There's a lot of discussion about a trading edge going down (for convenience sake, I'll say that "edge" is measured by profit factor, so what I mean is I see a lot of people saying their method's profit factor eventually degrades), but has anyone had theirs increase after, say, a few hundred (or more) trades? I have also seen a lot of discussion about non-normality of trade return and market price distributions, but if trade returns and price action are truly non-normal, wouldn't be be as likely to see traders who earn increasing returns relative to their past history as we are to see traders' returns decreasing over time? And, from a money management perspective, couldn't this mean that Kelly actually underestimates (for some traders) the truly optimal bet size? I grant that last point is kind of speculative, but if I'm right about the statistical implications of non-normality, I'm not sure why that question about bet size wouldn't be that, yes, it could be that even Kelly undersizes some traders' bets.
No, because volatility has an assymetric effect with such distributions of returns with negative impact being much greater and much persistent than positive. On the contrary IMO, it means that %kelly overestimated optimal bet size because it undrestimates risk due to fat tails. It may depend on the time frame. It probably undersizes trend-following systems and oversizes intraday systems. From a practical stand, anyone trading for longer-term and consistent returns should avoid %kelly and stick to small fixed percentages. Consistency is much more desirable than optimality.
That sounds like something you are asserting, rather than something which has been shown empirically. Also, my understanding is that volatility is mean-reverting, yet your statement claims it is persistent, which again seems like something you're asserting rather than proving. Also, I guess I don't understand why, if this were true, and volatility had been isolated as the cause of these negative effects, no one had developed a portfolio of strategies, one of which is designed to benefit from the negative and persistent impact of volatility on their returns distribution. That would depend on the system, no? What if your betting system always got you into an asset before that asset's pricing entered the fat part of the tail and either got you out before it entered the fat part of the tail (in which case you leave some on the table, but are otherwise fine, although your Kelly could take a hit if your winner/loser ratio goes down as a result of getting out before the fat part of the tail kicked in) or kept you in for a portion, at least, of the fat tail? I would think that entry methods which force you into an asset in a "contrarian" way would do just this, when they were right, provided you took every entry signal. Like many people, I have a contrarian strategy and I never miss the beginnings of a fat-tail move because I'm forced in to the market by price action. Does it fail sometimes and I take a loss? Of course, 40% of the time, to be exact. From a practical standpoint, isn't this one of the benefits of the advances in automation? Not so much automation of the HFT type, but automation of trading strategies to take the human element of valuing consistency over optimality?
There is substantial literature on this subject with studies of many worldwide indices that proves this, which you appear not to be aware off, so let us terminate right here. I have no time for disputes of well-known, proven facts.
well, defining an edge as a market inefficiency, then edges generally have declined over time. as for an edge increasing...randomness could be it. i'm a cynic i suppose, but i don't see many real, executable edges getting better over time. maybe you're just currently good side of this edge's actually volatile returns.
and, as for kelly, i always think it feels messy with these variable payouts in the real world. though, i'm not yet a kelly expert.
That's fine, although I notice again that rather than cite some of this literature, you assert that it both exists (which I don't doubt) and is definitive (which I do doubt, at least not without qualification). Also, by cutting off your response in such a way, you leave out the answer to my question about why no one would construct a portfolio to capture these effects, even when I stipulated they exist.
It could be random. Or, the initial decline the edge showed, relative to backtests, could have been the random part. Or, subsequent refinement of the method, using post-trade analysis and further development of tools to accompany it, could reveal periods of degradation which could be avoided in the future, when "similar" circumstances arise. "Addition by subtraction", if you will. Imagine a scenario in which a strategy degrades during market conditions which are identifiable to the 95% confidence level and then choosing not to trade under those conditions. Over time, this would increase your Kelly% and, so long as the number of trades didn't decrease too much, you'd be better off over time. Of course, if those trades you were giving up had positive expectancy, you might have second thoughts about not taking them, regardless of what that did to your Kelly %. I guess I'm just saying that out of the hundreds of thousands of traders around the world, it seems impossible that none of them experience a stable or even increasing edge, assuming they keep their information private, don't "rest on their laurels" and don't have to trade in such size as to negate the edge. As for Kelly, I don't claim to be an expert, but I have been reading up on it for over a year now and from what I know, it seems like the way to go, if you have the stomach for it and recalculate it after every trade. Anecdotally, it seems to be at least a portion of some of the biggest names in trading's repertoire. Yes, there are differences in the formula for discrete vs. continuous payoffs. My understanding is that in financial markets, as opposed to betting scenarios, you use Kelly to calculate the amount of leverage you should take on to maximize your wealth, although that is not how I am using it. http://epchan.blogspot.com/2006/10/how-much-leverage-should-you-use.html