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How advanced mathematics and gaming theory can help you as a trader
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How advanced mathematics and gaming theory can help you as a trader

  #71 (permalink)
Fortitudo et Honor
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Fat Tails View Post
@RM99 Your statement is not clear and confuses different subjects.

You really would need to differentiate between uncorrelated and correlated bets.

If you apply any progressive betting system to uncorrelated bets, it just becomes a tool for position sizing.

Strings have no meaning, if consecutive bets are uncorrelated, such as for a coin tosses.

Well, the posts above tend to prove otherwise. Unless you're trying to argue that trades aren't mutually exclusive, which is debateable, but difficult to prove.

I would argue that for an average expectation of 55%, each trade has an expectation of 55%, regardless of previous outcome. SOME strategies, might lend expectation, but for a totally random outcome distribution (as posted above) and 55%, you're STILL GOING TO OBSERVE STRINGS.

This is the part that you're refusing to realize. you CANNOT observe a 55% win rate and NOT observe random strings of winners that are longer and more common than equivalent losing string occurrences.

Whether the strings make up the winning percentage, or the winning percentage is what makes up the strings, it's semantics.

The FACT IS, that adjusting position size, even with mutually exclusive outcomes, and an observed rate <> 50%, it IS going to have an effect on the yield.

Just because I have an 85% win rate, doesn't mean that after a win I have any different expectation than the trade before. THAT is approaching the decision from a single event. However, IF you approach the decision from a total string point of view, over time, adjusting position size can and does have an effect on the outcome.

At this point, if you don't agree, then we'll simply have to agree to disagree.

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  #72 (permalink)
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RM99 View Post
Well, the posts above tend to prove otherwise. Unless you're trying to argue that trades aren't mutually exclusive, which is debateable, but difficult to prove.

I would argue that for an average expectation of 55%, each trade has an expectation of 55%, regardless of previous outcome. SOME strategies, might lend expectation, but for a totally random outcome distribution (as posted above) and 55%, you're STILL GOING TO OBSERVE STRINGS.

This is the part that you're refusing to realize. you CANNOT observe a 55% win rate and NOT observe random strings of winners that are longer and more common than equivalent losing string occurrences.

Whether the strings make up the winning percentage, or the winning percentage is what makes up the strings, it's semantics.

The FACT IS, that adjusting position size, even with mutually exclusive outcomes, and an observed rate <> 50%, it IS going to have an effect on the yield.

Just because I have an 85% win rate, doesn't mean that after a win I have any different expectation than the trade before. THAT is approaching the decision from a single event. However, IF you approach the decision from a total string point of view, over time, adjusting position size can and does have an effect on the outcome.

At this point, if you don't agree, then we'll simply have to agree to disagree.


We agree that you always will observe strings. We agree that if the win rate is higher there will be more and longer strings with a positive outcome. But now comes the catch:


(1) Non correlated bets (coin tosses, throwing dice, playing roulette, described by a binomial distribution)

The strings are random and have no meaning. You may increase your wager after each positive outcome. You may decrease it after each negative outcome. If the win rate is > 50% you will have more positive than negative outcomes by definition. So you will gradually increase your bets, which in turn has an impact on the yield. You have just increased your position size. You will get the same result, if you make a small increase in position size with every bet, such as you would obtain with fixed fractional position sizing.


(2) Correlated Bets (Black Jack, trending markets, reacting markets, fat tails)

(2a) Positive Correlation: A positive outcome of the prior bet increases the expectancy for the current bet.
(2b) Negative Correlation: A positive outcome of the prior bet decreases the expectancy for the current bet.

For Black Jack consecutive bets are negatively correlated. If you have had a number of losses, this increases your expectancy which can become larger than 50%. That is why some Black Jack players are watching for negative strings by counting cards. This gives them an edge. Casinos will respond by increase the card stacks to make it more difficult to overcome the edge of the casino.

To use this knowledge for trading, you have to find out whether consecutive price moves are positively or negatively correlated. This is not easy as correlations change. In a trending market, you may assume positive correlation, in a range bound market negative correlation. This really depends on the other players (traders) in the market. There are positive and negative feedback traders, and you do not know which group will dominate during the period of your next bet.

One way to look at this are the COT reports. Commercials shows anti-cyclical behavior (with a high crude price you will find a considerable net short position), Managed Money will have a net long position. However managed money traders can also generate negative feedback, when they start rushing to the exits.

What I want to show is that the concept of strings only makes sense, when the bets are correlated. For non-correlated bets there are strings as well, but they have no impact on the future outcome of bets. So increasing bet size after a positive string is just a money management tool.

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  #73 (permalink)
Fortitudo et Honor
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It would be interesting to see the results of a random distribution of 55% outcome probability with a fractional position increase of 50%,

Then compare that to the same distbrution with a fractional increase of 50% following winning outcomes, followed by a return to the original amount following a losing outcome.

A third iteration would be to incorporate both, by increasing fractionally following a winner, return to original following a loser and then a "reset" or increase of the base/original positionsize once the account has increased past a certain "reserve" or drawdown amount. (i.e. return to original position following a loser, up until the account has doubled, then double the base/original position size and continue from there).

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  #74 (permalink)
Live Your Bliss
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RM99 View Post
It would be interesting to see the results of a random distribution of 55% outcome probability with a fractional position increase of 50%,

Then compare that to the same distbrution with a fractional increase of 50% following winning outcomes, followed by a return to the original amount following a losing outcome.

