Thanks, very helpful analysis! Any thoughts on how much value it would create if someone set up a DAF for EAs that makes leveraged investments? (This is on my longlist of things that EA Funds could try to do.)
Historical long-run global equities have returned about 5% with a standard deviation of about 16% (source). Let’s use that as a rough forward-looking estimate.
With a relative risk aversion (RRA) coefficient of 1 (= logarithmic utility), the certainty-equivalent interest rate of an un-leveraged portfolio is 5% (logarithmic utility doesn’t care about standard deviation as long as geometric return is held constant). With optimal leverage (2.45:1), the certainty-equivalent rate is 7.7%. That means the ability to get leverage is as good as a guaranteed 2.7% extra return (= 7.7% − 5.0%).
With RRA=1.5, optimal leverage = 1.63:1, and the excess certainty-equivalent rate is 0.8%.
With RRA=2, optimal leverage = 1.22:1, and the excess certainty-equivalent rate = 0.14%.
I think altruistic RRA is probably somewhere around 1 to 1.5, so under these assumptions, the ability to use leverage is roughly as good as a guaranteed 1-3% extra return.
(FWIW I think you can also get better return by tilting toward the value and momentum factors, so if you’re willing to do that, that makes the ability to invest flexibly look relatively more important.)
(I don’t understand how you arrived at 2.45:1 optimal leverage with log utility. I get 5%/(.16^2*1)= 1.95, and the Samuelson formula in leverage.py seems to be the same. Same for the other values.)
5% is the geometric mean return, the Samuelson share formula uses the arithmetic mean on the numerator (see here. So the correct formula is (5% + 0.16^2/2)/(0.16^2 * 1) = 2.45.
Thanks! The above calculation compares an un-leveraged portfolio to a leveraged one, but at least under log utility and assuming a low risk of value drift, the relevant comparison is probably between a leveraged (tax-free) DAF and a leveraged taxable account? Presumably, that would be lower than 2.7%.
Also, do you happen to know how effortful and feasible tax loss harvesting might be for leveraged portfolios in taxable accounts?
Yeah, because adding leverage will increase taxes on dividends. My calculator correctly accounts for this, but I didn’t account for it in my previous comment. But it doesn’t lower the certainty-equivalent rate by much.
Also, do you happen to know how effortful and feasible tax loss harvesting might be for leveraged portfolios in taxable accounts?
It shouldn’t be too hard, but I don’t think you’d get much benefit from it. I’m not sure though, I’m not too familiar with the mechanics of tax loss harvesting.
If we set this up well, we might get $100 million in investments, and the value added would be ~1% excess certainty equivalent rate, i.e., a certainty equivalent of $1 million per year.
If setting up such a DAF takes a year of labor, maintaining it takes 0.25 FTE, and labor has an opportunity cost of $3 million per year, it would take 3/(1-3*0.25) = 12 years to break even (with a plausible range from two years to ‘never’).
Over a period of ten years, it would return around 10/(1+10*0.25) = $3 million per person-year (with a plausible range from $500k to $5 million).
That seems pretty good, but perhaps slightly less valuable than other things EA Funds could be doing.
I’d be keen to hear if you think this seems like a reasonable overall takeaway.
labor has an opportunity cost of $3 million per year
This seems really high. You could hire an experienced investment manager for a lot less than that. But the general structure of your analysis seems sound.
Another consideration is that you can probably reduce correlation to other altruists’ investments (I wrote about this a bit here, and I’m currently writing something more detailed). Uncorrelated investments have much higher marginal utility of returns, at least until they become popular enough that they represent a significant percentage of the altruistic portfolio. And leveraging uncorrelated investments looks particularly promising. So you could get more than a 1% excess certainty equivalent return that way.
Thanks, I look forward to your analysis of uncorrelated investments! In particular, I’ll be keen to see to what degree they rely on the same assumptions as value/momentum strategies, or if there are opportunities that are independent of that.
