This artice covers a research paper written by Jonathan Harris – you can find a link to it here.

This is a paper about how investors should think about their impact, and what they are trying to maximise when they construct a portfolio. A lot of this resonates very strongly with how we think about these questions at British International Investment, to the extent that there are passages that are almost identical to our internal guidelines and training material.

There are also some new ideas, although some of these are — I think — hard to apply in practice. And there is an attempt to capture everything formally in mathematical notation. Harris says this brings precision and coherence which “makes it suitable for both practical and academic applications.” I fear the formality might be more appealing to academics than practitioners.

This is a working paper that will be revised, and some of what I write here is informed by conversations with the author about that. It covers (at least) three topics: how to define what investors are trying to optimise and how to conceptualise total returns; how to think about the impact of investors and the firms they invest in; how to think about the question of impact relative to a counterfactual. I’ll take each of these in turn, starting with that probabilistic approach.

Harris insists that impact must be defined relative to a counterfactual.[1] His view is that you are not an impact investor unless you are genuinely altruistic and “genuine altruists gain utility from genuine impact.” He notes “some believe it is too hard to think carefully about the counterfactual. The simple solution is just to invest in ‘great’ companies and attribute a proportion of the enterprise impact to oneself.” Harris is not having that. He also notes that “economists already naturally think in terms of welfare improvement and counterfactual impact” and may be surprised to learn some impact investors do not.

However, if a large number of impact investors are competing for the same investment opportunities, it’s hard for any one of them to believe they are making any difference with their individual investment, relative to the counterfactual of them not investing. If investors took that seriously, perhaps nobody would invest because everyone would believe they wouldn’t make a difference! He likens this to the ‘irrationality’ of voting “despite the astronomically small odds of being the swing vote.” His solution is to think probabilistically.

This is music to my ears. In my paper The Elusive Quest for Additionality (with Nicolas Van de Sijpe and Raphael Calel) we suggest a probabilistic approach, and at BII we regard additionality as something in which we can have varying degrees of confidence, but we can never know. As Harris puts it “decision-relevant impact is always an assessment of expected impact never a measurement, because the counterfactual is never measurable.” That’s little too strong — but the point that you usually cannot know (and hence measure) both what will happen if you do and what will happen if you don’t, is right.

Harris suggests that altruistic investors should adopt what game theorists call a “mixed strategy”. That means instead of adopting a rule “in these circumstances, I will take this action”, players introduce some randomness: “in these circumstances, I will take this action with some probability”. He writes “if all investors choose a low, but non-zero probability that they will make an investment, then the number of investors who invest will be low on average” which means there is more chance that your investment will be the “swing vote” that makes a difference. In terms of expected impact, some chance of making a difference is enough to justify action.

I think the word “adopt” is misplaced here. Nobody is going to introduce randomness to their investment decisions. Investment is already uncertain. As Harris puts it: “one shouldn’t think in binary terms of others investing or not, but in terms of the probability that others will invest.” From our point of view, the uncertainty comes from the chance we will end up rejecting a prospective investment, or that the project sponsor will reject us. Our strategy is: “if the deal is mutually agreeable, we are in”.[2]

I think there is another way to think about the probability of impact — but rather than asking “what are the chances this investment would not go ahead without me” private impact investors can ask “what are the chances the overall quantity of impactful investment is higher because of me?”

BII is a public DFI, so the counterfactual that concerns us is what private investors might have done if we decline to invest — we want to have an impact relative to that. That makes less sense if you are a private investor, where your job entails competing with other private investors to win deals.[3]

Here’s a mental model that might be more useful, although it is still only applicable in less liquid markets. It is based on what economists call a “search and matching” model.

Firms search for investors and investors search for firms. This takes time and money. Sometimes one side finds a potential match but decides to keep searching for something better. There is competition for matches — firms meet multiple investors before finding a mutually agreeable match. Sometimes firms or investors stop searching after having failed to find a match. Firms and investors think about how likely they are to find a good match, and how much time and money it will take, before they decide whether to embark on a search.

When an impact investor enters and starts financing firms (“matching” with them) in a particular market segment where capital is relatively scarce, there is some probability those firms would not have made a match otherwise. There is also some probability that other investors in that market segment, beaten to those deals, will now make other matches they would not have otherwise. In that case the total volume of investment in the market will rise. The entrance of new investors should also push down required returns (making firms more likely to accept matches) and speed up the matching process, so more firms will embark on a search for external capital and the total volume of investment will rise for those reasons too.

