It is simple to prove that if the markets were truly a random walk it would be impossible to have a positive expectancy. Yes, random walks do exhibit trends, but no matter what kind of system you use, no matter how tight you make your stops, no matter how much you let your profits run, you could not gain an edge.
Simply stated, IF the markets were random, for any given trade you could make, the same trade in the opposite direction would have to have an equal expectancy. The only way two opposite trades could have the same expectancy is if it were zero for both. The same applies to any possible trading system, simply reverse its trades, and it must show the identical performance in a random market, i.e. zero. (Note that for the same reason it would also not be possible to design a losing system - before transaction costs that is)
One thing that would still be possible, is to play a game of "russian roulette" in the markets, a strategy that yields many small winning trades but which carries a possibility of a huge loss which balances out the many small winners, keeping the overall expectancy at zero.
Note that even in a non-random market, a trader with no predictive skill, whose trades would be the equivalent of random, could do this and appear to have a streak of good performance, entirely due to luck. It is this kind of trading that N. Taleb warns about in <i>Fooled by Randomness</i>. And the more traders playing this game, the more likely that we will hear about traders with exceptionally good performance runs, and many will attribute this to skill when in fact they simply had the same edge that a lottery winner had over the losers, i.e. pure chance.
I am not saying with this post that the markets are random, or that they are not. What I am trying to do is dispell some misconceptions I see quite often here.
- The existence of profitable (day)traders does not in itself prove that the markets are not random
- Keeping stops tight and letting winners run does not automatically improve your expectancy
- Just because you can see trends and patterns after the fact in a randomly generated series doesn't mean you'd have been able to "trade" them with a positive expectancy
- In a purely random market, no trading style can be better or worse than any other, in terms of overall expectancy.
- There is definitely a lot of noise in the intraday time frame. For the markets not to be purely random, there must also be some "signal" in that noise. If you claim the markets are random in the intraday time frame but not in the long term, then what you are really claiming is that during trading hours it is all noise and that non-randomness only happens when the markets are closed. This is hard to believe.