When to diversify? Breaking down mission-correlated investing

Note: This post was originally drafted earlier this year, but we never got around to posting it for various reasons (mostly being busy). We recently had time to revisit it, partly just as a natural result of our workflow, partly because the way this year has gone highlights the main message of this post.

Mission-correlated investing means investing so as to have more money when money is more valuable. For effective altruists, money is more valuable when giving opportunities are more cost-effective. Some, such as Open Philanthropy, have mentioned considering such strategies. How important is this? Is this something only for major donors or for all EAs?

In this post, we first introduce the concept of ‘mission-correlated returns’. We then estimate these ‘returns’ for three examples to illustrate the potential importance of mission correlation in different contexts. Tentatively, we expect the highest magnitude mission-correlated returns to be the negative returns associated with investments in which the EA ‘Total Portfolio’ is highly concentrated. This makes pursuing other investments, which diversify the portfolio, relatively attractive. However, for donors who are devoted to a single narrow cause area, it could make sense to make concentrated bets if there are investments with particularly positive mission correlation.

The FTX blowup shows how bad it can be when too much EA wealth is concentrated in a single risky company. This adds some circumstantial weight to our theoretical claims. We hope this post adds some mathematical weight to arguments for more diversification going forward.

While this post is about ‘investing to give’, we believe similar conclusions (like the importance of diversification) are relevant to other parts of EA strategy. In particular, the argument for working to increase funder diversity seems strong, as discussed here. Similar arguments can, for example, be made about PR. We encourage you to think about how you can help EA diversify, both financially and otherwise.

Key points

Mission-correlated investment strategies, including ‘mission hedging’, are about identifying investments whose returns are correlated with your future cost-effectiveness.
- They can be as much about ‘investing in good’ as ‘investing in evil’.
- They can be a reason to diversify, or a reason to make concentrated bets.
- They may be as or more important for small donors as for major donors.
‘Mission-correlated returns’—the covariance between an investment’s financial returns and your future cost-effectiveness—are a useful metric for assessing the importance of mission correlation for an investment.
- We show that these ‘mission-correlated returns’ could exceed 1% per year for certain investments.
- This underlines the importance of forecasting future cost-effectiveness, as well as efforts to better understand the composition of the ‘EA portfolio’.
The main implication for most donors is a reminder that it is important to diversify the EA ‘Total Portfolio’. Concentrating investments in the same companies and sectors as other EA donors incurs a large negative ‘mission-correlated return’.

Essentials

Note: You might be familiar with the term ‘mission hedging’ as this was the first term used for this concept. We use the more general term ‘mission correlation’ because the crux of the idea is increasing the correlation of your investment returns with your future impact per dollar (i.e. your ability to achieve your altruistic ‘mission’). Whether or not this is ‘hedging’ is a secondary consideration.

If you are ‘investing to give’, the total good you will do equals the value of your investment portfolio in the future multiplied by the impact per dollar that you can achieve by donating (and continuing to invest) that future value. Your portfolio’s future value will be equal to its current value multiplied by the portfolio financial return.

In deciding how to invest right now, what we care about is your expected future impact.

The definition of covariance tells us that we can break expected future impact into the following parts:

where the ‘relative impact per dollar’ in the covariance is the future impact per dollar divided by the expected impact per dollar.

Naive expected value maximization would tend to suggest divide and conquer strategies of focusing on increasing the Expected Portfolio Financial Return (e.g. high risk entrepreneurship) while maximizing Expected Impact per Dollar (e.g. making grants based on EA principles). Of course, both of these things are good (great even) up to a point. But pursuing them too naively ignores many important considerations (such as the general complexity of the world and diminishing returns to scale). It also ignores the covariance term. This term is one more reason it will often not be optimal to bet everything on whatever appears to have the maximum financial return.

Covariance is defined as the product of the volatility of your future relative impact per dollar, the volatility of your portfolio’s financial return, and their correlation:

It’s helpful to express considerations in terms of returns when reasoning about investing. Happily the covariance term in the equation for ‘Expected Future Impact’ acts just like a return. So we refer to this covariance as a ‘mission-correlated return’:

You can control the ‘mission correlation’ by picking investments whose returns themselves have a high ‘mission correlation’ with your future impact per dollar. The mission-correlated return of any investment is similarly:

This enables us to assess the importance of mission correlation for an investment in terms of variables that are relatively easy to reason about.

