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The Allocation of Socially Responsible Capital
Daniel Green & Benjamin N. Roth*
November 25, 2020
Abstract
A rapidly increasing share of asset allocation decisions
incorporate social values in addition
to financial considerations. We argue that the most common
strategies for socially motivated
investing, which only consider the social value of the firms in
an investors’ portfolio, are mis-
guided. We develop a tractable framework in which commercial and
social investors compete,
and identify alternative strategies for social investors that
result in higher social welfare and de-
liver higher financial returns. We discuss several normative
implications for socially-motivated
investors. From the enterprise perspective, we demonstrate that
a focus on increasing profitability
can have a greater social impact than a focus on direct social
value creation.
*[email protected], [email protected]. We thank Malcolm Baker, Vivek
Bhatacharya, Paul Brest, Robert Gertner (discus-sant), Oliver Hart,
Dean Karlan, Scott Kominers, Ernest Liu, Ludwig Straub, Mark
Wolfson and participants at HarvardBusiness School, Brandeis, and
the 2020 Economics of Social Sector Organizations conference for
helpful comments.
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1 Introduction
The last several decades have seen an invigoration of investing
in companies that rank favorably onmetrics of social value, such as
environmental stewardship, social responsibility, and good
governancepractices (collectively referred to as ESG). For
instance, one quarter of assets under management byprofessional
investors–$30 trillion– are now allocated with such considerations
(US SIF Foundation,2018). This large shift in investment strategies
has the potential to dramatically alter the allocation ofcapital in
the economy. In fact, many argue the entire purpose of this
movement is to help reallocateresources to socially beneficial uses
and away from socially harmful ones. Thus, it is centrally
im-portant to understand whether and how this style of investing
generates impact. This paper developsa general framework to explore
how investing with social convictions results in the creation of
socialvalue and which investment strategies generate social value
most efficiently.
We focus on “passive” strategies based entirely on selecting
which assets to hold or avoid. By farthe most common of such
strategies in practice are constructed with attention to the
financial returnsand the social value of the companies included in
an investor’s portfolio. For example, ESG indexfunds attempt to
track the returns of a benchmark index while maximizing some
composite measureof the social good of the companies in the
portfolio. Proponents of such “values-aligned” investingclaim that
they increase the valuation of (or equivalently decreases the cost
of capital for) economicendeavors that contribute the most
positively to society. This in turn shifts the set of projects
thatmarkets will finance towards those that create social value and
away from those that destroy it.
We argue that the folk wisdom justifying “values-aligned”
investing is misguided, and such in-vestment strategies are an
inefficient way to use asset allocation decisions to influence
social valuecreation. Our framework builds on the insight that an
investor’s true contribution to social value isnot reflected in the
social value of the companies in their portfolio, but rather by the
additional socialvalue created relative to if the investor did not
exist at all (e.g. Brest et al., 2016). The distinctionbetween
these perspectives is driven by the fact that many companies that
have high social valuecould attract investors with a purely
financial objective. Therefore, socially motivated investors
whofinance these companies may not be contributing to social value
creation. In fact, their behavior couldeven result in social value
destruction if it displaces investors unconstrained by social
considerationsinto financing socially harmful projects. We
formalize this critique in a general equilibrium modelof capital
allocation and characterize its implications for the behavior of
social investors. We furtheridentify an alternative to
“values-aligned” investment strategies that can generate more
impact andachieve higher financial returns.
To understand the basic logic of why social investors who attend
only to the social value of theirportfolio companies might achieve
sub-optimal outcomes, consider the following stylized example.
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Suppose there are two investors each of whom holds one unit of
capital. One commercial investorcares only about financial returns
and the other social investor cares about both financial returns
andsocial value. Suppose further that there are three enterprises,
each of whom needs one unit of capitalto survive:
• Firm A generates a 10% profit and 10 units of social
value.
• Firm B generates a 8% profit and 5 units of social value.
• Firm C generates a 9% profit and 0 units of social value.
Investors finance companies at prices that ensure them a
financial return no greater than the firm’stotal return on
investment. A social investor who makes investment decisions based
only on their ownreturns and the social value of the companies they
finance would want to invest in Firm A. Such aninvestor would be
willing to pay more for this opportunity than the commercial
investor, leaving thecommercial investor to finance Firm C and earn
a 9% return. As a result, the social investor financesFirm A,
enjoys a financial return of 9%, and 10 units of social value are
created. If instead the socialinvestor took a holistic view, they
would appreciate that Firm A is profitable enough to attract
thesupport of the commercial investor. The social investor might
then want to invest in firm B. In thiscase the social investor
would receive a financial return of 8% and 15 units of social value
would becreated.
This example highlights that social investors narrowly focused
on the social value attributable tocompanies in their own portfolio
are not effective at generating social value through their
investmentdecisions.1 We develop a framework to embed this logic in
a competitive financial market, in whichmany commercial investors
and social investors coexist and firms’ costs of capital are
determinedin equilibrium. To highlight the nuances arising from the
two approaches to social investing in theprevious example, we
introduce two types of social investors. Values-aligned social
investors formportfolios based on the financial returns and social
welfare generated by the companies they support.Sophisticated
social investors are similar, but consider implications of their
investment decisions fortotal social welfare, not just the social
value of firms in their portfolio.
Beyond admitting a tractable analysis of equilibrium behavior,
our model yields several normativeimplications for social investors
and entrepreneurs. First we demonstrate that capital held by
differentclasses of investors has different social values,
reflecting the investors’ contribution to social welfare.We define
the social value of capital for a particular class of investors as
the increase in total socialwelfare associated with marginally
expanding the pool of capital held by those investors. Both typesof
social investors have socially valuable capital. However,
values-aligned investors have a lower so-
1In fact, notice in this example that the social investor’s
choice of Firm A results in zero additional social value
creationrelative to an economy in which neither investor had
preferences for social value.
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cial value of their capital. Relative to sophisticated
investors, values-aligned investors over-prioritizecompanies that
have both high social impact and high profitability. These
companies could attractcommercial investment independent of whether
social investors support them. Values-aligned socialinvestors who
finance these companies bid up their prices, crowding out
commercial investors, whoinstead finance less profitable and
socially impactful firms.
While values-aligned social investors do lower the cost of
capital for socially valuable projects,their displacement of
commercial investors also lowers the cost of capital for, and
enables financing of,projects that the values-aligned social
investors themselves would not want to support. Sophisticatedsocial
investors, by definition, internalize this effect of their
investment behavior and do not supportprojects that could have been
financed by commercial investors in their absence.
An important implication of this result is that there are
improvements to the investment strategy ofvalues-aligned social
investors. Any capital that values-aligned investors deploy to fund
profitable butalso impactful projects that could have been
commercially financed should be redeployed to projectswith lower
profitability (and potentially lower social value). Perhaps
surprisingly, this can increaseboth the social impact and financial
return to this capital. Why? As the result of
values-alignedinvestors competing with each other to own shares in
certain projects, they are both pushing commer-cial investors into
lower impact projects and transferring excessive value to
entrepreneurs (or a firm’sexisting owners). Any financial
concession made to own a firm that could have attracted
commercialinvestment does not serve to expand the set of socially
valuable projects that are economically viable.This generates scope
to put a financial concession to more effective use. Instead
investing directly inprojects that are less profitable but more
impactful than what a displaced commercial investor wouldhave
chosen can thus result in higher social value creation and higher
financial returns to the socialinvestor.
Our baseline model considers an environment where all firms have
a fixed scale. In this case,socially conscious investors maximize
by investing in firms that could not attract any
commercialfinancing. This is not a realistic option for small
socially conscious investors, who are typically limitedto making
investments through established capital markets. We extend our
model to investigate theimplications of socially responsible
investing when firms have an intensive margin of scale and showthat
in this case there is scope for creating impact. However, this
depends on the ability of socialand commercial investors to provide
capital at different terms. When there is just a single security
forwhich all investors must pay the same price, social investors
can only subsidize a firm’s new projects ifthey are the marginal
investor in the security. Enabling new projects therefore requires
social investorsnot only to finance the new projects, but also to
displace existing commercial investors. The socialcapital used to
displace commercial investors generates no marginal social impact.
We argue thatthe creation of a second security, similar to existing
“green bonds,” provides more scope for social
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investors to generate impact. This allows social investors to
provide low-cost financing for sociallyvaluable projects without
displacing a firm’s existing commercial investors. However, green
bonds intheir current form do not necessarily serve this goal,
because they do not restrict proceeds to be usedonly to fund
investment that is not commercially viable.
