Kelly Criterion

[Dogpile 10]

This thread is an extension of the Martingale thread but deserves its own place. The Kelly Criterion is a forumula that maximizes growth of account. This is a high-risk, high-reward strategy and isn't recommended -- but the concept is valid and one can use this as a starting point and take down the risk. It is worthy of discussion.

 

http://en.wikipedia.org/wiki/Kelly_criterion

-----------

Basically, it computes a % of how much of your portfolio you should risk on the next trade given your long-run expected win rate (W) and the expected dollars won for a win vs dollars lost for a loss ®.

 

Drawdowns are problematic using this formula -- but growth of capital is awesome if your win rate is there.

 

-----------

K = W - (1-W)/R

 

K = Fraction of Capital for Next Trade

 

W = Historical Win Ratio (Wins/Total Trials)

 

R = Winning Payoff Rate

 

-------

For example, say a coin pays 2:1 with 50-50 chance of heads or tails. Then ...

 

K = .5 - (1 - .5)/2 = .5 - .25 = .25.

 

Kelly indicates the optimal fixed-fraction bet is 25%.

[Sparrow 10]

If i understand some of the implications of the kelly criterion correctly, one possible problem is that a string of losses of high probability trades could lead to big setbacks. The risk of blowing out ones account wouldn't be so bad though, since less money would be risked after every losing trade.

 

Of course if everything works out well, it is just the opposite.

 

Assuming market conditions stay the same and trade execution wouldn't change.

[darthtrader 10]

I got into this type of stuff last year when I was thinking about throwing caution to the wind. From what I remember I thought "optimal r" (i think thats what it was called?) was better than kelly.

 

This thread on elite though seemed to have the best money management strategy if you knew what your systems expectancy was:

 

System Development with acrary

http://www.elitetrader.com/vb/showthread.php?threadid=33654

 

Here is a text with all the replies stripped out. Someday I would like to get through this but its pretty hard. Easily the best thing I've ever read on elite though.

[darthtrader 10]

oops, forgot to attache the txt file.

acrary posts collection.txtFetching info...

[maildigger 10]

Lets say you have a 10K account and according to Kelly you have to risk 40% of your account. How do you do that ?:crap:

[nelo 10]

  maildigger said:

Lets say you have a 10K account and according to Kelly you have to risk 40% of your account. How do you do that ?:crap:

 

1/ Kelly number is based on huge amount of statistically consistent data - what most traders do not have from their trading - that is the first reason why it is so dangerous.

 

2/ Anyway, let us assume that you could have. Markets are changing (they are not like telephone line noise). What you get is based on past results, current trade "Kelly" is unknown variable, fluctuating wildly based on market conditions.

 

3/ There are also technical issues. Kelly works if you can bet infinite fraction but you can bet only in increments of one contract. If you bet that portion of your account at once and lose just few times in a row you might end up with too little money for your risk or margin to open even one contract. That is why in this direct way it is only useful for perfectly optimized diversified portfolios (~30 uncorrelated securities or more, various strategies, timeframes, etc.). Anyway, portfolio theory will be very long story.

 

4/ Then there are psychological issues. After 3 loses in a row you would lose about 80% of your account - can you stand it? With $10,000 account you can forget using Kelly this way.

 

There are other issues but what I found useful for average trader like me is using Kelly relative to maximum drawdown. Let's say you have $10,000 and think you are a consistent trader in changing market conditions. You start with single contract and make at least 100 trades. From that you calculate Kelly ratio and your maximum drawdown. Let's say your max DD is 3,000 and your Kelly is 40%. Then your risk could be 0.4 * 2,000 = $800 per trade. If you were risking $200 per trade you could trade 4 contracts.

 

For average speculator there are simpler, safer and more effective MM methods so you do not need to worry about Kelly too much.

[Jakew 10]

The Kelly is an absolute classic.

 

However, because:

 

a/ the payoffs in trading cannot be precisely assessed

b/ the psychological factors will interfere in a trader's execution of "otherwise winning strategy" - i.e. he will capitulate under a severe drawdown pressure

 

half Kelly or less is advised

 

Kelly is better for trading multiple - and uncorrelated - markets, then you just divide Kelly ...

[maildigger 10]

  nelo said:

 

For average speculator there are simpler, safer and more effective MM methods so you do not need to worry about Kelly too much.

 

Tell me ...

[nelo 10]

  maildigger said:

Tell me ...

 

In the beginning try to find a position sizing method which fits your psychology. It is important also later but in the beginning you maybe do not know so well that can happen and how will you react.

So think about money management not only from math point of view, but what is more important from psychological point of view. I found trading one contract quite difficult from psychological point of you, since I either took only a small profit from large move (fear) or loss when I wanted a bigger profit (greed). Two or three contracts and scaling out helped me a lot.

 

And regarding formulas, I spent long time testing various very complex position sizing methods and found three most useful: Fixed Ratio, Fixed Fraction and Larry Williams method. I should point out here that I daytrade single market, so it is different it you trade portfolio of 30 stocks with some automated strategy etc.

 

The last one (Larry's) is which I like the most:

contract traded = (account balance * risk percent) / largest loss

You set the risk percent based on your knowledge, skills and risk tolerance, usually between 5% and 15%. I like it because it takes into account two subjective numbers: your personality (risk percent) and your system (largest loss). You might hear to risk 1-2%, it is even safer and I also advise to start from that.

 

Traders never bust because they risked too little, they bust because they risked too much!

[Reaver 10]

  Jakew said:

The Kelly is an absolute classic.

 

However, because:

 

a/ the payoffs in trading cannot be precisely assessed

b/ the psychological factors will interfere in a trader's execution of "otherwise winning strategy" - i.e. he will capitulate under a severe drawdown pressure

 

half Kelly or less is advised

 

Kelly is better for trading multiple - and uncorrelated - markets, then you just divide Kelly ...

 

Please elaborate.....

[Jakew 10]

...you divide your method's Kelly fraction by the number of markets you trade, so if your method's Kelly is say 20% and you trade 10 markets with that method - you allocate 2% risk per position = per market

[Reaver 10]

Cool Jakew, thanks.