I’m not sure what prompted all of this effort, and I’ve rarely heard Kelly described as corresponding to log utility, only ever as an aside about mean-variance optimization. There, log utility corresponds to A=1, which is also the Kelly portfolio. That is the maximally aggressive portfolio, and most people are much, much more risk averse.
If anything, I’d say that the Kelly - log utility connection obviously suggests one point, which is that most people are far too risk-averse (less normatively, most people don’t have log utility functions). The exception is Buffett - empirically he does, subject to leverage constraints.
Did you take vitamin K? You really need that to process vitamin D. This LessWrong post goes into more detail. Quotes from the article:
Atli Arnarson makes the case in Is Vitamin D Harmful Without Vitamin K? that Vitamin D toxicity at high doses is usually about K2 deficiency because both are needed in the same pathways and more K2 is needed when there's more Vitamin D. Vitamin D toxicity leads to hypercalcemia where there's too much Calcium in the blood. Calcifediol moves some calcium from the bone to the blood and K2 is needed to put the calcium in the bones. Hypercalcemia is bad because it lead to blood vessel calcification. Observational studies link low Vitamin K2 levels to blood vessel calcification with K2 being more important than K1.
>The vast majority of the equity premium is unexplained. When people say "just buy stocks and hold for a long period and you'll make 10% a year", they're asserting that the unexplained equity premium will persist, and I have a problem with that assumption.
I completely agree with you here. My point is that this comment is different from the plain language interpretation of your top post. I know that is a seemingly small point, but I commented because I don't want to leave future readers with the wrong impression. If we did not have this conversation, I think they may have been left thinking that it is a puzzle that stocks go up at all. I don't view that as a simple caveat to the initial statement, but a different statement entirely.
Can we agree on the following statement? "While it is expected that stocks will go up, and go up more than bonds, it is yet to be explained why they have gone up so much more than bonds."
The equity risk premium puzzle is about a very different question, no? The equity premium puzzle is a puzzle because of how large the equity premium is to bonds, but it is totally expected that there is an equity premium or that bond and equity returns are positive. Concretely, the puzzle asks, why do equities earn 8% if the risk-free rate is 2%, instead of 3%? The puzzle is that 6% spread is much larger than what standard financial theory predicts (although a lot of the dispute ends up being around the right parameterization and benchmarks). But standard financial does predict (a) an equity premium to the risk-free rate and (b) positive returns for both equities and bonds.
I think you get to that understanding in your last sentence ("stock returns are way, way higher than the risk-free rate"), but this is a much different statement than "stocks shouldn't have gone up historically" or "people have grown accustomed to there being an equity premium to the extent that there's a default assumption that it'll just continue forever despite nobody knowing why it existed in the past." I don't want to be a pedant, but those are much different statements, because they state that the absolute return on stocks should be 0, and that the positive return of equities is some puzzle. Maybe I'm misunderstanding you, but the straightforward interpretation of what you were saying is quite bold, and not something I've heard of before or have seen on wikipedia (including what you linked).
Why shouldn't have stocks gone up historically? Isn't there more real wealth today than during the days of the East India Company? If a stock represents a piece of a businesses, and those businesses now have more real wealth today than 300 years ago, why shouldn't stock returns be quite positive? To be honest I'm bewildered by this perspective that stocks should never go up - I've never seen anyone in finance academically or professionally entertain this idea, so I'm surprised to hear you say "no one knows the answer," as if it's a common puzzle in the field. Why some stocks go up more than others is a good and open question, but that's one of relative valuation, not whether market returns on an absolute are greater than zero.
The biggest reason stocks go up is pretty simple, in my view: a lot of very smart and hardworking people are working very hard to make stocks go up. In addition, lots of less smart and less hardworking people are also working to make stocks go up. In contrast, very few people are trying to make stocks go down.
While there are shortsellers, they are generally not trying to make stocks go down, i.e. by destroying value. Instead, shortsellers are simply saying that some companies are overvalued, and time and effort is better spent on other companies.
What do I mean by "make stocks go up"? I mean it in a fundamental sense: employees are trying to create value by making products better or adding new markets. Their rewards include stock compensation, bonuses, and promotions, so they are indeed incentivized to create value in whatever way possible. Meanwhile, financiers are trying to allocate capital (an abstract representation of time, effort, and value) in the best way, by optimizing society's effort. These people are also rewarded with capital gains, bonuses, and promotions.
Given that there is so much effort and incentive to fundamentally increase the value of stocks, why should the market stay flat or neutral? I'm sure someone can try to find some elaborate corner case why this isn't true, but mostly the reasons stocks wouldn't go up is if no one is trying (no incentive) or if someone is trying to destroy asset value (expropriation, violent revolution, etc.). If people are trying to build stuff that makes stock prices go up, and there isn't much effort to destroy them, it's pretty straightforward that they go up.
For what it's worth, this is basically Buffett's view. Also note, the comments about equity risk premium, valuation puzzles, and the efficient market hypothesis miss the point: that's only a matter of relative returns, not absolute returns. (If your question is about beating the market, then those points are more relevant, but it's not clear anyone can beat the market today in developed economies outside narrow pockets of inefficiency.) As long as you can build new stuff, you'll have a reason to invest, which demands a return, hence the positive returns we see. If there's less "stuff" to build, you can expect lower prospective returns because capital competes for each opportunity, resulting in lower rates and a huge premium on growth opportunities, which is what we observe today.
One last way to think about it is in real terms. If you have a machine that can build more of itself, you will have more of those machines over time, which is a real return.
This is amazing. I've often used blocking extensions, only to remove them when I "needed" them - e.g., a google search about a health question resulted in an informative reddit thread. This is great, because now I can use these sites when I have a legitimate need (or at least when it's worth a 30 second delay). It's great for email in particular, because I use it both out of need and as a distraction.