The Myth of Mathematics

Discussions about Money Management and Risk Control.
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Chris67
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The Myth of Mathematics

Post by Chris67 » Thu Jan 15, 2004 10:09 am

Okay so I'm probably going to cause more controversy but here goes

One thing that never ceases to amaze me in the realm of mechanical trading platforms are peoples willingness to accept certain mathematical models that are simply not shown to be true in ''real-life '' trading.
The most astonishing for me is the theory of probability surrounding the liklihood of being stopped out of many U- correlated trades all at , approximately , the same time.

In the last 8 months it has happened to me 3 times that I have been stopped out of up to 10 different and un- correlated positions at once .. or at least within the same day or at most as a string of losing trades. Also in this period I have had 24 back to back losing trades.

The idea that the the liklihood of having 3 consecutive losing trades is 0.5 * 0.5 * 0.5 is actually extremely nonsensical and shows a thorough misunderstanding of the inter-relatedness of financial markets despite what correlations may tell us.

My conclusions are simply that risking more than perhaps 0.2 % per trade is not viable and that anyone trying to achieve a track record for the purposes of raising money better not risk this much

Good Luck

verec
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Post by verec » Thu Jan 15, 2004 10:28 am

I'm all for believing what you say, but it seems difficult for a single event -- your experience over the last 8 months -- to invalidate a whole theory, no?

Did you trade 0.2% as you imply? After the 24 consecutive lossing trades, what was your drawdown? How much less would it have been if you had used 0.1% ?

Forum Mgmnt
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Post by Forum Mgmnt » Thu Jan 15, 2004 10:38 am

I've addressed this before in the section on Monte-Carlo analysis, but the problem comes because most of the mathematics people use for trading is for independent events.

Markets are based on human behaviors. Humans having memory and emotions, don't behave like dice, cards or anything else that generates independent events.

So markets and trading system results come as a result of dependent events.

Still, I think there is value to the concepts and tendencies one can take from the statistics of independent events. I just don't think you can use the results from the specific calculations, and say for example, the probability of such and such an event is 4.54%.

Chris67
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Post by Chris67 » Thu Jan 15, 2004 11:01 am

Thanks 4 replies guys,

Verec .. my drawdown after my losing run was about 3.1 % .. I managed the positions .. I have to because I cannot have a 5 % drawdown .. im building a cta trackrecord at the moment. If I had followed the general perceived theory on risk per trade I would have probably been down 25 %
Basically what i do is take the general turtle trading system ( trendfollowing philosophy ) , because I believe it is undoubtedly the best way to trade , but I have adapted it for my own personality and What I believe from 15 years of trading experience .. I believe that trades vary in term of where stops should initially be and how quickly they move up with winners. I also believe its okay to use whatever you want to use as a signal for market entry as long as you always maintain very strong discipline around money management.

A good example is today .. I have been long Crude for a while , but today I have gone short. I dont need a reason other than its my view .. I know that if it trades back through 35.4o I am wrong and I dont need a 2 atr stop loss.. only 4o pips in this case .. I will keep adding IF it goes lower and bring stop to where I assume it shouldn't go back to.

Now you may say that I may sometimes/frequently miss big moves with this strategy -You would be correct !! However I dont have to catch all the big trends because I am not relying on a few big winners per year. Having said that I have taken 30 % of moves frequently recently and rarely risk more than 0.1 % on a trade.

I dont want to sound arrogant because this business is very hard and if it were as easy as programming a computer then I'm sure a lot of MIT grads would have figured out the holy grail .. THERE ISNT ONE .. yes you can put the odds in your favour and thats okay if you can weather the drawdowns

I dont know how many guys on this forum have actually traded and have long track records but i can assure you if you design a system and you see on paper it averages 40 % a year with max 20 % drawdowns ..when you get to 20 % down and perhaps 22 % down I would say 1 in 10,000 traders may stick to the rules from that point on .... and even then there is no guarantees ...


There are some traits that great traders have that simply cannot be programmed into a computer.

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Post by Douglas » Thu Jan 15, 2004 11:18 pm

Chris,

Have you tested your 1 in 10,000 claim? Perhaps we should take a poll on this forum. We’ll need at least 10,000 (many more would be better) newbies with excellent system design experience, knowledge of the markets, but with no trading experience, and, say, $100,000 of their own money to throw at their newly created, newly tested, never been traded system. Then we’ll have to wait a few years (let’s say 3) and see if they stuck to their system.

THEN we will poll them.

This all seems perfectly viable to me. Could we get one of the moderators on this?

(Although, in the end, it will be just another statistic and past performance does not necessarily indicate future results... :wink: )

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Theory of Runs

Post by Christian Smart » Fri Jan 16, 2004 9:26 am

Actually, Chris, the topic you've brought up is treated very extensively in mathematics and it's called the "theory of runs." Your example is the following: if the probability of a winning trade = 0.5, then the probability of three losses in a row in three trades is 0.5^3 = 0.125. You then seem to say this doesn't apply to a more real world problem of having k consecutive losses in a run of n trades. And you're right about that, because that's a different story. For a trading system with the probability of a winning trade = 0.5, the probability of a streak of at least three consecutive losses in, say, 8 trades, is much higher, 0.414.

More information on this topic can be found at:

http://www.ieiit.cnr.it/~muselli/papers/spl00.pdf

http://mathworld.wolfram.com/Run.html

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???

Post by shakyamuni » Sat Feb 07, 2004 3:34 pm

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Last edited by shakyamuni on Sat Jan 08, 2005 4:45 pm, edited 1 time in total.

Zeke
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correlation and dependency

Post by Zeke » Sun Feb 08, 2004 1:40 am

shakyamuni,

I agree, the key issue is dependency.

The identification between correlation and dependency does seem a bit simplistic.

Dependency is where one particular bet out of a series (example: series of bets in one market) has its odds to win effected by whatever else happens in the game (market) of that series.

Correlation is the relationship between two different series of bets. In some cases, losing periods of one series are matched with winning periods of the other series; in other cases, losing and winning periods of one series are matched haphazardly with losing and winning periods of the other series; and finally, winning periods of one series match up with winning periods of the other series.

Perhaps correlation and dependency have become conflated because they are both considerations for reducing risk of ruin.

The above is my articulation of the distinction between the two. I am interested in any additional insight or suggestions for investigation.

regards,

Zeke

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Correlation

Post by Christian Smart » Sun Feb 08, 2004 11:21 pm

Correlation can be handled using Monte Carlo simulation. Most decent Monte Carlo software packages, such as Crystal Ball and @Risk, allow for correlation.

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