This is my first post, so I would appreciate any feedback. This started out as a comment on one of the other threads but kept on expanding from there.
I’m also tempted to write “Contra Kelly Criterion” or “Kelly is just the start” where I write a rebuttal to using Kelly. (Rough sketch—Kelly is not enough you need to understand your edge, Kelly is too volatile). Or “Fractional Kelly is the true Kelly” (either a piece about how fractional Kelly accounts for your uncertainty vs market uncertainty OR a piece about how fractional Kelly is about power utilities OR a piece about fractional Kelly is optimal in some risk-return sense)
This was a pretty solid post, and outstanding for a first post. Well done. A few commenters said the tone seemed too strong or something along those lines, but I personally think that’s a good thing. “Strong opinions, weakly held” is a great standard to adhere to; at least some pushback in the comments is a good thing. I think your writing fits that standard well.
Of those, I think I would vote for one of the fractional-Kelly ones—providing arguments for something (fractional Kelly) rather than merely against naive Kelly. (Suppose I think one should “Kelly bet on everything”, and you write an article saying that Kelly is too volatile, and I read it and am convinced. Now I know that what I’ve been doing is wrong, but I don’t know what I should be doing instead. On the other hand, if instead I read an article saying that fractional Kelly is better in specific circumstances for specific reasons, then it probably also gives some indication of how to choose the fraction one uses, and now I have not merely an awareness that my existing strategy is bad but a concrete better strategy to use in future.)
I appreciated that you posted this, and I think your further proposed post(s) sound good, too!
To my personal taste, my main disappointment when reading the post was that you didn’t expand this section more:
Utilities and repeated bets are two sides of the same coin
I think this is fairly clear—“The time interpretation of expected utility theory” (Peters, Adamou) prove this. I don’t want to say too much more about this. This section is mostly to acknowledge that:
Yes, Kelly is maximising log utility
No, it doesn’t matter which way you think about this
Yes, I do think thinking in the repeated bets framework is more useful
But that’s a perfectly reasonable choice given (a) writing time constraints, (b) time constraints of readers. You probably shouldn’t feel pressured to expand arguments out more as opposed to writing up rough thoughts with pointers to the info.
Speaking of which, I appreciated all the references you included!
Yeah, I think I’m about to write a reply to your massive comment, but I think I’m getting closer to understanding. I think what I really need to do is write my “Kelly is Black-Scholes for utility” post.
I think that (roughly) this post isn’t aimed at someone who has already decided what their utility is. Most of the examples you didn’t like / saw as non-sequitor were explicitly given to help people think about their utility.
I think that (roughly) this post isn’t aimed at someone who has already decided what their utility is. Most of the examples you didn’t like / saw as non-sequitor were explicitly given to help people think about their utility.
Ah, I suspect this is a mis-reading of my intention. For a good portion of my long response, I was speaking from the perspective of a standard Bayesian. Standard Bayesians have already decided what their utility is. I didn’t intend that part as my “real response”. Indeed, I intended some of it to sound a bit absurd. However, a lotta folks round here are real fond of Bayes, so articulating “the bayesian response” seems relevant.
If you’d wanted to forestall that particular response, in writing the piece, I suppose you could have been more explicit about which arguments are Bayesian, and which are explicitly anti-Bayesian (IE Peters), and where you fall wrt accepting Bayesian / anti-Bayesian assumptions. Partly I thought you might be pretty Bayesian and would take “Bayesians wouldn’t accept this argument” pretty seriously. (Although I also had probability on you being pretty anti-Bayesian.)
Why teach about these concepts in terms of the Kelly criterion, if the Kelly criterion isn’t optimal? You could just teach about repeated bets directly.
This is my first post, so I would appreciate any feedback. This started out as a comment on one of the other threads but kept on expanding from there.
I’m also tempted to write “Contra Kelly Criterion” or “Kelly is just the start” where I write a rebuttal to using Kelly. (Rough sketch—Kelly is not enough you need to understand your edge, Kelly is too volatile). Or “Fractional Kelly is the true Kelly” (either a piece about how fractional Kelly accounts for your uncertainty vs market uncertainty OR a piece about how fractional Kelly is about power utilities OR a piece about fractional Kelly is optimal in some risk-return sense)
This was a pretty solid post, and outstanding for a first post. Well done. A few commenters said the tone seemed too strong or something along those lines, but I personally think that’s a good thing. “Strong opinions, weakly held” is a great standard to adhere to; at least some pushback in the comments is a good thing. I think your writing fits that standard well.
Of those, I think I would vote for one of the fractional-Kelly ones—providing arguments for something (fractional Kelly) rather than merely against naive Kelly. (Suppose I think one should “Kelly bet on everything”, and you write an article saying that Kelly is too volatile, and I read it and am convinced. Now I know that what I’ve been doing is wrong, but I don’t know what I should be doing instead. On the other hand, if instead I read an article saying that fractional Kelly is better in specific circumstances for specific reasons, then it probably also gives some indication of how to choose the fraction one uses, and now I have not merely an awareness that my existing strategy is bad but a concrete better strategy to use in future.)
I appreciated that you posted this, and I think your further proposed post(s) sound good, too!
To my personal taste, my main disappointment when reading the post was that you didn’t expand this section more:
But that’s a perfectly reasonable choice given (a) writing time constraints, (b) time constraints of readers. You probably shouldn’t feel pressured to expand arguments out more as opposed to writing up rough thoughts with pointers to the info.
Speaking of which, I appreciated all the references you included!
Yeah, I think I’m about to write a reply to your massive comment, but I think I’m getting closer to understanding. I think what I really need to do is write my “Kelly is Black-Scholes for utility” post.
I think that (roughly) this post isn’t aimed at someone who has already decided what their utility is. Most of the examples you didn’t like / saw as non-sequitor were explicitly given to help people think about their utility.
Ah, I suspect this is a mis-reading of my intention. For a good portion of my long response, I was speaking from the perspective of a standard Bayesian. Standard Bayesians have already decided what their utility is. I didn’t intend that part as my “real response”. Indeed, I intended some of it to sound a bit absurd. However, a lotta folks round here are real fond of Bayes, so articulating “the bayesian response” seems relevant.
If you’d wanted to forestall that particular response, in writing the piece, I suppose you could have been more explicit about which arguments are Bayesian, and which are explicitly anti-Bayesian (IE Peters), and where you fall wrt accepting Bayesian / anti-Bayesian assumptions. Partly I thought you might be pretty Bayesian and would take “Bayesians wouldn’t accept this argument” pretty seriously. (Although I also had probability on you being pretty anti-Bayesian.)
Why teach about these concepts in terms of the Kelly criterion, if the Kelly criterion isn’t optimal? You could just teach about repeated bets directly.
A couple of reasons:
For whatever reason, people seem to really like Kelly criterion related posts at the moment.
I think Kelly is a good framework for thinking about things
“Kelly is about repeated bets” could easily be “Kelly is about bet sizing”
“Kelly is Black-Scholes for utility”
Kelly is optimal (in some very concrete senses) and fractional-Kelly is optional in some other senses which I think people don’t discuss enough