Thanks, very helpful analysis! Any thoughts on how much value it would create if someone set up a DAF for EAs that makes leveraged investments? (This is on my longlist of things that EA Funds could try to do.)
We can estimate how valuable that would be by comparing the certainty-equivalent interest rates (I talked about this here).
Some quick analysis using leverage.py:
Historical long-run global equities have returned about 5% with a standard deviation of about 16% (source). Let’s use that as a rough forward-looking estimate.
With a relative risk aversion (RRA) coefficient of 1 (= logarithmic utility), the certainty-equivalent interest rate of an un-leveraged portfolio is 5% (logarithmic utility doesn’t care about standard deviation as long as geometric return is held constant). With optimal leverage (2.45:1), the certainty-equivalent rate is 7.7%. That means the ability to get leverage is as good as a guaranteed 2.7% extra return (= 7.7% − 5.0%).
With RRA=1.5, optimal leverage = 1.63:1, and the excess certainty-equivalent rate is 0.8%.
With RRA=2, optimal leverage = 1.22:1, and the excess certainty-equivalent rate = 0.14%.
I think altruistic RRA is probably somewhere around 1 to 1.5, so under these assumptions, the ability to use leverage is roughly as good as a guaranteed 1-3% extra return.
(FWIW I think you can also get better return by tilting toward the value and momentum factors, so if you’re willing to do that, that makes the ability to invest flexibly look relatively more important.)
(I don’t understand how you arrived at 2.45:1 optimal leverage with log utility. I get 5%/(.16^2*1)= 1.95, and the Samuelson formula in leverage.py seems to be the same. Same for the other values.)
5% is the geometric mean return, the Samuelson share formula uses the arithmetic mean on the numerator (see here. So the correct formula is (5% + 0.16^2/2)/(0.16^2 * 1) = 2.45.
Oh, thanks, I was under the mistaken impression that the Samuelson share formula used the geometric mean!
Thanks! The above calculation compares an un-leveraged portfolio to a leveraged one, but at least under log utility and assuming a low risk of value drift, the relevant comparison is probably between a leveraged (tax-free) DAF and a leveraged taxable account? Presumably, that would be lower than 2.7%.
Also, do you happen to know how effortful and feasible tax loss harvesting might be for leveraged portfolios in taxable accounts?
Yeah, because adding leverage will increase taxes on dividends. My calculator correctly accounts for this, but I didn’t account for it in my previous comment. But it doesn’t lower the certainty-equivalent rate by much.
It shouldn’t be too hard, but I don’t think you’d get much benefit from it. I’m not sure though, I’m not too familiar with the mechanics of tax loss harvesting.
Thanks, very helpful.
If we set this up well, we might get $100 million in investments, and the value added would be ~1% excess certainty equivalent rate, i.e., a certainty equivalent of $1 million per year.
If setting up such a DAF takes a year of labor, maintaining it takes 0.25 FTE, and labor has an opportunity cost of $3 million per year, it would take 3/(1-3*0.25) = 12 years to break even (with a plausible range from two years to ‘never’).
Over a period of ten years, it would return around 10/(1+10*0.25) = $3 million per person-year (with a plausible range from $500k to $5 million).
That seems pretty good, but perhaps slightly less valuable than other things EA Funds could be doing.
I’d be keen to hear if you think this seems like a reasonable overall takeaway.
This seems really high. You could hire an experienced investment manager for a lot less than that. But the general structure of your analysis seems sound.
Another consideration is that you can probably reduce correlation to other altruists’ investments (I wrote about this a bit here, and I’m currently writing something more detailed). Uncorrelated investments have much higher marginal utility of returns, at least until they become popular enough that they represent a significant percentage of the altruistic portfolio. And leveraging uncorrelated investments looks particularly promising. So you could get more than a 1% excess certainty equivalent return that way.
Edit: Published Uncorrelated Investments for Altruists
Thanks, I look forward to your analysis of uncorrelated investments! In particular, I’ll be keen to see to what degree they rely on the same assumptions as value/momentum strategies, or if there are opportunities that are independent of that.