stevehopwoodforex.com
https://www.stevehopwoodforex.com/phpBB3/
Print view

Kelly Criterion
https://www.stevehopwoodforex.com/phpBB3/viewtopic.php?t=233		 Page 3 of 4
Author:  hedgeitall [ Tue Apr 17, 2012 3:58 am ]
Post subject:  Re: Kelly Criterion
Hi,
Just saw this thread,
thought you might like to see my take on the Kelly formula

K=((100*(pt-lt)/count)+100)*0.5*0.01*lots;

K= Kelly Lots
pt= profit trades
lt= loss trades
count= number of trades
lots = optimized lots


If you have all wins K=lots.
if you have all losses K=0 (or 0.01 lots)
the more wins = the higher lot size
the more losses = lower lot sizes
Author:  hedgeitall [ Tue Apr 17, 2012 4:10 am ]
Post subject:  Re: Kelly Criterion
Also here is a reverse option.
this gives you lots + Reverse Kelly.. (lots + (more wins= less lots) (more losses = more lots)

K=(((100*(lt-pt)/count)+100)*0.01*lots)+lots;
Author:  garyfritz [ Wed Apr 18, 2012 4:53 pm ]
Post subject:  Re: Kelly Criterion
Those are arbitrary position-sizing calculations. They are **NOT** Kelly calculations. Kelly position sizing has very specific mathematical properties -- e.g. sizing at full Kelly will maximize your profits in the long run, and sizing at a given fraction of full Kelly gives you known probabilities of a particular drawdown level. Your formula doesn't do that.

Your first formula returns a negative position size if you have < 50% wins (so lt > pt). With 50% wins (lt = pt) it returns zero. Maybe you intended to use pt/count = pt/(lt+pt) ?
Author:  hedgeitall [ Thu Apr 19, 2012 9:55 am ]
Post subject:  Re: Kelly Criterion
Hi Gary,

You are right. I was not taking into consideration the b(odds) part of the equation. The reason is it did not have that much bearing on the outcome.
The outcome I wanted was just the percentage of x lots. Not the full lots according to the kelly formula.

The formula should be more like this adding b

k=((100*((b*pt)-lt)/b)+100)*0.5*0.01*lots;

b=(total profit / (total loss*-1)

Here is a graph, hope you can see lot sizes. it is calculating over the last 15 trades using a fixed lot size for "lots".
Author:  garyfritz [ Thu Apr 19, 2012 2:39 pm ]
Post subject:  Re: Kelly Criterion
I don't know how you're deriving these formulas. But unless I'm mistaken they really ARE NOT Kelly calculations (though they're closer with this recent change), so I'd appreciate it if you'd move the discussion to another thread. I don't want to confuse people any more than I already have. :D
Author:  AnotherBrian [ Fri May 11, 2012 2:21 pm ]
Post subject:  Re: Kelly Criterion
I recently received a PM from Gary on a different topic and he mentioned Kelly in the PM. I thought I'd follow up and read a little. I tried to read the paper that was posted....didn't get past page 1. I'm not a math wizard, when I see all those funny symbols it usually means statistical analysis followed by blurry vision and nap. So thanks for the summary on the Kelly calculation on the first page of this thread.

Let me explain why I am interested in Kelly and how it can help me. First, I don't plan to blindly follow the calculation, for me it is a high level guide.

I typically risk 0.5% to 3% per trade, most of the time its 2%. I adjust the risk based on "gut feel" on the set up. What I don't have a good handle on is the max risk I can take for a mathematically decent long term result. I'm not looking for exact numbers, rather a range. Is 10% way to high? What would happen if I risked 50%?

So I took my list of completed trades and found my Kelly. I have a live account and a demo where I trade the same system manually (discretionary). I'm going to combine the trades from both and calculate Kelly as well as find the Kelly for each separately. I do this only to expand on the number of trades in the calculation.

