Is “The S&P 500” actually a good comparison entity? The companies that make it up vary all the time, on average remaining in it just a few decades, while US treasuries are from the same US government as always. Is there any company whose stock has average “S&P 500 level” returns over the course of a century or more? And presumably if there is, no simple method can consistently predict which one? In that case, can (some of?) the premium come from the need to constantly have money in motion and rebalancing and deciding what to include in indexes at all?
Similarly, if I instead compare the S&P 500 to a portfolio of bonds from all the large countries over the past century and a half, i.e. if I have to include the USSR and the Ottoman Empire and Imperial China in a constantly-updating index of bonds as my comparison point, what does that do to my expected government debt rate of return?
How much, if at all, is this a result of the choice to measure returns in USD, a currency whose supply is controlled by one of the entities involved in the comparison? The US government can actually, literally guarantee that as long as it exists at all, it will have enough dollars to pay its debts. Would it matter if I measured both financial assets in some other metric (although IDK which one, maybe something commodity based?).
Would the premium remain the same in a world where humans were immortal? People and organizations generally don’t just save and invest money, they do it for some purpose, with some time horizon in mind. If I expected to live 1,000 years it would matter a lot less to me if a crash caused me to delay buying a house by an extra decade, if it meant I’d most likely be able to get one a year sooner, or get a more expensive one, on average. The idea of putting a significant fraction of my savings in a low-yield US treasury would seem silly to immortal-me. Note: does this relate to why large endowments of long-lived trusts and organizations get higher returns?
What matters is that it’s something you can invest in. Choosing the S&P 500 is not really that important in particular. There doesn’t have to be a single company whose stock is perfectly correlated with the S&P 500 (though nowadays we have ETFs which more or less serve this purpose) - you can simply create your own value-weighted stock index and rebalance it on a daily or weekly basis to adjust for the changing weights over time, and nothing will change about the main arguments. This is actually what the authors of The Rate of Return on Everything do in the paper, since we don’t really have good value-weighted benchmark indices for stocks going back to 1870.
The general point (which I hint at but don’t make in the post) is that we persistently see high Sharpe ratios in asset markets. The article I cite at the start of the post also has data on real estate returns, for example, which exhibit an even stronger puzzle because they are comparable to stock returns in real terms but have half the volatility.
I don’t know the answer to your exact question, but a lot of governments have bonds which are quite risky and so this comparison wouldn’t be appropriate for them. If you think of the real yield of bonds as consisting of a time preference rate plus some risk premium (which is not a perfect model but not too far off), the rate of return on any one country’s bonds puts an upper bound on the risk-free rate of return. Therefore we don’t need to think about investing in countries whose bonds are risky assets in order to put a lower bound on the size of the equity premium relative to a risk-free benchmark.
This only has a negligible effect because the returns are inflation-adjusted and over long time horizons any real exchange rate deviation from the purchasing power parity benchmark is going to be small relative to the size of the returns we’re talking about. Phrased another way; inflation-adjusted stock prices are not stationary whereas real exchange rates are stationary, so as long as the time horizon is long enough you can ignore exchange rate effects so long as you perform inflation adjustment.
This is an interesting question and I don’t know the answer to it. Partly this is because we don’t really understand where the equity premium is coming from to begin with, so thinking about how some hypothetical change in the human condition would alter its size is not trivial. I think different models of the equity premium actually make different predictions about what would happen in such a situation.
It’s important, though, to keep in mind that the equity premium is not about the rate of time preference: risk-free rates of return are already quite low in our world of mortal people. It’s more about the volatility of marginal utility growth, and there’s no logical connection between that and the time for which people are alive. One of the most striking illustrations of that is Campbell and Cochrane’s habit formation model of the equity premium, which produces a long-run equity premium even at infinite time horizons, something a lot of other models of the equity premium struggle with.
I think in the real world if people became immortal the long-run (or average) equity premium would fall, but the short-run equity premium would still sometimes be high, in particular in times of economic difficulty.