Examples

We present three examples to illustrate actual estimates of mission-correlated returns.

Each example is introduced below the table, but for more details please see the appendix here.

The examples are intended to be realistic, but the numbers are not based on extensive research, so don’t take them literally. That said, the ‘EA total portfolio’ and ‘AI’ examples were calibrated to be in line with publicly available data. In contrast, the ‘SpaceX’ example should be interpreted as a hypothetical example that applies equally well to any cause area that is plausibly dominated by the efforts of a single company.

Example	Mission- correlated asset	Relevant to	Mission- correlated return
Diversifying the EA ‘Total Portfolio’	Risky company with high weight in the ’Total Portfolio’	Any EA donor	–10% (–24% to –2%)
Concentrated bet: Relatively weak mission correlation	AI stocks	AI safety funders	1% (0.4% to 3%)
Concentrated bet: Relatively strong mission correlation	SpaceX	Space exploration / governance funders	8% (5% to 13%)

A Guesstimate model for these estimates is here. All returns are annualized.

How significant are these returns? As context, note that expected financial returns are generally in the range 0%–15% depending on the asset class. Thus, these mission-correlated returns are of the same order of magnitude as regular expected returns.

The first example illustrates the negative mission correlation that comes from being correlated with the EA ‘Total Portfolio’ (the portfolio of all assets that are devoted to effective giving across all cause areas). The results in the table assume that 30% of the EA Total Portfolio is concentrated in a single highly risky asset. You can avoid such negative mission-correlated returns by reducing how much you hold in assets that are overrepresented in the EA Total Portfolio (e.g. tech stocks, crypto) or even betting against them.

This first example is relevant to any EA that is investing to give in one or more cause areas where major donors have significant concentrations in a single risky asset or sector. The second and third examples focus on what mission correlation might mean for a donor focused on a single cause area.

The second example is for an AI risk donor who expects the cost-effectiveness of their giving to increase given rapid AI progress. Such a donor may be able to improve their portfolio’s mission correlation by buying AI stocks. The investment in this case has a relatively low mission correlation at 30%, and a relatively low volatility of impact per dollar. These estimates are based on Michael’s research on AI ‘mission hedging’. Nevertheless, given reasonable but low risk aversion, it is plausible that the AI risk donor may choose to hold 20% of their portfolio in such stocks to take advantage of this mission correlation.

The third example illustrates how mission-correlated investments can include betting on ‘good’ (from the investor’s point of view). In this example, a space governance funder (and space enthusiast) improves their portfolio’s mission correlation by investing in SpaceX. We set this hypothetical case up with much higher mission correlation and impact per dollar volatility than the second example. Because of the high mission correlation in this case, it is plausible that the donor devotes more than 50% of their portfolio to SpaceX.

The point of these two examples is not that mission correlation is more or less important for space governance or AI—we would want to see more research and expert input before forming such a view. Rather, the point of the SpaceX example is to demonstrate just how important mission correlation can plausibly be if you have a relatively narrow cause area (in terms of the relevant organizations) that includes a highly influential, investable company.

How much of a shift in investment do these returns suggest? This will depend on an investor’s ‘risk aversion’ and the risk of each investment. A given mission-correlated return will change the optimal investment size for an investor with high risk aversion less than for one with low risk aversion.

As discussed here, there is an argument that smaller donors should have much lower risk aversion (orders of magnitude lower). In practice, however, we believe this is dominated by practical considerations (e.g. limits to risk in small investment accounts), model uncertainty and ‘if everyone did this’ considerations.

We still expect smaller donors should have a lower risk aversion with their ‘investing to give’ money, but not orders of magnitude lower. In the Guesstimate models we show estimated weight changes for a ‘normal’ level of risk aversion.

Approaches to assessing the value of mission correlation

As summarized in the table below, we see three approaches one might use to assess the value of a mission-correlated investment.

In general, we recommend the analytic approximation as a default. It was used to generate the returns in the table above. Full simulation could be used to gain confidence if highly uncertain about a strategy. More basic scenario analysis can be intuitive, but it needs to be used with care as it can be easy to miss important features if only a small number of scenarios are used^[1].

