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5757 S. University Ave. Chicago, IL 60637 Main: 773.702.5599 bfi.uchicago.edu WORKING PAPER · NO. 2020-24 Sustainable Investing in Equilibrium Lubos Pastor, Robert F. Stambaugh, and Lucian A. Taylor FEBRUARY 2020 Sustainable Investing in Equilibrium Lˇubosˇ Pa′stor Robert F. Stambaugh Lucian A. Taylor* February 14, 2020 Abstract We present a model of investing based on environmental, social, and gover- nance (ESG) criteria. In equilibrium, green assets have negative CAPM alphas, whereas brown assets have positive alphas. Green assets’ negative alphas stem from investors’ preference for green holdings and from green stocks’ ability to hedge climate risk. Green assets can nevertheless outperform brown ones during good performance of the ESG factor, which captures shifts in customers’ tastes for green products and investors’ tastes for green holdings. The latter tastes pro- duce positive social impact by making firms greener and shifting real investment from brown to green firms. The ESG investment industry is at its largest, and the alphas of ESG-motivated investors are at their lowest, when there is large dispersion in investors’ ESG preferences. JEL classifications: G11, G12 Keywords: sustainable investing, socially responsible investing, ESG, social impact *Pa′stor is at the University of Chicago Booth School of Business. Stambaugh and Taylor are at the Wharton School of the University of Pennsylvania. Pa′stor and Stambaugh are also at the NBER. Pa′stor is additionally at the National Bank of Slovakia and the CEPR. The views in this paper are the responsibility of the authors, not the institutions they are affiliated with. We are grateful for comments from Rui Albuquerque, Malcolm Baker, George Constantinides, Alex Edmans, Gene Fama, Sam Hartzmark, John Heaton, Ralph Koijen, Yrjo Koskinen, Raghu Rajan, Jeff Wurgler, Josef Zechner, and seminar audiences at the University of Chicago, WU Vienna, and the National Bank of Slovakia. 1. Introduction Sustainable investing is an investment approach that considers not only financial but also environmental, social and governance (ESG) objectives. This approach initially gained pop- ularity by imposing negative screens under the umbrella of socially responsible investing (SRI), but its scope has expanded significantly in recent years. Assets managed with an eye on sustainability have grown to tens of trillions of dollars, and they seem poised to grow further.1 Given the rapid growth of ESG-driven investing, it seems important to understand its effects on asset prices and corporate investment. We analyze both financial and real effects of sustainable investing through the lens of a general equilibrium model. The model features many heterogeneous firms and many het- erogeneous agents, yet it is highly tractable, yielding simple and intuitive expressions for the quantities of interest. The model illuminates the key channels through which agents’ preferences for sustainability can move asset prices, tilt portfolio holdings, determine the size of the ESG investment industry, and cause real impact on society. In the model, firms differ in the sustainability of their activities. “Green” firms generate positive externalities for society, “brown” firms impose negative externalities, and there are different shades of green and brown. Agents differ in their preferences for sustainability, or “ESG preferences,” which have multiple dimensions. First, agents derive utility from holdings of green firms and disutility from holdings of brown firms. Second, agents care about firms’ aggregate social impact. In a model extension, agents additionally care about climate risk. Naturally, agents also care about financial wealth. We show that agents’ tastes for green holdings affect asset prices. The greener the firm, the lower is its cost of capital in equilibrium. Greener assets have lower CAPM alphas. Green assets have negative alphas, whereas brown assets have positive alphas. Consequently, agents with stronger ESG preferences, whose portfolios tilt more toward green assets and away from brown assets, earn lower expected returns. Yet such agents are not unhappy because they derive utility from their holdings. The model implies three-fund separation, whereby each agent holds the market portfolio, the risk-free asset, and an “ESG portfolio,” which is largely long green assets and short brown assets. Agents with stronger-than-average tastes for green holdings go long the ESG 1According to the 2018 Global Sustainable Investment Review, sustainable investing assets exceeded $30 trillion globally at the start of 2018, a 