 Well, thank you so much for this opportunity. It's an honor to be here. It's an honor to follow Dr. Schnabel's remarks. This paper is called Sustainable Investing in Equilibrium. My co-authors are Lubosz-Pastor and Rob Stambal. So there's, we know there's been growing interest in sustainable investing. This is an investing style that considers not just financial objectives, but also environmental, social, and governance, or ESG objectives. So for example, by one measure in the United States today, roughly one out of every three professionally managed dollars is sustainably managed. So there's been this tremendous growth. We need more theoretical guidance for how to think about sustainable investing. So in this paper, we build a simple equilibrium model of sustainable investing and we use it to analyze the effects of sustainable investing on asset prices and on firms' behavior. I'll summarize our predictions. Our first prediction is that greener assets have lower expected returns for two reasons. First, agents have green tastes, meaning they derive utility from holding green assets in their portfolios, where a green asset is a security of a socially responsible firm. The second reason is that green assets help to hedge climate risk. They perform relatively well when we get negative news about climate change. For both of those reasons, investors are willing to accept lower returns to hold green assets. So we predict that green assets have negative CAPM alphas and brown assets have positive alphas. So despite their lower expected returns, greener assets can outperform when what we call the ESG factor performs well. And this ESG factor is capturing shifts, unexpected shifts in customers and investors' ESG tastes. And our model produces a two-factor pricing model where the two factors are the market and this ESG factor. We find that ESG motivated investors earn lower expected portfolio returns. And that's because they tilt their portfolios toward green assets. Yet ESG investors earn what we call an investor surplus. They give up less return than they're willing to give up. And that's because of an equilibrium pricing effect that I'll explain. We show that the size of the ESG industry depends not just on how much we care about ESG, but it also depends on how dispersed investors' ESG tastes are. More dispersion creates a bigger ESG industry. Finally, we show sustainable investing leads to real positive social impact through two channels. First, by shifting capital, by inducing green firms to invest more, brown firms to invest less. And the second channel is that it induces all firms to become greener. So let me give you a graphical overview of the model. In our model, you have firms that produce financial payoffs and social impact. Investors care about both. The financial side is going to be completely standard. So let me focus on the social side. In our model, firms differ in their social responsibility. You have green firms that produce positive social externalities like cleaning up the environment. You have brown firms that produce negative externalities like polluting the environment. And there are different shades of green and brown. There are also different types of investors. Some investors care a lot about ESG. Those investors derive utility from holding green assets in their portfolios. And they have this utility from holding brown assets in the portfolio. But you also have investors who don't care at all about ESG. And they're indifferent about these companies' greenness. We use GN to denote how green firm N is. So green firms have positive Gs, brown firms have negative Gs. You can think of these GNs as being like an ESG score for the firm. We use DI to denote how much investor I cares about ESG with positive DIs for those who care. And if you don't care at all, your D is zero. We show that the average level of D in the economy, D-bar, has important asset pricing implications. So this is kind of the graphical version of the model. Formally, we add a few assumptions. We assume that excess stock returns are normally distributed. Their mean, mu, is going to be determined in equilibrium. And I've started, by the way, to say stock instead of asset. But remember, this model applies beyond stocks to really any asset, including sovereign bonds, green bonds, and so on. Then we have agents. We have a continuum of agents. They have exponential utility. And their utility has a financial component and a non-financial component. The financial component, again, it's completely standard. It depends on the agent's wealth. In their wealth, W is derived from a portfolio of N assets and the risk-free asset. The non-financial component, first of all, depends on DI, how much they care about ESG. And then this term in parentheses is the greenness of the portfolio they choose. G is a vector of those ESG scores and XI is the vector of the portfolio weights that this agent chooses. So if you care a lot about ESG, you derive utility from holding a green portfolio, disutility from holding a brown portfolio. So this is the entire model. It fits in one slide. We solve the model by, first of all, taking prices as given and solving for agent's optimal portfolio holdings X. Then we solve for asset prices by making the asset markets clear. So let me show you equilibrium-expected returns first at