ψS +1−ωLG + ηZG
ψS
P
and RM = ψP +1−ωLM + ηZM .
ψP(iii) The expected negative externalities generated by B-firms, G-firms, and the firms included in the market portfolio satisfy the following equations:
ZB + ZG = ZM ,

(21)

cRS
cRP
(2RG − RM ) − ηλ2(RM − RG − R0 ),
(22)
cZS
cZP
cRS
cRP
cRP
ZM = ZG0 + ZB0 − ηλ2(2RG − RM ) − ηλ2(RM − RG − R0 ) − η(RM − RG − R0 ),
cZS
cZP
cZP
(23)
ZG = ZG0 − ηλ2where RG and RM are given above.
SP
LG and PM = 1−ω
LM .
(iv) The prices of G-stocks and the market portfolio are PG = 1−ωψSψPThe restrictions R0 > max (ηZB0 + LB , ηZG0 + LG ), R0 − ηZG0 − LG > W , and W ≥W ensure that the liquidity investors’ holding ratio in each stock is positive, that is, xSG+ xP < 1. The restriction R0 > ηZG0 + LG guarantees that the S-fund finds it optimal
to diversify equally across all G-firms. Finally, the restriction W ≥ W further ensuresthat fund investors make a positive investment in an alternative investment opportunity
such as public bonds; that is, WS + WP < W .
As WS + WP < W , fund investors’ aggregate wealth is relatively large. Then, theiroutside options in negotiations are eventually limited by an alternative investment opportunity such as public bonds with the fixed return 0.24 In addition, given ψS ≥ ψP , the fee
charged by the S-fund is higher than that charged by the P-fund if the bargaining powerof the S-fund manager is equal to or exceeds that of the P-fund manager.
Some recent studies indicate the limited or even counterproductive impact of S-funds
on ESG because high-ESG firms have little scope for further improvement in their impact,
whereas low-ESG firms, which face an increase in financing costs, must produce large negative externalities (e.g., see Hartzmark and Shue, 2023). In the present model, the limited
impact of the ESG performance in G-firms in response to each fund manager’s eﬀort iscaptured by λ ∈ [0, 1). Indeed, if λ = 0, it follows from (21)—(23) that the following
24

To be consistent with the assumption of R0 − ηZG0 − LG > W that ensures xSG + xP < 1, we needto suppose the situation where R0 is also suﬃciently large. Hence, our analysis may be less applicable tothe case where the economy faces a financial crisis such that R0 is not suﬃciently large.

23

corollary is derived.
Corollary to Proposition 1: If λ = 0, shareholder engagement does not aﬀect the expected negative externality generated by G-firms, but it does aﬀect the expected negative
externality generated by B-firms and the firms included in the market portfolio.
Intuitively, even if λ = 0, the P-fund manager’s ESG engagement eﬀort is still eﬀective
such that it aﬀects the expected negative externalities generated by B-firms and the firms
included in the market portfolio.
In the subsequent analysis, we focus on the case of λ ∈ (0, 1)
4.5. Comparative statics.–
We examine the eﬀects of the key parameters of the model on the expected negative
externalities, the expected profits, and the asset management fees. The key parameters
are the intensity of investors’ ESG preference, η, the improvement of the ESG performancein high-ESG firms relative to that in low-ESG firms in response to each fund manager’s
eﬀort, λ, and the eﬀort cost parameter of each fund manager in ESG, cZS and cZP .
We first consider how growing interest in ESG aﬀects the ESG and pecuniary performances of firms. Then, we obtain the following proposition.
Proposition 2: Suppose that investors’ ESG preferences are strengthened (i.e., η increases).
(i) The expected negative externality released by G-firms, ZG , decreases if η is not large> ccZP. The expected profit of G-firms, RG , increases if η is notor if η is large and ccRP
RS
ZS
large.
(ii) The expected negative externality released by B-firms, ZB , decreases, whereas the expected profit of B-firms, RB , increases.
(iii) The expected negative externality released by all the firms in the market portfolio,> ccZP, whereas the expected profit
ZM , decreases if η is not large or if η is large and ccRP
RS
ZS
for the market portfolio, RM , increases if η is not large.
(iv) The asset management fees of both funds are unaﬀected.
cRP
cRS

is equal to the eﬀort cost ratio of the P-fund to the S-fund for improving the profit

is this eﬀort cost ratio for improving the negative externality. Aof firms, whereas ccZP
ZS
( ccZP) implies that increasing profits (decreasing the negative externalities) oflarger ccRP
RS
ZS
24

the portfolio firms is relatively less costly for the S-fund than for the P-fund. Thus, the( ccZP) can be interpreted such that the S-fund has a greater cost advantage inlarger ccRP
RS
ZS
improving profit (ESG performance) than the P-fund.
Considering this interpretation, Propositions 2(i) and 2(iii) show that when η increases,
ZG and ZM decrease if η is not large, or if compared with the P-fund, the S-fund has agreater comparative advantage in improving profit performance over ESG performanceis larger than ccZP). Propositions 2(i) and 2(iii) indicate that when η increases,(i.e., if ccRP
RSZS
RG and RM increase if η is not large. Proposition 2(ii) also suggests that an increase inη always decreases ZB and increases RB . Proposition 2(iv) states that an increase in η
does not aﬀect either the fees of either the P-fund or the S-fund.
The intuition behind Proposition 2 is as follows. For convenience, we begin by considering the eﬀect of an increase in η on the expected negative externality and the expected
profit by taking the management fee of each fund as given. Later, we clarify the eﬀect of
an increase in η in considering its eﬀect on the asset management fees. Now, the eﬀort
incentive for each fund manager to reduce the negative externality in a firm not only
depends on η directly, but also on the fund ownership stakes in the firm, as indicated in(8) and (90 ). The direct eﬀect of an increase in η on the eﬀort incentive increases theengagement eﬀorts for the S- and P-fund managers aSG and aP to reduce the negative
externality, thus decreasing ZG , ZB , and ZM .
However, an increase in η changes the fund ownership stakes in each firm, i.e., the fundownership eﬀect exists. Suppose that η is not large. Then, an increase in η increases
is not large. The larger ηZG
the expected disutilities of fund investors, ηZ, because η dZdηand ηZM increase fund investors’ rate of expected gross return from each fund (note)/∂(ηZ) > 0, where P = R − ηZ − L). However, in equilibrium, fundthat ∂( R−ηZ
P
investors must be indiﬀerent between investing in each fund and the alternative investment
opportunity (see (18)). In fact, the larger RG and RM decrease fund investors’ rate of)/∂R < 0, where P = R − ηZ −expected gross return from each fund (note that ∂( R−ηZ
PL). Thus, to restore (18), RG and RM need to increase in response to increases in ηZG

and ηZM .
To this end, note that RG and RM increase with the fund managers’ eﬀorts eSG andeP . Because eSG and eP are determined by (8) and (90 ), each fund needs to increase
its ownership stakes in each firm, xSG and xP , until the fund investors’ rate of expected25

gross return from the fund decreases so that their rate of expected net return goes backto 1. This implies that fund investors increase their investment in the S-fund (P-fund)and enable the S-fund (P-fund) to take increasingly large ownership stakes xSG (xP ) in
G-firms (all the firms in the market portfolio). Thus, the increases in xSG and xP reduce
the ownership stakes held by liquidity investors; that is, 1 − xSG − xP in G-firms and 1− xP in the market portfolio.