This is still a probabilistic approach. When you invest, it is not certain the overall quantity of investment in the market will rise as a result. We may presume the probability is higher in market segments where capital is scarcer, required returns are higher, and firms’ demand for capital is more responsive to market conditions. When an impact investor comes to think about their total impact return, they could weight the impact of investment by an assessment of this probability. That would imply an understanding of impact that is more about market segments, and less about individual deal characteristics.

The atomistic approach to rationality taken by economists is not the only way to think about reasonable behaviour. If we think collectively rather than individually, then we are better off, for example, if many of us vote to choose our government, relative to an undemocratic counterfactual. Personally, I think it is reasonable to be a team player, despite my individual vote almost certainly not changing the outcome. Likewise, we may be better off if many investors take decisions that incorporate altruistic considerations, relative to the counterfactual of few investors doing that, and its reasonable to want to join the team that collectively make a difference. Elsewhere in the paper Harris says it’s a mistake to treat impact as a “rival good” (if I have more of it, you have less of it). The “irrationality” of wanting to have impact when you are so unlikely to be “the investor that makes the difference”, which Harris seeks to overcome by pointing out there is still some probability of that, seems to assume rivalry — wanting impact to be cleanly attributable to an individual rather than a team.

This part of the paper (Section 2 starting on page 6) is hard going for the uninitiated, and I am very grateful to the author for walking me through it. Those steeped in financial economics should (I am told) recognise that it follows the logic behind the equations of modern portfolio theory and the intertemporal capital asset pricing model, due to Harry Markowitz and Robert Merton. But rather than only caring about wealth the investor now also cares about altruistic variables.

The investor has a “utility function”, based on the state of the world, as described by variables of different sorts, denoted by X. Some of these variables have intrinsic altruistic value (the number of malaria infections). Other things are only proxies for intrinsically valuable things (the number of bed nets distributed). Harris also discusses “warm glow” or “holding based variables”, such as what percentage of your investments qualify as climate finance, and “strategic variables”, which are things that will indirectly raise your long-term impact, if you continue to invest.[4]

Because the investor is altruistic, their utility can be read as an impact-oriented assessment of the state of the world. The investor chooses actions to maximise a “value function”, which is based on contemporary and expected future variables — this amounts to maximising your expected utility. The use of expectations here, which implies uncertainty, fits with the ‘probabilistic’ conception of investor impact described above, but otherwise there is no explicit connection between these two parts of the paper — the mathematical notation does not include any expression to capture the probability that the investor is making something happen that would not otherwise.

An action has a positive impact when it changes the state of the world (variables in X) to increase the investor’s expected utility. One of these variables is your wealth, W. The value function combines variables you care about (such as malaria infections) with your present and expected wealth, because wealth affects how many impactful investments you will be able to make in the future.

If it was possible to write down this value function mathematically, it would be something fearsomely complicated. Harris applies several steps that result in the following approximation to your expected utility:[5]

This approximation to your expected utility consists of three components:

1. Expected wealth

2. Monetised expected impact-relevant outcomes

3. A monetised outcome risk-adjustment

The terms in that approximation are defined as follows:

The terms with μ are expectations of future variables given their current state, the σ term captures variance (or risk) and the γ terms are how these things are monetised. Σ means adding it all up.

If this was standard investing, your expected utility would consist of two terms: expected wealth and a monetised adjustment for the risk in your future wealth.

Accounting for other, non-wealth, variables introduces the second term and expands the third term beyond financial risk (variation in your wealth) to include what might be called impact risk — the variation (risks) that arise from uncertainties and correlations between all the variables you care about.

These variables are not impact — impact arises when the investor takes actions to change them. Harris uses an operator ∆_A to express such changes. The impact of an action A on your expected utility is then:

Hence there are three ways in which your actions can raise your utility:

1. Increase your expected wealth

2. Improve the monetised expected outcomes

3. Reduce your monetised risk

An action has an ‘impact’ if it changes the value of the second term in the expected utility equation. This expression contains the term “μ_X” which represents expected outcomes X and “γ_X” represents how impact can be monetised by using an “exchange rate” based on how your utility U changes when “μ_X” changes, compared to how much your utility changes when your wealth changes.

Harris then divides the expression above by the investment required to carry out action A, to get the total return on an investment. Harris calls this ‘total portfolio returns’ because it represents the totality of what you care about (the returns you seek), not just your financial wealth. It’s a confusing choice of words — at first, I thought it meant the return on your whole (total) portfolio.