34% increase in two years. As of November 2019, more than 2,600 organizations have become signatories to the United Nations Principles of Responsible Investment (PRI), with more than 500 new signatories in 2018/2019, according to the 2019 Annual Report of the PRI. 1 portfolio, agents with weaker tastes go short, and agents with average tastes hold the market portfolio. If there is no dispersion in ESG tastes, all agents simply hold the market. Even if all agents derive a large amount of utility from green holdings, they end up holding the market if their ESG tastes are equally strong, because asset prices adjust to reflect those tastes. In this equal-taste case, the ESG investment industry does not exist: despite the strong demand for green holdings, a market index fund is all that is needed to satisfy investors. For the ESG industry to exist, some dispersion in ESG tastes is necessary. The larger the dispersion, the larger the industry. We illustrate the economic significance of the above effects by calibrating a case in which there are two types of investors, those sharing equal concerns about ESG and those not con- cerned at all. The key free parameter is , the maximum certain return an ESG-concerned investor is willing to forego in exchange for investing in her desired portfolio instead of the market. The negative alpha such investors earn is greatest, and the ESG industry is largest, when dispersion in ESG tastes is greatest (here meaning ESG investors constitute half of total wealth). That worst-case alpha is substantially smaller than , however, because equi- librium prices adjust to ESG demands, thereby pushing the market portfolio toward the portfolio desired by ESG investors. For example, when ESG investors have a of 4%, their worst-case alpha is only 2%. This difference between and alpha provides ESG investors with an “investor surplus”: In order to hold their desired portfolio, they sacrifice less return than they are willing to. The same price-adjustment mechanism lessens the impact of ESG investing on the ESG industry’s size, which we measure as the aggregate ESG dollar tilt away from the market portfolio. For example, if the ESG industry reaches 33% of the stock market’s value when is 1%, then doubling the strength of ESG concerns (raising to 2%) increases that maximum industry size by less than half, to 46% of the market’s value. Our model implies that sustainable investing leads to positive social impact. We define social impact as the product of a firm’s ESG characteristic and the firm’s operating capital. We show that agents’ tastes for green holdings increase firms’ social impact, through two channels. First, firms choose to become greener, because greener firms have higher market values. Second, real investment shifts from brown to green firms, due to shifts in firms’ cost of capital (up for brown firms, down for green firms). We obtain positive aggregate social impact even if agents have no direct preference for it, shareholders do not engage with management, and managers simply maximize market value. We introduce an “ESG factor” that captures unexpected changes in ESG concerns. These concerns can change in two ways: customers may shift their demands for goods of green providers, or investors may change their appreciation for green holdings. The ESG factor 2 affects the relative performance of green and brown assets, both ex post and ex ante. Ex post, the factor’s positive realizations boost green assets while hurting brown ones. If ESG concerns strengthen unexpectedly, green assets can outperform brown ones despite having lower expected returns. Ex ante, green and brown assets have opposite ESG factor exposures, which push these assets’ market betas in opposite directions. Finally, we extend the model by allowing climate to enter investors’ utility. Expected returns then depend not only on market betas and investors’ tastes, but also on climate betas, which measure firms’ exposures to climate shocks. Evidence suggests that brown assets have higher climate betas than green assets (e.g., Choi, Gao, and Jiang, 2019, and Engle et al., 2019), which pushes up brown assets’ expected returns in our model. The idea is that investors dislike unexpected deteriorations in the climate. If the climate worsens unexpectedly, brown assets lose value relative to green assets (e.g., due to new government regulation that penalizes brown firms). Because brown firms lose value in states of the world investors dislike, they are riskier, so they must offer higher expected returns. Greener stocks thus have lower CAPM alphas not only because of investors’ tastes for green holdings, but