Kaufmann Risk of Ruin

[kut2k2]

Quote from DontMissTheBus:

No kidding. I made the same point all over that thread and in the earlier thread by intradaybill that led to this one.

Which "that thread" are you referring to? There are only 2 threads in question, which third thread are you hallucinating about?

Quote from DontMissTheBus:

This entire thread's discussion is based on intradaybill's somewhat outlandish, but clearly stated assumptions.

Wrong again, this entire thread is based on virtualmoney's OP, which is only tangentially related to Bill's confused proposition.

Quote from DontMissTheBus:

By the way, you've done nothing to show my proof was wrong (other than pointing out a trival typo) - you actually copy and pasted something from google that actually showed I was right.

The Gambler's Ruin formula PROVES that your absurd conclusion of certain ruination is wrong. The fact that you and Bill and other mathematically challenged types can't see this is utterly laughable.

Do your own homework and go find the flaw in your "proof." It's there. Your pathetic attempts to claim I only copy and paste and don't "understand" what I post are falling flat, only you're not smart enough to see that. Ignorance is bliss.

 

[DontMissTheBus]

You are right. I meant to say 'that' thread.

That's the only thing you are right about, of course; The rest of what you wrote qualifies as abject nonsense. But, I'd be an idiot to argue with you;

Good luck with life.

Quote from kut2k2:


Wrong again, this entire thread is based on virtualmoney's OP, which is only tangentially related to Bill's confused proposition.

 

[Lucrum]

Quote from DontMissTheBus:

That's the only thing you are right about, of course; The rest of what you wrote qualifies as abject nonsense....

kunt2 has a long history of that here at ET.

 

[kut2k2]

Quote from DontMissTheBus:

By the way, you've done nothing to show my proof was wrong (other than pointing out a trival typo) - you actually copy and pasted something from google that actually showed I was right.

Having suffered through your "proof", I will now show where you went off the rails and are to this day oblivious to your crash.

Here's your post:

Quote from DontMissTheBus:

No problemo:

First, some notations: each trade is a biased coin toss with probability of head being p_win and tail being p_lose; you win +$a if you flip head, and -$b if you flip tail.

Let's say at some point, you have NAV of $n and you consider the next $n/$b tosses; The probability of ruin is getting tail for exactly $n/$b tosses - which is of course p_lose^($n/$b).

Now let's consider we start with capital $n0. If after $n0/$b tosses, we are still in business and have capital $n1, then the probability of getting to the end of toss $n1/$b is:

(p_lose^($n0/$b))*(p_lose^($n1/$b))

Since $n0/$b is always positive, and p_lose > 0, then (p_lose^($n0/$b))*(p_lose^($n1/$b)) > (p_lose^($n0/$b)).

That is to say, your probability of survival gets smaller at each step of $x/$b tosses, where $x is whatever your NAV happens to be at the end of the previous step.

NOTE: this is key: p_lose^($n/$b) can NEVER be greater than one regardless of of the size of $n and $b because $n >0 (or you are ruined) and $b > 0 (remember, you lose -$b, so $b is the magnitude of the loss).

Then as we keep multiplying these together, this series converges of 0 as the number of multiplications converges to infinity because each successive probability is zero.

Thus, as the probability of survival goes to zero at infinity, probability of ruin (1 - probability of survival, goes to 1).

QED

OK let's look at the expectation, E = p_win*a - p_lose*b.

IF E is positive, then we can expect the player's "NAV" (that word doesn't mean what you think it means btw ) to increase on average.

IOW the risk of ruin as you intuitively measure it as p_lose^(NAV/b) will decrease as NAV increases, and NAV is certainly expected to increase in a positive-expectation trading system. So your conclusion that the risk of ruin approaches 1 makes no sense even on an intuitive level, much less on an exact level as demonstrated by proof of the Gambler's Ruin theorem.

 

[virtualmoney]

Quote from intradaybill:

The reason he does not understand this and many others like thim is because they confuse the probability of a sequence of losses, which is very small in some cases, with the probability of ruin.
If someone tosses a fair coin, wins $1 for heads and pays $1 for tails, starts with $10, the probability of 10 tails in a row is tiny, yet the probability of ruin is 100% if the game goes without stop because the probability of such sequence coming up in infinite time is 100%.
He does not understand that. Many do not.

Professional traders/gamblers who deal with real $ know that this is not the case because streak of losses or winners always have a tendency to cluster together. It is for this reason that progressions(e.g,martingales) will not only fail but happens frequently. Since ROR is current balance$ path dependent, it also becomes increasingly difficult for one just to recover to starting point balance$ once a streak/cluster of losses happens as I mentioned earlier in the thread.
The theoretical prob. of 10 tails in a row seems tiny but 10 trials is also a tiny sample size in 1000 trades/bets where 10 tails in a row is very possible such that the house always defends itself from cheating accusations with the law of large numbers.
For practical purpose, whether the prob. of ruin is 100% is not as important(since you mentioned it will happen) as the rate of it happening fastest which is tied in to the study of bet size adjustment, N,max no. of consecutive losses.i.e. Identify when to totally stop algo or slow down ROR rate by varying size or other methods.

