Possible extensions and applications related to Pricing Investor Impact

This page lists possible extensions and applications of the supply and demand framework used in this Pricing Investor Impact. The list is in no particular order.

Empirical studies. Estimates for the parameters of different firms and investors. Analysis of how these parameters vary over time. Comparison of the optimal tilts suggested by reported ESG data and the real tilts of existing ESG or impact funds. Estimates in private markets and historical markets (a challenge due to data limitations).

Multiple time periods. The model may be extended to include multiple time periods, with model parameters varying over time. Betermier, Calvet, and Jo (2020) offer a multi-period version of their model. In a multi-period model the optimal policy of an impact-sensitive investor is likely to be significantly affect by considerations such as avoiding scenarios where investors with no taste for impact (or even opposite tastes) come to dominate the economy. Parameters like a_CF(n) and Σ_C can be made endogenous and time-varying in a multi-period model. Taste for strategic variables. In place of a full multi-period model, investor’s can simply be given a taste for strategic variables like the wealth of investors that share their beliefs and the percent of votes held by aligned shareholders in each firm. Higher order dependence on K. The dependence of cash flows and contributions to the public good on firm size K can be extended to include higher order terms. Uncertainty and robustness. Because of nonlinearities in each investor’s optimization problem, parameter uncertainty could have nontrivial effects on investors’ optimal policies.

Firm management tastes (for impact). The impact of firm management’s preferences on firm finances is an important topic in corporate finance. As an example, Morellec, Nikolov, and Schuerhoff (2012) provides evidence for the importance of firm manager’s taste for higher cash flows (as distinct from firm valuation). Chowdhry, Davies, and Waters (2019) and Gupta, Kopytov, and Starmans (2021) are examples of models with managers that have impact tastes. Mission correlation. In the same way that the correlation between returns and an investor’s marginal utility of personal consumption leads to risk premia, it is possible that correlations between returns and the impact per dollar of future opportunities may result in premia for impact-oriented investors. Roth Tran (2019) first proposed similar ideas in the context of an altruistic investor hedging their risk. Mission-correlated premia are a generalization that allows for the fact that altruistic investors may use assets with social-financial correlations to increase their expected utility, whether or not this decreases the dispersion of outcomes (see Harris (2021a) and Harris (2021b)). The premia associated with ESG supply and demand in Avramov et al. (2021), as well as the preference of environmentalists to hold polluting firms in Baker, Hollifield, and Osambela (2020), may arguably be seen as specific examples of mission-correlated premia for ESG and climate-motivated investors, respectively. Studies of historical examples of mission correlation could also be valuable for shedding light on the practical utility of strategies based on these correlations. Capital structure and blended finance. Different financial instruments can be offered by a single firm, with integrated capital schedules for each instrument. Betermier, Calvet, and Jo (2020) allows for riskless debt. More general extensions could be used to examine cases of blended finance, where different instruments are offered to investors with different impact preferences in order to produce a positive-sum result. Advanced market commitments. That is where a funder commits to pay for outcomes once they have occurred. Also called ‘retroactive funding’ or ‘impact certificates’ in some cases. Social impact bonds, and other performance-linked bonds, may be included in this class. Mechanism design. The Open Philanthropy Project, which grants more than $100 million a year to various organizations, has called on academics to develop mechanisms to combine different staff members’ views on the most effective giving opportunities, and also to help coordinate the giving of different philanthropic organizations (Muehlhauser, 2017). Interest in donor coordination mechanisms has also been expressed in the effective altruism community (Peters, 2019), many of whose members have pledged to donate 10% of their income to effective charities. Impact risk. The investor utilities in this paper are not sensitive to the volatility in each firm’s g(n). In reality, investors are likely to have preferences in this regard. Note that it should not be presumed that an investor’s impact risk aversion is similar to their financial risk aversion. Financial risk aversion has been thoroughly study by a large and still growing economic literature. Impact risk aversion is a topic that, while it can also be studied empirically, also demands analysis from a philosophical perspective. Different investors with beliefs that conform to different philosophies may have markedly different tastes regarding impact risk. For example, investors that subscribe to a precautionary principle may refuse to make investments that have even the slightest chance of causing harm. Extreme risks are another topic regarding both financial and impact risk that I have also not addressed in this paper. In particular, some philanthropists are explicitly focused on extreme risks. Such investors may have little concern over Gaussian volatility in a firm’s impact, but strong aversion to extreme negative impacts that could result from a firm’s activities. Effects on other investors beliefs. The narrative of many prominent impact investors (and ESG investors) is that there investment activities are not merely about shifting their allocation, but about leading other investors to update their beliefs and preferences (e.g. about g(n) or their price of impact). The model in this paper can be used to analyze such effects. I haven’t pursued this as I do not have a good sense of what how such changes might be produced (i.e. the affected investors, the scale, the operational costs).

