Gambler's fallacy vs. Theory of Probablity

Brokershopping,

In a game such as this, with independent events and fixed probabilities, you maximize profits by betting a constant size each time. The amount depends on how much risk you are willing to take. The higher the amount, the more money you make, but also the higher chance that you lose everything if enough failures occur at once.

If this was just a one time game with no real significance to me, I would bet 20% of my entire equity(as suggested by Tharp), since that allows me to fail up to 5 times before I'm wiped out. The chances of 5 failures in a row is 40%^5, which equals 1%, a very slim chance.

However, if this was an actual trading environment or I had alot of real capital on the time, I'd probably bet 10% of my entire equity, which is really conservative. That allows me 10 failures in a row, which occurs only 0.01% of the time. Of course, this is all a moot point since no system(that I know of), gives you a consistent 60% success and 40% failure rate.

And yes you are right that if an infinite number of betters risked 100% at this, there would still be an overall positive expectation because the tiny percentage of individuals who have 100 successes in a row would win much more than everyone else would lose.

The whole point of this example is to show how important money management and trade size is. The correct way to trade is often counterintuitive to the average individual.

Htrader
 
Skiley,
In answer to your question: By increasing your bet size when you win you DON'T expect to win anymore often. The odds stay the same. You're just in a better position to lose that's all. You have a little cushion from the previous win.

I'm currently experimenting with different position sizing strategies in my own trading. I'll keep you posted how the outcomes are. I'll tell you what I've done that's worked pretty well so far.

First find out what your min. risk amount is. I've decided to only risk 1-2% of my total capital on each individual trade. Next, look over a large sampling of your trades and find out what your hitting percentage is and what your average winner vs. average loser is. Over the last 3 months, I have won 56% of the time and the average winner was +.73 points with an average loser of -.51. The average loser is the number I'm interested in. So if I'm trading with a $20,000 account I would not want to put on a trade over 400 shares. (1/2 point loss on 400 shares = -$200 which is 1% of $20,000).

So here's what I've been doing lately. Whenever I'm up .60 to .70 of a point or so I increase the next trade by 100 shares. If I lose on the next trade my average of 1/2 point on 500 shares, I would lose $250 which is the exact same amount I won with the 400 share trade. I'm not out anything of my original capital. If I'm in a losing streak I just keep trading with my min. risk amount. It would take a long time to wipe out your account if you're only risking 1% at a time.

But in a winning streak you can really pump up the gains without ever risking any of your original capital. The idea is to bet a lot in a winning streak (risk the houses money, not your own) and bet as little as possible of your own money in a losing streak. Here is an example with 10 trades. 6 winners followed by 4 losers. I'll show you the position sizing vs. same share size. To simplify it we'll just assume that each winner is +.70 and each loser is -.50.

Position sizing:

1) 400 x .70=$280
2) 500 x .70=$350
3) 600 x .70=$420
4) 700 x .70=$490
5) 800 x .70=$560
6) 900 x .70=$630

7) 1000 x .50= -$500
8) 900 x .50= -$450
9) 800 x .50= -$400
10) 700 x .50= -$350

Net Profit: $1,030

Same Shares:

1-6) 400 x .70 x 6=$1,680
7-10) 400 x .50 x 4= -$800

Net Profit: $880

As you can see the most important thing is to have a positive expectancy. Position sizing won't do you a bit of good if your losers are bigger than your winners. With a positive outcome in your trading you'll make money no matter what share size you use. However you'll make more in a winning streak by adding to the winners and lose less by decreasing when you lose. The idea is to maximize those gains when winning and minimize the risk when losing. The results really get intereting on the next winning streak. Assume you had the same outcome on the next set of 10 trades. The results would be even better because now you're starting out with 700 shares instead of 400.

Net profit with position sizing would be: $1,690
Net profit without would be the same: $880.

You could get burned I suppose if you won one, lost one, won one, lost one, etc. because your losers would always be bigger share size. Again, the most important thing is to already be profitable. Making more on the average winner than average loser. If you are consistently doing that, I think this could really turbo charge your results. So far it's working well for me.

 
huby,

Recommending increasing the amount risked in each trade in a "winning streak" seems to suggest that your very next trade in this series is more probable than the same trade in a "losing streak", therefore maximize your gains from these better odds with increased size.

But didn't you just argue in your first paragraph that each possible trading outcome in a series is independent of the previous trade(s)?

Is there really such a thing as a "winning or losing streak"? Aren't streaks simply the end result of a series of random outcomes? I don't think it is appropriate to speak of a "streak" of luck.

The essence of what you suggest is simply risk more capital when you have more capital to risk. [shrug] No kidding. Bringing in "streaks" just confounds the matter.

tradeRX
 
Excellent thread !

It seems the only issue still debated is the change of size.
It is only a side issue imo. The big point is to understand the positive expectancy game and what the odds mean, and this was well covered.

changing size is an OPTIMIZATION.
you should not change size, ever. you bet always the same amount with your odds.. Only experience shows 'streaks' exist. It does not matter how you call them : there are periods with local imbalance in the game's odds, either in your favor or not.
When you decrease size with a 'loosing streak' you are optimizing to limit the drawdown on your capital. When you increase in a winning streak you make more greens.
But it is no obligation at all.