The eﬀect of the decrease in 1 − xSG − xP reduces ZG and raises RG . The reason isthat if the S- and P-funds replace the liquidity investors’ ownership in G-firms, the overall
eﬀorts to reduce ZG and raise RG increase because liquidity investors do not make any
engagement eﬀorts. Similarly, the eﬀect of the decrease in 1 − xP reduces ZG and ZM

and raises RG and RM . Given that B-firms are bought only by the P-fund and liquidity
investors, such changes in the fund ownership stakes also reduce ZB and raise RB . Because
the direct eﬀect of an increase in η derived above decreases ZG , ZB , and ZM , both thedirect eﬀect and the ownership structure eﬀect are consistent with each other in this case.
By contrast, suppose that η is large. Then, an increase in η may reduce the expected
is large. Then, we can show that the funddisutilities of fund investors, ηZ, because η dZdηownership eﬀect from the change in xG increases ZG and ZM but decreases RG and RM ,although the fund ownership eﬀect from the change in xP still decreases ZB and increases
RB . However, as mentioned above, the direct eﬀect of an increase in η on the eﬀort
incentive reduces the expected negative externality of each firm. Thus, combining these
two eﬀects, we find that the eﬀect of an increase in η can be ambiguous in G-firms and> ccZP, the fund ownership eﬀect ofmarket portfolio firms in this case. However, if ccRP
RS
ZS
increasing ZG and ZM from the change in xG is smaller than that of decreasing ZG and
ZM from the change in xP . Then, an increase in η reduces both ZG and ZM . Furthermore,for B-firms, the fund ownership eﬀect works only through the changes in the ownershipof the P-fund and liquidity investors. Consequently, an increase in η always decreases ZB
and increases RB .
We return to examining the eﬀect of an increase in η on the asset management fee of
each fund. An increase in η changes the expected gross return earned by fund investors.
The reason is that an increase in η changes the expected disutilities of fund investors, ηZ,
as discussed above. However, given (14), (16), (19), and (20), note that fund investors’, depends on the expected profit of portfolio
rate of expected gross return, (1 − f ) R−ηZP
26

firms of the fund, R, minus the expected disutility of the negative externality released by
the firms, ηZ. When η increases, the eﬀect of the increase in η on the expected disutility iscanceled out by its eﬀect on the expected profit to restore fund investors’ capital allocation
conditions (18). This implies that the change in η has no eﬀect on the fund investors’rate of expected gross return, and thus has no eﬀect on the management fee of either fundwhen fund investors’ bargaining power is fixed.25
Now, we proceed to discuss the comparative statics of λ, which is taken as the limited
impact on G-firms in response to each fund manager’s ESG eﬀort. Then, we have thefollowing proposition.
Proposition 3: Suppose that the improvement of the ESG performance of G-firms relative to that of B-firms in response to each fund manager’s ESG eﬀort is further limited(i.e., λ decreases).
(i) The expected negative externality and the expected profit of G-firms, ZG and RG , increase.
(ii) The expected negative externality and the expected profit of B-firms, ZB and RB , areunaﬀected.
(iii) The expected negative externality and the expected profit of all the firms in the market
portfolio, ZM and RM , increase.
(iv) The asset management fees of both funds are unaﬀected.
Proposition 3 indicates that when λ decreases, the ESG performances on G-firms andof all the firms in the market portfolio are negatively aﬀected, whereas the profit performances of these firms are improved. However, neither ESG performance nor profit
performance in B-firms is aﬀected. In addition, the asset management fees of both funds
are unaﬀected.
The intuition for Proposition 3 is as follows. Again, suppose that the management fee
is taken as given. Then, the lower λ directly decreases both the S-fund manager’s ESG
eﬀort in G-firms (see aSG = ηλfcSZSxSG ) and the P-fund manager’s ESG eﬀort in G-firms
P xP), thereby increasing both ZG and ZM directly. However, as discussed(see aP G = ηλfcZP

in the case of an increase in η, we also need to consider the eﬀect of a change in the fund25

Under fund investors’ capital allocation conditions (18), the S-fund (P-fund) investors’ rate of exG
Mpected gross return (1 − fS ) RGP−ηZ((1 − fP ) RMP−ηZ) must remain constant for a fixed ψS (ψP ).
G
M
Combining this with (19) ((20)), we can show that both the fund fee fS (fP ) and the rate of expectedGM
gross return RGP−ηZ( RMP−ηZ) must remain unaﬀected by the change in η.
GM27

ownership stakes. Because the larger ZG and ZM increase fund investors’ rate of expected]/∂Z > 0, where P = R
gross returns from both the S- and P-funds (see ∂[(1 − f ) R−ηZ
P

− ηZ − L), fund investors would increase their investment in the S- and P-funds. Suchan investment increase would force the S-fund (P-fund) manager to buy a larger numberof the shares of G-firms (all the firms in the market portfolio), thus increasing xSG (xP ).

However, the eﬀect of the larger xSG and xP also raise the fund managers’ eﬀorts regarding
xp
xSG
and eP = fcpRp). Hence, RG and RM increase.
firm profit (see eSG = fScRS, depends on
In fact, note that fund investors’ rate of expected gross return, (1 − f ) R−ηZP

the expected profit of the portfolio firms of the fund, R, minus the expected disutility of

the negative externality released by the firms, ηZ. When λ is lower, under fund investors’
capital allocation conditions (18), its negative eﬀect on the reduction of the expected
disutility, ηZ, cancels out its positive eﬀect on the expected profit, R. This implies thatthe change in λ has no eﬀect on fund investors’ rate of expected gross return, although it
continues to have the initial direct eﬀect on aSG and aP G , and the fund ownership eﬀect
through a change in xSG so that ZG , RG , ZM , and RM increase. Thus, given (18), thechange in λ has no eﬀect on the management fee of either fund.26 By contrast, as theseeﬀects do not operate in B-firms, neither ZB nor RB is aﬀected as long as the management
fee is taken as given.
Recently, various institutions and organizations have attempted to clarify and develop
ESG definitions and scores. Furthermore, they have reported how firms’ activities areevaluated from the viewpoint of the ESG definitions and scores. As a result, it has beeneasier for fund managers to intervene in the management of their portfolio firms fromthe perspective of ESG performance. In the context of our model, we can consider thesechanges as decreasing cZS and cZP .
Proposition 4: Suppose that the S-fund manager’s eﬀort cost parameter for reducing thenegative externality is lower (i.e., cZS is lower).
(i) The expected negative externality and the expected profit of G-firms, ZG and RG , bothdecrease.
(ii) The expected negative externality and the expected profit of B-firms, ZB and RB ,respectively, are unaﬀected.
(iii) The expected negative externality and the expected profit from all the firms in the26

A remark similar to that of footnote 25 also holds in this case.