Nonlinear effects and edge cases. I have glossed over the reality that many constraints (e.g. short-sales constraints) are likely to be binding on many investors. In some cases, the binding of these constraints may be important. For example, the investor impact of going from excluding to including a firm in an investor’s opportunity set. In particular, if a firm must raise a minimum amount to be viable, a marginal investor who enables them to reach this amount may have much more investor impact than would be naively calculated based on my linear model. Non-marginal effects. Many of the results in this paper have been derived assuming that the investors are small. There are likely to be interesting surprises about the optimal policies when one or more investor is large. Short selling. Are there cases, in theory or observed in practice, where short-selling is a key part of an investors impact policy? Or are the frictions and uncertainties too significant in practice? General equilibrium effects. If investor’s impact tastes are significant enough this could lead to large macro effects, changing the risk-free rate and investor consumption. The riskless bond could have an externality associated with it. Primary vs secondary markets. In this paper I have kept the market structure abstract, not distinguishing between primary and secondary markets. In reality there are likely important considerations unique to each form of market.

Search models and probabilistic interpretations. One feature of private markets is concentrated ownership. Often a single investor or a small group take large positions in a firm, whereas the model in this paper assumes that investment is split across all potential investors. In the former context, the investor impact studied in this paper may still be the correct counterfactual impact of an investor. But the interpretation of the contribution is better as the probability that another investor would make the investment if the investor in question declines it.

More heterogeneity. Investors may have different risk-free rates to reflect their different opportunity sets. They may also have different beliefs about the beliefs and preferences of other investors. Practical proxies for impact contribution. What proxies due practitioners currently use to assess the impact contribution of investments? What alternative variables might also be good proxies? Agent-based model. An agent-based model would allow for examination of the key ideas in this paper without many restrictions that are primarily motivated by analytical tractability (e.g. small investors). Machine learning tools could be used to solve such models. Attribution versus contribution. The contributions and investor impact returns are not (necessarily) attributions. ‘Attribution’ suggests that a central planner allocates a portion of outcomes to each investor and the sum of these portions equals the whole. This attribution may be done in more or less optimal ways, including using Shapley values (Shapley 1951). In contrast, investor impact returns are what is optimal for each investor to use in order to optimize their own utility. These contributions can turn out to be the same as an attribution, but need not be. Further work could explore the similarities and differences in different cases. Welfare costs. What is the implied welfare cost of observed ESG tilts, if they are indeed much larger than suggested by the relevant investor impact returns? Such an analysis requires looking at the actual distribution of g_i across firms.

Enterprise contribution. Empirical analysis of enterprise contribution would be valuable to establish how significant and variable it is in practice. This may be combined with theory to help develop heuristic metrics for enterprise contribution that can be used in practice. Another direction for research is to study the contribution of intermediaries like fund managers. Leverage and risk aversion. Risk aversion, in combination with the frictions an investor faces, determines how much leverage they should pursue. The appropriate risk aversion for an impact-focused investor, such as a foundation, may be substantially different from that of a consumption-oriented investor. In theory the impact-focused investor’s risk aversion should be set according to the curvature of the curve of their impact per dollar spent. Empirical studies of the curvature of these curves could help inform appropriate choices of risk aversion. However, model uncertainty and ambiguity aversion may also play a significant role in the policies such investors wish to pursue. Non-financial investor impact. Engagement, stewardship, activism. Potential links between capital allocation and engagement may be explored. For example, holding a significant position in a firm may increase the likelihood of a positive response to an engagement campaign. Beyond mean-variance utility. Higher order or alternative utility specifications may be explored. This may include using alternative risk metrics, such as Expected Shortfall, Var, CVaR and the Sortino ratio. Firm impact per dollar. A firm’s operations in a given time period can affect outcomes well into the future. There are many empirical and normative questions in this regard, including how to forecast future impacts, and how to discount future impacts for risk and uncertainty. Impact measurement and management. The investors in this paper form their strategies purely based on their forward-looking assessments of each firm’s expected future impact. Many practitioners, however, are tasked with measuring firm’s historical and recent impacts and engaging to help positively influence future impacts. It could be valuable to study how these perspectives of passive forward-looking assessment, backwards-looking measurement and active management can and do interact with each other. Nonprofits. Charitable opportunities are left separate and exogenous to the model in this paper. However, it could be extended to include nonprofit organizations, assuming investors who assign high impact returns to these organizations, and replacing financial risk with impact risk. Value of information. If the investors have the option to pay for more information on each opportunity, then assessing the value of information becomes necessary. Information on different parameters may have significantly different values. Firms with higher scalability are likely to offer higher value for information. Universal ownership. The off-diagonal elements in the firm cost sensitivity matrix offer a way to operationalize the impacts of each firm on others. This goes beyond standard portfolio theory, while generating similar results. Empirical and theoretical research is needed to build a better picture of what this matrix should look like. Extensions are also possible to intra-firm effects not just on costs, but also on profitability and impact per dollar.

Macroeconomic considerations. For example, labour.