Thank you for the post! I’m very interested to see more work on this topic.
I feel a little bit unsure about the focus on the bonds – would be very curious to hear any reflections on the below.
As you say, if real interest rates rise, that should affect all assets with positive duration.
Perhaps then the net effect of having the view that real interest rates will rise is just that you should reduce overall portfolio duration. A 60:40 portfolio has an effective duration of ~40 years, where most of that duration comes from equities. Perhaps someone who believes this should target, say, a 20 year average duration instead (through whatever means seems least costly, which could mean holding fewer equities).
Perhaps equivalently, if real interest rates are going to rise, then all financial assets are currently overpriced, so maybe the effect would be holding fewer financial assets in general, and holding more cash / spending more.
My understanding is that an important part of the reasoning for a focus on avoiding bonds is that an increase in GDP growth driven by AI is clearly negative for bonds, but has an ambiguous effect on equities (plus commodities and real estate), so overall you should hold more equities (/growth assets) and less bonds. Is that right?
That makes sense to me, but then I still feel unsure about, having tilted towards equities, whether your overall exposure should be higher or lower.
(And tilting towards equities will increase the effective duration of your portfolio, making an increase in real interest rates worse for you all else equal.)
If we use the merton’s share to estimate optimal exposure, that depends on the difference between the expected return of the asset and the expected real interest rate over your horizon. Perhaps with equities you might expect both returns and the interest rate to rise by 3%, which would cancel out, and you end up with the same exposure. But with bonds only the interest rate will rise, so you end up with much lower exposure (potentially negative exposure if your expected interest rate is higher than the expected returns). Is that basically the reasoning?
Thanks for these comments. In short, to all of your questions, the answer is “yes”. Some specific comments:
1. This is perhaps already clear, but it might be worth emphasizing that the economic logic is: real rates are particularly use for forecasting, since the sign of the effect is rather unambiguous for the TAI scenario; but it’s possible the expected returns could be higher for trading on other bets, if you’re willing to make stronger assumptions (e.g. “compute will be important”).
2. Re: equities, the appendix post (especially #4 there) summarizes how we’re thinking about this. To spell out a bit more:
An approximation for stock pricing is the Gordon growth formula, P=D/(r−g), where
P is stock price (i.e. market cap)
D is some initial level of dividends
r is the real rate
g is the growth rate of dividends over time
For the equity market as a whole, a natural approximation is that the growth rate of dividends equals the growth rate of the economy. And as we pointed out in section I, a first-order approximation for the Euler equation under certainty (“the Ramsey rule”) is
r=ρ+θg
Combining the Ramsey rule and the Gordon growth formula, we have
P=Dρ+(1−θ)g
How to interpret this? As a benchmark, suppose theta=1. That’s log utility (which I think is the benchmark used in a lot of EA, e.g. at OpenPhil, and has some support in the literature). Then you have P=D/rho. That is, price is future profits discounted by your rate of time preference—raising or lower the growth rate doesn’t affect the stock price at all, because it ‘cancels out’ in a specific way.
So, that denominator is picking up the ‘Merton optimality’ that you mention. And I guess the reason I wrote all of this out was to reply to this:
Perhaps with equities you might expect both returns and the interest rate to rise by 3%, which would cancel out
Yes! But also they might not cancel out. It could go either way depending on theta ¯\_(ツ)_/¯. To my knowledge it’s an active area of debate (‘financial economists think theta < 1, macroeconomists think > 1’).
If you really want to nerd out, Cochrane has extended wordy discussion here and Steinsson has long slides here (theta is the inverse of the elasticity of intertemporal substitution).
This is perhaps more than you asked for, and yet I’m not sure if this answered exactly what you were asking. Let me know if not!
Sorry for making you repeat yourself, I’d read the appendix and the Cochrane post :)
To summarise, the effect on equities seems ambiguous to you, but it’s clearly negative on bonds, so investors would likely tilt towards equities.
In addition, the sharpe ratio of the optimal portfolio is decreased (since one of the main asset classes is worse), while the expected risk-free rate over your horizon is increased, so that would also imply taking less total exposure to risk assets.
What do you think of that implication?
One additional piece of caution is that within investing, I’m pretty sure the normal assumption is that growth shocks are good for equities e.g. you can see the Chapter in Expected Returns by Anti Ilmanen on the growth factor, or read about risk parity. There have been attempts to correlate the returns of different assets to changes in growth expectations.