Our framework also has implications for evaluating the social
impact of a firm, sometimes calledits enterprise impact (Brest et
al., 2016). Enterprise impact depends not only on the amount of
capitalused by the enterprise, but also on the type of capital used
by the enterprise. All else equal, enterprisesthat attract the
capital of socially minded investors have lower contribution to
social welfare than thosethat attract the capital of purely
commercial investors. Holding fixed the social value created by a
firm,it can raise its enterprise impact by reducing its dependence
on social capital, freeing social capital tofund another enterprise
that is unable to obtain commercial financing. The more profitable
is a firm,the less likely it is to rely on scarce, socially
valuable capital. Our framework thus provides a newconnection
between the profitability of an enterprise and its contribution to
social welfare.
Finally we consider an extension in which social investors
exhibit varying degrees of altruism.When social investors are
values-aligned we identify a familiar result: social investors and
entrepreneursexhibit positive assortative matching, in that
investors who care more about social welfare match toentrepreneurs
that create more social value. However when social investors are
sophisticated, thisresult partially reverses. Holding fixed the
level of an entrepreneur’s profitability, social investorswho value
social welfare more highly match to entrepreneurs who create less
social value. This resultarises from the fact that social investors
have interdependent utility in that they internalize the
socialvalue created by all firms that receive financing.
Before reviewing the relevant literature, we make one note about
the interpretation of our modeland results. The investment
strategies adopted by values-aligned investors in our model
strongly mir-ror those of real-world socially conscious investors.
There are at least two ways to understand this.First, investors may
not care about social welfare creation, but instead derive utility
from associa-tion with social value. They may not want to be
associated with companies that are heavy pollutersand would be
willing to forgo higher returns from investing in those companies,
for example, evenif over-weighting low-polluting companies in their
portfolio does little to reduce aggregate pollution.According to
this interpretation of the motives of social investors, our
analysis should be understoodas exploring the positive implications
of values aligned versus sophisticated social investment
strate-gies on aggregate resource allocation. Alternatively,
real-world socially conscious investors could bemotivated by making
the world a better place, and therefore would be making a mistake
in adoptingvalues-aligned investment strategies. If they knew
better, they might prefer to invest in a way thathad a bigger
impact on social value and generated higher returns. If investors
are indeed making amistake, our model delivers normative
suggestions that can help investors improve asset allocation
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decisions. We return to this discussion in our conclusion.
This paper contributes to the literature on investing with
social preferences. A number of papersstudy financing environments
where social and commercial investors coexist, and ask how social
in-vestors should behave to maximize their impact. Oehmke and Opp
(2019) and Landier and Lovo(2020) both study activist social
investors who aim to resolve a moral hazard problem amongst
en-trepreneurs. The two papers investigate how the amount of social
and commercial capital influencesthe bargaining power of social
investors and their resulting social impact. Broccardo et al.
(2020)highlights that if activist investors all vote as if they are
pivotal, well-diversified investors with even asmall concern for
social welfare will vote in line with the social planner. Like in
our analysis, thesepapers consider social investors who care about
social value independently of if it was created by thecompanies
they support. In contrast to these papers, we study passive
investors in a complete infor-mation environment, whose goal is to
enable new projects by offering cheaper capital to firms
withsocially valuable projects.
Pedersen et al. (2019) and Pastor et al. (2020) study social and
commercial investors within aMarkowitz framework, derive the
optimal portfolios for each class of investors and shows an
ESG-adjusted CAPM emerges. The social investors in their framework
maximize a combination of finan-cial return and the impact of firms
in their portfolio, and hence correspond to our values-aligned
socialinvestors.2 Heinkel et al. (2001) demonstrates that when
socially motivated investors divest from so-cially unproductive
firms their stock price declines, as the remaining investors hold
more concentratedportfolios. In contrast to these papers, we study
a model without uncertainty, and focus our analysison the behavior
of sophisticated social investors who aim to maximize social
welfare rather than theimpact of their own portfolio.
Several papers analyze the behavior of individual firms and
their prosocial investors. Focusing onthe single investor case,
Chowdhry et al. (2019) and Roth (2020) analyze when a socially
mindedinvestor can have more impact through an investment in a
social enterprise than they can througha grant. Hart and Zingales
(2017) fleshes out several cases for a stakeholder view of the
firm, inwhich management’s objective encompasses more than profits
alone, and considers arrangements bywhich activist shareholders can
induce the firm to take socially efficient actions. Morgan and
Tum-linson (2019) argue that corporate social responsibility might
be a vehicle to overcome collectiveaction concerns amongst a firm’s
prosocial shareholders, and argues that corporate social
responsi-bility might be an efficient channel for prosocial actions
when the firm’s production imposes societal
2Pastor et al. (2020) considers an extension in which investors
incorporate the social value of all firms into theirobjective
function, but the analysis assumes that individual investors cannot
meaningfully influence the economy andhence their preferences for
financial return and the social value of firms within their own
portfolio fully determine theirinvestment decisions. In contrast
our sophisticated social investors value their own financial return
on the same order astheir contribution to total social value, and
hence the fact that they partially internalize the value created by
all firms doesinfluence their decisions. We expand on this
discussion in Section 2.1.
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externalities. This latter point is also highlighted in Nilsson
and Robinson (2017). Dewatripont andTirole (2020) study how
competition affects the degree to which firms’ behaviors reflect
the ethicalconcerns of their stakeholders.
Our study also relates to the broader economic literature on
altruistic motives. Andreoni (1990)highlights the distinction
between “pure altruists,” who derive utility from social welfare,
and “impurealtruists” who derive utility, or “warm glow” from
having directly improved social welfare. In thislight, our
sophisticated social investors can be understood as pure altruists,
and our values-alignedsocial investors can be understood as impure
altruists.
Our analysis bears a technical resemblance to assignment
matching models, commonly employedin trade and labor economics
(e.g. Roy, 1951, Becker, 1973, Sattinger, 1979, Costinot and
Vogel,2010). We contribute to this literature by providing a model
in which agents sort along two dimensionsof heterogeneity, as in
Gola (2020), and by studying an environment where one side of the
market hasinterdependent utility in the sense that they care not
only about their own match but also the matchesof others. As
discussed in Section 5, we show that this latter feature can
partially reverse the classicresult of positive assortative
matching.
The rest of the paper proceeds as follows. In Section 2 we
outline the model for the case whereentrepreneurs have binary
projects. In Section 3 we analyze the model separately for the case
whereall social investors are values-aligned and for the case where
all social investors are sophisticated. InSection 4 we study a
market in which both types of social investors coexist. In Section
5 we considerinvestors with varying degrees of concern for social
welfare. Section 6 concludes.
2 Model
Players, Technology, and Contracts
There is a mass E of entrepreneurs. Each one is endowed with a
project that requires one unit ofcapital. If entrepreneur i
receives the requisite capital, his project returns πi ∈ R+ profit
and wi ∈ R“social value,” where πi and wi represent the private and
social return of the project respectively.3 Weassume that πi and wi
have atom-less and full-support distribution with CDF F , and that
the featuresof each project are perfectly observable to all
players.
There is a mass C of commercial investors and a mass S of social
investors, each of whom controlsone unit of capital. We assume that
C+S < E so that some projects go unfinanced.
3We assume that wi encompasses the full social return of the
project, including the private return πi, as well as anyconsumer
and employee surplus and externalities arising from the
project.
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A contract between some investor and an entrepreneur i specifies
the transfer of one unit of capitalfrom the investor to the
entrepreneur at a price pi ≥ 1. The investor receives financial
return pi ontheir invested capital, the entrepreneur receives πi−
pi, and wi social value is created. Because weare studying a
complete information environment without contracting frictions,
this contract can beunderstood as either debt of equity.
Preferences
Index investors and entrepreneurs such that investor i matches
with entrepreneur i. Each en-trepreneur’s utility is their share of
the profit, (πi− pi)di and each commercial investor’s utility
istheir return on capital pidi. We will separately examine two
classes of social investors.
Values-aligned social investors make investment decisions based
on financial returns they receiveand the social value created by
the entrepreneur they’ve financed. That is, their utility is
(pi +θwi)di,
where θ represents the strength of investor i’s social
preference.
Sophisticated social investors receive utility from their income
and from the total social valuecreated by all entrepreneurs who
receive financing. That is, their utility is
pidi+θ∫
j∈Ēw jd j = (pi +θwi)di+θ
∫j∈Ē\i
w jd j,
where Ē is the set of entrepreneurs who receive financing. We
discuss the formalization of thesepreferences in Section 2.1. We
can observe that the difference between the utility functions of
values-aligned and sophisticated social investors is that
values-aligned investors do not derive utility fromthe social
output generated by entrepreneurs they do not finance, while
sophisticated social investorsderive utility equally from all
social output regardless of who financed it.
