# Reverse Martingale position sizing



## Gringotts Bank (29 August 2010)

Many of you would have heard of the Martingale system of betting (trading).  If you are winning, keep betting the same amount (position size).  At your first loss, you double up, and continue to do so til you win back everything you've lost, and start over.  It's not actually doubling, (there's a simple formula), but you get what I'm saying.  You might get lucky if you don't trade for too long, but the likelihood of not having the required capital to cover your nth losing bet is high.  Not recommended.

Reverse Martingale can be used successfully with share trading, I believe.  If your first bet wins you increase your bet size.  The more you win the more you increase the increment (with some limits obviously).  The idea behind this system is that it makes use of the 'winning streak' phenomenon.  First loss will cause you to reduce your bet size.  Lose again, reduce it again... and so on.   

Probably best for high frequency trading systems.


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## Garpal Gumnut (29 August 2010)

Gringotts Bank said:


> Many of you would have heard of the Martingale system of betting (trading).  If you are winning, keep betting the same amount (position size).  At your first loss, you double up, and continue to do so til you win back everything you've lost, and start over.  It's not actually doubling, (there's a simple formula), but you get what I'm saying.  You might get lucky if you don't trade for too long, but the likelihood of not having the required capital to cover your nth losing bet is high.  Not recommended.
> 
> Reverse Martingale can be used successfully with share trading, I believe.  If your first bet wins you increase your bet size.  The more you win the more you increase the increment (with some limits obviously).  The idea behind this system is that it makes use of the 'winning streak' phenomenon.  First loss will cause you to reduce your bet size.  Lose again, reduce it again... and so on.
> 
> Probably best for high frequency trading systems.




I can see a number of problems with the system.

1. You may not get all your order for stocks or instruments filled at the price you wish
2. Brokerage
3. Taxes and Bookkeeping on the Trades.
4. A run of very bad luck.

gg


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## Gringotts Bank (29 August 2010)

Sigh.....

None of your objections is relevant.  Read it again, it's a position sizing method.


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## Garpal Gumnut (29 August 2010)

Gringotts Bank said:


> Sigh.....
> 
> None of your objections is relevant.  Read it again, it's a position sizing method.




Sorry sirG I didn't mean to make you sigh.

I still reckon you'll go broke using that system, its a bit like replacing Rudd with Gillard.

sigh.....

gg


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## Gringotts Bank (29 August 2010)

But it's not a system of trading, it's a system of deciding how much to put on each trade of _your existing system._

It actually has safeguards against going broke through a run of bad luck.  It aims to give you less drawdown in times of losing streaks.  On the upside, it aims to capitalize on winning streaks (if you believe in such things).

Gillard has longer earlobes.  Should count for something.


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## tech/a (29 August 2010)

A subject rarely touched on but a very important one.
It makes sense and is a good idea.
There will always be strings of winners and losers in any system
However anticipating through analysis when those streaks are more likely is a wise idea.
Equity curve stops seem to work well but havent tested fully yet.

Seen and heard of it before it basically increases your risk each winning trade.
If you move to B/E (Or minimum risk) as soon as possible the risk is no more than any other trade.

Penfold discusses and tests a number of really interesting position size models in "The Universal Principals of Successful Trading"
Worth buying the book if for nothing else.

Mind you there is plenty of "ELSE".


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## skc (29 August 2010)

The underlying reason why martingale systems don't work is because the next trade has the same probability of success as any other individual trade. 

Of couse we will observe winning streak - that's the nature of statistics. Streak probabilities matter only when you look at them before the start of the streak, not after the streak has begun.

I am doubtful that the suggested reverse martingale actually improves the edge. 

It improves the outcome of course on a positive expectancy system - you trade bigger so you will have a bigger payout over time. But you have not improved your edge. By that I think the improvement in total profit will be linear to the increase in position size. 

Happy to be shown that this is wrong however.


