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.
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.