Values-aligned investors do not fully internalize the
implications of their investment decision onsocial welfare. This
does not imply that the preferences of values-aligned investors are
incorrect. Asdiscussed in the introduction, values-aligned
investors may derive intrinsic utility from owning firmsthat create
social value, similar to the conception of warm-glow altruists in
Andreoni (1990). In sucha case, the analysis to follow should be
understood as exploring the positive implications of these twomodes
of investment behavior. Alternatively values-aligned preferences
may represent the behaviorof socially conscious investors, while
sophisticated social preferences may more faithfully representthe
intentions of socially-conscious investors to affect social change.
Under this interpretation our
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analysis of the behavior of sophisticated social investors
offers normative guidance to real-worldinvestors with social
preferences. We return to this discussion in our conclusion.
Timing of Actions
The central focus of our analysis is to understand how social
investors make decisions given thatsome entrepreneurs can receive
commercial financing and some cannot. Therefore we study a modelin
which entrepreneurs’ “outside option” is to seek capital on the
commercial market if they cannotattract capital from social
investors. This is relevant not only for determining the price of
equity thatsocial investors must offer, but also for the
determination of which projects could attract financingwithout the
intervention of social investors. We follow Oehmke and Opp (2019)
and Broccardo et al.(2020) in assuming that commercial investors
make their decisions after observing those of socialinvestors.
Specifically, we study a two-period model. In period 1 each
social investor offers a contract toan entrepreneur. In period 2
each commercial investor observes the period 1 actions and then
offersa contract to an entrepreneur. Entrepreneurs who have
received at least one contract then choose atmost one contract to
accept, and payoffs are realized.
Equilibrium
The solution concept is Subgame Perfect Equilibrium. All
investors choose contracts that aremutual best responses. Among
other things this implies that no entrepreneur ever receives
offersfrom more than one investor. Therefore we maintain the
convention that entrepreneur i matches withinvestor i. Further, we
adopt the convention that an entrepreneur i who receives no offers
for financinghas a price of equity pi = πi.
Social Welfare
Our measure of social welfare is W =∫
i∈Ē wi , where Ē is the set of entrepreneurs that
receivefinancing. Our interpretation is that wi is the total social
value created by firm i if it receives financing,including the
value to the firm’s owners.4 Sophisticated social investors can
therefore be understoodto be maximizing a modified variant of
social welfare that increases the weight placed on their
ownconsumption.
4Under this interpretation, the value accruing to the firm’s
owners is determined independently of how ownership isdivided, i.e.
the welfare weights placed on entrepreneurs and investors are the
same.
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Note that we do not adopt a social welfare function that sums
over the utility of entrepreneursand investors. Doing so would
induce a standard analysis of public good provision, wherein none
ofthe investors we consider invest sufficiently in businesses that
produce high wi because they do notinternalize the benefit accruing
to other investors. Instead, we adopt the convention that the
socialplanner cares about value creation wi, but does not care
about the intrinsic “altruistic” utility thatsocial investors
derive from the creation of wi. In this sense we follow Hart and
Zingales (2017) andBroccardo et al. (2020).
2.1 Discussion of the Preferences of Sophisticated Social
Investors
Sophisticated social investors differ from values-aligned social
investors in that they value total so-cial value rather than
privileging the social value of the firms that they support.
Because we studya model with a continuum of projects, social
investors cannot influence aggregate social welfare∫
Ē w jd j. An intuitive formulation of the utility of
sophisticated social preference – which we donot employ – would
be
pi +θ∫
Ēw jd j (1)
Because a single investor cannot influence aggregate social
welfare, social investors with the abovepreferences would
single-mindedly optimize their financial return.5 To ensure that
sophisticated socialinvestors do not behave this way, we employ a
different modeling approach.
Formally, we model the preferences of sophisticated social
investors as arising from the limit of asequence of discrete
models, each of which has a finite but increasing number of
projects n that canbe financed. In each of these models we assume
that sophisticated social investors have utility
1n
(pi +θ ∑
j∈Ēw j
)=
1n
(pi +θwi)+θ ∑j∈Ē\i
w j
. (2)As the number of projects financed increases, the
contribution of investor i to social welfare as afraction of total
social welfare vanishes, yet so does the amount that she values her
own financialreturn. These preferences might be understood to
represent the fact that a sophisticated social investorplaces the
same relative value on her own financial return and the welfare of
a fixed set of others nomatter how large is the set of total
financed projects.
In contrast, the social preferences represented by Equation 1
can be understood as arising from the
5Indeed, this aligns with Pastor et al. (2020), which briefly
considers social investors who have preferences for aggre-gate
social value and concludes that this preference does not influence
investor behavior.
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continuous limit of the same set of discrete models, in which
social investor preferences are
pi +1n
θ ∑j∈Ē
w j.
This would correspond to the idea that relative to her own
financial return, a social investor places lessvalue on the welfare
of a fixed set of others, as the set of all financed projects
grows.
For the remainder of the analysis, we adopt the preferences in
Equation 2. In the continuous limit,we represent these preferences
as
pidi+θ∫
Ēw jd j.
3 Equilibrium Structure with Just One Type of Social
Investor
To understand the behavior of values-aligned and sophisticated
social investors we first characterizethe equilibrium the model in
which all investors are either values-aligned or sophisticated. In
Section4 we present our main results in the model in which both
types of social investors coexist.
3.1 Values-Aligned Social Investors
We begin by characterizing the equilibrium of the model where
all social investors are values-aligned.
In the period 2 commercial market, investors’ returns must be
equalized across all entrepreneurswho receive financing. That is,
prices offered to any two entrepreneurs i and j who are both
supportedby a commercial investor satisfy pi = p j ≡ π̄ . Further,
for any entrepreneur k who is not, it must beeither that πk ≤ π̄ ,
or that they have already received an offer from a social investor
with price pk ≤ π̄ .Entrepreneurs who do not receive support in
period 2 are those who cannot offer sufficiently highfinancial
return to commercial investors.
In period 1 prices offered to any two entrepreneurs i and j who
are both supported by a socialinvestor satisfy pi +θwi = p j +θw
j.6 And for an entrepreneur i supported by a social investor andan
entrepreneur k who is not, prices must satisfy pi +θwi ≥ pk
+θwk.
6The preceding equality holds so long as prices are finite. In
equilibrium a social investor may provide funding inexchange for
zero share of the proceeds (p = 0) if the project has sufficiently
high social impact (akin to philanthropy).In such a case, the above
equality need not hold.
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𝜋
𝑤ഥ𝑤
ത𝜋
𝐶
𝑆
Figure 1: Equilibrium investment with values-aligned social
investors
With the above pricing equations we can now characterize the set
of entrepreneurs financed byeach type of investor in equilibrium.
The equilibrium investment allocation is depicted in Figure 1.
Importantly, commercial investors only invest in projects with
social value below some w̄ and prof-its above some π̄ determined in
equilibrium. Marginally profitable projects remain unfinanced,
andbecause commercial investors could finance them in exchange for
100% of their proceeds, commercialinvestors earn returns of π̄
.
Because commercial investors support all entrepreneurs with
profit higher than π̄ and with socialvalue lower than w̄, π̄+θ w̄
is the social investor’s effective outside option utility. Prices
in equilibriumare set such that social investors achieve this
outside option utility. Social investors receive financialreturn of
π̄ − θ (wi− w̄). Thus, they are willing to pay (in terms of reduced
financial return) forprojects that generate high social value.
Commercial investors do not find it attractive to invest
incompanies with πi > π̄ and wi > w̄ precisely because social
investors are willing to invest in thesecompanies at higher
prices.
A formal characterization of equilibrium investment allocations
is relegated to the Appendix Sec-tion B.1.
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𝜋
𝑤𝑤′
𝜋 𝐶
𝐶
𝑆
Figure 2: Equilibrium investment with sophisticated social
investors
3.2 Sophisticated Social Investors
Next we analyze the equilibrium allocation of capital when
social investors are all sophisticated.The equilibrium allocation
is depicted in Figure 2.
Similar to the case with values-aligned social investors, there
is an equilibrium level of profit π̃below which commercial
investors do not fund projects, and all commercial investors
receive returnsof π̃ .