28

market portfolio, ZM and RM , respectively, decrease.
(iv) The asset management fees of both funds are unaﬀected.
Proposition 5: Suppose that the P-fund manager’s eﬀort cost parameter of reducing thenegative externality is lower (i.e., cZP is lower). Then, the statements of (i), (ii), and (iv)in Proposition 4 hold, whereas the expected negative externality and the expected profit of
B-firms both decrease.
Propositions 4 and 5 show that the lower cZS and the lower cZP both improve ESG
performance in G-firms and in all the firms in the market portfolio, but reduce profit
performance in G-firms and in all the firms in the market portfolio. However, these
propositions indicate that only the lower cZP improves ESG performance but harms profit
performance in B-firms; and neither the lower cZS nor the lower cZP aﬀects the asset
management fees of either funds.
Intuitively, the mechanism by which the lower cZS works is similar to that by which
the lower λ works except that the lower cZS directly increases only the S-fund manager’s
ESG eﬀort. Thus, the lower cZS decreases ZG , RG , ZM , and RM , but does not aﬀect ZB ,RB , or the asset management fees of either funds. For the eﬀect of the lower cZP , wecan apply a similar logic, except that the P-fund manager’s eﬀort in the market portfolio
firms reduces ZB and RB . Thus, the lower cZP also reduces ZB and RB .
Several remarks regarding Propositions 2—5 are in order. First, because the strong ESG
preference creates S-fund growth, Proposition 2 can be interpreted in the light of thisgrowth. In our model, S-fund growth changes the fund ownership stakes. Specifically,
whether S-fund growth crowds out fund investors’ allocations to the other fund or brings
new investor capital into the fund industry is related to whether S-fund growth replaces the
P-fund or liquidity investors. Accordingly, Proposition 2 shows the following: (i) S-fundgrowth decreases the expected negative externality released in G-firms and in all the firms
in the market portfolio if the ESG preference of investors is not strong and/or if the S-fund
has a comparative advantage over the P-fund in improving profit performance relative to
ESG performance; and (ii) S-fund growth always reduces the expected negative externality
released by B-firms. Conversely, if the above condition in (i) is not satisfied, Proposition
2 indicates that S-fund growth may increase the expected negative externality released by
G-firms or all the firms in the market portfolio. As some recent studies suggest, albeit for29

diﬀerent reasons than the limited or counterproductive impact of the S-fund, the latter
result theoretically suggests the possibility of S-fund growth preventing the reduction of
the expected negative externality if investors have a strong preference for ESG and if
the S-fund does not have a comparative advantage over the P-fund in improving profit
performance relative to ESG performance.
Second, Proposition 3 shows that when shareholders’ ESG engagement becomes lessvaluable for high-ESG firms, the ESG performance of the high-ESG firms and all thefirms in the market portfolio worsens, whereas their profit performances are improved.
Although this change aﬀects fund managers’ ESG eﬀorts toward G-firms in both the Sand P-funds, the ESG and profit performances in B-firms are unaﬀected because neither
the direct eﬀect nor the fund ownership eﬀect works in B-firms.
Third, it is empirically supported that the change in the fund ownership structure behind the mechanism working in Proposition 2 has first-order eﬀects. Even though S-fund
is taken as ESG-indexed funds, there is growing evidence that passive fund growth may
aﬀect information production and the information content of asset prices (see Israeli, Lee,
Sridharam, 2017; Glosten, Nallareddy, and Zou, 2021; and Coles, Health, and Ringgenberg, 2022). These changes may have first-order eﬀects on shareholders’ willingness tomake costly engagements in their portfolio firms.
Fourth, Goldstein, Kopytov, Shen, and Xiang (2022) suggest that an increase in thegreen investor share leads to an increase (a decrease) in the cost of capital and the expectedasset returns when most investors are traditional (green) investors. Their results dependon changes in the composition of the investor base and in the price informativeness.
Pástor, Stambaugh, and Taylor (2021b) indicate that higher ESG appetite leads green
firms to become greener but reduces the expected returns of green firms. Their results
depend on the shift of real investment from brown to green firms. By contrast, ourresults of growing interest in ESG are mainly derived from changes in the fund managers’
governance eﬀorts caused by both the direct eﬀect of the strengthened ESG preferences
and the change in the fund ownership stakes. Accordingly, our results depend on thestrength of investors’ ESG taste and the comparative advantage of each fund manager in
improving ESG performance relative to firm profit. Furthermore, our results suggest thatgrowing interest in ESG does not necessarily improve ESG performance in G-firms or in
all the firms in the market portfolio if investors have a strong preference for ESG, which30

is diﬀerent from the results of Pástor, Stambaugh, and Taylor (2021b).
Fifth, Corum, Malenko, and Malenko (2021) report that passive fund growth improves
the firm’s governance and increases the returns of firms if it replaces liquidity investors
with institutional investors, whereas its eﬀects on governance are subtler and depend on
the active and passive funds’ ownership stakes if the passive fund growth primarily aﬀects
the composition of active versus passive funds. Our results of growing interest in ESG
depend on the S- and P-funds’ ownership stakes. However, our model includes investors’
ESG preferences and the costly engagement of each fund manager in reducing the negative
externality in addition to the costly engagement of each fund manager to improve firm
profit. Hence, our results depend on the degree of investors’ ESG preferences and thecomparative advantage of improving ESG performance relative to firm profit for eachfund manager.
Sixth, Propositions 4 and 5 show that an improvement in the engagement cost in ESG
for the S-fund manager enhances ESG performance in both G-firms and all the firms
in the market portfolio, but does not aﬀect ESG performance in B-firms. By contrast,
an improvement in the engagement cost in ESG for the P-fund manager enhances ESG
performance even in B-firms. Regarding these results, one might think it is obvious thatthe lower engagement cost in ESG for each fund manager reduces the expected negative
externalities. However, the present model has an indirect channel through fund investors’
capital allocation that might block the reduction of the expected negative externalities. In
this sense, the comparative static results for cZS and cZP are not straightforward because
we need to examine the indirect channel.
Seventh, an interesting point is that under the multitask situation for fund managers,
the lower cZS (cZP ) increases aSG (aP ) but decreases eSG (eP ), even though the costsof these eﬀorts are additive. This implies that if the ESG eﬀort cost parameter of eachfund manager is lower, his eﬀort in increasing the firm profit substitutes for his eﬀort in
reducing the negative externality, although the costs of these eﬀorts are additive. This
result is diﬀerent from that of Holmström and Milgrom (1991). They formalize a multitask
principal—agent model in which complementarity or substitutability between tasks plays
an important role in deriving their key results. However, the mechanism behind our model
is diﬀerent from theirs because it depends on the adjustment of fund investors’ capital
allocation conditions.
31

5. Discussions and Empirical Implications
Propositions 2—5 provide several empirical predictions regarding the shareholder engagement eﬀects of growing interest in ESG, the limited impact of shareholder ESG
engagement in G-firms, and a decrease in each fund manager’s cost of engagement in
ESG on the expected negative externality and the expected financial return. To test thepredictions of our model empirically, although ESG performance includes various aspects,
one could rely on several proxies capturing diﬀerent ESG aspects that are proposed by
the empirical literature (e.g., see Pedersen, Fitzgibbons, and Pomorski, 2021).
To derive the empirical implications, using (12) and (16), we start by observing that the
expected financial returns of G-stocks, B-stocks, and the market portfolio for investors,
RG − PG , RB − PB , and RM − PM , are defined by
Rh − Ph = Lh + ηZh ,for h ∈ (G, B, M).

(24)

RG − PG , RB − PB , and RM − PM capture the expected financial returns (cost of capital)of G-stocks, B-stocks, and the market portfolio, respectively.

