Kelly Criterion - Optimizing risk

Hi,

I am using the Kelly Criterion to help me determine how much risk I should take in each trade, according to my win/loss ratio and winning probability (based on my track record). A concise and well written explanation of the method may be found here:
http://www.investopedia.com/articles...#axzz1bycGZb51

I have created an Excel spreadsheet that plots the expected % Payoff on each trade against the % Capital at risk according to the criterion. I know that taking the optimum risk pointed out may not be the best choice, so I always consider taking a fraction of it, using the optimum level as a reference.

The reason for starting this thread is that I am trying to figure out how to calculate the probability of a certain % drawdown against a chosen risk level. It is not just the compounded probability of a string of losses leading to the target drawdown. There may be winners among the losers - shifting the odds - so here I am trying to push the limits of my math background.

Attached is a screenshot of the %Payoff x %CAR plot from my spreadsheet. If there is anybody interested (or willing to help me) I may post the spreadsheet as well. Thanks and good trading to all.

Hi Jairo,
as far as i know kelly formula is better suited for casino games where wins and loses are constant (you know how much you lose you know how much you win on each hand) unlike trading.
of course the formula is of no value when your expected value is negative - trading or in gambling. Try to put your hands on Ralph Vince books he explains it better
cheers.
pipkeep

Thank you Pipkeep for the useful tip. I will dig slowly into it.

Hi Jairo,

I've just discovered the Kelly Criterion and find it quite interesting.

I would like to study your spreadsheet - would you be willing to send me a copy?

Cheers mate,

ggerhardt

Hi ggerhardt,

Here is the latest version of the spreadsheet (please see attachment). It is a work in progress. I use yellow cells to input data.

Best regards,
Jairo.

Here is a better (simplified) version of the spreadsheet. Got rid of some useless stuff.

Hi Jairo

I was also interested in the likelihood of a given drawdown using Kelly. I couldn't find anything... But you may be interested in these two links.

This first one explains the generalization of the formula for several outcomes. More suited for trading systems where you may have any kind of R:R, like trend following.
http://elem.com/~btilly/kelly_criterion/

This second gives an idea to "forcefully" limit the drawdown.
http://epchan.blogspot.fr/2010/04/ho...ing-kelly.html

Another question I couldn't answer is: "Let's suppose I did hit my max DD. What shall I do next?"

Best

Thank you PipMeUp for the interesting links. The math involved in this criterion is very challenging. I changed focus a bit after I got my spreadsheet done. I am using it now just for post-trade risk control (checking if my risk exposure is correct, according to my hit rate and profit factor) and as a consistency test.

If you upload your trades to MT4i or Myfxbook, you will get some estimated probability of %DD. Nothing perfect, but provides some reference. The Trade Explorer here in FF has useful statistics too.

About your question, I think that if you are trading profitably, once you hit your maximum drawdown you should continue to trade the same way. Probably your method will have provisions for lot ajustments, stop losses, etc, so drawdown is just part of the game.

Best regards.

Check these two articles I find them very useful: http://articles.mql4.com/631
http://articles.mql4.com/659

As far as I understand it, the maths behind the Kelly criterion is sound but in pragmatic terms its theoretical best point tends to assume a lot of risk for the average trader. This is because it was not originally developed for trading and the optimal point is just before the risk of ruin starts going vertical on the graph. In actual trading you'd probably want to be a lot more conservative and assume rather less risk per trade than the optimal Kelly point would indicate

Actually this was a joke to underline a paradox: How can you open a new position if you are already at your maximum DD? Per definition of "maximum" you cannot go any beyond ;-). Yet if you don't open a new trade how can you recover?
=> In short there is no maximum DD, except for total bankruptcy. You have to carry on.

Also I think it is exactly the time where you shall absolutely not try to modify the method at all! You have no way to know if it will be better this way (plus you're under stress). And if it was better why not using it beforehand instead of only in a deep DD? The "black swan" will happen. Just because the probability of N losers is not null.
That's the point where you have to remember the famous "Stick to the plan".


Back to Kelly formula: It is only valid under the assumption of the central limit theorem (law of large numbers). That is when you have taken an infinity of trades... It is a limit. That's why the value isn't the optimal bet size but the absolute maximum bet size.

In the first link (I admit quite hard to comprehend), the example of the poker tournament is interesting for traders: quite a lot of losers, winners are usually small and sometimes a home run.
Look the result: 1.48%. Now compare with the rule of thumb of 1% per position. Your conclusion? Yes 1% is already too big!


Olsen, thanks a lot for the links. A must read!

The Kelly Criteria is an interesting thing to play with. Works quite well in many ways, but has serious limitations when used for trading.
Works best when used in retrospect. One thing that complicates the matter is that short term results can vary widely from the long term.
For example, we might look over the last hundred trades and see we have a good system going that gives us 3 out of 4 winning trades.
Sounds good so far, but what happens during short segments of that run? Can we pick out a series of 4, 5, even 7 or more bad trades?
Happens all the time even when over the longer term we still show 75% profitable trades.
So, for me, I use the short term worst case series to figure the win percentage probability.
That and we must also realize that it isn't just position size at risk unless we trade with no leverage.
For reality, we must consider the value of the stop-loss as being what is at risk.
Consider as well that too tight of a stop-loss when entering a trade can hurt the chances of having a happy ending.
Market volatility is always lurking around hunting those tight stop outs.
So, first consider what stop position you have to allow for the trade to have a good chance of going your way, then work out the position size accordingly to that.

Here is an updated version of the spreadsheet. I am using it to trade, to keep record of trades and to analyse results. Monte Carlo Simulation was put in a separate file but it takes data from the main spreadsheet, named Toolbox. There is still some redundant and obsolete stuff in it but in general it works fine. Some minor corrections in the to do list. The best thing about this spreadsheet is that finally I seem to have arrived at a valid solution to the drawdown problem. Account growth can be deceiving if you don't take drawdown into serious consideration. I believe thousands of people have lost their accounts because they thought they were ready for the real market when in fact they were not. This has happened to me but I intend not to let it happen again.

There are better MM options than Kelly formula. I would recommend the book "Definitive Guide to Position Sizing" by Dr. Van Tharp.

Mades, thank you for your input. I was obsessed by the question "What is the ideal risk level?". Why cut losses at 0.5, 1, 2, 5, 10 or 30%? If you have a good edge, you may risk more. On the other hand, a profitable method may be ruined by too much risk exposure.

Corrected daily log ("Resumo do dia", DLog sheet) and uploaded new file.

My consistency test is brutal and I like it this way. It will mercilessly point out any flaw in your trading scheme. Limiting risk with no edge will only guarantee that you will destroy your account slowly instead of blowing it up in one day. Thanks again for your recommended reading.

A slightly improved version of my Toolbox is here. Got rid of some useless stuff, corrected some minor errors and added a few resources. The Q3 cell in the Open sheet, intended to monitor drawdown and hold the biggest value experienced during the last trading cycle (I name this way the period between two flat positions), still has an issue: it shows #N/D at spreadsheet start - only if there are open positions. I have tried my best to figure out why this happens but couldn't come up with a fix yet. It looks like an Excel bug to me, but maybe it's only my ignorance.

Fixed an error in the Starting Balance automatic update. Just a reminder: this "toolkit" is not a recommendation to use martingale, which is very dangerous. If you have an edge, please stick with it and don't play with fire. If you don't have, it will not provide you one.

Fixed some broken references in formulas. Not enough data yet to start (and test) the risk balancing mechanism. Maybe in a few sessions - if I can keep drawdown low.