In equilibrium, social investors and entrepreneurs in period 1
expect that those entrepreneurs withprofits above π̃ can receive
financing and earn πi− π̃ from a commercial offer in period 2.7
There-fore, sophisticated social investors recognize that by
supporting an entrepreneur i with profits πi ≥ π̃ ,their marginal
contribution to social welfare is not wi, but instead the social
value corresponding tomarginally expanding the set of entrepreneurs
supported by commercial investors.
We next determine the price offered to any entrepreneur
supported by a social investor.Lemma 1. For any entrepreneur i
supported by a social investor, pi = π̃ if πi ≥ π̃ and pi = πi
else.
Lemma 1 dictates that if a social investor were to support an
entrepreneur with profit πi ≥ π̃ ,they must offer contracts that
allow the entrepreneur to retain πi− π̃ of their profit, as this is
theprofit the entrepreneur could achieve from a commercial
investment. In contrast, social investors whosupport entrepreneurs
with πi < π̃ can extract the entrepreneur’s full profits. These
entrepreneursexpect not to be able to attract commercial financing
in period 2. Further, because sophisticated
7Note that this holds even if in period 1 there are more than a
mass C of entrepreneurs who meet this criterion, sinceall players
expect that in period 2 a mass of exactly C will meet this
criterion.
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social investors recognize that they cannot contribute to social
welfare by undercutting another socialinvestor, and because in
equilibrium all social investors prefer their investment to earning
π̃ andmarginally expanding the pool of commercial investments, no
social investor will undercut anotherwho is supporting an
entrepreneur with profits πi < π̃ .
In equilibrium, sophisticated social investors do not invest in
any projects that generate at least π̃profit, as they anticipate
that all of these projects will receive commercial financing.
Instead, theyinvest in the mass S of entrepreneurs i who have the
highest πi + θwi, amongst those that generateprofits πi < π̃ (so
that they would not receive commercial financing). This is depicted
in Figure 2.In Appendix Section B.2, we formally characterize the
allocation of sophisticated social investor’scapital.
3.3 Comparison of the Two Equilibria
Before analyzing the model where sophisticated and
values-aligned social investors coexist, wecompare social welfare
across the regimes with only one type of social investor. Recall,
our measure ofsocial welfare is W =
∫i∈Ē wi , where Ē is the set of entrepreneurs that receive
financing in equilibrium.
Proposition 1. Social welfare is higher when all social
investors are sophisticated than when allsocial investors are
values-aligned.
Though all social investors place weight θ on social value,
sophisticated social investors createmore social value in
equilibrium. This is because values-aligned social investors
prioritize investmentin entrepreneurs that have high social value
wi even if they could also attract investment in the com-mercial
market. The marginal contribution of these investments to social
welfare is not wi but ratherthe social value created by the
marginal project financed by commercial investors. In other words,
bysupporting an entrepreneur i that could have attracted commercial
financing, the investor’s marginalcontribution to social welfare is
not wi but rather the social value created by firm that the
displacedcommercial investor goes on to support. As commercial
investors focus single mindedly on financialreturns, the marginal
commercial investment has relatively low social value.8
In contrast, sophisticated social investors focus on the set of
entrepreneurs who could not attractfinancing on the commercial
market. Relative to values-aligned social investors, sophisticated
socialinvestors may support entrepreneurs with lower contributions
to social welfare. But the sophisticatedinvestor’s contribution to
social welfare is higher, as they are not displacing a commercial
investorwho would have supported the firm in their absence.
8Note, this does not require any assumption about the joint
distribution of profits and social value amongst projects inthe
population. Instead we are observing that in equilibrium, the
marginal projects that commercial investors support havelower
social value than the projects that social investors support, as
social investors place positive weight on social valuewhen making
their investment decision.
14
-
𝜋
𝑤ഥ𝑤
ത𝜋
𝐶 𝑆𝑁
𝑆𝑆
Figure 3: Equilibrium investment with both types of social
investors
4 Main Results
In this section we discuss a number of normative results about
social investing, in a market in whichboth sophisticated and
values-aligned social investors coexist. In particular, we
demonstrate that thereare investment strategies that deliver higher
financial returns and create more social value than thoseemployed
by values-aligned social investors. And we draw a new link between
the profitability of afirm and the firm’s social value.
First we characterize the equilibrium in the market with both
types of social investors.
4.1 Equilibrium Structure with Both Types of Social
Investors
Let there be a mass SN of values-aligned social investors, and
SS sophisticated social investors, sothat S≡ SN +SS.
There is no longer a unique equilibrium in this market.
Commercial investors’ behavior is stilluniquely pinned down as a
function of period 1 actions. But social investors may follow
multipleinvestment profiles in equilibrium leading to different
allocations of capital. In Appendix SectionB.3 we characterize the
full set of equilibria. In this section we focus on the unique,
welfare-optimalequilibrium, depicted in Figure 3.
As in Section 3.1 there is some w̄ such that values-aligned
social investors only support en-trepreneurs with social value
greater than w̄ and commercial investors only support
entrepreneurs
15
-
with social value less than w̄. Moreover, as in Section 3.1,
there exists a π̄ such that entrepreneurswith profits higher than
π̄ and social value less than w̄ are supported by commercial
investors.
To characterize the behavior of sophisticated social investors,
the following analogue of Lemma 1holds.Lemma 2. For any
entrepreneur i supported by a sophisticated social investor,
if πi ≥ π̄ and wi ≤ w̄, pi = π̄ ,
if min{πi, π̄}+θwi ≥ π̄ +θ w̄ then pi solves p+θwi = π̄ +θ w̄ if
such a p exists and pi = 0 if nosuch p exists
and pi = πi else.
The price that a sophisticated social investor pays is
disciplined by the commercial market if the en-trepreneur could
have attracted commercial financing, and by the values-aligned
social investors if theentrepreneur could have attracted financing
from values-aligned social investors. Else, a sophisticatedsocial
investor can demand an entrepreneur’s entire profit, as in Section
3.2.
The above lemmas apply across all equilibria. In the
welfare-optimal equilibrium sophisticatedsocial investors do not
compete with either commercial investors or values-aligned social
investors,and instead support the set of entrepreneurs i who
maximize πi + θwi amongst those who couldnot attract financing from
other investors. We defer formal characterization of this
equilibrium toAppendix B.3. For the remainder of our analysis we
focus on the welfare-optimal equilibrium toilluminate the model’s
comparative statics.
4.2 The Social Value of Capital
Next we discuss the social value of capital held by various
investors, defined to be the socialvalue created by marginally
expanding a given pool of capital. Let W (C,SN ,SS) be the total
socialvalue created in the investor-optimal equilibrium given
masses of investors C, SN , and SS. DefineνC ≡ dW (C,SN ,SS)dC to
be the social value of commercial capital, νSN ≡
dW (C,SN ,SS)dSN
to be the social value
of values-aligned social capital, and νSS ≡dW (C,SN ,SS)
dSSto be the social value of sophisticated social
capital. We have the following result.Lemma 3. The social value
of commercial capital is less than the social value of
values-alignedsocial capital, which is less than the social value
of sophisticated social capital: νC ≤ νSN ≤ νSS .
Figure 4 depicts how the equilibrium asset allocation changes as
each pool of capital is expanded.The grey lines define the
equilibrium prior to adding new capital. Each type of marginal
capital has a
16
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Expand Naïve Social Investors
Expand Sophisticated Social Investors
Expand Commercial Investors
Figure 4: Expanding the pool of Commercial, Values-aligned
Social, and Sophisticated Social Capital
different impact on the equilibrium set of funded projects and
which investors finance them. The bluelines denote the shift in the
equilibrium induced by expanding a particular set of capital.
Increasing the mass of commercial investors C results in the
least social value creation, as commer-cial investors disregard
social welfare entirely. New commercial investors create social
value in twoways. First, they fund previously unfinanced marginally
profitable projects that have incidental socialvalue. Second, they
bid up the price of claims on profits and displace social
investors, who substituteinto higher social value projects.
Increasing the mass of values-aligned social investors SN causes
a displacement of both commer-cial and sophisticated social
entrepreneurs, effectively expanding the pool of each. This results
in alarger increase in social welfare than does directly increasing
the mass of commercial investors, asit effectively expands the pool
of commercial capital by less and the pool of sophisticated capital
bymore.
17
-
Increasing the mass of sophisticated social investors SS
provides more social value than increas-ing the mass of
values-aligned social investors SN , as some of the firms that
values-aligned socialinvestors support could have attracted
commercial capital and therefore they merely serve to expandthe
pool of commercial capital. In contrast, expanding sophisticated
social capital does not result inthe displacement of either of the
other two types of investors.