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## AlterEgo (30 August 2010)

Fixed fractional position sizing already does this. As the account size increases, so do the position sizes (well technically it's the $ risked per trade that increases, but that's closely related to position size). As the account size shrinks, the position sizes reduce as well. But I guess you're talking about a much more aggressive approach than this?


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## howardbandy (30 August 2010)

Gringotts Bank said:


> Many of you would have heard of the Martingale system of betting (trading).  If you are winning, keep betting the same amount (position size).  At your first loss, you double up, and continue to do so til you win back everything you've lost, and start over.  It's not actually doubling, (there's a simple formula), but you get what I'm saying.  You might get lucky if you don't trade for too long, but the likelihood of not having the required capital to cover your nth losing bet is high.  Not recommended.
> 
> Reverse Martingale can be used successfully with share trading, I believe.  If your first bet wins you increase your bet size.  The more you win the more you increase the increment (with some limits obviously).  The idea behind this system is that it makes use of the 'winning streak' phenomenon.  First loss will cause you to reduce your bet size.  Lose again, reduce it again... and so on.
> 
> Probably best for high frequency trading systems.




Greetings --

As several other responders have commented, this is a position sizing method.  It relies on having a trading system that has a positive expectancy, then increasing position size when the system is winning.  

Thought of in gambling terminology:
1.  Anti-martingale methods are based on "betting the run of the table".  That is, bet that winning will be followed by winning.
2.  Increase bet size by using "the house money".

There are several good books that discuss position sizing:
1.  Any of Ralph Vince's books.  His latest is:
http://www.amazon.com/Leverage-Spac...=sr_1_2?ie=UTF8&s=books&qid=1283092336&sr=8-2
2.  Ryan Jones. 
http://www.amazon.com/Trading-Game-...=sr_1_1?s=books&ie=UTF8&qid=1283092386&sr=1-1
3.  Van Tharp.
http://www.amazon.com/Trade-Your-Wa...=sr_1_1?s=books&ie=UTF8&qid=1283092422&sr=1-1
4.  Advanced AmiBroker, when it becomes available.

Thanks,
Howard


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## Gringotts Bank (30 August 2010)

Correct alterego, it's exactly the same as fixed fractional betting but more aggressive.  Achieves the very same thing.

skc, I understand that the next coin toss will always be 50-50, mathematically speaking.  However I'm looking at this from a psychological perspective, not mathematical.  My assumption: that a win will tip the odds in your favour of picking correctly the next time because you're "on a roll".  The more of a roll you're on, the more you should bet, and vice versa.  Many of the hard stat/maths guys will look at this assumption and say "yeh right!".  Well that's fine, I do happen to believe in streaks that have a psychological cause (ie. non random).

Getting back to the statistical side of things, reverse Martingale does have 2 advantages over Martingale, as mentioned in my earlier posts.

I favour this over Van Tharp's stuff purely because of it's simplicity and psychological bent.  Van Tharp is the limit of my reading on this topic to date, but thanks for all those other great refs people have included here. 

Looking forward to Advanced Amibroker, Howard.  What are they planning to include?


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## Gringotts Bank (30 August 2010)

I thought Advanced Ami was a software upgrade, but I see it's howard's book.

http://www.advancedamibroker.com/advanced-amiBroker-contents.pdf


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## waza1960 (31 August 2010)

I have a presentation from Dr Bruce Vanstone of Bond Uni who has done work on Anti-Martingale systems and they seem to have an edge.


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## Gringotts Bank (31 August 2010)

Can you post a link or original text waza?


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## tech/a (31 August 2010)

Gringotts Bank said:


> Can you post a link or original text waza?




Send me a private message with your email address and I'll send you his thesis.


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## LimitBid100 (31 August 2010)

Gringotts,

In my trading system, I use risk management that increase trade size as my capital increase (ie, after a winning trade), as you suggest in this post.

However, more importantly, I use a leverage increasing risk management style within each trade as well. Ie, I open a trade with a tiny amount, and then add more as it goes in the money.....eventually ending up with a suitable size position.