On the other hand, I would guess theta is above one for the average investor.
To summarise, the effect on equities seems ambiguous to you, but it’s clearly negative on bonds, so investors would likely tilt towards equities.
“Negative for bonds” does not imply “shift investment from bonds to stocks”, though. It could mean “shift toward short bonds” or “shift investment from bonds, to just invest less overall”.
In addition, the sharpe ratio of the optimal portfolio is decreased (since one of the main asset classes is worse)
I would push back on this too, for a related reason—the optimal portfolio can include “go short bonds”, which might now have a higher expected return.
I think the standard asset pricing logic would be: there is one optimal portfolio, and you want to lever that up or down depending on your risk tolerance and how risky that portfolio is. So, whether you ‘take less total exposure to risky assets’ depends on whether the argument here updates your view on how ‘risky’ the future is (Tyler Cowen has argued this, I’m not sure it’s super clear cut though).
That makes sense. It just means you should decrease your exposure to bonds, and not necc buy more equities.
I’m skeptical you’d end up with a big bond short though—due to my other comment. (Unless you think timelines are significantly shorter or the market will re-rate very soon.)
I think the standard asset pricing logic would be: there is one optimal portfolio, and you want to lever that up or down depending on your risk tolerance and how risky that portfolio is.
In the merton’s share, your exposure depends on (i) expected returns of the optimal portfolio (ii) volatility / risk (iii) the risk free rate over your investment horizon and (iv) your risk aversion.
You’re arguing the risk free rate will be higher, which reduces exposure.
It seems like the possibility of an AI boom will also increase future volatility, also reducing exposure.
Then finally there’s the question of expected returns of the optimal portfolio, which you seem to think is ambiguous.
So it seems like the expected effect would be to reduce exposure.
A 60:40 portfolio has an effective duration of ~40 years, where most of that duration comes from equities.
I’m not really sure how you get that? The duration on the bond portion is going to be ~7-10y which would imply 60y duration for equities, which I think is wrong.
My understanding is that an important part of the reasoning for a focus on avoiding bonds is that an increase in GDP growth driven by AI is clearly negative for bonds, but has an ambiguous effect on equities (plus commodities and real estate), so overall you should hold more equities (/growth assets) and less bonds. Is that right?
That is their claim, but as I pointed out here the evidence isn’t so clear.
Thank you for the post! I’m very interested to see more work on this topic.
I feel a little bit unsure about the focus on the bonds – would be very curious to hear any reflections on the below.
As you say, if real interest rates rise, that should affect all assets with positive duration.
Perhaps then the net effect of having the view that real interest rates will rise is just that you should reduce overall portfolio duration. A 60:40 portfolio has an effective duration of ~40 years, where most of that duration comes from equities. Perhaps someone who believes this should target, say, a 20 year average duration instead (through whatever means seems least costly, which could mean holding fewer equities).
Perhaps equivalently, if real interest rates are going to rise, then all financial assets are currently overpriced, so maybe the effect would be holding fewer financial assets in general, and holding more cash / spending more.
My understanding is that an important part of the reasoning for a focus on avoiding bonds is that an increase in GDP growth driven by AI is clearly negative for bonds, but has an ambiguous effect on equities (plus commodities and real estate), so overall you should hold more equities (/growth assets) and less bonds. Is that right?
That makes sense to me, but then I still feel unsure about, having tilted towards equities, whether your overall exposure should be higher or lower.
(And tilting towards equities will increase the effective duration of your portfolio, making an increase in real interest rates worse for you all else equal.)
If we use the merton’s share to estimate optimal exposure, that depends on the difference between the expected return of the asset and the expected real interest rate over your horizon. Perhaps with equities you might expect both returns and the interest rate to rise by 3%, which would cancel out, and you end up with the same exposure. But with bonds only the interest rate will rise, so you end up with much lower exposure (potentially negative exposure if your expected interest rate is higher than the expected returns). Is that basically the reasoning?
Thanks for these comments. In short, to all of your questions, the answer is “yes”. Some specific comments:
1. This is perhaps already clear, but it might be worth emphasizing that the economic logic is: real rates are particularly use for forecasting, since the sign of the effect is rather unambiguous for the TAI scenario; but it’s possible the expected returns could be higher for trading on other bets, if you’re willing to make stronger assumptions (e.g. “compute will be important”).
