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Risk of Ruin


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Risk of Ruin

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  #31 (permalink)
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Nasdin94 View Post
In short, keep your drawdown low.

The higher your drawdown, the more difficult it is for you to recover.
It is an exponential curve.

Very true but the statement is entirely qualitative. So it doesn't give me any quantitative statement what my risk of ruin is.
But as I have said before, I have no optimal solution to that problem either, so I am certainly not entitled to complain about statements that need not to be argued upon as they are obviously correct!

vvhg

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  #32 (permalink)
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I am not an expert on risk of ruin, but I will try to formulate some basic ideas. Be aware please that I am not insisting that the following statements are entirely correct.


Calculating the Risk of Ruin Requires A Few Assumptions


(1) I assume fixed fractional betting, that is for every bet (trade) I am betting the same fixed percentage of my account.

(2) Definition of ruin: Ruin is achieved, when you cannot trade anymore. Ruin therefore depends on the initial account size and the maximum acceptable drawdown.

(3) Target: If you want to quadruple your account, the risk of ruin is higher than if you just intend to double your account, as you stay in the game for a longer time.

(4) Bet size: The bet size has the largest impact on the risk of ruin. I will express the betsize as a multiple of optimal f, which is the optiomal bet size derived from the Kelly criterion.


Example: Betting full Kelly with a target of quadrupling the account

Initial bank roll 100,000
Ruin : a = 0.25 (when the account has dropped to 25,000)
Success: b = 4 (when the account has reached 400,000)
Kelly Factor: k = 1 (known as full Kelly betting)

You can then calculate the probability that you reach the target size of the account prior to ruin. This probability only depends from a, b and k, but not from the expecation or the standard deviations of the bets.

The formula is

In the above case we would get P(0.25,4,1) = 80%.

The risk of ruin is the complementary probability and would accordingly show as 20%. This shows that betting full Kelly is quite risky.


Betting Half-Kelly

If you bet half Kelly, but leave the other parameters unchanged, you will get

P(0.25, 4, 0.5) = 98.5 %

The risk of ruin drops to 1.5 % (half Kelly) compared to 20% (full Kelly)!

This may explain why many professional gamblers rather bet half-Kelly than full-Kelly.


Tip
Provided you use a fixed fractional betting system and adjust your bet size according to the Kelly Formula, the risk of ruin does not depend on the expectancy, as the Kelly criterion already adjusts the bet size to match expectancy. The risk of ruin only depends on a, b and k, where

a: fraction of initial account size considered as ruin
b: multiple of initial account size used as target
k: Kelly factor describing the bet size in terms of optimal f


@ThatManFromTexas:

I am counting on you to check the formula.

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  #33 (permalink)
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Fat Tails View Post
@ThatManFromTexas:

I am counting on you to check the formula.

@Fat Tails

The ability to do math decreases exponentially inversely proportionally to an increase in aging .... it's gotten so bad... I don't even ask the strippers for change back... anymore....

I'm just a simple man trading a simple plan.

My daddy always said, "Every day above ground is a good day!"
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  #34 (permalink)
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The strippers should be to do the math in their head for your change. I mean they ARE "going to college" AHHH aren't they?? LMAO

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  #35 (permalink)
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Fat Tails View Post
(4) Bet size: The bet size has the largest impact on the risk of ruin. I will express the betsize as a multiple of optimal f, which is the optiomal bet size derived from the Kelly criterion.

Please help me understand where the bet size is determined in this example. Can you list an actual trade example (ie: entry, stop, target measured in terms of % risk or Kelly bet size)?

Thanks so much for contributing.

Mike

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  #36 (permalink)
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Fat Tails View Post
The formula is P(a,b.k) = ( 1 a 1-2/k) / (b 1-2/k a 1-2/k)

In the above case we would get P(0.25,4,1) = 80%.

The risk of ruin is the complementary probability and would accordingly show as 20%. This shows that betting full Kelly is quite risky.


Betting Half-Kelly

If you bet half Kelly, but leave the other parameters unchanged, you will get

P(0.25, 4, 0.5) = 98.5 %

The risk of ruin drops to 1.5 % (half Kelly) compared to 20% (full Kelly)!

This may explain why many professional gamblers rather bet half-Kelly than full-Kelly.

@ThatManFromTexas:

I am counting on you to check the formula.


As @ThatManFromTexas is aging exponentially (as he stated) I quickly ran a few calculations.
I believe you missed a few brackets, so the formula should read:
P(a,b.k) = ( 1 a (1-2/k)) / (b (1-2/k ) a (1-2/k))
Please correct me if I'm wrong!