 

[DontMissTheBus]

I once sat a roulette table for a few hours wasting some time before meeting buddies for drinks: there was this fella who sat there, betting on some magic number because it hasn't come up in awhile. So he keeps betting, keeps losing, keeps betting, keeps losing - all the while getting his wife to hand over wads of cash for more chips - and then... the number hits! He was overjoyed - and we were all happy for him - and so he continued betting on that number letting his winning streak run...

Financial prices, on the other hand, aren't as simple as roulette wheel - and trends cluster. But then, an ET trader doesn't even know how roulette wheel probabilities work and certainly can't distinguish the two - leading to idiocy such as what was posted below.

But what do I know - I just trade billions of dollars worth of fixed income security per day (don't worry, I probably made that up too - we all know there's no real traders on ET).

Quote from virtualmoney:

Professional traders/gamblers who deal with real $ know that this is not the case because streak of losses or winners always have a tendency to cluster together.

 

[virtualmoney]

Quote from DontMissTheBus:

I once sat a roulette table for a few hours wasting some time before meeting buddies for drinks: there was this fella who sat there, betting on some magic number because it hasn't come up in awhile. So he keeps betting, keeps losing, keeps betting, keeps losing - all the while getting his wife to hand over wads of cash for more chips - and then... the number hits! He was overjoyed - and we were all happy for him - and so he continued betting on that number letting his winning streak run...
Financial prices, on the other hand, aren't as simple as roulette wheel - and trends cluster. But then, an ET trader doesn't even know how roulette wheel probabilities work and certainly can't distinguish the two - leading to idiocy such as what was posted below.
But what do I know - I just trade billions of dollars worth of fixed income security per day (don't worry, I probably made that up too - we all know there's no real traders on ET).

Now we know where "billions of dollars" in the financial world has been misplaced.
You got Financial price trends,fixed roulette no. bet and system optimisation/evaluation all mixed up. Just like beer & other alcoholic drinks, they are not drunk mixed even they all contain alcohol.

 

[virtualmoney]

Consecutive losing or winning trades occur when trading systems designed to perform individually better in different market conditions(e.g, trending,ranging,breakouts) encounters one or the other, not to be confused with financial price trends in general.
The goal is to find optimal N to switch emphasis(halt or vary size) between 2 or more systems when some systems are doing better during certain periods & to smoothen the overall equity curve by reducing drawdowns.

 

[intradaybill]

Quote from kut2k2:

OK let's look at the expectation, E = p_win*a - p_lose*b.

IF E is positive, then we can expect the player's "NAV" (that word doesn't mean what you think it means btw ) to increase on average.

Hi lunatic. I know you have me on ignore. You avoid sanity checks.

Expectation can be positive you lunatic but depending on starting capital you can get ruined. Why doesn't that fit into your flat head?

You toss a bias coin with p= 0.6 you lunatic. The expectation for win = loss = $1 is:

E = 0.6 -0.4 = $0.2

Yet, if you have $2 in your pocket, the probability of ruin in the first two bets in 16% (0.4 x 0.4).

Yes you moron, in the longer term you will make N x $0.2, where N is the number of tosses.

But you may never get there depending on starting capital and bet size.

I wonder how much money you have lost gambling...

 

[kut2k2]

Quote from intradaybill:

Hi lunatic. I know you have me on ignore. You avoid sanity checks.

Congrats, bill, you're off ignore. For the sake of maintaining some reason in this thread and avoiding the train wreck of your thread.

Quote from intradaybill:

Expectation can be positive you lunatic but depending on starting capital you can get ruined. Why doesn't that fit into your flat head?

You toss a bias coin with p= 0.6 you lunatic. The expectation for win = loss = $1 is:

E = 0.6 -0.4 = $0.2

Yet, if you have $2 in your pocket, the probability of ruin in the first two bets in 16% (0.4 x 0.4).

Yes you moron, in the longer term you will make N x $0.2, where N is the number of tosses.

But you may never get there depending on starting capital and bet size.

I wonder how much money you have lost gambling...

Congrats again, bill, you've proven that the risk of ruin is greater than zero. But that was never the issue. You and DontMissTheBus have maintained that ruin is a certainty (RoR = 1).

You see, the vast majority of probabilities fall between the extremes of zero and one. Not everything (indeed, not most things) with a probability greater than zero has a probability of one.

Yes, the risk of ruin of a positive-expectation system is greater than zero. But that is not the definition of "certainty".

So please, no more lectures to me on how I'm the guy who doesn't understand probability theory. You've demonstrated beyond any doubt who that guy really is.

Quote from intradaybill:

Quote from abattia:

Quote from intradaybill:

Do you agree then that even if someone has an edge if he trades long enough the probability of ruin is inreasing?

For 0 < t1 < t2, for continuous t
P.of.Ruin(t1) < P.of.Ruin(t2)

But obviously, “higher risk of ruin” does not mean “certainty of ruin”. Working against “certainty of ruin” is risk management, etc.

Well, I was interested in the certainty of ruin, meaning P of Ruin = 1.

Quote from intradaybill:

Well, after the invaluable contributions of DontMissThe Bus, I will try to summarize as follows:

1. As number of trades tends to be very large, risk of ruin approaches certainty asymptotically 1.

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