4.3 Reallocating Values-Aligned Social Capital to Improve Social
Welfare andFinancial Returns
In this section we consider two thought exercises. First,
holding fixed the equilibrium behavior ofall other investors, we
consider the possibility of reallocating the investment of a single
values-alignedsocial investor. We demonstrate that generically, any
values-aligned social investor who supportsa firm with πi ≥ π̄
could reallocate their capital to increase total social welfare and
increase theirfinancial return. In this sense values-aligned
investors leave money on the table. We then considerthe possibility
of converting a values-aligned social investor into a sophisticated
social investor, andshow that this always leads to an increase in
social welfare and sometimes (but not always) leads toan increase
in the investor’s financial return.Proposition 2. Consider any
values-aligned social investor i that supports a firm with πi >
π̄ inequilibrium. Generically there exists an unfinanced firm j
with profits π j > pi, such that if the values-aligned social
investor i were to deviate and offer firm j financing at price π j,
total social welfarewould increase as would investor i’s financial
return.
The logic of Proposition 2 can be understood with reference to
Figure 5. Fix any values-alignedsocial investor i that supports a
firm i with profits πi ≥ π̄ and who earns financial return pi <
π̄(generically this holds for all values-aligned investors who
support firms with πi≥ π̄). These investorssupport the firms
highlighted in blue. And consider among the set of unfinanced firms
some firm jwith profits π j > pi and with social value w j
greater than the social value of the marginal firm
receivingcommercial support. This firm is guaranteed to exist by
the assumption that the distribution of firmshas full support, and
one such firm is highlighted in green.
The contribution to social welfare of the equilibrium investment
for investor i is low, regardless ofthe social value wi of firm i,
as investor i is merely displacing commercial investment. Firm j
createsless social value than any firm in the blue region of the
diagram, but by reallocating investor i’s capitalto firm j social
welfare increases, as firm j creates more social value than the
marginal firm no longersupported by a commercial investor.
18
-
!
"#"
$!
Figure 5: Reallocating Values-aligned Social Capital Out of
Equilibrium
Further, by offering firm j a cost of capital p j = π j,
investor i can earn higher financial returnas well. As with social
value, firm j earns lower profits than any firm in the blue region
of thediagram. But social investor i can demand the full profit of
firm j in exchange for financing, whereasthe price that
values-aligned investor i offered to firm i was disciplined by
competition with othervalues-aligned social investors.
Values-aligned social investors compete up the prices of firms
withlarge contribution to social value even when these firms could
have attracted commercial financing.The financial compromise made
by values-aligned investors to support such firms results in a
transferof wealth to the entrepreneur rather than expanding the
pool of socially valuable firms. In contrast, thefinancial
compromise made to support a firm that could not attract commercial
financing goes entirelytoward expanding the pool of socially
valuable firms rather than transferring rents to entrepreneurswhose
projects would anyway have been feasible.
Proposition 2 demonstrates that values-aligned social investors
leave money on the table in thesense that, relative to the firms
these investors support, there are unfinanced firms that could
deliverhigher financial returns and increase social welfare.
However, while it is straightforward to showthat converting
values-aligned social investors to sophisticated social investors
would result in highertotal social welfare, in general we cannot
guarantee that this conversion would lead investors to earnhigher
financial returns. The simple reason is that once values-aligned
investors have been convertedto sophisticated social investors,
while they would prefer to finance firms in the green region of
Figure5 relative to any firm in the blue region, there may be yet
another firm j′ which contributes more tosocial welfare but has
lower financial return than firms in the green region.
Nevertheless, we candemonstrate the following result.Proposition 3.
In the welfare-optimal equilibrium, there exists a set of
values-aligned social investors
19
-
𝜋
𝑤ഥ𝑤
ത𝜋
𝐶 𝑆𝑁
𝑆𝑆
Figure 6: Converting Values-aligned to Sophisticated
Investors
such that were they to be converted to sophisticated social
investors they would earn higher returns.
Moreover total social welfare would increase.
The logic of Proposition 3 is depicted in Figure 6. We identify
a mass of values-aligned socialinvestors, shaded in blue, who are
supporting entrepreneurs that satisfy two properties.
1. These entrepreneurs could attract commercial capital at
market rates, i.e. πi ≥ π̄ ,
2. These entrepreneurs have very high contribution to social
value wi, so that values-aligned socialinvestors make a large
financial compromise to support them.
By converting these values-aligned social investors to
sophisticated social investors, they instead sup-port the firms
shaded in yellow. As above, this results in an increase in social
welfare, as the firmsin yellow could not have attracted commercial
capital, and have contribution to social value higherthan rC.
Moreover, by identifying values-aligned social investors who were
making a sufficientlylarge financial compromise to support firms i
with high wi, we can guarantee that the newly
convertedsophisticated social investors earn higher profits, as
these sophisticated social investors can demandthe full profits of
the firms they support.
Finally, we note that while converting these values-aligned
social investors to sophisticated socialinvestors increases their
profits and total social welfare, it does not increase their
utility judged ac-cording to the utility function of values-aligned
social investors. Nevertheless, Proposition 3 offersencouraging
news about the prospect of converting values-aligned social
investors to sophisticatedsocial investors in practice. A
substantial amount of effort has gone into investigating the
hypothesisthat ESG investing can increase impact and financial
returns (e.g. Eccles et al., 2014), suggesting
20
-
investors are sensitive to the financial implications of values
investing. Our model demonstrates thatrelative to conventional ESG
strategies there is room for improvement in this dimension.
4.4 Enterprise Impact
How should one judge the contribution to social welfare of a
particular entrepreneur, sometimesreferred to as enterprise impact
(e.g. Brest et al., 2016)? On first pass it might seem natural for
wi tobe the measure of enterprise impact. However, in Section 4.2
we demonstrated that different socialvalue is attributable to
different classes of capital, suggesting that the impact of an
enterprise shouldalso reflect the social value of the capital it
employs. Along these lines, we define the enterpriseimpact of firm
i to be ei ≡ wi− νi where νi is the social value of capital
attributable to the investorwho supports entrepreneur i in the
welfare-optimal equilibrium. We define the enterprise impact to be0
for firms that do not receive financing.
This definition of enterprise impact might have practical value
for socially motivated investorsaiming to quantify the social value
of a particular enterprise. Frontier efforts in the impact
investingindustry often attempt to account for the social value
created by the enterprise and the amount ofcapital employed by the
enterprise, such as in the impact multiple of money method (Addy et
al.,2019). Our analysis highlights that it is also critical to
account for the composition of social capitalversus commercial
capital raised by an enterprise in judging its impact.
This definition of enterprise impact also highlights an
alignment between the enterprise impactand profitability of a firm.
Firms can increase their enterprise impact by increasing their
profitabilityeven holding fixed their social value wi. Increasing
the profitability of the firm makes it more likelyto attract
commercial capital, freeing up capital that is willing to accept
lower returns to fund highersocial value endeavors. In particular,
we have the following result.Proposition 4. Suppose firm i attracts
financing from some investor in equilibrium. Increasing itsprofits
πi while holding fixed its social value wi weakly increases its
enterprise impact ei and totalsocial value created in
equilibrium.
Proposition 4 states that making a firm more profitable
increases its enterprise impact even holdingits social value wi
fixed. Importantly, this result is not driven by an assumption that
a firm’s profitabil-ity and its social value are correlated.
Instead, this result is driven by the observation that the
moreprofitable is a company, the more likely it is to attract a
class of investor whose capital has low socialvalue. Every firm
that is successful in attracting financing is effectively crowding
out another firmthat could have attracted capital in its absence.
The more profitable is a firm, the less socially valuableis the
firm that it displaces from being funded.
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4.5 Impact on the Intensive Margin
So far we have assumed that every firm has a single project,
which is completed if and only if itraises a unit of capital.
Within this setting, we demonstrated that the sophisticated
investing strategycan outperform the values-aligned investment
strategy on both total social value creation and financialreturns.
However, the sophisticated approach required that investors
allocate their capital to firms thatare not commercially viable. In
reality, this would effectively relegate sophisticated social
investorsto private capital markets, which is likely infeasible for
small investors. In this section we consideran extension of the
model where firms have a non-trivial intensive margin of scale and
demonstratethat sophisticated social investors can have impact by
inducing commercially viable firms to changetheir scale of
operation. Therefore, there may be room for sophisticated social
investors to inducechange in public markets. We present this case
as a formal extension to the model in the Appendixand discuss the
results briefly here.