Harris breaks down the ‘total portfolio return’ into four components:

1. Excess financial returns

2. ‘impact returns’

3. ‘mission-correlated premia’

4. ‘altruistic uncertainty premia’

Excess financial returns are just the risk-adjusted improvement in returns you get from making an investment. ‘Impact returns’ are the monetized returns that you can view yourself as generating via your investor impact. These are somewhat like an “social return on investment”, but Harris’ expression differs from typical SROI formulations in two ways.

First, it emphasizes that what should be included in the calculation is only your investor impact (based on your probabilistic assessment of investor contribution). Second, Harris argues your monetised impact μ_X should equal the cost-effectiveness of the marginal dollar in your aid budget. This is quite different from traditional monetization practice. Many SROI calculations use things like statistical evaluations of the ‘value of a life’. That fits with what I have argued here — the optimal allocation of capital between DFIs and traditional aid should equalize marginal impact returns.

‘Mission-correlated premia’ come from the correlation between an investment’s financial returns and those strategic variables mentioned earlier. The essence of the idea is that its more valuable to have wealth when the conditions are ripe for you to carry out your mission. At a strategic level, governments might choose to give more money into DFIs when these premia are higher. From the author, I understand this concept has origins in a ‘mission hedging’ paper by Brigitte Roth Tran.

Finally, by considering ‘altruistic uncertainty premia’, Harris brings up the question of whether impact investors ought to be averse to uncertainty (impact risk) in a similar fashion to financial risk aversion. The justification for financial risk aversion comes from “diminishing returns” so that people tend to dislike minus $10 somewhat more than they like plus $10. Of course, we may often regard negative impacts (doing harm) as in a different moral category than positive impact (unlike positive and negative variation in wealth). But should we assume “diminishing returns” in positive impacts?

Take two positive things — cataract operations and clean cook stoves. Are the first 500 cataract operations more impactful than the second 500? It’s not obvious, if the profile of the people benefiting is unchanged. But if impact returns are diminishing, then we might prefer a diversified impact portfolio of cataract operations and cook stoves over going “all in” on cataracts. I have argued elsewhere that because there is uncertainty about which interventions will ultimately prove more effective at delivering on development goals, development interventions should be diversified.

I not sure practitioners will ever be in a position to write down equations that resemble these with real variables. But having a clear concept of how you should be thinking can be useful when it comes to trying to devise simpler, more practical, methods for assessing impact (and for seeing the flaws in easy answers). For example, these equations remind us that impact is about changing things out there in the world from where they started, so the impact of increasing someone’s income by $100 per year depends on their initial income and variables such as “farmers reached” really don’t cut it, in isolation. The formalisation also tells us that really impact investors should be explicit about how they would trade improvements in impact off against increases in wealth (those γ_X terms).

The third chunk of the paper concerns how to think about the ways in which enterprises and investors can have an impact.

The easiest way to think about the impact of an enterprise is to compare the scenario where it operates to the scenario where it ceases operations. Harris takes pains to emphasise that enterprise output is not the same as enterprise impact, despite the former being what most impact reporting consists of.

Enterprise impact gets complicated quickly once you start to think about how other firms might behave differently, in the enterprise’s absence. So, Harris suggests breaking it down into “simple enterprise impact” (SEI) and “dynamic enterprise impact” (DEI). SEI assumes that if the firm did not exist, then its activities would simply not be carried out, and Harris suggests using linear approximation based on marginal impact at the firm’s currently level of activity. If you know the hospital has 500 beds, and the impact of adding another bed would be Z, then your SEI is 500*Z.

We use these terms slightly differently at BII — we use “enterprise impact” to refer to the overall impact of the enterprise and “the impact of the investment” to refer to how that will change, as a result of the transcation we are participating in. Those two things are the same only when we are investing in greenfield projects. We care about the impact of the investment. If the investment will expand a 500-bed hospital to 1000 beds, we disregard the existing 500 beds.

But, as Harris would put it, we usually take the ‘simple’ approach of assessing that impact as if the activities resulting from the investment would not take place without it. We do that because if we are going to decide whether to participate in an investment to expand a hospital to 1000 beds, we want to understand everything that entails, not just the parts that we think might be attributable to us.

DEI can be broken down into what Harris calls “peer enterprise impact” (the effects of the enterprise on related firms) and “miscellaneous enterprise impact”, for indirect effects on the economy through mechanisms such as tax revenues, interest rates, FX availability and exchange rates.