also because of their ability to better hedge climate risk. The climate factor is likely to be related to the ESG factor because climate shocks are likely to affect both customers’ tastes for green products and investors’ tastes for green holdings. In the special case where climate shocks are the only reason behind shifts in agents’ tastes, the two factors coincide. A two-factor asset pricing model then prices all stocks, with the factors being the market portfolio and the ESG factor. In general, though, a multi-factor approach may be necessary to capture the risk associated with ESG investing because agents’ tastes may shift also for reasons unrelated to climate shocks. Our theoretical treatment of climate risk is related to recent empirical work on the im- plications of such risk for asset prices. Hong, Li, and Xu (2019) analyze the response of food stock prices to climate risks. Bolton and Kacperczyk (2019) argue that investors demand compensation for exposure to carbon risk in the form of higher returns on carbon-intensive firms. Ilhan, Sautner, and Vilkov (2019) show that firms with higher carbon emissions ex- hibit more tail risk and more variance risk. Engle et al. (2019) develop a procedure to dynamically hedge climate risk by constructing mimicking portfolios that hedge innovations in climate news series obtained by textual analysis of news sources. Bansal, Ochoa, and Kiku (2016) model climate change as a long-run risk factor. Krueger, Sautner, and Starks (2019) find that institutional investors consider climate risks to be important investment risks. Besides climate risk, studies have identified multiple other aspects of ESG-related risk. 3 Hoepner et al. (2018) find that ESG engagement reduces firms’ downside risk, as well as their exposures to a downside-risk factor. Luo and Balvers (2017) find a premium for boycott risk. We complement these studies with a theoretical contribution. We construct an ESG risk factor that is driven by unexpected shifts in ESG concerns of firms’ customers and market investors. We show that green and brown assets have opposite exposures to this factor, and we link these exposures to market betas. Prior studies report that green assets underperform brown assets, in various contexts. Hong and Kacperczyk (2009) find that “sin” stocks (i.e., stocks of public firms producing alcohol, tobacco, and gaming, which we would classify as brown) outperform non-sin stocks. They argue that social norms lead investors to demand compensation for holding sin stocks. Barber, Morse, and Yasuda (2018) find that venture capital funds that aim not only for financial return but also for social impact earn lower returns than other funds. They argue that investors derive nonpecuniary utility from investing in dual-objective funds. Baker et al. (2018) and Zerbib (2019) find that green bonds tend to be priced at a premium, offering lower yields than traditional bonds. Both studies argue that the premium is driven by investors’ environmental concerns. Similarly, Chava (2014) and El Ghoul et al. (2011) find that greener firms have a lower implied cost of capital. All of these results are consistent with the effects of tastes for green holdings on the cost of capital in our model. Some studies find the opposite result, based on different definitions of green and brown. Firms perform better if they are better-governed, judging by employee satisfaction (Edmans, 2011) or strong shareholder rights (Gompers, Ishii, and Metrick, 2003), or if they have higher ESG ratings in the 1992–2004 period (Kempf and Osthoff, 2007). These results are consistent with our model if ESG concerns strengthened unexpectedly over the sample period. Our model is related to prior theoretical studies of sustainable investing. Heinkel, Kraus, and Zechner (2001) build an equilibrium model in which exclusionary ethical investing affects firm investment. They consider two types of investors, one of which refuses to hold shares in polluting firms. The resulting reduction in risk sharing increases the cost of capital of polluting firms, depressing their investment. Albuquerque, Koskinen, and Zhang (2019) construct a model in which a firm’s socially responsible investments increase customer loyalty, giving the firm more pricing power. This power makes the firm less risky and thus more valuable. Unlike these models, ours features neither a lack of risk sharing nor pricing power; instead, the main force is investors’ tastes for holding green assets. Tastes for holding assets can affect prices, as emphasized by Fama and French (2007). Baker et al. (2018) build a model featuring two types of investors with mean-variance 