the level of the overall stock market. The predicted equity premium depends on the usual term. It depends on risk aversion, interacted with how much risk there is. But now we get a new term. This new term in red depends on the market's overall greenness. This is the vector of market weights times that vector of ESG scores. And that's multiplied by this negative term that has D bar in it. So what we're finding is the greener the market is, the lower the market's expected return is. And the intuition is that if investors care a lot about ESG and if the market is green, then investors don't require as much return to hold the market. Going forward though, we're going to assume that the market is ESG neutral and we do that so we can focus on the cross section which I showed starting here. So these are expected excess returns at the firm level. And I've collected those in this vector mu. They depend on the kind of the classic CAPM term. It depends on market betas, but now we get this new term in red. The new term in red is firms CAPM alphas. So what we're finding is that greener stocks have lower alphas. The alpha of stock in depends on how green that firm is interacted with D bar with a minus sign. So we're finding the greener the firm, the lower the expected return, we find that green stocks have negative alphas, brown stocks have positive alphas. This has an important corporate finance implication because remember the expected return is the firm's cost of capital. It's the discount rate the firm uses when evaluating projects. So we're finding greener firms have lower cost of capital. So what about at the agent level, the expected return on agent eyes portfolio is given here. It equals the market return minus this positive number times little delta I where little delta, it's how much this agent cares about ESG minus the average taste level. And what we're finding is the more an agent cares about ESG, the lower their expected portfolio return. And the reason is people who care a lot about ESG will optimally tilt their portfolio toward green assets. Let me show that here. So here are agent eyes equilibrium portfolio weights. So for agent eye, they've got this in by one vector of portfolio weights. Their weights equal the market portfolio weights plus a term we call the ESG tilt. That ESG tilt depends on delta I. So what we're really finding here is three fund separation agents form optimal portfolios by combining first of all the risk-free asset. Second, the market portfolio. And third is what we call the ESG portfolio. So what we're finding is that for agents with positive deltas, they optimally tilt toward green assets. Agents with negative deltas, they tilt toward brown assets. Agents who are exactly average whose delta, their delta is zero, they simply hold the market. So one kind of interesting corollary here is if you ever hear someone say, I don't care about ESG, so I'm just gonna hold the market. That person is not optimizing. If you do not care about ESG, then your delta is negative. So they should be tilting torn toward brown assets. Another corollary here is that if there's no dispersion in ESG tastes, everyone simply holds the market. And that's true even if people care a lot about ESG. And you can see it here. If everyone is the same, then everyone is average. So everyone's delta would be exactly zero. Everyone holds the market. So what we're finding is that in order for an ESG industry to exist, there must be dispersion in investors ESG tastes. So I'm gonna show some of those predictions in picture form here. These pictures come from a simple calibration of the model. And we're looking at a special case of the model here where there are just two types of investors. ESG investors and non-ESG investors. In this figure, I'm plotting on the vertical axis the expected return for an ESG investors portfolio minus the expected return for a non-ESG investor. And I'm plotting that against Lambda here where Lambda is defined as what fraction of investors are ESG investors. So first thing to notice is that all these gaps are negative. We're always finding that these ESG investors are expected to underperform. And that underperformance is especially strong when Lambda is big, when there are lots of ESG investors out there. You can get a similar message by plotting instead on this axis, the alphas of these ESG investors. Here I'm plotting that against Delta, big Delta. Big Delta is just another way to express DI, that ESG taste parameter for an ESG investor. So specifically Delta here is how much return an ESG investor is willing to sacrifice to hold their desired portfolio rather than the market. So first thing to notice is that all these alphas are negative. We're always finding that an ESG investor has negative portfolio alphas. And those alphas become especially strong the more ESG investors care about ESG. This picture also helps illustrate what we call the investor surplus. So now I've plotted this dashed line, which is just a 45 degree line. So the dashed line is plotting Delta. Remember these solid lines plot alphas. So for example, this point is how much return ESG investors actually sacrifice. This term is, or this point is how much return they're willing to sacrifice. That gap we define as the investor surplus and we can prove that gap is always positive. So