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Square root rule #475582
12/26/18 21:51
12/26/18 21:51
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HamSelv Offline OP
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Hi laugh

I have read about the square root rule in the Black Book and also in the forum. It makes good sense to me to protect the account from future unknown draw downs with this rule. There is one thing that confuses me a bit. I'm not an expert in statistics so please bear with me:

Let's say I'm trading a Z-system and I want to reinvest all the profits. My starting account is $1000 and I make $200 in profit. According to the square root rule I cannot reinvest the whole $200. I have to reinvest less. Fair enough.

If I stopped trading the system then that would give me $1000 + $200 = $1200 in total in my account. What if I then started trading the same Z-system right away. Then my starting amount would be $1200 meaning I have suddenly reinvested the whole $200 in profits. What am I missing here?

Thanks!

Regards

Last edited by HamSelv; 12/26/18 22:06.
Re: Square root rule [Re: HamSelv] #475584
12/26/18 22:59
12/26/18 22:59
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AndrewAMD Offline
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Many (if not most) trading systems have an expiration date.

By the time you have acquired your hard-earned $200, how much time has passed? 1 week? month? year? You will need to re-evaluate and fine-tune your system. Then, and only then, can you consider re-adjusting your capital after making a profit.

By the way, if you turn off the system after gaining 200, and then turn it on with the capital set at 1200, you are deliberately disobeying the rule! laugh

Re: Square root rule [Re: AndrewAMD] #475586
12/27/18 00:10
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HamSelv Offline OP
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Hi Andrew. Thanks for replying. I get your point about re-evaluating and fine-tuning. For a start I'm going to trade a Z-system so I assume it is already re-evaluated and fine-tuned laugh My understanding is that for a Z-system at any given time I can increase the capital after getting profits (according to the square root rule).

What rules am I deliberately disobeying please? Let me try to be more clear:

I stop trading a Z-system after earning $200 in profits so now I'm $1200 in total. Straight away I start to trade the same system all over again with $1200. So starting to trade the system again corresponds to trading the system for the very first time with $1200 start capital. Now I have re-invested all the profits and I don't have to use the square root rule. Does it make sense, I mean is my example clear?

Thanks.

Regards

Last edited by HamSelv; 12/27/18 00:14.
Re: Square root rule [Re: HamSelv] #475590
12/27/18 09:48
12/27/18 09:48
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I think your misunderstanding comes from not considering your MM rule at the begging. For example, the Z strategies chapter suggests:

"For avoiding margin calls, we recommend to set Capital not higher than about 80% of the account equity."

So, if you want to start trading with Capital Slider = $1000, your account's equity (or balance) should be $1250.

Re: Square root rule [Re: HamSelv] #475593
12/27/18 13:21
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MatPed Offline
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Originally Posted By: HamSelv
Hi laugh

I have read about the square root rule in the Black Book and also in the forum. It makes good sense to me to protect the account from future unknown draw downs with this rule. There is one thing that confuses me a bit. I'm not an expert in statistics so please bear with me:

Let's say I'm trading a Z-system and I want to reinvest all the profits. My starting account is $1000 and I make $200 in profit. According to the square root rule I cannot reinvest the whole $200. I have to reinvest less. Fair enough.

If I stopped trading the system then that would give me $1000 + $200 = $1200 in total in my account. What if I then started trading the same Z-system right away. Then my starting amount would be $1200 meaning I have suddenly reinvested the whole $200 in profits. What am I missing here?

Thanks!

Regards


You are right not missing anything. Starting with 1200 you are not using the sr rule. The sr rule gives you a statistically protection in long run AND for a winning TS, that you will not face a Margin call reinvesting your profit. The key words are "long run", "winning TS" and " "reinvesting your profit".

Re: Square root rule [Re: MatPed] #475595
12/27/18 15:46
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HamSelv Offline OP
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Hi people.

Thanks for your feedback. Hmm good point kvm even though the 80% is only mentioned for the Z8 system, so I guess it only applies for the Z8 system. For the rest of the Z-systems you need to look in the log files.