4 preferences, where one type also has tastes for green assets. Their model predicts that green assets have lower expected returns and more concentrated ownership, and they find support for these predictions in the universe of green bonds. Pedersen, Fitzgibbons, and Pomorski (2019) consider the same two types of mean-variance investors, but also add a third type that is unaware of firms’ ESG scores. This lack of awareness is costly if firms’ ESG scores predict their profits. The authors show that stocks with higher ESG scores can have either higher or lower expected returns, depending on the wealth of the third type of investors. They obtain four-fund separation and derive the ESG-efficient frontier characterizing the tradeoff between the ESG score and the Sharpe ratio. While these studies share some modeling features with ours, we offer novel insights that do not appear in those studies. We show that the size of the ESG investment industry, as well as investors’ alphas, crucially depend on the dispersion in investors’ ESG tastes. We relate market betas to assets’ exposures to an ESG risk factor. We show that this factor, along with the market, prices assets in a two-factor model. We also show that positive realizations of this factor, which result from shifts in customers’ and investors’ tastes, can result in green assets outperforming brown. We have a continuum of investors with multiple dimensions of ESG preferences. Including climate in those preferences, for example, results in the pricing of climate risk. Finally, we show that ESG investing has positive social impact. Positive social impact also emerges from the model of Oehmke and Opp (2020), but through a different channel. Key ingredients to generating impact in their model are fi- nancing constraints and coordination among agents. Our model does not include those ingredients, but it produces social impact nevertheless, through tastes for green holdings. To emphasize these tastes, we do not model shareholder engagement with management, which is another channel through which ESG investing can potentially increase market value (e.g., Dimson, Karakas, and Li, 2015). In our model, value-maximizing managers make their firms greener voluntarily, without pressure from shareholders, because greener firms command higher market values.2 Our assumption that some investors derive nonpecuniary benefits from green holdings has a fair amount of empirical support in the mutual fund literature. Mutual fund flows resp

ond to ESG-salient information, such as Morningstar sustainability ratings (Hartzmark and Sussman, 2019) and environmental disasters (Bialkowski and Starks, 2016). Flows to SRI mutual funds are less volatile than flows to non-SRI funds (Bollen, 2007) and less responsive 2Theoretical work on sustainable investing also includes Friedman and Heinle (2016), Gollier and Pouget (2014), and Luo and Balvers (2017). Empirical work includes Geczy, Stambaugh, and Levin (2005), Hong and Kostovetsky (2012), and Cheng, Hong, and Shue (2016), among others. For surveys of the early literature, see Bauer, Koedijk, and Otten (2005) and Renneboog, ter Horst, and Zhang (2008). 5 to negative past performance (Renneboog, ter Horst, and Zhang, 2011). Investors in SRI funds also indicate willingness to forgo financial performance to accommodate their social preferences (Riedl and Smeets, 2017). This paper is organized as follows. Section 2 presents our baseline model. Section 3 explores the model’s quantitative implications. Section 4 extends the baseline model by allowing ESG concerns to shift over time, giving rise to the ESG factor. Section 5 extends the baseline model by letting agents care about the climate, showing that climate risk commands a risk premium. Section 6 discusses social impact. Section 7 concludes. 2. Model The model considers a single period, from time 0 to time 1, in which there are N firms, n = 1, . . . , N . Let r n denote the return on firm n’s shares in excess of the riskless rate, rf , and let r be the N × 1 vector whose nth element is r n. We assume r is normally distributed: r = μ+ , (1) where μ contains equilibrium expected excess returns and ～ N(0,Σ). In addition to finan- cial payoffs, firms produce social impact. Each firm n has an observable “ESG characteristic” gn, which can be positive (for “green” firms) or negative (for “brown” firms). Firms with gn > 0 have positive social impact, meaning they generate positive externalities (e.g., clean- ing up the environment). Firms with gn < 0 have negative social impact, meaning they generate negative externalities (e.g., polluting the environment). In Section 6, we model