We assume that ZB0 is suﬃciently larger than ZG0 and the S-fund holds only G-firms.
Therefore, it follows from (3), (4), and (24) that if LG is not so diﬀerent from LB and if the
ESG engagement eﬀort of the P-fund manager in B-firms is not very large, the expectedfinancial returns of stocks with low-ESG proxies outperform those with high-ESG proxies.
Many empirical studies provide predictions about the relation between ESG aspects andfinancial returns of firms’ operations, but document mixed results. For example, Hong and
Kacperczyk (2009), El Ghoul, Guedhami, Kwok, and Mishra (2011), Chava (2014), Zerbib(2019), Bolton and Kacperczyk (2021), and Barber, Morse, and Yasuda (2021) reporta negative relation between ESG performance and financial returns. However, Derwall,
Guenster, Bauer, and Koedijk (2005), Kempf and Osthoﬀ (2007), and Pastor, Stambaugh,
and Taylor (2021a) report a higher financial return of stocks with better environmental
prospects. Green and Roth (2021) suggest that measurement issues are a significant
obstacle to resolving the problem of whether firms with good ESG performance face lower
financial returns. In addition, the opposite findings can be explained by the weak return
predictability of the overall ESG rating (Pedersen, Fitzgibbons, and Pomorski, 2021) and32

the presence of uncertainty about the ESG profile (Avramov, Cheng, Lioui, and Tarelli,2022). Indeed, until recently, the construction of ESG ratings has not been regulated or
unified. As a result, the methodology of ESG ratings is opaque and proprietary.27
Next, we examine the eﬀect of growing interest in ESG because many practitioners
and researchers wonder how growing interest in ESG really aﬀects ESG performance andfinancial returns. As mentioned in Section 3.1, the engagement eﬀort eih (aih ) exerted by
the fund manager i for i ∈ (S, P ) and h ∈ (G, B) includes any actions such as commu-

nicating with management, submitting shareholder proposals, nominating directors, andvoting on proxy contests.
Suppose that the S-fund is a sustainable active fund. In their review of the literature,

Brav, Malenko, and Malenko (2022) conclude that because actively managed funds andpassive funds have diﬀerent types of costs, and hence are likely to specialize in diﬀerent
types of engagement, passive funds may be in a better position to have an impact bysetting broad, market-wide governance standards, instead of focusing on firm-specific operational improvements.28 Given the diﬀerence in the engagement strategies, the P-fund
has a comparative advantage over the S-fund in improving ESG performance relative to
profit performance if improving ESG performance can be achieved to a certain extent by
setting broad, market-wide standards for ESG. This is because, in this situation, improving the profit performance of each firm needs more firm-specific operational engagements
than improving ESG performance. In addition, the engagement eﬀort regarding ESG ismore valuable for firms that lag behind in terms of ESG, although the S-fund invests
only in G-firms. This feature may be reflected in the comparative advantage argument,even though the parameter λ may mainly capture this feature in our model. Then,
cZP
cZS

becomes lower because setting, broad, market-wide standards for ESG is less costly,

becomes higher because improving the profit performance of each firm rewhereas ccRP
RS
duces more firm-specific operational engagements. Accordingly, we can assume that ccRP
RS
> ccZP
if improving ESG performance can be achieved to a certain extent by setting broad,
ZS
27
Avramov, Cheng, Lioui, and Tarelli (2022) report that there are substantial variations across diﬀerent
rating providers; that is, the average rating correlation is 0.48.
28
Kahn and Rock (2020) and Fish, Hamdani, and Solomon (2019) indicate that actively managed
funds may have an advantage over index funds in identifying firm-specific operational or financial issues
because they can specialize in collecting or acquiring such information as a byproduct of their investment
activities. They also argue that large passive funds are in a good position to enjoy economics of scale incollecting information on broad, market-wide issues and setting market-wide standards.

33

market-wide standards for ESG.
On the other hand, suppose that the S-fund is an ESG-indexed fund. If the engagement
eﬀort regarding ESG is more valuable for firms with low-ESG proxies and if this featureis also captured by the fund manager’s ESG engagement cost in G-firms relative to thatis suﬃciently low because the S-fund invests
in B-firms in addition to a lower λ, then ccZP
ZS
> ccZP.
only in G-firms. Hence, again, we may assume that ccRP
RS
ZS
Now, given that the strengthened ESG taste aﬀects both η and Zi (i = G, B, M) in(24), Propositions 2(i)—2(iii) along with (24) provide the following predictions (for the
proof, see Appendix A):
Prediction 1A: Suppose that investors do not have a strong preference for ESG. Then,
growing interest in ESG is likely to reduce the expected negative externalities releasedby any type of firm. It is also likely to raise the expected financial returns of any typeof firm.
Prediction 1B: Suppose that investors have a strong preference for ESG. If improving ESG performance can be achieved to a certain degree by setting broad, market-widestandards of ESG, growing interest in ESG is likely to reduce the expected negative
externalities released by firms with high ESG proxies and by all the firms in the market portfolio. However, growing interest in ESG always reduces the expected negative
externality by firms with low-ESG proxies and raises their expected financial returns.
If investors have a strong preference for ESG and if improving ESG performance cannot
be achieved to a certain degree by setting broad, market-wide standards for ESG, Prediction 1 does not necessarily suggest that growing interest in ESG is likely to improve ESG
performance in firms with high-ESG proxies and in all the firms in the market portfolio,or that growing interests in ESG is likely to raise expected financial returns in these firms.
By contrast, Prediction 1 suggests that growing interest in ESG always improves ESG
performance and the expected financial returns of firms with low-ESG proxies.
Now, we consider the eﬀect of the limited impact of shareholder ESG engagement in
G-firms. Because the increasing tendency for shareholder ESG engagement to have alimited impact on high-ESG firms is captured by a decrease in λ, it easily follows from
Propositions 3(i)—3(iii) along with (24) that the following predictions are obtained.
Prediction 2: When the impact of shareholder ESG engagement in G-firms is more34

limited, not only the expected negative externalities but also the expected financial returns
are increased for firms with high-ESG proxies and all the firms in the market portfolio,
but are unaﬀected in firms with low-ESG proxies.
Prediction 2 particularly suggests that when the impact of shareholder ESG engagementin G-firms relative to that in B-firms is limited and decreases, both ESG performance andfinancial returns in firms with high-ESG scores and market portfolio firms increase, but
those in firms with low-ESG proxies are unaﬀected.
We proceed to discuss the eﬀect of an improvement in the ESG eﬀort cost for eachfund manager. As argued, sustainable active funds are more likely to focus on firmspecific operational improvements, whereas ESG-indexed funds and P-funds are more
likely to have an impact by setting broad, market-wide governance standards. Thus, cZS islower when exerting firm-specific operational eﬀorts in improving ESG performance is lesscostly for sustainable active funds or when setting broad, market-wide ESG governancestandards is less costly for ESG-indexed funds, whereas cZP is lower when setting broad,market-wide ESG governance standards is less costly for P-funds. Hence, Propositions 4
and 5 with (24) immediately yield the following predictions:
Prediction 3A: Suppose that focusing on firm-specific operational improvements in ESG
is less costly for sustainable active funds and/or that setting broad, market-wide ESG
governance standards is less costly for ESG-indexed funds. Then, the expected negative
externalities released by firms with high-ESG proxies and by all the firms in the market
portfolio are reduced. The expected financial returns of firms with high-ESG proxies
and those of the market portfolio are also reduced.
Prediction 3B: Suppose that setting broad, market-wide ESG governance standards isless costly for P-funds. Then, the expected negative externalities released by any type offirm are reduced. The expected financial returns of any type of firm are also reduced.
Now, the profit of each firm in Propositions 2—5 can be interpreted as the operating
profits–that is, the EBITDA–of each firm. As a lower expected negative externality
implies higher ESG scores, Propositions 2—5 also provide empirical implications regarding
the association between ESG scores and the EBITDA achieved by each firm.
First, Propositions 2 and 3 imply the following predictions.
Prediction 4: Growing interest in ESG leads to a positive association between ESG
35