(MatPed) Ok, let me try to explain again with another example:

Person A starts trading $1000 using a Z-system. After getting $200 in profits he closes all his trades and removes Zorro from his computer. Now he has $1200 in his broker account.

Person B has never traded before. He gets a $1200 gift from his aunt and wants to trade it all.

Person A and person B now have $1200 each. They now both, at the same time, install Zorro on their computers and start trading the $1200 they each got. The system they trade is the same Z-system as person A traded when getting $200 in profits.

Person A and person B now both have the exact same starting point. Person A has re-invested all his old profits without using the square root rule. Using the square root rule wouldn't make any sense as he is starting all over again and hasn't made any profit (yet). So why should person A not re-invest the $200 in profits right away in the first place?

Maybe jcl would also like to comment?

Thanks! laugh

Regards

Last edited by HamSelv; 12/27/18 15:49.
Re: Square root rule [Re: HamSelv] #475596
12/27/18 16:03
12/27/18 16:03
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you forgot the elapsed time in your example. How much was the elapsed trading time of Person A? One month, or 5 years? the sr rule "protect" your account in the 5 years situation. I had a similar conversation months ago.
The main point is the time, because the probability of a larger draw-down increases with time. So longer time=higher risk.
If the person A of your example is trading from one week, has almost the same risk of person B.

HtH

Re: Square root rule [Re: MatPed] #475597
12/27/18 16:18
12/27/18 16:18
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HamSelv Offline OP
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In my example the $200 profits was made without re-investing any profits. It was made from the starting amount of $1000 and the Capital slider was never touched. So I'm trying to understand why to use the square root rule when I can work-around it using person A from my recent example. Does it make sense?

Regards

Re: Square root rule [Re: HamSelv] #475599
12/27/18 16:40
12/27/18 16:40
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It's with the square root rule as with all such rules: Don't merely follow it, but try to understand it. Statistics can be a bit counterintuitive, but I hope it's intuitively clear that just stopping and restarting your system is irrelevant for reinvesting.

So, I fear your person A will not keep her hard earned money, regardless of how often she stops and starts. Here's the formula to calculate how long the money will last, under "money management":

https://www.financial-hacker.com/build-better-strategies-part-3-the-development-process/

The square root rule is also explained in the black book and in short also in workshop 6.


Re: Square root rule [Re: jcl] #475603
12/27/18 19:11
12/27/18 19:11
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Hi all. OK, I'll take another stab at the square root rule and hope to learn more from the further comments of jcl and others.

As I understand it, the 2 critical things to understand are:

- Initial Capital: The wealth that was originally invested, not whatever it's grown to. Not trading system stops & restarts. Not changing the trading system. Not closing the account and opening another with the same funds. Etc. None of these things change the Initial Capital.

- Trading Time: Drawdown risk and magnitude grow as trading time accumulates. Account Balance is used as a convenient proxy for this in the square root formula.

In the simple case of a single trader trading in 1 account, just apply the formula. Don't try to get around it.

The more interesting cases involve more traders, etc.:

1) Person A gifts the $1200 to Person C. Does Person C trade using $1000 or $1200 as their square root rule starting point? I.e., does the square root rule tie to the Initial Capital traded ($1000) or to the person who's never traded before ($1200)?

2) Person B may never have traded before, but has the $1200 gift come from trading? If so, same question: What's the starting point?!

3) Person B's aunt traded to get the $1200. But she stopped trading decades ago and the $1200 came to Person B as an inheritance. Has so much time now passed that Person B can safely use the full $1200 as the square root rule's Initial Capital?

4) Or, what if Person B doesn't know the source of the $1200? What should Person B then use as Initial Capital?!

Look forward to comments.

Thanks.

Re: Square root rule [Re: DdlV] #475609
12/28/18 09:12
12/28/18 09:12
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Don't forget this case:

5) Person A blackmails person B's aunt for her $1200 trading returns, but is robbed by person C's nephew and loses $1000. Should person A invest the remaining $200 in Z9 or better in Z3, the square root of Z9?

