You seem to be predicting a diverging trend in that relation towards infinity, which is insane, as infinities tend to be.
I conclude from this you're misunderstanding the notion of "long term equilibrium" as stronger than it is in reality. Construct a model that simultaneously allows infinite divergence between securitized asset prices and their associated incomes, and disallows easy arbitrage, or we have nothing to talk about.
Every fool digs up that Keynes quote when his model is wrong.
OTOH, there's another story to why equity returns are higher than GDP returns: equity investors are being compensated for the higher risk.
This gets mentioned very often in such debates, but the implied causal connection is wrong: There is no guarantee that higher risk leads to higher returns. It's not like the stock market says "We should keep up increasing stock prices so that equity investors are being compensated for their risk."
Over long timespans, stock prices are coupled to the performance of the underlying companies (mostly their income streams), not to risk. So far, there has been a correlation, but there has never been a guaranteed causal relation between risk and stock returns.
The mechanism is much simpler: asset prices of risky assets today will fall because willing buyers demand a higher return for the risk.
E.g. you have a stock and a bond both at $100 with the same expected return. Investors aren't happy with that, so they refuse to buy the stock until its price falls and its implied return rises.
So despite the higher risk, and despite the fact that the stock's price is discounted, the investor did not make more profit from the stocks than from the bonds.
In practice, companies should grow faster than bonds (because they can reinvest their profits to increase their profit – although many companies fail at that), yielding higher returns. My point is, that those higher returns result from the different mechanisms underlying different security types, not from differences in risk.
Bonds are fundamentally less risky than stocks because in the event of bankruptcy bondholders are paid first. Real recovery rates are around 40% usually.
> Ten years later, the bonds are about to mature and are valued at $150 (50% profit)
No, the value of of the bond is mostly independent of how much the company's future revenues are (as long as they don't go bankrupt). There are few future paths where someone will pay you $150 in the future for a bond that you bought for $100 today.
Bonds mostly have downside risk (you can lose everything), but limited upside participation. OTOH, equity has worse downside risk (if a company has $700m in debt and $300m in equity, it only needs to lose $300m in assets to go bankrupt--but in that case, bondholders would still get paid), but full upside participation.
Another way of looking at this is that if a company triples in size, your equity stake also triples because you now own the same percentage of a much larger company, but the bond cashflows did not change because bonds do not have that upside.
Your reasoning was:
> The mechanism is much simpler: asset prices of risky assets today will fall because willing buyers demand a higher return for the risk. [...] Investors aren't happy with that, so they refuse to buy the stock until its price falls and its implied return rises.
I showed that this is not a valid argument, because if the market discounts the price of a stock by x% due to higher perceived risk, then it will discount its price by x% ten years later as well (unless there was a major change in the company's fundamentals, which is another story and not relevant here), meaning that the discounting of risk did not result in higher profit (compared to the return on stocks of a company which is deemed less risky).
Otherwise, how can you measure the return to risk?
> then it will discount its price by x% ten years later as well
That doesn't follow because you're missing a free parameter. Let's say a piece of stock ought to be worth $110 in 1 year if people weren't risk averse (based on how we think the company will do, etc.), but it'll only be worth $100 because of the risk. It can still be worth $91 today, implying a 10% return, for example.
For any path of future expected equity values, regardless of what future discount you apply, there is a price today that will imply an equity risk premium.
FYI, people have empirically measured the implied equity risk premium over long periods of time. The general consensus is that equity returns around 5-10% more per annum that a risk-free asset, but it varies greatly from decade to decade:
https://www.newyorkfed.org/medialibrary/media/research/staff...
Rational pricing requires perfect knowledge of future income streams. Unless you have such knowledge, you can't even know what concrete position reflects a bet that the market "reverts" (a misnomer, because it assumes that rationality is a normal state that is only in exceptional circumstances deviated from) to rational pricing.
Equity > GDP as a return to risk would require you to be able to "invest in GDP" in a relatively variance-free way. Social Security or seizing control of the government (or at least its taxing power) is about as close as you can get, but neither is really securitizable.
Technically no, it just requires one to be able to construct a basket that approximately returns GDP growth (along with GDP variance).
Note that total returns to equity include dividends, so you can easily have equity give outsize returns without total market cap approaching 100% of assets.
Perhaps, but then we are getting into rational expectations and not mathematical constraints. (Though, really, given that rationality requires perfect knowledge of future utilities, "the future will be perpetually irrational about asset prices" is pretty much guaranteed to be true except for intermittent times when it isn't momentarily largely by chance; even a consistent divergence in a particular direction from rationality isn't surprising, given what we the particular ways in which people tend to be deviate from economic rationality in practice.)
> There is indeed a mathematical relation between long run asset prices and the income generated by those assets.
No, there is a mathematical relation between reasonable asset prices and expected income streams that the assets will generate.
> In the short run you can do whatever you want, but the long run constraint is predictably enforced by arbitrage.
"In the long run, we're all dead" -- Keynes
Even granting your point for the sake of argument, what must ultimately be true in the long run assuming an infinite time horizon need never actually be true in the physical universe we inhabit. Irrationality in prices can be maintained indefinitely, even though not infinitely -- but then, the market can't actually exist infinitely, anyway.