An other strange thing i noticed is that if you bet very small like k/100 or so, the formula states a very high risk of ruin and although it would take long to reach b, I doubt that high a risk of ruin. I got P(0.25,4,0.01)=0.0653

Vvhg

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  #37 (permalink)
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vvhg View Post
As @ThatManFromTexas is aging exponentially (as he stated) I quickly ran a few calculations.
I believe you missed a few brackets, so the formula should read:
P(a,b.k) = ( 1 a (1-2/k)) / (b (1-2/k ) a (1-2/k))
Please correct me if I'm wrong!

An other strange thing i noticed is that if you bet very small like k/100 or so, the formula states a very high risk of ruin and although it would take long to reach b, I doubt that high a risk of ruin. I got P(0.25,4,0.01)=0.0653

Vvhg

@vvhg: Thank you for pointing this out. I did not omit any brackets, but had a problem with the editor of the forum software. It is not a WYSIWYG editor, everything was shown correctly until I saved it...

I have now replaced the formula with a picture file to avoid further confusion. Here it is:


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  #38 (permalink)
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Big Mike View Post
Please help me understand where the bet size is determined in this example. Can you list an actual trade example (ie: entry, stop, target measured in terms of % risk or Kelly bet size)?

Thanks so much for contributing.

Mike

I will respond to this question and produce an example, which shows how to calculate the risk of ruin for a series of trades.

But before doing this, I want to come back to the definition of risk of ruin.

Let us assume that you start with a bank roll of $ 100,000.
Ruin: The account drops to less than $ 25,000 (preventing you from placing anymore intraday trades)
Target: You have quadrupled your account to $ 400,000.


Definition of Risk of Ruin


You cannot calculate the Risk of Ruin, without defining ruin and setting a target to achieve. Once this is defined, you can calculate the probability that you will experience a drawdown to ruin (account value of less than $ 25,000) prior to having achieved your target of $ 400,000. This probability is the Risk of Ruin.


Probability of Success of Your Trading Concept

This really like creating a small enterprise. You have a concept and an edge, which translates into a positive expectancy for your trades.

Step 1: Fix the size of your initial account, your pain threshold (where you stop trading), and your target.

Step 2: Calculate the Kelly bet size from your expectancy by using the concept of opimal f. Make sure to include commissions and other trading cost, when calculating the expectancy

Step 3: Adjust the Kelly bet size according to your risk appetite. Can you live with a risk of ruin of 20%? Then you are a full-Kelly trader. Do you tolerate something like a risk of ruin of 2%? Then you are a half-Kelly trader.

The theoretical probability that the endeavour succeeds is 98% for a risk of ruin of 2%. But is this realistic?


Be aware that not all risk is accounted for

Whether this approach is practical, can be debated. There is more risk involved than can be calculated via a Kelly formula. Your computer or the exchange may burn. Your edge may have prove to be a temporary edge at best, which is later annihilated by a change in the way markets operate. You may suffer from mental or physical illness, etc.

The calculated risk of ruin, should therefore be considered as minimum risk you are willing to accept. Nevertheless this approach allows to find an appropriate bet size in line with risk appetite.

Compounding returns is the single most important criterion, provided that there is an edge and that the psychological implications of being a trader have been mastered.

I will come back with a specific example for trading YM with that account of $ 100,000.

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  #39 (permalink)
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Fat Tails, really good stuff.

Probably obvious, but think we should put it on paper. This all depends on independence of trades as Kelly does.

As I read it, the formula won't work for all possibilities. For (a stupid) example, wins 100 times losses, 90% win rate. You get an optimal f of 89.9%. Let a = 0.9, b = 1.1. Formula gives a 55% risk of ruin for optimal F, when anyone can tell you it should be 10% (as it would be for half kelly). I know this is a silly example, I just want to make sure I'm following correctly.

Secondly, I have written a small program to run account simulations. There are probably much better about, but I at least know what my code (supposedly) does. I'm really suspicious of the RNG funtion I'm using (I'm also very rusty), so don't trust it, maybe it will provide a base for someone to improve on. Plugged in some values of a system I have, namely:

p=82%
odds=0.5 (wins half the size of losses)

This gives us a Kelly of 46%.

Using a=0.25 and b=4, I got at 12.1% risk of ruin for full Kelly, and a 0.3% risk of ruin for half Kelly. This seems a bit out compared to your formula, but again, the RNG may be dodgy. It's probably my code, I'm sure I didn't have problems with RNGs before.

P.S. I know the coding is awful.
P.P.S. I have a terrible feeling I'm going to look a complete fool in a few short hours

Dovie'andi se tovya sagain.
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  #40 (permalink)
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Great stuffs guys.

I am becoming more and more convinced each day, the true edge in trading is not about finding the right indicators or even the best setups but in managing probability and R/R.

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