what we're finding is that an ESG investor never sacrifices as much return as they're willing to sacrifice. And that's good news for an ESG investor. And we find that result because of an equilibrium pricing effect. An equilibrium prices adjust and they adjust in a way that makes the market portfolio closer to the portfolio that an ESG investor wants to actually hold. Our simple model produces a two factor asset pricing model. So expected returns depend on the usual CAPM term plus a new term that depends on beta G. That's assets loadings on this ESG portfolio return. So excess returns obey a simple regression model. We've got excess returns on the left, market returns on the right and ESG portfolio returns on the right as well. Notice there's no intercept in this regression model. That tells you that assets have zero alphas with respect to this two factor model. But remember assets do have non-zero one factor alphas, CAPM alphas. So this sheds new light on those CAPM alphas. We can express CAPM alphas as depending on beta G. So that tells you CAPM alphas come from an omitted priced ESG risk factor. At the same time though, it's true that alphas fundamentally are coming from tastes, not from some aversion to ESG risk. And you see that by our old representation of alphas as depending on the average taste level, ESG taste level. So our model also produces an ESG factor. That's the excess return on a position in this ESG portfolio. In a special case, you can just think of this ESG factor as what you get if you go long green stocks and short brown stocks. And we also obtain two factor pricing with respect to the market portfolio and now this ESG factor. So this ESG factor, it's a risk factor. Where does ESG factor risk come from? We saw the simple extension of our model and it shows that ESG factor risk comes from the fact that the strength of ESG concerns can shift over time in two ways. First you've got the investor channel. The investors ESG tastes can shift over time. Then there's the customer channel. The idea there is that the demand for green versus brown products can unexpectedly shift. For example, due to government regulation. So we work out the math and we show that the return on this ESG factor depends on unexpected shifts in customer demand and unexpected shifts in investor tastes. So the important implication here is that greener assets, green stocks can perform better than expected. If these ESG concerns strengthen unexpectedly via either of those two channels. So this is a good place for me to kind of pause and recap. Our main predictions so far are that greener assets have lower expected returns. That's the ex-ante perspective. Yet they can have higher realized returns if these ESG concerns strengthen unexpectedly. That's the exposed perspective. So this kind of begs the question, well, if you look at the data, how have green assets actually performed? To answer that question, I want to take a quick digression and talk about a brand new paper that we've just come out with called dissecting green returns. This is an empirical paper that directly builds on our theory paper. One thing we do in this new paper is to construct empirically an ESG factor. We're going to focus on the environmental part of ESG. So we're going to call this factor the green factor. And you should think of it as a stock portfolio that goes long environmentally friendly stocks, and it goes short environmentally unfriendly stocks. And we construct this using US data with ESG environmental scores from MSCI. So here's how this green factor has performed since 2013. Green assets in recent years have performed very, very well. They have outperformed brown assets by about 35% over this time period. And remember, our model says that this can happen if during this time period, ESG concerns strengthened. Did they strengthen? We think the answer is yes. In particular, one way that ESG concerns strengthened is that people's concern about climate change grew dramatically during this time period. So I'm now overlaying in red a measure of the level of concern about climate change. And this is coming from a measure constructed by analyzing the text of newspaper articles. So we're finding that these green assets outperformed and it lines up pretty well with this increase in concern about climate change. What we show in the paper is that there's a strong statistical relation between the returns of green assets and unexpected changes in concerns about climate change. Basically, when people become more concerned about climate change, green assets perform relatively well. And we think that's intuitive, right? Say we all wake up one morning and we're more concerned about climate change. Well, we would then expect governments to act. For example, governments might increase carbon taxes. That's going to shift demand to green products away from brown products. That's going to make green assets outperformed. So then we do a counterfactual analysis. We ask, well, what would have happened to this green factor if there had been no increases in concerns about climate change? So let me show that here. This top line just shows you again what actually happened to the green factor, performed well. Then using our statistical model, we set those changes in climate concerns to zero, counterfactually to zero. When you do