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#467130 - 07/17/17 17:42 Square Root Rule & Additional Investment
DdlV Offline
Serious User

Registered: 06/10/13
Posts: 1293
Hi all. Looking to expand my understanding... laugh

The manual contains a description of the Square Root Rule for withdrawing and/or reinvesting: http://zorro-trader.com/manual/en/kelly.htm.

Once before in the Forum the question of adding additional funds to one's account came up, and the response was to simply treat this as a negative Withdrawal (W in the manual's formulas). (Unfortunately, can't now seem to find that thread/post... frown )

The question now in my mind is whether or not that's correct. Treating new investment funds as a negative Withdrawal has the effect of immediately subjecting them to the Square Root Rule, so that the mere action of depositing new funds makes a portion unavailable for withdrawal, which doesn't make sense to me.

For example, if I'd instead opened a new account with those new funds, wouldn't they have their own life and their own Square Root Rule progression?

So, bottom line: If new funds are added, whether to the same or a different account, doesn't each investment have its own independent timeline, Square Root Rule calculations, etc.?

Thanks.

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#467271 - 07/24/17 14:47 Re: Square Root Rule & Additional Investment [Re: DdlV]
DdlV Offline
Serious User

Registered: 06/10/13
Posts: 1293
Anyone can help clarify? jcl? laugh

Thanks.

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#467295 - 07/25/17 10:55 Re: Square Root Rule & Additional Investment [Re: DdlV]
jcl Online

Chief Engineer

Registered: 07/22/00
Posts: 25939
Loc: Frankfurt
I think you're right. Adding funds is independent of trading time and thus they are not subject to the square root rule.

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#467401 - 07/31/17 21:29 Re: Square Root Rule & Additional Investment [Re: jcl]
DdlV Offline
Serious User

Registered: 06/10/13
Posts: 1293
Thanks jcl.

Then would the correct process be:

1) From the add point forward, results (cumulative gain or loss) should be split pro-rata between the pre-existing investment(s) and the added funds.
2) Pro-rata results of the pre-existing funds would be subject to the same pre-existing square root rule.
3) Pro-rata results of the added funds would be subject to a new square root rule that starts at the time of the addition.

Is that correct?

Thanks.

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#467408 - 08/01/17 11:49 Re: Square Root Rule & Additional Investment [Re: DdlV]
jcl Online

Chief Engineer

Registered: 07/22/00
Posts: 25939
Loc: Frankfurt
Correct. The profit generated from your newly added funds are again subject to the square root rule.

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#467415 - 08/01/17 16:58 Re: Square Root Rule & Additional Investment [Re: jcl]
DdlV Offline
Serious User

Registered: 06/10/13
Posts: 1293
Thanks!

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#467416 - 08/01/17 18:07 Re: Square Root Rule & Additional Investment [Re: DdlV]
MatPed Offline
Senior Member

Registered: 02/28/15
Posts: 379
Loc: Milano, Italy
Interesting, wonder how to adapt the original spreadsheet. It was useful. Another item in the to-do list...

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#467574 - 08/14/17 05:22 Re: Square Root Rule & Additional Investment [Re: MatPed]
DdlV Offline
Serious User

Registered: 06/10/13
Posts: 1293
Hi jcl, MatPed,

I thought more about this over the weekend, and my thoughts have shifted as follows:

a) While from the time point of view different capital fundings are different, in fact Balance is being used as a proxy for time & number of trades, and so time is absent from the formulas. If Balance is then pro-rata'd over the fundings, and Withdrawals as well, then the square root formula gives the same f factor for all capital fundings, regardless of when they were done!

b) One could drop down from the account level to the individual trades, since at the time of an additional capital funding it has obviously no trades and until a new one is opened all Profits apply to the old funding's trades. This would, however, be a lot of extra work for probably not really much benefit. Especially since over some likely relatively short time all the old trades would be closed, at which point everything is pro-rata again.

What should really be done when multiple fundings are involved? How should time be incorporated?

Put another way in terms of the manual's example:

Capital of $1000 has grown to $1300 account balance. The investment grew by factor 1.3; the square root of 1.3 is 1.14. Therefore $1140 must stay and $160 can be withdrawn.

But what if the $1000 came from $500 invested 9 years ago and $500 invested last year? How does this change things? Should 90% of the $300 Profit be allocated to the 1st $500? Or...?

Thanks.

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#467575 - 08/14/17 10:01 Re: Square Root Rule & Additional Investment [Re: DdlV]
MatPed Offline
Senior Member

Registered: 02/28/15
Posts: 379
Loc: Milano, Italy
Just an idea but adding a capital to a running system, looks like to start a new system from zero.
Following your example is like you start a TS 9 years ago with 500 and another one one year ago. So the square root, and the other relevant parameters, may be calculated just adding the values of the two systems.
I have not the capabilities to prove it mathematically but it make sense to me: if the square root rule is correct for 2 user starting 2 TS independently one 9 years ago and one last year, should be correct for the sum of them...

ciao

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#467581 - 08/14/17 14:55 Re: Square Root Rule & Additional Investment [Re: MatPed]
DdlV Offline
Serious User

Registered: 06/10/13
Posts: 1293
Thanks MatPed. I'm in the same boat - lacking the framework/understanding/statistics skills to answer this... frown

According to the manual, the real statistical issue under the Balance proxy covers is time/number of trades. Therefore it seems to me that the $500 that's been trading for 9 years will have a higher risk of larger drawdown than the $500 that's only been trading for 1 year. Therefore, it seems I would need to leave more $$$ in the account to protect the older $500 than the newer $500. From the withdrawal perspective, I can't withdraw as much for the older $500 as the newer.

Now what does this really mean? Some possibilities are:

- $300 is the right withdrawal amount, $150 to each $500, and the underlying statistics just works out fine, somehow. laugh

- $300 is the right withdrawal amount, spread in some way between the 2 $500's based on time or ???

- Less than $300 (how much?) is the right withdrawal amount due to the increased drawdown risk of the older $500.

- Other???

Hopefully jcl can clarify.

Thanks!

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