Alright, I'm about to spew some dilettante statistical theory. It may be completely bunk, but what the hell, that's what forums are for! Anyway, I'm going to posit that if you take a wide random sample of stocks, hold them for a set period of time, then plot their returns, the resulting chart would look like a bell curve. Few big losers/winners, the bulk of returns would be in the middle. (I'm assuming going long/short so that bull/bear markets won't skew the sample). So in the middle of the curve, your little winners cancel out your little losers. Then your stop loses turn your few big losers into little losers. All you are left with is your big winners that you let run i.e. your final profit. So if the markets were random and one trades a large enough sample of stocks, can we assume that one can still make a profit using proper money management?
Unfortunately no. You are just looking at the endpoint of the stock price's meanderings during your set period of time. During the set period of time some of your stocks are going to wander down to your stop loss price and then come back up again. With your stop loss you will be turning many break even trades and small winners into small losers. If the distribution of the stock price changes is gaussian (bell curve) with a mean of zero. Then your distribution of P&L's using your stop loss money management is going to be truncated on the negative side and positively skewed, but it is still going to have a mean of zero. Your average winner will be greater than your average loser, but you will have more losers than winners.
The distribution of returns for stocks is not representative of a bell curve. It's more like a Pareto-Levy distribution with fat tails and a smaller middle. Random studies have been done where stops were set to the lowest 20% of the returns and found to be consistently profitable using random entries.
Ok, well then let's assume I am using a valid method to set my stops. So of those positions I enter, the vast majority when stopped out were going in the wrong direction. In other words, assume that when I get stopped out it's not premature and the stop prevented a larger loss. Then would bell curve money management still yield a profit in a random market?
I'll admit my system is based on this theory. Looking at this months results though would tend to support Aaron's theory. I try to breakeven in the chop and hold the outliers. The problem is no outliers this month, as well as poor discipline. I think you are on to something though in your theory. My system has had 13 profitable months in row using it. I'll predict this month will be profitable as well (for the system).
You contradict yourself implicitly... By saying they were "going in the wrong direction" you are implying you think they will keep going in that direction. But then you say it is a random market. In a random market, if a stock has price X (your stop price) then it is unknowable whether it will go up from there or continue down from there. If market prices are in a trend following mode, then, if the price is at price X, then it does matter if the past price has been falling. If it has been falling, you can expect it to continue falling, and you can cut your losses with a stop loss. In this case you can improve your results with a stop loss. If the market is "choppy" -- the inverse of trend following mode. Then if the price has been falling and reaches price X, you can expect it to turn around and rise. In this case you would be harming your results with a stop loss.
Ok. I think I get what you're saying. Either the market is random or it isn't. If it's random then I can't assume my stops have any significance because, well, they're random. Anyway, the theory has another inherent flaw when applied to the real world, in over-night trading anyway. Big gaps against me will register as big losers, screwing up my theory about never having any. But the theory could be applied in the 24 hour FX market where gaps don't happen.
I couldn't find one online that was so straight forward. Here's one that has a good introduction to the Pareto-Levy distribution and the distribution of stock returns. http://bschool.huji.ac.il/segel/moshe-l/SF.pdf