Is “The S&P 500” actually a good comparison entity? The companies that make it up vary all the time, on average remaining in it just a few decades, while US treasuries are from the same US government as always. Is there any company whose stock has average “S&P 500 level” returns over the course of a century or more? And presumably if there is, no simple method can consistently predict which one? In that case, can (some of?) the premium come from the need to constantly have money in motion and rebalancing and deciding what to include in indexes at all?
Similarly, if I instead compare the S&P 500 to a portfolio of bonds from all the large countries over the past century and a half, i.e. if I have to include the USSR and the Ottoman Empire and Imperial China in a constantly-updating index of bonds as my comparison point, what does that do to my expected government debt rate of return?
How much, if at all, is this a result of the choice to measure returns in USD, a currency whose supply is controlled by one of the entities involved in the comparison? The US government can actually, literally guarantee that as long as it exists at all, it will have enough dollars to pay its debts. Would it matter if I measured both financial assets in some other metric (although IDK which one, maybe something commodity based?).
Would the premium remain the same in a world where humans were immortal? People and organizations generally don’t just save and invest money, they do it for some purpose, with some time horizon in mind. If I expected to live 1,000 years it would matter a lot less to me if a crash caused me to delay buying a house by an extra decade, if it meant I’d most likely be able to get one a year sooner, or get a more expensive one, on average. The idea of putting a significant fraction of my savings in a low-yield US treasury would seem silly to immortal-me. Note: does this relate to why large endowments of long-lived trusts and organizations get higher returns?
Answering your questions in order:
What matters is that it’s something you can invest in. Choosing the S&P 500 is not really that important in particular. There doesn’t have to be a single company whose stock is perfectly correlated with the S&P 500 (though nowadays we have ETFs which more or less serve this purpose) - you can simply create your own value-weighted stock index and rebalance it on a daily or weekly basis to adjust for the changing weights over time, and nothing will change about the main arguments. This is actually what the authors of The Rate of Return on Everything do in the paper, since we don’t really have good value-weighted benchmark indices for stocks going back to 1870.
The general point (which I hint at but don’t make in the post) is that we persistently see high Sharpe ratios in asset markets. The article I cite at the start of the post also has data on real estate returns, for example, which exhibit an even stronger puzzle because they are comparable to stock returns in real terms but have half the volatility.
I don’t know the answer to your exact question, but a lot of governments have bonds which are quite risky and so this comparison wouldn’t be appropriate for them. If you think of the real yield of bonds as consisting of a time preference rate plus some risk premium (which is not a perfect model but not too far off), the rate of return on any one country’s bonds puts an upper bound on the risk-free rate of return. Therefore we don’t need to think about investing in countries whose bonds are risky assets in order to put a lower bound on the size of the equity premium relative to a risk-free benchmark.
This only has a negligible effect because the returns are inflation-adjusted and over long time horizons any real exchange rate deviation from the purchasing power parity benchmark is going to be small relative to the size of the returns we’re talking about. Phrased another way; inflation-adjusted stock prices are not stationary whereas real exchange rates are stationary, so as long as the time horizon is long enough you can ignore exchange rate effects so long as you perform inflation adjustment.
This is an interesting question and I don’t know the answer to it. Partly this is because we don’t really understand where the equity premium is coming from to begin with, so thinking about how some hypothetical change in the human condition would alter its size is not trivial. I think different models of the equity premium actually make different predictions about what would happen in such a situation.
It’s important, though, to keep in mind that the equity premium is not about the rate of time preference: risk-free rates of return are already quite low in our world of mortal people. It’s more about the volatility of marginal utility growth, and there’s no logical connection between that and the time for which people are alive. One of the most striking illustrations of that is Campbell and Cochrane’s habit formation model of the equity premium, which produces a long-run equity premium even at infinite time horizons, something a lot of other models of the equity premium struggle with.
I think in the real world if people became immortal the long-run (or average) equity premium would fall, but the short-run equity premium would still sometimes be high, in particular in times of economic difficulty.