that, the green factor's performance becomes this green line. So basically, once you turn off those climate shocks, the green outperformance vanishes. And then we turn off additionally in this red line, we turn off unexpected shocks to corporate earnings news, green versus brown earnings news. And then finally we turn off one other type of shock. These are flows into ESG investment funds. Once you turn off all those unexpected shocks, the green factor's performance, counterfactual performance, becomes negative. This agrees with our theory. Our theory says green assets can outperform if there are these unexpected shocks to ESG concerns. But once you turn off those shocks, you would expect the green factor to perform negatively. That wedge between realized and expected returns comes through even more clearly, we think, in the case study of German twin bonds. So Germany performed a nice experiment for us. They recently issued green bonds. And each green bond had a non-green twin. It was a twin in the sense that it was another German bond with exactly the same coupons in exactly the same maturity. So we can compare those two to measure the effects of greenness. The first thing we notice up here is that the green bonds had a slight greening at issuance. Their yield was slightly below their twin's yield. So what that tells you is that the green bonds were expected to underperform consistent with our prediction. Did they underperform? The answer is no. We show that below, where I'm plotting the cumulative realized return on the green bond minus its twin. So what we found is that the green bond actually outperformed. Why did the green bond outperformed? Why did it outperform? The answer is back up top. This greenium, this yield spread between the two bonds deepened during this period. What that means is the expected return on the green bond went down and down and down. That is what was responsible for the green bonds realized returns being higher. So again, this is another illustration of how there can be a wedge between expected returns and realized returns. And that wedge comes from shifts. In this case, shifts in expected green returns. Back to the theory. I want to mention two important extensions in our theory paper. The first is about climate change risk. We model climate in a very simple way by adding a new term to agents utility functions. We put a climate variable, a random variable C, in their utility. So we're saying agents dislike bad realizations of the climate. When you do that, you get a new expression for expected excess returns. We have the same black terms as before, but now we get this new red term. Now we find that firms expected returns depend on climate betas. That is, how do these firms co-vary with this climate variable? Next, we assume greener stocks are likely better climate hedges. Supporting that assumption are those empirical facts I just showed you. We show empirically green stocks perform relatively well. When people become more concerned about climate change. In that sense, green assets are safer. They perform better in bad states of the world. And because of that, we now get this kind of new expression for firms alphas. We now find that firms green stocks have lower alphas for two reasons. The first reason is green tastes exactly as before. But the second reason is now hedging risk. Since green assets are safer, they help hedge climate risk. Since they're safer, people require less return to hold them. Our last extension is about social impact. Here we're asking to sustainable investing have any real effects. So we define the social impact of firm in as the product of how green that firm is and how big that firm is. K is the firm's operating capital. So remember, green firms have positive G's. So they have positive social impact. Brown firms have negative G's. They have negative social impact. Bigger firms have more absolute impact. Next, we allow firms to choose their G and choose their K. Specifically, we assume each firm maximizes its market value. By choosing how much extra capital to buy that's corporate investment. And by how much to change their greenness. We endow firms with some initial amount of capital some initial level of greenness. And we assume firms face adjustment costs costs and adjusting their capital costs and adjusting how green they are. And what we show is that green tastes of investors generate positive social impact for every single firm. So for here we have for firm in. Here's its social impact if there were zero ESG tastes. We show that's lower than that exact same firm social impact. If they're positive ESG tastes. Social impact comes through two channels. The first is about a shift in capital. We find that green firms would invest more. And that's because these ESG investors lower the cost of capital for green firms. Conversely, brown firms invest less. And that's because their cost of capital is driven up by these ESG investors. So essentially we're predicting you would get more solar farms less coal mines. The second channel is that we predict all firms voluntarily choose to become greener. And that's because they understand if they become a little bit greener that will make their market value go up. And it's interesting we get this because remember our managers don't care about ESG. They simply care about maxing