We assume that each firm i operates at scale k ∈ N, producing πi
(k) profit and wi (k) social value,and we assume that πi (·) and
w(·) feature decreasing returns to scale. Though the model can
beused to study the behavior of either values-aligned or
sophisticated social investors, in this sectionwe restrict
attention to sophisticated social investors. We first consider the
case where all of a firm’sinvestors must offer capital at the same
terms.
For sophisticated social investors to have an impact they must
expand (or contract) the scale of afirm relative to if it were
financed exclusively by commercial investors. Simply put, to induce
firmsto adopt marginal high social value projects, social investors
need to offer the firm a lower cost ofcapital. But because all
investors provide capital at the same terms, previously marginal
commercialinvestors will not find these terms attractive. Social
investors would thus need to replace the capitalprovided by these
marginal commercial investors, which we have argued in the
binary-project caseis a low-impact use of social capital. We
further demonstrate that sophisticated social investors arenot only
prioritizing firms that have a high marginal social value project,
but also firms for which theelasticity of demand from commercial
investors is low, so that this displacement effect we highlightis
small.9
If sophisticated social investors can provide financing at
different terms than commercial investorsthen they can achieve
higher social value creation. In this case, social investors can
effectively providesubsidized capital to support high social-value
marginal projects in a way that does not dilute theclaims of
commercial investors. This allows social investors to exclusively
finance socially valuableinvestment opportunities that are not
profitable enough to be financed by commercial investors.
9In our model, investors are homogeneous and in equilibrium
every investor is marginal, so sophisticated investorswould need to
displace all commercial investors to impact the firm. Thus, in our
model inducing a firm to undertake agiven marginal socially
valuable project requires the displacement of less commercial
capital at smaller firms.
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The model outlined in the Appendix shows that the economics of
having impact is similar on theintensive and extensive margins. In
both cases the issue is adopting an investment strategy that
avoidsdisplacing commercial investors. On the extensive margin,
this is achieved by supplying capital tocompanies that could not
raise it in commercial markets. On the intensive margin,
sophisticatedsocial investors can have impact by inducing a change
in the scale of commercially viable firms, butonly if they are able
to provide subsidized financing.
This highlights the potential for companies to issue a new class
of security in order to facilitatesocial impact creation.
Importantly, this new security is only impactful if it is used to
finance marginalinvestment opportunities that are not feasible to
finance with commercial capital. This differs from theexisting
green bond market, which raises capital to finance socially
valuable investment, regardlessof their commercial viability.10
Thus, the efficacy of green bonds could be improved if a greenbond
certification required verification that the project being financed
would not create value at itscommercial cost of capital.
5 Extension: Heterogeneous Investor Altruism θ
In this section we consider an extension of the model in which
we allow the altruism parameter θto vary across investors. Our aim
is to explore the model’s implications with regards to
assortativematching. A classic exercise in the assignment matching
literature is to identify conditions underwhich agents exhibit
positive assortative matching (e.g. Roy, 1951, Becker, 1973,
Sattinger, 1979,Costinot and Vogel, 2010, Gola, 2020) -– i.e. when
do agents with higher “types” match with oneanother? We demonstrate
when social investors in our model are values-aligned, investors
with higheraltruism match with entrepreneurs with higher social
value for familiar reasons. In contrast, wheninvestors are
sophisticated, they exhibit a variant of negative assortative
matching. This latter resultarises from the fact that sophisticated
social investors have interdependent utility; their utility
dependsnot only on the terms of their own match but also on the
matches of other investors.
5.1 Model
The model is the same as in Section 2 with the exception that
for the set of social investors we nowindex their altruism
parameter θi by i, and let it vary across investors. Specifically
we assume that thereis a finite set Θ≡
{θ 1, . . . ,θ n
}of potential levels of altruism, with θ j < θ k for 1≤ j
< k≤ n. We make
10See VanEck (2020) for background on the green bond market.
There is mixed evidence on whether green bondsare valued at a
premium to conventional bonds (Baker et al. (2018), Larcker and
Watts (2020), and Partridge and Medda(2020).)
23
-
𝜋
𝑤ഥ𝑤1
ത𝜋
ഥ𝑤2 ഥ𝑤3
𝐶 𝑆1 𝑆2 𝑆3
Figure 7: Equilibrium sorting with values-aligned social
investors
no assumption about the distribution of θi. As before we let C
be the mass of commercial investorsand we now let Sl be the mass of
social investors with altruism parameter θ l . In both the
modelwith values-aligned social investors and the model with
sophisticated social investors, commercialinvestors can be
understood as having an altruism parameter of 0. We maintain all
other assumptionsof the model in Section 2.
5.2 Values-aligned Social Investors
We now characterize the equilibrium of the model where all
social investors are values-aligned anddemonstrate that social
investors and entrepreneurs exhibit positive assortative matching
on θ and w.
The period 2 commercial market operates in exactly the same
manner as in Section 3.1; there isa level π̄ such that firms that
generate profits πi ≥ π̄ and who do not already have investment
offerswith pi ≤ π̄ receive commercial financing at price pi = π̄
.
In period 1 prices offered to any two entrepreneurs i and j who
are both supported by a socialinvestor with type θ l satisfy pi+θ
lwi = p j +θ lw j.11 And for an entrepreneur i supported by a
socialinvestor of type θ l and an entrepreneur k who is not, prices
must satisfy pi +θ lwi ≥ pk +θ lwk.
With the above pricing equations we can now characterize the set
of entrepreneurs financed byeach type of investor in equilibrium.
The equilibrium investment allocation is depicted in Figure 7.
11The preceding equality holds so long as prices are finite. In
equilibrium a social investor may provide funding inexchange for
zero share of the proceeds (p = 0) if the project has sufficiently
high social impact (akin to philanthropy).In such a case, the above
equality need not hold.
24
-
𝜋
𝑤
𝜋
𝐶
𝑆1
𝑆2
𝑆3
Figure 8: Equilibrium sorting with sophisticated social
investors
Relative to Section 3.1 the principle novelty is that we can now
establish assortative matchingin equilibrium. Namely, investors
partition the set of entrepreneurs who receive financing such
thatinvestors with higher θi match with entrepreneurs who have
higher wi. This stems from the fact thatthe utility of investor i
is supermodular in θi and wi, and hence social investors with
higher altruismhave a higher willingness to pay for projects with
high social value. This positive assortative matchingechoes many
results in the assignment matching literature cited above. As we
will see in the followingsection, this result breaks down, and
partially reverses when social investors are sophisticated.
5.3 Sophisticated Social Investors
When social investors are sophisticated there is a multiplicity
of equilibria; Figure 8 depicts theinvestment allocation in the
welfare-optimal equilibrium. Appendix Section B.5 offers a formal
char-acterization of the welfare-optimal equilibrium.
Relative to when social investors are values-aligned, the
equilibrium allocation features two impor-tant differences. First,
as in Section 3.2, so long as social capital is sufficiently
scarce, sophisticatedsocial investors exclusively support firms
that could not attract commercial financing. Second, andnovel to
this section, positive assortative matching breaks down, even among
the set of firms supportedby social investors. In fact, holding
fixed a level of profits π ′, social investors exhibit negative
assor-tative matching; the higher is the social investor’s altruism
parameter θi, the lower is the social valuewi of the firm they
support. This negative assortative matching holds despite the fact
that the utility ofsophisticated social investors is still
supermodular in their altruism parameter θi and the social
value
25
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wi of the firm they support.12
In equilibrium, in order for a sophisticated social investor i
not to deviate and support a firm thatcould have attracted
commercial investment it must be that
πi +θiwi ≥ π̃ +θiw′
where π̃ is the equilibrium level of commercial returns and w′
is the social value created by the firmfinanced by the displaced
commercial investor. This incentive compatibility condition is
easier tosatisfy for social investors with higher altruism
parameters. Therefore in the welfare optimal equi-librium, it is
the sophisticated social investors who care the least about social
welfare that match tothe most impactful entrepreneurs for a given
level of profitability, as these are the entrepreneurs whoare most
able to entice social investors away from commercial markets. In
contrast, sophisticatedsocial investors with higher altruism
parameters are willing to forgo commercial returns to
supportentrepreneurs with lower contribution to social welfare for
a given profit level. And because sophisti-cated social investors
derive utility from the social value created by all firms supported
in equilibrium,social investors with high altruism parameters do
not compete with social investors with low altruismparameters, as
they recognize that doing so would not expand social value.
