In 1956, John Kelly introduced his “Kelly criteria” betting strategy: bet on each possible outcome in proportion to (your estimate of) that outcome’s chances of winning, regardless of the betting odds offered. More generally, a
I think they tend to be pretty well paid and pretty well off, more so than most other professions (all that is needed). And to some extent, being an economist is about learning how you *can't* just become rich with a little extra knowledge (no free lunches, efficient markets, that sort of thing).
Thanks - that all makes sense. #2 wouldn't be a problem, apparently, if I did have such an edge... but since I'm not even entirely sure what an edge is in this context (inside information? some sort of predictive ability? gobs of cash?), I probably don't!
I'm going to go off on two tangents that always puzzled me, because you seem knowledgeable and your mention of Buffet reminded me. Feel free to ignore them if you don't have the time or inclination, though; no worries.
1.) Are economists rich? Shouldn't they be?
They're not the highest-paid by salary, I know. But I always assumed that the knowledge required - about value, markets, investing, and the like; basically, "the science of money"(?) - would translate into turning small piles of money into big piles of money better than any other profession. I'm not quite certain this is so, though.
I've been meaning to go through and look at what the profession ends up making people the richest on average (and of course discounting things like inheritance)... if you know any insight on this, too, please let me know!
2.) Why is Buffet so good at investing? Does anyone know, beyond assumption of some sort of Kelly rule?
That is - it seems his "edge" is abnormally large, even accounting for obvious stuff like time, dedication, and education. I've read that his performance in the stock market is wildly, improbably good. I've also read that attempting to "beat the market" with any sort of investing strategy will always fail (except for lucky breaks); yet it seems he is clearly doing it. Or did it at one time, anyway. This might just be a misinterpretation of his career, though.
1. Kelly requires you to be committed to it as a strategy, you can't really 'time' it or anything. (If it was optimal at the start, it's optimal now even if you lost.) You may not have the emotional fortitude for it. (I learned this in practice betting Kelly on Intrade: http://www.gwern.net/Predic... This is a common criticism of Kelly in practice.2. Kelly requires you to be committed for a long time. In particular, as pointed out here already I think, you need to be able to think in centuries or millennia. With Kelly, as with many optimal strategies or results, 'in the long run we are all dead'. How soon do you need that money...?3. You need an edge of some kind, otherwise Kelly has no way to maximize your growth rate. As decades of research goes to show, most people trade too much (I think Hanson has linked in the past one paper on how overtrading damages returns and a gender correlation with overtrading) and are overconfident and cannot beat the markets, which are pretty efficient. The smaller your edge, obviously, the less Kelly can grow your investment.4. You need to estimate your edge correctly! If you think your edge is better than it is, that's as bad as thinking your edge is worse than it is.
Hopefully that's enough to explain why you probably don't want to use this particular strategy. Leave it to the Buffets and Swiss Res of the world.
It seems to me that the post is advocating it, but some people in the comments disagree with this assessment. Wei Da appears to be talking about something else entirely; only Chip seems to offer an actual criticism. Can you explain one or two of these 3-5 arguments to me?
> Should I be attempting to follow this Kelly Rule, or is my original strategy of investing in an index fund like the S&P 500 a better bet?
With all due respect, reading this post and the comments should have given you at least 3-5 arguments why you would not want to follow it for your investing. If you can't think of any, then you probably shouldn't do it in the first place because you don't actually understand it.
This article is extremely interesting. I've been a longtime lurker at LessWrong, but have not ventured over here; now I see what I've been missing.
If, however, someone could simplify this for me... I'm about to invest in the stock market, as I have come into some money ($5,000 - I know, very little for most people). Should I be attempting to follow this Kelly Rule, or is my original strategy of investing in an index fund like the S&P 500 a better bet?
I understand the point you're making in this post, and was making a connection to the previous post. Someone who wants to maximize expected number of descendants would not want to apply the Kelly rule, despite it being "optimal" in some sense. It seems worth pointing this out.
Wei this post is about financial prices, not the number of future descendants. Selection can reward the Kelly rule of investment even with zero effect of prices on the actual assets returns. So all these possible financial states could have exactly the same number of descendants.
Robin, the self indication assumption (which you previously said you "embraced") says that we should reason as if we are randomly selected from all creatures across all possible worlds (instead of first sampling a possible world, then sampling a creature within the chosen world). I pointed out in the linked comment that under such a sampling scheme you would expect the creature selected to be the descendent of an expected-descendants maximizer instead of an expected-log-descendants maximizer.
Empirically, fund inflows are convexly related to relative returns (mutual and hedge). Given this, I think there's an incentive to greater volatility than the Kelly Criterion in asset markets.
The book Fortune's Formula by William Poundstone contains many examples of successful real-world applications of the Kelly principle. (btw, if you are *that* CM, I have my students read your "Lessons from Habitat" paper, nice to meet you.)
Talosaga, it "gets better than average growth regardless of state, time, or prices."
Matthew, I think you misunderstand the rule, and its implications.Chris, Kelly rule can't go bankrupt, and Cochrane reviewed how prices now are way ignorant.