Approach	Description	Notes
Analytic approximation	The approach we used for the examples in this post and described in the appendix. Based on simplifying assumptions.	Easiest. Most likely to be a reasonable approximation on shorter time horizons and with less volatile investments. Good for quick assessment and back-of-the-envelope calculations (BOTECs).
Basic scenario analysis	Working out the potential result of the investment in a small number of scenarios (at least two) and calculating the expected result. Examples—We have put together this sheet for the AI & SpaceX examples, which builds on Jonas Vollmer and Hauke Hillebrandt’s models associated with this comment.	Relatively intuitive to set up each scenario, but will often require more work than the analytic approximation in order to make sure the scenarios tell a coherent story. Useful to develop intuition and for sense checking.
Full simulation	Simulating the result of the investment across a large number of scenarios and calculating the expected result. Examples—Michael’s research including: A Preliminary Model of Mission-Correlated Investing	Most technically difficult. Most flexible and able to capture all key considerations. Less intuitive than a scenario analysis, which makes bad assumptions harder to spot. Appropriate for thorough investigations, when necessary.

Other considerations

Mission correlation is likely most important when your wealth is small relative to the scale of the problem—larger donors are much more subject to diminishing returns to scale. Mission correlation is also most likely to suggest concentrated bets for altruists focused on a specific cause area (e.g. AI), as then it is relatively easy to assess how impact per dollar might evolve over time. EAs who aim to donate to whatever cause is the highest priority at a given time are less likely to find investments that are positively correlated with this ‘mission’, so the negative mission correlation of holding similar assets to other EAs seems likely to dominate.

Given the uncertainty in many of the key parameters relevant to mission-correlated investing, it is possible that mission correlation could be much more valuable than currently expected, and it could be applied to special situations as discussed here. It is also complementary with developing a more nuanced understanding of the value of impact under different scenarios as, for example, highlighted by Founders Pledge climate research^[2].

Another consideration that is typically brought up in regards to mission correlation is the direct impact of investing, which can suggest moving in the opposite direction of mission correlation (e.g. selling AI stocks, rather than buying them, to marginally slow AI progress). We agree that the direct impact of investing is important in general. Indeed, JH is actively researching this topic. For mission correlation, we think this simply means that one should prioritize strategies that involve highly liquid investments like major public equities, where one’s investments will have relatively little impact on the underlying company ^[3].

We see mission-correlated strategies and ‘impact investment’ strategies as the two main tools that differentiate altruistic investors from others. Mission-correlated strategies are complementary to impact investing, in that they are most likely to be useful in asset classes where impact investing doesn’t have a big effect (e.g. large, public tech stocks). That said, there are definitely cases of potential overlap. Indeed our SpaceX example could be viewed as both (for an early-stage SpaceX investor).

Conclusion and recommendations

In this post we reviewed how ‘mission correlation’ (including ‘mission hedging’) is all about the covariance of financial returns and future impact per dollar. We then presented Guesstimates of the ‘mission-correlated returns’ associated with three illustrative investment scenarios.

The current state of research on forecasting cost-effectiveness makes estimates of mission correlation (and covariance) highly uncertain. We would be excited to see research that makes quantitative forecasts of cost-effectiveness under different possible scenarios. We expect this research will be strategically useful in general, in addition to enabling better assessments of the potential for mission-correlated investing. Implementing a mission-correlated strategy may require significant upfront research, but will pay dividends for years as likely only occasional refinements will be required.

For most EAs, our main recommendation (as Michael has emphasized before) is to position your ‘investing to give’ portfolio to be as uncorrelated as reasonably possible with the EA ‘Total Portfolio’. Recent events with FTX emphasize how important it is for EA funding to be diversified. It’s not too late for us all to more prudently promote better diversification going forward. In practice, this may still mean underweighting certain (categories of) tech stocks and crypto.

^
A two scenario model only has two degrees of freedom for each variable in the model. Hence, in general, it cannot match all of the means, variances and covariances of all the variables, not to mention higher moments.
^
https://founderspledge.com/stories/changing-landscape: “it is much more important to shift from 5 to 4.5 degrees if we are in a 5-degree scenario than it is to shift from 3 to 2.5 degrees in a 2-degree world”
^
Total Portfolio Project’s estimate of the ‘impact on company size per marginal dollar invested’ is approximately $0.03$ for the average US publicly listed company. This is based on empirical data from prominent financial economics researchers. For the largest stocks this will be even lower on average. On top of this, we expect the ‘impact per dollar’ of most companies to be small (e.g. even the most CO2-intensive stocks have emissions of <0.01 tCO2e/$).