maximizing their firm's market values. And it's also interesting because remember there's no shareholder activism, no direct engagement in this model, yet we still find social impact. To conclude, in our model, we predict greener assets have lower expected returns. Yet green assets can outperform when this ESG factor performs well. This ESG factor is capturing unexpected shifts in customers and investors ESG tastes, possibly driven by government regulation. In our empirical follow on paper, we study shifts and climate change concerns, and we show that those shifts go a long way to explaining the outperformance we've seen in recent years in green versus brown assets. In our theory paper, we show the ESG motivated investors they earn lower expected returns, yet they enjoy this investor surplus. Finally, we show sustainable investing has real impacts, it leads to positive social impact by reallocating capital away from brown firms toward green firms, and by inducing every firm to voluntarily become greener. Thank you very much. Thank you, Lucian. The paper will be presented by Eugenie de Goua from the LSE. Thank you very much for this opportunity. So I'm going to try my best to provide a discussion on this paper, though before I get started, you know, I need to highlight that. First, I'm an environmental economist. I am not a financial economist. And so a lot of the thoughts that this paper inspired to me are very much from a perspective of somebody working on environmental issues. Very much so I focus a lot on innovation and technological change. And so obviously the discussion I'm providing here may be staying at a very high level in terms of the financial aspects. Also, this paper is already published. And congratulations to the authors for already the amazing amount of citation that this paper has put together. So my discussion is going to focus mostly on trying to understand the contribution of that theory and how it can help us understand the world, how in particular sustainable investing may be doing today. And that is really the starting point for this paper is trying to think about how sustainable investing works. There's been a really impressive growth in sustainable investing recently. We have put out some number here coming from a BNP Paribas report from two years ago. And you can see that the number is basically saying that in just two, three to four years, about a majority of asset owners and asset managers have had more than 25% funds invested in ESG funds. And they're obviously forecasting that this trend will continue. There are also many headlines about sustainable investing or ESG funds. And often you see some questions popping up like, okay, does it really matter or is this just really greenwashing? Is this doing anything that sort of matter for the thing in the real economy? Is it shifting, you know, how much pollution is being produced or is this changing anything about how firms treat their employees, for example? So this paper is a theory and does, you know, theory here is really helpful to clarify how we think about such an investment vehicle. And in particular here it is useful to help us clarify the different channels through which the different preferences that agents have that investors have for sustainability may matter. And exactly there are many different ways that investors may interact with firms and assets. But in this model, they really in fact start from their very simple starting point, which is to have a model that just have different agents with different preferences for sustainability. So stronger or weaker preferences for sustainability and then having green assets or brown assets providing a utility or a disunity. And really from the simple starting theoretical point, they look at several outcomes of interest. In particular, there's a big part of the paper as well as a talk that has focused on explaining how asset prices and portfolio holdings change or impacted by investors' preferences. But they're also trying to draw some conclusions about real impact. They're here, they're making this really valuable effort at the live in connecting the theory of asset pricing to, you know, the real impact on society, which they define as this combination between the intensity of the greenness of the firm and the scale of that firm. Right. So that is the definition that they adopt here of how a particular, how much impact a particular firm has. And so there's a key take where message here in a way they are implicitly one of the question that this paper is trying to answer is, you know, can ESG investors change the world, like do something very concrete about the directions of the world economy. And, and apparently sort of yes. Well, at least I would say that this theory tells us that while ESG invent investors push the world into the right direction. And there are several channels through which this is happening. The first one is that because you have some higher tests for green, this leads to an increase in asset prices of green. And there's already quite a sizable empirical literature, you know, was sometimes opposite findings and the more recent empirical work that the authors mentioned in the presentation also sort of added novel dimension to the connection between sustainable investing and the role of preferences or the role of climate