Therefore, that positive as-sortative matching breaks down, and
partially reverses when social investors are sophisticated
arisesfrom the fact that sophisticated social investors have
interdependent utilities in the sense that theirutility depends not
only on the firm they match to and the price they reach but also on
the matchingof other investors and entrepreneurs.
We close this section with one final remark. We view this result
as an interesting contribution tothe literature on assignment
matching models but are cautious in interpreting it as a normative
resultfor social investors, as it relies on a feature of the model
that may be our biggest departure from thereal world. Namely, while
sophisticated social investors recognize that firms they do not
finance canstill search for financing on the commercial market,
sophisticated social investors who support firmsthat are not
eligible for commercial financing are all pivotal. Consider an
equilibrium in which socialinvestor i with low altruism parameter
is assigned to support a high social value firm j that
cannotattract commercial investment. Because sophisticated social
investors all choose their investmentdecisions at the same time, if
social investor i deviated to invest in a higher profit firm, then
firmj would go unfinanced. However, in a richer model in which
social investors make their decisionsdynamically, social investor i
might expect that another social investor with higher altruism
parameterwould replace them if they were to deviate and leave firm
j unfinanced. In such a case, this negative
12All equilibria with the same investment frontier depicted in
Figure 8 are welfare-optimal. Therefore, formally, thereexists a
welfare-optimal equilibrium such that holding the level of
entrepreneur profit fixed, social investors engage innegative
assortative matching. But there may be other equilibria with
equivalent allocations that do not feature negativeassortative
matching.
26
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assortative matching result would break down.
The above not withstanding, we conjecture that some variant of
negative assortative matchingmight survive other extensions of the
model that more closely align with reality. Perhaps most
plau-sibly, if social investors’ utility was some combination of
values-aligned and sophisticated — i.e.social investors derive
utility from both total social value and also especially from the
social value ofthe firm they support — then social investors with
low altruism who were assigned to support the mostimpactful firms
might not be tempted to deviate even if they anticipated that
another social investorwould willingly replace them. And social
investors with higher altruism assigned to support lowersocial
value firms would now face an increased temptation to undercut
their competitors financinghigher social value firms, but the
knowledge that low altruism investors will only support high
socialvalue firms might still deter this kind of competition.
6 Conclusion
This paper provides a new framework understand to how
values-based investing generates impact.We consider a model in
which investors influence social outcomes only through their asset
allocation.Investors’ choices affect the set of companies or
projects that are financed in equilibrium. Preciselyhow socially
conscious investors think about social value when making investment
decisions matters.If investors act as if they only care about the
social value generated by companies in which they invest– what we
term values-aligned investing –they have limited impact on total
social value creation.
Investors following values-aligned investment strategies, which
closely resemble the constructionof conventional ESG and emissions
reduction portfolios, have limited impact because they
displacecommercial investors who do not care about social value
creation but would have supported somesocially valuable companies
anyway. The impact of socially conscious investors is therefore in
partdetermined by the preferences of the investors displaced by the
arrival of socially conscious capital.The mechanism for this
displacement further constrains their impact. By competing with
each otherto invest in high social value companies, values-aligned
investors are wasting a financial concessionthat could have been
better spent investing in a socially valuable project that could
not have attractedcommercial capital. Because of this, we show it
is possible for a values-based investor to alter theirinvestment
strategy in a way that generates more impact and delivers higher
financial returns.
The idea of displacement also has efficiency considerations from
a firm’s perspective. By investingin their own profitability,
companies are able to reduce their reliance on social capital,
freeing it toinvest in other endeavors and thus contributing to
social value creation. This represents a new linkbetween a firm’s
profitability and its social value.
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An important question not addressed by our analysis regards the
true preferences of socially awareinvestors. There has been an
explosive growth in investment strategies that resemble the
behaviorvalues-aligned preferences in our model, and are thus
consistent with preferences for association withsocial value rather
than creation of social value. If these are indeed the true
preferences of investors,our analysis delivers a positive
prediction that preferences for social value association result in
onlylimited social value creation.
On the other hand, it is not unreasonable to believe that
investors have preferences for social valuecreation, yet, perhaps
mistakenly, pursue strategies that are inefficient in generating
social value.Investment advisers and mutual fund managers
advertising ESG portfolios routinely allude to thepositive impact
of their investment strategies. For a few examples of many, Nuveen,
an investmentmanagement firm with one trillion dollars in assets
under management asserts that ESG investing isthe approach “that is
most likely to produce optimal financial and societal outcomes.”13
Candriam, asocially responsible investment fund with C130 billion
under management asserts on its webpage thatthey “invest in the
future, channeling capital for the common good. ”14 While these
quotes indicatethat ESG investment funds aim to attract investors
with a direct preference for the creation of socialvalue, Calvert,
another provider of ESG mutual funds with $23 billion in assets
under management,goes one step further; their website allows
investors to calculate the impact of their investment in aCalvert
mutual fund across a variety of outcomes.15
To the extent that ESG funds are marketed to investors that have
a preference for the creation ofimpact rather than merely being the
owner of impactful firms, our analysis offers normative
guidance.Namely, we offer investment strategies that dominate
typical ESG approaches on both financial returnand the creation of
social impact.
13See:
https://www.tiaa.org/public/pdf/how_nuveen_uses_responsible_investing_across_asset_classes.pdf
Last Ac-cessed: November 27, 2020
14See: https://www.candriam.com/en/private/about-us/ Last
Accessed: November 27, 202015In fact, Calvert’s calculation of the
impact of an investment conflates measures of social value of
portfolio companies
with the impact of an investor in these companies. For example,
it reports that a $10,000 investment in Calvert USLarge-Cap Core
Responsible Index Fund results in an annual reduction in emissions
equivalent to burning 147 gallons ofgasoline. This figure is based
on the difference between the value-weighted emissions of
constituents in the Calvert fundand the Russell 1000 Index. See:
https://www.calvert.com/what-is-your-impact.php Last Accessed:
November 27, 2020
28
-
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Sustainable investing in equilibrium. Journal
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A Model Extension to Firms with Variable Scale
A.1 Model
There is a mass E of entrepreneurs. Each entrepreneur i is
endowed with a production function thattakes as an input k ∈ N
capital. If entrepreneur i invests k capital, they produce πi (k) ∈
R+ profit andwi (k) ∈ R “social value,” where πi (k) and wi (k)
represent the private and social return of the projectrespectively.
We assume that πi (·) and wi (·) are perfectly observable to all
players. For expositionalclarity we assume that πi (k+1)−πi (k)>
πi (k+2)−πi (k+1) for all k > 0 and i, and similarly forwi.
Importantly, we do not assume that wi is positive or strictly
increasing, so social investors maydesire to reduce the scale of a
firm’s operations, for example a heavy polluter.
There is a mass C of commercial investors and a mass S of social
investors, each of whom controlsone unit of capital.
A contract between some investor and an entrepreneur i specifies
the transfer of one unit of capitalfrom the investor to the
entrepreneur at a price pi. Therefore, letting k̄i be the amount of
capitalinvested in entrepreneur i’s project, each of entrepreneur
i’s investors receive return pi on their investedcapital, the
entrepreneur receives πi
(k̄i)− pik̄i financial return, and wi
(k̄i)
social value is created.
Market Clearing Mechanism
We assume that the market is cleared via uniform price auction.
Each entrepreneur i reports anintention to raise ki units of
capital. Each investor then submits a bid pi ∈
[0, πi(ki)ki
]to some en-
trepreneur i. Entrepreneur i then accepts his ki highest bids.16
Each investor receives a return p̄iwhere p̄i is the ki’th lowest
bid that entrepreneur i received.
Preferences
Each entrepreneur i’s utility is their share of the
profit,(πi(k̄i)− p̄ik̄i
)di. Each commercial investor
who supports entrepreneur i has utility equal to her return on
capital p̄idi. We will separately examinetwo classes of social
investors.
Values-aligned social investors receive utility from their
financial return and from the averagesocial value per unit of
capital created by the entrepreneur they’ve financed. That is, a
values-aligned
16Entrepreneurs that fail to raise their goal of ki capital
instead raise nothing.
31
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social investor who supports entrepreneur i receives utility(p̄i
+θ
wi(k̄i)
k̄i
)di,
where θ represents the strength of the investor’s social
preference.
Sophisticated social investors receive utility from their income
and from the total social value cre-ated by all entrepreneurs who
receive financing. That is, a sophisticated social investor who
supportsentrepreneur i receives utility
p̄idi+θ∫
jw j(k̄ j)
d j.
