Trading Math - Part I

[DontMissTheBus]

Um.... this should be pretty obvious, no? If when you win, you win $1, and when you lose, you lose $0.0001; You start off with $100 - is your probability of ruin after 1000 tries risking a single bet the same as if the gain and losses are $1 and $10? Is the optimal betting sizing strategy the same in both cases?

No. It's not. The answer requires knowing both p_win and the amount of win vs loss. AND the initial capital level.

And this is only the case of a coin toss-like scenario; If you want to talk about returns, you'll have to model a lot more than that.

Is that enough details?

Quote from virtualmoney:

Please elaborate mathematically with examples.

 

[virtualmoney]

Quote from DontMissTheBus:

The answer requires knowing the amount of win vs loss.

That is unknown(until it becomes historical/statistics)... sounds like expectancy component crap.

 

[DontMissTheBus]

Well... yes - that's why it's a hard freaking' problem - one which can't be solved unless you make certain assumptions!

Moreover, isn't your p_win and p_lose also unknown in real life?

Sounds like you have zero clue as to what you are actually talking about.

Quote from virtualmoney:

That is unknown(until it becomes historical/statistics)... sounds like expectancy component crap.

 

[intradaybill]

Quote from virtualmoney:

That is unknown(until it becomes historical/statistics)... sounds like expectancy component crap.

No, it is not unknow for fixed bet systems, known as target and stop in trading systems.

 

[DontMissTheBus]

I think I made the mistake of thinking that guy is a rational guy that one can have a discussion with about technical topics.

I was wrong. I think he's a standard et loon.

Quote from intradaybill:

No, it is not unknow for fixed bet systems, known as target and stop in trading systems.

 

[virtualmoney]

Quote from DontMissTheBus:

Well... yes - that's why it's a hard freaking' problem - one which can't be solved unless you make certain assumptions!
Moreover, isn't your p_win and p_lose also unknown in real life?
Sounds like you have zero clue as to what you are actually talking about.

P(win) is an assumption, not past statistics no. of win/losses, if you cannot even differentiate that, you are the one with zero clue...

 

[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. But how large? This is the question.

2. For finite time/trades or cummulative profit stop, risk of ruin is path dependent. It may happen fast and it is a function of capital, risk management, win rate, price series, even commission, as I found out after reading this very interesting blog in which it is demonstrated that ruin may occur depending on starting capital and commission rate even though the strategy may be profitable in the longer term:

 

[DontMissTheBus]

sheesh, and my reply was that with different assumptions on gain and loss when win/lose, the answers all come out different.

My entire point was that the correct answer requires things you aren't factoring when just considering p_win and p_loss.

Further, you are telling me in real life, you know the p_win and p_loss of your trading system??

Quote from virtualmoney:

P(win) is an assumption, not past statistics no. of win/losses, if you cannot even differentiate that, you are the one with zero clue...

 

[virtualmoney]

Quote from intradaybill:

No, it is not unknow for fixed bet systems, known as target and stop in trading systems.

He said "amount of win, losses" not target and stop.

 

[intradaybill]

Quote from virtualmoney:

He said "amount of win, losses" not target and stop.

He said amount of win vs. loss. Maybe it is your English.