scores and the EBITDA attained by any type of firm if investors do not have a strong
preference for ESG. Even if investors are strongly ESG conscious, growing interest in ESG
leads to a positive association between ESG scores and the EBITDA attained in firms
with low-ESG proxies.
Prediction 5: The increasing tendency for shareholder ESG engagement to have alimited eﬀect in firms with high-ESG proxies causes a negative association between ESG
scores and the EBITDA attained in firms with high-ESG proxies and in all the firms inthe market portfolio.
If the ESG preference of investors is strong, Prediction 4 does not necessarily suggestthat S-fund growth creates a positive association between ESG scores and the EBITDA
attained by any type of firm.
Second, Propositions 4 and 5 imply the following predictions.
Prediction 6: The lower cost for sustainable active funds to exert firm-specific operational eﬀorts to improve ESG performance and/or the lower cost of ESG-indexed funds
in setting broad, market-wide ESG standards causes a negative association between ESG
scores and the EBITDA attained by firms with high-ESG proxies and by all the firms inthe market portfolio.
Prediction 7: The lower cost of P-funds setting broad, market-wide ESG standards
causes a negative association between ESG scores and the EBITDA attained by any typeof firm.
To the best of our knowledge, Predictions 1—6 have not yet been tested. As for Predictions 1A, 1B, and 4, many empirical studies report the expected financial returns of assets,
but they focus on cross-sectional analysis. In contrast with these cross-sectional studies,
Predictions 1A, 1B, and 4 provide time-series predictions created by the eﬀect of growinginterest in ESG. Conversely, the other predictions need to be tested using cross-sectional
and panel data analyses. To test Predictions 2 and 5, we need to identify the impact ofshareholder ESG engagement in each firm, which may be estimated using the method ofHartzmark and Shue (2022). To test Predictions 3A, 3B, 6A, and 6B, diﬀerences in theaccessibility and plausibility of ESG data in diﬀerent industries and/or the growing accessibility and variety of ESG proxies may be used to identify the cross-sectional diﬀerences
and the time-series changes in ESG engagement costs.
36

6. Conclusion
This paper considers how profit-motivated managers of S- and P-funds govern theirportfolio firms when these funds must attract capital from socially responsible investors
and when the impact of shareholder ESG engagement in high-ESG firms is limited. We
examine a multitask situation in which the manager of each fund must choose the fund’s
costly engagement eﬀort levels for mitigating negative externalities and increasing pecuniary returns in his portfolio firms.
Using the search model framework for fund managers and investors, we derive thefollowing implications:(i) If investors are generally not very interested in ESG, a growing interest in ESG is likely
to improve ESG performance and the expected financial returns of any type of firm. Even
when the investors have strong ESG preferences in general, growing interest in ESG is
likely to improve ESG performance in firms with high-ESG proxies and in all the firms
in the market portfolio if the S-fund has a comparative advantage in improving profit
performance over ESG performance when compared with the P-fund, whereas it always
improves ESG performance and expected financial returns in firms with low-ESG proxies.
However, in the latter case, growing interest in ESG does not generally contribute to the
reduction of the expected negative externality in all types of firms.
(ii) The increasing tendency for shareholder ESG engagement to have a limited impact infirms with high-ESG proxies reduces ESG performance but improves expected financial
returns of firms with high-ESG proxies and all the firms in the market portfolio, butdoes not aﬀect the ESG performance or expected financial returns of firms with low-ESG
proxies.
(iii) The lower ESG engagement cost of the S-fund (P-fund) improves ESG performance,
but reduces the expected financial returns of firms with high-ESG proxies and all thefirms in the market portfolio (in any type of firm).
In this paper, we focused on the fund manager’s multitask incentive problem in engaging
in the ownership of his portfolio firms, and fund investors’ investment allocation problems.
To shed light on these problems, we abstract from the tax and interest payments of theportfolio firms. Thus, in our model, the EBITDA and net income are indistinguishable.
However, in conducting empirical research, net income may be a more adequate measure37

of the profit of the portfolio firms for the fund manager. Hence, the tax and interest
payment considerations would be an interesting extension of the empirical analysis in
future research.

38

Appendix A
Proof of Proposition 1: We first derive statements (i), (ii), and (iv). Substituting PG
from (14) and fS from (19) into (18), we obtain(1 + ψS − ωS )LG = ψS (RG − ηZG ),SSLG + ηZG . Then, (14) yields PG = 1−ω
LG . Thus, it follows
which means RG = ψS +1−ω
ψS
ψS
S ψS
. Similarly, using (16), (18), and (20), we can derive thefrom (19) that fS = ψSω+1−ω
S
P ψP
P
P
, RM = ψP +1−ωLM + ηZM , and PM = 1−ω
LM . In addition, if
solution: fP = ψPω+1−ωψPψPPωS ≥ ωP , then ψS ≥ ψP implies that fS ≥ fP .

Next, we verify statement (iii). As the S-fund holds only the stock of G-firms, it follows
eG = RG , and E R
eB = RB
from (1) and (2) with RM = RG + RB , eP G = eP B = eP , E R
that

RM − RG = R0 + eP ,(A1)

2RG − RM = eSG .

(A2)

and

It is also found from (3) and (4) with ZM = ZG + ZB , E ZeG = ZG , and E ZeB = ZB that
ZG = ZG0 − λaSG − λaP G ,(A3)

ZM = ZG0 + ZB0 − λaSG − λaP G − aP B .

(A4)

and

Substituting aSG and eSG from (8) and aP and eP from (90 ) into (A3) and (A4) andrearranging them with (8), (90 ), (A1) and (A2), we obtain (22) and (23).
In the remaining part, we show that under the conditions of this proposition, (a) liquidity investors hold at least some shares in each type of stock, that is, xSG + xP < 1, (b)fund investors make a positive investment in an alternative investment opportunity suchas public bonds, that is, WS + WP < W , and (c) the S-fund finds it optimal to diversify
equally across all G-firms.
We first prove (a). Given that the S-fund holds only the stock of G-firms, it follows
39

from (1)—(4) and (13)—(16) with RM = RG + RB and eP G = eP B = eP thatxSG + xP =

WS WP
+
.
PG
PM

(A5)

Note that
PG = R0 + eSG + eP − ηZG − LG ≥ R0 − ηZG0 − LG > 0,
PM = 2R0 + eSG + 2eP − ηZM − LM ≥ R0 − ηZG0 − LG > 0,
because we focus on the cases of (eSG , aSG ) > 0 and (eP , aP G , aP B ) > 0 and because R0> max (ηZB0 + LB , ηZG0 + LG ) > 0. Given WS + WP < W derived below, (A5) leads
toxSG + xP ≤WS + WP
W<.
R0 − ηZG0 − LG
R0 − ηZG0 − LG

It follows from the condition W < R0 − ηZG0 − LG that xSG + xP < 1.

We next proceed to prove (b). Rearranging (8) and (90 ) with (A1) and (A2), we havecRS
(2RG − RM ),
fS

(A6)

cRP
(RM − RG − R0 ).
fP

(A7)

xSG =

xP =

S
It is found from (13), (15), (A6), and (A7) with RG = ψS +1−ωLG + ηZG , RM =ψSψP +1−ωP
LM + ηZM , (A3), and (A4) thatψP

WS + WPPG cRS
PM cRP= PG xSG + PM xP =(2RG − RM ) +(RM − RG − R0 )
fS
fP
µ
¶
ψS + 1 − ωS
ψP + 1 − ωP
PG cRS2
LG −LM + ηZG0 − ηλaSG − ηλaP G − ηZB0 + ηaP B
=
fS
ψS
ψP
µ
¶
ψS + 1 − ωS
PM cRP ψP + 1 − ωP
(A8)
LM −
LG − R0 + ηZB0 − ηaP B .
+
fP
ψP
ψS
Define∙¸
ψS + 1 − ωS
1 − ωS ψS + 1 − ωS
ψP + 1 − ωP
LG cRS 2
LG −LM + ηZG0
W≡
ψS
ωS ψS
ψS
ψP
40

1 − ωP ψP + 1 − ωP+
LM cRP
ψP
ωP ψP

µ

¶
ψP + 1 − ωP
ψS + 1 − ωS
LM −LG − R0 + ηZB0 .
ψP
ψS
(A9)

S ψS
P ψP
S
P
LG , PM = 1−ω
LM , fS = ψSω+1−ω, and fP = ψPω+1−ωwith theThen, given PG = 1−ω
ψS
ψP
S
P

assumption of ZB0 > aP B , comparing (A8) with (A9) verifies that WS + WP < W if W
≥ W.

