There’s something odd about the tone of this piece. It begins by saying three times (three times!) “Kelly isn’t about logarithmic utility. Kelly is about repeated bets.” Then, later, it says “Yes, Kelly is maximising log utility. No, it doesn’t matter which way you think about this”.
I think you have to choose between “You can think about Kelly in terms of maximizing utility = log(wealth), and that’s OK” and “Thinking about it that way is sufficiently not-OK that I wrote an article that says not to do it in the title and then reiterates three times in a row that you shouldn’t do it”.
I do agree that there are excellent arguments for Kelly-betting that assume very little about your utility function. (E.g., if you are going to make a long series of identical bets at given odds then almost certainly the Kelly bet leaves you better off at the end than any different bet.) And I do agree that there’s something a bit odd about focusing on details of the formula rather than the underlying principles. (Though I don’t think “odd” is the same as “wrong”; if you ever expect to be making Kelly bets, or non-Kelly bets informed by the Kelly criterion, it’s not a bad idea to have a memorable form of the formula in your head, as well as the higher-level concept that maximizing expected log wealth is a good idea.) But none of that seems to explain how cross you seem to be about it at the start of the article.
Thanks! That’s helpful. I definitely wrote this rather stream of consciousness and I definitely was more amped up about what I was going to say at the start than I was by the time I’d gotten halfway through. EDIT: I’ve changed the title an added a note at the top
I think the section where I say “it doesn’t matter how you think about this” I mean it something in the sense of: “Prices and vols are equivalent in a Black-Scholes world, it doesn’t matter if you think in terms of prices of vols, but thinking in terms of vols is usually much more helpful”.
I also agree that having a handy version of the formula is useful. I basically think of Kelly in the format you do in your comment I highlighted and I think I would never have written this if someone else hadn’t taken that comment butchered it a little but and it became a (somewhat) popular post. (Roughly I started writing a long fairly negative comment on that post, and tried to turn it into something more positive. I see I didn’t quite manage to avoid all the anger issues that entails).
There’s something odd about the tone of this piece. It begins by saying three times (three times!) “Kelly isn’t about logarithmic utility. Kelly is about repeated bets.” Then, later, it says “Yes, Kelly is maximising log utility. No, it doesn’t matter which way you think about this”.
I think you have to choose between “You can think about Kelly in terms of maximizing utility = log(wealth), and that’s OK” and “Thinking about it that way is sufficiently not-OK that I wrote an article that says not to do it in the title and then reiterates three times in a row that you shouldn’t do it”.
I do agree that there are excellent arguments for Kelly-betting that assume very little about your utility function. (E.g., if you are going to make a long series of identical bets at given odds then almost certainly the Kelly bet leaves you better off at the end than any different bet.) And I do agree that there’s something a bit odd about focusing on details of the formula rather than the underlying principles. (Though I don’t think “odd” is the same as “wrong”; if you ever expect to be making Kelly bets, or non-Kelly bets informed by the Kelly criterion, it’s not a bad idea to have a memorable form of the formula in your head, as well as the higher-level concept that maximizing expected log wealth is a good idea.) But none of that seems to explain how cross you seem to be about it at the start of the article.
Thanks! That’s helpful. I definitely wrote this rather stream of consciousness and I definitely was more amped up about what I was going to say at the start than I was by the time I’d gotten halfway through. EDIT: I’ve changed the title an added a note at the top
I think the section where I say “it doesn’t matter how you think about this” I mean it something in the sense of: “Prices and vols are equivalent in a Black-Scholes world, it doesn’t matter if you think in terms of prices of vols, but thinking in terms of vols is usually much more helpful”.
I also agree that having a handy version of the formula is useful. I basically think of Kelly in the format you do in your comment I highlighted and I think I would never have written this if someone else hadn’t taken that comment butchered it a little but and it became a (somewhat) popular post. (Roughly I started writing a long fairly negative comment on that post, and tried to turn it into something more positive. I see I didn’t quite manage to avoid all the anger issues that entails).