firms’ social impact in greater detail. There is a continuum of agents who trade firms’ shares and the riskless asset. The riskless asset is in zero net supply, whereas each firm’s stock is in positive net supply. Let Xi denote an N × 1 vector whose nth element is the fraction of agent i’s wealth invested in stock n. Agent i’s wealth at time 1 is W 1i = W0i (1 + rf +X ′ i r ), where W0i is the agent’s initial wealth. Besides liking wealth, agents also derive utility from holding green stocks and disutility from holding brown stocks.3 Each agent i has exponential (CARA) utility V (W 1i, Xi) = e AiW 1i b′iXi , (2) where Ai is the agent’s absolute risk aversion and bi is an N × 1 vector of nonpecuniary benefits that the agent derives from her stock holdings. Holding the riskless asset brings no 3We frame the discussion in terms of green and brown stocks, but our main ideas apply more broadly to any set of green and brown assets, such as bonds and private equity investments. 6 such benefit. The benefit vector has agent-specific and firm-specific components: bi = dig , (3) where g is an N×1 vector whose nth element is gn and di ≥ 0 is a scalar measuring agent i’s “ESG taste.” Agents with higher values of di have stronger tastes for the ESG characteristics of their holdings. In addition to having ESG tastes, agents care about firms’ aggregate social impact, but that component of preferences does not affect agents’ portfolio choice or asset prices. Therefore, we postpone the discussion of that component until Section 6.3. 2.1. Expected Returns Due to their infinitesimal size, agents take asset prices (and thus also the return distribution) as given when choosing their optimal portfolios, Xi, at time 0. To derive the first-order con- dition for Xi, we compute the expectation of agent i’s utility in equation (2) and differentiate it with respect to Xi. As we show in the Appendix, agent i’s portfolio weights are Xi = 1 ai Σ 1 ( μ+ 1 ai bi ) , (4) where ai ≡ AiW0i is agent i’s relative risk aversion. For tractability, we assume that ai = a for all agents. We define wi to be the ratio of agent i’s initial wealth to total initial wealth: wi ≡ W0i/W0, where W0 = ∫iW0idi. The market-clearing condition requires that x, the N × 1 vector of weights in the market portfolio, satisfies x = ∫ i wiXi di = 1 a Σ 1μ+ dˉ a2 Σ 1g , (5) where dˉ ≡ ∫iwididi ≥ 0 is the wealth-weighted mean of ESG tastes di across agents. Note that dˉ > 0 unless the mass of agents who care about ESG is zero. Solving for μ gives μ = aΣx dˉ a g . (6) Premultiplying by x′ gives the market equity premium, μM = x′μ: μM = aσ 2 M dˉ a x′g , (7) where σ2M = x ′Σx is the variance of the market return. In general, the equity premium depends on the average of ESG tastes, dˉ, through x′g, which is the overall “greenness” of the market portfolio. If the market is net green (x′g > 0) then stronger ESG tastes (i.e., larger 7 dˉ) reduce the equity premium. If the market is net brown (x′g < 0), stronger ESG tastes increase the premium. For simplicity, we make the natural assumption that the market portfolio is ESG-neutral, x′g = 0 , (8) so that the equity premium is independent of agents’ ESG tastes. In this case, equation (7) implies a = μM/σ 2 M . Combining this with equation (6) and noting that the vector of market betas is β = (1/σ2M)Σx, we obtain our first proposition. Proposition 1. Expected excess returns in equilibrium are given by μ = μMβ dˉ a g . (9) We see that expected excess returns deviate from their CAPM values, μMβ, due to ESG tastes for holding green stocks. Corollary 1. If dˉ > 0, the expected return on stock n is decreasing in gn. As long as the mass of agents who care about sustainability is nonzero, dˉ is positive, and expected returns are decreasing in stocks’ ESG characteristics. Because the alpha of stock n is defined as αn ≡ μn μMβn, equation (9) yields the following corollary. Corollary 2. The alpha of stock n is given by αn = dˉ a gn . (10) If dˉ > 0, green stocks have negative alphas, and brown stocks have positive alphas. Moreover, greener stocks have lower alphas. As long as some agents care about sustainability, equation (10) implies that the CAPM alphas of stocks with gn > 0 are negative, the alphas of stocks with gn < 0 are positive, and αn is decreasing with gn. Furthermore, the negative relation between αn and gn is stronger when risk aversion, a, is lower and when the average ESG taste, dˉ, is higher. Proposition 2. The mean and variance of the excess return on agent i’s portfolio are E(r i) = μM δi ( dˉ a3 g′Σ 1g ) (11) Var(r i) = σ 2 M + δ 2 i ( 1 a4 g′Σ 1g ) , (12) where δi ≡ di dˉ. 8 Both equations are derived