Finally, we prove (c). Indeed, applying a procedure similar to the proof of Lemma 2

in Online Appendix of Corum, Malenko, and Malenko (2021) under the condition R0 >
ηZG0 + LG and the assumption of a quadratic cost function, we can show that the S-fundfinds it optimal to diversify equally across all G-firms. k
SP
LG + ηZG and RM = ψP +1−ωLM
Proof of Propositions 2—5: Substituting RG = ψS +1−ωψSψP+ ηZM into (22) and (23) of Proposition 1(iii), we show that ZG , ZB , and ZM are determined by solving the following simultaneous equations
ZB + ZG = ZM ,(A10)

ZG = ZG0 − Γ1 − Γ2 ,(A11)

ZM = ZG0 + ZB0 − Γ1 − Γ2 − Γ3 ,

(A12)

where
µ
¶
ψS + 1 − ωS
ψP + 1 − ωP
2
LG + 2ηZG −LM − ηZM ,Γ1 ≡ ηλ
cZS
ψS
ψP
2 cRS

¶
ψP + 1 − ωP
ψS + 1 − ωS
Γ2 ≡ ηλLM + ηZM −LG − ηZG − R0 ,
cZP
ψP
ψS
µ
¶
cRP ψP + 1 − ωP
ψS + 1 − ωS
LM + ηZM −LG − ηZG − R0 .
Γ3 ≡ η
cZP
ψP
ψS
2 cRP

µ

Totally diﬀerentiating (A10)—(A12) with respect to ZB , ZG , ZM , η, λ, cZS , cZP , and ψP

41

yields

⎡

1
⎢
⎢
⎢ 0
⎣
0
⎡

1
∂Γ1
∂Γ2
1 + ∂Z
+ ∂Z
G
G
∂Γ1
∂Γ2
∂Γ3
+ ∂Z
+ ∂Z
∂ZG
G
G

0

⎤

⎤⎡

−1

⎤

dZB
⎥⎢
⎥
⎥
⎥
⎢
∂Γ1
∂Γ2
⎥
⎢
+
dZ
G ⎥
∂ZM
∂ZM
⎦⎣
⎦
∂Γ1
∂Γ2
∂Γ3
1 + ∂ZM + ∂ZM + ∂ZM
dZM
⎡

0

⎤

⎡

0

⎤

⎢
⎢
⎥
⎥
⎥
⎢ 2Γ1 2Γ2 ⎥⎢ Γ1 ⎥⎥dη+dλ+⎢ − λ − λ ⎥⎢ c ⎥ dcZS⎥⎣
⎣ ZS ⎦
⎦
⎦
∂Γ1
∂Γ2
∂Γ3
2Γ1
2Γ2
Γ1
− ∂η − ∂η − ∂η
− λ − λ
cZS
⎡
⎡
⎤
⎤
0
0
⎢
⎢
⎥
⎥
⎢ Γ2 ⎥
⎢
⎥
∂Γ
∂Γ
1
2
+ ⎢ c ⎥ dcZP + ⎢⎥ dψP .
− ∂ψP − ∂ψP
ZP
⎣
⎣
⎦
⎦
2Γ2
∂Γ1
∂Γ2
∂Γ3
−
−
−
cZP
∂ψP
∂ψP
∂ψP
⎢
⎢
=⎢
⎣

1
2
− ∂Γ
− ∂Γ
∂η
∂η

(A13)

S
P
Given (A6) and (A7) with RG = ψS +1−ωLG + ηZG and RM = ψP +1−ωLM + ηZM , note
ψS
ψP
2

2

fP xP
S xSG
(2RG − RM ) = ηλ cfZS
, Γ2 = ηλ2 ccRP
(RM − RG − R0 ) = ηλcZP, andthat Γ1 = ηλ2 ccRSZS
ZP

(RM − RG − R0 ) = ηfcPZPxP . It follows from (8) and (90 ) that the assumption
Γ3 = η ccRP
ZP
(eSG , aSG ) > 0 and (eP , aP G , aP B ) > 0 means that Γ1 > 0, Γ2 > 0, and Γ3 > 0.
Now, solving (A13), we show
¶
µ
¶µ
cRP
1
Γ3
dZB
2 2 cRS
< 0,
=−
ηZB
1+η λ
+
dη
∆
cZP
η
cZS
µ
¶
µ
¶
ηλ2 ZB cRS cRPηλ2 ZG cRS
cZP
dZG
2 cRP
1+η
−
=−
−
dη
∆ cZS
cZP
∆ cZP cRS
cZS
¶
¶
µ
µ
cRP
cRS
Γ2
Γ1
−
1 + η2
1 + η2
−
η∆
cZP
η∆
cZS
cRP
cZP
< 0, if η is not large or if η is large and
−
> 0,
cRS
cZS

(A14)

(A15)

µ
µ
¶
¸
∙
¶
cRP
cRP
dZM
ηλ2 ZG cRSηZB 2 2 cRP cRS
cRS
2 cRP
2
η
+
=−
η λ
+1 −
+λ
−
dη
∆ cZS
cZP
∆
cZP cZS
cZP
cZS
cZP
¶
µ
µ
¶
cRP
cRS
Γ3
Γ1
η2
2η2 λ2+1 −+ 1 + λ2 < 0,
−
η∆
cZP
η∆
cZS
42

if η is not large or if η is large and
dZB
= 0,
dλ

cRP
cZP
>
,
cRS
cZS

¶
µ
dZh
2(Γ1 + Γ2 )
2 cRP
< 0,
=−
1+η
dλ
λ∆
cZP

dZB
= 0;
dcZS

cRP
dZh
Γ1
=
) > 0,(1 + η2
dcZS
cZS ∆
cZP

(A16)

h = G, M,(A17)

h = G, M,

(A18)

dZB
cRS
cRS
Γ3
dZG
Γ2
=
) > 0,=) > 0,(1 + η 2 λ2
(1 + η2
dcZP
cZP ∆
cZS
dcZP
cZP ∆
cZS
cRS
dZM
Γ3
=
) > 0,(1 + λ2 + 2η2 λ2
dcZP
cZP ∆
cZS
¶
µ
dZB
(1 − ωP )ηLM cRP
2 2 cRP cRS
> 0,
=
+η λ
dψP
(ψP )2 ∆cZP
cZP cZSµ¶
dZG
cRP(1 − ωP )ηλ2 LM cRS cRP
cZP
cZP
R 0,
if and only if
=
−
R
,
2
dψP
(ψP ) ∆cZP cRS
cZS
cRS
cZS
∙
¸
dZM
(1 − ωP )ηLM cRS
2 cRP
2 2 cRP
2 cZP(1 + λ )
> 0,
=
+η λ
−λ
dψP
(ψP )2 ∆ cZP
cRS
cZS
cZS

(A19)

(A20)
(A21)

λ2
cRP
cZP
>
,
(A22)
c
RS
cRS
1 + λ2 + η 2 λ2 cZS cZS³´cRP
2 2 cRS cRP> 0. It follows from (A14)—(A19) that++η
λwhere ∆ = 1 + η2 λ2 ccRS
cZP
cZS cZP
ZS
if and only if

the results of the expected negative externalities in Propositions 2—5 are obtained.
Given Proposition 1(ii), we havedZh
dRh
= Zh + η
,
dη
dη
dZh
dRh
=η
,
dλ
dλ
dRh
dZh
=η
,
dcZi
dcZi
dRG
dZG
=η
;
dψP
dψP

h = G, M,(A23)

h = G, M,(A24)

h = G, M, and i = S, P.

