I took your spreadsheet and made a quick estimate for an AI mission hedging portfolio. You can access it here.
The model assumes:
AI companies return 20% annually over the next 10 years in a short-timelines world, but less than the global market portfolio in a long-timelines world,
AI companies have equal or lower expected returns than the global market portfolio (otherwise we’re just making a bet on AI),
money is 10x more useful in a short-timelines world than in a long-timelines world,
logarithmic utility.
In the model, the extra utility from the AI portfolio is equivalent to an extra 2% annual return.
My guess is that this is less than the extra returns one might expect if one believes the market doesn’t price in short AI timelines sufficiently, but it makes the case for investing in an AI portfolio more robust.
Caveat: I did this quickly. I haven’t thought very carefully about the choice of parameters, haven’t done sensitivity analyses, etc.
As an extension to this model, I wrote a solver that finds the optimal allocation between the AI portfolio and the global market portfolio. I don’t think Google Sheets has a solver, so I wrote it in LibreOffice. Link to download
I don’t know if the spreadsheet will work in Excel, but if you don’t have LibreOffice, it’s free to download. I don’t see any way to save the solver parameters that I set, so you have to re-create the solver manually. Here’s how to do it in LibreOffice:
Go to “Tools” → “Solver...”
Click “Options” and change Solver Engine to “LibreOffice Swarm Non-Linear Solver”
Set “Target cell” to D32 (the green-colored cell)
Set “By changing cells” to E7 (the blue-colored cell)
Set two limiting conditions: E7 ⇒ 0 and E7 ⇐ 1
Click “Solve”
Given the parameters I set, the optimal allocation is 91.8% to the global market portfolio and 8.2% to the AI portfolio. The parameters were fairly arbitrary, and it’s easy to get allocations higher or lower than this.
As of yesterday, my position on mission hedging was that it was probably crowded out by other investments with better characteristics[1], and therefore not worth doing. But I didn’t have any good justification for this, it was just my intuition. After messing around with the spreadsheet in the parent comment, I am inclined to believe that the optimal altruistic portfolio contains at least a little bit of mission hedging.
Some credences off the top of my head:
70% chance that the optimal portfolio contains some mission hedging
50% chance that the optimal portfolio allocates at least 10% to mission hedging
20% chance that the optimal portfolio allocates 100% to mission hedging
[1] See here for more on what investments I think have good characteristics. More precisely, my intuition was that the global market portfolio (GMP) + mission hedging was probably a better investment than pure GMP, but a more sophisticated portfolio that included GMP plus long/short value and momentum had good enough expected return/risk to outweigh the benefits of mission hedging.
EDIT: I should add that I think it’s less likely that AI mission hedging is worth it on the margin, given that (at least in my anecdotal experience) EAs already tend to overweight AI-related companies. But the overweight is mostly incidental—my impression is EAs tend to overweight tech companies in general, not just AI companies. So a strategic mission hedger might want to focus on companies that are likely to benefit from AI, but that don’t look like traditional tech companies. As a basic example, I’d probably favor Nvidia over Google or Tesla. Nvidia is still a tech company so maybe it’s not an ideal example, but it’s not as popular as Google/Tesla.
I believe the most important downside to a mission hedging portfolio is that it’s poorly diversified, and thus experiences much more volatility than the global market portfolio. More volatility reduces the geometric return due to volatility drag.
Example case:
Stocks follow geometric Brownian motion.
AI portfolio has the same arithmetic mean return as the global market portfolio.
Market standard deviation is 15%, AI portfolio standard deviation is 30%.
Market geometric mean return is 5%.
In geometric Brownian motion, arithmetic return = geometric return + stdev^2 / 2. Therefore, the geometric mean return of the AI portfolio is 5% + 15%^2/2 − 30%^2/2 = 1.6%. If we still assume a 20% return to AI stocks in the short-timelines scenario, that gives 1.3% return in the long-timelines scenario. And the annual return thanks to mission hedging is −1.1%.
(I’m only about 60% confident that I set up those calculations correctly. When to use arithmetic vs. geometric returns can be confusing.)
Of course, you could also tweak the model to make mission hedging look better. For instance, it’s plausible that in the short-timeline world, money is 100x more valuable instead of 10x, in which case mission hedging is equivalent to a 24% higher return even with my more pessimistic assumption for the AI portfolio’s return.
Yeah, in my model, I just assumed lower returns for simplicity. I don’t think this is a crazy assumption – e.g., even if the AI portfolio has higher risk, you might keep your Sharpe ratio constant by reducing your equity exposure. Modelling an increase in risk would have been a bit more complicated, and would have resulted in a similar bottom line.
I don’t really understand your model, but if it’s correct, presumably the optimal exposure to the AI portfolio would be at least slightly greater than zero. (Though perhaps clearly lower than 100%.)
To be clear, my model is exactly the same as your model, I just changed one of the parameters—I changed the AI portfolio’s overall expected return from 4.7% to 1.3%.
