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.
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!