nisiprius wrote: ↑Fri Mar 26, 2021 10:46 am
tradri wrote: ↑Fri Mar 26, 2021 7:33 amI had a look at the Wikipedia article of the Kelly Criterion, but from I understood, it mostly applies to situations where you either gain or lose money. Since (I think) we all assume that "stonks only go up" in the long-run, I don't see how I can calculate the probability of losing money. It's not like I have to realize my losses when investing in a leveraged ETF, so I should be able to sit out any market crash.
1) If you want to engage in long-term,
high risk investing, you
really owe it to yourself to understand the Kelly Criterion. (As in, understand it better than I do. I don't need to). If you are actually interested in learning, not confirmation of your pre-existing ideas, you
need to learn about it. You can reject the practical conclusions if you like, but only after you understand the ideas. 2) If you want to understand the Kelly Criterion, I suggest taking the time to read William Poundstone's book,
Fortune's Formula--which, incidentally, does not endorse the idea uncritically. It's a thoughtful and intelligent analysis, including discussions of the difference in opinion between traditional financial economists and practitioners of the Kelly Criterion in investing.
The intellectual problem is not simple. Briefly, traditional analysis suggests that the highest long-term return will be obtained by using as much leverage as possible.
I believe that's what you think. That you should use as much leverage as possible, limited only by personal risk tolerance, and that this will "obviously" give the highest long-term return. And that you are only setting a 3X limit for practical reasons... and that you also believe that financial ruin with 3X leveraged stocks and daily rebalancing is impossible
because you personally cannot envision a scenario of the S&P 500 losing more than 33.34% in a day, so you set the limit at 3X, not because you can actually tolerate it necessarily, but because you think that at 3X it is impossible for your intolerable risk ever to show up.
The Kelly criterion writing turns on goal definition. The goal is assumed to be to maximize the long-term return in the sense of compound average growth rate (CAGR). The key word here is "compound," and the key insight is that maximizing the average annual return (which is increased without limit by using more and more leverage) does
not maximize the long-term multi-year
compounded return.
The big problem in applying the Kelly criterion is that despite Poundstone's phrase "fortune's
formula," the only formulas for applying the Kelly criterion require idealized models in which you accurately know probabilities
a priori--for example, gambling games like roulette or dice where you know the probabilities from the physical design of the equipment, but not horse races or the stock market, where you do not.
It is made worse by the fact that financial data is ill-behaved, with extreme events occurring much more often than they do in statistical models based on the normal distribution.
Various stock market estimates based on the Kelly criterion come up with values of 1.2X or 1.4X leverage. Even there, there is a problem, because I have read that people who
really use the Kelly criterion think it is too due to inability to know the true odds. Therefore, the conventional rule-of-thumb is to go no more than farther than "half Kelly."
That would rationally suggest that a risk-tolerant stock investor might go beyond 100% stocks and consider 10% or 20% leverage.
The point is that there are rational, numerical, computational reasons for limiting leverage, and to much less than 2X. Of course there are other people who assert the opposite, but it's important to see there
is a cold hard argument for limiting leverage.
The second point is that even if we are not talking about personal financial ruin, if your hardnosed goal is to "maximize return" in the sense of longterm CAGR, using more than a small amount of leverage
probably will not do that.
A detail that's always argued in discussions of the Kelly criterion is whether it contains an assumption of a logarithmic utility function. That is, does it assume that $10,000 to someone with $10 million than to someone with $100,000? Some say that it absolutely does not. Some say that this assumption has surely been smuggled in. Even if it has been, I don't think it's all that crazy an assumption.
2) And of course even the appropriateness of the Kelly criterion has been challenged. The late economist Paul Samuelson had very strong views, and ultimately expressed them in a paper entitled
Why We Should Not Make Mean Log of Wealth Big Though Years to Act are Long. His point is that the goal of maximizing long-term average return (CAGR) is, in his opinion, wildly inappropriate. The odd title is that eventually he got so irritated that he wrote this paper literally in words of one syllable. Although it's a droll idea, unfortunately in this case using words of one syllable doesn't actually make the argument particularly clear, but at least when the topic came up he could say "I've explained this in words of one syllable."