Chip, Cohcrane reviewed how very simple stat track records give plenty good enough expectations for the Kelly rule to have better than average growth.
Wei, Kelly is not *equivalent* to log returns, though it can be close. Yes creatures that consistently max expect distant future returns will have the most expected returns, but we have little reason to expect to see the selection of such creatures.
Wei Dai: At the other end of this spectrum there is quantum lottery. Would you say that quantum lottery is also something that someone with a different psychological makeup could claim as a legitimate strategy?
Robin, Wikipedia says that Kelly criterion is equivalent to maximizing expected log returns, which reminds me that we never resolved our debate about whether evolution "selects for" creatures that maximize expected number of descendants, or creatures that maximize expected log descendants. In particular I don't think you responded to the point I made in this comment, beyond saying "that seems worth pondering".
To restate that point, creatures that maximize expected number of descendants will end up with a higher number of descendants averaged over all possible worlds, but their descendants are concentrated into a few possible worlds with very large total populations, whereas creatures that maximize log descendants end up dominating the population in most possible worlds.
Similarly, when you say Kelly rule "would win an evolutionary competition" you mean that portfolios following the Kelly rule would dominate the market in most possible worlds. But portfolios that maximize expected return instead of expected log return would dominate in the few possible worlds that turn out to be extremely rich.
Do you see any reason why we should be more concerned about "dominating in most possible worlds" instead of "taking over the few possible worlds that are really worth taking over"? It seems that you are more motivated by the former, but perhaps someone with a different psychological makeup could claim the latter as a legitimate preference?
I deduced the the Kelly criterion before hearing about it, and I still have problems remembering or understanding it. It seems to be one of those concepts that is slippery to the mind, like minimax with a-b pruning, or Gödels incompleteness proof.
The Kelly criterion sounds a like a principle that is both true and useless.
All this is predicated on investors' estimates of the probabilities of winning on each bet bearing some resemblance to reality (at least on evolutionary time scales). But if you had any kind of effective strategy for reasonably making such estimates, you would have already solved the problem. I suspect the majority of people who made bad bets during the real estate bubble, for example, lost out not because they had a bad rule for aligning their investment strategy with their expectations, but because their expectations were invalid.
Also, I believe it is very rare for most people to be able access their own expectations in quantifiable form, which, if I understand it correctly, the Kelly rule requires.
This whole argument puts me in mind of the Austrian critique of socialism in the 1930s: the socialists said "we'll just put all the data into this model and calculate what to do", to which the Austrians said, "yes, but you can't actually get the data". It seems to me that the Kelly rule requires knowledge that is not generally available.
> 1.) Are economists rich? Shouldn’t they be?
I think they tend to be pretty well paid and pretty well off, more so than most other professions (all that is needed). And to some extent, being an economist is about learning how you *can't* just become rich with a little extra knowledge (no free lunches, efficient markets, that sort of thing).
As for Buffet, I have no idea.
Thanks - that all makes sense. #2 wouldn't be a problem, apparently, if I did have such an edge... but since I'm not even entirely sure what an edge is in this context (inside information? some sort of predictive ability? gobs of cash?), I probably don't!
I'm going to go off on two tangents that always puzzled me, because you seem knowledgeable and your mention of Buffet reminded me. Feel free to ignore them if you don't have the time or inclination, though; no worries.
1.) Are economists rich? Shouldn't they be?
They're not the highest-paid by salary, I know. But I always assumed that the knowledge required - about value, markets, investing, and the like; basically, "the science of money"(?) - would translate into turning small piles of money into big piles of money better than any other profession. I'm not quite certain this is so, though.
I've been meaning to go through and look at what the profession ends up making people the richest on average (and of course discounting things like inheritance)... if you know any insight on this, too, please let me know!
2.) Why is Buffet so good at investing? Does anyone know, beyond assumption of some sort of Kelly rule?
That is - it seems his "edge" is abnormally large, even accounting for obvious stuff like time, dedication, and education. I've read that his performance in the stock market is wildly, improbably good. I've also read that attempting to "beat the market" with any sort of investing strategy will always fail (except for lucky breaks); yet it seems he is clearly doing it. Or did it at one time, anyway. This might just be a misinterpretation of his career, though.
Sure.
1. Kelly requires you to be committed to it as a strategy, you can't really 'time' it or anything. (If it was optimal at the start, it's optimal now even if you lost.) You may not have the emotional fortitude for it. (I learned this in practice betting Kelly on Intrade: http://www.gwern.net/Predic... This is a common criticism of Kelly in practice.2. Kelly requires you to be committed for a long time. In particular, as pointed out here already I think, you need to be able to think in centuries or millennia. With Kelly, as with many optimal strategies or results, 'in the long run we are all dead'. How soon do you need that money...?3. You need an edge of some kind, otherwise Kelly has no way to maximize your growth rate. As decades of research goes to show, most people trade too much (I think Hanson has linked in the past one paper on how overtrading damages returns and a gender correlation with overtrading) and are overconfident and cannot beat the markets, which are pretty efficient. The smaller your edge, obviously, the less Kelly can grow your investment.4. You need to estimate your edge correctly! If you think your edge is better than it is, that's as bad as thinking your edge is worse than it is.