I find this "micro reverse martingale" (for a lack of a better term) adds far more value to my trading than the reverse martingale risk management at a portfolio level. (That said, the portfolio level risk management is essential, and does add plenty of value on its own).

To put it in perspective for you, my initial position is only 1/6th of my final position. This means, that if a trade goes wrong quickly, i only lose on a tiny position. If it goes well....I trade up to a full position and let it run as best i can.

Hope this helps,

LimitBid.


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## Naked shorts (31 August 2010)

I have found that adjusting my position sizing relative to my confidence in the trade, to be optimal. Discretion in position sizing is an edge in itself, but is extreamly difficult to master and takes hundreds, if not thousands of hours to get right

"You got to know when to hold 'em, know when to fold 'em, / Know when to walk away and know when to run"


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## Gringotts Bank (31 August 2010)

Sounds good Limit.  My current system won't permit scaling in/out (due to brokerage costs) but I can see how that could add quite a bit to many systems.  Reminds me, Amibroker does allow coding for scaling positions and I should go and learn how it works.

Naked, there's a lot of truth in the lyrics of 'The Gambler' eh?


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## LimitBid100 (31 August 2010)

I dont see how scaling in and out adds to your brokerage....

If you do 2 contract, then 4 more, then another 6......you pay for 12 contracts.........if you dont scale in and just do 12 straight up, you still pay for 12 contracts?

Am I missing something here?


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## howardbandy (1 September 2010)

LimitBid100 said:


> Gringotts,
> 
> In my trading system, I use risk management that increase trade size as my capital increase (ie, after a winning trade), as you suggest in this post.
> 
> ...




Hi LimitBid --

Using one of your examples, where the initial position is one sixth of the final position, I assume that the size of the final position is the size that limits your risk.  (If it is the initial one-sixth that limits your risk, then every scale in amount is putting your account at greater risk than you probably intend.)  If the account risk is one percent of equity, and the final position goes badly, then no more than one percent is lost.  If the trade goes well, and it is expected to go well since every system being traded has a positive expectancy, then the amount participating in the trade was significantly less than allowed by the risk management calculation and you are leaving considerable profit "on the table". 

In general, scaling in hurts overall system performance.  And scaling out hurts overall system performance.  Best results come from calculating both the account risk and the system risk, then taking the maximum position allowed at the entry signal and exiting the entire position at the exit signal.  

A good way to test is to isolate each signal.  That is, create a separate signal for each scale in, including the initial entry, and a separate signal for each scale out.  Compare the results from following each of the signals with a fixed amount.

Thanks for listening,
Howard


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## LimitBid100 (1 September 2010)

Howard, 

I find that more than half of my trade lose money (actually closer to 70% lose money). Most of these go bad straight away, createing a loss on the 1/6th position. 

The trades that go well.....go really well, far outweighing the losses on my many bad trades.

Essentially, the scaling saves me a lot of money by reducing most of my losses to a trivial amount (about 0.12% of capital), while only reducing my winning trades (which are far less in number) by a smaller proportion.

There is no doubt that my winning trades would make more money if i didnt scale in. But my losing trade would cost me a lot more as well........much more than the extra gains in the winning trades.

LimitBid.


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## Gringotts Bank (1 September 2010)

Limit, if for example I buy a $30,000 position in one hit, that's $30,000x.11% = $33 brokerage to enter.  (Talking about ordinary shares here).

If I split it into 6 parts, it's 6x$15 = $90.

I guess if I had one of those brokers that allowed order splitting that would be different.


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## LimitBid100 (1 September 2010)

If you are serious about your trading, you would find a broker that suits your needs.  You wouldnt be lazy about your trading research, why be lazy about your broker.....they booth contribute to your P/L?


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## Gringotts Bank (1 September 2010)

Who do you use that allows order splitting?


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## LimitBid100 (1 September 2010)

I dont trade shares, i trade futures....I use Man.