(A25)

dRM
(1 − ωP )LM
dZM
=−
+η
,
2
dψP
(ψP )
dψP

(A26)

In addition,
dRB
dRM
dRG
=
−
,
dχ
dχ
dχ

χ = η, λ, cZS , cZP , ψP .
43

(A27)

Inspecting (A23)—(A25) and (A27) with (A14)—(A19), we prove the results of the expected
profits in Propositions 2—5.
Finally, it follows from Proposition 1(i) that
dfi
dfi
dfi
=
=
= 0,
dη
dλ
dcZj
dfS
= 0;
dψP

i = S, P ; j = S, P,

(A28)

dfP
ωP (1 − ωP )
=
> 0.
dψP
(ψP + 1 − ωP )2(A29)

It follows from (A28) that the results of the asset management fees in Propositions 2—5
are verified. k
Proof of Predictions 1A and 1B: Comparing Proposition 1(ii) with (24), we showi −Pi )i= dR
for i = G, B, M. Hence, it follows from Propositions 2(i)—2(iii) thatthat d(Rdηdη

the statements of Predictions 1A and 1B are obtained. k
Appendix B
B.1. Multiple S- and P-funds.–
Our basic model can be extended to the case of multiple funds in which there are NS
S-funds and NP P-funds. All NS S-funds only invest in and diversify the stocks of Gfirms, whereas all NP P-funds invest in the market portfolio. As we focus on symmetricequilibria, the same type funds choose the same eﬀort and bargaining strategies and thesame fund size. Then, under a quadratic cost function of eﬀorts, we can show that allof our propositions continue to hold by applying the discussion of Corum, Malenko, andMalenko (2021).
B.2. Non-sustainable funds and non-socially responsible investors.–
We can consider a third type of fund as a non-sustainable fund (N-fund), which invests
only in B-firms. The fund manager of the N-fund invests in B-firms on behalf of investors
and is interested purely in his monetary payoﬀs. There is also a large mass of non-socially
responsible investors, who have no ESG preference and are purely interested in theirmonetary payoﬀs. Then, we can discuss whether our results are robust to these changes.
For convenience, fund investors and liquidity investors in the basic model are denoted associally responsible investors.
44

For simplicity, we assume that because socially responsible investors have ESG preferences, they dislike the N-fund such that they do not want to invest in the N-fund.
By contrast, we assume that non-socially responsible investors have a certain amount ofwealth to invest, ε, and only determine whether they invest in the N-fund or the alternative investment opportunity such as public bonds.29 We denote their aggregate wealthby W + , which is given exogenously. Each non-socially responsible investor with wealth εmust search for and vet the N-fund manager by incurring a search cost ψN ε. After she
finds the N-fund manager, she negotiates the fee fN through generalized Nash bargaining.
Under these assumptions, we begin with the case in which the fund manager of the Nfund has no governance role in his portfolio firms because the N-fund is practically set up
to seek higher financial returns by arbitrage trading. Then, the basic model is modified asfollows. As shown in Section 4.4, in the basic model, the endogenous variables consistingof the eﬀort decisions, (eSG , aSG , eP , aP G , aP B ), the asset management fees, (fS , fP ), thetrading decisions and investment asset allocations, (xSG , xP , WS , WP ), the total expected
payoﬀs of the S- and P-funds, (RG − ηZG , RM − ηZM ), and the asset prices, (PG , PM ),are determined by (8), (90 ), (10), and (13)—(20). In this extended model, we additionallyneed to determine the asset management fee of the N-fund, fN , the holding shares of the
N-fund in B-firms, xNB , the investment amount of the N-fund in B-firms, WN , and theprice of B-firms, PB .
First, PB is given by (12). Second, for WN and fixed W + , xN B satisfy
xNB =

WN
W+
≤
.
PB
PB

(B1)

Third, the N-fund fee fN is determined by generalized Nash bargaining between the Nfund manager and non-socially responsible investors. Because both agents are purelyinterested in their pecuniary returns, their concern is to distribute RB PεB in this case.
29

As non-socially responsible investors have no ESG preference and are purely interested in theirmonetary payoﬀs, they can invest in assets that yield the highest rate of expected net return among
the S-fund, the N-fund, the P-fund, and the alternative investment opportunity such as public funds.
However, for simplicity, we focus on the case in which non-socially responsible investors invest only in
the N-fund, that is, the N-fund yields the highest rate of expected net return.

45

Hence, it follows from the discussion at the end of Section 4.3 thatµ¶PB
fN = ωN 1 −
,
RB

(B2)

where ωN is the bargaining power of the N-fund manager and RB is given by (2) for eP
determined from the above-mentioned equation system of the basic model.
The remaining problem is to show how WN is chosen by non-socially responsible investors. As non-socially responsible investors decide whether they invest in the N-fundor the alternative investment opportunity such as public bonds, we need to specify the
expected payoﬀ of non-socially responsible investors attained by investing in the N-fund.
This expected payoﬀ is represented by(1 − fN )RB− ψN .
PB(B3)

Because RB and PB are given by (2) and (12) for eP and aP B determined from the abovementioned equation system of the basic model, it follows from (B2) that the value of (B3)
may not be generically equal to 1; thus, it may be smaller than 1 or larger than 1. Hence,
if (B3) is larger than 1, non-socially responsible investors invest their entire wealth in the
N-fund, that is, WN = W + . Otherwise, they do not invest in the N-fund, that is, WN =0.
In either case, even in this extended model, the endogenous variables in the basic model
are still determined in the exactly same way as in the main text. Consequently, none ofour main results are aﬀected because Proposition 1 still holds in this extended model.
We next examine the case in which the fund manager of the N-fund exerts governance eﬀort eN B to increase the profit of B-firms by incurring a private engagement coste2 . Then, as the negative externality released by each firmcRN (eNB ), where cRN (e) = cRN2
is aﬀected by a fund ownership eﬀect because of a change in eNB , we cannot derive ourmain results generally. However, if socially responsible investors’ ESG preference, η, is notlarge, RB and PB are almost taken as exogenous because RB and PB are almost unaﬀected
by ZB . Thus, the eﬀect of a change in eNB is not large. Similarly, if the bargaining powerof the N-fund manager, ωN , is not large, and/or if the wealth of non-socially responsible
investors, W + , is not large, the eﬀect of a change in eNB is not large because eNB is not46

large in this case. Then, our main results are almost certainly true in these cases.
B.3. Eﬀect of P-fund growth.–
It has been discussed frequently that ESG investing is harmed by P-fund growth because
P-funds automatically invest their money in firms with lower ESG scores unlike S-funds.
However, as has been argued in this paper, P-funds have an ability to monitor theirportfolio firms and force the management of the firms to improve their ESG performance.
Hence, to investigate the above problem, we must analyze P-fund growth by incorporating
the P-fund manager’s engagement with their portfolio firms. A decrease in ψP can bethought of as indicating easy access to the P-fund over time and bring about P-fund growth
because it reflects more investor awareness about the fund and improved disclosure about
the investment strategy and the fee structure of the fund.30
We then have the following proposition.
Proposition 6: Suppose that access to the P-fund becomes easier (i.e., ψP is lower).
(i) The expected negative externality released by G-firms, ZG , decreases if

cRP
cRS

> ccZPZS

but increases otherwise. The expected profit of G-firms, RG , decreases if ccRP
> ccZP
but
RS
ZS
increases otherwise.
(ii) The expected negative externality released by B-firms, ZB , decreases, whereas the
expected profit of B-firms, RB , increases.
(iii) The expected negative externality released by all the firms in the market portfolio,> 1+λ2 +η12 λ2 cRS ccZP
but increases otherwise. The expected profit of
ZM , decreases if ccRP
RS
ZS
cZS

the market portfolio, RM , increases if investors do not have a strong preference for ESG(i.e., η is not large).
(iv) The asset management fee of the S-fund, fS , is unaﬀected, whereas that of the P-fund,
fP , decreases.
The intuition behind Proposition 6 is divided into two eﬀects: the fund fee eﬀect andthe fund ownership eﬀect. For convenience, we begin by discussing the eﬀect of the lower
ψP on the asset management fee of each fund, fS and fP . The eﬀect of the lower ψP on
fP follows from an eﬀect of the decrease in the rate of expected gross return earned by
the P-fund. The reason is that the lower ψP increases fund investors’ rate of expected net
30

