Wednesday, May 16, 2012

Statistics Part 1 - Probability of a Streak of Wins


I paper traded today and had one losing position and a scratch trade on GMCR after 4 minutes with no direction. There have been three days of good paper trading profits, from Friday through to today. This a step in the right direction because to me it means that I could not have done this due to chance alone, or at least it is unlikely. If the above is true, then the only other explanation is that my method seems to put the odds in my favour enough to turn a profit. I don't use anything other than price and price action, volume, and Bollinger bands to make my entries, so this is a very pure setup without any indicators to clutter the charts. The reason I bring this up is that indicators tend to work in one market condition but not in others, while price, volume, and standard deviation of mean price work in every condition.

Overall, that makes 3 days of profitable paper trading and 5 days of profitable live trading in a row without a draw down. Let's do some light statistics to get a different perspective. Assume that just like a coin flip, there is a 50/50 chance of a trade being profitable because price can go up just as likely as it can go down after entry. The size of the gain or loss is irrelevant. Also assume that each trade is selected during market hours in such a way that it is completely random. Further assume that each trading day is the cumulative of all trades for now and the amount of trades per day is not important.

Guessing 8 coin flips or having 8 profitable days in a row has a 0.39% chance of occurring while guessing 5 coin flips in a row (counting only live trading days) has a higher chance at 3.125%. Although 3.125% is quite high, it is still low enough to suggest that perhaps luck alone is not sufficient enough to explain the results thus far. 

Okay, but what if we want to know the probability of getting a streak of 5 profitable trading days in a sample of 100 days? This changes things up a bit and gives a different perspective all together. The calculations come up to 79.56%. This means that if I were to trade for 100 days, I have a 79% chance of having at least one streak of 5 profitable days. Not so impressive now is it. For all I know, this winning streak is about to end. I've tabulated the results for more streaks of trades below. Of course, my trading is not completely random (or at least shouldn't be) as I try to pick only the ones I think have a greater chance of turning out positively and it might skew the results. Then again, my decisions can appear just as random to any other trader. As can be seen, having 10 profitable trading days in a row out of a total of 100 trading days means you are really good - the probability of that happening is just 4.76%. Accomplishing that means you have a quantifiable edge. Of course, 9, 8, and 7 are all good too and desirable.
These results should only be taken at face value and I am well aware that the risk of ruin is present. This does not imply that I can now use more leverage or trade more aggressively. Furthermore, market conditions (choppy markets) can always abruptly change so that whatever edge I have will be diminished. If this were to happen, then something called random reinforcement may occur. Random reinforcement occurs either when an inexperienced trader has a streak of wins and attributes it to intuition and skill or when an experienced trader endures a streak of losses even though the trading methods have statistically worked in the past. The experienced trader will commit random reinforcement error when they attempt to adopt a new trading method instead of realizing that randomness can create both a streak of winners or losers regardless of trading experience. Misattributing the streak of losers to the system no longer working is how one commits this error since any new system they adopt has a lower probability of succeeding regardless, simply for the fact that the trader is unaccustomed to it. This is also partly why I rely mainly on price and volume, so that in the event that a random streak of losers occurs, I will know for a fact that the problem is not the trading system but my focus or mental state, since volume and price are as old as the market and can't be wrong.

And finally, the sample size is too small to make anything other than a preliminary conclusion - a more accurate measure would be to tabulate the total trades instead of profitable vs. unprofitable days. I'm going to do this in the future. For now, see the paper trading profits for today below and let's do one more quick analysis. Today I had a streak of two winners in the morning, then a loss which was followed by a 7 win streak in a row. There were a total of 10 trades all together, so that means that the probability of enduring a 7 win streak in 10 total trades is about 3.84%. Not bad.

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