If you want by $20k worth at $10, another $20k at $10.50, and another $20k at $11.00......that is three seperate orders....not 1 order split into 3.

Surely the brokerage is the same as for $60k in one hit?


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## AlterEgo (1 September 2010)

LimitBid100 said:


> Howard,
> 
> I find that more than half of my trade lose money (actually closer to 70% lose money). Most of these go bad straight away, createing a loss on the 1/6th position.
> 
> ...




I doubt very much that this approach makes more money overall than buying the entire position upfront. If fact I'm sure I've read articles that prove this. The stock would need to move much further for you to break even, plus you'd be paying more in brokerage. Eg. comparing 1 purchase of 20,000 shares at $1, vs. buying 4 x 5,000 positions at $1.00, $1.05, $1.10 & $1.15 would result in a breakeven price of $1.005 (1 tick) for the single position vs. $1.08 (16 ticks) for the 4 positions.

I have often read of this approach, but have never used it myself, because I've never been able to work out a way of doing it that hasn't reduced the system's overall profitability. Have you done a computer backtest that shows this approach making more money??


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## LimitBid100 (3 September 2010)

AlterEgo,

I have done numerous backtests over 15-20 years of data across 35 different futures. 

It is obvious that adding to a position wont make as much money as doing the entire position up front......on a winning trade. But on a losing trade, the losses can be greatly reduced by starting with a small position.

The total amount of money made is the sum of the profits and losses. You can improve this result by either, increasing the size of the winners, or, reducing the size of the losses.

I try and do both. My backtesting suggests that adding to positions to ensure many small loses creates a smoother growth of capital than hitting every trade as hard as possible to maximize the upside.

LimitBid


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## tech/a (3 September 2010)

Any chance of emailing me the results
Ill send you my email by private message.
Ive not been able to model anything that mirrors your results.
Where do you get your futures data for 35 types?
Is it EOD?
What software are you using to test with?
Im interested in your code for this averaging in approach.
I know in theory it seems logical but in practice Ive not seen any positive correlation.
You may well be the first and if so will certainly alter many peoples thinking.


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## LimitBid100 (3 September 2010)

Im not going to tell you exactly what I do......I will give you the vibe, which may or may not help you. If it gets you thinking about something new, that is a good result.....that is all I look for from these forums.

I got my data from a shop called pinnacle data, you can find them on the web. I did my backtesting using Excel. The data I use is end of day data (open, high, low, close).

If you have a high winning% in your trading, then adding to positions like this probably wont help. Where as, if you have a low winning% (but still positive expectation), this method should help reduce the damage on the many losing trades.

LimitBid


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## tech/a (3 September 2010)

As I expected.
thanks.


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## AlterEgo (4 September 2010)

LimitBid100 said:


> My backtesting suggests that adding to positions to ensure many small loses creates a smoother growth of capital than hitting every trade as hard as possible to maximize the upside.




Ok, so if I read this sentence correctly, you're saying it produces a smoother equity curve, but less total profit?


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## village idiot (4 September 2010)

AlterEgo said:


> I doubt very much that this approach makes more money overall than buying the entire position upfront. If fact I'm sure I've read articles that prove this. The stock would need to move much further for you to break even, plus you'd be paying more in brokerage. Eg. comparing 1 purchase of 20,000 shares at $1, vs. buying 4 x 5,000 positions at $1.00, $1.05, $1.10 & $1.15 would result in a breakeven price of $1.005 (1 tick) for the single position vs. $1.08 (16 ticks) for the 4 positions.




yeah but at the point the breakeven level becomes 1.08 , the stock is already at $1.15, and if the stock never reaches 1.15 then the breakeven level never reaches 1.08......

spookily enough i am just in middle of rereading "Reminiscences of a stock operator" after some years. page 127 he describes how this exact scaling in model is the basis for his trading. plus ca change...