Corum, Malenko, and Malenko (2021) provide the same interpretation of a decrease in the search
cost.

47

return of the P-fund from which ψP is deducted. In equilibrium, however, fund investors
are indiﬀerent between investing in the P-fund and the alternative investment opportunity(see (18)). To restore (18), fund investors increase their investment in the P-fund untilfund investors’ rate of expected gross return from the P-fund decreases so that their rateof expected net return returns to 1. A decrease in fund investors’ rate of expected gross
return from the P-fund then leads to a lower fP because the P-fund manager’s bargaining
power ωP is assumed to be fixed. Indeed, in the expression for the fund fee in Proposition
1(i), this eﬀect is featured as a dependence of fP on ψP . However, the lower ψP has noeﬀect on the S-fund fee because it does not aﬀect fund investors’ expected net return fromthe S-fund exclusive of the search cost ψS .
To examine the eﬀect of the lower ψP on the expected negative externality, we needto consider both the fund fee eﬀect and the fund ownership eﬀect: note that the eﬀort
incentive for each fund manager to reduce the negative externality depends on the fundfee and the fund ownership stakes for fixed η, λ, cZS and cZP , as indicated in (8) and (90 ).
For the eﬀect through the fund fee, a decrease in ψP reduces the P-fund fee fP , but does
not aﬀect the S-fund fee fS , as discussed above. This weakens the eﬀort incentive for the
P-fund manager to reduce the negative externality in all the firms in the market portfolio
and thus increases ZG and ZM . However, it has no eﬀect on the eﬀort incentive for the
S-fund manager to reduce the negative externality in G-firms.
A decrease in ψP also changes the fund ownership stakes in firms. If ψP decreases, fundinvestors increase their investment in the P-fund, WP , because fund investors’ expected
net return from the P-fund increases, as argued above. This enables the P-fund manager
to take increasingly large stakes xP in all the firms in the market portfolio. The increase
in xP reduces the stakes held by the S-fund, xSG , and those held by liquidity investors, 1− xSG − xP , in G-firms, while it also reduces the stakes held by liquidity investors, 1 −xP , in the market portfolio. Note that the S-fund does not buy the market portfolio. The

eﬀect of the decrease in xSG of the S-fund in G-firms reduces the engagement eﬀort of
the S-fund manager in G-firms and thus increases ZG and ZM . However, the eﬀect of thedecrease in 1 − xSG − xP (1−xP ) of liquidity investors in G-firms (in the market portfolio)

reduces ZG (both ZG and ZM ). The reason is that if the P-fund replaces liquidity investorsin G-firms’ ownership (in the market portfolio ownership), this eﬀect decreases ZG (both
ZG and ZM ) because liquidity investors do not make any engagement eﬀorts.
48

In evaluating the eﬀects of the lower ψP on ZG (ZM ), note that the total eﬀects throughchanges in the fund fees and the fund ownership stakes depend on the diﬀerence in ccRP
RS
and ccZP( 1+λ2 +η12 λ2 cRS ccZP). Accordingly, the lower ψP reduces ZG (ZM ) as long as ccRP
is
ZS
ZS
RS
cZS

( 1+λ2 +η12 λ2 cRS ccZP). However, for ZB , the total eﬀects of the lower ψP dolarger than ccZP
ZS
ZS
cZS

not include any eﬀect through a change in the fund ownership stakes in G-firms. As theeﬀect of replacing liquidity investors is dominant, the lower ψP always reduces ZB .
To investigate the eﬀect of the lower ψP on the expected profit, note that the expected
profit is positively associated with the expected negative externality in G-firms and in
market portfolio firms (see Proposition 1(ii)). Then, for RG , we show that the lower ψPdecreases RG as long as ccRP
is larger than ccZP
. However, for RM , there exists an additional
RS
ZS
direct eﬀect of the lower ψP through the P-fund fee on the eﬀort incentive for the P-fundmanager to increase the profit, which increases RM . Hence, we only suggest that the lower
ψP increases RM if η is not large. For RB , as the eﬀect of replacing liquidity investors isdominant, the lower ψP always increases RB .
The theoretical implication of Proposition 6 is that because P-fund growth aﬀects fundinvestors’ capital allocation and then changes the fund ownership stakes, the eﬀect of
P-fund growth on the expected negative externality strongly depends on the comparativeadvantage between each fund in improving ESG or profit performance, like the eﬀect ofgrowing interests in ESG. Accordingly, despite the recent argument about the P-fund
not contributing to ESG, P-fund growth does not necessarily avoid the reduction in the
expected negative externality.
Given the argument in Section 5, it easily follows from Propositions 6(i)—6(iii) alongwith (24) that the following predictions are obtained:31
Prediction 7A: Suppose that improving ESG performance can be achieved to a certain
degree by setting broad, market-wide standards of ESG. Then, the growth in P-funds
is likely to reduce the expected negative externalities released by firms with high-ESG
proxies and by all the firms in the market portfolio. It is also likely to reduce the expectedfinancial returns of firms with high-ESG proxies, whereas it is likely to raise the expectedfinancial returns for the market portfolio if investors’ ESG preference is not strong.
Prediction 7B: The growth in P-funds reduces the expected negative externalities
31

Note that ccRP
> ccZP
implies ccRP
> 1+λ2 +η12 λ2 cRS ccZP
.
RS
ZS
RS
ZS
cZS

49

released by firms with low-ESG proxies and raises the expected financial returns of firms
with low-ESG proxies.
Predictions 7A and 7B show that if improved ESG performance can be achieved to acertain degree by setting broad, market-wide standards of ESG, P-fund growth is likely
to improve ESG governance in any type of firm. However, its eﬀect on expected financial
returns in each type of firm is more complicated. This prediction suggests that P-fundgrowth does not necessarily hinder the improvement in ESG performance, unlike theargument of environmental activists.
Using the argument in Section 5, we also indicate
Prediction 8: P-fund growth causes a negative association between ESG scores and
EBITDA attained in firms with high-ESG proxies. However, it brings about a positive
association between ESG scores and EBITDA attained in firms with low-ESG proxies (inall the firms in the market portfolio if the ESG taste of investors is not strong).

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52




Time 0Fund investors
allocate theirwealth between
a S-fund, a Pfund, and outside
investment
opportunities.
Fund investors
search forfund managers.

Time 1Fund investors
and fundmanagers
negotiate amanagement
fee.

Fund managers
invest thedelegatedamount offund investors’
wealth.

Fund managers
Payoffs
exert theirareefforts regarding realized.
ESG andmonetary
performances.

Liquidity
investors
trade.

Figure 1. Timing of the model