Hopefully that's enough to explain why you probably don't want to use this particular strategy. Leave it to the Buffets and Swiss Res of the world.
It seems to me that the post is advocating it, but some people in the comments disagree with this assessment. Wei Da appears to be talking about something else entirely; only Chip seems to offer an actual criticism. Can you explain one or two of these 3-5 arguments to me?
> Should I be attempting to follow this Kelly Rule, or is my original strategy of investing in an index fund like the S&P 500 a better bet?
With all due respect, reading this post and the comments should have given you at least 3-5 arguments why you would not want to follow it for your investing. If you can't think of any, then you probably shouldn't do it in the first place because you don't actually understand it.
This article is extremely interesting. I've been a longtime lurker at LessWrong, but have not ventured over here; now I see what I've been missing.
If, however, someone could simplify this for me... I'm about to invest in the stock market, as I have come into some money ($5,000 - I know, very little for most people). Should I be attempting to follow this Kelly Rule, or is my original strategy of investing in an index fund like the S&P 500 a better bet?
I understand the point you're making in this post, and was making a connection to the previous post. Someone who wants to maximize expected number of descendants would not want to apply the Kelly rule, despite it being "optimal" in some sense. It seems worth pointing this out.
Wei this post is about financial prices, not the number of future descendants. Selection can reward the Kelly rule of investment even with zero effect of prices on the actual assets returns. So all these possible financial states could have exactly the same number of descendants.
Robin, the self indication assumption (which you previously said you "embraced") says that we should reason as if we are randomly selected from all creatures across all possible worlds (instead of first sampling a possible world, then sampling a creature within the chosen world). I pointed out in the linked comment that under such a sampling scheme you would expect the creature selected to be the descendent of an expected-descendants maximizer instead of an expected-log-descendants maximizer.
Empirically, fund inflows are convexly related to relative returns (mutual and hedge). Given this, I think there's an incentive to greater volatility than the Kelly Criterion in asset markets.
The book Fortune's Formula by William Poundstone contains many examples of successful real-world applications of the Kelly principle. (btw, if you are *that* CM, I have my students read your "Lessons from Habitat" paper, nice to meet you.)
Talosaga, it "gets better than average growth regardless of state, time, or prices."
Matthew, I think you misunderstand the rule, and its implications.Chris, Kelly rule can't go bankrupt, and Cochrane reviewed how prices now are way ignorant.
Chip, Cohcrane reviewed how very simple stat track records give plenty good enough expectations for the Kelly rule to have better than average growth.
Wei, Kelly is not *equivalent* to log returns, though it can be close. Yes creatures that consistently max expect distant future returns will have the most expected returns, but we have little reason to expect to see the selection of such creatures.
Wei Dai: At the other end of this spectrum there is quantum lottery. Would you say that quantum lottery is also something that someone with a different psychological makeup could claim as a legitimate strategy?
Robin, Wikipedia says that Kelly criterion is equivalent to maximizing expected log returns, which reminds me that we never resolved our debate about whether evolution "selects for" creatures that maximize expected number of descendants, or creatures that maximize expected log descendants. In particular I don't think you responded to the point I made in this comment, beyond saying "that seems worth pondering".
To restate that point, creatures that maximize expected number of descendants will end up with a higher number of descendants averaged over all possible worlds, but their descendants are concentrated into a few possible worlds with very large total populations, whereas creatures that maximize log descendants end up dominating the population in most possible worlds.
Similarly, when you say Kelly rule "would win an evolutionary competition" you mean that portfolios following the Kelly rule would dominate the market in most possible worlds. But portfolios that maximize expected return instead of expected log return would dominate in the few possible worlds that turn out to be extremely rich.
Do you see any reason why we should be more concerned about "dominating in most possible worlds" instead of "taking over the few possible worlds that are really worth taking over"? It seems that you are more motivated by the former, but perhaps someone with a different psychological makeup could claim the latter as a legitimate preference?
I deduced the the Kelly criterion before hearing about it, and I still have problems remembering or understanding it. It seems to be one of those concepts that is slippery to the mind, like minimax with a-b pruning, or Gödels incompleteness proof.
The Kelly criterion sounds a like a principle that is both true and useless.
All this is predicated on investors' estimates of the probabilities of winning on each bet bearing some resemblance to reality (at least on evolutionary time scales). But if you had any kind of effective strategy for reasonably making such estimates, you would have already solved the problem. I suspect the majority of people who made bad bets during the real estate bubble, for example, lost out not because they had a bad rule for aligning their investment strategy with their expectations, but because their expectations were invalid.
Also, I believe it is very rare for most people to be able access their own expectations in quantifiable form, which, if I understand it correctly, the Kelly rule requires.
This whole argument puts me in mind of the Austrian critique of socialism in the 1930s: the socialists said "we'll just put all the data into this model and calculate what to do", to which the Austrians said, "yes, but you can't actually get the data". It seems to me that the Kelly rule requires knowledge that is not generally available.