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## skyQuake (4 September 2010)

village idiot said:


> yeah but at the point the breakeven level becomes 1.08 , the stock is already at $1.15, and if the stock never reaches 1.15 then the breakeven level never reaches 1.08......
> 
> spookily enough i am just in middle of rereading "Reminiscences of a stock operator" after some years. page 127 he describes how this exact scaling in model is the basis for his trading. plus ca change...




Agree, 

If you're trading seriously, brokerage on 5 trades should be similar to brokerage on a large order.

What also needs to be noted is that if you bought 20k shares at $1, it could be fairly very hard to get out at $0.95

Whereas an average entry of 1.08 is a lot easier to manage when the price is already 1.15

If intraday, also pays to look at daily range before averaging up (or down)


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## lindsayf (5 September 2010)

Naked shorts said:


> I have found that adjusting my position sizing relative to my confidence in the trade, to be optimal. Discretion in position sizing is an edge in itself, but is extreamly difficult to master and takes hundreds, if not thousands of hours to get right
> 
> "You got to know when to hold 'em, know when to fold 'em, / Know when to walk away and know when to run"




Hi Naked

Im curious to understand why you would enter a trade you had little confidence in?  If you can make the distinction between low and high probability setups - why not just wait for the latter?

thanks

Lindsay


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## tech/a (5 September 2010)

lindsayf said:


> Hi Naked
> 
> Im curious to understand why you would enter a trade you had little confidence in?  If you can make the distinction between low and high probability setups - why not just wait for the latter?
> 
> ...




Somtimes a trade may evolve into an above average 
situation by say breaking decisively through an important resistance level


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## lindsayf (5 September 2010)

Hi techa
I understand that any 'marginal' setup could take off and there is no way to know in advance for sure.  To know if entering  these marginal/maybe trades with a small position and then scaling in has  an edge over a series of trades  you would have to backtest/forward test them.  So this is a seperate trading method to the other one  -  the 'non marginal setup'.  If this is right then Naked is saying she trades seperate methods - one with full position size and trade managment style 'A' and one with partial position sizing with scaling in and trade management 'B'.  If this is the case then it makes sense to me.

I gather that you use or are interested in a scaling in approach - it is something I have not looked into - scares me a bit - which tells me I need to learn more about it.


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## tech/a (7 September 2010)

> I gather that you use or are interested in a scaling in approach - it is something I have not looked into - scares me a bit - which tells me I need to learn more about it.




No I dont.

But I do trade full positions and if the market moves immediately and decisively in my direction I often double or more position size.
I' have scaled out! But again prefer to exit the whole position.
Im either in or out.


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## LimitBid100 (10 September 2010)

AlterEgo said:


> Ok, so if I read this sentence correctly, you're saying it produces a smoother equity curve, but less total profit?




AlterEgo,

The sentence may have not been entirely clear. What I meant was, that by reducing the maximum profit available on an individual trade, (and equally, reducing the maximum loss on an individual trade), I can generate a smoother equity curve.

Once I have a smoother equity curve, this allowd me to increase the size of all trades until I reach a level of equity curve volatility I am happy with. (Actcually, I only care about the downside volatility of the equity curve.....but that is going into technicalities).

So, profit (and more importantly, loss) may be curtailed in indiviual trades.....however this leads to a smoother equity curve, allowing for the use of more leverage, and thus greater over profits (for a similar level of risk tolerance).

Essentially, while the profit is reduced by pyramiding into trades, the ratio of "average profit/average loss" for a set of trades is increased....this is done primarily by reducing the size of the average loss.

I hope this clears up any confusion.....

LimitBid.


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## LimitBid100 (10 September 2010)

tech/a said:


> No I dont.
> 
> But I do trade full positions and if the market moves immediately and decisively in my direction I often double or more position size.
> I' have scaled out! But again prefer to exit the whole position.
> Im either in or out.




You say you are either "in or out"......surely this implies that you dont scale into positions.....as then you would be (at some stage) only partially in.

But then you say that if the markets moves your way, you double the position.....isnt this scaling in???

So do you scale into positions, or dont you?  I am confused........

LimitBid.