in the Appendix. Agents with δi > 0 earn below-market expected returns because their portfolios tilt toward stocks with negative alphas. In contrast, agents with δi < 0 earn above-market returns because they tilt toward positive-alpha stocks. All agents with δi 6= 0 hold portfolios more volatile than the market. Corollary 3. If dˉ > 0 and g 6= 0, agents with larger δi earn lower expected returns. Under the conditions of this corollary, the term in parentheses in equation (11) is strictly positive. Therefore, agents with stronger ESG tastes (i.e., larger δi) earn lower expected returns. The conditions are not satisfied if no agents care about ESG (dˉ = 0) or if all firms are ESG-neutral (g = 0); in that case, E(r i) is independent of δi because all agents hold the market. The effect of δi on E(r i) is stronger when the average ESG taste is stronger (i.e., when dˉ is larger), when risk aversion a is smaller, and when g′Σ 1g is larger. The low expected returns earned by ESG-sensitive agents do not imply these agents are unhappy. As we show in the Appendix, agent i’s expected utility in equilibrium is given by E { V (W 1i) } = Vˉ e δ2 i 2a2 g′Σ 1g , (13) where Vˉ is the expected utility if the agent has δi = 0. We see that expected utility is increasing in δ2i (note from equation (2) that Vˉ < 0), so it is larger for agents with larger absolute values of δi. The more an agent’s ESG taste di deviates from the average in either direction, the more ESG preferences contribute to the agent’s utility. High-δi investors derive utility from their holdings of green stocks, while low-δi investors derive utility from the positive alphas of brown stocks. 2.2. Portfolio Tilts Substituting for μ from equation (9) into equation (4), we obtain an agent’s portfolio weights: Proposition 3. Agent i’s equilibrium portfolio weights are given by Xi = x+ δi a2 ( Σ 1g ) . (14) Proposition 3 implies three-fund separation as each agent’s portfolio can be implemented with three assets: the riskless asset, the market portfolio x, and an “ESG portfolio” whose weights are proportional to Σ 1g. Agents with δi > 0 go long the ESG portfolio; agents with δi < 0 short the portfolio. Agent i’s portfolio departs from the market portfolio due to the second term in equation (14), which we refer to as agent i’s “ESG tilt.” 9 The ESG tilt is zero for agents whose ESG taste is average, in that di = dˉ. Such agents hold the market portfolio. Interestingly, agents with di = 0 hold a portfolio that departs from the market in the direction away from ESG. It is suboptimal for an investor to say “I don’t care about ESG, so I’m just going to hold the market.” Investors who do not care about ESG must tilt away from ESG, otherwise they are not optimizing. The market portfolio is optimal for investors who care about ESG to an average extent, but not for those who do not care about ESG at all. Corollary 4. If there is no dispersion in ESG tastes across agents then all agents hold the market portfolio. No dispersion in ESG tastes implies di = dˉ, and so zero ESG tilt, for all i. Interestingly, even if all agents derive a large amount of utility from green holdings, they end up holding the market if their tastes are equally strong. The reason is that stock prices adjust to reflect those tastes, making the market everybody’s optimal choice. Some dispersion in ESG tastes is necessary for an ESG investment industry to exist. If the covariance matrix Σ is diagonal, meaning all risk is idiosyncratic, then the ESG portfolio weights are positive for green stocks (whose gn > 0), negative for brown stocks (whose gn < 0), and lower for stocks with more volatile returns. A similar result obtains when Σ has a simple one-factor structure, allowing systematic risk: Σ = σ2ιι′ + η2IN , (15) where ι is an N × 1 vector of ones and IN is an identity matrix, because in that case4 Σ 1g = 1 η2 g gˉ η2 Nσ2 + 1 ι , (16) where gˉ = ι′g/N is the mean gn across firms. As N gets large, the ESG portfolio goes long stocks that are greener than average (gn > gˉ) and short stocks that are browner than average (gn < gˉ). The ESG portfolio’s positions are smaller when idiosyncratic risk η 2 is higher, because tilting toward the ESG portfolio exposes investors to more idiosyncratic risk. In general, the ESG tilt depends also on the covariances among stocks. If a stock is positively correlated with a greener stock, the former stock may be shorted by agents who want to hold the greener stock and hedge their risk exposure to it. In principle, even a green stock could be shorted if it is sufficiently correlated with a stock that is even greener. 