Re: Square root rule [Re: DdlV] #475612
12/28/18 10:30
12/28/18 10:30
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Lovely test!
1) 1200
2) 1200
3) (trading capital of person B) + (square root of profit) + 1200. The situation is similar to fund with extra money your trading. Its not reinvesting
4) as point 3)
5) totally lost...

Last edited by MatPed; 12/28/18 10:30.
Re: Square root rule [Re: MatPed] #475618
12/28/18 17:04
12/28/18 17:04
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Thanks for the bit of humor, jcl! laugh

But in the interest of any who read this thread later, I think it'd be good for you to explicitly state if the square root rule's trading time follows the Initial Capital, or each individual trader.

I.e., can one get around the square root rule by moving the funds/account around amongst relatives, friends, etc.? Or no matter how many traders/friends/relatives are involved the total trading time of the Initial Capital is what matters?

And in the case where Initial Capital isn't known, be very conservative!?

Thanks.

P.S. - @MatPed, or is it:

1) $1000
2) $1000
3) ?
4) ?

For example, if the $1200 came from, say, wages, then it's clearly the starting point. But if it came from any trading at all, is it "encumbered" with "baggage" and a smaller value must be used for Initial Capital?!

Re: Square root rule [Re: DdlV] #475619
12/28/18 18:13
12/28/18 18:13
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Ddlv,
we had already a similar discussion, I can not add much from what I already said. I do not understand why you make the SR rule so complicated, its easy.

1) You have a starting capital calculated from the needed capital for a TS
2) If you profit you should reinvest accordingly with SR rule.
3) If you add capital is like to start a separate TS so you do not need to reinvest using the SR rule.

Where you get the money to start trading is not relevant because you are at starting point.
You can have a margin call with your first trade if you are very unlucky. At the same time you can double your capital with the first trade using a fraction of the estimated needed capital, if you lucky.
If you survive in the market and you are profitable reinvest using the SR rule.

If you do not like my approach, use the most conservative condition you are confident with. You will be on the safe-side, maybe scarifying some profit, but in the long run it will not create much problem.

Ciao

Re: Square root rule [Re: MatPed] #475622
12/29/18 07:12
12/29/18 07:12
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Hi MatPed. If you're telling me I have a think head, you're in good company! laugh

Just trying to understand...

What you've described is that the square root rule's Initial Capital is per trader.

So, an even simpler example:

Uncle J has been investing for decades and has grown his $1000 to $50000.

For Uncle J to safely continue investing, he should reinvest per the square root rule, and move his Margin slider accordingly.

But, lamentably, Uncle J passes away. As his sole heir, the $50000 becomes yours. And you can therefore begin investing it as the whole $50000 without regard to any history or square root rule, correct?

In fact, you can just have the name on the existing account changed to yours and run that Margin slider right up, waving at the square root rule as you go by, correct?

All just because the trader's name changed, correct?

Thanks.

Re: Square root rule [Re: DdlV] #475623
12/29/18 09:24
12/29/18 09:24
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MatPed Offline
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hI DdlV I du not fully understand your first sentence anyway, I do not understand the distinction between the SR rule for Trader or for trading system.
This is what I do, without thinking too much, I guess...
I test the TS A and the results is that the required capital is 1.000€. i start the TS with 1.000€. The profit of the TS A will be reinvested accordingly with SR rule.

Then I test the TS B and the required capital is 1500€ I start the TS B with 1500€
The profit of the TS B will be reinvested accordingly with SR rule.

I treat the two TS as totally separated, I do not make any other consideration: one TS, one Capital required, one SR rule calculation for each of them.

Easy and simple. Ciao

Re: Square root rule [Re: MatPed] #475627
12/29/18 19:47
12/29/18 19:47
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MatPed,c'mon:-)
Quote:
Then I test the TS B and the required capital is 1500€ I start the TS B with 1500€
The profit of the TS B will be reinvested accordingly with SR rule.
Change this to :
Quote:
"Then I re-test TS B (which my uncle followed) and the required capital from the backtest is still 1000 ( because a bigger maxDD was still not hit). You have 50K accumulated in that account for over 3yrs,now under your name.
What do you use as base capital for TS B in your new account? And why/what are the calcs?

