Comment by TameAntelope
4 years ago
Kelly himself ended up using 1/n for his own personal portfolio management.
Gerd Gigerenzer has a lot to say about how harmful this model has been to finance and the world, because it creates "false certainty".
https://news.ycombinator.com/item?id=26325425 has further discussion.
The problem with anything that isn't 1/n is the large estimator variance of the mean of asset returns. There's such little signal there that Markowitz et al invariably fit to mostly noise, which reduces diversification, increases transaction costs, among other problems.
A similar phenomenon occurs in ensemble methods in statistics. It's often better to equal weight many estimates than try to fit weights to them, since that fitting process introduces lots of variance.
I'm not sure what you mean by using 1/n, but the Kelly criterion optimised on past returns for common portfolios of thickly traded assets does suggest something very close to 1/n very often.
I've always attributed this to market efficiency (if it suggested anything else, that's what investors would do until the mispricing went away) but maybe there's a deeper reason it happens.
This random person's thesis describes 1/N in a way I think is understandable:
> In circa 400 A.D. Jewish Rabbi Issac Bar Aha recommended always to invest a third into land, a third into merchandise and to keep a third at hand. This method later became well-known under the name “1/n asset allocation strategy”, “equal asset allocation strategy” or “naïve strategy” and is further defined by DeMiguel et al.(2009) as ”the one in which a segment 1/n of wealth is allocated to each of N assets available for investment at each rebalancing data.” The strategy requires investing an equal part of the capital in the different present assets. Nowadays this rule is often labelled as naïve and too simple, by McClatchy and VandenHul (2005) for example.
http://arno.uvt.nl/show.cgi?fid=129399
Gerd Gigerenzer has a number of books, the one I recently read was, "Risk Savvy" and he goes into some detail about the topic. All I'd do here is write a terrible book review, so if you're curious, I definitely recommend taking a look at the book. I'm not sure I totally agree with his arguments (I had a hard time understanding how he would suggest accounting for human bias), but they're definitely interesting.
Ah, that's what I thought, and what I'd expect Kelly optimisation to come up with too. So they're not really different approaches, 1/n is a special case of Kelly in somewhat efficient markets.
I will look up your references though!
I am confused so hope you will clarify. I thought the article argues that Markowitz mean variance has problems and 1/n is a reasonable estimator. You seem to be arguing for the opposite? Or perhaps you mean 1/n vs. Kelly but that article does not talk about Kelly.
Sorry, I didn't mean to argue any point really, just expose folks to Gerd Gigerenzer's work, as it seems relevant to this topic. He makes the arguments much more strongly than I ever could.
Any confusion or inconsistency I'm presenting is my fault, and I apologize!