As in Sections 3 and 4, the difference between the utility
functions of values-aligned and sophisticatedsocial investors is
that values-aligned investors do not derive utility from the social
value generatedby entrepreneurs they do not finance.
Timing of Actions
As before, we study a two period model. In period 1 each
entrepreneur i proposes to raise ki capitalafter which each social
investor submits a bid to an entrepreneur. In period 2 each
entrepreneur canrevise their target ki, but in doing so
relinquishes all bids placed in period 1.17 After observing all
prioractions, each commercial investor submits a bid to an
entrepreneur. Then the market clears accordingto the process
described above.
Equilibrium
Our solution concept is Subgame Perfect Equilibrium. All
investors choose contracts that aremutual best responses. When an
entrepreneur is indifferent between two capital targets, they
choosethe one that maximizes social value.
A.2 Results
For simplicity we focus separately on the case when all social
investors are values-aligned andwhen all social investors are
sophisticated.
17This is specified for completeness, but in equilibrium no
entrepreneur who receives bids from social investors everrevises
his target ki.
32
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Values-aligned Social Investors
The model with values-aligned social investors works much the
same way as in the single projectanalysis. There exists a cutoff π̄
such that all projects receive capital at least to the point where
themarginal unit of capital generates profits less than π̄ .
Values-aligned social investors attend to a firmi’s average social
value per unit of capital,
wi(k̄i)k̄i
, in equilibrium. Therefore in equilibrium there
is some cutoff w̄ such that firms i for which p̄i + θwi(k̄i)
k̄i> π̄ + θ w̄ are entirely financed by social
investors, firms that do not clear this hurdle but that yield
average profitπi(k̄i)
k̄i≥ π̄ are financed by
commercial investors, and firms that cannot clear either hurdle
remain unfinanced. Firms i supportedby social investors raise the
smallest amount of capital k̄i such that the next unit would
yield(
πi(k̄i +1
)+θwi
(k̄i +1
))−(πi(k̄i)+θwi
(k̄i))
< π̄ +θ w̄
and firms i supported by commercial investors raise the smallest
amount of capital k̄i such that thenext unit would yield
πi(k̄i +1
)−πi
(k̄i)< π̄
Therefore, the equilibrium size of a firm is determined by not
only the intrinsic properties of thefirm but also by the identity
of its marginal investor. Firms that attract social capital have
scalepinned down by the equilibrium opportunity cost of a social
investor, which is different from that of acommercial investor.
There are two important takeaways from the exposition of
values-aligned social investors whenprojects have variable scale.
First, the investment strategy of these investors closely mirrors
that ofESG investors, for example in public equities. Such
investors purchase shares of companies that theybelieve will have
high financial returns and whose existing operations are measured
in some way tobe socially desirable. In the model, values-aligned
social investors make investments to achieve high
financial returns and be associated with companies generating
high average impactwk(k̄i)
k̄i, regardless
of whether this impact would have occurred without the social
investors’ capital.
Second, an immediate feature of this model is that
values-aligned social investors never coinvestwith commercial
investors. This stark phenomenon arises because social and
commercial investorsdisagree on the relative value of companies
with the same profits but different contributions to so-cial value,
so there is no price at which both sets of investors would be happy
to finance the sameinvestment. Any company financed by social
investors is fully financed by social investors. Whilethis extreme
separation would not arise in a model with, for example,
diversification motives, it illus-trates an important point.
Disagreement about the value of a company among investors implies
that
33
-
to change the scale of the company requires displacing some of
its existing investors.
This idea is closely related to the observations of Heinkel et
al. (2001) and Broccardo et al. (2020),that commercial investors
will partially “undo” the actions of social investors, insofar as
social in-vestors may partially crowd-out commercial investors in
the firms they support. This notion of dis-placement is critical
for understanding the behavior of sophisticated social investors in
the next sectionand implications for security design in Section
A.2.
Sophisticated Social Investors
In this section we examine the behavior of sophisticated social
investors and draw out severalnormative implications. The analysis
in this section differs qualitatively from the case where
projectsare binary in Section 3.2, in that now all projects could
potentially attract some level of commercialcapital. Thus,
sophisticated social investors may no longer want to avoid
investing in projects thatcould have attracted a positive amount of
commercial capital. We demonstrate that, unlike values-aligned
social investors, sophisticated social investors have a preference
to support small firms.
In the welfare-optimal equilibrium, sophisticated social
investors allocate their capital to maxi-mize18
max{ki}
∫i∈Ē
{(πi (ki)−qCi +θwi (ki)
)I(ki > 0)+θwi
(kCi)I(ki = 0)
}di
such that ∫kidi = S.
Here, kCi is the amount of commercial capital that firm i could
attract in period 2, and letting pC be
the cost of capital in the commercial market, qCi ≡ π(kCi)−
pCkCi is the entrepreneur’s anticipated pay-
off from commercial investment. As in the binary project case,
Ē represents the set of entrepreneursthat receive a positive level
of financing in equilibrium. 19
The term πi (ki)− qCi represents the financial return that
sophisticated social investors draw frominvesting k capital in firm
i. Namely, they can demand the full return from the project minus
whatentrepreneur i could earn on the commercial market. The term
θwi (ki) represents the social valuecreated by firm i supported by
sophisticated social investors, and for all firms i not supported
bysophisticated social investors, θwi
(kCi)
social value is created. Recall from the previous section
thatany firm supported by social investors must be wholly supported
by social investors, as social and
18The welfare-optimal equilibrium can be found by solving a
maximization problem over the joint behavior of allsophisticated
social investors. Nevertheless one can readily verify that their
behavior is individually optimal in the sensethat it can be
supported in subgame perfect equilibrium.
19Note that kCi , pC, qCi , and Ē are all implicitly functions
of the allocation of social capital in period 1.
34
-
commercial investors disagree about the value of each firm.
Thus, the constraint that∫
kidi = S
represents the sophisticated social investors’ resource
constraint; the sum of capital allocated to allfirms that receive
social investors’ support must equal the sum of all social
investors’ capital.
Let{
kSi}
denote the solution to this maximization problem. Note that in
general, kSi may be lessthan kCi . In such a case, social investors
are effectively paying entrepreneurs to reduce their scalerelative
to their optimum if financed by commercial investors.
Implied by the above maximization problem, in the
welfare-optimal equilibrium, for each firm i,sophisticated social
investors maximize
vi (k)≡(
πi (k)−qCi +θ(
wi (k)−wi(
kCi)+ γkCi
))−λk (3)
where λ is the Lagrange multiplier on the resource constraint,
and γ is the social value of the marginalproject supported by
commercial investors in equilibrium.20 Sophisticated social
investors support thefirms i for whom maxk vi (k)≥ 0.
This maximization problem captures two ideas. First, relative to
values-aligned social investors, so-phisticated social investors
care about their marginal contribution to social value, wi
(kSi)−wi
(kCi)+
γkCi , rather than the firm’s total social value wi(kSi), as
they recognize that their contribution to social
value corresponds ot the additional social value of firm i
relative to if it had received commercialfinancing, plus the social
value created by the displaced commercial investors. This parallels
thedifference in concerns of values-aligned and sophisticated
investors discussed in Section 3.
Second, even though the marginal social value created by
sophisticated social investors corre-sponds only to the output
resulting from the final kSi − kCi invested capital plus the social
value of thedisplaced commercial capital, to achieve this change
they have to provide the full amount of capitalkSi , at cost λk
Si . This has important implications for social investors’
choice of which firms to support.
Consider investments in two firms i and j that would achieve the
same marginal contribution tosocial welfare and the same marginal
profits (for convenience, assume kSi > k
Ci and k
Sj > k
Cj ); i.e.
wi(
kSi)−wi
(kCi)= w j
(kSj)−w j
(kCj)
πi(
kSi)−πi
(kCi)= π j
(kSj)−π j
(kCj)
andkSi − kCi = kSj − kCj .
20Here we are taking kCi ,qCi and γ to be fixed at their levels
implied by
{kSi}
. Taking as given the level of socialinvestment for all firms
but j, v j (k) can be evaluated at any level of k without moving
other equilibrium objects as theinvestment in firm j has mass
0.
35
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Then sophisticated social investors prefer to support the firm
that requires displacing less commercialcapital, i.e. vi
(kSi)> v j
(kSj)
if and only if kCi < kCj .
21 In this sense sophisticated social investorsprefer to support
smaller firms. We codify this logic in the following
observation.Observation 1. When there is just one security for
which all investors must pay the same price (i.e.the model s