"SR rule" is quite a rough one. You will understand this once you try to re-create the specific calculations behind it.

The paper referenced by jcl states that the risk of a system ( a continuing sequence of bets) increases with time (regardless if smbdy actually trades it or not).

IMHO, Z systems should be implementing a corresponding "dampening" factor on trade size according to the continuously accumulating statistics - under the hood.

This would practically mean that if you start trading with 10K one year ago and today - the system would use different base trade sizes.

Last edited by Zheka; 12/29/18 19:49.
Re: Square root rule [Re: Zheka] #475629
12/29/18 20:32
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Hi Zheka, English is not my mother language and sometime I can not get the subtle meanings of some post. Trust me or not, but it is as it is.
I agree with you: "SR rule" is quite a rough one. This is why I do not invest too much time in evaluating several subtle situations. My idea is that I should stop a trade system way before a margin call thanks to tools like CBI or Equity trading. I use the SR rule only to be sure I am not reinvesting too much. If I stop a system and restart it after 2 months I consider it as a brand new one. Right or wrong is how I use the SR rule. But you can cut the reinvest profit by 10 (just an example) if you think that the standard rule is too much or do not reinvest at all and accumulate your profits...

Re: Square root rule [Re: MatPed] #475630
12/29/18 22:34
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Quote:
If I stop a system and restart it after 2 months I consider it as a brand new one. Right or wrong is how I use the SR rule.
In this case you do not really use it.

Without why and how such bare POV does not help us answer the question.

Re: Square root rule [Re: Zheka] #475631
12/29/18 23:11
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Well, I am using it, but you already answered to your point: "a continuing sequence of bets" if you stops for 1-2 months is not "continuing", so I treat it as a brand new start.
I have 1-2 more months of data. I have used that data for back-test and any "large dd" have been already taken into consideration and reflected in the initial capital.

Re: Square root rule [Re: MatPed] #475638
12/30/18 16:50
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Hi folks,
This question also puzzled me for a long time. I would like to share my understanding on this issue. I think some previous posts have already shed some light on this. Hopefully, my answer is more systematic and can make things more clear. Of course, any criticisms and suggestions are welcome.

My short answer is that there is no “absolutely correct” way to handle reinvestment ratio in order to fully maximize your gain without getting a margin call. The SR rule is more a subjective tradeoff choice rather than an objective rule.

First of all, SR rule is derived from a diffusion model. No model can really model financial markets or how a trading strategy exactly progresses in a financial market. SR rule is itself just one way to protect your account.

Secondly, we take a step back. Let’s just assume this diffusion model is a pretty accurate approximation on how a trading strategy will behave through time. Usually, we use max drawdown or maybe CBI index as a criterion to stop a trading strategy when experiencing drawdowns. If you use a higher reinvestment ratio (reinvest all profit generated so far, and thus higher trading lots), it is more likely your strategy will be expired given a usual expiring criterion (20% percent drawdown or 5% CBI index). If you use a lower reinvestment ratio and thus lower trading lots, you essentially give the strategy more chance and time for it to survive through current adverse market condition and work its way back into making profit again. So, the reinvestment ratio is the tradeoff between making more money when the market fits your strategy and the survivability when the market hits you hard given some drawdown related strategy expiring criterion.

Thirdly, if we think about the strategy development process, more things are subjective rather than objective. In strategy development process, whatever your approach is, backtesting is a step you can not omit. But the question is how long the history data you should use to backtest. Let’s say you want to develop a strategy that can not have more than 20% drawdown and you use 5 years of history. Once you have successfully developed such a strategy, you now set the trading size to the point where 20% drawdown is the maximum during the backtest. However, what if you test 1 more year back in history and you get a 30% drawdown, now should you use the previous initial trading size or modify the trading size corresponding to this new backtest result? If you do not get such drawdown in 1 more year, what about 2 more years back, or 5 more years back? Theoretically, your drawdown will increase given a fixed trading size when you backtest longer history, and thus your starting trading size will decrease when you go live. So, my point is that even the initial trading size (or required capital) is in fact subjective. Therefore, the SR rule based on the initial trading size will also be subjective.