However, increasing in a loosing streak is BAD for the reasons well explained earlier. If you ever averaged down in a negative expectancy game you know what I mean. [averaging down is not necessarly bad by the way, if it is a pyramiding optimization in a well defined system/strategy].

It is also interesting to not that 2 out of 40 only made it in the game. Traders make the same mistake, and that's partly why so many loose.

I only wonder sometimes what would happen if much more traders would finally understand how the game is played. Would it kill my ratio ?
But then I remember the game is played for decades with hundreds of books published and seminars and still I made the same stupid mistakes and it was very very difficult to finally understand the game.

Tharp's game with odds is a very important part of understanding how to play the biggest online game in the world [trading equities, bonds and futures].

Because it is a game, don't assume it's not very serious business. You play many games in the casino, but the owner takes it very very seriously to get your money. That's what any trader should do : be the bank in the casino [well, beside the brokers and exchanges, the real winners!].

neo
 
This is a great thread, with some many pertinent comments.

At the end of the day, good trade entry will only be effective over the long run with the correct application of statistical concepts to trading. Indeed, poor trade entry can be more successful over the long run if the practitioner has a sound grasp and application of statistical concepts.

It just goes to show that people who spend 90% of their time on working out techniques to time the market are deluding themselves. I would rather fund a trader with a sound mathematical mind and great discipline, who has somewhat mediocre timing.
 
TradeRX,

I guess there are two ways to look at this strategy for two different types of people. When trader 1 makes money, he gets all attatched to it and starts to count it as if he just got a check sent to him. Trader two thinks, "Hey, I still have my original capital and now I have some market money to play with as well". This strategy wouldn't work for trader one. The drawdowns would be too big and they wouldn't be able to handle the losing streaks.

But trader two (I believe) can make more money (if he has a positive outcome system) by taking more risk with "market money" than by keeping shares the same.

I'm not saying that you have any better luck in a winning streak either. Because you don't. Like you said, every trade is a random outcome. That's true. But it's also true that streaks do occur. Every trader will have series of several winners in a row and series of several losers in a row. If you knew when those were going to be then obviously you'd position size perfectly every time. You'd risk 100% and more on all the winners and you wouldn't play the losers at all. Since no one knows though, I've found this to be the next best thing.

I got the idea for this strategy from Van Tharp's position sizing game. http://www.iitm.com It has a postive outcome so you should make money either way but you really make a ton more if you add to your winners. I played it the first time and kept my share size at the same risk the whole game. Over the course of the game I turned my original $10,000 into about $50,000. The next game I increased my share size by 25-50% with each winner and I turned the $10k into 2 million! One thing I didn't like about the game is that the odds of a winner do increase after the first win which just isn't true in real life. But the point is to learn how to maximize your winning streaks.

Another thing to consider though is that there comes a point when you do need to raise your "stop on your equity". Money made in the market really is YOURS and you need to protect it. Once a certain equity goal is reached it would be smart to consider that as your starting capital and start over by being very conservative whenever you're at or under that amount. If you consider ALL of your gains 'house money' you could really get some wild swings and drawdowns.

 
Is there really such a thing as a "winning or losing streak"? Aren't streaks simply the end result of a series of random outcomes? I don't think it is appropriate to speak of a "streak" of luck.

The essence of what you suggest is simply risk more capital when you have more capital to risk. [shrug] No kidding. Bringing in "streaks" just confounds the matter.

A little sarcastic but an excellent point which helps clarify the good advice given by huby.

DJC


 
It doesn't seem unreasonable to me to think that their could be 'winning streaks'. For any strategy, wouldn't subtle (or not so subtle) changes in overall market conditions cause the probability of sucess to vary? You may have a technique that has a 55% probability of gain one month and 45% the next. Wouldn't it be advantageous to adapt your strategy to account for this?
 
wanted to comment on "streaks":

in "Beyond Greed and Fear" by Shefrin, he talks about asking a class full of students to pretend they are flipping coins and to write down what they got, heads or tails. How do you think their imagined coin flips would differ from a real random coin flip?

The difference was that when the students pretended, they would stops streaks of H or T. So it would look like this: HHTHTTHTHHTTTHTHT

But a real random flip of a coin may actually contain a really long streak, like this: HHHHTHHHTTTTTTHHTTTTTTTTT

interesting, huh?
 
When we are talking about flipping quarters the probability of heads will always be 50% on any one flip. So therefore the results should always revert back to the mean if there is a "streak." But with human behavior and countless variables and decisions involved in trading, the probability of you winning is always changing. So if you have a winning streak...this may be "luck" or a combination of luck and improved ability. Or maybe the market is just right for your style. Since nobody has been trading forever...there probabilites are based on finite data. So if you do have a long winning streak...it is actually increasing your winning percentage and your probability. But this is based on historical data. We know the quarter will have 2 sides every time we flip it.

 
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