I've calculated Kelly for the live account and have chosen to take 10% of that for my max risk level.

All said, this only give me some 'reasoning' or logic for my upper risk limit per trade. Where would I use such a high risk per trade? ...when the probability for a winner is high.

Overall, there are too many variables that continue to change to determine a solid and static number. My goal is to simply - keep the equity line rising and keep the draw down lower reasonable for me.
Author:  garyfritz [ Fri May 11, 2012 3:35 pm ]
Post subject:  Re: Kelly Criterion
I think that's a good approach, Brian. 10% of Kelly is reasonably conservative, while still giving you the opportunity to increase your returns above what a fixed 1% or 2% risk might provide. Judging by the equity curve on your mt4i account, I'd guess your Kelly value is fairly high.

According to the formula on the first page, the probability of drawdown D is P(D) = D^(2/K-1). K = 0.10 if you're trading at 10% of Kelly. So e.g. the chance of a 20% drawdown is (1-20%)^(2/0.1-1) = 0.8^19 = 1.44%. That's a pretty safe risk level.
Author:  mlewis [ Wed Aug 22, 2012 9:14 am ]
Post subject:  Re: Kelly Criterion
i found this EA in case anybody wasn't already aware of it:

http://www.forexfactory.com/showthread.php?t=153234

ML
Author:  dusktrader [ Sat Dec 08, 2012 9:18 pm ]
Post subject:  Re: Kelly Criterion
AnotherBrian pointed me to this formula / method and I have been studying it with great interest lately.

The system I trade (discretionary) has a known accuracy rate of at least 50% (from my history) and also a known risk:reward ratio of at least 3:1. Seems like these are the only two things that Kelly formula needs.

By the way, this is the calculator I'm using (its just a spreadsheet). In the formula, I use extra-conservative values of 40% accuracy and 2.5:1 reward ratio.

I'm not sure exactly what fraction of Kelly I'm using, but I know its very small. I guess for now I'm using the "holy crap that scares me!" method to know when it's too much.

Unlike what AnotherBrian mentioned above, I use the same sizing for every trade. Also, using his TT2P I equalize all trades with regard to equity at risk, so regardless of timeframe, etc. they are all the same. Either they work or they don't (and I know 50% or better will). The reward ratio of 3:1 is hopefully conservative as well, because TT2P allows a second leg to run for much higher profit. Whether or not it achieves that second leg (or any portion thereof) is a sortof bonus to me.

The problem I'm currently researching is how to know when my criminal will cut me off with regard to margin. For example, I know at some point they will probably say "not enough margin to open the trade". Each trade is currently set to 4% risk (that came from Kelly) but I don't know how many I can have simultaneously open at once yet.
Author:  garyfritz [ Sat Dec 08, 2012 10:22 pm ]
Post subject:  Re: Kelly Criterion
That calculator has some issues...

It's correct that the expectancy is $33.33. ($500 * 60% - $666.67 * 40% = $33.33.) Kelly is AvgTrade / AvgWin = Expectancy / AvgWin = 33.33 / 500 = 6.67%.

If you're going to use Kelly, you have to know how much you're risking on each trade, and use that to size your positions. That calculator seems to assume the "average loss" is the worst-case risk on each trade, which is probably not always true.

Bigger issue, though: it implies you should trade at full Kelly or, if you're conservative, drop down all the way to half Kelly.

That's insane. At full Kelly you're likely to see 95% drawdowns or worse. Even at half Kelly you're likely to see 50-70% drawdowns. Probability of drawdown to D when trading at Kelly fraction K is D^(2/K-1), where D = 0.40 for 60% drawdown. So at half Kelly it's 0.40^(2/.5-1) = 6.4% chance of 60% drawdown, 12.5% chance of 50% drawdown.

Personally I run at 10% of Kelly or lower. That generally keeps the drawdowns under 25% or so.
All times are UTC Page 3 of 4

Powered by phpBB® Forum Software © phpBB Limited