It’s not intuitively obvious to me whether, given the 1.3%-return assumption, the optimal portfolio contains more AI than the global market portfolio. I know how I’d write a program to find the answer, but it’s complicated enough that I don’t want to do it right now.
(The way you’d do it is to model the correlation between the AI portfolio and the market, and set your assumptions such that the optimal value-neutral portfolio (given the two investments of “AI stocks” and “all other stocks”) equals the global market portfolio. Then write a utility function that assigns more utility to money in the short-timelines world and maximize that function where the independent variable is % allocation to each portfolio. You can do this with Python’s scipy.optimize, or any other similar library.)
EDIT: I wrote a spreadsheet to do this, see this comment
I can’t follow this either but a study cited in Radical Markets suggests that a randomly chosen portfolio of as few as fifty stocks achieves 90% of the diversification benefits available from full diversification across the entire market.
Given that FAANG’s market cap alone is already $3 trillion and for almost 10% of the U.S. stock market’s total market capitalization of $31 trillion, AND you could further diversify then this, wouldn’t you get quite a lot of the diversification benefits?
50 randomly-chosen stocks are much better diversified than 50 stocks that are specifically selected for having a high correlation to a particular outcome (e.g., AI development).
This paper provides some more in-depth explanation of what I was talking about with the math. It’s fairly technical, but it doesn’t use any math beyond high school algebra/statistics.
The key point I was making is that, if markets are efficient, then you shouldn’t expect a 5% (or even 4.7%) geometric mean return from the AI portfolio. Instead, you should expect more like 1.3%. I might have messed up some of the details, but I’m confident that the geometric return for an un-diversified portfolio in an efficient market is meaningfully lower than the global market return. This is not to say that mission hedging is a bad idea, just that this is an important fact to take into account.
@Jonas: I think your model is interesting, but if we define transformative AI like OpenPhil does (” AI that precipitates a transition comparable to (or more significant than) the agricultural or industrial revolution.”), and you invest for mission hedging in a diversified portfolio of AI companies (and perhaps other inputs such as hardware) , then it seems conceivable to me to have much higher returns—perhaps 100x of crypto? This is the basic idea for mission hedging for AI, and in line with my prior, and I think this difference in returns might be why I find the results of your model, that Mission hedging wouldn’t have a bigger effect, surprising.
I took your spreadsheet and made a quick estimate for an AI mission hedging portfolio. You can access it here.
The model assumes:
AI companies return 20% annually over the next 10 years in a short-timelines world, but less than the global market portfolio in a long-timelines world,
AI companies have equal or lower expected returns than the global market portfolio (otherwise we’re just making a bet on AI),
money is 10x more useful in a short-timelines world than in a long-timelines world,
logarithmic utility.
In the model, the extra utility from the AI portfolio is equivalent to an extra 2% annual return.
My guess is that this is less than the extra returns one might expect if one believes the market doesn’t price in short AI timelines sufficiently, but it makes the case for investing in an AI portfolio more robust.
Caveat: I did this quickly. I haven’t thought very carefully about the choice of parameters, haven’t done sensitivity analyses, etc.
As an extension to this model, I wrote a solver that finds the optimal allocation between the AI portfolio and the global market portfolio. I don’t think Google Sheets has a solver, so I wrote it in LibreOffice. Link to download
I don’t know if the spreadsheet will work in Excel, but if you don’t have LibreOffice, it’s free to download. I don’t see any way to save the solver parameters that I set, so you have to re-create the solver manually. Here’s how to do it in LibreOffice:
Go to “Tools” → “Solver...”
Click “Options” and change Solver Engine to “LibreOffice Swarm Non-Linear Solver”
Set “Target cell” to D32 (the green-colored cell)
Set “By changing cells” to E7 (the blue-colored cell)
Set two limiting conditions: E7 ⇒ 0 and E7 ⇐ 1
Click “Solve”
Given the parameters I set, the optimal allocation is 91.8% to the global market portfolio and 8.2% to the AI portfolio. The parameters were fairly arbitrary, and it’s easy to get allocations higher or lower than this.
As of yesterday, my position on mission hedging was that it was probably crowded out by other investments with better characteristics[1], and therefore not worth doing. But I didn’t have any good justification for this, it was just my intuition. After messing around with the spreadsheet in the parent comment, I am inclined to believe that the optimal altruistic portfolio contains at least a little bit of mission hedging.
Some credences off the top of my head:
70% chance that the optimal portfolio contains some mission hedging
50% chance that the optimal portfolio allocates at least 10% to mission hedging
20% chance that the optimal portfolio allocates 100% to mission hedging
[1] See here for more on what investments I think have good characteristics. More precisely, my intuition was that the global market portfolio (GMP) + mission hedging was probably a better investment than pure GMP, but a more sophisticated portfolio that included GMP plus long/short value and momentum had good enough expected return/risk to outweigh the benefits of mission hedging.