shocks. So to speak. Now what I'm sort of was more interested in or the two other channels which, you know, are trying to tell us something about how sustainable investing may matter for real impacts. And the first channel here is by saying that the model shows that higher tastes for green leads to a lower cost of capital for green firm. And that's really interesting from my perspective because I immediately connected that to the literature and the economics of innovation. And in particular firms ability to innovate. So there is a literature thinking about market failures in risk and capital markets and how that constrain our and definancing for firms. So there's a seminal article here from Holland Learner 2010 that explains how the lack of collateral values and information asymmetries between investors and entrepreneurs may hinder the process of innovation and technological change in the in a context of green innovation. There is also a versioning literature here that to me really resonated strongly with that implication of the paper, the idea that green technologies or younger less mature they're more uncertainties maybe a higher chunk of cause that would be irreversible. So there's like two paper here that really speak very strongly to the fact that green firms indeed may be critically constrained that may hinder their ability to be innovative and develop, deploy their technologies. And so, in that sense, this, this sort of channel about lowering the cost of capital for green firm this sort of first theoretical, one of the theoretical finding that they have in this paper I thought was of prime importance for that reason. The second channel, going back to this sort of two sort of channel that's really sparked my inspiration is the one about where they do this exercise in one part of the paper where it's almost as if they end dogenize firms decision to be greener or dirtier. And that obviously rings a bell to the whole literature and directed technical change. Here I'm sort of putting out an example of one of the seminal article in that literature from Asimoglu, Agnion, Birston and Hemis 2012. And in that literature, you can conceptualize firms as being directed biased in terms of the technological change or the R&D work that they are doing. And there are several channels that influences the bias of their technologies. And you can mostly redirect to try to change the bias by either taxing their production of subsidizing clean research. And I, you know, this sort of inspired me to think a little bit about this presence of discretion in investor states as having a part of the distribution of investors as effectively taxing drawn assets. So I think that's how I thought about it. And I would be curious to see if that sort of resonates. Now sort of leaving the theory sort of behind I was drawn to think more about the empirical side and I think it'd be really interesting to try to find empirical evidence for these two channels that would argue that sustainable investing really matters for social impacts. And in particular the key question is, okay, what is the magnitude of that. And in particular, can we compare this with other types of things that other actions like environmental policies or regulations that are there to try to change the technologies that have been used and induced different type of innovation. And here the worry, of course, is that the sustainable investors or, you know, a much sort of weaker, less effective mechanism to really get anything to change and of course they are themselves impacted by the policies and regulations are going on. Another thought of thought on bringing the theory to the empirics is how complicated it is to really define what green is and also what counts as ESG. And I think that may prove a hurdle to really identify properly in the data whether ESG is doing something here again from this report on ESG investments. It is interesting to know that what investors said about what the key barriers to ESG integration was in fact data or the issue that data was inconsistent across asset classes and defined that often ESG ratings could be conflicting. Right. And so if we are struggling to really agree on this definition, then it's a bit complicated to argue, you know, whether these channels of investments are really helping this category. As a small sort of connective notabene here, but I and to some extent the author in the presentation clarified that point to me but I was really, it was striking to me that what a lot of asset managers are saying is that they're, they're interested in ESG. You know, values sort of was listed in the list of things that the reasons why they were interested in ESG, but really a big chunk of them are integrating ESG and their criteria to improve long term returns. And I think that talks to the, the, this aspect of their theory that when you have maybe shocks in preferences or shocks in terms of like how future investors are going to care about ESG. So, you know, you may have incentives today to be to invest so that later on in the long term, you are part of of the rallying to ESG values. So in a way it's a sort of a coordination problem, but the trade off is not so much about green versus brown assets here becomes more of a trade off between short terms versus long term gains, making the bet that in the