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## tech/a (10 September 2010)

> So do you scale into positions, or dont you? I am confused........





Sorry to hear that.

If I have a common position size of say 5 contracts and I trade 1 contract then add 2 then another 2 then thats scaling in to a full position size.

If However I have 5 contracts on a trade and I see an opportunity to add to that then thats (to me anyway) adding to a position.

Like if I feel like a Mars Bar and as Im eating it I just have to have another couple.
Different to buying a 1/3rd and adding to it.

So to help your confusion.
NO I DONT SCALE IN TO POSITIONS.


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## Gringotts Bank (3 March 2013)

Say I have a win rate of 80+% on a very basic system.  Small profitstop of 1% and wide stoploss of 5%.  Max consecutive losers is 2 on any bluechip tested.  Max consecutive winners of around 10.  The equity curve is basically flat for most securities, but can be optimized to slope upwards.

I wonder how this would go with a Martingale.  

Recovering 5% each loss is going to make for a huge position size after 2 losers.  I guess one could start small.

Any ideas?


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## tech/a (4 March 2013)

Gringotts Bank said:


> Say I have a win rate of 80+% on a very basic system.  Small profitstop of 1% and wide stoploss of 5%.  Max consecutive losers is 2 on any bluechip tested.  Max consecutive winners of around 10.  The equity curve is basically flat for most securities, but can be optimized to slope upwards.
> 
> I wonder how this would go with a Martingale.
> 
> ...




Personally I'd play around with the win rate 
I'd want to increase the profit stop while decreasing the stop loss
The objective is to decrease the gap when you have consecutive losers.

If you ever got 3 or 4 consecutive losers you'd need very deep pockets and may never get back.
Just my take.


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## howardbandy (4 March 2013)

HI GB --

I discuss the importance of using the entire distribution of trade results to answer questions such as you are asking in my book "Modeling Trading System Performance."  

In short summary:
1.  Final equity or terminal wealth, TW, of a set of trades can be computed as the geometric return per trade, G, raised to the power of the number of trades, N.  TW = G ^ N.  You must have a positive G -- a positive expectancy.  You want a large N.
2.  While the final equity of a set of trades is always the same without regard to the sequence in which they occur, the drawdown is very sequence dependent.  
3.  The reason most traders stop trading a system is that the drawdown exceeds their personal risk tolerance.
4.  Drawdown is determined primarily by the number and size of losing trades.
5.  Position size is independent of the logic of the trading system, including being independent of the exit methods, including whatever profit target and maximum loss exits are included in the system logic.  Position size depends on the relationship between the health of the system (the synchronization between the logic and the data over time) and the trader's personal risk tolerance.  

Given a list of trades (which can be any combination of real trades, paper, out-of-sample, in-sample, or hypothetical), you can determine the risk of drawdown, then maximum safe position size, then profit potential, using the techniques I describe.  

You need the list of trades, or a probability density function of the distribution that represents those trades, in order to do the analysis.  Knowing only the expectancy, or the mean and standard deviation, or even the first four moments (mean, standard deviation, skewness, and kurtosis) is insufficient.

Best regards,
Howard


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## Gringotts Bank (4 March 2013)

Thanks tech and howard.

Howard, I followed along until those last 2 paragraphs.  If possible, could you explain in more basic language?  Thanks.


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## howardbandy (4 March 2013)

Hi GB --

It took a large part of the book to explain the background, the concepts, and the techniques.  See if some of the articles on my blog site help:
http://www.blueowlpress.com/WordPress/

There are a couple of chapters of the book that give an introduction on the book's website:
http://www.modelingtradingsystemperformance.com/book.html
but the meat is in the chapters that are not posted.

Regards,
Howard


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## Gringotts Bank (4 March 2013)

howardbandy said:


> Hi GB --
> 
> It took a large part of the book to explain the background, the concepts, and the techniques.  See if some of the articles on my blog site help:
> http://www.blueowlpress.com/WordPress/
> ...




Thanks, will do.


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