4With Σ given in equation (15), we have Σ 1 = 1η2 ( IN 1η2/σ2+N ιι′ ) . 10 The ESG tilt is smaller when risk aversion, a, is higher, because the tilt exposes agents to additional risk (see equation (12)). Holding ESG preferences (δi) constant, those preferences are reflected less strongly in agents’ portfolios if agents’ risk aversion is higher. 3. Quantitative Implications To explore the model’s quantitative implications, we consider a special case with two types of agents: ESG investors, for whom di = d > 0, and non-ESG investors, for whom di = 0. ESG investors thus consume nonpecuniary benefits dg, whereas non-ESG investors consume no benefits (see equation (3)). Let λ denote the fraction of total wealth belonging to ESG investors, so that 1 λ is the corresponding fraction for non-ESG investors. 3.1 Expected Returns and Portfolio Tilts In this setting, dˉ = λd, so from equation (9) the vector of expected excess returns becomes μ = μMβ λd a g . (17) As λ increases, expected returns on green stocks decrease, whereas expected returns on brown stocks increase. In this comparative static sense, growing interest in ESG increasingly pushes stock prices in the direction of their ESG characteristics. The portfolio weights for each type of investor follow directly from equation (14), with δi = (1 λ)d for an ESG investor and δi = λd for a non-ESG investor: Xesg = x+ (1 λ) d a2 Σ 1g (18) Xnon = x λ d a2 Σ 1g . (19) Both ESG tilts depend on λ in an interesting way. As λ→ 0, all investing is non-ESG, and all capital is invested in the market portfolio x because Xnon → x. As λ → 1, all investing is ESG, and again, all capital is invested in the market because Xesg → x. In other words, whether λ → 0 or λ → 1, all portfolios converge to the market portfolio. When λ → 0, everybody holds the market because there are no ESG investors. When λ → 1, everybody holds the market because ESG preferences are fully embedded in market prices. From equation (11), the difference in expected excess returns earned by the two types of investors is E(r esg) E(r non) = λd 2 a3 g′Σ 1g . (20) 11 An ESG investor thus earns a lower expected return than a non-ESG investor. The performance gap is larger when there is a greater presence of ESG investors (i.e., when λ is larger). In this comparative static sense, growth in ESG investing deepens the performance gap. The gap is also larger when the two types of investors are further apart in their ESG tastes (i.e., when d is larger), when risk aversion a is smaller, and when g′Σ 1g is larger. 3.2. Parameter Specifications We further simplify our setting by assuming that Σ has the simple one-factor structure given in equation (15) and setting β = ι, x = (1/N)ι, ι′g = 0 (i.e., x′g = 0), and g′g = 1. With these assumptions, as the number of assets (N) grows large, the mean and variance of market returns, the certainty-equivalent return of ESG investors, and other aggregate quantities of interest do not depend on N , as will be evident below. This simple setting has five free parameters: λ, a, σ, η, and d. We present results over the entire (0, 1) range of λ. We specify a and σ so that the return on the market portfolio has a mean of μM = 0.08 and a standard deviation of σM = 0.20, corresponding roughly to annual empirical estimates. To translate these values of μM and σM into implied values for a and σ, first note that the above assumptions imply the variance of the market, x′Σx, is σ2M = 1 N2 ι′ ( σ2ιι′ + η2IN ) ι = σ2 + η2 N , (21) so we set σ2 = σ2M , taking the limit as N grows large. Next, recall from equation (7) that a = μM/σ 2 M . We set η 2 = (0.7/0.3)σ2, so that the common market factor explains 30% of the variance of each individual stock’s return. The remaining free parameter, d, reflects the strength of ESG tastes. We calibrate this parameter by choosing , the maximum rate of return that an ESG investor is willing to sacrifice, for certain, in order to invest in her desired portfolio rather than in the market portfolio. The sacrifice is greatest when there are no other ESG investors, i.e., when λ ≈ 0, because that is when the ESG investor’s portfolio most differs from the market portfolio. Specifically, we define ≡ r esg r M , where r esg is the ESG investor’s certainty equivalent excess return when investing in the optimal ESG portfolio, and r M is the same investor’s corresponding certainty equivalent if forced to hold the market portfolio instead. Both certainty equivalents are computed for λ = 0. For a given , the corresponding value of d is d = √ 2 a3η2 . (22) 12 We derive this equation, along with the expressions for r esg and r M , in the Appendix. In the following analysis, we consider four v