long term investors will have coordinated on valuing ESG. Now as we sort of a more open handed bigger question in this paper, and in this topic, what really matters is really tastes for ESG and therefore the bigger open handed question is what, what does it take to change this taste what does it take to make this taste also stick over time and not be transient. How can we make sure that this, all the externalities and particularly the negative externalities are being internalized. The voluntary mechanism that's where shown in this paper, maybe are useful there's a question mark on the, on the magnitude. And they are interesting empirical application here to better understand how salient shocks like the Drittattenberg effect here has been instrumental also in changing investors taste for such assets. Another kind of shocks that's happening in the background is in terms of the perception of the technologies and their costs in the world where solar wind and battery tax is getting cheaper and cheaper. It becomes less and less acceptable to rely on on fall on dirty fossil fuels. So all these things comes together and impact investor states and I think it would be interesting to have empirical studies that ended study the different drivers and try to identify and estimate their respective magnitudes. All right, I'll stop here because I think I may have to be out of time. Thank you very much. So there are two questions from the floor that I would like to add to this question. So one is something that is already touched upon, which is that in your paper Lucien, you really cover ESG, but in your presentation you spoke mostly about green. Of course, this is a green symposium, so I understand. But the question was, especially when you take this sort of to these empirical results, which is what you're currently working on. How much of these returns that are that you're showing are really about green versus the other dimensions of ESG? What is more important there? And the second question is a bit related to Virginia's discussion about preferences and basically your sort of starting point assumptions. What if they were more symmetric and you have some people, they prefer brown and some prefer green. Some care about ESG gets utility, but some actually would get this utility. Some would actually prefer to still use these dirty fossil fuels to whatever, which is still get the surplus. So with everything basically bowed down to everything being symmetric, just from a more tactical point of view, I guess. So back to you Lucien. Okay, thank you. Let me start by thanking Eugenia. I think it's, I love getting the perspective of a real environmental economist on this paper. And I think I love the questions you raised about magnitudes and measurement. I think those are kind of some of the key questions in this literature beyond our paper, of course. To the two questions, Luke, that you raised. First, what if investors care about ES and G separately? You can imagine a simple extension of our theory where investors have separate preferences for E, S, and G. You know, I imagine I'll speculate that what would happen is you would end up with three ESG factors, an E factor, an S factor, and a G factor. And I think it would be interesting empirically to explore that. The second question is what if you have symmetric tastes. Let me make that give a concrete example that I think is actually kind of plausible, which is about guns in America. Some people in America hate guns. Other people in America love guns. So how would that work in our model? Our model allows investors to have different perceived G's for the exact same firm. The G in our model is the wealth-weighted average. So for this gun company, the G in our model is the wealth-weighted average of investors G's for that gun company. And it's possible that those G's exactly cancel each other out so that I'll call the net G for the gun company would be exactly zero. Last question from the floor is how your results on the outperformance of stocks can be reconciled with the findings of another paper. I'm sure you're aware by Patrick Bolton and Marcin Kaspecic who showed that the CO2 emission firms stocks perform better because of transition risk being priced. That's a good question. And I don't know the details of that paper, so it's hard for me to answer. I'm guessing it goes a lot toward how we measure green. And we measure a company's greenness using these MSCI ESG data. MSCI is one of the leading providers of these ESG ratings. Okay, thank you. Do I have time? You cut me off, Luke, but I'd love to say one more thing about the discussion if I may. Absolutely. One question I like that was raised was, you know, this idea that, you know, when you look at people's motivations for ESG investing, it looks like the top motivation is improved long run returns. And indeed, when you look at how investment managers market their ESG products, they market them saying our products offer better returns. The point of our new paper is that that's pretty misguided. Why are asset managers doing this? They're doing it to make money. They know that they're earning huge fees off these ESG products. It's easy to point to green assets past performance, which has been good. But the point of our new papers, we should not expect that great past performance to continue.