Many of our investments (in the financial sector, transportation, power generation and other activities that we call “economic enablers”) are motivated by the indirect impact on firms across the economy. I presume these indirect effects are part of SEI, and the “peer enterprise impact” of an investment in a port, for example, would consist of its effect via other port operators, not via the firms that import and export. Peer effects are especially important for what DFIs call creating or catalysing markets, where the intention is to change the behaviour of other firms, often by prompting a competitive response.[6]

Some elements of DEI are probably too difficult to evaluate for practical purposes. Investments reduce poverty when they push up prevailing real wages across a market, for example. Trying to capture that would probably not be helpful for decision-making purposes (it might be possible to estimate for reporting purposes). We don’t tend to get into questions such as “if this hospital was not expanding, perhaps other hospitals would” either.

Turning to investor impacts, the distinction Harris makes between “investment impacts” and “engagement impacts” maps easily onto the categories of financial and non-financial additionality, used by DFIs. His definition of “simple investor impact” is “how much new capital will increase impact” multiplied by your share of the capital raised (equation 12). This resembles proposed methods for impact investors to attribute development outcomes amongst themselves.[7] The counterfactual seems to be that no capital is raised at all, and not “somebody else might supply the capital”, and hence this is not really a claim of investor impact in the sense that motivated Harris’ discussion of a probabilistic approach. This is where an expression to capture the probability of being additional — at the transaction or market level — should enter.

Harris then introduces two variants of dynamic investor impact. “System investor impact” captures impact created by the actions of other investors in other firms. Some of the dynamic (or indirect) aspects of enterprise impact presumably involve firms raising capital from other investors, so there is overlap here. Some of the investments we make are about trying to get certain segments of financial markets moving, so the behaviour of other investors is very much part of our thinking. The other category of dynamic investor impact “portfolio investor impact” left me scratching my head. It is the “sum of the simple investment impacts that the action induces in other enterprises.” This is explained with “If the investor moves capital into one enterprise it must come from somewhere. Even if it comes from short-term cash this will ultimately have some effect on how they allocate capital going forward”. As best I can make it out, that seems to be the opportunity cost of not investing elsewhere. If so, I would ignore it. I don’t see how thinking about what other enterprises might have done with our money helps in decision-making or impact reporting.

These categories of enterprise and investor impact may be useful in their own right, but they are not integrated into part of the paper about total returns, which is based on changes to the bundle of variables X, resulting from the investor’s actions, without regard for how.

This the first academic paper that I have seen that tries to break down everything an impact investor should be thinking about. At BII we have tried to translate a clear understanding of how what we do translates into the impact objectives we ultimately care about, and how everything fits together, into a set of tools that we use to manage impact. It is heartening to see so much of that thinking reflected in this paper. But our impact management tools often amount to asking the correct questions, and providing verbal answers (although we do use numerical rating systems in some places, we do not suppose they quantify impact). Some of the conceptual clarity introduced in this paper could serve to sharpen the questions that impact investors ask of themselves, but there is an enormous gulf to cross before we get anything that resembles a credible monetised impact return measure. I don’t know how to take the formal expressions Harris derives and translate them into a measure of total portfolio return that practitioners might use in practice. But hopefully others (and Harris in follow-up work) will explain how that can be done. Presumably it will involve trying to get the big things right, and setting aside a ton of detail.

Footnotes

[1] The “factual” is what happens after you do something; the “counterfactual” is what would have happened if you had not done something.

[2] Investment committee decisions are not just about objective criteria being met — group dynamics and subjective decisions no doubt display randomness for all sorts of reasons.

[3] Although some impact investors do think about what other less impact-oriented investors would have done. The approach BII takes to assessing additionality is described here.

[4] An investment that creates a useful relationship with a company or other investors that will generate future investment opportunities but makes no other immediate difference to things you care about, is an example of a strategic asset. Strategic assets can also raise the impact of other investors. At BII we may try to demonstrate that independent power projects are the best way of building renewable power generation quickly and inexpensively, for example. That would make it easier for investors to have a positive impact from financing IPPs in the future and ‘market creation’ has found its way into DFIs’ impact scoring tools (including ours). What matters here is the impact of more, cheaper renewable power, regardless of who the investors are.

[5] In the preamble the variables X and Y are defined in specific ways, but in these equations, they represent any pair of things among the many you care about

[6] The BII approach to managing impact is explained here: https://www.bii.co.uk/en/our-impact/what-impact-means-to-us/ Our impact framework requires us to articulate “how” impact will come about, and has three categories: direct impacts on workers and customers; indirect impacts via economic outputs (such as electricity or foreign exchange earnings) and catalysing market (indirect effects via behavioural changes). If I am reading Harris correctly, SEI covers direct and indirect via outputs, DEI covers catalysing markets, and we ignore some aspects of DEI.

[7] See my blog Attribution (not contribution) for an explanation.