A third iteration would be to incorporate both, by increasing fractionally following a winner, return to original following a loser and then a "reset" or increase of the base/original positionsize once the account has increased past a certain "reserve" or drawdown amount. (i.e. return to original position following a loser, up until the account has doubled, then double the base/original position size and continue from there).

Run it.

Btw, the Epstein text that Fat Tails references is a classic (with a second edition out now) and worth checking out.

"...the degree to which you think you know, assume you know, or in any way need to know what is going to happen next, is equal to the degree to which you will fail as a trader." - Mark Douglas
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  #75 (permalink)
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Lets try it like this. 1500 trades. Standard win/loss is 500. When there is a win then increase by 50%. Keep doing this until there is a loss then go back to 500.

I have added red blobs to show what would happen if you didn't alter the R. These are calculated as

(win% * 500 * 1500) - (lose% * 500 * 1500)

At low win rates you can make your results much worse but at modestly high win rates your results are improved by altering your R to take advantage of the fact that strings occur

This makes sense. If you had a 50% win rate and you got wlwlwlwlwlwlwlwl you would keep losing 750 and winning 500 and go broke very quickly. At 50% win rates the strings tend to be interupted by streaks of wlwlwlw which undo all the good work from a string of 5 or 6 wins in a row very quickly. the higher you win rate the less that happens so once you get in the 55% and over the altered position sizing improves your bank even though you wil get some doozies of losses. There were plenty of runs where the maximum loss is 4,000 (8 times your standard R yikes!) but the final profit is still way higher than using a flat 500

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  #76 (permalink)
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Changing position size like this is NOT equivalent to fixed fractional position sizing. The bet size is reduced dramatically as soon as a loss comes along. With FF the be size decreases a little each time a loss comes along

i.e. 100,000 risking 1% your next R is 1,000 if you just had a loss but may be 3,000 if you have had a string of wins.

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  #77 (permalink)
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For someone who knows excel it would be very easy to put this to rest with some spreadsheet modelling...wouldnt it?
Use the random number generator to model the win %
Run tests for w% of 45, 50, 52, 55, 60
start with $100000
initial bet size $1000
After a win increase position size by 1%
After a loss decrease it by 1%
Plot in format X axis is trade number, Y axis is equity in %
Run a simulation of 1000 trades for each w% - then compare to the curves for constant bet size
There may be more aggressive bet sizing formulae that could also be modelled.

Unfortunately it would take me days to work out how to do this..I would like to see the results...anyone?

The other way for RM99 to demonstrate application of his beliefs would be to run a forward test in a journal?

L


Last edited by Linds; April 9th, 2011 at 11:07 PM.
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  #78 (permalink)
Fortitudo et Honor
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Linds View Post
For someone who knows excel it would be very easy to put this to rest with some spreadsheet modelling...wouldnt it?
Use the random number generator to model the win %
Run tests for w% of 45, 50, 52, 55, 60
start with $100000
initial bet size $1000
After a win increase position size by 1%
After a loss decrease it by 1%
Plot in format X axis is trade number, Y axis is equity in %
Run a simulation of 1000 trades for each w% - then compare to the curves for constant bet size
There may be more aggressive bet sizing formulae that could also be modelled.

Unfortunately it would take me days to work out how to do this..I would like to see the results...anyone?

The other way for RM99 to demonstrate application of his beliefs would be to run a forward test in a journal?

L

Unfortunately, like I said, it's not really feasible for instruments like CL because of the discrete nature. Unless you're trading a lot of contracts, a 10% increase in position size isn't feasible.

I'm away from home, but I'll work on an excel analysis when I get back.

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  #79 (permalink)
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I didn't think this tactic would make sense - particularly when you set yourself up for a big loser at the end of a string - but am inclined to trust Nickemp's spreadsheets. Well done RM99.

Hopefully the debate will be as rigorous as to the best possible applications for trading.

I'm wondering if adding contracts while day trading futures - but only in the direction of the longer timeframe trend - might be a better alternative than a fixed fractional position size.

What would be the best stop loss and what time should these trades be initiated?

Sorry for having more questions than answers - I just swing trade futures and stocks now.

Here is a Fixed Fractional Position Sizing Calculator if helpful to anyone.

Attached Files
Register to download File Type: xls Calculator-FixedFractionalPositionSizing.xls (30.0 KB, 48 views)
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  #80 (permalink)
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Nickemp View Post
Lets try it like this. 1500 trades. Standard win/loss is 500. When there is a win then increase by 50%. Keep doing this until there is a loss then go back to 500.

I have added red blobs to show what would happen if you didn't alter the R. These are calculated as

(win% * 500 * 1500) - (lose% * 500 * 1500)

At low win rates you can make your results much worse but at modestly high win rates your results are improved by altering your R to take advantage of the fact that strings occur

This makes sense. If you had a 50% win rate and you got wlwlwlwlwlwlwlwl you would keep losing 750 and winning 500 and go broke very quickly. At 50% win rates the strings tend to be interupted by streaks of wlwlwlw which undo all the good work from a string of 5 or 6 wins in a row very quickly. the higher you win rate the less that happens so once you get in the 55% and over the altered position sizing improves your bank even though you wil get some doozies of losses. There were plenty of runs where the maximum loss is 4,000 (8 times your standard R yikes!) but the final profit is still way higher than using a flat 500


You just showed that

- if your expectancy is greater than 50%
- and if you gradually increase your position size,

this will improve your profits, compared to maintaining a fixed position sizing.

Not really unexpected.

This has nothing to do with strings, because strings are irrelevant, as long as your bets are not correlated. Nevertheless, increasing the position size, does increase returns, if the odds are in your favor. It also increase the risk of ruin, if your bet size grows faster than your equity.

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