EDIT: I should add that I think it’s less likely that AI mission hedging is worth it on the margin, given that (at least in my anecdotal experience) EAs already tend to overweight AI-related companies. But the overweight is mostly incidental—my impression is EAs tend to overweight tech companies in general, not just AI companies. So a strategic mission hedger might want to focus on companies that are likely to benefit from AI, but that don’t look like traditional tech companies. As a basic example, I’d probably favor Nvidia over Google or Tesla. Nvidia is still a tech company so maybe it’s not an ideal example, but it’s not as popular as Google/Tesla.
Very cool—thanks for doing this.
I agree that EA-related resources are skewed towards the US tech sector (see Ben Todd’s recent post) and that should definitely be taken into account.
Thanks for making this model extension!
I believe the most important downside to a mission hedging portfolio is that it’s poorly diversified, and thus experiences much more volatility than the global market portfolio. More volatility reduces the geometric return due to volatility drag.
Example case:
Stocks follow geometric Brownian motion.
AI portfolio has the same arithmetic mean return as the global market portfolio.
Market standard deviation is 15%, AI portfolio standard deviation is 30%.
Market geometric mean return is 5%.
In geometric Brownian motion, arithmetic return = geometric return + stdev^2 / 2. Therefore, the geometric mean return of the AI portfolio is 5% + 15%^2/2 − 30%^2/2 = 1.6%. If we still assume a 20% return to AI stocks in the short-timelines scenario, that gives 1.3% return in the long-timelines scenario. And the annual return thanks to mission hedging is −1.1%.
(I’m only about 60% confident that I set up those calculations correctly. When to use arithmetic vs. geometric returns can be confusing.)
Of course, you could also tweak the model to make mission hedging look better. For instance, it’s plausible that in the short-timeline world, money is 100x more valuable instead of 10x, in which case mission hedging is equivalent to a 24% higher return even with my more pessimistic assumption for the AI portfolio’s return.
Yeah, in my model, I just assumed lower returns for simplicity. I don’t think this is a crazy assumption – e.g., even if the AI portfolio has higher risk, you might keep your Sharpe ratio constant by reducing your equity exposure. Modelling an increase in risk would have been a bit more complicated, and would have resulted in a similar bottom line.
I don’t really understand your model, but if it’s correct, presumably the optimal exposure to the AI portfolio would be at least slightly greater than zero. (Though perhaps clearly lower than 100%.)
To be clear, my model is exactly the same as your model, I just changed one of the parameters—I changed the AI portfolio’s overall expected return from 4.7% to 1.3%.
It’s not intuitively obvious to me whether, given the 1.3%-return assumption, the optimal portfolio contains more AI than the global market portfolio. I know how I’d write a program to find the answer, but it’s complicated enough that I don’t want to do it right now.
(The way you’d do it is to model the correlation between the AI portfolio and the market, and set your assumptions such that the optimal value-neutral portfolio (given the two investments of “AI stocks” and “all other stocks”) equals the global market portfolio. Then write a utility function that assigns more utility to money in the short-timelines world and maximize that function where the independent variable is % allocation to each portfolio. You can do this with Python’s scipy.optimize, or any other similar library.)
EDIT: I wrote a spreadsheet to do this, see this comment
I can’t follow this either but a study cited in Radical Markets suggests that a randomly chosen portfolio of as few as fifty stocks achieves 90% of the diversification benefits available from full diversification across the entire market.
Given that FAANG’s market cap alone is already $3 trillion and for almost 10% of the U.S. stock market’s total market capitalization of $31 trillion, AND you could further diversify then this, wouldn’t you get quite a lot of the diversification benefits?
50 randomly-chosen stocks are much better diversified than 50 stocks that are specifically selected for having a high correlation to a particular outcome (e.g., AI development).
This paper provides some more in-depth explanation of what I was talking about with the math. It’s fairly technical, but it doesn’t use any math beyond high school algebra/statistics.
The key point I was making is that, if markets are efficient, then you shouldn’t expect a 5% (or even 4.7%) geometric mean return from the AI portfolio. Instead, you should expect more like 1.3%. I might have messed up some of the details, but I’m confident that the geometric return for an un-diversified portfolio in an efficient market is meaningfully lower than the global market return. This is not to say that mission hedging is a bad idea, just that this is an important fact to take into account.
Very interesting- thanks for elaborating!
@Jonas: I think your model is interesting, but if we define transformative AI like OpenPhil does (” AI that precipitates a transition comparable to (or more significant than) the agricultural or industrial revolution.”), and you invest for mission hedging in a diversified portfolio of AI companies (and perhaps other inputs such as hardware) , then it seems conceivable to me to have much higher returns—perhaps 100x of crypto? This is the basic idea for mission hedging for AI, and in line with my prior, and I think this difference in returns might be why I find the results of your model, that Mission hedging wouldn’t have a bigger effect, surprising.