Hopefully I am making some sense here. To answer the initial question, should one use SR rule after stopping a strategy and resuming it, or stopping and waiting some period of time then resuming it, it really depends on your knowledge and confidence on the particular strategy. However, if you don’t have enough information or confidence about a strategy, it is probably better to use SR rule to be safe if you know how much profit one strategy has already made. If you don’t know such information, you better test longer history to be on the safe side. After all, based on years of JCL’s experience on such matter, I assume his advice would be very valuable.

Re: Square root rule [Re: Seymour] #475643
12/31/18 11:09
12/31/18 11:09
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Valid arguments. The SR rule assumes a random distribution of wins and losses. This is normally a good model, but only a model, and real systems can deviate from it.

Even when the model is correct, we must deal with two facts that appear contradictory to the human mind. The longer you trade, the higher the probability for you to have encountered a bad drawdown at some point. But at any given day the chance of a bad drawdown is exactly the same as the day before. So the day we start a system has no special meaning. The bad drawdown can happen within the first week of trading with the same probability as in a week after 10 years trading the system. It only matters how long you traded, not when you started. Thats why the SR rule applies to trade profits, because for having them you must be already trading for some time during which you're exposed to the drawdown risk. In some situations the SR rule is not obvious:

You got two systems A and B. You invest $1000 in A. After a year, the account is at $2000. Now you stop A, go on a long round-the-world trip, then come back and start B. B has never been traded before. Do you invest the full $2000, or only $1440?

Your aunt has traded system A and has doubled her account to $2000 after a year. Now she gives you the $2000 and suggests that you use it for trading the same system. How much do you invest?

You know that your aunt has traded system A and has doubled her account to $2000 within a year. By chance you also have $2000 on your savings account. You now want to use it and start trading the same system. You have never traded before. Do you invest your $2000, or only $1440?

Re: Square root rule [Re: jcl] #487961
12/02/23 09:15
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Originally Posted by jcl
You got two systems A and B. You invest $1000 in A. After a year, the account is at $2000. Now you stop A, go on a long round-the-world trip, then come back and start B. B has never been traded before. Do you invest the full $2000, or only $1440?

Your aunt has traded system A and has doubled her account to $2000 after a year. Now she gives you the $2000 and suggests that you use it for trading the same system. How much do you invest?

You know that your aunt has traded system A and has doubled her account to $2000 within a year. By chance you also have $2000 on your savings account. You now want to use it and start trading the same system. You have never traded before. Do you invest your $2000, or only $1440?


I know this is an old thread but I would like to ask an additional question to your scenarios, in particular this one:
You got two systems A and B. You invest $1000 in A. After a year, the account is at $2000. Now you stop A, go on a long round-the-world trip, then come back and start B. B has never been traded before. Do you invest the full $2000, or only $1440?

Let's say I trade one of the Z-systems and then with a new release of Zorro, I update the .par and the .fac files. Am I now trading a "new" system? Is this a similar consideration like the above example?

Thank you!

Re: Square root rule [Re: HamSelv] #487984
12/13/23 16:08
12/13/23 16:08
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It is a similar consideration and it is not relevant whether it's a new or old system.

Re: Square root rule [Re: jcl] #488001
12/24/23 08:27
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Originally Posted by jcl
It is a similar consideration and it is not relevant whether it's a new or old system.


Thanks.

With regards to the whole model itself, the blog post https://financial-hacker.com/build-better-strategies-part-3-the-development-process/ it says that "On leveraged accounts with no limit to drawdowns, it can be shown from statistical considerations that the maximum drawdown depth Dmax grows proportional to the square root of time t".

--> Is there a source you can link to where this model/this statistical consideration is explained?

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