2. Re: equities, the appendix post (especially #4 there) summarizes how we’re thinking about this. To spell out a bit more:
An approximation for stock pricing is the Gordon growth formula, P=D/(r−g), where
P is stock price (i.e. market cap)
D is some initial level of dividends
r is the real rate
g is the growth rate of dividends over time
For the equity market as a whole, a natural approximation is that the growth rate of dividends equals the growth rate of the economy. And as we pointed out in section I, a first-order approximation for the Euler equation under certainty (“the Ramsey rule”) is
r=ρ+θg
Combining the Ramsey rule and the Gordon growth formula, we have
P=Dρ+(1−θ)g
How to interpret this? As a benchmark, suppose theta=1. That’s log utility (which I think is the benchmark used in a lot of EA, e.g. at OpenPhil, and has some support in the literature). Then you have P=D/rho. That is, price is future profits discounted by your rate of time preference—raising or lower the growth rate doesn’t affect the stock price at all, because it ‘cancels out’ in a specific way.
So, that denominator is picking up the ‘Merton optimality’ that you mention. And I guess the reason I wrote all of this out was to reply to this:
Yes! But also they might not cancel out. It could go either way depending on theta ¯\_(ツ)_/¯. To my knowledge it’s an active area of debate (‘financial economists think theta < 1, macroeconomists think > 1’).
If you really want to nerd out, Cochrane has extended wordy discussion here and Steinsson has long slides here (theta is the inverse of the elasticity of intertemporal substitution).
This is perhaps more than you asked for, and yet I’m not sure if this answered exactly what you were asking. Let me know if not!
Sorry for making you repeat yourself, I’d read the appendix and the Cochrane post :)
To summarise, the effect on equities seems ambiguous to you, but it’s clearly negative on bonds, so investors would likely tilt towards equities.
In addition, the sharpe ratio of the optimal portfolio is decreased (since one of the main asset classes is worse), while the expected risk-free rate over your horizon is increased, so that would also imply taking less total exposure to risk assets.
What do you think of that implication?
One additional piece of caution is that within investing, I’m pretty sure the normal assumption is that growth shocks are good for equities e.g. you can see the Chapter in Expected Returns by Anti Ilmanen on the growth factor, or read about risk parity. There have been attempts to correlate the returns of different assets to changes in growth expectations.
On the other hand, I would guess theta is above one for the average investor.
“Negative for bonds” does not imply “shift investment from bonds to stocks”, though. It could mean “shift toward short bonds” or “shift investment from bonds, to just invest less overall”.
I would push back on this too, for a related reason—the optimal portfolio can include “go short bonds”, which might now have a higher expected return.
I think the standard asset pricing logic would be: there is one optimal portfolio, and you want to lever that up or down depending on your risk tolerance and how risky that portfolio is. So, whether you ‘take less total exposure to risky assets’ depends on whether the argument here updates your view on how ‘risky’ the future is (Tyler Cowen has argued this, I’m not sure it’s super clear cut though).
That makes sense. It just means you should decrease your exposure to bonds, and not necc buy more equities.
I’m skeptical you’d end up with a big bond short though—due to my other comment. (Unless you think timelines are significantly shorter or the market will re-rate very soon.)
In the merton’s share, your exposure depends on (i) expected returns of the optimal portfolio (ii) volatility / risk (iii) the risk free rate over your investment horizon and (iv) your risk aversion.
You’re arguing the risk free rate will be higher, which reduces exposure.
It seems like the possibility of an AI boom will also increase future volatility, also reducing exposure.
Then finally there’s the question of expected returns of the optimal portfolio, which you seem to think is ambiguous.
So it seems like the expected effect would be to reduce exposure.
I’m not really sure how you get that? The duration on the bond portion is going to be ~7-10y which would imply 60y duration for equities, which I think is wrong.
That is their claim, but as I pointed out here the evidence isn’t so clear.
I think the effective duration on equities is roughly the inverse of the dividend yield + net buybacks, so with a ~2% yield, that’s ~50 years.
Some more here: https://www.hussmanfunds.com/wmc/wmc040223.htm
I don’t think that makes much sense tbh.
I think the key point is just equities will also go down if real interest rates rise (all else equal) and plausibly by more than a 20 year bond.
I agree, although I’ll give you good odds the 20y moves more.