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The Kelly Criterion was the subject of an incomprehensibly bitter argument in the 1970s/1980s. Paul Samuelson, considered by many to be the greatest economist o
by freddie_mercury 8y ago
The Kelly Criterion was the subject of an incomprehensibly bitter argument in the 1970s/1980s. Paul Samuelson, considered by many to be the greatest economist of the 20th century, believed the Kelly Criterion was wrong. And not just wrong but SO WRONG that anyone who believed it was an idiot.
The kind of idiot who could only understand single syllable words. So he wrote a paper in the Journal of Finance and Banking in words of only a single syllable saying why no one should use the Kelly Criterion.
http://www-stat.wharton.upenn.edu/~steele/Courses/434/434Context/Kelly%20Resources/Samuelson1979.pdf http://www-stat.wharton.upenn.edu/~steele/Courses/434/434Con...
- n4r9 8y agoInteresting. I don't know much about economics or the Kelly criterion, but my understanding of the argument is that maximising the growth rate is distinct from maximising actual profit arbitrarily far into the future. Would be cool if there was a simple toy example demonstrating a situation where these differ. Perhaps it even differs for the example in OP.
- norswap 8y agoHow is the growth rate determined? Since presumably it varies, is it averaged in some ways?
- imh 8y agoIf a big growth rate is a composition of a bunch of small changes with their own growth rate, then the overall change is the product of the individual ones, so geometric mean is appropriate.
- n4r9 8y agoI wrote a reply, but accidentally made it top-level: It's the expected growth rate, so yes it would vary in a real-world instance. I wondered for a while why they've taken the logarithm, but I think it's just because growth models are normally defined exponentially (with the rate being a parameter inside the exponential) - it shouldn't make a difference to the result. As for varying, that Samuelson article says: > For N as large as one likes, your growth rate can well (and at times must) turn out to be less than mine - and turn out so much less that my tastes for risk will force me to shun your mode of play.
- sesqu 8y agoMy understanding of the argument is that you have to assume you keep playing after you lose, so your stake is dictated by the risk. For the example in the article, the potential upside is 110% profit and the potential downside is 100% loss, so the optimal stake is relatively conservative in order to prevent any loss from impacting your future ability to invest. Imagine you get the expected result of one win and one loss and had staked 5%: you'll end up with 1.055×0.95=1.002 wealth. If you had picked a 50% stake, you'd be sitting at 1.55×0.5=0.775 wealth instead, since the loss more than erases your winnings. The unstated contrast is to models where e.g. there are only a limited number of investment opportunities, losses aren't total, or there are capital infusions.
- n4r9 8y agoApologies for the confusion but I was talking about Samuelson's argument against the Kelly criterion. If I was to make one gamble per day and wanted to maximise my profit after 50 years, I don't know if I'd use the Kelly criterion. I need to think about it.
- OscarCunningham 8y agoIf you just want to maximise the average amount of money that you end up with then you should bet your entire fortune every day. Of course you will be bankrupt if you ever lose your bet, which is very likely over the course of 50 years. But in the ridiculously unlikely event that you won every bet your fortune would be even more ridiculously large. So the average amount of money would be very large, even though you would very probably be bankrupt.
- n4r9 8y agoI see. What if I wanted to maximise the expected profit, given that the chance of bankruptcy should not exceed 1%? Does that sort of problem become difficult to solve?
- OscarCunningham 8y ago
- deleted 8y ago[deleted]
- soneca 8y agoThe irony is that using single syllable words makes it less understandable.
- soVeryTired 8y agoI find it pretty distasteful that someone should be able to publish a paper like that. Big names should be just as answerable to review and quality control as everyone else. Also, 'Losses' is two syllables. Thanks for playing Paul.
- anonu 8y agoAlso, Q.E.D technically references 2 polysyllabic words.
- bytematic 8y agoShould have just used the square. QED is a bit pretentious anyways
- hwillis 8y agoScientists and academics are not above humor: http://iopscience.iop.org/article/10.1088/1751-8113/44/49/492001/meta http://iopscience.iop.org/article/10.1088/1751-8113/44/49/49...
- LandR 8y ago>> should make us change our views on gains and losses - should taint our tastes for risk. Isn't losses 2 syllable ?
- fjsolwmv 8y agoDid Samuelson ever apologize for embarrassing himself with such a rude and irrational insult. Did JFB ever publish a retraction or apology for publishing a bad-economics article written in incomprehensible language?
- deleted 8y ago[deleted]
- evrydayhustling 8y agoThis is a pretty weird straw man argument. The Kelly Criterion is not, like, a lifestyle. It's a way of exposing how opportunities to reinvest should impact your investment sizing... so how useful it is really depends on whether you are making investment decisions on a time horizon where reinvestment opportunity is a big part of the picture. Does anyone know if Samuelson was responding to a particular strain of thought where people wanted to use Kelly for everything?
- joker3 8y agoSamuelson's argument basically comes down to the fact that the investments that maximize growth don't maximize your utility unless your utility is log(wealth), and to him it was completely obvious that people should act to maximize their own utilities. However, there have been a couple recent developments that somewhat undercut his line of thinking. First of all, to the extent that people's behavior can be described by utility theory, we all roughly have isoelastic utilities (https://en.wikipedia.org/wiki/Isoelastic_utility https://en.wikipedia.org/wiki/Isoelastic_utility) with a parameter not too much greater than one. As a result, the ideal investments for most of us are near Kelly. Second, there's a body of theory that asks what the optimal strategy for investment is given a certain number of years, and it turns out that the ideal strategy is to follow the Kelly approach until near the deadline and then to switch to the investments that maximize your own utility as the time to act grows short. This work is known as turnpike theory for reasons that never really made sense to me. There are still concerns about Kelly investments, but Samuelson's argument isn't really one of them.
- sarosh 8y agoThank you for this insight! Would you be so kind as to provide some pointers to the concerns you’ve mentioned? Any pointers on turnpike theory would also be appreciated!
- evrydayhustling 8y ago> investments that maximize growth don't maximize your utility unless your utility is log(wealth) This needs a slight adjustment to be exactly true: > investments that maximize growth don't maximize your utility at a specific time horizon unless your utility is log(wealth) The reason is that in situations of repeated investment, Kelly's policy actually does maximize many time-indefinite notions consistent with linear utility -- for example, if you have a fixed wealth goal (retirement) that is enough successful wagers away, Kelly will minimize the expected time to get there [1]. For me, the important limitation for Kelly is that it is designed around timescales that involve many many repeated bets. Like most asymptotic results, Kelly can win marathons and lose sprints -- so it's important to consider which situation you're in. [1] https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Ke...