I'm not sure I understand what this means. They are either random or they are not. "Worse than random" is similar to "better than random" in that neither is random. At least that's how I see it. Statistics is a useful discipline. However, I think it has far more descriptive value than it has predictive value. Further, given that you cannot even assume a normal distribution for market price activity, but must rely on an even wider distribution curve, I would think that the use of statistical theory has fairly limited value in a short-term trading environment concerned with strict loss containment. Just my opinion, of course.
Thanks for you comments thunderdog, as I find you one of the few posters I have come to respect on the boards. I should be more specific. When I refer to random, I am implicitly referring to random in the gaussian sense. Markets are very close to gaussian random and can be modeled as such if you remove the fat tail (black swan/10 sigma etc.. ) events. This is why when people run random generators on excel, they look so similar to market price action. It is also why most academics model them as such. It is the frequent price shocks that make markets non(gaussian) random. Note that while this implies they are not strictly (gaussian)random, the difference does not make the non-(g)random nature any more beneficial to modellers, rather it makes it worse (i.e. random, yet worse). Often people jump in and argue about randomness and modeling without making the distinction. When I say worse than random, what I mean is that you could come up with a pretty reliable methodology based on random modeling, it's the fat tail shocks that killed many well thought out systems like LTCM. These 10 sigma type events are what make it worse than random IMO. On a smaller scale, you can think about gap up and gap downs, certainly those are are advatages (order flow) available to the specialist that can wipe out the uninformed trader who expects well defined random behavior to be on his side. Hope that defines it a little better. In this sense, I don't really see how unforeseen gaps (which are the fat-tail "non-gaussian random" events on a smaller scale) are in the retail trader's favor. Regarding statistics, I am implying that structuring bets ( I.e. some form of risk management) hold more weight than betting based on reading charts. The structured bets are useful against systems that have a random bias (like roulette machines for example). I read a recent book on how norman leigh broke monte carlo's roulette machines based on a betting algorithm he devised. I think the key to success lies along these lines of thinking vs. reading charts and ascertaining future outcomes via expectations.
... When I refer to random, I am implicitly referring to random in the gaussian sense... You would be surprised how close the Markets are to the Gaussian distribution. If you divide the price of S&P by the daily true range you will get a precise bell curve, not a power law distribution. In other words, the hidden truth of the markets is that the price has to be presented in the units of its volatility not in the absolute numbers. The âperceivedâ positive bias of the markets is due to devaluation of the securities fairly presented in the corresponding volatility (average, annualized dollar swing per day). So, you my friend, are absolutely correct!
That is certainly one way to look at it. Another is that they were relying on mean reversion in the face of demonstrable bias not at all in their favor, and when the market showed them to be wrong and then very wrong, LTCM chose to increase the size of their bet rather than accept the inopportune timing of their trades. Good money after bad. In my mind, it is such overreliance on statistical theory in the face of an unaccommodating market that runs many quants into trouble. Further, LTCM made good money before its demise because it placed very highly leveraged trades. Management did not fully appreciate the fund's exposure. If it was not one "extreme" event that got them, it would have been another. However large they may have been, they were still diving for sandwiches in a pool of sharks.
Yes, relying on the reversion to the mean is a very dangerous game. The reason, of course, is that you are relying on the average outcome but at the same time you are forced to deal with a particular run of the random walk. The remedy to it is chopping the fat tail with options or running hundreds of independent runs on a set of uncorrelated securities.
It is very unusual to meet an intelligent person here on ET, so rare! I like the way you think and express your self. Very refreshing.
Thank you maestro, although I haven't read much of your work (since I joined), I look forward to seeing more.